Densities of solutions of NaCl and CsCl in mixtures of water and methanol are determined by experiment and molecular dynamics simulation. Both ex- periments and simulations cover the concentration range up to the solubility limit of the salt in the temperature range 288.15 T/ K318.15 at ambi- ent pressure. Non-polarizable molecular models from the literature are used for the ions and solvents. The partial molar volume of the salts at in nite dilution in the mixed solvent is determined from an empirical correlation of the data. The mixed solvent e ects on the density and the partial molar volumes of the salts are well predicted by the molecular models. Keywords: density measurement, molecular simulation, mixed solvent, 1Author to whom correspondence should be addressed. Electronic mail: maximilian.kohns@mv.uni-kl.de. Telephone: +49-631/205-3216. Fax: +49-631/205-3835. Preprint submitted to Fluid Phase Equilibria November 2, 2017 electrolyte solution 1. Introduction 1 A sound knowledge of thermophysical properties of electrolyte solutions is 2 important for the understanding of natural processes and the design of a 3 wide variety of industrial processes. Aqueous electrolyte solutions have been 4 studied extensively, and more recently, also non-aqueous electrolyte solutions 5 have drawn signi cant attention, because of their importance e.g. in energy 6 storage. However, solutions of salts in mixed solvents have been studied only 7 rarely up to now. In the present work, we therefore investigate the den- 8 sity and related volumetric properties in mixed solvent electrolyte solutions, 9 where the electrolytes are either NaCl or CsCl and the solvent is a mixture 10 of water and methanol. 11 Several experimental studies on densities of solutions of alkali halide salts in 12 mixtures of water and methanol have been reported in the literature. Take- 13 naka et al. [1{3] report densities of such solutions for seven of the 17 alkali 14 halide salts that are soluble both in water and in methanol, namely LiCl, 15 NaCl, KCl, NaBr, KBr, NaI, and KI. For solutions of NaCl, there are three 16 additional investigations [4{6], and Ivanov and Abrosimov [7] study solutions 17 of KBr. Furthermore, there is a detailed investigation by Raatschen [8] on 18 2 solutions of LiBr in mixtures of water and methanol. Werblan [5] reports 19 data on the cesium halides, however, inspection of these data shows consid- 20 erable scatter, cf. Section 4.3. 21 Interestingly, densities of solutions of electrolytes in mixtures of water and 22 methanol have hardly been studied with thermodynamic models. There are 23 several modeling studies dealing with phase equilibria in such systems [9{ 24 19], however, most of the these works employ models for the excess Gibbs 25 energy, so that solution densities cannot be obtained. Equations of state 26 (EOS), which enable density calculations, have only very recently been ex- 27 tended towards the modeling of mixed solvent electrolyte solutions. This 28 is e.g. the case for the ePC-SAFT EOS [17], the SAFT-VRE EOS [18] and 29 the electrolyte CPA EOS [19]. Molecular simulations are particularly attrac- 30 tive for modeling mixed solvent electrolyte solutions due to the low number 31 of adjustable parameters and a strong physical background. However, we 32 are aware only of the work of Strauch and Cummings [12], who investigate 33 the vapor-liquid equilibrium of solutions of NaCl in mixtures of water and 34 methanol and also report the densities of the coexisting phases. 35 In contrast, solutions of a salt - in most cases NaCl - in pure water have been 36 studied extensively with molecular simulations in the recent literature. In 37 3 these studies, mainly the di erences between polarizable and non-polarizable 38 models were investigated. Models including polarizability, such as the alkali 39 halide models developed around the polarizable water models SWM4-DP 40 [20] and BK3 [21], were found to perform better than non-polarizable ones in 41 some aspects, e.g. concerning the description of activity coecients [22, 23]. 42 Interestingly, this does not necessarily result in an improved prediction of the 43 salt solubility [23]. When considering other properties such as the density, 44 simple non-polarizable models are found to be of almost the same quality 45 as the polarizable ones [23]. Furthermore, non-polarizable models can in 46 principle describe a variety of properties of electrolyte solutions fairly well. 47 However, the systematic assessment of Orozco et al. [24] shows that none of 48 the existing model parameterizations is able to quantitatively describe sev- 49 eral properties at once. This suggests that better model parameterizations 50 can be found [25]. For a more detailed discussion of the recent advances in 51 the eld, see the comprehensive review by Nezbeda et al. [26]. 52 In the present work, we rst report new experimental density data for the 53 systems water-methanol-NaCl and water-methanol-CsCl. Our experiments 54 cover the entire concentration range up to the solubility limit of the salt, 55 and we report data for the temperatures 288.15, 293.15, 298.15, 308.15, and 56 4 318.15 K. Second, we address the question whether simple non-polarizable 57 molecular models based on Lennard-Jones (LJ) sites and partial charges can 58 predict volumetric properties of the studied electrolyte solutions. In our dis- 59 cussion, the partial molar volume of the salt at in nite dilution is of particu- 60 lar interest, because it is a very sensitive property and provides a descriptive 61 view of the salt-solvent interactions. 62 Throughout this work, the composition of a ternary solution of a salt CA, 63 which completely dissociates into the ions C+and A, in a mixture of wa- 64 ter and methanol is described by the methanol mole fraction of the salt-free 65 solvent mixture MeOH66 MeOH =nMeOH=(nMeOH +nW) (1) and the true mole fraction of the cation xC+ 67 xC+=nC+=(nC++nA+nMeOH +nW); (2) whereniare the mole numbers. 68 5 2. Experiments 69 Ultradry methanol ( 50 ppm water) with a purity of 99.9 % was pur- 70 chased from Roth. Deionized water was produced by an Elix Essential 5UV71 of Merck Millipore and degassed by boiling before use. NaCl was purchased 72 from Merck with a purity of 99.5 % and CsCl was purchased from Roth 73 with a purity of99.999 %. The salts were dried in a vacuum oven at 353 K 74 for 24 h. 75 The electrolyte solutions were prepared gravimetrically (AE240, Mettler- 76 Toledo) in a glovebox (GS Glovebox Technik). In case of mixed solvents, 77 about 200 ml of a stock solution of water + methanol of the desired com- 78 position MeOH was prepared rst. All reported experimental data for one 79 salt at one salt-free solvent composition MeOH were obtained using one sin- 80 gle stock solution. The solvent (pure or mixed) was then added to a known 81 amount of salt to yield samples of about 20 ml. Uncertainties in the compo- 82 sition variables MeOH andxC+were estimated from error propagation of the 83 uncertainty of the balance. Thereby, the uncertainty of the salt-free solvent 84 composition MeOH is found to be better than 0.00002 mol mol1. The 85 uncertainty of the mole fraction of the cation xC+is found to be better than 86 0.0002 mol mol1in most cases, except for the highly concentrated CsCl 87 6 solutions, for which it is up to 0.0009 mol mol1. 88 As a guide to the accessible concentration range in case of solutions of NaCl, 89 the solubility data of Pinho and Macedo [14] were used. They proved to be 90 reliable during the present experiments. In case of CsCl, the solubility is only 91 known for the pure solvents water [27] and methanol [28], but not for mixed 92 solvents. As an estimate, we assumed the same qualitative dependence of 93 the solubility on the composition of the solvent mixture as for NaCl. 94 The densities of the samples were measured with a vibrating tube densimeter 95 (DMA 4500 M, Anton Paar), which was calibrated with air and deionized 96 water. Based on the repetition of several experiments and the resolution 97 provided by the densimeter, the uncertainty of the reported densities is es- 98 timated to be better than 0.0001 g cm3. The temperature was measured 99 with the densimeter's built-in thermometer, for which the supplier claims an 100 uncertainty of0.1 K. 101 To obtain the partial molar volume of the salt at in nite dilution v1 saltin the 102 solvent from the measured densities, a simple empirical correlation is devel- 103 oped in the present work, cf. Sections 4.1 and 4.2. The uncertainty in the 104 numbers for v1 saltobtained from that correlation was estimated by randomly 105 disturbing the measured densities with their uncertainty and using these val- 106 7 ues for the ts. Thereby, the uncertainty in v1 saltis estimated to be better 107 than0:5 cm3mol1and thus of similar magnitude as the uncertainties 108 reported by Takenaka et al. [1]. 109 3. Molecular Simulation 110 In the present work, rigid, non-polarizable molecular models for the solvents 111 and ions are employed. The water model SPC/E is taken from the literature 112 [29], the ion models and the methanol model are taken from previous work 113 of our group. For methanol, we employ the molecular model of Schnabel et 114 al. [30], which was optimized with respect to the vapor-liquid equilibrium of 115 pure methanol. For the ions, molecular models of the Lennard-Jones (LJ) 116 + point charge type from the ion model set of Reiser et al. [31] are used. 117 The models of that set were trained together with the SPC/E water model 118 mainly using density data of dilute aqueous solutions of all alkali halide salts 119 [32]. Thus, the models used here for NaCl and CsCl were not optimized 120 for describing the individual salts, but taken from an ion model set which 121 includes all alkali and halide ions. Therefore, the Clmodel is the same for 122 both salts studied here. 123 Molecular dynamics (MD) simulations of methanol-water mixtures, employ- 124 8 ing the Schnabel et al. [30] model for methanol and several popular water 125 models (including SPC/E) were previously conducted by Guevara-Carri on 126 et al. [33, 34] and Pa rez et al. [35], but with a focus on transport proper- 127 ties. In another previous study [36], the predictions obtained from combining 128 the ion models of the set of Reiser et al. [31] with the methanol model of 129 Schnabel et al. [30] using the Lorentz-Berthelot combining rules were already 130 studied. Good agreement with experimental data for solutions of all alkali 131 halide salts in methanol was found even though the ion models had only 132 been trained with data on aqueous solutions. Altogether, these results from 133 previous studies suggest that the employed models are suited as a starting 134 point for modeling ternary solutions. 135 All models employ LJ sites and point or partial charges, so that the potential 136 writes [37] 137 U=ULJ+UC =N1X i=1NX j=i+1(nLJ iX a=1nLJ jX b=14ijab"ijab rijab12 ijab rijab6# +ne iX c=1ne jX d=11 4"0qicqjd rijcd) ; (3) 9 where the indices a;b;c; anddrefer to model interaction sites and iandj 138 refer to molecules (including ions), "0is the vacuum permittivity, ijaband 139 ijabare the Lennard-Jones energy and size parameters, rijabandrijcdare 140 site-site distances, and qicandqjdare the magnitudes of the point charges. 141 The interaction between unlike LJ sites is described by the modi ed Lorentz- 142 Berthelot combining rules [38, 39] 143 ijab=ijiiaa+jjbb 2; (4) ijab=piiaajjbb: (5) A binary interaction parameter ijdi erent from 1 is only employed in the 144 unlike interaction water-methanol and adjusted to experimental data of the 145 molar excess volume at 298.15 K, cf. Section 4.1. This correction is in- 146 troduced into the Lorentz rule here as the unlike size parameter obviously 147 shows a much larger in uence on densities than the unlike energy parameter, 148 which is in line with a general theoretical analysis by Fischer et al. [40]. The 149 adjustment was carried out to ensure a good description of the volumetric 150 properties of the salt-free solvent mixture. It has only a minor impact on the 151 10 results obtained for the properties of the electrolytes in the mixed solvent on 152 which we focus here. 153 Densities were obtained by standard MD simulations in the NpT ensemble 154 for the temperatures 288.15, 298.15 and 318.15 K. Simulation details are 155 given in Appendix A. For each studied salt-free solvent composition, the 156 simulations were carried up to the experimental solubility limit of the salt. 157 To obtain the partial molar volume of the salt at in nite dilution in the sol- 158 vent from the densities obtained in these simulations, the same correlation 159 as for the measured densities was employed, cf. Sections 4.1 and 4.2. 160 4. Results and Discussion 161 The solution densities obtained from the experiments and the molecular sim- 162 ulations are reported in Tables 1 - 4. The densities of the studied salt-free 163 solvents are reported together with the data for NaCl. To improve the read- 164 ability of the plots, in most gures we only display the experimental results 165 for 288.15, 298.15 and 318.15 K, and omit those for 293.15 and 308.15 K. 166 11 Table 1: Experimental data for the density of solutions of NaCl in mixtures of water and methanol at 1 bar. The uncertainties are: u( MeOH ) =0:00002 mol mol1,u() =0:0001 g cm3,u(T) =0:1 K. ForxNa+, the uncer- tainty of the last digit is given in parentheses, or omitted where it is below 0:0001 mol mol1. / g cm3 MeOH /xNa+/ T/ K mol mol1mol mol1288.15 293.15 298.15 308.15 318.15 0 0 0:9991 0:9982 0:9970 0:9940 0:9902 0.0099(1) 1:0222 1:0210 1:0196 1:0162 1:0121 0.0196(2) 1:0447 1:0432 1:0416 1:0378 1:0335 0.0291(2) 1:0658 1:0641 1:0623 1:0582 1:0536 0.0385(3) 1:0867 1:0848 1:0828 1:0785 1:0737 0.0476(3) 1:1074 1:1054 1:1033 1:0987 1:0938 0.0566(4) 1:1272 1:1250 1:1227 1:1180 1:1129 0.0654(4) 1:1471 1:1448 1:1424 1:1374 1:1322 0.25 0 0:9421 0:9393 0:9364 0:9301 0:9234 0.0040 0:9503 0:9475 0:9445 0:9382 0:9315 0.0098(1) 0:9603 0:9574 0:9544 0:9480 0:9413 0.0229(2) 0:9845 0:9815 0:9784 0:9719 0:9651 0.0336(2) 1:0043 1:0012 0:998 0:9914 0:9845 0.5 0 0:8892 0:8854 0:8815 0:8736 0:8653 0.0020 0:8921 0:8883 0:8844 0:8765 0:8682 0.0049 0:8968 0:8930 0:8891 0:8811 0:8729 0.0079(1) 0:9014 0:8975 0:8937 0:8857 0:8775 0.0117(1) 0:9074 0:9036 0:8997 0:8917 0:8835 0.0146(1) 0:9125 0:9087 0:9048 0:8968 0:8886 0.0192(1) 0:9189 0:9150 0:9111 0:9031 0:8949 12 Table 1 continued. / g cm3 MeOH /xNa+/ T/ K mol mol1mol mol1288.15 293.15 298.15 308.15 318.15 0.75 0 0:8398 0:8355 0:8312 0:8224 0:8134 0.0013 0:8418 0:8375 0:8332 0:8245 0:8155 0.0027 0:8437 0:8395 0:8352 0:8264 0:8175 0.0053 0:8471 0:8428 0:8385 0:8298 0:8209 0.0079 0:8509 0:8467 0:8424 0:8337 0:8248 0.0104(1) 0:8558 0:8516 0:8473 0:8387 0:8298 0.0130(1) 0:8584 0:8541 0:8498 0:8412 0:8323 1 0 0:7959 0:7913 0:7866 0:7771 0:7675 0.0010 0:7974 0:7927 0:7880 0:7786 0:7690 0.0020 0:7989 0:7943 0:7896 0:7802 0:7707 0.0030 0:8001 0:7955 0:7908 0:7814 0:7719 0.0040 0:8014 0:7968 0:7921 0:7827 0:7733 0.0050 0:8029 0:7983 0:7937 0:7843 0:7748 0.0060 0:8041 0:7995 0:7949 0:7855 0:7761 0.0070 0:8057 0:8011 0:7964 0:7871 0:7777 13 Table 2: Experimental data for the density of solutions of CsCl in mixtures of water and methanol at 1 bar. The uncertainties are: u( MeOH ) =0:00002 mol mol1,u() =0:0001 g cm3,u(T) =0:1 K. ForxCs+, the uncertainty of the last digit is given in parentheses, or omitted where it is below 0:0001 mol mol1. / g cm3 MeOH /xCs+/ T/ K mol mol1mol mol1288.15 293.15 298.15 308.15 318.15 0 0.0099(1) 1:0697 1:0684 1:0670 1:0635 1:0592 0.0196(2) 1:1373 1:1358 1:1341 1:1301 1:1255 0.0292(2) 1:2033 1:2016 1:1996 1:1952 1:1902 0.0385(3) 1:2662 1:2642 1:2620 1:2573 1:252 0.0536(7) 1:3670 1:3646 1:3621 1:3567 1:3509 0.0690(9) 1:4669 1:4641 1:4613 1:4553 1:4486 0.25 0.0192(3) 1:0661 1:0650 1:0623 1:0564 1:0501 0.0370(5) 1:1664 1:1635 1:1604 1:1540 1:1471 0.0536(7) 1:2534 1:2501 1:2466 1:2395 1:2311 0.5 0.0074 0:9248 0:9208 0:9169 0:9088 0:9004 0.0146(1) 0:9597 0:9557 0:9517 0:9435 0:9350 0.0215(1) 0:9916 0:9876 0:9835 0:9751 0:9665 0.0283(2) 1:0241 1:0200 1:0158 1:0073 0:9986 0.0349(2) 1:0564 1:0522 1:0480 1:0394 1:0305 0.75 0.0025 0:8511 0:8468 0:8424 0:8336 0:8246 0.0050 0:8611 0:8568 0:8524 0:8436 0:8346 0.0074 0:8712 0:8669 0:8625 0:8536 0:8445 0.0098(1) 0:8808 0:8764 0:8720 0:8631 0:8540 0.0122(1) 0:8901 0:8857 0:8813 0:8723 0:8632 1 0.0012 0:8008 0:7961 0:7913 0:7818 0:7723 0.0025 0:8055 0:8008 0:7960 0:7865 0:7769 0.0037 0:8099 0:8052 0:8005 0:7910 0:7814 0.0049 0:8145 0:8098 0:8051 0:7955 0:7859 14 Table 3: Molecular simulation data for the density of solutions of NaCl in mixtures of water and methanol at 1 bar. For the density, the uncertainty of the last digit is given in parentheses. / g cm3 MeOH /xNa+/ T/ K mol mol1mol mol1288.15 298.15 318.15 0 0 1:0042(2) 0:9996(2) 0:9879(2) 0.02 1:0407(2) 1:0357(2) 1:0232(2) 0.04 1:0762(2) 1:0708(2) 1:0577(2) 0.06 1:1107(2) 1:1045(2) 1:0907(2) 0.25 0 0:9493(2) 0:9407(2) 0:9237(2) 0.01 0:9646(2) 0:9559(2) 0:9385(2) 0.02 0:9789(2) 0:9710(2) 0:9531(2) 0.03 0:9945(2) 0:9867(2) 0:9679(2) 0.5 0 0:8931(2) 0:8838(2) 0:8644(2) 0.005 0:8995(2) 0:8904(2) 0:8710(2) 0.01 0:9061(2) 0:8966(2) 0:8778(2) 0.015 0:9127(2) 0:9036(2) 0:8838(2) 0.75 0 0:8427(2) 0:8337(2) 0:8141(2) 0.004 0:8484(2) 0:8391(2) 0:8196(2) 0.008 0:8533(2) 0:8436(2) 0:8246(2) 0.12 0:8584(2) 0:8489(2) 0:8299(2) 1 0 0:7974(2) 0:7880(1) 0:7687(1) 0.002 0:8002(2) 0:7910(2) 0:7717(1) 0.004 0:8029(1) 0:7938(1) 0:7743(1) 0.006 0:8056(2) 0:7963(2) 0:7770(1) 15 Table 4: Molecular simulation data for the density of solutions of CsCl in mixtures of water and methanol at 1 bar. For the density, the uncertainty of the last digit is given in parentheses. / g cm3 MeOH /xCs+/ T/ K mol mol1mol mol1288.15 298.15 318.15 0 0.02 1:1262(2) 1:1212(2) 1:1086(2) 0.04 1:2437(2) 1:2379(2) 1:2245(2) 0.06 1:3549(2) 1:3487(2) 1:3353(2) 0.25 0.02 1:0493(2) 1:0404(2) 1:0226(2) 0.04 1:1470(2) 1:1378(3) 1:1194(2) 0.06 1:2420(2) 1:2331(3) 1:2143(2) 0.5 0.01 0:9358(2) 0:9256(2) 0:9061(2) 0.02 0:9772(2) 0:9678(2) 0:9479(2) 0.03 1:0182(3) 1:0100(2) 0:9900(2) 0.75 0.004 0:8576(2) 0:8486(2) 0:8287(2) 0.008 0:8720(2) 0:8627(2) 0:8432(2) 0.012 0:8869(2) 0:8775(2) 0:8578(2) 1 0.002 0:8041(2) 0:7943(1) 0:7751(1) 0.004 0:8105(1) 0:8012(1) 0:7818(1) 0.006 0:8175(1) 0:8079(1) 0:7886(1) 16 4.1. Salt-free Solvent Mixture 167 Studying a ternary electrolyte solution rst requires an adequate description 168 of the salt-free solvent mixture. The volumetric behavior of the salt-free 169 solvent mixture water-methanol is discussed here based on the molar excess 170 volumevE171 vE(T; MeOH ) =v(T; MeOH ) MeOHvpure MeOH (T)(1 MeOH )vpure W(T);(6) wherevis the molar volume of the mixture, vpure iare the pure component 172 molar volumes, and the methanol mole fraction is MeOH in our notation. 173 Results for the molar excess volume of the mixture water + methanol at 174 298.15 K are shown in Fig. 1. 175 The experimental results from the present work are compared to a correlation 176 of experimental data of Coquelet et al. [41]. Excellent agreement is observed. 177 The deviations are below about 0:01 cm3mol1. Furthermore, molecular 178 simulation results from the present work are shown. They were obtained 179 usingWMeOH = 0:993. That parameter was t to reproduce the minimum 180 ofvE, which is found for equimolar composition both experimentally and 181 17 0 0:20:40:60:8 110:80:60:40:20 MeOH / mol mol1vE=cm3mol1Figure 1: Molar excess volume of mixtures of water and methanol at 298.15 K. ( ) experimental data, this work, ( ) molecular simulation data, this work, () correlation of experimental data by Coquelet et al. [41], ( ) correlation of the present molecular simulation data. in the simulations. The deviation of WMeOH from 1 is only small. Using 182 WMeOH = 1, the minimum of vEis about 15% above the experimental 183 result. Using the adjusted value of WMeOH , the dependence of vEon MeOH184 is predicted well by the simulation. 185 The density of the salt-free solvent mixture is the basis for the correlation 186 used here for describing the density of the ternary electrolyte solutions. As 187 Coquelet et al. [41], we employ a Redlich-Kister type correlation, which in 188 our notation writes as 189 18 vE(T; MeOH ) = (1 MeOH ) MeOHX kAk(T)(12 MeOH )k; k= 0;1;::: ; (7) where theAkare t parameters. We also use Eq. (7) here for correlating 190 the molecular simulation data. The Redlich-Kister coecients Akfor de- 191 scribing the molar excess volume of mixtures of water and methanol for all 192 temperatures studied here are presented in Appendix B, cf. Table B.1. Two 193 parameter sets are reported. The rst one describes the experimental data. 194 It is adopted from Coquelet et al. [41], but also describes the present exper- 195 imental results within their uncertainty. The second one is obtained from 196 a t to the present simulation data for the system water + methanol. The 197 densities of pure water and pure methanol, which are needed in addition to 198 the Redlich-Kister t to calculate the density of the mixture, are taken from 199 Tables 1 and 3. 200 4.2. Electrolyte Solutions 201 Fig. 2 shows the measured and simulated densities of solutions of NaCl and 202 of CsCl in mixtures of water and methanol at 298.15 K. 203 19 0 0.02 0.04 0.060.80.911.1 xNa+/ mol mol−1ρ/ g cm−3χMeOH = 0.00 0 0.01 0.02 0.030.80.911.1 xNa+/ mol mol−1ρ/ g cm−3χMeOH = 0.25 0 0.006 0.012 0.0180.80.911.1 xNa+/ mol mol−1ρ/ g cm−3χMeOH = 0.50 0 0.004 0.008 0.0120.80.911.1 xNa+/ mol mol−1ρ/ g cm−3χMeOH = 0.75 0 0.002 0.004 0.0060.80.911.1 xNa+/ mol mol−1ρ/ g cm−3χMeOH = 1.00 0 0.02 0.04 0.060.811.21.4 xCs+/ mol mol−1ρ/ g cm−3χMeOH = 0.00 0 0.02 0.04 0.060.811.21.4 xCs+/ mol mol−1ρ/ g cm−3χMeOH = 0.25 0 0.01 0.02 0.030.811.21.4 xCs+/ mol mol−1ρ/ g cm−3χMeOH = 0.50 0 0.004 0.008 0.0120.811.21.4 xCs+/ mol mol−1ρ/ g cm−3χMeOH = 0.75 0 0.002 0.004 0.0060.811.21.4 xCs+/ mol mol−1ρ/ g cm−3χMeOH = 1.00Figure 2: Densities of solutions of NaCl (left column) and CsCl (right col- umn) in mixtures of water and methanol over the cation mole fraction at 298.15 K. Results from the present work: ( ) experiment, () molecular simulation, () correlation of experimental data, ( ) correlation of molec- ular simulation data. 20 For both salts in pure water ( MeOH = 0), the increase in the density upon 204 addition of the salt is slightly underpredicted by the models. The salt models 205 used here are not individual models but taken from an ion model set for 206 all alkali halides, so that compromises regarding the performance for some 207 salts had to be made [32]. However, the higher the methanol content in 208 the mixture, the better the agreement between experiment and simulation. 209 This is a remarkable nding since in the development of the ion models, only 210 data on aqueous solutions were used. The in uence of adding methanol is 211 predicted surprisingly well by the models. 212 In previous work of our group [36, 42], it was found that both for aqueous 213 and methanolic solutions of alkali halide salts, the density of the solution is 214 an almost perfectly linear function of the ion mole fraction. That nding was 215 based on results for xC+0:05 mol mol1. The present results, both from 216 experiment and from molecular simulation, show that the linearity holds also 217 up to the solubility limit for the studied salts. Additionally, the linear relation 218 is also found to hold for mixed solvents. Thus, for the ternary electrolyte 219 solutions, we employ the correlation 220 21 (T; MeOH;xC+) =solv(T; MeOH ) +bsalt(T; MeOH )xC+ (8) withbsalt=@ @xC+ T; MeOH; (9) wheresolvis the density of the salt-free solvent mixture, which is obtained 221 as described in the previous section. The slope of the density bsaltwas t to 222 the data for each individual solvent composition. 223 In Fig. 3, the slope of the density bsaltdetermined from experimental and 224 molecular simulation data is shown for 288.15, 298.15 and 318.15 K. 225 0 0.20.40.60.8 11.21.41.61.822.2 χMeOH / mol mol−1bNaCl/g cm−3 0 0.20.40.60.8 14567 χMeOH / mol mol−1bCsCl/g cm−3 Figure 3: Slope of the density bsalt, cf. Eq. (9), of NaCl solutions (left) and CsCl solutions (right) over the composition of the salt-free solvent mixture water + methanol. Colors indicate the isotherms 288.15 K (blue), 298.15 K (gray) and 318.15 K (red). As the temperature in uence is small, the results overlap. Results from the present work: ( ) experiment, () molecular sim- ulation, () correlation of experimental data, ( ) correlation of molecular simulation data. 22 The experimental data of the NaCl solutions reveal a surprising behavior: 226 For aqueous solutions, the slope of the density decreases with increasing 227 temperature. This trend is reversed for methanolic solutions. Furthermore, 228 at approximately equimolar composition of the salt-free solvent mixture, the 229 slope of the density is independent of the temperature. This behavior is also 230 predicted by the molecular simulations. The experimental results show that 231 bNaCldoes not decline linearly with increasing MeOH . The trend is predicted 232 well by the molecular simulations. In the simulations, a shallow minimum is 233 found for all temperatures, which is present in the experimental data only 234 for the higher temperatures. 235 The experimental data of the CsCl solutions show a more steady decline of the 236 slope of the density when adding methanol to the solution. Comparing NaCl 237 and CsCl in pure methanol, the temperature dependence is reversed: bNaCl238 decreases with increasing temperature, while bCsClincreases with increasing 239 temperature. Consequently, for CsCl solutions the isotherms of the slope of 240 the density do not intersect. In general, the temperature dependence of bCsCl241 is weaker than the temperature dependence of bNaCl. All this is predicted 242 well by the molecular models. 243 To establish a correlation, bsaltis described by a polynomial of second degree: 244 23 bsalt(T; MeOH ) =b2;salt(T) 2 MeOH +b1;salt(T) MeOH +b0;salt(T) (10) The t parameters bk;salt were determined individually for each isotherm for 245 both the experimental and the simulation data and are given in Appendix 246 B, cf. Table B.2. 247 Together with the pure component molar volumes of water and methanol, 248 Eqs. (7), (8) and (10) fully determine the density in the ternary system 249 water-methanol-salt. From that correlation, it is possible to deduce any 250 volumetric property of interest. In the following, we focus on the partial 251 molar volume of the salt at in nite dilution v1 saltin the mixed solvent with 252 composition MeOH . It can be shown that, from the correlation developed 253 here, this quantity can be obtained as 254 v1 salt(T; MeOH ) =bsalt(T; MeOH )Msolv+Msaltsolv(T; MeOH ) solv(T; MeOH )2(11) Msolv= MeOHMMeOH + (1 MeOH )MW; (12) whereMiis the molar mass of component i. 255 The results for the partial molar volume of both salts at in nite dilution as 256 24 determined from experiments and predicted by the simulations are shown in 257 Fig. 4. 258 0 0.20.40.60.8 1−1001020 χMeOH / mol mol−1v∞ NaCl/cm3mol−1 0 0.20.40.60.8 12030405060 χMeOH / mol mol−1v∞ CsCl/cm3mol−1 Figure 4: Partial molar volume of the salt at in nite dilution v1 salt, cf. Eq. (11), of NaCl solutions (left) and CsCl solutions (right) over the composition of the salt-free solvent mixture water + methanol. Colors indicate the isotherms 288.15 K (blue), 298.15 K (gray) and 318.15 K (red). Results from the present work: () correlation of experimental data, ( ) correlation of molecular simulation data. Both for NaCl and CsCl, the partial molar volume of the salt is distinctly 259 lower in methanol than in water. This indicates that the ions have a strong 260 ordering e ect especially on methanol. For NaCl solutions, v1 NaCl depends 261 only weakly on MeOH for MeOH below about 0.5 mol mol1, while for larger 262 MeOH an important decrease of v1 NaClis observed. For CsCl solutions, the 263 decrease of v1 CsClis more steady. 264 The temperature dependence of v1 saltis weak both for NaCl and CsCl. While 265 v1 NaCl increases slightly with increasing temperature in water, it decreases 266 25 with increasing temperature in methanol. The same is true for v1 CsCl. For 267 both salts, there is a solvent composition for which the temperature depen- 268 dence vanishes. For high temperatures, the partial molar volume of NaCl 269 in methanol is negative. This is remarkable since despite addition of salt, 270 the volume of the solution decreases. In contrast, the partial molar volume 271 of CsCl in methanol is positive. Comparing both salts and considering that 272 they comprise the same anion shows that especially Na+ions have a strong 273 in uence on the structure of methanol. 274 The experimental ndings discussed above are correctly predicted by the 275 molecular simulations. However, there are some quantitative di erences 276 which are of the order of 10 cm3mol1for both salts. Fig. 4 clearly shows 277 that they are induced by the models of the systems salt + pure solvent, while 278 the e ects of the mixed solvents are well predicted. Taking into account that 279 the salt models were taken from an ion model set and not adjusted individ- 280 ually and the fact that adjustments of the ion models were only made using 281 experimental data for the solvent water, the predictions are of remarkable 282 quality. 283 To point out the di erent behavior of the salts in the two pure solvents water 284 and methanol more clearly, the temperature dependence of v1 saltin both pure 285 26 solvents is shown in Fig. 5. 286 290 300 310 320−1001020χMeOH = 0 χMeOH = 1 T/ Kv∞ NaCl/cm3mol−1 290 300 310 320204060χMeOH = 0 χMeOH = 1 T/ Kv∞ CsCl/cm3mol−1 Figure 5: Partial molar volume of the salt at in nite dilution v1 salt, cf. Eq. (11), of NaCl solutions (left) and CsCl solutions (right) over the temperature. The two sets of data in each plot correspond to pure water as the solvent ( MeOH = 0, top) and pure methanol as the solvent ( MeOH = 1, bottom). Results from the present work: ( ) experiment, () molecular simulation. Dotted lines are guides to the eye. As already known from Fig. 4, for both salts v1 saltincreases with increasing 287 temperature in an aqueous solution, while it decreases with increasing tem- 288 perature in a methanolic solution. This feature and also the quantitative 289 incline / decline is predicted well by the molecular simulations. It is instruc- 290 tive to interpret this behavior in the light of Kirkwood-Bu theory [43{45]. 291 The present results indicate that for both salts in water, the total correlation 292 of the ions with the solvent molecules is lowered with increasing temperature. 293 In contrast, for both salts in methanol the total correlation of the ions with 294 the solvent molecules is enhanced with increasing temperature. A rigorous 295 27 assessment of this relation might be carried out using additional simulations. 296 However, that study is beyond the scope of the present work as large system 297 sizes are needed to avoid nite size e ects [46] and Kirkwood-Bu integrals 298 usually show poor convergence [47], which is especially cumbersome for the 299 in nite dilution case studied here. 300 4.3. Comparison of Experimental Data from the Literature and the Present 301 Work 302 For both systems studied in the present work, density data have been re- 303 ported before. 304 There are four sets of data for NaCl in solutions of water and methanol: 305 Takenaka et al. [1] studied the system in great detail, covering the same con- 306 centration and temperature ranges as the present work. Khimenko [4] and 307 Werblan [5] studied only the isotherms 293.15 K and 298.15 K, respectively, 308 and their works also cover only parts of the concentration range. For these 309 two sets of data, the numbers were taken here from the Dortmund Data Bank 310 [48] because the original sources could not be retrieved. The fourth data set 311 on NaCl solutions is that of Guetachew et al. [6], who report densities at 312 298.15 K. Unfortunately, it is dicult to compare their data to any of the 313 other sets because their measurements were not carried out at constant com- 314 28 positions of the salt-free solvent mixture. That data set is therefore omitted 315 in the following discussion. 316 For solutions of CsCl in mixtures of water and methanol, densities have so 317 far only been reported by Werblan [5]. Also that data set was taken from 318 the Dortmund Data Bank because the original source could not be retrieved. 319 In Fig. 6, the experimental data from the literature are compared to the cor- 320 relation of experimental data developed in the present work. Since di erent 321 salt-free solvent compositions were studied in the literature, this comparison 322 is carried out based on the slope of the density bsalt( MeOH ) at 298.15 K. To 323 this end, the literature data were correlated using the same linear relation- 324 ship as for the data of the present work, cf. Eq. (8). The linear trend was 325 con rmed from inspection of the data of Takenaka et al. [1] and of Khimenko 326 [4], while the data of Werblan [5] showed considerable scatter. 327 For the pure solvents water and methanol, the results from experiments from 328 previous work of our group [36, 42] are also included in Fig. 6. They are 329 in very good agreement with the correlation developed in the present work. 330 For solutions of NaCl in mixtures of water and methanol, the agreement 331 between the data of Takenaka et al. [1] and the correlation to experimental 332 data obtained in the present work is excellent. The data of Khimenko [4], 333 29 0 0.20.40.60.8 11.522.5 χMeOH / mol mol−1bNaCl/g cm−3 0 0.20.40.60.8 14567 χMeOH / mol mol−1bCsCl/g cm−3Figure 6: Slope of the density bsalt, cf. Eq. (9), of NaCl solutions (left) and CsCl solutions (right) over the composition of the salt-free solvent mixture water + methanol. All displayed data are at 298.15 K except for the results of Khimenko [4], which are at 293.15 K. The lines represent the correlation of experimental data from the present work. Symbols denote experimental data from the literature: ( ) Takenaka et al. [1], ( ) Khimenko [4], ( ?) Werblan [5], (4) Reiser et al. [36, 42]. For solutions of NaCl and CsCl in pure water, the results of Reiser et al. [42] were interpolated between 293.15 and 303.15 K. which were reported only for high water concentrations, deviate considerably 334 from both our data and those of Takenaka et al. [1]. The same holds for most 335 of the data of Werblan [5], which scatter very strongly. 336 5. Conclusions 337 Densities of solutions of NaCl and CsCl in mixtures of water and methanol 338 were studied by experiment and molecular simulation. For the NaCl solu- 339 tions, the experimental data from the present work are found to be in very 340 good agreement to those reported by Takenaka et al. [1]. For the CsCl solu- 341 30 tions, up to now only the unreliable data of Werblan [5] were available. 342 The employed molecular models for the ions were taken from a set of models 343 for all alkali and halide ions, for which the parameters were obtained by a 344 t to density data of dilute aqueous solutions only. The ion models are com- 345 bined with established solvent models using the Lorentz-Berthelot combining 346 rules. The models show excellent predictions for the dependence of the elec- 347 trolyte solution density on the composition of the salt-free solvent mixture. 348 Also the temperature dependence is predicted correctly. Some quantitative 349 di erences are found, which stem, however, from deviations in the models 350 of the electrolytes in the pure solvents, for which no individual adjustments 351 were carried out. Altogether, taking into account that the employed molec- 352 ular models are very simple, the results are very encouraging. 353 Both salts are found to behave di erently in the two pure solvents water and 354 methanol. The present results indicate that the e ect of ions on methanol 355 is even more pronounced than their e ect on water. This is especially true 356 for the Na+ion. The good agreement between simulations and experiments 357 shows that the employed models give a realistic picture of the solution be- 358 havior. Therefore, subsequent molecular simulations should be carried out in 359 future work, as they can provide additional insight into the solution behavior 360 31 on the molecular level. 361 Acknowledgments 362 The authors gratefully acknowledge nancial support by the Reinhart Kosel- 363 leck Program (HA1993/15-1) of the German Research Foundation (DFG). 364 The present work was conducted under the auspices of the Boltzmann-Zuse 365 Society of Computational Molecular Engineering (BZS) and the simulations 366 were carried out on the Regional University Computing Center Kaisers- 367 lautern (RHRK) under the grant TUKL-TLMV, the High Performance Com- 368 puting Center Stuttgart (HLRS) under the grant MMHBF as well as the Leib- 369 niz Supercomputing Centre (LRZ) under the grant SPARLAMPE (pr48te). 370 Funding 371 This work was supported by the Reinhart Koselleck Program (HA1993/15-1) 372 of the German Research Foundation (DFG). 373 Appendix A. Simulation Details 374 In the present work, MD simulations were carried out with the molecular 375 simulation program ms2 [49]. Equilibration and production took 100,000 376 and 2,000,000 time steps of length 1.2 fs, respectively. The equations of 377 32 motion were integrated with a gear predictor-corrector scheme of fth or- 378 der. The simulations were run with a total of 1000 particles in the NpT 379 ensemble, employing the velocity scaling thermostat and Andersen's baro- 380 stat. All interactions were evaluated explicitly up to the cuto radius of 15 381 A. The usual LJ long-range corrections to the virial and the energy were 382 included. Electrostatic long-range interactions were calculated using Ewald 383 summation, where the real and reciprocal space cuto were 15 A. Statistical 384 simulation uncertainties were estimated with the block average method by 385 Flyvbjerg and Petersen [50]. 386 Appendix B. Correlation Parameters 387 Tables B.1 and B.2 contain the parameters of the empirical density correla- 388 tion developed in the present work. 389 33 Table B.1: Parameters of the Redlich-Kister ts for the molar excess volume of mixtures of water and methanol, cf. Eq. (7). ExperimentaSimulationb T/ KA0A1A2A3A4A5A0A1A2 288.154:0240:319 0:113 0:382 0:621 0:2914:147 0:3590:387 293.154:0470:314 0:125 0:462 0:4750:073 298.154:0690:299 0:121 0:492 0:3880:2834:094 0:1520:492 308.154:1110:219 0:082 0:378 0:3280:254 318.154:1460:090 0:001 0:105 0:437 0:2354:020 0:1390:697 aTaken from Coquelet et al. [41] bNo simulations were carried out for 293.15 K and 308.15 K 34 Table B.2: Parameters of the polynomial ts to the slope of the density, cf. Eq. (10). NaCl Experiment Simulationa T/ Kb2;NaClb1;NaClb0;NaClb2;NaClb1;NaClb0;NaCl 288.15 1:05061:9072 2:2658 0:99931:3956 1:7788 293.15 1:01671:8504 2:2444 298.15 0:98431:7991 2:2255 0:93301:3336 1:7662 308.15 0:98801:7470 2:1975 318.15 0:98291:6953 2:1778 0:96541:2788 1:7172 CsCl Experiment Simulationa T/ Kb2;CsClb1;CsClb0;CsClb2;CsClb1;CsClb0;CsCl 288.15 1:91785:0312 6:8499 1:69404:1679 5:8345 293.15 1:85804:9636 6:8225 298.15 1:84654:9312 6:8002 1:53204:0245 5:8094 308.15 1:78354:8498 6:7596 318.15 1:77804:8008 6:7170 1:56044:0167 5:7797 aNo simulations were carried out for 293.15 K and 308.15 K 35 Nomenclature 390 Abbreviations 391 EOS Equation of state LJ Lennard-Jones MeOH Methanol MD Molecular dynamics W Water Symbols 392 bsalt Slope of the density versus ion mole fraction  LJ energy parameter "0 Vacuum permittivity ni Number of moles of component i nj i Number of sites of type jon molecule i N Number of molecules ij Binary interaction parameter Mi Molar mass of component i q Point charge  Mass density r Distance 36  LJ size parameter T Temperature u(z) Uncertainty of the property z U Potential v Molar volume vEMolar excess volume vi Partial molar volume of component i vpure i Molar volume of pure component i xi Mole fraction of component i MeOH Methanol mole fraction in the salt-free solvent mixture Subscripts and Superscripts 393 a;b;c;d Site index e Electrostatic i;j Component / molecule index k Index for t parameters salt Either NaCl or CsCl solv Solvent 1 At in nite dilution 37