Viscosity of Dilute Model Bead Arrays at Low Shear: Inclusion of Short Range Solute−Solvent Interactions

Abstract

The intrinsic viscosity, [eta], of certain polymer-solvent systems, such as alkanes in benzene, are "anomalous" in the sense that [eta] for low molecular weight fractions are low and in certain cases negative (Dewan, K. K.; Bloomfield, V. A.; Berget, P. G.; J. Phys. Chem. 1974, 75, 3120). In this work, the theory of the viscosity of a dilute suspension of macromolecules at low shear is formulated that accounts for possible solute-solvent interactions. In doing so, we show that negative intrinsic viscosities are possible and are able to reproduce quite well the known length dependence of [eta] for alkanes in benzene. The coarse grained, solvent continuum, bead model developed here is an extension of previous work (Allison, S. A.; Pei, H. J. Phys. Chem. B 2009, 113, 8056). Following Fixman (Fixman, M. J. Chem. Phys. 1990, 92, 6858), we assume that solute-solvent interactions are short-range in character and can be separated from long-range hydrodynamic interactions between different beads. These interactions are accounted for by introducing three adjustable parameters specific to the transport of small "monomeric" solutes in the solvent of interest. Long range hydrodynamic interactions are accounted for to order a(J)(2)/r(IJ)(3) (a(J) is a bead radius and r(IJ) is an interbead distance). In modeling a macromolecule as an arbitrary array of N beads, the transport of the array is examined numerically in 5 different elementary shear fields. The most computationally demanding component of the procedure involves the inversion of a 12N by 12N matrix. In the present work, we restrict ourselves to systems with a maximum N of about 100. Our procedure is first applied to short rods and rings of from 2 to 10 beads which can be compared with independent results from the literature. Agreement is found to be better than 5%. Modeling macromolecules as wormlike chains, the procedure is then applied first to duplex DNA and then to alkanes in benzene. In both cases, it is possible to obtain excellent agreement between modeling and experiment.