Hybrid Monte Carlo Self-Consistent Field Approach to Model a Thin Layer of a Polyelectrolyte Gel near an Adsorbing Surface

A Hybrid Monte Carlo Self-Consistent Field Model of Physical Gels of Telechelic Polymers

We developed a hybrid Monte Carlo self-consistent field technique to model physical gels composed of ABA triblock copolymers and gain insight into the structure and interactions in such gels. The associative A blocks of the polymers are confined to small volumes called nodes, while the B block can move freely as long as it is connected to the A blocks. A Monte Carlo algorithm is used to sample the node configurations on a lattice, and Scheutjens-Fleer self-consistent field (SF-SCF) equations are used to determine the change in free energy. The advantage of this approach over more coarse grained methods is that we do not need to predefine an interaction potential between the nodes. Using this MC-SCF hybrid simulation, we determined the radial distribution functions of the nodes and structure factors and osmotic compressibilities of the gels. For a high number of polymers per node and a solvent-B Flory-Huggins interaction parameter of 0.5, phase separation is predicted. Because of limitations in the simulation volume, we did however not establish the full phase diagram. For comparison, we performed some coarse-grained MC simulations in which the nodes are modeled as single particles with pair potentials extracted from SF-SCF calculations. At intermediate concentrations, these simulations gave qualitatively similar results as the MC-SCF hybrid. However, at relatively low and high polymer volume fractions, the structure of the coarse-grained gels is significantly different because higher-order interactions between the nodes are not accounted for. Finally, we compare the predictions of the MC-SCF simulations with experimental and modeling data on telechelic polymer networks from literature.

Interactions between nodes in a physical gel network of telechelic polymers; self-consistent field calculations beyond the cell model

Triblock copolymers, with associative end-groups and a soluble middle block, form flower-like micelles in dilute solutions and a physical gel at higher concentrations. In a gel the middle blocks form bridges between domains/nodes that contain the ends. We combine the self-consistent field theory with a simple molecular model to evaluate the pair potential between the nodes. In this model the end-groups are forced to remain in nodes and the soluble middle blocks are in solution. When the distance between the centres of the nodes is approximately the corona diameter, loops can transform into bridges, and the pair potential is attractive. Due to steric hindrance, the interaction is repulsive at smaller distances. Till now a cell-model has been used wherein a central node interacts through reflecting boundary conditions with its images in a spherical geometry. This artificial approach to estimate pair potentials is here complemented by more realistic three-gradient SCF models. We consider the pair interactions for (i) two isolated nodes, (ii) nodes positioned on a line (iii) a central node surrounded by its neighbours in simple cubic ordering, and (iv) a central node in a face centred cubic configuration of its neighbours. Qualitatively, the cell model is in line with the more refined models, but quantitative differences are significant. We also notice qualitative differences for the pair potentials in the specified geometries, which we interpret as a breakdown of the pairwise additivity of the pair potential. This implies that for course grained Monte Carlo or molecular dynamics simulations the best choice for the pair potentials depends on the expected node density.

Bending rigidities of surfactant bilayers using self-consistent field theory

Self-consistent field (SCF) theory is used to find bending moduli of surfactant and lipid bilayers. Recently, we successfully applied low-memory search methods to solve the SCF equations. Using these we are now able to directly evaluate the Gaussian bending modulus for molecularly detailed models of bilayers by evaluating the excess Helmholtz energy of tensionless bilayers in a (part of the) Im3m cubic phase. The result prompted us to reconsider the protocol that has been used thus far to find the mean bending modulus kc and Gaussian bending modulus k[overline]. With respect to previous predictions, the value of kc is reduced by a factor of two and the Gaussian bending modulus is less negative and much closer to zero. In line with experimental data we now find that k[overline] can also become positive. In this paper we use the non-ionic surfactants series of the type CnEm for illustration.