The Enskog theory for transport coefficients of simple fluids with continuous potentials

Anomalous Colloidal Motion under Strong Confinement

Diffusion of biological macromolecules in the cytoplasm is a paradigm of colloidal diffusion in an environment characterized by a strong restriction of the accessible volume. This makes of the understanding of the physical rules governing colloidal diffusion under conditions mimicking the reduction in accessible volume occurring in the cell cytoplasm, a problem of a paramount importance. This work aims to study how the thermal motion of spherical colloidal beads in the inner cavity of giant unilamellar vesicles (GUVs) is modified by strong confinement conditions, and the viscoelastic character of the medium. Using single particle tracking, it is found that both the confinement and the environmental viscoelasticity lead to the emergence of anomalous motion pathways for colloidal microbeads encapsulated in the aqueous inner cavity of GUVs. This anomalous diffusion is strongly dependent on the ratio between the volume of the colloidal particle and that of the GUV under consideration as well as on the viscosity of the particle's liquid environment. Therefore, the results evidence that the reduction of the free volume accessible to colloidal motion pushes the diffusion far from a standard Brownian pathway as a result of the change in the hydrodynamic boundary conditions driving the particle motion.

Sensitivity of nonequilibrium relaxation to interaction potentials: Timescales of response from Boltzmann's H function

We investigate, by simulations and analytic theory, the sensitivity of nonequilibrium relaxation to interaction potential and dimensionality by using Boltzmann's H function H(t). We evaluate H(t) for three different intermolecular potentials in all three dimensions and find that the well-known H theorem is valid and that the H function exhibits rather strong sensitivity to all these factors. The relaxation of H(t) is long in one dimension, but short in three dimensions, longer for the Lennard-Jones potential than for the hard spheres. The origin of the ultraslow approach to the equilibrium of H(t) in one-dimensional systems is discussed. Importantly, we obtain a closed-form analytic expression for H(t) using the solution of the Fokker-Planck equation for velocity space probability distribution and compare its predictions with the simulation results. Interestingly, H(t) is found to exhibit a linear response when vastly different initial nonequilibrium conditions are employed. The microscopic origin of this linear response is discussed. The oft-quoted relation of H function with Clausius's entropy theorem is discussed.

Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids

We present a numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids established by Maimbourg et al. [Phys. Rev. Lett. 116, 015902 (2016)]. For soft sphere interactions, we obtain the numerical solution by an iterative algorithm and a straightforward discretization of time. We also discuss the case of hard spheres for which we first derive analytically the dynamical mean field theory as a non-trivial limit of that of soft spheres. We present numerical results for the memory function and the mean square displacement. Our results reproduce and extend kinetic theory in the dilute or short-time limit, while they also describe dynamical arrest toward the glass phase in the dense strongly interacting regime.

Sensitivity of nucleation phenomena on range of interaction potential

Theoretical and computational investigations of nucleation have been plagued by the sensitivity of the phase diagram to the range of the interaction potential. As the surface tension depends strongly on the range of interaction potential and as the classical nucleation theory (CNT) predicts the free energy barrier to be directly proportional to the cube of the surface tension, one expects a strong sensitivity of nucleation barrier to the range of the potential; however, CNT leaves many aspects unexplored. We find for gas-liquid nucleation in Lennard-Jones system that on increasing the range of interaction the kinetic spinodal (KS) (where the mechanism of nucleation changes from activated to barrierless) shifts deeper into the metastable region. Therefore the system remains metastable for larger value of supersaturation and this allows one to explore the high metastable region without encountering the KS. On increasing the range of interaction, both the critical cluster size and pre-critical minima in the free energy surface of kth largest cluster, at respective kinetic spinodals, shift towards smaller cluster size. In order to separate surface tension contribution to the increase in the barrier from other non-trivial factors, we introduce a new scaling form for surface tension and use it to capture both the temperature and the interaction range dependence of surface tension. Surprisingly, we find only a weak non-trivial contribution from other factors to the free energy barrier of nucleation.

Autocorrelation functions of a fluid of molecules interacting through steeply repulsive and attractive forces

A new method is presented for an extension of Enskog's approximation for the evaluation of the autocorrelation functions of a fluid, and this approach is used to evaluate these functions when the interaction between the molecules includes both steeply repulsive and steeply attractive forces. Consequently the correlation functions depend upon the temperature in a nontrivial way. As an example, the method is applied to calculate the velocity and force autocorrelation functions of a fluid when the molecules interact through the specific potential, V(r)=4epsilon[(sigma/r)2n-(sigma/r)n] when the parameter n is large. There is a relationship between this model and the "sticky sphere" one which is exploited in the theoretical computations. The results obtained from the theory are compared with molecular dynamics simulation for n=72 and 144 and for a range of temperatures from T=epsilon/kB down to epsilon/3kB. The two approaches agree very well for a range of state points, especially at short times. At later times the theory predicts a more oscillatory behavior than the simulation especially at very low reduced temperatures.

Memory function for a fluid of molecules interacting through steeply repulsive potentials

Previous studies of the properties of fluids of molecules interacting through steeply repulsive central potentials are extended to the investigation of the memory function. It is assumed that collisions are dominated by binary collisions and a general formula previously derived by Miyazaki, Srinivas, and Bagchi [J. Chem. Phys. 114, 6276 (2001)] is applied to the present problem. It is shown that the equations of motion of a pair of molecules can be solved explicitly and substitution of the result into the formula leads to a closed explicit expression for the memory function which is easily evaluated for any given state. In the limit of hard spheres this result leads to Enskog's equation and represents a generalization of that formula to fluids with softer potentials. The results obtained from the formula are compared with those derived from the molecular dynamics simulation. The velocity autocorrelation function was calculated using the generalized soft sphere potential, phi(r) = epsilon (sigma/r)(n), where epsilon and sigma set the energy and size of the molecule, and the exponent, n, is a variable. The two approaches agree very well for a range of state points for n large, especially at short times.

Molecular dynamics simulation study on the transient response of solvation structure during the translational diffusion of solute

The transient response function of the density profile of the solvent around a solute during the translational diffusion of the solute is formulated based on the generalized Langevin formalism. The resultant theory is applied to both neat Lennard-Jones fluids and cations in liquid water, and the response functions are obtained from the analysis of the molecular dynamics simulations. In the case of the self-diffusion of Lennard-Jones fluids, the responses of the solvation structures are in harmony with conventional pictures based on the mode-coupling theory, that is, the binary collision in the low-density fluids, the backflow effect from medium to high density fluids, and the backscatter effect in the liquids near the triple point. In the case of cations in water, the qualitative behavior is strongly dependent on the size of cations. The pictures similar to simple dense liquids are obtained for the large ion and the neutral molecule, while the solvent waters within the first solvation shell of small ions show an oscillatory response in the short-time region. In particular, the oscillation is remarkably underdumped for lithium ion. The origin of the oscillation is discussed in relation to the theoretical treatment of the translational diffusion of ions in water.

Memory effect in friction on a particle caused by a system of fixed or moving scatterers with power law potential

The memory function for friction on a particle caused by a system of fixed or moving scatterers is evaluated for power law interaction. For a dilute system the study extends the steady-state calculation based on the Boltzmann equation to the case of frequency dependence due to the dynamics of the scattering process. For a dense gas an Enskog approximation can be used. The power law potential leads to scaling behavior of the dynamical friction coefficient as a function of reduced mass, coupling coefficient, and energy.

Exact calculation of the linear term in the density expansion of the dynamic structure factor of a dilute gas

We evaluate the linear term in the density expansion of the dynamic structure factor for a classical gas using a generalized Enskog theory developed by one of the authors, which enables us to describe the dynamics at small time and length scales where the use of the Boltzmann equation is severely limited. Agreement of the theory with experiment and simulation is very good. We find that the linear term is very sensitive to the shape of the potential so that the dynamic structure factor can serve as a good probe to determine the intermolecular potentials of dilute gases.

Dynamic structure factor of a dilute Lennard-Jones gas

We calculate the leading correction term in the density expansion of the dynamic structure factor for a Lennard-Jones fluid using the Boltzmann equation. The qualitative behavior is found to be very similar to the hard-sphere result reported by Kamgar-Parsi et al. [Phys. Rev. A 35, 4781 (1987)]. A comparison was made with the results from the neutron scattering experiment by Verkerk et al. [Phys. Rev. Lett. 67, 1262 (1991)] for dilute argon gases. Several possibilities to explain the discrepancies of the present results from the experiment are proposed.