Evaluation of the Gaussian Blob Model for Coarse-Graining Hydrodynamic Interactions in Isolated Polymer Molecules

Prabhakar, R.
July 2008
AIP Conference Proceedings;7/7/2008, Vol. 1027 Issue 1, p309
Conference Proceeding
Hydrodynamic interactions (HI) are important in a variety of systems such as colloidal suspensions and polymer solutions, both near and well beyond equilibrium. Detailed particulate simulations are increasingly an important tool in exploring the behaviour of such systems. An accurate method for coarse-graining long-range HI is desirable for designing efficient simulations, particularly when no obvious spatial symmetries can be exploited, as in the case of isolated flexible polymer molecules in solution. A recent model [Prabhakar et al. Phys. Rev. E, 76:011809 (2007)] proposed coarse-graining HI in a dilute polymer solution by representing a macromolecule as a chain of axisymmetric ellipsoidal Gaussian density fields, whose instantaneous dimensions are derived from their end-to-end stretch and orientation by invoking the assumption of local equilibrium. In this “Gaussian Blob” (GB) model, an expression was derived for the tensor describing HI between any pair of blobs. By combining the resulting mobility matrix with entropic spring force laws also based on the local equilibrium assumption, the GB model provides an alternative to the conventional bead-spring chain model with Rotne-Prager-Yamakawa HI. The advantage of the new model is that it has no free parameters, and all model parameters are uniquely related back to the polymer contour length, the Kuhn step length and the hydrodynamic diameter of the polymer contour. Preliminary simulations indicated that the GB model achieved a considerable reduction in the variation of predictions with respect to the number of blobs N chosen to represent the chain in comparison with the conventional bead spring model, irrespective of whether chains are stretched, or coiled near equilibrium. In this talk, I present more detailed results to confirm the practical viability of the coarse-grained HI used in the GB model. Firstly, the universal viscoelastic features predicted by both the GB and conventional models are identical, in the linear response regime, in strong extensional flows, and during relaxation after being initially expanded. In addition, the much smaller variation with N observed with the GB model means that a single low choice of N∼5 can be used to perform reliable and computationally efficient simulations under a variety of conditions without the necessity for adjusting parameters. I also discuss applications of this model to model more complex structures and illustrate its use with simulations for linear and nonlinear rheological properties of rod-coil block co-polymers.


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