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.     

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.     

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     

Lattice Monte Carlo simulation of polymer adsorption at an interface, 1. Monodisperse polymer

Adsorption of a monodisperse polymer at a solid-liquid interface is comprehensively studied by Monte Carlo simulation. The distributions of total segment density and different adsorption configurations including trains, loops and tails are obtained. Effects of reduced exchange interaction energies $ \tilde \varepsilon $, bulk concentrations ϕ^*, reduced adsorption energies $ \tilde \varepsilon_a $ and chain lengths r on those distributions are studied. Comparisons with predictions of the Scheutjens-Fleer (SF) theory are also provided. Generally, the chain molecules are more easily adsorbed at an interface in non-solvents than in good solvents. Longer chains are more likely to be adsorbed than shorter ones. The reduced adsorption energy and the bulk concentration have shown strong effects on the segment-density distributions. In addition, the thickness of the adsorption layer is mainly determined by the extension of tails into the bulk solution, which are in turn determined by the chain length. The trains, loops and tails are overwhelmingly short. On the other hand, the amounts of trains and loops are usually much greater than that of tails. Though not perfect, satisfactory agreement is found in comparison with the theoretical predictions of the SF theory.     

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.     

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     

Monte Carlo simulation for the adsorption of symmetric triblock copolymers I. Configuration distribution and density profiles of adsorbed chains

Monte Carlo simulations for the adsorption of symmetric triblock copolymers from a nonselective solvent at a solid-liquid interface have been performed on a lattice model. In simulations, triblock copolymer molecules are modeled as self-avoiding linear chains composed of m segments of A and n segments of B arranged as A_m/2B_nA_m/2. Either segment A or segment B is attractive, while the other is non-attractive to the surface. The microstructure of the adsorbed layers, including the segment-density profiles and the size distribution of loops, tails and trains are presented. The effect of the adsorption energy, the bulk concentration, the chain composition, as well as the chain length on various adsorption properties has been studied. The results have shown that the size distribution of various configurations is dependent of the adsorption energy, the chain composition and the chain length. The mean length of the loops, trains and tails is insensitive to the bulk concentration. The mean length of the trains increases and that of the tails decreases as the adsorption energy and the length of the attractive segments increase. The mean length of the loops for the end-adsorbed copolymers appears a maximum and that for middle-adsorbed copolymers appears a minimum as the length of attractive segments increases. The length of the non-attractive segments affects mostly the size distribution of the tails. The longer the chain is, the larger the tail appears. The mean length of the tails and loops increases linearly as the length of the non-attractive segments increases, but that of the trains approximately is unchanged.     

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 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.     

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.     

Side‐Chain Engineering of Benzodithiophene‐Fluorinated Quinoxaline Low‐Band‐Gap Co‐polymers for High‐Performance Polymer Solar Cells

A new series of donor–acceptor co‐polymers based on benzodithiophene and quinoxaline with various side chains have been developed for polymer solar cells. The effect of the degree of branching and dimensionality of the side chains were systematically investigated on the thermal stability, optical absorption, energy levels, molecular packing, and photovoltaic performance of the resulting co‐polymers. The results indicated that the linear and 2D conjugated side chains improved the thermal stabilities and optical absorptions. The introduction of alkylthienyl side chains could efficiently lower the energy levels compared with the alkoxyl‐substituted analogues, and the branched alkoxyl side chains could deepen the HOMO levels relative to the linear alkoxyl chains. The branched alkoxyl groups induced better lamellar‐like ordering, but poorer face‐to‐face packing behavior. The 2D conjugated side chains had a negative influence on the crystalline properties of the co‐polymers. The performance of the devices indicated that the branched alkoxyl side chains improved the V_oc, but decreased the J_sc and fill factor (FF). However, the 2D conjugated side chains would increase the V_oc, J_sc, and FF simultaneously. For the first time, our work provides insight into molecular design strategies through side‐chain engineering to achieve efficient polymer solar cells by considering both the degree of branching and dimensionality.     

Span‐Length Distributions of Star‐Branched Polymers

Many relations between the physical, rheological or mechanical properties of linear polymers and their molar mass are well known. For disperse polymers, parameters that express these relations are typically related to (a combination of) the moments of the molar‐mass distribution. Properties of branched, nonlinear polymers have been far more difficult to describe in the form of general relations. Monodisperse star polymers or regular stars, with a distinct number of arms and equal arm length, are the simplest member of the family of branched polymers and have served as model compounds in many studies. For these regular stars, the relation between zero shear viscosity and arm or span length has been determined. To establish equivalent relations for disperse star‐branched polymers, it is important to assess the span‐length distribution and its moments; these parameters can be calculated when the distribution of the molar mass of the arms of a star‐branched polymer is known, for instance, for a known polymerization mechanism.

Span‐length probability functions of star‐branched polycondensates with x_n = 100: f = 1 (•), f = 2 (○), f = 3 (▪), f = 5 (□), and f = 10 (+).     

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.     

Combination of nitroxide‐mediated polymerization and SET‐LRP for the synthesis of high molar mass branched and star‐branched poly(n‐butyl acrylate) characterized by size exclusion chromatography and rheology

Branched and star‐branched polymers were successfully synthesized by the combination of two successive controlled radical polymerization methods. A series of linear and star poly(n‐butyl acrylate)‐co‐poly(2‐(2‐bromoisobutyryloxy) ethyl acrylate) statistical copolymers, P(nBA‐co‐BIEA)_x, were first synthesized by nitroxide‐mediated polymerization (NMP at T > 100 °C). The subsequent polymerization of n‐butyl acrylate by single electron transfer‐living radical polymerization (SET‐LRP at T = 25 °C), initiated from the brominated sites of the P(nBA‐co‐BIEA)_x copolymer, produced branched or star‐branched poly(n‐butyl acrylate) (PnBA). Both types of polymerizations (NMP and SET‐LRP) exhibited features of a controlled polymerization with linear evolutions of logarithmic conversion versus time and number‐average molar masses versus conversion for final M_n superior to 80,000 g mol^?1. The branched and star‐branched architectures with high molar mass and low number of branches were fully characterized by size exclusion chromatography. The Mark–Houwink Sakurada relationship and the analysis of the contraction factor (g′ = ([η]_branched/[η]_linear)_M) confirmed the elaboration of complex PnBA. The zero‐shear viscosities of the linear, star‐shaped, branched, and star‐branched polymers were compared. The modeling of the rheological properties confirmed the synthesis of the branched architectures. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Molecular mass distributions of star‐branched polycondensates

Of late much attention has been paid to star‐branched polymers, being a good reference model for branched polymers, in general. Usually, monodisperse or narrow disperse polymers are analysed. Knowledge of molecular mass distributions is a key factor in the analysis and study of these systems. Star‐branched polycondensates can be synthesised by reaction of a difunctional ( AB ) monomer with a compound RA _f . Weight and number molecular mass distributions of star‐branched polycondensates have been studied in relation to the initial molar ratio between R and the AB monomer (α), the average molecular mass per arm (β) and the number of arms (f ). Simple probability density functions can be derived at, if molecules are split into – R (without core R ) and + R (with core R ). This enables further the representation in molecular mass units next to the representation in monomer units. Proper choice of α, β and f can either give narrower or broader distributions compared to the most probable distribution, which is the theoretical distribution for the pure AB polymer (α = 0). The resulting polymer might either have a uni‐modal or a bi‐modal molecular mass distribution.     

On the theory of polyelectrolyte adsorption : The effect on adsorption behavior of the electrostatic contribution to the adsorption free energy

A theory has been developed for the adsorption of polyelectrolytes on charged interfaces from an aqueous salt solution. This adsorption is determined by the electrical charge density of the polyelectrolyte, the adsorption energy, the salt concentration, the molecular weight, solubility, flexibility, and concentration of polymer. The theory relates these parameters to the properties of the adsorbed polymer layer, i.e., the amount of polymer adsorbed, the fraction of the adsorbent interface covered, the fraction of the segments actually adsorbed on the interface versus the fraction of the segments in the dangling loops, the final surface charge density, and the thickness of the adsorbed layer. As polyelectrolyte adsorption should resemble nonionic polymer adsorption at high ionic strength of the solution or low charge density on the polymer, this work is an extension of the nonionic polymer adsorption theory to polyelectrolyte adsorption. The following effects are taken into account: (a) the conformational change upon adsorption of a coil in solution into a sequence of adsorbed trains interconnected by loops dangling in solution; (b) the interactions of the adsorbed trains with the interface and with each other; (c) the interaction of the dangling loops with the solvent; (d) the change in surface charge density of the adsorbent due to adsorption of charged trains and the accompanying changes in the electrical double layer which contains “small” ions as well as charged loops; (e) the (induced) dipole interaction of the adsorbed trains with the charged adsorbent interface. The theory is worked out for low potentials (Debye—Hückel approximation); in Appendix B an outline of a more complete treatment is given. The predicted adsorption isotherms have the experimentally observed high-affinity character. A relation between the adsorption energy, the surface charge density on the adsorbent, the degree of dissociation of the polymer, and the salt concentration predicts the conditions under which no adsorption will occur. For adsorbent and polymer carrying the same type of charge (both positive or both negative) the adsorption is predicted to decrease with increased charge density on polymer or adsorbent and to increase with salt concentration. If adsorbent and polymer carry different type charges, the adsorption as a function of the degree of dissociation, α, goes through a maximum at a relatively low value of α and, depending on the adsorption energy, an increase in the salt concentration can then increase or decrease the adsorption. At finite polymer concentration in solution the number of adsorbed segments and the fraction of the interface covered practically do not change with an increase in polymer concentration, whereas the total number of polymer molecules adsorbed increases slightly, as does the average fraction of segments in loops. The experimental results for polyelectrolyte adsorption have been reviewed in general and, as far as data are available, the predictions of the theory seem to follow the experimentally observed trends quite closely, except for the thickness of the adsorbed layer. This thickness is systematically overestimated by the theory and two reasons for this are given. The theoretical model implies a not too low ionic strength of the solution. Extrapolation of results to solutions of very low ionic strength is not warranted.     

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.     

Conformational structures and thermodynamic properties of compact polymer chains confined between two parallel plane boundaries

In this paper, the authors investigated the adsorption phenomenon of compact chains confined between two parallel plane boundaries using a pruned‐enriched Rosenbluth method. The authors considered three cases with different adsorption energies of ε = 0, ?1, and ?3 (in units of k_BT) for the confined compact chains of different chain lengths N, respectively. Several parameters were employed to describe the size and shape of compact chain, and some special behaviors in the conformational structures were investigated for the first time. For example, the size and shape of confined compact chains undergo distinct changes in the adsorption cases of ε = ?1 and ?3, and pass through the maximum values at the characteristic distances D_c. The authors found that this characteristic distance D_c could be scaled as D_c～ (N + 1)^ν (ν = 0.56 ± 0.01) in the case of ε = ?3. In addition, the microstructures of chains were investigated, and several significant results were obtained by analyzing the segment density distribution and the mean fractions of segment in tails, trains, bridges, and loops structures. On the other hand, the thermodynamic properties were also investigated for the confined compact chains, such as average energy per bond, Helmholtz free energy per bond, and elastic force per bond. Results show that elastic forces f have different behaviors in three cases, indicating that it is not necessary to exert an external force on the boundaries in the nonadsorption case. At the same time, the average contact energy of compact chain obviously changes when the distance between the two parallel boundaries D increases, which is similar to those of the size and shape parameters. The authors also conclude that these thermodynamic properties of compact chains depend strongly on not only the adsorption energies but also the chain lengths and the confined condition. In addition, several results of the conformational and thermodynamic parameters, such as the segment density distribution and free energy, were compared with the results from the self‐consistent field theory. These investigations may help us to deepen the knowledge about the adsorption phenomenon of confined compact chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2888–2901, 2006     

Junction‐Controlled Topological Polymerization

Methodology that enables the controlled synthesis of linear and branched polymers from an identical monomer will be a novel pathway for polymer synthesis and processing. Herein we first describe the control of one or both of the C(3)‐C(3′) and C(6)‐C(6′) coupling reactions of carbazolyl. In a second approach, an identical monomer containing two carbazolyls is polymerized using chemical and electrochemical oxidizers, leading to topologically controllable growth of linear polymers in weak oxidizer or of cross‐linked polymer chains in strong oxidizer, with satisfactory long chain propagation of step growth polymerization (M_n=6.0×10⁴ g mol^?1, M_w/M_n=2.3). This very simple polymerization with cheap reagents and low levels of waste has provided a flexible pathway for synthesis and processing of polymers.     

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.