Equation of state and critical behavior of polymer models: A quantitative comparison between Wertheim’s thermodynamic perturbation theory and computer simulations

110

We have calculated the interfacial properties of fully flexible chains formed from tangentially bonded Lennard-Jones beads by direct coexistence. The full long-range tails of the potential are accounted for by means of inhomogeneous long-range corrections consisting in slice by slice summation of interactions away from the truncation sphere. We show that the corrections may be transformed into an effective long-range pair potential plus a self term, thus allowing for a fast and easy implementation of the method. After addition of the effective pair potential, the coexistence densities agree very well with results from Gibbs-ensemble simulations with usual homogeneous long-range corrections. We calculate the surface tensions without the need for explicit evaluation of the virial by using the wandering interface and test area methods. Comparison with surface tensions obtained previously for chains of truncated Lennard-Jones beads show a very large contribution of interactions beyond truncation radii as large as four bead diameters. The percentage change is about 40% for low temperatures but may increase beyond 60% for high temperatures, thus revealing the need for proper account of long-range corrections for models with untruncated interactions. The study of interfacial properties with chain length shows asymptotic increase for the surface tension and related asymptotic decrease for the interfacial width.

Section: Resultsmentioning

confidence: 94%

Section: Model and Simulationsmentioning

confidence: 99%

Surface tension of fully flexible Lennard-Jones chains: Role of long-range corrections

MacDowell

Blas

2009

110

“…MacDowell et al 18 investigated the phase diagram of this system and found that for 10-mers, the critical temperature is equal to 1.98k B / ⑀. The ⌰ temperature was estimated to be equal to 3.3k B / ⑀.…”

Section: ͑2͒mentioning

confidence: 98%

Single-chain dynamics in a semidilute polymer solution under steady shear

Jose

Szamel

2008

We use Brownian dynamics computer simulations to investigate single-chain dynamics in a semidilute polymer solution undergoing a steady, uniform shear flow. In the presence of the shear flow, the system used in the present study exhibits anisotropic structure factors, often referred to as butterfly patterns, which rotate with increasing shear rate [P. P. Jose and G. Szamel, J. Chem. Phys. 127, 114905 (2007)]. The rotation of these patterns correlates with shear thinning of the solution. In order to elucidate the microscopic origin of this behavior, we have investigated the change in the single-chain dynamics in the solution: We have focused on the relaxation of the end-to-end vector, the Rouse modes, and the radius of gyration tensor. In equilibrium and for small shear rates, these quantities show double exponential relaxation. With increasing shear rate, they show oscillatory relaxation, which hints at the tumbling motion of the chain. In the high shear rate regime, the frequency of the oscillations of the end-to-end vector autocorrelation function shows a power law dependence on the shear rate. We have compared the single-chain dynamics in the semidilute solution with that in a dilute solution. An analysis of the instantaneous values of the radius of gyration tensor, the end-to-end distance, and the normal stress along the system's trajectory reveals a synchronization of the fluctuations of these quantities.

“…At our mixture density of 0.85, we are well to the right of the critical point and it is not unreasonable that we see only the UCST. These results, however, are complicated by the fact that recent estimates 44 based on Wertheim's equation-of-state 45 suggest that at 3 ϭ0.85 and k B T/⑀Ϸ1, the pure chain melt may be slightly within the gas/liquid coexistence region. Thus if there indeed is a UCST in the polymer solution, it may be unobservable because it may be preempted by the gas/liquid coexistence curve.…”

Section: Phase Behaviormentioning

confidence: 98%

An integral equation theory for polymer solutions: Explicit inclusion of the solvent molecules

Mendez

Curro

Pütz

et al. 2001

Self-consistent Polymer Reference Interaction Site Model ͑PRISM͒ calculations and molecular dynamics ͑MD͒ simulations were performed on athermal solutions of linear polymers. Unlike most previous treatments of polymer solutions, we explicitly included the solvent molecules. The polymers were modeled as tangent site chains and the solvent molecules were taken to be spherical sites having the same intermolecular potential as the polymer sites. The PRISM theory was solved self-consistently for both the single chain structure and intermolecular correlations as a function of chain length and concentration. The rms end-to-end distance from PRISM theory was found to be in agreement with corresponding MD simulations, and exhibited molecular weight dependence in accordance with scaling predictions in the dilute and concentrated solution limits. The presence of explicit solvent molecules had a significant effect on the packing of the polymer by inducing additional structure in the intermolecular radial distribution function between polymer sites. Using the direct correlation functions from the athermal solution and the random phase approximation, we were able to estimate the spinodal curves for solutions when polymer and solvent attractions were turned on. We found significant deviations from Flory-Huggins theory that are likely due to compressibility and nonrandom mixing effects.