Stoichiometric polyelectrolyte complexes as comb copolymers

The collapse behavior of a single comblike copolymer chain has been studied by Monte Carlo simulations. It has been supposed that the solvent is good for the side chains but the solvent quality for the backbone chain changes. It has been shown that depending on the structural parameters of the comb copolymer (the lengths of the backbone and side chains, grafting density of the side chains) various thermodynamically stable morphologies of the collapsed backbone chain can be realized. In addition to ordinary spherical globule we have observed elongated structures as well as necklace-like conformations. The proposed model can be used to describe conformational behavior of stoichiometric complexes between block copolymers with a polyelectrolyte short block and oppositely charged linear homopolymers.     

Mean field theory for the intermolecular and intramolecular conformational transitions of a single flexible polyelectrolyte chain

The diMarzio theory has been extended to elucidate the intermolecular and intramolecular phase segregations of a single flexible chain polyelectrolyte in dilute salt-free solutions. At the long chain limit, this theory yields the formalism obtained from the more sophisticated Edward Hamiltonian for polyelectrolyte problems. The calculated phase diagram exhibits the features of a first-order phase transition, with continuous and discontinuous transitions separated by a critical point. Under the discontinuous transition, the polyelectrolyte chain exhibits coexistent expanded and collapsed conformational states, same as intermolecular phase segregation. For a limiting long chain, the mean chain size at critical point is roughly 90% of the size of an ideal chain. Such a result implies that partial contraction within a chain molecule is required to collapse a flexible polyelectrolyte chain. Moreover, the theory predicts that for a longer chain, intramolecular segregated conformations differ significantly from intermolecular segregated conformations, but the difference becomes small for shorter chains. Besides, the charge needed to induce intramolecular segregation is smaller than that of intermolecular segregation for a given chain length. These findings are consistent with previous literature results.     

Chain conformations and phase separation in polymer solutions with varying solvent quality

Molecular dynamics simulations are used to investigate the conformations of a single polymer chain, represented by the Kremer-Grest bead-spring model, in a solution with a Lennard-Jones liquid as the solvent when the interaction strength between the polymer and solvent is varied. Results show that when the polymer-solvent interaction is unfavorable, the chain collapses as one would expect in a poor solvent. For more attractive polymer-solvent interactions, the solvent quality improves and the chain is increasingly solvated and exhibits ideal and then swollen conformations. However, as the polymer-solvent interaction strength is increased further to be more than about twice the strength of the polymer-polymer and solvent-solvent interactions, the chain exhibits an unexpected collapsing behavior. Correspondingly, for strong polymer-solvent attractions, phase separation is observed in the solutions of multiple chains. These results indicate that the solvent becomes effectively poor again at very attractive polymer-solvent interactions. Nonetheless, the mechanism of chain collapsing and phase separation in this limit differs from the case with a poor solvent rendered by unfavorable polymer-solvent interactions. In the latter, the solvent is excluded from the domain of the collapsed chains while in the former, the solvent is still present in the pervaded volume of a collapsed chain or in the polymer-rich domain that phase separates from the pure solvent. In the limit of strong polymer-solvent attractions, the solvent behaves as a glue to stick monomers together, causing a single chain to collapse and multiple chains to aggregate and phase separate.     

Chemical Communication between Organometallic Single-Chain Polymer Nanoparticles

Chemical communication between macromolecules was studied by observing the controlled single chain collapse that ensues the exchange of a metal cross-linker between two polymer chains. The rhodium (I) organometallic cross-linker transfer from a low molecular weight collapsed polybutadiene to a larger polymer was followed using size exclusion chromatography. The increased effective molarity in the larger polymer seems to be the driving force for the metal migration. Thus, we demonstrate here a strategy for transferring a molecular signal that induces chain collapse of a polymer chain based on non-covalent interactions, mimicking biological behaviors reminiscent of signal transductions in proteins.     

表面温敏聚合物刷的原子力显微镜和石英晶体微天平研究

通过表面引发的原子转移自由基聚合在硅片表面制备了聚（N-异丙基丙烯酰胺）（PNIPAAm）聚合物刷。用原子力显微镜（AFM）分别研究了PNIPAAm的接枝动力学、温度和溶剂性质对厚度的影响以及PNIPAAm链与原子力针尖间的粘附力。结果表明,PNIPAAm链在硅片表面的生长具有很好的可控性。常温下厚度为33nm的PNIPAAm膜在水溶液中的增加到82.4nm;而在甲醇/水（v/v,1:1）溶液中,PNIPAAm分子链处于坍塌收缩状态,厚度降低为45nm;在55℃下干燥所得厚度则仅为22nm。力-距离测量结果表明,在溶液中,PNIPAAm链与原子力针尖之间的粘附力远小于在干态下的粘附力。用石英晶体微天平（QCM-D）对PNIPAAm的可逆相转变进行了研究,结果表明PNIPAAm分子链随温度变化的构象转变是发生在30-34℃之间的连续过程。     

激光光散射研究聚(N-异丙基丙烯酰胺)单链及其智能凝胶微球在水中的相变(下)

（接上期）２聚（Ｎ－异丙基丙烯酰胺）微凝胶在水中的体积相变２．１理论部分凝胶体积相变热力学：聚合物凝胶的溶胀和蜷缩可以用膨胀因子α＝（Ｖ／Ｖ０）１／３＝（ΦＴ／ΦΘ）１／３来表征，其中ΦΘ的ΦＴ分别是温度Θ和Ｔ下凝胶网络的体积分数。在平均场理论中，中...     

Chain collapse by lattice simulation

Monte Carlo simulations have been performed on a self-avoiding simple cubic lattice chain with the nearest-neighbor interactions for a range of chain lengths N from 40 to 1000 segments to investigate equilibrium properties of polymer chains from an athermal to a collapsed state. Both the fraction of segments in the clusters and the number of contacts exhibit the three stage process for the chain collapse, consistent with our previous molecular dynamics simulations of a fully atomistic chain. In the collapse region corresponding to the nearest-neighbor interaction parameter larger than 0.5 for a segment-solvent pair, polymer chains are quite spherical and both ends lie nearly randomized within the sphere. The peak height of the specific heat is proportional to N(In N)^3/11, as predicted by the renormalization group theory.     

磁性高分子链的磁性质和构象性质的Monte Carlo模拟

采用退火 (Annealing)MonteCarlo方法 ,从高温到低温顺序模拟了简立方格点上考虑最近邻Ising相互作用的磁性高分子链在不同温度的磁性质和构象性质 .磁性高分子链在低温下存在自发磁矩 ,无限长链的临界温度Tc=1 77± 0 0 5J kB.在临界温度附近 ,高分子链经历了从伸展的无规线团到紧缩球体的塌缩相变 .对链的尺寸、形状、近邻数及能量的分析表明 ,高分子链的构象性质从温度Tc=1 77开始发生较明显的变化 ,这表明高分子Ising链的相变是Ising相互作用和链节运动协同作用的结果 .     

Intramolecularly ordered globules and the collapse of short chains

We investigate the poor-solvent collapse of short chains having different stiffness through self-consistent minimization of the intramolecular free energy under the constraint of fixed segment lengths between adjacent beads. At first the chains form the Random Gaussian Globule, where the beads are distributed at random at the same average distance from the centre of mass, while the segments show very little correlation. At a larger attractive potential, this collapsed globule undergoes a transition to one or more ordered compact states, depending on the chain stiffness. Under very strong contraction, all chains are described as a Compact Ordered Globule: the beads are again at a constant average distance from the centre of mass, while the segments jump back and forth at the globule's wall with a very large correlation. At intermediate contraction, the thinner and stiffer chains form the Oscillating Ordered Globule wherein the beads are alternatively distributed on two concentric on two concentric shells. In this case, we also find metastable states with nonsymmetrical conformations of the chain with respect to its ends. We also briefly discuss the thermodynamics of the coil-globule and globule-globule transitions, showing that in long polymer chains these ordered conformations cannot involve the whole chain. However, we suggest that they might still be found as local globules that form for kinetic reasons.     

Combined Molecular Dynamics Simulation and Rouse Model Analysis of Static and Dynamic Properties of Unentangled Polymer Melts with Different Chain Architectures

Chain architecture effect on static and dynamic properties of unentangled polymers is explored by molecular dynamics simulation and Rouse mode analysis based on graph theory. For open chains, although they generally obey ideal scaling in chain dimensions, local structure exhibits nonideal behavior due to the incomplete excluded volume(EV) screening, the reduced mean square internal distance(MSID) can be well described by Wittmer' theory for linear chains and the resulting chain swelling is architecture dependent, i.e., the more branches a bit stronger swelling. For rings, unlike open chains they are compact in term of global sizes. Due to EV effect and nonconcatenated constraints their local structure exhibits a quite different non-Gaussian behavior from open chains, i.e., reduced MSID curves do not collapse to a single master curve and fail to converge to a chain-length-independent constant, which makes the direct application of Wittmer's theory to rings quite questionable.Deviation from ideality is further evidenced by limited applicability of Rouse prediction to mode amplitude and relaxation time at high modes as well as the non-constant and mode-dependent scaled Rouse mode amplitudes, while the latter is architecture-dependent and even molecular weight dependent for rings. The chain relaxation time is architecture-dependent, but the same scaling dependence on chain dimensions does hold for all studied architectures. Despite mode orthogonality at static state, the role of cross-correlation in orientation relaxation increases with time and the time-dependent coupling parameter rises faster for rings than open chains even at short time scales it is lower for rings.     

Histogram Monte Carlo simulation on phase transitions in single‐polymer systems

Applying the histogram Monte Carlo simulation method and the bond‐fluctuation model, various phase transitions in single‐polymer systems were investigated. The critical transition temperature (Θ point) in the coil‐globule collapse transition of a macromolecular chain is accurately determined. Finite‐size scaling results near the transition point are verified. The first‐order transition associated with the freezing/crystallization of a polymer at a temperature below the Θ point is also observed. The free energy profiles associated with these two transitions are explicitly computed. Furthermore, the unfolding phase transition associated with stretching a collapsed polymer chain is investigated. The free energy profile associated with the transition is explicitly computed. Results on the energy cumulants and free energy profiles provide direct evidences for the first‐order nature of the unfolding phase transition.     

Development of knotting during the collapse transition of polymers

A dynamic Monte Carlo simulation of the collapse transition of polymer chains is presented. The chains are represented as self-avoiding walks on the simple cubic lattice with a nearest-neighbor contact potential to model the effect of solvent quality. The knot state of the chains is determined using the knot group procedure presented in the accompanying paper. The equilibrium knot spectrum and the equilibrium rms radius of gyration as functions of the chain length and the contact potential are reported. The collapse transition was studied following quenches from good-to poor-solvent conditions. Our results confirm the prediction that the newly formed globule is not yet at equilibrium, since it has not yet achieved its equilibrium knot spectrum. For our model system, the relaxation of the knot spectrum is about an order of magnitude slower than that of the radius of gyration. The collapse transition is also studied for a model in which both ends of the chain remain in good-solvent conditions. Over the time scale of these simulations, knot formation is frustrated in this inhomogeneous model, verifying that the mechanism of knotting is the tunneling of chain ends in and out of the globule.     

The phase diagram of a single polymer chain: New insights from a new simulation method

We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang-Landau sampling idea. Applying this new algorithm to the problem of the homopolymer collapse allows us to investigate not only the high temperature coil–globule transition but also an ensuing crystallization at lower temperature. Performing a finite size scaling analysis on the two transitions, we show that they coincide for our model in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil–globule transition. As a consequence, also the many chain phase diagram of this model can be predicted to consist only of gas and crystal phase in the limit of infinite chain length. This behavior is in agreement with findings on the phase behavior of hard-sphere systems with a relatively short-ranged attractive square well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2542–2555, 2006     

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.     

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.     

Temperature-induced self-assembly of triple-responsive triblock copolymers in aqueous solutions

A series of triple-thermoresponsive triblock copolymers from poly(N-n-propylacrylamide) (PNPAM, A), poly(methoxydiethylene glycol acrylate) (PMDEGA, B), and poly(N-ethylacrylamide) (PNEAM, C) was synthesized by sequential reversible addition-fragmentation chain transfer polymerizations. Polymers of differing block sequences, ABC, BAC, and ACB, with increasing phase transition temperatures in the order A < B < C were prepared. Their aggregation behavior in dilute aqueous solution was investigated using dynamic light scattering, turbidimetry, and NMR spectroscopy. The self-organization of such polymers was found to dependent strongly on the block sequence. While polymers with a terminal low-LCST (lower critical solution temperature) block undergo aggregation above the first phase transition temperature at 20-25 °C, triblock copolymers with the low-LCST block in the middle show aggregation only above the second phase transition. The collapse of the middle block is not sufficient to induce aggregation but produces instead stable, unimolecular micelles with a collapsed middle block, as supported by NMR and fluorescence probe data. Continued heating of all copolymers led to two additional thermal transitions at 40-55 and 70-80 °C, which could be correlated to the phase transitions of the B and C blocks, respectively. All polymers show a high tendency for cluster formation, once aggregation is induced. The carrier abilities of the triple responsive triblock copolymers for hydrophobic agents were probed with the solvatochromic fluorescence dye Nile Red. With passing through the first thermal transition, the block copolymers are capable of solubilizing Nile Red. In the case of block copolymers with sequences ABC or ACB, which bear the low-LCST block at one terminus, notable amounts of dye are solubilized already at this stage. In contrast, the hydrophobic probe is much less efficiently incorporated by the BAC triblock copolymer, which forms unimolecular micelles. Only after the collapse of the B block, when reaching the second phase transition at about 45 °C, does aggregation occur and solubilization becomes efficient. In the case of ABC and ACB polymers, the hydrophobic probe seems to partition between the originally collapsed A chains and the additional hydrophobic chains formed after the collapse of the less hydrophobic B block.     

The effect of hydrogen bonding on oligoleucine structure in water: A molecular dynamics simulation study

Molecular dynamics simulations were conducted in order to improve our understanding of the forces that determine polyleucine chains conformations and govern polyleucine self-assembly in aqueous solutions. Simulations of 10 repeat unit oligoleucine in aqueous solution were performed using the optimized potential for liquid simulations (OPLS) - all atom force field using the canonical ensemble for a minimum of 1.3 ns. These simulations provided information on conformations, chain collapse and intermolecular aggregation. Simulations indicate that single isotactic oligoleucine chains in dilute solution assume tightly packed, regular hairpin conformations while atactic oligoleucine assumes a much less regular and less compact structure. The regular, compact collapsed isotactic chain exhibited a greater degree of intramolecular hydrogen bonding and an increased level of hydrophobic t-butyl functional group aggregation compared to the atactic chain. This occurs at the expense of reduced leucine-water hydrogen bonding.     

Transitions of tethered polymer chains: a simulation study with the bond fluctuation lattice model

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density-of-states results have been evaluated for interaction parameters spanning the range from good- to poor-solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.     

The collapse of polyethylene rings on an attractive surface

Polymers exhibit extended structures at high temperatures or in good solvents and collapsed configurations at low temperatures or in poor solvents. This fundamental property is crucial to the design of materials, and indeed has been extensively studied in recent years. In this paper, the collapse of polyethylene rings on an attractive surface was investigated by using molecular dynamics simulations. It is found that the collapse of ring chains on the attractive surface is of distinct difference from their free counterparts, where the collapse becomes more continuous and a one-stage instead of two-stage collapse can be identified by the specific heat. Some hairpin-like crystal structures are found at low temperatures, which are induced by the adsorption interaction of polymer-surface. For a given chain length, the results were further compared with those of the adsorbed linear chains. Due to the topological constraint of ring chains, the number of hairpin structures is clearly less than that of the linear chains. These numerical simulations may provide some new insights into the folding of ring polymers under adsorption interactions.     

Collapsed conformation of poly(methacrylic acid) chain containing nonionic hydrophilic units

Copolymers of methacrylic acid (MAA) and a nonionic hydrophilic monomer N-vinylpyrrolidone (NVP) were synthesized by polymerization in aqueous solution in the absence of metal ions. The NVP content of the copolymers ranged from 2 to 36 mole % with sequences of MAA interrupted at random by a single unit of NVP at all compositions. The pH-induced conformational transition of these copolymers was followed by potentiometric titration and viscosity studies and the results were compared with those of pure poly(methacrylic acid) (PMAA). The negative free energy of transition from the un-ionized compact from to expanded structure showed a gradual decrease with increasing NVP content, and the collapsed conformation observable for PMAA at low degrees of ionization (0 < α < 0.3) disappeared at NVP contents greater than 15 mole%. These findings are supported by viscosity data. The results suggest that long-range methyl–methyl hydrophobic contacts still possible in higher NVP content copolymers are not sufficient to bring about the collapse of the molecule and a minimum average sequence length of about 20 MAA units is required to compact the molecule. Hydrophilic “shielding” of MAA chains by NVP segments could also partly destabilize the collapsed structure.