Properties of Star-Branched Polymer Chains Near a Surface

We considered two model systems of star-branched polymers near an impenetrable surface. The model chains were constructed on a simple cubic lattice. Each star polymer consisted of f = 3 arms of equal length and the total number of segments was up to 799. The excluded volume effect was included into these models only and therefore the system was studied at good solvent conditions. In the first model system polymer chain was terminally attached with one arm to the surface. The grafted arm could slide along the surface. In the second system the star-branched chain was adsorbed on the surface and the strength of adsorption was were varied. The simulations were performed using the dynamic Monte Carlo method with local changes of chain conformations. The internal and local structures of a polymer layer were determined. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. It was shown that the behavior of grafted and weakly adsorbed chains was similar to that of a free three-dimensional polymer, while the strongly adsorbed chains behave as a two-dimensional system.     

Induced orientation of free chains in a strained rubber: A deuterium magnetic resonance study

Linear free polydimethylsiloxane (PDMS) chains are dissolved in a PDMS model network. When the system is uniaxially stretched, the free chains, as well as the network chains themselves, acquire a uniaxial orientational order, which is monitored by ²H NMR. The induced orders measured on both kinds of chains are comparable. The order is then investigated as functions of the free chain length and concentration.     

Polymer chain dynamics at interfaces: role of boundary conditions at solid interface

Using classical molecular dynamics simulations, we study the dynamical properties of a single polymer chain dissolved in an explicit solvent and strongly adsorbed at solid-liquid interface. To circumvent a serious challenge posed by finite size effects due to long-range hydrodynamic effects, we developed a correction procedure that substantially limits the finite size effects. Concurrently, we provide an analysis of distinctly different size effects in the directions transverse and normal to the interface. We find that on analytically smooth interfaces, corresponding to the slip boundary condition, the motions of the polymer chain and the surrounding solvent are hydrodynamically coupled. This leads to the chain diffusion coefficient D scaling with the chain degree of polymerization N as D approximately N(-3/4), consistent with the Zimm dynamics for strongly adsorbed chains. Introduction of transverse forces at the interface results in loss of correlation between the motion of the polymer chain and the solvent. Consequently, D approximately N(-1), which is a characteristic of the Rouse dynamics.     

Large-scale molecular dynamics simulations of alkanethiol self-assembled monolayers

Large-scale molecular dynamics simulations of self-assembled alkanethiol monolayer systems have been carried out using an all-atom model involving a million atoms to investigate their structural properties as a function of temperature, lattice spacing, and molecular chain length. Our simulations show that the alkanethiol chains of 13-carbons tilt from the surface normal by a collective angle of 25 degrees along next-nearest-neighbor direction at 300 K. The tilt structure of 13-carbon alkanethiol system is found to depend strongly on temperature and exhibits hysteresis. At 350 K the 13-carbon alkanethiol system transforms to a disordered phase characterized by small collective tilt angle, flexible tilt direction, and random distribution of backbone planes. The tilt structure also depends on lattice spacing: With increasing lattice spacing a the tilt angle increases rapidly from a nearly zero value at a=4.7 A to as high as 34 degrees at a=5.3 A at 300 K for 13-carbon alkanethiol system. Finally, the effects of the molecular chain length on the tilt structure are significant at high temperatures.     

Computer simulation of linkage of two ring chains

We performed off-lattice Monte Carlo simulations of links of two model ring chains with chain length N up to 32,768 in the theta solution or amorphous bulk state by using a random walk model (Model I), and molecular dynamics simulations of two model ring chains in solution with excluded volume interaction (Model II) to investigate topological effects on the geometry of link and ring conformation. In the case of Model I, the mean squared linking number, its distribution, and the size of two chains with fixed linking number are investigated. Our simulation results confirm the previous theoretical prediction that the mean squared linking number decays as pe(-qs(2)) with the distance of centers of chain mass s, where p and q are found to be chain length dependent and q asymptotically approaches to 0.75 as chain length increases. The linking number distribution of two chains has a universal form for long chains, but our simulation results clearly show that the distribution function deviates from the Gaussian distribution, a fact not predicted by any previous theoretical work. A scaling prediction is proposed to predict the link size, and is checked for our simulations for the Model II. The simulation results confirmed the scaling prediction of the blob picture that the link with linking number m occupies a compact volume of m blobs, and the size of the link is asymptotic to R(L) ≈ bN(ν)m(1/3-ν), where N is the chain length, and v is the Flory exponent of polymer in solutions.     

Polymer fracture—A simple model for chain scission

A simple model for calculating the fracture process for a single extended-chain molecule such as polyethylene is considered. The model consists of a chain of N coupled Morse oscillators. There exists a critical overall extension ΔL_c below which the fracture is energetically unfavorable but above which fracture is favored both energetically and kinetically. This elongation ΔL_c scales as N^1/2. For the critically stretched chain, the activation energy for rupture increases with N. Long chains must be stretched beyond this critical value to fail within experimentally meaningful times. Chains of all lengths subjected to the same force will fail with the same activation energy, provided this force is large enough to stretch each chain to ΔL > ΔL_c. Observed activation energies are less than 1/3D_e, where D_e is the bond energy.     

Computer simulation of solutions of telechelic polymers with associating end-groups

We present the results of numerical Monte Carlo simulations of solutions of telechelic chains with strongly attracting end-groups. Formation of micelles (aggregates), their structure and structural characteristics of the system as a whole are studied in detail. The features revealed in computer experiments are qualitatively similar to the recent theoretical predictions. In particular, we show that micelles formed by telechelic chains attract each other even if the solvent is good for the soluble blocks forming micellar shells. As a result, A “micellar gel” structure with a number of chain “bridges” connecting micelles is formed. The bridging chains turn out to be significantly stretched. Furthermore, we observe a pronounced maximum in the wave-vector dependence of the static structure factor for the associating end-units which is a manifestation of a quasiperiodic pattern of alternating microdomains consisting of dense micellar cores and the swollen soluble chain blocks.     

Distribution functions and dynamical properties of stiff macromolecules

An analytically tractable model for chain molecules with bending stiffness is presented and the dynamical properties of such chains are investigated. The partition function is derived via the maximum entropy principle taking into account the chain connectivity as well as the bending restrictions in form of constraints. We demonstrate that second moments agree exactly with those known from the Kratky-Porod wormlike chain. Moreover, various distribution functions are calculated. In particular, the static structure factor is shown to be proportional to 1/q at large scattering vectors q. The equations of motion for a chain in a melt as well as in dilute solution are presented. In the latter case the hydrodynamic interaction is taken into account via the Rotne-Prager tensor. The dynamical equations are solved by a normal mode analysis. In the limit of a flexible chain the model reproduces the well-known Rouse and Zimm dynamics, respectively, on large length scales, whereas in the rod limit the eigenfunctions correspond to bending motion only. In addition, the coherent and incoherent dynamic structure factor is discussed. For melts we show that at large scattering vectors the incoherent dynamic structure factor is a universal function of only the combination q^8/3tp^1/3, where 1/(2p) is the persistence length of the macromolecules. The comparison of the theoretical results with quasielastic neutron and light scattering experiments of various polymers in solution and melt exhibits good agreement. Our investigations show that local stiffness strongly influences the dynamics of macromolecules on small length scales even for long and flexible chains.     

STUDIES ON ENHANCED CONDUCTIVITY OF STRETCHED CONDUCTING POLYMERS

A physical model of series of the conductivity on chain and the interchain conductivitybetween chains is proposed to explain enhanced conductivity of stretched conducting polymers.This model suggests that the enhanced conductivity for stretched conducting polymers might bedue to increasing of the interchain conductivity between chains along the elongation direction afterdrawing processes if the conductivity on chain is assumed much larger than that of the interchainconductivity between chains. According to this model, it is expected that the temperaturedependence of conductivity measured by four-probe method for stretched conducting polymers iscontrolled by a variation of the interchain conductivity between chains with temperature, whichcan be used to explain that a metallic temperature dependence of conductivity for stretchedconducting polymers is not observed although the conductivity along the elongation direction isenhanced by two or three orders of magnitude.     

Computer simulation of bottle-brush polymers with flexible backbone: good solvent versus theta solvent conditions

By molecular dynamics simulation of a coarse-grained bead-spring-type model for a cylindrical molecular brush with a backbone chain of N(b) effective monomers to which with grafting density σ side chains with N effective monomers are tethered, several characteristic length scales are studied for variable solvent quality. Side chain lengths are in the range 5 ≤ N ≤ 40, backbone chain lengths are in the range 50 ≤ N(b) ≤ 200, and we perform a comparison to results for the bond fluctuation model on the simple cubic lattice (for which much longer chains are accessible, N(b) ≤ 1027, and which corresponds to an athermal, very good, solvent). We obtain linear dimensions of the side chains and the backbone chain and discuss their N-dependence in terms of power laws and the associated effective exponents. We show that even at the theta point the side chains are considerably stretched, their linear dimension depending on the solvent quality only weakly. Effective persistence lengths are extracted both from the orientational correlations and from the backbone end-to-end distance; it is shown that different measures of the persistence length (which would all agree for Gaussian chains) are not mutually consistent with each other and depend distinctly both on N(b) and the solvent quality. A brief discussion of pertinent experiments is given.     

Conformational statistics of polymer chain terminally attached to wall (III) —NRW model loop chain

When the two end groups of a linear polymer chain are absorbed on a solid surface, the polymer chain forms the “loop” conformation. Investigation has been made on the conformational statistics of a model loop chain by the normal random walk (NRW) on a lattice confined in the half-infinite space. Based on the conformational distribution function of the NRW model tail chain, it is easy to deduce an analytical formula expressing the conformational number of the model loop chain. It was found that the ratio of the conformational number of the model loop chain to that of the free chain varies with the power functionN ^-2/3 when the chain lengthN→οο. The same result -was obtained by means of the recursion equation. The ratio of the mean square end-to-end distanceh ² for the model loop chain to its mean square bond lengthl ² is 2N/3. Compared with the free chain with the same lengthN, the mean square end-to-end distance of the model loop chain contracts to a certain extent. The basic relationships deduced were supported by the exact enumeration and Monte Carlo simulations. Project supported by the National Natural Science Foundation of China.     

Distributions of the unperturbed dimensions of Markov-chain copolymers

This investigation shows that Markov-chain copolymers can be regarded as random copolymers the segment lengths of which depend on the copolymerization parameters. It was possible to derive simple analytical formulae for the mean-square end-to-end distance (〈r²〉), the Kuhn length, and the distribution of r² under theta-conditions. The results of these equations are in excellent agreement with data from simulations. It is shown that 〈r²〉 as well as the non-uniformity of r² increase strongly with increasing probabilities of homopropagation, i.e., with increasing mean homosequence lengths. Furthermore it is demonstrated by simulation that even chains of identical length and composition show a distribution of r² because of different arrangements of the sequences inside the chains. For chains or chain segments shorter than the average homosequences, a double-peak distribution of r² is found. The equations derived in this paper can be applied to real copolymers as well as to chains the curvature of which is altered locally by the association of ligands.     

Superselective Adsorption of Multivalent Polymer Chains to a Surface with Receptors

Multivalent polymer chains exhibit excellent prospect in biomedical applications by serving as therapeutic agents. Using three-dimensional (3D) Langevin dynamics simulations, we investigate adsorption behaviors of multivalent polymer chains to a surface with receptors. Multivalent polymer chains display superselective adsorption. Furthermore, the range of density of surface receptors at which a multivalent polymer chain displays a superselective behavior, narrows down for chains with higher density of ligands. Meanwhile, the optimal density of surface receptors where the highest superselectivity is achieved, decreases with increasing the density of ligands. Then, the conformational properties of bound multivalent chains are studied systematically. Interestingly, we find that the equilibrium radius of gyration R_g and its horizontal component have a maximum as a function of the density of surface receptors. The scaling exponents of R_g with the length of chain suggest that with increasing the density of surface receptors., the conformations of a bound multivalent polymer chain first fall in between those of a two-dimensional (2D) and a 3D chain, while it is slightly collapsed subsequently.     

Is the alignment of nematics on a polymer slab always along the rubbing direction? A molecular dynamics study

ABSTRACT

We have studied the alignment and molecular organisation within a thin film of the popular nematic 5CB sandwiched between two flat polymer slabs, examining the effect of polymer chemical nature and morphology with atomistic molecular dynamics simulations. We have chosen two common polymers: polystyrene (PS) and polymethylmethacrylate (PMMA), either with their chains in random coil conformation (disordered) or with chains unidirectionally stretched (ordered). We found that, independently on the arrangement of the chains, both surfaces align planarly the liquid crystal, in accord with experimental observation. Moreover, while 5CB molecules align along the chains stretching direction of the PMMA ordered surface, on the combed PS surface they arrange on average perpendicularly to the stretching direction. This behaviour is attributed to the chemically specific interactions between the respective aromatic moieties of PS and 5CB.     

Structure of iodide ion arrays in iodinated nylon 6 and the chain orientation induced by iodine in nylon 6 films

Two species of iodide ions (I₃^? and I₅^?) are found in iodine—nylon 6 complexes. Orientation of I₅^? arrays (most likely I₂/I₃^? complex) along the polymer chain and I₃^? ions perpendicular to the chain axis in uniaxially drawn films and in films with planar orientation suggests that there is and intrinsic relation between the direction of iodide ion arrays and nylon 6 chains. When an unoriented film of nylon 6 in the amorphous or the α crystalline form is treated with an aqueous solution of iodine—potassium iodide, the I₃^? species in the resulting iodine—nylon complex lie in planes parallel to the surface of the film, and I₂/I₃^? units are oriented normal to the surface of the film. The γ form obtained by desorbing the iodine from this complex shows considerable uniaxial rientation with the nylon chains oriented perpendicular to the plane of the film; this orientation is maintained during the γ to α transition. It is proposed that the iodine-induced orientation of the nylon 6 chains is due to the nucleating effects of the iodide ion species as the iodine diffuses unidirectionally into the film.     

Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

Transitions of tethered polymer chains: a simulation study with the bond fluctuation lattice model

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density-of-states results have been evaluated for interaction parameters spanning the range from good- to poor-solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.     

Interaction between small colloidal particles and molecular chains with selectively adsorbing groups: computer simulation study

Using the Monte Carlo simulation technique and the method of simulated annealing, we study interactions between small (nanometric) particles and flexible‐chain polymers with sticker groups which selectively adsorb on the particles and also can strongly attract each other. For the chains with two end stickers (telechelic polymers), we find that the colloidal particles adsorbing on the polymers play the role of junction points (locks) which bind together the ends of different chains. This direct or indirect binding leads to the formation of a web‐like structure throughout the sample: colloidal particles and chain stickers group into mixed clusters – “drops of a fog” – which are wrapped by polymer chains and connected by bridges. Analyzing static structure factors, we show that the selectively adsorbing telechelic polymers can affect the equilibrium spatially homogeneous distribution of colloidal particles that results in the appearance of a quasiregular structure on the intermediate scale related to the average intercluster distance. At sufficiently strong attraction between particles and chain end‐groups, most of the telechelic chains (>90%) adopt either a loop‐like or a stretched bridge‐like conformation, the most typical morphology of the system being a combination of these two structural elements. In the mixed clusters, the colloidal particles and the chain ends pack locally on a binary grid corresponding to a local crystal‐like arrangement. For the chains without attracting end‐groups, we observe the formation of elongated, rugby‐ball‐like clusters having alternate layers of particles and adsorbing chain groups.     

Monte Carlo study of the coil-to-globule transition of a model polymeric system

Monte Carlo computer simulations of single, flexible, self-avoiding chains on a cubic lattice have been performed upon conditions of increasing segment–segment cohesive energy (deteriorating solvent quality). The simulations spanned a wide range of chain lengths (20–10,000, i.e., up to molecular weights of a few millions) and cohesive energies (0.0–0.45k_BT, i.e., from athermal to very poor solvents). The chain length dependence of the chain size in poor solvents was characterized by a wide plateau of almost null growth for intermediate chain lengths. This plateau was linked to the development of the incipient constant density core, while genuine power law dependence (1/3) was not reached even for the longest chains and poorest solvents simulated here. The mere appearance of a core required substantial chain lengths (higher than 1000; molecular weights of a few hundred thousands), while short chains underwent a gradual densification devoid of any qualitative changes in the density distribution. Sufficiently long chains became more but not quite spherical and underwent a reasonably sharp second order phase transition. The findings were generally in agreement with predictions of mean-field theory and with the use of the standard scaling variables, despite slight inconsistencies. Nevertheless, the results stress the fact that short chains never form a constant density core and that core-dominance on the globule's properties (“volume approximation”) is only valid for extraordinarily long chains [molecular weight of O(10⁹)], an effect linked to the relatively diffuse nature of the surface layer and originating from chain connectivity in conjunction with spherical geometry. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3651–3666, 2006     

Viscoelasticity of a stretched polymer chain with ends exposed to a constant force

The viscoelasticity of a stretched polymer chain with its end particles exposed to oppositely acting forces is studied via collisional molecular dynamics and analytically. A simple model according to which a polymer molecule is a chain of particles linked through freely jointed elastic bonds is adopted. The analytical theory is in good agreement with the results of the computer simulation of time correlation functions in the range of large-scale motions of a polymer molecule. It is found that the decay of correlation functions K _αβμν of fluctuations of the microscopic stress tensor of a chain, K _zzzz, K _zαzα , = K _zαzα , (α = x, y; z is the axis along which the forces act), is slowed down, and their value increases relative to the respective correlation functions of a chain with fixed ends. The greater the force, the higher this difference. The correlation functions that are transverse with respect to the z axis do not differ from those for chains with fixed ends. The results show that, in the calculation of time correlation functions of strongly stretched polymer chains, different statistical ensembles are not equivalent; this must be taken into account in the dynamic theories of heavily deformed polymers.