Apparent molar volume anomaly in water-dimethyl sulfoxide liquid mixtures. Molecular dynamics computer simulations

We have studied the composition dependence of density of liquid water-DMSO mixtures at different temperatures by using the isobaric-isothermal (NPT) molecular dynamics computer simulations. The non-polarizable semi-flexible, P1 and P2 models for the DMSO molecule combined with the TIP4P-2005 water model are considered. The excess mixing volume and the apparent molar volumes of the species are reported. We have established that the P1-TIP4P-2005 model for the mixture provides a very good description of the location of the minimum of apparent molar volume for DMSO species indicating the anomaly. Most important is that the temperature interval where the hydrophobic effect exists, is correctly captured with this modelling, in contrast to the P2-TIP4P-2005 model.

. Panel b: Similar to the panel a, but at 338.15 K. Experimental data (dashed line with triangles) are from [14].
As common, the strategy of exploration is to describe a desired property on composition and to capture its deviation from ideality as well. We do that for the mixture density at each fixed temperature. A set of results is shown in figure 1. The panel a of this figure refers to = 298.15 K and = 318.15 K, whereas the panel b illustrates the results at = 338.15 K. This temperature was also chosen in [5] due to the availability of experimental data. From the inspection of the results, we observe that the P1-TIP4P-2005 and P2-TIP4P-2005 are quite accurate in the interval of composition from pure water, dmso = 0, up to dmso ≈ 0.2. At a higher DMSO content in the mixture, the simulation data begin to deviate from the experimental results. The maximum density at a certain composition, dmso ≈ 0.58, is captured by both models in question. Nevertheless, it can be seen that the P1-TIP4P-2005 model performs much better than its P2-TIP4P-2005 counterpart. This latter model overestimates the density in the interval above dmso > 0.2. Moreover, the deviation from the experimental points does not decrease while the temperature grows from 298.15 K up to 338.15 K. The P1-TIP4P-2005 model exhibits a small inaccuracy for density at "intermediate" compositions, but performs much better than P2-TIP4P-2005. It is difficult to judge the precision of computer simulations data at low dmso values at the scale in the figure 1. Better insights follow from the excess properties.
We describe geometric aspects of mixing of the species in terms of the excess mixing volume defined as common, Δ mix = mix − − (1 − ) , where mix , and refer to the molar volume of the mixture and of the individual components, DMSO and water, respectively. Apparently, this property is not strongly dependent on temperature in the interval we deal with. This follows from the experimental results shown in figure 2. The mixing volume slightly decreases in magnitude upon increasing temperature, as expected. In general terms, computer simulation results show that the excess mixing volume is overestimated in the framework of models assumed. Thus, the mixture of water and DMSO species from simulations is predicted to be more non-ideal than its laboratory counterpart in almost entire composition range at = 298.15 K. The Δ mix values from simulations decrease in magnitude in agreement with experimental trends. However, the location of the minimum along dmso axis from simulations and experiments is slightly different. Finally, one can observe that the performance of the P1-TIP4P-2005 model is slightly better compared to the P2-TIP4P-2005 model.
In order to discern the contribution of each species of the mixture into the mixing volume, it is common to resort to the excess partial molar volumes as we have done recently [2]. However, similar insights into the geometric aspects of mixing on composition, both from experiments and simulations, can be obtained by resorting to the notion of the apparent molar volume of species, rather than to the partial molar volumes.   entire composition range, especially for higher temperatures. The respective figure at 298.15 K is given in [2] (figure 3d). It is necessary to mention, however, that the experimental results for DMSO-rich (more specifically, extremely rich) mixtures are difficult to obtain precisely, because high-purity DMSO is an exceedingly hygroscopic solvent, the discussion of this issue is given in [12].
To conclude, we have established that the P1 and P2 models for DMSO combined with the TIP4P-2005 water model yield a minimum of the apparent molar volume for DMSO species at low values for dmso . This behavior is the manifestation of hydrophobic effects in these mixtures at a specific composition interval. However, it appears that the predictions from P1-TIP4P-2005 model agree better with the experimental trends than the ones from P2-TIP4P-2005 model. Moreover, the P1-TIP4P-2005 model predicts the existence of a minimum of ( ) for DMSO within the correct temperature interval from 298.15 K up to 338.15 K. At this highest temperature, the minimum almost disappears, as deduced from experimental data. By contrast, P2-TIP4P-2005 model does not provide an accurate estimate for a peculiar composition interval and does not yield a decay for the hydrophobicity trends on temperature.
In various publications this model is claimed to be the best, see for example [18]. Here, we show that this conclusion is valid in certain aspects at a room temperature only. In addition, it is important to mention that the combination of the OPLS model for DMSO with TIP4P-2005 model for water does not provide a correct composition dependence of density at room temperature, cf. figure 2 of [2] and at temperatures of this study. In consequence, the anomaly of the apparent molar volume is not captured by this type of model at all. These results are available upon request. Previously, we explored the minimum of the methanol apparent molar volume on composition for water-methanol mixtures [16] at 298.15 K, see also [17] for the interpretation of the observed phenomena. This kind of system is the mixture of two hydrogen bonded liquids. By contrast, in the systems of the present study there is no bonding between the DMSO solutes in water. Apparently, the temperature trends should be slightly different for these two classes of systems.
In addition, it seems intriguing to investigate the evolution of trends of hydrophobicity in water-DMSO mixtures upon changing the external pressure as well. One can be guided by important experimental observations, see e.g., [19,20]. More generally, from the simulations perspective it is challenging to construct a more complete map of anomalies, in pressure, temperature and composition variables, that would involve, for example, the temperature of maximum density and the minimum of isothermal compressibility, even by using the non-polarizable models. These data would serve as a useful benchmark for the following development of polarizable models. In the case of water-DMSO mixtures, certain progress has been reached at this level of modelling in [21,22]. However, the BK3 polarizable water model seems to be a more convenient starting point, because the principal anomalies of pure water are quite well captured in this framework [23,24]. Some of these issues are under study in our laboratory.