Universal properties of a single polymer chain in slit: Scaling versus molecular dynamics simulations

We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyze their range of validity by means of comprehensive molecular dynamics simulations using a coarse-grained bead-spring model of a flexible polymer chain. The normal and parallel components of the average end-to-end distance, mean radius of gyration and their distributions, the density profile, the force exerted on the slit walls, and the local bond orientation characteristics are obtained in slits of width D=4/10 (in units of the bead diameter) and for chain lengths N=50/300. We demonstrate that a wide range of static chain properties in normal direction can be described quantitatively by analytic model-independent expressions in perfect agreement with computer experiment. In particular, the observed profile of confinement-induced bond orientation is shown to closely match theory predictions. The anisotropy of confinement is found to be manifested most dramatically in the dynamic behavior of the polymer chain. We examine the relation between characteristic times for translational diffusion and lateral relaxation. It is demonstrated that the scaling predictions for lateral and normal relaxation times are in good agreement with our observations. A novel feature is the observed coupling of normal and lateral modes with two vastly different relaxation times. We show that the impact of grafting on lateral relaxation is equivalent to doubling the chain length.     

The dimensions of a polymer chain at the coil-to-globule transition

Simple models of the star-branched and linear polymers were studied by means of a Monte Carlo method. The chains were confined on a simple cubic lattice. Star-branched polymers consisted of f=3 arms of equal length. The total number of beads in both types of polymers was varied from N=49 to N=799. The simulations were performed in different solvent qualities—from a good solvent to a collapsed globule regime. The static properties of the chains under consideration were measured as functions of the temperature of the system. It appeared that the ratio of the radius of gyration to the mean end-to-end vector is very sensitive to solvent quality. It shows that the coil-to-globule transition is a complicated phenomenon. The possible explanation of the phenomenon is discussed.     

Stepwise growth of a single polymer chain

By monitoring the modulation of an ionic current passing through a nanoreactor formed from a protein pore, the step-by-step growth of an individual polymer chain was monitored. The observation of polymer growth at the single-molecule level will be useful for studying the kinetics of chain growth or the movement of polymers under confinement. It might also be used to synthesize "molecular fishing lines" in situ, for applications in stochastic sensing.     

Molecular-dynamics simulations of dimethylsulfoxide-methanol mixtures

We present molecular-dynamics (MD) computer simulation results for the local structures, hydrogen (H)-bond distribution, and dynamical properties of methanol (MeOH) and dimethylsulfoxide (DMSO) binary mixtures at ambient conditions over the entire composition range. The simulated heat of mixing and site-site pair distribution functions suggest that the intermolecular structures of the pure liquids are not markedly altered upon mixing. Nevertheless, H-bonding statistics show that aggregates of the type 1DMSO:1MeOH are formed and represent the predominant form of molecular association in these mixtures. Only a small fraction (10%) of DMSO molecules in MeOH-rich mixtures (85% in mole) forms H-bonding trimers of type 1DMSO:2MeOH. No evidence of other types of interspecies association is found. The self-diffusion coefficient for DMSO (MeOH) increases (decreases) upon mixing. The characteristic reorientation time tau1 of both species increases in the mixture, but the composition dependence is weak. The frequency spectrum of MeOH reorientational time-correlation function shows significant redshifts of the principal librational band as DMSO is added to the system, whereas the librational band of DMSO shows small alterations upon mixing. Our results are discussed in the light of previous simulation analyses for a similar system, DMSO-water mixtures, and compared with available experimental results.     

Molecular-dynamics study of chain reptation in a gel

Specific features of the translational dynamics of free chains in a gel in which the occurrence of a fixed tube of the reptation model results from the presence of crosslinked chains and the molar concentrations of mobile chains are 5, 10, 20, and 30% are studied. The gels are prepared from a thermodynamically equilibrium melt composed of 200 chains, each of which contains 40 Lennard-Jones particles, via the spatial freezing of the first and, then, every fourth particle of a required number of chains. The known crosslink density makes it possible to estimate the diameter of the tube in which the free chains move; for the considered concentrations, the chains are isolated from each other most of the time. In addition to commonly used diffusion displacements of the center of mass of the chain and its middle units, the components of the displacement of the middle units normal to and along the tube axis are studied. The time dependence of the ratio of these two components passes through a deep minimum, which has never been observed before. This phenomenon suggests that the motion of free chains in gels has a reptation pattern.     

Molecular dynamics simulations of polymer transport in nanocomposites

Molecular dynamics simulations on the Kremer-Grest bead-spring model of polymer melts are used to study the effect of spherical nanoparticles on chain diffusion. We find that chain diffusivity is enhanced relative to its bulk value when polymer-particle interactions are repulsive and is reduced when polymer-particle interactions are strongly attractive. In both cases chain diffusivity assumes its bulk value when the chain center of mass is about one radius of gyration R(g) away from the particle surface. This behavior echoes the behavior of polymer melts confined between two flat surfaces, except in the limit of severe confinement where the surface influence on polymer mobility is more pronounced for flat surfaces. A particularly interesting fact is that, even though chain motion is strongly speeded up in the presence of repulsive boundaries, this effect can be reversed by pinning one isolated monomer onto the surface. This result strongly stresses the importance of properly specifying boundary conditions when the near surface dynamics of chains are studied.     

Molecular-dynamics simulations of methane hydrate dissociation

Nonequilibrium molecular-dynamics simulations have been carried out at 276.65 K and 68 bar for the dissolution of spherical methane hydrate crystallites surrounded by a liquid phase. The liquid was composed of pure water or a water-methane mixture ranging in methane composition from 50% to 100% of the corresponding theoretical maximum for the hydrate and ranged in size from about 1600 to 2200 water molecules. Four different crystallites ranging in size from 115 to 230 water molecules were used in the two-phase systems; the nanocrystals were either empty or had a methane occupation from 80% to 100% of the theoretical maximum. The crystal-liquid systems were prepared in two distinct ways, involving constrained melting of a bulk hydrate system or implantation of the crystallite into a separate liquid phase. The breakup rates were very similar for the four different crystal sizes investigated. The method of system preparation was not found to affect the eventual dissociation rates, despite a lag time of approximately 70 ps associated with relaxation of the liquid interfacial layer in the constrained melting approach. The dissolution rates were not affected substantially by methane occupation of the hydrate phase in the 80%-100% range. In contrast, empty hydrate clusters were found to break up significantly more quickly. Our simulations indicate that the diffusion of methane molecules to the surrounding liquid layer from the crystal surface appears to be the rate-controlling step in hydrate breakup. Increasing the size of the liquid phase was found to reduce the initial delay in breakup. We have compared breakup rates computed using different long-range electrostatic methods. Use of the Ewald, minimum image, and spherical cut-off techniques led to more rapid dissociation relative to the Lekner method.     

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory‐Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small‐angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb³) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self‐consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non‐additive monomer shapes, one has a large positive chain‐length‐independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10^–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non‐entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End‐functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off‐lattice simulations and analytical theories are briefly discussed.     

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).     

The properties of a single polymer chain in solvent confined in a slit: A molecular dynamics simulation

A single polymer chain in solvent confined in a slit formed by two parallel plates is studied by using molecular dynamics simulation method. The square radii of gyration and diffusion behaviors of polymers are greatly affected by the distance between the two plates, but they do not follow the same way. The chain size decays drastically with increasing h (h is the distance between two plates), until a basin occurs, and a universal h/〈R _g〉₀ dependence for polymer chains with different degrees of polymerization can be obtained. While, for the chain’s diffusion coefficient, it decays monotonously and there is no such basin-like behavior. Furthermore, we studied the radial distribution function of confined polymer chains to explain the reason why there is a difference for the decay behaviors between dynamic properties and static properties. Besides, we also give the degree of confinement dependence of the static scaling exponent for a single polymer chain. Our work provides an efficient way to estimate the dynamics and static properties of confined polymer chains, and also helps us to understand the behavior of polymer chains under confinement.     

Morphological variation in a toroid generated from a single polymer chain

A single semiflexible polymer chain folds into a toroidal object under poor solvent conditions. In this study, we examined the morphological change in such a toroidal state as a function of the cross-sectional area and stiffness of the chain together with the surface energy, which characterizes the segmental interaction parameter. Changes in the thickness and outer/inner radius on a toroid are interpreted in terms of these parameters. Our theoretical expectation corresponds to the actual morphological changes in a single giant DNA molecule as observed by electron microscopy.     

Melt‐state polymer chain dimensions as a function of temperature

The unperturbed chain dimensions (〈R²〉_o/M) of cis/trans‐1,4‐polyisoprene, a near‐atactic poly(methyl methacrylate), and atactic polyolefins were measured as a function of temperature in the melt state via small‐angle neutron scattering (SANS). The polyolefinic materials were derived from polydienes or polystyrene via hydrogenation or deuteration and represent structures not encountered commercially. The parent polymers were prepared via lithium‐based anionic polymerizations in cyclohexane with, in some cases, a polymer microstructure modifier present. The polyolefins retained the near‐monodisperse molecular weight distributions exhibited by the precursor materials. The melt SANS‐based chain dimension data allowed the evaluation of the temperature coefficients [dln 〈R²〉_o/dT(κ)] for these polymers. The evaluated polymers obeyed the packing length (p)‐based expressions of the plateau modulus, G = kT/np³ (MPa), and the entanglement molecular weight, M_e = ρN_anp³ (g mol^?1), where n_t denotes the number (～21) of entanglement strands in a cube with the dimensions of the reptation tube diameter (d_t) and ρ is the chain density. The product np³ is the displaced volume (V_e) of an entanglement that is also expressible as pd or kT/G. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1768–1776, 2002     

Computer simulations of polymer chain structure and dynamics on a hypersphere in four-space

There is a rapidly growing interest in performing computer simulations in a closed space, avoiding periodic boundary conditions. To extend the range of potential systems to include also macromolecules, we describe an algorithm for computer simulations of polymer chain molecules on S3, a hypersphere in four dimensions. In particular, we show how to generate initial conformations with a bond angle distribution given by the persistence length of the chain and how to calculate the bending forces for a molecule moving on S3. Furthermore, we discuss how to describe the shape of a macromolecule on S3, by deriving the radius of gyration tensor in this non-Euclidean space. The results from both Monte Carlo and Brownian dynamics simulations in the infinite dilution limit show that the results on S3 and in R3 coincide, both with respect to the size and shape as well as for the diffusion coefficient. All data on S3 can also be described by master curves by suitable scaling by the corresponding values in R3. We thus show how to extend the use of spherical boundary conditions, which are most effective for calculating electrostatic forces, to polymer chain molecules, making it possible to perform simulations on S3 also for polyelectrolyte systems.     

Influence of molecular topology on the static and dynamic properties of single polymer chain in solution

The influence of molecular topology on the structural and dynamic properties of polymer chain in solution with ring structure, three-arm branched structure, and linear structure are studied by molecular dynamics simulation. At the same degree of polymerization (N), the ring-shaped chain possesses the smallest size and largest diffusion coefficient. With increasing N, the difference of the radii of gyration between the three types of polymer chains increases, whereas the difference of the diffusion coefficients among them decreases. However, the influence of the molecular topology on the static and the dynamic scaling exponents is small. The static scaling exponents decrease slightly, and the dynamic scaling exponents increase slightly, when the topology of the polymer chain is changed from linear to ring-shaped or three-arm branched architecture. The dynamics of these three types of polymer chain in solution is Zimm-like according to the dynamic scaling exponents and the dynamic structure factors.     

Variation of polymer chain dimensions with temperature below the theta point

The temperature dependence of the intrinsic viscosity [η] for the system polystyrene-cyclohexane in the interval ?20 < (T ? ψ) ≤ 0 near the ideal temperature ψ has been investigated. The observed diminution in size of the molecular coil with decreasing temperature is attributable to attractive net polymer-solvent interactions, denoted by negative values for the excluded volume parameter z. The data thus comprise an interesting selection for comparison with the predictions of various excluded volume theories. Among the approximate, closed-form expressions the functional relationship of Flory (x⁵ ? α³ ～ z) appears to describe best the variation of [η] with temperature in the region examined. The behavior of the Huggins constant k′ derived from the intrinsic viscosity plots is also examined, in accordance with the Peterson-Fixman model, suitably extended to the temperature region below ψ.     

Monte Carlo simulations of single crystals from polymer solutions

A novel "anisotropic aggregation" model is proposed to simulate nucleation and growth of polymer single crystals as functions of temperature and polymer concentration in dilute solutions. Prefolded chains in a dilute solution are assumed to aggregate at a seed nucleus with an anisotropic interaction by a reversible adsorption/desorption mechanism, with temperature, concentration, and seed size being the control variables. The Monte Carlo results of this model resolve the long-standing dilemma regarding the kinetic and thermal roughenings, by producing a rough-flat-rough transition in the crystal morphology with increasing temperature. It is found that the crystal growth rate varies nonlinearly with temperature and concentration without any marked transitions among any regimes of polymer crystallization kinetics. The induction time increases with decreasing the seed nucleus size, increasing temperature, or decreasing concentration. The apparent critical nucleus size is found to increase exponentially with increasing temperature or decreasing concentration, leading to a critical nucleus diagram composed in the temperature-concentration plane with three regions of different nucleation barriers: no growth, nucleation and growth, and spontaneous growth. Melting temperatures as functions of the crystal size, heating rate, and concentration are also reported. The present model, falling in the same category of small molecular crystallization with anisotropic interactions, captures most of the phenomenology of polymer crystallization in dilute solutions.     

Doping properties of polydithienylmethine: a study on the correlation between polymer chain length, spectroscopy, and transport

(1S)-(+)-10-Camphorsulfonic acid-doped polydithienylmethine was prepared through an acid-catalyzed condensation reaction of alpha,alpha'-di-2-thienyl-(2,2'-bithiophene)-5,5'-dimethanol and was characterized by 1H NMR spectroscopy and size exclusion chromatography (SEC). The electronic and vibrational properties of the resulting polymer thin films vary with the loadings of the (1S)-(+)-10-camphorsulfonic acid. The dark conductivity and drift mobility, which is significantly high, of the polymer thin films were enhanced with increasing doping levels and reached maximum values of 8.0x10(-5) S.cm-1 and 3.5x10(-2) cm2.V-1.s-1, respectively, at a 7 mol % dopant loading. Higher doping levels (>7 mol %) result in nonuniform polymer thin films with degraded optical quality due to the formation of nanocrystalite and thus a decrease in conductivity and drift mobility was observed. The doped polydithienylmethine thin film also exhibited a photoconductivity response with an excitation at 457 nm and the highest photoconductivity (2x10(-4) S.cm-1) was again observed at the 7 mol % doping level. Spectroscopic investigation suggests that the enhanced transport properties can be attributed to polaronic species present. The electronic and vibrational changes which relate to such doping were characterized by electronic absorption spectroscopy, Raman spectroscopy, and FTIR spectroscopy. The changes in transport values can be directly related to the changes we see in our spectroscopic investigations.     

Self‐entanglement of a single polymer chain confined in a cubic box

We study the self‐entanglement of a single linear polymer chain with N monomers confined to a cubic box (L × L × L) using the bond‐fluctuation lattice model and primitive path analysis. We probe chains with N between 30 and 750 and vary the degree of confinement L/R_g0 between 0.4 and 12, where R_g0 is the radius of gyration of an unconfined polymer. We find that the conformational properties R_g/R_g0 and L_p/R_g0, where L_p is the average primitive path length, collapse onto a single master curve as a function of the degree of confinement. In the strongly confined regime, L/R_g0 < 1, we find that R_g/R_g0 ～ (L/R_g0)^0.8 and (L_p/R_g0) ～ (L/R_g0)^?2. We verify that the simulation methodology used is quantitatively consistent with experimental data, and the Colby‐Rubinstein entanglement model for unconfined concentrated polymer solutions. The most significant difference between unconfined and confined systems is the variation of L_p with monomer density ?; L_p ～ ?^5/9, in the former, and L_p ～ ?^2/3, in the latter. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1283–1290     

Charge carrier transport properties in polymer liquid crystals containing oxadiazole and amine moieties in the same side chain

Steady-state and transient photocurrent measurements were carried out to study the charge carrier transport properties of polymer liquid crystal (LC) containing oxadiazole (OXD) and amine moieties in the same side chain. The steady-state photocurrent measurement with asymmetric electrodes of ITO and Al and a short penetration depth of the illumination light indicated that both electrons and holes can be transported in this film. The transient hole photocurrent observed by time-of-flight (TOF) experiments was dispersive at room temperature. The hole drift mobility significantly depended on temperature and electric field and was determined to be 6.1 x 10(-8) cm2/Vs at a field of 9.1 x 10(5) V/cm. According to the disorder formalism, the Gaussian width of the density of states was determined to be 170 meV for holes. Despite the indication of possible electron transport in this film, we could not determine the electron mobility by TOF experiments due to strong dispersive photocurrent. We discuss the present charge transport properties of the film in relation to a large dipole attributed to an electrical push-pull structure of p-dimethylaminophenyl-substitited OXD moiety in polymer LC and its electroluminescent properties.     

Contributions of short-range and excluded-volume interactions to unperturbed polymer chain dimensions

A Monte Carlo study is made of the mean-square radius of gyration for the freely rotating chain with such fictitious excluded-volume interactions that the Lennard-Jones 6-12 potentials at the Theta temperature act only between the fourth-through (3+Delta)th-neighbor beads (Delta > or = 1) along the chain. The behavior of the asymptotic value (/n)infinity of the ratio /n as a function of the number n of bonds in the chain in the limit of n --> infinity is examined as a function of Delta. It is shown that the approach of (/n)infinity to its value for the real unperturbed chain with Delta = infinity is so slow that the interactions between even up to about 100th-neighbor beads should be taken into account in order to reproduce nearly its dimension. The result implies that the unperturbed polymer chain dimension as experimentally observed at the Theta temperature depends not only on short-range interactions but also to a considerable extent on the long-range excluded-volume interactions, and that the asymptotic value Cinfinity of the characteristic ratio Cn for the rotational isomeric state model in the limit of n --> infinity, which is determined only by the very local conformational energy, cannot be directly compared with the corresponding experimental value.