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Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the “freely draining” case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Microrheology of semidilute polymer solutions is investigated. In this paper we calculate a response function of a probe particle embedded in a semidilute polymer solution by analyzing the two-fluid model. We find that when the size of the probe particle is comparable to the viscoelastic length, the response from the longitudinal compression modes becomes more important than that of the transverse shear modes. As a result, depending on the circumstances, the obtained complex shear modulus cannot be well approximated by that measured in macroscopic rheology experiments. The present results are due to the dynamical asymmetry coupling and the existence of the cooperative dynamics, which are intrinsic to entangled polymer solutions. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we study the effect of the chromophores’ β tensor active components on the diffraction efficiency of a high Tg photorefractive polymer. In particular, we study the two simplest structures with nonvanishing dipole moment, the one-dimension push-pull systems, and the Λ-shaped chromophores. We have developed a model that relate the diffraction efficiency expression with experimental conditions and microscopic properties of the molecules used. Using this model we determine the optimum experimental conditions for both kinds of chromophores and the criteria for the design of chromophores with improved microscopic properties. The model was also used to evaluate the diffraction efficiency of the chromophore Disperse Red 1 (DR1) with a good agreement with experimental data present in bibliography, and of other chromophores selected with the criteria derived from the model, using quantum mechanical calculations to obtain the microscopic properties. Using the designed chromophores diffraction efficiencies more than one order of magnitude higher than that calculated for DR1 with the experimental conditions has been obtained in simulations. These chromophores also exhibit a low dependency of η on the electric field polarization in contrast to the DR1 or the low Tg photoreactive materials. © 2004 American Institute of Physics. [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]

We investigate asymptotic properties of long polymers grafted to convex cylindrical and spherical surfaces, and, in particular, distribution of chain free ends. The parabolic potential profile, predicted for flat and concave brushes, fails in convex brushes, and chain free ends span only a finite fraction of the brush thickness. In this paper, we extend the self-consistent model developed by Ball, Marko, Milner, and Witten [Macromolecules 24, 693 (1991)] to determine the size of the exclusion zone, i.e., size of the region of the brush free from chain ends. We show that in the limit of strong stretching, the brush can he described by an alternative system of integral equations. This system can he solved exactly in the limit of weakly curved brushes, and numerically for the intermediate to strong curvatures. We find that going from melt state to θ solvent and then to marginal solvent decreases relative size of the exclusion zone. These relative differences grow exponentially as the curvature decreases to zero. [ABSTRACT FROM AUTHOR]

We present a mathematical approach to the worm-like chain model of semiflexible polymers. Our method is built on a novel generating function from which all the properties of the model can be derived. Moreover, this approach satisfies the local inextensibility constraint exactly. In this paper, we focus on the lowest order contribution to the generating function and derive explicit analytical expressions for the characteristic function, polymer propagator, single chain structure factor, and mean square end-to-end distance. These analytical expressions are valid for polymers with any degree of stiffness and contour length. We find that our calculations are able to capture the fully flexible and infinitely stiff limits of the aforementioned quantities exactly while providing a smooth and approximate crossover behavior for intermediate values of the stiffness of the polymer backbone. In addition, our results are in very good quantitative agreement with the exact and approximate results of five other treatments of semiflexible polymers. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Our theory of dynamic barriers, slow relaxation, and the glass transition of polymers melts is numerically applied using parameters relevant to real materials. The numerical results are found to be in qualitative agreement with all the approximate analytic expressions previously derived with quantitative differences on the order of ∼20–30% or much less. The analytic prediction of a universal temperature dependence of the alpha relaxation time, and its intimate connection with the idea of a nearly universal crossover time, is established. Inter-relations between the breadth of the deeply supercooled regime, two definitions of the dynamic fragility, and the magnitude of the fast local Arrhenius process at the glass transition temperature are demonstrated and system-specific limitations identified. A quantitative application to segmental relaxation over 16 orders of magnitude in a polyvinylacetate melt yields encouraging results regarding the accuracy of the theory. The theoretical relaxation time results are well fit by multiple empirical forms (generally containing an assumed singular aspect) using parameters consistent with experimental studies. No physical significance is ascribed to this finding, but it does provide additional support for the temperature dependence of the alpha relaxation process predicted by the theory. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Recently we described a coarse-grained model of poly(ethylene oxide) and then employed that model to study the amount of spontaneous threading of cyclic molecules by linear chains in the melt [C. A. Helfer, G. Xu, W. L. Mattice, and C. Pugh, Macromolecules 36, 10071 (2003)]. Since the amount of statistical threading at equilibrium is small, there is interest in identifying physical changes in the system that will increase the threading. We now use that coarse-grained model to investigate the effect on threading of various hypothetical (but feasible) modifications to the two-component system of macrocycles and linear chains in the melt, and different confinement geometries, that can bring about correlations in the arrangement of the rings. Our work follows on the concept of an amphiphilic approach [C. Pugh, J.-Y. Bae, J. R. Scott, and C. L. Wilkins, Macromolecules 30, 8139 (1997)] for increasing the statistical threading in homopolyrotaxane melts. We investigate whether introducing such correlations in the macrocycles can increase the spontaneous threading. This paper shows that some of our modifications can yield more than double the amount of threading seen in purely statistical mixing. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to propose an idea to construct the volume function W for polymer glasses and calculate the volume of polymer glasses as a function of the compactivity X utilizing a statistical-mechanical method developed for semiflexible polymers. We also discuss the analogue for glasses of “tapping” experiments which show the validity of statistical mechanics and the entropy concept in powders. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, we present computer simulation results concerning interdiffusion of fully compatible components in symmetric binary (AB) polymer mixtures in solutions. The simulation is performed in two dimensions using the algorithm based on the dynamic lattice liquid model. The solvent molecules are taken into account explicitly. The evolution of the concentration profiles in time at an interface is studied for chain lengths N=2,4,8,16 for three polymer concentrations [lowercase_phi_synonym]=0.1,0.5,0.9. The tracer diffusion coefficients for polymer chains and for the solvent are obtained by monitoring the mean square displacements of their center of mass. The relationships between coefficients of interdiffusion and self-diffusion are tested. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the elastic behaviors of short compact polymers using the enumeration calculation method and the HP model on a two-dimensional square lattice. Both the mean-square end-to-end distance 〈R2〉 and the ratio of 〈R2〉/〈S2〉 increase with λ. However, when the elongation ratio becomes larger, the curves of 〈R2〉/〈S2〉 become smooth and they are close to the limit of 10.50 for different compact polymers. We also investigate the changes of interior conformations in the process of tensile elongation through calculating the probabilities of three bond angles (i.e., 90°, 180°, and 270°). The average energy and Helmholtz free energy per bond are both negative and increase with elongation ratio λ. In the meantime, the elastic force per bond (f ) also increases with elongation ratio λ, and the energy contribution to the elastic force (f[sub U]) increases first and then drops, and there exists the maximum of f[sub U] in the region of λ=1.40–1.80 for different sequences. The entropy contribution to force (f[sub S]) is close to zero at a small elongation ratio λ and then increases with λ. Some comparisons with different sequences (including nonfolding and folding sequences) are also made. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The dynamics of protein folding result from both enthalpic and entropic contributions to the free energy. In this paper we focus on entropic volume exclusion effects. We carry out computer simulations using a model that allows us to independently change the size or biochemical properties of amino acid residues. To determine the importance of excluded volume effects, we investigate the effects of changing the size of side chains on the unfolding dynamics of a model four-helix bundle protein. In addition, we also investigate the effects of changing the thickness of the chain’s backbone. This has relevance to the behavior of synthetic polymers where the size of the constituent units can be varied. We find that entropic excluded volume effects are crucially important for stabilizing the organized native state relative to the molten globule. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We investigate the influence of a shear flow on the process of nucleation. Mesoscopic nonequilibrium thermodynamics is used to derive the Fokker–Planck equation governing the evolution of the cluster size distribution in a metastable phase subjected to a stationary flow. The presence of the flow manifests itself in the expression for the effective diffusion coefficient of a cluster and introduces modifications in the nucleation rate. The implications of these results in condensation and polymer crystallization are discussed. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper extends previous methods for obtaining the probability distribution function of end-to-end distance for semiflexible polymers, and presents a general formalism that can generate conformational statistics of any continuum filament model of semiflexible chains with internal bends and twists. In particular, our focus is distribution functions for chains composed of straight or helical segments connected with discrete bends or twists. Prior polymer theories are not able to fully account for the effects of these internal shape discontinuities. We use the operational properties of the noncommutative Fourier transform for the group of rigid-body motions in three-dimensional space. This general method applies to various stiffness models of semiflexible chainlike macromolecules. Examples are given which apply the stiffness parameters defined in the Kratky–Porod model, Yamakawa helical wormlike chain model, and revised Marko–Siggia double-helix model to chains with intrinsic bends or twists in their undeformed (minimal energy) state. We demonstrate how the location and magnitude of internal bends in the chain affect the distribution of end-to-end distances for each of these models. This capability allows one to study the entropic effects of intrinsic shape changes (e.g., bend angle) in various models, and may lead to coarse-grained continuum mechanical models of processes that occur during transcription regulation. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Two improved versions of the pruned-enriched-Rosenbluth method (PERM) are proposed and tested on simple models of lattice heteropolymers. Both are found to outperform not only the previous version of PERM, but also all other stochastic algorithms which have been employed on this problem, except for the core directed chain growth method (CG) of Beutler and Dill. In nearly all test cases they are faster in finding low-energy states, and in many cases they found new lowest energy states missed in previous papers. The CG method is superior to our method in some cases, but less efficient in others. On the other hand, the CG method uses heavily heuristics based on presumptions about the hydrophobic core and does not give thermodynamic properties, while the present method is a fully blind general purpose algorithm giving correct Boltzmann-Gibbs weights, and can be applied in principle to any stochastic sampling problem. [ABSTRACT FROM AUTHOR]

In this paper a combined experimental and quantum chemical study of the geometry and opto-electronic properties of unsubstituted and dialkoxy-sustituted phenylene-vinylene oligomers (PV's) is presented. The optical absorption spectra for PV cations with different chain lengths and substitution patterns were measured using pulse radiolysis with time-resolved spectrophotometric detection from 1380 to 500 nm (0.9 to 2.5 eV). The geometries of the PV's studied were optimized using density functional theory (DFT) for both the neutral and singly charged molecule. The spectra for the PV radical cations were then calculated using singly excited configuration interaction with an intermediate neglect of differential overlap reference wave function method together with the DFT geometry. The agreement between experimental and theoretical absorption energies is excellent; most of the calculated radical cation absorption energies are within 0.15 eV of the experimental values. The pattern of dialkoxy-substitution is found to have a large effect on the optical absorption spectrum of the cation. Using the calculated charge distribution it is shown that the degree of delocalization of the charge correlates with the energy of the lowest absorption band. If alkoxy side chains are present on some of the rings the positive charge tends to localize at those sites. [ABSTRACT FROM AUTHOR]

We present a new real space Newton-based computational approach to computing the properties of inhomogeneous polymer systems with density functional theory (DFT). The DFT is made computationally efficient by modeling the polymers as freely jointed chains and obtaining direct correlation functions from polymer reference interaction site model calculations. The code we present can solve the DFT equations in up to three dimensions using a parallel implementation. In addition we describe our implementation of an arc-length continuation algorithm, which allows us to explore the phase space of possible solutions to the DFT equations. These numerical tools are applied in this paper to hard chains near hard walls and briefly to block copolymer systems. The method is shown to be accurate and efficient. Arc-length continuation calculations of the diblock copolymer systems illustrate the care required to obtain a complete understanding of the structures that may be found with this polymer-DFT approach. [ABSTRACT FROM AUTHOR]

Phase separated structure of ternary blends of A and B homopolymers and symmetric AB diblock copolymer is investigated using a lattice (real-space) self-consistent field theory. This paper includes the detailed description of our published results [Kodama, Komura, and Tamura, Europhys. Lett. 53, 46 (2001)] as well as more extended calculations. We consider the symmetric case, namely, (i) both A and B homopolymers have the same degree of polymerization N[sub A]=N[sub B]; (ii) AB diblock copolymer of length N[sub AB] is symmetric; (iii) average volume fractions of A and B homopolymers are equal. We looked into the influence of relative chain lengths α=N[sub A]/N[sub AB] on the phase separated structure. Our numerical simulations are performed in the real space without assuming the symmetry of the structure a priori. For the fixed copolymer length and α<1, the typical length scale of the microphase separated structure become smaller for relatively shorter homopolymer chains (small α). In other words, the homopolymers becomes more efficient to swell the microphase separated structure for longer homopolymer chains (large α). Detailed free-energy analysis revealed that the stability of the lamellar phase is marginal for small block copolymer volume fraction. For α>1, on the other hand, three-phase coexistence either between the disorder, A-rich and B-rich phases or between the lamellar, A-rich and B-rich phases is observed. [ABSTRACT FROM AUTHOR]

Statistical properties of flexible polymers with controlled molecular weights (length of arms) and branching patterns (topology) has been attracting strong interest. Basically, the lattice enrichment algorithms are suitable for simulating this kind of subject because they allow direct estimation of the total configuration number. However, it is difficult to apply this kind of algorithm for polymers with highly complicated structures, namely the comb-polymers. One of the difficulties is that the efficiency of simulation is severely limited. In this paper, a previously reported improvement technique is revisited, enhanced, and combined with several new ideas for developing a modified algorithm, which can solve such a situation. The validation and performance evaluation of the modified algorithm is presented. The algorithm is then applied to small scale polymer combs. In particular, the value of the critical exponent related to the configuration number is estimated on these combs. The result obtained for an H-shaped polymer is in accordance with previous simulations and a theoretical prediction formula already proposed. Possibilities for the future extension of the algorithm are briefly discussed. [ABSTRACT FROM AUTHOR]

The self-consistent-field (SCF) theory developed in Part I [J. Chem. Phys. 116, 7283 (2002), preceding paper] is employed to compute the interaction between particles coated by end-grafted homopolymers in good solvent, where the particles and the homopolymers have comparable sizes. The result shows that, contrary to the prediction of the conventional theory for colloidal stabilization and previous SCF studies, the interaction is attractive, repulsive, and attractive at large, intermediate, and small distances, respectively, for densely grafted particles, while it is purely attractive for sparsely grafted particles. The attractive interaction is a consequence of two important factors that were ignored in previous studies: (i) the sphere–sphere geometry of the system and (ii) the segment density associated with individual particle being deformed anisotropically, with respect to the particle, under the perturbation of other particles. We argue that the conventional wisdom that end-grafted homopolymers in good solvent always impart stability indeed is correct only in a kinetic sense and that our result will become more observable in systems composed of nanoparticles. Limitations of our prediction and considerations that must be carefully taken into account when generalizing our result to micron-sized particles and star polymers are discussed. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The frequency and molecular mass dependences of nuclear magnetic resonance spin-lattice relaxation and the time dependence of the mean-squared segment displacement of Kuhn segment chains confined in static straight and randomly coiled tubes with "soft" and "hard" walls were studied. "Soft" walls were modeled in the form of a cylindrical distribution of a harmonic radial potential. This scenario is analytically solvable in contrast to the situation of "hard" (reflecting) walls corresponding to an infinitely deep square-well radial potential. In the latter case, we have therefore employed Monte Carlo simulations using a modified Stockmayer chain model. In both situations, qualitatively equivalent results were obtained. Depending on the effective tube diameter (or width of the potential well) a crossover from Rouse to reptation behavior occurs which sets on already far beyond the Flory radius of the polymer. In terms of the spin-lattice relaxation dispersion, reptation reveals itself by T[sub 1] ∝ M[sup 0]ω[sup 3/4] in the chain mode regime, in good agreement with experimental data for polymers in artificial tubes reported in our previous paper by Kimmich et al. [ABSTRACT FROM AUTHOR]

Using extensive molecular dynamics simulations, we obtain the conformational phase diagram of a charged polymer in the presence of oppositely charged counterions and neutral attractive crowders for monovalent, divalent, and trivalent counterion valencies. We demonstrate that the charged polymer can exist in three phases: (1) an extended phase for low charge densities and weak polymer–crowder attractive interactions [Charged Extended (CE)]; (2) a collapsed phase for high charge densities and weak polymer–crowder attractive interactions, primarily driven by counterion condensation [Charged Collapsed due to Intra-polymer interactions [(CCI)]; and (3) a collapsed phase for strong polymer–crowder attractive interactions, irrespective of the charge density, driven by crowders acting as bridges or cross-links [Charged Collapsed due to Bridging interactions [(CCB)]. Importantly, simulations reveal that the interaction with crowders can induce collapse, despite the presence of strong repulsive electrostatic interactions, and can replace condensed counterions to facilitate a direct transition from the CCI and CE phases to the CCB phase. [ABSTRACT FROM AUTHOR]

We present the phase separation dynamics of a binary (AB), simple fluid (SF), and amphiphilic polymer (AP) mixture using dissipative particle dynamics simulation at d = 3. We study the effect of different AP topologies, including block copolymers, ring block copolymers (RCP), and miktoarm star polymers, on the evolution morphologies, dynamic scaling functions, and length scale of the AB mixture. Our results demonstrate that the presence of APs leads to significantly different evolution morphologies in SF. However, the deviation from dynamical scaling is prominent, mainly for RCP. Typically, the characteristic length scale for SF follows the power law R(t) ∼ tϕ, where ϕ is the growth exponent. In the presence of high AP, we observe diffusive growth (ϕ → 1/3) at early times, followed by saturation in length scale (ϕ → 0) at late times. The extent of saturation varies with constraints imposed on the APs, such as topology, composition ratio, chain length, and stiffness. At lower composition ratios, the system exhibits inertial hydrodynamic growth (ϕ → 2/3) at asymptotic times without clearly exhibiting the viscous hydrodynamic regime (ϕ → 1) at earlier times in our simulations. Our results firmly establish the existence of hydrodynamic growth regimes in low surfactant-influenced phase separation kinetics of binary fluids and settle the related ambiguity in d = 3 systems. [ABSTRACT FROM AUTHOR]

Block copolymers at homopolymer interfaces are poised to play a critical role in the compatibilization of mixed plastic waste, an area of growing importance as the rate of plastic accumulation rapidly increases. Using molecular dynamics simulations of Kremer–Grest polymer chains, we have investigated how the number of blocks and block degree of polymerization in a linear multiblock copolymer impacts the interface thermodynamics of strongly segregated homopolymer blends, which is key to effective compatibilization. The second virial coefficient reveals that interface thermodynamics are more sensitive to block degree of polymerization than to the number of blocks. Moreover, we identify a strong correlation between surface pressure (reduction of interfacial tension) and the spatial uniformity of block junctions on the interface, yielding a morphological framework for interpreting the role of compatibilizer architecture (number of blocks) and block degree of polymerization. These results imply that, especially at high interfacial loading, the choice of architecture of a linear multiblock copolymer compatibilizing surfactant does not greatly affect the modification of interfacial tension. [ABSTRACT FROM AUTHOR]

The presence of gradient softer outer layers, commonly observed in biological systems (such as cartilage and ocular tissues), as well as synthetic crosslinked hydrogels, profoundly influences their interactions with opposing surfaces. Our prior research demonstrated that gradient-stiffness hydrogel layers, characterized by increasing elasticity with depth, control contact mechanics, particularly in proximity to the layer thickness. We postulate that the distribution of polymers within these gradient layers imparts extraordinary stretch and adhesion characteristics due to network adaptability and stress-induced reorganization. To investigate this phenomenon, we utilized Atomic Force Microscopy nanoindentation to assess the depth-dependent adhesion behavior of polyacrylamide hydrogels with varying gradient layer thicknesses. Two gradient layer thicknesses were achieved by employing different molding materials: glass and polyoxymethylene (POM). Glass-molded hydrogels exhibited a thinner gradient layer alongside a stiffer bulk layer compared to their POM-molded counterparts. In indentation experiments, the POM-molded hydrogel had larger adhesion compared to glass-molded hydrogel. We find that indenting within the gradient layer engenders increased load-unload hysteresis due to heightened fluid transport in the sparse outer polymer network. Consequently, this led to augmented adhesion and work of separation at shallow depths. We suggest that the prominent stretching capability of the sparse outer polymer network during probe retraction contributes to enhanced adhesion. The Maugis–Dugdale adhesive model only fits well to indentations on the thin layer or indentations which engage significantly with the bulk. These results facilitate a comprehensive characterization of adhesion mechanics in gradient-stiffness hydrogels, which could foster their application across emerging contexts in health science and environmental domains. [ABSTRACT FROM AUTHOR]

A polymer model given in terms of beads, interacting through Hookean springs and hydrodynamic forces, is studied. A Brownian dynamics description of this bead-spring polymer model is extended to multiple resolutions. Using this multiscale approach, a modeller can efficiently look at different regions of the polymer in different spatial and temporal resolutions with scalings given for the number of beads, statistical segment length, and bead radius in order to maintain macro-scale properties of the polymer filament. The Boltzmann distribution of a Gaussian chain for differing statistical segment lengths gives a diffusive displacement equation for the multi-resolution model with a mobility tensor for different bead sizes. Using the pre-averaging approximation, the translational diffusion coefficient is obtained as a function of the inverse of a matrix and then in closed form in the long-chain limit. This is then confirmed with numerical experiments. [ABSTRACT FROM AUTHOR]

This paper is the first in a series of papers in which polymer adsorption on a surface is studied by computer simulation using the ‘‘scanning method.’’ This method is especially efficient to handle chain systems with finite interactions and geometrical constraints. Here we test the method by applying it to models of a single random walk (without excluded volume) on a simple cubic lattice, which are solved analytically; in the immediately following paper a self-avoiding walk model is treated. The scanning method is found to be extremely efficient, where walks of up to N=105 steps can be simulated reliably, leading thereby to very precise estimates of transition temperatures and critical exponents. In particular we test carefully for a lattice model the range of validity of scaling functions developed by Eisenrigler, Kremer and Binder [J. Chem. Phys. 77, 6296 (1982)] for a continuous model. We pay a special attention to corrections to scaling and demonstrate that they are strong above the transition temperature for ⊥, the perpendicular part of the mean-square end-to-end distance and for ρ(z), the monomer concentration profile. We show that at T=∞, the asymptotic regime, in which these corrections become negligible, is obtained for N≊40 000 for ⊥ but a significantly larger N is required for ρ(z). This means that this regime corresponds to a real polymer length that is not realized experimentally. [ABSTRACT FROM AUTHOR]

The Curtiss–Bird model of polymer melts has been extended to include polydisperse mixtures. The formula for the stress tensor derived in the last paper is used here to give explicit expressions for material functions in shear and elongational flow. Predictions are shown for viscosity, first normal stress coefficient, elongational stress growth viscosity, and steady elongational viscosity for Flory–Schulz and log–normal molecular weight distributions. It is also shown how generalizations that are observed experimentally for viscosity are predicted by the Curtiss–Bird model. In the next paper, these calculations are compared with experimental data. [ABSTRACT FROM AUTHOR]

Following the general scheme developed in the preceding paper (paper VII), dielectric and magnetic relaxation and fluorescence depolarization for flexible chain polymers in dilute solution are reinvestigated on the basis of the discrete helical worm-like chain in the higher-order subspace approximation. A comparison of theory with experiment is made with respect to the dielectric correlation time τD, the spin-lattice relaxation time T1, the spin–spin relaxation time T2, the nuclear Overhauser enhancement (NOE), the fluorescence emission anisotropy r(t), the average fluorescence anisotropy r, and the fluorescence correlation time τF. It is found that there is agreement between the diameters of the chains determined from these dynamic properties and those from chemical structures, better than in the previous crude subspace approximation, indicating that the theory is remarkably improved in the present approximation. The magnetic correlation time τM is in general not an observable, and therefore an empirical equation to be used for its determination from the observed T1 is constructed. It is then found that there is good correlation between the dynamic chain stiffness τX/τ0X and the static chain stiffness λ-1, where τ0X is the correlation time of the isolated subbody (monomer unit) with X=D, M, and F; τX/τ0X is a monotonically increasing function of λ-1 nearly independent of X as far as perpendicular dipoles are concerned. An explanation of this result is given. However, the dependence of τX on temperature cannot be explained very satisfactorily. [ABSTRACT FROM AUTHOR]

Recent experiments have shown that porous filters preadsorbed with polymer molecules exhibit an anomalously high pressure drop at high rates of flow. We have modeled the adsorbed polymers as dynamical systems and have found that the introduction of hydrodynamic interaction between molecules destabilizes at a high applied shear. As a direct result this instability will cause the molecules to unravel and stretch far into the cross section of the pore, and thus by inference, cause the observed anomalously high pressure drop. Although much of this paper is devoted to the stability characteristics of the deterministic system, Brownian motion is also considered, and an account of the statistics of the Brownian system when the deterministic system becomes unstable is given. The examples revealed in this paper are not of sufficient complexity to calculate with any accuracy the magnitude of this anomalous pressure drop. We simply present a procedure by which a large variety of more complex models could be undertaken and their ultimate effect clearly understood. [ABSTRACT FROM AUTHOR]

We consider a lattice model of a semiflexible homopolymer chain in a bad solvent. Beside the temperature T, this model is described by (i) a curvature energy εh, representing the stiffness of the chain; (ii) a nearest-neighbor attractive energy εv, representing the solvent; and (iii) the monomer density ρ=N/Ω, where N and Ω denote, respectively, the number of monomers and the number of lattice sites. This model is a simplified view of the protein folding problem, which encompasses the geometrical competition between secondary structures (the curvature term modelling helix formation) and the global compactness (modeled here by the attractive energy), but contains no side chain information. By allowing the monomer density ρ to depart from unity one has made a first (albeit naive) step to include the role of the water. In previous analytical studies, we considered only the (fully compact) case ρ=1, and found a first order freezing transition towards a crystalline ground state (also called the native state in the protein literature). In this paper, we extend this calculation to the description of both compact and noncompact phases. The analysis is done first at a mean-field level. We then find that the transition from the high temperature swollen coil state to the crystalline ground state is a two-step process for which (i) there is first a θ collapse transition towards a compact ‘‘liquid’’ globule, and (ii) at low temperature, this ‘‘liquid’’ globule undergoes a discontinuous freezing transition. The mean-field value of the θ collapse temperature is found to be independent of the curvature energy εh. This mean-field analysis is improved by a variational bound, which confirms the independence of the θ collapse temperature with respect to εh. This result is confirmed by a Monte Carlo simulation, although with a much lower value of the θ... [ABSTRACT FROM AUTHOR]

Estimates are evaluated for all constants in the theory of polymer dynamics developed in the preceding paper. These theoretical estimates are employed in calculations on the many chain systems simulated previously by Kremer and Grest and by Paul and co-workers. The agreement between the theoretical calculations and the simulations of Kremer and Grest is found to be very good for the bead mean squared displacement. The theoretically evaluated center of mass mean squared displacement is in good qualitative agreement with the Kremer–Grest simulations, although there are quantitative differences. Good qualitative agreement with the simulations of Paul and co-workers is also obtained. It is shown that quantitative agreement can be obtained with modest changes in the theoretical estimates of a few of the constants in the theory. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, an extensive analysis of free volume related properties of a lipid membrane is given. Using percolation theory, and comparing the free volume properties to those of a soft polymer, additional insights are obtained. The analyses are discussed within the framework of the four region model. It is concluded that the four regions have very different free volume properties. The region containing the dense part of the lipid tails resembles a soft polymer membrane to a large extent. The middle part of the membrane is more similar to a low density alkane. The consequences of the computed free volume properties on the permeation process of small penetrants are discussed. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present results from numerical analysis of the equations derived in the Gaussian self-consistent method for kinetics at the collapse transition of a homopolymer in dilute solution. The kinetic laws are obtained with and without hydrodynamics for different quench depths and viscosities of the solvent. Some of our earlier analytical estimates are confirmed, and new ones generated. Thus the first kinetic stage for small quenches is described by a power law decrease in time of the squared radius of gyration with the universal exponent αi=9/11 (7/11) with (without) hydrodynamics. We find the scaling laws of the characteristic time of the coarsening stage, τm∼Nγm, and the final relaxation time, τf∼Nγf, as a function of the degree of polymerization N. These exponents are equal to γm=3/2, γf=1 in the regime of strong hydrodynamic interaction, and γm=2, γf=5/3 without hydrodynamics. We regard this paper as the completion of our work on the collapse kinetics of a bead and spring model of a homopolymer, but discuss the possibility of studying more complex systems. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Understanding the interfacial organization of heteropolymers near solid surfaces is an issue of fundamental interest that is relevant for many technological and biological applications. In this paper we address several questions pertaining to the surface-induced ordering and the adsorption–desorption phase behavior of a dilute solution of two-letter random heteropolymers interacting with a solid surface. Our analysis is based on a statistical field theoretic formulation of the propagator for the problem of interest. We employ the replica trick to alleviate analytical difficulties which arise when considering averaging over the sequence distribution of the A and the B units. In order to highlight the effects of the surface, we consider the situation wherein the intersegment interactions are of the excluded volume type while the segment–surface interactions of the A and B segments are arbitrarily different. Within the replica symmetric solution, we show that proper coarse-graining of the interaction potentials leads to exact analytical expressions for the self-consistent propagator of the heteropolymer at theta conditions and for the case where excluded volume interactions prevail. One of our interesting findings is that heteropolymers undergo an adsorption–desorption transition in the vicinity of a surface that interacts with the different types of segments in arbitrarily different ways. This is consistent with our previous numerical findings for much more restricted circumstances.We explicitly analyze the influence of the fluctuations in the sequence distribution on the conformational organization of the adsorbed chains and obtain the scaling behavior of properties of interest in the vicinity of the adsorption–desorption threshold with respect to the disorder strength and other polymer interaction parameters. Specifically, invoking the Ehrenfest theorem we find that the adsorption–desorption transition at theta conditions is... [ABSTRACT FROM AUTHOR]

In this paper, we consider the behavior of random heteropolymers in a quenched disordered medium. We develop a field theory and obtain a mean-field solution that allows for replica symmetry breaking. The presence of an external disorder leads to the formation of compact states; a homopolymeric effect. We compute the phase diagram for two classes of problems. First, we consider the situation wherein the bare heteropolymer prefers like segments to segregate, and second, we examine cases where the bare heteropolymer prefers unlike segments to mix. For the first class of systems, we find a phase diagram characterized by a replica symmetry broken phase that exists below a particular temperature. This temperature grows with the strength of the external disorder. In the second class of situations, the phase diagram is much richer. Here we find two replica symmetry broken phases with different patterns separated by a reentrant phase. The reentrant phase and one of the two replica symmetry broken phases are induced by interactions with the external disorder. The dependence of the location of the phase boundaries on the strength of the external disorder are elucidated. We discuss our results from a physical standpoint, and note the testable experimental consequences of our findings. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The average size of long chains below the theta point is discussed in terms of a continuum model in which the chain is viewed as a collapsed phase perturbed by repulsive pair interactions. The representation of the collapsed phase makes use of the path integral formulation of a colored noise process introduced in an earlier paper [J. Chem. Phys. 99, 9230 (1993)], while the pair interactions are approximated as delta function pseudopotentials of strength v0. By treating the excluded volume perturbatively, the model can be described (at first order in v0) by renormalization group (RG) methods using dimensional regularization, ε expansion and minimal subtraction of poles. The nature of the fixed points of the RG transformation suggests that the collapse transition may be first order. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In recent years the fractional calculus approach to describing dynamic processes in disordered or complex systems such as relaxation or dielectric behavior in polymers or photo bleaching recovery in biologic membranes has proved to be an extraordinarily successful tool. In this paper we apply fractional relaxation to filled polymer networks and investigate the dependence of the decisive occurring parameters on the filler content. As a result, the dynamics of such complex systems may be well–described by our fractional model whereby the parameters agree with known phenomenological models. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Using the method of Born, Green, and Yvon we have recently derived a coupled set of integral equations for the intermolecular site–site distribution functions which describe the microscopic equilibrium structure of a fluid of flexible chain molecules. Here, we carry out an average over this set of equations to arrive at a single equation for the average intermolecular distribution function. Intramolecular distribution functions appearing in this equation are approximated by results for isolated chain molecules. Numerical calculations have been performed over a range of fluid densities for chains composed of 8, 16, 20, and 50 tangent hard spheres. The resulting intermolecular distribution functions are in good to fair agreement with simulation data. This structural information is used to compute second virial coefficients and pressure equations of state via the virial route to thermodynamics. Although the theory consistently underestimates the pressure, it gives very accurate results for the second virial coefficient for all chain lengths studied. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Two sets of integral equations are presented in this paper for dynamic pair correlation functions for polymeric liquids subjected to shearing. One set of the integral equations is a dynamic and polymeric extension of the Percus–Yevick integral equation for the equilibrium pair correlation function of a simple fluid, whereas the other is that of the hypernetted chain equation. These integral equations are coupled, in the case of uniform temperature, to the momentum balance equation and the constitutive equations for the stress tensor and the diffusion fluxes in the system. When this coupled system of evolution equations (generalized hydrodynamic equations) is solved subject to appropriate initial and boundary conditions, the dynamic structure factors and correlation functions can be computed for the polymeric liquid of interest. The first-order iterative solution of the integral equations for correlation functions is computed for the case of equilibrium polymers. It yields a qualitatively correct chain-length dependence of the maximum position of the end-to-end distance distribution function and thus the mean square end-to-end distance of the polymer. The shear-induced effect on the end-to-end distance distribution function is numerically computed based on the first-order perturbation solution, which indicates that the distribution becomes anisotropic, having two twofold symmetry axes, when the polymer is sheared. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Slow, large-amplitude chain motions play an important role in determining the macroscopic mechanical properties of polymers. Although such motions have been studied quantitatively by two-dimensional (2D) nuclear magnetic resonance (NMR) exchange experiments, overlapping anisotropic patterns hamper spectral analysis, and limit applications. Variable angle correlation spectroscopy (VACSY) has proven useful in resolving such problems for rapidly spinning samples by separating anisotropic spectral patterns according to isotropic chemical shifts. In a previous study [J. Am. Chem. Soc. 115, 4825 (1993)], we described a three-dimensional (3D) NMR experiment that incorporates the VACSY method and a hop of the rotor axis to correlate the isotropic chemical shifts to 2D anisotropic exchange patterns. The hop of the rotor axis, however, presents experimental difficulties and limits the range of motional rates that may be studied. We present in this paper a new 3D VACSY exchange experiment that obtains the same correlations without the need for the rotor axis hop. A series of 2D exchange spectra are recorded with the sample spinning at different rotation axis angles. Then using the scaling of the anisotropic frequency at the different angles, we construct the data onto a 3D matrix so that a Fourier transformation directly yields the desired correlations. The technique is applied to 13C exchange NMR to study the slow molecular motion of ordered isotactic polypropylene. [ABSTRACT FROM AUTHOR]

We calculate the average end-to-end distance of a polymer in a semidilute solution that is near the temperature Tc at which phase separation occurs. The calculation is carried out within the usual canonical partition function formalism, the Hamiltonian of the system being taken to comprise a reference term, in which the chains are represented as collapsed coils, and a perturbation, which originates in repulsive excluded volume interactions between different monomers. The description of the reference state employs the fractional Brownian walk approach developed in an earlier paper, while the perturbation is modeled by delta function pseudopotentials. The treatment of excluded volume follows the methods developed by Edwards, Singh, and Jeffers, which make use of the equations derived for an effective step length and an effective monomer–monomer potential to determine various polymer properties. In this way, we find that near Tc, R scales with chain length N as N0.462. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new theoretical approach to treat polymer systems with local aperiodic part efficiently. This approach is the combination of the elongation method with the supercell method which has been developed in our group, and we developed this approach to obtain the electronic structure of a polymer having local aperiodicity by considering the locality of the interaction between periodic and local aperiodic parts. In order to confirm the validity of this method, several model calculations were performed at the complete neglect of differential overlap (CNDO/2) level. That is, we applied this method to all-trans polyacetylene interacting with a small molecule, and to all-trans polyacetylene with partial substitution of hydrogen atoms by fluorine atoms. We compared the results obtained by this calculation with those obtained by usual crystal orbital calculation concerning total energy, computational time, and electron density distribution. The charge extension on the polymer chain under the influence of aperiodicity was also discussed. [ABSTRACT FROM AUTHOR]

This paper presents real values of photochemical hole-burning (PHB) parameters for dye-doped polymer systems. The cross section for purely electronic zero-phonon absorption σ*0, quantum efficiency of hole formation η and full-width at half-maximum of inhomogeneous broadening Δωi are determined by the least-squares fitting method. Our sample is sulfonated tetraphenylporphin doped in polyvinyl alcohol at 20 K. The determined values are σ*0 = (2.3 ± 0.2)× 10-15 cm2, η=(1.6±0.6)×10-2, and Δωi=(223±7) cm-1. The errors are of the order of a standard deviation. The η is much greater than previously reported values. The apparent quantum efficiencies of hole formation are derived under the assumption that the lowest-energy absorption band consists of transitions of one type. They exhibit a marked wavelength dependence, but their values are well explained quantitatively by the real values. There is no need to consider any wavelength dependence of σ*0 and η, at least at the initial stage of burning. The purely electronic transition component is about half of the lowest-energy absorption band. The other component is ascribed to at least two kinds of vibronic transitions of the dye. The Debye–Waller factors for these two vibronic transitions are roughly estimated to be in the order of 10-2. This result means the site-selectivity in PHB is not perfect in a wide range of the lowest-energy absorption band. [ABSTRACT FROM AUTHOR]

The integral equations for intramolecular and intermolecular correlation functions are derived for nonrigid polymeric (polyatomic) liquids by the device of the Kirkwood charging parameters. These integral equations are cast into mean-field-type equations by using the potential elimination method, reported previously for dense simple fluids. Based on the mean-field integral equations, we examine the superposition approximations for various levels of correlation. The present theory provides a means to make systematic corrections for superposition approximations for correlation functions of various orders. Upon using the superposition approximations for the triplet correlation functions in the Kirkwood hierarchy and an assumption or another concerning the charging parameter dependence of the cavity functions, we derive a set of generalized Percus–Yevick and hypernetted chain integral equations for the intramolecular and intermolecular pair correlation functions for beads (sites) of polymeric (polyatomic) liquids. This set of integral equations allows the intramolecular and intermolecular correlation functions to be determined self-consistently. The connection of this set of integral equations to the bead–bead (molecular) Ornstein–Zernike relation is pointed out. The integral equations for the intramolecular correlation functions will be numerically solved for some properties of a single polymer chain in the infinite dilution limit in the sequel to this paper. [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]

In this paper we develop a general mean-field lattice model, in the spirit of the Scheutjens and Fleer theory of polymer solutions [J. M. H. M. Scheutjens and G. J. Fleer, J. Phys. Chem. 83, 1619 (1979); Macromolecules 18, 1882 (1985)], of an N-component polymer blend in the vicinity of an impenetrable surface. We consider the special case of N=3, model one component as noninteracting holes and obtain the bulk density of this system by using the Sanchez–Lacombe equation of state. The free surface of a polymer blend is then modeled by considering the interphase which forms when this ternary mixture is phase separated. One sample case corresponding to the free surface of a symmetric isotopic polystyrenelike blend is probed and we find that the deuterated component is partitioned to the air surface in agreement with experiment. The application of the concept of the Gibbs dividing surface relative to the polymer density profile at the free surface is then examined, and we show that all comparisons to experiment must be conducted relative to this hypothetical plane. Finally, comparisons of the concentration profiles predicted by this theory to existing square gradient theories of binary polymer blends, as well as Monte Carlo simulations, are performed to highlight the usefulness of these calculations to realistic systems. [ABSTRACT FROM AUTHOR]

The chemical potential of lattice polymers is calculated in two alternative ways: by the Widom insertion method using the Rosenbluth and Rosenbluth sampling technique and by the modified Widom method, based on the insertion of one segment to an existing polymer chain. In the first part of this paper we present a detailed derivation of the modified Widom technique for lattice systems. We then proceed to calculate the chemical potential for chains of up to 50-mers in monomeric and polymeric solvents. We observe marked odd-even effects on the chemical potential. The density dependence of the chemical potential is found to vary with chain length. For most temperatures and densities studied the chemical potential of chain molecules in a fixed environment becomes linear in chain length for molecules longer than 10–20 segments. The results are compared to the classical lattice theories, which are found to be best at high densities, as expected based on previous investigations. [ABSTRACT FROM AUTHOR]

The Edwards path-integral description of chain statistics is used to derive an effective φ4 field theory of polymer solutions that is applicable near the temperature of critical phase separation Tc. The present formalism, an extension of the mean-field approach discussed in paper I [R. E. Goldstein and B. J. Cherayil, J. Chem. Phys. 90, 7448 (1989)], makes use of standard results from the theory of continuous phase transitions to account for the effects of previously neglected density fluctuations, and to obtain thereby, among other results, estimates for the temperature and molecular weight-scaling exponents of the coexistence curve in the vicinity of Tc. The critical monomer volume fraction ρc of the solution is shown to scale as the osmotic second virial coefficient below the theta point, providing a rigorous approach to the calculation of the molecular weight dependence of ρc. Experimental data on the phase separation of solutions of polystyrene in methylcyclohexane are shown to lie on a single universal curve when expressed in terms of the scaling variables suggested by the present analysis. [ABSTRACT FROM AUTHOR]

By time-of-flight photocurrent techniques, hole transport has been investigated in vapor deposited films of the title compound. The measurements were made over a wide range of fields and temperatures which encompassed the glass transition temperature. The results are described within the framework of the disorder formalism due to Bässler and co-workers. The formalism is based on the assumption that transport occurs by hopping in a manifold of states subject to both energetic (diagonal) and positional (off-diagonal) disorder. In this paper, we describe (1) the field and temperature dependencies of the photocurrent transients, (2) the role of polymer dynamics on charge transport at temperatures above the glass transition temperature, and (3) the spectroscopy of interfacial hole states derived from an analysis of photocurrent transients in terms of computer simulations conducted under the premise of energy selective carrier injection into a Gaussian distribution of states. [ABSTRACT FROM AUTHOR]