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Polymer models describing the statistics of biomolecules under confinement have applications to a wide range of single-molecule experimental techniques and give insight into biologically relevant processes in vivo. In this paper, we determine the transverse position and bending correlation functions for a wormlike chain confined within slits and cylinders (with one and two confined dimensions, respectively) using a mean-field approach that enforces rigid constraints on average. We show the theoretical predictions accurately capture the statistics of a wormlike chain from Monte Carlo simulations in both confining geometries for both weak and strong confinement. We also show that the longitudinal correlation function is accurately computed for a chain confined to a slit and leverages the accuracy of the model to suggest an experimental technique to infer the (often unobservable) transverse statistics from the (directly observable) longitudinal end-to-end distance. [ABSTRACT FROM AUTHOR]

Functionalizing nanoparticles with organic ligands, such as oligomers, polymers, DNA, and proteins, is an attractive way to manipulate the interfacial interactions between the nanoparticles and the medium the particles are placed in, and thus control the nanoparticle assembly. In this paper we have conducted a Monte Carlo simulation study on copolymer grafted spherical nanoparticles to show the tremendous potential of using monomer sequence on the copolymers to tune the grafted chain conformation, and thus the effective interactions between copolymer grafted nanoparticles. We have studied AB copolymers with alternating, multiblock, or diblock sequences, where either A monomers or B monomers have monomer-monomer attractive interactions. Our focus has been to show the nontrivial effect of monomer sequence on the conformations of the grafted copolymers at various particle diameters, grafting densities, copolymer chain lengths, and monomer-monomer interactions in an implicit small molecule solvent. We observe that the monomer sequence, particle diameter, and grafting density dictate whether (a) the grafted chains aggregate to bring attractive monomers from multiple grafted chains together (interchain and intrachain monomer aggregation) if the enthalpy gained by doing so offsets the entropic loss caused by stretching of chains, or (b) each grafted chain folds onto itself to bring its attractive monomers together (only intrachain monomer aggregation) if the entropic loss from interchain aggregation cannot be overcome by the enthalpic gain. For six copolymers of chain length N=24 grafted on a spherical particle of diameter D=4, interchain and intrachain monomer aggregation occurs, and the radius of gyration varies nonmonotonically with increasing blockiness of the monomer sequence. At larger particle diameters the grafted chains transition to purely intrachain monomer aggregation. The radius of gyration varies monotonically with monomer sequence for intrachain monomer aggregation because as the sequence becomes blockier (like monomers are grouped together), the copolymer chain has to fold less compactly to maximize the enthalpically favorable contacts while maintaining high conformational entropy. The radius of gyration of alternating and diblock copolymers scales with chain length N through a power law (1/2) = alphaN(nu) with the prefactor alpha and scaling exponent nu, varying with monomer sequence and monomer-monomer attraction strength.

Hypothetical scanning Monte Carlo (HSMC) is a method for calculating the absolute entropy S and free energy F from a given MC trajectory developed recently and applied to liquid argon, TIP3P water, and peptides. In this paper HSMC is extended to random coil polymers by applying it to self-avoiding walks on a square lattice--a simple but difficult model due to strong excluded volume interactions. With HSMC the probability of a given chain is obtained as a product of transition probabilities calculated for each bond by MC simulations and a counting formula. This probability is exact in the sense that it is based on all the interactions of the system and the only approximation is due to finite sampling. The method provides rigorous upper and lower bounds for F, which can be obtained from a very small sample and even from a single chain conformation. HSMC is independent of existing techniques and thus constitutes an independent research tool. The HSMC results are compared to those obtained by other methods, and its application to complex lattice chain models is discussed; we emphasize its ability to treat any type of boundary conditions for which a reference state (with known free energy) might be difficult to define for a thermodynamic integration process. Finally, we stress that the capability of HSMC to extract the absolute entropy from a given sample is important for studying relaxation processes, such as protein folding.

The nonlinear viscoelastic behavior of the Fraenkel-chain model is studied with respect to the constitutive equation of the Rouse model. Distinctly different from the results of the Rouse model, the Fraenkel-chain model gives the following characteristic nonlinear behavior: (a) The two distinct dynamic modes in the relaxation modulus GS(t,λ)—as observed in the linear region reported in Paper I [Y.-H. Lin and A. K. Das, J. Chem. Phys. 126, 074902 (2007), preceding paper]—or in the first normal-stress difference function GΨ1(t,λ) are shown to have different strain dependences: strain hardening for the fast mode and strain softening for the slow mode. (b) The Lodge–Meissner relation GS(t,λ)=GΨ1(t,λ) holds over the whole time range, which has been shown both analytically and by simulation. (c) The second normal-stress difference is nonzero, being positive in the fast-mode region and negative in the slow-mode region. The comparisons between orientation and stress for all tensor components consistently confirm the strong correlation of the slow mode as well as its entropic nature with the segmental-orientation anisotropy as shown in the linear region studied in Paper I. A consequence of this correlation is the applicability of the stress-optical rule in the slow-mode region. This also leads to the expectation that the damping function h(λ)=GS(t,λ)/GS(t,λ→0) and the ratio between the first and second normal-stress differences, N2(t,λ)/N1(t,λ), are described by the orientation tensor which has the same form as that given by Doi and Edwards [J. Chem. Soc. Faraday Trans. 2 74, 1789 (1978); 74, 1802 (1978)] with independent-alignment approximation for an entangled system. The similarity between the slow mode of an entanglement-free Fraenkel-chain system and the terminal mode of an entangled polymer system as observed in the comparison of theory, simulation, and experiment suggests that the close correlation of the entropic nature of the mode with the orientation anisotropy—as of the Fraenkel segment or the primitive step in the Doi–Edwards theory—is a generally valid physical concept in polymer viscoelasticity. [ABSTRACT FROM AUTHOR]

In the first paper of this series, we developed a new one-dimensional Monte Carlo approach for the study of flexible chains that are translocating through a small channel. We also presented a numerical scheme that can be used to obtain exact values for both the escape times and the escape probabilities given an initial pore-polymer configuration. We now present and discuss the fundamental scaling behaviors predicted by this Monte Carlo method. Our most important result is the fact that, in the presence of an external bias E, we observe a change in the scaling law for the translocation time τ as function of the polymer length N: In the general expression τ∼Nβ/E, the exponent changes from β=1 for moderately long chains to β=1+ν or β=2ν for very large values of N (for Rouse and Zimm dynamics, respectively). We also observe an increase in the effective diffusion coefficient due to the presence of entropic pulling on unbiased polymer chains. [ABSTRACT FROM AUTHOR]

The rheological behaviors of polymer brush under oscillatory shear flow were investigated by nonequilibrium Monte Carlo simulation. The grafted chain under oscillatory shear flow exhibited a waggling behavior like a flower, and the segments were found to have different oscillatory phases along the chain contour. Stress tensor was further obtained based on the statistics of sampled configuration distribution functions. The simulation reproduced the abrupt increase of the first normal stress difference N1 with the flow velocity over a critical value, as observed in the experiment of Klein et al. [Nature (London) 352, 143 (1991)]. However, our simulation did not reproduce the brush thickening with shear velocity increased, which was suggested to be responsible for the abrupt increase of N1 in the above-mentioned paper. This simulation demonstrates that the increase of normal stress might be an inherent behavior of polymer brush due to chain deformation under flow. [ABSTRACT FROM AUTHOR]

This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the θ-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of “good solvents” and “θ-solvents” in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types. [ABSTRACT FROM AUTHOR]

Morphology of symmetric ABCD tetrablock quaterpolymers in melt was studied by the Monte Carlo (MC) simulation, where the volume fractions of the block chains, f, kept the relationships of fA = fD and fB = fC, and the volume fraction of the two mid-blocks φ was defined as φ = fB + fC. Previous self-consistent field theory for ABCD reported morphological change including several structures; however, the scope was limited within a two-dimensional system. To the contrary, in this paper, MC simulations were carried out in three dimensions with changing the φ value finely, which resulted in finding a tetracontinuous structure in the range of 0.625 ⩽ φ ⩽ 0.75. Moreover the tetracontinuous structure has been found to be the gyroid structure, and the mean curvature of the B/C interface is nearly zero. We concluded that the B/C interface must be the Schoen gyroid surface, one of three-dimensional periodic minimal surfaces. The geometrical nature of the A/B interface should be equivalent to that of the C/D interface, and they stand as level surfaces to the Schoen gyroid surface. [ABSTRACT FROM AUTHOR]

In efforts to produce polymeric materials with tailored physical properties, significant interest has grown around the ability to control the spatial organization of nanoparticles in polymer nanocomposites. One way to achieve controlled particle arrangement is by grafting the nanoparticle surface with polymers that are compatible with the matrix, thus manipulating the interfacial interactions between the nanoparticles and the polymer matrix. Previous work has shown that the molecular weight of the grafted polymer, both at high grafting density and low grafting density, plays a key role in dictating the effective inter-particle interactions in a polymer matrix. At high grafting density nanoparticles disperse (aggregate) if the graft molecular weight is higher (lower) than the matrix molecular weight. At low grafting density the longer grafts can better shield the nanoparticle surface from direct particle-particle contacts than the shorter grafts and lead to the dispersion of the grafted particles in the matrix. Despite the importance of graft molecular weight, and evidence of non-trivial effects of polydispersity of chains grafted on flat surfaces, most theoretical work on polymer grafted nanoparticles has only focused on monodisperse grafted chains. In this paper, we focus on how bidispersity in grafted chain lengths affects the grafted chain conformations and inter-particle interactions in an implicit solvent and in a dense homopolymer polymer matrix. We first present the effects of bidispersity on grafted chain conformations in a single polymer grafted particle using purely Monte Carlo (MC) simulations. This is followed by calculations of the potential of mean force (PMF) between two grafted particles in a polymer matrix using a self-consistent Polymer Reference Interaction Site Model theory-Monte Carlo simulation approach. Monte Carlo simulations of a single polymer grafted particle in an implicit solvent show that in the bidisperse polymer grafted particles with an equal number of short and long grafts at low to medium grafting density, the short grafts are in a more coiled up conformation (lower radius of gyration) than their monodisperse counterparts to provide a larger free volume to the longer grafts so they can gain conformational entropy. The longer grafts do not show much difference in conformation from their monodisperse counterparts at low grafting density, but at medium grafting density the longer grafts exhibit less stretched conformations (lower radius of gyration) as compared to their monodisperse counterparts. In the presence of an explicit homopolymer matrix, the longer grafts are more compressed by the matrix homopolymer chains than the short grafts. We observe that the potential of mean force between bidisperse grafted particles has features of the PMF of monodisperse grafted particles with short grafts and monodisperse grafted particles with long grafts. The value of the PMF at contact is governed by the short grafts and values at large inter-particle distances are governed by the longer grafts. Further comparison of the PMF for bidisperse and monodisperse polymer grafted particles in a homopolymer matrix at varying parameters shows that the effects of matrix chain length, matrix packing fraction, grafting density, and particle curvature on the PMF between bidisperse polymer grafted particles are similar to those seen between monodisperse polymer grafted particles. [ABSTRACT FROM AUTHOR]

The classical bond-fluctuation model (BFM) is an efficient lattice Monte Carlo algorithm for coarse-grained polymer chains where each monomer occupies exclusively a certain number of lattice sites. In this paper we propose a generalization of the BFM where we relax this constraint and allow the overlap of monomers subject to a finite energy penalty [variant_greek_epsilon]. This is done to vary systematically the dimensionless compressibility g of the solution in order to investigate the influence of density fluctuations in dense polymer melts on various static properties at constant overall monomer density. The compressibility is obtained directly from the low-wave vector limit of the static structure factor. We consider, e.g., the intrachain bond-bond correlation function P(s) of two bonds separated by s monomers along the chain. It is shown that the excluded volume interactions are never fully screened for very long chains. If distances smaller than the thermal blob size are probed (s≤g) the chains are swollen according to the classical Fixman expansion where, e.g., P(s)∼g-1s-1/2. More importantly, the polymers behave on larger distances (s>g) like swollen chains of incompressible blobs with P(s)∼g0s-3/2. [ABSTRACT FROM AUTHOR]

In this paper, we construct an effective model for the dynamics of an excluded-volume chain under confinement by extending the formalism of Rouse modes. We make specific predictions about the behavior of the modes for a single polymer confined to a tube. The results are tested against Monte Carlo simulations using the bond-fluctuation algorithm which uses a lattice representation of the polymer chain with excluded-volume effects. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations of a model fluid in which the particles interact via a continuous potential that has a logarithmic divergence at a pair separation of σ, which we introduced in J. G. Powles et al., Proc. R. Soc. London, Ser. A 455, 3725 (1999), have been carried out. The potential has the form, [lowercase_phi_synonym](r)=-ε ln(f(r)), where ε sets the energy scale and f(r)=1-(σ/r)m. The value of m chosen was 12 but the qualitative trends depend only weakly on the value of m, providing it is greater than 3. The potential is entirely repulsive and has a logarithmic divergence as ∼-ln(r/σ-1) in the r→σ limit. Predictions of the previous paper that the internal energy can be computed at all temperatures using the standard statistical mechanics formula for continuous potentials are verified here. The pressure can be calculated using the usual virial expression for continuous potentials, although there are practical limitations in resolving the increasingly important contribution from the r→σ limit at reduced temperatures greater than ∼5. The mean square force ≤F2≥ and infinite frequency shear G∞ and bulk K∞ moduli are only finite for T*=kBT/ε<1. The logarithmic fluid’s physical properties become increasingly more like that of the hard sphere fluid with increasing temperature, showing a sharp transition in the behavior of the mean square force and infinite frequency elastic constants at T*=1. The logarithmic fluid is shown to exhibit a solid-fluid phase transition. [ABSTRACT FROM AUTHOR]

Proteins contain many voids, which are unfilled spaces enclosed in the interior. A few of them have shapes compatible to ligands and substrates and are important for protein functions. An important general question is how the need for maintaining functional voids is influenced by, and affects other aspects of proteins structures and properties (e.g., protein folding stability, kinetic accessibility, and evolution selection pressure). In this paper, we examine in detail the effects of maintaining voids of different shapes and sizes using two-dimensional lattice models. We study the propensity for conformations to form a void of specific shape, which is related to the entropic cost of void maintenance. We also study the location that voids of a specific shape and size tend to form, and the influence of compactness on the formation of such voids. As enumeration is infeasible for long chain polymer, a key development in this work is the design of a novel sequential Monte Carlo strategy for generating large number of sample conformations under very constraining restrictions. Our method is validated by comparing results obtained from sampling and from enumeration for short polymer chains. We succeeded in accurate estimation of entropic cost of void maintenance, with and without an increasing number of restrictive conditions, such as loops forming the wall of void with fixed length, with additionally fixed starting position in the sequence. Additionally, we have identified the key structural properties of voids that are important in determining the entropic cost of void formation. We have further developed a parametric model to predict quantitatively void entropy. Our model is highly effective, and these results indicate that voids representing functional sites can be used as an improved model for studying the evolution of protein functions and how protein function relates to protein stability. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper reports the first computational estimation of the comb polymers’ third virial coefficients. The number of the chains in the comb polymers range from 5 to 11. An algorithm that counts the contributing terms of the third virial coefficients in an accelerated manner is presented along with its efficiency dependence on the polymers’ size. In addition, the second virial coefficients are estimated for the comb polymers and compared to previously reported results. [ABSTRACT FROM AUTHOR]

Large scale molecular dynamics and grand canonical Monte Carlo simulation techniques are used to study the behavior of the interdiffusion of a solvent into an entangled polymer matrix as the state of the polymer changes from a melt to a glass. The weight gain by the polymer increases with time t as t1/2 in agreement with Fickian diffusion for all cases studied, although the diffusivity is found to be strongly concentration dependent especially as one approaches the glass transition temperature of the polymer. The diffusivity as a function of solvent concentration determined using the one-dimensional Fick’s model of the diffusion equation is compared to the diffusivity calculated using the Darken equation from simulations of equilibrated solvent-polymer solutions. The diffusivity calculated using these two different approaches are in good agreement. The behavior of the diffusivity strongly depends on the state of the polymer and is related to the shape of the solvent concentration profile.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we present a comprehensive lattice Monte Carlo study of long chain conformations at solid–polymer melt interfaces. Segmental scale interfacial features, like the bond orientational distribution were found to be independent of surface–segment energetics, and statistically identical with Helfand’s predictions for the full-occupancy, infinite chain length limit. Conformational statistics of chains longer than 5–6 statistical segments followed the predictions of the Scheutjens–Fleer theory and the same power laws as a single ideal chain at the critical value of the surface–segment adsorption free-energy. Our simulations tested the predictions of random walk next to a ‘‘reflective’’ surface statistics for the spatial variations of chain dimensions and chain center of mass density. It was found that these statistics furnish the correct long chain limit, independently of surface–segment energetics. The random walk next to a ‘‘reflective’’ boundary predictions for the ‘‘adsorbed’’ amount and the distributions of tail, loop, and train number, as well as tail and loop size were in quantitative agreement with the simulation data. The correspondence between random walks and real (or simulated) chains required the knowledge of a single, microscopic parameter, the number of chemical segments per statistical segment, a∞. This quantity was very close to the average length of adsorbed sequences (trains), in the long chain limit. Our simulations tested thoroughly and established firmly the validity of ‘‘reflective’’ boundary statistics in the melt. The inevitability of these statistics has broad implications on ‘‘desorption’’ kinetics, chain mobility, and chain relaxation, which are currently under study. [ABSTRACT FROM AUTHOR]

Stretching of semicrystalline polymer materials is fundamentally important in their mechanical performance and industrial processing. By means of dynamic Monte Carlo simulations, we compared the parallel stretching processes between the initially bulk amorphous and semicrystalline polymers at various temperatures. In the early stage of stretching, semicrystalline polymers perform local and global melting-recrystallization behaviors at low and high temperatures, while the memory effects occur upon global melting-recrystallization at middle temperatures. However, the final crystallinities, crystalline bond orientations, chain-folding probabilities, residual stresses, and crystallite morphologies at high enough strains appear as the same at each temperature, irrelevant to the initially amorphous and semicrystalline polymers, indicating that the common post-growth melting-reorganization processes determine the final products. In addition, both final products harvest the highest crystallinities in the middle temperature region because the postgrowth stage yields the vast nuclei followed with less extent of crystal growth in the low temperature region and few nuclei followed with large extent of crystal growth in the high temperature region. Our observations imply that a large enough strain can effectively remove the thermal history of polymers, similar to the thermal treatment at a high enough temperature; therefore, the fracture strength of semicrystalline polymers depends upon their final structures in stretching, not related to their nascent semicrystalline structures. [ABSTRACT FROM AUTHOR]

The process during which a polymer translocates through a nanopore depends on many physical parameters and fundamental mechanisms. We propose a new one-dimensional lattice Monte Carlo algorithm that integrates various effects such as the entropic forces acting on the subchains that are outside the channel, the external forces that are pulling the polymer through the pore, and the frictional effects that involve the chain and its environment. Our novel approach allows us to study the polymer as a single Brownian particle diffusing while subjected to a position-dependent force that includes both the external driving forces and the internal entropic bias. Frictional effects outside and inside the pore are also considered. This Monte Carlo method is much more efficient than other simulation methods, and it can be used to obtain scaling laws for various polymer translocation regimes. In this first part, we derive the model and describe a subtle numerical approach that gives exact results for both the escape probability and the mean translocation time (and higher moments of its distribution). The scaling laws obtained from this model will be presented and discussed in the second part of this series. [ABSTRACT FROM AUTHOR]

We simulated the translocation process of a polymer chain from a source container to a drain container through a short nanochannel. We utilized the bond fluctuation model coupled with Monte Carlo dynamics in our simulations. The calculation results show that the excluded volume effect significantly affects the polymer’s translocation time τ. This time depends nonmonotonically on the polymer length N. For a fixed nanochannel length, τ decreases when the polymer length increases. τ, however, increases when the polymer length exceeds a certain threshold. This observation differs from those predicated for a Gaussian chain. In this paper, we will further present our findings to explain this phenomenon. The knowledge we gain from this research can enhance the understanding of complex transport processes in many biological systems. [ABSTRACT FROM AUTHOR]

Bounded potentials are good models to represent the effective two-body interaction in some colloidal systems, such as the dilute solutions of polymer chains in good solvents. The simplest bounded potential is that of penetrable spheres, which takes a positive finite value if the two spheres are overlapped, being 0 otherwise. Even in the one-dimensional case, the penetrable-rod model is far from trivial, since interactions are not restricted to nearest neighbors and so its exact solution is not known. In this paper the structural properties of one-dimensional penetrable rods are studied. We first derive the exact correlation functions of the penetrable-rod fluids to second order in density at any temperature, as well as in the high-temperature and zero-temperature limits at any density. It is seen that, in contrast to what is generally believed, the Percus-Yevick equation does not yield the exact cavity function in the hard-rod limit. Next, two simple analytic theories are constructed: a high-temperature approximation based on the exact asymptotic behavior in the limit T→∞ and a low-temperature approximation inspired by the exact result in the opposite limit T→0. Finally, we perform Monte Carlo simulations for a wide range of temperatures and densities to assess the validity of both theories. It is found that they complement each other quite well, exhibiting a good agreement with the simulation data within their respective domains of applicability and becoming practically equivalent on the borderline of those domains. A comparison with numerical solutions of the Percus-Yevick and the hypernetted-chain approximations is also carried out. Finally, a perspective on the extension of our two heuristic theories to the more realistic three-dimensional case is provided. [ABSTRACT FROM AUTHOR]

Studies the phase behavior of single homopolymers in a simple hydrophobic/hydrophilic off-lattice model with sequence independent local interactions. Monte Carlo methods used in the study; Dynamics of the algorithms; Measurement of specific heat and bond-bond correlation function.

In this paper, we present the results of Monte Carlo simulations of the static properties of polymer melts confined between hard walls. The simulations are conducted in the canonical ensemble with a method that is a combination of reptation and crankshaft motions. 1250 polymer chains each comprising of 100 connected beads are placed in a box which allows for the simulation of a typical polymer melt confined between two hard plates at a separation of 51 bead diameters. Noncovalently bonded beads are assumed to interact with an empirical 6-12 Lennard-Jones potential which has parameters chosen to simulate a polyethylene melt at 400 K. From the analysis of the simulation results we show the existence of two relevant length scales in the problem. Single-chain statistics are perturbed by the wall, and this effect is screened out only after one proceeds to a distance comparable to twice the unperturbed radius of gyration of the polymer chain. However, many-chain statistics, i.e., packing and orientation of chain segments, are screened out as soon as one proceeds about three times the bead size from the wall. The simulation also allows for the study of the conformations of chains near the wall, and we observe that chains near the surface are flattened into nearly two-dimensional structures. The interface therefore corresponds to a region where chain configurations gradually evolve from this nearly two-dimensional structure to the unperturbed, three-dimensional Gaussian configurations in the bulk. [ABSTRACT FROM AUTHOR]

The three-parameter model of excluded volume is employed to calculate both the moments {n=2,3,...} of the end-to-end vector distance of a linear homopolymer and the average square moment for a single branch of an f-armed star. These results complement the calculations of , the radius of gyration RG, the Kirkwood approximation to the hydrodynamic radius RH, and the second virial coefficient A2 for linear chains given in paper I. These calculations are intended to check the self-consistency of the ternary interaction theory against recent simulation data for lattice chains under theta conditions (A2=0) using the fact that higher moments and properties of branched polymers are more sensitive to the presence of ternary interactions. No free parameters are involved in the comparison, and the agreement between theory and numerical data is quite satisfactory. In addition, a general discussion is provided of differences in values of various polymer properties that can result from different methods of regularizing the continuum theory. [ABSTRACT FROM AUTHOR]

Fluid–fluid phase separation in a simple model for a colloid dispersed in a solution of stiff rodlike polymers is studied by means of Gibbs ensemble Monte Carlo simulations. The fluid–solid transition for this model is computed using first-order perturbation theory. The phase diagrams clearly show that a stable critical point is not possible for polymer lengths smaller than 30% of the colloidal particle diameter. At very large rod length, the fluid coexistence curve can be derived directly from the hard-sphere equation of state. © 1994 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present computer simulations of dense polymer mixtures composed of flexible and semiflexible chains. It is found that a demixing transition takes place below a certain degree of flexibility, even without introducing repelling interactions between the two polymers except the excluded volume condition. Computing the equilibrium concentration of phases for various temperatures, a phase diagram for the binary mixture is found. The results show qualitative agreement with the Flory lattice theory of stiff chains. [ABSTRACT FROM AUTHOR]

The adsorption of hard chains in slitlike pores is studied via an integral equation theory. The theory uses the growing adsorbent model in conjunction with the polymer reference interaction site model (polymer-RISM) theory to predict the wall–fluid correlation functions; wall–fluid and fluid–fluid correlations are treated using the Percus–Yevick closure relations. The theory is compared to Monte Carlo simulation data for the density profiles of 4-mers and 8-mers in slitlike pores; the theory is fairly accurate, though it tends to overestimate the density at the wall at low densities and underestimate the density at the wall at high densities. The theory also underestimates the amplitude of the oscillations in the density profile. The theory is very accurate, however, for the adsorption isotherm of 4-mers and 8-mers. [ABSTRACT FROM AUTHOR]

The equilibrium conformation of a polymer molecule in an external field is often used in field theories to calculate macroscopic polymer properties of melts and solutions. We use a mathematical method called a Brownian bridge to exactly sample continuous polymer chains to end in a given state. We show that one can systematically develop such processes to sample specific polymer topologies, to confine polymers in a given geometry for its entire path, to efficiently generate high-probability conformations by excluding small Boltzmann weights, or to simulate rare events in a rugged energy landscape. This formalism can improve the polymer sampling efficiency significantly compared to traditional methods (e.g., Monte Carlo or Rosenbluth). [ABSTRACT FROM AUTHOR]

We introduce a novel coarse-grained bead-spring model for flexible polymers to systematically examine the effects of an adjusted bonded potential on the formation and stability of structural macrostates in a thermal environment. The density of states obtained in advanced replica-exchange Monte Carlo simulations is analyzed by employing the recently developed generalized microcanonical inflection-point analysis method, which enables the identification of diverse structural phases and the construction of a suitably parameterized hyperphase diagram. It reveals that icosahedral phases dominate for polymers with asymmetric and narrow bond potentials, whereas polymers with symmetric and more elastic bonds tend to form amorphous structures with non-icosahedral cores. We also observe a hierarchy in the freezing transition behavior associated with the formation of the surface layer after nucleation. [ABSTRACT FROM AUTHOR]

Interaction between two simple ring chains catenated in a molecule was estimated by a Metropolis Monte Carlo simulation, and the result was compared with a model. We employed catenated ring chains in this study; they were composed of two simple ring chains, and the topology was kept as 2 1 2 . The temperature dependence of the distance between two ring chains in a molecule was discussed using Flory's scaling exponent, ν, in Rg ∝ Nν, where Rg is the radius of gyration of a simple ring chain catenated in a molecule. In the simulation, the topology of the component rings and their links were kept because chain crossing was prohibited. The excluded volume of chains was screened by the attractive force between polymer segments, and the strength of the attractive force depends on temperature, T. At the θ temperature for trivial ring polymers, where the condition ν = 1/2 holds, their trajectories can be described statistically as a closed-random walk, i.e., a closed-phantom chain model. The temperature at which interaction between trivial ring polymers, i.e., inter-molecular interaction, is repulsive; trivial ring polymer molecules show the excluded volume generated with keeping their own topology, 01. A catenated molecule is composed of two simple rings, and so forth a component ring can be affected by the existence of the counterpart rings. Under that temperature, the mean-square distance between two rings in a catenated molecule, ⟨L2⟩, was obtained and compared with that of the simple model composed of two circles in three-dimensions, where interaction between circles is set as zero. It has been found that the simulated ⟨L2⟩ values were constantly larger than those of the model owing to the excluded volume of rings in a molecule. [ABSTRACT FROM AUTHOR]

We investigate the structural phases of single poly(3-hexylthiophene) (P3HT) polymers that are adsorbed on a two-dimensional substrate with a striped pattern. We use a coarse-grained representation of the polymer and sophisticated Monte Carlo techniques such as a parallelized replica exchange scheme and local as well as non-local updates to the polymer's configuration. From peaks in the canonically derived observables, it is possible to obtain structural phase diagrams for varying substrate parameters. We find that the shape of the stripe pattern has a substantial effect on the obtained configurations of the polymer and can be tailored to promote either more stretched out or more compact configurations. In the compact phases, we observe different structural motifs, such as hairpins, double-hairpins, and interlocking "zipper" states. [ABSTRACT FROM AUTHOR]

We present an analytical theory to describe conformational changes as a function of salt for polymers with a given sequence of charges. We apply this model to describe Intrinsically Disordered Proteins (IDPs) by explicitly accounting for charged residues and their exact placement in the primary sequence while approximating the effect of non-electrostatic interactions at a mean-field level by effective short-range (two body and three-body) interaction parameters. The effect of ions is introduced by treating electrostatic interactions within Debye-Huckle approximation. Using typical values of the short-range mean-field parameters derived from all-atom Monte Carlo simulations (at zero salt), we predict the conformational changes as a function of salt concentration. We notice that conformational transitions in response to changes in ionic strength strongly depend on sequence specific charge patterning. For example, globule to coil transition can be observed upon increasing salt concentration, in stark contrast to uniformly charged polyelectrolyte theories based on net charge only. In addition, it is possible to observe non-monotonic behavior with salt as well. Drastic differences in salt-induced conformational transitions is also evident between two doubly phosphorylated sequences—derived from the same wild type sequence—that only differ in the site of phosphorylation. Similar effects are also predicted between two sequences derived from the same parent sequence differing by a single site mutation where a negative charge is replaced by a positive charge. These effects are purely a result of charge decoration and can only be understood in terms of metrics based on specific placement of charges, and cannot be explained by models based on charge composition alone. Identifying sequences and hot spots within sequences—for post translational modification or charge mutation—using our high-throughput theory will yield fundamental insights into design and biological regulation mediated by phosphorylation and/or local changes in salt concentration. [ABSTRACT FROM AUTHOR]

Depletion forces and macromolecular crowding govern the structure and function of biopolymers in biological cells and the properties of polymer nanocomposite materials. To isolate and analyze the influence of polymer shape fluctuations and penetrability on depletion-induced interactions and crowding by nanoparticles, we model? polymers as effective penetrable ellipsoids, whose shapes fluctuate according to the probability distributions of the eigenvalues of the gyration tensor of an ideal random walk. Within this model, we apply Monte Carlo simulation methods to compute the depletion-induced potential of mean force between hard nanospheres and crowding-induced shape distributions of polymers in the protein limit, in which polymer coils can be easily penetrated by smaller nanospheres. By comparing depletion potentials from simulations of ellipsoidal and spherical polymer? models with predictions of polymer? field theory and free-volume theory, we show that polymer depletion-induced interactions and crowding depend sensitively on polymer shapes and penetrability, with important implications for bulk thermodynamic phase behavior. [ABSTRACT FROM AUTHOR]

The second virial coefficient, A2, for trivial-ring polymers in dilute condition was estimated from a Metropolis Monte Carlo (MC) simulation, and the temperature dependence of A2 has been discussed with their Flory's scaling exponent, v, in Rg ∝ Nv, where Rg is radius of gyration of a polymer molecule. A limited but not too small number of polymer molecules were employed in the simulation, and the A2 values at various temperatures were calculated from the molecular density fluctuation in the solution. In the simulation, the topology of ring polymers was kept, since chain crossing was prohibited. The excluded volume effects can be screened by the attractive force between segments, which depends on the temperature, Tα, defined in the Metropolis MC method. Linear and trivial-ring polymers have the v value of 1/2 at Tα = 10.605 and 10.504. At Tα = 10.504, the excluded volume effects are screened by the attractive force generated between segments in a ring polymer, but the A2 value for ring polymers is positive. Thus, the temperature at A2 = 0 for a ring polymer is lower than that at v = 1/2, and this fact can be explained with the following two reasons. (a) Rg value for a ring polymer is much smaller than that for a linear polymer at the same temperature and molecular weight, where interpenetration of a ring polymer chain into neighboring chains is apparently less than a linear chain. (b) The conformation of trivial rings can be statistically described as a closed random walk at v = 1/2, but their topologies are kept, being produced topological constraints, which strongly relate not only to the long-distance interaction between segments in a molecule but also the inter-molecular interaction. [ABSTRACT FROM AUTHOR]

The problem of demixing in the Asakura-Oosawa colloid-polymer model is considered. The critical constants are computed using truncated virial expansions up to fifth order. While the exact analytical results for the second and third virial coefficients are known for any size ratio, analytical results for the fourth virial coefficient are provided here, and fifth virial coefficients are obtained numerically for particular size ratios using standard Monte Carlo techniques. We have computed the critical constants by successively considering the truncated virial series up to the second, third, fourth, and fifth virial coefficients. The results for the critical colloid and (reservoir) polymer packing fractions are compared with those that follow from available Monte Carlo simulations in the grand canonical ensemble. Limitations and perspectives of this approach are pointed out. [ABSTRACT FROM AUTHOR]

Multi-scale aggregation to network formation of interacting proteins (H3.1) are examined by a knowledge-based coarse-grained Monte Carlo simulation as a function of temperature and the num-ber of protein chains, i.e., the concentration of the protein. Self-assembly of corresponding homo- polymers of constitutive residues (Cys, Thr, and Glu) with extreme residue-residue interactions, i.e., attractive (Cys-Cys), neutral (Thr-Thr), and repulsive (Glu-Glu), are also studied for comparison with the native protein. Visual inspections show contrast and similarity in morphological evolutions of protein assembly, aggregation of small aggregates to a ramified network from low to high tem-perature with the aggregation of a Cys-polymer, and an entangled network of Glu and Thr polymers. Variations in mobility profiles of residues with the concentration of the protein suggest that the seg- mental characteristic of proteins is altered considerably by the self-assembly from that in its isolated state. The global motion of proteins and Cys polymer chains is enhanced by their interacting network at the low temperature where isolated chains remain quasi-static. Transition from globular to random coil transition, evidenced by the sharp variation in the radius of gyration, of an isolated protein is smeared due to self-assembly of interacting networks of many proteins. Scaling of the structure fac-tor S(q) with the wave vector q provides estimates of effective dimension D of the mass distribution at multiple length scales in self-assembly. Crossover from solid aggregates (D ∼ 3) at low temperature to a ramified fibrous network (D ∼ 2) at high temperature is observed for the protein H3.1 and Cys polymers in contrast to little changes in mass distribution (D ∼ 1.6) of fibrous Glu- and Thr-chain configurations. [ABSTRACT FROM AUTHOR]

The coil-bridge transition in a self-avoiding lattice chain with one end fixed at height H above the attractive planar surface is investigated by theory and Monte Carlo simulation. We focus on the details of the first-order phase transition between the coil state at large height H ≥ Htr and a bridge state at H ≤ Htr, where Htr corresponds to the coil-bridge transition point. The equilibrium properties of the chain were calculated using the Monte Carlo pruned-enriched Rosenbluth method in the moderate adsorption regime at (H/Nα)tr ≤ 0.27 where N is the number of monomer units of linear size a. An analytical theory of the coil-bridge transition for lattice chains with excluded volume interactions is presented in this regime. The theory provides an excellent quantitative description of numerical results at all heights, 10 ≤ H/&945; ≤ 320 and all chain lengths 40 < N < 2560 without free fitting parameters. A simple theory taking into account the effect of finite extensibility of the lattice chain in the strong adsorption regime at (H/Nα)tr ≥ 0.5 is presented. We discuss some unconventional properties of the coil-bridge transition: the absence of phase coexistence, two micro-phases involved in the bridge state, and abnormal behavior in the microcanonical ensemble. [ABSTRACT FROM AUTHOR]

The effect of nano-sized fillers on the equilibrium and dynamical properties of a linear polymer is studied by using off-lattice Monte Carlo simulation. Fillers are arranged periodically in the system with period d and Lennard-Jones interaction between polymer and fillers is considered. Results show that the statistical dimension and dynamical diffusion of the polymer are dependent on the polymer-filler interaction strength Épf and the relative size between RG0 and d, here RG0 is the radius of gyration of polymer in dilute solution. Normal diffusion of polymer is always observed in the regime 2RG0 > d. And the diffusion coefficient D is scaled with chain length N as D â N â'α, where the exponent α increases with Épf. Whereas in the regime 2RG0 < d â% Nl 0 with l 0 the mean bond length of polymer, normal diffusion is observed only at Épf < 2, but the polymer will be adsorbed on the fillers and cannot diffuse at Épf > 2. In addition, we find that there is a critical interaction strength É* pf = 2 in our model system. [ABSTRACT FROM AUTHOR]

Using Monte Carlo simulations based on the bond fluctuation model we study the adsorption of starburst dendrimers with flexible spacers onto a flat surface. The calculations are performed for various generation number G and spacer length S in a wide range of the reduced temperature τ as the measure of the interaction strength between the monomers and the surface. Our simulations indicate a two-step adsorption scenario. Below the critical point of adsorption, τc, a weakly adsorbed state of the dendrimer is found. Here, the dendrimer retains its shape but sticks to the surface by adsorbed spacers. By lowering the temperature below a spacer-length dependent value, τ*(S) < τc, a step-like transition into a strongly adsorbed state takes place. In the flatly adsorbed state the shape of the dendrimer is well described by a mean field model of a dendrimer in two dimensions. We also performed simulations of star-polymers which display a simple crossover-behavior in full analogy to linear chains. By analyzing the order parameter of the adsorption transition, we determine the critical point of adsorption of the dendrimers which is located close to the critical point of adsorption for star-polymers. While the order parameter for the adsorbed spacers displays a critical crossover scaling, the overall order parameter, which combines both critical and discontinuous transition effects, does not display simple scaling. The step-like transition from the weak into the strong adsorbed regime is confirmed by analyzing the shape-anisotropy of the dendrimers. We present a mean-field model based on the concept of spacer adsorption which predicts a discontinuous transition of dendrimers due to an excluded volume barrier. The latter results from an increased density of the dendrimer in the flatly adsorbed state which has to be overcome before this state is thermodynamically stable. [ABSTRACT FROM AUTHOR]

A complex composed of a charged flexible polymer chain irreversibly attached with its ends to surfaces of two nanoparticles was investigated using the Metropolis Monte Carlo method on a simple cubic lattice. The simulations were performed in the presence of explicit ions. The bridging chain and the nanoparticles bearing the same and the opposite sign charges were considered. Changes in the free energy of the complex upon its stretching or compression, together with the magnitude of the elastic force, were examined. The relative roles of energetic and entropic effects in determining the properties of the complex were identified. Also, the adsorption of charged monomers on the opposite-sign charged nanoparticles and its influence on the examined quantities was studied. Moreover, a simple semi-analytical approach to the thermodynamics of the polymer bridge was derived. [ABSTRACT FROM AUTHOR]

We studied equilibrium conformations of trivial-, 31-knot, and 51-knot ring polymers with finite chain length at their θ-conditions using a Monte Carlo simulation. The polymer chains treated in this study were composed of beads and bonds on a face-centered-cubic lattice respecting the excluded volume. The Flory's critical exponent ν in Rg ∼ Nν relationship was obtained from the dependence of the radius of gyration, Rg, on the segment number of polymers, N. In this study, the temperatures at which ν equal 1/2 are defined as θ-temperatures of several ring molecules. The θ-temperatures for trivial-, 31-knot, and 51-knot ring polymers are lower than that for a linear polymer in N <= 4096, where their topologies are fixed by their excluded volumes. The radial distribution functions of the segments in each molecule are obtained at their θ-temperatures. The functions of linear- and trivial-ring polymers have been found to be expressed by those of Gaussian and closed-Gaussian chains, respectively. At the θ-conditions, the excluded volumes of chains and the topological-constraints of trivial-ring polymers can be apparently screened by the attractive force between segments, and the g2> values for trivial ring polymers are larger than the half of those for linear polymers. In the finite N region the topological-constraints of 31- and 51-knot rings are stronger than that of trivial-ring, and trajectories of the knotted ring polymers cannot be described as a closed Gaussian even though they are under θ-conditions. [ABSTRACT FROM AUTHOR]

An athermal solution of semiflexible macromolecules with excluded volume interactions has been studied at various concentrations (dilute, semidilute, and concentrated solutions) in a film of thickness D between two hard walls by grand canonical Monte Carlo simulations of the bond fluctuation lattice model. Analyzing profiles of orientational order parameters across the film, we find that for thick films two phase transitions occur at chemical potentials of the polymers (or polymer densities, respectively) where the bulk polymer solution still is in the disordered isotropic phase. At rather small polymer densities, polymers accumulate at the walls due to an entropic attraction and undergo a transition to two-dimensional nematic order. Due to the properties of the lattice model, this order has Ising character, and the simulation results seem to be compatible with a second-order transition. Increasing the polymer density, nematically ordered 'wetting' layers form at both walls; the increase of thickness of these layers is compatible with a logarithmic divergence when the chemical potential of the isotropic-nematic transition in the bulk is approached. In a system of finite width, D, between the walls, this leads to capillary nematization, exhibiting a reduction of the transition chemical potential inversely proportional to D. This transition exists only if D exceeds some critical value Dc, while the transition from the isotropic phase to the two-dimensional nematic state is suggested to persist down to ultrathin films. [ABSTRACT FROM AUTHOR]

The fractal globule, a self-similar compact polymer conformation where the chain is spatially segregated on all length scales, has been proposed to result from a sudden polymer collapse. This state has gained renewed interest as one of the prime candidates for the non-entangled states of DNA molecules inside cell nuclei. Here, we present Monte Carlo simulations of collapsing polymers. We find through studying polymers of lengths between 500 and 8000 that a chain collapses into a globule, which is neither fractal, nor as entangled as an equilibrium globule. To demonstrate that the non-fractalness of the conformation is not just the result of the collapse dynamics, we study in addition the dynamics of polymers that start from fractal globule configurations. Also in this case the chain moves quickly to the weakly entangled globule where the polymer is well mixed. After a much longer time the chain entangles reach its equilibrium conformation, the molten globule. We find that the fractal globule is a highly unstable conformation that only exists in the presence of extra constraints such as cross-links. [ABSTRACT FROM AUTHOR]

By use of an intramolecular criterion, i.e., the direct proportionality between mean square dimension and chain length, theta conditions for linear chains and ring shaped polymers are evaluated for several types of cubic lattice chains (simple cubic, body centered cubic, and face centered cubic). The properties of the rings are evaluated for the same thermodynamic conditions under which they are prepared thus allowing for a natural amount of knots which have been identified by use of Alexander polynomials. For the limit of infinite chain lengths the same theta parameter is found for linear chains and rings. On the contrary, a significant theta point depression occurs due to an additional excluded volume effect if unknots are exclusively regarded. Parameters characteristic of the shape of rings and chains under theta conditions extrapolated to infinite chain length fairly well coincide with respective data for random walks. Mean square dimensions (characteristic of the size) of theta systems are slightly in excess as compared to nonreversal random walks due to the necessity of avoiding overlaps on a local scale. Furthermore athermal systems are studied as well for comparison; mean square dimensions are described by use of scaling relations with proper short chain corrections, shape parameters are given in the limit of infinite chain length. [ABSTRACT FROM AUTHOR]

The effect of crowded environment with static obstacles on the translocation of a three-dimensional self-avoiding polymer through a small pore is studied using dynamic Monte Carlo simulation. The translocation time τ is dependent on polymer-obstacle interaction and obstacle concentration. The influence of obstacles on the polymer translocation is explained qualitatively by the free energy landscape. There exists a special polymer-obstacle interaction at which the translocation time is roughly independent of the obstacle concentration at low obstacle concentration, and the strength of the special interaction is roughly independent of chain length N. Scaling relation τ ∼ N1.25 is observed for strong driving translocations. The diffusion property of polymer chain is also influenced by obstacles. Normal diffusion is only observed in dilute solution without obstacles or in a crowded environment with weak polymer-obstacle attraction. Otherwise, subdiffusion behavior of polymer is observed. [ABSTRACT FROM AUTHOR]

This article reports the first attempt to apply the relaxation mode analysis method to a simulation of a biomolecular system. In biomolecular systems, the principal component analysis is a well-known method for analyzing the static properties of fluctuations of structures obtained by a simulation and classifying the structures into some groups. On the other hand, the relaxation mode analysis has been used to analyze the dynamic properties of homopolymer systems. In this article, a long Monte Carlo simulation of Met-enkephalin in gas phase has been performed. The results are analyzed by the principal component analysis and relaxation mode analysis methods. We compare the results of both methods and show the effectiveness of the relaxation mode analysis. [ABSTRACT FROM AUTHOR]

Based on the success of the maximum entropy principle (MEP) in the study of semiflexible treelike polymers [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)], it is of much interest to establish MEP's potential for general semiflexible polymers which contain loops. Here, we embark on this endeavor by considering discrete semiflexible polymer rings in a Rouse-type scheme. Now, for treelike polymers a beads-and-bonds (i.e., a discrete) picture is essential for an easy inclusion of branching points. Moreover, one may envisage (similar to our former work [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)]) to impose for each angle between two bonds a distinct stiffness condition. Working in this way leads already for a polymer ring to a complicated problem. Hence, we follow a reduced variational approach as applied earlier to polymer chains, in which a single Lagrange multiplier is used for each set of identical conditions imposed on topologically equivalent bonds and bonds' orientations. In this way, we obtain for the discrete ring an analytically closed form which involves Chebyshev polynomials. This expression turns out to lead to a series of solutions: Apart from the regular solution, several other solutions appear. One may be tempted to discard the other solutions, since for them the potential energy matrix is not positive definite. A more careful analysis based on topological features suggests, however, that such solutions can be assigned to rings displaying knots. Monte Carlo simulations which take excluded volume interactions into account agree with our interpretation. [ABSTRACT FROM AUTHOR]

In this work, thermo-responsive polyelectrolyte gels have been simulated using polymer networks of diamond-like topology in the framework of the primitive model. Monte Carlo simulations were performed in the canonical ensemble and a wide collection of situations has been systematically analysed. Unlike previous studies, our model includes an effective solvent-mediated potential for the hydrophobic interaction between non-bonded polymer beads. This model predicts that the strength of the attractive hydrophobic forces increases with temperature, which plays a key role in the explanation of the thermo-shrinking behaviour of many real gels. Although this hydrophobic model is simple (and it could overestimate the interactions at high temperature), our simulation results qualitatively reproduce several features of the swelling behaviour of real gels and microgels reported by experimentalists. This agreement suggests that the effective solvent-mediated polymer-polymer interaction used here is a good candidate for hydrophobic interaction. In addition, our work shows that the functional form of the hydrophobic interaction has a profound influence on the swelling behaviour of polyelectrolyte gels. In particular, systems with weak hydrophobic forces exhibit discontinuous volume changes, whereas gels with strong hydrophobic forces do not show hallmarks of phase transitions, even for highly charged polyelectrolyte chains. [ABSTRACT FROM AUTHOR]

The thermodynamic properties of a simple fluid confined by effective wall forces are calculated using Monte Carlo simulations in the grand canonical ensemble. The solvation force produced by polymer brushes of two different lengths is obtained also. For the particular type of model interactions used, known as the dissipative particle dynamics method, we find that it is possible to obtain an exact, simple expression for the effective force induced by a planar wall composed of identical particles that interact with those in the fluid. We show that despite the short range of all forces in the model, the solvation force can be finite at relatively large distances and therefore does not depend only on the range of the interparticle or solvent-surface forces. As for the polymer brushes, we find that the shape of the solvation force profiles is in fair agreement with scaling and self-consistent field theories. The applications and possible extensions of this work are discussed. [ABSTRACT FROM AUTHOR]

We consider polymer structures which are known in the mathematical literature as 'cospectral.' Their graphs have (in spite of the different architectures) exactly the same Laplacian spectra. Now, these spectra determine in Gaussian (Rouse-type) approaches many static as well as dynamical polymer characteristics. Hence, in such approaches for cospectral graphs many mesoscopic quantities are predicted to be indistinguishable. Here we show that the introduction of semiflexibility into the generalized Gaussian structure scheme leads to different spectra and hence to distinct macroscopic patterns. Moreover, particular semiflexible situations allow us to distinguish well between cospectral structures. We confirm our theoretical results through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]