Rouse Chains with Excluded Volume Interactions:  Linear Viscoelasticity

Abstract

Linear viscoelastic properties for a dilute polymer solution are predicted by modeling the solution as a suspension of non-interacting bead-spring chains. The present model, unlike the Rouse model, can describe the solution's rheological behavior even when the solvent quality is good, since excluded volume effects are explicitly taken into account through a narrow Gaussian repulsive potential between pairs of beads in a bead-spring chain. The use of the narrow Gaussian potential, which tends to the more commonly used δ-function repulsive potential in the limit of a width parameter d going to zero, enables the performance of Brownian dynamics simulations. The simulations results, which describe the exact behavior of the model, indicate that for chains of arbitrary but finite length, a δ-function potential leads to equilibrium and zero shear rate properties which are identical to the predictions of the Rouse model. On the other hand, a non-zero value of d gives rise to a prediction of swelling at equilibrium, and an increase in zero shear rate properties relative to their Rouse model values. The use of a δ-function potential appears to be justified in the limit of infinite chain length. The exact simulation results are compared with those obtained with an approximate solution which is based on the assumption that the non-equilibrium configurational distribution function is Gaussian. The Gaussian approximation is shown to be exact to first order in the strength of excluded volume interaction, and is found to be accurate above a threshold value of d, for given values of chain length and strength of excluded volume interaction.

Viscosity Radius of Polymers in Dilute Solutions: Universal Behavior from DNA Rheology and Brownian Dynamics Simulations

“…N, while, for flexible polymers, the strength of excluded volume interactions is determined by the excluded volume parameter, [5,37] …”

An alternative to the bead-rod model: Bead-spring chains with successive fine graining

“…The dimensionless zero-shear rate viscosity (η * p,0 ) for a free draining bead-spring model derived using a retarded motion expansion is given by [9,29]:…”

“…The analytical calculations are carried out for the case where both HI and EV interactions are absent. Most of previous results derived in the literature for the linear viscoelastic properties for free draining bead-spring chains without EV are the functions of the spring parameters and the number of beads and hence, cannot be used directly to compare with results for Kramers bead-rod chains [4,28,29] (the exception are the results of infinitely stiff Fraenkel spring [4,28]). In our work, we have used expressions Table 1 The values of the coefficients for the series approximation, which accurately fit the obtained numerical values of the ILC and WLC force laws for the zero-shear rate viscosity and zero-shear rate first normal stress coefficient which, in literature, are expressed in term of the beads N, the second moment Q * 2 eq and the fourth moment Q * 4 eq of the end to end vector given in Refs.…”

“…In our work, we have used expressions Table 1 The values of the coefficients for the series approximation, which accurately fit the obtained numerical values of the ILC and WLC force laws for the zero-shear rate viscosity and zero-shear rate first normal stress coefficient which, in literature, are expressed in term of the beads N, the second moment Q * 2 eq and the fourth moment Q * 4 eq of the end to end vector given in Refs. [4,28,29] to derive expressions which can be directly compared to the bead-rod results.…”

“…For free draining chains without EV, we have also derived alternative analytical expressions for linear viscoelastic properties using the results given previously in Refs. [4,28,29]. We have manipulated the expressions for linear viscoelastic properties in such as way that the final expressions derived in Refs.…”