Dr Gilles Tessier

Dr Dorin Dadarlat

Corinne Kolinsky

Abdelylah Daoudi

Philippe Hus

Fabrice Goutier

Mathieu Bardoux

Abdelaziz Elass

Remi Deram

Aoumeur Boulerouah

Yahia Boussoualem

Alejandro Segovia

Dr Rajesh Ravindran Nair

Preethy

Nisha Radha

Anu Philip

Prof. Raghu O Ginson T J Subin

Prof K P Manjusha

Prof. Viji Chandra

Prof A V Alex

Prof Benjamin

late prof Sreeprasanth & Satish

Joice Krishna

Thomas

Sandeep Nithya

Sangameswaram

Parvathy

Vinay & Dhanya

Lathesh K C & Santhi

Rany & Ramya

Applonia, Rini, Minta Doni

Suchithra Liya

Dr Rojin Sundaram

Mohanan Sumitha

Latha Chettan

Mahesh Chechi

Vyloppilly

Lakshmi

Liju Kuriakose

Maju Kuriakose

Michael Depriester

Roch Chan

Yu King

Frédérick Roussel

Abdelhak Hadj

Sahraoui Measurement

M Streza

A H Sahraoui

Wagner Maxwell

Sillars

S Delenclos

Effect as a Means for Thermal Characterization of Nanocomposites Based On Intrinsically Conducting Polymers and Carbon Nanotubes

If there is a person who can claim, through

Acknowledgement

There is always a world of people behind the scenes, with supports, sacrifices and good hopes in order to accomplish each and every piece of work. My PhD thesis wouldn't exist without all of those my well wishers and supporters. Therefore, I would like to use this opportunity to thank everyone those who helped me to carry out this thesis work and also all those who have supported me to be what I am at present, as a professional and as a person.

Firstly, I would like to thank Dr. Jean-Marc BUISINE, Director of the Unité de Dynamique et Structure des Matériaux Moléculaires (UDSMM), for accepting my candidature as well as providing me all the necessary supports for my entire stay in France during the thesis work.

Equally, I am thankful to Dr. Abdelhak Hadj Sahraoui (Professor) and Dr. Michael Depriester (Maître de Conférences) for welcoming me as their student and giving me all scientific supports to do this PhD in UDSMM, Université du littoral côte d'opale (ULCO), Dunkerque.

Dr. Abdelhak has been an excellent mentor in all respects-kind, efficient, firm and meticulous in weeding out all weak links in my work, attitude and in my thesis. I am very happy and proud to say that I have been a part of his group. I am also grateful to him for being generous with my holidays whenever I wanted to visit my family in India, for all the conference trips that he funded and giving proper guidance and word of supports in the midst of difficult situations.

Michael has been a good friend, daily supervisor and upto a certain extend, my local guardian too, all rolled into one during the last two and a half years. He was sincerely attentive to all my doubts and ideas. He has been always with helping mentality and without his helps my earlier days in France, hardly knowing french, would be a real tragedy. I am grateful to both of you for all your supports, corrections and reviews of my thesis versus amplitude varying applied electric field (EF) with constant frequency as well as versus frequency varying electric field with constant amplitude. For amplitude varying experiments, we find the thermal properties are increased from an initial value to a maximum until a threshold field is reached and stay unaltered with further increase in the amplitude of the applied EF. The changes are attributed to the effect of EF on aligning the liquid crystal director in the direction of the EF. Using effective medium theory, we deduce the kapitza resistance at the LC droplet-PS matrix boundaries. These results are also used to calculate reorientation angle (θ) of the liquid crystal droplets. Investigation on thermal parameters of PDLC samples under frequency dependent EF with constant threshold amplitude corresponding to the saturation point of increase in thermal parameters (found from the amplitude varying studies) are used to analyse depolarization field effects called as Maxwell-Wagner-Sillars (MWS) effect. Our results clearly show the thermal properties of the samples are prone to depolarizing field effects at the lower frequencies of the applied EF. The experimental results are modelled against existing theories to predict electric properties of the sample composites. We have also deduced the droplet elastic constant (K). As obtained values for K are slightly lower than the reported bulk values of 5CB.

Second part of the manuscript describes the development of a novel photothermal technique based on thermoelectric (TE) effect. This technique, so called photothermoelectric (PTE), is particularly useful for thermally characterizing thermoelectric materials without using a separate sensor for measuring induced temperature changes. PTE technique is presented both theoretically and experimentally. The experiments are done on polyaniline (PANI) -carbon nanotube (CNT) composite pellets by measuring Seebeck voltage generated by the samples upon heating by a modulated laser beam alike other photothermal experiments using a lock-in amplifier. Additional PTR experiments are done on the same samples and the results are in good agreement with the one found by PTE technique. Later on, the chapter experimentally describes the possibility of PTE technique to be used for finding thermal transport properties of materials by using TE materials as photothermal sensors with known thermal properties. Two methods have been developed to find thermal effusivity and diffusivity of samples under investigation. In the first method, so called front-PTE, the TE sensor in contact with the sample via a coupling liquid having known thermal parameters, is irradiated with a chosen chopping frequency of the laser beam and

Résumé

Les investigations des propriétés du transport thermique dans les substances hétérogènes avec des techniques existantes ou nouvellement développées sont décrites dans ce mémoire de thèse. Dans une première partie, une nouvelle méthode, précise et hautement sensible de caractérisation des paramètres thermiques de liquides par radiométrie photothermique (PTR) est présentée. Une configuration à 3 couches où l'échantillon liquide est emprisonné entre 2 fenêtres transparentes est proposée. Des dépôts opaques appliqués sur la surface des milieux transparents à l'interface fenêtre-liquide absorbent le faisceau laser et permettent la génération de chaleur. De plus, la fenêtre avant (en CaF2) est transparente aux radiations infrarouges émises à son interface avec l'échantillon. Dans ce type de configuration, l'échantillon peut être chauffé aussi bien par le dessus que par le dessous. Nous proposons 2 configurations. La première s'appelle la ≪ configuration arrière ≫ (B-PTR) dans laquelle la perturbation de l'échantillon et du matériau de référence s'effectuent par la face arrière et la seconde est nommée la ≪ configuration avant-arrière ≫ (BF-PTR) où les faces avant et arrière de l'échantillon sont successivement chauffées. La B-PTR donne deux paramètres thermiques simultanément (diffusivité et effusivité ou conductivité thermiques) et nécessite le remplacement de l'échantillon liquide par un liquide de référence tandis que la BF-PTR fournit la diffusivité thermique absolue sans requérir à un quelconque liquide de référence.

Nos résultats expérimentaux montrent que les incertitudes sur les paramètres thermiques sont similaires aux techniques photothermiques classiquement utilisées pour les liquides avec ici l'avantage d'offrir une mesure sans contact. Par la suite, ces 2 configurations ont été utilisées pour l'étude de polymères dispersés dans des cristaux liquides (PDLC).

Des échantillons de polystyrène (PS)-5 CB (4-Cyano-4'-pentyl-biphenyle) ont été préparés par mélange de ces éléments avec un solvant, suivi d'une évaporation de ce dernier. Deux échantillons de 5CB/PS aux fractions massiques différentes ont été préparés (85/15 % et 73/27 %). Chaque échantillon a été observé aux microscopes polarisants Résumé et la taille des gouttelettes dans la matrice PS a été évaluée. Les propriétés thermiques dynamiques de chaque échantillon ont été mesurées en fonction de l'amplitude du champ électrique appliqué à une fréquence constante aussi bien qu'en fonction de la fréquence du champ électrique à une amplitude fixe. Pour les expériences où l'amplitude du champ électrique est la variable, nous trouvâmes que la valeur des paramètres thermiques s'accroît jusqu'à atteindre une limite qui ne peut être dépassée par tout accroissement additionnel du champ. Ces changements sont attribués à l'alignement des directeurs des cristaux liquides dans la direction du champ électrique. Par l'utilisation de la théorie des milieux effectifs, nous déduisîmes la résistance de Kapitza aux interfaces gouttelette -matrice.

Ces résultats ont alors été utilisés pour calculer l'angle de réorientation (θ) des gouttes

Introduction

In the ever extending fields of research, studies on thermal transport properties of materials are significant in many technological areas such as electronics [START_REF] Michael J Rightley | Advancement in Thermal Interface Materials for Future High-Performance Electronic Applications : Part 1[END_REF], energy [START_REF] Ribeiro | Thermal Properties of Ionic Liquids and Ionanofluids[END_REF]3], safety [4],

heat exchangers [START_REF] Ding | Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids)[END_REF][START_REF] Assael | Thermal Conductivity of Nanofluids-Experimental and Theoretical[END_REF], health [START_REF] Matvienko | Robust multiparameter method of evaluating the optical and thermal properties of a layered tissue struc-ture using photothermal radiometry[END_REF][START_REF] Shen | Synthesis and phase behavior of aqueous poly(N-isopropylacrylamide-coacrylamide), poly(N-isopropylacrylamide-co-N,N-dimethylacrylamide) and poly(Nisopropylacrylamide-co-2-hydroxyethyl methacrylate)[END_REF] etc. As the technology grows, the ever shrinking sizes and increasing performance of instruments are always raising questions about thermal management and heat dissipation [START_REF] Onkaraiah | Mitigating heat dissipation and thermomechanical stress challenges in 3-D IC using thermal through silicon via (TTSV)[END_REF]10]. Since heat is one of the unwanted by-product of almost all energy conversion processes, there is a huge interest to reduce the wastage of energy as heat as well as to remove heat effectively from the point of generation, in order to protect the device from over heating and thereby preventing system failure. The leap from micro to nano scale designing are also facing challenges on the successful implementation of the techniques. At nano scale, the physical behaviour of materials changes abruptly than while considering its properties in the bulk state. The factors like: grain boundary effects [START_REF] Feng | Prediction of size effect on thermal conductivity of nanoscale metallic films[END_REF], inter facial thermal resistance [START_REF] Lu | Effect of interfacial characteristics on effective conductivities of composites containing randomly distributed aligned long fibers[END_REF][START_REF] Shenogin | Role of thermal boundary resistance on the heat flow in carbonnanotube composites[END_REF], surface roughness effects etc. are dominant at low dimensions. These effects may produce anomalous behaviour such as: changes in different phonon modes [START_REF] Seo | Infrared spectroscopy of CaTiO3, SrTiO3, BaTiO3, Ba0.5Sr0.5TiO3 thin films, and (BaTiO3)5/(SrTiO3)5 superlattice grown on SrRuO3/SrTiO3(001) substrates[END_REF][START_REF] Zollner | Optical properties of bulk and thin-film SrTiO 3 on Si and Pt[END_REF], thermal conductivity [START_REF] Feng | Prediction of size effect on thermal conductivity of nanoscale metallic films[END_REF][START_REF] Liang | Size-dependent thermal conductivity of nanoscale semiconducting systems[END_REF], phonon mean free path [START_REF] Richardson | YBa2Cu307-a films : Calculation path of the thermal conductiwity and phonon mean free path[END_REF],

refractive index [START_REF] Zollner | Optical properties of bulk and thin-film SrTiO 3 on Si and Pt[END_REF] and so forth in the physical properties of materials [START_REF] David | Nanoscale thermal transport[END_REF].

As part of this PhD work, we investigate thermal transport properties of two different classes of technologically important material composites by studying them while considering all possible and aforementioned thermophysical behaviour of materials and keeping their design aspects in mind. In these, the first class contains polymer dispersed liquid crystal samples (PDLC) and the second deals with polymer thermo-electic (TE) composites. Both of these classes of material samples have been studied [START_REF] Houriez | Etude du Transport Thermique dans des Fluides Complexes par Calorimetrie Photopyroelectric[END_REF][START_REF] Bouchaour | Equilibrium phase diagram of poly(2-phenoxyethylacrylate) and 5CB[END_REF][START_REF] Maschke | Equilibrium phase properties of polymer/liquid crystal blends: Theory and experiments[END_REF][START_REF] Chan | Carbon nanotube-polyaniline nanohybrids: Influence of the carbon nanotube characteristics on the morphological, spectroscopic, electrical and thermoelectric properties[END_REF] and being investigated in our laboratory by many researchers to understand their physical and chemical properties. So our present work is an extension to give more insight into the thermophysical properties of these materials.

Polymer dispersed liquid crystals have been attracted the scientists and manufactures Introduction because of its many advantages over conventional liquid crystal (LC) displays. Manufacturing easiness, cost effectiveness and extended working conditions are some of its advantages.

Electro-optic and thermo-dynamic behaviours of PDLCs were widely studied because of its direct application on practical implementations. So far, to the best of our knowledge, no studies were reported on PDLC's thermal behaviour other than the one reported from our lab [START_REF] Hadj Sahraoui | Heat transport in polymer-dispersed liquid crystals under electric field[END_REF].

On a fundamental point of view, PDLCs are heterogeneous mixtures and the transport properties are dependent on their constituent ratios, LC droplet size and shape, applied electric or magnetic fields, temperature, time and so on. Since these systems are more vulnerable and very sensitive to such process parameters, PDLCs are inherently more complex and often difficult to predict their behaviour without having a sound understanding versus different precess conditions.

Most often, since the PDLCs are operated by applied electric fields, their dielectric properties are also playing an important role in its working. Because of the system's heterogeneity, the difference in dielectric parameters lead to the manifestation of polarization The second part of this manuscript deals with polymer thermoelectric materials and their thermal studies. The energy consumption [START_REF] Darby | Literature review for the Energy Demand Research Project[END_REF] and thus the loss of energy, particularly in the form of heat, are increased in this modern era. Since the efficiency stays roughly less than 50% for most of the energy conversion systems (eg. automotive engines [START_REF] Morita | Automotive power source in 21st century[END_REF]), the necessity to improve performance is a major concern for the entire world. This is not only due to the scarcity and running out of the energy sources but also because of its contribution towards the global warming [START_REF] Gervet | Global Warming is mainly a result of Heat Emissions[END_REF]. These threats lead researchers to perform studies on improving the efficiency of various energy converters [START_REF] White | The hydrogen-fueled internal combustion engine: a technical review[END_REF][START_REF] Thamir K Ibrahim | Improvement of gas turbine performance based on inlet air cooling systems : A technical review[END_REF] and waste heat energy recovery [START_REF] Michael | Review THERMOELECTRIC WASTE HEAT RECOVERY AS A RENEWABLE ENERGY SOURCE[END_REF][START_REF] Yokokawa | Materials for clean energy conversion[END_REF] possibilities.

Recently, the research on heat energy to electricity converters, which are called as thermoelectric generators (TEG), are more intensified. Thermoelectric energy harvesting could be an additional solution for the energy crisis in the near future. Since these materials are solid state converters, electricity is generated without any mechanical movements, their developments are much promising. Though various kinds of semi conducting or metallic TEGs are already available in the market, their wide applications are restricted due to the insufficient efficiency. So the researchers are working by relying on various theoretical concepts in order to develop high efficiency TEGs.

Polymer TE materials are also introduced after the findings of electrically conducting polymers. Until now, these materials are showing lower efficiencies than metallic or semiconducting TEGs. But these materials are potentially interesting because of their low cost, easiness in processing, light weight and flexibility.

Thermal properties of TEGs are involved in controlling material's energy conversion efficiency. Usually the classical thermal characterization methods like 3ω, photothermal techniques, hotwire methods etc. have been using to find their thermal properties. Since all these measurement techniques use a separate sensor, the results are prone to be erroneous due to factors such as deviations in sensor's thermal properties, interface thermal resistance of sample-sensor assembly in contact methods etc.

In order to overcome such errors and to carry out measurements in a much more reliable way, we introduce a novel thermal characterization technique for TE samples in which the TE sample itself serves as the sensor. Here the seebeck voltage generated by TE materials Introduction upon absorbing an intensity modulated laser beam is used to find the thermal parameters of the irradiated TE sample. We present the thermal transport studies on certain polymer nanotube composite TE materials by this newly developed method, so called Photothermoelectric (PTE) technique, and validates the obtained results using classical PTR technique.

Further, we present the use of PTE technique for the thermal characterization of solid and liquid samples while using TE materials as sensors as if pyro materials in PPE technique.

Chapter 4 contains the developments, validation and application of novel PTE technique.

It particularly compares the results from a set of polyaniline-carbon nanotube composites.

These are prepared in a special chemical method in which the polymer is wrapped around nanotubes by in-situation polymerization process. The chapter ends by opening the potential use of TE sensors as photothermal sensors to characterize solid and liquid samples by presenting various experimental results.

Chapter 1

Photothermal Techniques:-An

Overview

The studies on thermal transport properties of materials have extensive applications in diverse areas. Knowledge of thermal properties of materials give one to optimize the usage where he/she can find applications. In high functioning materials, for example electrically insulated and heat conducting coatings on copper windings in power transformers, a better knowledge of thermal properties of the coating material and the heat transfer at coating-substrate interfaces are important; since these properties are vital for the lifetime and functionality of transformers. On the other hand, by knowing the thermal properties, we can find the thickness of the coating layer on a substrate with high accuracy (inverse problem). Photothermal spectroscopy with a handful of flexible and accurate measuring methods give us the possibility of measuring thermal properties of matter in a non-destructive manner. This chapter gives an introduction about various photothermal methods.

Photothermal phenomena

The discovery of photoacoustic effect by Alexander Graham Bell in the nineteenth century was originally pioneered the field of thermal investigation of materials in an optically activated means. Bell's invention was first reported in 1880 of his work on the photophone (fig. 1.1). Later he demonstrated that the strength of the acoustic signal strongly depends on the amount of incident light absorbed by the material in the cell [START_REF] Alaxander | Production of Sound by Radiant Energy[END_REF]. Nevertheless, the difficulty in quantifying the phenomenon, which was mainly due to the lack of detection mechanism (the investigator's ear was the detector), obstructed further developments until 1970s. Eventually after the findings of some measuring techniques, revived the research on photoacoustic effect and gave a rebirth to the field.

The word 'photothermal' represents the process of absorption of photons in a material which accounts for the generation of heat and thus a temperature increase. This process gives rise to a number of physical phenomena including refractive index change (thermo refluctance) [START_REF] He | Theory of photothermal spectroscopy in an optically dense fluid[END_REF][START_REF] Nie | Separation of surface and volume absorption by photothermal deflection[END_REF], acoustic wave generation (thermoelastic effect) [START_REF] Käding | Transient thermal gratings at surfaces for thermal characterization of bulk materials and thin films[END_REF][START_REF] Gusev | Theory of Scholte, leaky Rayleigh, and lateral wave excitation via the laser-induced thermoelastic effect[END_REF], pyroelectric effect [START_REF] Mandelis | Theory of photopyroelectric spectroscopy of solids[END_REF], infrared emission in a material sample under study. The common choice of the source for thermal excitation is a laser source with power ranging from micro watts to a few watts.

Figure (1.2) shows some of these signals generated inside a sample after the thermal excitation. More over, all of these following phenomena are material dependent and thus by measuring these physical changes may reveal us the thermal properties of material under investigation.

In the photothermal field, the existing techniques can be classified into two categories: contact and non-contact techniques. In contact techniques, a temperature or heat flux measuring sensor is placed in contact with a material sample, detects directly the thermal

Contact Photothermal Techniques

Generally, contact techniques directly measures the dynamic temperature variations of a sample due to the periodical heating. Since it needs direct contact, any of them (the sample or the sensor), must have the property of sticking together without making any void space or air gap in between. So the applications are limited but can be overcome by the [START_REF] Kawaguchi | Fully automated apparatus to measure the thermal conductivity of liquids by the transient hot-wire method[END_REF][START_REF] Takahashi | An improved transient hot-wire method for studying thermal transport in condensed matter[END_REF][START_REF] Richard | A transient hot-wire method for measuring the thermal conductivity of gases and liquids[END_REF] and 3ω techniques [START_REF] Cahill | Thermal conductivity of amorphous solids above the plateau[END_REF]. Here we are restricting our reviews only on techniques based on photothermal effect.

Photopyroelectric Technique (PPE)

Pyroelectric effect is based on the ability of a material to generate temporary voltage due to a change in heat flux through the material. The variation of temperature in the material produces a change in material's electrical polarization, which results in charge generation.

In photopyroelectric technique (PPE), a modulated light source provides necessary temperature oscillations inside the sensor, directly or through the sample which is in contact with the sensor generate electrical signals. As generated photothermal signals contain both the thermal and optical properties of the sample-sensor assembly. Analysing these obtained signals with suitable theoretical model reveal the thermal properties of sample materials [START_REF] Mihailescu | Theory of the photopyroelectric method for investigation of optical and thermal materials properties[END_REF][START_REF] Longuemart | Study on Liquid Crystal and ferro fluids using Photopyroelectric Technique[END_REF][START_REF] Delenclos | On the accurate determination of thermal diffusivity of liquids by using the photopyroelectric thickness scanning method[END_REF]. PPE techniques can be used to characterize solids [START_REF] Dadarlat | Combined FPPE-PTR Calorimetry Involving TWRC Technique II. Experimental : Application to Thermal Effusivity Measurements of Solids[END_REF], liquids [START_REF] Preethy Chirukandath Menon | High accuracy, self-calibrating photopyroelectric device for the absolute determination of thermal conductivity and thermal effusivity of liquids[END_REF] and gases [START_REF] Caerels | Photopyroelectric thermal wave setup for the absolute measurement of the thermal conductivity of low density gases[END_REF]. The advantages of high sensitivity, large bandwidth (typically milli Hz to several kHz of dynamic response), high signal to noise ratio and simplicity to implement [START_REF] Mandelis | Theory of photopyroelectric spectroscopy of solids[END_REF][START_REF] Zammit | Invited Review Article: Photopyroelectric calorimeter for the simultaneous thermal, optical, and structural characterization of samples over phase transitions[END_REF] have

q(t) = pA l p lp 0 T (z, t)dz = pAT (t) (1.1)
where, t ⇒ time z ⇒ arbitrary direction l p ⇒ thickness of pyro sensor A ⇒ area of the sensor

T (z, t) ⇒ temperature p ⇒ pyroelectric coefficient T (t) ⇒ spacially averaged temperature
Using eq. ( 1.1) we can find out the temperature fields of a sample-sensor stacked system and it gives the thermal properties of the sample.

Piezoelectric detection

An alternative technique in the photothermal field is based on the piezoelectric properties of certain materials used as sensors (such as a lead zirconate titanate (PZT) ceramic), to find thermal properties of samples [START_REF] Farrow | Piezoelectric detection of photoacoustic signals[END_REF][START_REF] Hordvik | Photoacoustic measurements of surface and bulk absorption in HF/DF laser window materials[END_REF][START_REF] Helander | Separation of bulk and surface light adsorption with an open photoacoustic cell[END_REF]. Temperature fluctuations produce a usual spatially averaged thermal expansion on both surfaces and also a thermal decay along the thickness of the sample causes expansion of the front surface than the rear. The latter results in bending of the sample proportional to the average thermal gradient inside the sample. The net expansion on the sample surface caused by these two mechanisms produce a voltage between the two ends of the PZT sensor, which is in contact with the sample and thus the thermal properties can be found from these piezoelectric signals.

Photothermoelectric Technique (PTE)

This novel PT technique introduced as part of this thesis work [START_REF] Kuriakose | Photothermoelectric effect as a means for thermal characterization of nanocomposites based on intrinsically conducting polymers and carbon nanotubes[END_REF] which is based on the Seebeck effect of certain materials (A property which produce electrical potential difference between the ends when it is subjected to a temperature difference between the same ends). The sensors are made of thermoelectric materials and this new method can be used efficiently to find thermal transport properties of thermoelectric materials directly by considering the sample itself as sensor. PTE technique is also capable of characterizing materials thermally in a similar manner as PPE works. The temperature dependent potential difference from the sensor is given by:

1.3. Non-Contact Photothermal Techniques ∆V = S T z=0 T z=l dT (1.2)
where, l ⇒ thickness of thermo sensor S ⇒ Seebeck Coefficient

An elaborate theoretical and experimental details are added in the later chapters of this manuscript.

Non-Contact Photothermal Techniques

Non-contact photothermal spectroscopy contains a wide variety of techniques. In these, each one of them stands out for their own distinctiveness in measuring ability or application possibility. The advantage of non-contact probing opens more applicability than the contact techniques (e.g., nano-meter thick film characterization, dealing with hazardous or highly reacting materials). Some of these widely using photothermal techniques are mentioning hereafter.

Photoacoustic Spectroscopy (PA)

Photoacoustic phenomena is based on the acoustic wave generation in materials due to the absorption of photons. The revival of photothermal techniques based on photoacoustic effect was experimentally and theoretically pioneered by the works of Kreuzer [START_REF] Kreuzer | Ultralow Gas Concentration Infrared Absorption Spectroscopy[END_REF] and Rosencwaig [START_REF] Rosencwaig | Photoacoustic scpectroscopy of solids[END_REF]. Typically, a dedicated microphone detects the pressure variations near to a sample under light induced periodical thermal excitations. These detected signals from the microphone, contains the thermal information about the sample specimen under investigation. PA techniques have been gained a great acceptance even from its beginning and rapidly expanded [START_REF] Vargas | Photoacoustic and related photothermal techniques and related photothermal[END_REF] with successful methods to characterize different types of material samples and under different process conditions (e.g., under magnetic field). Even though the poor bandwidth, restricts the applicability of this technique. Its sensitivity and non-contact investigation possibility are major advantages.

Photothermal Beam Deflection (PBD)

Photothermal Beam Deflection spectroscopy based on the mirage effect, was introduced by Boccara, Fournier, and Badoz [START_REF] W B Jackson | Photothermal deflection spectroscopy and detection[END_REF][START_REF] Boccara | Thermo-optical spectroscopy: Detection by the "mirage effect[END_REF]. A sample under periodical thermal excitation produce thermal perturbation in the gas medium in contact with the heating surface.

These thermal perturbations produce a refractive index change in the medium. If a second probe beam passing in parallel to the sample surface, through the gas phase where the refractive index changes happened, can get deflected in proportion to the temperature rise in the sample specimen. These deflected probe beams, can be detected by using positionsensitive diode detectors, contain the thermal properties of the sample under investigation.

Using proper theoretical models, one can find the thermal properties of the sample in relation with the detector output.

Impulsive Stimulated Scattering

Impulsive stimulated scattering (ISS) is a time domain experimental technique which has the advantage to measure directly the density dynamics on subnanosecond to millisecond time scales [START_REF] Yang | Impulsive stimulated light scattering from glass-forming liquids. I. Generalized hydrodynamics approach[END_REF]. In this technique [START_REF] Maznev | Optical heterodyne detection of laserinduced gratings[END_REF], an impulsive stimulated scattering of probe laser beam crossing the bulk of a (semi-) transparent sample (in transmission mode) gives the thermal as well as acoustic information about the sample. The scattering was induced by photothermal and photoacoustic excitation of the sample by a pulsed laser with picosecond pulse duration. Practically, in the case of a heterodyne type of detection, both the pump and probe laser beams are split in two diffraction orders by means of a phase mask, and recombined on the sample using a 2-lens telescope with a given magnification, which is essentially imaging the optical phase modulation induced by a phase mask with known grating space onto an equivalent light intensity pattern in the crossing region. Due to partial optical absorption of the pulsed pump laser, impulsive heating and thermal expansion occurs according to the intensity grating pattern. This launches two counterpropagating acoustic wave packets with the same spatial periodicity as the optical grating, on top of the thermal expansion grating, which is slowly washing out due to thermal diffusion between the hot (illuminated) and cold (dark) parts of the grating. The spatially periodic dynamic density changes resulting from both the thermal expansion and acoustic wave evolution results in proportional diffraction of the probe laser beams, which, by virtue This heterodyne mixing allows to optically amplify the light intensity modulation of both light beams on the photodetectors. By tuning the optical phases of these light beams by means of a glass slide or wedge in the optical path of one or both probe beams in between the lenses, the heterodyned signal components can be made opposite in sign. Differential detection of both probe beams then results in a signal in which the total heterodyne component has a double magnitude, while the dc components of the reference beams, as well as the homodyne components, are removed from the signal. It allows to find the thermal and acoustic responses of a sample. ISS by heterodyne diffraction used in such transmission configuration allows to accurately determine on one hand the longitudinal speed of acoustic waves by determining the frequency f signal of the periodical part of the signal (induced by the propagating acoustic wave density grating), and calculating the corresponding acoustic velocity as cL=λf signal , with λ, the spatial period of the optical grating, which can be controlled by choosing the spatial periodicity of the phase mask, and the optical magnification factor of the lens telescope. On the other hand, the decay of the 1.4. Summary thermal expansion grating evolves exponentially according to exp(-q 2 α th t), with q=2π/λ, the wave number of the grating, and α th , the thermal diffusivity of the sample. By analyzing the periodic and decaying components of the signal ISS thus allows to simultaneously determine the longitudinal velocity and thermal diffusivity of materials [START_REF] Slayton | Transient grating measurements of film thickness in multilayer metal films[END_REF][START_REF] Dora | Impulsive stimulated thermal scattering study of structural relaxation in supercooled glycerol[END_REF][START_REF] John | Study of Lamb acoustic waveguide modes in unsupported polyimide f Urns using real-time impulsive stimulated thermal scattering[END_REF].

Photothermal Radiometry (PTR)

Photothermal Radiometry or Photothermal Infrared Radiometry is an extensively using non-contact PT technique mainly for the thermal characterization of coating materials.

The technique is based on the detection of infrared radiation, which comes out of the sample specimen due to the periodical thermal excitation by laser absorption. It posses a broad frequency response range, typically from mHz to a few MHz depending on the detection mechanism, and accuracy to find thermal properties of samples having thickness down to sub-micron scales [START_REF] Mandelis | Non-contacting measurements of photocarrier lifetimes in bulk-and polycrystalline thin-film Si photoconductive devices by photothermal radiometry[END_REF]. Generally, the PTR experiments are less complex and experimental requirements can be easily fulfilled in comparison with many other noncontact techniques, e.g., PA technique needs an air tight photoacoustic cell. Since PTR is the major part of this thesis work, more details in the theoretical and experimental point of view can be found in the subsequent chapters of this manuscript.

The field of photothermal calorimetry contains a variety of experimental techniques and methods mentioned other than here. One can find a broader review on these topics from different resources [START_REF] Vargas | Photoacoustic and related photothermal techniques and related photothermal[END_REF][START_REF] Vargas | Photothermal techniques applied to thermophysical properties measurements (plenary)[END_REF][START_REF] Busse | Optoacoustic and photothermal material inspection techniques[END_REF][START_REF] Zammit | Invited Review Article: Photopyroelectric calorimeter for the simultaneous thermal, optical, and structural characterization of samples over phase transitions[END_REF][START_REF] Almond | Photothermal Science and Techniques[END_REF].

Summary

In this chapter, we have given an overview of photothermal phenomena and different photothermal techniques. All the techniques have been described under two main categories: contact, and non-contact. The applicability of different techniques and the sensing mechanisms are also being described qualitatively.

Chapter 2

Theory of Heat Transfer Through

Multi-layered Systems

Introduction

The fashion of adjusting a body to its surrounding temperature changes depends on its thermal properties such as: specific heat (C, the amount of heat per unit mass required to raise the temperature by one degree Celsius, unit: Jkg -1 K -1 ), Thermal Diffusivity (α, a parameter which describes how far the thermal diffusion modulation travels away from the source, unit: m 2 s -1 ), Thermal Conductivity (κ, a parameter which describes how efficiently it conducts heat through its body, unit: Wm -1 K -1 ), Thermal Effusivity (e, square root of thermal inertia, unit: JK -1 m -2 s -1/2 ) etc. On the process of irradiating an opaque homogeneous isotropic sample, heat diffuses from its surface to interior, undergoes damping and phase shift. The mechanism of heat transfer also depends on the time period of irradiation (modulation frequency) and thermal properties of the surrounding media.

Fourier law of heat transfer defines how the heat diffuses inside a material in the form of differential equations. Thus, by solving the heat diffusion equation with clearly defined experimental boundaries, one can quantitatively find the process of heat transfer in a material.

This chapter gives the theoretical background necessary for the investigation of thermal transport properties of various material samples studied in this thesis.

Heat transfer through multi layered Systems

Heat transfer inside a medium is basically a diffusion process rather than wave motion. A.

Salazar gave a comprehensive view on classical Fourier law of heat diffusion and proposed relation between first derivative of the temporal component with the second derivatives of spatial terms which satisfies parabolic heat transfer equation, in comparison to electromagnetic wave equation which satisfies a hyperbolic relation. Nevertheless, we can assume that the heat propagation posses wave properties even though, unlike electromagnetic waves, heat waves do not carry energy i.e., the average intensity over a period is zero [START_REF] Salazar | Energy propagation of thermal waves[END_REF].

Heat diffusion equation governs the heat transfer through a material specimen. Let us consider an infinitesimally small volume dV of homogeneous isotropic medium in space with dimensions dx, dy and dz in the arbitrary X, Y and Z directions respectively, as in fig.

(2.1). Now, when a heat flux, q z , allowed to pass through this volume in the Z direction, can produce a change in its thermodynamic state of equilibrium if the energy is absorbed by the specimen. As gained extra energy will in turn completely stored or partly stored and dissipates the remaining, over the course of time. The complete description of such situation based on the principle of conservation of energy may include four processes:

the amount of energy received into the specimen, the amount of energy generated inside the specimen, the amount of energy stored in the specimen and the amount of energy flown out of the specimen. The heat diffusion equation derives from these physical processes.

In the following section, the four previously mentioned physical processes are described mathematically in order to derive the heat diffusion equation [START_REF] Almond | Photothermal Science and Techniques[END_REF][START_REF] Rosencwaig | Theory of the photoacoustic effect with solids[END_REF].

Heat Diffusion Equation

1. Energy Received: The entrance (or travel) of energy in the form of heat into the unit volume specimen can be: by conduction, by convection, by radiation or by the combination of either two or three of these phenomena. In our experimental conditions, it is reasonable to assume that the heat transfer is only via conduction because of the contributions via convection or radiation are negligibly smaller since the induced temperature changes are smaller than a few milli Kelvin and each measurement lasts only for a short period of time (usually upto milli seconds). Thus, the heat flux, q i (where i can be x, y or z depending on the direction of heat flux), entered into a unit volume via convection in arbitrary X, Y , and Z directions, can be expressed by the aid of Fourier's law as: where, κ is the proportionality constant known as thermal conductivity of the medium.

q x = -k ∂T ∂x x dydz q y = -k ∂T ∂y y dzdx q z = -k ∂T ∂z z dxdy (2.1)
The negative sign is because of the heat transfer is in the direction of decreasing temperature.

The total energy received by the system from all the three directions can be expressed as,

E r = q x + q y + q z (2.2)
2. Energy Generated: Let us consider a periodically heating laser source having peak intensity, I 0 , travelling in the z direction with angular frequency ω = 2πf ,

I (z) = I 0 cos (ωt -ψ) (2.3)
where, f is the frequency of modulation, t is the time (sec) and ψ is the phase shift.

Without loosing generality, further we can consider ψ = 0 and since the incident laser intensity only contribute to sample's periodical heating (and hence the generated heat wave is completely in the positive upper axis), we can rewrite the above equation as,

I (z) = 1 2 I 0 [1 + cos (ωt)] (2.4)
and in polar form (generally the imaginary sinusoidal term can be ignored),

I (z) = 1 2 I 0 1 + e iωt (2.5)
The incident laser beam (photons) on materials produce thermal excitation via light absorption. This generation of heat depends on material's optical absorption coefficient (β)

and the efficiency of conversion of absorbed light into heat (η) by non radiative excitation at a particular wavelength. Thus, the heat density generated at any point z because of the incident radiation can be written as:

E g = βe βz η I 0 2 1 + e iωt , (z ≤ 0) (2.6)
Inverse of optical absorption coefficient is known as the optical absorption length or penetration depth (µ β ). Equation (2.6) has a frequency dependent dynamic part and also a stationary part. Apparently we are interested only in the dynamic part of E g .

Energy Stored:

Considering the energy received in the system completely redistributed as the kinetic energy, then the stored energy can be identified as the rate of temperature change, ∂T /∂t (T is the temperature and t is time), of the specimen and which depends on its density (ρ) and the specific heat (C). Then the stored energy can be represented as:

E st = ρC ∂T ∂t dx dy dz (2.7)

Energy flown out:

The heat flux leaving the system is the space derivative of the flux entering into the volume. Tailor expansion of the heat flux over the space gives the amount of heat flux exiting the specimen and is given by, omitting the higher order terms, E f =q x+dx + q y+dy + q z+dz =q x + ∂q x ∂x dx + q y + ∂q y ∂y dy + q z + ∂q z ∂z dx (2.8)

Combining four of these above mentioned contributions of heat energy [eqs. (2.2), (2.6),

(2.7), (2.8)] in unit volume, dV , we obtain the complete picture of heat propagation in dV , which is given by:

E r + E g -E st -E f = 0 (2.9)
which gives: q x + q y + q z + E g -q x + ∂q x ∂x dx + q y + ∂q y ∂y dy + q z + ∂q z ∂z dx -ρC ∂T ∂t dx dy dz = 0 (2.10)

Simplifying and rearranging eq. (2.10) gives:

∂ 2 T ∂x 2 + ∂ 2 T ∂y 2 + ∂ 2 T ∂z 2 + E g κ = ρC κ ∂T ∂t (2.11)
Equation (2.11) is known as the "Heat Diffusion Equation" in three dimensions.

Dealing with the heat diffusion equation in three dimensions is more complex and needs much computational tasks. So we are only dealing with the one-dimensional form of heat propagation in all our experimental and theoretical studies. This assumption is quite valid and reasonable if the direction of heat transfer is only in one direction (say, in the Z direction) and there is no heat diffusion (∆T = 0) in the other two directions (towards X and Y directions).

Solution of 1-Dimensional Heat Diffusion Equation for Periodically Varying Temperature Field

One dimensional heat equation having heat propagation only in the Z direction can be written as:

∂ 2 T ∂z 2 = 1 α ∂T ∂t -Q (2.12)
where, Q = E g /κ, is the source term and α = κ/ρC is the thermal diffusivity. The periodically oscillating temperature field as a function of angular frequency (ω) and time (t), similar to eq. (2.5) for the oscillating intensity, can be written as, excluding the stationary part:

T (ω, t) = T 0 e iωt (2.13)
where, T 0 is the peak value of the temperature oscillations. Equation (2.12), in the form of partial differential equation can be solved by the separation of variable method (see Appendix of this chapter).

Hence, a proposed solution for the 1-Dimensional heat transfer equation (2.12) for periodically oscillating temperature field and including the transient part of the source term (Q) explicitly, is given by:

T (z, t) = Ae σz + Be -σz -Eβe βz η I 0 2κ e iωt (2.14)
where, A, B and E are constants which can be found by solving the equation using proper boundary conditions and σ is the complex wave number.

Solving eq. (A-6) for finding σ gives:

σ 2 F = iω F α (2.15) ∴ σ = iω α = (1 + i) πf α (2.16) = (1 + i) 1 µ s (2.17)
here, µ s is known as the thermal diffusion length.

Temperature Field for Different Layers

In the last subsection 2.1.2, we have derived the general solution for the temperature field of a sample specimen with a heat flux flowing in the z direction. This can be extended for any number of layers. In most of our experiments, we are dealing with a system of three layers in which each of them having its own thermophysical properties. the equations for the temperature fields T 0 , T 1 and T 2 corresponding to layer-0, layer-1 and layer-2 respectively, can be written as:

T 0 = A 0 e σ 0 z + B 0 e -σ 0 z e iωt (z ≥ 0) (2.18) T 1 = A 1 e σ 1 z + B 1 e -σ 1 z -Eβe -βz η I 0 2κ 1 e iωt (0 ≥ z ≥ -d) (2.19) T 2 = A 2 e σ 2 z + B 2 e -σ 2 z e iωt (z ≤ -d) (2.20)
The eq. (2.19) contains both the heat conduction part and the source term. The coefficient E in the source term is determined by forcing function and it is given by the eq. ( 2.24). So the constant part (i.e., the term excluding e βz and e iωt ) of the source term (further calls by 'ǫ') is given by:

ǫ = βηI 0 2κ 1 (β 2 -σ 2 1 ) (2.21)
By substituting eq. (2.14) in eq. ( 2.12) we obtain:

σ 2 1 T 1 + E βe βz ηI 0 2κ 1 e iωt -β 2 E βe βz ηI 0 2κ 1 e iωt = iω α 1 T 1 - βe βz ηI 0 2κ 1 e iωt (2.22) σ 2 1 T 1 + E E g κ 1 -β 2 E E g κ 1 = σ 2 1 T 1 - E g k 1 (2.23) ∴ E = 1 β 2 -σ 2 1 (2.24)
Certainly the eqs. (2.18, 2.19, 2.20) have unknown coefficients and need to be solved against proper boundary conditions in order to find out its values. Before that, It is also reasonable to assume that the coefficient A 0 in eq. (2.18) is zero since the temperature at infinity is zero. Also in the same way, the coefficient B 2 in eq. (2.20) becomes zero. While looking for the boundary conditions, we can assume that the heat flux is continuous and the temperatures are same at the layer-layer interface. These can be written as:

κ 0 ∂T 0 ∂t = κ 1 ∂T 1 ∂t , T 0 =T 1 , (z = 0) (2.25) κ 1 ∂T 1 ∂t = κ 2 ∂T 2 ∂t , T 1 =T 2 , (z = -d) (2.26)
Now we have three equations for the temperatures with four unknowns and four boundary conditions. Applying the boundary conditions into the eqs (2.18, 2.19) at z = 0 gives:

-b 01 B 0 -A 1 + B 1 = - β σ 1 ǫ (2.27) B 0 -A 1 -B 1 = -ǫ (2.28)
Similarly, by applying boundary conditions to the eqs. (2.19, 2.20) at z = -d gives:

A 1 e -σ 1 d -B 1 e σ 1 d -b 21 A 2 = β σ 1 ǫe -βd (2.29) A 1 e -σ 1 d + B 1 e σ 1 d -A 2 = ǫe -βd (2.30)
Here, b 01 and b 21 are given by:

b 01 = k 0 σ 0 k 1 σ 1 = e 0 e 1 (2.31) b 21 = k 2 σ 2 k 1 σ 1 = e 2 e 1 (2.32)
where, e 0 , e 1 and e 2 are the thermal effusivities of layer-0, layer-1 and layer-2 respectively.

Equations (2.28, 2.28, 2.30, 2.30) in matrix form is given by:

        -b 01 -1 1 0 1 -1 -1 0 0 e -σ 1 d -e σ 1 d -b 21 0 e -σ 1 d e σ 1 d -1                 B 0 A 1 B 1 A 2         =         -β σ 1 E -E β σ 1 Ee -βd Ee -βd         (2.33)
Using Cramer's rule, one can solve the above matrix and the unknowns are given by:

B 0 = ǫ (1 + b 21 ) e σ1d β σ1 -1 + (1 -b 21 ) e -σ1d β σ1 + 1 + 2e -βd b 21 -β σ1 (1 + b 01 ) (1 + b 21 ) e σ1d -(1 -b 01 ) (1 -b 21 ) e -σ1d
(2.34)

A 1 = ǫ e σ1d (1 + b 21 ) b 01 + β σ1 + e -βd (1 -b 01 ) b 21 -β σ1 (1 + b 01 ) (1 + b 21 ) e σ1d -(1 -b 01 ) (1 -b 21 ) e -σ1d
(2.35)

B 1 = ǫ e -βd (b 01 + 1) b 21 -β σ1 + e -σ1d (1 -b 21 ) b 01 + β σ1 (1 + b 01 ) (1 + b 21 ) e σ1d -(1 -b 01 ) (1 -b 21 ) e -σ1d
(2.36)

A 2 = ǫ σ 1 -e σ1d-βd (1 + b 01 ) σ 1 + β σ1 + e -σ1d-βd (1 -b 01 ) σ 1 -β σ1 + 2σ 1 b 01 + β σ1 (1 + b 01 ) (1 + b 21 ) e σ1d -(1 -b 01 ) (1 -b 21 ) e -σ1d (
T 0 = ǫ (1 + b 21 ) e σ1d β σ1 -1 + (1 -b 21 ) e -σ1d β σ1 + 1 + 2e -βd b 21 -β σ1 (1 + b 01 ) (1 + b 21 ) e σ1d -(1 -b 01 ) (1 -b 21 ) e -σ1d
e -σ0z e iωt , (z ≥ 0)

(2.38)

T 1 = ǫ   e σ1d (1 + b 21 ) b 01 + β σ1 + e -βd (1 -b 01 ) b 21 -β σ1 (1 + b 01 ) (1 + b 21 ) e σ1d -(1 -b 01 ) (1 -b 21 ) e -σ1d e σ1z + e -βd (b 01 + 1) b 21 -β σ1 + e -σ1d (1 -b 21 ) b 01 + β σ1 (1 + b 01 ) (1 + b 21 ) e σ1d -(1 -b 01 ) (1 -b 21 ) e -σ1d e -σ1z -e βz   e iωt , ( 0
≥ z ≥ -d) (2.39) T 2 = ǫ σ 1 -e d(σ1-β) (1 + b 01 ) σ 1 + β σ1 + e d(-σ1-β) (1 -b 01 ) σ 1 -β σ1 + 2σ 1 b 01 + β σ1 (1 + b 01 ) (1 + b 21 ) e σ1d -(1 -b 01 ) (1 -b 21 ) e -σ1d e σ2(z+d) e iωt , (z ≤ -d) (2.40)
Equations (2.38, 2.39, 2.40) represent the complete solution in order to find the temperature fields at different depths of a three layer system. Even though all these equations seem to be lengthier and consists of many parameters, usually the case studies make it smaller and much more interesting.

Special Cases and Approximations

Thermal characterisation of materials needs different modes of experimentations depending on the sample of interest. For example, a transparent glass needs an absorbing layer for the incident laser beam while a steel sample not; a semitransparent sample allows the laser radiation upto a longer depth and thereby the point of heat generation also stretch forth, which means that the condition for volume absorption is met. The plausibility to determine the thermal parameters is also depending on the physical dimensions of the sample, because, the thermal diffusion length governs the depth upto where a thermal wave can travel. So the experimental situations can differ according to the sample's optical, physical, dimensional or thermal properties. Here we are mentioning only a few special cases that suits to our experiments. A more broader study about different special cases can be found in literatures [START_REF] Rosencwaig | Theory of the photoacoustic effect with solids[END_REF][START_REF] Santos | Theory of the photothermal radiometry with solids[END_REF][START_REF] Mandelis | Theory of photopyroelectric spectroscopy of solids[END_REF].

Optically Opaque Sample (A Surface Absorption Model)

Let us consider a situation at which the intensity of the laser excitation for heat generation is attenuated by a factor of 1/e inside a sample layer (say, layer-1 ), then the optical absorption length (µ β = β -1 ), inverse of the optical absorption coefficient, is smaller than the sample thickness, d, and thus the sample is optically opaque. Again, if the penetration depth, µ β , is much lesser than the thermal diffusion length of the sample layer, then the material is optically opaque and the criterion for 'surface absorption' is also met. Thus the condition for optically opaque sample with surface absorption is given by:

µ s ≫ µ β , Surface absorption d > µ β , Optically opaque
Under these conditions and at nominal experimental frequency range, it is pretty reasonable to assume that:

e -βd ≈ 0 β/σ 1 ± 1 ≈ β/σ 1 β 2 -σ 2 ≈ β 2
The incident light to heat conversion efficiency, η, is usually considered as one. All these approximation can be applied to eqs. (2.38, 2.39, 2.40). We are mainly interested in temperature fields at the top and bottom surfaces of layer-1, at z = 0 and z = -d. Thus rewriting eq. ( 2.38) at (z = 0) for layer-1 gives:

T 0 (ω, z = 0) = I 0 2σ 1 k 1 (1 + b 01 ) 1 + ℜ 2 e -2σ 1 d 1 -ℜ 0 ℜ 2 e -2σ 1 d e iωt (2.41)
where, ℜ 0 and ℜ 2 are given by:

ℜ 0 = 1 -b 01 1 + b 01 ℜ 2 = 1 -b 21 1 + b 21 (2.42)
The quantities b 01 and b 21 are the ratios of effusivities of adjacent layers given by eqs.

(2.31 and 2.32). It represents the thermal mismatch between the layers. While measuring single layered solid samples, the top and bottom surrounding layers are air, having a lowest

effusivity of 5.7 JK -1 m -2 s -1/2 [69]
. This makes the effusivity ratios become much smaller than one. Again, if it is the case of liquid samples, the top and bottom layers could be of glass or similar type of materials which will be chosen in such a way that the thermal mismatch is minimized in order to obtain highest accuracy [START_REF] Dadarlat | Combined FPPE-PTR Calorimetry Involving TWRC Technique II. Experimental : Application to Thermal Effusivity Measurements of Solids[END_REF][START_REF] Dadarlat | Photopyroelectric calorimetry of liquids; recent development and applications[END_REF], resulting, b 01 and b 21 are much smaller in comparison to the quantity β/σ 1 . So the eq. ( 2.39) at (z = -d) can be approximated and rewritten as:

T 1 (ω, z = -d) = I 0 e -σ 1 d 2σ 1 k 1 (1 + b 01 )(1 + b 21 ) 2 1 -ℜ 0 ℜ 2 e -2σ 1 d e iωt
(2.43)

Summary

Or in another form,

T 1 (ω, z = -d) = I 0 2σ 1 k 1 (1 + b 01 ) (1 + ℜ 2 ) e -σ 1 d 1 -ℜ 0 ℜ 2 e -2σ 1 d e iωt (2.44)
Now the equations of temperature fields look fairly simple compared to the full equations and yet valid. Further we can neglect also the temporal term, since the experiments are conducted in frequency domain.

Summary

This chapter principally contains the necessary theoretical descriptions which suits to the chosen photothermal experiments those have been used in this thesis work. It started by deriving the heat diffusion equation and then solving it for one dimensional heat transfer for a three layer system. Later the solutions are being treated under practical circumstances by special cases and approximations, under which, theoretical models can be developed for measuring liquid and solid samples. Finally, it presents the studies on polarization field effects on the thermal properties of Polymer Dispersed Liquid Crystal (PDLC) samples using the newly developed PTR techniques. Experiments on PDLC samples have been mainly aimed for the investigation on the variation of their thermal properties as a function of frequency of the applied electric field. Our observations are confirming this thermal dependence on frequency (of the applied electric field) due to the presence of polarization field effects, which is also known as Maxwell-Wagner-Sillars (MWS) effect. The obtained results are modelled against existing theories on MWS effect for finding the elastic and electrical properties of PDLC samples from their thermal informations.

Photothermal Infrared Radiometry (PTR)

Photothermal Infrared Radiometry [START_REF] Nordal | Photothermal Radiometry[END_REF][START_REF] Santos | Theory of the photothermal radiometry with solids[END_REF] (PTR) is an efficient and accurate nondestructive technique able to find the thermal properties of materials. As the name specifies, it uses the infrared radiation coming out of the material under investigation and gives us the advantage of investigating materials in a non contact manner. Because of the non-contact ability of PTR, it is mainly used to characterize solid materials, where the contact techniques can produce errors due to the contact resistance at the sample-sensor interface. Considering the thermal investigation capability of layered systems [START_REF] Sheard | Measurement of opaque coating thickness using photothermal radiometry[END_REF][START_REF] Frederikse | Heat conductivity of oxide coatings by photothermal radiometry between 293 and 1173[END_REF][START_REF] Lazare | Investigation of Thermal Transport in Layered Sytems and Micro-structured Semiconductor Devices by Photothermal Techniques and Finite Element Simulations[END_REF],

thin films [START_REF] Visser | Measurement of thermal diffusion in thin films using a modulated laser technique: Application to chemical-vapor-deposited diamond films[END_REF], liquids [START_REF] Kusiak | Measuring the thermal conductivity of liquids using photo-thermal radiometry[END_REF][START_REF] Sreekumar | Measurement of thermal effusivity of liquids using a photothermal imager[END_REF] etc., PTR has its own space in the field of thermal characterisation of materials.

Thermal Parameters from Radiometry signals

Dealing with the experimental data and retrieving back the thermal informations is an important part of thermal analysis. Usually the data consists of frequency dependent amplitude and phase measured and recorded by a lock-in amplifier represented by the complex relation:

V(z, ω) = Z(ω)Γ(z, ω) (3.2)
Here, Z(ω) represents the instrumental transfer function and Γ(z, ω) contains the thermal information of the sample. Due to the difficulty in quantifying the frequency dependent instrumental transfer function, the experimental analysis needs normalization of the data obtained by dividing two separate frequency scans:

-a usual sample scan and a reference scan with different material in exactly identical experimental conditions.

-a sample scan followed by a reference scan on the same sample using different experimental configuration.

This normalised signal, free from the instrumental transfer function and contains only the thermal parameters of the sample and the reference material. By analytically solving or numerically fitting this normalised signal against proper equation(s) derived for the temperatures in the last section 2.2, unveils the thermal properties of the sample.

Measuring Liquid Samples Using Photothermal Radiometry (A Novel Approach)

Generally measuring liquid samples need proper holder or encapsulation because of its flowing nature. As a result it increases the experimental difficulties also. In order to reduce the complexity of the data analysis and thereby increasing the accuracy and certainty of the measured thermal properties, a three layer system with liquid sample at the centre of two transparent semi infinite windows has been considered in this novel approach [START_REF] Kuriakose | Improved methods for measuring thermal parameters of liquid samples using photothermal infrared radiometry[END_REF],

as shown in the fig. 3.2. The possibility of irradiating the sample from the top, at the interface of layer-0 and layer-1, as well as from the bottom, at the interface of layer-1 and layer-2, has been used for these measurements.

Since the experimental signal is in the infrared (IR) region (λ ∼10µm) and since the signal detection is from the top of the sample, a visible -infrared (VIR) transparent CaF 2 upper window (layer-0 ) was chosen. At the bottom, we have used visible transparent glass.

Consequently a laser absorbing coating at the liquid interface side of both of the windows has been accomplished in order to completely block the laser beam at each of the sample boundaries and to provide necessary thermal excitation. with eq. ( 2.41) and it can be written as:

Γ BF (ω) = T 1 (ω, z = -d) T 0 (ω, z = 0) = I b 2κ 1 σ 1 I f 2σ 1 κ 1 2e -σ 1 d 1 + ℜ 2 e -2σ 1 d (3.3)
where, I b and I f are the peak intensities of the laser radiation for the back and front excitation respectively. Doing further simplification one can arrive at:

Γ BF (ω) = A f e -σ 1 d 1 1 + ℜ 2 e -2σ 1 d (3.4)
with,

A f = 2 I b I f (1 + b 21 ) , ℜ 2 = (1 -b 21 ) (1 + b 21 ) , b 21 = e 2 e 1
Further, at higher modulation frequencies, the term exp(-2σ 1 d) in eq. (3.4) can be approximated to zero. Thus the equation for the BF-PTR configuration can be written as: still it is evident that the experiment can be realised in a well extended frequency domain. Here, both the amplitude and phase independently carry the information about the thermal diffusivity. So relation for finding thermal diffusivity analytically is:

Γ BF (ω) = A f e -σ 1 d (3.5)
from amplitude, α 1 = πf d ln(A f /A) 2 (3.6) from Phase, α 1 = πf d θ 2 (3.7)
where, A and θ are the experimental amplitude and phase respectively. Both equations (3.7 and 3.7) reveal us that the thermal diffusivity can be calculated from any single frequency and it depends only on the thickness of the sample.

Back PTR (B-PTR) :-For Simultaneous Detection of Diffusivity and Effusivity

Alike back photopyroelectric (BPPE) technique [START_REF] Mandelis | Theory of photopyroelectric spectroscopy of solids[END_REF][START_REF] Chirtoc | Theory of the photopyroelectric method for investigation of optical and thermal materials properties[END_REF], the so called Back-PTR (B-PTR) configuration posses high sensitivity and allows simultaneous detection of thermal diffusivity and effusivity of the sample. As in the case of BF-PTR, here also we are bounded to some maximum range of modulation frequency. As shown in figure 3.2(b), the heat is generated at the backing-sample interface and the signal detection is from the CaF 2 -Sample interface for both scans, the sample and reference scans. The normalized equation derived from eq. (2.43) is given by:

Γ B (ω) = T 1 (ω, z = -d) T ′ 1 (ω, z = -d) = e ′ 1 e 1 1 + b ′ 01 1 + b ′ 21 e σ ′ 1 d (1 + b 01 ) (1 + b 21 ) e σ 1 d 1 -ℜ ′ 0 ℜ ′ 2 e -2σ ′ 1 d 1 -ℜ 0 ℜ 2 e -2σ 1 d (3.8)
The variables with prime show the thermal parameters of the reference material and without prime represent the sample. The trends of these plots demonstrate that the sensitivity towards thermal diffusivity of the sample is monotonically increasing with the increase in modulation frequency for both the amplitude and phase. It is also evident that the amplitude is sensitive to the thermal effusivity in the entire frequency range while the phase is sensitive only at the lower frequency region. Apparently, for such measurements which needs a physical replacement of the sample with a reference material, a varying proportionality factor (A f ) may be needed to consider in the fitting domain in order to nullify the offset that can come in the signal amplitude because of many reasons, restricts the use of amplitude alone for finding thermal parameters. Thus, in this case, an effusivity sensitive phase data in the lower frequency region is needed to determine both of the thermal parameters from eq. (3.8).

Diffusivity Effusivity Conductivity

(m 2 s -1 ) (Jm -2 K -1 s -1/2 ) (Wm -1 K -1 )
Further more, B-PTR gives the advantage of finding thermal diffusivity and effusivity simultaneously from a single frequency for those measurements in which A f is kept fixed (means: no physical sample-reference replacement). This is the case when the used reference material is the sample itself in a particular condition (ambient temperature, zero applied electric field etc.) where its thermal parameters are known. It helps to avoid time consuming frequency scans while preserving better accuracy. Sample's thermal diffusivity can be calculated from the phase and the effusivity from the combined amplitude and phase signals. The analytical expression for sample's thermal diffusivity, α 1 , and effusivity, e 1 , are given by equations (3.9) and (3.10) respectively. Both of these equations are derived from equation (3.8) considering that the sample is at quasi thermally thick (µ s ≈ d) frequency regime and thus the negative exponential term has negligible contribution (e -2σ 1 d ≈ 0).

α 1 = d √ α r πf d √ πf -θ √ α r 2 (3.9) e 1 = - 1 2 L -R + (L -R) 2 -4J (3.10)
where,

R = exp(θ) e r A e 2 r + e r L + J L = e 0 + e 2 J = e 0 e 2
A is the normalized amplitude and θ is the normalized phase. α r and e r are thermal diffusivity and effusivity of the reference material respectively. f represents the modulation frequency and d is the sample thickness.

Front-PTR (F-PTR)

Rather easier but less sensitive than the rear detection involved models, this, so called front-PTR configuration is depicted as in Fig.

Γ F (ω) = 1 + R 2 e -2σ 1 d 1 -R 0 R 2 e -2σ
(α 1 =1.48×10 -7 m 2 s -1 , e 1 =650 Jm -2 K -1 s -1/2
) and d =30 µm with steel as backing and CaF 2 as the top layer. The normalisation has been done with the same sample while making it semi infinite.

one and together, for a typical liquid sample having distinctive values of thermal parame-

ters (α 1 =1.48×10 -7 m 2 s -1 , e 1 =650 Jm -2 K -1 s -1/2
). The sample is sandwiched between a CaF 2 window (layer-0) and a steel substrate (layer-2) holding thermal parameters as in the table 3.1. Here the choice of steel substrate is because of its high thermal effusivity that improves the sensitivity via the increased thermal mismatch between the sample and backing. This configuration allows one to find out the thermal diffusivity and effusivity of a liquid sample simultaneously knowing the thermal parameters of the surrounding layers and the sample thickness. The zero crossing method [START_REF] Depriester | New methodology for thermal parameter measurements in solids using photothermal radiometry[END_REF] is also valid for finding the thermal diffusivity of the sample from the normalised phase knowing only the thickness (d)

and zero crossing frequency (f (θ=0) ) and is given by:

α 1 = 4d 2 f (θ=0) π , n = 1, 2, 3... (3.12)

Photothermal Radiometry Experimental Set Up

The general procedure for conducting PTR experiments is relatively simple [START_REF] Almond | Photothermal Science and Techniques[END_REF]. Like other photothermal techniques [START_REF] Vargas | Photothermal techniques applied to thermophysical properties measurements (plenary)[END_REF], the sample under investigation is heated periodically at a frequency, f = ω/2π, where ω is the angular frequency, using an intensity modulated laser beam. These heat pulses diffuse into the sample layers and produce periodic temperature 3.7

Electronic Circuitry and Signal Recording

The detector signal was converted to voltage and pre amplified by PA 300 pre-amplifier.

This amplified signal was then connected to a Lock-in amplifier ( SIGNAL RECOVERY,

Temperature Controlling

A home made heater powered by a programmable power supply (Instek, PSS-2005, 0-20V, 0-5A) was used for heating the sample cell. This helped to conduct experiments under constant temperature as well as to carry out measurements under varying temperature. As used temperature controller, controlled by a computer based PID (Proportional Integral Derivative) controller, had the ability to regulate temperature better than 10 mK inside the sample cell.

Electric Field Varying Experiments

For electric field varying measurements (e.g., liquid crystal re-orientation), signal from a function generator (RIGOL, DG2021A) was amplified with a ×20 Voltage amplifier (model:F20A) and applied to the sample cavity. Least Square Analysis and Error Calculation :

(m 2 s -1 ) (Jm -2 K -1 s -1/2 ) (Wm -1 K -1 )
In table 3.3, the best fit values and their statistical uncertainties (σ p ) for diffusivity (α 1 ) (one of the fitted parameter) calculated from each type of experimental signals (amplitude, phase and complex) are presented. The χ 2 cost function is calculated by:

χ 2 = 1 N N j=1 [Γ exp (ω j ) -Γ theory (ω j , p)] 2 (3.13)
with N , the number of summed quadratic differences of the experimental and theoretical values; ω j (j = 1...N ), the experimentally available frequencies; Γ exp (ω j ), is the normalized experimental signal; Γ theory (ω j , p), corresponding theoretical normalized signal. p is the set of fitting parameters. Least square analysis finds best set of fit parameters by varying all of them (fit parameters) so that a lowest χ 2 value is achieved. Then the fitting uncertainty σ p for each fit parameter, e.g. α 1 , is calculated by varying its value around the best fit while keeping all other parameters constant.

σ p = 2 (N -P ) ∂ 2 dp 2 ( χ 2 (p) / χ 2 (p 0 ) ) (3.14)
Here, p 0 is the optimised set of fitted parameters corresponding to the lowest χ 2 value obtained from the least square analysis and p is the set of parameters containing the varying parameter for which the uncertainty to be calculated. In eq. (3.14), the second order partial derivative of χ 2 function was obtained by fitting a parabola through χ 2 (p), where p is the varying parameter during the χ 2 analysis. The steepness of this parabola is inversely proportional to the fit parameter's uncertainty.

Interestingly the small values of the uncertainties comparable with the PPE measurement results represent the high sensitivity of the method and quality of the experimental Analyses on amplitude (a); phase (b); and on complex (c) data.

signal. The experimental results on ethylene glycol (E.G) and lanolin (wool wax) [START_REF] Mitchell | Lanolin and Its Derivatives[END_REF] are also included in table 3.3. Nematic liquid crystals tend to align themselves parallel to one another along an arbitrary principle axis (n). While cholesteric phase happens when there is a "twisting" of the nematic director between consecutive layers, usually in helix form. In smectic phase, the molecules align parallel to one another within a layer and inter layer translational movements are restricted. Figure 3.12 schematically explains these LC phases.

Liquid crystals in its crystalline phase are opaque and turbid fluid to our naked eye but it shows characteristic optical textures due to its strong birefringence property when looking through a polarizing microscope. In normal form, direction of the director, n, can be in any arbitrary direction within the mesophase. Interestingly, these directions and thereby their properties can be controlled by different ways, e.g, rubbing or surface treatment of the material in contact, applying electric or magnetic field etc. These unusual optical properties and the possibility to control it have attracted the scientific world to use it in various areas. The thermal diffusivity variation is about 9% without doing any pre surface treatments which is necessary to obtain high degree planar alignment and thereby increased thermal parameter contrast [START_REF] Marinelli | Thermal conductivity and thermal diffusivity of the cyanobiphenyl (nCB) homologous series[END_REF]. This behaviour of the thermal diffusivity of 5CB as a function of electric field is similar to the one obtained with PPE in reference [START_REF] Hadj Sahraoui | Heat transport in polymer-dispersed liquid crystals under electric field[END_REF]. α and e as in figure 3.16(a). It shows closed curves around the best fitting pair of values which confirms the absence of any interdependency between the two thermal parameters.

Results obtained with B-PTR configuration

Most Squares Inversion and Multi-Fold Degeneracy :

Assessment of two fold degeneracy (between any two fitting parameters) can be brought out by plotting contour plots but a three fold or higher (multi fold) degeneracy cannot be viewed in 2-D plots. Here a third fitting parameter called proportionality factor (A f ) which comes from the sample-reference replacement (A f has effect only on the amplitude and not on the phase. A possible reason for including A f is coming from the small changes in absorbed laser intensity due to the sample cell rearrangements which can alter the amount of photothermal heat generation) may introduce the chances to have a three fold degeneracy (same results for different sets of input parameters) between the three unknown fitting parameters (α, e and A f ). It can be brought out by doing so called "Most Squares Inversion" [START_REF] Preethy Chirukandath Menon | High accuracy, self-calibrating photopyroelectric device for the absolute determination of thermal conductivity and thermal effusivity of liquids[END_REF][START_REF] Jackson | Most Squares Inversion[END_REF]. In classical least-squares error analysis procedure (described in section 3.2.1.1), each parameter vary around its best fit value keeping all other parameters fixed unambiguously and calculates the error. While in the case of most squares error analysis, each chosen value of a selected parameter (e.g., α) around its best fit is optimized by varying all other fitted parameters until minimizing the χ 2 cost function. So, for each value of the selected parameter, an additional least square analysis by minimizing the χ 2 cost function is being carried out in order to optimize the full set of fit parameters. The results from the most squares analysis can be analysed as in the following way. If the analysis shows a single minimum, which means that the obtained set of values are unique. On the other hand if it shows a flat line, it indicates a multi-fold degeneracy which means that the fit parameter set satisfies more than one solution for the same experimental data. Figure 3. 16(b,c)

shows the least square and most-squares analysis for the thermal diffusivity and effusivity.

The parabolic shape of the plots indicate the absence of degeneracy with all other fitting parameters for each of these thermal quantities. The sharpness of the parabola is a proof of lower statistical uncertainty and high accuracy of the experimental method. From fig.

3.16(b, c) it can be noted that the most squares curves are broader than the χ 2 curves. This is because the most squares analysis take into account of covariance with the other fitting parameters. Employing B-PTR experimental method, we have also investigated the variations of α and e for 5CB liquid crystal sample with varying electric field. The obtained results are from the scans performed at high sensitive frequency region, where the sample was in quasi thermally thick regime. The frequency scan at zero electric field was taken as the reference signal for normalisation for all other signals with applied electric field, thus the A f kept fixed. The reference thermal parameters for the 5CB at zero electric field for thermal diffusivity was from the BF-PTR result on 5CB and for the effusivity was from reference [START_REF] Hadj Sahraoui | Heat transport in polymer-dispersed liquid crystals under electric field[END_REF]. Figure 3.17 Since B-PTR has the advantage of finding thermal diffusivity and effusivity simultaneously from a single frequency for those measurements in which A f is kept fixed, it helps to avoid time consuming frequency scans while preserving better accuracy. Sample's thermal diffusivity can be calculated from the phase and the effusivity from the combined amplitude and phase signals considering the sample is at quasi thermally thick (µ s ≈ d) frequency regime where the negative exponential term in equation (3.8) can be approximated to zero (e -2σ 1 d ≈ 0). The analytical expression for α and e are given by:

α s = d √ α r πf d √ πf -θ √ α r 2 (3.15) e s = - 1 2 L -R + (L -R) 2 -4J (3.16)
where,

R = exp(θ) e r A e 2 r + e r L + J L = e c + e b J = e c e b
and A is the normalized amplitude and θ is the normalized phase. e r , e s , e c and e b are the thermal effusivities of reference, sample, CaF 2 window and backing respectively. α s and α r are the thermal diffusivities of sample and reference respectively. f represents the modulation frequency and d is the sample thickness. Figure 3.19 shows the variation of thermal diffusivity, effusivity and conductivity (calculated from α and e) vs. temperature for the 5CB liquid crystal. The temperature dependent experimental signal was normalized with the signal at the isotropic phase and the reference values were chosen from reference [START_REF] Marinelli | Thermal conductivity and thermal diffusivity of the cyanobiphenyl (nCB) homologous series[END_REF].

The experiment has been done with a single stage temperature controller with temperature resolution better than 10 mK.

Results obtained Using F-PTR configuration

In order to validate F-PTR method, we have measured thermal diffusivity and effusivity of glycerol. The experiment has been conducted as described in section 3.1.2 and the normalisation has been done with the same semi infinite sample. The results on glycerol as the sample are included in table 3.4. The sample is sandwiched between the CaF 2 window, which acts as the semi infinite top layer, and a highly effusive steel backing in order to obtain better sensitivity to sample's thermal parameter changes. The sample space is created by an O-ring shaped mica film and placed in between the top layer and the backing. The thickness of the sample space has been calibrated using water as the sample having known thermal parameters as indicated in table 3. The obtained results from our experiments are in good agreement with the already reported values and also with the results obtained with B-PTR experiments. The uncertainties in the experimental results, obtained from the least squares error analysis by minimizing the χ 2 cost function, for each thermal parameters, are also included in table 3.4. Since this configuration has less sensitivity towards sample's thermal parameters, the results have bigger uncertainties than the results from BF-PTR or B-PTR configurations.

Plausibility of PTR Methods for Characterizing Liquid Sample's Thermally

Until now, the most used method for liquids thermal characterization is probably the PPE calorimetry. The main advantage of this method compared to other PT techniques is its simplicity: it measures directly the temperature variation of the sample with the special feature for liquids of a perfect liquid/pyroelectric sensor thermal contact. In this work, we propose the PTR technique as an alternative calorimetry. Concerning the accuracy of the investigations, in both techniques, when using sandwiched detection cells, it was demonstrated [START_REF] Dadarlat | Photopyroelectric calorimetry of liquids; recent development and applications[END_REF][START_REF] Dadarlat | Combined FPPE-PTR Calorimetry Involving TWRC Technique II. Experimental : Application to Thermal Effusivity Measurements of Solids[END_REF] that it is connected with the values of the thermal parameters of the layers of the detection cell; more exactly, the accuracy is increased when the values of the thermal effusivity of the liquid and backing layers are close. In the PTR configurations proposed in this work, the backing layer is glass with a thermal effusivity rather close to the typical liquids, so the experiment is optimized in order to obtain high accuracy. While considering the signal to noise ratio, PPE outperforms PTR, which limits the temperature resolution granted by the PTR in highly resolved temperature dependent measurements. Some recent advances in IR detection technologies promising us improved sensing possibilities [START_REF] Zeng | Carbon nanotube arrays based high-performance infrared photodetector[END_REF] which in principle allows to perform experiments at extremely low laser powers than it requires now. The requirement of IR transparency of the first layer of the proposed PTR detection cell can be easily fulfilled, a lot of commercially available materials satisfying this criterion.

Thermal Transport Studies in Polymer Dispersed

Liquid Crystals (PDLC) Under Frequency Dependent Electric Field

Polymer Dispersed Liquid Crystals (PDLCs) are the subject of study in our lab for the past few years. Until now only the different aspects governing the thermodynamic of the phase separation and the electro-optical performances (transmission properties, drive voltage, switching times, etc.) of these materials have been extensively investigated. The studies on thermal transport properties of PDLC samples can be very interesting in this heterogeneous material composite. We have used the PTR technique developed for liquid studies to determine the thermal behaviour of the PDLC systems under applied electric field.

PDLCs are modified edition of the conventional LC technology. These are made up of micron or sub-micron sized LC droplets encapsulated inside a polymer matrix. One of the usual procedure of preparation is in-situation polymerization of host polymer matrix in the presence of LC proceeded by phase separation. This manufacturing procedure is especially simple and avoids the requirements of surface aligning or cell filling and sealing which are needed in the case of twist cells. Conventional LC (super twist cells, twisted nematic (TN) cells, π-cell) needs the use of polarisers while PDLC's do not require any polarisers.

Maxwell-Wagner-Sillars Effect

Polymer dispersed liquid crystal assembly is a heterogeneous mixture of LC and polymer.

Because of the difference in dielectric characteristics (ability to hold charges) and electrical conductivities in these material mixture components, an additional charge polarisation occur at each LC-polymer boundaries upon the application of an EF as in fig 3 .22. At lower frequencies, the blocking inner charges at the boundaries start to build up and produce reduction in the equivalent applied EF strength. This interfacial polarisation effect, also known as Maxwell-Wagner-Sillars (MWS) effect [START_REF] Sillars | The properties of a dielectric containing semi-conducting particles of various shapes[END_REF][START_REF] Wagner | Erklärung der dielektrischen Nachwirkungsvorgänge auf Grund Maxwellscher Vorstellungen[END_REF] in a multiple phase mixture, vanishes at sufficiently high frequencies of applied EF at which the movement of charges become frozen out and the development of depolarisation field interrupts. droplet under sinusoidal field [START_REF] Kelly | Dielectric losses in a polymer-dispersed liquid crystal film. volume 1257 of Liquid Crystal Displays and Applications[END_REF][START_REF] Drzaic | Liquid Crystal Dispersion[END_REF], which is given by:

E drop (ω e ) = 3ǫ ⋆ M ǫ ⋆ LC + 2ǫ ⋆ M -φ LC (ǫ ⋆ LC -ǫ ⋆ M )
E a e -iωet (3.17) and,

ǫ ⋆ M = ǫ ′ M -i σ M ω e ǫ 0 (3.18) ǫ ⋆ LC = ǫ ′ LC -i σ LC ω e ǫ 0 (3.19)
where,

φ LC ⇒ Phase separated LC fraction.
E a ⇒ Magnitude of the applied electric field. Inside PDLC, a part of the LC dissolves into the polymer. The amount of LC which dissolves into the polymer is defined as solubility limit (β) and it can be found by doing DSC measurements. The undissolved part will form droplets. Knowing β and the amount of LC added to the polymer, x, one can calculate the phase separated LC fraction (φ LC ) using [START_REF] Roussel | Phase diagrams and morphology of polymer dispersed liquid crystals based on nematic-liquid-crystalmonofunctional-acrylate mixtures[END_REF][START_REF] Benmouna | Equilibrium phase diagram of polystyrene and 8cb[END_REF][START_REF] Smith | Study of formation, phase behavior, and microdroplet size of a polyurethane-based polymer-dispersed liquid crystal[END_REF]:

φ LC = 100 x x -β 100 -β , x β (3.20)
where, all the quantities are in weight percentage. Value of β is about 55% at room temperature has been used to calculate φ LC using eq. (3.20) for finding the amount of LC droplet phase separated inside the polymer matrix.

In this section, we are analysing the MWS effect on dynamic thermal properties of PS/5CB composites and model it using eq. (3.17). Since the improved PTR methods for measuring liquid samples are capable of measuring thermal parameters with enough resolution, we have chosen B-PTR method (section 3.2.2) for experimental characterisation of the PDLC system. Because of the non-contact capability of the PTR technique, the measured thermal informations are free from electric field induced errors compared to contact techniques, for which, the signal can be affected by the electric field applied to the PDLC and making the measurements more tricky.

Heat Flow (a.u.)

Chemical Synthesis

PDLC was prepared by dissolving liquid crystal and polymer in solvent and evaporating the solvent completely afterwards. 5CB and PS monomers in required amounts were dissolved in equal amount of chloroform firstly. After completely dissolving both 5CB and PS in chloroform, the mixture was placed in an oven and allowed for a complete evaporation of chloroform for more than 24 hours to obtain a final PDLC sample. Upon the solvent evaporation, LC-PS phase separation happens and 5CB droplets of the order of micron or sub-micron size develops throughout entire polymer matrix. Micrographs of as prepared PDLCs for the two different samples are shown in fig. 3.24. The pictures are taken using a polarising microscope with crossed polarisers. For the PTR experiment, required amount of PDLC sample was cast onto a quartz cell, prearranged with electric contacts for the electro-thermal measurements (see section 3.1.3 for the experimental procedure), using a spatula and heated it up above LC clearing temperature and closed the cell. The measurements were carried out by keeping the sample temperature constant at ∼ 28 0 C in order to avoid temperature dependent thermal property changes. Sample holder cell thickness used was 50±2µm.

PDLC Under Varying Electric Field

We are interested on thermal properties of PDLCs under varying electric field is because of these composites offer the opportunity to modify the thermal characteristics of the inclusions (LC droplets) without changing physical properties of the system (same number, size and dispersion of inclusions). This is due to the fact that electric field reorients the molecules of liquid crystal in the droplets thereby change their thermal properties. In this manner, one can study and evaluate the contribution of the inclusions to the effective heat transport in the films.

Since the interfacial thermal resistance between different constituent phases in a com-posite can play a critical role in the thermal behaviour of composite systems, the effect of this thermal resistance on the effective thermal conductivity of PDLC with different liquid crystal concentrations has been studied. Firstly, we have investigated the variation of thermal parameters of both PDLC samples, (85% LC and 73% LC) under varying electric field at constant frequency (f e = 1 kHz) and the results are depicted as in fig. 3.25. The PTR experiments were conducted by fixing the laser modulation frequency, f = 18Hz, at which the sample is in quasi-thermally thick regime, and varying EF strength successively. The displayed results are from the mean of three consecutive EF scans. We have also made an additional filtering by plotting volumetric heat capacity (ρC = e/ √ α)

and by taking data points lie within ±1% or ±0.55% (depending on the population of experimental data points) from the linear fit value of ρC as shown in fig. 3

Effective Medium Theory and Interfacial Thermal Resistance:

In all heterogeneous mixtures, thermal transport is hindered by interfacial boundaries.

Nan et al [START_REF] Ce-Wen Nan | Effective thermal conductivity of particulate composites with interfacial thermal resistance[END_REF] has given an estimation of effective thermal conductivity (κ PDLC ) of such heterogeneous mixtures with spherical inclusions on the basis of effective medium approach by taking into account of interfacial thermal resistance:

κ PDLC = κ m κ LC (1 + γ) + 2κ m + 2φ LC [κ LC (1 -γ) -κ m ] κ LC (1 + γ) + 2κ m -φ LC [κ LC (1 -γ) -κ m ] (3.21)
where, γ = r k /r d , is the ratio of Kapitza radius (r k ) and mean droplet radius (r d ). κ m and κ LC are thermal conductivities of polymer matrix and LC respectively.

γ is a dimensionless parameter which compares the Kapitza radius r k to the droplet radius r d . The Kapitza radius is related to thermal interfacial resistance and describes the transition when interfaces begin to play a significant influence on the effective thermal conductivity of PDLC. When γ ≪ 1 the influence of the interfaces may be ignored but if γ > 1 the contribution of the interfaces to the effective thermal conductivity becomes more important than that of the volume of the inclusions.

By knowing the thermal conductivities of polymer matrix and LC as well as by experimentally finding κ PDLC and φ LC (eq. (3.20)), one can calculate γ by rearranging eq. (3.21), which is given by:

γ = κm κ PDLC (κ LC + 2κ m + 2φκ LC -2φκ m ) -κ LC -2κ m + φκ LC -φκ m 2κ LC + φκ LC + 2 κmκ LC κ PDLC (φ LC -1) (3.22)
Equation (3.22) allows to compute r k , once we know the mean radius of the droplets.

Apparently, fig. 3.24 may not be sufficient to calculate the size of the droplets precisely.

However, a rough estimation of droplet diameters lie around 1 to 5µm for 85% LC and 0.5 to 2µm for 73% LC, from the figure.

Nematic droplets in our system possess the bipolar configuration, at zero field the nematic is aligned tangentially at the droplet wall (fig. Table 3.5 contains the thermal conductivity values used for calculations and the results obtained for γ values. These values, less than unity, are indicating that the volume of the LC droplets are involved in the thermal transport. Moreover it is less prominent in 73% LC sample where γ shows higher value than 85% LC sample. Apparently, due to the reduction in droplets' sizes at lower LC concentrations, increase the ratio, γ, for the same Kapitza radius values. Interestingly, these values are comparable to the one found previously for PS-5CB composites [START_REF] Hadj Sahraoui | Heat transport in polymer-dispersed liquid crystals under electric field[END_REF].

Above results are indicating the thermal transport inside PDLCs are influenced both by the applied electric field and the average droplet size. It is also noteworthy that, both the other dynamic thermal parameters, diffusivity and effusivity, shows the same trend as the thermal conductivity does, thus giving an opportunity to study the thermal behaviour of these samples by finding any one of these thermal parameters. and filtered out the points lie outside ±0.9% of the ρC mean value. Results on 73% LC samples are also consistent with the behaviour of ρC as expected.

Both results, from 73% and 85% PDLC samples, are clearly showing the frequency dependence of the dynamic thermal properties of PDLC samples. At higher frequencies, the charge accumulation at the LC-polymer interfaces due to the mobility of free charges (conductivity effect) are interrupted and the effect of depolarisation field vanishes. This makes the molecules better aligned in the direction of the EF and hence the thermal transport also increases and reaches its maximum. On the other hand, at lower frequencies, the dominant depolarisation field diminish the electric field inside the droplets (E drop ) and it worsen molecular alignment which lower the heat flow normal to the surface of the PDLC material [START_REF] Drzaic | Liquid Crystal Dispersion[END_REF]. can estimate the mean thermal conductivity of LC droplets, given by: Considering κ LC⊥ and κ LC the thermal conductivity perpendicular to or along the molecular long axis, and θ-the angle between this long axis and a given direction (fig.

κ LC = κ m [2κ m (1 -φ) -κ PDLC (2 + φ)] κ PDLC [(1 + 2γ) -φ (1 -γ)] -κ m [1 + 2γ + 2φ (1 -γ)] (3.
3.32), the thermal conductivity along this direction may be express as:

κ LC = κ LC cos 2 θ + κ LC⊥ sin 2 θ (3.24)
Using the values of κ LC and κ LC⊥ , the variation in orientation angle, θ, can be extracted from the thermal conductivity experimental data: the stamped down variations of thermal conductivity values in both samples.These frequency behaviour of PDLC contains informations on several physical phenomenon. In the subsequent sections, we have used the obtained results on θ and κ LC for finding different physical parameters.

θ = asin κ LC -κ LC κ LC⊥ -κ LC (3.

Frequency Dependent Thermal Conductivity and MWS Effect

The relation between droplet electric field, E drop , and the angle of molecular orientation, θ, is given by [START_REF] Drzaic | Liquid Crystal Dispersion[END_REF] :

2cos 2 θ = 1 + e 2 -1 + 2cos 2 ψ (e 2 -1) 2 + 4e 2 cos 2 ψ (3.26)
where, ψ is the equilibrium angle of the droplet directors at zero electric field obtained from EF varying experiments (values are displayed in table 3.6), e is the reduced field parameter and which can be expressed as: e = E drop /E 0 and E 0 is the threshold reorientation electric field. E 0 can be defined as the electric field necessary to reorient LC molecules in its direction (threshold electric field). Its value depends on the droplet radius (r d ), elastic constant (K) and the dielectric anisotropy (∆ǫ) of the LC material. ǫ 0 is the permittivity of free space (8.85×10 -12 F/m). The relation for E 0 is given by [START_REF] Drzaic | Liquid Crystal Dispersion[END_REF]:

E 0 ≈ 1 r d K ǫ 0 ∆ǫ (3.27)
In order to determine the effective thermal conductivity variations of PDLCs as a function of frequency of the applied electric field, one can insert the equation for E drop (f e ) (eq. (3.17)) into the equation for the angle of reorientation (θ, eq. (3.26)), the resultant then put into the expression for LC droplet thermal conductivity (κ LC , eq. (3.24)) and finally to the expression for κ PDLC (f e ) (eq. (3.21)), as shown below:

E drop (f e )
Eq. (3.17)

→ θ

Eq. (3.26)

→ κ LC Eq. (3.24) → κ PDLC (f e )
The outcome of the above relation for κ PDLC (f e ) can be used to model the frequency dependent effective thermal conductivity results of PDLC samples (figures 3.30 and 3.28)

to find electrical parameters of LC and polymer matrix as well as the threshold electric field E 0 . x ψ (rad.) LC respectively as a function of frequency. The values of the EF were chosen from a previous electric field scan (fig. 3.25) so that the LC molecules were aligned parallel to the EF at a frequency high enough to nullify the MWS effects. During the fitting procedure, E 0 as well as electrical conductivities of both the polymer matrix and LC were kept as free parameters. Values of the materials' dielectric properties were taken from literatures. The results obtained from fitting are displayed in table 3.6.

σ M (S/m) σ LC (S/m) E 0 (V/m) f 0 (Hz) E a (V/m) 85% 0.6 (1.27±0.09)×10 -9 (4.9±0.3)×10 -8 (6.8±0.3)×10 4 21 ± 2 1.27×10 5
Figure 3.37 contains the simulated plots for 85% LC and 73% LC samples having the values used in or obtained from the theoretical fitting of the experimental data. These plots show the evolutions of E drop and κ PDLC for both samples. The threshold electric fields (E 0 ) and the corresponding frequencies (f 0 ) are also labelled inside the plots and also included in table 3.6. The electrical parameters for 85% LC found from fitting are in good agreement with the values found in literatures (ref. section 3.3.2). While for 73% LC sample, the results are showing relatively higher values than reported. One of the reasons for this difference could be due to the possible variations in the solubility limit of the LC. In addition, the system properties are vulnerable to change during the course of time, temperature and synthesizing conditions.

The main interesting parameter in our study is the threshold field (E 0 )or frequency (f 0 ). These values are indicating the necessary field needed to align the LC molecules in the direction of the applied EF. Obviously, the values of these parameters increase with decreasing LC concentration. This behaviour is expected since the droplet size decreases with decreasing concentration and thus the field across the droplet must be higher for aligning the molecules. In the case of f 0 , the depolarisation field increases with decreasing frequency thus the equivalent field acting on the droplets is linear to the applied frequency.

Table 3.7: Elastic constants for the PDLC samples.

x ∆ǫ r d (µm) E 0 (V/m) K (N) 85% 10 0.5/2.5 (6.8±0.3)×10 4 9.4 × 10 -14 /2.8 × 10 -12 73% 10 0.25/1 (7.2±0.1)×10 4 2.8 × 10 -14 /4.7 × 10 -13

We can also deduce the elastic constant, K, knowing E 0 and the droplet radius using eq.

(3.27). Values found for K for both of the PDLC samples are displayed in table 3.7. These effective values of elastic constants govern the interaction between the anchoring forces at the droplet-polymer boundaries, which make the droplet to be aligned in a particular direction, and the elastic forces acting in the bulk of the LC droplet. The studied samples are showing the values of K lower than that the value reported for bulk nematic 5CB (4.1x10 -12 ) [START_REF] Doane | Polymer Dispersed Liquid Crystals for Display Application[END_REF]. This is attributed due to the increased anchoring forces at the LCpolymer boundaries. Apparently, the K values are more closer and even similar for the 3.4. Summary of the Experimental Results on Liquid Samples biggest droplets in the case of 85% LC to the reported bulk values, where the molecules available away from the boundaries are higher than 73% LC sample.

Summary of the Experimental Results on Liquid Samples

We have explored the ability of photothermal infrared radiometry for studying thermal properties of liquid samples and demonstrated its capability to give results with high accuracy. The two presented configurations are described theoretically followed by experimental results. BF-PTR gives the absolute thermal diffusivity of a sample knowing only the sample's thickness and also the result is independent of the thermal parameters of surrounding

Introduction

Certain materials produce an electrical potential difference when they are subjected to a temperature gradient [START_REF] Hendricks | Engineering Scoping Study of Thermoelectric Generator Systems for Industrial Waste Heat Recovery[END_REF]. This phenomenon is called Seebeck effect and these solid-state materials are called thermoelectric (TE) materials. Even though, at present, TE materials are less efficient than other energy harvesting systems like photovoltaic, they have attracted the scientific community over the past decades [START_REF] Michael | Review THERMOELECTRIC WASTE HEAT RECOVERY AS A RENEWABLE ENERGY SOURCE[END_REF]. New interests on TE materials started since the theoretical predictions suggested that the thermoelectric efficiency could be strongly improved with nano-structuring [START_REF] Snyder | Complex thermoelectric materials[END_REF][START_REF] Li | Thermal Transport in Nanostructured Solid-State Cooling Devices[END_REF][START_REF] Liu | Recent advances in thermoelectric nanocomposites[END_REF][START_REF] Chen | Phonon engineering in nanostructures for solid-state energy conversion[END_REF]. The performance depends mainly on the dimensionless quantity called figure of merit ZT = S 2 σ k T , where S, σ, κ, T are the Seebeck coefficient, electrical conductivity, thermal conductivity and the absolute temperature. Polymer thermoelectrics are new class of materials interestingly emerged out after the finding of electrically conducting doped polyacetylene [START_REF] Shirakawa | Synthesis of electrically conducting organic polymers: halogen derivatives of polyacetylene, (CH) x[END_REF]. Since

∆V = S [T (z = 0) -T (z = d)] (4.2)
Referring back to the derived expressions in chapter 2 for the temperature fields for an optically opaque sample of thickness d in contact with a semi-infinite substrate and air as the top layer (layer-0 ), excited by a modulated laser beam is given by, including the terms for convection heat transfer loss(H 1 ) [START_REF] Mandelis | Diffusion-Wave Fields, Mathematical Methods and Green Functions[END_REF]:

T (z, ω) = I 0 (1 + H 1 ) 4k 1 σ 1 1 + ℜ 2 exp(-2σ 1 (d + z)) 1 -H 1 ℜ 2 exp(-2σ 1 d) exp(σ 1 z) (z ≤ 0) (4.3)
where I 0 , k 1 , ℜ 2 and σ 1 are intensity of the incident radiation, sample's thermal conductivity, thermal wave reflection coefficient (eq. (2.42)) and the complex thermal wave number (eq. (2.17)) respectively, as mentioned earlier. H 1 is a parameter depending on convection coefficient h 1 , followed by the relation:

H 1 = k 1 σ 1 -h 1 k 1 σ 1 + h 1 (4.4)
It should be pointed out that h 1 can be neglected for a given sample for high frequency. In the following section 4.2.1 we have carried out simulations to show the suitable frequency range where h 1 can be neglected. By equating eq. ( 4.3) into eq. ( 4.2) and after rearranging, the potential difference between the two surfaces can be expressed as:

∆V = SI 0 (1 + H 1 ) 4k 1 σ 1 1 + ℜ 2 exp(-2σ 1 d) -(1 + ℜ 2 ) exp(-σ 1 d) 1 -H 1 ℜ 2 exp(-2σ 1 d) (4.5)
The normalized signal is obtained by realising frequency scans with separate substrates, e.g., air and glycerol. When the substrate is air, ℜ 2 becomes ℜ 0 (eq. (2.42)) and the voltage difference is given by:

∆V 0 = SI o (1 + H 1 ) 4k 1 σ 1 1 + ℜ 0 exp(-2σ 1 d) -(1 + ℜ 0 ) exp(-σ 1 d) 1 -H 1 ℜ 0 exp(-2σ 1 d) (4.6)
Further, considering that the thermal transport by conduction largely outweighs the thermal transport by convection, the real part of k 1 σ 1 ≫ h 1 , then the quantity H 1 can be approximated to 1 and also, since the air effusivity is too low ℜ 0 ≈ 1. Then the normalized voltage V n , obtained by dividing ∆V with ∆V 0 is given by, after simplification:

V n = ∆V ∆V 0 = 1 + (1 -ℜ 2 ) exp(-σ 1 d) 1 -ℜ 2 exp(-2σ 1 d) . (4.7)
Apparently, the phase (normalized phase) from eq. (4.7) decreases with frequency and becomes zero for a first time at a value d/µ 1 = π. Thus, the thermal diffusivity of the sample, α 1 , can be extracted from, as previously reported for photopyroelectric techniques [START_REF] Hadj Sahraoui | The application of the photopyroelectric method for measuring the thermal parameters of pyroelectric materials[END_REF]:

α 1 = d 2 f 0 π , (4.8)
where, f 0 is the zero crossing frequency. Knowing α 1 , the thermal effusivity can be obtained after some rearrangements of eq. (

:

e 1 = e 2 1 + ℜ 2 1 -ℜ 2 . (4.9)
where, ℜ 2 is given by:

ℜ 2 = (V n -1) -exp(-σ 1 d) (V n -1) exp(-2σ 1 d) -exp(-σ 1 d) . (4.10)
Therefore, both thermal parameters of the TE sample (as sensor) can be determined either by a direct least squares fitting of eq. (4.7) to experimental data or analytically using eqs.

(4.8), (4.9) and (4.10) provided that the effusivity of backing is known.

Simulations on Convection Effects and Sensitivity

Due to the poor thermal conductivity of polymers, the measurements need to be carried out at lower frequencies, meaning that convection effects can not be neglected. In order to take into account of this phenomenon, the influence of the convection effect on the PTE signal is investigated numerically.

Experimental Results using PTE technique 4.2.2.1 Intrinsically Conducting Polymers

Polymer composite materials identifies as an indispensable stuff in our scientific arena. It creates a new distinguished class of material, which are light in weight and mechanically stronger in utility. The ease of preparation and possibility of reprocessing opens cost effective solutions for many applications using polymer composites. Polymers were previously known as electrically insulting materials until the recent findings of appreciable electrical conductivity in them. This circumstantial findings lead to the developments on using such intrinsically conducting polymers (ICPs) as bio-materials [START_REF] D D Ateh | Polypyrrole-based conducting polymers and interactions with biological tissues[END_REF], actuators [START_REF] John | Application of Polypyrrole Actuators : Feasibility of Variable Camber Foils[END_REF], fabrics [START_REF] Hu | Development of a cooling fabric from conducting polymer coated fibres: Proof of concept[END_REF], corrosion inhibitors [START_REF] Uffana Riaz | High performance corrosion protective DGEBA/polypyrrole composite coatings[END_REF], in electronics [START_REF] Baibarac | Nanocomposites Based on Conducting Polymers and Carbon Nanotubes from Fancy Materials to Functional Applica-tions[END_REF], organic LEDs and PVs, charge dissipating (antistatic) layers and chemical sensor research. ICPs are polymers with extended π-conjugation along the molecular backbone. Their conductivity can be changed by several orders of magnitude from a semiconducting state to a metallic state by doping. Usually p-doping is achieved by partial oxidation of the polymer by a chemical oxidant or an electrochemical method, and causes depopulation of the bonding π orbital (HOMO) with the formation of "holes" [START_REF] Macdiarmid | Synthetic Metals" : A Novel Role for Organic Polymers ( Nobel Lecture )[END_REF]. The possibility of generating electricity [3,[START_REF] Xuan | Thermoelectric properties of conducting polymers: The case of poly(3-hexylthiophene)[END_REF][START_REF] Kim | Improved thermoelectric behavior of nanotube-filled polymer composites with poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate)[END_REF] ing are described elsewhere [START_REF] Chan | Carbon nanotube-polyaniline nanohybrids: Influence of the carbon nanotube characteristics on the morphological, spectroscopic, electrical and thermoelectric properties[END_REF]. Each surface of the pellets were covered with a sputtered silver electrode on which electrical leads were silver pasted and plugged into an EG&G 7260 lock-in amplifier (Fig. 4.1).

Experimental Details

Conducting experiments based on PTE technique are more or less similar to the phototpyroelectric (PPE) experiments [START_REF] Longuemart | Study on Liquid Crystal and ferro fluids using Photopyroelectric Technique[END_REF][START_REF] Chirtoc | Development of the frontdetection photopyroelectric ( FPPE ) configuration for thermophysical study of glassforming liquids[END_REF]. For PTE, the sensor is a thermoelectric (TE) device rather than a pyroelectric generator as in PPE. For making sensors all the PANI-CNT pellets were coated on both sides with gold or silver using a sputter coater (Cressington 108)

or silver painted and attached electrical contacts on both sides. The electrically conducting coatings integrate all the generated charges on both surfaces of the sensor. A lock-in amplifier in voltage mode, connected directly to the PTE sensor, was used to detect the signal.

We have used pure PANI samples and also composites with carbon nanotubes (CNT) as sensors. Typical electrical resistance between the terminals of the sensor measured was only a few ohms. The laser power used was also comparatively high (∼ 750 mW) in order to get enough signal. Typically the signal was around 10 µV at a modulation frequency of 2 Hz and the noise level was as low as 50 nV. The laser power was chosen so that the signal to noise ratio stays better than 10 in the highest modulation frequency used for the experiment. Amplitude (upper plot) and Phase (lower plot).

Results and Discussion

Experiments have been carried out using the setup described in Fig. These results for OxSWNT-PANI sample were also calculated analytically using the zero crossing frequency (f 0 = 11.5 Hz) of the normalized phase using eq. (4.8). It led to a thermal diffusivity value of (4.45 ± 0.10)×10 -7 m 2 s -1 . Based on this value, thermal effusivity has also been calculated from eq. (4.10) and obtained, e = 1212 ± 37 Ws 1/2 m -2 K -1

and the corresponding thermal conductivity value is 0.81 ± 0.04 Wm -1 K -1 . Conducting measurements on solid samples using PTR are well established and extensively using for the accurate determination of thermal parameters [START_REF] Depriester | New methodology for thermal parameter measurements in solids using photothermal radiometry[END_REF][START_REF] Park | Optical Measurements of Thermal Diffusivity of a Material[END_REF][START_REF] Ravi | Optothermal depth profiling by neural network infrared radiometry signal recognition[END_REF]. The method for simultaneous determination of thermal diffusivity and effusivity of free standing thin layers is of interest [START_REF] Streza | Photothermal radiometry (PTR) investigation of dynamic thermal parameters of dental composites[END_REF]. Theoretical model for our experiments considers a three layer configuration with air as the top layer (layer-0 ), the sample as layer-1 and air or liquid with well known thermal parameters as the backing (layer-2 ), depicted as in fig. 2.2.

The sample is considered as optically opaque and the backing is thermally semi infinite.

Using the surface absorption model described by eq. (2.41), at z = 0, can be used to find the temperature field at the sample surface and it reveals the thermal parameters of the sample. The reference signal for the normalisation can be obtained by performing the experiment with another backing material (e.g., air replaced with water) without altering the sample and layer-1. This means ℜ 2 , in eq. (2.41), is the only modifying parameter.

Thus the equation for the normalised signal obtained by dividing two frequency scans with two different backing materials can be written as:

Γ F (ω, z = 0) = I 0 2σ 1 k 1 (1 + b 01 ) 1 + ℜ 2 e -2σ 1 d 1 -ℜ 0 ℜ 2 e -2σ 1 d × 2σ 1 k 1 (1 + b 01 ) I 0 1 -ℜ 0 ℜ 2r e -2σ 1 d 1 + ℜ 2r e -2σ 1 d (4.11)
where, ℜ 2 is replaced by ℜ 2r in the reference (normalization) signal.

Approximation while using 'air' interfaces:-Because of the extremely low effusivity of air medium makes the effusivity ratios b 01 and b 21 at both the sample interfaces will become negligibly small. The approximated terms are:

b 01 ≈ 0, b 21 ≈ 0, ℜ 0 ≈ 1, ℜ 2 ≈ 1
So the eq. (4.11) can be rearranged and rewritten as:

Γ F (ω, z = 0) = 1 + e -2σ 1 d 1 -e -2σ 1 d 1 -ℜ 2r e -2σ 1 d 1 + ℜ 2r e -2σ 1 d (4.12)
Multiplying the terms in the above eq. (4.12) and neglecting the higher order exponential term e -4σ 1 d , which has again negligible contribution, will result in: the usual higher thermal conduction property of SWNTs. Among all the four composites, oxidized nanotube composites are showing a little lower thermal conductivity values than their un-oxidized counter parts. This might be due to the presence of oxide layer along the surface of the nanotubes, which, upto a small extend, hindering the heat transport at the matrix-nanotube boundaries. Electrical conductivity studies on this same set of samples [START_REF] Chan | Carbon nanotube-polyaniline nanohybrids: Influence of the carbon nanotube characteristics on the morphological, spectroscopic, electrical and thermoelectric properties[END_REF] are also confirming the same trend as from our thermal studies. Of interest, it is also pointing out that, regardless of the nature of the inclusions, the thermal effusivities stay roughly constant, which indicate the thermal conductivity behaviour is mainly controlled by the thermal diffusivity. Here, the higher thermal conductivities of individual SWNTs in comparison with individual MWNTs attributed to the higher thermal conductivity values of SWNT-PANI composites. Although it is acknowledged that SWNTs present a higher interfacial thermal resistance than the MWNTs [START_REF] Ce-Wen Nan | Interface effect on thermal conductivity of carbon nanotube composites[END_REF], this property, however, is not sufficient to mitigate the effects of thermal conductivity differences between the aforementioned tubes. We believe, this is due to the strong polymer-nanotube interaction that came from the in situ polymerization procedure. Further, the thermal conductivities of oxidized nanotubes based composites are lower than their unoxidised counterparts. This behaviour can be explained by the oxidation process of CNTs which induces defects on the nanotubes.

Γ F (ω, z = 0) = 1 + (ℜ 2r -1)e -2σ
These defects scatter the phonons, and, thus, lower the thermal conductivity. A similar behaviour has been suggested for the lowering of the electrical conductivity in the case of oxidized CNT due to induced carrier scattering centres. have been calculated from these parameters using the formula ZT = S 2 κe k T , at ambient temperature (T = 300K). The results are displayed in figure 4.10. It is obvious from the figure that the ZT is considerably enhanced with the incorporation of carbon nanotubes into the polymer material even with a small fraction of CNT (6.6 wt-%). Overall, nanocomposites containing unoxidized and single-walled CNTs exhibit better thermophysical properties than their oxidized or multiple-walled counterparts. Among the investigated samples, PANI/unoxidized SWNT nano-composite showed the most promising TE characteristics. This result can be explained by i) the electrical con-ductivity improvement provided by the high SWNT electrical conductivity ,and, ii) the weak thermal conductivity increase resulting from interfacial thermal resistances between nanotubes and PANI. The CNT oxidization process creates defects on the nanotubes leading to a decrease of the thermal conductivity.

PTE Technique for Thermal Investigation of

Solids samples

TE materials can also be used as temperature sensors for the characterization of materials thermally. Similar to the PPE methods, the detection configurations can be classified as:

(i) the "front" one (sensor directly irradiated and sample in back position) coupled with TWRC method (scan of the liquid's thickness), for thermal effusivity measurements [START_REF] Shen | Thermal-wave resonator cavity[END_REF][START_REF] Balderas-López | Thermal-wave resonator cavity design and measurements of the thermal diffusivity of liquids[END_REF][START_REF] Balderas-López | Self-normalized photothermal technique for accurate thermal diffusivity measurements in thin metal layers[END_REF] and (ii) the "back" one (sample directly irradiated and sensor in back position), together with the chopping frequency scan, for thermal diffusivity investigations [START_REF] Marinelli | Photopyroelectric study of specific heat, thermal conductivity, and thermal diffusivity of Cr2O3 at the Neel transition[END_REF].

Further we are deriving the equations for these two configurations, so called Front-PTE (FPTE) and Back-PTE (BPTE).

Front Photothermoelectric Configuration (FPTE)

Theoretical model for the FPTE configuration is depicted as in figure 4.11. Here the model has to accommodate one more layer than we have derived in the previous chapter. Since the basic procedure for any number of layers are same, we are expanding the already derived three layer model with extra terms in order to obtain a theoretical model for a four layer configuration. A proposed solution for the temperature field T 3 for an additional fourth layer can be written as:

T 3 = A 3 e σ 3 z + B 3 e -σ 3 z e iωt [z ≤ -(d + b)] (4.14)
where, d and b are the thickness of layer: 2 and layer: 3. A 3 and B 3 are the unknown constants. The boundary conditions for solving the equation are:

κ 2 ∂T 2 ∂t = κ 3 ∂T 3 ∂t , T 2 =T 3 , [z = -(d + b)] (4.15)
After solving the equations for temperatures for all layers including this fourth layer, one can arrive at an expression for voltage induced on the TE sensor given by: ∆V = S T (z=0) The easiest way to normalize the signal described by eq. 4.23 is to perform a measurement with empty sensor. If d = 0, the normalization signal becomes:

T (z=-d) dT = S[T (z = 0) -T (z = -d)] (4.16) ∆V = S I 0 2κ 1 σ 1 (1 + Q)(e σ 1 d -1) + (1 -Q)(e -σ 1 d -1) (1 -Q)e -σ 1 d -(1 + Q)e σ 1 d (4.
∆V 0 = - SI 0 2κ 2 σ 2 (4.24)
and the normalized one:

∆V n = 2 exp(-σ 1 d) (b 12 + 1) -(b 12 -1) exp(-2σ 1 d) (4.25)
If, additionally, the sample is at quasi thermally thick frequency regime then e -2σ

Comparison with PPE

When using the photopyroelctric (PPE) technique, in the same FPPE configuration and approximation (thermally thin sensor and coupling fluid), the normalized FPPE voltage is

given by [START_REF] Dadarlat | Photopyroelectric calorimetry of solids[END_REF]:

V F P P E n = σ 1 d + b 21 (σ 1 d) + b 21 1+ℜ 32 e -2σ 2 b 1-ℜ 32 e -2σ 2 b (4.27)
with ℜ 32 = (b 32 -1)/(b 32 + 1) which is practically identical with eq. (4.21). When working with PPE, in the back (BPPE) configuration, in the thermally thick regime for the pyroelectric sensor we obtain:

V BP P E n = 2 (b 12 + 1) e -σ 1 d (4.28)
which is different from eq. (4.25), but in the thermally thick limit for the sample, the two detection configurations lead to the same result.

Mathematical simulations

As pointed out before [START_REF] Dadarlat | High Performance Photopyroelectric Calorimetry of Liquids[END_REF], when it is possible, we use as source of information only the phase of the signal because, being only a time delay, the phase is less noisy than

Experiments on Solid Samples Using PTE technique

In the FPTE configuration, the sensor is glued on a rotating stage. The backing material is situated on a micrometric stage. The modulated radiation (800 mW YAG laser, f=0.3Hz) is partially absorbed by the (blackened) front electrode of the sensor. The space between the sensor and the backing material accommodates the liquid layer. The liquid's thickness variation is performed with a step of 0.03µm (9062M-XYZ-PPP Gothic-Arch-Bearing Pi- comotor) and the data acquisition was taken each 30 th step. The "rough" control of the liquid's thickness and the parallelism between backing and sensor are assured by 3 and 6

-axis micrometric stages. During the scanning procedure, the sample's thickness variation is very rigorously controlled, but the absolute sample's thickness is not precisely known.

Its correct value is obtained as a result of a fitting procedure [START_REF] Dadarlat | Photopyroelectric calorimetry of liquids; recent development and applications[END_REF]. The coupling fluid was ethylene glycol (e 2 = 890Ws -1/2 m -2 K -1 ; α 2 = 9.36e -8 m 2 s -1 ) with thickness ranging from 0 to 1mm. The normalized signal is obtained with thermally thick (thickness larger than 700µm) coupling fluid. All the measurements were performed at room temperature. The PTE signal was processed with an SR 830 lock-in amplifier. Even if the signal generated by TE was rather small (10µV-50µV), the signal to noise ratio was good (S/N>100). Several backing solids with different values of thermal effusivity (Al, glass, teflon, polypropylene, processed as disks with 10 mm diameter and thicknesses of about 1 cm) were selected for investigations, thus covering a large range for the typical effusivity spectrum of solids. At 0.3 Hz chopping frequency, the request of the particular detection case (thermally thin regime for the sensor and thermally thick for the backing) was respected. The coupling fluid changes the thermal regime from thermally thick to thin at about 600µm. As demonstrated in the theoretical section, the information was collected in the thermally thin regime for the coupling fluid.

In In order to prove the suitability of the BPTE method, as a challenge, the thermal diffusivity of a largely used pyroelectric sensor (500µm thick LiTaO3 single crystal) was measured.

Experimental Results

The results obtained for the measurements performed in the FPTE configuration are displayed in figs. Consequently, the only differences and possible advantages of this new technique come from the values of the sensors' (pyro and TE) thermal and/or electrical parameters. For example, in the case of the TE used in this work, both thermal effusivity and diffusivity of the TE are about 3 times smaller than the similar parameters of a LiTaO 3 pyroelectric sensor. Consequently, in order to fulfil the conditions for particular detection cases (thermally thin/thick regime for different layers of the detection cell), different ranges for the scanning parameters are required. This can be an advantage or disadvantage, depending on the type of investigated material. A huge difference between the TE and pyroelectric sensors is their electrical resistivity. From experimental point of view, the low electrical resistivity (few Ohms) of TE is correlated with low signal voltage (tens of µV), but also with very low noise signal (tens of nV). The typical S/N ratio is larger than 10 2 -10 3 , similar with that obtained with pyroelectric sensors. To go on with the comparison of the two methods, the PTE needs higher levels of incident radiation (hundreds of mW), but the TE generators are not limited in temperature by a critical one, as in the case of pyroelectric sensors (Curie point).

Here, some applications on some solids, covering a large range for the typical values of thermal parameters (Aluminium, Glass, Teflon, Polyethylene and even a largely used pyroelectric material, LiTaO 3 ), were described, in order to demonstrate the suitability of the method. The results obtained for the values of the thermal parameters are in agreement with literature data. In conclusion, a new photothermal technique, the photothermoelectric method, was proposed for calorimetric investigations. The method is an alternative to the PPE; it is very similar with the PPE technique, but it is based on a new class of materials with different properties.

Summary

A novel technique, based on the photothermoelectric (PTE) effect has been introduced

for thermal characterization of TE generators. For that, the voltage generated in TE sen-4.6. Summary sors due to the temperature variations between the two sides were modelled in terms of temperature fields and solved the heat diffusion equations. As obtained, equations for temperature fields contains the thermal transport properties of TE material. Thereby, we can thermally characterize the thermoelectrics without using a secondary sensing mechanism.

We have also proposed the very same technique as an alternative calorimetry tech- Polymer dispersed liquid crystal (PDLC) samples are chosen because of their rich physical properties, so that we can consider them as a model system to interpret many physical phenomena. One of its interesting nature is coming from the heterogeneity of the system by the presence of spherical inclusions of liquid crystals whose thermophysical properties can be controlled by external means without making any physical interruption to the sample system. The PDLC samples used in this studies are made of polystyrene (PS) and 4-Cyano-4'-pentylbiphenyl (5CB) liquid crystal. Samples having two different liquid crystal (LC) concentrations (73 wt% and 85 wt%) were prepared using a procedure based on solvent induced phase separation (SIPS).

We have chosen photothermal radiometry (PTR) technique to investigate the thermal properties of samples because of the experimental simplicity and non-contact nature. The latter property helps to conduct measurements on samples under external electric field with greater freedom in sample cell erection than contact photothermal (PT) methods.

In order to perform the thermal investigations with high accuracy and resolution similar to the one obtained using contact PT techniques like photopyroelectric (PPE), we have developed novel methods with PTR, so called back-front-PTR (BF-PTR) and back-PTR (B-PTR), to study liquid samples. In this novel approach, a small amount (about 5 µl) of liquid sample is enclosed between two transparent windows (a quvette is used as bottom window having known sample space thickness) in which the top window (made of CaF 2 and facing PTR detector) has been chosen so that it is transparent to infrared radiation specified by the detector. The sample cell is prepared to contain sample at the middle and thin opaque coatings are made at faces of each top and bottom windows on the sample touching surface to obtain laser heating exactly at the surface of the sample. In B-PTR, the heating of the sample is from the bottom window side for both the sample and reference scans. This method gives thermal diffusivity and effusivity of the sample. But the sample has to be replaced by a reference liquid for realizing the reference scan. Apart from this, in BF-PTR configuration, there is no sample replacement needed, while, frequency scans of the laser intensity modulations are performed from bottom side is normalized by a second frequency scan of the sample from top. Here, thermal diffusivity is the only parameter which can be deduced.

Both PTR methods are validated and compared with results from existing techniques and found they can be used for the thermal characterization of liquid samples with high accuracy and certainty. A possible disadvantage of these methods are coming from the higher laser power (a few tens of milliwatts) to be used for sample heating than compared to the PPE techniques. This may limit the temperature resolution in the case of high resolution phase transition studies are being performed.

We have studied thermal transport properties of PDLC samples under amplitude varying (at fixed frequency) and frequency varying (at fixed amplitude) electric field (EF). The This thesis primarily focused on the investigation of thermal transport studies of PDLC samples. Studies on these system's thermophysical properties vs. temperature, LC concentration, various kinds of LCs and polymer matrix will help to understand thermal transport behaviour in different circumstances. In a thermal point of view, these studies not only help to understand fundamental heat transport in heterogeneous systems but also contribute to the developments of electrically controlled heat shutters.

In the field of thermoelectric material research, a broad and extensive research works are being conducted by various research teams around the world to develop high efficient heat conversion materials. Our works on the thermal behaviour of certain samples by a chosen method must be investigated further by different nanotube concentrations, lengths of nanotubes, different host polymer matrices etc. in order to optimize them for producing highest efficiency. More than that, samples prepared by various methods (e.g., mechanical mixing, in situation polymerization and so on) could give more insight on the thermal transport through nano-composites and the role of Kapitza resistance with respect to nanotube addition to the host matrix. Temperature dependent measurements are also needed to predict their performances in different temperatures.

As part of the PTE technique, further studies are needed to develop or find sensors which work at lower laser powers. This could be directly related to the Seebeck coefficients of materials. At the same time materials with higher electrical resistance (typically more than a few tens of ohms through sensor thickness) is preferable for the collection of generated majority carriers from both surface of the sensor efficiently via thin coatings.

Introduction 1

 1 Photothermal Techniques:-An Overview 1.1 Photothermal phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Contact Photothermal Techniques . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Photopyroelectric Technique (PPE) . . . . . . . . . . . . . . . . . . 1.2.2 Piezoelectric detection . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Photothermoelectric Technique (PTE) . . . . . . . . . . . . . . . . 1.3 Non-Contact Photothermal Techniques . . . . . . . . . . . . . . . . . . . . 1.3.1 Photoacoustic Spectroscopy (PA) . . . . . . . . . . . . . . . . . . . 1.3.2 Photothermal Beam Deflection (PBD) . . . . . . . . . . . . . . . . 1.3.3 Impulsive Stimulated Scattering . . . . . . . . . . . . . . . . . . . . 1.3.4 Photothermal Radiometry (PTR) . . . . . . . . . . . . . . . . . . . 1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Theory of Heat Transfer Through Multi-layered Systems 2.1 Heat transfer through multi layered Systems . . . . . . . . . . . . . . . . . 2.1.1 Heat Diffusion Equation . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Solution of 1-Dimensional Heat Diffusion Equation for Periodically Varying Temperature Field . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Temperature Field for Different Layers . . . . . . . . . . . . . . . . 2.2 Special Cases and Approximations . . . . . . . . . . . . . . . . . . . . . . viii CONTENTS ix 2.2.1 Optically Opaque Sample (A Surface Absorption Model) . . . . . . 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Polarisation Field Effects on Heat Transport in PDLCs-Investigations Using Improved Photothermal Radiometry Techniques 3.1 Photothermal Infrared Radiometry (PTR) . . . . . . . . . . . . . . . . . . 3.1.1 Thermal Parameters from Radiometry signals . . . . . . . . . . . . 3.1.2 Measuring Liquid Samples Using Photothermal Radiometry (A Novel Approach) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2.1 Back-Front PTR (BF-PTR) :-For Finding Absolute Thermal Diffusivity . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2.2 Back PTR (B-PTR) :-For Simultaneous Detection of Diffusivity and Effusivity . . . . . . . . . . . . . . . . . . . . 3.1.2.3 Front-PTR (F-PTR) . . . . . . . . . . . . . . . . . . . . . 3.1.3 Photothermal Radiometry Experimental Set Up . . . . . . . . . . . 3.1.3.1 From Laser Excitation to Infrared Detection . . . . . . . . 3.1.3.2 Electronic Circuitry and Signal Recording . . . . . . . . . 3.1.3.3 Temperature Controlling . . . . . . . . . . . . . . . . . . . 3.1.3.4 Electric Field Varying Experiments . . . . . . . . . . . . . 3.1.3.5 Cell for Liquid Samples . . . . . . . . . . . . . . . . . . . 3.2 Validation of PTR Methods for Liquids . . . . . . . . . . . . . . . . . . . .3.2.1 Results obtained with BF-PTR configuration . . . . . . . . . . . . . 3.2.1.1 BF-PTR experiment with water . . . . . . . . . . . . . . . 3.2.1.2 BF-PTR experiment on 5CB with varying electric field . . 3.2.2 Results obtained with B-PTR configuration . . . . . . . . . . . . . 3.2.2.1 B-PTR experiment on glycerol . . . . . . . . . . . . . . . 3.2.2.2 B-PTR experiment on 5CB with varying electric field . . . 3.2.2.3 B-PTR experiment on 5CB with varying temperature . . . 3.2.3 Results obtained Using F-PTR configuration . . . . . . . . . . . . . 3.2.4 Plausibility of PTR Methods for Characterizing Liquid Sample's Thermally . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 PDLC Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Abstract droplet sizes inside PS matrix. Dynamic thermal properties of both samples are analysed

  de cristaux liquides. Les analyses sur les paramètres thermiques d'échantillons PDLC en fonction de la fréquence du champ électrique, pour une amplitude fixée correspondant à la valeur de saturation des paramètres thermiques, sont utilisées pour analyser les effets du champ de dépolarisation appelé effet Maxwell-Wagner-Sillars (MWS). Nos résultats montrent clairement que les propriétés thermiques sont sujettes aux effets du champ de dépolarisation aux basses fréquences. Les résultats expérimentaux sont modélisés selon les théories prédisant les propriétés électriques des composites. Nous en avons également déduit la constante élastique des gouttelettes (K) qui se trouve être plus faible que celle reportée dans la littérature pour le 5 CB pur. La seconde partie de ce manuscrit décrit la nouvelle technique photothermique basée sur l'effet thermoélectrique (TE). Cette technique également appelée photothermoélectricité (PTE) est particulièrement utile pour caractériser thermiquement les matériaux thermoélectriques sans avoir à recourir à un capteur extérieur pour mesurer le changement de température. Cette technique est présentée à la fois théoriquement et expérimentalement. Ces expériences sont réalisées avec des composites polyaniline/nanotubes de carbone (PANI/NTC) par mesure de la tension Seebeck générée par l'échantillon thermoélectrique chauffé par un faisceau laser. Des mesures additionnelles à l'aide de la PTR sur ces mêmes échantillons ont été réalisées et les résultats sont en bon accord avec ceux trouvés avec la PTE. Plus loin, ce chapitre évoque la possibilité d'utiliser les matériaux thermoélectriques comme capteur photothermique (aux caractéristiques thermiques connues) pour mesurer les paramètres thermiques via deux approches. Pour la première méthode, appelée PTE ≪ avant ≫, le capteur TE, en contact avec l'échantillon par l'intermédiaire d'un fluide Résumé de couplage aux paramètres thermiques connus, est illuminé avec un faisceau laser à une fréquence de modulation adéquatement choisie et le signal est enregistré en fonction de l'épaisseur du fluide de couplage par l'implémentation d'une cavité résonnante à ondes thermiques (TWRC). Cette méthode est utilisée pour obtenir l'effusivité thermique de l'échantillon. Dans la seconde méthode appelée PTE ≪ arrière ≫, l'échantillon est irradié directement par le faisceau laser et le signal photothermique provenant du capteur TE est analysé afin d'en extraire la diffusivité thermique de l'échantillon. La validation des méthodes a été réalisée en sélectionnant des matériaux aux paramètres connus.

1. 1 .Figure 1 . 1 :

 111 Figure 1.1: Bell's photophone and related experiments for sound transmission and reproduction by the aid of sunlight [31].

Figure 1 . 2 :

 12 Figure 1.2: Photothermal signals generated by the thermal excitation on a sample material

  attracted the researchers significantly to use PPE techniques widely. Common pyroelectric sensors used to carry out PPE measurements are polyvinylidene difluoride (PVDF or PVF2) and LiTaO 3 single crystals. Normally, the pyro slabs are cut so that the permanent polarization fields are oriented in orthogonal direction with respect to the transducer surface. These polarization charges are coupled with the conducting electrode coatings on each surface of the transducer. When a temperature fluctuation comes, the thermal equilibrium looses and thereby a spontaneous polarization builds up. It produces the charge imbalance and opens the way to flow charges through the connected external circuitry. This charge flow in relation with the temperature fluctuations can be 1.2. Contact Photothermal Techniques written as:

1. 3 .

 3 Non-Contact Photothermal Techniques of the symmetry of the optical configuration, are automatically mixed with their reference counterparts, as depicted in fig. 1.3.

Figure 1 . 3 :

 13 Figure 1.3: Heterodyne Detection set-up for thermal and acoustic wave propagation

Figure 2 . 1 :

 21 Figure 2.1: Heat transfer model

Figure 2 . 2 :

 22 Figure 2.2: A three layer system

  with the theoretical and experimental results obtained by photothermal radiometry (PTR) technique to measure thermal properties of liquid samples with novel approaches. The chapter primarily gives the underlying theory for analysing signals from PTR experiments and secondly, it deals with the development of two novel PTR methods which give high accuracy on results than the existing PTR methods for thermal characterization of liquids. In addition, the chapter also contains the validation experiments on thermal investigation of some common liquids as well as temperature dependent phase transition studies and electric field (EF) dependent thermal transport studies of 5CB (4-Cyano-4'-pentylbiphenyl) liquid crystal (LC).

Figure 3 . 1 :

 31 Figure 3.1: Black body radiation

3. 1 . 2 . 1 Figure 3 . 2 :

 12132 Figure 3.2: Theoretical model for liquid measurement using photothermal radiometry. (a) Front detection. (b) Rear (back) detection.

Figure 3 .Figure 3 . 3 :

 333 Figure 3.3(c, d) shows the percentile error in amplitude, phase and thermal diffusivity (α) from each, while using approximated model, eq. (3.5), instead of the full model, eq. (3.4), simulated with water as the sample and thickness, d=100µm. The plots show the valid frequency domain of the approximated model for conducting experiments. This domain will change according to the material properties and the sample thickness. But

  From eq. (3.5), we can find the absolute thermal diffusivity of the sample layer. Though the term A f contains the effusivity of the sample and the substrate, it remains undetectable and just acts as an offset for the amplitude. Equation (3.5) is particularly useful due to its rather direct and only exponential term to find sample's thermal diffusivity evolution as a function of time, temperature or electric field. The sensitivity to the thermal diffusivity of the sample increases with the modulation frequency as shown in fig.3.3(a, b). So it is advisable to conduct the measurements in the high sensitive experimental region at which the sample becomes quasi thermally thick.

Figure 3 . 4 :

 34 Figure 3.4: Simulated plots of frequency dependent amplitude and phase of a typical liquid sample (α 1 =1.48 ×10 -7 m 2 s -1 , e 1 =650 Jm -2 K -1 s -1/2 , d= 50µm) showing the percentile change in amplitude (upper plot) and phase (lower plot) with +1% change in α 1 and e 1 , (circles); +1% change in e 1 keeping 0% change in α 1 (dotted line with cross) and +1% change in α 1 keeping 0% change in e 1 (dashed line).

Figure 3 .

 3 Figure 3.4 contains the simulations using equation (3.8) for the percentage variation of the frequency dependent normalized amplitude and phase plotted with +1% change in

  3.2(a). The laser excitation and the signal detection are from the same side (CaF 2 face), at the interface between CaF 2 (layer: 0 ) and Sample (layer: 1 ), of the sample cell assembly for both the sample and reference scans. The temperature field at the sample surface (z = 0) is described by the eq.(2.41) which is obtained from the surface absorption model. To avoid the use of a second reference material and thereby minimizes errors due to possible distortions in the experimental setup due to the sample-reference replacement and also uncertainties on the reference material's thermal properties, we have carried out the reference scan with the same sample with semi infinite thickness. Hence it gives better accuracy on the results and provides the possibility of measuring the absolute values of sample thermal parameters. The equation for F-PTR model with sample of known thickness, d, normalised with same semi infinite sample is obtained from eq. (2.41) and can be written as:

Figure 3 . 5 :

 35 Figure 3.5 shows the frequency dependent procentile sensitivity variations of the normalised amplitude and phase for 5% change in thermal diffusivity and effusivity, one by

  variations, thus emitting infrared (IR) waves. These emitted IR signals are collected by the aid of proper optical arrangements and focused into an IR detector. A lock-in amplifier locked at the same modulation frequency of excitation quantify the output from IR detector. As obtained signal contains both the thermal parameters of the sample layers and the contribution from instrumental transfer function which comes from the underlying electronic circuitry. A proper normalisation procedure allows one to filter out the signal that depends only on thermal parameters of the sample layer system. Figure3.6 shows the schematic representation of a classical PTR set up.3.1.3.1 From Laser Excitation to Infrared DetectionLaser source:-Laser beam of wavelength (λ =532 nm) corresponding to the green color in the electromagnetic spectrum has been used as the source (manufacturer Laser Quantum, He-Ne, Ventus HP 532, 1.4 mm spot size).

Figure 3 . 6 :

 36 Figure 3.6: Photothermal infrared Radiometry set up

Figure 3 . 7 :

 37 Figure 3.7: A photograph of the experimental setup

Figure 3 .

 3 Figure 3.8 is the LabVIEW front panel for controlling and recording the experiments automatically.

Figure 3 . 8 :

 38 Figure 3.8: Front panel of the LabVIEW program used for the automation of experiments.

Figure 3 . 9 :

 39 Figure 3.9: Photograph of the cell assembly used for liquid measurements using PTR technique

Figure 3 .

 3 Figure 3.10: Normalized BF-PTR signal amplitude (upper plot) and phase (lower plot), plotted as a function of square root of the modulation frequency for water sample (d =100µm). The circles are from the experimental data and the full line represents the best fit. CaF 2 window is used as the top layer and quartz cell as the backing.

Figure 3 . 11 :

 311 Figure3.11: χ 2 analyses in the neighbour hood of its minimum for calculating the statistical uncertainty.

3. 2 . 1 . 2

 212 BF-PTR experiment on 5CB with varying electric field Liquid Crystals and their Physical Characteristics : Liquid crystal (LC) compounds are special class of materials exhibiting crystal ordering in liquid state. Because of such unique property, LCs unfolded improved class of optical devices which are thin, light in weight and even foldable. Thermodynamically, this liquid crystalline phase exists in between the melting point and the isotropic clearing temperature of material. Ordinarily, LCs may display one or more mesophases depending on the molecular symmetry and three major classes of these mesophases are: nematic, smectic and cholesteric. The differences between these mesophases are coming from their lattice order parameter.

Figure 3 . 12 :Figure 3 . 13 :

 312313 Figure 3.12: Three of the main liquid crystal phases.

Figure 3 . 15 :

 315 Figure 3.15: Experimental result on glycerol (sample) normalized with water (reference) plotted as a function of f . Amplitude (upper plot) and phase (lower plot) are fitted simultaneously. The symbols show the experimental curve and the full line represents the best fit (d =50µm).

Figure 3 . 16 :

 316 Figure 3.16: Contour plot (a) showing the closed curves with χ 2 minima around the best fitting values of α and e confirms the absence of degeneracy. Most square error analysis (full line) plotted along with the least-square (dashed line) for thermal diffusivity (b) and effusivity (c) confirming that the results are unique. The statistical uncertainty is inversely proportional to the sharpness of the parabolic minima. The analysis is for the B-PTR experiment (fig. 3.15) with glycerol as sample and water as the reference.

Figure 3 . 17 :

 317 Figure 3.17: Normalized experimental signals (symbols) and the best fits(lines) are plotted vs. laser modulation frequency for 5CB liquid crystal sample under three different electric fields. Signals are fitted to obtain α and e keeping A f fixed. The reference signal was from the sample at zero electric field.

Figure 3 . 18 :

 318 Figure 3.18: Variation of thermal diffusivity,(a) and thermal effusivity,(b) with error bar of 5CB liquid crystal as a function of electric field. Results from B-PTR experiments done at 28 0 C.

Figure 3 . 19 :

 319 Figure 3.19: Experimental results on variations of thermal diffusivity (a), thermal effusivity (b) and thermal conductivity (c) from the temperature varying B-PTR experiment around the Nematic -Isotropic (NI) phase transition of 5CB. The experiment has been done at f =32Hz (laser modulation frequency) and d =36µm. The thermal conductivity has been calculated from e and α.

2 .Figure 3 . 20 :

 2320 Figure 3.20: Normalized experimental signal for Glycerol sample (d =38µm) using F-PTR plotted as a function of laser modulation frequency. Normalisation has been done with semi infinite sample. Circles show the experimental data and the full line represents the best fit.

  It particularly reduces the power loss due to the absence of polarisers (polarisers absorb ∼ 50% incident light in LC cells) and thereby increases the device efficiency. Moreover, in high temperatures, polarisers often degrade or peel off. Sturdy environmental properties, fast switching time and low production costs are other attractions of PDLC technology. Some of its electro-optical applications are: flexible displays[START_REF] Fergason | Polymer encapsulated nematic liquid crystals for display and light control applications[END_REF][START_REF] Doane | Field controlled light scattering from nematic microdroplets[END_REF][START_REF] Basile | Optical phase shift of polymer-dispersed liquid crystals[END_REF], window shutters, projection displays[START_REF] Lin | High contrast polymer-dispersed liquid crystal in a 90 0 twisted cell[END_REF], optical switches[START_REF] Hsiao | Optically switchable, polarization-independent holographic polymer dispersed liquid crystal (H-PDLC) gratings[END_REF], focus tunable lenses[START_REF] Loiko | Focusing of light by polymer-dispersed liquidcrystal films with nanosized droplets[END_REF] etc.

Figure 3 . 21 :

 321 Figure 3.21: PDLC before and after applying electric field E. The downward arrows showing the light path.

Figure 3 . 22 :

 322 Figure 3.22: Maxwell-Wagner-Sillars effect in a heterogenious medium

LC⇒

  ǫ ′ M ⇒ Dielectric permittivity of polymer matrix ǫ ′ Dielectric permittivity of LC aligned with E a σ LC ⇒ Electrical conductivity of LC in the direction of E a σ M ⇒ Electrical conductivity of Polymer matrix in the direction of E a

Figure 3 . 23 :

 323 Figure 3.23: Thermogram of pure 5CB, showing crystalline (C) , Nematic (N) and Isotropic (I) phases of 5CB liquid crystal. Figure obtained from reference[START_REF] Bouchaour | Equilibrium phase diagram of poly(2-phenoxyethylacrylate) and 5CB[END_REF]

Figure 3 . 24 :

 324 Figure 3.24: PDLC micrographs taken on a polarising microscope with crossed polarisers. Images of PS:5CB=27:73 (73% LC) (left) and PS:5CB=15:85 (85% LC) (right).

Figure 3 . 25 :

 325 Figure 3.25: Variation of thermal diffusivity (top) , thermal effusivity (middle) and thermal conductivity (bottom) vs. varying electric field (at constant frequency (f e ), 1kHz) for PDLC samples (85% LC and 73% LC).

  3.27.a). Upon application of the field, the nematic within the center of each droplet aligns quickly with the field. This process leads to a droplet where the bulk of the nematic is aligned with the applied field, but near the wall of the droplet the nematic molecules are still aligned tangentially to the droplet surface (fig.3.27.b). The orientation of the molecules along the surface of the droplets remaining unchanged in the presence and in the absence of the electric field brought us to consider that the thermal interfacial resistance is constant and independent of the electric field. For calculating γ, we have used thermal conductivities when the LC molecules aligned in the direction parallel to the EF, at which κ PDLC = κ PDLC and κ LC = κ LC .

Figure 3 . 27 :

 327 Figure 3.27: Schematic of nematic alignment in bipolar droplets (a) at zero field and (b) high field state.

3. 3 . 5 PDLC

 35 Under Frequency Varying Electric Field 3.3.5.1 Experimental Results on PDLCs as function of Frequency Subsequently, we have investigated the polarization field effects in PDLC samples due to interfacial polarisation at polymer-LC boundaries.

Figure 3 .Figure 3 . 28 :

 3328 Figure 3.28 shows the variation of thermal parameters of PDLC sample with 85% LC as a function of f e at constant EF of 0.127 V/µm. The results are obtained from the mean of four f e scans (upper plots), done at 18, 20, 22 and 30 Hz of laser modulation frequencies.In order to smooth the obtained results, we have plotted volumetric heat capacity (ρC) (fig.3.29) and took the points lie within ±0.65% from the mean value. The parameter, ρC is not affected by the orientation of the LC molecules. So the EF as well as the the frequency dependent EF do not change the volumetric heat capacity of the samples.

Figure 3 . 29 :

 329 Figure 3.29: ρC plotted for both PDLC samples vs. frequency of applied electric field.

Figures 3 . 1 )Figure 3 . 30 :

 31330 Figures 3.30 and 3.28 are evidencing for the first time to the best of our knowledge the MWS effect via the thermal properties of PDLC materials.

Figure 3 . 31 :

 331 Figure 3.31: Thermal conductivity of the confined liquid crystal as a function of frequency of the applied electric field. Squares are showing the results on 85% LC and circles represents 73% LC.

25 )Figures 3 .Figure 3 . 32 :

 253332 Figures 3.33 and 3.34 are showing the variation of equilibrium angle of the directors, θ, of LC droplets for both samples as a function of frequency of the applied electric field. Evaluating the evolutions of θ in conjunction with the variations of κ LC (fig. 3.31) reveal

Figure 3 . 33 :

 333 Figure 3.33: Angle (in radian) of the director with respect to heat flow direction as a function of frequency of the applied electric field for 73% LC sample.

Figure 3 . 34 :

 334 Figure 3.34: Angle (in radian) of the director with respect to heat flow direction as a function of frequency of the applied electric field for 85% LC sample.

Figure 3 . 35 :

 335 Figure 3.35: PDLC 85% LC experimental data (circle) and theoretical fit (full line).

73% 0. 9 ( 3 .

 93 5±0.1)×10 -8 (4.8±0.1)×10 -7 (7.2±0.1)×10 4 221 ± 5 1.80×105

Figures 3 .Figure 3 . 36 :

 3336 Figures 3.35 and 3.36 are showing the experimental results (circles) and the best fits (full line) on effective thermal conductivity (κ PDLC ) variations of PDLC 85% LC and 73%

Figure 3 . 37 :

 337 Figure 3.37: Simulations on E drop and κ PDLC with values used and obtained in fitting for PDLC 85% LC (upper plot) and PDLC 73% LC (lower plot).

  Photothermoelectric (PTE)

Figure 4 . 1 :

 41 Figure 4.1: Investigated sample configuration

Figure 4 . 1 Figure 4 . 2 :

 4142 Figure 4.2 shows the evolution of the normalized phase vs. reduced parameter d/µ 1 ,where µ 1 is the thermal diffusion length. h 1 is varied for values 0, 10 and 100 Wm -2 K -1 keeping ℜ 2 fixed at -0.2. It is apparent that, above d/µ 1 = 1, convection has little or no effect on the normalized signal, thus the eq. (4.7) without convection factor is valid for

Figures 4 . 3 -

 43 Figures 4.3 -(a & b) are showing the sensitivity of experimental signal vs. d/µ 1 for various values of ℜ 2 for a 1% change in thermal diffusivity. The sensitivity increases with decreasing ℜ 2 value, indicating that a substrate with high effusivity need to be used for the determination of the thermal diffusivity. While in the case of sensitivity studies on effusivity variations, the best frequency range found is 0.5 ≤ d/µ 1 ≤ 2 (fig. 4.3 -(c & d) plotted with 1% change in e 1 around each ℜ 2 values keeping zero percentage change in α 1 ). However, in order to avoid convection during experiments, the frequency scans are restricted to d/µ 1 ≥ 1, limiting the available frequency range to 1 ≤ d/µ 1 ≤ 2. As expected, sensitivity on thermal effusivity increases when the thermal effusivity contrast increases, means ℜ 2 goes far from 0.

Figure 4 . 3 :

 43 Figure 4.3: Simulations for the variation of normalized amplitude in percentage (a & c) and phase difference in degree (b & d) vs. d/µ 1 for various ℜ 2 values. In a & b the thermal diffusivity (α 1 ) is varied 1% for all the plots. For c & d, 1% change in e 1 is introduced around each ℜ 2 values while keeping 0% change in α 1 . Values used for simulations are: α 1 = 3.2 × 10 -7 m 2 s -1 , e 1 = 1184 Jm -2 K -1 s -1/2 , d =200µm and e 2 = 1581 Jm -2 K -1 s -1/2

Figure 4 .

 4 4 shows the SEM images of each samples of polyaniline-CNT nano hybrides. These images are confirming that the in situ polymerization of aniline has been taken place and as grown PANI-CNTs evidently forming fibrous hybrids with a minimum size bigger than the smallest nanotube diametrically. The longer lengths of all the hybrid nano fibres (fig. 4.4 b,c,d,e) than the pristine PANI fibres (fig. 4.4 a) are also justifying the guided growth of PANI along the CNT backbone.

Figure 4 . 4 :

 44 Figure 4.4:

Figure 4 . 5 :

 45 Figure 4.5: Experimental Signals obtained from PANI-OxSWNT using air and glycerol as backings.

4 . 1 .

 41 A typical Amplitude and phase data of a photothermoelectric (PTE) experimental signal for a 348.5µm thick doped PANI-OxSWNT are presented in fig.4.5 using either air or glycerol as substrates. Though the measured voltages for the signal amplitudes were weak (≤ 10 µV), it can still be exploited with a satisfactory signal to noise ratio. Amplitude ratios and phase differences for the OxSWNT-PANI signals in fig. 4.5 are calculated and depicted as in fig.4.6. Thermal parameters are retrieved by fitting the signal against eq.(4.7) while considering h 1 = 0 ; the thermal diffusivity of α 1 = (4.68 ± 0.04)×10 -7 m 2 s -1 and a thermal effusivity of e 1 = (1212 ± 25) Ws 1/2 m -2 K -1 are obtained. Then the thermal conductivity was calculated using the relationship k 1 = e 1 √ α 1 and the result is k 1 = (0.83 ± 0.02) Wm -1 K -1 .

Figure 4 . 6 :

 46 Figure 4.6: Normalized amplitude (upper plot) and phase (lower plot) from PTE experiment on OxSWNT-PANI

1 d 1 -Figure 4 . 8 :

 148 Figure 4.8: Thermal parameters with error bar of different PANI-CNT composites measured using PTR technique. The results are also displayed in table 4.2.

Figure 4 . 9 :

 49 Figure 4.9: Experimental results of thermal parameters for PANI-CNT composites (PTE results)

4 ZTFigure 4 . 10 :

 4410 Figure of Merit for the PANi-CNT Composites

17

 17

  )

Figure 4 . 11 :Q = b 21 ( 1 +2κ 1 σ 1 b

 4112111 Figure 4.11: Front Configuration

Figure 4 . 12 :

 412 Figure 4.12: Front Configuration. Opaque sample and thermoelectric sensor

Figure 4 . 13 : 13 Figure 4 .

 413134 Figure 4.13: Normalized phase of the PTE and PPE signals, in front configuration, for two e 3 /e 2 ratios. b 32 = 0.67 -backing bad thermal conductor; b 32 = 26.97 -backing good thermal conductor.

Figure 4 . 14 :

 414 Figure 4.14: Normalized phase of the BPTE signal as a function of √ f for Al, brass and LiTaO 3 . Layers'

Figure 4 .

 4 Figure 4.21 presents the behaviour of the phase of the BPTE signals, as a function of sqrt(f), in the linear region, for two good thermal conductors (Al and brass) and a LiTaO 3

Figure 4 . 15 :

 415 Figure 4.15: Normalized phase of the FPTE signal as a function of coupling fluid's thickness for aluminium sample

Figure 4 . 16 :Figure 4 . 19 :

 416419 Figure 4.16: Normalized phase of the FPTE signal as a function of coupling fluid's thickness for teflon sample

2 )Figure 4 . 21 :

 2421 Figure 4.21: Normalized phases of the PTE signals, in back configuration, as a function of sqrt(f) for brass (violet circles), Al (red diamonds) and LiTaO 3 (green squares).

  nique for measuring dynamic thermal parameters of solid samples. In order to show the various technical possibilities, we have used both back and front detection configurations, coupled with laser chopping frequency as well as thickness scanning procedures. The front PTE configuration, together with the thermal-wave resonator cavity (TWRC) method as scanning procedure, has been used to measure the value of thermal effusivity. The back PTE configuration, together with the chopping frequency of incident radiation as scanning parameter, lead to the direct measurement of thermal diffusivity. The theory of the two detection configurations was developed. In principle, the general results obtained for the PTE voltage in both front and back configurations are different from PPE ones, but when using particular cases of experimental interest ((i) front configuration with opaque sensor, thermally thin sensor and coupling fluid, and semi-infinite backing, or (ii) back configuration with optically opaque sample and thermally thick sample and sensor) they are identical.General Conclusions and FutureOutlookThis thesis work is intended to investigate on the thermal transport properties of material composites using photothermal techniques. As a continuation of past research works in our laboratory, this work is aimed to study thermal properties of two different classes of technologically important materials. The first class deals with polymer dispersed liquid crystals and the second class is about thermoelectric (TE) polymer nano composites.

  measurements have been carried out using B-PTR configuration. Here, the EF varying results are obtained using experiments with single chopping frequency of the laser source, which is one of the advantages of this configuration if the sample properties are known at zero electric field. The amplitude (of the EF) varying experiments are confirming our already published works and the frequency (of the EF) varying experiments clearly showing the Maxwell-Wagner-Sillars (MWS) effect (polarization field effect) on thermal properties of PDLC samples. Relations between thermal conductivity of PDLCs and existing MWS model are established and the results are numerically fitted to find electrical properties (electrical conductivities of PS and LC as well as the threshold electric field (E 0 ) for LC droplet alignment) of both PDLC samples (of 73% LC and 85% LC). Obtained results for E 0 has been used to calculate droplet elastic constants. Our results are showing that the amplitude of the threshold electric field increases with reducing droplet size (or LC concentration) as expected. An interesting outcome of PDLC results from frequency (of EF) varying experiments have shown, for the first time to the best of our knowledge, that the thermal transport through PDLCs can be controlled via changing the frequency of the applied EF. In other words, the thermal transport properties of PDLC films are also affected by depolarization field effects as in the case of optical transmission properties. Moreover, the experimental results give access to find various physical properties such as: elastic constants, threshold electric field, Kapitza resistance, average molecular long axis orientation of LC droplets. The second part of this thesis work is concerned about thermal investigation of thermoelectric (TE) polymer nano-composites. Studies on TE materials are particularly interesting because of their growing importance in waste heat energy harvesting technology. As part of this work, we have developed novel photothermal technique based on photothermoelectric (PTE) effect to measure thermal properties of TE materials directly. The PTE technique is established theoretically and validated experimentally by finding thermal properties of the same set of samples using classical photothermal radiometry technique. The samples used are composites made of polyaniline (PANI), a widely used conducting polymer, and carbon nanotubes (CNT). Four sample composites are prepared at 6.6 wt% of four kinds of CNTs (un-oxidized or oxidized / single or multi walled nanotubes). Comparing with other already reported studies on PANI-CNT materials, our samples are stay aside due to its novel preparation method and oxidation levels of CNTs. A chemical synthesis procedure in which the CNTs are wrapped around by PANI and form hybridized composites via an in situation polymerization procedure. Scanning electron microscope (SEM)images of these as grown PANI-CNT composites are used to confirm their physical structures. Results from thermal properties of these samples showed that single walled CNT composites are more thermally conductive than multi-walled CNT composites. Moreover, composites with oxidized nanotubes have lower conductivity than their unoxidised counter parts. The results have shown that the maximum enhancement in thermal conductivity is only about 2.5 times higher than the pure PANI sample while the measured electrical conductivity and seebeck coefficients are about 650 times and 6 times higher than pure PANI, respectively. This observation is particularly interesting and highly recommended because, the efficiency of TE materials are proportional to electrical conductivity and see-beck coefficient while it is inversely proportional to sample's thermal conductivity. The experimental observations are analysed in the light of nanotube physical properties and interfacial thermal resistance.We have also described PTE technique for measuring thermal properties of solid samples while using TE materials as thermal sensors. The developed techniques are classified under back-PTE (B-PTE), in which the sample is periodically heated directly, and front-PTE (F-PTE), in which the sensor is heated directly. In B-PTE, a scan has been done by varying laser chopping frequency and the thermal diffusivity is the outcome. On the other hand, in F-PTE, a thickness scan of the coupling fluid in between the sample and sensor is used to find sample's thermal effusivity. Validation experiments have been conducted by choosing solid samples in wide range of thermal properties.This novel PTE technique has some notable advantages like, possibility of direct thermal characterization of TE materials and its inherent simplicity. This technique can be used to thermally characterize different TE materials regardless their nature (polymers, glasses, metallic or semiconducting materials). At the same time, due to the lower electrical resistivity of used TE materials, the noise levels were observed as low as 50 nV in the experimental frequency domain. On the other hand, a higher laser power (about 750 mW at 8 mm spot size) is used to conduct the experiments.

Table 3 . 1 :

 31 Thermal parameters used for simulations.

  Ref.[START_REF] Lide | CRC Handbook of Chemistry and Physics[END_REF] water at 20 0 C. thermal diffusivity and effusivity of a typical liquid sample (circles) (α 1 =1.48 ×10 -7 m 2 s -1 ,

	CaF 2 Quartz 8.4 ×10 -7 3.58 ×10 -6 Water b 1.43 ×10 -7	5135 1590 -	9.71 a -0.598

a Data sheet, Crystran Ltd.

b

e 1 =650Jm -2 K -1 s -1/2

) having thickness, d = 50µm, sandwiched between CaF 2 top layer and bottom glass substrate (table 3.1). The dotted line with cross shows a change in thermal effusivity (e 1 ) by +1% keeping original diffusivity (α 1 , 0%) while the dashed line represents +1% change in diffusivity and original effusivity (e 1 , 0%).

Table 3 . 2 :

 32 Thermal parameters used as input data for fitting.

	Diffusivity	Effusivity	Conductivity
	Material

  The normalized experimental amplitude and phase for water sample plotted as a function of square root of modulation frequency is shown in figure3.10. A least square fitting has been done on the experimental amplitude, phase and complex (fitting amplitude and phase data together simultaneously) data against theoretical model described in eq. (3.5) in order to extract the thermal diffusivity of the sample under investigation. The best fitting results corresponding to lowest χ 2 values are given in table3.3 together with other literature values for comparison. The agreement of the results with the thermal diffusivity values from literature support the validity of the method. The precision cells helped to minimize the errors due to thickness uncertainties and which are neglected in the calculations.

	3.2.1 Results obtained with BF-PTR configuration
	3.2.1.1 BF-PTR experiment with water
	CaF 2	3.58 ×10 -6	5135	9.71 a
	Quartz	8.4 ×10 -7	1506	1.38
	Water b	1.43×10 -7	1581	0.598
	Steel	-	7535	-

Table 3 . 3 :

 33 Thermal Diffusivity from BF-PTR.

			BF-PTR
		Amplitude	Phase	Complex
	Sample				Literature
		fitting	fitting	fitting
			10 -7 (m 2 s -1 )		10 -7 (m 2 s -1 )
	Water	1.441±0.005	1.435± 0.006	1.436± 0.006	1.437±0.008 a , 1.43 b
	E.G	0.926±0.006	0.924±0.007	0.922±0.009	0.918±0.002 c
	Lanolin	0.50±0.02	0.49±0.02	0.53±0.03	-

a [45] at 25 0 C; b [81] at 20 0 C; c [83].

Table 3 .

 3 4: B-PTR and F-PTR Experimental results on Glycerol.

			Diffusivity	Effusivity
		Method
			×10 -8 (m 2 s -1 )	(JK -1 m -2 s -1/2 )
		Amplitude fit	9.45 ± 0.02	958 ± 2
	B-PTR	Phase fit	9.425 ± 0.007	940 ±10
		Complex fit	9.43 ± 0.02	945 ± 3
	F-PTR	Complex fit	9.5 ± 0.3	945 ±11
	Ref.[81] (25 0 C)	9.99	923

  .26. Here, the behaviour of ρC is independent of the applied electric field as expected. The molecular reorientation in LC do not make any contributions towards ρC and hence it stays unchanging. Nevertheless, liquid crystal concentration changes produce difference in ρC values.The behaviour of the thermal conductivity (fig.3.25) is intimately linked with the reorientation of molecules in LC droplets. At zero field, the symmetry axis of each LC droplet in the nematic phase varies randomly and for the heat entering the film, the effective thermal conductivity is reduced. At high fields, each droplet's symmetry axis is aligned with the external field which is parallel to the heat flow. The thermal conductivity of the droplets increases leading to an increase of the effective thermal conductivity of the PDLC film.

		1.92	x 10 6		ρC from EF varying Experiments
	ρC (Wsm -3 K -1 )	1.82 1.84 1.86 1.88 1.9				85% Experiment filtered (±1%) Linear fit
		1.8
		1.78	x 10 6 0	0.1	0.2	0.3	0.4	0.5
		1.86				73% Experiment filtered (±0.55%)
	ρC (Wsm -3 K -1 )	1.78 1.8 1.82 1.84				Linear fit
		1.76
			0	0.1	0.2	0.3	0.4	0.5
					Electric Field (Vrms/µm)

Figure 3.26: ρC plotted as a function of EF for both concentrations of PDLCs. Experimental data points shown are within ±1% for 85% LC and ±0.55% for 73% LC from the mean value of ρC.

Table 3 . 5 :

 35 Physical properties of PDLC samples derived from EF varying experiments.

	LC volume% (x)	κ PDLC	κ LC	φ LC	γ	r d (µm)
	85%	0.18	0.24 *	0.78 0.079	0.5/2.5
	73%	0.138	0.24 *	0.55 0.178	0.25/1

* Reference

[START_REF] Marinelli | Thermal conductivity and thermal diffusivity of the cyanobiphenyl (nCB) homologous series[END_REF]

  [START_REF] Hadj Sahraoui | Heat transport in polymer-dispersed liquid crystals under electric field[END_REF] Evolution of the mean thermal conductivity of LC droplets, κ LC , for PDLC samples of 73%LC and 85% LC are shown in fig.3.31. Calculations are done using the previously obtained γ and φ LC values from table 3.5.

Table 3 . 6 :

 36 Electrical parameters of PDLC samples from MWS fit.

  ZT = S 2 σT /κ. Here S, σ, T and κ are the Seebeck coefficient(V/K), electrical conductivity(S/m), absolute temperature(K) and thermal conductivity(W/mK) respectively. Until now, metallic or semi-metallic composites are showing the best ZT and the highest reported value is about 2.2[START_REF] Biswas | High-performance bulk thermoelectrics with all-scale hierarchical architectures[END_REF] at around 900 0 C. Even though these ZT values are far below in comparison with the equivalent efficiency of compressor type cooling systems. This restricts the use of TE materials from efficient application oriented implementations. The class of polymer thermoelectrics have even lower ZT values, typically < 1. Even though, a significant interest on TE research stems on the solid state and cost effective energy conversion possibility and waste heat recovery advantages. Thus many of the researchers are being focused on improving the ZT values of both types (polymer and metallic) of TE materials by hoping on different theoretical predictions and possibilities such as nano structuring, doping etc. to increase S, σ and/or to decrease κ. Recent studies on conducting polymers have shown improved ZT values on the tailor-made polymer nano-composites than pure polymers. These composites exhibit high electrical conductivities, depending on the amount of nano inclusions, without a major increase in thermal conductivity. SO 3 H/oxidized MWNT (PANI/oxMWNT). Details of sample pellet process-

	due to its thermoelectric (TE) properties, based on the Seebeck effect (property of a material to generate a potential difference between the ends when it is subjected to a tempera-ture difference at those ends), is also a live research area. The conversion efficiency of thermo-electricity generation is governed by the dimensionless quantity known as figure of The TE samples are pressed pellets (diameter: 13 mm) of Methanesulfonic acid (CH 3 SO 3 H) doped nanofibrous Polyaniline (PANI) used as sheath to wrap CNT core yielding nanos-tructured composite materials (Fig. 4.1). The Carbon Nanotubes (CNT) mass fraction is ≈ 6.6 wt-%. Four composites are investigated: PANI-CH 3 SO 3 H/unoxidized Single-Walled Carbon Nanotubes (PANI/unoxSWNT), PANI-CH 3 SO 3 H/unoxidized Multi-Walled Car-bon Nanotubes (PANI/unoxMWNT), PANI-CH 3 SO 3 H/oxidized SWNT (PANI/oxSWNT) merit, 4.2.2.2 Sample Preparation and PANI-CH 3

Table 4 . 1 :

 41 Thermal parameters retrieved using PTE techniques for the PANI-OxSWNT composite; α: thermal diffusivity; e: thermal effusivity, k: thermal conductivity.

	Parameter	PTE (fit)	PTE (analytic)
	Diffusivity (× 10 -7 m 2 /s) 4.68± 0.04 4.45± 0.10
	Effusivity (J/Km 2 s 1/2 )	1212 ± 25	1212 ± 37
	Conductivity (W/mK)	0.83 ± 0.02 0.81 ± 0.04

Table 4 . 2 :

 42 Thermal diffusivity, effusivity and conductivity results of PANI-CNT samples (PTR results).

	PANI-	Thermal diffusivity Thermal effusivity Thermal conductivity
	composite	×10 -7 α (m 2 s -1 )	e (JK -1 m -2 s -1/2 )	κ (Wm -1 K -1 )
	PANI	1.44±0.06	1132±133	0.43 ±0.01
	-OxMWNT	2.87±0.01	1084±10	0.581±0.002
	-UnOxMWNT	2.89±0.02	1293±21	0.695±0.001
	-OxSWNT	4.3±0.1	1292±72	0.850±0.007
	-UnOxSWNT	4.38±0.07	1523±53	1.01 ±0.004

Table 4 . 3 :

 43 Thermal diffusivity, effusivity and thermal conductivity Results of PANI-CNT samples.

	PANI-	Thermal diffusivity ×10 -7 α (m 2 /s)	Thermal effusivity e (J/Km 2 s 1/2 )	Thermal conductivity κ (W/mK)
		PTR PTE	PTR PTE	PTR PTE
	PANI	1.44±0.06 1.2±0.05 1132±133 1129±103 0.43 ±0.01 0.39±0.01
	-OxMWNT	2.87±0.01 2.94±0.02 1084±10 1070±25 0.581±0.002 0.58±0.01
	-UnOxMWNT 2.89±0.02 2.8±0.2	1293±21 1402±191 0.695±0.001 0.74±0.03
	-OxSWNT	4.3±0.1 4.68±0.04 1292±72 1212±25 0.850±0.007 0.83±0.02
	-UnOxSWNT 4.38±0.07 4.87±0.08 1523±53 1316±40 1.01 ±0.004 0.92±0.01

Table 4 .

 4 4 shows the Seebeck coefficient, electrical conductivity and thermal conductivities values obtained for various composites. Figure of merit (ZT ) for each material samples

Table 4 . 4 :

 44 Seebeck coefficient, electrical conductivity and thermal conductivity Results.

	Material	Seebeck Coefficient Electrical Conductivity Thermal Conductivity S (µV/K) κ e (S/m) κ (W/mK)
	PANI		5.8	0.82	0.39±0.01
	PANI-OxMWNT		13.5	14	0.58±0.01
	PANI-UnOxMWNT	10.6	70.1	0.74 ±0.03
	PANI-OxSWNT		12	132.23	0.83±0.02
	PANI-UnOxSWNT		33	530.98	0.92±0.004

  Equation 4.26 indicates that a similar scan of the phase of the BPTE signal as a function of the chopping frequency (at constant thickness), or thickness of the layer 1 (for liquid samples, at constant frequency) can lead to the direct measurement of sample's thermal diffusivity. The amplitude can also be used for thermal effusivity measurement.

			1 d ≈ 0
	and eq. (4.25) reduces to:
	∆V n =	2e -σ 1 d (b 12 + 1)	(4.26)

  the back detection configuration (BPTE), the sample (disks of d = 10mm and d ≤ 1mm) has glued on the surface of the sensor with a thin layer of silicon grease. The irradiated surface of the sample was blackened to assure good optical absorption. In this configuration, PTE has the same problem as PPE: due to the attenuation of the thermal wave in the sample, generally, good thermal conductors (as Al and brass in our work) can be selected as samples. The thermal isolators (at about 1mm thickness) attenuate too much the thermal wave, and the signal to noise ratio is too small to be useful. If trying to polish bad thermal conductors at thickness of 100-200µm, they become transparent, and one request of the particular detection case (opaque sample) is not fulfilled. The scanning parameter was in this case the chopping frequency of radiation; the typical scanning range was 0.3-3 Hz. At such low frequencies, 1mm thick good thermal conductors as Al and brass are normally thermally thin but, due to the properties of the adjacent layers (air on one

side), as demonstrated by Chirtoc et al.

[START_REF] Chirtoc | The Effective Thermal Thickness: A New Concept for Photothermal Investigation of Layered Systems[END_REF]

, the critical frequency (the crossing frequency from thermally thin to thick regime) is in fact much lower and they can be considered thermally thick.

  4.15, 4.16, 4.17 and 4.18 together with the best fits (eq.(4.21)). The room temperature values of the thermal effusivity for the investigated materials are in rather good agreement with literature data[START_REF] Mandelis | Principles and perspectives of photothermal and photoacoustic phenomena[END_REF][START_REF] Dadarlat | Contact and non-contact photothermal calorimetry for investigation of condensed matter[END_REF][START_REF] Touloukian | Thermophysical Properties of High Temperatures Solid Materials[END_REF].

	Typical behaviours of the phase of the PTE signal, in the BPTE configuration, for the
	brass/TE sensor system, and for the empty sensor (signal used for normalization) as a
	function of the laser modulation frequency are presented in fig. 4.19. Figure 4.20 displays
	the normalized phase as a function of sqrt (f) for this system (brass/TE sensor) together

with the best fit performed in order to obtain the value of thermal diffusivity of brass.

  Normalized phase as a function of sqrt(f) for the BPTE signal from brass sample. single crystal. Their room temperature values of the thermal diffusivities are displayed in table 4.5 together with the values measured using PPE and infrared thermography (IRthermography) techniques on the same samples. These measured values are also in good agreement with the available literature data[START_REF] Dadarlat | Contact and non-contact photothermal calorimetry for investigation of condensed matter[END_REF][START_REF] Nakamura | Anisotropy of thermal conductivities in non-and Mg-doped near-stoichiometric LiTaO3 crystals[END_REF].

		-1.8
			Experimental
			Fit
		-2.0
	normalized phase (rad)	-2.6 -2.4 -2.2	sample:brass (1mm thick) slope:0.4030 =(19.34 +/-0.64) x10 -6 m 2 /s
		-2.8
			2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2
			sqrt(f) (Hz)
	Figure 4.20:

Table 4 . 5 :

 45 Thermal diffusivities of aluminium, brass and LiTaO 3 measured using PTE, PPE and IRthermography techniques.Summary of PTE Experimental Results on Solid SamplesThe theory of the two detection configurations was developed and the results compared with PPE technique in section 4.5.3. In principle, the general results obtained for the PTE 4.6. Summary voltage in both front and back configurations are different from PPE ones, but when using particular cases of experimental interest ((i) front configuration with opaque sensor, thermally thin sensor and coupling fluid, and semi-infinite backing, or (ii) back configuration with optically opaque sample and thermally thick sample and sensor) they are identical.

	Material	Thermal Diffusivity (×10 -6 m 2 /s) PTE PPE IR-Thermography
	Aluminium (alloy) 27.20±0.57 36.94±0.20	30±1
	Brass	19.34±0.64 17.93±0.21	20±1
	LiTaO 3	1.24±0.03 1.00±0.01	-
	4.5.5.2

a Data sheet, Crystran Ltd., b Ref.[START_REF] Lide | CRC Handbook of Chemistry and Physics[END_REF] water at 20 0 C.

I am deeply indebted to him for introducing me this research field and providing me scholarship for my stay as well as grants for various research activities.

these materials are cost effective and easily processable than the conventional 'state of the art' metal/semiconductor composite materials [START_REF] Minnich | Bulk nanostructured thermoelectric materials: current research and future prospects[END_REF], a renewed interests on polymer thermoelectrics arise to improve their efficiency.

Here, our experimental studies are focused on the investigation of thermal transport properties of thermoelectric materials, in which, the characterisation of Polyaniline (PANI) -Carbon Nanotube (CNT) nanohybrids, prepared using a novel approach called CNTtemplated polymerization process, are being analysed. Carbon nanotubes used for experiments are either oxidized or unoxidized, single-or multiple-walled, and the as prepared hybrids exhibit cable-like morphology with CNTs as cores, wrapped by nanofibrous polyaniline (PANI) [START_REF] Chan | Carbon nanotube-polyaniline nanohybrids: Influence of the carbon nanotube characteristics on the morphological, spectroscopic, electrical and thermoelectric properties[END_REF].

In this work, we introduce, for the first time, a novel application of the thermoelectric effect as a means to investigate the thermal properties of both TE and other materials by using TE materials as sensors. All the presented results, in this chapter, are obtained by the newly developed photothermoelectric technique (PTE), where the samples themselves serve as sensors. Results obtained from PTE measurements are then being compared with those retrieved from conventional photothermal radiometry (PTR) as a validation of the PTE technique. Furthermore, we have used PTE technique for the thermal characterization of solid samples. Here, the TE material as a PT sensor operate under two configurations: (i) Front-PTE (FPTE), and (ii) Back-PTE (BPTE).

A Novel PhotoThermoElectric Technique (PTE)

The potential difference (∆V ) between two points of a thermoelectric material can be described by the following relation provided that the temperature fluctuations are weak:

with, d is the thickness of the sample in the negative z-direction, T z=0 and T z=d are the temperature at the surface z = 0 and at thickness z = d respectively. S is considered as constant for small temperature variations. Figure Normalized phase (rad)

Glass -Experiment (e=1160 Ws 1/2 m -2 K -1 ) Glass -Fit

where, β is known as the attenuation coefficient (or optical absorption coefficient), given by:

In such condition for absorption, the optical intensity of the light wave, (I), is exponentially reduced while travelling through the medium. Reciprocal of β is called penetration depth, the depth at which the intensity reduced by a factor of 1/e of the original signal.

Extinction Coefficient: The optical absorption coefficient can also be expressed as,

where, λ is the wavelength of the incident radiation and K is the extinction coefficient.

Solving by separation of variable method: The temperature field (T (z, t)), function of space and time, can be expressed as the product of two ordinary differential equations,

given by:

Substituting eq. (A-1) into eq. (2.12) and dividing by the product f g and excluding the source term gives:

Since both sides of the eq. (A-2) can vary quite independently of each other, the only way that this can happen is if the two side are equal to a constant. So both sides of the equation can be written as: Substituting Λ from eq. (A-5) in the z dependent eq. (A-4) gives:

This can also be expressed as an exponential solution, say [e σz ].