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.     

Star-branched polymers in an adsorbing slit: a Monte Carlo study

A coarse-grained model of star-branched polymer chains confined in a slit was studied. The slit was formed by two parallel impenetrable surfaces, which were attractive for polymer beads. The polymer chains were flexible homopolymers built of identical united atoms whose positions in space were restricted to the vertices of a simple cubic lattice. The chains were regular star polymers consisted of f = 3 branches of equal length. The chains were modeled in good solvent conditions and, thus, there were no long-range specific interactions between the polymer beads-only the excluded volume was present. Monte Carlo simulations were carried out using the algorithm based on a chain's local changes of conformation. The influence of the chain length, the distances between the confining surfaces, and the strength of the adsorption on the properties of the star-branched polymers was studied. It was shown that the universal behavior found previously for the dimension of chains was not valid for some dynamic properties. The strongly adsorbed chains can change their position so that they swap between both surfaces with frequency depending on the size of the slit and on the temperature only.     

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 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 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.     

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.     

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.     

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.     

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.     

Structure of Adsorbed Polymer Chains: A Monte Carlo Study

The structure of adsorbed polymer chains was studied using simplified lattice models. The model chains were adsorbed on an impenetrable surface with an attractive potential. The dynamic Monte Carlo simulations based in the Metropolis scheme were carried out using these models. The influence of the internal chain architecture (linear, star‐branched and ring chains) and the degree of adsorption on the chain's structure was studied. It was shown that for weakly adsorbed chain regime the ring polymers which exhibit an almost twice as high degree of adsorption compared to linear and star chains have a higher number of adsorbed parts of chain (trains). But the length of such train remains almost the same for all types of a polymer chain. Star‐branched chains exhibit a slightly different change in number and the mean length of trains, loops and tails with the temperature and the chain total length compared to two other types of chain.     

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.     

Properties of star-branched polymer brushes

A simple model of a polymer brush was constructed. The star polymers with three arms were terminally attached with one arm (the stem) to an impenetrable surface with the other two arms (branches) free. The excluded volume effect was included into the model as the only interaction. Therefore, the system was studied in good solvent conditions. The simulations were carried out by means of the dynamic Monte Carlo method using the local changes of chain conformations to sample efficiently the conformational space. The influence of both the number of chains (the grafting density) and the length of chains on the static properties of the polymer brush was studied. The internal and local structure of a formed polymer layer was determined. It was shown that the size of the stems increased rapidly with the increase of the grafting density, while the size of the branches diminished. The changes of the spatial orientations of the stems and the branches for different grafting densities were shown and discussed.     

Molten globule state in homopolymers:A Monte Carlo study

Simple models of polymer chains were based on a simple cubic lattice. The model chains were star‐branched with f = 3 and f = 6 branches. The attractive potential between polymer segments was introduced to study the properties of polymer chains in the different temperature regimes. The computer simulations were carried out by means of the dynamic Monte Carlo method. It was found that contrary to recent real experiments, the ratio of the radius of gyration to the hydrodynamic radius did not exhibit a maximum near the coil‐globule transition but decreased monotonically with the temperature. The distribution of polymer‐polymer contacts and their lifetimes were also studied. It appeared that in homopolymer chains the lifetimes of these contacts were very short. At low temperatures contacts were distributed over the entire chain and at high temperatures only contacts that were close to the chain survived longer times.     

Properties of grafted amphiphilic chains. A computer simulation study

The model of a heteropolymer film formed by polypeptide chains was used for theoretical considerations. The linear chains consisting of amino acid residues were approximated by alpha carbon chains. Each chain was constructed on a very flexible [310] lattice. The inter- and intramolecular interactions consisted of the long-range contact potential between residues. The chains were built of hydrophilic and hydrophobic residues. Chains were terminally attached to an impenetrable surface with lateral motions possible. The Monte Carlo simulations of this model were carried out by using the Metropolis algorithm. The influence of the grafting density, the sequence of the amino acid residues, and the temperature on the static properties of the formed layer were studied and discussed. It was shown that homopolymer chains collapsed at higher temperature than the heteropolymers. The size of the polymers forming brush was smaller for homopolymers than for heteropolymers. The structure of the resulting polymer film and of its external surface was determined. The block copolymers formed well defined hydrophobic and hydrophilic layers, while for the amphiphilic case the composition of the brush layers changed continuously at high temperature. It was observed that the latter effect vanished at the collapsed amphiphilic copolymer.     

Hard-surface effects in polymer self-consistent field calculations

We have investigated several effects due to the confinement of polymer melts by impenetrable (hard) surfaces in the self-consistent field calculations. To adequately represent such confinement, the total (normalized) polymer segmental density (volume fraction) is usually constrained to an imposed profile that continuously decreases from 1 in the interior of confined melts to 0 at the surfaces over a short distance. The choice of this profile strongly influences the numerical performance of the self-consistent field calculations. In addition, for diblock copolymers A-B the hard-surface confinement has both energetic and entropic effects: On one hand, the decrease of polymer density from 1 reduces A-B repulsion and favors morphologies with more A-B interfaces near the surfaces. On the other hand, the enrichment of chain ends and depletion of middle segments near the surfaces favor parallel morphologies where chains orient mainly perpendicular to the surfaces. These two effects are comparable in magnitude, and for asymmetric diblock copolymers result in an entropic preference of a neutral surface for the shorter block as proposed previously [Q. Wang et al., Macromolecules 34, 3458 (2001)]. The hard-surface effects are weak in practice and thus manifested only when the surfaces are nearly neutral.     

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.     

Oligo(ethylene glycol) containing polymer brushes as bioselective surfaces

The nitroxide-mediated polymerization of styrenic monomers containing oligo(ethylene glycol) (OEGn) moieties was chosen for the preparation of biocompatible polymer brushes tethered to silicon oxide surfaces due to the broad range of monomer structures available and the use of a nonmetallic initiator. These surfaces were characterized by near-edge X-ray absorption fine structure and water contact angle measurements. The biocompatibility of these grown polymer brushes was studied and compared with deposited assemblies of surface-bound OEGn-terminated silanes with selected chain lengths. Grown polymer brushes with short OEGn side chains suppressed protein adsorption significantly more than the deposited assemblies of short OEGn chains, and this was attributed to higher surface coverage by the brushes. Cell adhesion studies confirmed that OEGn-containing polymer brushes are particularly effective in preventing nonspecific adhesion. Studies of protein adsorption and cell localization carried out with specific ligands on surfaces patterned demonstrated the potential of these surface-tethered polymer brushes for the formation of micro- and nanoscale devices.     

Electroless deposition of nickel on fluoropolymers modified by surface graft copolymerization

Surface modification of Ar plasma-pretreated poly(tetrafluoroethylene) (PTFE) and poly(vinylidene fluoride) (PVDF) films via UV-induced graft copolymerization with 4-vinylpyridine (4VP), 2-vinylpyridine (2VP) or 1-vinylimidazole (VIDz) was carried out. Electroless deposition of nickel could be carried out on these graft-modified fluoropolymer surfaces after PdCl₂ activation. The surface compositions of the graft-modified films were studied by X-ray photoelectron spectroscopy. The adhesion strength between the surface graft-copolymerized fluoropolymer film and the electrolessly deposited nickel was affected by the type of monomers used for graft copolymerization and the graft concentration. The optimum T-peel adhesion strengths of the electrolessly deposited Ni on the 4VP graft-copolymerized PTFE and PVDF surfaces were about 7 and 13 N/cm, respectively. The metal/fluoropolymer assemblies delaminated by cohesive failure inside the fluoropolymer substrates. The enhanced adhesion between the electrolessly deposited Ni and the surface-modified fluoropolymers is attributable to the interfacial charge transfer interactions between the grafted polymer chains and the deposited metals (Pd and Ni), the spatial distribution of the graft chains into the metal matrix and the covalent tethering of the graft chains on the fluoropolymer surface.     

Short-chain behaviour of star-branched nonreversal random walks embedded in a tetrahedral lattice

Analytical results are presented for the mean-square dimensions of star-branched nonreversal random walk polymers on a tetrahedral lattice considering short-chain effects and the influence of the core (centre) of the star. They are checked against numerical results obtained from highly precise Monte Carlo calculations. Short-chain effects are studied in detail. In addition, the deviation from proportionality between mean-square dimensions and the total chain-length is evaluated and compared to that for self-avoiding chains and stars near theta-conditions, the total chain-lengths ranging from 125 to 3845 segments.     

Synthesis of asymmetric star-branched polymers consisting of three or four different segments in composition by means of living anionic polymerization with a new dual-functionalized 1,1-bis(3-chloromethylphenyl)ethylene

A series of four-armed A₂BC, AB₂C, and ABC₂ asymmetric star-branched polymers with a three-component system, the A, B, and C segments of which are polystyrene, polyisoprene, and poly(4-trimethylsilylstyrene), respectively, have been successfully synthesized with a methodology based on living anionic polymerization with dual-functionalized 1,1-bis(3-chloromethylphenyl)ethylene ( 1 ). These star-branched polymers have well-defined architectures and precisely controlled chain lengths, as confirmed by size exclusion chromatography, ¹H and ¹³C NMR, vapor pressure osmometry, and static light scattering analyses. A simple and convenient one-pot process for star-branched polymer synthesis is an additional advantage of this methodology. One problem to be solved is that the synthetic route is limited in some cases by the inherently low reactivity of polyisoprenyllithium toward the 1,1-diphenylethylene functionality of in-chain-functionalized polymers. A new four-armed ABCD star-branched polymer, the A, B, C, and D segments of which are polyisoprene, poly(4-methoxystyrene), polystyrene, and poly(4-trimethylsilylstyrene), could also be synthesized through the extension of the methodology using 1 to a four-component system. The successful results strongly demonstrate the synthetic versatility and potential of this methodology for a wide variety of well-defined asymmetric star-branched polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4535–4547, 2004