The effects of particle softness on the dynamics of molecular and colloidal systems

We extend previous studies of the dynamical relaxation in liquids consisting of particles interacting with the soft-sphere or inverse power potential, phi (r) = is an element of(sigma/r)(n), where is an element of and sigma set the energy and length scales, respectively, and n is the steepness or stiffness parameter. In previous work we have simulated these systems using molecular dynamics ( MD) simulation. Here we include model colloidal particles interacting with this potential, executing the position Langevin equation of motion as implemented in the Brownian dynamics ( BD), method. A formal statistical mechanical expansion of the force autocorrelation function for such particles was carried out in both cases. Using the ( molecular) Liouville operator this gives at short time a scaling with time, t, in terms of a reduced time, x = n(1 + d/n)(1/2) t, where d depends on the state point, and for the colloidal case, the Smoluchowski operator gives the reduced time, x = n(2)(1 + d/n)t. The first term accounts for the leading two-body contributions to the relaxation, and the second term, in d, represents additional two-body, and the leading three-body contribution. d depends mainly on the packing fraction and only weakly on n for ca. n >= 18. In the colloidal case, because of the greater sensitivity to n, the simulations were limited to relatively small values ( in the range, 18 - 72). In this range of n values, the term in d is shown to make a significant contribution and is necessary to produce collapse at short times for both the MD and BD data. We also show that in this n range there is a collapse of the correlation functions at short times with an alternative (empirical) definition of the reduced time similar to n(alpha)t, with alpha < 1 for the molecular case and alpha < 2 for the colloids. This applies not only to the force autocorrelation function but also for the shear stress and deviatoric pressure autocorrelation functions. In the 18 - 72 range, the alpha were typically 10% lower than the large n limiting value ( 1 and 2 for MD and BD, respectively). The optimum value of alpha for the various time correlation functions depended on the packing fraction and choice of correlation function. The shear stress correlation functions for these finite n have alpha values closer to 1 ( MD) and 2 ( BD) than the pressure and force autocorrelation functions.