Nouara Benmessaoud

Salah Hamri

Tewfik Bouchaour

Ulrich Maschke

Swelling and thermal behavior of a cross-linked polymer networks poly (2-phenoxyethyl acrylate): exploitation by the Voigt viscoelastic model

Keywords: Cross-linked network, UV photopolymerization, Glass transition temperature, Swelling, Voigt model

The response-ability to the external and internal environmental condition qualifies the smart polymer material to be successfully applied in artificial muscle, drug delivery and water treatment. A three-dimensional polymer network based on the phenyl monomer, 2phenoxy ethyl acrylate (PEA), was polymerized under ultraviolet (UV) radiation using the Darocur 1173 as an initiator of the polymerization reaction, and the 1,6-hexane-diol diacrylate (HDDA) as a chemical cross-linker. The analysis of the thermophysical properties of this elaborated polymeric material represents the main goal of the present work. The infrared spectroscopy (FTIR) and the dynamic scaling calorimetry (DSC) were used to examine, respectively, the vibration of the carbon double bond (C=C) and the glass transition temperature T g . It is found that parameters, the rate of reticulation and monomer composition have a remarkable effect on the variation of T g . The swelling behavior of the cross-linked poly(PEA/ HDDA) was investigated; the effects of solvent nature, the degree of cross-linking, temperature and chemical structure have a significant influence on material swelling properties. The theoretical investigation based, especially on the Voigt model, Flory-Rehner theory and solubility approximation, permits to give much information about several parameters such as the swelling time constant, swelling equilibrium constant, solubility prediction, entropy and enthalpy. It ended interestingly that the Voigt model shows a good agreement with swelling experimental results.

Introduction

Intelligent material has a smart behavior toward the internal and external conditions such as temperature [START_REF] Abdelaty | Environmental functional photo-crosslinked hydrogel bilayer thin films from vanillin (part 2): temperatureresponsive layer A, functional, temperature and pH layer B[END_REF], pH of the medium [START_REF] Tally | Synthesis and characterization of pHsensitive superabsorbent hydro-gels based on sodium alginate-gpoly(acrylic acid-co-acrylamide) obtained via an anionic sur-factant micelle templating under microwave irradiation[END_REF], magnetic and electric field [START_REF] Zhao | In situ synthesis of magnetic field-responsive hemicellulose hydrogels for drug delivery[END_REF][START_REF] Doi | Deformation of ionic polymer gels by electric fields[END_REF]. The investigation of the intelligent comportment of such material was the principle motivation for many researchers and encourages them to invent mechanisms, techniques, experimental and theoretical tools [START_REF] Yang | Analytical methods for polymer characterization[END_REF][START_REF] Ganji | Theoretical description of hydrogel swelling: a review[END_REF].

Among the experimental method, the swelling study permits to analyze the physical properties of substances [START_REF] Mark | Physical properties of polymers handbook[END_REF][START_REF] Treloar | The physics of rubber elasticity[END_REF]. Material with swelling capacity can be used in numerous applications; in drug delivery, the polymer networks can be used to release a medicament after swelling in the stomach; pH in this application was considered as a stimulus [START_REF] Karimi | Chitosan hydrogels crosslinked with tris(2-(2-formylphenoxy) ethyl) amine: swelling and drug delivery[END_REF]. In the oil and gas sector, swelling elastomers have been successfully deployed in zonal isolation where it is used to separate between unwanted and production zones, and this permits to avoid the mixing of redundant fluids. Furthermore, it can be applied to be a partial replacement of cement and to slim the down of wells [START_REF] Qamar | Performance evaluation of water-swelling and oil-swelling elastomers[END_REF]. It helps also to improve the volume of production and the recovery rate of hydrocarbons, thus reducing the impact on the environment. Additionally, the swelling polymer has been widely used for the cleanup of the water surface from organic solvents and petroleum waste [START_REF] Kizil | Oil loving hydrophobic gels made from glycerol propoxylate: efficient and reusable sorbents for oil spill clean-up[END_REF][START_REF] Zhang | Synthesis of MnO 2 /poly(n-butyl-acrylate-co-butyl methacrylate-comethyl methacrylate) hybrid resins for efficient oils and organic solvents absorption[END_REF][START_REF] Hoang | An absorption capacity investigation of new absorbent based on polyurethane foams and rice straw for oil spill cleanup[END_REF].

The phenomenon of swelling of polymer networks is a classical subject of polymer science. Many years ago, Flory and Rehner [START_REF] Flory | Statistical mechanics of cross-linked polymer networks II[END_REF] developed a theory of rubber elasticity, suggesting that the swelling equilibrium is reached when the osmotic pressure of small solvent molecules that promote swelling is balanced by the elastic forces at the cross-links opposing network strand extension. In 1978, Tanaka [START_REF] Tanaka | Collapse of gels and the critical endpoint[END_REF] discovered that polymer gels change volume discontinuously and reversibly in response to external environmental changes such as pH, temperature and solvent composition. Since the discovery of this phenomenon, the study of polymer gels has progressed rapidly.

Recently, Kowalski et al. [START_REF] Kowalski | Synthesis and effect of structure on swelling properties of hydrogels based on high methylated pectin and acrylic polymers[END_REF] studied the effect of the structure on the swelling properties of poly(acrylic acid) high methylated pectin hydrogels which are obtained by free radical polymerization/grafting reaction. It was found that the introduction of a small amount of pectin to the hydrogel increases the swelling capacity, but the further increase in pectin content causes a deterioration of these properties.

Idaat et al. [START_REF] Ida | Effect of monomer sequence along network chains on thermoresponsive properties of polymer gels[END_REF] evaluated the effect of monomer sequence along the network chain of polymer gels on the swelling behavior by utilizing two gel synthetic methods, copolymerization and co-cross-linking. It was found that the swelling measurement of the obtained gels showed totally different behaviors between the copolymerization and the cocross-linking gels.

Bendahma et al. [START_REF] Bendahma | Conformational modeling of the system pollutant/threedimensional poly(2-hydroxyethyl methacrylate) (PHEMA) in aqueous medium: a new approach[END_REF] presented a study about the removal of eosin Y from water; the three-dimensional poly(2-hydroxyethyl methacrylate)-designed poly(HEMA) was used as retention support.

Uptake of water by swelling of hydrogel permits to the pollutant, eosin Y, to be well retained by the porous polymer network poly(HEMA).

In the present work, the polymer network based on an aromatic acrylic monomer was elaborated by the UV light curing technique with many advantages such as the carries out at room temperature, no solvent required and time reduction. The difunctional monomer HDDA was used to cross-link the polymer chains which product a three-dimensional architecture of the elaborated polymer.

To our knowledge of the literature, there is no study of the swelling and determination of thermophysical properties peculiarly for the polymer networks poly(2-phenoxy ethyl acrylate)-designed poly(PEA). The Polymer architecture was varied by two parameters, the degree of reticulation and the degree of copolymerization; the first parameter was increased by the increase in the HDDA cross-linker quantity, whereas the copolymerization was realized by the introduction of another

Experimental part

Materials

The acrylic monomer used in this study is 2-phenoxy ethyl acrylate

Sample preparation and FTIR examination

The elaboration of polymer networks was made by irradiating the mixtures of three basic components (monomer, cross-linker and photoinitiator) using a UV lamp (Philips TL08 type with a wavelength characteristic, λ = 365 nm and intensity of I 0 = 1.5 mW/cm 2 ) in an inert atmosphere, created by a stream of nitrogen gas cir-culating in a quartz chamber that contains the sample holder (a cylindrical Teflon mold).

Fourier transform infrared FTIR spectra were recorded in the range of 4000-600 cm -1 with PerkinElmer Frontier FTIR model spectrometer, in ATR mode, with a spectral resolution of 4 cm -1 . The number of scans accumulated was 16.

The reagent solution was examined by FTIR, before and after

Swelling measurements

To study the swelling kinetic behavior, a cylindrical sample was weighed and immersed in a different solvent at room temperature.

The sample was taken out at regular intervals of time, wiped with a filter paper to remove the free liquid on the surface and then weighted. The degree of swelling is calculated from the following expression 1:

(1

)
where τ (%) is the degree of swelling. m t is the weight of the swollen network at time t. m 0 is the weight of initially dried network.

Theoretical part

The exploitation of the Voigt viscoelastic model allows analyzing efficiently the swelling kinetics results. The Flory-Rehner model permits to determine the phase diagrams of the polymer/solvent mixture.

The thermodynamic parameters especially, the enthalpy, entropy and free energy, were determined by van't Hoff's equation. The solubility calculation predicts the solubility of polymer networks in the chosen solvent.

The Voigt model

The Voigt model is based on Eq. 2 which relates between swelling rate and two important parameters, the swelling time constant and the power parameter.

(

) 2
where Q(t) is the rate of swelling at time t. Q max called the power parameter which measures the resistance to the polymer network expansion and the equilibrium degree of swelling. τ s called the swelling time constant or rate parameter which measures the resistance to solvent diffusion.

Solubility model

It is theoretically possible to predict, approximately the solubility of the polymer in a solvent, as expressed by Eq. 3:

(

) 3
where δ p is the solubility parameter of the polymer and δ s is that of the solvents calculated by the method of Hoftyzer and Van Krevelen (HVK) [START_REF] Van Krevelen | Properties of polymers: correlations with chemical structure[END_REF][START_REF] Barton | CRC handbook of solubility parameters and other cohesion parameters[END_REF] as it is expressed in Eq. 4. The units for these (5)

F and F p are, respectively, the molar attractant constants for the dispersive and polar components. E h is the cohesion energy that describes the contribution of the hydrogen bond, and this parameter is calculated based on the Small method [START_REF] Small | Some factors affecting the solubility of polymers[END_REF]. V is the molar volume of the unit of material.

.

Σ

Phase diagrams

The phase diagrams provide information on the thermodynamic stability of the coexistence phases as a function of temperature and composite. Experimentally, it can be obtained by plotting temperature versus solvent weight fraction (φ S ) which can be calculated from Eq.

8:

(8)

The phase diagrams can be determined by means of the FloryRehner theory.

Flory-Rehner theory

The main hypothesis of this theory is that the change in free energy consists of sepa-rable and additive quantities [START_REF] Flory | Statistical mechanics of cross-linked polymer networks I. Rubber-like elasticity[END_REF]. These are the free energy of mixing ΔG mix and the free energy of elastic strain ΔG el as expressed in Eq. 9:

(9)

In order to determine the phase diagram, the chemical potential which can be obtained from the derivative of the free energy. The chemical potentials [START_REF] Benmouna | Model phase diagrams of binary nematic mixtures. A comparative study between linear and crosslinked polymers[END_REF] of solvent and polymer noted, respectively, μ s and μ p , are defined on Eqs. 10 and 11 as follows:

(10) [START_REF] Kizil | Oil loving hydrophobic gels made from glycerol propoxylate: efficient and reusable sorbents for oil spill clean-up[END_REF] where P is the pressure, T is the absolute temperature, n s and n p are numbers of molecules of solvent and polymers, respectively.

Thermodynamic quantities, ΔH, ΔS, ΔG

In order to calculate the heat of absorption ΔH, the equilibrium absorption constant K s was calculated from considerations of the equilibrium process occurring in the liquid phase at constant temperature and pressure, as expressed on Eq. 15:

(15)

Thus, by realizing the relations between K s and various thermodynamic quantities, enthalpy ΔH and entropy ΔS can be calculated using Eq. 16 of van't Hoff [START_REF] Aithal | Diffusivity, permeability, and sorptivity of aliphatic alcohols through polyurethane membrane at 25, 44, and 60 °C[END_REF].

(

) 16
ΔG values were obtained using the expression 17:

(17)

Results and discussion

Glass transition examination

To examine the glass transition temperature, two parameters will be varied, the degree of cross-linked and the degree of co-monomers.

Influence of the degree of cross-linking

As shown in Fig. 3, the increase in the cross-linker percentage increases the glass transition temperature of a polymer matrix poly(PEA/HDDA). This effect can be explained in terms of the internal mobility of the system. Indeed, the presence of cross-linking points between the polymer chains reduces the overall mobility of the system. Thus, a reduction in the mobility of the molecules leads to an increase in the T g because it requires more thermal energy to cause the movements of the polymer chains. On Fig. 4, the T g increases as the degree of cross-linking increases and seems to be exponential. On Fig. 5, the evolution of the heat capacity ΔC p (related to the glass transition) as a function of the degree of cross-linking is presented. It appears that cross-linking has no significant influence on ΔC p which remains substantially constant. On Fig. 8, the heat capacity decreases slightly as the degree of comonomer (wt% LA) increases.

Influence of the degree of comonomer

Swelling behavior investigation

The effects of the cross-linking agent and copolymerization on the swelling ratio were studied. The swelling time constant and equilibrium degree of swelling are obtained from Eq. 2.

Fig. 9 Kinetics swelling of poly(PEA/HDDA) networks in toluene.

Solid curves are the fit to Eq. 2 Solid curves are the fit to Eq. 2

Effect of the cross-linking agent

The comparative study of the swelling behavior of poly(PEA/HDDA) in two solvents was presented; it is clear from Figs. 9 and 10 that the polymer network low cross-linked has the largest swelling, nature solvent effect shows a remarkable effect; in fact, the polymer network swells highly in toluene and attained a swelling rate about 130%, whereas in MIBK, the swelling rate is registered at 68%. Solubility approximation can be calculated based on Eq. 3, it concluded from Table 1 that toluene is more miscible with the poly(PEA) network than MIBK, which confirms the experimental results of swelling, for the system poly(PEA/0.1% wt HDDA). where C represents the degree of cross-linking of polymer networks (% wt HDDA).

Figure 12 illustrates a power-law relationship between the equilibrium degree of swelling and degree of cross-linker as you can see on Eq. 20:

(

) 20
where a and b are constants for an individual gel, and their values are shown in Table 2. The diffusion of a solvent through a polymer matrix results in the relaxation of the polymer chains previously entangled. Thus, cavities are formed between the cross-linking points allowing mobility and diffusion of the solvent molecules.

However, a highly cross-linked polymer structure will inhibit the transport process more than a low cross-linked polymer network because such chains are more closely bonded together and resist to the increase in the polymer porosity and consequently, increases the diffusion of solvent molecules and the energy required to create such porosity will be important. where C′ represents the ratio of the co-monomer (wt% LA).

Effect of copolymerization

As the degree of lauryl acrylate (wt% LA) increases, the diffusion capacity of the solvent molecules inside the polymer network increases. This returns to two reasons, firstly, the geometric change of networks, i.e., a magnification at the mesh levels. Due secondly to the linear chemical structure of the new introduced monomer, therefore the interaction in the system, solvent/poly(PEA-co-LA), can be varied.

The variation behavior of the equilibrium degree of swelling as a function of the degree of the co-monomer (wt% LA) is illustrated in

The swelling equilibrium increases proportionally with the degree of lauryl acrylate co-monomer (wt% LA). This is due to the internal mobility increases, which 3.

The positive ΔH values obtained for both solvents suggest that the absorption, in this case, is dominated by the Henry model [START_REF] Bamgbose | Equilibrium swelling and kinetic studies of highly swollen chitosan film[END_REF] with endothermic contributions. However, ΔS values are positive.

Table 3 Values of ΔH, ΔS and ΔG of the swelling process

The change in ΔG was obtained using expression 17; the standard Gibbs absorption energy ΔG is positive at room temperature for the poly(PEA)/MIBK system which was an indication of the nonspontaneity of the mixing solubility. In contrast, the negative value of ΔG of the poly(PEA)/toluene system indicates the feasibility and spontaneity of the swelling process.

Conclusions

A cross-linked poly(PEA) was elaborated by facile, cleanest method, the UV photopolymerization technique. Samples were studied by swelling and DSC characterization; the Voigt model was applied to analyze the swelling results.

Based on the differential enthalpy analysis, the increase in the crosslinking degree increases the glass transition temperature of poly(PEA), whereas the copolymerization by an aliphatic monomer decreases the T g temperature. This is due to the internal mobility of the system.

The degree of swelling of poly(PEA) is proportional to the degree of copolymerization by aliphatic lauryl acrylate monomer; this is explained by the exploitation of the Voigt viscoelastic model, and the model shows that the variation in swelling rate follows a power law related to the degree of cross-linking. The inclusion of a small amount of aliphatic lauryl acrylate monomer between the aromatic monomers of the main chains increases both the mobility and the viscosity of the chains; therefore, the degree of swelling is increased.

Analysis of the swelling rates shows that toluene is a good solvent compared to MIBK. Theoretically confirmed by the calculation of the solubility parameter using the model Hoftyzer and Van Krevelen HVK, the solubility of poly(PEA) in toluene and MIBK is, respectively, 2.69 and 8.06.

The thermal study shows that the temperature does not influence the power parameter Q max , but it has an effect on the rise to reach the plateau at equilibrium swelling.

The temperature increases the chain's flexibility of the polymer network, which activates the movement of the solvents molecules; consequently, their diffusion in polymer networks was more quickly.

The variation of τ s as a function of temperature has an exponential form that corresponds well to Arrhenius law.

The free Gibbs energy indicates that ΔG is positive at 20 °C for the poly(PEA)/MIBK system which is an indication of the nonspontaneity of the mixing solubility. The negative value of ΔG of the poly(PEA)/Toluene system indicates the feasibility and spontaneity of the swelling process.

monomer 2 -

 2 photopolymerization under UV radiation.

(

  photopolymerization agent used is 2-hydroxy-2-methyl-1-phenyl-pro-

2 -Fig. 1 Fig. 2

 212 Fig. 1 Chemical structure of the components of the initial mixtures

  MPa) 1/2 . The solubility parameter can be expressed according to the three solubility parameter:[START_REF] Doi | Deformation of ionic polymer gels by electric fields[END_REF] where δ d , δ p and δ h are the Hansen solubility parameters for the dispersion, polar and hydrogen bonding interactions, respectively, which can be estimated from the group contributions using Eqs. 5, 6 and 7:

  Equations 12 and 13 correspond to the chemical potentials of the solvent and the polymer, respectively, obtained from Eqs. 10 and 11: parameters α and β are obtained from Petrovic model, Eq. 14:[27] (14) where α and β represent the network elasticity parameters. f being the functionality of the monomers. k B is the Boltzmann constant. φ S and φ P represent, respectively, the volume fraction of the solvent and the polymer. N c represents the average number of repetitive units at two consecutive cross-linking points. φ 0 is the volume fraction of the polymer network in the reference state (dried network). χ is the interaction parameter of Flory-Huggins.

Fig. 3

 3 Fig. 3 DSC thermograms of polymer networks poly(PEA/HDDA)

Figure 6 Fig. 4 Fig. 5 Fig. 6 Figure 7

 64567 Figure 6 represents the DSC thermograms of different copolymer

Fig. 7 Fig. 8

 78 Fig. 7 Glass transition temperature T g versus (wt% LA)

Fig. 10

 10 Fig. 10 Kinetics swelling of poly(PEA/HDDA) networks in MIBK.

Table1:

  The solubility of poly(PEA) model networks/ solvents. Based on Eq. 2, the experimental data permit to determine the τ s and Q max values. A good correlation is noted between theoretical and experimental data justified by the value of the coefficient of determination, R 2 ≈ 0.99 for all curves. The variation of the swelling time constant τ s as a function of the degree of cross-linking (wt% HDDA) is shown in Fig. 11. The linear relationship is determined and expressed in Eqs. 18 and 19 which relate between the two previous parameters, for the solvents, toluene and MIBK, respectively:

Fig. 11 Fig. 12 Table 2 :

 11122 Fig. 11 Swelling time constant (τ s ) versus (wt% HDDA). Lines are

Figures 13 and 14 Fig. 13 2 Fig. 14

 1413214 Figures 13 and 14 show the influence of the copolymerization rate on

Fig. 16 .Fig. 16

 1616 Fig. 16. Equations 23 and 24 express the linear relationship found

Fig. 17 2 Fig. 18

 17218 Fig.[START_REF] Ida | Effect of monomer sequence along network chains on thermoresponsive properties of polymer gels[END_REF] Thermal effect on the kinetics swelling of poly(PEA/0.1wt%

Figure 20 Fig. 19 Fig. 20

 201920 Figure 20 illustrates the variations of the temperature as a function of

Acknowledgements

The authors gratefully acknowledge the support of the Algerian Ministry of Higher Education and Scientific Research MESRS and the French Ministry of Higher Education, Research and Innovation MESRI.

Affiliations


I Benammar
email: benammar.ikram@yahoo.fr

R Salhi

J.-L Deschanvres

R Maalej

The effect of rare earth element (Er, Yb) doping and heat treatment on suspension stability of Y2O3 nanoparticles elaborated by sol-gel method

Keywords: Y2O3, rare earth, nanoparticles, suspension, Hamaker 2 program. I

    The effect of rare earth element (Er, Yb) doping and heat treatment on suspension stability of Y2O3 nanoparticles elaborated by sol-gel method I. Benammar, R. Salhi, J.-L. Deschanvres, R.

Introduction

The new light emitting materials have received a lot of attention in recent decades for their versatile applications in optical fibre amplifiers, lasers, waveguides, X-ray imaging, bioimaging, electroluminescent emission field [START_REF] Blasse | Luminescent Materials[END_REF][START_REF] Justel | [END_REF]3,4,5,6,7,8,9] and the application of solar energy [START_REF] Blasse | Luminescent Materials[END_REF][START_REF] Justel | [END_REF]. Considerable research activity is underway to explore the new luminescent materials, to improve their chemical stability, and to adapt the chemistry of their materials for the production of the technology for each application. To produce optically active components, some materials are doped with metal ions and with levels rarely exceeding a few atomic percent.

The doping nature fixes many of the component parameters. In particular, the rare earths ions incorporated in high refractive index media allow the improvement of luminescence in the photovoltaic application [5]. Rare earth elements are widely used because of their large transitions numbers [10,11], covering a spectral range extending from near ultraviolet to infrared [12,13,14,15]. They also possess a spectral insensitivity to the matrix into which they are introduced. For example, an erbium-doped crystal or glass always appears pink [16,17].

Transition metals do not exhibit this stability. Thus chromium gives the red color to alumina (ruby) and the green to silica.

Among the various doped oxide with luminescent lanthanide ions, we are also interested to yttrium oxide. Yttrium oxide, assimilated to the family of rare earth oxides because of the strong similarities on the outer electronic layers between yttrium and lanthanides, brings together several very interesting characteristics that fully justify its study: high point melting point (2450°C) [18], high free energy formation [19], excellent dielectric properties (kY2O3 ≈ 12-18) [20] and optical properties (high refractive index n = 1.9) [21], host matrix for metal nanoparticles [22], photoluminescence when doped with other rare earths [23], good resistance for ions irradiation [24]. The physical properties of these materials can be strongly modified by changing their composition or by introducing defects. The doping of yttrium oxide with other rare earths leads, for example, to a modification of the optical properties (photoemission) [25].

The ionic conduction properties can also be considerably increased by creating and by stabilizing the disorder on the oxygen vacancies [26]. The quality of the powders is crucial for the production of high performance ceramics. The powders must have a high purity, a fine grain size, a narrow size distribution and a good dispersion. However, the particles at the nanoscale tend to agglomerate because of their larger surfaces, which affects the frittability of the powder and the ceramic properties.

The suspending is an important step for the photovoltaic application to fabricate nanostructured thin films. Indeed, the formation of a dense and homogeneous deposit and/or the incorporation of Y2O3 nanoparticles into pores are possible only from a stable suspension [27].

From theoretical studies, the sedimentation rate is due to the possible collisions, which occur between nanoparticles, and to their concentration. Derjaguin, Verway, Landau and Overbeek (DVLO) [28,29] have introduced a theory that the nanoparticles stability is due to the combination of the Van der Waals force (attractive) and double layer strength (repulsive). Some procedures are used to stabilize nanoparticles as: ultrasonic vibration; surfactants; pH variation of the base particles, which influences the Zeta potential around the nanoparticles, as described by Sharma et al. [30] and Ghadimi et al. [31].

As their name suggests, dispersants have the function of maintaining an homogeneous dispersion of the various solid particles, in suspension, avoiding the formation of particle aggregates, possibly leading to the separation of liquid and solid phases (sedimentation) [32].

Dispersants fulfil their role by adsorbing on the particles surface, creating additional repulsive forces between particles. Some dispersants act primarily by electrostatic repulsion while others prevent NPs from approaching each other by steric repulsion. These stabilization mechanisms are seen in previous studies [27].

Taking the above in consideration, in the present study, we have focused to the synthesis of doped and undoped Y2O3 nanopowder by sol-gel method and its characterization. Then, preparation of doped and undoped Y2O3 liquid suspensions using the ultrasonic agitation for use in coating preparation. The effect of RE dopant element, solvents and heat treatment to enhance the stability of the suspension were determined.

II.

Experimental Procedure

Sample Synthesis

The preparation of doped and undoped Y2O3 nanoparticles with Er and/or Yb is based in two steps: the preparation of yttria solution and the drying in supercritical condition of ethanol. For the preparation of yttrium oxide (Y2O3), a precise mass of yttrium acetate ([C5H7O2]3•xH2O, Sigma-Aldrich) is dissolved in ethanol. Then, a well-defined volume of methanol (solvent) and acetic acid (catalyst) was added. In situ production of water is formed by esterification reaction between acetic acid and methanol. To prepare a doped solution, a specific percentage of erbium (III) nitrate pentahydrate (Er(NO3)3.5H2O, Sigma-Aldrich) and ytterbium nitrate pentahydrate (Yb(NO3)3.5H2O, Sigma-Aldrich) as lanthanide precursors was mixed with the solution. Each solution was stirred magnetically for 30 minutes. The solution obtained was then placed in an autoclave heated up to 243°C and pressurized to overcome the critical point of ethanol (Tc = 243°C, Pc = 63 bar). After maintaining the temperature at 243°C for 1h, the sol gelation occurred. To evacuate the interstitial solvent, depressurization for 1h down to room temperature was conducted with nitrogen gas. Finally, after cooling of the autoclave at room temperature, a very fine powder was recovered and annealed at 500 °C and 800°C for 2h.

Preparation of nanoparticles suspension

According to preliminary studies, 0.05g/100ml was chosen as the optimal concentration for the elaborated nanoparticles dispersion. For this aim, a mother solution consists to mix 0.05 g of doped and undoped Y2O3 with 100 ml of distilled water or 100 ml of ethanol or methanol. All prepared suspensions were then stirred magnetically for 24 hours to disagglomerate the aggregates of the nanoparticles. In order to promote disagglomeration [33] and to form homogenous dispersions before any tests, ultrasonication was applied for 1h. The ultrasonic exposure time has been optimized in previous studies [27].

Characterizations

The thermal properties of the Y2O3 nanopowders were performed using a simultaneous thermal analyser (Setaram SETSYS Evolution 1750) by heating to 1300°C at a heating rate of 10°C/min (20°C/min in descent) in air. The structural properties of the samples are determined by using Siemens D8 θ/2θ diffractometer (XRD) with CuKα radiation (λ = 1.54Å). The X-ray diffraction patterns were acquired over the 2θ range from 20° to 90° at a sampling width of 0.05°. The morphology and chemical composition of the doped and undoped Y2O3 nanoparticles was examined by field-emission scanning electron microscope (FE-SEM, Philips XL 30) using an accelerating voltage of 20 keV.

The stability of doped and undoped yttrium oxide suspension was estimated from the variation of its optical absorbance using UV/vis Perkin Elmer Lambda 950 spectrometer operating from 250 to 1400 nm. Zeta potential measurements and particle size distribution of the doped and undoped Y2O3 suspensions elaborated in different solvents was studied using a zeta potential analyzer DTS 1060 C model clear disposable zeta cell (Malvern Instruments). The interparticle interactions of these nanoparticles suspensions was determined using the Hamaker 2.2 software.

III. Results and discussion

Characterization of Y2O3 Nanoparticles

In order to estimate beforehand the calcination temperature allowing to obtain a well crystallized oxide, the nanopowders of Y2O3 were analyzed by the TG-DTA analysis and the results for the Y2O3 nanoparticles are presented in Figure 1. The TG curves for the Y2O3 nanopowders show a weight loss in three stages between 20 and 300°C, from 350 to 500°C and from 500 to 772°C, respectively. The recorded weight loss is characterized by two endothermic peaks of the ATD curve which could be attributed to the loss of water molecules and the partial decomposition of the adsorbed solvents inducing the dehydration of the sample [34]. At temperatures between 350 and 500°C, the weight loss is assigned to the decomposition of the acetate groups and the oxidative decomposition of the organic matter which has according to the ATD curve two exothermic peaks. At temperatures between 500 and 772°C, the weight loss could be attributed to the combustion of organic substances bonded to nanopowders [35] resulting in an exothermic process as detected in corresponding DTA curve. The last region exceeds 772°C and shows no loss of mass and no peak indicating the complete formation of cubic particles of yttria and the crystallization of elaborated nanopowders: it is the thermal stability [36]. The ATG and ATD curve of yttria shows a thermal stability from 750°C and confirms a good stability of the prepared material so this temperature is taken for the annealing of the sample and becomes well crystallized.

The XRD pattern of Y2O3 nanopowder annealed at different temperatures 500°C and 800°C for 2 h are shown in Fig. 2. Before heat treatment, yttrium oxide nanoparticles remain amorphous but after annealing the crystallinity of the nanopowders improves with the increase of the synthesis temperature. The obvious diffraction peaks of the cubic Y2O3 structure in the range of resolution of XRD were well defined with treatment, which indicated good crystallinity of the synthesized Y2O3 nanopowder annealed at 800°C. In fact, the diffraction peaks at 2θ (degree) of 20.54°, 29.18°, 33.71°, 39.84°, 43.49°, 48.62° and 57.69° were indexed as (211), ( 222), (400), ( 411), (332), ( 440) and (622) planes of the pure cubic phase Y2O3 (PDF n° 72 -0927). The cubic phase of Y2O3 according to the hanawalt method [37] has been characterized by plane (222), ( 400) and (440), the most intense peaks in 29.2, 33.7 and 48.4 diffraction angles, respectively. XRD diagrams of Er and/or Yb doped Y2O3 nanoparticles and treated at 500°C and 800°C for 1h (Fig. 3) revealed that the structure is still pure cubic after doping and that the doping does not affect the yttria matrix structure [38]. Indeed, no additional peaks of the Er2O3 phase or of the Yb2O3 phase for the elaborated nanoparticles thus showing the good incorporation of the Er 3+ and Yb 3+ ions into the Y2O3 matrix during the heat treatments. Yb 3+ and Er 3+ occupy the lattice sites of Y 3+ ions [START_REF] Markose | Proc. of SPIE[END_REF].

The grain sizes of Y2O3 have been calculated using Scherer's equation:

D = K λ/ β cosθ (1)
Where K = 0.9; D represents the crystallite size; λ is the wavelength of Cu (Kα) radiation and β is the corrected half width of the diffraction peak. The average particle size of Y2O3 nanopowder calculated according to Eq. ( 1) is shown in Table 1.

The size of the elaborated yttria nanoparticles annealed at 800°C decreases after the doping that limits the magnification of the nanoparticles size. The photovoltaic application requires the smallest nanometric size to decrease the loss of light.

The morphological characterization of the yttria powder by SEM (Fig. 4) shows that the powder consists of spherical heterogeneous particles. The particles are well separated and their boundaries are clearly visible. These spheres are bubbles of the 500 nm order enriched with small agglomerated grains with a size of about 10 nm, in accordance with the size estimated by the Debye Scherrer equation from the XRD analyses.

Characterization of Y2O3 suspension

The effect of heat treatment, the effect of doping and the effect of solvents will be studied in order to evaluate the suspensions stability of elaborated nanopowders.

a. Effect of solvents on suspension stability

The stability of 5%Er:Y2O3 suspensions at various solvents was measured on the base of the zeta potential. A potential zeta is about at least 30 mV (positive or negative) was normally necessary to acquire a reasonable stability dispersion [START_REF]Zeta Potential: An Introduction in 30 Minutes[END_REF]. Fig. 5 shows the effect of solvents Van der Waals between the nanoparticles. On the other hand, the repulsive force of the suspension, when water is a solvent, is dominant between particles.

b. Effect of the doping on the suspension stability

In order to study the doping influence on the suspension, measurements of absorbance spectra as a function of wavelengths without and with doping of the elaborate nanopowders dispersed in water were performed. According to the Fig. 6, it can be observed that the suspensions of the nanopowders are strongly influenced by the presence of the dopants of rare earth ions Er and/or

Yb. In all the absorbance spectra, it is clear that the suspension of the treated and untreated Er doped Y2O3 nanoparticles, dispersed in in water, has the highest absorbance. This result shows that the doping of Y2O3 nanoparticles with Er promotes the dispersion quality and gives well stabilized and well dispersed solutions. This limits the aggregation of nanoparticles and therefore improves their stability.

Zeta potential is often used as an indicator of the suspension stability. It is clear in Fig. 7 that the aqueous suspension prepared by the Er-doped Y2O3 nanoparticles has the highest zeta potential. In fact, it increases from 37.5 mV for the 5%Er-5%Yb:Y2O3 to 48.1 mV for the 5%Er:Y2O3. This result indicates that the suspension which gives the highest zeta potential in absolute value is therefore the best stable solution which is the suspension prepared with 5%Er:Y2O3. Nevertheless, we also note that there are high zeta potential values that correspond to solutions that are stable during time using water as the solvent. Zeta potential measurements confirm the results obtained with UV-visible spectroscopy. The doping of Y2O3 nanoparticles with Erbium improves suspensions to disagglomerate and remain stable since Y2O3 is a promising host material for Er 3+ and Er2O3 and Y2O3 have the same crystal structures with a very similar constant network, and the trivalent ions Y 3+ and Er 3+ have almost the same ionic radiation [41].

c. Thermal treatment effect of the nanopowders on the suspension

To investigate the effect of heat treatment of powders on the suspension, absorbance measurements as a function of the wavelengths (from 250 nm to 1400 nm) of the raw nanopowders and treated at 500°C and 800°C dispersed in water were performed. The UVvisible spectra illustrated in Fig. 8 show that the absorbance strongly depends on the annealing temperature of the doped and undoped elaborated Y2O3 nanoparticles. Indeed, the intensity of the absorbance band of the raw nanopowders is the highest in all the spectra. Thus, the nanopowders treated at 800°C have the intensity of the weakest absorbance band. The solutions of the treated nanopowders decant quickly compared to the suspensions of untreated powders.

This observation shows that the repulsive forces of the raw Y2O3 suspension are greater than the attraction forces. This confirms that the heat treatment has a negative effect on the stability of the powders suspensions. This result was explained by the increase in grain size during heat treatment of the nanoparticles by increasing the annealing temperature as shown by the XRD analysis. Naturally, more the size of nanoparticles augments more there is possibility of having an agglomeration.

To explain this result, zeta potential measurements have been performed. The zeta potential of different nanoparticles suspensions prepared in water are provided in Fig. 9. It can be seen that the zeta potential decreases with increasing annealing temperature of elaborate nanopowders.

More in details, it increases from 1.59 mV to 47.2 mV for the treated nanoparticles at 800°C and the raw nanoparticles, respectively. The same fall of the zeta potential in all the spectra of the nanopowders was observed. The heat treatment of the elaborate nanopowders negatively influences on the zeta potential and the suspensions stability. These results are confirmed by the results of UV-Visible spectra.

The average size of aggregates increased with increasing annealing temperature. To support this result, the grain size (nanoparticles) of the untreated 5%Er:Y2O3 aqueous suspension and annealed at 500°C and 800°C / 2h was measured by the Zeta Sizer. Fig. 10 shows that the particle size of the nanopowders in suspension decreases as a function of the annealing temperature. The lowest average size intensity distributions were obtained with the aqueous dispersions of the treated nanoparticles. The lowest measured size values were around 2000 to 3000 nm, for nanoparticles in suspension annealed at 500°C and at 800°C for 2 hours, which are higher than the particle size of the untreated powders which is about 700 to 800 nm. The heat treatment of the elaborated nanoparticles improves the agglomeration and rapid decantation of the suspension and the solutions become unstable. This observation is in good agreement with the analysis by UV-Visible spectroscopy and the measurement of the zeta potential.

d. Interparticle potential calculation

The Interparticle interaction calculations were used to predict or explain either the good dispersion or the coagulation of all or part of the suspension. These interactions of repulsive forces and attraction forces are described by the DLVO theory. In this work, Hamaker 2.2 software was used to calculate the potential interaction between particles. Using this program, the interaction potentials can be calculated taking into account Van der Waals, electrostatic interaction and steric interaction in ceramic suspensions [42,43]. Hamaker constant A can be calculated by the following equation Eq. ( 2) [44]:

A= (3/4) KT( 𝜀 𝑚 -𝜀 𝑝 𝜀 𝑚 +𝜀 𝑝 ) 2 + 3ℎ𝜔(𝑛 𝑝 2 -𝑛 𝑚 2 ) 2 16√2(𝑛 𝑝 2 +𝑛 𝑚 2 ) 3/2 (2)
Where h is Planck's constant, h=6.626×10 -34 J s, k is Boltzmann's constant, k=1.381×10 -23 J/K, T is the absolute temperature, T=300K. np and nm are the refractive indexes of particles and medium, respectively. ɛp and ɛm are the dielectric constants of particles and medium, respectively. ω is UV adsorptive frequency, ω=3.0×10 15 s -1 . According to the Fig. 11, it can be noticed that the Er-Yb:Y2O3 nanopowders suspension has a low interparticle potential which results in an important interaction, whereas the nanoparticles agglomerate and the suspension becomes unstable. The Y2O3 and Yb:Y2O3 suspensions are less dispersed since they have lower interactions. Nevertheless, the Er:Y2O3 suspension has high potential, leading to a lower interparticle interaction. This observation indicates that the suspension is homogeneous and well dispersed. While the Er:Y2O3 suspension dispersed in water was the suspension that has the best stability and the most stable solution. These results are in a good agreement with the results of UV-Visible spectroscopy and zeta potential. The Fig. 12 shows that the interparticle potential of suspensions becomes low by increasing the annealing temperature of the Er:Y2O3 nanopowders, indicating that the interaction between the particles becomes more important and high. Therefore, the treated nanopowders could strongly attract and aggregate and their suspensions become unstable. This result confirms our previous studies.

IV.

Conclusion

The host matrix Y2O3 would allow the incorporation of erbium concentration much higher than that of other oxides. In this context, we have been able to develop Y2O3 nanoparticles undoped and doped with Erbium and/or Ytterbium by sol-gel method using the supercritical drying of ethanol. The obtained nanopowders are in spherical form. Thus, they are well crystallized at 800°C/2h in the cubic phase and the dopants are well incorporated without a structural distortion. Then, the nanoparticles are dispersed in various solvents such as water, ethanol and methanol and then sonicated in order to break the agglomerates into small agglomerates and very fine aggregates. Homogeneous and stable solutions were successfully prepared. The 5%Er:Y2O3 suspension in water was well dispersed and demonstrate an excellent stability. The disagglomeration process and the suspensions stability were improved by the doping with Er.

These stable suspensions of undoped and Er and/or doped elaborated Y2O3 nanoparticles will be used for the synthesis of the thin layers on glass or silicon substrates for our photovoltaic application.

(

  figure that the potential value varies depending on the type of used solvent. Indeed, the zeta potential increases by 4.5 mV for the suspension dispersed in methanol to 10.5 mv for the suspension prepared in ethanol and 48.1 mv when the water used as a solvent. The suspension with the highest stability potential is obtained in water. Whereas for the suspensions dispersed in ethanol and methanol are supposed flocculate quickly and agglomerate. Repulsive force is

Fig. 11 and

 11 Fig.11and Fig.12show the interparticle potential of the doped and undoped Y2O3 nanoparticles suspensions and the Er doped Y2O3 nanoparticles suspensions raw and treated at 500°C and 800°C for 2 h dispersed in water, respectively. Taking into account in our previous studies the Er doped Y2O3 nanopowders suspension presents the best solution and it has a good stability.

Figure 1 : 18 Figure 2 : 19 Figure 3 : 20 Figure 4 : 21 Figure 5 : 22 Figure 6 : 23 Figure 7 : 24 Figure 8 : 25 Figure 9 : 26 Figure 10 : 27 Figure 11 : 28 Figure 12 :

 1182193204215226237248259261027112812 Figure 1: Thermogravimetric and thermo-differential analyzes of Y2O3 nanopowders. ......... 18

Figure 1 :Figure 2 :

 12 Figure 1: Thermogravimetric and thermo-differential analyzes of Y2O3 nanopowders.

Figure 3 :

 3 Figure 3: Diffractograms of doped and undoped Y2O3 aerogels and annealing at (a) 500°C and (b) 800°C.

Figure 4 : 3 Figure 5 :Figure 6 : 3 Figure 7 : 3 Figure 8 :Figure 9 :

 435637389 Figure 4: SEM micrograph of Y2O3 nanoparticles.

Figure 10 :Figure 11 :Figure 12 :

 101112 Figure 10: Determined particle size distribution of 5%Er:Y2O3 (a) untreated, (b) T.T 500°C/2h and (c) T.T 800°C/2h.

Table 2

 2

and table 3 list the data used for interparticle potential calculations through Hamaker 2 toolkit.

Table . 1. Particle size (nm) of prepared Y2O3 nanopowder with different concentrations of Er/Yb.

 .

	Sample	d (nm) 500°C	d (nm) 800°C
	Y2O3	10	38
	5%Yb:Y2O3	9	30
	5%Er:Y2O3	8	29
	5%Er-5%Yb:Y2O3	10

Table . 2.Parameters used in the Hamaker 2 calculations for different nanopowders developed dispersed in water.

 .

	Nanopowder (in water)	Y2O3	5%Yb:Y2O3 5%Er:Y2O3	5%Er-5%Yb:Y2O3
	Zeta potential (mV)	47.2	44.8	48.1	37.5
	Zeta plane (nm)	0.5	0.5	0.5	0.5
	Ionic strength (M)	0.001	0.001	0.001	0.001
	Particle density (g/cm 3 )	5.03	5.03	5.03	5.03
	Particle diameter (nm)	9	8	7	9
	Hamaker constant (×10 -19 J)	0.4	0.4	0.4	0.4
	Dielectric constant (water)	80.1	80.1	80.1	80.1
	Refractive index (water)	1.33	1.33	1.33	1.33
	Dielectric constant of powders	18	18	18	18
	Refractive index of powders	1.93	1.93	1.93	1.93

Table . 3. Parameters used in the Hamaker 2 calculations for the aqueous suspension of the Er doped and treated nanoparticles.

 .

	Nanopowder (in water)	Er:Y2O3	Er:Y2O3 T.T 500°C	Er:Y2O3 T.T 800°C
	Zeta potential (mV)	48.1	10.5	4.5
	Zeta plane (nm)	0.5	0.5	0.5
	Ionic strength (M)	0.001	0.001	0.001
	Particle density (g/cm 3 )	5.03	5.03	5.03
	Particle diameter (nm)	7	8	29
	Hamaker constant (×10 -19 J)	0.4	0.4	0.4
	Dielectric constant (water)	80.1	80.1	80.1
	Refractive index (water)	1.33	1.33	1.33
	Dielectric constant of	18	18	18
	powders
	Refractive index of powders	1.93	1.93	1.93