Excess entropy scaling of transport properties of Lennard-Jones chains

Abstract

Excess-entropy scaling relationships for diffusivity and viscosity of Lennard-Jones chain fluids are tested using molecular dynamics simulations for chain sizes that are sufficiently small that chain entanglement effects are insignificant. The thermodynamic excess entropy S_e is estimated using self-associating fluid theory (SAFT). A structural measure of the entropy S₂ is also computed from the monomer-monomer pair correlation function, g_m(r). The thermodynamic and structural estimators for the excess entropy are shown to be very strongly correlated. The dimensionless center-of-mass diffusivities, D_cm, obtained by dividing the diffusivities by suitable macroscopic reduction parameters, are shown to conform to the excess entropy scaling relationship, D_cm = A_nexp(a_nS_e), where the scaling parameters depend on the chain length n. The exponential parameter α _n varies as -(1/n) while A_n varies approximately as n^-0.5. The scaled viscosities obey a similar relationship with scaling parameters B_n and β_n where β_n varies as 1/n and B_n shows an approximate n^0.6 dependence. In accordance with the Stokes-Einstein law, for a given chain length, α _n = -β_n within statistical error. The excess entropy scaling parameters associated with the transport properties therefore display a simple dependence on chain length.