Studies on the behavior of nanoconfined homopolymers with cyclic chain architecture

We have performed Monte Carlo simulations to study the effect of cyclic architecture on the behavior of homopolymer chains under several conditions of confinement. The collapse of the rings in two stages, a coil-to-globule and a liquidlike-to-solidlike transition, was observed even at extreme confinement. Both transitions were observed at lower temperatures than for linear chains of the same length, 2%-5% lower for unconfined systems, and 10%-15% lower for wall separations below three bond lengths due to the effect of confinement. When the plates separation approached the two-dimensional regime, the coil-to-globule transition shifted to lower temperatures. The inverse trend was observed when the chain length was increased. In the collapsed state, the average size and conformations of linear and cyclic molecules of same length were similar independently of confinement. At temperatures near the coil-to-globule transition, the radius of gyration of unconfined linear chains, [R(g)(2)](linear), became larger than for the cyclic chains, [R(g)(2)](cyclic), and this difference increased considerably with confinement. The radius of gyration ratio [R(g)(2)](linear)/[R(g)(2)](cyclic) in this region decreased rapidly. The decrease was more pronounced and occurred at lower temperatures for slit width confinements. At higher temperatures, in the coil state, the radius of gyration ratio became nearly constant for a given separation, and varied from 0.56 for unconfined systems to 0.47 when the chain was completely confined between the walls. This reduction was attributed to the higher increase in the average size of linear chains with confinement when compared with cyclic chains, due to architectural restrictions.     

线形、梳形和星形高分子静态和动态性质的模拟

以梳形高分子为纽带,基于粗粒化分子动力学模拟方法,研究了线形、梳形和星形拓扑结构高分子的静态和动态性质,以揭示稀溶液中高分子链行为与链拓扑结构依赖关系的一般性规律.研究结果表明,随着线形-梳形-星形的链拓扑结构转变,回转半径的标度关系由仅依赖分子聚合度转变为同时依赖链聚合度与臂数或侧链数.分析了星形高分子和梳形高分子的静态和动态性质的特征规律.星形高分子的臂数增加使其尺寸迅速减小,形状则由长椭球形转变为类球形,且扩散系数也随之增加;其均方回转半径(〈R_g〉)和扩散系数(D)与分子聚合度(N)及臂数(f)的标度规律为〈R_g〉~N~(0.581)f~(-0.402),D~N~(-0.763)f~(0.227).梳形高分子的静态与动态性质与分子聚合度及侧链数的依赖关系为〈R_g〉~N~(0.597)f~(-0.212)(每个支化点只有一条侧链)和〈R_g〉~N~(0.599)f~(-0.316)(每个支化点有多条侧链).     

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.     

Synthesis and solution properties of star‐shaped poly(tert‐butyl acrylate)

A series of star polymers consisting of poly(tert‐butyl acrylate) arms and an ethyleneglycol dimethacrylate (EGDMA) microgel core were synthesized using anionic polymerization. The effect of various parameters (precursor length, ratio [[EGDMA]/[Initiator], reaction time, and overall concentrations) on the average number of arms was investigated. Molecular weights were determined using GPC coupled with an online viscometer and MALLS. The exponents for the relation between intrinsic viscosity or radius of gyration and molecular weight, respectively, are extremely low, indicating that the dimensions of the star polymers only slightly increase with the number of arms. After a certain number of arms is reached the intrinsic viscosity even decreases with molecular weight. Computer simulations for star polymers were carried out where the radius of gyration was calculated as a function of the number of arms. The results are in good agreement with the experimental data.     

Monte Carlo Simulation of Coil-to-Globule Transition of Compact Polymer Chains: Role of Monomer Interacting

Coil-to-globule transitions are fundamental problems existing in polymer science for several decades; however, some features are still unclear, such as the effect of chain monomer interaction. Herein, we use Monte Carlo simulation to study the coil-to-globule transition of simple compact polymer chains. We first consider the finite-size effects for a given monomer interaction, where the short chain exhibits a one-step collapse while long chains demonstrate a two-step collapse, indicated by the specific heat. More interestingly, with the decrease of chain monomer interaction, the critical temperatures marked by the peaks of heat capacity shift to low values. A closer examination from the energy, mean-squared radius of gyration and shape factor also suggests the lower temperature of coil-to-globule transition.     

Structural properties of star-shaped polyions: Entropic sampling

The method of entropic sampling within the Wang–Landau algorithm (a modern variant of the Monte Carlo method) is used to determine the densities of energy states of a strongly charged star-shaped polyelectrolyte within the framework of the lattice model. The equilibrium thermal and structural properties of the polyelectrolyte with the number of arms f ≤ 6 and the length of arms N _arm ≤ 73 in a wide temperature range are determined from the density of states. Such characteristics as the free energy, the mean-squared radius of gyration, its components, and the parameters characterizing the shape of a polyion are calculated. It is found that the concentration, length, and number of arms affect the thermal and structural properties. The main attention is focused on the effect of temperature on these properties. The coil-to-globule transition is detected, while for the polyion with the highest length of arms (N _arm = 24) the transition from the liquid globule to the crystal-like one is observed. Differences in the properties of the star-shaped and corresponding linear polyions are characterized.     

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.     

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).     

Synthesis and Characterization of Star Polymer with Comb-like Poly(lauryl methacrylate) Arms by Atom Transfer Radical Polymerization via One-pot ‘Arm-First’ Method

Atom transfer radical polymerization (ATRP) was used to prepare core crosslinked star polymers with comb-like poly (lauryl methacrylate) (LMA) arms by one-pot “arm-first” method, involving the synthesis of comb-like PLMA arms, followed by their crosslinking, using a mixture of LMA monomer and ethylene glycol dimethacrylate (EGDMA) crosslinker. By adjusting the feeding time and level of EGDMA, a series of star-like polymers with various comb-like arms length and number can be obtained. The molecular architecture including radius of gyration (Rg), hydrodynamic radius (Rh) and intrinsic viscosity (η_i) etc. were characterized by a triple-detector gel permeation chromatography (GPC) equipped with a refractive index detector, viscometer detector and a multi-angle static laser light scattering (MALLS) detector. The thermal property and shearing stability of these star-like polymers were also investigated.     

聚羧酸系高性能减水剂分子在稀溶液中尺寸及其在体积排除色谱表征中表观分子量的模型研究

针对被称为"第一代聚羧酸高性能减水剂"(以下简称为MPEG-type PCE)的甲基丙烯酸(MAA)/烯酸甲酯(MAA-MPEG)梳状共聚物分子,从高分子物理基础理论出发,构建等效自由连接链模型,结合前人的理论结果和实验数据,得到了MPEG-type PCE分子的回转半径、流体力学半径及其相应的支化参数的数学表达式.在此基础上,报道了以下三方面的工作:首先,将计算结果与文献中的实验结果进行比较,检验模型的合理性;其次,利用所建立的数学模型考察主链分子量、侧链分子量和侧链接枝密度对PCE分子的回转半径和流体力学半径的影响;最后,结合近年来发展的体积排除色谱分离理论,对PCE分子的真实分子量与其常规体积排除色谱"表观分子量"(又被称为GPC分子量)两者之间的差异进行了分析.本文所提出的计算模型和数学表达式没有不确定的指前因子,可用来估算MPEG-type PCE分子在稀水溶液中的尺寸以及根据其GPC分子量估算真实分子量.     

Simulation analysis of the temperature dependence of lignin structure and dynamics

Lignins are hydrophobic, branched polymers that regulate water conduction and provide protection against chemical and biological degradation in plant cell walls. Lignins also form a residual barrier to effective hydrolysis of plant biomass pretreated at elevated temperatures in cellulosic ethanol production. Here, the temperature-dependent structure and dynamics of individual softwood lignin polymers in aqueous solution are examined using extensive (17 μs) molecular dynamics simulations. With decreasing temperature the lignins are found to transition from mobile, extended to glassy, compact states. The polymers are composed of blobs, inside which the radius of gyration of a polymer segment is a power-law function of the number of monomers comprising it. In the low temperature states the blobs are interpermeable, the polymer does not conform to Zimm/Stockmayer theory, and branching does not lead to reduction of the polymer size, the radius of gyration being instead determined by shape anisotropy. At high temperatures the blobs become spatially separated leading to a fractal crumpled globule form. The low-temperature collapse is thermodynamically driven by the increase of the translational entropy and density fluctuations of water molecules removed from the hydration shell, thus distinguishing lignin collapse from enthalpically driven coil-globule polymer transitions and providing a thermodynamic role of hydration water density fluctuations in driving hydrophobic polymer collapse. Although hydrophobic, lignin is wetted, leading to locally enhanced chain dynamics of solvent-exposed monomers. The detailed characterization obtained here provides insight at atomic detail into processes relevant to biomass pretreatment for cellulosic ethanol production and general polymer coil-globule transition phenomena.     

The Effect of Number of Arms on the Aggregation Behavior of Thermoresponsive Poly(N-isopropylacrylamide) Star Polymers

The thermoresponsive nature of aqueous solutions of poly(N-isopropylacrylamide) (PNIPAAM) star polymers containing 2, 3, 4, and 6 arms has been investigated by turbidity, dynamic light scattering, rheology, and rheo-SALS. Simulations of the thermosensitive nature of the single star polymers have also been conducted. Some of the samples form aggregates even at temperatures significantly below the lower critical solution temperature (LCST) of PNIPAAM. Increasing concentration and number of arms promotes associations at low temperatures. When the temperature is raised, there is a competition between size increase due to enhanced aggregation and a size reduction caused by contraction. Monte Carlo simulations show that the single stars contract with increasing temperature, and that this contraction is more pronounced when the number of arms is increased. Some samples exhibit a minimum in the turbidity data after the initial increase at the cloud point. The combined rheology and rheo-SALS data suggest that this is due to a fragmentation of the aggregates followed by re-aggregation at even higher temperatures. Although the 6-arm star polymer aggregates more than the other stars at low temperatures, the more compact structure renders it less prone to aggregation at temperatures above the cloud point.     

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.     

Synthesis and characterization of multiarm star-branched polyisobutylenes: Effect of arm molecular weight

A series of star-branched polyisobutylenes with varying arm molecular weights was synthesized using the 2-chloro-2,4,4-trimethylpentane/TiCl₄/pyridine initiating system and divinylbenzene (DVB) as a core-forming comonomer (linking agent). The resulting star-branched polymers were characterized with regard to the weight-average number of arms per star molecule (N̄_w) and dilute solution viscosity behavior. As the molecular weight of the arm (M̄_{w, arm}) was increased, dramatically longer star-forming reaction times were needed to produce fully developed star polymers. It was calculated that N̄_w varied from 50 to 5 as the M̄_{w, arm} was increased from 13,000 to 54,000 g/mol. The radius of gyration, R_g, of the star polymers was observed to increase as M̄_{w, arm} was increased. The solution properties of the star polymers were evaluated in heptane using dilute solution viscometry. It was determined that the stars had a much higher [η] compared to the respective linear PIB arms, but a much lower [η] compared to a hypothetical linear analog of an equivalent molecular weight. The dependence of [η] on temperature for the stars and linear arms was very small over the temperature range 25 to 75°C, with only a very slight decrease with increasing temperature. [η]_star was also determined to increase with increasing M̄_{w, arm}, but decrease with increasing M̄_{w, star}. The branching coefficient, g′, calculated for the stars at 25°C, increased as N̄_w decreased and agre ed well with literature values for other star polymer systems. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 3767–3778, 1997     

Second-order phase transitions in amorphous gallium clusters

Ion mobility and calorimetry measurements have been used to probe the nature of the phase transitions in gallium clusters with 29-55 atoms. While most clusters appear to undergo a first-order transition between solidlike and liquidlike phases, a few show the signature of melting without a significant latent heat. These transitions appear to be the finite size analogue of a second-order phase transition, and they presumably occur for some cluster sizes because their solidlike phase is amorphous.     

Structural properties of thermoresponsive poly(N-isopropylacrylamide)-poly(ethyleneglycol) microgels

We present investigations of the structural properties of thermoresponsive poly(N-isopropylacrylamide) (PNiPAM) microgels dispersed in an aqueous solvent. In this particular work poly(ethyleneglycol) (PEG) units flanked with acrylate groups are employed as cross-linkers, providing an architecture designed to resist protein fouling. Dynamic light scattering (DLS), static light scattering (SLS), and small angle neutron scattering (SANS) are employed to study the microgels as a function of temperature over the range 10 °C ≤ T ≤ 40 °C. DLS and SLS measurements are simultaneously performed and, respectively, allow determination of the particle hydrodynamic radius, R(h), and radius of gyration, R(g), at each temperature. The thermal variation of these magnitudes reveals the microgel deswelling at the PNiPAM lower critical solution temperature (LCST). However, the hydrodynamic radius displays a second transition to larger radii at temperatures T ≤ 20 °C. This feature is atypical in standard PNiPAM microgels and suggests a structural reconfiguration within the polymer network at those temperatures. To better understand this behavior we perform neutron scattering measurements at different temperatures. In striking contrast to the scattering profile of soft sphere microgels, the SANS profiles for T ≤ LCST of our PNiPAM-PEG suspensions indicate that the particles exhibit structural properties characteristic of star polymer configurations. The star polymer radius of gyration and correlation length gradually decrease with increasing temperature despite maintenance of the star polymer configuration. At temperatures above the LCST, the scattered SANS intensity is typical of soft sphere systems.     

Star‐shaped polymers by Ru(II)‐catalyzed living radical polymerization. II. Effective reaction conditions and characterization by multi‐angle laser light scattering/size exclusion chromatography and small‐angle X‐ray scattering

Star poly(methyl methacrylate)s (P*) of various arm lengths and core sizes were synthesized in high yields by the polymer linking reaction in Ru(II)‐catalyzed living radical polymerization. The yields of the star polymers were strongly dependent on the reaction conditions and increased under the following conditions: (1) at a higher overall concentration of arm chains ([P*]), (2) with a larger degree of polymerization (DP) of the arm chains (arm length), and (3) with a larger ratio (r) of linking agents to P* (core size). In particular, the yields sharply increased in a short time at a higher temperature, in a polar solution, and at a higher complex concentration after the addition of linking agents. These star polymers were then analyzed by multi‐angle laser light scattering to determine the weight‐average molecular weight (3.8 × 10³ to 1.5 × 10⁶), the number of arm chains per molecule (f = 4–63), and the radius of gyration (R_z = 2–22 nm), which also depended on the reaction conditions (e.g., f and R_z increased as [P*], DP, and r increased). Small‐angle X‐ray scattering analyses of the star polymers showed that they consisted of spheres for which the radius of the microgel core was 2.7 nm. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2245–2255, 2002     

Melting mechanism of monolayers adsorbed in cylindrical pores: the influence of the pore wall roughness

We have analyzed the mechanism of melting of molecular layers adsorbed in porous materials with cylindrical pores and rough pore walls. The working example studied here is a monolayer of methane molecules adsorbed in MCM-41 pore of diameter 2R=4 nm. Both experimental (neutron scattering) and simulation (Monte Carlo) results demonstrate the strong influence of the wall roughness on the melting mechanism. In particular, the transformation between solidlike and liquidlike monolayer phases adsorbed on a rough surface is observed over a broad temperature range, and solidlike properties persist even above the bulk methane melting temperature.     

Pair distribution function and related properties of star‐branched chains

Pair configurations of linear and star‐branched chains with F = 4, 8 and 12 arms embedded in the tetrahedral lattice were investigated. Pair data were determined by exact enumeration of all possible pair configurations. When the separation between two (linear) chains reached zero (r → 0) the pair distribution function g (r) read ≈ 0.15 for athermal and ≈ 0.6 for theta conditions in full accordance with former work. For star‐branched chains, g (r) approached a value zero at small separations for both thermodynamic conditions and the range of g (r) = 0 increased with an increase of the number of arms. As a consequence, the characteristic maximum of g (r) for theta conditions was the more pronounced the larger the number of arms. For stars, the extent to which mean squared dimensions and shape parameters depend on intermolecular distance was similar to that of linear chains, at least in the region of intermediate and large intermolecular separations. Transformation of the data into a concentration dependence revealed that with an increase in concentration, the dimensions decreased in the case of athermal solvents while they increased for θ‐solvents regardless of the functionality given.     

Electrophoretic separation of large DNAs using steric confinement

We report an alternative method for electrophoretic separation of large DNAs using steric confinement between solid walls, without gel or obstacles. The change of electrophoretic mobility vs confinement thickness is investigated using fluorescence video microscopy. We observe separation at small confinement thicknesses followed by a transition to the bulk behavior (no separation) at a thickness of about 4 mum (a few radii of gyration for the studied DNA chains). We present tentative explanations of our original observations.