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.     

Properties of star-branched and linear chains in confined space: a computer simulation study

We studied the properties of simple models of linear and star-branched polymer chains confined in a slit. The polymer chains were built of united atoms and were restricted to a simple cubic lattice. Two macromolecular architectures of the chain linear and star-branched with three branches (of equal length) were studied. The excluded volume was the only potential introduced into the model and thus, the system was athermal. The chains were put between two parallel and impenetrable surfaces. Monte Carlo simulations with a sampling algorithm based on chain’s local changes of conformation were carried out. The differences and similarities in the global size and the structure and of linear and star-branched chains were shown and discussed.     

The Structure of Star-Branched Chains in a Confined Space

Summary. We studied the properties of a simplified model of star-branched polymers confined in a slit formed by two parallel and impenetrable surfaces. The chains were built of identical united atoms (segments) whose positions were restricted to vertices of a simple cubic lattice. The polymer excluded volume and polymer segment-surface contact interactions were also introduced into the model. The properties of the model chains were determined by means of Monte Carlo simulations with a Metropolis-type sampling algorithm based on local changes of chain’s conformation. The structure of star-branched chains was investigated and the influence of the confinement and the temperature on the chain dimensions and structure was studied. It was shown that for chains in the adsorbing slits their sizes do not exhibit a universal behavior contrary to confined athermal polymers. The polymers in narrow slits at higher temperatures still exhibited features of a three-dimensional chain. It was also shown that chains in small slits and at low temperatures were fully adsorbed at one of the surfaces but could also switch the surface rapidly.     

Dynamics of star branched polymers in a matrix of linear chains — a Monte Carlo study

A simple cubic lattice model of the melt of 3-arm star-branched polymers of various length dissolved in a matrix of long linear chains (n₁ = 800 beads) is studied using a dynamic Monte Carlo method. The total polymer volume fraction is equal to 0,5, while the volume fraction of the star polymers is about ten times smaller. The static and dynamic properties of these systems are compared with the corresponding model systems of isolated star-branched polymers and with the melt of linear chains. It has been found that the number of dynamic entanglements for the star polymers with arm length up to 400 segments is too small for the onset of the arm retraction mechanism of polymer relaxation. In this regime dynamics of star-branched polymers is close to the dynamics of linear polymers at corresponding concentration and with equivalent chain length. The entanglement length for star polymers appears to be somewhat larger compared with linear chains.     

Properties of Star-Branched Polymer Chains Near a Surface

We considered two model systems of star-branched polymers near an impenetrable surface. The model chains were constructed on a simple cubic lattice. Each star polymer consisted of f = 3 arms of equal length and the total number of segments was up to 799. The excluded volume effect was included into these models only and therefore the system was studied at good solvent conditions. In the first model system polymer chain was terminally attached with one arm to the surface. The grafted arm could slide along the surface. In the second system the star-branched chain was adsorbed on the surface and the strength of adsorption was were varied. The simulations were performed using the dynamic Monte Carlo method with local changes of chain conformations. The internal and local structures of a polymer layer were determined. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. It was shown that the behavior of grafted and weakly adsorbed chains was similar to that of a free three-dimensional polymer, while the strongly adsorbed chains behave as a two-dimensional system.     

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.     

Properties of simple models of polymer networks. A Monte Carlo simulation

A model polymer network was constructed from branched chains. Each chain was built on a simple cubic lattice forming a star-branched polymer consisting of f = 3 arms of equal lengths. The fragment of network under consideration consisted of 1, 2 and 3 star polymers with different topology of connections. The only potential used was excluded volume (athermal chains). The properties of the network were determined by the means of computer simulations using the classical Metropolis sampling algorithm (local micromodifications of chain conformation). The behaviour of linear chains of the same molecular weight was also studied as a state of reference. The influence of attaching the next star-branched chain to the network on its static and dynamic properties was studied. The short-time dynamic behaviour of chain fragments was determined and discussed.     

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.     

The dimensions of a polymer chain at the coil-to-globule transition

Simple models of the star-branched and linear polymers were studied by means of a Monte Carlo method. The chains were confined on a simple cubic lattice. Star-branched polymers consisted of f=3 arms of equal length. The total number of beads in both types of polymers was varied from N=49 to N=799. The simulations were performed in different solvent qualities—from a good solvent to a collapsed globule regime. The static properties of the chains under consideration were measured as functions of the temperature of the system. It appeared that the ratio of the radius of gyration to the mean end-to-end vector is very sensitive to solvent quality. It shows that the coil-to-globule transition is a complicated phenomenon. The possible explanation of the phenomenon is discussed.     

Choose sides: differential polymer adhesion

AFM-based single molecule desorption measurements were performed on surface end-grafted poly(acrylic acid) monolayers as a function of the pH of the aqueous buffer to study the adhesion properties of polymers that bridge two surfaces. These properties were found to depend on the adhesion forces of both surfaces in a differential manner, which is explained with a simple model in analogy to the Bell-Evans formalism used in dynamic force spectroscopy. The measured interaction forces between the poly(acrylic acid) chains and silicon nitride AFM tips depend on the grafting density of the polymer monolayers as well as on the contour length of the polymer chains. This study demonstrates that the stability of polymer bridges is determined by the adhesion strengths on both surfaces, which can be tuned by using pH-dependent polyelectrolyte monolayers.     

A simple model of stiff and flexible polymer chain adsorption: the influence of the internal chain architecture

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.     

Computer Simulation of Adsorbed Polymer Chains with a Different Molecular Architecture

Simulations of simple models of polymer chains were carried out by the means of the dynamic Monte Carlo method. The model chains were confined to a simple cubic lattice. Three different chain architectures were studied: linear, star‐branched and ring chains. The polymer model chain interacted with an impenetrable surface with a simple contact attractive potential. It was found that size parameters of all these polymers obey scaling laws. The temperatures of the transitions from weakly to strongly adsorbed chain were determined. It was shown for weakly adsorbed chains that ring polymers are always ca. 50% more adsorbed than linear and star‐branched ones. The properties of adsorbed linear and star‐branched polymers are very similar in the length of chain and the strength of adsorption studied. Strongly adsorbed ring polymers are still more adsorbed but differences between all kinds of chains become less pronounced.     

Tethered polymer chains: surface chemistry and their impact on colloidal and surface properties

In this review the grafting of polymer chains to solid supports or interfaces and the subsequent impact on colloidal properties is examined. We start by examining theoretical models for densely grafted polymers (brushes), experimental techniques for their preparation and the properties of the ensuing structures. Our aim is to present a broad overview of the state of the art in this field, rather than an in-depth study. In the second section the interactions of surfaces with tethered polymers with the surrounding environment and the impact on colloidal properties are considered. Various theoretical models for such interactions are discussed. We then review the properties of colloids with tethered polymer chains, interactions between planar brushes and nanocolloids, interactions between brushes and biocolloids and the impact of grafted polymers on wetting properties of surfaces, using the ideas presented in the first section. The review closes with an outlook to possible new directions of research.     

Effect of branching and confinement on star-branched polymeric systems

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.     

Control of macromolecular architecture of polyamides by poly-functional agents. 2. Use of oligomerization in polycondensation study

In the first paper of the series, a statistical model for star-branched polycondenzation of AB type monomers in the presence of a polyfunctional agent RA_f was completely developed. The analytical expressions obtained for the number-average (D̄P̄_n̄) and weight-average (D̄P̄_w̄) degree of polymerization, and the dispersion index (D) for whole polymer species, linear and star macromolecular chains, are now derived as function of the feed and of end-group analysis. Also the important molecular parameter, mole fraction of star-branched polymer, can be evaluated. Some numerical examples are presented. It is illustrated that the molecular weight properties of the linear and star-branched polymers in the mixture of the products, very important factors for the application of this kind of polymeric materials, can be determined starting from the feed and terminal group analysis. Polymerization and oligomerization of 6-aminocaproic acid were carried out in the presence of trimesic (T3) acid and 2,2,6,6-tetra(β-carboxyethyl)cyclohexanone (T4) and EDTA as tri- and terra-functional agents. The molecular weights calculated are in good agreement with those obtained by Size Exclusion Chromatography (SEC), end group analysis and NMR spectra.     

Af+AB星型聚合体系的统计热力学

应用统计力学和热力学原理研究了 A_f+AB星型聚合体系的性质. 首先从两种不同的角度给出了与聚合反应相应的配分函数, 并据此得到反应体系的平衡自由能、质量作用定律及数量分布函数, 进而得到了体系的平衡状态方程和比热. 在此基础上, 以反应体系的回转半径为例研究了溶剂效应对星型高分子空间尺度的影响.     

The properties of a single polymer chain in solvent confined in a slit: A molecular dynamics simulation

A single polymer chain in solvent confined in a slit formed by two parallel plates is studied by using molecular dynamics simulation method. The square radii of gyration and diffusion behaviors of polymers are greatly affected by the distance between the two plates, but they do not follow the same way. The chain size decays drastically with increasing h (h is the distance between two plates), until a basin occurs, and a universal h/〈R _g〉₀ dependence for polymer chains with different degrees of polymerization can be obtained. While, for the chain’s diffusion coefficient, it decays monotonously and there is no such basin-like behavior. Furthermore, we studied the radial distribution function of confined polymer chains to explain the reason why there is a difference for the decay behaviors between dynamic properties and static properties. Besides, we also give the degree of confinement dependence of the static scaling exponent for a single polymer chain. Our work provides an efficient way to estimate the dynamics and static properties of confined polymer chains, and also helps us to understand the behavior of polymer chains under confinement.     

Static and dynamic properties of the interface between a polymer brush and a melt of identical chains

Molecular-dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model, which includes excluded volume and backbone connectivity of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and nonequilibrium molecular-dynamics simulations at constant temperature and volume using the dissipative particle dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The obtained boundary conditions and slip length show a rich behavior as a function of grafting density and shear velocity.     

Monte Carlo Simulations of Polymers in Nanoslits

Summary: Monte Carlo computer simulations have been performed for model polymers confined in slits of thickness comparable to the transverse diameter of the chains. The density of polymer within the slits is allowed to vary with the slit thickness in such a way that the content of the slits is always in equilibrium with a large reservoir of bulk polymer. The calculations reveal the presence of polymer‐mediated attractive or repulsive interactions between the slit plates, oscillating with the slit thickness in good agreement with experimental results.

The base cell used in the simulations.     

Successive Synthesis of Well-Defined Star-Branched Polymers by “Convergent” Iterative Methodology Using Core-Functionalized 3-Arm Star-Branched Polymer and a Specially Designed 1,1-Diphenylethylene Derivative

The synthesis of well-defined regular and miktoarm star-branched polymers by a convergent iterative methodology using core-functionalized 3-arm star-branched polymer with 1,1-diphenylethylene (DPE) moiety and a specially designed DPE derivative is described. The methodology involves the following two reaction steps in the entire iterative synthetic sequence: 1) a coupling reaction of a star-branched polymer having an anion at the core with a DPE derivative with two benzyl bromide moieties, 1-{4-[5,5-bis(3-bromomethylphenyl)-7-methylnonyl]phenyl}-1-phenylethylene, and 2) an addition reaction of the resulting core-DPE-functionalized star-branched polymer with sec-BuLi to convert the DPE moiety to a DPE-derived anion. The iterative synthetic sequence including these two reaction steps, 1) and 2), was repeated to successively synthesize star-branched polymers with more arms. Iteration of this synthetic sequence doubled the number of the arms in the star-branched polymer. With this methodology, 6-arm, 12-arm, and 14-arm regular star-branched polystyrenes as well as 6-arm A₂B₂C₂, A₄B₂, and 12-arm A₄B₄C₄ and A₈B₄ miktoarm star-branched polymers with well-defined structures have been successfully synthesized.