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.     

Mechanochemical energy conversion of neutral polymer gels

Mechanochemical energy conversion exhibited by water-swollen poly(vinyl alcohol) gels has been studied. The effective mechanical work produced as well as the chemical energy converted were measured simultaneously. It is shown theoretically and experimentally that the mechanical work developed during the swelling of the mechanochemical system increases with increase of the external load (m), the degree of cross-linking (DC) and the deswelling ratio (ϕ/ϕ_e, i.e. the ratio of the volume fraction of network polymer (ϕ) to that of the same gel in equilibrium with pure diluent (ϕ_e)). The chemical energy converted was found to be practically independent of m. The efficiency of energy conversion increased with increase of m and DC, and significantly decreased with increase of ϕ/ϕ_e. Comparison is made between theoretical predictions and experimental findings.     

Generalization of Hardy–Littlewood maximal inequality with variable exponent

Let $p(·)$ be a measurable function defined on ${\mathbb{R}}^d$ and $p_{-}:={inf}_{x\in {\mathbb{R}}^d}p(x)$. In this paper, we generalize the Hardy–Littlewood maximal operator. In the definition, instead of cubes or balls, we take the supremum over all rectangles the side lengths of which are in a cone-like set defined by a given function ψ. Moreover, instead of the integral means, we consider the $L_{q(·)}$-means. Let $p(·)$ and $q(·)$ satisfy the log-Hülder condition and $p(·)=q(·)r(·)$. Then, we prove that the maximal operator is bounded on $L_{p(·)}$ if and is bounded from $L_{p(·)}$ to the weak $L_{p(·)}$ if $1\le r_{-}\le \infty$. We generalize also the theorem about the Lebesgue points.     

Calcium induced volume transition in polyelectrolyte gels

The osmotic properties and the small angle neutron scattering (SANS) behaviour of fully neutralized sodium polyacrylate gels are investigated in the presence of calcium ions. Analysis of the SANS response displays three characteristic length scales, two of which are of thermodynamic origin, while the third, associated with the frozen-in structural inhomogeneities, is static. The SANS results are consistent with direct osmotic observations which indicate that the thermodynamic properties cannot be adequately described by a single correlation length. The concentration dependence of the osmotic pressure displays a power law behaviour with an exponent that decreases with increasing calcium concentration.     

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.     

Synthesis and Characterization of Poly(ethylene glycol) Dimethacrylate Hydrogels

Facile synthesis and detailed characterization of photo-polymerizable and biocompatible poly(ethylene glycol) dimethacrylates (PEGDM) and their hydrogels are described. Combined analyses of ¹H NMR and MALDI-TOF MS confirmed the formation of prepolymers of high purity and narrow mass distribution (PD < 1.02). A systematic investigation into the structure and mechanical properties of PEGDM hydrogels was performed to characterize the relationships between the network structure and gel properties. Small-angle neutron scattering was used to characterize the structural features of hydrogels with respect to their semidilute solution precursors. A well-defined structural length scale (correlation length) manifested as a maximum in the scattering intensity was observed for hydrogels derived from high molecular mass PEGDMs and/or high oligomer mass fractions. Hydrogels derived from lower molecular mass PEGDMs and/or low oligomer mass fractions exhibited multiple correlation lengths suggesting the formation of inhomogeneous gel structures. The shear moduli, determined from uniaxial compression measurement, showed that the gel structures correlate well with the gel mechanical properties.