Stress–strain behavior of swollen polymeric networks

The network parameters of swollen, solution-crosslinked polymer filaments can be collected from deswelling measurements in solutions of nonpermeating polymer or, as shown in this paper, from the stress–strain relation when in equilibrium with the surrounding solvent. The degree of swelling, at which the partial molar free energy of elasticity equals zero, is found to vary with solvent power in agreement with earlier findings on other systems. Comparison with results of studies on rubber networks crosslinked in the absence of diluent show that previously observed discrepancies between theory and experiment can be attributed to the deficiency of the single term involving the one-third power of the volume fraction of polymer in the swollen network to describe the contribution of the partial elastic free energy.     

Osmotic deswelling of polymer gels

The osmotic deswelling of polymer networks swollen in a good solvent by transferring it into a solution of a linear polymer in the same solvent is investigated using the modified Flory model proposed previously. The predicted results obtained using this simple model are compared to the experimental data available in the literature. We further examine the variation of the degree of deswelling, the degree of swelling and the partition coefficient with the molecular weight, and the volume fraction of the linear polymer chains in the surrounding polymer solution. Also, the role of the packing factor is briefly discussed.© 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2525–2535, 1998     

Diffusion in glassy polymers. II

The Fickian diffusion coefficient of methylene chloride in a glassy epoxy polymer is calculated with the use of Crank's model of discontinuous change of D with concentration C. The diffusion constant is obtained as 1.93 × 10^?6 cm²/sec. The swollen layer behind the advancing solvent front is essentially in the rubbery state of the same polymer. The case II swelling by benzene is discussed in terms of a convective transport arising from the partial stress (internal) tensor of the penetrant. The superposition of Fickian and case II diffusion found with mixtures of methylene chloride and benzene is also discussed briefly.     

The "Le Chatelier's principle"-governed response of actin filaments to osmotic stress

Actin filaments inhibit osmotic stress-driven water flow across a semipermeable membrane in proportion to the filament concentration (Ito, T.; Zaner, K. S.; Stossel, T. P. Biophys. J. 1987, 51, 745). When the filaments are cross-linked by F-actin binding protein, filamin A, this flow is stopped completely (Ito, T.; Suzuki, A.; Stossel, T. P. Biophys. J. 1992, 61, 1301). No conventional theory accurately accounts for these results. Here, this response is analyzed by formulating the entropy of the system under osmotic stress. Results demonstrate that the response of the actin filaments to osmotic stress is governed by the Le Chatelier's principle, which states that an external interaction that disturbs the equilibrium brings about processes in the body that tend to reduce the effects of this interaction. In the present case, disrupting equilibrium by osmotic stress brings about a reaction that decreases the chemical potential of water in the F-actin solution, reducing the effect of the applied osmotic disturbance. This decrease in the chemical potential of the water in the F-actin solution is caused by an increase in the chemical potential of F-actin, which is induced by isothermal absorption of heat by F-actin aided by work done by osmotic stress. As a result, F-actin has an inhibitory effect on the osmotic stress-driven water flow, and can even completely stop the flow when it is cross-linked. This is the first report demonstrating that the Le Chatelier's principle applies to the reaction of biopolymers against equilibrium disturbances such as osmotic stress.     

Mean‐field‐theory for polymers in mixed solvents. Thermodynamic and structural properties

Theoretical aspects of polymers in mixed solvents are considered using the Edwards Hamiltonian formalism. Thermodynamic and structural properties are investigated and some predictions are made when the mixed solvent approaches criticality. Both the single and the many chain problems are examined. When the mixed solvent is near criticality without solute, addition of a small amount of polymers shifts the criticality towards either enhanced compatibility or induced phase separation depending upon the value of the parameter describing the interaction asymmetry of the solvents with respect to the polymer. The polymer‐solvent effective interaction parameter increases strongly when the solvent mixture approaches criticality. Accordingly, the apparent excluded volume parameter decreases and may vanish or even become negative. Consequently, the polymer undergoes phase transition from a swollen state to an unperturbed state or even takes a collapsed configuration. The effective potential acting on a test chain in strong solutions is calculated and the concept of Edwards screening discussed. Structural properties of ternary mixtures of polymers in mixed solvents are investigated within the Edwards Hamiltonian model. It is shown that the effective potential on a test chain in strong solutions could be written as an infinite series expansion of terms describing interactions via one chain, two chains etc. This summation can be performed following a similar scheme as in the Ornstein‐Zernike series expansion.     

Theoretical analysis of sorption of a binary solvent in a polymer phase. II. Occurrence of maxima and minima in the curve of total sorption

It has been shown that sorption equilibrium in the system polymer–mixed solvent and the total sorption as one of its manifestations can be derived from osmotic equilibrium. The equilibrium relation for the dependence of the osmotic pressure II (as the potential for total sorption) on the composition of the ternary polymer-containing phase also includes the preferential sorption ε. This complication leads to difficulties in the analysis of the dependence of II on composition: for this reason, analysis has been limited to the case of a very dilute polymer phase. If preferential sorption is neglected, the occurrence of an extremum on the curve representing the dependence of the total sorption on the composition of the mixed solvent is affected by the Flory-Huggins parameters as in the occurrence of an inversion in preferential sorption, with the exception that in the former case the difference in the molar volumes of the solvent components contributes a term smaller by a factor of two. In the general case, however, the contribution of preferential sorption to the osmotic pressure (which has always a negative sign) also plays its role. Consequently, while total sorption, at a low preferential sorption and at a large positive value of the solvent–solvent interaction parameter χ₁₂, can exhibit a maximum, a larger preferential sorption can overcompensate the effect of the parameter χ₁₂, so that a minimum appears. The coexistence of a minimum with a maximum on the same curve is possible in some cases with positive χ₁₂. The latter theoretical predictions have not yet been confirmed experimentally. At a negative χ₁₂ the extremum is always a minimum.     

A differential approach to calculating osmotic equilibrium for multisolvent systems

A differential approach to the calculation of osmotic pressure of multisolvent systems within the Lewis–Randall framework is presented in this paper. Exact differential equations relating the osmotic pressure and the system composition along paths of constant solvent chemical potential are obtained and numerically solved. Although even for the simple case of an ideal solution no analytic expression for the osmotic pressure can be obtained, the system of differential equations does not pose numerical difficulties to be solved. Examples of the use of the proposed methodology are presented using the two-suffix Margules and Flory–Huggins equations, allowing an assessment of the influence of liquid-phase non-ideality on the performance of the method, and showing that it can be applied even for systems wherein liquid–liquid phase equilibrium occurs.     

Dynamic swelling performance of hydrophobic hydrogels

Conventional gels manifest monotonous swelling or shrinking performance upon immersing in solvents until reaching an equilibrium state. Recently, we discovered that the “hydrophobic hydrogels” prepared from hydrophobic polymer networks demonstrated dynamic swelling performance without equilibrium states. Upon water immersion, the gels expanded tremendously at the first stage until reaching a swelling peak; subsequently, the gels shrunk at an extremely slow rate. While this phenomenon endows the ...     

Quasi-elastic neutron scattering in gels and solutions

Measurements of swelling pressure, neutron spin-echo scattering, and dynamic light scattering were made in an end-linked poly(dimethylsiloxane) (PDMS) gel swollen to equilibrium in a good solvent (toluene) and also in the equivalent solution. The macroscopic osmotic modulus is depressed in the gel. Neutron spin echo observations at intermediate and high values of the scattering vector Q reveal that the mobility of the monomers is unaffected by cross-linking. Elastic neutron scattering at small Q detects non-uniformities in the polymer concentration distribution, which are absent from the solution. These non-uniformities play a major role in the dynamic response of the system at lower Q, and and appear to be the cause of the observed reduction in osmotic pressure.     

从溶胀平衡研究玻璃态高聚物的凝聚缠结网络

在13~15℃室温条件下对聚苯乙烯(PS)颗粒在二氧六环/水混合溶剂中的溶胀情况进行目视观察,可以看到,当减小混合溶剂二氧六环/水中的水含量时,PS颗粒从玻璃态到溶胀的玻璃态、溶胀的高弹态、流体态的转变,与PS颗粒升温时从玻璃态到高弹态、流体态的转变相对应.选定混合溶剂二氧六环/水(水6·8wt%)对一个单分散PS试样(Mw=1·68×105)在30℃进行分相平衡和溶胀平衡的测定.分相平衡是先将PS/二氧六环/水(混合溶剂水含量6·8wt%)体系加热到130℃使PS溶解成一均相溶液,然后在冷却过程中分相,在30℃达分相平衡(30天)时,浓相高分子体积浓度p″=0·304,稀相几乎为纯溶剂.从Flory-Huggins相平衡理论得出此体系的高分子-溶剂相互作用参数χ=0·63.本工作使用的单分散PS试样在选定的混合溶剂,即二氧六环/水(水6·8wt%)中,30℃时不能溶解只能溶胀,单分散PS颗粒淬冷试样(密度ρp=1·0451g/mL)到达溶胀平衡(80天)时浓相高分子体积浓度p″=0·308.而此淬冷试样经在80℃热处理100h后的老化试样(ρp=1·0470g/mL)达溶胀平衡(70天)时p″=0·312.从溶胀过程中浓相体积变化曲线可知试样经在80℃热处理过程中凝聚网络趋向于更均一,更接近热处理温度下的平衡态,试样密度增大,网络产生了新的链间凝聚,物理交联密度增大(凝聚点间分子量减小).从溶胀平衡理论并取χ=0·63(分相平衡)可得到淬冷试样的物理交联点间分子量Mc=11·6×104,老化试样的物理交联点间分子量Mc=6·9×104.实验结果说明溶胀过程及溶胀平衡的测定可以反映玻璃态高聚物中的凝聚网络结构的细节,而且非常敏感.     

A simplified molecular-thermodynamic model of a microphase-separated ionic gel swollen in salt solution

A molecular-thermodynamic model [A.I. Victorov, C.J. Radke, J.M. Prausnitz, Mol. Phys., 2004, submitted for publication] of diblock copolymer ionic gels swollen in brine is simplified by deriving asymptotic expressions for electrostatic terms. This model derived recently from the self-consistent field theory in the limit of strong segregation gives thermodynamic functions for gels of lamellar, bicontinuous, cylindrical and spherical morphologies and details the gel structure including equilibrium microdomain spacing, distribution of mobile ions, polymer segments, and the electric potential across the microdomains. The model reflects the copolymer chain composition, length, rigidity, ionization degree and the effective polymer–polymer and polymer–solvent interactions. Several asymptotic regimes are considered that lead to simple formulae for the solvent chemical potential. Applicability of asymptotic relations is tested. Equilibrium uptakes of salt are calculated for gels of varying ionic charge over a wide range of solution salinity.     

Reversible Morphology Control in Block Copolymer Films via Solvent Vapor Processing: An In Situ GISAXS study

The real time changes occurring within films of cylinder-forming poly(α-methylstyrene-block-4-hydroxystyrene) (PαMS-b-PHOST) were monitored as they were swollen in tetrahydrofuran (THF) and acetone solvent vapors. In situ information was obtained by combining grazing incidence small angle X-ray scattering (GISAXS) with film thickness monitoring of the solvent vapor swollen films. We show that for self assembly to occur, the polymer thin film must surpass a swollen thickness ratio of 212% of its original thickness when swollen in THF vapors and a ratio of 268% for acetone vapor annealing. As the polymer becomes plasticized by solvent vapor uptake, the polymer chains must become sufficiently mobile to self assemble, or reorganize, at room temperature. Using vapors of a solvent selective to one of the blocks, in our case PHOST-selective acetone, an order-order transition occured driven by the shift in volume fraction. The BCC spherical phase assumed in the highly swollen state can be quenched by rapid drying. Upon treatment with vapor of a non-selective solvent, THF, the film maintained the cylindrical morphology suggested by its dry-state volume fraction. In situ studies indicate that self-assembly occurs spontaneously upon attaining the threshold swelling ratios.     

Thermal Effects in Mechanochemistry

Fundamental thermodynamic equations are presented for anisotropic bodies with account forthermal effects. Definitions for Gibbs energy, partial molar quantities with respect to a direction chosen inan anisotropic phase, as well as expressions for the chemical potential tensor of an immobile component of asolid and for the chemical affinity tensor for a physicochemical process (including chemical reactions) in terms of the strain tensor variables and mixed variables including one component of the stress tensor are proposed. Conditions of stationary affinity and phase equilibrium are deduced. The mechanochemistry of polymorphous transformations is formulated for the cases of first- and second-order phase transitions.     

Swelling measurement of some ethylene copolymers crosslinked by dicumyl peroxide

Swelling equilibrium of crosslinked ethylene copolymers prepared by the curing of ethylene–vinyl acetate (EVA), ethylene–ethyl acrylate (EEA), and ethylene–acrylic acid (EAA) with dicumyl peroxide (DCP), has been measured in toluene at 23°C. The stress–strain behavior of the swollen EVA and EEA networks was in accord with that predicted from the statistical rubber elasticity theory, while that of the swollen EAA network was divergent. The concentration dependence of the polymer–solvent interaction parameter for the EAA network–toluene system was observed to be highest, while that for the EVA network–toluene system remained nearly zero. The order of the reactivity of pendant groups in the copolymers by radicals from DCP was estimated to be carboxyl > acetyloxy > ethoxycarbonyl group.     

Unusual swelling behavior of films of polyvinyl- and polyvinylidene/fluorides in various solvents

The swelling of PVF and PVDF films in various solvents was investigated. It was found that in the swollen state both polymers show little tendency to retain the solvent that leaks out under a mild pressure and evaporates quickly when the specimen is exposed to air. The equilibrium swelling ratios were measured in numerous solvents. From the results it is concluded that the solubility parameters are δ_PVDF = 12.0–12.3, δ_PVF = 12.0–12.1. The unusual swelling behavior is explained by strong polymer–polymer interactions via dipoles which tend to replace polymer–solvent interactions once the sample is withdrawn from the solvent.     

Membrane equilibria in concentrated polymer solutions

Membrane equilibria in concentrated polymer solutions are investigated. A three-component system (solvent, a polymer and an arbitrary solute) is considered. Starting with the virial expansion of the osmotic pressure, the Gibbs-Duhem equation for the system is integrated and the chemical potentials of the different components are evaluated. From the latter the equilibrium conditions are derived for a variety of experimental situations. The treatment is extended to the study of partition equilibria in gels, using a concentrated polymer solution as a model for the gel.     

Swelling Behaviour of Isotropic Poly(n-butyl acrylate) Networks in Isotropic and Anisotropic Solvents

Summary: The swelling properties of photochemically crosslinked poly(n-butyl acrylate) (PABu) networks in isotropic and anisotropic solvents were investigated experimentally. The purpose of this study was to examine the swelling kinetics of PABu networks in isotropic solvents and to compare the results obtained which those observed in the case of the low molecular weight liquid crystal 4-cyano-4′-n-pentyl-biphenyl known as 5CB. The phase diagrams were established in terms of composition and temperature for isotropic solvents, as toluene, acetone, cyclohexane, and methanol, and 5CB, using the plateau values corresponding to equilibrium states of swelling. The polymer networks were prepared via free radical polymerization/crosslinking processes by ultraviolet (UV) radiation of initial mixtures made up from a monomer, a crosslinker, and a photoinitiator. PABu networks with several crosslinking densities were formed using different quantities of difunctional monomer hexanedioldiacrylate (HDDA). Immersion of these networks in excess solvent allows measuring the solvent uptake by determination of the weight in isotropic solvents and diameter in an anisotropic solvent (5CB). Swelling data were rationalized by calculating weight and diameter ratios considering swollen to dry network states of the samples.     

Kinetics of styrene uptake by a polyurethane network during the formation of interpenetrating polymer networks

Due to insolubility of the components, formation of interpenetrating polymer networks (IPNs) requires particular ways of synthesis. Among others, IPNs can be prepared by the sequential technique where a network is swollen in a monomer and its crosslinker, which are then polymerized in situ. The simplest case is to swell at equilibrium; however this leads to IPNs of a given composition. For obtaining other compositions, swelling has to be stopped before equilibrium, or the swollen network (gel) has to be deswollen to a certain extent. Therefore, diffusivity of the monomer within the gel has to be known. The kinetics of monomer uptake was studied for a polyether urethane/styrene-divinylbenzene system which gives transparent materials despite the difference in refractive indexes. This allows direct visual observations of the monomer progress within the network. The results are not fully in agreement with the theories of Tanaka and of Candau which both predict the progression of a solvent in a polymeric gel. Two regimes of swelling depending on the concentration distribution of the monomer within the gel were found.