Contraction of swollen coil of flexible polymer chain below theta temperature

In our previous study on thermodynamic equilibrium at infinite dilution, chain segments at the periphery of a polymer coil were shown to be more extended than the average expansion of the coil. This is because such segments are in contact with pure solvent, whereas inside the coil there is a concentration of the segments. In a subsequent work examining the low concentration range, this excess extension of the segments was shown to diminish as the concentration was increased. Having more and more neighboring coils, the chain segments at the periphery of the coil have less and less excess extension, because the concentration difference between the inside and the outside of the coil decreases. In the present work the range below the theta temperature is examined; for polymers of finite molecular weights there are soluble ranges including partial and critical miscibility. When the limits of miscibility are approached either by lowering the temperature at a constant concentration or by increasing concentration at a constant temperature, the excess extension of the chain segments at the periphery of the coil disappears. The calculation makes use of a modified Maron theory. The required input data are intrinsic viscosity and polymer-solvent interaction parameter as a function of polymer concentration. These parameters must be known as functions of temperature and molecular weight. The example used in this work is the polystyrene-cyclohexane system.     

Nonuniform extension of chain segments of a polymer coil in dilute solution

An isolated, flexible polymer chain in dilute solution assumes a random configuration. In reality such a polymer coil is not completely random, because an excluded volume effect requires a modification from randomness. In addition, the coil placed in a better solvent is more expanded than that in a poor solvent. In other words, the polymer chain segments in a better solvent are more extended, compared to those in a neutral solvent. In the present study we have discovered an indication that the chain segments lying on the periphery of the coil are more extended than those in the interior. This discovery has been made in the course of relating intrinsic viscosity to thermodynamic interaction between polymer and solvent. The resulting relationship provides a means of evaluating the thermodynamic interaction parameter from the measured value of intrinsic viscosity, if the molecular weight of the polymer, its intrinsic viscosity in a neutral solvent, and the degree of excess extension of chain segments are known. The last is the parameter discovered in this work. This observation is independent of particular thermodynamic theory, so long as the experimental data are used in a consistent manner. In this work Maron's theory was used, because it is applicable to infinite dilution as well as concentrated solutions.     

Influence of Mixed Solvents and Temperature on the Solution Properties of Quaternized Polysulfones

Modification of intrinsic viscosity and the preferential adsorption coefficients of quaternized polysulfones with various contents of ionic chlorine in N,N‐dimethylformamide/water and methanol/water mixed solvents was investigated at different compositions and temperatures. The polyelectrolyte effect induced by an enhanced dissociation of the ionizable groups determines both the modification of the swelling degree of the polymer coil and the difference in composition of the mixed solvent inside and outside the coil. The results obtained were correlated with the interaction parameters of the above‐mentioned polymer/solvent/solvent systems.     

Effect of temperature on the intrinsic viscosity of poly(ethylene glycol) in water/dimethyl sulfoxide solutions

In this work, the intrinsic viscosities of poly(ethylene glycol) with molar mass of 20 kg mol^− 1 were measured in water/dimethyl sulfoxide solutions from (298.15 to 318.15) K. The expansion factors of the polymer chains were calculated from the intrinsic viscosity data. The expansion factor were decreased by increasing temperature; therefore the chain of PEG shrinks and the end-to-end distance become smaller by increasing temperature. Perhaps the interactions of segment-segment are favored toward segment-solvent by increasing temperature; therefore the hydrodynamic volumes of the polymer coils become smaller by increasing temperature. The thermodynamic parameters (entropy of dilution parameter, the heat of dilution parameter, theta temperature and polymer-solvent interaction parameter) were derived by the temperature dependence of the polymer chain expansion factor. The thermodynamic parameters indicate that the interactions of segment-segment were increased by increasing temperature.     

Influence of the Substitution Degree on the Dilute Solution Properties of Cellulose Acetate

Modification of intrinsic viscosity, coil size, and preferential adsorption coefficients of cellulose acetate with various substitution degrees in single and mixed solvents was investigated at different temperatures. Miscibility is attained by specific competitive interactions between the solvent-solvent and solvent-polymer systems, which induce modification in the composition of solvent mixtures both inside and outside the polymer coil. The conformational properties in solutions were correlated with the preferential adsorption coefficients, known as depending on the interaction parameters of the polymer/solvent/solvent systems. The intermolecular interactions observed in the cellulose acetate solutions assure the main properties necessary for obtaining membranes with different applications.     

Equilibrium swelling and mesoscopic structure of a diblock copolymer gel in a selective solvent

Our previous analytic model [A.I. Victorov, C.J. Radke, J.M. Prausnitz. Molec. Phys., 100, 2277 (2002)] of a block-copolymer gel swollen in selective solvent was obtained from self–consistent field theory in the strong–segregation approximation; it takes into account the structure of the gel on the mesoscopic scale but is restricted to the case where the solvent–selective polymer subchains are located in the inner (minority) domains. In this work, the model is generalized to include swollen outer domains. The dependence of the equilibrium microdomain size on solvent uptake has been established. We calculate equilibrium swelling and determine relative stabilities for gels of different morphologies. Predicted equilibrium profiles of polymer segments are compared with computer simulation. Based on the average–solvent–fraction approximation, results obtained for an athermal solvent are very close to those from equilibrium profiles. Attention is given to the effect of partial restrictions in self–assembly of polymer chains on microdomain spacing and on equilibrium swelling.     

Effect of Temperature on Cononsolvency of Polyvinylpyrrolidone in Water/Methanol Mixture

The behavior of polyvinylpyrrolidone in mixed water/methanol solvents was studied by rheoviscosimetry over a temperature range of 20°C–40°C. For the lower temperatures of this range, the intrinsic viscosity variation of the polymer vs. methanol molar fraction shows structural transitions (coil–globule–coil). This transition, which is usually attributed to the cononsolvency phenomenon, agrees with our previously published results obtained by dynamic light scattering. For higher temperatures, near 40°C, the intrinsic viscosity increase shows an expansion of the polymer over the alcohol molar fraction range 0.2 < X _A < 0.5. This last result can be attributed to the water/alcohol complex destruction under temperature increase. The “excess viscosity” of the polymer-mixed solvents vanishes with increasing temperature and becomes positive at 40°C. So, the polymer chain tends to transit from a globular to an ideal chain in the middle composition range of the mixed solvents.     

Flow pattern in a polymer coil placed into a stationary longitudinal flow

The flow pattern of solvent in a polymer coil placed into a stationary flow is examined. In contrast to the previous works, the flow of solvent at large distances from the macromolecule has a constant longitudinal gradient. The calculations are based on a simple model of macromolecule dynamics in flowing solutions proposed earlier. An analysis of the results shows that, in the first-order approximation in the longitudinal velocity at a certain threshold value of the parameter of hydrodynamic interactions P, the coil acquires a hydrodynamic boundary at which the radial component of the flow velocity is zero. The threshold value of P coincides with that for a stationary shear flow, determined earlier. At large P, i.e., large molecular mass, the hydrodynamic boundary of the coil encompasses a major part of the macromolecule, while the longitudinal intrinsic viscosity takes a form analogous to that characteristic of a suspension of solid balls with a radius equal to the radius of inertia of the polymer coil. In the second-order approximation in the flow velocity, the radial component of the flow velocity is nonzero. As a result, the mass transfer of solvent between the regions separated by the hydrodynamic boundary only slows down, without hindering the speedup of reactions by mixing the reagents and macromolecules.     

Effect of Alkyl Side Chain on the Conformational Properties of Polysulfones with Quaternary Groups

Modification of intrinsic viscosity, temperature coefficient, and preferential adsorption coefficient of polysulfones with different alkyl side groups in N,N-dimethylformamide/methanol and N,N-dimethylformamide/water was investigated at different compositions and temperatures. The specific interactions, such as hydrogen bonding and polyelectrolyte effect induced by an enhanced dissociation of the ionizable groups, determine both the modification of the solvation power of the polymer coil and the difference in the composition of the mixed solvent inside and outside the coil.     

分子链缠结对核-壳结构复合凝胶非均匀变形行为的影响

凝胶分子形成凝胶网络时,分子链段间会相互缠绕形成物理交联,显著影响其力学行为.为研究凝胶分子链段间相互缠结形成的物理交联对核壳结构复合凝胶变形行为与溶剂分布的影响,基于slip-link链缠结模型和张量推导建立核壳结构复合凝胶变形过程的一般数学表达式.结果表明：受刚性核影响,凝胶壳的拉伸是各向异性的,凝胶壳内溶剂的分布也是非均匀的,由内向外呈非线性变化,溶剂在凝胶内的扩散不满足菲克扩散定律;分子链缠结度越高凝胶壳的径向和周向伸长比越低,凝胶的溶胀率也越低.     

Single-molecule elasticity measurements of the onset of excluded volume in poly(ethylene glycol)

A polymer must reach a certain size to exhibit significant excluded-volume interactions and adopt a swollen random-walk configuration. We show that single-molecule measurements can sense the onset of swelling by modulating the effective chain size with force: as the force is reduced from a large value, the polymer is first highly aligned, then a Gaussian coil, then finally a swollen chain, with each regime exhibiting a distinct elasticity. We use this approach to quantify the structural parameters of poly(ethylene glycol) and show that they vary in the expected manner with changes in solvent.     

Grafted polymers with annealed excluded volume: A model for surfactant association in brushes

We present an analytical self-consistent-field (SCF) theory for a neutral polymer brush (a layer of long polymer chains end-grafted to a surface) with annealed excluded volume interactions between the monomer units. This model mimics the reversible adsorption of solute molecules or aggregates, such as small globular proteins or surfactant micelles, on the grafted chains. The equilibrium structural properties of the brush (the brush thickness, the monomer density profile, the distribution of the end segments of the grafted chains) as well as the overall adsorbed amount and the adsorbate density profile are analyzed as a function of the grafting density, the excluded volume parameters and the chemical potential (the concentration) of the adsorbate in the solution. We demonstrate that, when the grafting density is varied, the overall adsorbed amount always exhibits a maximum, whereas the root-mean-square brush thickness either increases monotonically or passes through a (local) minimum. At high grafting densities the chains are loaded by adsorbed aggregates preferentially in the distal region of the brush, whereas in the region proximal to the grafting surface depletion of aggregates occurs and the polymer brush retains an unperturbed structure. Depending on the relative strength of the excluded volume interactions between unloaded and loaded monomers both the degree of loading of the chains and the polymer density profile are either continuous or they exhibit a discontinuity as a function of the distance from the grafting surface. In the latter case intrinsic phase separation occurs in the brush: the dense phase consists of unloaded and weakly extended chains and occupies the region proximal to the surface, whereas a more dilute phase consisting of highly loaded and strongly extended chains forms the periphery of the brush. Received 26 November 1998 and Received in final form 2 April 1999     

Distinct conformational properties determined by implicit and explicit representation of protein-solvent interactions. An analytical and computer simulation study

In the protein folding problem, solvent-mediated forces are commonly represented by intra-chain pairwise contact energy. Although this approximation has proven to be useful in several circumstances, it is limited in some other aspects of the problem. Here we show that it is possible to achieve two models to represent the chain-solvent system, one of them with implicit and other with explicit solvent, such that both reproduce the same thermodynamic results. Firstly, lattice models treated by analytical methods, were used to show that the implicit and explicitly representation of solvent effects can be energetically equivalent only if local solvent properties are time and spatially invariant. Following, applying the same reasoning used for the lattice models, two inter-consistent Monte Carlo off-lattice models for implicit and explicit solvent are constructed, being that now in the latter the solvent properties are allowed to fluctuate. Then, it is shown that the chain configurational evolution as well as the globule equilibrium conformation are significantly distinct for implicit and explicit solvent systems. Actually, strongly contrasting with the implicit solvent version, the explicit solvent model predicts: (i) a malleable globule, in agreement with the estimated large protein-volume fluctuations; (ii) thermal conformational stability, resembling the conformational heat resistance of globular proteins, in which radii of gyration are practically insensitive to thermal effects over a relatively wide range of temperatures; and (iii) smaller radii of gyration at higher temperatures, indicating that the chain conformational entropy in the unfolded state is significantly smaller than that estimated from random coil configurations. Finally, we comment on the meaning of these results with respect to the understanding of the folding process.     

Temperature-Induced Swelling of Alkali Metal Polyacrylate Gels in Aqueous Organic Solvent Mixtures

It has been known that some polyelectrolyte systems, e.g., betaine polymer and polycations, have an upper critical solution temperature (UCST) in water while polyanions seldom show such a temperature-dependent phase separation. Recently we have found a significant counterion- and solvent-specific UCST-type behavior for alkali metal poly(acrylate)s (PAAM) in aqueous organic solvent mixtures. Namely, the reduced viscosity significantly increased with increasing temperature which was ascribed to disintegration of the ion-clusters or the aggregated ion-pairs formed at the lower temperature. In the present study, we prepared PAAM gel samples by irradiating the aqueous solutions with γ-rays in variable doses to find that a significant gel swelling was induced by a temperature jump from 5 to 40°C in various kinds of aqueous organic solvent mixtures. The UCST-type behavior and the counterion- and solvent-specificities for the gel swelling turned out to be parallel to those for the corresponding solution systems. In addition to these expected results, an appreciable LCST-type deswelling was unexpectedly observed for collapsed gels in a relatively higher solvent concentration region. Further, the γ-ray doses, i.e., the degree of crosslinking, proved to affect the UCST behavior; the gel swelling ratio was more significant for gels prepared with higher doses.     

Nematic ordering problem as the polymer problem of the excluded volume

Based on a solution of the polymer excluded volume problem, a technique is proposed to estimate some parameters at the isotropic-nematic liquid crystal phase transition (the product of the volume fraction of hard sticks and the ratio of the stick length, L, to its diameter, D; the maximum value of this ratio at which one cannot regard the stick as hard). The critical exponents are estimated. The transition of a swelling polymer coil to ideal is revealed as the polymerization degree of a macromolecule increases. The entanglement concentration obtained agrees with experimental data for polymers with flexible chains. The number of monomers between neighbor entanglements is assumed to be the ratio L/D. A comparison of the theory with other ones and recent experimental data is made.     

Monte Carlo simulation of polymers in solution and bulk

The behavior of polymers in solution depends on both temperature and concentration. At least four different regions of the concentration-temperature plane exist in which the physical properties are fundamentally different. These regions are known as the dilute good solvent, theta solvent, semidilute, and concentrated regions. In this investigation, Monte Carlo simulations were performed in order to examine how properties change in going from one region to another. Two series of simulations were performed. In the first series, properties were studied as a function of concentration so that crossover from dilute, to semidilute, and then to concentrated was obtained. In the concentrated or bulk region, it was found that the second and fourth moments of the end-to-end distance were characteristic of ideal chains (without excluded volume), consistent with neutron scattering results. In the semidilute region, the concentration dependence of the mean square end-to-end distance was not in agreement with scaling theory. In the second series of simulations, the temperature was changed for an isolated chain (zero concentration limit), so that crossover from good solvent to theta solvent behavior was obtained. Over the chain length range studies (10–300), no evidence was seen for the existence of “thermal blobs.” In addition, expansion of the average internal conformation over the expected result was observed and found to be increasingly important as the temperature increases from the theta temperature.     

Helix coil mixing in twist-storing polymers

Twist-storing polymers respond with elastic energy penalty to coherent or random twisting along the local chain axis away from its equilibrium, which can be straight (as in “ribbons”) or helical (as in DNA and other biopolymers). Here we study the equilibrium conformation of such polymers, focusing on the thermodynamic balance between twist and writhe, resulting from the competition between the random coil entropy and the potential energy stored in superhelical portions of the polymer chain. Two macroscopic variables characterise such a chain, the end-to-end distance R and the link number Lk, which is a topological invariant of a given polymer with clamped ends. We find that with increasing link number Lk, the chain accommodates its excess twist in growing plectonemes, unless forced out of this state by stretching its end-to-end distance R. We calculate the force-extension relation, which exhibits crossovers between different deformation regimes. Received 16 November 2000 and Received in final form 6 February 2001     

Chemical Modification of Polyamide 6 by Chain Extension with Terephthaloyl-biscaprolactam

The chain extension behaviors of terephthaloyl-biscaprolactam (TBC), 2,2′-bis(2-oxazoline)(BOZ), 2,2′-(1,3-phenylene)bis(2-oxazoline)(MPBO), TBC/BOZ, and TBC/MPBO, were studied to evaluate the coupling effect on polyamide 6 (PA6) in a Haake Rheocord mixer and an extruder. For the chain extension of PA6 with TBC only, the coupling results showed that there was an optimal dosage of chain extender, shortage of which caused incomplete chain extensions and excess of which led to more blocking reactions. When the added amount of TBC chain extender in PA6 was 0.684 wt%, the intrinsic viscosity of the PA6 increased from 1.630 to 1.848 dl/g, and the concentration of the amine end groups in the chain-extended PA6 decreased from the initial 5.12 × 10^?5 to 1.96 × 10^?5 mol/g. However, for the chain extension of PA6 with TBC/BOZ and TBC/MPBO mixtures, the intrinsic viscosity of PA6 increased to 2.189 dl/g and 2.097 dl/g, respectively, while at the same time both the concentration of carboxyl end-groups and amine end-groups of chain-extended PA6 decreased. The effect of temperature on the time needed for the completion of the chain extension reaction was not obvious, and the time needed for the completion of the reaction was about 200 sec. The chain-extended PA6 dissociated at high temperature, and the degradation is suggested to proceed simultaneously from the onset of the chain extension reaction. Furthermore, the effects of chain extenders on the thermal properties of chain-extended PA6 were investigated. The thermal stability of chain-extended PA6 was slightly improved.     

Relationship between dynamic mechanical property and thermodynamic interaction parameter of concentrated polymer solutions

The use of concentrated polymer solutions is one of the basic techniques in the application of polymers. They may be coating materials, plasticized polymers, and oil-extended rubber. In these applications the solubility relation is one of the key requirements. The polymer-solvent interaction is expected to influence the mechanical property of the mixture. It is the intent of this study to explore how the dynamic mechanical property is affected by the change of thermodynamic interaction parameter in concentrated polymer solutions. The theoretical development is based on several assumptions: (1) a polymer chain in the amorphous state and in its own environment assumes unperturbed configuration; (2) a polymer chain in a good solvent (poor) is expanded (contracted) relative to the unperturbed dimension; (3) the expanded (contracted) chain configuration results in the higher (lower) entanglement density; (4) both expanded and contracted chains store an elastic energy, the magnitude of which may be estimated; (5) the elastic energy of the deformed chain is balanced by the thermodynamic energy of interaction. The paper focuses on the development of a theory. Also, limited examples of the application of the theory are presented.