Zhiqiang Yang

Alain Valtz

Christophe Coquelet
email: christophe.coquelet@mines-paristech.fr.

Jiangtao Wu

Jian Lu

Critical properties and vapor-liquid equilibrium of two near-azeotropic mixtures containing HFOs

Keywords: Refrigerant blend, low-GWP alternatives, vapor-liquid equilibrium, critical properties, modeling

come

Introduction

Climate change is one of the biggest challenges facing all humanity. The main driver of climate change is the greenhouse effect caused by a huge amount of greenhouse gas emissions. The dominate refrigerants are mainly hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs), which exhibit high global warming potential (GWP).

The direct emissions of these refrigerants account for about 3% of the total global greenhouse gas emissions [START_REF] Mclinden | New refrigerants and system configurations for vapor-compression refrigeration 1-7[END_REF]. In order to protect the global environment, the international community has signed a series of international conventions such as Montreal Protocol, the Paris Agreement, F-Gas Regulations (European Parliament and The Council of the European Union, 2006), Kigali Agreement (UNEP, 2016), etc., to restrict high GWP refrigerants on a global scale. Reducing greenhouse gas emissions and exploring environmentally friendly refrigerants with low greenhouse effect have become urgent issues facing the refrigeration industry.

3,3,3-trifluoropropene (R1243zf) is one of attractive alternative refrigerants which has been recently proposed to replace R134a in air-conditioning and other applications [START_REF] Lai | Thermodynamic properties of HFO-1243zf and their application in study on a refrigeration cycle[END_REF]. R1243zf has zero ODP, and a remarkably low GWP of 0.29 compared to R134a of 1430 [START_REF] González | Hydroxyl radical reaction rate coefficients as a function of temperature and IR absorption cross sections for CF3CH=CH2 (HFO-1243zf), potential replacement of CF3CH2F (HFC-134a)[END_REF]. Furthermore, R1243zf exhibits similar thermodynamic behavior as R134a. The thermodynamic properties [START_REF] Akasaka | Recent trends in the development of Helmholtz energy equations of state and their application to 3,3,3-trifluoroprop-1-ene (R-1243zf)[END_REF][START_REF] Brown | Saturated pressure measurements of 3,3,3-trifluoroprop-1-ene (R1243zf) for reduced temperatures ranging from 0.62 to 0.98[END_REF][START_REF] Di Nicola | Subcooled liquid density measurements and PvT measurements in the vapor phase for 3,3,3trifluoroprop-1-ene (R1243zf)[END_REF][START_REF] Higashi | Measurements of PvT Properties, Saturated Densities, and Critical Parameters for 3,3,3-Trifluoropropene (HFO1243zf)[END_REF] and cycle performance [START_REF] Brown | Thermophysical properties and heat transfer and pressure drop performance potentials of hydrofluoro-olefins, hydrochlorofluoro-olefins, and their blends[END_REF][START_REF] Lai | Thermodynamic properties of HFO-1243zf and their application in study on a refrigeration cycle[END_REF] of R1243zf have been extensively studied. The selection of refrigerant requires comprehensive consideration of environmental, thermodynamic properties, refrigeration performance, safety, economy and other factors [START_REF] Bobbo | Low GWP halocarbon refrigerants: A review of thermophysical properties[END_REF]. Whereas, taking these factors into consideration, ideal pure refrigerants are almost non-existent because of each pure substance has different degrees of defects [START_REF] Mclinden | Limited options for low-global-warming-potential refrigerants[END_REF]. The defects of R1243zf is flammable, it's assigned as A2L from the ASHRAE classification. The solution to expand the application range of R1243zf is to develop mixed refrigerants, because the components in mixed refrigerants can complement each other. The mixed refrigerant technology provides a way for applications where pure refrigerant cannot meet. For instance, adding HFC compounds to R1234yf such as R-134a, could improve the cooling capacities in one hand and inhibits the flammability on the other [START_REF] Raabe | Molecular simulation studies on the thermophysical properties of the refrigerant blend R-445A[END_REF].

High-temperature heat pumps are one of the effective ways to utilize waste heat, which can reduce energy consumption and carbon dioxide emissions accordingly. The design of subcritical cycle heat pumps depends closely on thermodynamics properties, especially vapor-liquid equilibrium (VLE) and critical properties of mixture, when mixtures are involved in thermodynamics cycle. This work is one of our series of studies [START_REF] Jia | Compressed liquid densities of binary mixtures of difluoromethane (R32) and 2,3,3,3-tetrafluoroprop-1-Ene (R1234yf) at temperatures from (283 to 363) K and pressures up to 100 MPa[END_REF][START_REF] Kou | Experimental measurements and correlation of isothermal vapor-liquid equilibria for HFC-32 + HFO-1234ze (E) and HFC-134a + HFO-1234ze (E) binary systems[END_REF][START_REF] Yang | Phase Equilibria of Difluoromethane (R32), 1,1,1,2-Tetrafluoroethane (R134a), and trans-1,3,3,3-Tetrafluoro-1-propene (R1234ze(E)) Probed by Experimental Measurements and Monte Carlo Simulations[END_REF][START_REF] Yang | Experimental measurement and modelling of vapor-liquid equilibrium for 3,3,3-Trifluoropropene (R1243zf) and trans-1,3,3,3-Tetrafluoropropene (R1234ze(E)) binary system[END_REF][START_REF] Yang | Experimental measurements of saturated vapor pressure and isothermal vapor-liquid equilibria for 1,1,1,2-Tetrafluoroethane (HFC-134a) + 3,3,3-trifluoropropene (HFO-1243zf) binary system[END_REF] alpha function, and combined with van der Waals (vdW) and modified Huron-Vidal second-order (MHV2) mixing rules [START_REF] Dahl | High-pressure vapor-liquid equilibrium with a UNIFAC -based equation of state[END_REF].

Experimental

Materials

The information of samples is summarized in Table 1. The purities of samples are verified by gas chromatographic analysis. All the samples are used without further purification (only degassing). The information of gas chromatography method is described in the Supplementary Information and gas chromatograph conditions are given in Table S1.

Measurement of critical properties

The apparatus of critical properties designed based on static-synthetic method was built by CTP at Mines ParisTech (patent of Mines ParisTech -Armines). The apparatus is used to measure the vapor-liquid coexistence point (temperature, pressure, and saturated density in The loading part is very similar to the work described by [START_REF] Soo | Determination of critical properties of pure and multi-component mixtures using a "dynamic-synthetic[END_REF]. It includes a thermostatic syringe pumps (ISCO, model 260D), a variable volumetric cell, and pressure resource (compressed nitrogen). The variable volumetric cell is specially designed to prepare the mixture, and the syringe pump is used to store the synthesized mixture and deliver them to the optical cell. The body of syringe pump is surrounded with an external jacket within which tap water thermally regulates and maintains the pump contents at room temperature. The syringe pump has two control modes: constant flow rate and constant pressure. The latter mode is utilized to load components into the optical cell.

The core unit of the measuring part is the optical cell which is self-developed by CTP and consists of top flange, bottom flange, and sapphire tube. The sapphire tube and two flanges are sealed with golden O ring. The operating temperature and pressure limits of the optical cell are up to 493 K and 20 MPa. The inner volume of the optical cell is calibrated by filling it with ethanol at room temperature, and the calibration value was 12.915 ± 0.014 cm3.

The optical cell is installed in a visual air thermostatic oven (AT) with temperature fluctuation less than 0.1 K. In order to enhance the visibility of the vapor-liquid interface and critical opalescence, a light source is installed in the air thermostatic oven. The volume variation of the optical cell caused by temperature and pressure is negligible, and detailed information for the volume variation can be found in the Appendix SC of Supplementary Information .

The temperature in the optical cell is measured by using a 100 Ohm platinum resistance thermometer probe which extends down along the central axis of the sapphire tube from the top flange. Another two platinum probes are inserted into the top flange and the bottom flange, respectively, to monitor the temperature gradient between the top and bottom of the optical cell. The pressure of the optical cell is measured by using two pressure transducers (DRUCK, Model PTX611), one connected to the top flange, the other connected to the bottom flange.

The two pressure transducers are maintained at a constant temperature of 373 K using a heating cartridge regulated by a PID regulator (WEST, Model 6100). Another pressure transducer (DRUCK, Model PTX611) is used for measuring the pressure of loading line. The signals from the temperature probes and pressure transducers are recorded by a computer linked to a data acquisition unit (Agilent; HP34970A). The temperature probes, pressure sensors, and volume of the critical cell are well calibrated before measurement, and the information of calibration is described in Supplementary Information. The uncertainty of temperature, pressure and density measurement is carefully analyzed, and the information of uncertainty analysis can be found in Appendix SA in Supplementary Information. The extended uncertainties (k=2) are estimated as U(T) = 0.06 K, U(p) = 0.001 MPa, and U(ρ) = 6.4 kg/m 3 for critical property measurement. The mixture is prepared in the variable volumetric cell and the concentration of the synthesized mixture can be accurately determined by weighing on a balance (Mettler Toledo, model XP2004S), as illustrated in Figure 2. Then the mixture is compressed and transferred to the syringe pump.

The transfer of sample is carried out in the monophasic liquid state at elevated pressures.

Before loading the sample into the optical cell, the sample is compressed again to monophasic liquid and maintained at high pressure for a sufficient amount of time. Such a loading process ensures the composition of the sample remains unchanged. Since the pressure, temperature, and composition of the sample remain unchanged during the loading process, the mass of loaded sample is equal to the compressed density of the sample multiplied by the volume change of the syringe pump. The saturated density (vapor or liquid phase) is calculated by Eq. For the calculation of saturated density of mixture, Eq. ( 1) is modified as:

(2) where and are the compressed liquid density of components 1 and 2 at loading temperature and pressure; x 1 and x 2 are mole fraction of components 1 and 2.

The mole fraction of each component is determined by Eq. (3)

(3)

Where m 1 and m 2 are the mass of components 1 and 2 loaded into the variable volumetric cell, and M 1 and M 2 are their corresponding molar mass. The components mass (m 1 and m 2 ) are measured by the Mettler Toledo balance, and the accuracy of mass measurement is less than ±0.1 mg. The uncertainty of mole fraction is calculated by following Eq. ( 4):

(4) Where g.

The experimental procedure of critical properties measurement is described in Supplementary information. Transition of the measuring sample from subcritical to the critical state on density increase is shown in Figure 3. For each measurement, the temperature-increasing and temperature-decreasing processes are repeated several times.

Measurement of vapor liquid equilibrium

The vapor liquid equilibrium (VLE) is measured by a PVT apparatus which has been designed to allow simultaneous determination of bubble pressure through pressure versus volume measurements. The principle of measurement is based on the static-synthetic method which is the same as the previous literature presented by our laboratory [START_REF] Coquelet | Vapour-liquid equilibrium measurements and correlation of the difluoromethane (R32) + propane (R290) + 1,1,1,2,3,3,3-heptafluoropropane ([END_REF][START_REF] Meskel-Lesavre | Bubble Pressures and Liquid Molar Volumes of the System Chlorotrifluoromethane-1,1,2-Trichlorotrifluoroethane[END_REF][START_REF] Rousseaux | A static method for determination of vapour-liquid equilibria and saturated liquid molar volumes at high pressures and temperatures using a new variable-volume cell[END_REF]Meekel-leeavre et al., 1981). The version of the apparatus used by [START_REF] Valtz | Bubble pressures and saturated liquid molar volumes of difluoromonochloromethane-fluorochloroethane binary mixtures: experimental data and modelling[END_REF]

Modeling

modeling of critical point

For the critical point measurement, whatever dynamic method or static method was utilized, the critical point was normally determined in consideration of the meniscus disappearing level as well as the intensity of critical opalescence, such a criteria can be found in the open literature [START_REF] Higashi | Measurements of PρT properties, vapor pressures, saturated densities, and critical parameters for R 1234ze(Z) and R 245fa[END_REF][START_REF] Akasaka | Measurements of saturated densities and critical parameters for the binary mixture of 2,3,3,3-tetrafluoropropene (R-1234yf) + difluoromethane (R-32)[END_REF][START_REF] Soo | Determination of critical properties of pure and multi-component mixtures using a "dynamic-synthetic[END_REF][START_REF] Juntarachat | Validation of a new apparatus using the dynamic and static methods for determining the critical properties of pure components and mixtures[END_REF]. Different with current visual method, we present a new modeling method that determined the critical point via modeling vapor-liquid coexistence points to the combined equations of the asymptotic law and rectilinear diameters law.

Close to the critical point, fluid exhibit large density fluctuation, and the phase behavior is determined by the size and nature of fluctuation rather than by the particular feathers of the molecular interaction. The phase behavior exhibits universal critical exponents for all fluid in the vicinity of the critical point, which is also called the scaling law or the asymptotic law behavior.

The temperature versus density curve exhibits critical exponent relationship for all pure or mixed systems:

(5)

Where is a characteristic universal exponent, is critical temperature, and represent saturated density at vapor and liquid phase, and parameter B is a substance dependence constant.

It is also assumed that saturated densities of the coexisting liquid and vapor obey the so-called law of rectilinear diameters:

(6)

Combining Eq. ( 5) with Eq. ( 6), saturated liquid density ρ L and saturated vapor density ρ V can be expressed as:

(7) (8)
These equations were previously used by [START_REF] Coquelet | Experimental measurement of vapor pressures and densities of pure hexafluoropropylene[END_REF] for the modeling of the volumetric properties of hexafluoropropane at saturation and close to its critical point.

Besides, in the critical region, the change of density with pressure obeys following critical exponent principle of the scaling law:

(9)

Where the +sign refer to density versus pressure curve in the liquid phase, while -sign refer to density versus pressure curve in the vapor phase. Parameters C and D are substance dependence constant, is a characteristic universal exponent.

By separating Eq. ( 9) into two ranges, ρ L and ρ V can be expressed as following equations:

(10)

For an investigated pure or mixture system, the vapor-liquid coexistence curve in critical region should satisfy the equations of ( 7), ( 8), ( 10

At least eight data points (four in vapor phase, and four in liquid phase in the vicinity of the critical point) are used for the critical property regression.

modeling of vapor liquid equilibrium

The experimental bubble pressures were modeling using the Peng-Robinson [START_REF] Peng | A New Two-Constant Equation of State[END_REF]) equation of state (PR78 EoS) associating with Mathias-Copeman (MC) alpha function [START_REF] Mathias | Extension of the Peng-Robinson equation of state to complex mixtures: Evaluation of the various forms of the local composition concept[END_REF]. The classical van der Waal one fluid mixing rules and one of excess Gibbs energy (g E ) mixing rules, namely modified Huron-Vidal second-order mixing rules (MHV2) [START_REF] Dahl | High-pressure vapor-liquid equilibrium with a UNIFAC -based equation of state[END_REF], are employed to describe the VLE behavior of mixture. The NRTL model [START_REF] Renon | Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures[END_REF]) is used to calculate g E in the MHV2 mixing rule. Actually, any activity coefficient model, for instances NRTL, Wilson, or UNIFAC, can be used to calculate g E . The binary interaction parameters of the NRTL model are treated as regressed parameters for the VLE correlation. The PR-MC-vdW and PR-MC-MHV2 models applied in this work have been described in our previous publications, more details about this model can be found in Appendix SB of Supplementary Information or in references [START_REF] Yang | Experimental measurement and modelling of vapor-liquid equilibrium for 3,3,3-Trifluoropropene (R1243zf) and trans-1,3,3,3-Tetrafluoropropene (R1234ze(E)) binary system[END_REF]. The binary interaction parameter k ij of vdW mixing rule and interaction energy parameters and of NRTL equation are determined by fitting bubble pressure to the following Objective Function (Eq.13):

(13)

The Critical properties and coefficients of Mathias-Copeman alpha function used in this work are listed in Table 2. The Critical properties of R1243zf, R1234yf are taken from REFPROP 10.0 [START_REF] Lemmon | NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP)[END_REF] and that of R245cb are taken from [START_REF] Weber | Vapor Pressure of 1 , 1 , 1 , 2 , 2-Pentafluoropropane[END_REF]. The Mathias-Copeman alpha function coefficients (m 1, m 2, and m 3 ) for R1243zf, R1234yf and R245cb are taken from our previous work [START_REF] Valtz | Experimental measurements and modelling of vapour-liquid Mesures expérimentales et modélisation de l ' équilibre vapeur-liquide du système[END_REF]Yang et al., 2020).

Results and discussion

Vapor-liquid coexistence curves

The vapor-liquid coexistence curves of pure R1243zf, R1234yf + R1243zf and R1243zf + R245cb binaries are measured by observing the meniscus and critical opalescence. The experimental results are presented in Tables 3 andTables 5-8. Symbol T, p, and ρ represent temperature, pressure, and density, respectively; n is the number of repeated measurements; and are the uncertainties of repeatability for temperature and pressure measurement respectively, which represent the measurement errors caused by visual observation.

The critical point can be determined through two methods by using the static-synthetic apparatus. The first one is the visual method [START_REF] Akasaka | Measurements of saturated densities and critical parameters for the binary mixture of 2,3,3,3-tetrafluoropropene (R-1234yf) + difluoromethane (R-32)[END_REF][START_REF] Higashi | Measurements of PρT properties, vapor pressures, saturated densities, and critical parameters for R 1234ze(Z) and R 245fa[END_REF][START_REF] Juntarachat | Validation of a new apparatus using the dynamic and static methods for determining the critical properties of pure components and mixtures[END_REF]. If the sample of the desired mass is loaded into the optical cell at critical density, the critical point can be determined by visual observation. The second one is the proposed modeling method which determined the critical point by modelling the vapor -liquid coexistence points to the combined equations of the asymptotic law and rectilinear diameters law. For the measurement of R1243zf, both two methods are utilized to determine the critical point. Seven densities in vapor-phase and eight densities in liquid-phase are obtained in the temperature range from 371.79 to 376.93 K as listed in Table 3. The critical opalescence is observed at three densities of 379.3, 419.6, and 451.5 kg/m 3 (marked with an asterisk in Table 3). At the densities of 379.3 and 451.5 kg/m 3 , critical opalescence occurs only in the vapor or liquid phase, but at density of 419.6 kg/m 3 the critical opalescence is observed simultaneously in both vapor and liquid phases, and the intensity of critical opalescence is the strongest compare with the other densities. According to the criteria of visual method [START_REF] Akasaka | Measurements of saturated densities and critical parameters for the binary mixture of 2,3,3,3-tetrafluoropropene (R-1234yf) + difluoromethane (R-32)[END_REF][START_REF] Higashi | Measurements of PρT properties, vapor pressures, saturated densities, and critical parameters for R 1234ze(Z) and R 245fa[END_REF][START_REF] Juntarachat | Validation of a new apparatus using the dynamic and static methods for determining the critical properties of pure components and mixtures[END_REF][START_REF] Soo | Determination of critical properties of pure and multi-component mixtures using a "dynamic-synthetic[END_REF], the density of 419.6 kg/m 3 is considered to be very close to the critical density. Finally, the critical properties of R1243zf are determined to be T c = 376.50 K, P c = 3.517 MPa, and ρ c = 419.6 kg/m 3 based on the visual method.

By contrast, the saturated densities of R1243zf are correlated to the combined equations of the asymptotic law and rectilinear diameters law by proposed modeling method. The critical properties T c , p c , and ρ c of R1243zf are treated as adjusted parameters, and the optimal values are found to be 376.66 K, 3.518 MPa, and 419.0 kg/m 3 . The experimental data and modeling results are also shown in Fig. 5. The critical properties determined by the modeling method are quite agreed with those determined by the visual method. Obtaining the critical density by visual method requires multiple adjustments of the sample mass loaded into the critical cell, which is a time-consuming process. The advantage of the proposed modeling method is that it provides a way to accurately determine the critical point and avoids the time-consuming process. Thus, in this work, the critical properties of investigated systems are taken from the modeling method rather than the visual method. 2013), and present ρ c by the group contribution method. Therefore, these data resources are taken less consideration. The T c of this work is consistent with that of [START_REF] Higashi | Measurements of PvT Properties, Saturated Densities, and Critical Parameters for 3,3,3-Trifluoropropene (HFO1243zf)[END_REF] and the value of REFPROP 10.0 [START_REF] Lemmon | NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP)[END_REF], while the reported T c of Daubert et al. [START_REF] Daubert | Vapor pressure of 18 pure industrial chemicals[END_REF]) is higher than other's. The p c of this work is very agree with that of [START_REF] Higashi | Measurements of PvT Properties, Saturated Densities, and Critical Parameters for 3,3,3-Trifluoropropene (HFO1243zf)[END_REF] For the critical point measurement of mixture, the measurement procedure is quite similar to that of pure R1243zf. The difference is that the mixture needs to be prepared and loaded (keep the composition unchanged) into the optical cell and the selection of the right pressure transducer for measurement of vapor or liquid phase densities. The R1243zf + R1234yf binary mixture is prepared at three different mole fractions of 0.2774, 0.4954, and 0.7509, and the R1243zf + R245cb binary is prepared at mole fraction of 0.4971.

The critical point of mixture is not determined by the visual method but the modeling method. The vapor-liquid coexistence curves of R1243zf (1) + R1234yf (2) binary at three mole fractions were measured in temperature range of 363.24 to 373.97 K as summarized in

Tables 567, and the experimental temperatures, pressures, and saturated densities are correlated to the combined equations of the asymptotic law and rectilinear diameters law. The determined T c , p c , and ρ c of R1243zf (1) + R1234yf (2) binary for each composition is listed in Table 10. For each composition, sixteen saturated densities were obtained. The critical opalescence is observed at the densities marked with asterisks. (2) binary show parallel lines in the experimental range, but in theory, it will intersect somewhere. The regressed critical points are almost at the maximum for the T -ρ or p -ρ curves. However, it is not the case for the p -ρ curve on mole fraction of 0.4954. At the densities of 411.2 and 439.8 kg•m -³, their pressure deviations on repeated measurement are 0.012 and 0.013 MPa respectively, resulting in big errors with the modeling p -ρ curve.

Therefore, for this p -ρ curve, the critical pressure lower than the maximum pressure is caused by the error of pressure measurement. Besides, the pure R1243zf p -ρ curve of this work does not well agreed with that of REFPROP 10.0, more experimental data are needed to verify the experimental results.

The critical properties of the R1243zf (1) + R1234yf (2) binary mixture is correlated using the Redlich-Kister type equation as following Eqns. ( 14), ( 15) and ( 16). The critical properties T c , p c , and of the binary mixture can be regarded as the sum of ideal contributions (the first two terms) and non-ideal contribution (summation term).

(

) (15) 14
where T c,mix , p c,mix , and are the critical temperature, pressure, and density of the binary mixture; T c,i , p c,i , and are the critical temperature, pressure, and density for pure component i; n is the number of coefficients, n=3; a j , b j and c j are the empirical coefficients which are determined by minimizing the relative mean standard deviation (RMSD):

(17

)
where M = T c or p c, and N is the number of data points.

The experimental and correlated binary critical properties T c , p c , and are plotted in Figure 7. The coefficients for each binary system are listed in Table 9. The vapor-liquid coexistence curve of R1243zf (1) + R245cb (2) binary system was measured with mole fraction of 0.4971. Experimental data are summarized in Table 8. Six densities in vapor-phase and four densities in liquid-phase were obtained in the temperature range of 369.54 -377.36 K. The determined T c , p c , and of R1243zf (1) + R245cb (2)

binary system are lists in Table 10. The T -ρ curve and p -ρ curve of R1243zf (1) + R245cb

(2) binary system along with that of pure R1243zf and R245cb are shown in (kg/m 3 )

x 1 coexistence curve for pure R245cb. Therefore, we use literature data to observe the relationship of the critical properties and the composition for R1243zf (1) + R245cb (2) binary system.

To our knowledge, [START_REF] Shank | Thermodynamic properties of 1,1,1,2,2-pentafluoropropane (refrigerant 245)[END_REF] presented critical parameters and saturated properties of R245cb in 1967. The critical properties (T c =380.11 K, p c = 3.137 MPa, and = 498.8 kg/m 3 ) were determined graphically from large-scale plots of P-V-T data, and the saturated liquid and vapor densities were generated from BWR equation of state. [START_REF] Weber | Vapor Pressure of 1 , 1 , 1 , 2 , 2-Pentafluoropropane[END_REF] presented vapour pressure of R245cb in 1996, and they used T c =380.38 K and = 498.8 kg/m 3 for regression of vapour pressure equation. Those critical parameters of R245cb

were private communicated with Schmidt, NIST in 1995. [START_REF] Defibaugh | Compressed and saturated liquid densities for 18 halogenated organic compounds[END_REF] presented saturated liquid density equations of R245cb in 1997, and they also adopted Schmidt's critical parameters for data regression. Therefore, T c =380.38 K and = 498.8 kg/m 3 from Schmidt's critical parameters, and p c = 3.1483 MPa from Weber's Wagner equation [START_REF] Weber | Vapor Pressure of 1 , 1 , 1 , 2 , 2-Pentafluoropropane[END_REF] are utilized in this work. The generated saturated densities in critical region (3 in vapor phase, and 3 in liquid phase) of [START_REF] Shank | Thermodynamic properties of 1,1,1,2,2-pentafluoropropane (refrigerant 245)[END_REF] are agree with saturated liquid density equation of [START_REF] Defibaugh | Compressed and saturated liquid densities for 18 halogenated organic compounds[END_REF] as displayed in Fig. 8. Hence, those two data sets are utilized as well. However, it is difficult to observe the relationship between the critical parameters and the molar fraction for the R1243zf (1) + R245cb (2) system due to the lack of enough data for the mixture. [START_REF] Weber | Vapor Pressure of 1 , 1 , 1 , 2 , 2-Pentafluoropropane[END_REF] [START_REF] Defibaugh | Compressed and saturated liquid densities for 18 halogenated organic compounds[END_REF]; (○): generated saturated density of R245cb from BWR equation [START_REF] Shank | Thermodynamic properties of 1,1,1,2,2-pentafluoropropane (refrigerant 245)[END_REF]. solid lines: combined equations of asymptotic law behavior and rectilinear diameters law; dash lines: saturated liquid density of R245cb from [START_REF] Defibaugh | Compressed and saturated liquid densities for 18 halogenated organic compounds[END_REF]; Table 9. The Redlich-Kister constants for Eqns. ( 14), ( 15) and ( 16) for the R1243zf+R1234yf binary mixtures in this work.

System

Regressed constants

R1243zf+R1234yf

Eq. ( 14) a 1 /K a 2 /K a 3 /K -2.606 0.894 -2.234 Eq. ( 15) b 1 /MPa b 2 /MPa b 3 /MPa 0.008 -0.017 -0.019 Eq. ( 16) c 1 /kg m -3 c 2 /kg m -3 c 3 /kg m -3 -2.61×10 -4 -1.78×10 -4 4.97×10 -4

Table 10. The correlated critical properties and constants of investigated systems from the combined equations of asymptotic law behavior and rectilinear diameters law.

x 1 ρ c / kg•m -3 T c /K p c /

Vapor liquid equilibrium

Saturated vapor pressures of pure R1243zf, R1234yf, and R245cb were measured by using PVT apparatus at four temperatures of 293.45, 313.47, 333.46, and 353.55 K. The results are presented in Table 11. The vapor pressure of the three pure compounds was obtained from the break point of P-V T curve. The vapor pressures of R1243zf and R1234yf were compared with calculated values of REFPROP 10.0, and the vapor pressures of R245cb were compared with vapor pressure equation of [START_REF] Valtz | Experimental measurements and modelling of vapour-liquid Mesures expérimentales et modélisation de l ' équilibre vapeur-liquide du système[END_REF]. The absolute deviations (Δp) between measured vapor pressures and calculated values are within ± 0.017 MPa.

Considering the extended uncertainty of pressure measurement for PVT apparatus is 0.015 MPa, the measured results are correct and reliable. The vapor phase line is very close to the liquid phase line at each investigated temperature for the two binary systems. The two systems show near-azeotropic phase behavior with slightly positive deviations from ideality, and the phase diagrams are very similar to previous studied R1243zf + R1234ze(E) system [START_REF] Yang | Experimental measurement and modelling of vapor-liquid equilibrium for 3,3,3-Trifluoropropene (R1243zf) and trans-1,3,3,3-Tetrafluoropropene (R1234ze(E)) binary system[END_REF]. The systems of R1234yf +R1243zf and R1243zf + R245cb show type I phase behavior based on the classification scheme of van [START_REF] Van Konynenburg | Critical lines and phase equilibria in binary van der Waals mixtures[END_REF] [START_REF] Coquelet | Experimental determination of phase diagram and modeling: Application to refrigerant mixtures[END_REF]. The average relative deviation of pressure (ARDP) and the average bias of pressure (BIASP) are defined to evaluate the accuracy of the two models:

where N is the number of experimental points, the subscripts exp and cal represent experimental and calculated pressure respectively.

The calculated ARDP and BIASP of PR-MC-MHV2 model are identical or smaller than that of PR-MC-vdW model at each isotherm for the two systems as presented in Table 13.

Base on the results of calculated ARDP and BIASP along with the deviation Figs 10 and 12, we can draw the conclusion that the PR-MC-vdW and PR-MC-MHV2models perform almost same ability in VLE prediction for the two binaries, and the accuracy of the

  critical region) by visually observing the critical opalescence and the disappearance or reappearance of vapor-liquid interface. The experimental apparatus consists of loading and measurement parts, as shown in Fig. 1, and it's similar to that of Soo et al. (2010), Juntarachat et al. (2012), and Gil et al. (2008).

Figure 1 .

 1 Figure 1. Schematic diagram of the critical properties measurement apparatus. PS: pressurized source; VVC: variable volumetric cell; SP: syringe pump; VP: vacuum pump; EM: electric motor; MS: magnetic stirrer; ST: sapphire tube; VC: visual cell; AT: air thermostat oven; TP: platinum resistance temperature probe; PT: pressure transducer; TR: temperature regulator; DAS: data acquisition system; CPU: central processor unit; V: valve.

Figure 2 .

 2 Figure 2. Flow diagram of mixture preparation. C1: more volatile compound; C2: less volatile compound; V: valve; VVC: variable volumetric cell; W: balance; VP: vacuum pump.

  of vapor or liquid; is the volume of the optical cell; is the mass of loaded sample; is the volume change of ISCO pump; is the compressed liquid density of sample at loading temperature and pressure. The uncertainty of discussed in Appendix SA of Supplementary Information.

Figure 3 .

 3 Figure 3. Transition of a fluid from subcritical to the critical state on density increase. From left to right: classical vapor liquid mixture (the two phases are perfectly separated by a thin meniscus); saturated vapor phase (the vapor-liquid interface disappear at the bottom of the optical cell); saturated liquid phase (the vapor-liquid interface disappear at the top of the optical cell. The meniscus becomes thicker and thicker and the liquid phase become cloudy and milky); critical opalescence (vapor-liquid interface disappear at the center level of optical cell, and the meniscus become darkness and occupies the entire optical cell).

  has been upgraded to version of this work, and the schematic diagram of PVT apparatus is shown in Figure4. The variable volume cell has been improved to visible sapphire cell. The structure of the sapphire cell is similar to that of critical properties measurement. The sapphire cell contains an automatically controlled piston to perform internal volume changes. When the piston moves from the top towards the bottom, the components in the sapphire cell will be compressed from the state of vapor-liquid coexistence to the state of monophasic liquid. The displacement of the piston can be accurately controlled via an homemade software with the help of servomotor and ball screws.The internal volume is determined by means of a displacement transducer attached to the piston. The sapphire cell is immersed in a visual thermostat bath (NORMALAB, Model ASTM D 445). The temperature in the cell is measured by using two platinum probes which are inserted into the top flange and the bottom flange, respectively. The pressure in the cell is measured by a miniature pressure transducer (KULITE, Model CPC 8000) which is installed at the bottom of the variable volume cell. The temperature probe and pressure sensors are calibrated before measurement, and the information concerning calibration as well as the experimental procedure of bubble pressure measurement is described in Supplementary Information. The uncertainty analysis on temperature and pressure measurements is discussed in Appendix SA of Supplementary Information. The extended uncertainties (k=2) are estimated as U(T) = 0.06 K and U(P) = 0.015 MPa for bubble point measurement.

Figure 4 .

 4 Figure 4. Schematic diagram of the PVT measurement apparatus. VSC: visual sapphire cell; LV: loading valve; SB: stirrer bar; PM: piston monitor; SD: digital stirrer; P: piston; ST: sapphire tube; VC: visual cell; PP: platinum resistance thermometer probe; PT: pressure transducer; TR: temperature regulator; LB: liquid bath; VVC: variable volume cylinder; DT: displacement detector; GC: gas cylinder; R: refrigerant; V: valve; CPU: central processor unit; VP: vacuum pump.

  ), and (11). The critical temperature T c , critical pressure p c , and critical density can be determined based on the knowledge of several liquid-vapor coexistence points. The critical properties T c , p c , , and constants A, B, C, and D can be regressed by fitting saturated densities to the following objective function Eq. (12).

Figure 5 .

 5 Figure 5. Experimental saturated densities and modeling results of R1243zf in the critical region. (•): vapor phase; (▲): liquid phase; (*): critical point of this work; (■): critical point of REFPROP 10.0; solid lines: combined equations of scaling law and rectilinear diameters law.

  and the value of REFPROP 10.0, while the reported p c of Di Nicola et al. (2013) and Daubert et al. (1987) exhibit positive error of 0.1 MPa. The ρ c reported in the literature is close to each other, especially the value of Higashi et al. (2018) and REFPROP 10.0. The ρ c of this work is consistent with REFPROP 10.0 with positive error of 5.98 kg/m 3 .

Fig 6

 6 Fig 6 shows the vapor-liquid coexistence curve of R1243zf (1) + R1234yf (2) along with that of pure R1243zf and R1234yf. Whether it is the experimental data of this work or the data of REFPROP 10.0, it was found that the p -ρ curves of R1243zf intersected with that of R1234yf, and the p -ρ curves of R1243zf+R1234yf mixture intersected with both pure R1243zf and R1234yf. This suggests that the p -ρ curve intersection is characteristic of the mixture itself and not due to measurement error. The T -ρ curves of R1243zf (1) + R1234yf

5 Figure 6 .Figure 7 .

 567 Figure 6. Vapor-liquid coexistence curves of R-1243zf (1) + R-1234yf (2) mixtures. (): vapor phase R1243zf; (△): liquid phase R1243zf; (•) saturated vapor phase of R1243zf + R1234yf mixture; (▲): saturated liquid phase of R1243zf + R1234yf mixture; (■): critical point of this work; (◊): critical point of R1234yf from REFPROP 10.0; solid lines: combined equations of scaling law and rectilinear diameters law; dash lines: vapor-liquid coexistence curves of R1234yf and R1243zf from REFPROP 10.0; dot line: critical line calculated by Redlich-Kister equation.

Fig. 8 .

 8 Due to the lack of sufficient samples of R245cb, we failed to complete the measurement of vapor-

Figure 8 .

 8 Figure 8. Vapor-liquid coexistence curves of R1243zf (1) + R-245cb (2) mixtures. (): vapor phase R1243zf ; (△): liquid phase R1243zf; (•) saturated vapor phase of R1243zf + R-245cb mixture; (▲): saturated liquid phase of R1243zf + R-245cb mixture; (■): critical point of this work; (◊): critical point of R245cb from literature[START_REF] Weber | Vapor Pressure of 1 , 1 , 1 , 2 , 2-Pentafluoropropane[END_REF][START_REF] Defibaugh | Compressed and saturated liquid densities for 18 halogenated organic compounds[END_REF]; (○): generated saturated density of R245cb from BWR equation[START_REF] Shank | Thermodynamic properties of 1,1,1,2,2-pentafluoropropane (refrigerant 245)[END_REF]. solid lines: combined equations of asymptotic law behavior and rectilinear diameters law; dash lines: saturated liquid density of R245cb from[START_REF] Defibaugh | Compressed and saturated liquid densities for 18 halogenated organic compounds[END_REF];

  k=2): U(T)= 0.10 K,U(p)= 0.042 MPa, = 6.4 kg m -³,U(x 1 ) = 5.8× 10 -5

  The phase curves displayed by the PR-MC-vdW and PR-MC-MHV2 models are almost the same, as shown in Figs 9 and 11. In order to further analyze the correlation results, the pressure deviations of two models are presented in Figs 10 and 12. Both the two models show almost the same deviations at each isothermal.

Figure 10 .Figure 11 .Figure 12 .

 101112 Figure 10. Relative deviation of pressure for the R1234yf (1) + R1243zf (2) binary system from PR-MC-vdW and PR-MC-MHV2 model. (△): PR-MC-vdW model; (■): PR-MC-MHV2 model.

Table 1 .

 1 Chemical information.

	Compound	Chemical Name	CAS number	Supplier	Purity a (Mass%)
	3,3,3-trifluoropropene	R1243zf	677-21-4	Synquestlabs	99 %
	2,3,3,3-tetrafluoropropene	R1234yf	754-12-1	Climalife	99.5%
	1,1,1,2,2-pentafluropropane	R245cb	1814-88-6	Synquest	99 %

a Gas Chromatograph analysis

Table 2 .

 2 Critical properties and coefficient of Mathias-Copeman alpha function for R1243zf, R1234yf and R245cb.

		Critical properties		Mathias-Copeman coefficients
	Components
		T c /K	p c /MPa		m 1	m 2	m 3
	R1243zf	376.93 a 3.5182 a	0.261 a	0.80529 c	-0.57580 c	1.64180 c
	R1234yf	367.85 a 3.3822 a	0.276 a	0.8049 d	-0.4242 d	1.7469 d
	R245cb	380.38 b 3.1483 b	0.297 b	0.8920 d	-1.2280 d	4.7966 d

a REFPROP 10.0

[START_REF] Lemmon | NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP)[END_REF]

b

[START_REF] Weber | Vapor Pressure of 1 , 1 , 1 , 2 , 2-Pentafluoropropane[END_REF]

c

Yang et al.(2020) d Valtz et al. (2019)

Table 3 .

 3 Saturated vapor density and saturated liquid density of R1243zf a

	Phase	T/K	p /MPa	ρ/kg•m -3	n	T/K a	p /MPa b U(ρ)/kg m -³
		372.38	3.244	245.3	9	0.05	0.003	1.3
		375.41	3.439	300.1	6	0.08	0.004	1.6
	Saturated	376.11	3.487	329.9	5	0.01	0.001	1.7
	vapor	376.50*	3.515*	379.3*	6	0.02	0.002	2.0
	phase	374.43	3.374	273.9	6	0.05	0.002	1.4
		376.43	3.510	359.4	4	0.03	0.002	1.9
		374.01	3.347	262.6	4	0.01	0.001	1.4
		376.50*	3.517*	419.6*	7	0.08	0.005	2.2
		376.46	3.516	450.8	6	0.01	0.001	2.3
		376.47*	3.518*	451.5*	6	0.02	0.003	2.3
	Saturated	376.14	3.495	518.5	6	0.02	0.002	2.7
	liquid	375.51	3.451	562.9	5	0.03	0.002	2.9
	phase	371.79	3.218	619.7	5	0.06	0.007	3.2
		376.02	3.472	548.8	5	0.02	0.002	2.7
		373.72	3.368	626.1	4	0.02	0.001	3.0
		372.57	3.290	527.5	5	0.02	0.003	3.2
	*Critical opalescence was observed
	a Extended uncertainty (k=2), U(T)= 0.17 K; U(p)= 0.014 MPa;	= 6.4 kg m -³
	a
	b

Table 4 .

 4 Available critical properties for R1243zf

	Authors	ρ c /kg•m -3	T c /K	p c /MPa
	Daubert et al. (1987)	-	378.59	3.609
	Higashi et al. (2018)	414	376.93	3.518
	Di Nicola et al. (2013)	422.58	378.59	3.6306
	REFPROP 10.0 (Lemmon et al., 2013)	413.02	376.93	3.518
	This work a	419.0	376.66	3.518
	a Extended uncertainty (

Table 5 .

 5 Saturated vapor density and saturated liquid density of R1243zf + R1234yf binary mixture at mole fraction of 0.2774

	Phase	T/K	p /MPa	kg m -³	n	T/K	p /MPa	/kg m -³
		367.45	3.264	293.9	6	0.09	0.005	1.3
		369.02	3.374	343.7	4	0.01	0.001	1.5
		369.55	3.412	388.7	5	0.02	0.001	1.7
	Saturated	369.61*	3.417*	425.3*	5	0.01	0.001	1.9
	vapor phase	368.11	3.310	312.2	6	0.04	0.002	1.4
		368.47	3.335	323.1	5	0.02	0.001	1.4
		369.31	3.394	362.1	5	0.01	0.001	1.6
		369.53	3.410	389.4	5	0.01	0.001	1.7
		369.61*	3.422*	482.4*	5	0.01	0.002	2.1
		369.54	3.417	519.7	5	0.01	0.001	2.0
		368.96	3.379	576.4	5	0.02	0.001	2.5
	Saturated	367.72	3.296	617.7	5	0.04	0.003	2.7
	liquid phase	369.58	3.420	499.4	6	0.01	0.001	2.1
		369.37	3.406	545.4	4	0.01	0.001	2.3
		368.49	3.347	593.7	5	0.02	0.002	2.5
		367.24	3.269	627.7	4	0.01	0.008	2.7
	*Critical opalescence was observed
	a Extended uncertainty (k=2), U(T)= 0.19 K; U(p)= 0.016 MPa;		= 6.4 kg m -³; U(x 1 ) =1.8×
	10 -4

Table 6 .

 6 Saturated vapor density and saturated liquid density of R1243zf + R1234yf binary mixture at mole fraction of 0.4954

	Phase	T/°K	p /MPa	kg m -³	n	T/K	p /MPa	/kg m -³
		367.78	3.192	260.4	5	0.04	0.022	1.1
		370.64	3.390	311.4	6	0.10	0.024	1.3
		371.46	3.440	384.0	5	0.01	0.004	1.6
	Saturated vapor phase	371.50 371.50 368.38	3.454 3.457 3.226	411.2 439.8 269.9	6 5 5	0.01 0.01 0.08	0.012 0.013 0.004	1.7 1.8 1.1
		369.38	3.294	287.9	5	0.07	0.003	1.3
		371.23	3.422	346.5	5	0.05	0.003	1.5
		371.46*	3.441*	393.0*	4	0.02	0.001	1.7
		371.51	3.450	466.8	5	0.03	0.002	1.8
		371.49	3.450	509.1	5	0.06	0.004	1.9
	Saturated liquid phase	371.23 370.38* 368.28	3.432 3.375* 3.239	548.3 592.0* 643.4	5 5 5	0.01 0.03 0.03	0.001 0.002 0.022	2.1 2.3 2.5
		371.54	3.452	503.8	4	0.04	0.003	1.9
		371.17	3.429	557.8	5	0.02	0.002	2.1
	*Critical opalescence was observed
	a Extended uncertainty (k=2): U(T)= 0.21 K, U(p)= 0.048 MPa,	= 6.4 kg m -³, U(x 1 ) =5.8×10 -5
	Table 7. Saturated vapor density and saturated liquid density of R1243zf + R1234yf binary
	mixture at mole fraction of 0.7509
	Phase	T/K	p/MPa	/kg m -³	n	T/K	p /MPa	/kg m -³
		371.38	3.298	269.6	5	0.04	0.002	1.2
		373.53	3.448	329.6	4	0.02	0.001	1.6
		373.93	3.477	371.8	5	0.02	0.001	1.8
	Saturated vapor	373.97*	3.481*	411.0*	5	0.01	0.001	2.0
	phase	372.17	3.355	286.8	4	0.01	0.001	1.4
		372.73	3.393	300.0	5	0.02	0.002	1.5
		373.64	3.456	337.0	5	0.03	0.002	1.6
		373.81*	3.469*	353.2*	4	0.01	0.001	1.7
		373.94*	3.483*	443.7*	4	0.01	0.001	1.8
		373.93	3.483	483.2	5	0.03	0.002	2.0
		373.70	3.468	528.6	5	0.02	0.001	2.2
	Saturated liquid	373.14	3.431	563.1	5	0.01	0.001	2.3
	phase	373.93	3.483	451.5	6	0.02	0.001	1.9
		373.82	3.477	504.7	5	0.02	0.001	2.1
		371.99	3.356	592.8	5	0.05	0.000	2.5
		372.54	3.391	577.0	5	0.02	0.002	2.4
	*Critical opalescence was observed

a Extended uncertainty (

Table 8 .

 8 Saturated vapor density and saturated liquid density of R1243zf + R245cb binary mixture at composition of 0.4971 a

	Phase	T/K	p/MPa	kg m -³	n	T/K	p/MPa	/kg m -³
		369.54	2.829	225.0	7	0.08	0.002	0.9
		373.03	3.024	261.5	5	0.05	0.001	1.0
	Vapor	375.82	3.198	309.8	5	0.03	0.001	1.2
	phase	377.33* 3.303*	442.8*	6	0.01	0.001	1.7
		377.30	3.298	391.1	6	0.01	0.001	1.5
		377.34	3.302	414.7	4	0.01	0.002	1.6
		377.36	3.296	484.5	6	0.01	0.001	1.9
	Liquid	377.33	3.295	537.2	5	0.02	0.002	2.0
	phase	375.90	3.207	619.5	5	0.03	0.001	2.3
		370.49	2.890	712.9	5	0.03	0.001	2.7
	*Critical opalescence was observed

a Extended uncertainty (

Table 11 .

 11 Experimental and calculated vapor pressures of pure components a . Δp =p exp -p ref e δp =100×(p exp -p ref )/p exp .

	Component	T/K	p exp /MPa	p ref /MPa	Δp d /MPa	δp e /%
	R1243zf	293.45	0.518	0.515 b	0.003	0.65
		313.38	0.891	0.890 b	0.001	0.16
		333.43	1.436	1.442 b	-0.006	-0.41
		353.54	2.203	2.211 b	-0.008	-0.34
	R1234yf	293.42	0.596	0.596 b	-0.004	-0.69
		313.40	1.042	1.025 b	0.017	1.67
		333.49	1.664	1.655 b	0.010	0.57
		353.57	2.532	2.541 b	-0.009	-0.37
	R245cb	293.45	0.409	0.403 c	0.006	1.47
		313.47	0.731	0.715 c	0.016	2.23
		333.46	1.170	1.176 c	-0.006	-0.51
		353.55	1.816	1.833 c	-0.017	-0.94
	a Extended uncertainty (k=2), U(T)= 0.06 K; U(P)= 0.015 MPa
	b REFPROP 10.0 (Lemmon et al., 2018)
	The bubble pressures of R1243zf + R1234yf and R1243zf + R245cb binary systems with
	three different compositions were measured by using the PVT apparatus in the range of
	293.45 to 353.55 K. Table 12 and Table 13 show the experimental bubble pressures of the
	two binaries. T and p represent the experimental temperature and pressure; n is the number of
	repeated measurements; x 1 are the liquid phase mole fraction;	and	are the
	uncertainty of measurement repeatability for temperature and pressure respectively; p cal and
	y 1.cal represent the calculated value of pressure and vapor phase mole fraction from selected
	cubic EoS respectively;	are the uncertainty of liquid phase mole fraction.
	The bubble pressures of R1234yf +R1243zf and R1243zf + R245cb systems are
	correlated by PR-MC-vdW and PR-MC-MHV2 models respectively. The regressed binary
	interaction parameter	of vdW mixing rules and interaction energy parameters	and
	of MHV2 mixing rules are presented in Table 14. The vapor liquid equilibrium (VLE)
	of the R1243zf + R1234yf and R1243zf + R245cb systems are predicted by PR-MC-vdW and
	PR-MC-MHV2 models respectively, and the phase diagrams are illustrated in Figs 9 and 11.

c Valtz et al. (2019). d

Table 12 .

 12 Vapor liquid equilibrium of R1234yf (1) +R1243zf (2) binary system

									The calculated results
			The experimental data
								PR-MC-vdW	PR-MC-MHV2
	T/K	δT/K	x 1	Δx 1 /(10 -5 ) P exp /MPa δP/MPa n P cal /MPa y 1.cal P cal /MPa	y 1.cal
					T = 293.44 K
	293.42 0.02	0	-	0.512	0	4	0.512	0	0.512	0
	293.41 0.03 0.2057	3.3	0.530	0.001 7	0.530	0.2201	0.517	0.2278
	293.51 0.03 0.4874	3.2	0.553	0.003 5	0.553	0.5331	0.544	0.5194
	293.42 0.04 0.7229	2.6	0.573	0.001 4	0.573	0.7599	0.575	0.7474
	293.45 0.07	1	-	0.596	0.001 4	0.596	1	0.596	1
					T = 313.42 K
	313.40 0.06	0	-	0.885	0.002 4	0.885	0	0.885	0
	313.31 0.02 0.2057	3.3	0.921	0.001 4	0.913	0.2272	0.921	0.2285
	313.30 0.03 0.4874	3.2	0.964	0.001 3	0.963	0.5234	0.964	0.5153
	313.41 0.05 0.7229	2.6	0.995	0.008 4	1.003	0.7453	0.995	0.7412
	313.44 0.08	1	-	1.025	0.002 4	1.025	1	1.025	1
					T = 333.42 K
	333.49 0.08	0	-	1.437	0.002 3	1.437	0	1.437	0
	333.29 0.04 0.2057	3.3	1.506	0.004 4	1.494	0.2266	1.506	0.2275
	333.36 0.10 0.4874	3.2	1.580	0.002 3	1.579	0.5165	1.580	0.5101
	333.46 0.03 0.7229	2.6	1.624	0.003 4	1.637	0.7380	1.624	0.7349
	333.52 0.06	1	-	1.656	0.004 6	1.656	1	1.656	1
					T = 353.55 K
	353.57 0.03	0	-	2.223	0.005 3	2.223	0	2.223	0
	353.74 0.01 0.2057	3.3	2.296	0.007 4	2.294	0.2174	2.296	0.2175
	353.33 0.07 0.4874	3.2	2.390	0.002 4	2.390	0.5034	2.390	0.5030
	353.58 0.02 0.7229	2.6	2.465	0.002 4	2.467	0.7340	2.465	0.7338
	353.54 0.01	1	-	2.550	0.002 2	2.550	1	2.550	1
	a Extended uncertainty (k=2): U(T)= 0.06 K, U(P)= 0.015 MPa, U(x 1 ) = 6.6*10 -5

Table 13 .

 13 Vapor liquid equilibrium of R1243zf (1) + R245cb(2) binary system

							The calculated results
			The experimental data
							PR-MC-vdW	PR-MC-MHV2
	T/K	δT/K	x 1	Δx 1 /(10 -5 ) P exp /MPa δP/MPa n P cal /MPa	y 1.cal	P cal /MPa	y 1.cal
					T = 293.43 K
	293.45	0.03	0	-	0.410	0.001 5	0.399	0	0.399	0
	293.46	0.02 0.4971	3.1	0.482	0.003 3	0.479	0.5516	0.479	0.5437
	293.38	0.03 0.7494	3.0	0.496	0.001 4	0.501	0.7723	0.498	0.7709
	293.42	0.08 0.2699	3.7	0.450	0.000 3	0.448	0.3321	0.452	0.3294
	293.45	0.02	1	-	0.518	0.000 4	0.512	1	0.512	1
					T = 313.41 K
	313.47	0.08	0	-	0.731	0.003 4	0.707	0	0.707	0
	313.41	0.02 0.4971	3.1	0.835	0.003 3	0.831	0.4971	0.830	0.5342
	313.41	0.07 0.7494	3.0	0.858	0.002 4	0.867	0.7494	0.862	0.7675
	313.36	0.04 0.2699	3.7	0.787	0.002 4	0.783	0.2699	0.789	0.3173
	313.38	0.06	1	-	0.891	0.002 4	0.886	1	0.885	1
					T = 333.45 K
	333.46	0.01	0	-	1.155	0.005 4	1.166	0	1.167	0
	333.47	0.01 0.4971	3.1	1.323	0.006 4	1.321	0.5325	1.321	0.5292
	333.43	0.02 0.7494	3.0	1.379	0.014 4	1.385	0.7707	1.381	0.7701
	333.46	0.04 0.2699	3.7	1.260	0.019 4	1.256	0.3032	1.260	0.3021
	333.43	0.08	1	-	1.436	0.002 3	1.440	1	1.438	1
					T = 353.52 K
	353.55	0.02	0	-	1.806	0.003 4	1.828	0	1.828	0
	353.53	0.02 0.4971	3.1	2.038	0.017 4	2.048	0.5224	2.047	0.5272
	353.50	0.01 0.7494	3.0	2.163	0.002 3	2.142	0.7650	2.158	0.7666
	353.50	0.08 0.2699	3.7	1.946	0.020 2	1.953	0.2934	1.940	0.2942
	353.54	0.03	1	-	2.203	0.005 3	2.226	1	2.222	1
	a Extended uncertainty (k=2): U(T)= 0.06 K, U(P)= 0.015 MPa, U(x 1 ) = 7.4*10 -5

Table 14 .

 14 The binary interaction parameters adjusted by the model stated as above at each

		temperature
			PR-MC-vdW			PR-MC-MHV2
	T /K	k 12	OF	ARDP/% BIASP/%	/J mol -1	/J mol -1	OF	ARDP/%	BIASP /%
					R1234yf (1) + R1243zf (2)
	293.43 0.000 0.0247	1.41	-0.54	-960.85	1418.55 0.0092	0.86	0.33
	313.41 0.005 0.0288	1.61	0.69	-795.98	1121.60 0.0267	1.56	0.67
	333.45 0.012 0.0054	0.57	0.14	-765.19	1084.35 0.0031	0.50	0.15
	353.52 0.002 0.0027	0.36	-0.32	-407.29	474.26	0.0027	0.33	-0.32
					R1243zf (1) + R245cb (2)
	293.43 0.021 0.0188	1.16	0.66	-469.14	706.99	0.0169	1.07	0.68
	313.41 0.020 0.0260	1.19	0.75	-564.60	830.13	0.0238	1.03	0.76
	333.45 0.008 0.0027	0.39	-0.24	-574.93	750.80	0.0022	0.28	-0.23
	353.52 0.007 0.0072	0.78	-0.38	1165.33	-842.11 0.0053	0.62	-0.39

lines: PR-MC-MHV2 model.

Acknowledgment

The authors gratefully acknowledge financial support from the China Scholarship Council for Z. Yang's Visiting (No. 201905290003).


Rémi Cogranne

Source-based Detection of Malicious Behavior in Cloud Environment

Keywords: Cybersecurity in Telecommunication and Networks ; Signal processing applied to telecommunications Statistical detection, signal processing, Security, Malicious behavior

This short paper summarized our research and our contributions on the problem of source-based detection of BotCloud at large scale. We carefully took into account two major constraints of the reallife context: the tenant privacy and the cloud architecture in which tenant containers are spread out over different servers which requires a distributed detection solutions. In addition, one of the main strength of our works rests on the assessment over a real dataset collected on PlanetLab research infrastructure in which we created containers executing DDoS-type attacks with several software.

Introduction and Context

Cloud computing has gained an important role in providing high quality and cost-effective IT services by outsourcing part of their operations to dedicated cloud providers. If intrinsic security issues of this architecture have been extensively studied, it has recently been considered as a ready-to-use platform able to perform malicious activities, thus offering new targets for indirect threats. However, its large scale, the heterogeneous and dynamic nature of the activities it executes, as well as multi-tenancy and privacy-related issues, make the security operation complex. Consequently, cloud providers can hardly detect and mitigate malicious activities they unknowingly host. The works presented in this paper form a contribution to the source-end detection of malicious activities a Cloud Service Providers can host unknowingly. We proposed a practical and efficient method for source-end detection of malicious activities in large scale virtualized environments while preserving tenants privacy.

Summary of the Proposed Method

The problem of source-based detection of malicious activities for Cloud Service Providers is threefold :

 First, the various type of malicious activities may exhibit very different pattern ; for instance, brute-force attacks for cracking passwords requires a lot of computing resources while DDoS attacks over-flood network interfaces. In addition, the legitimate activities of containers are also of very different activities.  Second, cloud environment may be of very large scale hence the need of fully distributed and scalable solutions.  Last and not least, the Cloud Service Provider must guarantee the tenants' privacy. It is indeed simple to look at the name of the running processes but that is not acceptable because it clearly violates the tenants privacy. However, for the sake of pricing of resource management, the Cloud Service Provider can access the use of each and every container at large (disk usage, network I/O, memory and CPU usage) other simple task such as load balancing and pricing would not even be possible. To summarize, the proposed solution must be distributed and scalable, adaptative to allow the analysis of a very large range of traffic and can only use coarse grain metrics on the usage of the container.

The solution we have proposed is not a breakthrough in terms of statistical detection theory but it carefully takes into account all those constraints related with the operational context. We developed an original method based on legitimate activity self-adaptation which is used for background rejection and we use only the remaining data (that are not part of legitimate behavior) to detect matches with known malicious behaviors. The proposed detection method if fully decentralized, hence scalable, and its principle is based on the three following steps :

1. The legitimate "workload" is estimated using the well-celebrated Principale Component Analysis (PCA) ; the PCA allows us to estimate the main "legitimate behavior patterns" adaptively using all containers metrics. Note that in practice PCA would require all metrics from all containers to be centralized at one central node. To allow a fully distributed implementation, we developed an interactive and decentralized method for the estimation of principal components (for benchmarking purpose it was implemented using gossip for epidemic information diffusion). 2. Using the PCA one can reject what is considered as the "leigitimate" workload by projecting (at containers level) the metrics onto the orthogonal complements spanned by the first principal components ; in other words, the metrics are projected on the linear subspace spanned by the principal components (which is considered as "legitimate" part) and the remaining part (lying into the orthogonal complement subspace) are the residues. 3. The detection is based on the matching of the residues with the traces left by the malware it is aimed at detecting which is measured simply by the projection onto "signatures" (metric values measured offline executing the BotCloud alone in separated containers).

The deployment of the proposed methodology in depicted in Figure 1 and leverages the distribution of tenants containers over different servers. First, at the server level, the metrics from all containers a server host are used to compute "local PCA"; then those estimations are shared by all containers from the same tenant from different servers. In the next iterations, the estimations of PCA are used and we used for benchmarking the method the Gossip epidemic diffusion process. We showed that this method allows an accurate estimation of the first principal components within only a few iterations.

Figure 1 :

 1 Figure 1: Representation of the distributed PCA estimation in two steps, gathering estimations from containers and then merging at tenants level.

Numerical Results

Due to the space limitations we will only present two main results. First Figure 2 shows the interest of the theoretical methodology. On the left, Figure 2 (a) compares the difference between the expected and theoretically established distribution of the decision statistics and the empirical one. Note that two types of data are used, some randomly generated and hence simulated (in dashed green) which fits very well with the established results. The dashed red line presents the results obtained from real data, using the monitoring of planetLab containers. On this real dataset it can be seen that the decision threshold fits well the empirical results for false-positive rate up to 2x 10e-3. Beyond that our autoadaptative model based on distributed PCA is not accurate enough which create too much falsepositive as compared to the desired rate. On the right, Figure 2 (b) show, using a box plot emphasizing the average and 95% confidence interval, the evolution of the "angle" (in radians) between the first two principal components and the ground truth (obtained using a centralized computation). It can be clearly seen that the first principal components converge extremely fast. However, the distributed estimation of the second PCA requires more iterations. This can be explained in part by the fact that PCAs are computed with respect to each other: the second PCA can only be estimated when the first is already estimated accurately. However, a careful look shows that for very high infection rate (32%) the trends go in the exact opposite direction. When looking at figure 3 (d)-(f) one can even note that the detection becomes quite poor when the attack payload becomes very large (as compared to the overall legitimate traffic); that is when either the payload and/or the infection rate are very large. This apparently counterintuitive phenomenon can be explained by the estimation of legitimate "workload". Our method relies on the PCA on the collective metrics themselves to estimate the main behaviors. When the attack payload become much larger than it starts representing a majority of the traffic, it becomes naturally modeled within the principal components analysis and hence becomes parts of what our method consider as the legitimate background activity.

Follow-up Works and Conclusion

We have proposed a fully-decentralized method for estimation of containers workload and have exploited this method in a statistical well-founded detection method. While our method is not perfect, is original and has been shown rather efficient on a real and large dataset in terms of both computing complexity and detection accuracy. A follow-up works we are currently finishing is to implement this source-based detection method using in-network-caching system instead of the resources-consuming gossip epidemic diffusion and shown that a good trade-off between accuracy with large cache-size requirement and low complexity can be obtained.

Additional information


Rémi Cogranne

The ALASKA project: An interesting mix of theoretical advances and open science 1

Keywords: Cybersecurity in Telecommunication and Networks ; Signal processing applied Statistical detection, Security, Secret communication, Image processing, AI

This article provides a brief review of the ALASKA project (ANR-18-ASTR-0009: https://alaska.utt.fr), which is continuing through the European Horizon 2020 project UNCOVER (No 101021687). The interest in presenting this project lies mainly in the two very different, but complementary, aspects of the project which aimed at applying scientific methods in media security "outside of academic conditions".

Introduction and Context

Steganalysis covers all the techniques used to conceal a message in a digital medium. The operation of inserting the message must not change the properties of the media (in the vast majority of cases, a digital image) so that the embedding of secret data and, thus, the confidential communication remains as stealthy as possible. Steganalysis, on the other hand, referred to all techniques for detecting the presence of hidden information in media.

Steganography and steganalysis are still mainly studied in the context of academic laboratories and therefore in very restricted conditions, often not representative of the practical context that one may find by inspecting media on the Internet or in a firewall. The goal of the ALASKA project (Application on LArge and heterogeneous images database of Steganalysis techniK for Advances "into the wild") was to take steganography and steganalysis out of their academic context, through two different but complementary approaches. Let us state first that the main difficulties when shifting the current steganography and steganalysis methods into an operational context lies in the extremely large diversity of digital images (to focus only of this type of media) according to their origin (camera), the acquisition settings and the post-acquisition processing.

Theoretical advances for practical uses

We have considered two very different but complementary approaches in order to bring academic work closer to practical use cases. The first one is based essentially on statistical methods and aims at characterizing qualitatively and quantitatively the factors generating discrepancies in steganalysis results using artificial intelligence. While AI-based methods, although very efficient in the field of hidden information detection, their performances largely depends on the training base which must be as close as possible to real conditions. This particularly holds true in the field of steganalysis whose objective is to detect a "very weak" signal hidden in a complex media content that can change radically. Before our works, there was nearly no study analyzing which factors allow to define consistent sources of images (i.e. on which the training leads roughly to the same results). It is clear that without knowing how to define a "source" of similar images it is out of reach to train a steganalysis method that is adapted to the properties of this "source". Our first work was mostly of experimental in nature: using images from many different cameras and simulating an image processing chain, we were able to show that it is essentially the post-acquisition processing of a digital image that most defines "how to detect hidden information". We then hypothesized that the correlation between neighboring pixels, which is the fundamental characteristic allowing to detect hidden information, is mostly impacted by these processes. As often for this type of experimental studies, our results need to be confirmed and extended in order to understand better the relationship between pixel correlation and the transfer capacity of machine learning based steganalysis.

However, we were able to continue this work in an adversarial approach for steganography: our studies confirming how AI-based steganalysis is essentially aimed at detecting changes in the correlation of neighboring pixels we have (1) statistically demonstrated that the optimal steganographic signal is the one that has the same covariance matrix as the original pixels and (2) developed a method for estimating pixels correlations as a function of the post-acquisition processing chain in order to propose a new data hiding method. This method outperforms significantly the current state of the art; however, it remains hardly possible to apply in practice, in real conditions, as it requires RAW images to estimate the processing pipeline and its impact on pixels correlations [START_REF] Giboulot | JPEG Steganography with side Information from the Processing Pipeline[END_REF][START_REF] Giboulot | Synchronization minimizing statistical detectability for side-informed jpeg steganography[END_REF][START_REF] Giboulot | Detectability-based JPEG steganography modeling the processing pipeline: The noise-content trade-off[END_REF].

Applications to the open science context:

The aim of this ALASKA project was to allow the members of the consortium to study how to apply steganalysis in real-life contexts, but also to draw the attention of the whole community to the difficulty that this represents, in particular because of the simplifying assumptions used in the academic world (i.e. a vast majority of the works use RAW images coming from the same camera and processed in the same way then largely resized and converted into gray levels…). With this objective in mind, we proposed two steganalysis challenges under conditions that we considered closer to the real-life without, however, having its great complexity, at the risk of making the challenge unsuccessful. For this purpose, we have built a base of 80,000 RAW images coming from more than 50 cameras, among which half are smartphones (in order to catch up with their recent massive use in photography). We also developed a RAW image development script that simulates post-acquisition processing while keep controlling the level of diversity of resulting images. All these materials, JPEG as well as RAW images development script and embedding simulators, were provided on the project website (alaska.utt.fr) under CC-BY-ND license. For the contest, images were available with and without hidden information (using different algorithms from the academic community) and an additional set 5,000 of images, from the same "source", was used as the evaluation testing set.

Participants were asked to rank these test images from most "likely" steganographic to most "likely" covers. The first contest that served as a benchmark was held as part of a special session at the ACM Information Hiding and Multimedia Security conference [START_REF] Cogranne | The ALASKA steganalysis challenge: A first step towards steganalysis[END_REF]; among other things, one of the participating teams proposed a highly original and extremely effective attack on images compressed with the highest JPEG quality factor [START_REF] Yousfi | Breaking alaska: Color separation for steganalysis in jpeg domain[END_REF][START_REF] Butora | Reverse jpeg compatibility attack[END_REF]. The second contest [START_REF] Cogranne | ALASKAv2: Challenging academic research on steganalysis with realistic images[END_REF] was opened on the platform Kaggle (www.kaggle.com) dedicated to competitions in the AI community. We managed to offer a $25,000 prize for the top three teams (split into $12,000 for the winner, $8,000 for the runner-up and $5,000 for the third place). This second challenge was an unprecedented success with more than 1,000 teams and over 2,000 participants (who can gather into teams of up to 5 competitors) and a lot of information shared in the dedicated forum. This challenge leads to the development of steganalysis methods whose performance significantly outperform the state of the art and remains the current reference; in addition, the main lessons the community learned from this challenge are the following: (1) the usual AI methods can be adapted to detect hidden information in a very efficient way (2) learning on an extremely large and diverse training base allows current AI methods to circumvent only partially the heterogeneity of the sources (3) the use of CNNs models "pre-trained" on very large sets of images for pattern recognition is extremely efficient ; For more details, the reader is referred to the papers [START_REF] Cogranne | ALASKAv2: Challenging academic research on steganalysis with realistic images[END_REF][START_REF] Yousfi | Imagenet pretrained CNNs for jpeg steganalysis[END_REF][START_REF] Chubachi | An ensemble model using cnns on different domains for alaska2 image steganalysis[END_REF]. Eventually, we wished to decrease the advantage of the steganography community by using a new embedding method and, to this aim, we used the method presented in the previous section while simplifying very much the statistical model by neglecting pixel correlations (which cannot be estimated blindly on a given image). Surprisingly, we have found that this method still outperforms the state of the art which shows the margin of progress that better considering the correlation between neighboring pixels could offer [START_REF] Cogranne | Steganography by minimizing statistical detectability: The cases of JPEG and color images[END_REF][START_REF] Cogranne | Efficient steganography in jpeg images by minimizing performance of optimal detector[END_REF].

Let us also conclude by announcing that, in the framework of the European project UNCOVER, we will organize a third and last challenge. This last one will use images from the Internet, and thus with a much higher heterogeneity, but we will use steganography software popular on the Internet which are much less secure than the methods used in the academic community. Furthermore, we will provide a larger images test set in order to favor proposals that reach high detection accuracy with a very low false-positive rate (another crucial issue for the use of steganalysis in practice, but which remains little studied in the academic literature and in the ML and AI communities in general).

Conclusion

Within the framework of the ALASKA project, the main objective was to bring the academic community in steganography and steganalysis closer to realistic conditions where the diversity of media, in particular, is far too complex. Although we cannot claim to have solved all the difficulties raised such an application in operational conditions, we proposed two different approaches, one rather theoretical and statistical to explain and take into account the very large diversity of images in steganalysis and the second towards open and participative science. Both approaches allowed us to obtain satisfactory results and, above all, to discover paths that we were not familiar with and that remains unusual in research, but extremely interesting.

The work presented in this paper was funded by National Research Agency (ANR-18-ASTR-0009, https://alaska.utt.fr) and by European Union's Horizon

research and innovation program (project "UNCOVER", grant No 101021687).

Additional information


Rémi Cogranne
email: remi.cogranne@utt.fr

The ALASKA project: An interesting mix of theoretical advances and open science

This article provides a brief review of the ALASKA project (ANR-18-ASTR-0009: https://alaska.utt.fr), which is continuing through the European Horizon 2020 project UNCOVER (No 101021687). The interest in presenting this project lies mainly in the two very different, but complementary, aspects of the project which aimed at applying scientific methods in media security "outside of academic conditions".

I. INTRODUCTION AND CONTEXT

Steganalysis covers all the techniques used to conceal a message in a digital medium. The operation of inserting the message must not change the properties of the media (generally a digital image) so that the concealment of the data, and thus the confidential communication, remains as stealthy as possible. Steganalysis, on the other hand, concerns techniques for detecting the presence of hidden information in media.

Steganography and steganalysis are still mainly studied in the context of academic laboratories and therefore in very restricted conditions, not even representative of the practical ones that some might find by inspecting media on the Internet or in a firewall. The goal of the ALASKA project (Application on LArge and heterogeneous images database of Steganalysis techniK for Advances into the wild) was to take steganography and steganalysis out of their academic context, through two different but complementary approaches. Let us specify that the main difficulty in the operational implementation of the current steganography and steganalysis methods lies in the incredible diversity of digital images (to speak only of this type of media) according to their origin (camera), the conditions of acquisition of the images and the post-acquisition treatments.

II. THEORETICAL ADVANCES FOR PRACTICAL USES

We have considered two very different but complementary approaches in order to bring academic work closer to practical use cases. The first of these approaches, essentially statistical and methotodological, aimed at characterizing qualitatively and quantitatively the factors generating variability in steganalysis methods using artificial intelligence. However, AIbased methods, although very efficient in the field of hidden information detection, see their performances being very

The work presented in this paper received funding from French National Research Agency (project "ALASKA" : https://alaska.utt.fr, grant No ANR-18-ASTR-0009) and from the European Union's Horizon 2020 research and innovation programme (project "UNCOVER", grant No 101021687). largely conditioned by the use of a training base which must be as close as possible to real conditions. It is particularly noteworthy that in the field of steganalysis the objective is to detect a "very weak" signal hidden in an environment that masks it in a very important way (the media content). Before our work, there was practically no study analyzing which factors allow to define coherent sources of images (i.e. on which the performances of a steganalysis method are similar). It is clear that without knowing how to define a "source" of similar images it is inconceivable to train a hidden information detection method that is adapted to the characteristics of this "source". Our first work was experimental in nature: using images from many different cameras and simulating an image processing chain, we were able to show that it is essentially the postacquisition processing of a digital image that most defines "how to detect hidden information". We then hypothesized that the correlation between neighboring pixels, which is the fundamental characteristic allowing to detect hidden information, is mostly impacted by these processes. As is often the case in this type of experimental study, our results need to be confirmed and extended in order to better understand the relationship between pixel correlation and the learning transfer capacity of steganalysis.

However, we were able to pursue this work in a steganography approach: our study confirming how AI-based steganalysis is essentially aimed at detecting changes in the correlation of neighboring pixels we have (1) statistically demonstrated that the optimal steganographic signal is the one that has the same covariance matrix as the original pixels and (2) developed a method for estimating the pixel correlation as a function of the post-acquisition processing chain in order to propose a new steganography method. This work has shown that this approach, although relatively methodological and difficult to apply in real conditions, compares very favorably with the state of the art, as long as the steganography has RAW images allowing to estimate the processing chain [START_REF] Giboulot | JPEG Steganography with side Information from the Processing Pipeline[END_REF]- [START_REF] Giboulot | Detectability-based JPEG steganography modeling the processing pipeline: The noise-content trade-off[END_REF]

III. APPLICATIONS TO THE OPEN SCIENCE CONTEXT

The aim of this ALASKA project was to allow the members of the consortium to study the possibilities of steganalysis in real conditions, but also to draw the attention of the whole community to the difficulty that this represents, in particular because of the simplifying assumptions used in the academic world (i.e. the very vast majority of the works use RAW images coming from the same camera and processed in the same way then largely resized and converted into grey levels). With this objective in mind, we proposed two steganalysis competitions in conditions that we considered closer to the field reality, without however having the great complexity, at the risk of making the competition unsuccessful. For that we have built a base of 80, 000 RAW images coming from more than 50 cameras, almost half of which are mobile phones (the latter having become widely used for taking photographs). We also developed a RAW image development script that simulates post-acquisition processing while maintaining control over the level of diversity of the resulting images. All these data were published on the project website https://alaska.utt.fr. These images were provided in RAW and JPEG formats and will remain available to the community (under CC-BY-ND license). For the contest, images were available with and without hidden information (using different algorithms from the academic community) and an additional 5, 000 worth of test images from the same "source" were provided. Participants were asked to rank these test images from most "likely" steganographic to most "likely" healthy. The first contest that served as a "benchmark test" was held as part of a special session at the ACM Information Hiding and Multimedia Security conference [START_REF] Cogranne | The alaska steganalysis challenge: A first step towards steganalysis[END_REF]; among other things, one of the participating teams demonstrated a highly original and extremely effective attack on images compressed to the highest JPEG quality [START_REF] Yousfi | Breaking alaska: Color separation for steganalysis in jpeg domain[END_REF], [START_REF] Butora | Reverse jpeg compatibility attack[END_REF]. The second contest [START_REF] Cogranne | Alaskav2: Challenging academic research on steganalysis with realistic images[END_REF] was opened on the platform Kaggle dedicated to competitions in the AI community. We managed to offer a $25, 000 prize for the top three teams (split into $12, 000 for the winner, $8, 000 for the runner-up and $5, 000 for the third place). This second challenge was an unqualified success with more than 1, 000 teams and 2, 500 participants (participants can form a team of up to 5 people) and a lot of information shared in the discussion forum. This resulted in steganalysis methods whose performance significantly exceeded the state of the art at the time and remains the benchmark today; in addition, the main lessons the community learned from this competition are the following : (1) the usual AI methods can be adapted to detect hidden information in a very efficient way (2) learning on an extremely large and diverse training base allows current AI methods to circumvent only partially the heterogeneity of the sources (3) the use of "pretraining" models on very large bases for object recognition is extremely interesting in terms of computation time For more details, the reader can consult the articles [START_REF] Cogranne | Alaskav2: Challenging academic research on steganalysis with realistic images[END_REF]- [START_REF] Chubachi | An ensemble model using cnns on different domains for alaska2 image steganalysis[END_REF]. Finally, we wished to decrease the steganography community advantage by using a new insertion method and for that we used the method presented in section II while simplifying very largely the statistical model by neglecting the pixel correlation (which cannot be estimated blindly on a given image). To our surprise, we found that this method still performs favorably compared to the state of the art which shows the margin of progress that the better consideration of the correlation between neighboring pixels could offer [START_REF] Cogranne | Steganography by minimizing statistical detectability: The cases of jpeg and color images[END_REF], [START_REF] Cogranne | Efficient steganography in jpeg images by minimizing performance of optimal detector[END_REF].

Let us also note that, in the framework of the European project UNCOVER, we will organize a third and last challenge. This last one will use images from the Internet, and thus with a much higher heterogeneity, but we will use steganography software popular on the Internet which are much less secure than the methods used in the academic community. Furthermore, we will provide a larger test base in order to favor proposals that allow to obtain a very low falsepositive rate, which is a crucial issue for the use of steganalysis in practice, but which remains little studied in the academic literature (and in the ML and AI communities in general).

IV. CONCLUSION

Within the framework of the ALASKA project, the main objective was to bring the current academic working methods in steganography and steganalysis closer to real conditions where the diversity of media, in particular, is far too complex. Although we cannot claim to have solved all the difficulties raised by an application in operational conditions, we proposed two different approaches, one rather theoretical and statistical to explain and take into account the very large diversity of images in steganalysis and the second one with an open and participative science vocation. Both approaches allowed us to obtain satisfactory results and, above all, to venture on paths that we were not familiar with and that remain unusual in research, but extremely interesting.