Simulating the collapse transition of a two-dimensional semiflexible lattice polymer

It has been revealed by mean-field theories and computer simulations that the nature of the collapse transition of a polymer is influenced by its bending stiffness epsilon(b). In two dimensions, a recent analytical work demonstrated that the collapse transition of a partially directed lattice polymer is always first order as long as epsilon(b) is positive [H. Zhou et al., Phys. Rev. Lett. 97, 158302 (2006)]. Here we employ Monte Carlo simulation to investigate systematically the effect of bending stiffness on the static properties of a two-dimensional lattice polymer. The system's phase diagram at zero force is obtained. Depending on epsilon(b) and the temperature T, the polymer can be in one of the three phases: crystal, disordered globule, or swollen coil. The crystal-globule transition is discontinuous and the globule-coil transition is continuous. At moderate or high values of epsilon(b) the intermediate globular phase disappears and the polymer has only a discontinuous crystal-coil transition. When an external force is applied, the force-induced collapse transition will either be continuous or discontinuous, depending on whether the polymer is originally in the globular or the crystal phase at zero force. The simulation results also demonstrate an interesting scaling behavior of the polymer at the force-induced globule-coil transition.     

Phase behavior of a single polyethylene chain confined between two adsorption walls

The phase behavior of a single polyethylene chain confined between two adsorption walls is investigated by using molecular dynamics simulations. In the free space, it is confirmed in our calculation that the isolated polymer chain exhibits a disordered coil state at high temperatures, and collapses into a condensed state at low temperatures, that is, the coil‐to‐globule transition, and the finite chain length effects are considered since the critical region depends on chain lengths. When the chain is confined between two attractive walls, however, the equilibrium properties not only depend on the chain length but also depend on the adsorption energy and the confinement. Mainly, we focus on the influence of polymer chain length, confinement, and adsorption interaction on the equilibrium thermodynamic properties of the polyethylene chains. Chain lengths of N = 40, 80, and 120 beads, distances between the two walls of D = 10, 20, 30, 50, and 90 Å, and adsorption energies of w = 1.5, 2.5, 3.5, 6.5, and 8.5 kcal/mol are considered here. By considering the confinement–adsorption interactions, some new folding structures are found, that is, the hairpin structure for short chain of N = 40 beads, and the enhanced hairpin or crystal like structures for long chains of N = 80 and 120 beads. The results obtained in our simulations may provide some insights into the phase behaviors of confined polymers, which can not be obtained by previous studies without considering confinement–adsorption interactions. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 370–387, 2008     

Monte Carlo Computer Simulation of a Single Semi-Flexible Macromolecule at a Plane Surface

Summary: The properties of a single semiflexible mushroom chain at a plane surface with a long-ranged attracting potential are studied by means of lattice Monte Carlo computer simulation using the bond fluctuation model, configurational bias algorithm for chain re-growing and the Wang-Landau sampling technique. We present the diagram of states in variables temperature T vs. strength of the adsorption potential, ε_w, for a quite short semiflexible chain consisting of N = 64 monomer units. The diagram of states consists of the regions of a coil, liquid globule, solid isotropic globule, adsorbed coil and cylinder-like liquid-crystalline globule. At low values of the adsorption strength ε_w the coil–globule and the subsequent liquid–solid globule transitions are observed upon decreasing temperature below the adsorption transition point. At high values of ε_w these two transitions change into a single transition from an adsorbed coil to a cylinder-like liquid-crystalline solid globule. We conclude that for a semiflexible chain the presence of a plane attracting surface favors the formation of a globule with internal liquid-crystalline ordering of bonds.     

Study of the phase transition of poly(N,N‐diethylacrylamide) in water by rheology and dynamic light scattering

Poly(N,N‐diethylacrylamide) (PDEA) possesses a lower critical solution temperature (LCST) in aqueous media. The solution properties of PDEA at various temperatures have been characterized with techniques such as rheology and dynamic light scattering. There is a decrease in the coil size before the phase transition due to a coil‐to‐globule transition. At the LCST, rheological and dynamic light scattering studies have also confirmed an aggregation phenomenon. This aggregation modifies the rheological properties of the polymer solutions. High frequencies hinder the phase‐transition process and reduce the LCST of the polymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1627–1637, 2003     

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.     

Counterion mixing effects on the conformational transitions of polyelectrolytes. II. Counterion binding as measured by NMR spectroscopy of alkali metal poly(acrylate)s

Bound states of counterions during the coil‐globule transition of poly(acrylic acid) in water/organic solvent mixtures were investigated by NMR spectroscopy of alkali metal cations (Li⁺, Na⁺, Cs⁺). Accompanying the transition, the line widths of the respective NMR peaks significantly increased with increasing the organic solvent composition in the medium. Although this line width broadening suggests that some specific counterion binding with desolvation is involved with the coil‐globule transition, the most marked broadening was observed in higher organic solvent compositions than those of the coil‐globule transition region detected by the viscometry. Namely, the specific counterion binding with desolvation proceeds even after the polymer chain collapsed. This means in turn that such a strong counterion binding is not a prerequisite for the coil‐globule transition, at least at the stage of the onset. For the Li⁺/Cs⁺ mixed counterion system in 60 vol % DMSO, where our previous conductivity data suggested that the specific counterion binding occurred only for Cs⁺ during the coil‐globule transition induced on mixing with Li⁺, a significant increase in the line width was also observed only for Cs⁺. The coincidence between the conductivity and the NMR results for the Li⁺/Cs⁺ mixed counterion system strongly supports a working hypothesis, “size‐fitting effect,” that has been proposed to determine the counterion specificity observed for the conformational transitions of polyelectrolytes. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2132–2139, 2009     

The size of a polymer in a symmetric solvent

Using a simple thermodynamic model, we derive an expression for the excluded volume parameter v of a polymer chain in a symmetric solvent (solvated by its own monomers). For a chain with a given segment length and number of monomers, this parameter determines whether the chain is collapsed or expanded. For the latter it determines the degree of expansion. Using a simple off-lattice version of Flory's model [P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, 1953)] and relaxing the assumption of incompressibility, we obtain the result v=(1-kappa)rho(0), where kappa is the dimensionless compressibility and rho(0) the number density of solvent. In the incompressible limit (in the sense that kappa-->0) the chain is expanded and the inverse of the solvent number density determines the degree of expansion of the chain. Using the van der Waals equation of state to estimate kappa (allowing for nonzero compressibility in a system that can undergo a gas-liquid phase transition), the model predicts that upon raising the temperature at constant pressure there is both a lower (coil to globule) and upper (globule to coil) Flory temperature. This is in quantitative agreement with experiment and computer simulations.     

Coil‐Globule Collapse in Flexible Macromolecules

The transition of a solvated flexible macromolecular chain from random coil behavior in the θ‐state to a globular compact form in the collapsed state has been the subject of extensive theoretical and experimental studies. Most of the coil‐globule transition studies of macromolecules have concentrated on the prototypical polystyrene‐cyclohexane system. However, chain contractions reported in this system have been around 75% of those in the unperturbed θ‐state. This relatively small decrease in size does not satisfy the criterion for a densely packed, collapsed globule. Experimentally, the collapse from a coil to a true compact globular state has now been established for two flexible macromolecules: poly(N‐isopropylacrylamide) in water and poly(methyl methacrylate) in various solvents. In this contribution, we review recent theoretical studies covering phenomenological and Langevin models as well as computer simulations. In addition, we outline recent experimental studies of the coil‐globule transition of various flexible polymers, copolymers, and polyelectrolytes.

Expansion factor, αequation/tex2gif-stack-1.gif, versus temperature for NaPSS in 4.17 M aqueous NaCl solution. (•): NaPSS‐1, (○): NaPSS‐2.     

Conformational relaxation dynamics of a poly(N-isopropylacrylamide) aqueous solution measured using the laser temperature jump transient grating method

We observed phase transition and phase relaxation processes of a poly(N-isopropylacrylamide) (PNIPAM) aqueous solution using the heterodyne transient grating (HD-TG) method combined with the laser temperature jump technique. The sample temperature was instantaneously raised by about 1.0 K after irradiation of a pump pulse to crystal violet (CV) molecules for heating, and the phase transition was induced for the sample with an initial temperature just below the lower critical solution temperature (LCST); the following phase relaxation dynamics was observed. Turbidity relaxation was observed in both the turbidity and HD-TG responses, while another relaxation process was observed only in the HD-TG response, namely via the refractive index change. It is suggested that this response is due to formation of globule molecules or their assemblies since they would have nothing to do with turbidity change but would affect the refractive index, which is dependent on the molar volume of a chemical species. Furthermore, the grating spacing dependence of the HD-TG responses suggests that the response was caused by the counter propagating diffusion of the coil molecules as a reactant species and the globule molecules as a product species and the lifetime of the globule molecules ranged from 1.5 to 5 seconds. Thus, we conclude that the turbidity reflects the dynamics of aggregate conditions, not molecular conditions. The coil and globule sizes were estimated from the obtained diffusion coefficient. The sizes of the coil molecules did not change at the initial temperatures below the LCST but increased sharply as it approaches LCST. We propose that the coil-state molecules associate due to hydrophobic interaction when the initial temperature was higher than LCST minus 0.5 K and that the globule-state molecules generated from the coil-state molecules showed a similar trend in temperature. The phase transition was also induced by heating under a microscope, and the relaxation process was followed using the fluorescence peak shift of a fluorescent molecule-labeled PNIPAM. The result also supports the existence of a globule molecule or its assembly remains for several seconds in the phase relaxation.     

Attenuated total reflectance/fourier transform infrared studies on the phase‐separation process of aqueous solutions of poly(n‐isopropylacrylamide)

Temperature‐induced phase separation of poly(N‐isopropylacrylamide) in aqueous solutions was studied by attenuated total reflectance (ATR)/Fourier transform infrared spectroscopy. The main objectives of the study were to understand, on a molecular level, the role of hydrogen bonding and hydrophobic effects below and above the phase‐separation temperature and to derive the scenario leading to this process. Understanding the behavior of this particular system could be quite relevant to many biological phenomena, such as protein denaturation. The temperature‐induced phase transition was easily detected by the ATR method. A sharp increase in the peaks of both hydrophobic and hydrophilic groups of the polymer and a decrease in the water‐related signals could be explained in terms of the formation of a polymer‐enriched film near the ATR crystal. Deconvolution of the amide I and amide II peaks and the O? H stretch envelope of water revealed that the phase‐separation scenario could be divided, below the phase‐separation temperature, into two steps. The first step consisted of the breaking of intermolecular hydrogen bonds between the amide groups of the polymer and the solvent and the formation of free amide groups, and the second step consisted of an increase in intramolecular hydrogen bonding, which induced a coil–globule transition. No changes in the hydrophobic signals below the separation temperature could be observed, suggesting that hydrophobic interactions played a dominant role during the aggregation of the collapsed chains but not before. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1665–1677, 2001     

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 .     

Collapse and swelling of poly(N‐isopropylacrylamide‐co‐sodium acrylate) copolymer brushes grafted on a flat SiO2 surface

Poly(N‐isopropylacrylamide‐co‐sodium acrylate) copolymer brushes grafted on SiO₂‐coated quartz crystal surface were prepared with a surface‐immobilized initiator. The collapse and swelling of the thermally sensitive copolymer brushes in water were studied with quartz crystal microbalance in situ. The frequency and dissipation changes with the temperature increasing in the range 20–38 °C indicate that the brushes undergo a continuous collapse transition. Our results show that the copolymer brushes collapse to a state where the brushes were prepared. A hysteresis was observed in the cooling process. Fourier transform infrared (FTIR) results revealed that the formation of some additional hydrogen bonds within the copolymer chains at their collapsed state is responsible for the hysteresis. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 770–778, 2006     

What's so special about polymers? A little known organizing principle gives rise to an abundance of polymer phase transitions

We argue that if an organizing principle exists it must have to do with the linear connectivity of the monomers since this feature is what distinguishes polymers from all other materials. We then compare a linear polymer threading a pore in a membrane (PTM) with an equal number of unconnected monomers which are also allowed to transit through a pore in a membrane. The crucial difference between the two cases is that the connected monomers are distinguishable from one another by virtue of their location along the polymer chain whereas the disconnected monomers are indistinguishable. Because of this, the disconnected monomers obey the ideal gas laws while the connected monomers undergo a first-order thermodynamic phase transition! Four other phase transitions occurring in isolated linear polymer molecules are known. They are the helix to random coil (HR) transitions in biological polymers, surface adsorption (SA), polymer collapse (C), and a model of polymerization (P). These five kinds of transitions can be coupled to one another resulting in a sizable number of exactly solvable minimal models of phase transitions. There are also five classes of phase transitions in many polymers systems. The coupling of these 10 classes of transitions to each-other results in a plethora of phases. These in turn provide the basis for the many polymer structures observed in the world about us. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2612–2620, 2006     

Adsorption of a single polymer chain on a surface: A molecular dynamics simulation study

We performed simulations of the physical adsorption of a single globular chain on a surface of hemispherical shape by means of molecular dynamics simulations. For the chain, we took advantage of a united atom model. Interactions within the chain were limited to stretching, bending, and torsional as well as nonbonded interactions between the nonadjacent atoms. The interaction between each chain element and the surface formation are reigned by a Lennard–Jones potential. In this article, we focused on differences in the behavior of the adsorbed globule to the free unadsorbed one particularly in two different zones of the immediate vicinity of the surface. There were strong indications for a localized acceleration of the dynamics as compared with the bulk that appears in an increase of trans–gauche switches. For explanation we came up with an adsorption scenario. Special attention was given to the shift of the percentage of trans and gauche conformations within the globule in dependence on the strength of the adsorption potential that might be related to crystallization or glass transition. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2333–2339, 2001     

Collapse of a two-state sticky hard sphere chain

The collapse of a homopolymer gaussian chain into a globule is represented as a transition between two states, viz., extended and collapsed. Appropriately, this model has been labeled as the all-or-none view of chain collapse. In the collapsed state, the single polymer partition function is expressed by a single Mayer diagram with the maximum number of f-bonds arising from nonbonded square well interactions. Our target is the dependence of the transition temperature on chain length and the interaction range of the square well, as indicated through the behavior of the radius of gyration and the constant volume heat capacity. Properties of the collapse transition are calculated exactly for chains with three to six backbone atoms and heuristically for long chains using arguments derived from the small chains and from conditions of integrability. Comparison with simulation studies is made.     

端基附壁高分子模型链的塌缩转变

借MonteCarlo和模拟退火方法研究了端基附壁高分子尾形链在不同温度下的形态变化 ,链的模型采用有最近邻相互吸引作用的自避行走 .计算机实验结果表明 ,对于端基附壁的高分子尾形链 ,与自由链一样 ,当温度逐渐降低时高分子链会发生从松散的无规线团到紧密球体的塌缩转变 .计算机模拟得到了端基附壁链的均方末端距及其分量 ,均方回转半径及分布随温度的变化 .由于刚性壁的影响 ,使得有限链长的高分子尾形链与自由链相比 ,其表示链尺寸 温度关系的曲线要稍低 .模拟还发现 ,在高温时壁对链形状的影响比较大 ,壁垂直方向上尺寸明显大于平行方向的尺寸 ,后者接近于自由链的尺寸分量 .然而 ,低于θ温度时 ,尤其是完全塌缩之后 ,壁对链形状的影响已经很小 .     

Atomistic insights on the LCST behavior of PMEO2MA in water by molecular dynamics simulations

Fully atomistic molecular dynamics simulations of poly(2‐[2‐methoxyethoxy]ethyl methacrylate) (PMEO₂MA) in water at temperatures below and above its lower critical solution temperature (LCST) were performed to improve the understanding of its LCST behavior. Atomic trajectories were used to calculate various structural and dynamic properties. Simulation results show that PMEO₂MA undergo a distinct coil‐to‐globule transition above LCST. Detailed analyses of the number of first hydration shell water molecules around various atomic regions are revealed that the water solubility of PMEO₂MA below LCST is mainly provided by the hydrophobic hydration around the side chain carbon atoms. This is achieved by the cage‐like water network formations which are disrupted when the temperature is increased above LCST, accompanied by significant amount of water molecule release and local water‐ordering reduction, which leads to the LCST phase transition. Furthermore, other analyses such as the number of hydrogen bonds and hydrogen bond lifetimes suggest that intermolecular hydrogen bondings between polymer and water molecules have little effect on the phase transition. Our results will contribute to a better understanding on the LCST phase transition of oligo(ethylene glycol) methyl ether methacrylate (OEGMA)‐based homopolymers at atomistic level that will be useful when designing homo‐ and co‐polymers of OEGMAs with desired properties. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 429–441     

Saccharide‐structure effects on poly N‐isopropylacrylamide phase transition in aqueous media; Reflections on protein stability

Protein stability in aqueous solutions is important in numerous fields, particularly biotechnology and food‐science. To shed new light on the protective effect of carbohydrates on proteins, we studied saccharide‐structure effects in aqueous solutions on the coil‐to‐globule transition occurring at the lower critical solution temperature (LCST) of poly‐N‐isopropylacrylamide (PNIPA), an isomer of polyleucine, as a simple model representing certain key behaviors of proteins (e.g., denaturation/renaturation). We systematically selected sugars and polyols to relate structural and physical characteristics of these carbohydrates to their effect on PNIPA solutions. Using isothermal titration‐microcalorimetry, we showed that no significant binding of saccharides to the polymer occurs. Using micro‐DSC, we studied the decreasing polymer LCST temperature with rising carbohydrate concentration. Beyond the expected observation that steric exclusion is important, we observed previously‐unreported significant differences among the effects of isomeric aldohexoses and also among the effects of isomeric diglucoses on PNIPA LCST. We found good correlation between the sugar hydration number and its effect on LCST. We conclude that the larger and denser the hydrated cluster a carbohydrate forms, the worse a cosolvent is for the polymer, and the stronger it's lowering effect of the coil‐to‐globule transition. Such favoring of the compact globule state provides a protective effect against denaturation of globular proteins. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2307–2318, 2008     

Discontinuous molecular dynamics simulation study of polymer collapse

Discontinuous molecular dynamics simulations were used to study the coil-globule transition of a polymer in an explicit solvent. Two different versions of the model were employed, which are differentiated by the nature of monomer-solvent, solvent-solvent, and nonbonded monomer-monomer interactions. For each case, a model parameter lambda determines the degree of hydrophobicity of the monomers by controlling the degree of energy mismatch between the monomers and solvent particles. We consider a lambda-driven coil-globule transition at constant temperature. The simulations are used to calculate average static structure factors, which are then used to determine the scaling exponents of the system in order to determine the theta-point values lambda(theta) separating the coil from the globule state. For each model we construct coil-globule phase diagrams in terms of lambda and the particle density rho. Additionally, we explore for each model the effects of varying the range of the attractive interactions on the phase boundary separating the coil and globule phases. The results are analyzed in terms of a simple Flory-type theory of the collapse transition.     

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...