Relaxation of intermediate wave-vector density fluctuations in dense binary liquids

Binary liquids are known to be better glass formers than one component liquids. To understand this, we carried out a theoretical study of relaxation of density fluctuations in a dense liquid of binary hard spheres. This study is based on a coupled, modified, Smoluchowski equations where effects of interparticle interactions are included through two particle direct correlation functions of the binary mixture. Such a modified Smoluchowski equation description is reliable at intermediated values of wave vector k, but not at small k, so we have limited our study only to intermediate k. We find that the eigenvalues of the coupled equations show rich structure that depends on the composition of the binary liquid and also on the size ratio of the two constituents. At high density, the larger of the two eigenvalues becomes positive at intermediate wave vectors, indicating an instability of density fluctuation at that wave vector. As the density is further increased, the range of k over which the eigenvalue is positive, also increases. Although nonlinearities in density fluctuations and coupling with other hydrodynamic modes (neglected in this calculation) must be considered to gain an understanding of glass transition, the present results do indicate that the relaxation of density fluctuations in a binary liquid mixture is considerably different from that in a one component liquid