A fast Monte Carlo algorithm for studying bottle-brush polymers

The Journal of Chemical Physics, 2011

By molecular dynamics simulation of a coarse-grained bead-spring-type model for a cylindrical molecular brush with a backbone chain of Nb effective monomers to which with grafting density σ side chains with N effective monomers are tethered, several characteristic length scales are studied for variable solvent quality. Side chain lengths are in the range 5 ⩽ N ⩽ 40, backbone chain lengths are in the range 50 ⩽ Nb ⩽ 200, and we perform a comparison to results for the bond fluctuation model on the simple cubic lattice (for which much longer chains are accessible, Nb ⩽ 1027, and which corresponds to an athermal, very good, solvent). We obtain linear dimensions of the side chains and the backbone chain and discuss their N-dependence in terms of power laws and the associated effective exponents. We show that even at the theta point the side chains are considerably stretched, their linear dimension depending on the solvent quality only weakly. Effective persistence lengths are extracted b...

The Journal of Chemical Physics, 1997

A three dimensional continuous space Monte Carlo computer simulation study is presented to discuss the extension of flexible, linear polymer chains due to the presence of equally flexible side chains. We consider the enhancement of the persistence length of bottle-brush structures in an athermal solution due to steric interactions between the side chains. The largest structure studied consists of a backbone of 100 beads with 50 side chains of 20 beads each. The persistence length is evaluated in two different ways using the radius of gyration of the backbone and the bond angle correlation function, respectively. A correct description of the backbone conformations is shown to require at least two characteristic lengths. At a small length scale the backbone behaves flexible; the extension occurs at a larger length scale. There is a strong indication that the ratio between the persistence length and the diameter, which is the determining factor for lyotropic behavior of conventional semiflexible chains, levels off as a function of the side chain length. The value of this ratio is, moreover, too small to induce lyotropic behavior along this line. Recent experimental observations of lyotropic behavior of polymacromonomers are discussed in terms of these findings.

Macromolecular Theory and Simulations, 2007

Scaling predictions and results from selfconsistent field calculations for bottle-brush polymers with a rigid backbone and flexible side chains under good solvent conditions are summarized and their validity and applicability is assessed by a comparison with Monte Carlo simulations of a simple lattice model. It is shown that under typical conditions, as they are also present in experiments, only a rather weak stretching of the side chains is realized, and then the scaling predictions based on the extension of the Daoud-Cotton blob picture are not applicable. Also two-component bottle brush polymers are considered, where two types (A,B) of side chains are grafted, assuming that monomers of different kind repel each other. In this case, variable solvent quality is allowed for, such that for poor solvent conditions rather dense cylinderlike structures result. Theories predict "Janus Cylinder"type phase separation along the backbone in this case. The Monte Carlo simulations, using the pruned-enriched Rosenbluth method (PERM) then are restricted to rather short side chain length. Nevertheless, evidence is obtained that the phase separation between an A-rich part of the cylindrical molecule and a B-rich part can only occur locally. The correlation length of this microphase separation can be controlled by the solvent quality. This lack of a phase transition is interpreted by an analogy with models for ferromagnets in one space dimension.

The Journal of Chemical Physics, 2006

simulations are presented for the static properties of highly branched polymer molecules. The molecules consist of a semiflexible backbone of hard-sphere monomers with semiflexible side chains, also composed of hard-sphere monomers, attached to either every backbone bead or every other backbone bead. The conformational properties and structure factor of this model are investigated as a function of the stiffness of the backbone and side chains. The average conformations of the side chains are similar to self-avoiding random walks. The simulations show that there is a stiffening of the backbone as degree of crowding is increased, for example, if the branch spacing is decreased or side chain length is increased. The persistence length of the backbone is relatively insensitive to the stiffness of the side chains over the range investigated. The simulations reproduce most of the qualitative features of the structure factor observed in experiment, although the magnitude of the stiffening of the backbone is smaller than in experiment.

Journal of Molecular Modeling, 2013

A linear chain on a simple cubic lattice was simulated by the Metropolis Monte Carlo method using a combination of local and non-local chain modifications. Kink-jump, crankshaft, reptation and end-segment moves were used for local changes of the chain conformation, while for non-local chain rearrangements the "cut-andpaste" algorithm was employed. The statistics of local micromodifications was examined. An approximate method for estimating the conformational entropy of a polymer chain, based on the efficiency of the kink-jump motion respecting chain continuity and excluded volume constraints, was proposed. The method was tested by calculating the conformational entropy of the undisturbed chain, the chain under tension and in different solvent conditions (athermal, theta and poor) and also of the chain confined in a slit. The results of these test calculations are qualitatively consistent with expectations. Moreover, the obtained values of the conformational entropy of self avoiding chain with ends fixed over different separations, agree very well with the available literature data.

Journal of Molecular Modeling, 2017

The static properties of two-dimensional athermal polymer solutions were studied by performing Monte Carlo lattice simulations using the cooperative motion algorithm (CMA) and taking into account the presence of explicit solvent molecules. The simulations were performed for a wide range of polymer chain lengths N (16-1024) and concentrations φ (0.0156-1). The results obtained for short chains (N < 256) were in good agreement with those given by previous simulations. For the longest chains (512 or 1024 beads), some unexpected behavior was observed in the dilute and semidilute regimes. A pronounced change in the concentration dependence of chain size and shape was observed below a certain critical concentration (0.6 for the longest chains under consideration, consisting of 1024 beads). Longer chains became more extended below this concentration. The behavior of the single-chain structure factor confirmed these changes in the fractal dimension of the chain as a function of the concentration. The observed phenomena are related to the excluded volume of solvent molecules, which causes the chain statistics to be modified in the vicinity of other chains; this effect is important in strictly 2D systems.

Macromolecules, 2010

We present a powerful connectivity-altering Monte Carlo (MC) algorithm for simulating atomistically detailed models of long-and short-chain branched polymers. Based on a mix of advanced and simple moves, the algorithm allows the robust simulation of chain systems with a variety of molecular architectures: H-shaped, A 3 AA 3 multiarm (pom-pom), and short-chain branched (SCB) ones. For the H-shaped and A 3 AA 3 architectures (A denotes the backbone and A the arm), in particular, the recently developed intermolecular double bridging (DB) move effecting a new bridging between the chain backbones or the branches of two different chains and the intramolecular double rebridging (IDR) move effecting a new bridging between two branches of the same chain [Karayiannis et al. J. Chem. Phys. 2003, 118, 2451 are shown to provide a robust sampling of their structural and conformational characteristics at the chain level. The double concerted rotation (d-CONROT) and H-shaped branch rebridging (H-BR) moves, on the other hand, which are important in relaxing internal degrees of freedom in the chain and the local structure around branch points, allow complete equilibration at the segmental level, which is prerequisite for the correct prediction of the volumetric and packing properties of the simulated systems. For the case of SCB polymers, a continuum configurational bias move for branched polymers (Br-CCB) has been designed capable of sampling changes in the atomic coordinates in the vicinity of branch points. Along with an effective implementation of the conventional end-bridging (EB) move, this has resulted in a powerful method for simulating SCB polymers with a prespecified distribution of branch points along the chain and given (i.e., fixed) number of carbon atoms per branch. To deal with polydispersity in the simulated systems, the algorithm is executed in a semigrand canonical ensemble by making use of the set of chain relative chemical potentials which for a bulk, linear system produces a uniform distribution of chain lengths [Pant and Theodorou Macromolecules 1995, 28, 7224]. Consistent with recent considerations by Ramos et al. [Macromolecules 2007, 40, 9640], two different chain length distributions should be simultaneously controlled in the course of the simulation for branched systems. The new, generalized MC algorithm is capable of thoroughly equilibrating model H-shaped, multiarm A 3 AA 3 , and SCB polymers at all length scales and adequately sampling fluctuations in their structural, volumetric, and conformational properties. Overall, we find that branched polymers are characterized by a stiffer conformation than linear analogues of the same total chain length. For the H-shaped and A 3 AA 3 architectures, in particular, we have observed that each dangling arm exerts an entropically driven tensile force on the chain crossbar (the part of the chain between the two branch points), causing significant chain stretching. Our results extend the previous works of Karayiannis et al. [J. Chem. Phys. 2003, 118, 2451 on the simulation of H-shaped polymers to A 3 AA 3 PE polymers and of Ramos et al. [Macromolecules 2007, 40, 9640] on the simulation of model ethylene-1-hexene copolymers to copolymers with longer R-olefinic side groups, such as the ethylene-1-octene and ethylene-1-decene ones.

The Journal of Chemical Physics, 2008

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond-fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density of states results have been evaluated for interaction parameters spanning the range from good to poor solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and twodimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.

Bottlebrush polymers consist of a linear backbone with densely grafted side chains which impact the rigidity of the molecule. The persistence length of the bottlebrush backbone in solution is influenced by both the intrinsic structure of the polymer and by the local environment, such as the solvent quality and concentration. Increasing the concentration reduces the overall size of the molecule due to the reduction in backbone stiffness. In this study we map out the size of a bottlebrush polymer as a function of concentration for a single backbone length. Small-angle neutron scattering (SANS) measurements are conducted on a polynorbornene-based bottlebrush with polystyrene side chains in a good solvent. The data are fit using a model which provides both the long and short axis radius of gyration (R g,2 and R g,1 , respectively), providing a measure for how the conformation changes as a function of concentration. At low concentrations a highly anisotropic structure is observed (R g,2 /R g,1 ≈ 4), becoming more isotropic at higher concentrations (R g,2 /R g,1 ≈ 1.5). The concentration scaling for both R g,2 and the overall R g are evaluated and compared with predictions in the literature. Coarse-grained molecular dynamics simulations were also conducted to probe the impact of concentration on bottlebrush conformation showing qualitative agreement with the experimental results.

Journal de Physique II, 1997

Monte Carlo simulations of both the single chain structure factor h(q) and the inter-chain structure factor HD(q) of flexible polymers in solutions are presented over a wide range of both wavenumber q and concentration c from the dilute to the concentrated regime, for chain lengths up to N = 256. The single chain properties (gyration radius (R(), h(q)) are in reasonable agreement with the expected theoretical behavior, showing a crossover from swollen chains ((R() oc N~", h(q) oc q~~/") to Gaussian chains, and the data comply with a scaling description, ~&.ith a correlation length ( oc c~"/~~"~~). However, the inter-chain structure factor HD(q) disagrees with the corresponding predictions, we find a behaviour HD(q) oc q~~only in an intermediate range but this is accidental: rather it is found that HD(q) smoothly bends over from its saturation value at small q to a behavior close to q~4 at q m 1Ii, I being the length of effective bonds. This failure is traced back to the condition that the la~v HD(q) c~q ~should only be observed for (~~< q < i~~, a condition reached neither in the simulation nor in experiments. lve also compare our results for HD IQ) with the random phase approximation and find strong deviations. 1.