Velocity autocorrelation functions ͑VACF͒ of a fluid confined in a slit pore have been modeled using the memory equation. Models for the VACF are based on both the truncation and analytic closure approximations of the Mori's continued fraction representation. The performance of the models is evaluated for gas to liquid-like pore densities and pore widths which accommodate one to four atomic layers. In all cases we compare the predictions from the models with the VACF obtained from molecular dynamics simulations. The truncation models predict an oscillatory behavior for the in-plane VACF with better agreement at lower densities. Among the analytical closure models we observe that the sech model applied at the first level of closure is not only able to capture the short-time dynamics but is also seen to give the best predictions to the in-plane diffusivities at liquid-like pore densities. Although the minima in the VACFs are captured accurately by the sech model, the subsequent plateau regions in the VACF typically observed in confined systems are not predicted. This aspect is due to the slower relaxation of the actual memory kernel, which is not captured by the model. Predictions of the in-plane diffusivities using different levels of analytic closure have been compared with diffusivities obtained from the simulations.
Molecular dynamic simulations of a strongly inhomogeneous system reveals that a single-component soft-sphere fluid can behave as a fragile glass former due to confinement. The self-intermediate scattering function, F(s)(k,t), of a Lennard-Jones fluid confined in slit-shaped pores, which can accommodate two to four fluid layers, exhibits a two-step relaxation at moderate temperatures. The mean-squared displacement data are found to follow time-temperature superposition and both the self-diffusivity and late α relaxation times exhibit power-law divergences as the fluid is cooled. The system possesses a crossover temperature and follows the scalings of mode coupling theory for the glass transition. The temperature dependence of the self-diffusivity can be expressed using the Vogel-Fulcher-Tammann equation, and estimates of the fragility index of the system indicates a fragile glass former. At lower temperatures, signatures of additional relaxation processes are observed in the various dynamical quantities with a three-step relaxation observed in the F(s)(k,t).
The density of states for bulk and confined fluids have been modeled using a recently proposed gamma distribution (Krishnan, S. H.; Ayappa, K. G. J. Chem. Phys. 2004, 121, 3197). The gamma distribution results in a closed form analytical expression for the velocity autocorrelation function and the relaxation time of the fluid. The two parameters of the gamma distribution are related analytically to the second and fourth frequency moments of the fluid using short time expansions. The predictions by the proposed gamma model are compared with the velocity autocorrelation functions obtained using the theory of instantaneous normal modes (INMs) and from molecular dynamics simulations. The model is applied to a bulk soft sphere liquid and fluids confined in a spherical cavity and slit-shaped pores. The gamma model is able to capture the resulting changes in relaxation time due to changes in density and temperature extremely well for both the bulk liquid and confined inhomogeneous fluid situations. In all cases, the predictions by the gamma model are superior to those obtained from the INM theory. In the case of the fluid confined in a slit pore, the loadings were obtained from a grand canonical Monte Carlo simulation where the pore is equilibrated with a bulk fluid. This is similar to a confinement situation in a surface force apparatus. The predicted relaxation times vs pore widths from the gamma model are seen to accurately capture the oscillations due to formation and disruption of layers within the slit pore.
We propose a model for the short-time dynamics of fluids confined in slit-shaped pores. The model has been developed from the observation that the real lobe of the instantaneous normal mode density of states (INM DOS) closely follows a gamma distribution. By proposing that the density of states of the confined fluid can be represented by a gamma distribution, the resulting velocity autocorrelation function (VACF) is constructed such that it is accurate upto the fourth frequency moment. The proposed model results in an analytical expression for the VACF and relaxation times. The VACFs obtained from the model have been compared with the VACFs obtained from molecular dynamic simulations and INM analysis for fluids confined in slit-shaped pores over a wide range of confinement and temperatures. The model is seen to capture the short-time behavior of the VACF extremely accurately and in this region is superior to the predictions of the VACF obtained from the real lobe of the INM DOS. Although the model predicts a zero self-diffusivity, the predicted relaxation times are in better agreement with the molecular dynamics results when compared with those obtained from the INM theory.
An accurate model for the density of states (DOS) for strongly inhomogeneous and bulk fluids has been proposed based on gamma distributions. The contribution to the density of states from the collective dynamics is modeled as an incomplete gamma distribution and the high frequency region is obtained from the solution of the memory equation using a sech memory kernel. Using only the frequency moments as input, the model parameters for the collective dynamics are obtained by matching moments of the resulting distribution. The model results in an analytical expression for the self-diffusivity of the fluid. We present results for soft sphere fluids confined in slit-shaped pores as well as bulk soft sphere liquids. Comparisons of the DOS, velocity autocorrelation functions, and memory kernels with molecular dynamics simulations reveal that the model predicts features in the DOS over the entire frequency range and is able to capture changes in the DOS as a function of fluid density and temperature. As a result the predicted VACFs, memory kernels, and self-diffusivities are accurately predicted over a wide range of conditions. Since the frequency moments for bulk liquids can be obtained from pair correlation functions, our method provides a direct route from fluid structure to dynamics. For fluids confined in slit-shaped pores, where the frequency moments are obtained from molecular dynamics simulations, the predicted self-diffusivities capture the resulting oscillations due to variations in the solvation pressure, and in the case of smooth walled pores, the predictions are superior to those obtained using kinetic theory.
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