A Shah

M S Sannaikar

S R Inamdar

B Duponchel

R Douali

D P Singh

Photoluminescence modulation in the graphene oxide dispersed 4-n-octyl-4'-cyanobiphenyl molecular system

Keywords: Liquid crystal material, Graphene oxide, Photoluminescence, UV-visible absorbance, fluorescence decay lifetime

Herein, we investigate the mechanism of photoluminescence modulation (PLM) in the 4-n-octyl-4'-cyanobiphenyl liquid crystal (LC) in the presence of various doping concentrations (0.02 to 0.4 wt%) of 2D-GO (two-dimensional graphene oxide) nanoflakes. The role of intermolecular interactions on PLM and the subsequent effect on the decay lifetime is also examined via time-resolved PL measurements. The presence of intermolecular interactions is additionally confirmed by means of differential scanning calorimetry and polarized optical microscopy.

The successive addition of GO nanoflakes sharpens the absorption band of pure 8CB LC; consequently, it is blue shifted. The PL properties of the 8CB LC enhance due to the addition of GO nanoflakes which might be attributed to electron-phonon interaction between 8CB molecules and GO nanoflakes. The PL enhancement has been further supported by the time-resolved PL decay time measurement. The longest and shortest fluorescence lifetimes have been recorded for the 0.1 and 0.4 wt % GO/8CB composites, respectively. The investigated composites have shown their potential applications for fluorescent optical devices; however, the quantum efficiency needs to be further improved.

Introduction

After the first demonstration of polarised organic light-emitting diodes (OLEDs) in 1995, luminescent liquid crystalline (LLC) materials have attracted immense interests for organic optoelectronic applications, in particular the linearly polarised emission, as it combines the easy alignment of molecules and their luminescence properties [START_REF] Wang | Recent progress in luminescent liquid crystal materials: design, properties and application for linearly polarised emission[END_REF][START_REF] He | Graphene oxide liquid crystals for reflective displays without polarizing optics[END_REF]. Calamitic LC materials are comparatively insignif-icant for OLED application in comparison to the discotic LC materials which shows visible light emission [START_REF] Gowda | Charge Transport in Novel Phenazine Fused Triphenylene Supramolecular Systems[END_REF][START_REF] Bala | Room temperature discotic liquid crystalline triphenylene-pentaalkynylbenzene dyads as an emitter in blue OLEDs and their charge transfer complexes with ambipolar charge transport behaviour[END_REF]. In contrast, calamitic LC exhibits the ultraviolet absorption and emission that could also be transformed via doping a nanostructured materials [START_REF] Singh | Electrooptical, UV absorbance, and UV photoluminescence analysis of Se95In5 chalcogenide glass microparticle doped ferroelectric liquid crystal[END_REF][START_REF] Goel | Evolution of excitation wavelength dependent photoluminescence in nano-CeO2 dispersed ferroelectric liquid crystals[END_REF][START_REF] Joshi | Tuning the photoluminescence of ferroelectric liquid crystal by controlling the size of dopant ZnO quantum dots[END_REF][START_REF] Kumar | Stacking of ultra-thin reduced graphene oxide nanoparticles in supramolecular structures for optoelectronic applications[END_REF][START_REF] Roy | Photoluminescence behavior of TiO2 nanoparticles doped with liquid crystals[END_REF][START_REF] Singh | CuInS2/ZnS QD-ferroelectric liquid crystal mixtures for faster electro-optical devices and their energy storage aspects[END_REF][START_REF] Singh | Preparation and photophysical properties of soft-nano composites comprising guest anatase TiO2 nanoparticle and host hekates mesogens[END_REF][START_REF] Singh | Transmuting the blue fluorescence of hekates mesogens derived from tris(N-salicylideneaniline)s core via ZnS/ZnS:Mn2+ semiconductor quantum dots dispersion[END_REF][START_REF] Roy | Plasmonic resonance instigated enhanced photoluminescence in quantum dot dispersed nematic liquid crystal[END_REF]. Such transformation in PL property of a host matrix remarkably depends on several factors like shape, size, concentration, excitation wavelength, etc. of the guest dopant. Moreover, the absorption and emission properties of the dopant is one of the factors that determines the overall PL properties of the composites. For example, the behavior of metallic [START_REF] Roy | Plasmonic resonance instigated enhanced photoluminescence in quantum dot dispersed nematic liquid crystal[END_REF], semiconducting [START_REF] Joshi | Tuning the photoluminescence of ferroelectric liquid crystal by controlling the size of dopant ZnO quantum dots[END_REF] and insulating nanoparticles [START_REF] Roy | Photoluminescence behavior of TiO2 nanoparticles doped with liquid crystals[END_REF][START_REF] Singh | Preparation and photophysical properties of soft-nano composites comprising guest anatase TiO2 nanoparticle and host hekates mesogens[END_REF] in the liquid crystalline matrices is found to be completely state of affairs for enhancing or quenching the PL properties. Some reports show the enhancement in PL emission of the LC materials due to the dispersion of different nanoparticles [START_REF] Roy | Photoluminescence behavior of TiO2 nanoparticles doped with liquid crystals[END_REF][START_REF] Roy | Plasmonic resonance instigated enhanced photoluminescence in quantum dot dispersed nematic liquid crystal[END_REF]; meanwhile, on the other hand, the presence of quantum materials has quenched photoluminescence of LCs [START_REF] Singh | Quenching of photoluminescence and enhanced contrast of ferroelectric liquid crystal dispersed with Cd 1-X Zn X S/ZnS core/shell nanocrystals[END_REF][START_REF] Singh | Mn2+ doped ZnS quantum dots in ferroelectric liquid crystal matrix: Analysis of new relaxation phenomenon, faster optical response, and concentration dependent quenching in photoluminescence[END_REF][START_REF] Singh | Phase Contraction, fluorescence quenching and formation of topological defects in chiral smectic C matrix by Cd 0[END_REF]. Moreover, the incorporation of specific nanoparticles has also produced an induced photoluminescence in a non-luminescent LC material [START_REF] Singh | The phenomenon of induced photoluminescence in ferroelectric mesophase[END_REF]. Despite using several kinds of nanoparticles and quantum dots, fewer investigations have been carried out with the two-dimensional (2D) nanosheets or flakes like graphene oxide (GO) or reduced graphene oxide (rGO) [START_REF] Singh | Effect of graphene oxide interlayer electron-phonon coupling on the electro-optical parameters of a ferroelectric liquid crystal[END_REF][START_REF] Singh | 13 Dual Photoluminescence and Charge Transport in alkoxy biphenyl benzoate ferroelectric liquid crystalline-Graphene Oxide Composite[END_REF].

Graphene shows superior electronic and mechanical properties as compared to its mother element graphite and it represents a single layer of graphite, in which sp 2 bonded carbon atoms are hexagonally arranged. GO is derived from graphite by chemical oxidation and subsequent exfoliation and it is readily dispersible in aqueous medium. The physical properties of GO depend on the degree of oxidation. The dispersion of graphene, GO and rGO has revealed some superior properties in the LCs [START_REF] Ahmad | Optimization of particle size for high birefringence and fast switching time in electro-optical switching of graphene oxide dispersions[END_REF][START_REF] Basu | Faster in-plane switching and reduced rotational viscosity characteristics in a graphene-nematic suspension[END_REF][START_REF] Özgan | Thermal and electro-optic properties of graphene oxide-doped hexylcyanobiphenyl liquid crystal[END_REF][START_REF] Singh | Orientation of 4-n-octyl-4-cyanobiphenyl molecules on graphene oxide surface via electron-phonon interaction and its applications in nonlinear electronics[END_REF][START_REF] Singh | Spectroscopic, dielectric and nonlinear current-voltage characterization of a hydrogenbonded liquid crystalline compound influenced via graphitic nanoflakes: An equilibrium between the experimental and theoretical studies[END_REF]. The most of investigated regimes with the dispersion of graphene, GO and rGO include the study of electro-optical, electronic and thermal properties, but it has not been done so well for the photoluminescence. Therefore, this field has plenty of opportunities for further investigations to realize better composites for next-generation fluorescent displays and photonic devices.

In our previous article [START_REF] Singh | Orientation of 4-n-octyl-4-cyanobiphenyl molecules on graphene oxide surface via electron-phonon interaction and its applications in nonlinear electronics[END_REF], we have investigated the graphene oxide (GO) dispersed 4-n-octyl-4'-cyanobiphenyl (8CB) hybrid system to disclose the longrange molecular interactions between GO and 8CB molecules. In this report, it has been seen that the orientation of 8CB molecules successively changes from planar to homeotropic depending on the dispersion concentration of GO. This study was focused on the molecular interaction and electronic properties of the hybrid system, but the investigation of photophysical properties for the hybrid system along with the pristine 8CB material has not been performed so far; therefore, in the present article, we have quantitatively studied the photoluminescence modulation in the 4-n-octyl-4'-cyanobiphenyl (8CB) liquid crystalline material dispersed with various concentrations of 2D-graphene oxide nanoflakes.

The photoluminescence modulation (PLM) depends upon the intermolecular interactions between the 8CB molecules and the 2D-GO nanoflakes. The reduction in full width at half maxima (FWHM) of the absorption band and slight shifting in the PL band supports the existence of intermolecular interactions.

2

The underlined mechanism has been further supported by the time-resolved PL measurements. The investigated composites indicate their applications for optical energy storage which is discussed within the scope of this paper.

Experimental details

Dopant material: Graphene oxide nanoflakes

2D-GO nanoflakes were synthesized from commercially available graphite following the Hummers method as previously described in our previous articles [START_REF] Singh | Effect of graphene oxide interlayer electron-phonon coupling on the electro-optical parameters of a ferroelectric liquid crystal[END_REF][START_REF] Singh | 13 Dual Photoluminescence and Charge Transport in alkoxy biphenyl benzoate ferroelectric liquid crystalline-Graphene Oxide Composite[END_REF][START_REF] Singh | Orientation of 4-n-octyl-4-cyanobiphenyl molecules on graphene oxide surface via electron-phonon interaction and its applications in nonlinear electronics[END_REF]. We have utilized the same 2D-GO nanoflakes in this study which is already reported in our previous articles [START_REF] Singh | 13 Dual Photoluminescence and Charge Transport in alkoxy biphenyl benzoate ferroelectric liquid crystalline-Graphene Oxide Composite[END_REF][START_REF] Singh | Orientation of 4-n-octyl-4-cyanobiphenyl molecules on graphene oxide surface via electron-phonon interaction and its applications in nonlinear electronics[END_REF]. To prepare GO suspension in DMF, 0.65 mg of 2D-GO nanoflakes were dissolved in 160 microliter of DMF and sonicated for 2.5 hours. This suspension was deposited on a Si wafer by drop casting technique and dried for 4 hours at 50 o C. The SEM image of 2D-GO nanoflakes is presented in figure 1(b). The width size distribution of 2D-GO nanoflakes was in the range of 10-40 nm, whereas the lateral size distribution was found to be ¤ 50 nm-25 µm. As the characterization data of 2D-GO nanoflakes have already been published; therefore, we are not providing all characterization data here and only referring to the size and SEM image of nanoflakes.

2.3. Preparation of the 8CB/GO composites 0.1 mg ml 1 suspension of 2D-GO was first prepared in the toluene. The sus- pension was homogenized by ultrasonication for several hours. After obtaining a homogenous suspension, it was added to the 8CB LC maintaining the wt/wt% from 0.02 to 0.4. The higher dispersion concentrations of GO were deferred as they started showing a high tendency of agglomeration beyond the 0.4 wt%.

Differential scanning calorimetry (DSC)

Usually, the dispersion of an external guest dopant causes the shifting of the mesophase transition temperatures of a LC material; therefore, it is essential to study the phase transitions of the 8CB/GO composites. For this purpose, phase thermograms were obtained using the TA Instruments Q1000 differential scanning calorimeter with a 2 K min 1 heating/cooling rate. Later on, the DSC thermograms were normalized according to the weight of the samples taken for the DSC study.

Polarized optical microscopy (POM)

Polarized optical microscopy is a fundamental tool to ensure the homogenous distribution of dopants in a LC matrix; therefore, polarized optical microscopic (POM) observations were performed on the ZEISS AXIO equipped with Infinity2 image capturing software. During the POM measurements, the temperature of materials was controlled with a Linkam TMS 94 hotstage. The pure 8CB and its GO nanoflakes composites were filled in 50 µm thick unaligned commercial sample cells (purchased from AWAT, Poland) to perform polarized optical microscopy.

UV-visible absorption spectroscopy

UV-visible absorption measurements were performed using a NIR-UV-VIS Spectrophotometer (Jasco, V670). UV-visible spectra were recorded in the solution state (concentration = 1 mg ml 1 ), using toluene as solvent [START_REF] Singh | Preparation and photophysical properties of soft-nano composites comprising guest anatase TiO2 nanoparticle and host hekates mesogens[END_REF][START_REF] Singh | Transmuting the blue fluorescence of hekates mesogens derived from tris(N-salicylideneaniline)s core via ZnS/ZnS:Mn2+ semiconductor quantum dots dispersion[END_REF].

Absorption measurements were carried out in the range from 200 to 750 nm by keeping the both entrance and exit slit width equal to 5nm. The baseline and background corrections were done before performing the absorption measurements for the pristine 8CB LC and mixtures.

Photoluminescence (PL) studies

The photoluminescence spectra of pure 8CB and its 2D-GO composites were recorded with the help of a Fluoromax-4 Spectrofluorometer (JY, Horiba). All the samples were excited by a monochromatic light of wavelength 300 nm since the 8CB and 8CB/GO composites have a strong absorption band at this wavelength as rendered from UV-visible absorption measurements.

Time-resolved PL Measurements (TRPL)

In steady-state spectral measurement, the detector adds up all the photons emitted by the sample molecules, starting with the instance of excitation and ending with a time when the last excited molecule is decayed to the ground state. Time-resolved measurements, using time correlated single photon counting (TCSPC) technique, were performed; since they contain more information than is available from the steady-state data. Owing to spectral overlap of absorption and emission, it is usually not possible to resolve the emission from the multiple residues from the steady-state data. Further, one can distinguish between static and dynamic quenching using lifetime measurements. Moreover, probe concentration can change during the measurement due to photobleaching leading to difficulty in making quantitative use of the local intensities. In contrast, fluorescence lifetimes are typically independent of the probe concentration and are not influenced by the fluctuations in the lamp intensity. We have used a pulsed LED as an excitation source (296 nm) to measure the decay times of these composites at their maximum PL peak using a time-domain based ISS ChronosBH TCSPC Spectrometer. All the optical measurements were carried out at room temperature.

Results and discussion

Differential scanning calorimetric (DSC) study

The effect of GO dispersion on the mesophase transition temperatures of the 8CB LC material has been studied. As the dispersion concentration of GO is successively increased, the molecular orientation of the 8CB changes accordingly, and a homeotropic orientation has been achieved for the dispersion 0.4 wt% of GO. At this particular concentration of GO, global homeotropic orientation is visible (figure 3k,l); however, some illuminated regions are also observed which is might be due to the scattering of incident light through the edges of GO flakes. The observed homeotropic orientation is because of the interaction between the polar C¡N functional group of the 8CB molecules with the GO surface via an electron-phonon interaction.

This postulate is recently reported by us [START_REF] Singh | Orientation of 4-n-octyl-4-cyanobiphenyl molecules on graphene oxide surface via electron-phonon interaction and its applications in nonlinear electronics[END_REF]. For the intermediate dispersion concentration of 2D-GO nanoflakes, the orientation of 8CB molecules represents a merged state of the planar and homeotropic orientations.

UV-visible absorption study

The absorption spectrum of any material is the result of its electronic, vibrational, and rotational transitions. The absorption peak corresponds to the electronic transition line, and the rest of the spectrum is formed by a series of lines that correspond to rotational and vibrational transitions. Therefore, the absorption spectrum provides in-depth information about the structure and transitions. The UV-visible absorption spectra of the pure 8CB LC and 8CB/2D-GO nanoflakes composites containing different GO concentrations (i.e. 0.02, 0.1, 0.2, 0.3 and 0.4 wt%) were recorded. These spectra were taken in the solution having toluene as solvent and 1mg/ml solution concentration. Figure 4 shows the normalized absorption spectra of the pure 8CB LC and 8CB/2D-GO nanoflakes composites.

It is noticed that the 8CB LC shows a strong absorption band nearly at 300 nm which is attributed to π-π* transitions in

1 A 1g 1 B 1u . The 1 A 1g 1 B 1u
is a spin allowed, symmetry-forbidden, but vibronically allowed transition [START_REF] Singh | Time-resolved fluorescence and absence of Förster resonance energy transfer in ferroelectric liquid crystal-quantum dots composites[END_REF].

Additionally, we have previously reported that the 2D-GO flakes exhibit two ab-sorption peaks at 230 and 300 nm,(supplementary figure S1), attributed to π-π* transitions of C=C bonds and to n-π* transitions of C=O bonds, respectively [START_REF] Singh | 13 Dual Photoluminescence and Charge Transport in alkoxy biphenyl benzoate ferroelectric liquid crystalline-Graphene Oxide Composite[END_REF][START_REF] Eda | Blue Photoluminescence from Chemically Derived Graphene Oxide[END_REF]. In 8CB/2D-GO composites, the successive addition of increasing weight concentration of GO results a trivial narrowing in the absorption bandwidth.

Inset of figure 4 depicts the full-width half maxima (FWHM) for the pure 8CB and 8CB/2D-GO nanoflakes composites. The FWHM varies nonlinearly with the increasing concentration of GO nanoflakes in the solution. Besides, the narrowing in the FWHM of the absorption band also caused a feeble blue shifting.

Steady-state spectral parameters are represented in Table 1. The sharpening in the UV-visible absorption spectra of the 8CB/GO composites can be explained by the modified Beer-Lambert law [START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF], which is as follows-

I I o c¦ n exp l¦ (1)
where, I o and I are the intensities of the incident and transmitted radiations, respectively. c and l are the solution concentration and optical path length, respectively, and is the absorption coefficient. n is the power exponent.

In our study, the sharpness of the absorption band (slightly blue shifting) might be associated with the dipole-dipole interactions between the 8CB LC molecules and GO nanoflakes. If the dipole-dipole interaction is strong, the energy required for an absorption will also be large, i.e., the position of the absorption band will be located at lower wavelengths [START_REF] Mahesh | Carbon dots dispersed hexabutyloxytriphenylene discotic mesogens: Structural, morphological and charge transport behavior[END_REF][START_REF] Albani | Fluorescence Spectroscopy Principles[END_REF].

Photoluminescence (PL) study

The room temperature PL spectra of the pure 8CB LC and its composites with GO nanoflakes are presented in figure 5. The pure 8CB LC exhibits a strong PL emission peak at 336 nm, whereas 2D-GO nanoflakes emit a violet band of 362 nm, (see supplementary figure S2), attributed to the n-π* transition of the isolated sp 2 domains within the carbon-oxygen sp 3 matrix [START_REF] Singh | 13 Dual Photoluminescence and Charge Transport in alkoxy biphenyl benzoate ferroelectric liquid crystalline-Graphene Oxide Composite[END_REF][START_REF] Eda | Blue Photoluminescence from Chemically Derived Graphene Oxide[END_REF]. In this study, we have not contemplated about the contribution of the disorderinduced long-wavelength PL band (visible at ¤ 700 nm) of the GO nanoflakes as the 8CB/GO composites only show a single PL emission nearly at 340 nm.

Interestingly, PL intensity of the 8CB/GO composites increases as compared to the pure 8CB LC. This modulation in the PL emission might be related to the combined effect of the change in optical density of 8CB LC after the addition of different concentrations of GO nanoflakes and electron-phonon interaction between the 8CB molecules and GO surface. In addition to this, the change in molecular orientation could also be a factor that leads to PL modulation in the composites. The optical density of a material is related to the PL emission in the following manner.

At a particular excitation wavelength, the PL emission intensity can be explained as follows [START_REF] Albani | Fluorescence Spectroscopy Principles[END_REF]-

I P L λ¦ 2.3I O λ¦ clφ P L (2)
where,φ P L is the photoluminescence quantum yield and other abbreviations are the same as explained in equation 1.

It is clear by the aforementioned equation that the PL intensity is proportional to the optical density i.e. cl. With the addition of GO nanoflakes in the 8CB LC, optical density changes nonlinearly due to the interfacial properties of GO surface and 8CB molecules that govern the changes in the PL emission.

Besides, a nonlinearity in the PL emission as a function of GO concentration for the 8CB/GO composites has also been observed. For the composites, maximum and minimum PL intensities have been observed for the 0.4 and 0.3 wt% of GO, respectively. In addition to the change in the PL intensity, the broadening of the PL band has also changed. The change in the broadening of the PL band is probably due to the contribution of the PL of GO nanoflakes. We have also analyzed this nonlinear change in the photophysical property by plotting the Stokes shift versus GO concentration in the 8CB LC which is shown in figure 6.

A maximum Stokes shift (difference between the emission and absorption peak wavelengths) of about 48 nm is detected for 0.1 % wt GO. A comparison of the steady-state spectral properties of the 8CB LC and its composites with various GO nanoflakes concentrations are listed in Table 1.

The fluorescence quantum yield of a sample is determined using a relative optical method. The absorption factor should be estimated accurately for solutions with a low absorbance, typically A © 0.1, to avoid internal filter effects and errors arising from uneven distribution of the excited species in the detected volume. The fluorescence quantum yields (ϕ s ) were obtained by comparison with a standard dye using Equation-

ϕ s ϕ r ¥ I s A r n 2 s I r A s n 2 r (3)
where, I s and I r are the integrated fluorescence emissions of the samples (binary mixtures) and the standard dye (Coumarin 440, QY = 0.98) in ethanol, respectively [START_REF] Wang | Molecular Wires Comprising π-Extended Ethynyl-and Butadiynyl-2,5-Diphenyl-1,3,4-Oxadiazole Derivatives:FIXME Synthesis, Redox, Structural, and Optoelectronic Properties[END_REF]. A s and A r , respectively, are the absorbances at the excitation wavelength of the samples and the reference, while ϕ s and ϕ r , respectively, are the quantum yields of the sample and the reference, n being the refractive index. The values of I s and I r are determined from the photoluminescence spectra corrected for the instrumental response, by integrating the emission intensity over the desired spectral range.

The results substantiate that the monotonical increase of quantum yield for 0.02, 0.2 and 0.4wt% of GO is in accordance with the results of photoluminescence modulation of 8CB upon addition of GO. Further, quantum efficiency for 0.1 and 0.2 wt% of GO are more as compared to that of pure 8CB. Hence, GO has modulated and enhanced the photoluminescence properties of the 8CB system.

Time Resolved Photoluminescence Measurements (TRPL)

The fluorescence decay profiles of the pure 8CB LC and 8CB/GO composites are presented in figure 7. The decay curves were fitted by a bi-exponential decay function and results are listed in Table 2. The average decay lifetime, (τ ), was calculated from the following equation [START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF]-

τ τ 1 A 1 τ 2 A 2 A 1 A 2 (4)
where, τ 1 and τ 2 represents the shorter and longer lifetime components with their normalized amplitude components A 1 and A 2 , respectively. The fast decay process with a lifetime around 1 ns,(τ 1 ), can be attributed to the non-radiative re-combination, while the slow decay process (τ 2 ) originates from the radiative decay.

The pure 8CB LC has a fluorescence decay lifetime of 1.32 ns; however, after the dispersion of GO into various proportions, the decay lifetime also changes.

The gradually increasing dispersion concentration of GO in the 8CB LC from 0.0 to 0.1 wt % leads to an enhancement of the decay lifetime from 1.32 ns to 1.81 ns. Further addition of GO into the 8CB LC, reduces the decay lifetimes.

The longest fluorescence lifetime is detected for the 8CB+0.1 wt % GO composite; whereas, the shortest decay lifetime is noticed for the 0.

Figure 1 :

 1 Figure 1: (a) Molecular structure of the 4-n-octyl-4'-cyanobiphenyl (8CB) liquid crystalline material and (b) scanning electron microscopic (SEM) image of 2D-graphene oxide (2D-GO) nanoflakes.

Figure 2

 2 shows the normalized differential scanning calorimetric (DSC) curves of the 8CB and its composites having different concentrations of 2D-GO nanoflakes. As stated in the experimental section, the 8 CB LC exhibits smectic A (SmA) and nematic (N) mesophases.The SmA-N and N-Iso phase transitions took place at 33.63 and 40.72 o C, respectively during the heating process. It is observed in all composites that the addition of different concentrations of GO in the 8CB causes a lowering in the N-Iso phase transition temperature. As the nematic-to-isotropic (NI) is a weakly first-order transition; therefore, it might be due to lowering of the orientational order of the pure 8CB material after the dispersion of GO into different concentrations. In addition to this, it is also observed that the SmA-N phase transition has been weakened. It is probably due to lowering in the positional order of the SmA phase originated because of the change in layer arrangement.Usually, 2D-GO nanoflakes align with orientational directions along their long axes and the 8CB molecules tend to align along with the flakes; however, the global orientation does not relay in a single direction resulting in the reduction in the order parameter.

3. 2 .

 2 Polarized optical microscopic study Polarized optical micrographs (POMs) of the 8CB and its GO nanoflakes composites are presented in figure 3. In general, the molecules of the pure 8CB LC material preferentially orient along with the director ( n). The pristine 8CB LC material renders the typical fan-shaped texture of in smectic A phase (figure 3a, at 25 o C) and traditional schlieren texture in the nematic phase (figure 3b, at 35 o C). The temperature for recording the POMs of 8CB/GO composites in a desired phase was chosen from their corresponding phase schemes. It is observed that the presence of 2D-GO flakes significantly changes the molecular orientation of the 8CB; as a result, the exemplary optical textures of the SmA and N phases have not been observed for the composites because of the GO flakes migrate closer to ITO substrate/LC interface due to viscous drift [23].

Figure 2 :

 2 Figure 2: Normalized differential scanning calorimetric (DSC) curves of (a) 8CB, (b) 8CB + 0.02, (c) 8CB + 0.1, (d) 8CB + 0.2, (e) 8CB + 0.3 and (d) 8CB + 0.4 wt% dispersion of 2D-GO nanoflakes with a heating/cooling rate of 2 K min 1 .

8 .

 8 4 wt % GO/8CB composite. The variation of average decay lifetime of the 8CB LC and its composites with different concentrations of 2D-GO nanoflakes is presented in figure The increased decay lifetimes indicate that the PL properties of the 8CB LC have been enhanced after the dispersion of GO concentration up to 0.1 wt%. In this situation, PL decays are dominated by the radiative process. Beyond this critical concentration, average decay lifetime decreases which suggests that the non-radiative decay processes are taking place in the composites and might be resulting in the quenching of PL intensity. This study indicates that the small dispersion concentration of 2D-GO nanoflakes are superior in PL properties; thus, such composites could be used for fluorescent displays and optical devices.

  In conclusion, various concentrations of 2D-GO nanoflakes were dispersed in a commercially available 4-n-octyl-4'-cyanobiphenyl (8CB) liquid crystalline (LC) material and characterized via differential scanning calorimetry (DSC), polarized optical microscopy, UV-visible, photoluminescence and time-resolved PL techniques. DSC thermograms reveal that the dispersion of GO nanoflakes lowers the weakly first-order nematic-isotropic (N-Iso) phase transition temperature. This lowering of the N-Iso phase transition temperature might be due to weaker orientational order parameter in the composites. The change in the smectic A to nematic (SmA-N) phase transition is associated with the reduction of positional ordering in the composites. 8CB LC exhibits a strong absorption band at 300 nm attributing to the π-π* transitions, whereas GO nanoflakes show two absorption peaks at 230 and 300 nm attributed to π-π* transitions of C=C bonds and to n-π* transitions of C=O bonds, respectively. The dispersion of GO nanoflakes causes the sharpening of the absorption band which has been explained by the modified Beer-Lambert law. The presence of GO nanoflakes has enhanced the PL emission of 8CB LC which is probably associated with the combined effects of electron-phonon interaction and change in optical density.

Figure 3 :

 3 Figure 3: Polarized optical micrographs (POMs) of the (a),(b) 8CB, (c),(d) 8CB + 0.02, (e),(f) 8CB + 0.1, (g),(h) 8CB + 0.2, (i),(j) 8CB + 0.3 and (k),(l) 8CB + 0.4 wt% dispersion of 2D-GO nanoflakes in the smectic A and nematic phases, respectively. The crossed arrows represent the crossed polarizer-analyzer condition at which POMs have been taken. The scale bar is 100 µm in all POMs.

Figure 4 :

 4 Figure 4: Absorption spectra of the 8CB and its composites with 2D-GO nanoflakes. Inset shows the variation of full width at half maxima (FWHM) of absorption band with the variation of dispersion concentration of GO. The concentration of solution was equivalent to 1mg/ml.

Figure 6 :

 6 Figure 6: Stokes shift of the pure 8CB LC and it's composites having different concentrations of 2D-GO nanoflakes.

Figure 7 :

 7 Figure 7: Time-resolved decay profile of the 8CB LC and it's composites having different concentrations of 2D-GO nanoflakes. The 8CB-GO pairs were excited by 296 nm wavelength.

Figure 8 :

 8 Figure 8: Variation of average decay lifetime with the change in 2D-GO nanoflakes concentrations in the 8CB LC.

Table 1 :

 1 Steady-state spectral properties of the 8CB LC and its composites having different concentrations of 2D-GO nanoflakes. QY is abbreviated for quantum yield. *Quantum yield of reference dye. .02 wt% GO 1.20 3.35 87.35 12.65 1.47 1.2506 8CB + 0.1 wt% GO 1.28 3.55 76.63 23.37 1.81 1.2173 8CB + 0.2 wt% GO 1.03 2.68 86.95 13.05 1.24 1.3294 8CB + 0.3 wt% GO 0.95 1.40 59.73 40.27 1.12 1.0605 8CB + 0.4 wt% GO 0.20 1.10 4.3 95.7 1.06 1.0722

	Sample	λ abs FWHM abs	λ em	Stokes shift PL Intensity	QY
	(nm)	(nm)	(nm)		( ∆λ, nm)		(arb. units)
	8CB	300	34.00		336		36		11838	0.0976
	2D-GO nanoflakes	300	-		362		62		11335	-
	8CB + 0.02 wt% GO	299	29.85		341		42		30698	0.5448
	8CB + 0.1 wt% GO	297	30.10		345		48		26764	0.3951
	8CB + 0.2 wt% GO	297	25.74		337		40		43419	0.6362
	8CB + 0.3 wt% GO	297	30.09		337		40		19265	0.3924
	8CB + 0.4 wt% GO	297	25.73		335		38		112279	0.8180
	C440 (C120)				430				0.9800*
	Sample	τ 1	τ 2	A 1		A 2	τ	χ	2
		(ns) (ns)	(%)	(%)	(ns)
	8CB	0.21 1.35 2.47 97.53 1.32 1.2209
	2D-GO nanoflakes	1.29 1.15 96.81 3.19 1.28	1.2
	8CB + 0

Table 2 :

 2 Fluorescence decay parameters of 8CB and 8CB+GO mixtures fitted by biexponential fit.

Acknowledgment

DPS gratefully acknowledges the financial assistance provided by the UDSMM, ULCO. Prof. A. Hadj Sahraoui, Director UDSMM is highly acknowledged for his kind support. We are thankful to Prof. François Delattre and Mr. Steven Ruellan for his help in NMR measurement.

The enhancement in PL properties has been further supported by the timeresolved PL measurements. The longest fluorescence lifetime has been detected for the 8CB+0.1 wt % GO composite; whereas, the shortest decay lifetime is noticed for the 0.4 wt % GO/8CB composite and their recorded values were found to be 1.81 and 1.06 ns, respectively. All the optical properties including the quantum efficiency were found to be nonlinear as a function of GO concentration. The nonlinearity in the optical properties might be due to the interfacial properties of 8CB molecules and GO surface. The enhanced PL properties for small dispersion concentration of GO nanoflakes would be interesting for the fluorescent displays and optical devices.

Conflict of interest

The article is original and has been written by the stated authors who are aware of its content and approve its submission. This article has neither been published previously nor under consideration for the publication elsewhere. We also declare "No conflict of interest exists".


Mohamed Moussa

E L Idi

Mustapha Karkri

Heating and cooling conditions effects on the kinetic of phase change of PCM embedded in metal foam

Keywords: Thermal energy storage, numerical simulation, phase change material, metal foam

Phase change materials (PCM) are attractive candidates for energy storage. They can store large quantities of energy in small volumes at nearly constant temperatures. Despite their advantage, their thermal conductivity is very low with a high-volume change during the melting and solidification process. One way to increase their poor thermal conductivity is to embed them into open cell metallic foams. In this paper, a numerical study is conducted on the effect of the heating and cooling conditions on phase change kinetics of paraffin embedded in a metal foam. Constant heating and sinusoidal heating are similarly investigated. For the constant heat flux, a step function ranging from +1800 W/m 2 to -1800 W/m 2 is considered, while for the variable heat flux, a sinusoidal function having a similar area as step function is considered at one wall of the container to provide heating and cooling of the PCM/ Metal foam composite. A new mathematical model based on the Brinkmann-Forchheimerextended Darcy equation and the local thermal non-equilibrium model (LTNE) is proposed by applying a two-energy equation. The paraffin phase change is modeled using the enthalpy-porosity method. The numerical results are validated by comparing them with the experimental data. The results showed that at the time of melting it has reduced with sinusoidal heating. The results also showed that the heat losses on the boundary have a greater effect in a sinusoidal heat flux case than in constant heat flux case and this effect is more important on the solidification than on the melting process of the paraffin.

Introduction

Phase change materials (PCM) offers the possibility to store and release a large amount of heat at the time of phase change in small volumes. They are widely used to improve energy efficiency. [START_REF] Sharma | Review on thermal energy storage with phase change material and applications[END_REF][START_REF] Moussa | Méthode inverse pour la détermination expérimentale des propriétés thermophysiques des matériaux à changement de phase[END_REF]. However, most PCM have low thermal conductivity, this limit the heat storage efficiency in real applications. [START_REF] Sharma | Review on thermal energy storage with phase change material and applications[END_REF][START_REF] Moussa | Méthode inverse pour la détermination expérimentale des propriétés thermophysiques des matériaux à changement de phase[END_REF][START_REF] Boussaba | Elaboration and properties of a composite bio-based PCM for an application in building envelopes[END_REF]. Normal paraffin of type CnH2n+2 is an excellent PCM for latent heat storage because of its high latent heat, good stability, and absence of subcooling and toxicity. However, its widespread utilization is hampered by several bottleneck issues. A major drawback is its low thermal conductivity of 0.2-0.4 W/(m.K) [START_REF] Nihal | Organic phase change materials and their textile applications: An overview[END_REF][START_REF] Moussa | Melting and solidification behavior of paraffin embedded in metal foam[END_REF], which leads to low heat storage/release rates and low utilization efficiency of the stored energy. PCM thermal conductivity can be enhanced through the addition of materials with high thermal conductivity such as fins [START_REF] Biwole | Influence of fin size and distribution on solid-liquid phase change in a rectangular enclosure[END_REF], porous-graphite [START_REF] Jegadheeswaran | Conductivity particles dispersed organic and inorganic phase change materials for solar energy storage-an energy based comparative evaluation[END_REF], nanoparticles [START_REF] Arıcı | Melting of nanoparticle-enhanced paraffin wax in a rectangularenclosure with partially active walls, Melting of nanoparticle-enhanced paraffin wax in a rectangular enclosure with partially active walls[END_REF], and high porosity-metal cells [START_REF] Tauseef-Ur-Rehman | A critical review on heat transfer augmentation of phase changematerials embedded with porous materials/foams[END_REF][START_REF] Moussa | Etude numérique de stockage d'énergie thermique dans un composite: mousses métalliques/matériaux à changement de phase[END_REF]. Among these heat transfer enhancers, the high porosity open-cell metal foam is found to be especially effective in improving the performance of PCM because of its high thermal conductivity, large surface area to volume ratio, highly interconnected structure and natural fluid mixing effect. The study of the thermal behavior and transfer mechanisms of PCM/metallic foam composites has attracted increasing research attention. [START_REF] Yang | Design and operating evaluation of a finned shell-and-tube thermal energy storage unit filled with metal foam[END_REF][START_REF] Yang | Experimental study on the solidification process of fluid saturated in fin foam composites for cold storage[END_REF].

For optimal use of PCM/metal foam composites such as a thermal storage unit or thermal management system, it is necessary to study the effect of the metal foam microstructure (morphology), the thermal conductivity of metal foam, and the heating and cooling condition. These effects studies led to find the vital parameters that can be used to optimize the performance of PCM/metal foam composites for the given application. Various researches have been carried out to study metal foam thermal conductivity and microstructure effects on the effective thermal conductivity of PCM/metal foam composites and phase change kinetics. However, studies are lacking on the effect of the heating and cooling conditions, especially in a continuous process (cyclical heating and cooling). Xia et al. [START_REF] Xiao | Effective thermal conductivity of open-cell metal foams impregnated with pure paraffin for latent heat storage[END_REF] studied the effective thermal conductivity of paraffin/nickel foam composites and paraffin/copper foam composites with high metal foam porosity (>95%). The study was carried out with the effect of porosity on the effective thermal conductivity of paraffin/metal foam composite. The results show that the effective thermal conductivity increases as the porosity decreases. Xiang Huang et al. [14] conducted an experimental study to investigate the thermal conductivity enhancement of myristyl alcohol (MA) by impregnation in metal foam. The MA/metal foam composite was elaborated by vacuum melting infiltration and the impregnation was evaluated by the impregnation ratio, which is the ratio between MA mass and MA theoretical mass. Two types of foam were investigated. The results show that if we compare with the use of pure MA, the use of the copper foam increases the effective thermal conductivity of MA/copper foam by 7.51 times, and the use of nickel foam increased the thermal conductivity by 1.80 times. Sriharsha S. et al [15] carried out a numerical study on the effect of the pores size of aluminum foam on the effective thermal conductivity of paraffin/aluminum foam composites using an analysis of finite elements. To study the effect of the pores size, an aluminum foam with 0.94 porosity and varying pores sizes, from 5μm to 100μm were considered. It was found that a smaller pore size results in a higher thermal conductivity. On average the thermal conductivity more than doubles, from 5W/(m.K) to 12W/(m.K), when the pore size is reduced from 100μm to 25μm. El idi [START_REF] Idi | A numerical investigation of the effects of metal foam characteristics and heating/cooling conditions on the phase change kinetic of phase change materials embedded in metal foam[END_REF] studied the effect of metal foam morphology and thermal conductivity effects on the phase change kinetic. The results show that the thermal conductivity plays an essential role in the kinetic phase change of PCM embedded in a metal foam. The melting of PCM embedded in metal foam is almost proportional to the metal foam's thermal conductivity. The melt fraction of PCM embedded in the metal foam increases with the decrease in porosity. The PCM melting and solidification rates for both increase with higher pore density. Small pore density increases permeability and natural convection, and large pore density leads to low permeability that weakens or suppresses natural convection, thus weakening the overall heat transfer. Y. Zhao et al. [START_REF] Zhao | Modeling metal foam enhanced phase change heat transfer in thermal energy storage by using phase field method[END_REF] carried out another numerical study on the effect of porosity and pores density on the melting and solidification cycle. The phase change of PCM in metal foam was modeled by the phase field method. To study the effect of the metal foam structure on the melting and solidification process, four metal foams with the same pore density of 20PPI and different porosity (0.80, 0.85, 0.90 and 0.95) were used. The same methodology was used to study the effect of pore densities. That is to say, four metal foams with the same porosity of 0.9 and different pore densities (5PPI, 10PPI, 20PPI and 40PPI). It was found that the foam morphology (porosity and pore density) play an essential role in the PCM melting and solidification cycle. The melting fraction of PCM embedded in a metal foam increases with the decrease of porosity, and similarly increases with the increase of pore density. S. Abishek et al. [START_REF] Abishek | Effect of microstructure on melting in metal-foam/paraffin composite phase change materials[END_REF], studied the microstructure effect on the melting of paraffin in metal foam. The authors were modeling the phase change using the enthalpy-porosity method and used additional volume fraction and field to account for the degree of melting. Furthermore, they used chtMultiRegionFoam in OpenFOAM, a conjugate heat transfer and fluid dynamics solver, to simulate the melting process in paraffin aluminum foam composites with a given porosity but varying microstructures. The results show that the specific area, which is the ratio between surface and volume, plays an essential role in the melting of paraffin embedded in the aluminum foam. Recently, Xiaohu Yang et al [START_REF] Yang | Gradient design of pore parameters on the melting process in a thermal energy storage unit filled with open-cell metal foam[END_REF] performed numerical simulation on the phase change kinetic of a novel latent heat thermal energy storage unit filled by metal foams with gradient in pore parameters. The gradients were designed by packaging metal foam blocks with an increase or decrease in porosity or pore density. The metal foam with positive gradient in pore parameters showed a better temperature uniformity. Hence, there is a need to study the cyclic heating and cooling of PCM/ Metal foam composites, which will, in turn, affect the performance of thermal energy storage systems. The study of heating and cooling conditions on the kinetics of phase change will be very interesting and will complete previous studies done in the field.

Among other important applications of PCM, is the use of PCM composites to cool electronic devices that generate a constant heat flux and passive solar energy storage, which is additionally affected by the variation in solar radiation. It is for these reasons that we have chosen to study the constant and sinusoidal heating and cooling. In this paper, we focused on the study of the heating and cooling conditions on the phase change kinetics of paraffin embedded in aluminum foam and stored energy. The amount of energy stored is directly related to the liquid fraction, and the storage kinetics is related to the temporal evolution of the liquid fraction. For the constant heat flux, a step function ranging from +1800 W/m 2 to -1800 W/m 2 is used and for variable heat flux, a sinusoidal function having a similar area as step function was considered at one wall of the container to provide heating and cooling of the PCM/metal foam composite. A new mathematical model is proposed based on the Brinkmann-Forchheimer-extended Darcy equation and the local thermal non-equilibrium model (LTNE) by applying a two-energy equation. The paraffin phase change is modeled by the enthalpy-porosity method. The numerical results are validated by comparing them with the experimental data. The results will be presented and discussed in order to make the optimal use and sizing choice of a thermal energy storage unit for the given application.

properties

(J.K -1 .kg -1 ) 1800 2100 Thermal conductivity -liquid (W.K -1 .m -1 ) 0.15 0.2 β (K -1 )
0.5x10 -3 1.1x10 -4 Table 1: Thermophysical properties of paraffin RT27, RT58 and aluminum foam.

Modeling method 2.1. Physical problem

The physical problem is illustrated in Fig. 1. A square cavity with the dimensions of 4cmx4cm is filled with paraffin wax, RT27, and embedded in an aluminum foam with porosity of 0.93 and pores density of 40PPI. A heat flux is applied in the left wall cavity. There are a two types of cycling heating and cooling applied to the PCM/metal foam composite. The first is at a constant flux of +1800 W/m 2 provided from the heated wall at 60mins, and then its value becomes negative at the same magnitude for the next 60mins. The second, is a sinusoidal function having the similar area under the curve it's provide for the same time, as shown in the Fig. 2. The equation for the boundary condition in the left wall is presented in Eq. [START_REF] Sharma | Review on thermal energy storage with phase change material and applications[END_REF]. The rest of the wall cavity is insulted. Initially, the metal foam and the PCM in the cavity are placed under a uniform melting temperature at 294.15K. The proprieties of paraffin RT27 used for the present study are given in Table1 [START_REF] Aadm | Heat transfer characteristics of thermal energy storage of a composite phase change materials: Numerical and experimental investigations[END_REF].

( )

w w W m t q W m t t q π π  ≤ ≤  =  - < ≤   = × × × (1)

Assumptions

• The liquid is considered as incompressible and the flow is laminar • The natural convection caused by buoyancy is subject to the Boussinesq approximation • The thermal radiation is neglected in the metal foam during melting and solidification • The metal foam is considered as isotopic and homogeneous.

• The volume expansion is neglected.

Mathematical model

In the model developed in this paper, a volume-averaging technique is used [START_REF] Whitaker | The Method of Volume Averaging[END_REF]. Based on the above assumptions, the mathematical model for the present problem can be expressed by the following equations:

Continuity equation:

0 u v x y ∂ ∂ + = ∂ ∂ (2)
Momentum equations: 2 2 ( ).

( )

P P P u C u p V u u u u S t x K k ρ ρ ρ µ µ ε ε ε ∂ ∂ + ∇ = - + ∇ - + + ∂ ∂ ur ur (3) 2 2 (
). ( ) ( )

P P P v P ref C v p V v v v v S g T T t y K k ρ ρ ρ µ µ ρ β ε ε ε ∂ ∂ + ∇ = - + ∇ - + + + - ∂ ∂ ur ur (4) Where 2 3
(1 )

u b S A u B b - = + , and 2 3
(1 )

v b S A v B b - = +
denoted the source term to damping the velocity in solidified phase (A and B are two constants). They are deducted from Carmen-Kozney relation [START_REF] Viswanath | A comparison of different solution methodologies for melting and solidification problems in Enclosures[END_REF]. In this study we take A=10 5 and B=10 -3 . For the solidified phase, 0 b = leads the item to be infinity to damp the velocity in the momentum equation. For fluid phase, 1 b = leads the item to be zero.

( ) b T can be defined as:

0 ( / 2) / 2 ( ) ( ) ( ) 2 2 1 ( / 2) m m m m m T T T T T T T T b T T T T T T T T < -∆   -+ ∆ ∆ ∆  = - ≤ < +  ∆  > + ∆   (5)
The dynamic viscosity is modified by using to have an extremely high value when the PCM is at a temperature below its melting temperature.

( ) (1 ( ))

P P l T S T µ ρ = + (6)
There exists a large difference in thermophysical properties between metal foam and PCM saturating [START_REF] Yao | Pore-scale visualization and measurement of paraffin melting in high porosity open-cell copper foam[END_REF]. We have two non-equilibrium equations:

Energy equation for PCM:

2 ) ) ( (

f
T T T T h a C C u v k T x x T ερ ρ τ ∂ ∂ ∂ + + = ∂ + - ∂ ∂ ∇ (7)
The density variation of PCM can be given by: ( ) ( ). ( )

P Ps Pl Ps T b T ρ ρ ρ ρ = + - (8)
The phase change temperature interval is taken at 3°C [START_REF] Idi | A numerical investigation of the effects of metal foam characteristics and heating/cooling conditions on the phase change kinetic of phase change materials embedded in metal foam[END_REF]. The specific heat of PCM can be written as [START_REF] Biwole | Influence of fin size and distribution on solid-liquid phase change in a rectangular enclosure[END_REF][START_REF] Ali | Simulating phase change heat transfer using comsol and fluent: Effect of the mushy-zone constant[END_REF]:

( ) . ( ) ( )

P P P s P l P s f C C C C b T L D T = + - + (9)
Where f L is the latent heat of fusion:

( ) ( ) ( ) 2 2 2 4 4
( )

m T T T T D T e π   - -     ∆     ∆         = (10)
D is a smoothed Delta Dirac function which is zero everywhere except in the interval [24]. Its integral is equal to 1. The use of this function ensures that the latent heat is conserved during the melting process. The thermal conductivity of PCM can be given as: ( ) ( ). ( )

P Ps Pl Ps k T k k k b T = + - (11)
Energy equation for metal foam:

2

) ( ( 1 )

S PS PS S P S S PS S T h a

k T T T c ε ρ τ ∇ ∂ - = ∂ - - (12)
Where P e k , S e k , P S h are the effective thermal conductivity of paraffin, effective thermal conductivity of metal foam and the interstitial heat transfer coefficient between the porous metallic surface and saturating PCM. The following expression was used to estimate P S h [START_REF] Zhu | Numerical analysis on the energy storage efficiency of phase change material embedded in finned metal foam with graded porosity[END_REF].

( )

0.5 0.6 1/ 3 4(1 ) 1 0.5 1 Re Pr P PS f k h d ε ε ε  -    = + + -         (13)
Many models having been developed to describe effective thermal conductivity. The tetrakaidecahedron cell model proposed by Boomsma and Poulikakos [START_REF] Boomsma | On the effective thermal conductivity of a three dimensionally structured fluidsaturated metal foam[END_REF] was adopted to describe the thermal conductivity in the present study as shown in the following equations:

( ) ( ) 2
= - + - - - (16)
( )

2 2 2 4 D s f e R e k e k = + - (17)
( )

2 2 eff A B C D k R R R R = + + + (18)
Where ( ) The effective thermal conductivity of PCM and metal foam can be defined as:

0 Pe eff s k k k = = (19) 0 Se eff f k k k = = (20)

Thermophysical and structural proprieties of metal foam

Thermophysical proprieties of aluminum foam used in this study are presented in Table 1. Many researches have been carried out to develop analytical model for predicting permeability and the inertial coefficient of metal foam [START_REF] Du Plessis | Pressure drop prediction for flow through high porosity metallic foams[END_REF][START_REF] Calmidi | Transportation phenomena in high porosity fibrous metal foams[END_REF][START_REF] Bhattacharya | Thermophysical properties of high porosity metal foams[END_REF][START_REF] Tadrist | Topin About the use of fibrous materials in compact heat exchangers[END_REF][START_REF] Dukhan | Correlations for the pressure drop for flow through metal foam[END_REF][START_REF] Yang | A simplistic analytical model of permeability for open-cell metallic foams[END_REF][START_REF] Calmidi | Forced Convection in High Porosity Metal Foams[END_REF]. In this work, we use the model of Calmidi [START_REF] Calmidi | Transportation phenomena in high porosity fibrous metal foams[END_REF] to calculate permeability and the inertial coefficient.

Permeability:

1 .1 1 2 0 .2 2 4 0 .0 0 0 7 3 (1 )

f p p d K d d ε - -   = -       (21)
Inertial coefficient:

1 .6 3 2 0 .1 3 2 0 .0 0 2 1 2 (1 )

f p p d C d d ε - -   = -       (22)
Where f d denotes the equivalent diameter of metal foam fibers and p d pores diameter [START_REF] Calmidi | Transportation phenomena in high porosity fibrous metal foams[END_REF]:

(1 ) / 0 .0 4 The specific area PS a can be calculated by the following formula [30].

1 1 1 .1 8 1 f p d d e ε ε π -- -  =   -   (23)
(

Numerical procedure and model validation

The numerical model is solved by using a finite element analysis with the COMSOL Multiphysics 5.3a software [START_REF]COMSOL Multiphysics User's Guide[END_REF]. The numerical model developed in this study was validated by comparing the predicted results with the experimental data of the study by Zhao et al. [START_REF] Zhao | Heat transfer enhancement for thermal energy storage using metal foams embedded within phase change materials (PCMs)[END_REF]. In the study conducted by Zhao et al. [START_REF] Zhao | Heat transfer enhancement for thermal energy storage using metal foams embedded within phase change materials (PCMs)[END_REF], a copper foam sample with dimensions of 200mm, 120mm and 25mm, pores density of 10PPI, and 95% porosity filled with paraffin wax RT58, was heated with a constant heat of 1600 W/m2. The heat loss coefficient generated by the natural convection of air is estimated at about 3W/m 2 . The experimental device developed by Zhao is presented in Fig. 3. The proprieties of RT58 are given in Table 1. Fig. 4. displays a comparison between the calculated temperature evolutions of the PCM at 8 mm away from the bottom of the copper foam composite and the experimental data. We can observe from the figure that during the melting process, from 1200s to 4000s, there is a small discrepancy between the results of the present model as well as after the melting process. The authors assume that the small difference is mainly due to the estimation of the thermo-physical properties of the RT58 paraffin wax and the heat transfer coefficient used to estimate heat losses and also to the estimation of other thermal and structural properties. It can be concluded that the results obtained by the present model is in accordance with the experimental data on the whole, and the present model is reliable reasonable.

Results and discussion

Heat supply effect on the kinetics of phase change

The liquid fraction evolution with constant and sinusoidal heat flux is illustrated in Fig. 5. It can be seen from this figure that the melting of paraffin with constant heat flux starts before the melting with sinusoidal heat flux. The melting of paraffin with constant heat flux starts after 40 seconds and starts after about 5mins with variable sinusoidal heat flux. The melt fraction of both becomes the same after 28mins, after which the fraction with variable heat becomes higher as shown in Fig. 5. Then all the paraffin in the aluminum foam becomes liquid (melting fraction equals 1) for heating with sinusoidal heat flux in 41mins and with constant heat flux after 48min. This can be explained by the fact that the behavior of melting fraction evolution is related to the heat supply types. In the constant heat flux case, the heating rate is constant with a magnitude of 1800W/m 2 . Whereas, in the case of heating with sinusoidal heat flux, the heating ratio is zero at the start of the melting process and increases in time in a sinusoidal manner and reaches its maximum at 30mins, (see Eq [START_REF] Sharma | Review on thermal energy storage with phase change material and applications[END_REF]). It can be seen that under the same conditions and with the same amount of energy supplied all paraffin filled in an aluminum foam becomes liquid with sinusoidal heating faster than with constant heating. In the solidification process of PCM, the solidification with sinusoidal heating starts 10mins after comparing to the solidification with constant heating after 33minutes we have a same liquid fraction with constant heat flux and sinusoidal heat flux. In the both cases the paraffin is not completely solidified. The fact that the paraffin is not fully solidified can be explained by the fact that the paraffin RT27 has lower thermal conductivity in liquid states (see table 1) which weakens the effective thermal conductivity of the paraffin/foam composite and therefore on the liquid-solid phase change kinetics.

Sinus Constant Fig. 5. Liquid fraction during melting and solidification.

Storage and release of energy

The energy stored in paraffin/aluminum foam composite was calculated for numerical element as: With T<Tm

With T=Tm

0 0 ( ) (1 ) ( ) 2 ps f ps pl s ps p m F f p m Q C T T L C T T ρ ρ ε ρ ε ρ +   = - + + - -     (27)
With T>Tm

0 0 ( ) ( ) (1 ) ( ) 2 ps pl f ps pl s ps p m F pl p P m f p S Q C T T L C T T C T T ρ ρ ε ρ ρ ε ρ +   = - + + - + - -     (28)
The energy stored is then calculated by integrating the right expression for the energy over the volume for each of the elements, resulting in a total amount of energy stored in the entire volume. The energy stored during melting and solidification of paraffin is shown in Fig. 6.

At the initial stage of melting the stored energy in paraffin / aluminum foam with constant heating is higher than compared to variable heating due to the corresponding heater heating rate. It is also noted that the amount of energy stored and is not released at the same period of time. This can be explained by that the paraffin in the liquid state has a lower thermal conductivity than in the solid state and therefore the thermal transfer is less intense during the solidification process than during melting. This result is very interesting for sizing PCM/ Metal foam to used as thermal energy storage unit. A such result will necessarily lead to an accumulation of heat in the PCM/ Metal foam composite and therefore an increase of temperature. After several cycles the temperature of the PCM/ Metal foam composite can be reached at a temperature higher than the temperature of melting of PCM at the beginning of the heating. This means that there is lose of storage by latent heat which is the reason why we use the PCM. Fig. 6. Thermal energy stored and discharge.

Heat loss effect

In order to study the effect of heat loss at the boundary, thermal insulation from the right-side boundary was removed. The environment temperature is 294.15K. Three heat loss coefficients generated by natural convection of the air were investigated (5W/m 2 , 10W/m 2 and 15W/m 2 ). Fig. 7 (a). presents the liquid fraction evolution with heat loss compared to the liquid fraction without heat loss in the right boundary with constant heating. Fig. 7 (b). illustrates the same process with sinusoidal heating. The result shows that for the melting process with constant heating as well as with sinusoidal heating, a weak effect of heat loss tooks place by natural convection of air in the right boundary. Also, there was a larger effect on the solidification process in comparison to the melting process. At first, the average temperature of the paraffin/aluminum foam composite is equal to the environment temperature, and therefore the right wall too. The heat loss in the right boundary is zero and increases with time until it reaches the maximum temperature value. In contrast, during the solidification process the temperature is at its maximum at the beginning and decreases with a slower rate than the increase reat as the thermal conductivity of the paraffin is lower at the liquid state than at solid state. All this leads to a greater convective heat flux during the solidification process than during the fusion process. Therefore, the heat losses are more important during the solidification cycle than the melting cycle. The full solidification time of paraffin for the cases with heat losses was summarized in Table 2. We can deduce from Fig. 8, Fig. 7(b). and table 2 that the heat losses have a greater impact on the solidification processes in the case of sinusoidal cooling than in constant cooling case. This is due to the fact that the heat transfer rate is constant in the case of constant heat flux.. Whereas, in the case of sinusoidal heat flux, the heat transfer rate is zero at the start of solidification and increases with the time in a sinusoidal manner before reaching its maximum value at 30mins, Eq [START_REF] Sharma | Review on thermal energy storage with phase change material and applications[END_REF]. Therefore, in the sinusoidal heat flux case, the right wall will keep its maximum temperature for a longer period than in the case of constant heat flux. As seen earlier, the amount of stored energy depends on the liquid fraction. This led to deduce that the heat losses from the right wall have a greater effect in the case of a sinusoidal heat flux than in the case of constant heat flux. Moreover, this effect is more important on the solidification process than on the melting process of the paraffin.

Conclusion

A numerical study was carried out on the energy supply efficiency of cyclical heating and cooling. The Brinkmann-Forchheimer-extended Darcy equation and the local thermal non-equilibrium model assumption were used due to the larger difference in thermal properties between the metal foam and the PCM. The phase change is modeled by the enthalpy-porosity method. The phase change material used paraffin RT27. The numerical model was developed and validated by comparison with experimental data coming from the literature. The heating and cooling conditions of the phase change kinetic of paraffin embedded in aluminum foam and stored energy was carried out. It was discovered that with sinusoidal heating the initial melting rate is low and becomes higher after some time. Furthermore, it was showed that with sinusoidal heating the melting time of PCM filled in a metal foam is reduce compared to when it was subject to a constant heating and the same behavior during the solidification cycle. The results also show that the heat losses on the boundary have a greater effect in a sinusoidal heat flux than in the case of constant heat flux and this effect is more important on the solidification than on the melting process of the paraffin. Future studies will aim to find the best compromise between foam proprieties, heat supply, energy storage density and time of the storage process.

PC

  Specific heat capacity, (J. kg -1 .K -1 ) C Inertial coefficient, (W.m -2 .K -1 ) ρ Density, (kg/m 3 )

Fig. 1 .Fig. 2 .

 12 Fig. 1. Physical model

Fig. 3 .Fig. 4 .

 34 Fig. 3. Experimental device[START_REF] Zhao | Heat transfer enhancement for thermal energy storage using metal foams embedded within phase change materials (PCMs)[END_REF]

Fig. 7 .

 7 Liquid fraction evolution with and without heat loss: (a) constant, (b) sinusoidal

Table 2 :

 2 Solidification time

	Heat loss coefficient	5 W/(m 2 .K)	10 W/(m 2 .K)	15 W/(m 2 .K)