Similarities between polyelectrolyte gels and biopolymer solutions

Small angle neutron scattering (SANS) measurements and osmotic swelling pressure measurements are reported for polyelectrolyte gels and solutions under nearly physiological conditions. A synthetic polymer (sodium-polyacrylate) and three biopolymers (DNA, hyaluronic acid, and polyaspartic acid) are studied. The neutron scattering response of these anionic polyelectrolytes is closely similar, indicating that at larger length scales the organization of the polymer molecules is not significantly affected by the fine details of the molecular architecture (e.g., size and chemical structure of the monomer unit, type of polymer backbone). The results suggest that specific interactions between the polyelectrolyte chains and the surrounding monovalent cations are negligible. It is found that the osmotic compression modulus of these biopolymer solutions determined from the analysis of the SANS response decreases with increasing chain persistence length. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3679–3686, 2006     

Ionic and pH effects on the osmotic properties and structure of polyelectrolyte gels

We investigate the effects of salt concentration and pH on neutralized poly(acrylic acid) (PAA) gels in near physiological salt solutions. Either adding calcium ions or decreasing the pH is found to induce reversible volume transitions but the nature of these transitions seems to be different. For example, the osmotic pressure exhibits a simple power law dependence on the concentration as the transition is approached in both systems, but the power law exponent n is substantially different in the two cases. On decreasing the pH the value of n gradually increases from 2.1 (at pH = 7) to 3.2 (at pH = 1). By contrast, n decreases with increasing calcium ion concentration from 2.1 (in 100 mM NaCl solution) to 1.6 (0.8 mM CaCl₂ in 100 mM NaCl solution). In both systems, a strong increase of the small-angle neutron scattering intensity (SANS) is observed near the volume transition. The SANS results reveal that calcium ions favor the formation of linearly aligned regions in PAA gels. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2803–2810, 2008     

Inhomogeneity control in polymer gels

Inhomogeneities, that is, nonrelaxing frozen concentration fluctuations, are inevitably present in polymer gels because they are introduced during the crosslinking of the constituent polymer chains in a solvent. Therefore, inhomogeneities increase as the number of crosslinks increases in a gel. The ionization of polymer gels is one of the methods used to suppress inhomogeneities. However, because crosslinking also means a freezing‐in of the conformation and topology of polymer chains in a solvent according to the chemistry of crosslinking, inhomogeneity control is quite sophisticated. In this article, we discuss the relationship between the inhomogeneities and the molecular/environmental parameters of polymer gels, such as the polymer concentration, the degree of crosslinking, the degree of ionization, and the interaction parameter, by considering the memory effect of gels. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 617–628, 2005     

Calcium-induced volume transition in polyacrylate hydrogels swollen in physiological salt solutions

Osmotic and small-angle neutron-scattering measurements are performed to study the volume transition that occurs in sodium polyacrylate gels swollen in sodium chloride solutions when calcium ions are introduced. In the presence of calcium ions, the osmotic pressure depends sensitively on the sodium chloride concentration, indicating that calcium preferentially replaces condensed sodium ions. This substitution modifies the effective attractive interaction between polymer chains. Analysis of the osmotic data in terms of the Flory–Huggins theory reveals a sharp increase in the third-order ternary thermodynamic interaction parameter upon introduction of calcium ions. The neutron-scattering response at low scattering vectors q displays power-law behavior with a slope of approximately −3.6, consistent with scattering from surfaces of large objects. These results are in agreement with the development of dense polymer-rich regions dispersed in a soft polymer matrix. At larger q, a region with slope −1 is observed, characteristic of rigid linear structures.

Small-angle neutron-scattering spectra of polyacrylate hydrogels swollen by 40 mM sodium chloride solutions containing different amounts of CaCl₂ (+: 0.5 mM , ○: 0.85 mM , ×: 1.7 mM ). The dashed curve shows the least squares fit of the 0.85 mM CaCl₂ data to Equation ( 5 ) in which the first term is replaced by Equation ( 8 ), and the second term is approximated by a simple power law.     

Thermodynamic interaction parameters in polymer solutions and gels

Polymer-solvent interaction parameters are reported for poly(vinyl acetate)-acetone, poly(vinyl acetate)-toluene, and poly(dimethyl siloxane)-toluene systems using different techniques. Results obtained by osmotic deswelling are compared with those from quasi-elastic light scattering and small-angle neutron scattering (SANS). In gels, the latter techniques involve separation of the time-dependent from the static component of the scattered radiation+ Separation is achieved in quasi-elastic light scattering through the heterodyning properties of the light, and in SANS by subtracting an appropriate static structure factor. The interaction parameters obtained by different separation procedures are consistent with measurements using the osmotic method. © 1995 John Wiley & Sons, Inc.     

Theory of volume transition in polyelectrolyte gels with charge regularization

We present a theory for polyelectrolyte gels that allow the effective charge of the polymer backbone to self-regulate. Using a variational approach, we obtain an expression for the free energy of gels that accounts for the gel elasticity, free energy of mixing, counterion adsorption, local dielectric constant, electrostatic interaction among polymer segments, electrolyte ion correlations, and self-consistent charge regularization on the polymer strands. This free energy is then minimized to predict the behavior of the system as characterized by the gel volume fraction as a function of external variables such as temperature and salt concentration. We present results for the volume transition of polyelectrolyte gels in salt-free solvents, solvents with monovalent salts, and solvents with divalent salts. The results of our theoretical analysis capture the essential features of existing experimental results and also provide predictions for further experimentation. Our analysis highlights the importance of the self-regularization of the effective charge for the volume transition of gels in particular, and for charged polymer systems in general. Our analysis also enables us to identify the dominant free energy contributions for charged polymer networks and provides a framework for further investigation of specific experimental systems.     

Ion condensation in a polyelectrolyte gel

Anomalous small angle X-ray scattering is used to determine the distribution of divalent ions in a neutralized polyelectrolyte gel of sodium polyacrylate in the vicinity of the volume transition. At the five different energies of the incident beam used to vary the contrast, the scattering curves have similar shapes, and are separated only by constant multiplying factors. This result, in conjunction with SANS results from the same sample, indicates that the divalent ion (strontium) is confined on the polymer backbone.     

Kinetics of the volume phase transition in poly(n‐isopropylacrylamide) gels prepared under high pressure

New poly(N‐isopropylacrylamide) gels were prepared under high pressure (ca. 200 MPa) during gelation. The preparation‐pressure dependence of the deswelling speed of the gels was measured with a conventional T‐jump method. The deswelling time of a gel rod 2.2 mm in diameter prepared at 193 MPa was about 200 s, 1000 times faster than that of a homogeneous poly(N‐isopropylacrylamide) gel. Moreover, the collective diffusion coefficient, the thermal fluctuation, and the ensemble‐average intensity of the swollen gel networks were obtained with dynamic light scattering measurements. Both the enthalpy and entropy of the gels were estimated from equilibrium swelling curves with the Flory–Huggins interaction parameter evaluated with mean field theory based on the Flory‐type of the Gibbs free‐energy formula. It was found that the networks of the gels had an inhomogeneous structure newly introduced by the preparation pressure. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2315–2325, 2001     

Boson peak and fast relaxation process near the glass transition in polystyrene

Atactic polystyrene, both side group and main chain deuterated, was investigated by inelastic neutron scattering in a wide temperature range around the glass transition from 2 to 450 K. In the glass the Boson peak position is only very weakly influenced by the deuteration of the phenyl group. In the neighborhood of the glass transition temperatureT _g we find a fast relaxation process similar to other glasses. The onset of the fast relaxation in polystyrene, however, is observed already at temperaturesT _g — 200 K. Results from partially deuterated polystyrene suggest a change of the phenyl ring dynamics already far belowT _g.     

Critical fluctuations and static inhomogeneities in polymer gel volume phase transitions

Thermoresponsive polymer gels exhibit pronounced swelling and deswelling upon changes in temperature, accompanied by dynamic concentration fluctuations that have been interpreted as critical opalescence. These fluctuations span lengthscales similar to that of static structures in the gels, such as the gel polymer‐network meshsize (1–10 nm) and static polymer‐network crosslinking inhomogeneities (10–1000 nm). To systematically investigate this overlay, we use droplet‐based microfluidics and fabricate submillimeter‐sized gel particles with varying static heterogeneity, as revealed on a molecular scale by proton NMR. When these microgels are probed by small‐angle neutron scattering, the detection of dynamic fluctuations during the volume phase transitions is strongly perturbed by the co‐existing static inhomogeneity. Depending of the type of data analysis employed, the temperature‐dependent evolution of the correlation length associated to the dynamic fluctuations does or does not agree with predictions by the critical scaling theory. Only the most homogeneous sample of this study, prepared by controlled polymer crosslinking in droplet microfluidics, shows a diverging correlation length in agreement to the critical scaling theory independent of the specific approach of data analysis. These findings suggest that care must be taken about polymer‐network heterogeneity when gel volume phase transitions are evaluated as critical phenomena. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1112–1122     

Conformation of a chain polyelectrolyte in solution with low molecular weight salt: small angle neutron scattering measurements

Small angle neutron scattering measurements have been carried out on the tetramethylammonium salt of the polystyrenesulfonic acid withDP _w =310 and 1060 in water solution with tetramethylammonium chloride with ionic strength between 0.02 M and 1.0 M. The scattering curves in the scattering vector range 0.05 nm^–1Q1.8nm^–1 have been fitted using the form factor of a worm-like chain of finite thickness. The conformational parameters mean square radius of gyration, statistic chain element, mass per unit length and mean square radius of the cross-section have been determined experimentally and used for describing the conformation of the coils. By these molecular weights and ionic strengths, excluded volume is not necessary to explain the conformation changes depending on the salt content of the solutions; relatively short coil molecules can be described in their unperturbed dimensions even in a thermodynamically good solvent: a change in the stiffness of the chain according to Odijk's theory succeeds in describing the conformation of the polyions. Together with a slow decrease of the coil dimension by increasing salt content, a transition at ionic strength 0.1–0.5 M between two different conformations has been observed. The conformation at lower ionic strength is characterized by higher stiffness of the chain and lower mass per unit length than the form at higher salt concentration.     

Growth and aging phenomena in silica gels

Growth and aging of silica aggregates are influenced both by temperature and by catalyzing fluorine ions as shown by SAXS and BET. It was found that both fluorine and increased temperature slightly increased the fractal dimension Df during aging, but the fluorine catalyzed system showed a lower BET surface area.To understand the effect of fluorine and increased temperature on the aggregates, 2D aggregations and SAXS simulations were carried out using two new programs GRASP and DALAI. In agreement with experiments it was found that binary RLCCA aggregates have a slightly higher Df value compared to DLCCA aggregates and that branch-flexibility during aging increases Df even further.     

Free‐volume change in volume phase transition of polyacrylamide gel as studied by positron annihilation: Salt dependence

Variation of free‐volume parameters—average radius size, number concentration, and size distribution—of a polyacrylamide (PAAm) gel containing 4 mol % carboxylate anions is studied during a volume phase transition (VPT) caused by a change of sodium chloride (NaCl) concentration. A positron annihilation lifetime technique is used for the determination of the free‐volume characteristics. The measurement is performed in an acetone–water 3 : 2 (v/v) [0.27 : 0.73 (mol/mol)] mixed solvent at 20°C, and the free‐volume parameters deduced from the analysis of a positron annihilation curve are utilized. An average free‐volume size of the swollen PAAm gel, ∼ 0.32 nm in radius, almost agrees with that of the mixed solvent for a corresponding salt concentration, while the size of the collapsed gel, which is ∼ 0.28 nm in radius, is smaller than that of the mixed solvent. The results for the collapsed gel indicate that the hydrogen bond plays a significant role in the nanoscopic environment. The radius of the free‐volume of the swollen PAAm gel seems to be influenced by the composition between acetone and water. An inhomogeneity of the nanoscopic structure inside the PAAm gels is discussed in terms of a dispersion of a size distribution of the free‐volume. It is concluded that a change of the nanoscopic environment of the PAAm gel during the VPT can be monitored through the free‐volume parameters obtained by the positron annihilation lifetime technique. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2634–2641, 1999     

Monomer volume fraction profiles in pH responsive planar polyelectrolyte brushes

Spatial dependencies of monomer volume fraction profiles of pH responsive polyelectrolyte brushes were investigated using field theories and neutron reflectivity experiments. In particular, planar polyelectrolyte brushes in good solvent were studied and direct comparisons between predictions of the theories and experimental measurements are presented. The comparisons between the theories and the experimental data reveal that solvent entropy and ion‐pairs resulting from adsorption of counterions from the added salt play key roles in affecting the monomer distribution and must be taken into account in modeling polyelectrolyte brushes. Furthermore, the utility of this physics‐based approach based on these theories for the prediction and interpretation of neutron reflectivity profiles in the context of pH responsive planar polyelectrolyte brushes such as polybasic poly(2‐(dimethylamino)ethyl methacrylate) (PDMAEMA) and polyacidic poly(methacrylic acid) (PMAA) brushes is demonstrated. The approach provides a quantitative way of estimating molecular weights of the polymers polymerized using surface‐initiated atom transfer radical polymerization. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 956–964     

A theoretical interpretation of free volume at glass transition

We device a relaxed lattice model (RLM) to study the mechanism of glass transition,which unifies the cageeffects from particle-particle interaction and entropy.By analyzing entropy in RLM with considering the influence of interactions on equilibrium,we demonstrate that glass transition is a second-order phase transition.For a perfect onedimensional linked particle system like linear polymer under normal pressure,the free volume at glass transition is rigorously deduced out to be 2.6％,which provides a theoretical basis for the iso-free volume of 2.5％ given by Willian,Landel and Ferry (WLF) equation.Extending to system with dead particles linked with higher dimensions like branched or cross-linked chains under positive or negative pressure,free volume at glass transition is varied,based on which we construct a phase diagram of glass transition in the space of free volume-dead particle-pressure.This demonstrates that free volume is not the single parameter determining glass transition,while either dead particles like cross-linked points or external force fields like pressure can vary free volume at the glass transition.     

Synergistic depression of volume phase transition temperature in copolymer microgels

Microgels consisting of poly-N,N-diethylacrylamide (PDEAAM) and copolymer microgels consisting of N,N-diethylacrylamide-co-N-isopropylacrylamide (PDEAAM-co-PNIPAM) have been synthesized via free radical polymerizations. The volume phase transition of the microgels in aqueous solution was investigated by means of dynamic light scattering. All samples revealed a volume phase transition upon heating and the size change was fully reversible. An unusual dependence of transition temperature on the composition of the copolymer microgels was observed and samples were obtained with a transition temperature that was lower than that of both corresponding homopolymer particles. This synergistic behavior could be caused by strong hydrogen bonding between the mono- and the disubstituted acrylamide repeating units at nearly equimolar composition of the microgel.     

Free‐volume change during the volume phase transition of polyacrylamide gel studied by positron annihilation: Solvent‐composition dependence

Changes in the free‐volume parameters of polyacrylamide (PAAm) gels during the volume phase transition (VPT) were studied with the positron annihilation lifetime technique. The VPT was induced through the variation of the solvent composition in a mixture of acetone and water. The PAAm gels containing 0 and 4 mol % carboxyl groups in their polymer chains were adapted to compare the effect of the presence of ionic groups on the microscopic environment. The change of the free‐volume property is discussed on a nanoscopic scale, with attention paid to the interactions between the polymer chains and the solvent molecules. It is proven that the variations of the free‐volume parameters correlate significantly with the VPT phenomenon. The results of the free volume for both gels are well‐explained when an interaction parameter, ε_g, is assumed. The interpretation suggests that the state of the interactions among the components (the polymer chain, acetone, and water molecules) plays an important role in the change of the free volume of PAAm gels during the VPT. An increase of the dispersion of the free‐volume size near the VPT point was observed for the ionized PAAm gel. The broadened size distribution of the free volume of the ionized PAAm gel around the VPT point lay between those of pure water and the corresponding mixed solvent, suggesting that a local minimum of the average free‐volume size at the VPT point is caused by the increase of a specific interaction, hydrogen bonding. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 922–933, 2000