Sagar S. Rane

Cluster size distribution of voids in a polymer melt

By extending a recently developed Bethe lattice theory, we calculate the cluster size distribution and average cluster size of voids in the presence of polymers. Because of the presence of interactions and because polymers have a size different from that of voids, the model we investigate is a correlated percolation model. The effects of interactions, the pressure P, the degree of polymerization (DP) M, the coordination number q, and the possibility of void percolation on the above properties are evaluated. It is found that small-sized clusters are in overwhelming majority and constitute a large fraction of the total free volume in cases of interest. Attractive monomer–monomer interactions favor the formation of larger clusters. As a function of the DP, the average cluster size shows very different behavior in two regions: with void percolation and without void percolation. The following results are valid at constant temperature and pressure. In the presence of percolation, the average cluster size increases with M, whereas in the absence of percolation it decreases with M. In the absence of void percolation, the average cluster size decreases with increasing q due to the decrease in the total free volume. We present and discuss the results and compare them with those from experiments, simulations and randompercolation. We conclude that we are able to qualitatively explain experimental results if we assume that there is no void percolation.

Monte Carlo simulation of solvent effects on the threading of poly(ethylene oxide)

Recently, we described a coarse-grained model of poly(ethylene oxide) (PEO) and then employed that model to study the amount of spontaneous threading of cyclic molecules by linear chains in the melt (Helfer et al Macromolecules at press). We now use that coarse-grained model to determine how the amount of threading is affected by dilution of the PEO melt with good, Θ, or poor solvents. We employ two distinctly different methods for incorporating the solvent. One method employs explicit coarse-grained solvent molecules, which have the same size as a coarse-grained bead of the polymer. Solvents of different quality are produced by changes in the values of the interaction energies between solvent and polymer beads. The other method does not employ explicit solvent particles but simply modifies the attractive part of the discretized Lennard-Jones potential that describes the pair-wise long-range interaction of coarse-grained PEO while leaving unchanged the rotational isomeric state model that describes the short-range intramolecular interactions. The thermodynamic quality of this implicit solvent is inferred from its effect on the mean square radius of gyration of PEO. The intermolecular pair correlation functions show that cyclic and linear molecules aggregate together in a poor solvent, which contributes to the increase in the amount of threading, relative to the situation found at the same concentration in a good solvent. However, the magnitude of this effect of the poor solvent is insufficient to overcome the decrease in threading upon increasing dilution expected from simple application of the law of mass action. Although the qualitative effects are similar for the two different methods of treating the solvent, quantitative comparison suggests that the use of explicit solvent particles gives a stronger connection with the anticipated behaviour of real systems. The present results for equilibrium structures in a Monte Carlo simulation are not as sensitive to the details of the treatment of the solvent as were earlier results (Chang and Yethiraj 2001 J. Chem. Phys. 114 7688) for the dynamics of the collapse of a single chain in a poor solvent.

Modification of statistical threading in two-component pseudorotaxane melts using the amphiphilic approach and variations in the confinement geometry.

Recently we described a coarse-grained model of poly(ethylene oxide) and then employed that model to study the amount of spontaneous threading of cyclic molecules by linear chains in the melt [C. A. Helfer, G. Xu, W. L. Mattice, and C. Pugh, Macromolecules 36, 10071 (2003)]. Since the amount of statistical threading at equilibrium is small, there is interest in identifying physical changes in the system that will increase the threading. We now use that coarse-grained model to investigate the effect on threading of various hypothetical (but feasible) modifications to the two-component system of macrocycles and linear chains in the melt, and different confinement geometries, that can bring about correlations in the arrangement of the rings. Our work follows on the concept of an amphiphilic approach [C. Pugh, J.-Y. Bae, J. R. Scott, and C. L. Wilkins, Macromolecules 30, 8139 (1997)] for increasing the statistical threading in homopolyrotaxane melts. We investigate whether introducing such correlations in the macrocycles can increase the spontaneous threading. This paper shows that some of our modifications can yield more than double the amount of threading seen in purely statistical mixing.

Calculation of pressure using the virtual-volume-variation method and the virial method from chain conformations obtained by Monte Carlo simulations on the second nearest neighbor diamond lattice

For a model system of polyethylene of chain lengths 40 and 100 carbon atoms, we calculated the pressure at different densities and compared them with the experimental values. The simulation was conducted on the second nearest neighbor diamond lattice, and the pressure was calculated using the virtual-volume-variation method after the system was reverse mapped to its fully atomistic form in continuous space and energy minimized. In addition, the pressure was also calculated from the virial route by conducting a short molecular dynamics simulation starting from the energy minimized structure. We show that the pressure obtained from our simulations is quite reasonable in the length of simulation time (in Monte Carlo steps) normally employed in our group. These results provide additional evidence for the equilibration of our model systems, and methodology to calculate the pressure in our lattice models.

Liquid–liquid phase separation in solutions of living semiflexible polymers

We consider a model of living semiflexible polymers in a solution and obtain results for the liquid–liquid phase separation, which has been a subject of growing interest in the literature and has been studied in some recent experiments. The tetrahedral lattice model is solved exactly on a Husimi cactus of coordination number q=4. The exact solution on the Husimi cactus forms the approximate theory for the original lattice. We consider the end groups to be a different species from the middle groups. This allows us to incorporate the end-group effects in our calculations, which become important at low molecular weights. We investigate the effect of chain rigidity, end-group/middle-group interactions, solvent quality, and the chemical potential of the end-group on the liquid–liquid coexistence curve. We also calculate the average molecular weights of the coexisting liquid phases. The bending penalty e is found to shift the phase diagram only slightly. Attractive end-group/middle-group interaction enhances th...

Applicability of partial monomer volumes derived from the regular solution theory

We demonstrate that the regular solution theory is qualitatively successful in describing the composition dependence of partial monomer volumes in a compressible binary mixture of polymers only when the mixture is symmetric (see text for proper definition). For asymmetric mixtures, the partial monomer volumes can be non-monotonic with composition under ordinary conditions of temperature and pressure, which contradicts the prediction of the regular solution theory. The investigation enables us to conclude that the composition dependence of the partial monomer volumes obtained from the regular solution theory can be considered trustworthy only for a low degree of asymmetry.

Interior segment regrowth configurational-bias algorithm for the efficient sampling and fast relaxation of coarse-grained polyethylene and polyoxyethylene melts on a high coordination lattice

We demonstrate the application of a modified form of the configurational-bias algorithm for the simulation of chain molecules on the second-nearest-neighbor-diamond lattice. Using polyethylene and poly(ethylene-oxide) as model systems we show that the present configurational-bias algorithm can increase the speed of the equilibration by at least a factor of 2-3 or more as compared to the previous method of using a combination of single-bead and pivot moves along with the Metropolis sampling scheme [N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953)]. The increase in the speed of the equilibration is found to be dependent on the interactions (i.e., the polymer being simulated) and the molecular weight of the chains. In addition, other factors not considered, such as the density, would also have a significant effect. The algorithm is an extension of the conventional configurational-bias method adapted to the regrowth of interior segments of chain molecules. Appropriate biasing probabilities for the trial moves as outlined by Jain and de Pablo for the configurational-bias scheme of chain ends, suitably modified for the interior segments, are utilized [T. S. Jain and J. J. de Pablo, in Simulation Methods for Polymers, edited by M. Kotelyanskii and D. N. Theodorou (Marcel Dekker, New York, 2004), pp. 223-255]. The biasing scheme satisfies the condition of detailed balance and produces efficient sampling with the correct equilibrium probability distribution of states. The method of interior regrowth overcomes the limitations of the original configurational-bias scheme and allows for the simulation of polymers of higher molecular weight linear chains and ring polymers which lack chain ends.