Monte-Carlo modeling of dense polymer melts near nanoparticles

Using Monte-Carlo techniques, we study polymer chain conformations near nanoparticles for dense melts of high molecular weight. Our results indicate the presence of a thin interfacial region (1-2 nm in thickness) within which polymer segments orient tangentially to the particle surface causing a stretching and widening of the chain ellipsoid. That region is also characterized by an accumulation of chain ends and a decrease in polymer density. Nanoparticles also affect polymer properties far away into the bulk. Thus, at small particle radius, we observe an overall swelling of the polymer chains when the distance between the centers of mass of nearest-neighbor particles becomes smaller than the radius of gyration of the chains.     

Properties of branched polymer chains adsorbed on a patterned surface

The aim of this study was to investigate the properties of polymer chains strongly adsorbed on a planar surface. Model macromolecules were constructed of identical segments, the positions of which were restricted to nodes of a simple cubic lattice. The chains were in good solvent conditions, thus, the excluded volume was the only interaction between the polymer segments. The polymer model chain interacted via a simple contact potential with an impenetrable flat surface with two kinds of points: attractive and repulsive (the latter being arranged into narrow strips). The properties of the macromolecular system were determined by means of Monte Carlo simulations with a sampling algorithm based on the local conformational changes of the chain. The structure of adsorbed chains was found to be strongly dependent on the distance between the repulsive strips, whenever this distance was very short. The mobility of the chains was also studied and it was found that diffusion across repulsive strips was suppressed for large distances between the strips.     

All solid-state polymer electrolytes prepared from a hyper-branched graft polymer using atom transfer radical polymerization

We propose an all solid-state (liquid free) polymer electrolyte (SPE) prepared from a hyper-branched graft copolymer. The graft copolymer consisting of a poly(methyl methacrylate) main chain and poly(ethylene glycol) methyl ether methacrylate side chains was synthesized by atom transfer radical polymerization changing the average chain distance between side chains, side chain length and branched chain length of the proposed structure of the graft copolymer. The ionic conductivity of the SPEs increases with increasing the side chain length, branched chain length and/or average distance between the side chains. The ionic conductivity of the SPE prepared from POEM₉ whose POEM content = 51 wt% shows 2 × 10⁻⁵ S/cm at 30 °C. The tensile strength of the SPEs decreases with increases the side chain length, branched chain length and/or average distance between the side chains. These results indicate that a SPE prepared from the hyper-branched graft copolymer has potential to be applied to an all-solid polymer electrolyte.     

Elastic behavior of adsorbed single compact chains

Elastic behaviors of short single two-dimensional compact chains adsorbed on the attractive surface are investigated in this paper by using the enumeration calculation method. In our model a single compact chain is fixed with one of its end at a position above the impenetrable surface, and then it is pulled away from the attractive surface slowly through elastic force acting. We investigate the chain size and shape of adsorbed compact chains, such as mean-square end-to-end distance per bond 〈R²〉/N mean-square radii of gyration per bond 〈S²〉_x/N and 〈S²〉_y/N, shape factors 〈δ〉, and fraction of adsorbed monomers f_a in order to illuminate how the size and shape of adsorbed compact chains change during the process of tensile elongation. Especially for strong attraction interaction there are some special behaviors in the chain size and shape during this process. If there exits adsorption interaction, single compact chain is first almost pulled down to the adsorption surface and then moves in the direction of force until to leave the adsorption surface. These changes become more obvious with strong adsorption interaction. Our calculation can show this elastic process of adsorbed compact chains visually and simply. On the other hand, some thermodynamics properties are also studied here. We use average energy per bond, average Helmholtz free energy per bond, elastic force f and energy contribution to elastic force f_u to study the elastic behavior of adsorbed single compact chains in the process of tensile elongation. Elastic force f has a long plateau during the tensile elongation for strong adsorption interaction, which agrees well with experimental and theoretical ones. These investigations can provide some insights into the elastic behaviors of adsorbed protein chains.     

Properties of a single chain embedded into a polymer matrix of varied thermodynamic quality and density

The properties (squared dimensions, anisotropy, numbers of intra- and intermolecular contacts) of a single five-way cubic lattice chain embedded into an environment (matrix) of chains of the same length n = 50 were evaluated as a function of matrix volume fraction (matrix density) v and intermolecular interaction between the matrix polymer and the minority chain segments, characterized by a parameter ?. No convincing evidence was found for the occurrence of a coil-globule transition in the range of matrix densities (v ≤ 0.7) and repulsive interactions between matrix and minority chain (? ≤ 0.2) investigated. For moderate attractive interaction (? ≈ ?0.17) a compensation of the chaincompressing action of the matrix and the chain-expanding interaction with the matrix was observed resulting in a zero-dependence of the size and shape of the minority chain on matrix density. It further turned out that there are fixed relations among the various size and shape data irrespective of the specific combination of matrix density and thermodynamic interaction by which a particular polymer dimension is produced. These interrelations are fairly the same as those evaluated for isolated chains the size of which is varied by an intramolecular energy parameter ?_i.     

The Wulff Shape of Alumina: I, Modeling the Kinetics of Morphological Evolution

The rate at which fully facetted nonequilibrium shaped particles and pores approach their equilibrium (Wulff) shape via surface diffusion was modeled, and calculations relevant to alumina were performed to guide experimental studies. The modeling focuses on 2-D features, and considers initial particle/pore shape, size, surface energy anisotropy, and temperature (surface diffusivity) as variables. The chemical potential differences driving the shape change are expressed in terms of facet-to-facet differences in weighted mean curvature. Two approaches to modeling the surface flux are taken. One linearizes the difference in the mean chemical potential of adjacent facets, and assumes the flux is proportional to this difference. The other approach treats the surface chemical potential as a continuous function of position, and relates the displacement rate of the surface to the divergence of the surface flux. When consistent values for the relevant materials parameters are used, the predictions of these two modeling approaches agree to within a factor of 1.5. As expected, the most important parameters affecting the evolution times are the cross-sectional area (volume in 3-D) and the temperature through its effect on the surface diffusivity. Pores of micrometer size are predicted to reach near-equilibrium shapes in reasonable times at temperatures as low as 1600°C. The detailed geometry of the initial nonequilibrium shape and the Wulff shape appear to have relatively minor effects on the times required to reach a near-equilibrium shape.     

Relation between molecular orientation and morphology of a multiblock copolymer melt confined in cylindrical nanopores

The morphologies of multiblock copolymer melts (for simplicity, we consider tetra blocks) and their configurations when they are confined in cylindrical nanopores were examined by Lattice Monte Carlo simulations. The dependence of their morphologies and of the configurations of the copolymers (through the radius of gyration) on the nanopore diameter, intersegment interaction energies (repulsive interaction energies between different kinds of segments of the copolymers), and attractive interactions between one kind of segments and the surface of the nanopore was investigated. The results indicate that the morphology of a copolymer melt is connected to the configuration of the copolymer chain. It was found that: (i) stacked disks are generated when the polymer chains are preferentially directed along the nanopore axis, and (ii) helixes or lamellae parallel to the nanopore axis are formed when the copolymer chains are preferentially directed normal to the nanopore axis.     

Small-Angle X-ray Scattering Study of the Thermal Decomposition of Magnesium Hydroxide

The submicroscopic porous structure developed in the isothermal decomposition of Mg(OH)₂ was studied in situ by means of small-angle X-ray scattering (SAXS). The scattering intensity in the 100% decomposed system has a good fit with an exponential correlation function, g(r) = exp(- r/a ) (where a is the correlation distance), according to the Debye, Anderson, and Brumberger (DAB) model which holds for a random distribution of pore shape and size in the solid. The DAB correlation distance is about 3.2 nm for systems decomposing at 583 and 623 K. According to the available pore volume fraction, such a correlation distance would imply a porous structure built up by pores of 7-nm mean size randomly distributed in a solid skeleton of 6-nm mean particle size.     

Effect of Pt nano-particle size on the microstructure of PEM fuel cell catalyst layers: Insights from molecular dynamics simulations

The effect of Pt nano-particles size on the microstructure of catalyst layers in a Polymer Electrolyte Fuel Cell is investigated by means of molecular dynamics simulations. The catalyst layer model includes carbon-supported platinum, perfluorosulfonate ionomer (PFSI), hydronium ions and water molecules. Three different Pt nano-particle sizes, i.e. 1, 2 and 3 nm, are studied, and simulations provide visualization of the distinct micro-morphologies of the CL corresponding to each nano-particle size. The results are analyzed using pair correlation functions, showing that different microstructures are obtained for different Pt nano-particle sizes, and also that inclusion of PFSI in the simulations impacts significantly the final configuration of Pt nano-particles. Water molecules are found to distribute near the side chains of PFSI and surface of Pt nano-particles, but far from the graphite surface. Side chains form clusters and exhibit different dispersion toward the Pt surface. The orientations of the side chains in the vicinity of the Pt surface are analyzed in detail. The dispersion of perfluorosulfonate ionomer is found to strongly influence the merging of Pt nano-particles and, consequently, the CL microstructure formation.     

Different diffusion behavior of cyclic chains under confinement

Molecular dynamics simulations of merging process of two isolated cyclic chains and that of linear chains have been performed, in order to find the difference between the two kinds of chain in bulk and in vacuum, where surface of the system restrains thousands of configurations showing up. Analysis indicates that in such confinement the chain ends at most moments float on the surface layer, and their mobility is much larger than the mean value of all atoms in linear chains, or that in cyclic chains. Comparison of the merging processes of cyclic chains and their linear counterparts was intensively carried out by several means of analyzing the trajectory files in statics and in dynamics. It was found that the segments of cyclic chains showed almost the same behavior of motion with that of linear chains. This is different diffusion behavior from that in bulk systems, where the cyclic chain has much higher diffusion rate. This modeling therefore indicates that in these confined systems because of the surface energy, the end groups are involuntarily kept on the surface, and lost the capacity of leading chain reptation through the other polymer chains, which is possibly the origin that the difference of diffusion behavior between the linear chain and the cyclic chain in the bulk almost disappears in the case of the confinement.     

Elastic behavior of compact polymer chain transporting through an infinite adsorption channel

The elastic behavior of a single compact chain transporting through an infinite adsorption channel is investigated using the pruned-enriched-Rosenbluth method (PERM). In our model, single compact chain is fixed with one of its first monomer at a position in an infinite adsorption channel, is then pulled slowly along the direction of z-axis. We first calculate the chain size and shape of compact chains transporting through an infinite channel, such as mean-square end-to-end distance per bond 〈R²〉/N, mean-square radii of gyration per bond 〈S²〉/N, 〈S²〉_xy/N and 〈S²〉_z/N, and shape factor 〈δ〉 for the changes in the size and shape of compact chains during the translocation process. If there are strong adsorption interactions between the monomers and the channel, some special behaviors for the size and shape of compact chains are obtained during the process. On the other hand, some thermodynamics properties are also investigated, such as average energy bond, average Helmholtz free energy per bond, elastic force per bond f and energy contribution to elastic force per bond f_E. During the translocation process, elastic force f is less than zero, and has some plateaus in some special regions for strong adsorption interaction, which may explain how the adsorption interaction drives chains through narrow channels or pores in many biological systems because f<0 means that the translocation process need no external force on the chains. These investigations can provide some insights into the mechanics of proteins infiltrating through membrane. In the meantime, by recording and comparing these force-extension curves, we may also investigate the complex interactions between biopolymers (such as protein, RNA, and DNA) and the membranes, and determine indirectly the complicated structure of the channel.     

Diffusion of polymer chains in porous media. A Monte Carlo study

In order to determine the structure and the dynamical properties of branched polymers in a random environment an idealized model was developed and studied by means of the Monte Carlo method. All atomic details were suppressed and the chain was represented as a sequence of identical beads. The model chains were star-branched with three arms of equal length. The chains were embedded to a simple cubic lattice and the polymer systems were confined between two parallel surfaces. The confining surfaces were attractive for polymer segments. A set of irregular obstacles was also introduced into the slit which can be viewed as a model of porous media. A Metropolis sampling algorithm employing local changes of chain conformation was used to sample the conformational space. It was shown that the mean dimensions of the chain depend strongly on the strength of surface's attraction and the concentration of obstacles. It was found that the size of the chains scales with the exponent close to the 2-dimensional case rather than to the 3-dimensional system. The long-time (diffusion) dynamic properties of the system were studied. The differences in the mobility of chains depending on the confinement, on the filling of the slit and on the internal macromolecular architectures were shown and discussed. The possible mechanism of chain's motion was shown: during the migration of the chain in the obstacles dense environment it can be trapped in the region of local lower density of obstacles (a ‘cavity’) and after some time it can leave the place moving into another cavity.     

Adsorption of Homopolymer Chains on a Strip-Patterned Surface: A Monte Carlo Study

In this study we investigated the process of chemisorption of polymers on solid surfaces. The formation of a strongly adsorbed polymer film was studied by Monte Carlo simulations. The adsorbing planar surface was patterned with strip-like repulsive sites. The polymer chains were represented by a sequence of schematically constructed objects (united atoms) and we considered star-branched macromolecules with f = 3 arms of equal length. The chains were studied at good solvent conditions and thus the excluded volume was the only potential of interaction between the polymers. A Metropolis-like sampling algorithm was employed in order to calculate the properties of the adsorbed chains. The influence of the chain length, the system density and the type of the pattern on the adsorbing surface on size of chains and the structure of the polymer film were determined and discussed. We found that the roughness of the polymer film surface depends non-monotonics on the number of polymer beads in the system. The shape of this surface reflects the pattern imposed on the substrate.     

Self-Consistent Field Analysis of Molecular Bottle-Brushes with Primary and Secondary Side Chains: Induced Persistence Length and Lateral Thickness

Macromolecules may feature liquid crystalline behavior when the chain aspect ratio, that is the ratio between the chain persistence length and the cross-sectional thickness of its segments, is large. Scaling theory suggests that for molecular bottle-brushes under good solvent condition the induced persistence length does not depend on the chain architecture but only on the amount of segments in the side chains per unit length of the backbone. Numerical self-consistent field results are presented for macromolecular bottle-brushes with side chains of variable architecture attached at regular intervals along the backbone chain. We consider side chains (flexible “flagstaffs”), which feature one branch-point onto which secondary side chains (the “flag”) emanate. We varied the distance of this branch-point from the main chain as our tuning parameter, resembling the “raising of the flag.” For a given height of the flags, that is when the mass-distribution along a side chain is architecturally fixed, the induced persistence length is a function of the branching parameter (ratio between the length of the longest path and the total number of segments in the graft). We found that the induced persistence length and hence the chain aspect ratio, vary non-monotonically with the height of the flags. The lowest aspect ratio is found when the flag is raised to about a quarter of the full height of the flagstaff. The induced persistence length is independent of this height when upon bending the translocation of the side chains from compressed to expanded regions is artificially suppressed, which leads us to speculate that the non-monotonic behavior of aspect ratio is related to the efficiency of side chains to partly translocate themselves upon bending.     

Segmented block copolyetheramides based on nylon 6 and polyoxypropylene. III. SAXS analysis

Morphologic characteristics of segmented block copolyetheramides based on nylon 6 and polyoxypropylene (POP) were investigated as a function of the compositions and block lengths of the hard and soft segments using small angle X-ray scattering (SAXS). Three POPs with different molecular weights were used as a soft segment. One-dimensional correlation functions were obtained from the desmeared intensity SAXS curves using the method developed by Vonk and Kortleve. The interdomain spacings were determined from the correlation distance at the peak position of the correlation function. From the dependence of the correlation distance on soft segment content, we deduced that an increase in the hard-segment length may lead to crystal formation by a chain-folding mechanism. The thickness of phase boundary was determined from the smeared intensity data using the method of Koberstein. A decrease in the phase boundary thickness with increasing soft-segment content suggests that an increase in the chain mobility by soft segment facilitates the regular arrangement of the hard segment, resulting in the formation of the hard domain with a narrow interfacial region. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 2155–2163, 1997     

Some aspects of autoignition delays and flammability limits of polyurethane based on diphenyl methane diisocyanate (MDI) and propoxylated trimethylol propane

The main purpose of this work is a better understanding of the physicochemical phenomena involved during an unpiloted ignition. We intend to characterize the step corresponding to the degradation of the material, the production of combustible gases, and their combustion with the surrounding oxidizing gas, leading to the flame. The degradation gases which are essentially alkanes, alkenes, and aldehydes undergo oxidation by degenerate chain branching mechanism. The initiating chain propagates very quickly and creates intermediate species of increased stability which initiate new active centers leading to secondary chains. Then, ignition can occur after a relatively large induction period. We suggest that this period may be defined as the time to reach a critical rate of production of the intermediate species. A study of the active center distribution near the surface as a function of time and of the distance to the surface allows us to explain the experimental variation of ignition delays vs. oxidant pressure. The ignition limits of this polyurethane, i.e., temperature–pressure curves in air and in oxygen, have also been determined. It has been possible to correlate pressure and temperature and to specify the influence of nitrogen on the ignition process.     

Steered molecular dynamics simulation of the detaching process of two parallel surfaces glued together by a single polyethylene chain

The detaching process of two parallel surfaces glued together by a single polyethylene chain in vacuo was investigated with a steered molecular dynamics method. Various statistical properties were analyzed in detail, including the mean‐square end‐to‐end distance; parallel and perpendicular mean‐square radii of gyration; shape factor; segment density distribution; average percentages of the microstructure of the chain of the tail, train, bridge, and loop; average surface adsorption energy; average total energy; and average pulling force (〈f〉). All these properties depended strongly on the pulling velocity (v). There existed a peak in the curve of 〈f〉 as a function of the detaching distance. Further, the relation between the maximum value of 〈f〉 and v showed three distinctive regions: a region of weak dependence at v < 10^?2 Å/ps, a region of strong dependence at 10^?2 Å/ps < v < 6.50 Å/ps, and a region of weak dependence at v > 6.50 Å/ps. These investigations may provide some insight into the microcosmic principle of the failure process of polymeric adhesives. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Influence of Chlorinating Solution Concentration on the Interactions Produced Between Chlorinated Thermoplastic Rubber and Polyurethane Adhesive at the Interface

Chlorination of a thermoplastic styrene-butadiene-styrene rubber (S0) with different amounts of trichloroisocyanuric acid (TCI) solutions in ethyl acetate improved its adhesion to polyurethane adhesives. A strong interaction of the PU (polyurethane) adhesive and the chlorinated S0 rubber chains is produced at the interface. The increase in the concentration of TCI from 0.5 wt% up to 2-7 wt% resulted in the deposition of crystallites of unreacted TCI on the rubber surface. The remaining TCI on the rubber surface migrates through the PU adhesive producing some chlorination of the PU chains. The failure of the joint is located in this interface composed of both chlorinated S0 rubber and partially-chlorinated PU adhesive.     

Free energy barrier for compact chains escaping from a small sphere

In this paper, the process of compact polymer chains escaping from a small sphere to a large one in the view of thermodynamics is investigated in detail based on the pruned-enriched-Rosenbluth method (PERM), which is quite efficient for the three-dimensional polymers on the simple-cubic lattice. In our simulation, three representative states of a polymer chain during the escaping process are studied, and some statistical properties of the chain size and the chain shape, such as mean-square radius of gyration per bond 〈S²〉/N and the shape factor 〈δ^∗〉 are investigated. Our aim is to illuminate how the size and shape of the compact chains change during the escaping process. The changes of 〈S²〉/N and 〈δ^∗〉 are not monotone and it is due to the fact that the chain should stretch itself in the escaping process. In the meantime, some thermodynamic properties are also calculated here. The hole is designed to be small enough to allow only one monomer at a time and it thus reduces the number of allowed chain conformations and breaks contacts between monomers at the beginning of the process. Additionally, we discuss the free energy barrier per bond H₂ − H₁ = ΔH of a compact chain, and here H₂ is the maximum free energy per bond during the process and H₁ is the minimum one when the compact chain is within the small sphere. Averaging free energy barrier over chain length N is convenient for the comparison with different chain lengths. ΔH as a function of chain length N and radius r₁ of the small sphere is also studied and our result shows that ΔH for longer chains is lower means that it is relatively easier for each bond in longer chains to surmount the free energy barrier to escape. Some discussions about the self-avoiding walk (SAW) and swollen chains are also made for the comparison, and our results also show that the restriction of the small sphere on the SAW and the swollen chains is more effective because of their relatively looser intrinsic structure.     

Influence of Chlorinating Solution Concentration on the Interactions Produced Between Chlorinated Thermoplastic Rubber and Polyurethane Adhesive at the Interface

Chlorination of a thermoplastic styrene-butadiene-styrene rubber (S0) with different amounts of trichloroisocyanuric acid (TCI) solutions in ethyl acetate improved its adhesion to polyurethane adhesives. A strong interaction of the PU (polyurethane) adhesive and the chlorinated S0 rubber chains is produced at the interface. The increase in the concentration of TCI from 0.5 wt% up to 2-7 wt% resulted in the deposition of crystallites of unreacted TCI on the rubber surface. The remaining TCI on the rubber surface migrates through the PU adhesive producing some chlorination of the PU chains. The failure of the joint is located in this interface composed of both chlorinated S0 rubber and partially-chlorinated PU adhesive.