Monte Carlo Self-consistent Field Research Articles

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.

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

The use of thin layers of a surface bound (polyelectrolyte) hydrogels for measuring the concentration of metal ions from electrolyte solutions is our motivation for modeling such hydrogels. The gels are composed of polymeric species with conformational degrees of freedom on the nanometer scale. The polymer conformations are affected by the presence of cross-links in the gel on a five to ten times larger length scale, and the repulsive interactions generated by the charges along the chains. Here we present a hybrid computational Monte Carlo Self-consistent field (MC-SCF) approach to model such hydrogels. The SCF formalism is used to evaluate the conformational properties of the chains, implementing a freely jointed chain model, in between featureless cross-links. The Monte Carlo simulation method is used to sample the (restricted) translational degrees of freedom of the cross-links in the gel. We consider the case that the polymers in the gel have an affinity for surface positioned at the edge of the simulation volume. The polymer density decays as a power-law from the surface to the gel-density with an exponent close to -4/3. The gel features relatively large density fluctuations which is natural for a gel with a low density (φ ≈ 0.035), a low degree of cross-linking (average of three chainparts per cross-link), and relatively large chains (N = 50) in between the cross-links. Some parts of the gel can break loose from the gel and sample the adjoining volume. Representative snapshots exemplify large density fluctuations, which explain the large pore size distribution observed in experimental counterparts.

Approximate one-electron density matrix functionals for the electron–electron repulsion energy from the hypervirial theorem

Application of the hypervirial theorem to a certain class of two-electron operators yields the electron–electron repulsion energy as an approximate functional of the Hartree–Fock one-electron reduced density matrix. This functional is entirely parameterized by a single screening function that, upon the assumption of transferability, can be readily retrieved from the known correlation energy of the homogeneous electron gas. Invoking the properties of the actual electronic Hamiltonian, the new formalism explicitly incorporates dispersion effects that are not accounted for by the conventional density functional approaches. Even more importantly, it affords analogous functionals for other variational methods such as Monte Carlo self-consistent field (MC SCF). Since such functionals are bi- and trilinear in the occupied orbitals, their fully analytical computation should be feasible with a carefully chosen approximate representation of the screening function.

Generalized Mo/ller–Plesset perturbation theory: Second order results for two-configuration, open-shell excited singlet, and doublet wave functions

The recently proposed consistent generalization of the Mo/ller–Plesset perturbation theory to arbitrary reference states is reviewed and compared to previous methods. We have implemented the second order of this theory (GMP2) for systems which can be described by a two-configuration wave function. GMP2 is applied here to bond-breaking potential curves: HF, F2, CH3–H, and twisted ethylene, as well as to the geometry and dipole moment of ozone, to the electron affinity of the cyano radical, to the vertical ionization potentials of ethylene, and to the excited singlet states of formaldehyde. In general, the performance of GMP2 is very good and comparable to the two-configuration based doubles CI method. However, like all methods based on a single reference function, GMP2 is not applicable in nearly degenerate situations. We also discuss the continuity of potential surfaces in Monte Carlo self-consistent-field (MC-SCF) theory.