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The conformation of a polymer chain in solution is coupled to the local structure of the surrounding solvent and can undergo large changes in response to variations in solvent density and temperature. The many-body effects of solvent on the structure of an n-mer polymer chain can be formally mapped to an exact n-body solvation potential. Here, we use a pair decomposition of this n-body potential to construct a set of two-body potentials for a Lennard-Jones (LJ) polymer chain in explicit LJ solvent. The solvation potentials are built from numerically exact results for 5-mer chains in solvent combined with an approximate asymptotic expression for the solvation potential between sites that are distant along the chain backbone. These potentials map the many-body chain-in-solvent problem to a few-body single-chain problem and can be used to study a chain of arbitrary length, thereby dramatically reducing the computational complexity of the polymer chain-in-solvent problem. We have constructed solvation potentials at a large number of state points across the LJ solvent phase diagram including the vapor, liquid, and super-critical regions. We use these solvation potentials in single-chain Monte Carlo (MC) simulations with n ≤ 800 to determine the size, intramolecular structure, and scaling behavior of chains in solvent. To assess our results, we have carried out full chain-in-solvent MC simulations (with n ≤ 100) and find that our solvation potential approach is quantitatively accurate for a wide range of solvent conditions for these chain lengths.

The present article gives an analysis of XYX triblock copolymers in a good solvent and in a theta solvent, the segments of type X and type Y being repulsive for each other. The results are compared to homopolymers as well as to copolymers in a selective solvent that is a good one for the outer blocks and a theta solvent for the inner one and vice versa, the strength of repulsion between blocks being the same as in the present types of copolymers. A lattice model is used for the investigations and the concentration ranges from a volume fraction phi = 0 up to phi = 0.8. In the limit phi --0 the triblocks in good solvent are slightly more expanded than homopolymers and in theta solvent mean square dimensions of triblocks are considerably increased compared to homopolymers due to the repulsion between blocks. With increasing concentration the dimensions decrease but then they increase again and for large concentrations they become similar for all types of copolymers studied, as the effect of the solvent levels off making the repulsive interaction between blocks the dominant interaction. This leads to an orientation effect and as a consequence to microphase separation which is demonstrated by the concentration dependence of various quantities as well as by visualization of snapshots.

Using the configurational-bias Monte Carlo method combined with the parallel tempering technique, solvent driven changes in polymer conformations in a supercritical solvent are systematically investigated using simple molecular models. The solvent is modelled as a square-well fluid, and the polymer is made up of a flexible chain of tangentially touching hard spheres and/or square-well spheres. The mean square end-to-end distance and radius of gyration are computed for various ratios of square-well and hard-sphere segments and a range of thermodynamic conditions. The simulation results show that conformation behavior of amphiphilic chains is rather complex and it is not a simple combination of the conformation behavior of the attractive and repulsive chains. The main finding is that the conformations of amphiphilic chains is determined primarily by attractive intermolecular interactions between the polymer segments and molecules of the solvent.

We have used molecular dynamics methods to investigate the effects of cyclic chain architecture on the properties of dilute solutions. In order to include solvent effects in estimating these properties, we use a van der Waals scaling factor determined for each solvent by matching to the theta condition. We predict that the theta temperature (theta) of cyclic PE (c-PE) is ~10% lower than for the linear case (l-PE). This can be compared to the experimental results for polystyrene (PS), where theta for cyclic PS is 2% lower. For conditions corresponding to n-pentane solvent, we predict that g2>cyclic/g2>linear is 0.59 for all temperatures above 350 K. The deviation from the ratio of 0.50–0.53 expected from analytic theory is due to the competition between chain stiffness and excluded volume effects. To calculate the intrinsic viscosity of c-PE and l-PE we extended the Bloomfield–Zimm type theory to include chain stiffness corrections. We find that for the theta temperature, the ratio of viscosities for c-PE and l-PE is 0.71, which is 7% higher than the value of 0.66 from the freely jointed chain model. This difference is caused by the larger value of g2>cyclic/g2>linear from the simulations.

We study the equilibrium behavior and dynamics of a polymer collapse transition for a system composed of a short Lennard-Jones (LJ) chain immersed in a LJ solvent for solvent densities in the range of ρ=0.6–0.9 (in LJ reduced units). The monomer hydrophobicity is quantified by a parameter λ∈[0,1] which gives a measure of the strength of attraction between the monomers and solvent particles, and which is given by λ=0 for a purely repulsive interaction and λ=1 for a standard LJ interaction. A transition from the Flory coil to a molten globule is induced by increasing λ. Generally, the polymer size decreases with increasing solvent density for all λ. Polymer collapse is induced by changing the hydrophobicity parameter from λ=0 to λ⩾0.5, where the polymer is in a molten globule state. The collapse rate increases monotonically with increasing hydrophobicity and decreases monotonically with increasing solvent density. Doubling the length of the chain from N=20 to N=40 monomers increases the collapse time roughl...

Self-consistent Polymer Reference Interaction Site Model (PRISM) calculations and molecular dynamics (MD) simulations were performed on athermal solutions of linear polymers. Unlike most previous treatments of polymer solutions, we explicitly included the solvent molecules. The polymers were modeled as tangent site chains and the solvent molecules were taken to be spherical sites having the same intermolecular potential as the polymer sites. The PRISM theory was solved self-consistently for both the single chain structure and intermolecular correlations as a function of chain length and concentration. The rms end-to-end distance from PRISM theory was found to be in agreement with corresponding MD simulations, and exhibited molecular weight dependence in accordance with scaling predictions in the dilute and concentrated solution limits. The presence of explicit solvent molecules had a significant effect on the packing of the polymer by inducing additional structure in the intermolecular radial distribution function between polymer sites. Using the direct correlation functions from the athermal solution and the random phase approximation, we were able to estimate the spinodal curves for solutions when polymer and solvent attractions were turned on. We found significant deviations from Flory–Huggins theory that are likely due to compressibility and nonrandom mixing effects.

Partitioning of polymer chains in the theta solution with a confined space of a slit was studied in a wide range of concentrations by using lattice Monte Carlo simulations. The slit width was equal to or greater than the radius of gyration of the theta chains. In the low concentration limit, the partitioning of the theta chains was indistinguishable from that of athermal chains compared at the same chain dimension. At higher concentrations but below the overlap concentration in the solution surrounding the slit, the partition coefficient was nearly independent of the concentration. With a further increase in the concentration, the partition coefficient increased toward unity, as the motional unit in the solution changed from a single chain to the concentration blob of the semidilute theta solution and the blob size decreased with an increasing concentration. The increase in the partition coefficient occurred, however, at concentrations much higher than those for the athermal solutions that showed a simila...

We have performed Brownian dynamics simulations of bead–rod chains under shear using the algorithm introduced by Ottinger. We have investigated the effect of excluded volume and hydrodynamic interactions on material functions and configurational quantities. The model exhibits shear thinning and a negative second normal stress coefficient. We find that excluded volume interactions increase the magnitude of rheological quantities. Hydrodynamic interactions lower the viscosity for small shear rates and long chains and do not contribute significantly to the viscosity for high shear rates. The shear thinning behavior of a chain in theta solvent with hydrodynamic interactions ends at lower shear rates in comparison with other combinations of interactions. We find that chains in theta solvent expand more relative to their quiescent state than chains in good solvent for small and intermediate shear rates. Their expansion, however, is much smaller than predicted by the Rouse or Zimm model, in agreement with recent experiments. The size of chains in theta solvent with hydrodynamic interactions shrinks for very high shear rates. Chains in good solvent orient more into the shear flow than chains in theta solvent if plotted versus the absolute shear rate.

Solvent effects play a major role in controlling electron–transfer reactions. The solvent dynamics happens on a very high-dimensional surface, and this complex landscape is populated by a large number of minima. A critical problem is to understand the conditions under which the solvent dynamics can be represented by a single collective reaction coordinate. When this unidimensional representation is valid, one recovers the successful Marcus theory. In this study the approach used in a previous work [V. B. P. Leite and J. N. Onuchic; J. Phys. Chem. 100, 7680 (1996)] is extended to treat a more realistic solvent model, which includes energy correlation. The dynamics takes place in a smooth and well behaved landscape. The single shell of solvent molecules around a cavity is described by a two-dimensional system with periodic boundary conditions with nearest neighbor interaction. It is shown how the polarization-dependent effects can be inferred. The existence of phase transitions depends on a factor γ proport...

Using the polymer reference interaction site model (PRISM) approximation and hybrid self-consistent MC/RISM method which combines the traditional Monte Carlo (MC) simulation with the numerical solution of the site–site Ornstein–Zernike-type (RISM) integral equation, we study solvent–mediated interactions and the conformational behavior of a single flexible-chain polymer immersed in a monoatomic solvent. The PRISM theory and the self-consistent MC/RISM method predict that in the vicinity of the solvent critical point there is an effective intrachain attraction between monomeric units of the chain. However, the strongly fluctuating solvent can induce significant conformational changes only if there is rather strong attraction between polymer segments and solvent particles. At such conditions, the collapse transition of long chains is possible near the solvent critical point. The equilibrium microstructure of the chain is modulated as a result of the competition between the intrachain short-range excluded vo...

Using the Monte Carlo (MC) calculations, we study the conformational behavior of a two-dimensional (2D) single flexible-chain polymer dissolved in a monoatomic solvent. It is shown that near the solvent critical region the polymer chain can contract. Such a behavior is observed if the radius of fluctuations of solvent density is smaller than the natural size of the N-unit chain with excluded volume interaction [R∼Nν, where ν≈3/(d+2) is the Flory–Edwards exponent]. On the other hand, the chain goes back to the initial swollen state when the solvent correlation length becomes larger than R. Under these conditions, the polymer chain is effectively confined in a large solvent droplet. We find that the strongly fluctuating solvent can induce significant conformational changes only if there is a rather strong attraction between polymer segments and solvent particles. In this case, the average chain size is a nontrivial function of polymer–solvent attraction: At rather weak affinity of polymer and solvent, the average chain size grows with the increase of this attraction; with further increase of affinity of polymer and solvent, the chain begins to contract. Thus, in the case of high affinity of polymer and solvent, the polymer chain can undergo the complex coil–globule–coil transition. In general, the results of the MC simulations are in reasonable agreement with those obtained from the self-consistent integral-equation calculations.

A fully many-body solvent influence functional for hard-sphere polymer chains in hard-sphere solvents is derived from scaled particle theory. Monte Carlo simulation of single chains in this “solvation potential” is used to calculate conformational properties of 3mers, 4mers and 10mers dissolved in 1mers. Comparison is made to the exact results of Monte Carlo simulation of the whole polymer+solvent fluid, and with the predictions of pairwise-additive integral-equation-based solvation potentials. The greater accuracy of the many-body potential suggests that at least in these systems solvent influence on polymer conformation is a strongly many-body phenomenon.

We use the bond fluctuation model with explicit solvent to study single polymer chains under poor solvent conditions. Static and dynamic properties of the bond fluctuation model with explicit solvent are compared with the implicit solvent model, and the Θ-temperatures are determined for both solvent models. We show that even in the very poor solvent regime, dynamics is not frozen for the explicit solvent model. We investigate some aspects of the structure of a single collapsed globule and show that rather large chain lengths are necessary to reach the scaling regime of a dense sphere. The force-extension curve of a single polymer chain under poor solvent conditions in the fixed end-to-end distance ensemble is analyzed. We find that the transition of the tadpole conformation to the stretched chain conformation is rather smooth because of fluctuation effects, which is in agreement with recent experimental results.

A detailed light scattering study of polystyrene (PS) in diethyl malonate (DEM) semidilute solution has been carried out. DEM is a theta solvent for PS at 32 °C. Dynamic light scattering measurements carried out at temperatures closed to the theta temperature show only a diffusion mode in the intensity autocorrelation function; no slow modes are found in the semidilute PS/DEM solution with concentration up to more than 18 times the overlap concentration. For this system, the mutual diffusion coefficient is found to be mainly determined by the osmotic modulus, with the solution stress modulus making a negligible contribution. A slowing down of the mutual diffusion coefficient as the temperature approaches the critical temperature (at the critical concentration) is observed. These results show that despite considerable chain entanglements existing in the semidilute/concentrated PS/DEM solution, no viscoelastic slow modes are found. These results are not in agreement with the existing literature data for the...

Conformation and dynamics of charged polymer chains in counter‐ion solvent is studied by a Monte Carlo simulation in two and three dimensions. The nodes of the chains are positively charged while the solvent particles possess negative charge. The concentration of the polymer (p), and the empty sites (pe) is varied along with the temperature. Reptation, kink‐jump, and a buckling governed by the interaction energy are considered in moving the chain segments. The variation of the root mean square (rms) displacement of the center of mass, and the relaxation of the radius of gyration of the chains with time are studied as a function of polymer concentration and temperature. The rms displacement of the polymer chains exhibits various power laws in different time regimes which depend on the concentration of the chains. Relaxation of the radius of gyration is enhanced on increasing the temperature; the relaxation time seems to decrease on reducing the chain length and increase on increasing the concentration. The...

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 $\varepsilon_h$, representing the stiffness of the chain (ii) a nearest-neighbour attractive energy $\varepsilon_v$, representing the solvent (iii) the monomer density $\rho={N \over \Omega}$, where $N$ and $\Omega$ 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..., Comment: 17 pages, plain tex, 2 figures available upon request

Two‐dimensional chains with C=4 up to C=20 segments are investigated by hard disks molecular dynamics simulations. Solvent particles are explicitly taken into account. In addition, the ratio S/σC of the diameters of the solvent molecules S and the chain segments C is varied between 0.5≤σS/σC≤40.0. Several equilibrium properties show that the polymer dimensions strongly depend on the solvent size. The data are compared to results obtained for a single chain generated by a Monte Carlo simulation. Studies of the mean square (m.sq.) end‐to‐end distance 2〉, the m.sq. radius of gyration 2〉 and some distribution functions indicate that the polymer coil becomes more compact in the presence of solvent molecules. Irrespective of C the most coiled configurations are found for systems with S/σC=1. For very large S/σC all quantities considered correctly approach the values found for isolated chains.

We have performed a Monte Carlo study of the dimensions (radius of gyration) and the intrinsic viscosity for three dimensional linear chains of different lengths. The chains are composed of Gaussian units which interact through a 6–12 Lennard‐Jones potential. From the study of the radius of gyration, the theta state has been characterized for this model. Moreover, the results for different temperatures and chain lengths have been plotted in terms of transition curves in order to analyze the collapse and excluded volume limiting behaviors. Also, a lower bound for the viscosity parameter Φ has been obtained in the theta state, as well as in the collapse and excluded volume regimes.

In this work, two-dimensional lattice-based self-consistent field theory is used to study the free energy cost associated with the insertion of a nanoparticle into a polymer brush. The nanoparticle is modeled as a cylinder and the self-consistent field equations are formulated on a cylindrical lattice. The use of two-dimensional formalism makes it possible to take into account the distortion of the brush density profile due to the embedded nanoinclusion. The insertion free energy penalty is analyzed as a function of the particle size, the brush grafting density, and the solvent quality. In agreement with the earlier simulation work, we find that the insertion free energy cost increases both with the particle size and the brush grafting density and decreases with deteriorating solvent quality. For nanoparticles located deep inside the brush, the insertion free energy is shown to scale with either squared (good solvent) or cubed (poor solvent) monomer volume fraction profile, in agreement with the earlier theoretical results. For shallow nanoinclusions located close to the brush surface, the insertion free energy is shown to scale linearly with the monomer volume fraction profile under both good and theta solvent conditions, again in agreement with the earlier work.

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.

By Molecular Dynamics simulation of a coarse-grained bead-spring type model for a cylindrical molecular brush with a backbone chain of $N_b$ effective monomers to which with grafting density $\sigma$ side chains with $N$ effective monomers are tethered, several characteristic length scales are studied for variable solvent quality. Side chain lengths are in the range $5 \le N \le 40$, backbone chain lengths are in the range $50 \le N_b \le 200$, and we perform a comparison to results for the bond fluctuation model on the simple cubic lattice (for which much longer chains are accessible, $N_b \le 1027$, and which corresponds to an athermal, very good, solvent). We obtain linear dimensions of side chains and the backbone chain and discuss their $N$-dependence in terms of power laws and the associated effective exponents. We show that even at the Theta point the side chains are considerably stretched, their linear dimension depending on the solvent quality only weakly. Effective persistence lengths are extracted both from the orientational correlations and from the backbone end-to-end distance; it is shown that different measures of the persistence length (which would all agree for Gaussian chains) are not mutually consistent with each other, and depend distinctly both on $N_b$ and the solvent quality. A brief discussion of pertinent experiments is given., Comment: 30 pages, 13 figures, 1 table

The average conformation of a flexible chain molecule in solution is coupled to the local solvent structure. In a dense solvent, local chain structure often mirrors the pure solvent structure, whereas, in a dilute solvent, the chain can strongly perturb the solvent structure which, in turn, can lead to either chain expansion or compression. Here we use Monte Carlo (MC) simulation to study such solvent effects for a short Lennard-Lones (LJ) chain in monomeric LJ solvent. For an n-site chain molecule in solution these many-body solvent effects can be formally mapped to an n-body solvation potential. We have previously shown that for hard-sphere and square-well chain-in-solvent systems this n-body potential can be decomposed into a set of two-body potentials. Here, we show that this decomposition is also valid for the LJ system. Starting from high precision MC results for the n = 5 LJ chain-in-solvent system, we use a Boltzmann inversion technique to compute numerically exact sets of two-body solvation potentials which map the many-body chain-in-solvent problem to a few-body single-chain problem. We have carried out this mapping across the full solvent phase diagram including the dilute vapor, dense liquid, and supercritical regions and find that these sets of solvation potentials are able to encode the complete range of solvent effects found in the LJ chain-in-solvent system. We also show that these two-site solvation potentials can be used to obtain accurate multi-site intramolecular distribution functions and we discuss the application of these exact short chain potentials to the study of longer chains in solvent.

A recently introduced bead‐spring type model of polymer chains with purely repulsive interactions between the beads is modified to allow for attractive forces at intermediate distances. This new model is suitable for the study of thermal properties of three‐dimensional polymer solutions and melts and can be efficiently simulated with Link–Cell Monte Carlo methods. As a first step, the single chain lengths up to N=128 beads are studied and the theta temperature θ is located. It is shown that the data are compatible with the theoretically predicted crossover scaling behavior, and that the properties of collapsed chains can be studied for reasonably low temperatures T

Molecular dynamics simulations have been performed for a bead–spring model chain of 30 beads immersed in 738 solvent molecules. The solvent–solute interaction energy ebs has been varied in the range 0.1≤ebs≤0.8 kcal/mol to assess the role and importance of solvent type on the dynamic and equilibrium properties of the chain. Radial distribution functions for polymer bead–solvent and bead–bead pairs indicate the enhancement of more expanded chain configurations with increasing quality of the solvent. The translational diffusivity D of the chain exhibits an inverse linear dependence on ebs, thus decreasing in the presence of more favorable polymer–solvent interactions. Molecular dimensions of the chain such as the mean‐square end‐to‐end distance 〈r2〉 and the radius of gyration Rg are examined in various solvent environment. The ratio 〈r2〉/Rg2 approximates the limiting value of 6 corresponding to infinitely long freely jointed chains. A linear dependence of D on 1/Rg is observed, in conformity with the Zimm t...

We study some dynamical aspects of grafted polymer layers in a solvent. The structure of the brush is described in a θ solvent by the self‐consistent mean field theory and in a good solvent using scaling laws. The Rouse–Zimm model including hydrodynamic interactions is used for the dynamic properties. A given chain end explores the entire thickness of a free grafted layer in a time Te proportional to the cube of the thickness. The exploration time is much larger than the Rouse time that characterizes the relaxation of the fluctuations of the chains conformations. In a θ‐solvent we give a detailed study of the relaxation of the density of a few labeled chain ends towards its equilibrium value. The bridging kinetics between a grafting plate and a plate adsorbing the free ends is also discussed. When adsorption proceeds, an exclusion zone grows in the vicinity of the adsorbing plate. To cross the exclusion zone and adsorb, a chain end must overcome an energy barrier. The typical adsorption time is the first ...

The concentration dependence of the characteristic frequency, ΔΓ1(c), for the overall intra‐ coil relaxation of linear polystyrene in good and theta solvents was determined using photon correlation spectroscopy. This dependence was unusually strong in good solvent and absent in theta solvent. In good solvent, coil–coil collisions, whose frequency depended on concentration, contributed to coil shrinkage and to the interruption of overall intracoil relaxations resulting in an unusually strong concentration dependence for ΔΓ1(c). In marked contrast to the good solvent behavior, coils interpenetrated readily at theta interacting only very weakly and as a result ΔΓ1(c) exhibited little, if any, concentration dependence.

The adsorption of strongly charged polyelectrolyte chains to an oppositely charged planar surface is studied using computer simulation. In addition to an explicit solvent model, two implicit solvent models are considered: one where the solvent induces an implicit Lennard-Jones (ILJ) interaction between polymer sites and one where the solvent induces a many body interaction that depends on the solvent accessible surface area (SASA) of the monomers. Molecular and Brownian dynamics simulations are reported for the explicit and implicit solvent models, respectively. All three models give similar results for the adsorption of the chains in good solvent. The electrostatic attraction between the surface and the polymers is not sufficient to drive the strong adsorption that is seen in experiments. In poor solvents, the models give different results for the adsorption excess and the mechanism for polyelectrolyte adsorption. With explicit solvent, thick adsorbed layers are formed at both charged and neutral surfaces. With the SASA model, adsorbed layers are formed on the charged but not on the neutral surface. With the ILJ model, adsorbed layers are not formed on any surfaces. The results show that the solvent plays a dominant role in the adsorption of polyelectrolytes under poor solvent conditions and that many-body solvent effects have a qualitative effect on the adsorption characteristics and mechanism. In particular, SASA and depletion effects could possibly play an important role; the former can be incorporated in the SASA model, but the latter cannot. The results suggest that accurate computational models for polymer adsorption under poor solvent conditions must incorporate the solvent explicitly.

We report on results of molecular dynamics simulations for supported polymer films with explicit solvent. The simulation represents the polymers by bead-spring chains and the solvent particles by monomers. The interaction between polymer and solvent favors mixing. We find that the solvent acts as a plasticizer. The glass transition temperature T(g) is reduced relative to the pure polymer film. Near T(g) we explore equilibrium properties as a function of temperature and solvent concentration. We find that the structure and dynamics of the films are spatially heterogeneous. The solvent density is enriched at the supporting wall and at the free surface where the film is in equilibrium with solvent vapor. At both interfaces the solvent dynamics is fast, but smoothly crosses over to bulk dynamics when moving from the interfaces toward the center of the film. A smooth gradient from enhanced dynamics at the interfaces to bulk behavior in the film center is also found for the monomers. We show that the same formula used to parametrize the spatial gradient of the dynamics in the pure polymer film may also be applied here. Furthermore, we determine the concentration dependence of the relaxation time of the solvent in the center of film and compare this dependence to models proposed in literature.

The coil-globule transition of a polymer in a solvent has been studied using Monte Carlo simulations of a single chain subject to intramolecular interactions as well as a solvent-mediated effective potential. This solvation potential was calculated using several different theoretical approaches for two simple polymer/solvent models, each employing hard-sphere chains and hard-sphere solvent particles as well as attractive square-well potentials between some interaction sites. For each model, collapse is driven by variation in a parameter which changes the energy mismatch between monomers and solvent particles. The solvation potentials were calculated using two fundamentally different methodologies, each designed to predict the conformational behavior of polymers in solution: (1) the polymer reference interaction site model (PRISM) theory and (2) a many-body solvation potential (MBSP) based on scaled particle theory introduced by Grayce [J. Chem. Phys. 106, 5171 (1997)]. For the PRISM calculations, two well-studied solvation monomer-monomer pair potentials were employed, each distinguished by the closure relation used in its derivation: (i) a hypernetted-chain (HNC)-type potential and (ii) a Percus-Yevick (PY)-type potential. The theoretical predictions were each compared to results obtained from explicit-solvent discontinuous molecular dynamics simulations on the same polymer/solvent model systems [J. Chem. Phys. 125, 194904 (2006)]. In each case, the variation in the coil-globule transition properties with solvent density is mostly qualitatively correct, though the quantitative agreement between the theory and prediction is typically poor. The HNC-type potential yields results that are more qualitatively consistent with simulation. The conformational behavior of the polymer upon collapse predicted by the MBSP approach is quantitatively correct for low and moderate solvent densities but is increasingly less accurate for higher densities. At high solvent densities, the PRISM-HNC and MBSP approaches tend to overestimate, while the PRISM-PY approach underestimates the tendency of the solvent to drive polymer collapse.

We represent ring polymers with the off‐lattice rod‐bead model. We produce perfect unbiased model instances that have between 32 and 2048 beads. These rings are produced at several different values of bead radius, to represent polymers in solvents of different quality. These instances are subject to a novel smoothing operation that facilitates the determination of their topological state, which is represented with the Alexander polynomial. We observe that the probability of observing a trivial knot (P) has a decreasing exponential dependence on the contour length (N) of the polymer, or that P=exp(−N/N0). The characteristic length (N0) varies by many orders of magnitude depending on chain flexibility and solvent quality. For Gaussian rings in a theta solvent, the characteristic length (N0) is 2.6×102. For a good solvent, N0∼8×105. We also explore the expectation value of the minimum number of crossings and suggest that it probably cannot be represented as a power law or exponential function of N. We also suggest that sufficiently large rings will always be composite, and not prime.

The light scattering by an initially monodisperse population of Gaussian random coils in a theta solvent is described by the well known Debye function: P(θ)=D[u(θ)] =(2/u2)(e−u−1+u), where u=u0≡〈S2〉q2. S is the radius of gyration, and q=(4πn/λ)sin(θ/2) is the magnitude of the scattering vector, λ being the vacuum wavelength of the incident light, n the index of refraction, and θ the scattering observation angle. If the molecules undergo random scission, P(θ)=D(u0+r), where r is the average number of scissions per original molecule. In a good solvent, one should include the effect of the second virial coefficient A2 on the light scattering. In the single contact approximation this can be done by using Kc/R=1/MP(θ)+2A2c for an originally monodisperse solution. K is a constant, R the absolute Rayleigh scattering ratio, and c the concentration. The above equation is generalized to originally polydisperse solutions and branched random coils without loops. We discuss its mathematical limits and range of valid...

We present a theoretical study of the lamellar structure of diblock copolymers blended with neutral solvent. The calculations are based on numerical solutions of the equations of the mean field self‐consistent theory of incompressible polymer/solvent blends, from the weak through to the strong segregation limits. For idealized model systems of symmetric copolymers and perfectly nonselective solvent, we examine the variation of the equilibrium lamellar thickness with molecular weight, Flory χ parameter, solvent quality, and copolymer volume fraction, as well as the distribution of solvent and polymer within the subdomains. We also examine a real system which has been extensively studied experimentally, namely PS‐b‐PI with the (nearly) nonselective solvent toluene.

In a side‐by‐side comparison, the q dependence of the collective internal decay constant ∼(ΔΓ)∼qγ of linear polystyrene in good and theta solvents was determined using photon correlation spectroscopy. The results q2.9 and q3.9 for the theta and good solvents, respectively, correspond to relatively strong hydrodynamic interactions (nondraining) when excluded volume effects are minimal for the compact coil at theta and to relatively weak hydrodynamic interactions (partial draining) when excluded volume effects are manifest in the swollen coil in good solvent.

The authors have performed the Langevin dynamics simulation to investigate the unforced polymer translocation through a narrow nanopore in an impermeable membrane. The effects of solvent quality controlled by the attraction strength lambda of the Lennard-Jones cosine potential between polymer beads and beads on two sides of the membrane on the translocation processes are extensively examined. For polymer translocation under the same solvent quality on both sides of the membrane, the two-dimensional and three-dimensional simulations confirm the scaling law of tautrans approximately N1+2upsilon for the translocation in the good solvent, where tautrans is the translocation time, N is the chain length, and upsilon is the Flory exponent. For the three-dimensional polymer translocation under different solvent qualities on two sides of the membrane, the translocation efficiency may be notably improved. The scaling law between tautrans and N varies from tautrans approximately N1+2upsilon to tautrans approximately N with the increase of the difference of solvent qualities, and the crossover occurs at the theta temperature point, where a scaling law of tautrans approximately N1.27 is found. The simulation results here also show that the translocation time changes from a wide and asymmetric distribution with a long tail to a narrow and symmetric distribution with the increase of the difference of the solvent qualities.

Vapor pressures (headspace sampling in combination with gas chromatography) and glass transition temperatures [differential scanning calorimetry (DSC)] have been measured for solutions of polystyrene (PS) in either toluene (TL) (10-70 degrees C) or cyclohexane (CH) (32-60 degrees C) from moderately concentrated solutions up to the pure polymer. As long as the mixtures are liquid, the vapor pressure of TL (good solvent) is considerably lower than that of CH (theta solvent) under other identical conditions. These differences vanish upon the vitrification of the solutions. For TL the isothermal liquid-solid transition induced by an increase of polymer concentration takes place within a finite composition interval at constant vapor pressure; with CH this phenomenon is either absent or too insignificant to be detected. For PS solutions in TL the DSC traces look as usual, whereas these curves may become bimodal for solutions in CH. The implications of the vitrification of the polymer solutions for the determination of Flory-Huggins interaction parameters from vapor pressure data are discussed. A comparison of the results for TL/PS with recently published data on the same system demonstrates that the experimental method employed for the determination of vapor pressures plays an important role at high polymer concentrations and low temperatures.

Results of molecular simulations are presented for the entropy-driven collapse of a single chain in an athermal solvent. The mean square radius of gyration (〈Rg2〉) is calculated for a flexible chain of length N immersed in a hard-sphere medium having a specified solvent chemical potential. For a ratio of chain bead diameter to solvent diameter of 0.2 and packing fraction η=0.44, we find that 〈Rg2〉∝N2ν with ν∼0.36 for N⩾100; such exponent is consistent with that predicted by renormalization group arguments for the poor solvent regime (ν=1/3). The effects of chain length and density on 〈Rg2〉 are consistent with the predictions of the Edwards–Muthukumar theory for a chain in a quenched, random medium.

By computer simulation, Dijkstra et al. [M. Dijkstra, D. Frenkel, and J. P. Hansen, J. Chem. Phys. 101, 3179 (1994)] reported the first entropy‐driven polymer chain collapse in an athermal solvent. To gain a better understanding of chain collapse physics in the absence of attractive interactions, we performed on‐lattice NVT Monte Carlo simulations on a single polymer chain immersed in a hard‐core solvent of variable size, shape, and density. In general, solvent quality decreases with increasing solvent density and incipient chain collapse occurs at a unique critical density for a given solvent size and shape. The critical density is smaller for large solvent molecules, but solvent shape also plays a role. Unfavorable solvent‐chain excluded volume (EV) interactions drive the collapse transition. The EV interaction is reduced and the solvent entropy increases when the chain collapses, but there is an accompanying and unfavorable loss of chain conformational entropy. At the transition density these opposing ...

The conformation of a polymer chain in solution is intrinsically coupled to the thermodynamic and structural properties of the solvent. Here we study such solvent effects in a system consisting of a flexible interaction-site n-mer chain immersed in a monomeric solvent. Chain conformation is described with a set of intramolecular site-site probability functions. We derive an exact density expansion for these intramolecular probability functions and give a diagrammatic representation of the terms contributing at each order of the expansion. The expansion is tested for a short hard-sphere chain (n=3 or 4) with site diameter sigma in a hard-sphere solvent with solvent diameter D. In comparison with Monte Carlo simulation results for 0.2< or =D/sigma< or =100, the expansion (taken to second order) is found to be quantitatively accurate for low to moderate solvent volume fractions for all size ratios. Average chain dimensions are predicted accurately up to liquidlike solvent densities. The hard-sphere chains are compressed with both increasing solvent density and decreasing solvent size. For small solvent (D

The effects of solvent quality on the internal stratification of polymer brushes formed by dendron polymers up to third generation were studied by means of molecular dynamics simulations with Langevin thermostat. The distributions of polymer units, of the free ends, the radii of gyration, and the back folding probabilities of the dendritic spacers were studied at the macroscopic states of theta and poor solvent. For high grafting densities we observed a small decrease in the height of the brush as the solvent quality decreases. The internal stratification in theta solvent was similar to the one we found in good solvent, with two and in some cases three kinds of populations containing short dendrons with weakly extended spacers, intermediate-height dendrons, and tall dendrons with highly stretched spacers. The differences increase as the grafting density decreases and single dendron populations were evident in theta and poor solvent. In poor solvent at low grafting densities, solvent micelles, polymeric pinned lamellae, spherical and single chain collapsed micelles were observed. The scaling dependence of the height of the dendritic brush at high density brushes for both solvents was found to be in agreement with existing analytical results. (C) 2013 AIP Publishing LLC. Journal of Chemical Physics

Measurements of diffusion and driven motion by probe particles in polymer solutions constrain theoretical models of polymer solution dynamics. In this paper, motions of large, intermediate (smaller than a polymer chain, larger than a solvent molecule), and small (solvent, ion) probes through polymer solutions and viscous small-molecule solvents are analyzed. The resulting constraints limit the physical models that can plausibly be used to describe polymer motion and separately limit the mathematical structures that might be used to obtain quantitative predictions from those models. A transition in small-molecule mobility through polymer solutions, at polymer concentrations near 400 g/l, is explained in terms of the size of a solvent molecule relative to the gaps between pairs of chain segments on adjacent polymer molecules.

We have performed classical density functional theory calculations to study the behavior of mixed polymer brushes tethered to a planar surface. We assume no lateral segregation of the polymer at the grafting density studied and consider an implicit solvent. For a binary mixture of short and long athermal polymer chains, the short chain is compressed while the long chain is stretched compared with corresponding pure polymer chains at the same grafting density, which is consistent with simulation. This results from configurational entropy effects. Furthermore, we add a mean-field interaction for each polymer brush to simulate their different response towards a solvent. The long chain is forced to dislike the solvent more than the short chain. Through the interplay between the solvent effects and configurational entropy effects, a switch of the polymer brush surface (or outer) layer is found with increasing chain length of the long chain. The transition chain length (long chain) increases with increasing the solvent selectivity, and decreases with increasing the grafting density of the long chain. These results can provide guidance for the design of smart materials based on mixed polymer brushes.

A coarse-grained model for molecular dynamics simulations of polymer solutions with variable solvent quality is proposed. This model allows solvent quality to be varied over the whole range from very poor to very good solvent conditions by varying a single parameter. The model has several advantages. All interactions are short ranged and repulsive, making the model very computationally efficient compared with other explicit solvent models that include the long-ranged attractive part of the interactions; the solvent is included explicitly, ensuring that the theta condition corresponds to a genuine cancellation of the solvent-mediated polymer-polymer interactions; and hydrodynamic interactions and entanglement can occur for all solvent conditions. The theta point is determined and the conformational properties of a 50-bead chain system are investigated over the whole concentration range from the dilute limit to the melt as a function of solvent quality.

The behavior of a linear polymer chain is studied in a solvent with high affinity for the polymer. The coil dimensions and specific heat are calculated as a function of chain length, solvent concentration, and polymer-solvent attraction strength epsilon(ps). All other interactions are limited to excluded volume repulsion, which implies that the Flory-Huggins chi parameter is negative. Using both on-lattice and off-lattice models of a polymer chain in explicit solvent, we study a transition from weak to strong association regimes. In all cases studied, the system's heat capacity is a nonmonotonic function of epsilon(rhos) with a maximum at attraction strengths of the order of several k(B)T. This peak originates from restriction of local conformational degrees of freedom due to the associated solvent rather than from a partial chain collapse which onsets as attractive solvent content is decreased.

The structure and thermodynamic properties of a system of end-grafted flexible polymer chains grafted to a flat substrate and exposed to a solvent of variable quality are studied by molecular dynamics methods. The macromolecules are described by a coarse-grained bead-spring model, and the solvent molecules by pointlike particles, assuming Lennard-Jones-type interactions between pairs of monomers (epsilon(pp)), solvent molecules (epsilon(ss)), and solvent monomer (epsilon(ps)), respectively. Varying the grafting density sigma(g) and some of these energy parameters, we obtain density profiles of solvent particles and monomers, study structural properties of the chain (gyration radius components, bond orientational parameters, etc.), and examine also the profile of the lateral pressure P( parallel)(z), keeping in the simulation the normal pressure P( perpendicular) constant. From these data, the reduction of the surface tension between solvent and wall as a function of the grafting density of the brush has been obtained. Further results include the stretching force on the monomer adjacent to the grafting site and its variation with solvent quality and grafting density, and dynamic characteristics such as mobility profiles and chain relaxation times. Possible phase transitions (vertical phase separation of the solvent versus lateral segregation of the polymers into "clusters," etc.) are discussed, and a comparison to previous work using implicit solvent models is made. The variation of the brush height and the interfacial width of the transition zone between the pure solvent and the brush agrees qualitatively very well with corresponding experiments.

We use bead-spring models for a polymer coupled to a solvent described by multiparticle collision dynamics to investigate shear thinning effects in dilute polymer solutions. First, we consider the polymer motion and configuration in a shear flow. For flexible polymer models we find a sharp increase in the polymer radius of gyration and the fluctuations in the radius of gyration at a Weissenberg number approximately 1. We then consider the polymer viscosity and the effect of solvent quality, excluded volume, hydrodynamic coupling between the beads, and finite extensibility of the polymer bonds. We conclude that the excluded volume effect is the major cause of shear thinning in polymer solutions. Comparing the behavior of semiflexible chains, we find that the fluctuations in the radius of gyration are suppressed when compared to the flexible case. The shear thinning is greater and, as the rigidity is increased, the viscosity measurements tend to those for a multibead rod.

Monte Carlo simulation has been used to investigate the effects of linear solvent molecular size on polymer chain conformation in solutions. Increasing the solvent molecular size leads to shrinkage of the polymer chains and increase of the critical overlap concentrations. The root-mean-square radius of gyration of polymer chains (R(g)) is less sensitive to the variation of polymer concentration in solutions of larger solvent molecules. In addition, the dependency of R(g) on polymer concentration under normal solvent conditions and solvent molecular size is in good agreement with scaling laws. When the solvent molecular size approaches the ideal end-to-end distance of the polymer chain, an extra aggregation of polymer chains occurs, and the solvent becomes the so-called medium-sized solvent. When the size of solvent molecules is smaller than the medium size, the polymer chains are swollen or partially swollen. However, when the size of solvent molecules is larger than the medium size, the polymer coils shrink and segregate, enwrapped by the large solvent molecules.

The time-resolved diffraction signal from a laser-excited solution has three principal components: the solute-only term, the solute-solvent cross term, and the solvent-only term. The last term is very sensitive to the thermodynamic state of the bulk solvent, which may change during a chemical reaction due to energy transfer from light-absorbing solute molecules to the surrounding solvent molecules and the following relaxation to equilibrium with the environment around the scattering volume. The volume expansion coefficient alpha for a liquid is typically approximately 1 x 10(-3) K(-1), which is about 1000 times greater than for a solid. Hence solvent scattering is a very sensitive on-line thermometer. The decomposition of the scattered x-ray signal has so far been aided by molecular dynamics (MD) simulations, a method capable of simulating the solvent response as well as the solute term and solute/solvent cross terms for the data analysis. Here we present an experimental procedure, applicable to most hydrogen containing solvents, that directly measures the solvent response to a transient temperature rise. The overtone modes of OH stretching and CH3 asymmetric stretching in liquid methanol were excited by near-infrared femtosecond laser pulses at 1.5 and 1.7 microm and the ensuing hydrodynamics, induced by the transfer of heat from a subset of excited CH3OH* to the bulk and the subsequent thermal expansion, were probed by 100 ps x-ray pulses from a synchrotron. The time-resolved data allowed us to extract two key differentials: the change in the solvent diffraction from a temperature change at constant density, seen at a very short time delay approximately 100 ps, and a term from a change in density at constant temperature. The latter term becomes relevant at later times approximately 1 mus when the bulk of liquid expands to accommodate its new temperature at ambient pressure. These two terms are the principal building blocks in the hydrodynamic equation of state, and they are needed in a self-consistent reconstruction of the solvent response during a chemical reaction. We compare the experimental solvent terms with those from MD simulations. The use of experimentally determined solvent differentials greatly improved the quality of global fits when applied to the time-resolved data for C2H4I2 dissolved in methanol.

The gelation of physically associating triblock copolymers in a good solvent was investigated by Monte Carlo simulation, and the effect of the solvent size on the gelation was discussed in detail. The solvent size can greatly affect the conformation distribution of the polymer chains, the size distribution of the micelle, and the mechanism of the gelation on microscale, mesoscale, and macroscale. Our results indicate that the effect of the solvent size on the physical gelation exhibits three distinct regions. The gelation closely couples to the chain conformation transition when the solvent size is normal or quasinormal; the gelation occurs simultaneously with phase separation when the solvent size approaches the ideal end-to-end distance of the polymer chains; the gelation follows a glass transition mechanism upon increasing the solvent size to much larger than the ideal end-to-end distance of polymer chains. We also found that the volume fraction of the gel point can shift from 0.20 to 0.06, a range much broader than that reported in the literature.

Solvation forces between large surfaces in athermal polymer solutions, in which both solvent particles and polymers are adsorbed at the surfaces, are studied with density functional theory. We investigate how the range of the surface potential affects the net interaction between the surfaces. Predictions from treatments in which the solvent is explicitly induced are compared with those obtained with more approximate models, where the solvent is either neglected, or enters the description implicitly. The results are interpreted via comparisons with simpler model systems. It is shown that a long-ranged surface potential, acting equally on monomers and solvent, leads to a solvent dominated repulsive solvation force, while polymer specific contributions dominate the net interactions when the adsorption potential has a short range. Effects of preferential polymer adsorption are also investigated.