| dc.description.abstract | In this paper, we have presented molecular dynamics (MD) simulations and mode coupling theory (MCT) calculations of the composition dependence of viscosity in binary mixtures. We have proposed two models to capture the essence of the wealth of experimental results available in the literature.
Model I: The two components like each other more than they like themselves. In this case, we find non-ideality in the positive direction.
Model II: The two components dislike each other. This model is delicate because it often shows phase separation. We have studied this model at somewhat higher temperatures. This model shows non-ideality of the negative kind.
In both cases, agreement between theory and simulation is quite good, although not fully satisfactory. However, it is satisfying to note that both theory and simulations can capture the qualitative aspects of the composition dependence of viscosity.
The main reason for the anomalous composition dependence seems rather easy to understand. It arises from a similar dependence of the mean square stress fluctuation (MSSF) on the composition of the mixture. Thus, it is fair to say that the anomaly has a structural, rather than a dynamic origin. The dynamics, of course, play an important role in augmenting the effect. The reason for the non-monotonous composition dependence of MSSF arises from its dependence on the force acting on each molecule.
It is worth emphasizing that in both models, the components have the same radius and the same mass. In addition to the emergence of significant non-ideality, we found an important result: non-ideality in both models is driven by the zero-time value of the shear stress autocorrelation function, which is proportional to the infinite-frequency shear modulus, G?G_{\infty}G??. Dynamical correlations seem to follow the lead given by the static correlations, as is most often the case at normal liquid temperatures far above the glass transition temperature.
In this work, we have not explored the composition dependence that can arise from differences in sizes of A and B. Work in this direction is under progress.
We have already stressed that the MCT calculations presented here are not self-consistent. The reason for this is that an accurate short-time description of the partial intermediate scattering function F12(q,t)F_{12}(q,t)F12?(q,t) is not available. Thus, we could not proceed via the usual route of constructing a continued fraction representation of Fij(q,t)F_{ij}(q,t)Fij?(q,t) and then solve the mode coupling theory expression for friction consistently with the viscosity. Earlier experience has shown that non-self-consistent theories provide reasonably accurate estimates (within 10–20%) of the zero-frequency value of the friction and viscosity, so long as one is far above the glass transition temperature, as is the case here.
The composition dependence of viscosity, diffusion, and excess volume of binary mixtures is a problem of great importance in solution chemistry. Unfortunately, however, no model-based theoretical study of this problem has been carried out which shows the diverse behavior exhibited by these mixtures. Much of the theoretical studies have been directed to supercooled liquids or to phase separation kinetics. The work presented here is perhaps the first detailed study of the anomalous composition dependence of viscosity, diffusion, and excess volume.
The novel aspect of this study is the introduction of two new models which are sufficiently simple to allow detailed investigation. In order to capture the commonly held wisdom that the anomalies in composition dependence arise from “structure making” or “structure breaking” among the two constituent species, the two models are made to represent the two extremes. However, we needed to carry out (NPT) MD simulations in order to allow for fluctuations in the total volume of the system.
In this paper, we have reported results of such constant temperature and pressure (NPT) MD simulations and searched for correlations between excess volume and excess viscosity. The simulations show that these two are strongly but inversely correlated for both the attractive and repulsive model liquids, with the trends themselves opposite for the two models. We have also shown the re-entrant nature of excess viscosity with excess volume in the direction of changing solute composition. We have calculated diffusion coefficients (D1D_1D1? and D2D_2D2?) for both models, which show non-monotonic behavior against composition. Finally, results show the breakdown of the Stokes–Einstein law for these complex systems.
Future work shall consider variation of solute–solvent size ratio and also pressure dependence of viscosity and excess volume of non-ideal binary mixtures. | |
