Calculation of self-diffusion coefficients in supercritical carbon dioxide using mean force kinetic theory

This paper presents an application of mean force kinetic theory (MFT) to the calculation of the self-diffusivity of CO₂ in the supercritical fluid regime. Two modifications to the typical application of MFT are employed to allow its application to a system of molecular species. The first is the assumption that the inter-particle potential of mean force can be obtained from the molecule center-of-mass pair correlation function, which in the case of CO₂ is the C-C pair correlation function. The second is a new definition of the Enskog factor that describes the effect of correlations at the surface of the collision volume. The new definition retains the physical picture that this quantity represents a local density increase, resulting from particle correlations, relative to that in the zero density homogeneous fluid limit. These calculations are facilitated by the calculation of pair correlation functions from molecular dynamics (MD) simulations using the FEPM2 molecular CO₂ model. The self-diffusivity calculated from theory is in good agreement with that from MD simulations up to and slightly beyond the density at the location of the Frenkel line. The calculation is compared with and is found to perform similarly well to other commonly used models but has a greater potential for application to systems of mixed species and to systems of particles with long range interatomic potentials due to electrostatic interactions.

A theory for the temperature effect on the chain length dependence of the diffusivity of oligomers

The effect of temperature on the chain length (N) dependence of the diffusivity of oligomers (with N = 10-60 carbon atoms) was theoretically studied using the free volume theory of Wong and Choi [Soft Matter, 2019, 15, 9300-9309] along with the experimental data of von Meerwall et al. [J. Chem. Phys., 1998, 108, 4299-4304]. Experimental data showed that D_cm∼N^v and that becomes less negative as temperature increases but is always stronger than -1 as obtained in the Rouse model. The theory successfully predicts the exponent v as a function of temperature.

A free volume theory on the chain length dependence of the diffusivity of linear polymers

A free volume theory was developed to account for the crossover of the chain length dependence of the center-of-mass self-diffusion coefficient of linear polymers from unentangled to entangled regimes. Similar to the original free volume theory of Cohen and Turnbull, this theory requires information about the free volume overlapping factor (α), critical free volume per bead (v), and mean free volume per bead (〈v_f,i〉). However, one additional parameter is needed and it is the critical fraction of beads having free volume greater than or equal to αv termed as φ⁺. Here, α and v can be readily determined from the intermolecular and intramolecular radial distribution functions (i.e., g(r) and g^intra(r)) obtained from molecular dynamics (MD) simulation and they were found to be 0.5 and 0.0257 nm³, respectively, for polyethylene melts and it is not dependent on N. 〈v_f,i〉 was determined using the generic van der Waals (GvdW) equation of state and it had a value of 0.01 nm³ and the volume available to each bead can also be determined by Voronoi tessellation (VT) on the corresponding MD simulation trajectories. VT yielded exact probability of finding a certain amount of free volume and the free volume distribution was found in the form of the gamma distribution that is consistent with the positron annihilation lifetime spectroscopy observation. Finally, φ⁺ was calculated using the experimentally measured activation energies for diffusion per polyethylene molecule with different chain lengths and was found to be approximately 0.22 that was in line with what was found from MD simulations.

A new Monte Carlo method for getting the density of states of atomic cluster systems

A novel Monte Carlo flat histogram algorithm is proposed to get the classical density of states in terms of the potential energy, g(E(p)), for systems with continuous variables such as atomic clusters. It aims at avoiding the long iterative process of the Wang-Landau method and controlling carefully the convergence, but keeping the ability to overcome energy barriers. Our algorithm is based on a preliminary mapping in a series of points (called a σ-mapping), obtained by a two-parameter local probing of g(E(p)), and it converges in only two subsequent reweighting iterations on large intervals. The method is illustrated on the model system of a 432 atom cluster bound by a Rydberg type potential. Convergence properties are first examined in detail, particularly in the phase transition zone. We get g(E(p)) varying by a factor 10(3700) over the energy range [0.01 < E(p) < 6000 eV], covered by only eight overlapping intervals. Canonical quantities are derived, such as the internal energy U(T) and the heat capacity C(V)(T). This reveals the solid to liquid phase transition, lying in our conditions at the triple point. This phase transition is further studied by computing a Lindemann-Berry index, the atomic cluster density n(r), and the pressure, demonstrating the progressive surface melting at this triple point. Some limited results are also given for 1224 and 4044 atom clusters.