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Conformations of wormlike chains in cylindrical pores with attractive walls are explored for varying pore radius and strength of the attractive wall potential by molecular dynamics simulations of a coarse-grained model. Local quantities such as the fraction of monomeric units bound to the surface and the bond-orientational order parameter as well as the radial density distribution are studied, as well as the global chain extensions parallel to the cylinder axis and perpendicular to the cylinder surface. A nonmonotonic convergence of these properties to their counterparts for adsorption on a planar substrate is observed due to the conflict between pore surface curvature and chain stiffness. Also the interpretation of partially adsorbed chains in terms of trains, loops, and tails is discussed.

Binary mixtures of semiflexible polymers with the same chain length, but different persistence lengths, separate into two coexisting different nematic phases when the osmotic pressure of the lyotropic solution is varied. Molecular Dynamics simulations and Density Functional Theory predict phase diagrams either with a triple point, where the isotropic phase coexists with two nematic phases or a critical point of unmixing within the nematic mixture. The difference in locally preferred bond angles between the constituents drives this unmixing without any attractive interactions between monomers.

The interplay of the isotropic-nematic transition and phase separation in lyotropic solutions of two types of semiflexible macromolecules with pronounced difference in chain stiffness is studied by Density Functional Theory and Molecular Dynamics simulations. While the width of the isotropic-nematic two-phase coexistence region is narrow for solutions with a single type of semiflexible chain, the two-phase coexistence region widens for solutions containing two types of chains with rather disparate stiffness. In the nematic phase, both types of chains contribute to the nematic order, with intermediate values of the order parameter compared to the corresponding single component solutions. As the difference in bending stiffness is increased, the two chain types separate into two coexisting nematic phases. The phase behavior is rationalized by considering the chemical potentials of the two components and the Gibbs excess free energy. The geometric properties of the chain conformations under the various conditions are also discussed.

The adsorption transition and the structure of semiflexible adsorbed macromolecules are studied by a molecular dynamics simulation of a coarse-grained, bead-spring type model. Varying chain length N and stiffness κ (which is proportional to the persistence length lp in d = 3 dimensions) as well as the strength ϵwall of the adsorption potential, the adsorbed monomer fraction, orientational bond order parameter, and chain linear dimensions are studied. In the simulations, excluded volume interactions normally are included but can be “switched off,” and thus, the influence of excluded volume (leading to deviations from predictions of the wormlike chain model) can be identified. It is shown that the variation in the adsorption threshold ϵwallcr with lp is compatible with the predicted law ϵwallcr∝lp−1/3. In the vicinity of the adsorption threshold, the coils are still three-dimensional, and for large lp, the effect of the excluded volume is almost negligible, while for strongly adsorbed chains it is always felt. Near the transition, the decay length of orientational correlations along the chain contour increases gradually from lp to 2lp. While the latter value is expected for strictly two-dimensional chains from the Kratky–Porod model, this model is inaccurate for the description of lateral chain dimensions of long, strongly adsorbed, semiflexible polymers due to its neglect of excluded volume. The significance of these findings for the interpretation of pertinent experiments is briefly discussed.

Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness &kappa, as well as the strength of the adsorption potential ϵ w a l l are varied over a wide range. The excluded-volume (EV) interactions inherent in this model can also be &ldquo, switched off&rdquo, to provide a discretized version of the Kratky&ndash, Porod wormlike chain model. We study both local order parameters (fraction f of monomers within the range of the potential, bond-orientational order parameter &eta, ) and the mean square gyration radius parallel, &lang, R g 2 &rang, | , and perpendicular, &lang, &perp, to the wall. While for strongly adsorbed chains EV has negligible effect on f and &eta, we find that &lang, | is strongly affected when the chain contour length exceeds the persistence length. Monomer coordinates in perpendicular (&perp, ) direction are correlated over the scale of the deflection length which is estimated. It is found that f , &eta, and &lang, converge to their asymptotic values with 1 / N corrections. For both weakly and strongly adsorbed chains, the distribution functions of &ldquo, loops&rdquo, &ldquo, trains&rdquo, and &ldquo, tails&rdquo, are analyzed. Some consequences pertaining to the analysis of experiments on adsorbed semiflexible polymers are pointed out.

Rigid spheres with a short-range attractive potential are taken as a coarse-grained model of vesicles, which contain a solution of semiflexible polymers in their interior. Assuming good solvent conditions with an implicit description of the solvent, effective monomers experience bond-length and bond-angle potentials as well as excluded-volume interaction. Due to the attractive vesicle surface, phase separation occurs between a thin shell of adsorbed monomers at the surface and a rather dilute, and therefore, disordered polymer solution in the sphere interior. While at a planar attractive surface the wormlike chains would exhibit liquid crystalline (nematic and smectic) order, the curvature of the sphere frustrates this order, causing the existence of defects in the orientational order. In the dense monolayer of surface-attached polymers, the stiff chains acquire a curvature corresponding to banana-like shapes for rather small contour length, causing a local nematic order of biaxial type. These orderings are compared to related phenomena in spheres densely filled with semiflexible polymers. We complement the results obtained by Molecuar Dynamics simulations by corresponding Density Functional Theory calculations.

Molecular dynamics simulations of semiflexible polymers in a good solvent reveal a dense adsorbed layer when the solution is exposed to an attractive planar wall. This layer exhibits both a nematic and a smectic phase (smA for short and smC for longer chains) with bond vectors aligned strictly parallel to the wall. The tilt angle of the smC phase increases strongly with the contour length of the polymers. The isotropic-nematic transition is a Kosterlitz-Thouless transition and also the nematic-smectic transition is continuous. Our finding demonstrates thus a two-dimensional realization of different liquid crystalline phases, ubiquitous in three dimensions, that occurs in a single monomolecular layer ordered at least over mesoscopic scales.

Conformations of partially or fully adsorbed semiflexible polymer chains are studied varying both contour length $L$, chain stiffness, $\ensuremath{\kappa}$, and the strength of the adsorption potential over a wide range. Molecular dynamics simulations show that partially adsorbed chains (with ``tails,'' surface attached ``trains,'' and ``loops'') are not described by the Kratky-Porod wormlike chain model. The crossover of the persistence length from its three-dimensional value (${\ensuremath{\ell}}_{p}$) to the enhanced value in two dimensions ($2{\ensuremath{\ell}}_{p}$) is analyzed, and excluded volume effects are identified for $L\ensuremath{\gg}{\ensuremath{\ell}}_{p}$. Consequences for the interpretation of experiments are suggested. We verify the prediction that the adsorption threshold scales as ${\ensuremath{\ell}}_{p}^{\ensuremath{-}1/3}$.

The backbone conformations of individual, unperturbed synthetic macromolecules have so far not been observed directly in spite of their fundamental importance to polymer physics. Here we report the dilute solution conformations of two types of linear dendronized polymers, obtained by cryogenic transmission electron stereography and tomography. The three-dimensional trajectories show that the wormlike chain model fails to adequately describe the scaling of these thick macromolecules already beyond a few nanometers in chain length, in spite of large apparent persistence lengths and long before a signature of self-avoidance appears. This insight is essential for understanding the limitations of polymer physical models, and it motivated us to discuss the advantages and disadvantages of this approach in comparison to the commonly applied scattering techniques.

The intrinsic local stiffness of a polymer is characterized by its persistence length. However, its traditional definition in terms of the exponential decay of bond orientational correlations along the chain backbone is accurate only for Gaussian phantom-chain-like polymers. Also care is needed to clarify the conditions when the Kratky-Porod wormlike chain model is applicable. These problems are elucidated by Monte Carlo simulations of simple lattice models for polymers in both d = 2 and d = 3 dimensions. While the asymptotic decay of the bond orientational correlations for real polymers always is of power law form, the Kratky-Porod model is found to be applicable for rather stiff (but not too long) thin polymers in d = 3 (but not in d = 2). However, it does not describe thick chains, e.g., bottle-brush polymers, where stiffness is due to grafted flexible side-chains, and the persistence length grows proportional to the effective thickness of the bottle-brush. A scaling description of bottle-brushes is validated by simulations using the bond fluctuation model.

A topical review of recent theoretical work on the properties of lyotropic solutions and melts containing semiflexible polymers in thermal equilibrium is given, with a focus on the liquid-crystalline and smectic order of these systems in the bulk and under confinement. Starting with a discussion of single chain properties in terms of the Kratky-Porod worm-like chain model and its limitations, extensions along the lines of Onsager’s theory for the isotropic-nematic transition of solutions of hard rods are briefly reviewed. This discussion is followed by a review of recent Molecular Dynamics simulations and classical Density Functional Theory calculations. It is argued that, even in the simplest case of athermal solutions, coarse-grained polymer models must include three lengths: the contour length L, the persistence length ℓ p , and the effective chain thickness D. The discussion is then extended to semiflexible polymers in solutions with thermally driven transitions, where the isotropic-isotropic phase separation competes with the isotropic-nematic transition. Basic physical phenomena due to confinement of these systems in thin films with either repulsive or attractive walls are briefly reviewed, and conditions for the formation of strongly ordered surface layers are identified.

Molecular dynamics simulations of a chemically realistic model for 1,4-polybutadiene in a thin film geometry confined by two graphite walls are presented. Previous work on melts in the bulk has shown that the model faithfully reproduces static and dynamic properties of the real material over a wide temperature range. The present work studies how these properties change due to nano-confinement. The focus is on orientational correlations observable in nuclear magnetic resonance experiments and on the local intermediate incoherent neutron scattering function, Fs(qz, z, t), for distances z from the graphite walls in the range of a few nanometers. Temperatures from about 2Tg down to about 1.15Tg, where Tg is the glass transition temperature in the bulk, are studied. It is shown that weakly attractive forces between the wall atoms and the monomers suffice to effectively bind a polymer coil that is near the wall. For a wide regime of temperatures, the Arrhenius-like adsorption/desorption kinetics of the monomers is the slowest process, while very close to Tg the Vogel-Fulcher-Tammann-like α-relaxation takes over. The α-process is modified only for z≤1.2 nm due to the density changes near the walls, less than expected from studies of coarse-grained (bead-spring-type) models. The weakness of the surface effects on the glass transition in this case is attributed to the interplay of density changes near the wall with the torsional potential. A brief discussion of pertinent experiments is given.

Semiflexible polymers in lyotropic solution confined inside spherical nanoscopic “containers” with repulsive walls are studied by molecular dynamics simulations and density functional theory, as a first step to model confinement effects on stiff polymers inside of miniemulsions, vesicles, and cells. It is shown that the depletion effects caused by the monomer-wall repulsion depend distinctly on the radius R of the sphere. Further, nontrivial orientational effects occur when R, the persistence length ℓp, and the contour length L of the polymers are of similar magnitude. At intermediate densities, a “shell” of wall-attached chains is forming, such that the monomers belonging to those chains are in a layer at about the distance of one monomer from the container wall. At the same time, the density of the centers of mass of these chains is peaked somewhat further inside, but still near the wall. However, the arrangement of chains is such that the total monomer density is almost uniform in the sphere, apart from a small layering peak at the wall. It is shown that excluded volume effects among the monomers are crucial to account for this behavior, although they are negligible for comparable isolated single semiflexible chains of the same length.

A chemically realistic model of 1,4-polybutadiene confined by graphite walls in a thin film geometry was studied by molecular dynamics simulations. The chemically realistic approach allows for a quantitative determination of a variety of experimentally accessible relaxation functions (e.g., dielectric, NMR, or neutron scattering responses). The simulations yield these experimental observables. Additionally, the simulations can be resolved as a function of distance to the solid interface on a much finer scale than experimentally possible, providing a detailed mechanistic picture of the segmental and large scale motions of polymers in the interfacial region between bulk polymer melts and solid walls. Extending the study of 1,4-polybutadiene on graphite to temperatures close to the glass transition temperature, we also address the question to what extent growing length scales associated with the glass transition influence the melt dynamics in the interphase. It was found that there is an interplay of this in...

Force versus extension behavior of flexible chains and semiflexible bottle-brush polymers adsorbed from a good solvent on a planar substrate is studied by Monte Carlo simulation of the bond fluctua...

The interaction of a ring polymer brush with a solution containing oligomers or free linear flexible macromolecules is studied by Monte Carlo simulation, varying the chain length of the free chains, and in selected cases also the lengths of the rings. Two grafting densities are studied, corresponding to semidilute and very concentrated conditions, and a comparison with the corresponding case of brushes formed from grafted linear chains is made. Although the ring polymer linear dimensions in the brushes show an anomalous scaling with ring length, similar to (noncatenated) ring polymer melts, the concentration profiles of oligomers and long macromolecules in ring polymer brushes differ only very little from their linear polymer brush counterparts.

Polymers grafted with one chain end to an impenetrable flat hard wall which attracts the monomers with a short-range adsorption potential (of strength e) are studied by large scale Monte Carlo simulations, using the pruned–enriched Rosenbluth method (PERM). Chain lengths up to N = 25600 steps are considered, and the intrinsic flexibility of the chain is varied via an energy penalty for nonzero bond angles, eb. Choosing qb = exp(−eb/kBT) in the range from qb = 1 (fully flexible chains) to qb = 0.005 (rather stiff chains with a persistence length of about lp=52 lattice spacings), the adsorption transition is found to vary from about e/kBTc ≈ 0.286 to e/kBTc ≈ 0.011, confirming the theoretical expectation that e/kBTc∝1/lp for large lp. The simulation data are compatible with a continuous adsorption transition for all finite values of lp, while in the rigid rod limit (lp→∞) a first order transition seems to emerge. Scaling predictions and blob concepts on the structure of weakly adsorbed semiflexible polymers...

The Wang-Landau (WL) algorithm is a Monte Carlo simulation technique providing a direct computation of the density of states of a many-body system. The temperature independent density of states function encodes all thermodynamic information about a system, and thus, its construction allows for a very efficient determination of phase behavior. Here we describe the application of the WL approach to continuum interaction-site polymer chains and compute single-chain phase diagrams for three specific models (flexible and semiflexible homopolymer chains built from square-well sphere monomers and a flexible AB-heteropolymer comprised of alternating square-well and hard-sphere monomers). We provide details on the implementation of the WL algorithm, the underlying Monte Carlo move set, and the subsequent thermodynamic and structural analysis required to characterize phase behavior.

The interaction between two spherical polymer brushes in solvents of variable quality is studied by molecular dynamics simulation and by self-consistent field theory, varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to-end distance of grafted chains, etc.) It is found that for rather short chain lengths and not too large grafting densities, isolated spherical brushes in the poor solvent regime exhibit incomplete coverage of the nanoparticle, rather than a complete coverage, i.e., a core–shell structure where the nanoparticle is covered homogeneously by a dense polymeric film. This latter case occurs for long chains and/or high grafting densities. When two su...

Bottle-brush polymers contain a long flexible macromolecule as a backbone to which flexible side chains are grafted. Through the choice of the grafting density and the length of the side chains the local stiffness of this cylindrical molecular brush can be controlled, but a quantitative understanding of these phenomena is lacking. Monte Carlo simulation results are presented and discussed which address this issue, extractingmesoscopic length scales (such as the cross-sectional radius, persistence length, and contour length of these objects). Large-scale simulations of the bond fluctuation model are combined with simulations of the simple selfavoiding walk (SAW) model with flexibility controlled by a bond-angle potential, using the pruned-enriched Rosenbluth algorithm. It is shown that under good solvent conditions the bottle-brush polymers never display a pre-asymptotic Gaussian regime that would be described by the Kratky–Porod worm-like chain model, unlike the semiflexible SAWmodel. Implications of these results for the proper interpretation of experiments are discussed.

We consider the ejection dynamics of a flexible polymer chain out of confined environment. This situation arises in different physical contexts, including a flexible synthetic polymer partially confined in a nanopore and a viral genome partially ejected from its capsid. We describe the chain release from confinement both analytically and by means of dynamic Monte Carlo simulation. We find two distinct regimes of ejection dynamics depending on whether the chain is fully or partially confined. Partially confined chains are ejected from a pore of length L and diameter D after a typical time τ ∝ L2D5/3, regardless of their contour length N. The process is driven by a constant force f ≈ 5kBT/D and follows a “capillary” law. The force value is model-independent as long as the pore diameter exceeds the persistence length of the polymer chain and for pore walls that do not attract the segments of the polymer. In contrast, the ejection of fully confined chains is largely diffusive, the residence time being a nonmo...

A coarse grained model of a flexible macromolecule end-grafted on the inside of a sphere or a cylinder under good solvent conditions is studied by Monte Carlo simulations. For cylindrical confinement, two regimes are found: when the cylinder radius R exceeds the gyration radius R 90 of the polymer mushroom grafted to a planar surface, a simple scaling description holds. In the opposite case, a non-monotonic crossover to a cigar-like quasi-one-dimensional structure occurs, and the distribution P e (x) of the free chain end in the x-direction along the cylinder axis becomes bimodal. Spherical confinement, on the other hand, causes a crossover from dilute to semidilute behavior of the structural properties.

Conformations of a bottle-brush polymer with two types (A,B) of grafted side chains are studied by molecular dynamics simulations, using a coarse-grained bead−spring model with side chains of up to...

The spontaneous rise of a fluid in a brush-coated nanocapillary is studied by molecular dynamics simulation of a coarse-grained model. The cases of changing wettability of both the capillary walls and the brush were examined. We also investigated the impact of polymer chain length on the transport of fluid along the nanotube. We found that capillary filling takes place in both lyophilic and lyophobic tubes, provided that the polymer brush coating is wetted by the fluid. In all the cases studied, capillary rise proceeds by a time-square law, but the mechanisms behind them (Lucas-Washburn or diffusive propagation) differ, depending on the chain length N. For a wettable wall, the speed of fluid imbibition decreases steadily with growing N, whereas the meniscus speed goes through a minimum at intermediate chain lengths. The polymer brush coating reorganizes into "channels" parallel to the tube axis and forms a dense plug of monomers in the vicinity of the meniscus, which moves with the meniscus along the nanotube. For lyophobic capillary walls (covered with a wettable polymer brush), depending on the chain length N, one finds three regimes: (1) short chains--one observes no meniscus motion, but an influx of fluid through the wet brush; (2) intermediate chain lengths--the fluid creates "fluid walls" inside the brush by diffusive spreading, whereby a meniscus is formed and moves up within the fluid walls; and (3) long chains--a "negative curvature" meniscus rises up the capillary by means of diffusive propagation.

We present an efficient method for direct determination of the excess free energy Δ F of a nanoparticle inserted into a polymer brush. In contrast to Widom's insertion method, the present approach can be efficiently implemented by Monte Carlo or Molecular Dynamics methods also in a dense environment. In the present investigation the method is used to determine the free energy penalty Δ F ( R , D ) for placing a spherical particle with an arbitrary radius R at different positions D between the grafting plane and the brush surface. Deep inside the brush, or for dense brushes, one finds Δ F ∝ R 3 whereas for shallow nanoclusions Δ F ∝ R 2 , regardless of the particle interaction (attractive/repulsive) with the polymer. The pressure and density fields around spherical nanoinclusions in a polymer brush are also investigated. Extensive Monte Carlo simulations show that the force, exerted on the particle by the surrounding brush, depends essentially on the proximity of the nanocolloid particle to the brush surface not only in strength but also with respect to its angular distribution. For shallow nanoinclusions close to the brush surface this angular distribution is shown to result in a growing buoyant force while deep inside the brush this effect is negligible.

We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method. The nanotube is a long channel opened at one end and its diameter $D$ is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position $x$ inside the tube: the free energy of confinement, the average end-to-end distance, the average number of imprisoned monomers, and the average stretching of the confined part of the chain for various values of $D$ and for the number of monomers in the chain, $N$. We show that when the chain end is dragged by a certain critical distance $x^*$ into the tube, the polymer undergoes a first-order phase transition whereby the remaining free tail is abruptly sucked into the tube. This is accompanied by jumps in the average size, the number of imprisoned segments, and in the average stretching parameter. The critical distance scales as $x^*\sim ND^{1-1/\nu}$. The transition takes place when approximately 3/4 of the chain units are dragged into the tube. The theory presented is based on constructing the Landau free energy as a function of an order parameter that provides a complete description of equilibrium and metastable states. We argue that if the trapped chain is released with all monomers allowed to fluctuate, the reverse process in which the chain leaves the confinement occurs smoothly without any jumps. Finally, we apply the theory to estimate the lifetime of confined DNA in metastable states in nanotubes., Comment: 13pages, 14figures

We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang–Landau sampling idea. Using the micro-canonical density of states obtained with this method we will discuss the ability of an analysis in the micro-canonical ensemble to locate the coil-globule (continuous) and liquid–solid (first-order) transitions found for this problem using a canonical analysis.

A brief review is given of methodological advances made during the past decade with the Monte Carlo sampling of equilibrium properties of simple lattice models of polymer systems, and representative applications of these new algorithms are summarized. These algorithms include Wang−Landau (WL) sampling, the pruned-enriched Rosenbluth method (PERM), and topology violating dynamic Monte Carlo algorithms such as combinations of local moves, slithering snake moves, and “double bridging” moves for the bond fluctuation model. The applications mentioned concern phase-transition-like phenomena of single chains (collapse and crystallization in bad solvents; interplay of collapse and adsorption; escape of chains from confining tubes; microphase separation in binary bottle brushes) and nontrivial correlation effects in dense systems of many chains (intramolecular long-range correlations in melts; fluctuation effects of micelles in homopolymer−block copolymer blends.) While all these examples refer to work on lattice ...

The structure of bottle-brush polymers with a rigid backbone and flexible side chains is studied in three dimensions, varying the grafting density, the side chain length, and the solvent quality. Some preliminary results of theoretical scaling considerations for one-component bottle-brush polymers in a good solvent are compared with Monte Carlo simulations of a simple lattice model. For the simulations a variant of the pruned-enriched Rosenbluth method (PERM) allowing for simultaneous growth of all side chains in the Monte Carlo sampling is employed. For a symmetrical binary (A,B) bottle-brush polymer, where two types (A,B) of flexible side chains are grafted with one chain end to the backbone in an alternating way, varying repulsive binary interactions between unlike monomers and the solvent quality, it is found that phase separation into an A-rich part of the cylindrical molecule and a B-rich part can occur only locally. Long range order (in the direction of the backbone) does not occur, and hence the transition from the randomly mixed state of the bottle-brush to the phase-separated structure is strongly rounded, in contrast to the corresponding mean field predictions of a sharp transition to a Janus cylinder phase-separated structure. This lack of a phase transition can be understood from an analogy with spin models in one dimension. By estimating the correlation length for this phase separation along the backbone as a function of side chain length and solvent quality, we present strong evidence that no sharp phase transition occurs.

Semiflexible polymers end-grafted to a repulsive planar substrate under good solvent conditions are studied by scaling arguments, computer simulations, and self-consistent field theory. Varying the chain length N, persistence length lp, and grafting density σg, the chain linear dimensions and distribution functions of all monomers and of the free chain ends are studied. Particular attention is paid to the limit of very small σg, where the grafted chains behave as "mushrooms" no longer interacting with each other. Unlike a flexible mushroom, which has a self-similar structure from the size (a) of an effective monomer up to the mushroom height (h/a ∝ N(v), ν ≈ 3/5), a semiflexible mushroom (like a free semiflexible chain) exhibits three different scaling regimes, h/a ∝ N for contour length L = Nalp, a Gaussian regime, h/a ∝ (Llp)(1/2)/a for lp ≪ L ≪ R* ∝ (lp(2)/a), and a regime controlled by excluded volume, h/a ∝ (lp/a)(1/5)N(ν). The semiflexible brush is predicted to scale as h/a ∝ (lpaσg)(1/3)N in the excluded volume regime, and h/a ∝ (lpa(3)σ(2))(1/4)N in the Gaussian regime. Since in the volume taken by a semiflexible mushroom excluded-volume interactions are much weaker in comparison to a flexible mushroom, there occurs an additional regime where semiflexible mushrooms overlap without significant chain stretching. Moreover, since the size of a semiflexible mushroom is much larger than the size of a flexible mushroom with the same N, the crossover from mushroom to brush behavior is predicted to take place at much smaller densities than for fully flexible chains. The numerical results, however, confirm the scaling predictions only qualitatively; for chain lengths that are relevant for experiments, often intermediate effective exponents are observed due to extended crossovers.

In this work we report on molecular dynamics simulations of the embedding process of a nano-particle into a polymeric film as a function of temperature. This process has been employed experimentally in recent years to test for a shift of the glass transition of a material due to the confined film geometry and to test for the existence of a liquid-like layer on top of a glassy polymer film. The embedding process is governed thermodynamically by the prewetting properties of the polymer on the nano-particle. We show that the dynamics of the process depends on the Brownian motion characteristics of the nano-particle in and on the polymer film. It displays large sample to sample variations, suggesting that it is an activated process. On the timescales of the simulation an embedding of the nano-particle is only observed for temperatures above the bulk glass transition temperature of the polymer, agreeing with experimental observations on noble metal clusters of comparable size.

The structure of a polymer nanodroplet adsorbed on a flat lyophobic substrate chemically decorated with a lyophilic stripe of width 2RD is studied by molecular dynamics simulation of a coarse-grained bead–spring model of short macromolecules (containing N = 20 effective monomers). Varying the stripe width, the strength of the monomer–wall attraction and the temperature, the equilibrium morphology of the resulting droplets is studied and discussed in terms of current phenomenological theories. In the second part, the behaviour of a liquid bridge connecting two such lyophilic stripes a distance L apart is analysed. It is shown that for large enough L such free-standing films are unstable and rupture, after a hole has nucleated and grown into an elongated cavity in the lateral direction leaving only a cylindrical bridge between the stripes immediately before break-up. The forces acting between the two walls of the slit pore in equilibrium due to the thin film forming the liquid bridge are also estimated as a function of distance between the walls.

Using Monte Carlo simulations of a coarse-grained bead-spring model we study the lateral structure formation of one-component polymer brushes in a bad solvent and of a mixed polymer brush upon increasing the incompatibility of the two species. We compare the morphology of the brush with a regular distribution of grafting points and with a random arrangement. Density or composition fluctuations of the grafting points enhance the formation of irregular structures but randomness prevents the formation of long-range order. Even small fluctuations of the grafting points are sufficient to pin the lateral structures of the brush.

We study the translocation of a coarse-grained flexible polymer through a nanopore in a membrane induced by its adsorption on the trans side of the membrane. Dramatic differences in the threading behavior are observed if the adhesion to the membrane wall, e w , is below or above the adsorption threshold e c r . For e w e c r (weak adsorption) the activation barrier for translocation is at c cis 0 ≈ N / 2 (in terms of the fraction of chain c cis = N cis / N before the pore), independent of chain length N. For e w > e c r this barrier is at a constant (vanishing) number of passed trans monomers for all N. The mean time of chain passage τ trans ∝ c cis 1.3 when c cis c cis 0 . It scales with chain length as τ trans ∝ N 2 ν + 1 for e w e c r , and as τ trans ∝ N 1.6 beyond the threshold e c r .

We present simulation results for the phase behavior of flexible lattice polymer chains using the Wang-Landau sampling idea. These chains display a two-stage collapse through a coil-globule transition followed by a crystallization at lower temperatures. Performing a finite-size scaling analysis on the two transitions, we show that they coincide in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil-globule transition.

The interplay between chain conformations and phase separation in binary symmetric polymer mixtures confined into thin films by "neutral" hard walls (i.e., walls that do not preferentially attract or repel one of the two components of the mixture) is studied by Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice in the semi grand canonical ensemble, we locate the critical temperature of demixing via finite size scaling methods for a wide range of chain lengths (16/= N/= 256 effective monomers per chain) and film thicknesses (2/= D/= 19 lattice spacings). Simultaneously, we investigate the geometrical structure of the chains, showing that despite using melt densities there are pronounced "correlation hole effects", in particular for the smaller values of D. Also the components of the radius of gyration and end-to-end distance parallel and perpendicular to the confining walls are analyzed and their scaling behavior is studied. Evidence is presented that for strictly two-dimensional polymers (as occur for D = 2) the average number of intermolecular contacts scales with chain length N as z(c) proportional, variant N(-3/8) and therefore the critical temperature scales as T(c) proportional, variant N(5/8), whereas for values of D that exceed the excluded volume screening length, z(c) remains nonzero for N --infinity, and hence T(c) proportional, variant N. However, strong deviations from the Flory-Huggins theory occur as long as the unperturbed chain dimension exceeds D, and the critical behavior falls in the universality class of the two-dimensional Ising model for any finite value of D.

Dynamic Monte Carlo simulation of a bead-spring model of flexible macromolecules threading through a very narrow pore in a very thin rigid membrane are presented, assuming at the cis side of the membrane a purely repulsive monomer-wall interaction, while the trans side is attractive. Two choices of monomer-wall attraction epsilon are considered, one choice is slightly below and the other slightly above the "mushroom to pancake" adsorption threshold epsilon(c) for an infinitely long chain. Studying chain lengths N=32, 64, 128, and 256 and varying the number of monomers N(trans) (time t=0) that have already passed the pore when the simulation started, over a wide range, we find for epsilonepsilon(c) (nonadsorbing case) that the translocation probability varies proportional to c(trans)=N(trans)(t=0)/N for small c(trans), while for epsilonepsilon(c) a finite number N(trans)(t=0) suffices that the translocation probability is close to unity. In the case epsilonepsilon(c), however, the time it takes for those chains to get through the pore to complete the translocation process scales as tau proportional, variant N(2.23+/-0.04). This result agrees with the suggestion of Chuang, Kantor, and Kardar [Phys. Rev. E 65, 011802 (2001)] that the translocation time is proportional to the Rouse time, that scales under good solvent condition as tau(Rouse) proportional, variant N(2nu+1), with the excluded-volume exponent nu approximately 0.59 in d=3 dimensions. Our results hence disagree with the suggestions that the translocation time should scale as either N(2) or N(3). For epsilonepsilon(c), we find that the translocation time scales as tau proportional, variant N(1.65+/-0.08). We suggest a tentative scaling explanation for this result. Also the distribution of translocation times is obtained and discussed.

We present a comparison between results, obtained from different simulation models, for the static properties of end-tethered polymer layers in good solvent. Our analysis includes data from two previous studies--the bond fluctuation model of Wittmer et al. [J. Chem. Phys. 101, 4379 (1994)] and the off-lattice bead-spring model of Grest and Murat [Macromolecules 26, 3108 (1993)]. Additionally, we explore the properties of a similar off-lattice model simulated close to the Theta temperature. We show that the data for the bond fluctuation and the Grest-Murat model can be analyzed in terms of scaling theory because chains are swollen inside the Pincus blob. In the vicinity of the Theta point the structure of the chains is essentially Gaussian in the Pincus blob. Therefore, the data for the second off-lattice model can be compared quantitatively to the self-consistent field theory. Different ways to determine the parameters of the self-consistent field theory are discussed.

The spreading of polymer nanodroplets upon a sudden change from partial to complete wetting on an ideally flat and structureless solid substrate has been studied by molecular dynamic simulations using a coarse-grained bead-spring model of flexible macromolecules. Tanner's law for the growth of the lateral droplet radius {R(f) t 0.1 } is found to hold as long as the droplet does not disintegrate into individually moving chains. The data for the contact angle θ following from Tanner's law correspond to a dependence on time {θ(t) t -0.3 }. Our analysis of the mean square displacements of the polymer centers of mass reveals several dynamic regimes during the process of spreading. PACS numbers: 68.10.Gw, 05.70.Ln, 61.20.Ja, 8.45.Gd.

The adsorption of long flexible chains from dilute solution is studied by Monte Carlo simulation of a coarse-grained bead-spring model, and the results are interpreted in terms of phenomenological theories, using both mean field approaches and scaling concepts. It is shown that the surface excess, i.e., the integral of the local density difference of the monomers close to the surface relative to the bulk changes its sign very close to the adsorption transition (that is a sharp transition in the limit where the chain length diverges to infinity) for long chains, and it can be described in terms of the standard scaling description that has previously been tested for polymers with one end anchored on the surface (“polymer mushrooms”). Attention is also paid to the question on how this description changes when the temperature T of the polymer solution approaches the theta temperature Θ. Since the theta point can also be considered as an end point of a line of critical points, where the polymer solution phase ...

Molecular dynamic simulations are reported for system of semi-flexible linear rod-like molecules. The molecules are composed of N c tangent soft spheres, connected by elastic springs. Rigidity is introduced by additional springs between all pairs of spheres along the molecule. The formation of only a nematic LC phase is shown for all systems with N c = 8 and different flexibility. The effect of flexibility on the order parameter and the volume fraction at the LC phase transition is compared with theoretical predictions by Khokhlov-Semenov and with available simulation data. The dependence of the anisotropy of diffusion on chain flexibility in LC phase was studied. The polymer brushes consisting of flexible and semi-flexible (composed of linear rod-like segments) chains were simulated at different grafting densities. Height of brush, order parameter, distribution of density and chain ends in brush were obtained in both cases and compared with theoretical predictions.

This paper presents a topical overview of molecular-dynamics and Monte Carlo simulations for polymer systems close to solid interfaces. The simulations utilize simplified coarse-grained models: The polymers are represented by bead-spring chains, and the walls by a crystalline layer of Lennard-Jones particles or by a smooth impenetrable barrier. This approach has two advantages. First, it reduces the complexity of the simulation. Often, it is only then possible that the interesting length and time scales can be studied at all. Second, the approach concentrates on generic features that are believed to determine the physics of the problem under consideration. The results of the simulation can thus help to single out those features which should be incorporated in an analytical treatment. In this paper, we want to illustrate the versatility of these models by applying them to a broad spectrum of different problems. The situations considered range from the adsorption of a polymer from dilute solution onto a wall, over the importance of sub-monolayer monomeric or polymeric lubricants for kinetic friction, to the crystallization or glass transition of dense polymer films.

The thermodynamics, structure and the chain configurations of symmetrical polymer mixtures confined into ultrathin films are studied by Monte Carlo simulations of the bond fluctuation model. It is shown that the Flory-Huggins–type scaling of the critical temperature (Tc ~ N) with chain length N in the bulk is replaced by a weaker increase, Tc ~ N1/2, in an ultrathin film, and this is interpreted in terms of geometric arguments. The pair-correlation function g(r) of monomers from different chains exhibits a pronounced correlation hole, and the density of intermolecular contacts zc decreases with N as zc ~ N−1/2.

After a brief review of the scaling concepts for static and dynamic properties of polymer brushes in good solvents and Theta solvents, the Monte Carlo evidence is discussed. It is shown that under typical conditions the diameter of the last blob is of the order of 10-20% of the brush height, and therefore pronounced deviations from the self-consistent field predictions occur. In bad solvents, lateral microphase separation occurs leading to an irregular pattern of "dimples". Particularly interesting is the response of brushes to shear deformation, and the interaction between two interpenetrating brushes. Recent attempts to understand the resulting shear forces via molecular-dynamics simulations are briefly described, and an outlook on related experiments is given.

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.