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.     

Globular structures of a helix-coil copolymer: self-consistent treatment

A self-consistent-field theory was developed in the grand canonical ensemble formulation to study transitions in a helix-coil multiblock globule. Helical and coil parts are treated as stiff rods and self-avoiding walks of variable lengths correspondingly. The resulting field theory takes, in addition to the conventional Zimm-Bragg, [J. Chem. Phys. 31, 526 (1959)] parameters, also three-dimensional interaction terms into account. The appropriate differential equations which determine the self-consistent fields were solved numerically with finite element method. Three different phase states are found: open chain, amorphous globule, and nematic liquid-crystalline (LC) globule. The LC-globule formation is driven by the interplay between the hydrophobic helical segment attraction and the anisotropic globule surface energy of an entropic nature. The full phase diagram of the helix-coil copolymer was calculated and thoroughly discussed. The suggested theory shows a clear interplay between secondary and tertiary structures in globular homopolypeptides.     

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.     

Conditions of formation of liquid crystals from biopolymer solutions

Using the representation of a completely stiff macromolecule as a long rigid rod and the representation of a semiflexible macromolecule as a chain of freely rotating connected effective rigid rods, the conditions of formation of the liquid-crystalline phase in the solutions of such macromolecules are obtained and the diagram of states for the corresponding phase transitions in the variables temperature-volume fraction of polymer in the solution is constructed.     

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.     

Simulation study on the coil‐globule transition of adsorbed polymers

Coil‐globule transition of adsorbed polymers on attractive surface is simulated by using dynamic Monte Carlo simulation. The effect of surface attraction strength E_PS and intrachain attraction strength E_PP on polymer phases is investigated. The coil‐globule transition point is dependent on E_PS, while the globule conformation is dependent on both E_PS and E_PP. At small E_PS, the conformation of adsorbed polymer is three‐dimensional layer structure. While at large E_PS, the conformation of adsorbed polymer is roughly two‐dimensional (2D) at E_PP = 0, and we observe a 2D coil‐globule transition at E*_PP and a layer‐forming transition from 2D conformation to three‐dimensional layer structure at E*_PP,L > E*_PP. The layer‐forming transition point E*_PP,L increases with E_PS as E*_PP,L = E_PS ? 1.4. In addition, we find that the adsorption suppresses the coil‐globule transition, i.e., the coil‐globule transition point E*_PP increases with the increase in E_PS. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2359–2367     

Coil-globule transition: Self-assembly of a single polymer chain

The coil collapse problem is of interest not only because it represents the simplest model of protein folding, but also because of its fundamental importance as related to polymer nanostructures and fractionation. It is extremely difficult to observe the coil-to-globule transition experimentally because at finite concentrations in a poor solvent, the macromolecules tend to aggregate due to phase separation when the collapsed state is being achieved. In the mid-1980s, two-stage kinetics of a single-chain collapse was proposed theoretically.^1,2 The first successful experimental observation of a two-stage coil-to-globule transition was achieved by quenching a dilute solution of polystyrene (PS) in cyclohexane.³ By using a thinnest capillary tube cell with a wall thickness of 0.01 mm and a diameter of 5 mm for dynamic light scattering, two relaxation times, τ_crum for the crumpled globule state and τ_eq for the compact globule state, were determined⁴ for the first time. The relaxation times were much slower than expected. From the size of the crumpled globule and that of the compact globule and by assuming the intraglobular density to be uniform, the volume fraction of the PS chain in the crumpled globule state, ϕ_crum, and that in the compact globule state, ϕ_comp, can be estimated, with ϕ_crum = 0.02 and ϕ_comp ∼ 0.24-0.4 at 28°C for polystyrene in cyclohexane. The results imply that a single-chain globule contains a large amount of solvent. It should also be noted that ϕ_comp is temperature dependent, i.e., one would have to go to hypothetically low temperatures in order to squeeze out all the solvent (cyclohexane) in the compact PS globule. The single-chain coil collapse state could be achieved under equilibrium conditions by using a high molecular weight, M_w ∼ 1.08 × 10⁷ g/mol; M_w/M_n < 1.06) poly(N-isopropylacrylamide) (PNIPAM) in water,<⁵ even though the ten million molecular weight for PNIPAM was substantially lower than that for polystyrene (M_w ∼ 50 × 10⁶ g/mole).⁶ Under equilibrium conditions, it was feasible to determine both the hydrodynamic radius R_h and the radius of gyration R_g. The ratio of R_g/R_h changed from 1.45 to 0.77, clearly demonstrating the transition from the theta coil state to the compact globule state. At the maximum value of the scaled expansion factor α_s³ |τ| M_w^1/2, R_g/R_h = 1.33 where α_s = R_g/R_g (θ) and τ = |T-θ| / θ with θ being the theta temperature. In the compact globule, R_g/R_h was of the order of 0.7, implying that the PNIPAM compact globule in water still contained ∼80% water, of the same order of magnitude as the PS compact globule in cyclohexane at 7° below its theta temperature (35°C).     

Study of Phase Separation of Poly(N-isopropylacrylamide-co-styrene) Aqueous Solutions with Rayleigh Scattering Technique

A thermally sensitive copolymer, poly(N‐isopropylacrylamide‐co‐styrene) [P(NIPAM‐co‐St)] (M_n?9.5×10⁵ g/mol and M_w/M_n?1.51) was synthesized by soap‐free emulsion polymerization. The phase separation of the copolymer in water was investigated by Rayleigh scattering (RS) technique. The RS spectra revealed the transition of molecular conformation and the aggregation of molecular chains in the course of phase separation. The coil‐to‐globule and globule‐to‐coil transitions of P(NIPAM‐co‐St) chains were found in one heating‐and‐cooling cycle. By means of Avrami formula, apparent activation energy of phase separation of P(NIPAM‐co‐St) aqueous solutions was estimated. Moreover, a model was proposed to describe the phase separation process.     

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     

Adsorption of Semiflexible Chains on Nanostriped Surfaces: Monte Carlo Simulations

Monte Carlo simulations were carried out to investigate the adsorption of semiflexible chains from a semidilute solution to substrates with periodic stripes of width w. The chains are made of fused N = 10 monomers of diameter σ interacting with each other through excluded volume interactions and with the stripes via a square‐well potential of depth ε and width σ. The surface coverage was found to increase upon increasing the chain stiffness and decreases on increasing the width of the stripes. At small w, more flexible chains are adsorbed than stiff chains. Analysis of the radius of gyration for the chains showed that when w < 8σ, the component along the stripe direction is significantly larger than the others. Orientational order parameter reveals that, for small w, chains have preference to align along the stripe direction.

     

Adsorption Transition of a Polymer Chain at a Weakly Attractive Surface: Monte Carlo Simulation of Off‐Lattice Models

A bead‐spring model of a polymer chain with one end attached to a wall is studied by Monte Carlo simulations for chain lengths 16 ≤ N ≤ 256. Two types of adsorption potentials, 9‐3 and 10‐4 Lennard‐Jones (LJ) potentials, between the effective monomers and the wall are assumed. For both cases the adsorption transition where the chain changes its asymptotic statistical properties from a three‐dimensional to a two‐dimensional configuration is located using a scaling analysis. It is shown that the crossover exponent φ = 0.50 ± 0.02 is the same for both LJ potentials. This value is compatible with recent theoretical predictions and simulation results for lattice models with short‐range wall potentials. The results of our study support the expectation that the exponents describing the adsorption transition are universal, i.e., they are not influenced by the precise form and the long‐range character of the adsorption potentials used. The technical aspects of the simulations (which use configurational bias methods as well as histogram re‐weighting) are also carefully discussed.

Snapshot pictures of a bead‐spring model of a polymer chain with N = 256 beads with one end anchored on the surface: (a)“mushroom configuration”, (b) ε_a ≈ ε_w at the adsorption transition, and (c)“pancake configuration” of a strongly adsorbed chain.     

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     

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...     

Molecular Simulation of the Adsorption of Rod/Coil Blends on Nano‐Patterned Surfaces

The adsorption of rod/coil blends onto patterned surfaces with periodic stripes of width w was simulated using Monte‐Carlo methods. The rods and the coils were taken to be fused monomers of diameter σ, interacting with the stripes by a square‐well potential of depth ε and width σ. When the interaction was through excluded‐volume interactions only, we observed segregation of the components in the adsorbed layer. The adsorbed rods are strongly aligned along the stripe for w = σ, but lose their orientational order for larger w. When a repulsive interaction between the rods and the coils was introduced, an increase in the surface coverage of the rods with better recognition of the stripes was observed.

     

Statistics of stiff polymer chains near an adsorbing surface

The exact solution of the problem of adsorption of a long ideal polymer chain with variable degree of stiffness on a plane surface is presented. It is shown that the adsorption of stiff polymer chains is a second-order phase transition; in the adsorbed state “train” (i.e. adsorbed) sections are relatively longer and loop sections relatively shorter than for flexible chains. This effect is very pronounced: already for moderately stiff chains the number of Kuhn segment lengths in one “train” section at the temperature T = T_cr/2 (T_cr is the critical temperature for adsorption transition) can reach several thousands, and deviation from the surface occurs only in the form of small “hairpins”. The maximum length of the chain, which at the given conditions would flatten completely on the surface, is estimated.     

Dynamics of Adsorbed Star‐Branched Polymer Chains: A Computer Simulation Study

The simple cubic‐lattice model of polymer chains was used to study the dynamic properties of adsorbed, branched polymers. The model star‐branched chains consisted of f = 3 arms of equal lengths. The chain was modeled with excluded volume, that is, in good solvent conditions. The only interaction assumed was a contact potential between polymer segments and an impenetrable surface. This potential was varied to cover both weak and strong adsorption regimes. The classical Metropolis sampling algorithm was used for models of star‐branched polymers in order to calculate the dynamic properties of adsorbed chains. It was shown that long‐time dynamics (diffusion constant) and short‐time dynamics (the longest relaxation time) were different for weak and strong adsorption. The diffusion of weakly adsorbed chains was found to be qualitatively the same as for free nonadsorbed chains, whereas strongly adsorbed chains behaved like two‐dimensional polymers. The time‐dependent properties of structural elements such as tails, loops, and trains were also determined.

The mean lifetimes of tails, loops, and trains versus the bead number for the chain with N = 799 beads for the case of the weak adsorption ε_a = −0.3.     

Dynamic light scattering studies of atactic and syndiotactic poly(methyl methacrylate)s in dilute theta solution

The present article considers the coil‐to‐globule transition behavior of atactic and syndiotactic poly(methyl methacrylates), (PMMA) in their theta solvent, n‐butyl chloride (nBuCl). Changes in Rh in these polymers with temperature in dilute theta solutions were investigated by dynamic light scattering. The hydrodynamic size of atactic PMMA (a‐PMMA‐1) in nBuCl (M_w: 2.55 × 10⁶ g/mol) decreases to 61% of that in the unperturbed state at 13.0°C. Atactic PMMA (a‐PMMA‐2) with higher molecular weight (M_w: 3.3 × 10⁶ g/mol) shows higher contraction in the same theta solvent (α_η = R_h(T)/R_h (θ) = 0.44) at a lower temperature, 7.25°C. Although syndiotactic PMMA (s‐PMMA) has lower molecular weight than that of atactic samples (M_w: 1.2 × 10⁶), a comparable chain collapse was observed (α_η = 0.63) at 9.0°C. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2253–2260, 1999     

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.     

Well-defined side-chain liquid-crystalline polysiloxanes

A route to well-defined side-chain liquid-crystalline polysiloxanes (ratio of weight-to number-average molar masses M̄_w/M̄_n < 1.2 is reported. Anionic ring-opening polymerization of pentamethylvinylcyclotrisiloxane yielded a poly(dimethylsiloxane-co-methylvinylsiloxane) backbone. A flexible disiloxane spacer was used to connect 4-(ω-alkenyloxy)-4′-cyanobiphenyl mesogenic molecules to the vinyl groups which belong to the backbone, leading to a side-chain liquid-crystalline polysiloxane (SCLCP) which has its mesogens distributed regularly along the main chain. Preliminary measurements indicate an electro-optic switching time τ_s = 1 min at 20°C and 7 s at 32°C (dc, 5 V/μm)).     

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