Modeling velocity autocorrelation functions for confined fluids using γ distributions

Krishnan, S. H.; Ayappa, K. G.

doi:10.1063/1.1768939

Cited by 4 publications

(11 citation statements)

References 28 publications

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“…The relaxation time is based on assuming that the normalized VACF is modeled as an exponentially decaying function, e - t /τ . Hence, provides a measure of the relaxation time of the VACF. , Using this definition of τ and carrying out the integral in eq 8 up to 0.4 ps, the τ obtained for Li + in the reverse micelle was 0.026 ps and from the VACF reported for Li + at infinite dilution 37 the value was 0.036 ps. The smaller relaxation time in the reverse micelle is a consequence of the smaller amplitude of oscillations observed for the VACF in the reverse micelle (Figure a) when compared with the VACF reported for bulk water .…”

Section: Resultsmentioning

confidence: 99%

Ion Exchange in Reverse Micelles

et al. 2004

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The distribution and dynamics of alkali cations inside Na-AOT reverse micelles have been investigated using Monte Carlo and molecular dynamics simulations. Water is modeled using the extended simple point charge (SPC/E) model. Simulations were carried out for alkali salts of Li+, Na+, K+, and Cs+ placed into the aqueous core of the reverse micelle, for situations corresponding to one and three molecules of added salt. In all cases, we observe that the larger K+ and Cs+ ions exchange with the Na+ counterion; however, the smaller Li+ ion prefers to remains solvated within the core of the reverse micelle. Our study reveals that the oil-water interface of the Na-AOT reverse micelle has the greatest selectivity toward Cs+ followed by K+ and Li+. A model based on enthalpic contributions illustrates that the solvation energies of the different cations in water control the ion-exchange process. The hydration number of the first water shell for Li+ situated in the aqueous core of the reverse micelle with radius R = 14.1 A was similar to that observed at infinite dilution in bulk water.

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Section: Resultsmentioning

confidence: 99%

Ion Exchange in Reverse Micelles

et al. 2004

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“…As u(0) is proportional to the force experienced by a particle, eqn (28) can also be expressed using the zero time force autocorrelation function. 38,39 Hence,…”

Section: Simulation Detailsmentioning

confidence: 98%

“…From eqn (27), the frequency moments can be directly related to particle velocities 38,39 using the following expressions,…”

Section: Simulation Detailsmentioning

confidence: 99%

“…Although time correlation functions have provided a fundamental starting point for understanding the dynamics of homogeneous liquids, only recently have these ideas been applied to predict time correlation functions for fluids confined in nanopores. [38][39][40][41][42] Within the framework of time correlation functions, the self-diffusivity, D, of a fluid is determined from the Velocity AutoCorrelation Function (VACF). Our efforts in this direction have been aimed at developing a model for the complete single particle dynamics of the fluid by using the Density of States (DOS) as the starting point.…”

Section: Introductionmentioning

confidence: 99%

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Using ? distributions to predict self-diffusivities and density of states of fluids confined in carbon nanotubes

Choudhary

Ayappa

2007

Phys. Chem. Chem. Phys.

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The density of states of rare gas atoms confined in carbon nanotubes is analyzed using a recently proposed model based on gamma distributions [Krishnan and Ayappa, J. Chem. Phys., 124 144503 (2006)]. The inputs into the model are the 2nd and 4th frequency moments that are obtained from molecular dynamics simulations. The predicted density of states, velocity autocorrelation functions and self-diffusivities are compared with those obtained from molecular dynamics simulations, for different nanotube loadings and temperatures. All results are reported for argon confined in a (16,16) carbon nanotube. The model predictions are extremely accurate at intermediate reduced densities of rhosigma(3) = 0.3, 0.4, where the majority of the self-diffusivity predictions lie within 10% of the simulation results. Since the frequency moments can be also obtained from Monte Carlo simulations, the study suggests an alternate route to the system dynamics of strongly confined fluids.

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“…Mode coupling theories have been reasonably successful in this regard. 27 This proposition results in a closed form expression for the VACF, and the two parameters of the distribution can be related to the frequency moments of the fluid. 18,19 Time correlation functions, which are central dynamical variables for a theory of transport, can be modeled either in the time or frequency domain.…”

Section: Introductionmentioning

confidence: 95%

Model for dynamics of inhomogeneous and bulk fluids

Krishnan

Ayappa

2006

The Journal of Chemical Physics

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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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Modeling velocity autocorrelation functions for confined fluids using γ distributions

Cited by 4 publications

References 28 publications

Ion Exchange in Reverse Micelles

Ion Exchange in Reverse Micelles

Using ? distributions to predict self-diffusivities and density of states of fluids confined in carbon nanotubes

Model for dynamics of inhomogeneous and bulk fluids

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