Molecular Modelling of the Viscoelastic Behaviour of Polymeric Liquids

Significant Achievements, Anticipated Outcomes and Future Work

Development of accurate constitutive models is essential for modelling the behaviour of polymeric liquids in complex flow simulations. The recent growth of micro-macro simulation techniques that enable the use of arbitrarily complex constitutive equations makes such an enterprise highly worthwhile. Theoretical developments in the past few years have shown that a truthful representation of the physics at the microscopic scale is a must in order to obtain an accurate constitutive equation. The fact that two parts of a polymer chain cannot occupy the same place at the same time, the so called "excluded volume" effect, is now widely recognised as one such microscopic phenomenon that must be faithfully modelled. Significant progress has been achieved in the course of this work on understanding the role played by excluded volume effects in determining the macroscopic behaviour of dilute polymer solutions. The approach developed by us to investigate the consequences of the presence of excluded volume interactions has led to very accurate predictions of universal equilibrium properties. It also promises to be a systematic means by which excluded volume effects can be examined in a consistent and unified manner far from equilibrium. For instance, the same framework has been used to show that excluded volume interactions lead to "shear thinning" in a polymer solution.

Computational Techniques Used

Brownian dynamics simulations of polymer chains with a large number of degrees of freedom are carried out using a FORTRAN code written by us to solve the governing stochastic differential equations. The finite chain results obtained in this manner are subsequently extrapolated to the limit of infinite chain length. This procedure leads to the prediction of material properties that are independent of the mechanical model used to describe the polymer. The scaling of CPU time as N cubed, where N is a measure of the length of the polymer chain, has so far prevented realistic molecular modelling of polymeric liquids. The availability of the large number of parallel processors at the APAC National Facility makes it feasible for the first time to explore the influence of non-linear microscopic phenomenon on macroscopic properties.

Publications, Awards and External Funding

External Funding and Awards

R. P. Jagadeeshan, Polymer Solution Rheology with a Realistic Meso-scale Polymer Model, Victorian Partnership for Advanced Computing, Expertise Grant Scheme, 2003, $30,000.

Publications

K.S. Kumar and J. R. Prakash, Equilibrium swelling and universal ratios in dilute polymer solutions: Exact Brownian dynamics simulations for a delta function excluded volume potential, Macromolecules, 36, 7842-7856 (2003).
K. S. Kumar, and J. R. Prakash, Universal shear rate dependence of the viscosity of dilute polymer solutions in the presence of excluded volume interactions, CHEMECA 2003, 31st Australasian Chemical Engineering Conference, Adelaide, South Australia, September 2003.