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.     

Simulation study of the coil-globule transition of a polymer in solvent

Molecular dynamics simulations are used to study the coil-globule transition for a system composed of a bead-spring polymer immersed in an explicitly modeled solvent. Two different versions of the model are used, 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 lambdatheta separating the coil from the globule states. For each model we construct coil-globule phase diagrams in terms of lambda and the particle density rho. The results are analyzed in terms of a simple Flory-type theory of the collapse transition. The ratio of lambdatheta for the two models converges in the high density limit exactly to the value predicted by the theory in the random mixing approximation. Generally, the predicted values of lambdatheta are in reasonable agreement with the measured values at high rho, though the accuracy improves if the average chain size is calculated using the full probability distribution associated with the polymer-solvent free energy, rather than merely using the value obtained from the minimum of the free energy.     

Structures of stiff macromolecules of finite chain length near the coil‐globule transition: A Monte Carlo simulation

Using a coarse‐grained model of a semiflexible macromolecule, the equilibrium shapes of the chain have been studied varying both the temperature and the chain stiffness. We have applied Monte Carlo techniques using the bond fluctuation model for a chain length of N = 80 effective monomers, and two different types of interactions: a potential depending on the angle between successive bonds along the chain to control the chain stiffness, and an attractive interaction between non‐bonded effective monomers to model variable solvent quality. In a diagram of states where chain stiffness and inverse temperature are used as variables, we find regions where the chain exists as coil, as spherical globule, and as toroidal globule, respectively. Some of these regions are not limited by sharply defined boundaries, but rather wide two‐state coexistence regions occur in between them, where also intermediate metastable structures (such as rods and disks) occur. Recording histograms of energy, orientational order parameters, etc., which exhibit a two‐peak structure in the two‐state coexistence regions, we perform a subensemble analysis of the individual structures corresponding to these peaks.     

Knots in globule and coil phases of a model polyethylene

We examine the statistics of knots with numerical simulations of a simplified model of polyethylene. We can simulate polymers of up to 1000 monomers (each representing roughly three CH(2) groups), at a range of temperatures spanning coil (good solvent) and globule (bad solvent) phases. We quantify the abundance of knots in the globule phase and in confined polymers, and their rarity in the swollen phase. Since our polymers are open, we consider (and test) various operational definitions for knots, which are rigorously defined only for closed chains. We also associate a typical size with individual knots, which are found to be small (tight and localized) in the swollen phase but large (loose and spread out) in the dense phases.     

Equilibrium conformational dynamics of a polymer in a solvent

Molecular dynamics simulations were used to study the conformational dynamics of a bead-spring model polymer in an explicit solvent under good solvent conditions. The dynamics of the polymer chain were investigated using an analysis of the time autocorrelation functions of the Rouse coordinates of the polymer chain. We have investigated the variation of the correlation functions with polymer chain length N, solvent density rho, and system size. The measured initial decay rates gamma(p) of the correlation functions were compared with the predictions from a theory of polymer dynamics which uses the Oseen tensor to describe hydrodynamic interactions between monomers. Over the range of chain lengths considered (N = 30-60 monomers), the predicted scaling of gamma(p) proportional to N(-3nu) was observed at high rho, where nu is the polymer scaling exponent. The predicted gamma(p) are generally higher than the measured values. This discrepancy increases with decreasing rho, as a result in the breakdown in the conditions required for the Oseen approximation. The agreement between theory and simulation at high rho improves considerably if the theoretical expression for gamma(p) is modified to avoid sum-to-integral approximations, and if the values of (R(p)2), which are used in the theory, are taken directly from the simulation rather than being calculated using approximate scaling relations. The observed finite-size scaling of gamma(p) is not quantitatively consistent with the theoretical predictions.     

Phase transitions of a polymer threading a membrane coupled to coil-globule transitions

We theoretically study phase transitions of a polymer threading through a pore imbedded in a membrane. We focus on the coupling between a partition of the polymer segments through the membrane and a coil-globule transition of the single polymer chain. Based on the Flory model for collapse transitions of a polymer chain, we calculate the fraction of polymer segments and the expansion factor of a polymer coil on each side of the membrane. We predict a first-order phase transition of a polymer threading a membrane; polymer segments in one side are discontinuously translocated into the other side, depending on solvent conditions and molecular weight of the polymer. We also discuss the equilibrium conformation of the polymer chain on each side of the membrane.     

AFM imaging of adsorbed Nafion polymer on mica and graphite at molecular level

Perfluorosulfonic acid ionomer (PFSA, specifically Nafion at EW = 975 g/mol) was visualized at the single molecule level using atomic force microscopy (AFM) in liquid. The diluted commercial Nafion dispersion shows an apparent M(w) = 1430 kg/mol and M(w)/M(n) = 3.81, which is assigned to chain aggregation. PFSA aggregates, imaged on mica and HOPG during adsorption from EtOH-H(2)O solvent at pH(e) 3.0 (below isoelectric point), showed a stable, segmented rod-like conformation. This structure is consistent with earlier NMR, SAXS/SANS, and TEM results that support a stiff helical Nafion conformation with long persistence length, a sharp solvent-polymer interface, and an extension of the sulfonated side chain into solution. Adsorption of Nafion structures on HOPG was observed at even higher pH(e) from EtOH due to screening of the repulsive electrostatic interaction in lower dielectric constant solvent, while the chain adopted an expanded coil conformation. These measurements provided direct evidence of the chain aggregation in EtOH-H(2)O solution and revealed their equilibrium conformations for adsorption on two model surfaces, highly ordered pyrolitic graphite (HOPG) and mica. The commercial Nafion dispersion was autoclaved at 0.10% w/w in nPrOH/H(2)O = 4:1 v/v solvent at 230 °C for 6 h to give a single-chain dispersion with M(w) = 310 kg/mol and M(w)/M(n) = 1.60. The autoclaved chains adopt an electrostatically stabilized compact globule conformation as observed by AFM imaging of the single PFSA molecules after rapid deposition on mica and HOPG at a low surface coverage.     

MOLECULAR DYNAMICS SIMULATION OF THE RELAXATION OF A FULLY EXTENDED POLYETHYLENE CHAIN

Molecular dynamics simulation of the relaxation at 300 K of a fully extended polyethylene chain of800 CH_2 units has been carried out by following the changes in morphology, van der Waals energy, radius ofgyration in the sense of mechanics and gyration radius in the sense of Flory, population of trans-conformation and orientation factor. The relaxation went through three stages: (1) relaxation from themorphology of a straight rod of 100 nm length to the molphology close to a random coil of gyration radius5.9 nm in 110 ps; (2) collapse of the morphology of a coil to a highly compact globule close to a sphere ofgyration radius 1.3 nm after 178 ps as the result of intersegmental van der Waals attractive interactions; (3)lateral ordering of the folded chain segments in the globule without appreciable changes in the chaindimension up to 1600 ps, the time limit of present simulation. Nearly complete relaxation of local segmentalorientation was performed much faster than the relaxation of globule chain orientation even for a single chainof low degree of polymerization and at a temperature some 155℃above its T_g. The lateral ordering of thechain segments during the period 178 to 680 ps of the simulation time was found to obey the Avramiequation with an Avrami index of 1 .44.     

Simulation Study on the Coil‐Globule Transition and Surface Adsorption of HP Chains

The coil‐globule transition of short hydrophobic‐polar (HP) chains, composed of 24 hydrophilic monomers and 24 polar monomers, in solution and on hydrophobic surface and the adsorption of the HP chain on hydrophobic surface are simulated. The coil‐globule transition point of the HP chain is dependent on sequence of chain but is roughly independent of the surface adsorption strength. Whereas the critical adsorption point of the HP chain is roughly independent of sequence. In addition, the lowest energy states can be obtained for the HP chain in solution or on surface by Monte Carlo simulated annealing method. Results show that the statistical conformation is strongly dependent on the intrachain H‐H attraction strength and the surface adsorption strength.

     

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...     

Study of the semidilute solutions of poly(N,N-dimethylacrylamide) by fluorescence and its implications to the kinetics of coil-to-globule transitions

The large scale motions of poly(N,N-dimethylacrylamide) chains randomly labeled with pyrene (Py-PDMA) were monitored by steady-state and time-resolved fluorescence in semidilute solutions of naked PDMA in acetone and DMF for polymer concentrations ranging from 0 to 550 g/L. Although increasing the polymer concentration of the solution led to a decrease of the mobility of the chromophore attached onto the PDMA backbone, this reduction was rather modest when compared to the large increase of the macroscopic viscosity. This result indicated that locally, the monomer constituting the chains experienced freedom of movement despite the high solution viscosity. The restricted mobility of the chromophore was characterized by the number of monomers occupying the volume probed by the excited chromophore during its lifetime, referred to as a fluorescence "blob". The number of monomers constituting a fluorescence blob, N(F)(-)(blob), and the volume of a fluorescence blob, V(F)(-)(blob), were found to decrease as the polymer concentration of the solution increased, reflecting the decreased mobility experienced by the chromophore. In DMF, the radius of an F-blob was found to scale as N(nu)(F)(-)blob, where nu equaled 0.66 +/- 0.03, very close to the expected value of the Flory exponent of 0.6 for a polymer in a good solvent. The combined knowledge of how N(F)(-)(blob) varies with the fluorescence lifetime of the chromophore and the coil density of the polymer was used to propose a new means of studying coil-to-globule transitions with potential implications for predicting the rate of protein folding.     

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.     

Exploring polymer solubility with thermally-responsive Diels-Alder monomers: Revisiting the monkey's fist

Thermo-responsive monomers were designed to contain a Diels-Alder (DA) adduct such that cyclo-reversion would yield either the maleimide or the furan unit attached to the polymer chain. These thermally responsive monomers were then copolymerized with N-isopropylacrylamide (NIPAM) via reversible addition-fragmentation chain-transfer (RAFT) polymerization to yield linear gradient-copolymer structures as a comparison to existing nanogel/starlike systems to understand how polymer topology and composition influence solution-state properties. Using UV–Vis spectroscopy, it was determined that solution-state properties were thermally dependent and influenced by a number of variables such as comonomer feed ratio, polymer chain end functionality, and polymer backbone length and composition. Manipulation of the feed ratio allowed for control over the cloud point, including the breadth and location of phase separation. Thermal treatment of these copolymers revealed tunable and predictable variations in previously observed transitions, directly correlated to cleavage of the DA adducts and change in polymer backbone composition. Finally, on cooling cycles, a double sigmoid was sometimes observed, indicating a complex globule to random coil transition correlated to polymer chain end composition. These studies help understand how to untie the “monkey's fist.”     

Dense orientationally ordered states of a single semiflexible macromolecule: an expanded ensemble Monte Carlo simulation

Using a coarse-grained model we perform a Monte Carlo simulation of the state behavior of an individual semiflexible macromolecule. Chains consisting of N = 256 and 512 monomer units have been investigated. A recently proposed enhanced sampling Monte Carlo technique for the bond fluctuation model in an expanded ensemble in four-dimensional coordinate space was applied. The algorithm allows one to accelerate the sampling of statistically independent three-dimensional conformations in a dense globular state. We found that the temperature of the intraglobular liquid-solid transition decreases with increasing chain stiffness. We have investigated the possible intraglobular orientationally ordered (i.e., liquid-crystalline) structures and obtained a diagram of states for chains consisting of N = 256 monomer units. This diagram contains regions of stability of coil, two spherical globules (liquid and solid), and rod-like globule conformations. Transitions between the globular states are rounded first-order ones since the states of liquid, solid, and cylinder-like globules do have different internal symmetry.     

Polysoaps in Backbone‐Selective Solvents: Effects of Side‐Chain Length on Collapse Dynamics

Abstract

Molecular dynamics (MD) simulations of model comb‐graft heteropolymers were performed to understand general mechanistic features of coil‐to‐micelle relaxation after instantaneous quench from a nonselective solvent to solvent conditions selective for the backbone monomers and poor for the side‐chain monomers. The systems considered were single bead‐spring molecules with backbones of 30 monomers and 10 equally spaced side chains of 1, 5, 10, or 20 monomers each, immersed in dense liquids of 20,000 simple solvent particles. We find that the coil‐to‐micelle relaxation time, τ _r , averaged over 50 independent trajectories for each set of topological parameters considered, decreases with increasing side‐chain length. A two‐stage relaxation mechanism is observed: (1) a fast collapse and aggregation of neighboring side chains to form a chain of “protomicelles,” followed by (2) a slow intramolecular aggregation of protomicelles. Fast collapse dominates for molecules with relatively longer side chains due to relatively higher probabilities of initial contacts between side‐chain monomers in different side chains, while slow intramolecular aggregation dominates for molecules with relatively shorter side chains.     

Monte Carlo simulation of DNA electrophoresis

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.     

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     

Microphase Separation within a Comb Copolymer with Attractive Side Chains: A Computer Simulation Study

Computer simulation modelling of a flexible comb copolymer with attractive interactions between the monomer units of the side chains is performed. The conditions for the coil‐globule transition, induced by the increase of attractive interaction, ε, between side chain monomer units, are analysed for different values of the number of monomer units in the backbone, N, in the side chains, n, and between successive grafting points, m. It is shown that the coil‐globule transition of such a copolymer corresponds to a first‐order phase transition. The energy of attraction (ε) required for the realisation of the coil‐globule transition decreases with increasing n and decreasing m. The coil‐globule transition is accompanied by significant aggregation of side chain units. The resulting globule has a complex structure. In the case of a relatively short backbone (small value of N), the globule consists of a spherical core formed by side chains and an enveloping shell formed by the monomer units of the backbone. In the case of long copolymers (large value of N), the side chains form several spherical micelles while the backbone is wrapped on the surfaces of these micelles and between them.     

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