Equilibration and aging of liquids of non-spherically interacting particles

• Published in: arXiv.org
• Main Authors: Cortes-Morales, E C, Elizondo-Aguilera, L F, Medina-Noyola, M
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 15.05.2016
• Subjects: Balancing; Covariance; Dipoles; Evolution; Fourier transforms; Irreversible processes; Liquids; Quenching; Spherical harmonics; Structure factor; Time correlation functions; Variations
• ISSN: 2331-8422

The non-equilibrium self-consistent generalized Langevin equation theory of irreversible processes in liquids is extended to describe the positional and orientational thermal fluctuations of the instantaneous local concentration profile \(n(\mathbf{r},\Omega,t)\) of a suddenly-quenched colloidal liquid of particles interacting through non spherically-symmetric pairwise interactions, whose mean value \(\overline{n}(\mathbf{r},\Omega,t)\) is constrained to remain uniform and isotropic, \(\overline{n}(\mathbf{r},\Omega,t)=\overline{n}(t)\). Such self-consistent theory is cast in terms of the time-evolution equation of the covariance \(\sigma(t)=\overline{\delta n_{lm}(\mathbf{k};t) \delta n^{\dagger}_{lm}(\mathbf{k};t)}\) of the fluctuations \(\delta n_{lm}(\mathbf{k};t)=n_{lm}(\mathbf{k};t) -\overline{n_{lm}}(\mathbf{k};t)\) of the spherical harmonics projections \(n_{lm}(\mathbf{k};t)\) of the Fourier transform of \(n(\mathbf{r},\Omega,t)\). The resulting theory describes the non-equilibrium evolution after a sudden temperature quench of both, the static structure factor projections \(S_{lm}(k,t)\) and the two-time correlation function \(F_{lm}(k,\tau;t)\equiv\overline{\delta n_{lm}(\mathbf{k},t)\delta n_{lm}(\mathbf{k},t+\tau)}\), where \(\tau\) is the correlation \emph{delay} time and \(t\) is the \emph{evolution} or \emph{waiting} time after the quench. As a concrete and illustrative application we use the resulting self-consistent equations to describe the irreversible processes of equilibration or aging of the orientational degrees of freedom of a system of strongly interacting classical dipoles with quenched positional disorder.