Binary Mixture of Charged Particles

The dynamics of colloidal mixtures provided by the previous extension of the SCGLE theory was illustrated in reference [21] with its application to a binary mixture of particles interacting through a hard-core pair potential of diameter a (assumed to be the same for both species), and a repulsive Yukawa tail of the form 

The dimensionless parameters that define the thermodynamic state of this system are the total volume fraction ( ) = (nl6)n (with n being the total number concentration, n = n, + n, the relative concentrations = njn, and the potential parameters K2, and z. The free-diffusion coefficients D° are also assumed identical for both species, that is, D = D = D°. Explicit values of the parameters a and D are not needed, since the dimensionless dynamic properties, such as t), only depend on the dimensionless parameters specified above, when expressed in terms of the scaled variables ka and t/to, where to = a /D . Besides solving the SCGLE scheme, in reference [21] Brownian dynamics simulations were generated for the static and dynamic properties of the system above. 

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In practice, in describing a binary mixture of charged particles, another set of dynamic variables is widely used, namely, instead of partial densities nk,a or the set (43), the mass density pk and the charge density qk are utilized. However, it should be mentioned that due to the electroneutrality constraint the charge density qk can be simply connected with the mass-concentration density xk, introduced above. In particular, one has,... 

Hence, one may conclude that in the limit k —> 0 the dynamics of the charge fluctuations is completely determined by relaxation processes with the finite (nonzero) relaxation time. In this sense we can speak about the fast kinetic-like behavior of the charge fluctuations in the model considered. This results in the effective independence of the other hydrodynamic Eqs. (44), (46), and (47), from the time evolution of fast charge subsystem, so that the hydrodynamics of a binary mixture of charge particles becomes rather similar to the case of simple liquids. However, we have to remember that in the hydrodynamic limit the additional (comparing with simple liquids) well-defined transport coefficients, namely the mutual D and />r thermal diffusion coefficients, exist in the system that play a crucial role in the electric and the thermoelectric properties, respectively. 

Optic-like collective excitations are not a unique feature of binary mixture of charged particles. Such modes can also be found in binary mixtures of neutral particles. However, the behavior of mode contributions to time correlation functions in small k range in these two cases is quite different. In particular, amplitude of optic-like modes to the mass concentration autocorrelation function tends to zero for the latter case, whereas for the former one these modes produce the finite contribution even in the hydrodynamic limit. 

General theoretical approach for the study of collective behavior of multicomponent mixture of charged particles has been developed. In particular, this approach has been applied to the comparison of binary mixtures of neutral and charged particles. 

In this study we restrict our consideration by a class of ionic liquids that can be properly described based on the classical multicomponent models of charged and neutral particles. The simplest nontrivial example is a binary mixture of positive and negative particles disposed in a medium with dielectric constant e that is widely used for the description of molten salts [4-6], More complicated cases can be related to ionic solutions being neutral multicomponent systems formed by a solute of positive and negative ions immersed in a neutral solvent. This kind of systems widely varies in complexity [7], ranging from electrolyte solutions where cations and anions have a comparable size and charge, to highly asymmetric macromolecular ionic liquids in which macroions (polymers, micelles, proteins, etc) and microscopic counterions coexist. Thus, the importance of this system in many theoretical and applied fields is out of any doubt. 

In this contribution we have reviewed the recent results concerning the collective dynamics of charged liquids. In order to establish the role of long-range Coulombic interactions we have concentrated our attention on the comparison of the results obtained for binary mixtures of neutral and charged particles. Such a comparison has been performed on two levels of consideration - on the level of analytical theories and numerical simulations. The main conclusions from our studies are as follows. 

According to Klemm and Schafer (1996) it is assumed that the binary mixture of molten salts M1X-M2X consists of five kinds of particles, three of which are charged and two are neutral M, mJ, X , MiX, and M2X. The sum of mole fractions of all the particles equals unity... 

W. Lin, M. Kobayashi, M. Skaiba, C. Mu, P. Galletto, M. Borkovec, Heteroaggregation in binary mixtures of oppositely charged colloidal particles. Langmuir 22(3), 1038-1047 (2006). doiilO. 1021/la0522808... 

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