Polymer Chains In Good Solvent Research Articles

Does Preferential Adsorption Drive Cononsolvency?

Cononsolvency refers to the effect in which a polymer chain in good solvent collapses when it is mixed with an increasing concentration of a second good solvent. An important question is if universality of nonspecific attraction between monomers and cosolvent explains the cononsolvency phenomenon. We report results obtained with computer simulations of coarse-grained models and show that the above universality does not exist. We demonstrate that cononsolvency can occur with or without the preferential adsorption of the cosolvent on the polymer chain and discuss experimental systems corresponding to these cases.

Phase Behavior of a Flexible Star Polymer Chain in Good Solvent near an Attractive Surface

AbstractThe phase behavior of a flexible star polymer chain in good solvent near an attractive surface is investigated by multicanonical Monte Carlo simulations where the specific heat, the parallel and the perpendicular components of the gyration tensor, and the fraction of adsorbed monomers are computed. Temperature–surface attraction strength pseudo‐phase diagrams are constructed for three chain lengths (N = 31, 41, 61) with three numbers of arms (f = 3, 4, 6). The star polymer chain adopts a desorbed expanded conformation for high temperatures and low surface attraction strength. With decreasing temperature and for sufficient surface attraction strength, the star polymer chain undergoes a transition from 3D to a 2D structure. At low temperatures, the chain is mostly adsorbed for low surface attraction strength and adopts a two‐layer arrangement at high values of the latter. In this context, it is also found that the phase behavior of flexible star polymer chains in good solvent near an attractive surface is affected by the number of arms f and that a star polymer chain with a high number of arms is necessary for a precise classification of all intermediate pseudo phases.

Interaction between Surfactants and Colloidal Latexes in Nonpolar Solvents Studied Using Contrast-Variation Small-Angle Neutron Scattering

The interaction between deuterium-labeled Aerosol OT surfactant (AOT-d34) and sterically stabilized poly(methyl methacrylate) (PMMA) latex particles dispersed in nonpolar solvents has been studied using contrast-variation small-angle neutron scattering (CV-SANS). The electrophoretic mobilities (μ) of the latexes have been measured by phase-analysis light scattering, indicating that μ is negative. Two analogues of the stabilizers for the particles have been studied as free polymers in the absence of PMMA latexes: poly(12-hydroxystearic acid) (PHSA) polyester and poly(methyl methacrylate)-graft-poly(12-hydroxystearic acid) (PMMA-graft-PHSA) stabilizer copolymer. The scattering from both PHSA in dodecane and PMMA-graft-PHSA in toluene is consistent with extended polymer chains in good solvents. In dodecane, PMMA-graft-PHSA forms polymer micelles, and SANS is consistent with ellipsoidal aggregates formed of around 50 polymer chains. CV-SANS measurements were performed by measuring SANS from systems of PHSA, PMMA-graft-PHSA, and PMMA latexes with 10 and 100 mM surfactant solutions of AOT-d34 in both polymer/particle and AOT contrast-matched solvent. No excess scattering above the polymer or surfactant was found for PHSA in dodecane or PMMA-graft-PHSA in dodecane and toluene. This indicates that AOT does not significantly interact with the free polymers. Excess scattering was observed for systems with AOT-d34 and PMMA latexes dispersed in particle contrast-matched dodecane, consistent with the penetration of AOT into the PMMA latexes. This indicates that AOT does not interact preferentially with the stabilizing layers but, rather, is present throughout the colloids. Previous research ( Langmuir 2010, 26, 6967-6976 ) suggests that AOT surfactant is located in the latex PHSA-stabilizer layer, but all the results in this study are consistent with AOT poorly interacting with alkyl-stabilizer polymers.

Explaining the Absence of High-Frequency Viscoelastic Relaxation Modes of Polymers in Dilute Solutions

Using multiscale modeling, including molecular dynamics simulations, with both united-atom and coarse-grained force fields, as well as Brownian dynamics simulations with still higher levels of coarse-graining, we explain the long-mysterious absence of high frequency modes in the viscoelastic spectrum of isolated polymer chains in good solvents, reported years ago by Schrag and co-workers. The relaxation spectrum we obtain for a chain of 30 monomers at atomistic resolution is, remarkably, a single exponential, while that of a coarse-grained chain of 100 monomers is well fit by only two modes. These results are very surprising in view of the many degrees of freedom possessed by these chains, and in view of the many relaxation modes present in melts of such chains. However, the result agrees perfectly with experimental observations of Schrag and co-workers. We also performed Brownian dynamics (BD) simulations in which the explicit solvent molecules are replaced by a viscous continuum, using chain models of varying degrees of resolution, both in the presence and absence of hydrodynamic interactions (HI). Although the local dynamics is suppressed by the addition of bending, torsion, side groups and excluded volume interactions (as suggested in Jain and Larson(15)), none of the BD simulations predict a single exponential relaxation for a short polymer chain. The comparison of the relaxation of the bond vectors from different models indicates an additional slow-down in the presence of explicit solvent molecules, which is critical to obtain a single exponential relaxation for short chains. Our results indicate that the chain dynamics at small length scales (down to a few Kuhn steps) are significantly different from the predictions of models based on a continuum solvent, and finally help explain the experimental results of Schrag and co-workers.

Formation and properties of surface-anchored amine-terminated poly(dimethylsiloxane) assemblies with tunable physico-chemical characteristics

Surface-anchored amine-terminated poly(dimethysiloxane) (PDMS) assemblies with tunable physico-chemical characteristics were fabricated with a simple two-step procedure. Firstly, 3-glycidoxypropylmethyldimethoxysilane (GPDMS) molecules were self-assembled on silicon surface, and then coupled to PDMS through a surface ring-opening reaction. The structure and morphology of the amine-terminated PDMS assemblies were characterized with various techniques such as ellipsometry, contact angle goniometer, grazing angle attenuated total reflectance-Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, and atomic force microscopy. The GPDMS monolayers were truly monomolecular films with a virtually normal molecular orientation of densely packed molecules, which were firmly tethered to the hydroxylated silicon substrate. Self-assembly of PDMS molecules resulted in the formation of homogeneous films ~ 6.3 nm thick with the surface roughness ~ 0.898 nm. The calculation of grafting parameters from experimental measurements indicated that the presence of homogeneous and densely grafted PDMS films allowed us to predict a “brushlike” regime for the polymer chains in good solvents.

Calculation of the Segmental Order Parameter for a Polymer Chain in Good Solvent

AbstractWe have calculated the segmental tensor order parameter (second moment of orientation distribution function) of flexible polymer chains in a weak good solvent with fixed end‐to‐end distance and fixed segment length. Using the Edwards model for polymer chains with excluded volume interaction, we have performed direct perturbation expansions to obtain the two‐vector correlation function in one loop order. Our results indicate that distribution of tensor order parameter is not homogeneous along the chain as expected for ideal Gaussian statistics. Segmental order is lower as compared to Gaussian chains and decays toward the chain ends. These results are in agreement with computer simulation studies.magnified image

Low-temperature and high-temperature approximations for penetrable-sphere fluids: Comparison with Monte Carlo simulations and integral equation theories

The two-body interaction in dilute solutions of polymer chains in good solvents can be modeled by means of effective bounded potentials, the simplest of which being that of penetrable spheres (PSs). In this paper we construct two simple analytical theories for the structural properties of PS fluids: a low-temperature (LT) approximation, that can be seen as an extension to PSs of the well-known solution of the Percus-Yevick (PY) equation for hard spheres, and a high-temperature (HT) approximation based on the exact asymptotic behavior in the limit of infinite temperature. Monte Carlo simulations for a wide range of temperatures and densities are performed to assess the validity of both theories. It is found that, despite their simplicity, the HT and LT approximations exhibit a fair agreement with the simulation data within their respective domains of applicability, so that they complement each other. A comparison with numerical solutions of the PY and the hypernetted-chain approximations is also carried out, the latter showing a very good performance, except inside the core at low temperatures.

Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories

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

Computer simulations of the conformations of strongly adsorbed chains at the solid–liquid interface

We have utilized molecular dynamics simulations to critically study the conformation of isolated polymer chains adsorbed on surfaces in the presence of explicit solvent. The changes in conformations of the polymer chain in good solvent as it adsorbs onto a substrate is mapped. The quasi two-dimensional pancake conformation of a well adsorbed polymer chain is confirmed. The effect of wetting characteristics of the solvent on the adsorption transition of polymer chain is also studied. We found that a non-wetting solvent aids adsorption of the polymer chain even at low sticking energies compared to wetting solvent.

Dynamics and scaling of polymers in a dilute solution: Analytical treatment in two and higher dimensions

We consider the dynamical scaling of a single polymer chain in good solvent. In the case of two-dimensional systems, Shannon and Choy [Phys. Rev. Lett. 79, 1455 (1997)] have suggested that the dynamical scaling for a dilute polymer solution breaks down. Using scaling arguments and analytical calculations based on the Zimm model, we show that the dynamical scaling of a dilute two-dimensional polymer system holds when the relevant dynamical quantities are properly extracted from finite systems. Most important, the polymer diffusion coefficient in two dimensions scales logarithmically with system size, in excellent agreement with our extensive computer simulations. This scaling is the reason for the failure of the previous attempts to resolve the dynamical scaling of dilute two-dimensional polymer systems. In three and higher dimensions our analytic calculations are in agreement with previous results in the literature.

Corrections to scaling in the hydrodynamic properties of dilute polymer solutions

We discuss the hydrodynamic radius RH of polymer chains in good solvent, and show that the leading order correction to the asymptotic law RH∝Nν (N degree of polymerization, ν≈0.59) is an “analytic” term of order N−(1−ν), which is directly related to the discretization of the chain into a finite number of beads. This result is further corroborated by exact calculations for Gaussian chains, and extensive numerical simulations of different models of good-solvent chains, where we find a value of 1.591±0.007 for the asymptotic universal ratio RG/RH, RG being the chain’s gyration radius. For Θ chains the data apparently extrapolate to RG/RH≈1.44, which is different from the Gaussian value 1.5045, but in accordance with previous simulations. We also show that the experimentally observed deviations of the initial decay rate in dynamic light scattering from the asymptotic Benmouna–Akcasu value can partly be understood by similar arguments.

Polymer chains in good solvent facing impenetrable walls: what is the distance to the wall in lattice Monte Carlo simulations

Monomer density profile of polymer chains in the good solvent condition near an impenetrable wall was examined in lattice Monte Carlo simulation. It was found that a positive penetration depth γ is necessary for the density profile to follow the prediction of the scaling theory. In dilute solutions, γ was 0.13–0.22 of the lattice unit from a weak confinement to a strong confinement. With an increasing concentration, γ increased gradually to a value close to 0.36. These findings corroborate our hypothesis that the need of the positive γ and a greater γ at higher concentrations result from non-even chain transport due to a large difference in site occupancy, especially at higher concentrations.

Monte Carlo simulations for a fluctuating sphere labeled on a flexible polymer chain in good solvents

Monte Carlo simulations are conducted to investigate a model composed of a fluctuating sphere labeled on one chain end of an isolated flexible chain polymer in good solvents. The labeled sphere is to model the instantaneous size of a bound flexible chain segment or a vibrating chromophore on a polymer chain. We assume the vibration of the sphere is governed by a harmoniclike potential, and the sphere size stays positive. We first address the issue regarding the confinement effect induced by a flexible chain. To rationalize the simulation results, we carry out a detailed analysis for a simple case containing a dimer grafted onto a fluctuating sphere. Using the sphere with a large size fluctuation, we find that the fluctuating sphere can be confined within the coiled polymer chain, and even trapped inside the grooves between neighboring monomers. The results imply the confinement effects may influence the properties of chromophores labeled on polymers or drugs bound to biopolymers. Moreover, in a separate study, we show the fluctuating sphere model can be used to fit a bound flexible chain segment, and provides a means to parameterize a polymer chain to a dumbbell, with possible applications in the dynamics of dilute polymer solutions.

Bridging of an Isolated Polymer Chain

Lattice Monte Carlo simulations are used to analyze a single polymer chain in good solvent confined between two adsorbing walls. Results are reported for the number and size distribution of bridge conformations and the resultant attractive force between the surfaces as a function of intersurface distance, H, and the effective adsorption energy, ε, between the polymer segment and the wall. The results are consistent with indirect experimental measurements of bridging in a multichain system and additionally yield information on the mechanism of bridging. In the case of single chains and strong adsorption (ε > 0.5 kBT), the force per bridge fbr is independent of separation and depends only on the adsorption energy, in agreement with scaling analysis. In the case of weak adsorption (or for multichain systems) it is explicitly shown that steric interactions (loop−loop, loop−bridge interactions, etc.) are important. The “force per bridge” again has a roughly constant magnitude (appropriately diminished by steric interactions) but cannot be related unequivocally to the adsorption energy at the surface.

Equation of state for polymer chains in good solvents

A free-energy model is developed for polymer chains in good solvents. This model, which combines the ideas of polymer field theory with liquid-state theory, is valid in the dilute, semidilute, and concentrated regimes. The model is compared against computer simulation data for the equation of state of tangent hard-sphere chain fluids. At low concentrations, it accurately describes the thermodynamics of tangent hard-sphere chains, reproducing the universal scaling behavior of long chains. At high concentrations, the model has an accuracy comparable to those of previous equations of state for tangent hard-sphere chains.

From Oil-Swollen Wormlike Micelles to Microemulsion Droplets: A Static Light Scattering Study of the L1 Phase of the System Water + C12E5 + Decane

The microstructure of the ternary system pentaethyleneglycol monododecyl ether (C12E5), decane and water was investigated by static light scattering in the water-rich region of the phase diagram at constant temperature (22 °C). Micellar size and shape were determined along several pseudobinary sections of constant oil-to-surfactant ratio. The main focus was on dilute solutions (cm ranging from 0.0004 g cm-3 up to 0.3 g cm-3, where cm denotes the mass concentration of oil plus surfactant in the aqueous phase) and small oil content (α up to 0.35, where α denotes the mass fraction of oil in the oil + surfactant mixture). Our data analysis supports the presumed existence of wormlike micelles at low α. The concentration dependence of the apparent molar mass Mapp of the micelles can be represented over a wide concentration range (up to the semidilute regime) by a model that combines a power law Mw ∝ cma with the structure factor S(q = 0) for flexible polymer chains in good solvents. For α ≤ 0.10 the fitted valu...

Molecular Dynamics Study of Relaxation Modes of a Single Polymer Chain

Relaxation modes and rates of a single polymer chain with the excluded volume interaction is studied by molecular dynamics simulations. The variational method for the estimation of the relaxation modes and rates proposed by Takano and Miyashita [J. Phys. Soc. Jpn. 64 (1995) 3688] is generalized to cases where the detailed balance condition is not satisfied and applied to the results of the present simulations. The relaxation modes and rates estimated by the generalized method describe the behaviors of the autocorrelation functions of relative velocities and relative positions of the segments well. For a polymer chain with N segments, the behavior of the p th slowest relaxation rate λ p with p / N ≪1 is consistent with the theoretical prediction λ p ∝( p / N ) 2ν+ 1 , where ν is the exponent for the size of a polymer chain in good solvent.

Monte Carlo Study of Relaxation Modes of a Single Polymer Chain

The relaxation modes and rates of a single polymer chain are studied by Monte Carlo simulations of the bond fluctuation model. On the basis of the method proposed by Takano and Miyashita [J. Phys. Soc. Jpn. 64 (1995) 3688], the approximate relaxation modes and rates are obtained by solving a generalized eigenvalue problem for the correlation matrices C i , j ( t )= / 3 , where R i ( t ) denotes the position of the i th segment relative to the center of mass of the polymer chain. For a chain of N segments with the excluded volume interaction, the contribution \(\tilde{g}_{i,p}\) of the p th slowest mode to R i shows the i -dependence \(\tilde{g}_{i,p} \propto \cos [(i-\frac{1}{2})p \pi / N]\), which is the same as that of the Rouse model. The behavior of the relaxation rate λ p of the p th slowest mode is in good agreement with the theoretical prediction λ p ∼( p / N ) 2ν+ 1 , where ν≃0.588 is the exponent for the swelling of a polymer chain in good solvent.

Polymer chains in good solvent within attracting walls

AbstractIt is known that a polymer chain in an ideal solvent confined within parallel attracting walls undergoes a second‐order transition at the temperature T* satisfying the equation exp[‐ε/(kBT*)]=6/5; here the model consists of a chain placed on a cubic lattice, and ε (<0) is the attractive energy experienced by a chain segment contacting a wall.We then investigate the effect induced by a good solvent upon the chain behavior. A single chain is considered; within the Gaussian approximation, we assume that its partition function may be factorized in two terms, one across the wall planes and another parallel to them. For an interplanar distance L significantly smaller than the average radius of gyration the compressed chain is assumed to reach a uniform density, so that the free energy contribution due to the intrachain atomic contacts is a function of the density alone. It may be shown that the effective value of ε/(kBT*)(=σ) is the difference between the value to be expected “in vacuo” and β/(z‐2), where z is the degree of coordination of the lattice and β is the excluded‐volume parameter. As a result, for large values of L we may have an attractive effect exerted by the chain on the walls whereas at small L's we invariably have a repulsion. For the cubic lattice we have a repulsion and an attraction for large L approximatively for σ < ln(6/5)+β/(z‐2) and for σ > (ln(6/5)+β/(z‐2), respectively, whereas we have inversion between the two regimes at some distance L for intermediate values of σ. In the limit of an infinite molecular weight the inversion translates into a thermodynamic transition.We believe the present model may explain some important features seen in polymer adhesion.

Long polymer chains in good solvent: beyond the universal limit

We analyze the effects of finite segment size and weak chain stiffness on the properties of polymer solutions in the dilute limit. We consider both weak coupling (cross over from Θ- to excluded volume - conditions) and strong coupling (very good solvents), pointing out that the renormalization group in its standard field theoretic implementation allows for two universal branches corresponding to these two different situations. The strong coupling branch implicitly relies on the existence of a finite segment size, a feature which however does not explicitly show up in the renormalized results. Beyond the leading «corrections to scaling» described by the standard renormalization group flow, the strong coupling branch necessarily is affected by nonuniversal corrections. In field theoretic renormalization we include the first order effects of finite segment size or stiffness in terms of an expansion of the scaling functions about the universal limit. We compare to direct renormalization, where finite segment size or stiffness are included into the renormalization group equations. This somewhat magnifies the effects, but still the nonuniversal corrections are negligible for chains longer than about 500 freely rotating units. Qualitatively the effects in both renormalization schemes are the same, consistent with experimental or Monte Carlo results