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We have used two different types of coarse graining techniques in this work: Multiple Particle Collision Dynamics¹ (MPCD) and Molecular Dynamics (MD) simulations using a bead-spring model of polymers.

MPCD is a mesoscopic model for solvent dynamics, in which the solvent is described as N point particles, whose dynamics is divided into two steps:¹(a) Streaming process: The particles move ballistically in this step¹ and (b) Collision process: The particles are sorted into cells. Collision is simulated via rotation of velocities of all the particles in a given cell relative to the center of mass velocity¹.

For coarse grained MD simulations, polymer beads are connected to each other via springs modeled by the FENE potential. In addition, all of the polymer and solvent beads interact with each other by the Lennard-Jones potential. These simulations are carried out using the LAMMPS package².

Two aspects of polymer solution behavior were studied in this work:

(A) Structural and dynamic behavior of ring polymer solutions:

The shear thickening behavior of wormlike micelles just below the overlap concentration has been hypothesized to be due to the formation of large rings in the wormlike micelles³. Given the importance of chain topology in determining the dynamic and rheological properties of polymers, we studied the effect of chain architecture on polymer properties by focusing on linear chains, ring polymers and catenated ring polymers.

For the MPCD simulations, 20 and 40 bead polymers were studied in a system with solvent particle density of 10. The MD calculations were also done for 20 and 40 bead polymers with a system density of 0.8. Both the simulations were carried out at a constant temperature of 1 (all quantities are in reduced units).

The properties of interest are the diffusion coefficient ratios, Dring/Dlinear and Dcatenated/Duncatenated, and the radius of gyration ratios, Rg ring/Rg linear and Rg catenated/Rg uncatenated.

The diffusion coefficients were calculated from the slope of the mean squared displacement vs. time plot, and the results are as follows:

Table 1: Values of diffusion coefficients and radii of gyration squared for the MPCD and MD simulations for bead-spring polymers of length 20 and 40.

Table 2: Ratios of diffusion coefficients and radii of gyration squared showing a comparison between MPCD and MD simulation approaches. Catenated rings of size 20 indicate 2 catenated rings of 10 beads each.

As the chain topology changes from linear chain to uncatenated ring to catenated ring chain, the chain size decreases while the diffusion coefficient increases. The two coarse grained simulation methods give quantitatively similar results for the effect of chain topology on the structural and dynamical properties studied.

(B) Effect of Solvent Quality and Temperature on the Properties of Polymers in Solution:

An interesting property of wormlike micelles, solvent-temperature superposition, is suggested⁴, according to which the effect of temperature and solvent concentration on the viscoelastic moduli is very similar. To determine the molecular origins of this phenomenon, we investigated the effect of varying solvent quality and temperature on the structural properties of polymers in solution. We used MD simulations with a coarse grained model of the system where polymers are represented by bead-spring chains that are dissolved in a particulate solvent.

The solvent quality was varied in the system by changing the interaction parameter of the LJ interaction potential between the solvent atoms and the polymer beads. The solvent quality is thus expected to increase as the value of this parameter increases. The effect of solvent quality is shown in Fig. 1:

Fig. 1: Effect of solvent quality on Rg for bead-spring polymers with 20 and 40 beads. The interaction parameter for solvent-solvent and polymer-polymer interactions was set to 1.

To study the effect of temperature on chain structural properties, the interaction parameter for all the interactions in the system was set to 1, while the temperature was varied from 0.5 to 2. The variation of radius of gyration with temperature is shown below:

Fig. 2: Effect of temperature on Rg for bead-spring polymers with 20 and 40 beads. Rg is plotted vs. the reciprocal of temperature.

Our results suggest that increasing the solvent quality has a similar effect on chain size as the effect of lowering the temperature. However, there are quantitative differences; effect of solvent quality appears to be stronger.

Impact of the research on the PI and the graduate student:

The PI (Khare) has a strong track record of molecular dynamics simulations of transport phenomena and properties of polymeric systems. The development of the MPCD simulation code in this project has allowed the PI to further expand his research portfolio in the field of mesoscopic modeling. The graduate student (Govind Hegde) working on this project received multidisciplinary training in the areas of mesoscale simulations, polymer physics and rheology of complex fluids. He is also scheduled to present a poster based on this research at the Annual Meeting of the Society of Rheology to be held in October 2010.

References:

1. Malevanets, A.; Kapral, R.; J. Chem. Phys., 110, 17, 8605-8613 (1999).
2. Plimpton, S.J.; J. Comp. Phys., 117, 1-19 (1995).
3. Cates, M.E.; Candau, S.J.; Europhys .Lett., 55 (6), 887-893 (2001).
4. Siriwatwechakul,W.; LaFleur, T.; Prud'homme, R.K.; Sullivan, P.; Langmuir, 20, 8970-8974 (2004).