Hongrui Ren,Jibin Song,Qinqin Xu,Jianzhong Yin*

State Key Laboratory of Fine Chemical,School of Chemical Machinery,Dalian University of Technology,Dalian 116024,China

Keywords:Supercritical carbon dioxide Silver nitrate Solubility parameter Correlation model

A B S T R A C T Solubilityofthesilvernitrateinthesupercriticalcarbondioxidecontainingethanolandethyleneglycolasdouble cosolvents was measured under certain pressure and temperature range(10-25 MPa,323.15-333.15 K).The impact of the pressure and temperature on the solubility was also investigated.Based on the experiment data,a correlation model concerning solid's solubility in supercritical fluids was established by combining the solubility parameter with the thermodynamic equation when a binary interaction parameter and a mixed solvent solubility parameter were defined.Experiments show the solubility of AgNO3increases with the pressure at a certain temperature.However,the influence of temperature is related to a pressure defined as the turnover pressure(12.3MPa).Whenthepressureishigher(orlower)thanthisturnoverpressure,silvernitrate'ssolubility shows increasing(or decreasing)trend as the temperature rises.Satisfactory accuracy of our presented model was revealed by comparing experimental data with calculated results.

1.Introduction

Supercriticalcarbondioxide(scCO2,Tc=304.2K,pc=7.376MPa),as oneofthemostwidelyusedsupercriticalfluids(SCF),isappliedinchemical[1-4]and biochemical[5,6]processes as a green solvent to reduce environmental hazard because of its chemical inertness,nontoxicity,noninflammability and designable solvent strength depending on its density.Hence,studies on the solubilities of various substances in scCO2have significant values from a practical perspective.Bartle[7]and Lucien[8]reviewed extensive studies concerning the solubilities of pure low volatile compounds and solid mixtures in scCO2with their coworkers respectively.But meanwhile,the solvent power of scCO2is seriously limited due to the low polarity of the CO2molecule itself and the consequent lack of solute-solvent interactions.Joshi and Prausnitz[9]proposed that a slight second solvent(called cosolvent or entrainer)that could form preferential intermolecular interactions with the solute,such as hydrogen-bonding,could be added to the primary solvent to increase the solute's solubility.Since then,numerous studies have been reported about determining the solubility of different solutes in scCO2with different cosolvents both experimentally[10,11]and theoretically[12-14].Abouttheessenceofthecosolventeffect,itisgenerallybelieved to be the intermolecular interactions[15,16]between the solute and cosolvent molecules,which involve physical forces(electrostatic,induction,and dispersion forces)and specific chemical forces.By analyzing solubility data of phenanthrene and benzoic acid in supercritical fluids with the existence of various cosolvents,Schmitt and Reid[17]came up with the notion that the cosolvent should not only be a modifier of the fluid's P-V-T properties,but also be as a chemical ameliorant to improve the fluid's solvent power.

The theoretical model used to quantitatively determine the solute's solubility in SCF could be generally divided into two categories:the thermodynamic model and the empirical correlation model.Prausnitz et al.[18]presented the thermodynamic model for calculating solid solute's solubility in SCF and analyzed the mechanism of the solubility enhancement phenomenon,which occurred when comparing the solubility of a solute in SCF with that in low pressure gas.Using this model,saturated vapor pressure,molar volume,and high-pressure fugacity coefficient of the solute are needed.In order to precisely determine the solute's fugacity coefficient in the SCF phase,compressed gas model and expanded liquid model[19]are usually adopted to characterize the thermodynamic behavior of the SCF phase.However,due to the complexity of the fluid's thermodynamic behavior in the supercritical region and the lack of the comprehension for the microscopic interactions between various substances,the thermodynamic model is not accurately suitable in every situation.At this time,the correlation model could be of significant values in achieving solubility data within certain experiment condition range by interpolating.Brennecke and Eckert[20]considered the correlation model proposed by Chrastil[21]as the most successful one,which based on the density of SCF and contained three regulating parameters.On the other hand,the solute's solubility can also be correlated with the extended Hansen method,which divided the original Hildebrand solubility parameter(δ,Eq.(1))into δd, δp,and δh,representing the dispersion,polar and hydrogen-bonding components of the total solubility parameter[22].δhcould be further divided into a Lewis-acid term,δa,and a Lewis-base term,δb,as reported in[23].The solubility parameter,originally defined as the square root of the cohesive energy density,was thought to better reveal the nature of dissolution because of the direct connection between the internal pressure(cohesive force,the resultant force of the intermolecular interactions)and the cohesive energy density.

Because of the wide application of the supercritical fluid extraction(SCFE)in food and biomedical engineering,the current research interests mainly involve the dissolution of various organic compounds in the SCF with or without cosolvents.The solubility of inorganic salts is seldom reported,which is significantly important for chemical processes like synthesizing nanomaterials using the SCF deposition method[24-26].The silver nitrate can be used as a metal precursor to be deposited on mesoporous template using the scCO2deposition method.With subsequent thermal or chemical reduction of the deposited silver nitrate,silver nanoparticles or nanowires can be synthesized,which have extensive applications in catalysis,optics,sensors,or electronic devices.As a precursor,the silver nitrate is very cheap,whichconstitutesa majoradvantageover its organometallic compound counterpart and facilitates the industrial application of the scCO2deposition method.However,a precursor of scCO2deposition must have a relatively large solubility in the scCO2,which cannot be fulfilled bymixingthe silver nitratewithscCO2alone.From ourpracticalexperience,pure silver nitrate could hardly dissolve in scCO2even when a reasonable amount of a single kind of cosolvents was added.However,adding a mixed cosolvent that consisted of two different kinds of cosolvents could considerably enhance the silver nitrate's solubility in scCO2.Thus,the gist of this paper is to propose a double-cosolvent strategy to increase the silver nitrate's solubility in scCO2and identify corresponding solubility data under specific conditions.On the other hand,a solubility correlation model that incorporates the solubility parameterintotheregularthermodynamicmodelmaybetterconsiderthe interactions between the solute and the mixed solvent as well as those among different components of the mixed solvent,which is critical to accurately predict the solubility data due to the complex composition of the system treated here.

In this paper,the solubility of thesilver nitrateinscCO2with ethanol and ethylene glycol as double cosolvents was measured using the static measuring method.The dissolution behavior of the silver nitrate in scCO2was analyzed and a solubility correlation model was established by associating the thermodynamic model with the solubility parameter theory.The selection of the ethanol and ethylene glycol as double cosolvents is inspired by our experimental discoveries about the correlationofthesolute'ssolubility(essentiallyistheintermolecularinteraction)in one of four different binary solutions,which can be AgNO3in C2H4(OH)2,C2H4(OH)2in scCO2,AgNO3in C2H5OH,or C2H5OH in scCO2.To be more specific,although the solubility of the silver nitrate in the ethylene glycol is great,that of the ethylene glycol in scCO2is small,which is not favorable for enhancing the silver nitrate's solubility in scCO2.To overcome this,the ethanol because of its considerable solubility(about 20 times greater compared with C2H4(OH)2)in scCO2is chosen.However,since the silver nitrate can barely solubilize in the ethanol,the ethylene glycol needs to be there and collaborate with the ethanol to increase the silver nitrate's solubility in scCO2.

2.Materials and Methods

2.1.Materials

Carbon dioxide gas,99%purity,was supplied by Dalian Guang Ming Gas Corporation of China.Ethanol,analytical purity,was purchased from Tianjin Fuyu Fine Chemical Co.Ltd.Ethylene glycol,analytical purity,wasobtained from Tianjin Chemical ReagentFactory.Silver nitrate,analytical purity,was provided by Dalian Institute of Chemical Physics,Chinese Academy of Sciences.All chemicals were used without any further purification.

2.2.Solubility measuring apparatus and procedures

Fig.1.Solubility measuring apparatus:(1)CO2cylinder;(2)control valve for the cylinder;(3),(10),(15)pressure gage;(4)filter;(5)cooling coil;(6)piston pump;(7)check valve;(8),(11),(18),(19)needle valve;(9)buffer tank;(12)high-pressure stainless steel reactor;(13)sample bottle;(14)magnetic stirrer;(16)electric thermostatic drying oven;(17)thermocouple;(20)heating tape;(21)cold trap;(22)wet gas flow meter.

Equilibrium solubility of the silver nitrate in scCO2with ethanol and ethylene glycol as double cosolvents was measured by static measuring method using the apparatus described in Fig.1.The temperature was measured using a thermocouple with an accuracy of ±0.1 °C and the pressure was measured by a pressure transducer(DG1300-BZ-A-2-40,SENEX,Guangzhou,China)with an accuracy of approximately±0.1 MPa.Mass was measured using an electronic scale(JA3003)with an accuracy of±0.1 mg.Firstly,the sample bottle(20.5 ml)containing a certain amount of solid silver nitrate was sealed with cotton and placed hanging inside the high-pressure stainless steel reactor(85 ml),at the bottom of which was a desired amount of preadded ethanol and ethylene glycol(indicated by the blue ellipses in the graphical abstract).Then the high-pressure stainless steel reactor was preheated inside the electric thermostatic drying oven(DHG-9240A,the following procedures were conducted by keeping the reactor inside the thermostatic oven)with the specific experiment temperature for an hour.After that,the reactor was slowly pressurized with CO2to a little lower pressure(identified empirically)than the target pressure.Suspend pressurizing enough time to allow the CO2to fully expand in the reactor under the present temperature.Once the pressure in the reactor was stable,proceed to infuse CO2to the target pressure.Then the reactor was kept rested for appropriate time(20 h)to let the components blend sufficiently and achieve equilibrium under this temperature and pressure.Finally,the high-pressure stainless steel reactor was depressurized at the rate about 0.5×105Pa·min?1.The sample bottle was then taken out of the reactor and weighed after being desiccated in a 100°C dryer for 4 h.The solubility was ultimately obtained by subtracting this final weightfrom the initial sample bottle weight.Under each condition,solubility data shown in Table 1 were averaged from three repeated experiments with a combined expanded uncertainty within 6%,coverage factor k=2.

2.3.Correlation model and mixed solubility parameter

The solubility correlation model in this paper(Supporting Information)is established by using the solubility parameter and the expanded liquid model,which treats the supercritical fluid-phase mixture as an expanded liquid.

The concept of the mixed solubility parameter[27]was adopted to treat the solvent(scCO2)and cosolvents(ethanol and ethylene glycol)as a mixed solvent.If the mixed solvent attained its mixed critical point and became homogeneous,this multicomponent system would have been simplified as containing two phases,namely the solidphase and SCF-phase.The mixed solubility parameter can be evaluated by

SubstitutingδMforδ1inEq.(9)orEq.(11)(S.I.),thesolute'ssolubility in the multicomponent system can be calculated or correlated.

Table 1 Experimental conditions and results of the solubility of AgNO3

3.Evaluation of the Solubility Parameters

3.1.Mixed solvent

The solubility parameter of the carbon dioxide is computed using Eq.(3)from reference[28],while that of ethanol(δethanol=26.5MPa1/2)and ethylene glycol(δglycol=32.8MPa1/2)is evaluated with their partial-solubility parameters(δd,δpand δh)listed in Table 3 using Eq.(4)respectively,which is a defined relationship equation in the Hansen solubility parameter scheme about calculating the total solubilityparameterfromitsthreedifferentpartial-solubilityparameter components.ThenEq.(2)isusedtogeneratethesolubilityparameterof the mixed solvent.All necessary data in calculating the solubility parameter of the mixed solvent can be found in Table 2.

3.2.Solute:silver nitrate

The solubility parameter of the silver nitrate is calculated using the method proposed by Beerbower et al.[29]and modified by Bustamante et al.[30,31],which involves regression analysis for the expanded parameter system as described by the following regression equation under the condition of knowing both the solute's solubility in various solvents(X2)and the partial-solubility parameter of the corresponding solvent(δ1d,δ1pand δ1h).

ThenthecoefficientsinEq.(5),namelyCi(i=0,1,2,3,4,5,6),canbe obtained through regression analysis.Because there are seven coef ficients in the regression equation Eq.(5),at least eight pairs of X2and the corresponding solvent's partial-solubility parameter must be provided to fit out Ciand the accuracy will be improved by increasing the number of solute-solvent pairs.In this paper,Ciis fitted out with the data of ten solute(silver nitrate)-solvent pairs listed in Table 3.Finally,the partial-solubility parameter of the solute(δ2d,δ2pand δ2h)can be generated by substituting the value of Ciinto the following Eq.(6):

Table 2 Data used in determining the solubility parameter of the mixed solvent δM

Table 3 Partial-solubility parameters[32]of the used solvents and the solubility of the silver nitrate in these solvents

With the solubility data of the silver nitrate in 10 solvents and the partial-solubility parameters of these solvents listed in Table 3,Ciin Eq.(5)can be obtained through nonlinear fitting as

Therefore,the partial-solubility parameters of the silver nitrate is determined by substituting the Ciinto Eq.(6)as

The total solubility parameter of the silver nitrate is computed by substituting its partial-solubility parameter components into Eq.(4),yielding 33.9MPa1/2.

4.Results and Discussion

4.1.Experimental solubility of the silver nitrate

The solubility of silver nitrate was measured under three different temperatures:323.15K,328.15 K,and333.15 K.The experimentresults are plotted in Fig.2 along with each corresponding temperature and pressure,vertical coordinates are the solubility of silver nitrate and the horizontal coordinates are the experiment pressure.

From Fig.2 it can be seen that under a certain temperature,the solubility of the silver nitrate becomes higher as the pressure increases and the rising trend becomes more and more gentle till a plateau appears in the high pressure region.On the other hand,a turnover pressure(about 12.3 MPa)exists as depicted by the dashed line in Fig.2,below which the lower temperature is in favor of enhancing the dissolution of the silver nitrate.When the pressure is above this turnover pressure,the solubility will be enlarged as the temperature goes up.

Fig.2.Experimental solubility of AgNO3in scCO2with ethanol and ethylene glycol as double cosolvents under three different temperatures:323.15 K,328.15 K,and 333.15 K.

Table 4 Comparison between experimental and calculated solubilities of AgNO3

4.2.Comparison between experimental and calculated solubilities

The experimentally measured solubility data of the silver nitrate in scCO2with ethanol and glycol as double cosolvents were processed by applying Eq.(11)(S.I.),four regulating parameters of which were fitted as k1=?290.7501,k2=?403.5007,k3=18.1535,and k4=2.7113×105.Then the solubility of silver nitrate was calculated by utilizing Eq.(11)(S.I.)with this four parameters and compared with experimentresults.Comparativedataunderdifferentexperimentconditions were listed in Table 4 with the relative error of each pair and the whole average absolute relative deviation(AARD).For better interpretation of the data,this comparative data were also plotted in Fig.3.

By comparing the calculated solubility with the experimental value,it could be seen that the proposed model had an AARD about 8.52%.Thus,this model could be utilized to calculate thesolubility of inorganic salts in the supercritical carbon dioxide containing cosolvents with satisfactory accuracy.

5.Conclusions

The solubility data of the silver nitrate in the supercritical carbon dioxide with ethanol and ethylene glycol as double cosolvents were preciselymeasuredundercertainconditions,withwhichacorrelationmodel combining the thermodynamic model with the solubility parameter theory was established to correlate the solubility.The solubility data have significant reference values in developing new chemical processes and techniques involving scCO2,like synthesizing silver nanoparticles.Meanwhile,the theoretical correlation model that integrates the solubility parameter with the thermodynamic model may better consider the interactions between different components of the multi-component system and thus generate accurate prediction of solubilities.

Nomenclature

ciiCohesive energy density of a pure substance

cijCohesive energy density of a mixture composed of two different substances

Fig.3.Comparison between experimental and calculated solubilities of the silver nitrate under three different temperatures:323.15 K,328.15 K,and 333.15 K.

l12Binary interaction parameter between the solvent and the solute

p Pressure of the system

R Gas constant

T Temperature of the system

TmNormal melting point of the solute

VLMolar volume of a substance in its liquid state

VSMolar volume of a substance in its solid state

y2Mole fraction of the solute in the supercritical-fluid phase.

γ2Activity coefficient of the solute at temperature T and pressure p0

δiSolubilityparameterof componenti,i=1forthesolvent,i=2 for the solute

φiVolumefractionofcomponenti,i=1forthesolvent,i=2for the solute

Supplementary Material

Supplementary data tothis article canbefoundonlineathttps://doi.org/10.1016/j.cjche.2018.06.011.