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.     

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.     

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.     

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.     

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.     

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.     

Silicon surface modification with trialkoxysilyl‐functionalized star‐shaped polymers

The synthesis of trimethoxysilane end‐capped linear polystyrene (PS) and star‐branched PS and subsequent silicon (Si) surface modification with linear and star polymers are described. Trimethoxysilane terminated PS was synthesized using sec‐butyl lithium initiated anionic polymerization of styrene and subsequent end‐capping of the living anions with p‐chloromethylphenyl trimethoxysilane (CMPTMS). ¹H and ²⁹Si NMR spectroscopy confirmed the successful end‐capping of polystyryllithium with the trimethoxysilane functional group. The effect of a molar excess of end‐capper on the efficiency of functionalization was also investigated, and the required excess increased for higher molar mass oligomers. Acid catalyzed hydrolysis and condensation of the trimethoxysilane end‐groups resulted in star‐branched PS, and NMR spectroscopy and SEC analysis were used to characterize the star polymers. This is the first report of core‐functionalized star‐shaped polymers as surface modifiers and the first comparative study showing differences in surface topography between star and linear polymer modified surfaces. Surface‐sensitive techniques such as ellipsometry, contact angle goniometry, and AFM were used to confirm the attachment of star PS, as well as to compare the characteristics of the star and linear PS modified Si surfaces. The polymer film properties were referenced to polymer dimensions in dilute solution, which revealed that linear PS chains were in the intermediate brush regime and the star‐branched PS produced a surface with covalently attached chains in the mushroom regime. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3655–3666, 2005     

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.     

Monte Carlo simulations of star‐branched polymers in a network of obstacles

A simple model of branched polymers in space confined between two parallel plates is developed. Star‐branched polymer molecules are built on a simple cubic lattice with excluded volume and no attractive interactions. A single star molecule is immersed in a network of irregularly dispersed linear rod‐like obstacles. The classical Monte Carlo Metropolis sampling algorithm is employed in the simulation. The aim of this study is to determine the effects of changes in dynamic properties of the star‐branched polymer as functions of the length of the molecule and the concentration of obstacles. Also the mechanism of motion of the polymer is 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.     

Relation between Polymer Conformational Structure and Dynamics in Linear and Ring Polyethylene Blends

Atomistic molecular dynamics simulations of ring‐linear polyethylene blends are employed to understand the relationship between chain conformational structure and the melt dynamics of these blends. As observed in previous studies, this study confirms that ring polymers in pure melts do not exhibit screened excluded volume interactions, contrary to linear polymers. Moreover, the average molecular shapes of the rings are quite distinct from both swollen and ideal ring polymers under theta conditions, and instead rather resemble branched polymers with screened binary excluded volume interactions, e.g., percolation clusters. Upon adding linear chains to a melt of pure rings, we find significant swelling of the rings and a corresponding shape change that is qualitatively similar to dissolving rings in a small molecule good solvent. This swelling, arising from altered self‐excluded volume interactions, translates into a large decrease in ring diffusivity, an effect that becomes more amplified when the polymer melt is entangled.     

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.     

Effective interaction parameter between branched and linear polystyrene

Values of the effective interaction parameter (χ) between regular, long‐branched polystyrene chains and their linear analogues were measured with small‐angle neutron scattering for several star‐branched chains and one comb‐type polymer. The contribution to this interaction due to architecture alone increases monotonically with star functionality for the set of polymers studied here. The interaction appears to be less sensitive to variations in arm size than would be expected from fluctuation theory predictions by G. H. Fredrickson, A. Liu, and F. S. Bates (Macromolecules 1994, 27, 2503) for a purely entropic interaction due to architecture. The change in χ with the volume fraction of the star in the blend is in agreement with the theory, however. The magnitudes of the interaction in the star/linear blends are small enough that bulk phase separation is unlikely, whereas that in the comb/linear blend is about 20 times higher for the same number of arms. Thus, bulk phase separation can be readily expected for comb/linear blends at commercially relevant values of molecular weights. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2549–2561, 2001     

Precise synthesis of well‐defined dendrimer‐like star‐branched polymers by iterative methodology based on living anionic polymerization

Dendrimer‐like star‐branched polymers recently developed as a new class of hyperbranched polymers, which resemble well‐known dendrimers in branched architecture, but comprise polymer chains between junctions, are reviewed in this highlight article. In particular, we focus on the precise synthesis of various dendrimer‐like star‐branched polymers and block copolymers by the recently developed methodology based on iterative divergent approach using living anionic polymers and 1,1‐bis(3‐tert‐butyldimethylsilyloxymethylphenyl)ethylene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6659–6687, 2006     

Characterization of hydrophilic networks synthesized by group transfer polymerization

Group transfer polymerization was used to synthesize several series of hydrophilic random and model networks. Cationic random networks were prepared both in bulk and in tetrahydrofuran (THF) using a monofunctional initiator and simultaneous polymerization of monomer and branch units, while a bifanctional initiator was employed in THF for the synthesis of model networks comprising basic or acidic chains. Upon polymerization of the monomer, the latter initiator gives linear polymer chains with two “living” ends, which are subsequently interconnected to a polymer network by the addition of a branch unit. Homopolymer network star polymers were also synthesized in THF by a one‐pot procedure. The synthesis involved the use of a monofunctional initiator and the four‐step addition of the following reagents: (i) monomer, to give linear homopolymers; (ii) branch unit, to form “arm‐first” star polymers; (iii) monomer, to form secondary arms and give “in‐out” star polymers; and, finally (iv) branch unit again, to interconnect the “in‐out” stars to networks. Different networks were prepared for which the degree of polymerization (DP) of the linear chains between junction points was varied systematically. For all networks synthesized, the linear segments, the “arm‐first” and the “in‐out” stars were characterized in terms of their molecular weight (MW) and molecular weight distribution (MWD) using gel permeation chromatography (GPC). The degrees of swelling of both the random and model networks in water were measured and the effects of DP, pH, and monomer type were investigated.     

Surface segregation of highly branched polymer additives in linear hosts

Entropy‐driven segregation of various branched and hyperbranched polymeric additives in chemically similar linear polymer hosts is studied using self‐consistent (SCF) mean‐field lattice simulations. The simulations account for the effect of molecular architecture on local configurational entropy in the blends, but ignores the effect of architecture on local density and blend compressibility. Star, dendrimer, and comb‐like additives are all found to be enriched at the surface of chemically identical linear host polymers. The magnitude of their surface excess increases with increased number of chain ends and decreases with increased segmental crowding near the branch point. Provided the number of arms and molecular weight of the branched additives are maintained constant, we find that the simplest branched architecture, the symmetric star, exhibits the strongest preference for the surface of binary polymer blends. We show that a single variable, here termed the “entropic driving force density,” controls the relative surface affinities of branched additives possessing a wide range of architectures. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1788–1801, 2008     

Simulation of GPC‐Distribution Coefficients of Linear and Star‐Shaped Molecules in Spherical Pores

Simulations of the distribution coefficients of linear and star‐shaped polymers in spherical pores were performed in order to predict the GPC‐elution behavior of star‐shaped polymers relative to that of linear polymers. Self avoiding walks were generated on a tetrahedral lattice to simulate good solvent conditions. It was found that neither the molecular weight nor the mean squared radius of gyration of the polymer serves as a universal factor to determine the distribution coefficient. However, the calculated distribution coefficients correlate well with the calculated hydrodynamic radii even for different topologies. For molecules at same elution volume the ratios of molecular weights of star and linear polymer agree well with exact calculations for Gaussian chains. These ratios are nearly independent of pore geometry (spherical or cylindrical).     

A comparative study on branched polymers formed by T‐shaped junctions and by H‐shaped junctions

In this paper, a statistical model is developed to determine the number‐average and weight‐average molecular weights of a branched polymer system formed through random branching of polymer chains. The average properties of the branched structures formed by T‐shaped junctions and by H‐shaped junctions through random branching of polymer chains are compared in detail. The model indicates that the H‐shaped chain connections can form a gel molecule while the T‐shaped chain connections alone can not cause gelation. Because only the randomly branched polymers for an equilibrium system are considered (under Flory's simplifying assumptions), the present results would not be a rigorous proof that the H‐shaped junctions are required to form a gel molecule in any type of reaction system. However, the present paper shows that the Macosko‐Miller model can be applied to this type of problem in a straightforward manner. The gel point for the branched structures formed by H‐shaped junctions can also be determined by the model.     

Self‐Assembly and Covalent Fixation for Topological Polymer Chemistry

A novel methodology (electrostatic self‐assembly and covalent fixation) has been proposed for designing various nonlinear polymer topologies, including monocyclic and polycyclic polymers, cyclic macromonomers and cyclic telechelics (kyklo‐telechelics), a‐ring‐with‐a‐branch topology polymers and polymeric topological isomers, as well as branched model polymers, such as star polymers and polymacromonomers. Thus, new telechelic polymer precursors having a moderately strained cyclic onium salt group as single or multiple end groups and carrying multifunctional carboxylates as the counterions were prepared through an ion‐exchange reaction. A variety of electrostatic self‐assemblies of these polymer precursors, formed particularly in dilute organic solution, was then subjected to heat in order to convert the ionic interactions into covalent linkages by ring‐opening reaction, and to produce topologically unique, nonlinear polymer architectures in high efficiency.