Xi Wu*,Shiming Xu,Debing Wu,Huan Liu

Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education,School of Energy and Power Engineering,Dalian University of Technology,Dalian 116024,China

Keywords:Conductivity Alcohol Electrochemistry Solution Mixtures

A B S T R A C T Salinity gradient energy between the concentrated and diluted electrolyte solutions can be converted to electric energy by using reverse electrodialysis(RED)technology.Electrolyte solution is a vital factor that impacts the energy conversion efficiency.Potassium acetate(KAc)was chosen as solute,and water,ethanol,2,2,2-trifluoroethanol(TFE),2-propanol(IPA)and several of their binary mixtures were selected as solvents.Electric conductivity of these solutions were measured under varying conditions.KAc was easily ionized in water and possessed the maximum electric conductivity,following by KAc–H2O–TFE and KAc–H2O–ethanol,and then KAc in pure TFE,ethanol,and IPA respectively.For electric convertibility of these solutions working in a RED power generation system,it was found that the KAc–H2O possessed the maximum power density,and the KAc–ethanol–H2O possessed the larger open circuit voltage than aqueous KAc solution under the same working condition.Besides,it was observed that both the electric conductivity and electric convertibility were significantly influenced by the concentration and temperature of solution.With the increasing of concentration,electric conductivity of these solutions increased firstly and then reached to the peak,but later it decreased.Solution temperature took a positive impact role to the electric conductivity.Electric conductivity of these solutions can be estimated by using a modified amplitude version of Gaussian peak function.

1.Introduction

1.1.A closed type RED power generation system driven by thermal energy

Salinity gradient energy exists between the concentrated and diluted electrolyte solutions,and which can be converted to electric energy by using reverse electrodialysis(RED)power generation technology.The RED power generation technology is firstly proposed by Pattle in 1954[1],and attracting increasing researchers in energy field recently with the rapid development of ion exchange membrane(IEM)[2,3].A simple RED apparatus consists of many alternately distributed cation exchange membranes(CEM,only permeable for positive ions)and anion exchange membranes(AEM,only permeable for negative ions),sandwiched between two polar plates with electrodes at each side respectively,as well as some feeding pumps and tubes,as Fig.1 shown.

When pumping the concentrated and diluted electrolyte solutions into the alternating compartments respectively,anion ions in the concentrated solution compartments can diffuse spontaneously across the AEM and transport to the adjacent diluted solution compartments.In contrast,cation ions move towards the opposite direction by passing through the CEM.At this time,a net diffusion current is generated,and the chemical potential difference between the concentrated and diluted solutions generates a voltage across each IEM[4].Oxidizing reaction and reduction reaction are ongoing respectively near each electrode with the looping of electrode rinse solution.If connecting an external load to the electrodes,then the inner ionic current can be converted into the external electrical current[5].

The outgoing electrolyte solutions from the RED apparatus are collected and regenerated in the distiller by using the multi-effect distillation(MED)technology,driven by the low temperature thermal energy[6],such as solar energy,geothermal energy,engine waste heat,etc.Then,the mixed electrolyte solution is separated to the concentrated solution and diluted solution again with the harvestable chemical potential difference.By means of integrating the above two processes together,a closed type thermal energy driven power generation cycle is available[6–8],and the schematic of which has been drawn as Fig.2.This is a novel technology in electrochemical energy engineering fields[9].

Fig.1.Schematic of salinity gradient energy power generation system with RED method.

Fig.2.Schematic of a closed type thermal energy driven power generation cycle with RED method.

1.2.Potential working solutions for the RED power generation system

Further study results indicate that the electrolyte solution looping in this power generation system is one of the vital factors that directly impact the energy conversion efficiency(ECE).And the ECE can be calculated by using Eq.(1)[5,7],

where ηs_Eis the efficiency of process of converting salinity gradient energy to electric energy;

ηH_Sis the efficiency of process of converting thermal energy to salinity gradient energy.

The ηH_Scan be calculated by using Eq.(2),thus it can be seen that the absorbent of working solution should be easily evaporated by absorbing thermal energy as little as possible[5,7].

where,?C/Dis the chemical potential difference between the concentrated and diluted solution;

hHOVis the latent heat of vaporization of mixed solution.

Most of the current attention in this field has been paid to the sodium chloride(NaCl)aqueous solution and natural sea–river water[1–4,10,11],while some researchers preferred to the ammonium bicarbonate(NH3HCO3)aqueous solution[12,13]and aqueous solutions of lithium chloride(LiCl)and lithium bromide(LiBr)[5].As a matter of fact,the pure water is not an ideal absorbent here due to its relative huge latent heat of vaporization and relative high operating temperature(NH3HCO3aqueous solution is an exception),resulting in the severe efficiency reduction during the process of solution regeneration.An ideal working solution,for the energy conversion system shown in Fig.2,needs to possess various practical characteristics in the aspects of thermophysical and transportation properties,electrochemistry characteristics,environmental influence,safety,cost,etc.Methodology of assessing the available working solutions can be found in the previous report,and it has been suggested that the binary or ternary solutions consisted of some monovalent salts and appropriate organic solvents or blends solvents may be workable[8,14],due to their relative higher solubility and electric conductivity,relative lower latent heat of vaporization,acceptable electric convertibility,and suitable boiling point temperature.Recently,working solutions consist of potassium acetate(CH3COOK,or KAc),water and organic solvents have been taken into consideration.

1.3.Physical and chemical properties of KAc in water and organic solvents

Potassium acetate,with molecular weight of 98.1423 g·mol-1,is one of food additives and medicine ingredients,and also used as anti-freeze and de-icing products[15].The normal physical form of KAc is white flakes or crystalline powder,while it is hygroscopic[16].Solubility of KAc in water is 256 g·(100 ml H2O)-1at 20°C[16],269 g·(100 ml H2O)-1at 25°C[16],283 g·(100 ml H2O)-1at 30°C[17],and 324 g·(100 ml H2O)-1at 40°C[17],respectively.The saturated vapor pressure of potassium acetate aqueous is 0.581 kPa at 25°C,and the molar enthalpies of vaporization is 4560 J·mol-1at the same temperature condition[18].KAc can be ionized in water,and the approximate effective ionic radii is 0.3 nm for K+and 0.45 nm for CH3COO—respectively at 25°C[17].KAc is less soluble in ethanol(C2H5OH)than in water,and which tends to form association complexes in the liquid phase preferentially with the water molecules over those of the alcohol[19].Molar electric conductivity at infinite dilution for aqueous KAc solution is 40.9 Ω-1·mol-1·cm2at 25°C[16].The calculated value of limiting conductance of KAc in heavy water(D2O)was 94.7 K.U.(Kohlrausch units)[20].

Some efforts have been made on the conductivity of KAc in different organic solvents.Ref.[21]reported the electric conductance behavior of KAc in mixed solvent(20%acetic acid and 80%acetonitrile,wt.%),and also calculated the values of limiting conductance at 35°C according to the Fuoss–Hsia equation,Fuoss–Kraus extrapolation technique and Shedlovsky technique,respectively.Sah et al.studied the molar conductance of KAc in aqueous 2-butanol solutions with an alcohol mass fraction of 0.7,0.8 and 0.9 at 25°C,30°C,and 35°C respectively,and the limiting molar conductivities,ion-association constants were also estimated by using Fuoss conductance–concentration equation[22].More practical information on properties of KAc in some other organic solvents(with the lower boiling temperature and lower latent heat of vaporization than water)are desiderated,so as to estimate their usability for the closed type RED power generation system driven by thermal energy.

The purpose of this work is to explore some new available working solutions for above introduced power generation system by means of measuring and analyzing two key parameters,the electric conductivity and electric convertibility.Here,KAc is selected as the solute,and the following substances are selected as the solvents,including water,ethanol(C2H5OH),2,2,2–trifluoroethanol(C2H3F3O,also named TFE),2–propanol(C3H8O,also named IPA)as well as their several binary blends.The experimental temperature and concentration conditions are variable,and which are set carefully according to the practical operating requirements of the working solutions looping in the power generation system as Fig.2 shown.

2.Electric Conductivity of Solutions

2.1.Experimentation

2.1.1.Experimental materials and apparatus

Purity of NaCl is≥99.5%(Sinopharm Chemical Reagent,China);KAc is analytical purity(Tianjin DaMao Chemical Reagent,China);Purity of TFE is≥99.5%(Jiangsu Blue-Star Green Tech.,China)and purity of IPA is≥99.7%(Tianjin DaMao Chemical Reagent,China).Anhydrous ethanol is better than 99.7%(Tianjin Guangfu Tech.,China).Deionized water was produced in laboratory,and the electric conductivity of which is less than 1 μS·cm-1.Both NaCl and KAc were dried in an electrical oven at 423.15 K for more than 3 h with periodic grinding.All experimental materials were weighed by using an electronic analytical balance(Ohaus,U.S.)with accuracy of 0.001 g.Some key thermophysical properties of these solvents are listed in Table 1[23].

Table 1Some key thermophysical properties of these four solvents[23]

Fig.3 showed the test rig schematic of electric conductivity measurement.A jacketed glass reaction vessel was designed to contain the solution hermetically.A thermal resistance temperature sensor(with accuracy of±0.15°C)and a corrosion resistance electrode(Model:inlab 710)were inserted into the solution directly.The tail of electrode was connected with a conductivity meter(Model:FE38-Standard;available range:10-5mS·cm-1to 500 mS·cm-1),both of which were produced by Mettler Toledo(Switzerland)with accuracy of±0.5%.The reaction vessel was placed on the platform of a stirrer(Tianjin Honour Instrument,China)with rotating speed variation of 0–2000 r·min-1.The stirring rod was covered by polytetra fluoroethylene outside to guard againstreaction with the solution.Temperature of solution was maintained by looping water supplied from thermostatic bath(Julabo Instrument,Germany)with temperature stability of ±0.03°C.The maximal temperature fluctuation of solution was 0.2°C during the whole experimental process.Computer,programmable logic controller(Siemens S7–200,Germany)and some matched modules were used to acquire data and control testing conditions.

Fig.3.Experimental apparatus of conductivity measurement.1 Glass reaction vessel;2 stirrer;3 stirring rod;4 thermostatic bath;5 cycling water pump;6 temperature sensor;7 electrode;8 conductivity meter;9 data acquisition system.

2.1.2.Reliability test and error analysis

Reliability tests were carried out to confirm the availability of this experimental method and apparatus.Electric conductivity of NaCl aqueous were tested out under different concentrations at 18°C firstly and then compared with the literature[24],seen in Fig.4.The measured results and the reference data were closed to each other with an average relative error of 2.32%.

Fig.4.Conductivity data comparison of NaCl aqueous solution at 18°C.

Uncertainty of measured conductivity data has also been analyzed and drawn along with the experimental results in the figures.The experimental error can be calculated by Eq.(3).

whereΔκis the error of displayed value of conductivity meter;XEcomes from the error of repetition test;XTcomes from the error of solution temperature condition;XCcomes from the error of standard solution;XIis the inherent error of testing system.

The first part of uncertainty of measured data caused by error of repetition tests that can be calculated by Eqs.(4)and(5)[25,26],

where Siis the standard deviation;n is the total times of tests;κiis conductivity value under the test of sequence number i,mS·cm-1;κaveis the average conductivity value,mS·cm-1.

The second part of uncertainty of measured data caused by solution temperature condition can be calculated by Eqs.(6)and(7)[26].

where κRand κTare conductivity value at reference temperature and current solution temperature,mS·cm-1;αTis temperature coefficient of conductivity measurement;△T is the uncertainty of solution temperature,°C;t and tRare the current temperature and reference temperature of solutions,°C.

The third part of uncertainty of measured data caused by standard solution,can be calculated by[25].

where uEis the expanded uncertainty of standard solution.In this test,standard solutions certificated by Mettler Toledo Co.were used,with an expanded uncertainty of 1.5%at 25°C.

The forth part of uncertainty of measured data is inherent error of testing system that can be predicted by Eq.(9)[25].

where uTis the accuracy of apparatus,given as±0.5%of the measured value in this work.

The compound uncertainty u(Δκ)can be estimated as Eq.(10).

The expanded uncertainty U(Δκ)of measurements can be estimated by Eq.(11).

2.2.Results and discussions on electric conductivity

2.2.1.Electric conductivity of KAc in water

Electric conductivity of aqueous KAc solution have been tested out and listed in Table 2 under different temperature(20°C,40°C and 60°C)and mass concentrations conditions(from 0.5%to 60%),with the unit of mS·cm-1(1 mS·cm-1=1000 μS·cm-1).The maximum tested value is 273.2 ± 5.451 mS·cm-1at the concentration of 40.11 wt.%when the solution temperature is 60°C.The tested peak values of electric conductivity are (133.8 ± 2.544)mS·cm-1and (202.3 ±3.957)mS·cm-1at 20°C and 40°C respectively.The relationships of the concentration,temperature and electric conductivity of solutions are drawn in Fig.5,with the experimental uncertainty.Eqs.(14)and(15)show,the number of free ions are further reduced,consequently leading to the electric conductivity reduction.

Table 2Conductivity data of aqueous KAc solution under different conditions

Fig.5.Electric conductivity of aqueous KAc solution under varying conditions.

2.2.2.Electric conductivity of KAc in ethanol,TFE and IPA

Electric conductivity of KAc in organic solvents(ethanol,TFE,IPA)was measured under varying temperature(20 to 60°C)and concentrations(up to 15.09%)conditions,and the results are listed in Table 3.KAc still can be ionized in these organic solvents,while the effective transport amount of cation ions(K+)and anion ions(CH3COO—)are not as abundant as that of aqueous KAc solution.The measured electric conductivity of KAc–ethanol and KAc–TFE solutions are both smaller

As Fig.5 shown, firstly,temperature of solution is a positive impact factor on the electric conductivity under the testing conditions.The most powerful influence region of temperature on the electric conductivity of aqueous KAc solution is Region I in Fig.5,where the peak values of the electric conductivity appear.In contrast,the influence of solution temperature is quite feeble on the electric conductivity of the extremely diluted concentration solutions,seen Region II in Fig.5.

Secondly,with the increasing of solution concentration,electric conductivity increases at the first half time and then reaches the peak value,but later it decreases gradually,as Fig.5 displayed.The reason can be explained by using the free ions theory.Solvent can be regarded as a continuous molecular medium in solution,theoretically,which provides the spaces for motions of free ions.Electric conductivity of solution usually depends on the amount of free ions and their transport velocities[27].The amount of free ions is found to be affected significantly by three factors,the ionic concentration,ionic association and solvation[28].The influence of ionic association and ionic solvation are negligible when the solution is in low concentration,since that the distances are large enough among the free cation ions and anion ions.At this time electric conductivity can be enlarged if the amount of free ions is increased by adding more crystal KAc into its aqueous solution.While,the curve slopes of electric conductivity turn down to be negative for the extremely concentrated solutions.At this moment,cation and anion ions(also including hydrated ions)are closed to each other,and ionic association may occur between the ions with opposite charges.

Ion pairing in aqueous KAc solutions exists,as described by equilibrium Eq.(12)of Bjerrum type.Products of ionic association are electroneutral,which have no positive contribution to electric conductivity of solutions.

Influence of ionic solvation also become obvious when solution is in high concentration.At this situation,the relaxation effect and electrophoretic effect increase with the reduction of interionic distances[27],and the drift of ions is retarded,thus resulting in the decrease of electric conductivity of solution.Besides,different with the hydration process of normal alkalis salt aqueous solution,as description in Eq.(13),CH3COO—ions(proton acceptors)exist in solution that can be connected with H+,according to Br?nsted–Lowry's acid–base theory and Robinson–Harned's localized hydrolysis hypothesis[29].Due to this connection,asthan that of aqueous KAc solution,and most of which are less than 10 mS·cm-1under the testing conditions.The maximum electric conductivity of KAc–TFE solution is(9.402 ± 0.189)mS·cm-1at 60°C,and it is(6.310 ± 0.126)mS·cm-1for KAc–ethanol solution under the same temperature.The solubility of KAc in IPA is less than 1.91%in weight percentage,and the electric conductivity of KAc–IPA solution is quite small,with the maximum value of(80.8 ± 1.63) μS·cm-1at 60°C under this experimental conditions.KAc seems to prefer water molecules to ethanol or TFE molecules in their solvation,and resist dissolving in IPA.The extremely weak ability of ionization,dissolution and conduction of KAc–IPA solution would lead to the quite low out put voltage,power density,and energy efficiency of the RED power generation system,thus the KAc–IPA solution should be excluded.

Table 3Electric conductivity of KAc in three organic solvents

The relationships of the concentration,temperature and electric conductivity of these solutions are drawn in Figs.6–8,with uncertainty analysis.Solution temperature is still observed to take a positive impact role for electric conductivity of solutions regardless of whether the solvent is water or organics.The influence mechanism can be explained as[27,28]:with the increase of the temperature of solution,(I)the viscosity of solution decreases,bringing down the friction and irreversible loss during the process of ions transport;(II)the solubility of some electroactive species from the environment decreases,promoting the reduction of external disadvantageous interference;(III)the average kinetic energy of ions increases,leading to the reinforcement of thermodynamic movement of ions;(IV)electrophoretic effect become weaken,reducing the obstruction of ions transport;(V)effects of hydrolysis and solvolysis become weaken,shrinking the effective interactive radius and retarding interionic constraint.

Fig.6.Electric conductivity of KAc–TFE solution under varying conditions.

From Figs.5-8,it can be seen that the electric conductivity of these four binary solutions is in the ranking of KAc–H2O ＞ KAc–TFE ＞ KAc–ethanol＞ KAc–IPA,which is coincident with the relationship of their solubility.The results can be analyzed by introducing a parameter Bjerrum length(β).β represent the separation at which the electrostatic interaction between two elementary charges is comparable in magnitude to the thermal energy scale[30],which is described as Eq.(16),

Fig.7.Electric conductivity of KAc–ethanol solution under varying conditions.

Fig.8.Electric conductivity of KAc–IPA solution under different conditions.

where KBis the Boltzmann constant;e is the elementary charge;ε0is the vacuum permittivity;and εris the relative dielectric constant.The value of εrcan be found from references[17,31–33],and the β of solvents(water,TFE,ethanol,IPA as well as the mixture of 90%water and 10%TFE)are calculated and shown in Fig.9 under the temperature from 20°C to 60°C.Compared Fig.9 with Table 3,it can be concluded that solution consist of KAc and some a solvent that with the relative small β value may possess the better electro conductibility.This conclusion is helpful for selecting new suitable solvents for the closed type RED power generation system driven by thermal energy.

The phenomena of ionic association and solvation still exist for the solutions consist of KAc and organic solvents.Thermal motion and interionic forces establish a steady state,and each ion in solution are in one of three categories,the unpaired ion,the solvent separated pair or the contact pair,basing on Fuoss theory[34],as Eq.(17)described.

According to the hypothesis of localized hydrolysis[29,35],the water molecules in cation hydration shell can be polarized,and then a part of anions can interact with hydrogen atom of the polarized water.This leads to the formation of a solvent separated ionic pair as follows[36].

Fig.9.Bjerrum length of several solvents.

The hypothesis of localized hydrolysis can be considered as a particular case for aqueous solutions of the general pattern of ionic association,named localized solvolysis[37].Ionic association,taking place by localized solvolysis pattern as both cation and anion of the ion pairs,are connected with different parts of the separated solvent molecules by donor-acceptor bonding.The higher the concentration of solution is,the more remarkable the connections are[37].In solvents of ethanol and TFE,the ionic pair are likely to be in the structures as Eqs.(19)and(20)shown respectively.

Consequently,for the extremely concentrated solutions,the amount of free ions with opposite charges are decreased due to the connections of ion pairs with the separated parts of the solvent molecules,and resulting in the reduction of electric conductivity.In order to increase the amount of free ions and electric conductivity,it is necessary to take action to create the protective solvating shells around ions to prevent the interionic attraction and connection.Two examples of the effective actions are to add surfactants and use the solvents with small β value.Next section,blending solvents will be tried,due to their appropriate β value and possibility of facilitating a protective construction.

2.2.3.Electric conductivity of KAc in blending solvents

Electric conductivity of KAc in four bending solvents(90%H2O–10%TFE,80%H2O–20%TFE,90%H2O–10%ethanol,and 80%H2O–20%ethanol)have been measured,and the results are listed in Table 4.

From Fig.10,it can be seen that the goal of improving the electric conductivity of KAc in organic solvents can be really achieved by means of adding a certain proportion of water,and the more the proportion ofwater in blending solvent,the larger the electric conductivity of the measured solution.Here it must be emphasized again,the pure water is not an ideal absorbent for the closed type RED power generation system driven by thermal energy,due to its relative huge latent heat of vaporization(needing much more heat input during the process of solution regeneration)and its relative high operating temperature(requiring the heat source with a higher temperature or operating the system under the negative pressure state),seen in Table 1.

Table 4Electric conductivity results of KAc–H2O–ethanol and KAc–H2O–TFE

Fig.10.Electric conductivity of KAc in blending solvents under vary conditions.

Besides,as illustrated in Fig.10 visibly,electric conductivity of solution KAc–H2O–TFE is larger than solution of KAc–H2O–ethanol at the same experimental condition.In addition,the electric conductivity curves of KAc–H2O–TFE are closer to the aqueous KAc solution than that of the KAc–H2O–ethanol solution,and far above than the solution of KAc in either pure TFE or pure ethanol.If using 20%ethanol(or TFE)to replace 20%water,then the maximum electric conductivity of KAc–H2O–ethanol solution reduces about 40%relative to the aqueous KAc solution,and as for solution KAc–H2O–TFE,itis only about a quarter reduction in its electric conductivity.While at this situation the good news is that the thermal energy consumptions during the solution regeneration process(supposing at 80°C)are only a half for of a RED power generation system working with KAc–H2O–ethanol,and only a third for KAc–H2O–TFE,compared to the aqueous KAc solution.Another benefit of using these blending solvents rather than the pure water is that the whole system can be operated in positive pressure state so that it is not necessary to particularly enhance the leak proof ness of the whole system.

2.3.Electric conductivity estimation

Electric conductivity of diluted solutions can be described by using Kohlrausch equation[28],Onsager limiting equation[28],Fuoss conductance–concentration equation[22],Fuoss–Hsia equation[21],Foss–Chen–Justice equation[38],etc.with the accepted accuracy.However,most of those equations are no longer available for estimating the electric conductivity of concentrated solutions.Researchers in this field made a major improvement over the classical theories by means of formulating a linear response theory in which Onsager continuity equations were combined either with the mean spherical approximation(MSA)or the hypernetted chain equations(HNC)[39,40].This method was applied by Bernard et al.to study the self–diffusion[40]and electrical conductance[41]for 1–1 binary electrolyte solutions(such as aqueous NaCl solution or aqueous KBr solution),with the concentration below 1 mol·L-1.Dufrêche et al.found the combined Smoluchowski–MSA theory of the primitive model was able to describe simultaneously the different transport and equilibrium properties of aqueous alkali chloride(LiCl,NaCl and KCl)solutions with higher concentrations 1–2 mol·L-1[42].Shi et al.further improved the traditional Brownian dynamics simulation method for electrolyte solution estimation on self-diffusion coefficient and molar conductivity by takingthe hydrodynamic interaction effect into account,and resulting a good agreement between the simulation values and the tested data for both aqueous NaCl solution and aqueous KCl solution up to 3 mol·L-1[43,44].Gao et al.extended the Dufrêche et al.’s work by adding the parameter of effective cationic diameter(was a function of total ionic strength),and by means of which,the mutual diffusion coefficients of 18 uni-valence electrolyte solutions were investigated under a wider concentration ranges(0–4 mol·L-1)[39].

Table 5Coefficients of equation for estimating electric conductivity of KAc solutions

Some other efforts were made on developing the electric conductivity theories of mixtures of electrolytes in aqueous solutions.By following Wu et al.'s work[45]and Young's rule[46],Miller found that the simple linear approximations to the specific conductance of a mixture solution(NaCl–MgCl2–H2O,1–2 mol·L-1)could be written in terms of various solute fractions(molar,equivalent,or ionic strength)and the specific conductance of its constituent blending systems[47].Young's rule was also developed by Chen et al.to predict the conductivity of ternary solutions of[PP1,6]Br(N-hexyl,methylpyrrolidinium bromide)–[PP1,4]Br(N-butyl,methylpyrrolidinium bromide)–H2O[48].Hu et al.proposed a simple equation for predicting the electric conductivity of ternary electrolyte solution based on the semi-ideal solution theory and Eyring absolute rate theory,and the accuracy of which was verified by comparing the predicted results with the tested data on NaCl–LaCl3–H2O solution[49],KCl–CdCl2–H2O solutions[47],and[C6mim][Cl](1–hexyl–3–methylimidazolium chloride) –[C6mim][BF4] (1–hexyl–3–methylimidazolium tetra fluoroborate)–H2O solution[50].

Here,a modified amplitude version of Gaussian peak function is used to estimate the electric conductivity of binary and ternary solutions under the wide range of solution concertation.Besides,the format of Arrhenius equation is referred due to its advantage on indicating the impact of temperature factor on chemical reaction rate of solution.The electric conductivity estimation equation is expressed as the follows,

where κTis conductivity value at current solution temperature T(K),mS·cm-1;A1,A2and A3is offset coefficient,amplitude coefficient and width coefficient;Cxis the current solution concentration,by mass percentage;Cm,is the solution concentration at maximum conductivity,by mass percentage.The coefficients of Eq.(21)are listed in Table 5.

The calculated results of electric conductivity of solutions have been drawn in lines and compared with the measured results,which can be seen in Figs.5–8 and 10.Almost all of the measured data are located nearby the estimated lines under different temperature and concentration conditions,and most of the average relative errors are less than 3%(kick off the first test point),and the total average relative error between the measured results and estimated data is about 2.06%.

3.Electric Convertibility of Solutions

3.1.Experimentation

In order to test out the electric convertibility(from salinity gradient energy to electric energy)of the solutions consist of KAc(as solute)and H2O,TFE,ethanol as well as their binary blends(as solvents),a test rig has been designed and built,as Fig.11 illustrated.The RED cells was the key component in this experimental system.Totally 11 CEMs and 10 AEMs(Asahi glass,Japan)were used,and each IEM was in size of 20 cm×10 cm and with effective area of 78.75 cm2.IEM was separated by polyamide woven spacer(Tianwei membrane Tech.,China)and silicone gasket combination with the total thickness of 0.35 mm.Endplates and electrodes were made of polymethyl methacrylate and titanium plates coated with Ru/Ir mixed metal oxide.Peristaltic pumps(Longer Pump,China)were used to feed the weak and strong solutions into the RED cells with the velocity of 0.1 cm·s-1,and to cycle the electrode rinse solutions with flow rate of 100 ml·min-1.Electrode rinse solution was mixed by aqueous solution of KAc,K4Fe(CN)6and K3Fe(CN)6.Three solutions tanks were placed into a thermostatic bath(Julabo,Germany)and controlled at 293.15 K.Power output of the RED cells was measured by the potentiostat(CHI 660E,Chenhua,China).The chronopotentiometry(CP)was applied to measure the internal resistance(Rstack),open circuit voltage(EOCV),and terminal voltage(EVact)[51].The gross output power(P)and power density(Pd)can be estimated as follows:

where Rextis external load resistance,Ω;NIPis number of IEM pairs;Aeis the effective area of IEM.

Fig.11.Schematic diagram of test rig to measure electric convertibility of solutions.

Several pre-experiments were carried out by using aqueous NaCl solution or aqueous LiCl solution to test the usability of this experimental system as well as to reduce the inherent errors as little as possible.Much more details about the experimentation can be seen in the previous introductions[52].

3.2.Results and discussions

3.2.1.Variations of voltage and power density

The output voltage and power density of the RED cells working with six working solution pairs have been tested out under the above introduced experimental conditions,and the six working solution pairs are(1)aqueous KAc solutions(0.05 mol·kg-1as weak solution and 2.5 mol·kg-1as strong solution);(2)KAc in blending solvents consist of 90%water and 10%ethanol(0.05 mol·kg-1as weak solution and 2.5 mol·kg-1as strong solution);(3)KAc in blending solvents consist of 80%water and 20%ethanol(0.05 mol·kg-1as weak solution and 2.5 mol·kg-1as strong solution);(4)aqueous KAc solutions(0.05 mol·kg-1as weak solution and 5 mol·kg-1as strong solution);(5)KAc in blending solvents consist of 90%water and 10%TFE(0.05 mol·kg-1as weak solution and 5 mol·kg-1as strong solution);(6)KAc in blending solvents consist of 80%water and 20%TFE(0.05 mol·kg-1as weak solution and 5 mol·kg-1as strong solution).The test results have been shown in Figs.12 and 13.

Fig.12.Variation relationships of voltage with current for different solutions.

Fig.13.Variation relationships of power density with current for different solutions.

First of all,as Fig.12 drawn,the output voltage of this RED cells is decreased with the increase of current,and their variation relationships are almost linear.Secondly,the output voltage is observably influenced by the solvents.RED cells working with solution pair(4)(0.05 mol·kg-1as weak solution and 5 mol·kg-1as strong solution)possesses the highest output voltage than the other five solution pairs.With the increase of percentage of the TFE(or ethanol)in the blending solvents,the output voltage decreases gradually under this tests.Thirdly,the output voltage is distinctly influenced by the concentration difference between the feeding week solution and the feeding strong solution.Taking the results gained from the tests under working pair(4)(aqueous KAc solutions,0.05 mol·kg-1:5 mol·kg-1)and working pair(1)(aqueous KAc solutions,0.05 mol·kg-1:2.5 mol·kg-1)into to comparison,it can be found that the average output voltage of former(symbol:open square in Fig.12)is about twice than that of the latter(symbol:solid square in Fig.12).It is worth mentioning of that the predicted output voltage cannot be always enlarged with the increase of concentration difference between the feeding solutions.

The output power density of this RED cells is found to be increased with the increase of current firstly,and then reach to the peak value,but later it goes down,seen in Fig.13.RED cells working with aqueous KAc solution possess the highest power density than either the KAc–H2O–TFE solution or the KAc–H2O–ethanol solution.The more the TFE(or ethanol)percentage in bending solvents is,the smaller the output power density of this RED cells.Besides,it is one of ways to enlarge the power density by extending the concentration difference between the feeding strong and weak solutions within a certain range.Finally,the convex parabolic curve relationship in Fig.13 indicates that the maximum power density exists.

3.2.2.Maximum power density and open circuit voltage

The maximum power density(Pdmax)and open circuit voltage(EOCVmax)of this experimental system running with the working solutions consist of KAc,water,TFE,ethanol,or their blends have been tested out and listed in Table 6.The following results are gained:(1)It can be seen that electric convertibility of KAc solutions is equivalent in order of magnitudes with that of NaCl aqueous reported in Ref.[53–55],and better than that of NH3HCO3solution reported in Ref.[15].(2)RED cells working with aqueous KAc solution possesses the biggest Pdmaxthan both of KAc–H2O–TFE and KAc–H2O–ethanol solutions.(3)RED cells working with KAc–H2O–ethanol solution has a bigger EOCVmaxthan the aqueous KAc solution when other testing conditions are the same.(3)When keeping the weak solution of KAc–H2O as a concentration of 0.05 mol·kg-1,but concentrating its strong solution from 0.25 mol·kg-1to 0.5 mol·kg-1,the measured EOCVmaxand Pdmaxare found to be increased 17.9%and 66.2%respectively.The concentration different between the strong solution and weak solution that flow separately in the neighboring compartments of the RED cells is an important factor on electric convertibility.Usually,the concentration different between the feeding solutions can be enlarged by further concentrating the strong solution or further diluting the weak solution.However,their variable range are not unlimited,since that for one hand electric resistivity must be significant for the excessive weak solution,and for another hand electric conductivity will be decreased for the excessive concentrated solution,thus leading to the reduction of EOCVmaxand Pdmax.

To further enlarge the EOCVmaxand Pdmax,the following actions may be workable.For instances,(1)reducing the thicknesses of IEM and gasket(even integrating them together by 3D print technology);(2)reducing the effect of concentration polarization around the IEM;(3)improving the ions permselectivity;(4)increasing solution temperature(but cannot exceed the thermostability of IEM);(5)using practicable feeding solutions with suitable concentrations;(6)adding more pairs of IEMs(such as fifty pairs);(7)adjusting the matched electrode rinse solution with the suitable velocity,and so on.

4.Conclusions

This work reports the measured electric conductivity and electric convertibility of potassium acetate in water,ethanol,2,2,2–trifluoroethanol,2–propanol,water–ethanol blends and water–TFE blends within the wide ranges of solution concentration(up to about 60%in mass concentration)and solution temperature(from 20°C to 60°C)conditions.The experimental temperature and concentration conditions are selected carefully according to the practical operating requirements of working solutions in a closed type RED power generation system that is developed to convert the low grade thermal energy to electric energy.The following conclusions can be gained:

(1)KAc can be ionized in water,ethanol,and TFE,as well as their mixtures,and electric conductibility ranking of these solutions are in the following order of KAc–H2O ＞ KAc–90%H2O–10%TFE ＞ KAc–90%H2O–10%ethanol＞ KAc–TFE ＞ KAc–ethanol＞ KAc–IPA under the same temperature and concentration conditions.The maximum tested electric conductivity is(273.2 ± 5.451)mS·cm-1gained at the concentration of40.11%and the temperature of60°C.

(2)Electric conductivity is influenced by both temperature and concentration factors of solutions.With the increasing of concentration,electric conductivity of solution increases firstly and then reaches the peak value,but later it decreases.Solution temperature plays a positive influence role to the electric conductivity,and the most powerful influence region of temperature on the electric conductivity of solution is located at the place where the peak electric conductivity appears.

(3)Electric conductivity of binary solutions(KAc–H2O,KAc–TFE,KAc–ethanol and KAc–IPA)and ternary solutions(KAc–H2O–ethanol and KAc–H2O–TFE)are verified to be estimable by using a modified amplitude version of Gaussian peak function with a similar format as the Arrhenius exponential equation.The total average relative error between the measured results and estimated data of fifteen solutions is about 2.06%.

Table 6Measured maximum power density and open circuit voltage

(4)Electric convertibility of binary solutions(KAc–H2O)and ternary solutions(KAc–H2O–ethanol and KAc–H2O–TFE)are measured.RED cells working with KAc–H2O solution possesses the biggest output power density(1.428 W·m-2)than both of KAc–H2O–TFE and KAc–H2O–ethanol solutions,while as for maximum open circuit voltage,KAc–H2O working pair is medium in this test,which is larger than KAc–H2O–TFE solutions but smaller than KAc–H2O–ethanol solutions under the same experimental condition.The concentration difference between the feeding strong solution and weak solution is found to be an important impact factor on electric convertibility.

(5)Due to its extremely weak ability of ionization,dissolution and conduction,the KAc–IPA solution is suggested to be excluded for RED power generation system.The solutions of KAc–TFE,KAc–H2O–TFE,and KAc–H2O–ethanol are recommended due to their relative higher solubility and electric conductivity,acceptable electric convertibility,as well as their relative lower latent heat of vaporization and suitable boiling point temperature.