3. Stability of HLSs characteristics under operational conditions CONCLUSIONS

3.2. Temperature dependences of intrusion and extrusion pressures 3.

productivity at high level from the first day of postgraduate work until the defense. I can't thank enough Prof. Jean-Pierre Grolier for always being open to help in any kind of problems, for being a bright example of successful scientist and kind person and for being unbelievably hard working with me all the time. I am very grateful to Prof. Jean-Marie Nedelec for his wide and strategic vision of the scientific problems and for being strong, but at the same time very positive boss.

I want to thanks to Dr. Victor Stoudenets and Nikolay Tsirin for their constant support and fruitful discussions during this work. I am much obliged to Prof. Stanislaw Randzio for his huge help on the handling and technical support of scanning transitiometer used as the main experimental equipment for this work.

I am very thankful to Dr. Leticia Carbajal for not only being a great friend, but also helping colleague especially for mercury porosimetry, gas sorption and DSC techniques. I want to thank to Dr. Geraldine Torin Ollarves for sharing her experience in scanning transitiomerty and for being a wonderful friend. Many thanks to Dr. Sandrine Renaudin for her help with XRD and FTIR experiments. I also want to express my thanks to principal constructor at Thermomolecular Energy (TME) laboratory Ivan Piatiletov for his useful advices on technical design and help with the graphics. I am glad I had an opportunity to work with great PhD-students of TME laboratory Oleksiy Ievtushenko, Artem Popik, Elisabeth Suzdalska and Tatiana Yarosh. I want to thank Prof. Elizabeth Charlaix and Prof. Philip Llewellyn for their agreement to be reviewers of this work. I want to thanks to Prof. Valerii I. Deshko the head of Department of Thermal Engineering and Energy Saving of NTUU "KPI" for his support and positive attitude. Special thanks to Prof. Helen Homonay for being an exceptionally inspiring professor and her great influence on my overall perception of our physical universe and the phenomenology to describe it. I'm deeply indebted to the Grolier family for their warm welcoming me in France and their great help during my stay in this wonderful country. I want to thanks my good friends PhD-students of UBP Alex Lowe and Barbara Liborio for their active participation in my after-work activities in Clermont-Ferrand. I am very thankful to my family for their constant support and for always providing me with the freedom of my choices. My heartfelt and deepest thanks are expressed to my wife Maria for her strong support and understanding, for her profound and inspiring vision of our world and for her infinite beauty, which inspires me for newer and newer achievements.

I want to thanks to many people, who were not mentioned, but in different ways helped me in the preparation of this work.

I want to dedicate this collaborative work between France and Ukraine to so many Ukrainians currently struggling on the painful path to the new free future where their country is a part of Europe.

INTRODUCTION

The problem of rational energy consumption is one of the most important global problems of contemporary humanity, which greatly stimulates the scientific community to search for new sources of energy as well as methods for its efficient utilization and storage. In particular a problem of efficient thermal energy storage is one of unsolved challenges today.

The use of surface energy on 'solid -liquid' interface as a working body for mechanical and thermal energy storage and transformation was proposed as an alternative to conventional methods by Prof. Eroshenko in the 1980's. It was shown that naturally such surface energy becomes dominant for systems with large specific surface (from 400 m 2 /g and higher) and reversible operational cycle (reversible interface area development-reduction) can be realized using highly porous Heterogeneous Lyophobic Systems (HLSs), that is an ensemble of a highly porous solid and a non-wetting liquid. Due to its nature such working bodies demonstrate distinguished properties and characteristics in comparison with conventional working bodies:

high energy capacity, ability to simultaneously store (restore) both mechanical and thermal energy during compression (decompression), most frequently being in the form of a suspension an HLS has strongly nonlinear and orders of magnitude higher compressibility compared to simple liquid together with the ability to operate at very high frequencies without overheating.

Apart from energy storage and transformation, HLSs with large stored-restored energy hysteresis were proposed to be used for efficient energy dissipation applications.

First publications on the properties and applications of HLS were in the form of classified patents by Eroshenko (Eroshenko 1981), (Eroshenko 1980(Eroshenko , 1982(Eroshenko , 1983(Eroshenko , 1985a(Eroshenko , 1985b(Eroshenko , 1986(Eroshenko , 1987a) 1 . In the beginning of the 1990's works in this area became unclassified (Eroshenko 1987b[START_REF] Eroshenko | Les proprietes Non-Ordinaires d'un Systeme Thermodynamique Complexe[END_REF][START_REF] Eroshenko | Non-Compressibilite et Non-Dilatabilite Adiabatiques d'un Systeme Thermodynamique Complexe[END_REF][START_REF] Eroshenko | Dimensionnalite de l'Espace Comme Potentiel Thermodynamique d'un Systeme[END_REF][START_REF] Eroshenko | Amortisseur a Haut Pouvoir Dissipatif[END_REF][START_REF] Eroshenko | [END_REF][START_REF] Eroshenko | A new paradigm of mechanical energy dissipation. Part 1: theoretical aspects and practical solutions[END_REF] smart applications in the field of energy storage, dissipation and transformation and their characteristics [START_REF] Han | Pressure induced liquid infiltration in nanopores[END_REF], 2007a, 2007b, 2007c, 2007d, Liu et al. 2008, 2009a[START_REF] Han | The dependence of infiltration pressure and volume in zeolite Y on potassium chloride concentration[END_REF], Kong and Qiao 2005a, 2005b, Han et al. 2006, 2008a, 2008b, 2008c[START_REF] Han | Effects of decomposition-treatment temperature on infiltration pressure of a surface modified nanoporous silica gel[END_REF], 2008e, 2009a[START_REF] Han | The dependence of infiltration pressure and volume in zeolite Y on potassium chloride concentration[END_REF] [START_REF] Coiffard | Thermomechanics of the variation of interfaces in heterogeneous lyophobic systems[END_REF]) and Bellat and co-workers [START_REF] Karbowiak | Thermal Effects of Water Intrusion in Hydrophobic Nanoporous Materials[END_REF](Karbowiak , 2010a(Karbowiak , 2010b[START_REF] Karbowiak | Confinement of water in hydrophobic nanopores: effect of the geometry on the energy of intrusion[END_REF]. The investigations focused on percolation effects during HLS operation can be found in the works of Borman et al. [START_REF] Borman | Investigation of the percolation transition in a nonwetting liquid-nanoporous medium system[END_REF][START_REF] Borman | Observation of dynamic effects in the percolation transition in a "nonwetting liquidnanoporous body" system[END_REF][START_REF] Borman | The mechanism of mechanical energy accumulation in a nonwetting liquid-nanoporous solid system[END_REF][START_REF] Borman | The percolation transition in filling a nanoporous body by a nonwetting liquid[END_REF][START_REF] Borman | Investigation of the dynamics of a percolation transition under rapid compression of a nanoporous body-nonwetting liquid system[END_REF][START_REF] Borman | The infiltration of nonwetting liquid into nanoporous media and the thermal effect[END_REF][START_REF] Borman | Observation of a dispersion transition and the stability of a liquid in a nanoporous medium[END_REF]. Some important microscopic insights for HLS can be found in the works of Bushuev and Sastre [START_REF] Bushuev | Feasibility of pure silica zeolites[END_REF], 2011, 2012).

Despite significant advances in the study of the properties of HLSs in recent years, the relevance of in-depth study of their thermodynamics properties is very high. Parameters of HLSs such as working (intrusion/extrusion) pressure, thermal effects, heat capacity, thermal conductivity and others are seldom studied in a wide temperature range, however, the investigation of the temperature dependence of the thermodynamic properties of HLSs is essential for expanding the class of devices based on them, as well as improving the efficiency of existing models, an in-depth thermodynamic description of HLSs is not yet proposed and operational mechanism of nano-HLSs is not fully understood.

Based on the above indicated problems the following tasks for this work were chosen.

1. Develop a mathematical description of HLSs by means of a thermodynamic of complex systems approach, including equation of state for real HLSs.

2. Making use of the results of the thermodynamic analysis, to implement an experimental and theoretical investigation of the properties and characteristics of HLSs, which are prominent in the processes of energy storage, dissipation and transformation, in a wide temperature range.

3. On the basis of the preceding tasks explore both experimentally and theoretically ways to improve, i.e. tune, the characteristics of HLSs for optimizing their use.

The thesis is organized in the following way. The Introduction is followed by Chapter 1 explaining the operational principles of the object of the study, which is porous Heterogeneous Lyophobic System (HLS), including the description of known types of HLSs and of their main characteristics. It also contains a short review of literature results, which is aimed at highlighting the evolution of the investigations of HLSs and topical problems still to be solved. In the following Chapter 2 the experimental techniques, equipment, materials and procedure of HLSs A typical scanning transitiometer consists in the following parts: 1) the sensitive differential calorimeter (located in the solid state thermostat); 2) digital precise temperature and pressure controllers; 3) high-pressure pump driven by stepping motor; 4) a pair of identical thermopiles housing the measurement and reference cells.

Figure 2.1 shows a diagram of the thermodynamic relationships between selected independent variables of the system (P, V, T) and heat flux (q). The scheme shows that in addition to the classical scanning calorimetry at a controlled temperature (differential scanning calorimetry), where the calorimetric signal (heat flux) that is recorded in proportion to heat generated, for scanning transitiometry two additional important regimes are available: 1) scanning calorimetry at a controlled pressure where calorimetric signal is proportional to coefficient of isobaric thermal expansion; 2) scanning calorimetry at a controlled volume where calorimetric signal is proportional to isochoric pressure coefficient. Simultaneous recording of calorimetric signal, allows using Maxwell relations, direct experimental measurement of thermodynamic derivatives fully describing a thermodynamic system. Below, the main derivatives are explained.

The enthalpy may be written as:

d ( , ) = d + d = δ + d . (2.1)
It can be seen from eq. (2.1) that simultaneous recording of heat and PV-diagram with the scanning transitiometry technique allows obtaining the enthalpy of the system as a function of T and P.

Similarly, we can write for the internal energy:

d ( , ) = d + d = δ -d , (2.2)
The calorimetric signal can be measured in four different modes depending on three variables (P,V,T): ( ) -heat flux provoked by compression-decompression of the sample by controlled pressure variation at isothermal conditions, ( ) -heat flux provoked by heatingcooling of the sample by controlled temperature variation at isobaric conditions, ( ) -heat flux provoked by heating-cooling of the sample by controlled temperature variation at isochoric conditions, ( ) -heat flux provoked by compression-decompression of the sample by controlled volume variation at isothermal conditions.

Four indicated modes are presented in Fig. 2.2 and may be described as follows:

1) Recording the volume change of the investigated system as a result of a given change in pressure with time t at a constant controlled temperature:

= ⟹ d = 0; = + ⟹ d = d .
Next using classical thermodynamic transformation one may write:

δ = - d ⟹ δ d = -.
On the other hand using Maxwell relations it can be written:

d = ( ) = = - .
It can be seen that the heat flux measured under isothermal conditions ( ) is proportional to the isobaric coefficient of thermal expansion .

2) Recording the pressure change of the investigated system as a result of a given change in volume with time t at a constant controlled temperature:

= ⟹ d = 0; = + ⟹ d = d .
Similarly to previous regime one may write:

δ = + d ⟹ δ d = + ,
and

δ d = ( ) = = .
It can be seen that heat flux measured as a function of volume variation under isothermal conditions ( ) is proportional to isochoric coefficient of pressure .

3) Recording the volume change of the investigated system as a result of a given change in temperature with time t at a constant controlled pressure:

= ⟹ d = 0; = + ⟹ d = d . δ d = ( ) = = .
The heat flux measured as a function of temperature variation under isobaric conditions ( ) is proportional to isobaric the heat capacity .

4) Registration of the pressure change of the system as a result of a given change in temperature with time t at a constant controlled volume:

= ⟹ d = 0; = + ⟹ d = d . δ d = ( ) = = .
The heat flux measured as a function of temperature variation under isochoric conditions ( ) is proportional to isochoric the heat capacity . Given the wide range of functional diversity of porous heterogeneous lyophobic systems (HLSs), the availability of the described modes allows to investigate the thermomechanical properties that are important for understanding the fundamental principles of the HLSs, and to directly quantitatively document the characteristics of the process of accumulation, dissipation and energy conversion.

Transitiometer ST-7M

As the main experimental equipment for implementation of this work a transitiometer ST-7M (BGR Tech) was used, detailed chart of which is shown in Figure 2.3 and photo in Figure.

2.4. ST-7M consists of a calorimeter equipped with two high-pressure working cambers (calorimeter cells), PVT-system and corresponding software.

The two calorimeter detectors made from 622 thermocouples each, set differentially and connected to nano-volt amplifier. Calorimeter detectors placed in a metal calorimeter block, the temperature of which is directly controlled to within ± 10 -4 K through automatic digital feedback circuit (PID controller) with a resolution of 22 bits. Calorimeter block is surrounded by solid state thermostat. The temperature difference between the thermostat and calorimetric block can be set to 5, 10, 20 or 30 K and controlled by an additional analog regulator. Registration of the temperature (both absolute and differential) is done using calibrated platinum resistance thermometer with 100 Ohm sensor. Heaters are evenly installed on the outside of calorimetric block and solid state thermostat. All design is additionally thermoisolated and set into a stainless steel casing mounted on a stand that allows one to move the calorimeter up and down. In the lower position working chambers are inside the calorimetric block.

For the experiments with the temperatures below 273 K calorimeter is ventilated by dry air to prevent condensation. In the improved version of the instrument (ST-7M), the unit ''stepping motor + HP-pump'' is still present, but is not used for volume variation registration. Changes in the system's volume are recorded by the induction volumeters (LVDT), which noticeably improved the metrological characteristics of the instrument. Recording of pressure in the hydraulic system was made via a pressure sensor (press.det.1) built in the hydraulic line connecting the pump to the transitiometric vessels (see Fig. Hydraulic lines are made of thin capillaries of stainless steel. High pressure piston-pump is driven by a stepping motor in manual or automatic (via software) mode. Total capacity of transmission medium (which is oil in our case) that can be introduced in the hydraulic PVTsystem is 9 cm 3 Each step of a motor provides a pumping volume of (5.24 ± 0.04 ) • 10 cm .

Pressure sensor -Vitaram BSS 245 -has a working range of 0-200 MPa and error of ± 0,15

MPa, as declared by the manufacturer. The pressure sensor, the output of calorimeter amplifier and the stepping motor are connected to a multifunction NI PCI-MIO-16XE-50 board via a shielded connecting block NISCB-68. Recording the temperature and digital control of the calorimetric unit are made via a digital port. The software is realized through LabView V language and operates as a virtual instrument. Overall it consists of 90 sub-devices, each of which is responsible for its own function: measuring pressure, temperature, volume change, calorimetric signal, etc. Each of these devices is independent, but they form a hierarchical structure. In the main window (Fig. 2.6.) operator can observe all independent variables (P, V, T, CS) as a function of time (CS stands for calorimetric signal).

For the temperatures below room temperature additionally a cryostat Thermo Haake K20 was used (Fig. 2.7).

Cryostat Thermo Haake K20 has a wide operating temperature range (from -28 to 150 °C).

The temperature stability is up to ±0.04 °C according to the supplier. Cooling power is 320 W.

Volume baths for refrigerant is 4.5 liters. Account of inertia of calorimeter. Fig. 2.9. represents the calorimetric signal and the pressure as a function of time in the experiment for the isothermal compression of {Zif-8 + Water} HLS. As can be seen during bulk phase compression calorimetric signal is close to constant. Upon reaching the intrusion pressure for which the development of "liquid -solid" interphase area occurs, endothermic effect takes place and that is accompanied by significant changes of calorimetric signal (calorimetric peak). Comparison of calorimetric signal time dependence and of the pressure time dependence clearly shows that at the end of the intrusion process (neat break in the pressure change) the calorimetric signal does not immediately return to the baseline value. This is due to the inertia of the calorimeter, which must be taken into account when processing calorimetric measurements.

Fig. 2.9. Time dependence of the pressure (black line), original (red line) and corrected (green line) calorimetric signal during compression of system the {Zif8 + Water} HLS at isothermal conditions.

Unfortunately, most calorimeters do not directly measure the thermal energy (heat flux ( )) generated or released by the sample, but they deliver the temperature difference in the form of thermogram. Heat generated, by endothermal or exothermal effects, exchanges with the environment (in the case of transitiometer with the calorimetric block). This means that the resulting thermogram depends not only on the energy processes occurring in the measuring cell, but also on the calorimetric system used. Having also some limited ability to respond to fluctuations in heat generated by the sample, the value of the heat flux will be distorted because of the specific heat capacity of the calorimetric cell and the block. Consequently there is inertia of calorimetric system.

According to the theory of differential calorimetry relationship between the actual heat flow ( ) and calorimetric signal ΔCS in the first approximation is given by:

( ) = ℵ ∆ ( + ) + d∆ ( + ) d , (2.3)
where is the characteristic time of calorimeter inertia, is the time delay in reaction of the calorimeter to the heat flow change.

As can be seen from Fig. 2.9 direct calorimetric signal delay is negligibly small. While inertia of calorimeter obviously requires consideration.

To find value equation (2.3) should be integrated from time , which is the initial time when ( ) = 0, and taking into account = 0, we obtain:

∆ ( ) = ∆ ( ) - - . (2.4)
For the example in Fig. 2.9 the inertia time is τ = 503,1 s. Corrected due to the calorimeter inertia the calorimetric signal is presented by the green line in Fig. 2.9. It can be seen that indicated correction makes the calorimetric signal synchronized with pressure (and volume)

signal, as required.

The inertia time was determined for each sample. In general, this value is between 400 -550 s, which may depend on the sample, rate and direction of scan.

Bellows calibration

In order to find LVDT coefficient L (for conversion of values of LVDT (in millimeters) to unit of volume (cm 3 )) experiments were performed on isothermal compression of reference samples of known volume and compressibility. Distilled water (working chamber is completely filled with water) and lead of a 99.96% purity (chamber filled with water and submerged in it lead) were used as reference samples.

Obtaining compressibilities of reference samples and knowing their reference values, the LVDT coefficient can be defined by the formula:

L = - d d - d d , (2.5)
where is the volume of lead, is isothermal compressibility of water, is isothermal compressibility of lead, and are the values of LVDT in the experiment with water and lead + water respectively. Fig. 2.10 represents the Pl -isotherms of reference samples. Using equation (2.5) and obtained Pl -dependences, the value of L = 0,066 сm is obtained.

The uncertainty of volume measurement is ±3,3 • 10 cm according to supplier (Peltron Ltd., Poland) with maximum non-linearity of -0,555% for extreme value of LVDT which is 10.00 mm.

Sample preparation

The gas contained in the pores and in the interparticle space must be removed before preparing an HLS (mixing non-wetting liquid and porous matrix), since presence of gas may prevent the complete intrusion of liquid into the pores. This effect is known in practice of mercury porosimetry. Under considerable external pressure gas can be dissolved in water, but the presence of gas in the interparticle space leads to the presence of parasitic changes of the volume of the system at low pressure, which negligibly increases the energy capacity of the HLS and largely increases its specific volume. to make the detachment possible. Next the degasation cork is removed, which is followed by excessive liquid expulsed from the cell (bellow retracts itself to the equilibrium state) filling the volume which took the cork and forming a meniscus on the surface of the cell. The degasation cork is quickly (less than 1 second) replaced be the high-pressure cork (Fig. 2.12d). During closing the cell with the high-pressure cork liquid which was in contact with air is expulsed from the cell through specially designed for that matter hole. The cell is now ready for the experiment.

An ultrasound degasation bath FB 15051 (Fisher Scientific) was used to degas water during 2 hours at temperature of 60 °С.

Isothermal experiments

In order to obtain PV-isotherms of studied porous Heterogeneous Lyophobic Systems (HLSs) prepared according to the above described procedure the investigated sample was subjected to compression with the rate pressure variation 1 MPa/min. After reaching the required pressure the system was maintained at a constant pressure for about 1 hour to achieve the equilibrium value of calorimetric signal. Next the pressure in the system was reduced with a similar rate to atmospheric value. Then the system again was kept under constant pressure to establish the equilibrium value of calorimetric signal. Next the compression-decompression cycle was repeated at least three times to check the good repeatability of registered results.

Along with recording PV-diagram the calorimetric signal proportional to the thermal effect of compression/decompression is simultaneously recorded.

Isobaric experiments

The transitiometer ST-7M was used to study the temperature dependence of heat-capacity and the thermal expansivity of HLSs under controlled constant pressure with accuracy of ±0.15 MPa. The temperature scanning rate was = 5 • 10 K/s. The value of heatcapacity was obtained as follows: ≡ = , where heat flow was measured simultaneously with all thermodynamic parameters (P,V,T).

2.1.1.2.6.

Experiments under constant load

The "constant load" operational mode of given HLS is a mode where the system experiences a constant external load (force), which creates the initial pressure in the system that exceeds atmospheric pressure. Hence, the pressure and the volume of the system changes due to the temperature variation. These conditions are close to those in which the HLS is used as a working body in the cycle of heat energy into mechanical transformation (Eroshenko 1981[START_REF] Laouir | Thermal machines based on surface energy of wetting: Thermodynamic analysis[END_REF]). In principle these conditions are equivalent to the ones shown on Fig. 2.13: some constant force (in this representation -the gravitational force which affects the load) acts on the system and does not change during the temperature variation of the system, which provokes both pressure and volume change. In these experiments the initial pressure is manually reached. does not exceeds intrusion pressure of HLS at the initial temperature . After reaching the required initial pressure the stepping motor is turned off and is not used during the experiment. Next heatingcooling cycle is performed in an automatic regime. After reaching the specified maximum temperature system is maintained at this temperature for at least an hour before cooling to a initial temperature . Thus, the heating-cooling cycle is performed, which provokes intrusion and extrusion of the fluid and, consequently, a significant reversible volume variation of the system.

ADDITIONAL TECHNIQUES

Some additional techniques were used to characterize porous materials before and after experiment with HLSs.

2.2.1. X-ray diffraction X-ray Diffraction (XRD) patterns of pristine powders and of powders modified after intrusion/extrusion cycle were recorded on an X'Pert Pro PANalytical diffractometer θ-θ geometry, using Cu K radiation ( = 1.54184 Å). XRD patterns were recorded at room temperature in the interval of 3° < 2θ < 120°, with a step size of Δ2θ = 0.0167° and a counting time of 119 s for each data value. A total counting time of about 200 min was used for each sample.

Fourier Transform Infra-Red spectroscopy

Fourier Transform Infra-Red spectroscopy (FTIR) spectra were recorded in transmission mode using the KBr pellet technique with a Nicolet 5700 spectrometer from Thermo Scientific.

Scanning Electron Microscopy

Scanning Electron Microscopy (SEM) micrographs were recorded on a Zeiss supra 55-VP microscope working at electron energy of 1.0 kV.

MATERIALS

The following porous materials were used to form the HLSs investigated in this work.

Waters Symmetry Prep C8 is a nanoporous grafted silica gel also known as SymmetryPrep C8, 7 μm supplied by Waters. The grafting was done with C8 chains octylsilanes with density 2.1 groups/nm 2 according to the data provided by the supplier. The pore size distribution is very narrow for this type of material, formed by the aggregation of elementary particles. The average pore radius of the material before grafting is 4.6 nm, but the effective calculated pore radius is CHAPTER 3.

PROPERTIES OF HLSs

In this Chapter (particularly in Paragraph 3.1) an attempt to formulate the general thermodynamic description of a heterogeneous lyophobic system as a complex thermodynamic system (taking into account both bulk and interface phenomena) is presented. First of all we introduce a thermal equation of state which takes into account pore size distribution function of the porous matrix used for the HLS. Next using this equation in classical thermodynamics of complex systems some of important properties and transformations are highlighted. An important question is the possibility to realize an equilibrium quasi-static operational regime of the HLS; this point is discussed.

This thermodynamic analysis demonstrates that temperature dependence of intrusion and extrusion pressures is essential for nearly all potential and existing HLS applications. For that reason great attention was paid to experimental and theoretical investigation of such dependence, which is reported in Paragraph 3.2.

The stability of the characteristics of HLSs (which is associated with stability of porous matrix) during operational cycle is obviously important characteristic for practical applications.

Investigation on stability of operational characteristics of HLSs is presented in Paragraph 3.3 focusing on HLSs based on Silicalite-1 and ZIF-8 metal-organic framework since for these systems (contrary to the ones based on grafted silica gels) under certain conditions the HLS operational cycles may cause irreversible changes in the porous matrix structure.

DESCRIBING HLS AS COMPLEX THERMODYNAMIC SYSTEM

Limitations of usage of equilibrium thermodynamics

Two limitations for using the concept of equilibrium thermodynamics were determined for HLS:

1. Pore size. The object of thermodynamics is a macroscopic system. Since some of the matrices used for HLS have pore size comparable to the size of a molecule of the liquid (Silicalite-1, ZIF-8 see. Table 2.2), it is important to determine the critical pore size in which the liquid can still be considered as a macroscopic substance. Based on literature data, the minimum diameter of 2-3 nm was considered. Hence only for mesoporous (not microporous) HLSs the thermodynamic description may be applied. It is important to note that a microporous HLS as a whole is still a macroscopic system allowing to use relations between macroscopic parameters (such as P, V, T, Q, W, etc.), but describing its parameters which are determined by the properties of the liquid confined in micropores obviously requires the microscopic comprehensive approach of phenomena, then macroscopic parameters (such as contact angle, surface tension, etc.) should not be used.

2. Speed of intrusion/extrusion of fluid during HLS operation. Within the framework of equilibrium thermodynamics only quasi-static processes can be described. The process of liquid intrusion (index «int») into the pores of the matrix occurs when pressure in the system reaches Laplace capillary pressure, which depends on the liquid surface tension σ, the advancing contact angle (for extrusion the index is «ext» and the contact angle is receding ), the pore radii r, and the geometry of the pore space k (k = 0,5 cylinders, k = 0,33 for spheres) 2 : This means that such process is non-controlled and is non-equilibrium.

On the other hand if pore sizes are described by some smooth (continuously differentiable)

function ( = ⟹ , =
), the process of intrusion/extrusion becomes controlled, as infinitesimal variation of pressure under isothermal conditions leads to infinitesimal variation of the volume due to infinitesimal amount of pores being filled:

, ≠ ∞
Hence, some smooth pore size distribution can be considered as criterion of the possibility of realization of a quasi-static process for HLS and the possibility of applying the concept of equilibrium thermodynamics to describe it.

To account for such pore size distribution in thermodynamic description of HLS, a distribution function was introduced as part of the equation of state of HLS, which is described below.

Thermal equation of state

To take into account the pore size distribution function of the matrix the following general form of thermal equation of state of HLS was proposed:

( , , ) + ( , , ) = 0 (3.2)
where ( , , ) is a function describing the relation between the pressure , temperature and the volume variation due to the development/reduction of interface area Ω in the system during intrusion/extrusion process. And ( , , ) is the eqation of state of the whole bulk part of HLS (mainly the liquid and the porous matrix with no account for the interface phenomenon).

The relation ( , , ) may be defined by known thermal coefficients of the components of the HLS. The explicit form of ( , , ) is determined by the type of the distribution function the porous matrix. For example if the pores are distributed according to a Cauchy function and the isothermal compressibility of the bulk phase as taken from experiment (compression before and after intrusion).

Validation of equation (3.2) and (3.3) using different distribution functions is presented below to model the thermal coefficients, the thermal effects of compression/decompression and heat capacity of the HLS.

Maxwell relations and thermal coefficients

Differential Maxwell relations are extremely useful tools for the thermodynamic analysis that allows obtaining thermomechanical properties difficult to measure otherwise. These relations may be derived using Bernoulli-Euler's theorem on equality of the second mixed derivatives applied to thermodynamic characteristic functions (U, H, F, G).

For simple thermodynamic systems, each of the characteristic functions depends on two independent variables so there are only four macroscopic variables ( , , , ) determining the above characteristic functions; being entropy. For HLS number of this variables is five:

, , Ω, , . Using the classical definitions of the thermodynamic characteristic functions, the work of interface development (

= = + , = - , , see eq.
(1) of Chapter 1) and the volume of HLS, which is

d = d -dΩ ≡ d + d (3.4)
the characteristic functions for HLS may be written as follows.

Internal energy:

d = d -d = d -d - dΩ (3.5)
Enthalpy:

d = d + d = d + ( -Ω)d (3.6)
Helmholtz free energy:

d = -d -d = -d - dΩ -d (3.7)
Gibbs energy:

d = d -d = ( -Ω)d -d (3.8)
To obtain the Maxwell relations for complex thermodynamic system involves rotation of all parameters held constant for each characteristic function in order to use the Bernoulli-Euler's theorem. Thus the Maxwell relations for HLS can be written as follows (for mathematical details see Appendix A):

Ω , = - S , (3.9) , = - S , (3.10) , = Ω , (3.11) = , (3.12) = - Ω (3.13) - = - (3.14)
As shown, relation (3.10) and (3.12) in which left-hand-side and right-hand-side derivatives are taken at constant surface Ω, coincide with the classical Maxwell relations for simple thermodynamic system, which is logical. While equations (3.13) and (3.14) becomes similar to corresponding relations if surface phenomena are negligible (Ω ≈ ). Which means that obtained relations are consistent with the correspondence principle.

Some of useful applications of obtained relations are presented below.

Relation (3.9) shows change of the temperature of the system during the interface development/reduction (compression/decompression of HLS) under adiabatic conditions neglecting the elastic compressibility of the liquid and the matrix.

The equation for entropy of HLS may be written:

d ( , , Ω) = , d + , d + Ω , dΩ = d + , d + d d dΩ, (3.15) where =
, is the isochoric heat capacity of the liquid and the matrix.

Using relations (3.9) and (3.15) allows to obtain the following relation:

Ω , = - , , (3.16)
which shows that under adiabatic conditions the compression of HLS (dΩ > 0) leads to the decrease of the temperature of the system, while the decompression (dΩ < 0) induces temperature increase, in the case where

On the other hand we may write , = -, where is pore size distribution function which normally is identification characteristics of the matrix or may be found from some of the characterization methods of mercury porosimetry or gas sorption.

Using previously proposed equation of state let us now define the thermal (thermophysical) coefficients of HLS (for mathematical details see Appendix B).

The isobaric coefficient of thermal expansion: , =

, is the isobaric coefficient of thermal expansion of the liquid and the matrix. The temperature dependence of α for the process of intrusion (temperature increase) is shown on Fig. 3.3., compared to the literature temperature dependence of for water. From Fig. 3.3 it can be seen that after reaching the certain temperature for which the value of intrusion pressure becomes equal to the value of the pressure in the system (in this case P = 15 MPa), α becomes negative, which means that the system reduces its volume while temperature is increasing. This phenomenon is known as Negative Thermal Expansion (NTE) and presents significant scientific interest in science and technology. The phenomenon of NTE for HLSs will be discussed in details in Paragraph 3.1.6. The isochoric coefficient of pressure:

, = 1 = - d , d , 1 - , (3.20)
It is important to note that if the interface effects are negligible for an HLS , → 0 , correspondence principle is satisfied: that is the thermal coefficients of HLS become equal to the thermal coefficients of the liquid and the matrix of an HLS, and if dispersion of the pore radii is negligibly small (dispersion of intrusion/extrusion is also small

Thermal effects of compression/decompression

In the previous paragraph it was shown that using the Maxwell relations thermal effects of compression/decompression (due to interface development(intrusion)/reduction(extrusion)) may be calculated using parameters of the matrix and the liquid used for HLS. In the reference (Eroshenko and Grosu 2013b) analysis of such thermal effects as well as some operational properties are presented. The reprint of this publication is given hereafter. The prediction of such thermal effects, but while taking into account bulk thermal coefficients is also discussed in the next paragraph. Temperature dependence of thermal effects of compression/decompression was investigated for the {Hypersil C18 + water} HLS (Fig. 3.3 and Fig. 3.4).

For intrusion as expected from the thermodynamic analysis the thermal effect is endothermal (interface development) and for extrusion it is exothermal (interface reduction), see Interestingly for the {Hypersil C18 + water} HLS compression-decompression cycle becomes reversible (system returns to initial state when pressure returns to initial value after intrusion) only at temperatures higher than 325 K (Fig. 3.6) and at lower temperatures liquid is not completely expulsed from the pores. However if after such irreversible intrusion HLS is heated up to at least 325 K at atmospheric pressure the liquid extrudes from the pores and the HLS operates reversibly. Such effect is shown for the first time. In fact in the literature this HLS was tested only at room temperature and since it was shown to be only partially reversible at these conditions (which is consistent with results presented here), it was considered as nonuseful [START_REF] Suciu | Novel and global approach of the complex and interconnected phenomena related to the contact line movement past a solid surface from hydrophobized silica gel[END_REF]. But it seems this HLS can operate quite well, but only at higher temperatures. Transition from non-reversible (at lower temperatures) to reversible (at higher temperatures) behavior of the {Hypersil C18 + water} HLS allowed realizing new regime of HLS operation: that is extrusion of the liquid provoked by heating (Fig. 3.8). First system was compressed at 275 K temperature. After decompression no extrusion was observed (Fig. 3.6a).

Next system was heated up to 335 K at controlled atmospheric pressure (Fig. 3.8), which leads to extrusion of the liquid and pronounced increase of the volume of HLS. Figure3S. 33 compression-decompression cycles of the {ZIF-8 + water} system: 2 nd -30 th cycles are at 300K; 31 st cycle is after keeping system at 360K and 0.1MPa during 24h; 32 nd cycle is with a 24h pause at 30 MPa; 33 rd cycle is at 300K after all mentioned above cycles.

CONCLUSIONS

The main results of this work are focusing on a deeper understanding of the operating mechanisms of porous Heterogeneous Lyophobic Systems (HLS) in energy applications. Also important part of this work is dedicated to determination of optimal conditions and regimes of HLSs operation, realized by recording their thermomechanical characteristics in extended temperature and pressure ranges.

Some striking results are highlighted:

1.

An equation of state for an HLS, which takes into account pore size distribution as well as compressibility and thermal expansion of the liquid and the matrix, was proposed. Using this equation, it was shown that pressure and temperature dependences of the thermal (thermomechanical) coefficients, the thermal effects of compression/decompression, and the heat capacities of HLS may be tuned using porous materials with different pore size distribution functions.

2.

Using a rigorous thermodynamic analysis it was demonstrated that the temperature dependence of intrusion and extrusion pressures of an HLS plays a dominant role in the applicability of their energetic characteristics. It was shown that an intrusion/extrusion process for an HLS is a second order phase transition process. For example the change of isobaric heat capacity caused by intrusion/extrusion during heating/cooling of an HLS can be described by Erenfest equation.

3.

For a mesoporous HLS a system of equations was proposed, which allows to calculate the intrusion/extrusion temperature dependences using the capillarity and bubble nucleation approach, where the size effects are taken into account with the concept of line tension, while the temperature dependences of advancing and receding contact angles are obtained by means of the "sharp-kink" approximation.

4.

The energetic characteristics of four distinct HLSs were collected in a wide temperature range. It was shown that the capacity to storing/restoring thermal energy for investigated systems increase with temperature. As regards the capacity to storing/restoring mechanical energy, a more complex (non-linear) temperature dependence was observed, mainly due to a more complex temperature dependence of the intrusion/extrusion pressure.

5.

Investigation of performance stability of HLS demonstrated that the main reason for the degradation of the energetic characteristics under high pressure and/or temperature is irreversible changes in the structure of the porous matrix. For the {Silicalite-1 + water} HLS such irreversible changes are associated with silanol defects formation, while for the {ZIF-8 + water} HLS with the change of the symmetry of the structure: from cubic to orthorhombic. Such change of the structure of ZIF-8 was shown for the first time.

6.

It was shown both experimentally and by means of the thermodynamic analysis that an HLS can be used to obtain an effect of Negative Thermal Expansion (NTE) within a controlled temperature window, with NTE-coefficient orders of magnitude higher compared to best known materials. The thesis is devoted to the theoretical and experimental investigations of thermodynamic and operational properties of nanoporous Heterogeneous Lyophobic Systems (HLS) and their temperature dependences in order to determine optimal conditions and increase efficiency of HLS-based energetical devices.

The thesis reflects results obtained in three main directions of research: 1. Thermodynamic analysis; 2. Characteristics of HLS in a wide temperature range; 3. Stability of HLS under different operational conditions. Maximum temperature range investigated is to 2 -150 ° C. Pressure range is 0.1 -120 MPa. Particularly, results include proposed equation of state for real HLS, which takes into account pore size distribution function; the energetic characteristics of four (two mesoporous and two microporous) HLSs collected in a wide temperature range; some new operation regimes of HLSs were investigated under controlled isobaric conditions; proposed concept of usage of HLS as a system with pronounced negative thermal expansion. Keywords: storage, conversion, dissipation of energy; interface, porous body, complex thermodynamic system. RESUME La thèse est consacrée à l'étude théorique et expérimentale des propriétés thermodynamiques et d'usage de Systèmes Hétérogènes de Lyophobes nanoporeux (SHL) et leurs dépendances en fonction de la température afin de déterminer les conditions optimales et accroître l'efficacité des dispositifs énergétiques à base de SHL.

La thèse présente les résultats obtenus dans trois directions principales de recherche: 1. Analyse thermodynamique; 2. Caractéristiques des SHL dans une large plage de température; 3. Stabilité de SHL dans différentes conditions opérationnelles. La gamme maximale de température étudiée est à 2 -150 °C et 0.1 -120 MPa pour la pression. En particulier, les résultats comprennent une équation d'état pour décrire des SHL réels qui prend en compte la distribution de taille des pores; les caractéristiques énergétiques de quatre (deux mésoporeux et deux microporeux) SHLs mesurées dans une large plage de température; certains nouveaux régimes de fonctionnement de SHLs ont été étudiés dans des conditions isobares contrôlées; enfin le concept d'utilisation de SHL comme système avec dilatation thermique négative prononcée est proposé.

Mots clés: stockage, conversion, dissipation de l'énergie; interface, matériaux poreux, système thermodynamique complexe.

1 0 2 , 1 ,

 121 of liquid and matrix of HLS, m3 Initial volume of liquid and matrix of HLS, thermal expansion of HLS, K -Isobaric coefficient of thermal expansion of liquid and matrix of HLS, K -1 β int,ext Isochoric coefficient of pressure of HLS, K -1 β 0Isochoric coefficient of pressure of liquid and matrix of HLS, K -1 σ surface tension of liquid, J/m coefficient of isothermal compressibility of HLS, Pa -1 coefficient of isothermal compressibility of liquid and matrix of HLS, Pa -coefficient of adiabatic compressibility of HLS, Pa -1 coefficient of adiabatic compressibility of liquid and matrix of HLS, Pa -

  preparation are described. Next Chapter 3 presents an attempt to build the thermodynamic description of HLS by mean of equilibrium thermodynamics of complex systems by proposing an equation of state of an HLS, which includes pores size distribution function of the matrix (Paragraph 3.1). Special attention in Paragraph 3.2 is paid to experimental and theoretical investigation of the temperature dependence of the intrusion/extrusion pressure of HLSs as one of their most important characteristic. In Paragraph 3.3 the conditions (especially temperature ranges) which provide stability of characteristics of HLS are described. The last part of the thesis is Conclusions followed by the References. Appendixes providing additional information are placed at the end of the present document. Most of the results presented in the Thesis were published in peer reviewed journals and are presented as reprints of corresponding papers (overall 10 papers). The citations are made in the (author year) form, which differs from the forms of citations used in reprints of the papers presented in here.

Fig. 2 .

 2 Fig. 2.1. A scheme of thermodynamic foundations for various types of PVT-controlled scanning calorimetry.

Fig. 2 .

 2 Fig. 2.2. A thermodynamic functional scheme of scanning transitiometry.

Fig. 2 . 3 .Fig. 2 . 5 .

 2325 Fig. 2.3. Scheme of transitiometer ST-7M.

  2.3.). Measurements are performed by controlling precisely the three thermodynamic variables, namely: pressure within ± 0.15 MPa, volume within ± 3.3 • 10 cm and temperature within ± 0.01 K.

Fig. 2 . 6 .

 26 Fig. 2.6. Main window of transitiometer ST-7M software.

Fig. 2 . 8 .

 28 Fig. 2.8. Peak of calorimetric signal obtained for the fusion of а) p-di-Bromobenzene, b) p-Bromochlorobenzene.

Fig. 2 .

 2 Fig. 2.10. Pl -isotherms of compression of water (blue line) and lead immerged in water (black line).

Fig. 2 .

 2 Fig. 2.11. Vacuum line for degasing the porous matrix of HLS а) scheme, b) photo

Fig. 2 .

 2 Fig. 2.12. Scheme of preparation of an HLS.

Figure 2 .

 2 Figure 2.12 shows a simplified scheme of degasation of investigated porous heterogeneous lyophobic systems. Weighted porous matrix in the form of powder is placed in a metal capsule, which is then closed with a porous ceramic-metal bottom. Pore sizes of the bottom are in the range of a few micrometers, excluding elutrition of the particles of the porous powder. In the experiments performed the powder weight was within 0.3 -1 g for different samples. Metal capsule with porous matrix is placed into the empty measuring cell. Next the cell is closed with the degasation cork through which the cell is connected to the vacuum line (Fig. 2.12a). The position of T-valve excludes non-wetting liquid to enter the vacuum line. The degasation is performed during 2 hours at 5•10 -2 mbar vacuum. After the degasation the T-valve is placed in the position shown in Fig. 2.12b which allows the non-wetting liquid to flow into measuring cell, while excluding its flow to the vacuum line. A small external force is applied to the piston of the

Fig. 2 .

 2 Fig. 2.13. Schematic representation of experiment with constant load.

1 )

 1 If the porous matrix of an HLS can be considered as uniporous (all the pores have the same radius) equation (3.1) under isothermal conditions can be written as Which means that during the intrusion/extrusion process the volume change takes place at2 In the Paragraph 3.2 it is shown that additionally to equation (3.1) the bubble nucleation must occur for liquid to extrude from the pores of the matrix.

, > 0 ,

 0 which is expected. A detail analysis of temperature dependences of surface tension and contact angle is discussed in Paragraph 3.2. The above property of HLSs is unusual for traditional working bodies (gas/vapor) and can be effectively used in engineering applications. For example it allows for an HLS-based shock absorber to operate at frequencies above 20 Hz (Eroshenko et al. 2007) (and theoretically even at much higher frequencies (Michelin-Jamois et al. 2013)) without overheating. The relation (3.11), using well-known equation δ = d , shows that thermal effect of the isothermal compression/decompression is determined by the temperature dependence of the surface tension and of the contact angle: 3.13) allows finding a very important, but difficult to measure experimentally, pressure dependence of temperature of an HLS during an adiabatic compression/decompression. Using relation (3.15) the partial derivatives in the right-hand-side of equation (3.13) may be written as follows =

Fig. 3 . 2 .

 32 Fig. 3.2. Coefficient of isobaric thermal expansivity of the {Waters C8 + water} HLS for the intrusion process. Solid line is model according to equation (3.17), dashed line is coefficient of isobaric thermal expansivity of water according to available data (NIST Chemistry WebBook).

, → 0

 0 ) they become equal to the thermal coefficients of an HLS based on uniporous matrix. It should be noted that obtained relations and thermal coefficients do not take into account the pore radii change during the compression/decompression process. An attempt to analyze such phenomena is presented here after in the reference (Eroshenko and Grosu 2013a), see the following reprint. Eroshenko V. A., Grosu Y. G. (2013a). Journal of Technical Physics. V. 58., No. 8., P. 1087 -1093.

  Eroshenko V. A., Grosu, Y. G. (2013b).. Int. J. of Thermodynamics. 16(1), P. 1-9.

Fig. 3 . 3 .

 33 Fig. 3.3. Such behavior is consistent with calorimetric studies for other HLSs available in the literature (Coiffard et al. 2005, Karbowiak et al. 2010a).

Fig. 3 . 3

 33 Fig. 3.3 Thermal effects of a) intrusion and b) extrusion of the {Hypersil C18 + water} HLS: solid line is experiment; dashed line is the model according to eq. (3.21)

Fig. 3 . 5 .Fig. 3 . 6 .

 3536 Fig. 3.5. Isobaric heat capacity of the {Waters C8 + water} HLS at = ( ) calculated according eq. (3.23) for intrusion provoked by temperature increase. Solid line is for HLS; dashed line is for water.

Fig. 3 . 7 .

 37 Fig. 3.7. Temperature dependence of a) intrusion and extrusion pressures: dotes are experiment, solid lines are theoretical dependence calculated taking into account contact angles temperature dependences; dashes line are theoretical dependences calculated considering constant contact angles b) Hysteresis of intrusion and extrusion pressures of the {Hypersil C18 + water} HLS.

Fig. 3 . 8 .

 38 Fig.3.8. Tmperature dependence of the volume of {Hypersil C18 + water} HLS at atmospheric pressure after one compression-decompression cycle at 275 K.

3. 3 .

 3 Stability of HLSs characteristics under operational conditionsStability of the characteristics of HLSs is of paramount importance for practical applications. In the references[START_REF] Ievtushenko | Evolution of the energetic characteristics of {silicalite-1+ water} repulsive clathrates in a wide temperature range[END_REF]) and[START_REF] Ya | Synergetic effect of temperature and pressure on energetic and structural characteristics of {ZIF-8 + water} molecular spring[END_REF]) some of the aspects of instability of HLSs characteristics which may be caused by the effect of high operational pressure or temperature (or by their simultaneous effect) are described. Since the stability of the characteristics of HLSs are investigated in a wide temperature range this publications have also information on temperature dependences of intrusion/extrusion pressures of investigated HLSs and their thermal effects. Reprints of indicated papers are presented hereafter. Ievtushenko O. V., Eroshenko V. A., Grosu Y. G., Nedelec J. M., Grolier J. P. E. (2013). Physical Chemistry Chemical Physics. 15(12), P. 4451 -4457. Grosu Ya., Renaudin G., Eroshenko V., Nedelec J.-M., Grolier J.-P.E. (2015b). Nanoscale. 7, p. 8803-8810.

FigureFigure1S.

  Figure 1S represents the work of intrusion and extrusion of {ZIF-8 + water} molecular spring at different temperatures and the hysteresis of their values, calculated as follows:

Figure

  Figure 2S represents the FTIR spectra of ZIF-8 before and after 25 cycles of intrusion-extrusion at temperatures in the range of 275 -360K.

7 .,

 7 Some new operation regimes of HLSs were investigated under controlled isobaric conditions: intrusion of the liquid by cooling a {ZIF-8 + water} HLS; extrusion of the liquid by heating a {HC18 + water} HLS. Such effects are associated with huge changes of the isobaric heat capacity of the HLSs. Such relation does not have physical sense. Since we consider quasi-static regime of an HLS operation, the interface development (dΩ ≠ 0) is impossible without considering variation of the volume of the bulk phase , which makes left-hand-side derivative null. While the surface tension as well as the contact angle do not depend on the volume of the bulk phase .Let us repeat this algorithm for all thermodynamic characterization functions.Enthalpy of an HLS: d = d + ( -Ω)d .

  .2013, 2014). Impressive success in the development of devices for mechanical energy dissipation applications was achieved by Suciu, especially in the development of HLSs-based car shock-absorber[START_REF] Suciu | Study of a novel squeeze film damper and vibration generator[END_REF](Suciu et al. , 2003[START_REF] Suciu | Novel Principle of Mechanical Energy Dissipation (Part 1-Static Performances of Colloidal Damper)[END_REF][START_REF] Suciu | Novel and global approach of the complex and interconnected phenomena related to the contact line movement past a solid surface from hydrophobized silica gel[END_REF](Suciu et al. , 2010a, 2010b, 2010c, Iwatsubo et al. 2007, Suciu and Yaguchi 2009, Suciu 2008, 2010, Suciu and Tobiishi 2012, Suciu and Kimura 2012, Suciu and Buma 2013). Qiao and co-workers investigated a number of potential HLSs-based

, Eroshenko and Fadeev 1995, Fadeev and Eroshenko 1997, Eroshenko et al. 2001, 2002, 2007, Eroshenko and Stoudenets 2002, Coiffard and Eroshenko 2006, Eroshenko and Lazarev 2012) and stimulated the development of mentioned above ideas in number of laboratories in different countries. Particularly a great number of porous materials coupled with water and aqueous solutions were investigated by Patarin and coworkers focusing on the energetic characteristics and operational stability of HLSs (Trzpit et al. 2007a, 2007b, 2008, 2009a, 2009b, Cailliez et al. 2008, Karbowiak et al. 2010a, Saada et al. 2010a, 2010b, Tzanis et al. 2011, 2012a, 2012b, 2014, Ortiz et al. 2013, 2014a, 2014b, Khay et 1 Multiple reference No. 30.

al

  , Kong et al. 2005, Qiao et al. 2006, 2007, Surani et al. 2005, 2006, Surani and Qiao 2006a, 2006b, 2006c, Cao et al. 2008a, 2008b, Chen et al. 2006, 2008, Qiao and Han 2007, Xu et al. 2011a, 2011b). Several important insights into the physical mechanisms of HLSs operation

can be found in the works supervised by Prof. E. Charlaix (Lefevre et al. 2004a, 2004b, Guillemot 2010, Guillemot et al. 2012a, 2012b, Michelin-Jamois et al. 2014). Highly valuable and still rare calorimetric measurements for HLSs were performed by Grolier and co-workers

  Reference samples used and their characteristics are presented in Table2.1. Where m is mass, ΔH F is enthalpy of fusion, T F is melting point temperature, ℵ is obtained by the conversion coefficient of the calorimeter. All the samples were encapsulated in glass capsules that were previously degassed.

	2.1.1.2. Experimental procedures and sample preparation
	2.1.1.2.1.	Calorimeter calibration
	Calibration of the calorimeter was carried out by recording the thermal effects of melting
	of reference samples. Comparison of calorimetric peak area corresponding to the phase transition
	of the reference samples (Fig. 2.8.) with the reference value of the enthalpy of fusion was used to
	calculate the conversion coefficient of calorimetric signal CS	. While comparison of
	recorded temperature of phase transition to reference one was used for calibration of temperature
	detectors. Table 2.1.
	Characteristics of reference samples used for calibration of the calorimeter.
	Reference sample	m, g	ΔH F , J/g	T F , K	ℵ, W/Volt
	p-Bromochlorobenzene	0,24315	97,99	337,70	0.08790
	p-di-Bromobenzene	0,23260	87,03	360,45	0.09287
	Benzoic Acid	0.14670	147.9	395.55	0.10254
	Indium	0.56205	28.59	429.75	0.01069

  K gives a porous volume of 0.53 cm 3 /g and an average pore radius of 4.2 nm, obtained from the desorption branch using the classical Barrett-Joyner-Halenda equation[START_REF] Coiffard | Temperature effect on water intrusion/expulsion in grafted silica gels[END_REF]). Combined with water indicated porous matrix achieved considerable attention in the field of mechanical energy dissipation[START_REF] Eroshenko | A new paradigm of mechanical energy dissipation. Part 1: theoretical aspects and practical solutions[END_REF]

	et al. 2007, Suciu and Yaguchi 2009); primarily due to strong hysteresis and good resistance to
	mechanical stress.
	Hypersil 5u HS C18 is a mesoporous silica grafted by linear chains of octylsilanes, but
	with greater length than the previous sample -C18 chains (C 18 H 37 ). In previous studies it was
	found (Suciu 2003) that at room temperature {Hypersil 5u HS C18 + water} HLS demonstrates
	satisfactory performance for mechanical energy dissipation processes only for the first
	compression-decompression cycle. The lack of results for such HLS in a wide temperature range
	indicates the need to determine the optimal conditions for its use.
				Table 2.2.
		Characteristics of porous materials
		Waters	Hypersil 5u	Silicalite-1	Zif-8
		SymmetryPrep C8	HS C18	(MFI-F)
	Porosity (cm 3 /g)	0,51	0,40	0,14	0,38
	Area (m 2 /g)	221	138	400	1800
	Average pore radius (nm)	4,0	3,9	0,3	0,17

3.8 nm

[START_REF] Coiffard | Temperature effect on water intrusion/expulsion in grafted silica gels[END_REF]

, taking into consideration grafting thickness

(Fadeev and Staroverov 1988, Eroshenko and Fadeev 1995)

. Nitrogen sorption measurements on the grafted material at 77 Silicalite-1 (prepared in fluoride medium) sample was bought from Sigma Aldrich. The pore space of Silicalite-1 has a simple topology (MFI) having almost ideal cylindrical pores with radius r ~ 0.3 nm and high hydrophobicity. ZIF-8 (Zeolitic imidazolate framework). The structure of ZIF-8 consists of cage-like pores of ~11.6 Å diameter connected by 6-ring windows of only ~ 3.4 Å and is characterized by a huge specific surface area of c.a. 1800 m 2 /g. ZIFs is a subclass of metal-organic frameworks (MOFs).

Analytical formula for ZIF-8 is С 8 Н 12 N 4 Zn; particle size is 4.9 μm. Some of the characteristics of described above are summarized in table 2.2.

As non-wetting liquid, distilled water was used. HLSs based on water present advantages of ecological safety, low price and availability.

Table 3 .

 3 1.

	Work of intrusion and extrusion for the {Hypersil C18 + water} HLS at different
	temperatures
	T, K	275	300	325	350	370	400	420
	W int , J/g	7,3	7,1	6,9	6,6	6,4	5,9	5,5
	W ext , J/g	0	0,3	0,6	0,9	1,1	1,2	1,2

Table 1S .

 1S Energetic characteristics of the {ZIF-8 + water} molecular spring

	T,K	275	300	310	320	330	340	350	360
	W int [J g -1 ]	8.8	9.6	9.8	9.9	9.9	9.9	9.8	9.5
	W ext [J g -1 ]	5.7	7.0	7.5	7.9	8.2	8.4	8.4	8.3
	Q int [J g -1 ]		4.4	7.4	9.4	14.4	13	26.3
	Q ext [J g -1 ]			5.4	6.3	12.7	12.9	25.7
	P int [MPa]	23.0	24.6	25.3	25.8	26.0	25.9	25.5	24.9
	P ext (1 st peak) [MPa] P ext2 (2 nd peak) [MPa]	18.8 14.6	21.8 18.3	22.5 19.8	23.0 20.8	22.9 21.6	22.2	22.3	21.9
	V int,ext [cm 3 g -1 ]	0.43	0.40	0.38	0.37	0.36	0.34	0.33	0.31

ACKNOWLEDGEMENTS

I would like to express my deepest gratitude to Prof. Valentin Eroshenko for inspiring me for the preparation of this work and for his exemplary incentive to keep my motivation and

is the pores volume of the matrix; and are initial pressure and temperature of the system, respectively;

is the volume of the whole bulk phase (liquid and the matrix), which may change due to elastic compression/decompression or due to thermal expansion/contraction; = -, is the isothermal compressibility of the liquid and the matrix; = , is the isobaric coefficient of thermal expansion; is the initial whole volume of the system (volume of the liquid plus the volume of the matrix);

, is the dispersion of the values if intrusion and extrusion pressures, which can be determined from the dispersion of pore radii from their average value using equation (3.1).

In principle pores may be distributed according to any function or in case of a HLS based on several matrices may be described by superposition of known distribution functions. Coefficient of adiabatic compressibility of an HLS was determined taking into account the temperature variation during adiabatic compression/decompression of an HLS:

Where ∆ is the density difference between water and its vapor and , is Wan der Waals integral for intrusion and extrusion process.

To obtain this equation temperature dependence of contact angles was used calculated by means of "Sharp-kink" approximation, which is in details described in reference (Grosu et al. 2014c). Reprint of this publication is presented in paragraph 3.2.

Equation (3.21) allows calculating the thermal effect with at least 15% error, which may be considered satisfactory (Fig.

As was demonstrated in Paragraph 3.1.3 thermal expansivity may become negative for some HLS under certain conditions. Such effect is called effect of Negative Thermal Expansion (NTE)

and attracts great attention due to its wide range of practical applications. Detailed experimental and theoretical investigation is presented in references (Grosu et

APPENDIXES Appendix А

Maxwell relations for HLS

The internal energy of HLS may be written as follows:

Next we consider three possible conditions, which are = , Ω = , = .

1)

Next using following relation = one obtains Maxwell relation:

For other two cases the procedure is similar.

2)

Apendix B Thermal coefficients

Adiabatic coefficient of compressibility of HLS may be written using its definition and equation (3.4):

Next we using function in the form of Cauchy distribution function one may write:

In this differential equation separation of variables is possible, which allows to integrate it:

Where constant may be found from initial conditions ( = ) = .

In order to determine Isochoric Coefficient of Pressure (ICP) of HLS let us write the full differential of pressure as function of , , Ω as follows:

By solving system of equations (B.5) and (B.6) one obtaines:

Appendix C

Thermal effects of compression-decompression

In order to obtain the pressure derivative of the heat of compression/decompression of HLS at isothermal conditions we use equation (3.15) and (3. The temperature coefficient of surface tension normally is a known characteristic of the liquid, the derivative may be rewritten using the generalized Young equation:


Dora Boviz
email: dora.boviz@alcatel-lucent.com

Aravinthan Gopalasingham
email: gopalasingham.aravinthan@alcatel-lucent.com

Chung Shue Chen
email: cs.chen@alcatel-lucent.com

Laurent Roullet
email: laurent.roullet@alcatel-lucent.com

Physical Layer Split for User Selective Uplink Joint Reception in SDN Enabled Cloud-RAN

To meet quality of service requirements on the uplink of future cellular networks, we need to exploit intercell interference among users eligible for cooperation. Cloud Radio Access Network (C-RAN) architecture is particularly favorable to realize cooperation between users in neighboring cells, since signal detection is realized in the same processing unit. The novel technology of Software Defined Networking (SDN) increases the flexibility of network optimization and scalability of computational resources. We propose a C-RAN based architecture and a practical scheme of realizing uplink joint processing in critical scenarios where strong interference would affect cell-edge users. We consider characteristics of a real network and novel technological solutions necessary for reliable transmission over the radio access network. The central idea is to split the physical layer processing between Remote Radio Heads (RRHs) and the central processing unit only for selected users in enabling cooperation and maintaining affordable fronthaul transport infrastructure. In practice, the joint detection for selected few co-channel users would simplify the required multiuser channel estimation while improving overall performance and cell-edge users' quality-of-service (QoS).

I. INTRODUCTION

One of the main challenges for next generation cellular communication systems is to transmit with higher spectral efficiency, since frequency resources are limited but the amount of data traffic is growing very rapidly [START_REF] Andrews | What will 5G be?[END_REF]. To be able to meet quality-of-service requirements, particularly for cell-edge users, without using large amount of bandwidth or transmit power, frequency reuse is applied. User equipments (UEs) transmitting on the same physical resource block (PRB) can lead to severe co-channel interference. Their transmissions can be accurately decoded if their respective base stations (BSs) cooperate [START_REF] Gesbert | Multi-cell MIMO cooperative networks: A new look at interference[END_REF]. Distributed and centralized schemes of cooperative processing were reported in the literature [START_REF] Singh | Distributed downlink resource allocation in cellular networks through spatial adaptive play[END_REF]. Decentralized processing was built for today's already deployed distributed RAN infrastructures. However, their cooperative processing gain remains quite limited. Its disadvantages such as high latency and large overhead needed for sharing data also orient the industry towards the use of a centralized architecture. In conventional uplink (UL) transmission, PRBs are reused for each cell. Inter-cell interference is expected and could lead to very low signal-to-interference-plus-noise ratio (SINR) especially to received signal from cell-edge user. Though the realization of large-scale multi-cell processing would be too complex, orchestration between the schedulers of each cell will allow better sharing of radio resources and joint detection (JD) of received signals. In this paper, we propose a centralized architecture in which users from neighboring cells can be allocated on the same PRB and their signals are detected jointly through sharing data between Baseband Units (BBUs) of their respective cells.

Exploiting inter-cell interference via multi-cell processing instead of avoidance [START_REF] Gesbert | Multi-cell MIMO cooperative networks: A new look at interference[END_REF] is one of the most interesting features for future cellular networks but also a very challenging task because of practical system limitations. Finite communication bandwidth between various network elements and potential multi-user channel estimation error [START_REF] Marsch | Uplink CoMP under a constrained backhaul and imperfect channel knowledge[END_REF] can easily decrease the system performance and expected theoretical gain. The trend is to use possible cooperation thanks to today's adoption of C-RAN architecture. Here, we will discuss the use of software defined networking (SDN) technology for radio access networks, which offers the possibility of efficient network control by separating control plane and data plane. Low latency data flow routing using network-wide control information increases network scalability and adaptability for features such as joint detection.

The aim of this paper is to highlight UL inter-cell cooperation in a centralized framework. We first review and compare existing techniques in the light of their applicability to C-RAN. We point out key innovations for allowing an efficient implementation of uplink coordinated multi-point transmission (CoMP). Then, we define an architecture with a physical layer (PHY) split that copes with system limitations and allows cooperation in today's C-RAN platform. Finally, we show by simulations and numerical studies the benefit of multicell cooperation which is implementable to today's Long Term Evolution (LTE) cellular networks.

We use the following technical terms in the coming discussion. The user or UE is the cellular device which sends data over the uplink channel. The data is then received by one or several antennas at the cell sites where only radio frequency or possibly physical layer signal processing is performed; we call them Remote Radio Heads (RRHs). If complete BBU is located there, it is then a base station (BS). Then the data is forwarded using fronthaul (FH) links to the central processing unit hosting BBUs of several cells, which is called BBU-pool.

The remainder of the paper is organized as follows. In Section II, we describe the idea of uplink cooperation in cellular networks and existing techniques. Section III presents the proposed C-RAN architecture and implementation integrated with SDN controller and carrier Ethernet fronthauling. Section IV shows how these technological solutions enable the proposed user selective cooperation scheme and its performance. Finally, Section V concludes the paper.

II. UPLINK COOPERATIVE PROCESSING

The idea of interference management through BS cooperation spans over several aspects of a cellular network regarding the amount of available channel state information (CSI) and shared data (compressed signal or decoded data), the FH network architecture (distributed or centralized processing), the communication infrastructures between BSs (e.g., fiber, microwave) and cooperation technique used (e.g., coordinated scheduling, joint detection). In this section, we investigate the state-of-the-art of uplink cooperative techniques already used in today's cellular networks or reported in standards and research papers.

A. The Network MIMO concept

In theory, we can assimilate multi-cell Multiple-Input Multiple-Output (MIMO) network without limitation in fronthaul connections to conventional multi-user MIMO (MU-MIMO), so that in the uplink, with full cooperation, the capacity of each cell should be the same as that in an interferencefree scenario [START_REF] Hanly | Capacity and power control in spread spectrum macrodiversity radio networks[END_REF]. Unfortunately, this capacity result cannot be applied to real cellular networks due to several theoretical and practical constraints as already pointed out in [START_REF] Gesbert | Multi-cell MIMO cooperative networks: A new look at interference[END_REF]. Still, we can have several methods to exploit the inter-cell interference with fully or partially centralized signal detection [START_REF] Marsch | Coordinated Multi-Point in Mobile Communications: From Theory to Practice[END_REF]. Multi-cell joint detection can be realized like that in single-cell MIMO case using either Maximum Likelihood (ML) or Minimum Mean Square Error (MMSE) detection. However, the high complexity of ML does not allow implementation in real-time systems. On the other hand, joint MMSE is suboptimal but requires more reasonable computational cost. It is also possible to apply Successive Interference Cancellation (SIC) detection to each signal. The drawback of SIC is the possible error propagation if first signals cannot be accurately detected. A main difficulty of joint detection is to forward received signal to the collective processing unit (see sub-section II-C). Signal compression before sending on the fronthaul links can address this practical constraint, but can affect accuracy of detection.

Compression followed by SIC detection was studied in [START_REF] Zhou | Uplink multicell processing with limited backhaul via per-base-station successive interference cancellation[END_REF]. In [START_REF] Miyamoto | Uplink joint reception with LLR forwarding for optical transmission bandwidth reduction in mobile fronthaul[END_REF] authors propose to forward to the BBU-pool a quantized version of demodulated symbols which is then used in joint processing. Amount of data sent over fronthaul links can also be reduced if a BS forwards already decoded signal that can be used to perform SIC for the other. Another form of decodeand-forward scheme is that a part of the message is individually decoded at the BS while the other part is forwarded for joint decoding in the BBU-pool [START_REF] Sanderovich | Uplink macro diversity of limited backhaul cellular network[END_REF]. Decentralized cooperation similar to decode-and-forward was investigated in [START_REF] Balachandran | Nice: A network interference cancellation engine for opportunistic uplink cooperation in wireless networks[END_REF], where decoded data is shared among neighboring BSs instead of a central unit. Where C-RAN architecture will be adopted in future cellular networks, we can benefit from low latency communication between collocated BBUs and consider more optimal scheme of multi-cell cooperation.

B. UL CoMP in Long Term Evolution (LTE)

In LTE, there are two classes of uplink CoMP: (i) coordinated scheduling (CS) which shares only control data between BBUs, and (ii) joint reception (JR) which requires large FH bandwidth to share received data signals. It should be noted that full multi-cell scheduling would also have a high computational complexity and cannot improve cell throughput beyond a limit in case of heavy load.

C. Constraints: FH capacity and multi-cell channel estimation

For reliable communication between RRHs and BBU-pool, low latency and low jitter links are required. Meanwhile, they have to be efficiently used for system cost. Optical fiber links of 10 Gbps capacity transporting signals encapsulated in Common Public Radio Interface (CPRI) packets are often used as fronthaul links. However, in future networks that may coordinate many antennas at a cell site, this capacity would be a bottleneck to transmit I/Q samples. To offer a cost-effective solution, transmitting demodulated symbols or decoded bits between cell site and BBU-pool should be considered since this can significantly decrease the required FH bandwidth.

A basic constraint for CoMP is the necessity of multi-cell CSI at the central processing unit. Orthogonal pilot symbols need to be sent by each UE so that channel gain can be accurately estimated. If several users are transmitting on the same PRB, larger pilot-length is needed. This will consume extra bandwidth. Note that in LTE, cyclic shift of pilot symbols is proposed for multi-user signal detection [START_REF] Gpp | Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation[END_REF]. However, the number of allowable co-channel users is still limited.

III. KEY TECHNOLOGIES FOR COOPERATIVE TRANSMISSIONS

A. C-RAN 1) Advantages of centralization: As aforementioned, a centralized architecture can facilitate inter-cell cooperation. Where possible to deploy, C-RAN is particularly appropriate for low-latency communications between BBUs of different cells since these are located in the same processing unit. Centralization of BBUs also facilitates the handover procedure which otherwise would require coordination and communication between distributed BSs through for example the 3GPP X2 interface [START_REF]X2 application protocol (X2AP)," 3rd Generation Partnership Project (3GPP)[END_REF].

The need for such an architecture is not only for improving network performance, but also for reducing deployment and operational costs. To satisfy future data rate and coverage requirements, antenna density should be increased while operators' per-subscriber income decreases. In order to deploy denser networks at lower cost (the Capital Expenditure, CAPEX), processing capacity should be centralized so that system scalability, energy efficiency and flexibility to upgrade and manage computational units can be guaranteed, which will result in lower Operational Expenditure (OPEX) [START_REF] Checko | Cloud RAN for mobile networks -a technology overview[END_REF]. Since several BBUs are located in the same server, the overall dimension of computational resources can be reduced thanks to pooling. BBU-pools are also susceptible to be shared between several operators using the concept of RAN as a Service [START_REF] Sabella | RAN as a service: Challenges of designing a flexible RAN architecture in a cloud-based heterogeneous mobile network[END_REF], which allows to have several instances of various standalone modules that can be attributed to different operators. Nonetheless, this centralization of BBUs requires resource management and data flow control. This can be provided by the emerging technology of SDN, to be discussed in subsection III-B.

2) Fronthaul transport using CPRI: In existing C-RAN deployments, RRHs are connected to BBU-pool through dedicated point-to-point fiber link on which synchronous CPRI packets containing baseband I/Q symbols are sent. As pointed out in [START_REF] Yuan | Rethink fronthaul for soft RAN[END_REF], this type of infrastructure cannot meet future network requirements such as dynamic mapping and network resource allocation between RRHs and BBU-pool. Ethernet based Fronthaul technology connected through a CPRI-to-Ethernet gateway is a good candidate for transport CPRI packets [START_REF] Checko | Cloud RAN for mobile networks -a technology overview[END_REF]. Since today's FH cannot guarantee to transport baseband I/Q symbols for large scale MIMO transmissions, the common target of centralizing all the baseband processing cannot be ensured. In general, the distribution of PHY processing between the RRH and the BS depends on the available fronthaul rate measured on the BBU-pool side. However, to benefit from C-RAN and CoMP features, we have to design a dynamic architecture allowing the centralization of PHY functions.

B. SDN controller in the BBU pool 1) Data and control plane separation: The separation between control plane and data plane in SDN architecture is to enable them to operate independently for high flexibility and programmability so that operators can have a complete control over the network from a centralized point [START_REF] Yeganeh | On scalability of software-defined networking[END_REF]. This would allow network operators to deploy their applications and services and to adjust network policies easily, see for example [START_REF] Mendonca | The case for softwaredefined networking in heterogeneous networked environments[END_REF]. Load balancing and scheduling can also be easily deployed. Software defined networking has been used in wide variety of network environments such as enterprise networks, data centers and infrastructure-based wireless access networks.

2) OpenFlow for network management: OpenFlow has been the first protocol for SDN. It has two key components. The controller has a complete control over all the OpenFlow switches in the network, i.e., it controls all network functions, whereas the OpenFlow switch forwards the first packet of each new flow to the controller for routing decision. The controller can update the forwarding table depending on some pre-defined rules or new policies. Though OpenFlow has programmability and flexibility in managing and controlling various network elements in SDN, there are some concerns of its efficiency during heavy traffic load. DevoFlow [START_REF] Curtis | DevoFlow: Scaling flow management for highperformance networks[END_REF] is a modification of OpenFlow protocol for maintaining flow visibility and reducing controller load and overhead. DevoFlow can reduce the switch flow table entries and also the control messages by more than ten times [START_REF] Curtis | DevoFlow: Scaling flow management for highperformance networks[END_REF]. It would be very suitable to offer efficient switching and routing solutions for high performance networks like C-RAN.

3) SDN approach for wireless networks: The importance of SDN is to bring dynamic programmability into the control and data planes. This will definitely also benefit mobile operators by incorporating SDN to wireless networks. OpenRoads [START_REF] Yap | OpenRoads: Empowering research in mobile networks[END_REF] and OpenRadio [START_REF] Bansal | OpenRadio: A programmable wireless dataplane[END_REF] are examples of bringing SDN into RAN by enabling dynamic programmability of RAN especially at physical and MAC layer. In [START_REF] Gopalasingham | Generalized software defined network platform for radio access networks[END_REF], generalized SDN framework for RAN is demonstrated based on OpenDayLight Controller for possible load balancing, interference management and dynamic radio resource sharing [START_REF] Checko | Cloud RAN for mobile networks -a technology overview[END_REF]. One can see that the flexibility, programmability and the single point control of SDN framework can support various objectives in C-RAN especially CoMP, where coordination between multiple BBUs is essential. It can also fit well for providing QoS-based dynamic switching between RRHs and BBUs in C-RAN and for sharing fronthaul network among operators.

Fig. 1 shows C-RAN with SDN controller. Signals are processed in the RRHs and the BBUs dedicated to each cell can communicate between one another inside the BBU-pool. The controller orchestrates data flows from RRHs towards the BBU-pool and inside it via control plane connections. Northbound (NB) applications are in charge of the coordination of specific features. Through the NB interface, they get measures and parameters from the controller and also send commands to the network and BBU-pool.

IV. MULTICELL CENTRALIZED DETECTION

In the previous sections, we have studied C-RAN architecture with its key elements. This framework, by its centralized architecture, enables the execution of multicell joint MMSE detection function for selected users. A NB application of the SDN controller realizes the coordination of this feature by Fig. 2: Physical layer split for fronthaul enabling joint detection for selected users and user-PHY offload. flow routing and signaling. We present the proposed physical layer split to enable joint processing and fronthaul offloading in Fig. 2, where Cell-PHY contains RF processing, cyclic prefix (CP) removal, inverse fast Fourier transform (IFFT) and subcarrier demapping, and User-PHY includes inverse discrete Fourier transform (IDFT), demodulation, and parallel-to-serial conversion and decoding. Data flow routing is realized by the SDN agent in the RRH using information from the NB application on PRBs allocated to JD. For users not involved in the joint detection Cell-and User-PHY are both processed at the RRH, for other users I/Q symbols are forwarded to the BBU-pool to apply joint MMSE detection in order to retrieve QAM symbols sent by each UE.

A. Use case

In case of network congestion (heavy traffic load) in an area supported by several RRHs, severe interference for cell-edge users managed by Coordinated Scheduling would decrease their data rate. The more effective solution to provide reliable high data-rate uplink transmissions is to exploit interference signal from co-channel users through joint detection. We can schedule on the same PRB two interfering users and have their signals received by two RRHs. These received signals are then forwarded to the central processing unit, where we can use both of them to jointly detect the data sent by each user for high performance.

B. Selective joint processing

As expected, in large network, we cannot transmit every users' I/Q symbols to the BBU-pool even if high capacity fronthaul solution can be available. To realize efficient cooperation in C-RAN, we choose critical users who are suffering from high inter-cell interference and forward their I/Q samples to jointly process them in the BBU-pool with the signal of the interfering users. Other users' PHY processing is completed at the RRH and then signal is forwarded, so each one of them uses less than 5% of the fronthaul bandwidth needed for a JD user [START_REF] Institute | C-RAN -the road towards green RAN[END_REF]. This would allow us to target cell-edge users in joint detection and hence improve overall performance.

As stated in [START_REF] Yuan | Rethink fronthaul for soft RAN[END_REF], performing cell-related PHY processing at the BS would allow fronthaul capacity to be load-dependent. This feature is interesting and can be maintained by our design, since the PHY split for the joint detection is at the limit of cell-PHY and user-PHY processing. In addition, our approach makes a further decrease of required fronthaul capacity thanks to the possibility of performing user-PHY processing of nonselected users at the BS.

A difficulty for CoMP JD is joint multi-cell channel estimation at the receiver side. In LTE, cyclic shift is defined to enable multi-user channel estimation [START_REF] Sesia | LTE -The UMTS Long Term Evolution: From Theory to Practice[END_REF], i.e., Demodulation Reference Signals (DMRS) are shifted in order to make them orthogonal between users. Since we schedule only a limited number of users on the same PRB, we can use cyclic shift without being affected by the limitation of its signaling to 3 bits. Pilot symbols of users selected for joint detection need to be transferred as well to estimate their channel conditions to the receiver antennas, but again, for a few users it introduces less overhead than that required for large-scale joint detection.

C. Coordination by a NB application of SDN controller

An application connected to the SDN controller through its NB interface can activate joint detection and optimize user pairing and selection. Depending on applications, the architecture should allow any algorithm to be easily plugged for different optimization. Adaptability to various network dynamics is important. In our design, the SDN controller has access to all system measurements that are stored in the associated database. This allows network applications connected through the NB interface to ask for the measurements needed to run optimization algorithm. When the optimization is done, the controller sends instructions back to the network elements involved to execute.

For the cell coordination and joint detection, we propose the following process that aims at overall cell throughput improvement as well as good QoS for cell-edge users. To begin with, we consider cooperation in pairs of two cells and especially for cell-edge users, while cell-center users can transmit lower power for minimal interference. An adaptation of the proposed process can also be applied to joint detection in more than 2 cells. We perform this optimization regularly when the cell-load, channel or user position changes. For sum-rate and throughput computation, we can have closed-form expressions with respect to given channel link gains.

D. Performance evaluation

We validate the proposed joint processing scheme in two steps. First, we check whether symbols can be accurately detected for the jointly scheduled users. Secondly, we evaluate the throughput improvement in the case where many users are in each cell and jointly detected users are selected between them.

In our first simulation study, we implement a single carrier model where one user in each cell transmits simultaneously towards the receivers (RRHs) who share the received signals for joint detection using multi-cell MMSE. We use LTE urban macro-cell channel model [START_REF] Gpp | Spatial channel model for Multiple Input Multiple Output (MIMO) simulations[END_REF], where 16-QAM modulated symbols are sent. We compare error rate after QAM demodulation without any repeat mechanism. Since our joint detection scheme does not affect user-PHY processing, it is appropriate to evaluate error rate at this point. Fig. 3 shows the error rates in the following cases for comparison: (i) interference-free transmission, (ii) 2-user cooperation, (iii) 3-user cooperation, and (iv) non-cooperative detection.

We see that in the JD cases we need slightly higher transmit power to reach the same error rate as in singleuser transmission, but we transmit on one PRB only instead of using one for each user. This confirms that if frequency resources become scarce, using JD in the BBU-pool enables accurate high-rate transmission on the uplink. We notice also that higher cluster-size requires higher power since meansquare error at detection can increase with the dimension of received signal. It appears also clearly that without cooperation at the receiver side, the SINR is too low to perform accurate detection.

We show in Fig. 4 the overall SNR = i j |hij xi| 2 σ 2 n required for achieving symbol error rate of 10 -1 in joint detection for different cooperation cluster sizes and the improvement of energy efficiency using JD with respect to the case when each user transmits on a different PRB. The number of cooperating RRHs is set equal to the number of interfering users in each joint detection. We observe that per-user transmission power needs to be increased with the size of the cooperation cluster, but the required additional power for adding a user becomes lower as the cluster size increases. Thus, energy efficiency gain increases with cluster size. Note that in general the symbol error rate can be improved by some retransmission and coding schemes for low bit error rate criteria.

As the complexity of the joint MMSE detection scales as O(n 2 ) where n is the number of jointly detected users, we studied the possibility of reducing this complexity by realizing the JD over a subset of the cooperation cluster only. This would allow jointly detected users to benefit from CSI of all co-channel users, but we should deal with interference coming from non-JD users. In addition, it turns out that for users transmitting with the same power and having pathlosses of the same order, overall SINR =

i =k j |hij xi| 2 j |h kj x k | 2 +σ 2 n
does not scale with the transmission power, so JD cannot achieve target error rate unless all co-channel users are jointly detected. Note that to handle potential implementation complexity, one can also consider to distribute the joint MMSE function among BBUs, in a parallelized system implementation.

To evaluate how much the system average throughput and cell-edge throughput are improved by user selective joint detection, in our current work we are implementing system simulations with realistic traffics. By adding a joint scheduling optimization algorithm and joint detection function for selected subcarriers in full-stack LTE base stations, we can simulate a full-load network scenario where we expect system performance improvement.

V. CONCLUSION AND FUTURE WORK

In this paper, we explore C-RAN architecture as an enabler for CoMP, including its limitations and the perspectives for next-generation cellular networks. We investigate the network elements required for C-RAN such as SDN-controller and evolved fronthaul transport. They can greatly facilitate the implementation of uplink cooperation between users, taking into account the practical limitations. The proposed joint detection method satisfies real network constraints and can improve cell throughput and cell-edge QoS.

In the next step of our work, we plan to transfer this implementation to real-time software C-RAN platform, where we can evaluate the benefit of the inter-cell coordination and joint processing as a northbound application with the SDN controller in our testbed. We can also evaluate the impact of adding this joint detection and its actual computation time. The evolution of C-RAN from today's physical BBU centralization towards future SDN-based dynamic configurations is in line with our idea of having a functional split in the physical layer with the possibility of placing user-PHY processing either in the BBU-pool or in the RRH. Benefiting from the possibility of low-latency multi-cell cooperation in C-RAN, it is expected that the proposed approach and user selective uplink joint detection scheme would be important for addressing inter-cell interference problems in future very dense cellular networks.

Fig. 1 :

 1 Fig. 1: C-RAN architecture with SDN controller.

• Step 1 :

 1 Select users on the common edge of cooperating neighboring cells. • Step 2: Pair these users, one from each cell in a pair (see in Fig. 2), by searching among these cell-edge users the sum-rate maximizing pair combination. • Step 3: Select the user pair having the maximum sumrate. • Step 4. If overall cell throughput of both cells increases by scheduling the selected user pair, activate joint detection for this pair. Iterate from Step 3.

Fig. 3 :

 3 Fig. 3: A comparison of the symbol error rates: interferencefree transmission, 2-user joint detection, 3-user joint detection, and non-cooperative detection.

Fig. 4 :

 4 Fig. 4: Required SNR for achieving 10 -1 symbol error rate during the joint detection and improvement of energy efficiency w.r.t. the 1 user/PRB case.

ACKNOWLEDGEMENT

Special thanks to J. Hoydis for precious comments and Y. El Mghazali for discussions and ideas about future networks. This work was supported in part by the 7th Framework Programme for Research of the European Commission HARP project under Grant HARP-318489.