Computer simulation of relaxation phenomena in star‐branched polymers. Temperature dependence

Dynamic Monte Carlo simulations of simple models of star‐branched polymers were conducted. A model star macromolecule consisted of f = 3 arms of equal length with a total number of polymer segments up to 800. The chain was confined to a simple cubic lattice with simple nearest neighbor attractive interactions. The relaxation phenomena were studied by means of autocorrelation functions in wide ranges of temperatures. Short‐time‐scale dynamic processes in the entire star‐branched chain were examined. It was found that under good solvent conditions the longest relaxation time of the end‐to‐center vector decreases with decreasing temperature. For low temperatures (below the Θ‐point) where the chain is collapsed, the dependence of the relaxation time on the temperature is opposite.     

A Monte Carlo study of a tethered polymer chain in a uniform field

We study the non‐uniform stretching and relaxation of a long flexible end‐anchored polymer chain of N monomers (32 ≤ N ≤ 1 024) in a uniform field B by means of an off‐lattice bead‐spring Monte Carlo model. Our simulational results for the case of a Rouse‐like polymer in the good solvent regime confirm the existence of “trumpet”‐ and “flower”‐type chain conformations, predicted recently by scaling analysis based on the notion of Pincus tensile blobs. The observed elongation of the chain and the critical fields, separating three different regimes of chain deformation, are found to obey the predicted scaling behavior. The segment density distribution matches that of a DNA molecule pulled from one end at constant velocity in a good solvent. As expected, the relaxation of the stretch to coil transition of the polymer of length N is determined by the typical Rouse time τ ∝ N^2ν+1.     

Monte Carlo study of chain conformations in the swollen middle layer of onion‐skin polymeric micelles

Conformations of chains in swollen middle layers of onion‐skin micelles were studied by Monte Carlo simulations on a tetrahedral lattice under conditions that mimic real systems of swollen onion‐skin micelles. Polymer blocks are modeled as tethered self‐avoiding chains, enclosed in a narrow spherical layer. Average density of segments, 〈g_S〉 ca. 0.6, corresponds to swollen micellar systems. Only the excluded volume effect was taken into account since it plays the most important role in dense polymer systems. Individual chains are described by equivalent ellipsoids of gyration. Distributions of the ellipsoid half‐axes were calculated during simulations. Results based on a large series of simulations indicate that the middle layer‐forming blocks may be described as prolonged ellipsoids oriented preferentially perpendicular to the radial direction. Analysis of the data concerning the orientations of end‐to‐end vectors and distributions of segments within one chain indicates that individual chains are strongly interpenetrated and the multi‐chain system is fairly disordered.     

Motion of star‐branched chains in polymer networks: a Monte Carlo study

A simple model of branched polymers in confined space is developed. Star‐branched polymer molecules are built on a simple cubic lattice with excluded volume and no attractive interactions (good solvent conditions). A single star molecule is trapped in a network of linear polymer chains of restricted mobility. The simulations are carried out using the classical Metropolis algorithm. Static and dynamic properties of the star‐branched polymer are determined using various networks. The dependence of the longest relaxation time and the self‐diffusion coefficient on chain length and network properties are discussed and the proper scaling laws formulated. The possible mechanism of motion is discussed. The differences between the motion of star‐branched polymers in such a network are compared with the cases of a dense matrix of linear chains and regular rod‐like obstacles.     

Partitioning of star branched polymers into pores at three chromatography conditions

The partitioning of star branched polymers into a slit pore at three different chromatography conditions, namely, size exclusion chromatography (SEC), liquid chromatography at the critical condition (LCCC), and liquid adsorption chromatography (LAC) have been investigated with lattice Monte Carlo simulations. Two different chain models are used: random walks (RW) that have no excluded volume interaction and self-avoiding walks (SAW) that have excluded volume interaction. The simulation data obtained for the two chain models are compared to illustrate the effect of excluded volume interactions on the partitioning of star branched polymers. The two most outstanding effects observed due to the introduction of excluded volume interactions are: (i) stars with a high number of arms can be excluded from the pore at condition corresponding to the LCCC of the linear polymers; (ii) the partition coefficient of stars in LAC mode is not dependent only on the total number of monomers on the chain. These effects illustrated by the current study should be taken into account when interpreting experimental chromatography data for branched polymers.     

Effect of alkyl side chain length on the properties of polyetherimides from molecular simulation combined with experimental results

Three polyetherimides (PEIs) with the same backbone of Ultem 100 but different lengths of the alkyl side chains were simulated by using molecular dynamics and molecular mechanics techniques to investigate the effect of side chain length on their properties and physical mechanism behind. Simulation results, which are consistent to the experimental data, show that PEI‐5 with four methylene units in each alkyl side chain has higher T_g (glass transition temperature) and higher tensile strength, but lower tensile elongation at break than those of PEI‐6 with five and PEI‐8 with seven methylene units in each alkyl side chain. However, unlike the traditional phenomena, conformational analysis provides that PEI‐5 with the highest T_g gives the highest flexibility to the polymer chain, whereas PEI‐8 with the lowest T_g imparts the lowest flexibility resulting from attachment of longer alkyl side chain increase the rigidity of backbone. From the calculated ratio of the accessible volume to the total volume for each system, the highest ratio of PEI‐8 indicates that long alkyl side chains generate more free volume than short side chains, acting as an internal plasticizer in bulk structure. It is the internal plasticizing effect that is predominantly responsible for the abnormal properties, instead of the rigidity from side chains. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 595–599, 2010     

Response of the mean-square optical anistropy of chain molecules to the imposition of excluded volume

The influence of the chain expansion produced by excluded volume on the mean-square optical anisotropy has been studied in six types of polymers. The mean-square optical anistropy for a specified configuration is calculated using the valence optical scheme. Realistic rotational isomeric state models are used for the configurational statistics of the unperturbed chains. Excluded volume is introduced by hard sphere interactions. Results obtained with chains of 100, 200, 300, and 400 bonds permit extrapolation to the behavior expected for much longer chains. The mean-square optical anisotropy of polyethylene is insensitive to excluded volume. A similar conclusion was obtained several years ago in a study of chains confined to a tetrahedral lattice and weighted in a manner appropriate for the short-range interactions in polyethylene.² Different behavior is seen in poly(vinyl chloride), poly(vinyl bromide), polystyrene, poly(p-chlorostyrene), and poly(p-bromostyrene). The mean-square optical anisotropy of these five vinyl polymers is sensitive to the imposition of excluded volume if the stereochemical composition is exclusively racemic. Much smaller effects are seen in meso chains and in chains with Bernoullian statistics and an equal probability for meso and racemic dyads.     

A coarse-grained model and associated lattice Monte Carlo simulation of the coil-helix transition of a homopolypeptide

A new coarse-grained lattice model neglecting atomic details is proposed for the coil-helix transition and a new physical parameter is suggested to characterize a helical structure. In our model, each residue is represented by eight lattice sites, and side groups are not considered explicitly. Chirality and hydrogen bonding are taken into consideration in addition to chain connectivity and the excluded volume effect. Through a dynamic Monte Carlo simulation, the physical properties of the coil-helix transition of a single homopolypeptide have been produced successfully within a short computing time on the PC. We also examined the effects of the variation of chain configurations including chain size and chain shape, etc. A spatial correlation function has been introduced in order to characterize periodicity of a helical chain in a simple way. A propagation parameter and a nucleation parameter have also been calculated, which compares favorably with the results of the Zimm-Bragg theory for the coil-helix transition.     

Conformational properties and dynamics of molecular bottle‐brushes: A cellular‐automaton‐based simulation

Extensive computer simulation was performed using the bond‐fluctuation model and cellular‐automaton (CA)‐based simulation technique to probe the equilibrium structure and dynamical behavior of comb‐branched polymers in which the flexible side chains of a given length are placed regularly along the backbone and the number of branches increases linearly with total molecular weight. By applying very efficient CA algorithm – the “lattice molecular dynamics” (LMD) method – we have been able to study the properties of sufficiently large structures (up to 5880 monomeric units). Depending on the length of main and side chains as well as on interbranch spacing, we have calculated mean chain dimensions, local fractal dimensionalities, particle scattering functions, time autocorrelation functions, etc. The following main conclusions may be drawn from the results presented in our study: (i) The critical exponent, governing the mean size of the main chain, remains unchanged from its value known for a 3d self‐avoiding walk (SAW). On the other hand, two‐dimensional branched macromolecules with one‐sided branches are effectively in a collapsed state even under conditions of a good solvent, forming specific helical superstructures. (ii) Comparison of the simulated data with the predictions of the scaling model indicates that the latter is valid in describing the mean dimensions of the backbone as a function of side‐chain length and interbranch spacing. (iii) The excluded volume interaction between side chains dramatically slows down the relaxation of the backbone chain.     

Dynamics of grafted star-branched polymers. A Monte Carlo study

Monte Carlo simulations of simple models of star-branched polymers were carried out. The model chains were confined to simple cubic lattice and consisted of f = 3 branches of equal length and the total number of polymer segments as well as the density of grafted chains on the surface were varied. The chains have had one arm end attached to an impenetrable plate. The simulations were performed by employing the set of local micromodifications of the chain conformations. The model chains were athermal, i.e. good solvent conditions were modeled, the excluded volume effect was present at the model. The density of grafted chains on the surface was varied from a single chain up to 0.3. The static and dynamic properties of the system were studied. The influence of polymer concentration as well as the polymer length on static and dynamic properties of the system studied was shown. The relation between the structure and short-time dynamics (relaxation times) was discussed.     

Hydrolytic degradation of poly(rac‐lactide) and poly[(rac‐lactide)‐co‐glycolide] at the air–water interface

The understanding of the simultaneous transport and chain‐scission phenomena involved in the hydrolysis of bulk‐degrading polymers requires the experimental separation of chain cleavage and water diffusion. The hydrolytic chain cleavage of poly(rac‐lactide) rac‐(PLA) and poly[(rac‐lactide)‐co‐glycolide] (PLGA) is analysed on the basis of monolayer degradation experiments combined with an improved data reduction procedure. Different, partly contradictory models of the hydrolytic degradation and erosion mechanism of PLA and PLGA, namely random chain scission and chain‐end scission, are discussed in the literature. The instantaneous linear area reduction observed for the polymer Langmuir films indicates a chain‐end scission mechanism. As monolayers of end‐capped and non‐end‐capped polymers degrade with exactly the same rate, the observed differences in the degradation kinetics of bulk samples do clearly result from differences in the water penetration into these polymers. A pronounced ‘auto‐inhibition’ effect is observed for the polymers degraded at initially high pH of the aqueous subphase in the absence of buffers. Copyright © 2007 John Wiley & Sons, Ltd.     

Distribution Function and Thermodynamic Potentials of a Self‐Avoiding Chain

Summary: An explicit expression is derived for the distribution function of end‐to‐end vectors for a flexible self‐avoiding chain. Based on this relation, analytical formulas are developed for the free and internal energies of a chain with excluded‐volume interactions. Force–stretch relations are obtained at uniaxial tension and compression. The effects of strength of segment interactions on the shapes of the distribution function and the force‐displacement diagram, as well as on the mean‐square end‐to‐end distance and stiffness of a chain are studied numerically.

The dimensionless distribution function P versus the dimensionless end‐to‐end vector Q^* for self‐repellent chains with χ = 0.0, 0.4, 0.8, 1.2, and 1.6, from top to bottom, respectively.     

Two forms of aluminium phosphate tridymite from X‐ray powder data

Monoclinic and triclinic (pseudo‐orthorhombic) AlPO₄ tridymites have been refined from X‐ray powder diffraction data using the silica analogues as starting models. The framework structures of both forms of tridymite are made up of six‐membered rings of tetrahedra which differ in the distortion patterns of the ring shapes. Ordered occupation of alternate tetrahedra by Al and P leads to a doubling of the a lattice parameter for monoclinic AlPO₄ tridymite (space group Pc) and loss of the C‐centring with respect to the isotypic silica tridymite (space group Cc). Triclinic AlPO₄ tridymite was refined in the same space group (F1) as the SiO₂ analogue.     

Dynamics of Adsorbed Star‐Branched Polymer Chains: A Computer Simulation Study

The simple cubic‐lattice model of polymer chains was used to study the dynamic properties of adsorbed, branched polymers. The model star‐branched chains consisted of f = 3 arms of equal lengths. The chain was modeled with excluded volume, that is, in good solvent conditions. The only interaction assumed was a contact potential between polymer segments and an impenetrable surface. This potential was varied to cover both weak and strong adsorption regimes. The classical Metropolis sampling algorithm was used for models of star‐branched polymers in order to calculate the dynamic properties of adsorbed chains. It was shown that long‐time dynamics (diffusion constant) and short‐time dynamics (the longest relaxation time) were different for weak and strong adsorption. The diffusion of weakly adsorbed chains was found to be qualitatively the same as for free nonadsorbed chains, whereas strongly adsorbed chains behaved like two‐dimensional polymers. The time‐dependent properties of structural elements such as tails, loops, and trains were also determined.

The mean lifetimes of tails, loops, and trains versus the bead number for the chain with N = 799 beads for the case of the weak adsorption ε_a = −0.3.     

Physicochemical Characterization of Transport in Nanosized Membrane Structures

The understanding of polymer–solvent interactions is highly important for the development of tailored membrane manufacturing procedures and for the prediction of membrane performance from transport mechanisms. This study examines the permeation performance of organic solvents through state‐of‐the‐art polyimide membranes (STARMEM, Membrane Extraction Technology Ltd.). Solvents are systematically selected to allow investigation of the effects of key physicochemical transport parameters by keeping constant all other parameters thought to be relevant. The effect of the solubility parameter, polarity (dielectric constant), surface tension, and viscosity are studied in detail. Dead‐end permeation experiments are carried out at 20 bar with STARMEM 122 and STARMEM 240 membranes. Results for the selected solvents show higher permeation rates for ketones over alcohols and aromatics as well as for acids. It is suggested that the viscosity and polarity have a greater influence than the other parameters. The effect of solvent molar volume is also investigated. Transport of solvents with high molar volume, independent of their polarity and compatibility with the membrane material, is slower in all cases than for solvents with smaller molar volume. The solubility parameter does not show any significant effect on transport phenomena.     

The behavior of the structure function at large wavevectors for polymers in different regimes

Off‐lattice Monte Carlo simulations employing the pivot algorithm are used to generate ideal and excluded volume linear polymers in three dimensions. The structure function at large wavevectors is calculated from the resulting configurations. This is compared to the exact equation for ideal chains and to experimental data and 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 structure function leads to close agreement with the experimental and Monte Carlo data.     

Anisotropic and enhanced self-diffusion of a macromolecular chain under simple shear flow as revealed by Monte Carlo simulation on lattices

Two-dimensional simple shear flow of a self-avoiding macromolecular chain is simulated by a lattice Monte Carlo (MC) method with a pseudo-potential describing the flow field. The simulated velocity profile satisfies the requirements of simple shear flow unless the shear rate is unreasonably high. Some diffusion problems for a free-draining bead-spring chain with excluded volume interaction are then investigated at low and relatively high shear rates. Three diffusion coefficients are defined and examined in this paper: the conventional self-diffusivity in zero field, D_self, the apparent self-diffusivity in flow field, D_app, and the flow diffusivity in simulation, D_flow reflecting actually the transport coefficient. It is found that these three diffusivities for a flexible chain are different from each other. What is more important is that self-diffusion exhibits a high anisotropy in the flow field. The apparent self-diffusion along the flow direction is enhanced to a large extent. It is increased monotonically with the increase of shear time or shear strain, whereas the chain configuration can achieve a stationary anisotropic distribution following an interesting overshoot of the coil shape and size. Besides a single self-avoiding chain, an isolated Brownian bead and a group of self-avoiding beads with a quasi-Gaussian spatial distribution are also simulated. According to the comparison, the effects of the connectivity of the chain on the diffusion behavior are revealed. Some scaling relations of D_app versus t are consistent with the theoretical analyses in the pertinent literature.     

Monte Carlo simulation studies of ring polymers at athermal and theta conditions

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.