Studies on the behavior of nanoconfined homopolymers with cyclic chain architecture

We have performed Monte Carlo simulations to study the effect of cyclic architecture on the behavior of homopolymer chains under several conditions of confinement. The collapse of the rings in two stages, a coil-to-globule and a liquidlike-to-solidlike transition, was observed even at extreme confinement. Both transitions were observed at lower temperatures than for linear chains of the same length, 2%-5% lower for unconfined systems, and 10%-15% lower for wall separations below three bond lengths due to the effect of confinement. When the plates separation approached the two-dimensional regime, the coil-to-globule transition shifted to lower temperatures. The inverse trend was observed when the chain length was increased. In the collapsed state, the average size and conformations of linear and cyclic molecules of same length were similar independently of confinement. At temperatures near the coil-to-globule transition, the radius of gyration of unconfined linear chains, [R(g)(2)](linear), became larger than for the cyclic chains, [R(g)(2)](cyclic), and this difference increased considerably with confinement. The radius of gyration ratio [R(g)(2)](linear)/[R(g)(2)](cyclic) in this region decreased rapidly. The decrease was more pronounced and occurred at lower temperatures for slit width confinements. At higher temperatures, in the coil state, the radius of gyration ratio became nearly constant for a given separation, and varied from 0.56 for unconfined systems to 0.47 when the chain was completely confined between the walls. This reduction was attributed to the higher increase in the average size of linear chains with confinement when compared with cyclic chains, due to architectural restrictions.     

聚乙烯单链松驰过程的分子模拟

利用分子模拟方法研究了不同链长聚乙烯单链折叠过程和相关的松弛和坍塌机理．发现在链长短于１０００ＣＨ２单元时,聚乙烯的链段主要通过整体塌缩机理进行折叠和取向;而链长超过１０００ＣＨ２单元时,可以明显地观察到局部取向团簇的形成,聚乙烯单链通过局部塌缩机理进行折叠和取向．通过对各阶段团簇数目,体系取向链段长度的表征,说明体系在模拟时间范围内表现了很强的松驰特性．     

Effect of solvent quality on the conformations of a model comb polymer

The effect of solvent quality on the equilibrium structure of a densely branched comb polymer is investigated based on the structure factor analyses by off-lattice Monte Carlo simulations. First, theta temperature (theta(infinity)) must be determined to identify the solvent condition. We locate the characteristic temperature theta(A)(N) at which the second virial coefficient vanishes and the transition temperature theta(R)(N) at which radius of gyration R(g) of the chain varies most rapidly with temperature, i.e., d(2)R(g)/dT(2)|(theta(R)) = 0. N represents the total number of monomers of a comb. As N --> infinity, theta(A) and theta(R) coincide to a point that is identified as the true theta temperature (theta(infinity)). The structure factors of the main chain, the side chain, and the whole polymer are calculated, respectively. It is found that at T = theta(infinity), the structural factors S(qR(g)) for the overall comb polymers match quite well with those of their Gaussian counterparts. When T< theta(infinity), the overall comb polymer assumes collapsed conformations, similar to a homogeneous sphere. However, the structure factor of the side chain indicates that it always remains in an expanded state regardless of the solvent condition. It is attributed to the strong interactions between side chains. The same effect leads to enhanced rigidity of the main chain in comparison to the linear chain, as clearly observed from the rescaled Kratky plot.     

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.     

Development of knotting during the collapse transition of polymers

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

Localization and freezing of a Gaussian chain in a quenched random potential

The Gaussian chain in a quenched random potential (which is characterized by the disorder strength Delta) is investigated in the d-dimensional space by the replicated variational method. The general expression for the free energy within so-called one-step-replica symmetry breaking (1-RSB) scenario has been systematically derived. We have shown that the replica symmetrical (RS) limit of this expression can describe the chain center-of-mass localization and collapse. The critical disorder when the chain becomes localized scales as Delta(c) approximately b(d)N(-2+d/2) (where b is the length of the Kuhn segment length and N is the chain length) whereas the chain gyration radius R(g) approximately b(b(d)/Delta)(1/(4-d)). The freezing of the internal degrees of freedom follows to the 1-RSB-scenario and is characterized by the beads localization length D(2). It was demonstrated that the solution for D(2) appears as a metastable state at Delta=Delta(A) and behaves similarly to the corresponding frozen states in heteropolymers or in p-spin random spherical model.     

DIMENSIONS OF ATACTIC POLY（α-METHYLSTYRENE） CHAINS WITH SIDE GROUPS

An improved configurational-confomational statistical method is developed and the mean-square radius of gyration for atactic poly(α-methylstyrene)(PαMS)chains is studied,in which the effect of large side groups is considered. The deduced formulas,based on the rotational isomer state theory,are used to investigate the configuration-dependent properties of the atactic polymer chain,and the statistical correlation of the unperturbed polymer chain dimension and structure parameters are calculated.For the fraction of meso dyads w_m=0.4,the dependence of the radius of gyration R_g and the intrinsic viscosity[η]on the molecule mass M are R_g=2.63×10~(-2) M~(0.50) nm and[η]=7.36×10~(-2) M~(0.497),respectively, which are in agreement with the previous experimental data for the PαMS samples.A small hump is detected in the curve of the characteristic ratio of the unperturbed mean-square radius of gyration versus the chain length for short PαMS chains.The R_g increases linearly with the temperature T,and the effects of the chain length and the tacticity on the temperature coefficient are remarkable.These are quite different from the results for PαMS chains not considering side groups or for the monosubstituted polystyrene chain.     

Polymer translocation through a nanopore: a two-dimensional Monte Carlo study

We investigate the problem of polymer translocation through a nanopore in the absence of an external driving force. To this end, we use the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. To overcome the entropic barrier without artificial restrictions, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau required for the polymer to completely exit the pore on either end. We find numerically that tau scales with the chain length N as tau approximately N(1+2nu), where nu is the Flory exponent. This is the same scaling as predicted for the translocation time of a polymer which passes through the nanopore in one direction only. We examine the interplay between the pore length L and the radius of gyration R(g). For LR(g), we find tau approximately N. In addition, we numerically find the scaling function describing crossover between short and long pores. We also show that tau has a minimum as a function of L for longer chains when the radius of gyration along the pore direction R( parallel) approximately L. Finally, we demonstrate that the stiffness of the polymer does not change the scaling behavior of translocation dynamics for single-segment dynamics.     

Electron bubbles in helium clusters. II. Probing superfluidity

In this paper we present calculations of electron tunneling times from the ground electronic state of excess electron bubbles in ((4)He)(N) clusters (N=6500-10(7), cluster radius R=41.5-478 A), where the equilibrium bubble radius varies in the range R(b)=13.5-17.0 A. For the bubble center located at a radial distance d from the cluster surface, the tunneling transition probability was expressed as A(0)phi(d,R)exp(-betad), where beta approximately 1 A(-1) is the exponential parameter, A(0) is the preexponential factor for the bubble located at the cluster center, and phi(d,R) is a correction factor which accounts for cluster curvature effects. Electron tunneling dynamics is grossly affected by the distinct mode of motion of the electron bubble in the image potential within the cluster, which is dissipative (i.e., tau(D)tau(0)) in superfluid ((4)He)(N) clusters, where tau(D) is the bubble motional damping time (tau(D) approximately 4 x 10(-12) s for normal fluid clusters and tau(D) approximately 10 s for superfluid clusters), while tau(0) approximately 10(-9)-10(-10) s is the bubble oscillatory time. Exceedingly long tunneling lifetimes, which cannot be experimentally observed, are manifested from bubbles damped to the center of the normal fluid cluster, while for superfluid clusters electron tunneling occurs from bubbles located in the vicinity of the initial distance d near the cluster boundary. Model calculations of the cluster size dependence of the electron tunneling time (for a fixed value of d=38-39 A), with lifetimes increasing in the range of 10(-3)-0.3 s for N=10(4)-10(7), account well for the experimental data [M. Farnik and J. P. Toennies, J. Chem. Phys. 118, 4176 (2003)], manifesting cluster curvature effects on electron tunneling dynamics. The minimal cluster size for the dynamic stability of the bubble was estimated to be N=3800, which represents the threshold cluster size for which the excess electron bubble in ((4)He)(N) (-) clusters is amenable to experimental observation.     

Mean-square radius of gyration of polymer chains

The calculations of the mean-square radius of gyration for more than thirty sorts of polymer chains are reviewed on the basis of a unified approach. A general expression of the mean-square radius of gyration was developed for polymer chains with side groups and/or heteroatoms. It consists of two parts. The first part is the mean-square radius of gyration of a model chain, in which every side group, R, was considered to be located in the centroid of the substituent flanking the related skeletal atom, and the second one is the total contribution of the square radius of gyration of every substituent around its centroid. Numerical calculations showed that the logarithmic relationship between the mean-square radius of gyration and the degree of polymerization becomes linear when x is greater than 100, and the dependence of the mean-square radius of gyration on the molecular weight can be expressed by the general formula 〈S²〉 = aM^b, which was supported by a number of experimental measurements. A comparison of our expression for the mean-square radius of gyration with that reported by Flory was made. The difference is obvious in the range of lower molecular weight, and gradually declines with increasing degree of polymerization.     

Monte Carlo Simulation of Coil-to-Globule Transition of Compact Polymer Chains: Role of Monomer Interacting

Coil-to-globule transitions are fundamental problems existing in polymer science for several decades; however, some features are still unclear, such as the effect of chain monomer interaction. Herein, we use Monte Carlo simulation to study the coil-to-globule transition of simple compact polymer chains. We first consider the finite-size effects for a given monomer interaction, where the short chain exhibits a one-step collapse while long chains demonstrate a two-step collapse, indicated by the specific heat. More interestingly, with the decrease of chain monomer interaction, the critical temperatures marked by the peaks of heat capacity shift to low values. A closer examination from the energy, mean-squared radius of gyration and shape factor also suggests the lower temperature of coil-to-globule transition.     

The size of RNA as an ideal branched polymer

Because of the branching arising from partial self-complementarity, long single-stranded (ss) RNA molecules are significantly more compact than linear arrangements (e.g., denatured states) of the same sequence of monomers. To elucidate the dependence of compactness on the nature and extent of branching, we represent ssRNA secondary structures as tree graphs which we treat as ideal branched polymers, and use a theorem of Kramers for evaluating their root-mean-square radius of gyration, ?R(g)=√R(g)(2). We consider two sets of sequences--random and viral--with nucleotide sequence lengths (N) ranging from 100 to 10,000. The RNAs of icosahedral viruses are shown to be more compact (i.e., to have smaller ?R(g)) than the random RNAs. For the random sequences we find that ?R(g) varies as N(1/3). These results are contrasted with the scaling of ?R(g) for ideal randomly branched polymers (N(1/4)), and with that from recent modeling of (relatively short, N ≤ 161) RNA tertiary structures (N(2/5)).     

Chaperone-assisted translocation of a polymer through a nanopore

Using Langevin dynamics simulations, we investigate the dynamics of chaperone-assisted translocation of a flexible polymer through a nanopore. We find that increasing the binding energy ε between the chaperone and the chain and the chaperone concentration N(c) can greatly improve the translocation probability. Particularly, with increasing the chaperone concentration a maximum translocation probability is observed for weak binding. For a fixed chaperone concentration, the histogram of translocation time τ has a transition from a long-tailed distribution to a gaussian distribution with increasing ε. τ rapidly decreases and then almost saturates with increasing binding energy for a short chain; however, it has a minimum for longer chains at a lower chaperone concentration. We also show that τ has a minimum as a function of the chaperone concentration. For different ε, a nonuniversal dependence of τ on the chain length N is also observed. These results can be interpreted by characteristic entropic effects for flexible polymers induced by either the crowding effect from a high chaperone concentration or the intersegmental binding for the high binding energy.     

Role of methyl in the phase transition of poly(N-isopropylmethacrylamide)

Poly(N-isopropylmethacrylamide) (PiPMA) has one more methyl group at each monomeric unit than poly(N-isopropylacrylamide) (PiPA). By use of laser light scattering (LLS) and ultrasensitive differential scanning calorimetry (US-DSC) we have investigated the association and dissociation of PiPMA chains in water. LLS studies reveal that PiPMA chains form larger aggregates at a temperature above its lower critical solution temperature (LCST) as the chain molar mass (Mw) decreases. In comparison with PiPA aggregates, PiPMA aggregates show a larger ratio of average radius of gyration to average hydrodynamic radius (/), indicating that PiPMA aggregates are looser. US-DSC studies show PiPMA chains have smaller enthalpy change (DeltaH) and entropy change (DeltaS) than PiPA chains during the phase transition, indicating that PiPMA chains have smaller conformational change. Our experiments demonstrate that the additional methyl groups in PiPMA chains restrain the intrachain collapse and interchain association, leading the phase transition to occur at a higher temperature.     

The phase behavior of polyethylene ring chains

The equilibrium properties of an isolated polyethylene ring chain are studied by using molecular dynamics (MD) simulations. The results of an 80-bond linear chain are also presented, which are in agreement with previous studies of square-well chains and Lennard-Jones (LJ) homopolymers. Mainly, we focus on the collapse of polyethylene ring chains. At high temperatures, a fully oblate structure is observed for the ring chains with different chain lengths. For such an oblate structure, a shape factor of delta(*)=0.25 and a rodlike scaling relation between the radius of gyration and chain lengths could be deduced easily in theory, and the same results are obtained by our MD simulations. Such an oblate structure can be obtained by Monte Carlo simulation only for sufficient stiff ring chains. When the temperature decreases, an internal energy barrier is observed. This induces a strong peak in the heat capacity, denoting a gas-liquid-like transition. This energy barrier comes mainly from the local monomer-monomer interactions, i.e., the bond-stretching, the bond-bending, and the torsion potentials. A low temperature peak is also observed in the same heat capacity curve, representing a liquid-solid-like transition. These numerical simulation results support a two-stage collapse of polyethylene ring chains; however, the nature should be different from the square-well and LJ ring chains.     

Effect of branching and confinement on star-branched polymeric systems

The effect of confinement, number of branches (functionality), and size of the molecules on various properties as a function of temperature of star-branched polymers confined between two walls was studied using Monte Carlo simulations with the parallel tempering technique. The coil-to-globule transition and the liquidlike to solidlike transition, similar to those observed for linear chains, were characterized in all systems by changes in the heat capacity, internal energy, and radius of gyration. The transitions were also characterized by the most probable isomeric structure at a given temperature. The radius of gyration of the star polymers was smaller than the values of linear chains when the number of arms f increased. For star chains with more than f=5 arms the values of the radius of gyration, and therefore the size of the molecules, were similar for every condition of confinement studied, especially at higher temperatures. As confinement was increased, the difference in the radius of gyration of linear chains and star polymers became even larger. The coil-to-globule transition temperatures shifted to higher temperatures as the size of the chains and the number of arms in a molecule were increased. Effects of confinement were higher on the properties of the system at the smallest separations (less than twice the monomer diameter), where the coil-to-globule transition shifted to lower temperatures. The liquidlike to solidlike transition was present at almost the same temperature for different conditions of confinement, chain size, and number of arms. The behavior of the systems for separations between the walls greater than five bead diameters was similar to the behavior in the unconfined case. Hence, no considerable effect of confinement was found above this separation.     

Scale-free center-of-mass displacement correlations in polymer melts without topological constraints and momentum conservation: a bond-fluctuation model study

By Monte Carlo simulations of a variant of the bond-fluctuation model without topological constraints, we examine the center-of-mass (COM) dynamics of polymer melts in d = 3 dimensions. Our analysis focuses on the COM displacement correlation function C(N)(t)≈?(t) (2)h(N)(t)/2, measuring the curvature of the COM mean-square displacement h(N)(t). We demonstrate that C(N)(t) ≈ -(R(N)∕T(N))(2)(ρ?/ρ)?f(x = t/T(N)) with N being the chain length (16 ≤ N ≤ 8192), R(N) ～ N(1/2) is the typical chain size, T(N) ～ N(2) is the longest chain relaxation time, ρ is the monomer density, ρ(*)≈N/R(N) (d) is the self-density, and f(x) is a universal function decaying asymptotically as f(x) ～ x(-ω) with ω = (d + 2) × α, where α = 1/4 for x ? 1 and α = 1/2 for x ? 1. We argue that the algebraic decay NC(N)(t) ～ -t(-5/4) for t ? T(N) results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains.     

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength E, length of the chain N, and length of the pore L on forced translocation. As our main result, we find a crossover scaling for the translocation time tau with the chain length from tau approximately N2nu for relatively short polymers to tau approximately N1+nu for longer chains, where nu is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains v approximately N-nu, which crosses over to v approximately N(-1) for long polymers. The reason for this is that with increasing N there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which R parallel, the radius of gyration Rg along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large N, however, the asymptotic scaling tau approximately N1+nu is recovered. In this regime, tau is almost independent of L. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for R parallel approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.     

Effect of temperature and surfactant type on the stability and aggregation behavior of styrene-acrylate copolymer colloids

The colloidal stability, aggregation kinetics, and cluster structure of two styrene-acrylate copolymer latexes, stabilized with an aliphatic sulfonate and an aliphatic carboxylate surfactant, respectively, have been investigated experimentally in the temperature range between 283 and 323 K. The main objective of this study is to investigate the role of temperature and surfactant type on the aggregation kinetics and cluster structure. For this, the values of the Fuchs stability ratio and the time evolutions of the average radius of gyration, hydrodynamic radius, and structure factor of the clusters have been determined using static and dynamic light scattering techniques at different temperatures. It is found that although the two latexes exhibit a somewhat different dependence of the colloidal stability on temperature, all of the values of the average radius of gyration (or hydrodynamic radius) measured at different temperatures and surfactant types, which are plotted as a function of a properly defined dimensionless time, collapse to form a single master curve. Similarly, all of the measured average structure factors also collapse to form a single master curve when they are plotted as a function of the wavevector normalized using the average radius of gyration. These results indicate that, at least for the conditions investigated in this work, the aggregation mechanism and cluster structure are independent of temperature and surfactant type.     

Structure of polyelectrolyte complexes by Brownian dynamics simulation: effects of the bond length asymmetry of the polyelectrolytes

Brownian dynamics simulations were performed to study the structure of polyelectrolyte complexes formed by two flexible, oppositely charged polyelectrolyte chains. The distribution of monomers in the complex as well as the radius of gyration and structure factor of complexes and individual polyelectrolytes are reported. These structural properties were calculated for polyelectrolyte chains with equal number of monomers, keeping constant the bond length of the negative chain and increasing the bond length of the positive chain. This introduces an asymmetry in the length of the chains that modulates the final structure of the complexes. In the symmetric case the distribution of positive and negative monomers in the complex are identical, producing clusters that are locally and globally neutral. Deviations from the symmetric case lead to nonuniform, asymmetric monomer distributions, producing net charge oscillations inside the complex and large changes in the radius of gyration of the complex and individual chains. From the radius of gyration of the polyelectrolyte chains it is shown that the positive chain is much more folded than the negative chain when the chains are asymmetric, which is also confirmed through the scaling behavior of the structure factors.