Shear-Thinning in Oligomer Melts-Molecular Origins and Applications.

We investigate the molecular origin of shear-thinning in melts of flexible, semiflexible and rigid oligomers with coarse-grained simulations of a sheared melt. Entanglements, alignment, stretching and tumbling modes or suppression of the latter all contribute to understanding how macroscopic flow properties emerge from the molecular level. In particular, we identify the rise and decline of entanglements with increasing chain stiffness as the major cause for the non-monotonic behaviour of the viscosity in equilibrium and at low shear rates, even for rather small oligomeric systems. At higher shear rates, chains align and disentangle, contributing to shear-thinning. By performing simulations of single chains in shear flow, we identify which of these phenomena are of collective nature and arise through interchain interactions and which are already present in dilute systems. Building upon these microscopic simulations, we identify by means of the Irving-Kirkwood formula the corresponding macroscopic stress tensor for a non-Newtonian polymer fluid. Shear-thinning effects in oligomer melts are also demonstrated by macroscopic simulations of channel flows. The latter have been obtained by the discontinuous Galerkin method approximating macroscopic polymer flows. Our study confirms the influence of microscopic details in the molecular structure of short polymers such as chain flexibility on macroscopic polymer flows.

Spinodal decomposition of polymer solutions: molecular dynamics simulations of the two-dimensional case.

As a generic model system for phase separation in polymer solutions, a coarse-grained model for hexadecane/carbon dioxide mixtures has been studied in two-dimensional geometry. Both the phase diagram in equilibrium (obtained from a finite size scaling analysis of Monte Carlo data) and the kinetics of state changes caused by pressure jumps (studied by large scale molecular dynamics simulations) are presented. The results are compared to previous work where the same model was studied in three-dimensional geometry and under confinement in slit geometry. For deep quenches the characteristic length scale ℓ(t) of the formed domains grows with time t according to a power law close to [Formula: see text]. Since in this problem both the polymer density ρ(p) and the solvent density ρ(s) matter, the time evolution of the density distribution P(L)(ρ(p),ρ(s),t) in L × L subboxes of the system is also analyzed. It is found that in the first stage of phase separation the system separates locally into low density carbon dioxide regions that contain no polymers and regions of high density polymer melt that are supersaturated with this solvent. The further coarsening proceeds via the growth of domains of rather irregular shapes. A brief comparison of our findings with results of other models is given.

Interactions between polymer brush-coated spherical nanoparticles: the good solvent case.

The interaction between two spherical polymer brushes is studied by molecular dynamics simulation varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. A coarse-grained bead-spring model is used to describe the macromolecules, and purely repulsive monomer-monomer interactions are taken throughout, restricting the study to the good solvent limit. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to-end distance of the grafted chains, etc.). When the nanoparticles approach very closely, some chains need to be squeezed out into the tangent plane in between the particles, causing a very steep rise of the repulsive interaction energy between the particles. We consider as a complementary method the density functional theory approach. We find that the quantitative accuracy of the density functional theory is limited to large nanoparticle separation and short chain length. A brief comparison to Flory theory and related work on other models also is presented.

Molecular-dynamics simulation of evaporation processes of fluid bridges confined in slitlike pores.

A simple fluid, described by pointlike particles interacting via the Lennard-Jones potential, is considered under confinement in a slit geometry between two walls at distance L_{z} apart for densities inside the vapor-liquid coexistence curve. Equilibrium then requires the coexistence of a liquid "bridge" between the two walls, and vapor in the remaining pore volume. We study this equilibrium for several choices of the wall-fluid interaction (corresponding to the full range from complete wetting to complete drying, for a macroscopically thick film), and consider also the kinetics of state changes in such a system. In particular, we study how this equilibrium is established by diffusion processes, when a liquid is inserted into an initially empty capillary (partial or complete evaporation into vacuum), or when the volume available for the vapor phase increases. We compare the diffusion constants describing the rates of these processes in such inhomogeneous systems to the diffusion constants in the corresponding bulk liquid and vapor phases.

Spinodal decomposition of polymer solutions: a parallelized molecular dynamics simulation.

In simulations of phase separation kinetics, large length and time scales are involved due to the mesoscopic size of the polymer coils, and the structure formation on still larger scales of length and time. We apply a coarse-grained model of hexadecane dissolved in supercritical carbon dioxide, for which in previous work the equilibrium phase behavior has been established by Monte Carlo methods. Using parallelized simulations on a multiprocessor supercomputer, large scale molecular dynamics simulations of phase separation following pressure jumps are presented for systems containing N=435136 coarse-grained particles, which correspond to several millions of atoms in a box with linear dimension 447 A . Even for large systems the phase separation can be observed up to the final, macroscopically segregated, equilibrium state. It is shown that in the segregation process the two order parameters of the system (density and concentration) are strongly coupled. The system does not follow the predicted growth law for the characteristic domain size l(t) proportional, variant t in binary fluid mixtures for the range of times accessible in the simulation. Instead, it exhibits a distinctly slower growth, presumably due to the dynamic asymmetry of the constituents.

Phase separation of an asymmetric binary-fluid mixture confined in a nanoscopic slit pore: molecular-dynamics simulations.

As a generic model system of an asymmetric binary-fluid mixture, hexadecane dissolved in carbon dioxide is considered, using a coarse-grained bead-spring model for the short polymer, and a simple spherical particle with Lennard-Jones interactions for the carbon dioxide molecules. In previous work, it has been shown that this model reproduces the real phase diagram reasonably well, and also the initial stages of spinodal decomposition in the bulk following a sudden expansion of the system could be studied. Using the parallelized simulation package ESPResSo on a multiprocessor supercomputer, phase separation of thin fluid films confined between parallel walls that are repulsive for both types of molecules are simulated in a rather large system ( 1356 x 1356 x 67.8 A{3} , corresponding to about 3.2-million atoms). Following the sudden system expansion, a complicated interplay between phase separation in the directions perpendicular and parallel to the walls is found: In the early stages the hexadecane molecules accumulate mostly in the center of the slit pore, but as the coarsening of the structure in the parallel direction proceeds, the inhomogeneity in the perpendicular direction gets much reduced. Studying then the structure factors and correlation functions at fixed distances from the wall, the densities are essentially not conserved at these distances, and hence the behavior differs strongly from spinodal decomposition in the bulk. Some of the characteristic lengths show a nonmonotonic variation with time, and simple coarsening described by power-law growth is only observed if the domain sizes are much larger than the film thickness.

How Well Can Coarse-Grained Models of Real Polymers Describe Their Structure? The Case of Polybutadiene.

Coarse-graining of chemical structure of macromolecules in the melt is investigated using extensive molecular dynamics simulation data which are based on a united atom force-field model of polybutadiene. Systematically increasing the number, n, of the united atoms approximated by an effective coarse-grained monomer, we study the influence of degree of coarse-graining on the structure functions such as the segment-segment intermolecular and intramolecular correlation functions. These results are compared to Monte Carlo simulations of the corresponding coarse-grained bead-spring model and Chen-Kreglewski potential for chain molecules. In contrast to the atomistic chemically realistic model of polybutadiene, the bending and torsional potentials are not included into the coarse-grained models. Nevertheless, for a range of intermediate values of n a good qualitative agreement between intra- and intermolecular coarse-grained correlations of the atomistic model and the coarse-grained bead-spring model is found on large and intermediate length scales, but deviations occur on length scales well below one nanometer. The structure functions obtained for the Chen-Kreglewski chains exhibit many artificial features.

Artificial multiple criticality and phase equilibria: an investigation of the PC-SAFT approach.

The perturbed-chain statistical associating fluid theory (PC-SAFT) is studied for a wide range of temperature, T, pressure, p, and (effective) chain length, m, to establish the generic phase diagram of polymers according to this theory. In addition to the expected gas-liquid coexistence, two additional phase separations are found, termed "gas-gas" equilibrium (at very low densities) and "liquid-liquid" equilibrium (at densities where the system is expected to be solid already). These phase separations imply that in one-component polymer systems three critical points occur, as well as equilibria of three fluid phases at triple points. However, Monte Carlo simulations of the corresponding system yield no trace of the gas-gas and liquid-liquid equilibria, and we conclude that the latter are just artefacts of the PC-SAFT approach. Using PC-SAFT to correlate data for polybutadiene melts, we suggest that discrepancies in modelling the polymer density at ambient temperature and high pressure can be related to the presumably artificial liquid-liquid phase separation at lower temperatures. Thus, particular care is needed in engineering applications of the PC-SAFT theory that aims at predicting properties of macromolecular materials.

A global investigation of phase equilibria using the perturbed-chain statistical-associating-fluid-theory approach.

The recently developed perturbed-chain statistical-associating-fluid theory (PC-SAFT) is investigated for a wide range of model parameters including the parameter m representing the chain length and the thermodynamic temperature T and pressure p. This approach is based upon the first-order thermodynamic perturbation theory for chain molecules developed by Wertheim [M. S. Wertheim, J. Stat. Phys. 35, 19 (1984); ibid. 42, 459 (1986)] and Chapman et al. [G. Jackson, W. G. Chapman, and K. E. Gubbins, Mol. Phys. 65, 1 (1988); W. G. Chapman, G. Jackson, and K. E. Gubbins, ibid. 65, 1057 (1988)] and includes dispersion interactions via the second-order perturbation theory of Barker and Henderson [J. A. Barker and D. Henderson, J. Chem. Phys. 47, 4714 (1967)]. We systematically study a hierarchy of models which are based on the PC-SAFT approach using analytical model calculations and Monte Carlo simulations. For one-component systems we find that the analytical model in contrast with the simulation results exhibits two phase-separation regions in addition to the common gas-liquid coexistence region: One phase separation occurs at high density and low temperature. The second demixing takes place at low density and high temperature where usually the ideal-gas phase is expected in the phase diagram. These phenomena, which are referred to as "liquid-liquid" and "gas-gas" equilibria, give rise to multiple critical points in one-component systems, as well as to critical end points and equilibria of three fluid phases, which can usually be found in multicomponent mixtures only. Furthermore, it is shown that the liquid-liquid demixing in this model is not a consequence of a "softened" repulsive interaction as assumed in the theoretical derivation of the model. Experimental data for the melt density of polybutadiene with molecular mass Mw=45,000 gmol are correlated here using the PC-SAFT equation. It is shown that the discrepancies in modeling the polymer density at ambient temperature and high pressure can be traced back to the liquid-liquid phase separation predicted by the equation of state at low temperatures. This investigation provides a basis for understanding possible inaccuracies or even unexpected phase behavior which can occur in engineering applications of the PC-SAFT model aiming at predicting properties of macromolecular substances.