Single-chain Monte Carlo Simulations Research Articles

A Hybrid Approach for Microscopic Properties and Self-Assembly of Dendrimers between Two Hard Walls

Dendrimers are of interest in a number of applications and theoretical studies due to their interesting and complex architectures. We use a hybrid approach to investigate the microstructure of hard dendrimers and self-assembly of diblock dendrimers confined between two hard walls. In the hybrid approach, a single-chain Monte Carlo simulation is used to evaluate the ideal-gas contribution of the Helmholtz energy and a density functional theory is employed to calculate the excess Helmholtz energy. In our calculations, a coarse-grained model is used to represent the dendrimers of generations 1-4. The effects of generation and bulk packing fraction on the microscopic properties of the hard dendrimers are explored. With the increase of generations, the complexity of the dendritic architecture increases. Accordingly, the depletion effect becomes stronger with the generation at etabulk = 0.1. Furthermore, it is found that the more complex the molecular architecture and the higher the molecular stiffness, the smaller is the partitioning coefficient of confined dendrimers. In addition, we also investigate the effects of the width of the slit and the interaction (epsilon*AA) between hydrophilic segments on the self-assembly of diblock dendrimers in the slit. With the increase of epsilon*AA, we observe that the curves of average packing fraction of the dendrimers in the slit exist an abrupt jump, which corresponds to the first-order phase transition from a disordered state to a lamellar ordered structure. In the slit of H = 11sigma, it is at epsilon*AA = 8 rather than epsilon*AA = 10 or epsilon*AA = 12 that the minimum critical bulk packing fraction appears. This observation is distinctively different from the case of self-assembly of rod-like molecules in the slit, where the critical bulk concentration increases with the decrease of the head-head interaction linearly.

“Intrinsic” and “Topological” Stiffness in Branched Polymers

Single-chain Monte Carlo simulations were carried out, in continuous space, of polymers with various topologies (branched and linear) in the good solvent. Using an inherently flexible bead-and-spring model, the backbone of linear polymers with either linear or dendritic side-groups attached was found to be elongated, indicative of an induced stiffness. This “topological stiffness” was compared to the “intrinsic stiffness” of semiflexible linear polymers in terms of various observables. Semiflexible comb polymers, which contained both types of stiffness, were also considered.

Monte Carlo Simulations of Amphiphilic Co-Dendrimers in Dilute Solution

Single-chain Monte Carlo simulations of amphiphilic diblock dendritic copolymers (co-dendrimers) with single and binary trifunctional cores were carried out in continuous space using implicit solvent. Two distinct topologies were studied: dendrimers with the hydrophobic blocks attached to the core, and dendrimers with the polar blocks attached to the core. Both topologies were found to be capable of forming micellar-type structures. As well as in terms of simulation snapshots, the systems were quantitatively compared via asphericity characteristics, monomer density profiles, mean-squared distances of monomers from the center of mass, and mean-squared bond lengths. Increasing the number of generations or increasing the number of spacers between branch points both yielded more well-defined shapes. Although increasing the number of generations of branching initially resulted in more spherical conformations (as for homodendrimers), it was found that high generation co-dendrimers adopted elongated cigar-like conformations for the single core case and dumbbell-like conformations for the binary core case. This phenomenon appears to involve the dendron segregation which occurs at the core of these large co-dendrimers.

Monte Carlo simulations of infinitely dilute solutions of amphiphilic diblock star copolymers

Single-chain Monte Carlo simulations of amphiphilic diblock star copolymers were carried out in continuous space using implicit solvents. Two distinct architectures were studied: stars with the hydrophobic blocks attached to the core and stars with the polar blocks attached to the core, with all arms being of equal length. The ratio of the lengths of the hydrophobic block to the length of the polar block was varied from 0 to 1. Stars with 3, 6, 9 or 12 arms, each of length 10, 15, 25, 50, 75 and 100 Kuhn segments, were analyzed. Four distinct types of conformations were observed for these systems. These, apart from studying the snapshots from the simulations, have been quantitatively characterized in terms of the mean-squared radii of gyration, mean-squared distances of monomers from the center of mass, asphericity indices, and static scattering form factors in the Kratky representation as well as the intrachain monomer–monomer radial distribution functions.

Self‐Consistent Integral Equation Theory for Semiflexible Polyelectrolytes in Poor Solvent

AbstractSelf‐consistent hybrid MC/PRISM method is presented for calculating properties of polyelectrolytes in semidilute and more concentrated regimes in a poor solvent. The static structure and conformational behavior of salt‐free polyelectrolyte solutions composed of semiflexible polyions and monovalent counterions are studied using the approach which combines the traditional Monte‐Carlo (MC) simulation with the numerical solution of the polymer integral PRISM equation. The MC technique is applied to generate the configurations of a single chain molecule and obtain the averaged intrapolymer correlation function. The PRISM equation is then numerically solved for a given monomer density to obtain the various correlation functions and the medium‐induced intrapolymer potential. This is used in a single chain MC simulation, where the polymer sites interact via the bare Coulomb potential together with the short range attractive potential and a self‐consistently determined medium‐induced potential. The monomer‐monomer pair correlation functions and static structure factors are calculated for a large variety of parameters. Conformational properties such as the radius of gyration and visual images are obtained as a function of attractive short‐range interaction, monomer density, Bjerrum length, and chain stiffness. The MC/PRISM study predicts that there is a range of hydrophobicity and monomer density for which polyion chains can form the toroidal structure in a poor solvent. Nonmonotonic dependence of the chain size on monomer density is predicted over the entire range of parameters. Polyion structure factor peak position as a function of density is described. Two concentration regimes in which the polyion structure factors exhibit physically different peaks were found. Over the entire concentration regime considered polyelectrolyte chains undergo strong compression with Rg ∝ l.Conformation of a polyion chain for lB = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.imageConformation of a polyion chain for lB = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.

Application of density functional theory to tethered polymer chains: Athermal systems

Athermal, tethered chains are modeled with density functional (DFT) theory for both the explicit solvent and continuum solvent cases. The structure of DFT is shown to reduce to self-consistent-field theory in the incompressible limit where there is symmetry between solvent and monomer, and to single-chain-mean-field (SCMF) theory in the continuum solvent limit. We show that by careful selection of the reference and ideal systems in DFT theory, self-consistent numerical solutions can be obtained, thereby avoiding the single chain Monte Carlo simulation in SCMF theory. On long length scales, excellent agreement is seen between the simplified DFT theory and molecular dynamics simulations of both continuum solvents and explicit-molecule solvents. In order to describe the structure of the polymer and solvent near the surface it is necessary to include compressibility effects and the nonlocality of the field.

Microstructure of 2,3 erythro di-isotactic polynorbornene from atomistic simulation

A new RIS model was developed for erythro di-isotactic polynorbornene that included long-range steric interactions that are needed to properly model its conformation. These interactions were included by extracting RIS states from an approximate energy state map for the heptamer of this polymer. The RIS model predicted a novel helix-kink conformation for this polymer in which helices were occasionally disrupted by a backbone kink and a value of approximately 1.9 for the exponent “a” from the Mark–Houwink–Sakurada equation at the θ condition. These RIS results were consistent with independent single chain Monte Carlo simulations and were also used to generate bulk periodic structures of this polymer. The results of these simulations compare well to both experimental viscometry and wide angle X-ray diffraction results for two polymer samples synthesized using Pd and zirconocene homogeneous polymerization catalysts. These results indicated that the likely stereochemical configuration for polymers produced using these catalysts is the erythro di-isotactic form. They also suggested that polymers of similar structure such as cis poly(t-butyl acetylene) may also adopt this kink-helix conformation.

Density functional theory of simple polymers in a slit pore. I. Theory and efficient algorithm

Previous applications of density functional (DF) theory required a single chain Monte Carlo simulation to be performed within a self-consistent loop. In the current work, a methodology is developed which permits the simulation to be taken out of the iterative loop. Consequently, the calculation of the self-consistent, medium-induced potential, or field, is decoupled from the simulation. This approach permits different densities, different forms of UM(r), and different wall–polymer interactions to be investigated from a single Monte Carlo simulation. The increase in computational efficiency is immense.

Comparisons between integral equation theory and molecular dynamics simulations for realistic models of polyethylene liquids

Molecular dynamics (MD) simulations were performed on dense liquids of polyethylene chains of 24 and 66 united atom CH2 units. A series of models was studied ranging in atomistic detail from coarse-grained, freely-jointed, tangent site chains to realistic, overlapping site models subjected to bond angle restrictions and torsional potentials. These same models were also treated with the self-consistent, polymer reference interaction site model (PRISM) theory. The intramolecular and total structure factors, as well as, the intermolecular radial distribution functions g(r) and direct correlation functions C(r) were obtained from theory and simulation. Angular correlation functions were also obtained from the MD simulations. Comparisons between theory and simulation reveal that PRISM theory works well for computing the intermolecular structure of coarse-grained chain models, but systematically underpredicts the extent of intermolecular packing, and overpredicts the compressibility, as more realistic details are introduced into the model. We found that the PRISM theory could be considerably improved by adding a tail function to C(r) beyond the effective hard core diameter. The range of this tail function was determined by requiring the theory to yield the correct compressibility. The intermolecular radial distribution functions from this modified PRISM theory were in excellent agreement with g(r)’s obtained from the simulations.

Self-Consistent Integral Equation Theory of Polyolefins and Comparison to X-ray Scattering Experiments

Self-consistent, polymer reference interaction site model (PRISM) calculations were performed on realistic models of three polyolefin melts: polyisobutylene (PIB), isotactic polypropylene (iPP), and syndiotactic polypropylene (sPP). In these calculations, both the intramolecular and intermolecular structure of the polymer liquid are determined in a self-consistent manner. The multiple-chain problem is mapped to an equivalent single-chain Monte Carlo simulation by representing the effect of the other chains through a “medium-induced” pairwise-additive potential calculated from PRISM theory. The intramolecular structure factor, intermolecular radial distribution functions, and medium-induced potentials are obtained numerically from a series of Monte Carlo simulations and PRISM calculations performed iteratively until a self-consistent solution is obtained. The resulting melt structure factors are in close agreement with X-ray scattering experiments on PIB at 25 °C and iPP and sPP liquids at 180 °C. The ind...

Theory for the Phase Behavior of Polyolefin Blends: Application to the Polyethylene/Isotactic Polypropylene Blend

A microscopically realistic theory for modeling the structure, thermodynamics, and phase behavior of polyolefin blends is developed on the basis of the polymer reference interaction site model (PRISM theory). The thermodynamics of mixing is treated using perturbation theory with the corresponding athermal mixture as the reference system. As an illustration of the approach we modeled the polyethylene/isotactic polypropylene blend (PE/i-PP). The polypropylene monomers were constructed from three independent interaction sites representing the CH 2 , CH, and CH 3 united atom groups constituting the monomer. Likewise polyethylene monomers consisted of two identical interaction sites, each representing a CH 2 moiety. The intramolecular structure functions, required as input to PRISM theory, were determined from single-chain Monte Carlo simulations using the rotational isomeric state approximation. The Suter-Flory rotational isomeric state parameters were used for isotactic polypropylene. PRISM theory was used to compute the ten independent intermolecular pair correlation functions needed to characterize the intermolecular packing of the athermal blend. The enthalpic contribution to the free energy was then computed from first-order perturbation theory. The entropy of mixing, heat of mixing, and spinodal curve were computed as a function of composition for the blend consisting of PE and i-PP chains of 200 monomer units. The blend was found to be highly incompatible with UCST behavior. Local or short range correlations were found to significantly increase the heat of mixing, resulting in critical temperatures approximately 10-15 times larger than predicted on the basis of Flory-Huggins theory under the assumption of random mixing.