Molecular segregation and nucleation of poly(ethylene oxide) crystallized from the melt. IV. Computer modeling

A crystal surface is modelled and Monte Carlo simulations are attempted to learn about conformations and motion of a macromolecule that could lead to crystallization. Chains with up to 200 mobile segments have been analyzed. The diffusion distance of a given chain segment increases with positioning closer to the chain end, and completion of crystallization accelerates with decreasing length of remaining amorphous chain ends and increasing temperature.     

Self-assembling of chain molecules in low dimensions: A Monte Carlo study

We studied the self-assembling of linear chain molecules in insoluble monolayers due to attractive interactions. We used lattice Monte Carlo simulations in a two-dimensional system. The molecules consist of segments occupying adjacent lattice sites. The head segments are confined to move along a line whereas the chain segments can arrange in a plane above the heads. Only one interaction parameter is applied. At high densities and small interaction energy the system shows percolation behavior. At moderate and small densities it can be characterized by a monotonous cluster size distribution. Self-assembling occurs at small densities for strong attractive interactions. The corresponding cluster size distributions indicate preferred cluster sizes which depend upon density and interaction strength. With increasing density the clusters grow. The internal cluster structure depends on the cluster size and the interaction parameter. The clusters tend to minimize their total energy. Molecules at cluster margins contribute less to the cluster energy and are mainly disordered. They cause that the cluster properties strongly depend on the cluster size. Large clusters only have minimum energy if the molecules in the cluster are in stretched-out conformation. With decreasing interaction strength the clusters get disordered thereby producing less energy-minimized domain boundaries.     

Effect of surface active sites on adsorption of associating chain molecules in pores: A Monte Carlo study

This work describes the adsorption behavior of associating and non-associating chains and their mixtures in pores with activated surfaces. The systems are studied using Gibbs ensemble Monte Carlo molecular simulations. Fluid molecules are modeled as freely jointed Lennard-Jones chains. Associating chains have, additionally, an associating square-well site placed in an end sphere. The pores are modeled as regular slit pores via an integrated Lennard-Jones potential (10-4-3); activation is achieved by placing specific association sites protruding from the surface. Two different solid-fluid interaction parameters are used, one of which corresponds roughly to alkanes on graphite, the other being a much weaker interaction. Adsorption isotherms are presented for several different cases: associating and non-associating chains confined within both neutral and activated walls. Mixtures of associating and non-associating chains are also considered. The effects of pore size, temperature and chain length are quantified. Selectivities obtained are in the range of those seen in adsorption experiments of alkane-alkanol mixtures.     

Free energies and phase equilibria of chain molecules

In this Article, a review is presented of recent developments in Monte Carlo simulations of chain molecules. The Rosenbluth chain insertion technique is used to calculate the free energy of the chain molecules. Furthermore, this insertion method is used to generate biased Monte Carlo moves. It is shown that this bias can be removed by adjusting the acceptance rules such that configurations are generated with their correct Boltzmann weight. This configurational-bias Monte Carlo method can be combined with the Gibbs-ensemble technique which results in an efficient method to simulate phase equilibria of chain molecules.     

A perturbation density functional theory for the competition between inter and intramolecular association

Using the framework of Wertheim's thermodynamic perturbation theory we develop the first density functional theory which accounts for intramolecular association in chain molecules. To test the theory new Monte Carlo simulations are performed at a fluid solid interface for a 4 segment chain which can both intra and intermolecularly associate. The theory and simulation results are found to be in excellent agreement. It is shown that the inclusion of intramolecular association can have profound effects on interfacial properties such as interfacial tension and the partition coefficient.     

Properties of branched confined polymers

A model of star-branched polymer chains confined in a slit formed by two parallel surfaces was studied. The chains were embedded to a simple cubic lattice and consisted of f=3 branches of equal length. The macromolecules had the excluded volume and the confining surfaces were impenetrable for polymer segments. No attractive interactions between polymer segments and then between polymer segments and the surfaces were assumed and therefore the system was a thermal. Monte Carlo simulations were carried out employing the sampling algorithm based on chain's local changes of conformation. Lateral diffusion of star-branched chains was studied. Dynamic properties of star-branched chains between the walls with impenetrable rod-like obstacles were also studied and compared to the previous case. The density profiles of polymer segments on the slit were determined. The analysis of contacts between the polymer chain and the surfaces was also carried out.     

Density functional theory of adsorption in pillared slit-like pores

We propose a density functional theory to describe adsorption of Lennard-Jones fluid in pillared slit like pores. Specifically, the pillars are built of chains that are bonded by their ends to the opposite pore walls. The approach we propose combines theory of quenched-annealed systems and theory of nonuniform fluids involving chain molecules. We compare the results of theoretical predictions with grand canonical ensemble Monte Carlo simulations and compute theoretical capillary condensation phase diagrams for several model systems.     

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.     

Molecular weight distribution effects on the structure of strongly adsorbed polymers by Monte Carlo simulation

Monte Carlo simulations are reported to study the structure of polymers adsorbed from solution onto strongly attractive, perfectly smooth substrates. Six systems spanning a range of molecular weight distributions are investigated with a coarse-grained united atom model for freely rotating chains. By employing a global replica exchange algorithm and topology altering Monte Carlo moves, a range of monomer-surface attraction from weak (0.27kT) to strong (4kT) is simultaneously explored. Thus for the first time ever, equilibrium polymer adsorption on highly attractive surfaces is studied, with all adsorbed molecules displaying similar properties and statistics. The architecture of the adsorbed layers, including density profiles, bond orientation order parameters, radii of gyration, and distribution of the adsorbed chain fractions, is shown to be highly dependent on the polydispersity of the polymer phase. The homology of polymer chains, and the ergodicity of states explored by the molecules is in contrast to the metastable, kinetically constrained paradigm of irreversible adsorption. The structure of more monodisperse systems is qualitatively similar to experimental results and theoretical predictions, but result from very different chain conformations and statistics. The polydispersity-dependent behavior is explained in the context of the competition between polymers to make contact with the surface.     

Monte Carlo simulation for the adsorption of symmetric triblock copolymers I. Configuration distribution and density profiles of adsorbed chains

Monte Carlo simulations for the adsorption of symmetric triblock copolymers from a nonselective solvent at a solid-liquid interface have been performed on a lattice model. In simulations, triblock copolymer molecules are modeled as self-avoiding linear chains composed of m segments of A and n segments of B arranged as A_m/2B_nA_m/2. Either segment A or segment B is attractive, while the other is non-attractive to the surface. The microstructure of the adsorbed layers, including the segment-density profiles and the size distribution of loops, tails and trains are presented. The effect of the adsorption energy, the bulk concentration, the chain composition, as well as the chain length on various adsorption properties has been studied. The results have shown that the size distribution of various configurations is dependent of the adsorption energy, the chain composition and the chain length. The mean length of the loops, trains and tails is insensitive to the bulk concentration. The mean length of the trains increases and that of the tails decreases as the adsorption energy and the length of the attractive segments increase. The mean length of the loops for the end-adsorbed copolymers appears a maximum and that for middle-adsorbed copolymers appears a minimum as the length of attractive segments increases. The length of the non-attractive segments affects mostly the size distribution of the tails. The longer the chain is, the larger the tail appears. The mean length of the tails and loops increases linearly as the length of the non-attractive segments increases, but that of the trains approximately is unchanged.     

嵌段高分子尾形链构象性质的Monte Carlo研究

基于简立方格点模型对AB两嵌段高分子尾形链的构象性质及其链节的空间分布进行了MonteCarlo模拟.结果表明,链的尺寸、形状和链节的空间分布等统计性质和B链节与平面壁之间的相互吸引能有关.随着B链节与壁之间的吸引能的增加,链的尺寸和形状均呈现出先下降后升高的变化趋势,而且B链节的比例越大,这种变化越明显.     

Different growth regimes on prepatterned surfaces: consistent evidence from simulations and experiments

Molecule deposition on a prepatterned substrate is a recently developed technique to generate desired structures of organic molecules on surfaces via self-organization. For the case of prepatterned stripes, the time-resolved process of structure formation is studied via lattice Monte Carlo simulations. By systematic variation of the interaction strength, three distinct growth regimes can be identified: localized growth, bulge formation, and cluster formation. All three growth regimes can be recovered in the experiment when choosing appropriate organic molecules. Some key microscopic observables, reflecting the properties of the structure formation, display a non-monotonous dependence on the interaction strength.     

Phase behavior of a fluid confined in slitlike pores with walls modified by preadsorbed chain molecules

We have studied the microscopic structure, thermodynamics of adsorption, and phase behavior of Lennard-Jones fluid in slitlike pores with walls modified due to preadsorption of chain molecules. The chain species are grafted at the walls by terminating segments. Our theoretical considerations are based on a density functional approach in the semigrand canonical ensemble. The applied constraint refers to the constant number of grafted chain molecules in the pore without restriction of the number of chains at each of the walls. We have observed capillary condensation of Lennard-Jones fluid combined with the change of the distribution of chains from nonsymmetric to symmetric with respect to the pore walls. The phase diagrams of the model are analyzed in detail, dependent on the pore width, length of chains, and grafted density.     

Shielding effects in polymer-polymer reactions. IV. Intermolecular contact formation between star-branched molecules

Pairs of star-branched molecules--taken from ensembles of athermal five-way cubic lattice chains prepared by Monte Carlo simulation--are analyzed for the relative probability of mutual contact formation between particularly specified segments i and j belonging to different chains within these pairs. These contact probabilities--termed shielding factors K(ij)--are calculated by means of exact enumeration as a function of chain length ranging from n = 8 to 256 bonds per arm, as a function of functionality (i.e., the number of arms) ranging from F = 2 to 6 arms, and as a function of segment position within the arms ranging from central to terminal segments. In addition, changes of properties that characterize the size and shape of the involved molecules while approaching and penetration are evaluated as a function of chain separation.     

Computer simulation studies of aggregates of associating polymers: Influence of low-molecular-weight additives solubilizing the aggregates

The structure of aggregates in solutions of chain molecules with associating groups at one of the ends is studied by Monte Carlo computer simulations using the bond fluctuation model. The main attention is paid to the influence of additives of low-molecular-weight solvent solubilizing the aggregates. It is shown that upon the addition of solvent the aggregates adopt a three-layer structure with the ‘lake’ of the solvent molecules in the central region surrounded by the layer of associating end-groups of polymer chains, which in turn is surrounded by the outer corona formed by the chain tails. The equilibrium form of the aggregates becomes close to that of a droplet of low-molecular-weight liquids. The regimes are found when the addition of the low-molecular-weight solvent stabilizes the multiplets and even induces the aggregate formation.     

Self-assembled structures of block copolymers in selective solvents reproduced by lattice Monte Carlo simulation

A lattice Monte Carlo (MC) simulation was applied to the study of block copolymers in selective solvent or amphiphilic surfactant solution on the segment level, hydrodynamic interactions being neglected. The code was found to be very efficient, employing a partial reptation mode as the elementary movement of the self-avoiding lattice chains. Typical self-assembled structures of block copolymers such as micelle, lamellae, hexagonal cylinder and bicontinuous networks have been successfully reproduced without any priori specification of structure. Order–disorder and order–order transitions of diblock copolymers are systematically studied by adjusting the temperature, the concentration or the block length ratio in a series computer simulations. The structural differences between micelles composed of ABA and BAB triblock copolymers are also explicitly revealed by direct visualisation of the underlying chain configurations. The simulation results are consistent with the experimental observations in the literature. This simulation approach is thus a very useful tool in the extensive investigation of self-assembled structures. It has the advantage that both micro-domains and chain configurations can be studied with only a comparatively modest call on computational resources.     

Motion of a branched polymer chain in confinement: a Monte Carlo study

The aim of the study was a theoretical investigation of the polymer molecules located between two parallel and impenetrable surfaces which were also attractive for polymer segments. The chains were constructed of identical segments and were restricted to knots of a simple cubic lattice. Since the chains were at good solvent conditions the only interactions between the segments of the chain were the excluded volume. The properties of the model chains were determined by means of Monte Carlo simulations with a sampling algorithm based on the chain's local changes of conformation. The differences and similarities in the structure for different adsorption regimes and the size of the slit were shown and discussed. It was observed that at certain conditions the polymer chain was adsorbed at one of the confining surfaces, and then after a certain period of time it detached from this surface and approached the opposite wall; this switch was repeated many times. The influence of the strength of the adsorption, the size of the slit, and the chain's length on the frequency of these jumps were determined. The mechanism of the chain's motion during the switch was also shown.     

Monte Carlo simulation of mixed lennard-jones nonionic surfactant adsorption at the liquid/vapor interface

New Monte Carlo simulations are presented for nonionic surfactant adsorption at the liquid/vapor interface of a monatomic solvent specifically investigating the roles of tail attraction and binary mixtures of different tail lengths. Surfactant molecules consist of an amphiphilic chain with a solvophilic head and a solvophobic tail. All molecules in the system, solvent and surfactant, are characterized by the Lennard-Jones (LJ) potential. Adjacent atoms along the surfactant chain are connected by finitely extensible harmonic springs. Solvent molecules move via the Metropolis random-walk algorithm, whereas surfactant molecules move according to the continuum configurational bias Monte Carlo (CBMC) method. We generate thermodynamic adsorption and surface-tension isotherms and compare results quantitatively to single-surfactant adsorption (Langmuir, 2007, 23, 1835). Surfactant tail groups with attractive interaction lead to cooperative adsorption at high surface coverage and higher maximum adsorption at the interface than those without. Moreover, adsorption and surface-tension isotherms with and without tail attraction are identical at low concentrations, deviating only near maximum coverage. Simulated binary mixtures of surfactants with differing lengths give intermediate behavior between that of the corresponding single-surfactant adsorption and surface-tension isotherms both with and without tail attraction. We successfully predict simulated mixture results with the thermodynamically consistent ideal adsorbed solution (IAS) theory for binary mixtures of unequal-sized surfactants using only the simulations from the single surfactants. Ultimately, we establish that a coarse-grained LJ surfactant system is useful for understanding actual surfactant systems when tail attraction is important and for unequal-sized mixtures of amphiphiles.