Search

This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the θ-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of “good solvents” and “θ-solvents” in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types. [ABSTRACT FROM AUTHOR]

Bounded potentials are good models to represent the effective two-body interaction in some colloidal systems, such as the dilute solutions of polymer chains in good solvents. The simplest bounded potential is that of penetrable spheres, which takes a positive finite value if the two spheres are overlapped, being 0 otherwise. Even in the one-dimensional case, the penetrable-rod model is far from trivial, since interactions are not restricted to nearest neighbors and so its exact solution is not known. In this paper the structural properties of one-dimensional penetrable rods are studied. We first derive the exact correlation functions of the penetrable-rod fluids to second order in density at any temperature, as well as in the high-temperature and zero-temperature limits at any density. It is seen that, in contrast to what is generally believed, the Percus-Yevick equation does not yield the exact cavity function in the hard-rod limit. Next, two simple analytic theories are constructed: a high-temperature approximation based on the exact asymptotic behavior in the limit T→∞ and a low-temperature approximation inspired by the exact result in the opposite limit T→0. Finally, we perform Monte Carlo simulations for a wide range of temperatures and densities to assess the validity of both theories. It is found that they complement each other quite well, exhibiting a good agreement with the simulation data within their respective domains of applicability and becoming practically equivalent on the borderline of those domains. A comparison with numerical solutions of the Percus-Yevick and the hypernetted-chain approximations is also carried out. Finally, a perspective on the extension of our two heuristic theories to the more realistic three-dimensional case is provided. [ABSTRACT FROM AUTHOR]

We investigate the structural phases of single poly(3-hexylthiophene) (P3HT) polymers that are adsorbed on a two-dimensional substrate with a striped pattern. We use a coarse-grained representation of the polymer and sophisticated Monte Carlo techniques such as a parallelized replica exchange scheme and local as well as non-local updates to the polymer's configuration. From peaks in the canonically derived observables, it is possible to obtain structural phase diagrams for varying substrate parameters. We find that the shape of the stripe pattern has a substantial effect on the obtained configurations of the polymer and can be tailored to promote either more stretched out or more compact configurations. In the compact phases, we observe different structural motifs, such as hairpins, double-hairpins, and interlocking "zipper" states. [ABSTRACT FROM AUTHOR]

Depletion forces and macromolecular crowding govern the structure and function of biopolymers in biological cells and the properties of polymer nanocomposite materials. To isolate and analyze the influence of polymer shape fluctuations and penetrability on depletion-induced interactions and crowding by nanoparticles, we model? polymers as effective penetrable ellipsoids, whose shapes fluctuate according to the probability distributions of the eigenvalues of the gyration tensor of an ideal random walk. Within this model, we apply Monte Carlo simulation methods to compute the depletion-induced potential of mean force between hard nanospheres and crowding-induced shape distributions of polymers in the protein limit, in which polymer coils can be easily penetrated by smaller nanospheres. By comparing depletion potentials from simulations of ellipsoidal and spherical polymer? models with predictions of polymer? field theory and free-volume theory, we show that polymer depletion-induced interactions and crowding depend sensitively on polymer shapes and penetrability, with important implications for bulk thermodynamic phase behavior. [ABSTRACT FROM AUTHOR]

Using Monte Carlo simulations based on the bond fluctuation model we study the adsorption of starburst dendrimers with flexible spacers onto a flat surface. The calculations are performed for various generation number G and spacer length S in a wide range of the reduced temperature τ as the measure of the interaction strength between the monomers and the surface. Our simulations indicate a two-step adsorption scenario. Below the critical point of adsorption, τc, a weakly adsorbed state of the dendrimer is found. Here, the dendrimer retains its shape but sticks to the surface by adsorbed spacers. By lowering the temperature below a spacer-length dependent value, τ*(S) < τc, a step-like transition into a strongly adsorbed state takes place. In the flatly adsorbed state the shape of the dendrimer is well described by a mean field model of a dendrimer in two dimensions. We also performed simulations of star-polymers which display a simple crossover-behavior in full analogy to linear chains. By analyzing the order parameter of the adsorption transition, we determine the critical point of adsorption of the dendrimers which is located close to the critical point of adsorption for star-polymers. While the order parameter for the adsorbed spacers displays a critical crossover scaling, the overall order parameter, which combines both critical and discontinuous transition effects, does not display simple scaling. The step-like transition from the weak into the strong adsorbed regime is confirmed by analyzing the shape-anisotropy of the dendrimers. We present a mean-field model based on the concept of spacer adsorption which predicts a discontinuous transition of dendrimers due to an excluded volume barrier. The latter results from an increased density of the dendrimer in the flatly adsorbed state which has to be overcome before this state is thermodynamically stable. [ABSTRACT FROM AUTHOR]

By use of an intramolecular criterion, i.e., the direct proportionality between mean square dimension and chain length, theta conditions for linear chains and ring shaped polymers are evaluated for several types of cubic lattice chains (simple cubic, body centered cubic, and face centered cubic). The properties of the rings are evaluated for the same thermodynamic conditions under which they are prepared thus allowing for a natural amount of knots which have been identified by use of Alexander polynomials. For the limit of infinite chain lengths the same theta parameter is found for linear chains and rings. On the contrary, a significant theta point depression occurs due to an additional excluded volume effect if unknots are exclusively regarded. Parameters characteristic of the shape of rings and chains under theta conditions extrapolated to infinite chain length fairly well coincide with respective data for random walks. Mean square dimensions (characteristic of the size) of theta systems are slightly in excess as compared to nonreversal random walks due to the necessity of avoiding overlaps on a local scale. Furthermore athermal systems are studied as well for comparison; mean square dimensions are described by use of scaling relations with proper short chain corrections, shape parameters are given in the limit of infinite chain length. [ABSTRACT FROM AUTHOR]

The absorption of free linear chains in a polymer brush was studied with respect to chain size L and compatibility ψ with the brush by means of Monte Carlo (MC) simulations and density functional theory (DFT)/self-consistent field theory (SCFT) at both moderate, σg=0.25, and high, σg=1.00, grafting densities using a bead-spring model. Different concentrations of the free chains 0.0625≤[lowercase_phi_synonym]o≤0.375 are examined. Contrary to the case of ψ=0 when all species are almost completely ejected by the polymer brush irrespective of their length L, for ψ<0 we find that the degree of absorption (absorbed amount) Γ(L) undergoes a sharp crossover from weak to strong (≈100%) absorption, discriminating between oligomers, 1≤L≤8, and longer chains. For a moderately dense brush, σg=0.25, the longer species, L>8, populate predominantly the deep inner part of the brush, whereas in a dense brush σg=1.00 they penetrate into the “fluffy” tail of the dense brush only. Gyration radius Rg and end-to-end distance Re of absorbed chains thereby scale with length L as free polymers in the bulk. Using both MC and DFT/SCFT methods for brushes of different chain length 32≤N≤256, we demonstrate the existence of unique critical value of compatibility ψ=ψc<0. For ψc([lowercase_phi_synonym]o) the energy of free chains attains the same value, irrespective of length L whereas the entropy of free chain displays a pronounced minimum. At ψc all density profiles of absorbing chains with different L intersect at the same distance from the grafting plane. The penetration/expulsion kinetics of free chains into the polymer brush after an instantaneous change in their compatibility ψ displays a rather rich behavior. We find three distinct regimes of penetration kinetics of free chains regarding the length L: I (1≤L≤8), II (8≤L≤N), and III (L>N), in which the time of absorption τ grows with L at a different rate. During the initial stages of penetration into the brush one observes a power-law increase of Γ∝tα with power α∝-ln [lowercase_phi_synonym]o, whereby penetration of the free chains into the brush gets slower as their concentration rises. [ABSTRACT FROM AUTHOR]

Mesopores present in inorganic barrier films have a unique structure since the bottom sides are blocked by underlying polymer substrates. Characterization of pore blockage by water condensation is important in understanding gas transport mechanisms because the pore blockage changes the transmission behavior of water vapor itself as well as other gases. In this study a water condensation behavior inside mesopores is investigated analytically and numerically. Appropriate modifications from the classical Kelvin equation-based solution are suggested to account for local and discrete molecular interactions and submolecular meniscus tip geometry. Grand canonical Monte Carlo simulations are also conducted to simulate the present problem and the result is compared with the analytical solutions. [ABSTRACT FROM AUTHOR]

We studied equilibrium conformations of ring polymers in melt over the wide range of segment number N of up to 4096 with Monte-Carlo simulation and obtained N dependence of radius of gyration of chains Rg. The simulation model used is bond fluctuation model (BFM), where polymer segments bear excluded volume; however, the excluded volume effect vanishes at N→∞, and linear polymer can be regarded as an ideal chain. Simulation for ring polymers in melt was performed, and the ν value in the relationship Rg∝Nν is decreased gradually with increasing N, and finally it reaches the limiting value, 1/3, in the range of N≥1536, i.e., Rg∝N1/3. We confirmed that the simulation result is consistent with that of the self-consistent theory including the topological effect and the osmotic pressure of ring polymers. Moreover, the averaged chain conformation of ring polymers in equilibrium state was given in the BFM. In small N region, the segment density of each molecule near the center of mass of the molecule is decreased with increasing N. In large N region the decrease is suppressed, and the density is found to be kept constant without showing N dependence. This means that ring polymer molecules do not segregate from the other molecules even if ring polymers in melt have the relationship ν=1/3. Considerably smaller dimensions of ring polymers at high molecular weight are due to their inherent nature of having no chain ends, and hence they have less-entangled conformations. [ABSTRACT FROM AUTHOR]

A Monte Carlo study is made of the mean-square radius of gyration ≤S2≥ and second virial coefficient A2 for the two freely rotating chains with the Lennard-Jones (LJ) 6-12 potential and the hard-sphere (HS) one in the range of the bond angle θ from 109° (typical flexible chain) to 175° (typical semiflexible or stiff chain) and in the range of the number n of bonds from 6 to 1000. It is shown that a value may be properly assigned to the collision diameter of the HS potential so that ≤S2≥ of the chain with the HS potential agrees well with that of the chain with the LJ one whose parameter values correspond to a good-solvent condition irrespective of the chain stiffness. It is then found that A2 of the latter chain becomes remarkably smaller than that of the former as the chain stiffness is increased. The result implies that the binary-cluster approximation does not seem to work well for typical semiflexible and stiff polymers [ABSTRACT FROM AUTHOR]

In this study, we investigated the process of random sequential adsorption of stiff and flexible polymer chains on a two-dimensional square lattice. The polymer chains were represented by sequence of lattice points forming needles, T shapes, and crosses as well as flexible linear chains and star-branched chains consisted of three and four arms. The Monte Carlo method was employed to generate the model systems. The percolation threshold and the jamming threshold were determined for all systems under consideration. The influence of the chain length and the chain architecture on both thresholds was calculated and discussed. The changes in the ordering of the system were also studied. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations were performed on semiflexible polymer chains with the goal of delineating their isotropic-nematic (IN) and gas-liquid coexistence envelopes. The chain monomers are spherical beads that interact via a square-well potential with all other beads. Bonded beads are connected by strings chosen so that bond length varies between 1.01σ and 1.05σ (where σ is the hard sphere diameter). The stiffness of the molecules is controlled via a potential between beads separated by two bonds; this potential restricts the distance between these beads to be between 2.02σ and 2.1σ. The vapor-liquid coexistence and IN coexistence curves are obtained using computer simulations. An IN transition is found for 10≤=Nb≤30. Both the density at which the IN transition occurs and the location of the gas-liquid coexistence go through a maximum with increasing Nb. For longer chains, behavior expected from theory is found and both of these coexisting densities decrease with increasing length. [ABSTRACT FROM AUTHOR]

We consider a lattice model of a mixture of repulsive, attractive, or neutral monodisperse linear polymers of two species, A and B, with a third monomeric species C, which may be taken to represent free volume. The mixture is confined between two hard, parallel plates of variable separation whose interactions with A and C may be attractive, repulsive, or neutral, and may be different from each other. The interactions with A and C are all that are required to completely specify the effect of each surface on all three components. We numerically study various density profiles as we move away from the surface, by using the recursive method of Gujrati and Chhajer [J. Chem. Phys. 106, 5599 (1997)] that has already been previously applied to study polydisperse solutions and blends next to surfaces. The resulting density profiles show the oscillations that are seen in Monte Carlo simulations and the enrichment of the smaller species at a neutral surface. The method is computationally ultrafast and can be carried out on a personal computer (PC), even in the incompressible case, when Monte Carlo simulations are not feasible. The calculations of density profiles usually take less than 20 min on a PC. [ABSTRACT FROM AUTHOR]

The structure and phase behavior of oppositely charged macroions in solution have been studied with Monte Carlo simulations using the primitive model where the macroions and small ions are described as charged hard spheres. Size and charge symmetric, size asymmetric, and charge asymmetric macroions at different electrostatic coupling strengths are considered, and the properties of the solutions have been examined using cluster size distribution functions, structure factors, and radial distribution functions. At increasing electrostatic coupling, the macroions form clusters and eventually the system displays a phase instability, in analogy to that of simple electrolyte solutions. The relation to the similar cluster formation and phase instability occurring in solutions containing oppositely charged polymers is also discussed. [ABSTRACT FROM AUTHOR]

A density-functional theory is presented to study the structure of polymers, having attractive interactions, confined between attractive surfaces. The theory treats the ideal-gas free-energy functional exactly and uses weighted density approximation for the hard-chain contribution to the excess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained from generalized Flory equation of state and the attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions are found to be in quite good agreement with the Monte Carlo simulation results for varying densities, chain lengths, and different interaction potentials. The results confirm important implications of using different approximations for the hard-sphere and attractive interactions. [ABSTRACT FROM AUTHOR]

We study a system of grafted polymers in a poor solvent by self-consistent-field methods as well as Monte-Carlo simulation methods. We observe a number of different morphological structures including an inverted solvent micelle or hole in the polymer layer, a lamella-like micelle structure, and fused, spherical micelle structures. These structures can be obtained by either varying the grafting density or chain length. We also develop a scaling theory for the existence of these structures and find reasonable agreement between this theory and our numerical calculations. [ABSTRACT FROM AUTHOR]

Elastic behaviors of single polymer chains adsorbed on the attractive surface are first investigated using Monte Carlo simulation method based on the bond fluctuation model. We investigate the chain size and shape of adsorbed chains, such as mean-square radius of gyration 〈S2〉, mean-square bond length 〈b2〉, shape factors 〈sfi〉 and 〈δ*〉, and the orientation of chain segments P2〈cos θ〉, to illuminate how the shape of polymer chains changes during the process of tensile elongation. There are some special behaviors of the chain size and shape at the beginning of elongation, especially for strong attraction interaction. For example, mean fraction of adsorbed segments decreases abruptly in the region of small elongation ratio and then decreases slowly with increasing elongation ratio. In fact, the chain size and shape also changes abruptly for small elongation ratio with strong attraction interaction. Some thermodynamics properties are also investigated here. Average Helmholtz free energy increases fast for elongation ratio λ<1.15, especially with strong attraction, and increases slowly for λ>1.15. Similar behaviors are obtained for average energy per bond. Elastic force (f ) and energy contribution to force (fU) are also studied, and we find that elastic force decreases abruptly for λ<1.15, and there is a minimum of elastic force for strong attraction interaction, then increases very slowly with increasing elongation ratio. However, there are different behaviors for weak attraction interaction. For energy contribution to force (fU), there is a maximum value for strong attraction interaction in the region of λ<1.15. Some comparisons with the atomic force microscopy experiments are also made. These investigations may provide some insights into the elastic behaviors of adsorbed polymer chains. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A computational strategy to model the amorphous phase of comblike polymers is presented. The strategy, denoted SuSi/CB (CB—configurational bias), combines the strength of an algorithm recently developed to generate reliable microstructures of dense amorphous polymers, which is based on a random search of energy minima, and configurational bias Monte Carlo method. The influence of different parameters used to define the characteristics of SuSi/CB on both the reliability of the generated structures and the computational effort has been examined in detail. Finally, we have modeled and characterized the supramolecular organization of poly(octadecyl acrylate) in the amorphous state. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The effect of confinement, number of branches (functionality), and size of the molecules on various properties as a function of temperature of star-branched polymers confined between two walls was studied using Monte Carlo simulations with the parallel tempering technique. The coil-to-globule transition and the liquidlike to solidlike transition, similar to those observed for linear chains, were characterized in all systems by changes in the heat capacity, internal energy, and radius of gyration. The transitions were also characterized by the most probable isomeric structure at a given temperature. The radius of gyration of the star polymers was smaller than the values of linear chains when the number of arms f increased. For star chains with more than f=5 arms the values of the radius of gyration, and therefore the size of the molecules, were similar for every condition of confinement studied, especially at higher temperatures. As confinement was increased, the difference in the radius of gyration of linear chains and star polymers became even larger. The coil-to-globule transition temperatures shifted to higher temperatures as the size of the chains and the number of arms in a molecule were increased. Effects of confinement were higher on the properties of the system at the smallest separations (less than twice the monomer diameter), where the coil-to-globule transition shifted to lower temperatures. The liquidlike to solidlike transition was present at almost the same temperature for different conditions of confinement, chain size, and number of arms. The behavior of the systems for separations between the walls greater than five bead diameters was similar to the behavior in the unconfined case. Hence, no considerable effect of confinement was found above this separation. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The effect of solvent quality on dilute and semidilute regimes of polymers in solution is studied by means of Monte Carlo simulations. The equation of state, adsorption near a hard wall, wall–polymer surface tension, and effective depletion potential are all calculated as a function of concentration and solvent quality. We find important differences between polymers in good and θ solvents. In the dilute regime, the physical properties for polymers in a θ solvent closely resemble those of ideal polymers. In the semidilute regime, however, significant differences are found. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Off-lattice Monte Carlo simulations employing the PIVOT algorithm are used to generate ideal and excluded volume linear polymers in two dimensions. The form factor at small and large wave vectors is calculated from the resulting configurations and compared to the exact equation for ideal chains and to both scaling and renormalization group predictions for excluded volume chains. It is found that using the des Cloizeaux form for the distance distribution function in an analytic calculation of the form factor leads to close agreement with the Monte Carlo data and that simple expressions for both the small and large wave vector expansions reproduce the essential features of the form factor. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Examines a cubic lattice model of star-branched polymers using Monte Carlo simulations. Analysis of a shape of branched macromolecules by means of the gyration tensor principal moments and asphericity factor; Changes of the parameters during the transition from a random coil to a collapsed globule; Formation of an isotropic globule in lower temperatures.

Using the pruned-enriched Rosenbluth Monte Carlo algorithm, the scattering functions of semiflexible macromolecules in dilute solution under good solvent conditions are estimated both in d = 2 and d = 3 dimensions, considering also the effect of stretching forces. Using self-avoiding walks of up to N = 25 600 steps on the square and simple cubic lattices, variable chain stiffness is modeled by introducing an energy penalty [variant_greek_epsilon]b for chain bending; varying qb = exp (-[variant_greek_epsilon]b/kBT) from qb = 1 (completely flexible chains) to qb = 0.005, the persistence length can be varied over two orders of magnitude. For unstretched semiflexible chains, we test the applicability of the Kratky-Porod worm-like chain model to describe the scattering function and discuss methods for extracting persistence length estimates from scattering. While in d = 2 the direct crossover from rod-like chains to self-avoiding walks invalidates the Kratky-Porod description, it holds in d = 3 for stiff chains if the number of Kuhn segments nK does not exceed a limiting value nK* (which depends on the persistence length). For stretched chains, the Pincus blob size enters as a further characteristic length scale. The anisotropy of the scattering is well described by the modified Debye function, if the actual observed chain extension (end-to-end distance in the direction of the force) as well as the corresponding longitudinal and transverse linear dimensions - 2, g,⊥2> are used. [ABSTRACT FROM AUTHOR]