Polymers In Good Solvent Research Articles

Molecular conformations of dumbbell-shaped polymers in good solvent.

We study conformational properties of diluted dumbbell polymers composed of two rings attached to both ends of a linear spacer segment. Our investigation involves analytical methods of field theory and bead-spring coarse-grained molecular dynamics simulations. We focus on the influence of the relative length of the spacer segment to the length of side rings on the shape and the relative size of dumbbells as compared to linear polymers of equal mass. We find that dumbbells with short spacers exhibit a significantly more compact structure than linear polymers. Conversely, as the spacer length increases, the influence of the side rings on the size of the dumbbells becomes negligible. Consequently, dumbbell molecules with long spacers attain a size comparable to corresponding linear chains. Our analytical theory accurately predicts a quantitative conformational crossover between the behaviors of short-spacer and long-spacer dumbbells, which is further confirmed by our numerical simulations.

Arabinoxylan in Water through SANS: Single-Chain Conformation, Chain Overlap, and Clustering.

Using small-angle neutron scattering (SANS), we examine the structure and conformational behavior of wheat arabinoxylan (AX) prepared at various concentrations in a sodium phosphate aqueous buffer. As for another major hemicellulose, xyloglucan, we observe a small number of large clusters surrounded by AX chains that behave exactly as a polymer in good solvent with a Flory exponent ν = 0.588. The fit of the data at high q-values to a standard worm-like chain model gives the persistence length lp = 45 Å and cross section of the chains 2Rc = 11-12 Å. In addition, using a dedicated modeling approach, we extract from the SANS data at the intermediate q-range the correlation length ξ of the solutions in the semidilute regime. The decay of ξ with concentration follows a scaling law that further confirms the self-avoiding statistical behavior of the AX chains. This first comprehensive study about the properties of water-soluble AX at different length scales may help in the development of products and processes involving AX as a substitute for fossil carbon molecules.

Understanding the Structure and Rheology of Galactomannan Solutions with Coarse-Grained Modeling

Understanding and predicting the behavior of aqueous solutions of galactomannans is of significant interest for a variety of fields and applications, such as hydraulic fracturing in the petroleum industry and thickening in the food industry. Herein, we devise and validate a coarse-grained (CG) model of guar gum─a galactomannan─and study its structure and rheology in aqueous solution. The CG model is computationally efficient, utilizing an implicit solvent and one CG bead per monosaccharide, and exhibits good quantitative agreement with experiments with respect to the radius of gyration of the chain, aggregate structure in solution, and solution viscosity. Using both simulations and experiments, we show that the behavior of guar gum in water can be explained by scaling theory for polymers in good solvents. Namely, the radius of gyration of the chain shows a self-avoiding random walk behavior, and the solution specific viscosity ηsp exhibits the expected power-law scaling with the reduced concentration in different solution regimes (i.e., ηsp ∼ (c[η])1.3 in semidilute and ηsp ∼ (c[η])3.9 in entangled solutions). By extending our CG model to other galactomannans with different mannose-to-galactose ratios (M/G ratios) and different arrangements of unsubstituted mannose units, we show that high M/G ratios and long blocks of unsubstituted mannose units are responsible for aggregate formation in galactomannan solutions, which can reduce solution viscosity moderately.

Forces between mica and end-grafted statistical copolymers of sulfobetaine and oligoethylene glycol in aqueous electrolyte solutions

This study quantified the interfacial forces associated with end-grafted, statistical (AB) co-polymers of sulfobetaine methacrylate (SBMA) and oligoethylene glycol methacrylate (OEGMA) (poly(SBMA-co-OEGMA)). Surface force apparatus measurements compared forces between mica and end-grafted copolymers containing 0, 40, or 80 mol% SBMA. Studies compared forces measured at low grafting density (weakly overlapping chains) and at high density (brushes). At high density, the range of repulsive forces did not change significantly with increasing SBMA content. By contrast, at low density, both the range and the amplitude of the repulsion increased with the percentage of SBMA in the chains. The ionic strength dependence of the film thickness and repulsive forces increased similarly with SBMA content, reflecting the increasing influence of charged monomers and their interactions with ions in solution. The forces could be described by models of simple polymers in good solvent. However, the forces and fitted model parameters change continuously with the SBMA content. The latter behavior suggests that ethyene glycol and sulfobetaine behave as non-interacting, miscible monomers that contribute independently to the interfacial forces. The results suggest that molecular scale properties of statistical poly (SBMA-co-OEGMA) films can be readily tuned by simple variation of the monomer ratios.

Ionic strength dependent forces between end-grafted Poly(sulfobetaine) films and mica

The molecular surface properties of zwitterionic polymer coatings are central to their ultra-low fouling properties and effectiveness as steric stabilizers in concentrated salt solutions. Here, Surface Force Apparatus measurements quantified the molecular forces between end-grafted poly(sulfobetaine) methacrylate thin films and mica, as a function of the chain grafting density and ionic strength. These results demonstrate that, at the ionic strengths considered, end-grafted poly(sulfobetaine) films can be described by models for polymers in good solvent. Parameters determined from data fits to the Milner-Witten-Cates or Dolan and Edwards models for dense or dilute chains, respectively, varied with ionic strength, in ways that reflect poly(sulfobetaine) swelling and the increased excluded volume strength of chain segments. These force measurements provide new insight into how polymer coverage and salt cooperate to regulate repulsive poly(sulfobetaine) steric barriers. These findings have implications for the design of grafted poly(sulfobetaine) as colloidal stabilizers or nonfouling surface coatings.

Plate-model applied on concentration effects in size exclusion chromatography

A universal procedure of modeling chromatography separation, based on the plate model, has been developed. On each plate, the equilibrium between the analyte in the mobile and stationary phases is established. This equilibrium may be described by the concentration-dependent partition coefficient. The establishment of the equilibrium on each plate is followed by the displacement of the analyte in the mobile phase by one plate, establishment of new equilibrium, etc. The result is a series of elution curves with positions of maxima dependent on injected mass of the polymer. The procedure has been tested on modeling concentration effects on the basis of dependences of the partition coefficient on local concentrations on each plate. By comparison with the experiment, the slope of the concentration dependence of the partition coefficient of polystyrene in benzene was estimated. It is in qualitative agreement with the literature data obtained by a computer simulation of chromatography separation of polymers in good solvents.

Chain flexibility and dynamics of alginate solutions in different solvents

Mechanical rheometry, specifically rotational rheometry, squeeze flow, and capillary rheometry, and two microrheology methods, namely multiple-particle tracking (MPT) and diffusing wave spectroscopy (DWS) have been used to get new insight into structural and dynamical properties of alginate dissolved in solvents widely used for bioprinting, namely deionized water, phosphate-buffered saline (PBS), and Dulbecco Modified Eagle Medium (DMEM) cell media. Results demonstrate that alginate rheological properties depend on the solvent quality at concentrations higher than 1 wt.%. In this high concentration regime, in aqueous salt-free and PBS solutions, experimental scaling exponents for the concentration dependence of the specific viscosity ηsp and the plateau modulus G0 agree well with theoretical predictions for neutral polymers in good solvent whereas for the terminal relaxation time TR, the exponent is slightly higher than theoretically predicted, presumably due to the formation of aggregates. For alginate dissolved in DMEM, all exponents for ηsp, G0, and TR agree with predictions for polymers in theta solvents, which might be related to the formation of polyelectrolyte complex as a result of interactions between alginate and amino acids. Chain persistence length lp values, as determined directly from high frequency rheometry for the first time, are independent of alginate concentration and temperature. Lower absolute lp values were found for DMEM solutions compared with the other solvents. Moreover, scaling exponents for ηsp, G0, and TR do not change with temperature, within 20 and 60 °C. These findings suggest no change in the conformation of alginate chains with temperature.Graphical abstractAlginate rheological properties depend on the solvent quality

Influence of solvent quality on conformations of crowded polymers.

The structure and function of polymers in confined environments, e.g., biopolymers in the cytoplasm of a cell, are strongly affected by macromolecular crowding. To explore the influence of solvent quality on conformations of crowded polymers, we model polymers as penetrable ellipsoids, whose shape fluctuations are governed by the statistics of self-avoiding walks, appropriate for a polymer in a good solvent. Within this coarse-grained model, we perform Monte Carlo simulations of mixtures of polymers and hard-nanosphere crowders, including trial changes in polymer size and shape. Penetration of polymers by crowders is incorporated via a free energy cost predicted by polymer field theory. To analyze the impact of crowding on polymer conformations in different solvents, we compute the average polymer shape distributions, radius of gyration, volume, and asphericity over ranges of the polymer-to-crowder size ratio and crowder volume fraction. The simulation results are accurately predicted by a free-volume theory of polymer crowding. Comparison of results for polymers in good and theta solvents indicates that excluded-volume interactions between polymer segments significantly affect crowding, especially in the limit of crowders much smaller than polymers. Our approach may help to motivate future experimental studies of polymers in crowded environments, with possible relevance for drug delivery and gene therapy.

Structures and Surface States of Polymer Brushes in Good Solvents: Effects of Surface Interactions

The influence of the surface interaction on the mesoscopic structure of grafted polymers in good solvents has been examined. At high surface coverage, tethered polymers are in the brush state and the parabolic segment density profile is confirmed by self-consistent field theory (SCFT) calculations. It is found that this is a universal behavior for a whole range of surface interactions from complete repulsion to strong attraction. More interestingly, finite surface repulsion may lead to the maximum in the proximal layer of its segment density profile, which is significantly different from both the depletion layer of pure repulsion and the adsorbing layer of attraction. In addition to the brush state on both repulsive and attractive surfaces, three additional surface states were identified by analyzing the scaling behavior of the layer thickness of polymer brushes: the mushroom state on repulsive substrates, the dilute and the semidilute surface states on attractive substrates.

FORCE-INDUCED DESORPTION OF SEMI-FLEXIBLE POLYMERS IN NON-HOMOGENEOUS MEDIA

Force-induced desorption of semi-flexible linear polymers in good solvents and non-homogeneous media is studied. We apply the model of self-avoiding walk with bending rigidity on 3-simplex fractal lattice. One boundary of the lattice represents an adsorbing wall, while an external force (perpendicular to the wall) pulls the polymer from the wall. Due to the hierarchical structure of the lattice under study, the phase diagram of polymer critical behavior can be exactly studied by real-space renormalization group method. Temperature dependence of the critical force, at which desorption occurs, is obtained and discussed for various values of the bending rigidity. Influence of the force and the polymer rigidity on the nature of desorption phase transition is also analyzed. All obtained results are compared with the related previous ones.

Influence of Solvent Quality on the Force Response of Individual Poly(styrene) Polymer Chains.

Single molecule mechanics of poly(styrene) polymer chains is investigated in different organic solvents with atomic force microscopy (AFM). The acquired force-extension profiles can be well fitted with a modified freely jointed chain (FJC) model. The model describes the force-extension profiles in terms of an apparent Kuhn length and an elasticity constant. The elasticity constant is found to be the same for all different solvents investigated. Best fit of the force-extension profiles with the FJC model reveals that the Kuhn length varies systematically with solvent quality. In fact, one can establish a good correlation between the Kuhn length and the Flory-Huggins interaction parameter. The increase in the Kuhn length with increasing solvent quality reflects the larger extent of swelling of the polymer in good solvents.

Conformational transition of polystyrene in good solvents studied by fluorescence spectroscopy

In this paper, the conformational transition of polystyrene (PS) in good solvents (i.e., dichloroethane and decalin) is studied by intramolecular fluorescence resonance energy transfer (FRET, NRET). The characteristics of FRET and PS excimer fluorescence spectroscopy in the analysis of polymer solution are systematically described. We find that FRET is prior to PS excimer fluorescence spectroscopy due to the superior sensitivity and better spectroscopic signal resolution. Based on the FRET results, it can be concluded that the chain conformation almost keeps unchanged with the increase of polymer concentration before the concentration reaches the critical overlap concentration ( C *). This spectroscopic observation excludes the existence of dynamic contact transition. In the expected C * regime, a sharp break point is observed for the fluorescence intensity versus the increase of the concentration, which is in exactly agreement with the theoretical value of C *. Additionally, the polymer chain undergoes severe collapse when the concentration reaches the semidilute regime and increases continuously. This work demonstrates that intramolecular FRET is a robust technique to sensitively characterize C *. C * could be used as a threshold to describe the conformational transition of polymer in good solvents.

Comparing Solvophobic and Multivalent Induced Collapse in Polyelectrolyte Brushes.

Coarse-grained molecular dynamics enhanced by free-energy sampling methods is used to examine the roles of solvophobicity and multivalent salts on polyelectrolyte brush collapse. Specifically, we demonstrate that while ostensibly similar, solvophobic collapsed brushes and multivalent-ion collapsed brushes exhibit distinct mechanistic and structural features. Notably, multivalent-induced heterogeneous brush collapse is observed under good solvent polymer backbone conditions, demonstrating that the mechanism of multivalent collapse is not contingent upon a solvophobic backbone. Umbrella sampling of the potential of mean-force (PMF) between two individual brush strands confirms this analysis, revealing starkly different PMFs under solvophobic and multivalent conditions, suggesting the role of multivalent "bridging" as the discriminating feature in trivalent collapse. Structurally, multivalent ions show a propensity for nucleating order within collapsed brushes, whereas poor-solvent collapsed brushes are more disordered; this difference is traced to the existence of a metastable PMF minimum for poor solvent conditions, and a global PMF minimum for trivalent systems, under experimentally relevant conditions.

End-anchored polymers in good solvents from the single chain limit to high anchoring densities.

An increasing number of applications utilize grafted polymer layers to alter the interfacial properties of solid substrates, motivating refinement in our theoretical understanding of such layers. To assess existing theoretical models of them, we have investigated end-anchored polymer layers over a wide range of grafting densities, σ, ranging from a single chain to high anchoring density limits, chain lengths ranging over two orders of magnitude, for very good and marginally good solvent conditions. We compare Monte Carlo and molecular dynamics simulations, numerical self-consistent field calculations, and experimental measurements of the average layer thickness, h, with renormalization group theory, the Alexander-de Gennes mushroom theory, and the classical brush theory. Our simulations clearly indicate that appreciable inter-chain interactions exist at all simulated areal anchoring densities so that there is no mushroom regime in which the layer thickness is independent of σ. Moreover, we find that there is no high coverage regime in which h follows the predicted scaling, h ∼ Nσ1/3, for classical polymer brushes either. Given that no completely adequate analytic theory seems to exist that spans wide ranges of N and σ, we applied scaling arguments for h as a function of a suitably defined reduced anchoring density, defined in terms of the solution radius of gyration of the polymer chains and N. We find that such a scaling approach enables a smooth, unified description of h in very good solvents over the full range of anchoring density and chain lengths, although this type of data reduction does not apply to marginal solvent quality conditions.

Mutual macromolecular crowding as the basis for polymer solution non‐ideality

Semidilute polymer solutions differ greatly from dilute solutions in properties such as viscosity, relaxation time, elastic modulus, colloid osmotic pressure, and light scattering. Previously, Matsuoka and Cowman proposed a single semiempirical expression for the nonideality contribution due to the concentration and intrinsic viscosity dependence, which has no other adjustable parameters, but quantitatively fits data for flexible, semiflexible, and rigid polymers in good solvents. In this report, the excluded volume theory as proposed by Ogston and Laurent is generalized to include mutual crowding between identical polymers based on hydrodynamic volumes, and applied to derive the expression for the nonideality contribution to specific viscosity, colloid osmotic pressure, and light scattering. Additionally, consideration of the contribution of mutual macromolecular crowding to the effective solvent viscosity allows prediction of polymer relaxation time and elastic modulus in semidilute solutions. This theoretical approach now allows the prediction of semidilute polymer solution properties based only on concentration and intrinsic viscosity, and conversely allows intrinsic viscosity (and thus average molecular weight) to be calculated from measurements made on semidilute solutions of known concentration. Copyright © 2016 John Wiley & Sons, Ltd.

The drag of the tails: Diffusion of sticky nanoparticles in dilute polymer solutions.

We devise a simple coarse-grained model of a nanoparticle exhibiting attractive interactions with a polymer in good solvent and use Monte Carlo simulations to study how adsorption of the polymer affects the hydrodynamic properties of the nanoparticle. We show that the hydrodynamic radius of the polymer-decorated nanoparticle increases with increasing polymer chain length or concentration. The slowdown of diffusion of the sticky nanoparticles is predicted to occur at polymer concentrations many orders of magnitude below the overlap concentration, in contrast with the case of non-sticky nanoparticles. To rationalize our findings, we employ the concept of trains, loops, and tails, which has been used in earlier theoretical studies of polymer adsorption at interfaces. We show that dominant contribution to the increase of the hydrodynamic radius of the polymer-decorated nanoparticles comes from the tails, which stretch far from the surface. On the contrary, the much more numerous but shorter loops and tails play only a minor role.

Conformation of the Linear-Dendritic Block Copolymers of Hyperbranched Polyphenylenegermane and Linear Poly(methylmethacrylate)

Dilute solutions of linear-dendritic block copolymers of linear poly(methylmethacrylate) with hyperbranched polyphenylenegermane were investigated by light scattering methods. The obtained results were compared with characteristics of functionalized poly(methylmethacrylate) with -Ge(C6F5)3 terminal groups, linear poly(methylmethacrylate), and hyperbranched polyphenylenegermane. The investigated samples differ by molar masses of the linear components. It was shown that molecules of functionalized poly(methylmethacrylate) in solution have a conformation that is typical for linear polymers in good solvent, while the linear-dendritic polymers in dilute chloroform solution have compact structure and high density in comparison with linear poly(methylmethacrylate).

Self-consistent field theory of tethered polymers: one dimensional, three dimensional, strong stretching theories and the effects of excluded-volume-only interactions.

We examine end-tethered polymers in good solvents, using one- and three-dimensional self-consistent field theory, and strong stretching theories. We also discuss different tethering scenarios, namely, mobile tethers, fixed but random ones, and fixed but ordered ones, and the effects and important limitations of including only binary interactions (excluded volume terms). We find that there is a "mushroom" regime in which the layer thickness is independent of the tethering density, σ, for systems with ordered tethers, but we argue that there is no such plateau for mobile or disordered anchors, nor is there one in the 1D theory. In the other limit of brushes, all approaches predict that the layer thickness scales linearly with N. However, the σ(1/3) scaling is a result of keeping only excluded volume interactions: when the full potential is included, the dependence is faster and more complicated than σ(1/3). In fact, there does not appear to be any regime in which the layer thickness scales in the combination Nσ(1/3). We also compare the results for two different solvents with each other, and with earlier Θ solvent results.

Polymer crowding and shape distributions in polymer-nanoparticle mixtures.

Macromolecular crowding can influence polymer shapes, which is important for understanding the thermodynamic stability of polymer solutions and the structure and function of biopolymers (proteins, RNA, DNA) under confinement. We explore the influence of nanoparticle crowding on polymer shapes via Monte Carlo simulations and free-volume theory of a coarse-grained model of polymer-nanoparticle mixtures. Exploiting the geometry of random walks, we model polymer coils as effective penetrable ellipsoids, whose shapes fluctuate according to the probability distributions of the eigenvalues of the gyration tensor. Accounting for the entropic cost of a nanoparticle penetrating a larger polymer coil, we compute the crowding-induced shift in the shape distributions, radius of gyration, and asphericity of ideal polymers in a theta solvent. With increased nanoparticle crowding, we find that polymers become more compact (smaller, more spherical), in agreement with predictions of free-volume theory. Our approach can be easily extended to nonideal polymers in good solvents and used to model conformations of biopolymers in crowded environments.

Polymeric Assembly of Gluten Proteins in an Aqueous Ethanol Solvent

The supramolecular organization of wheat gluten proteins is largely unknown due to the intrinsic complexity of this family of proteins and their insolubility in water. We fractionate gluten in a water/ethanol mixture (50/50 v/v) and obtain a protein extract which is depleted in gliadin, the monomeric part of wheat gluten proteins, and enriched in glutenin, the polymeric part of wheat gluten proteins. We investigate the structure of the proteins in the solvent used for extraction over a wide range of concentration, by combining X-ray scattering and multiangle static and dynamic light scattering. Our data show that, in the ethanol/water mixture, the proteins display features characteristic of flexible polymer chains in a good solvent. In the dilute regime, the proteins form very loose structures of characteristic size 150 nm, with an internal dynamics which is quantitatively similar to that of branched polymer coils. In more concentrated regimes, data highlight a hierarchical structure with one characteristic length scale of the order of a few nm, which displays the scaling with concentration expected for a semidilute polymer in good solvent, and a fractal arrangement at a much larger length scale. This structure is strikingly similar to that of polymeric gels, thus providing some factual knowledge to rationalize the viscoelastic properties of wheat gluten proteins and their assemblies.