We present a theory of the kinetics of the swelling of a gel. The characteristic time of swelling is proportional to the square of a linear dimension of the gel and is also proportional to the diffusion coefficient of the gel network, which is defined as D=E/f where E is the longitudinal bulk modulus of the network, and f is the coefficient of friction between the network and the gel fluid. This constitutes an essential difference between the present theory and the previous theory which is based on the assumption that the swelling time is determined by the diffusion coefficient of the fluid molecules. Experimental data are shown for spheres of 5% polyacrylamide gels and are analyzed using the present theory. The value of the diffusion coefficient obtained from the macroscopic swelling experiments shows excellent agreement with that obtained microscopically using laser light scattering spectroscopy.

Kinetics of swelling of gels

This review examines the stages of drying, with the emphasis on the constant rate period (CRP), when the pores are full of liquid. It is during the CRP that most of the shrinkage occurs and the drying stresses rise to a maximum. We examine the forces that produce shrinkage and the mechanisms responsible for transport of liquid. By analyzing the interplay of fluid flow and shrinkage of the solid network, it is possible to calculate the pressure distribution in the liquid in the pores. The tension in the liquid is found to be greatest near the drying surface, resulting in greater compressive stresses on the network in that region. This produces differential shrinkage of the solid, which is the cause of cracking during drying. The probability of fracture is related to the size of the body, the rate of evaporation, and the strength of the network. A variety of strategies for avoiding fracture during drying are discussed.

Theory of Drying

A large quantity of small molecules may migrate into a network of long polymers, causing the network to swell, forming an aggregate known as a polymeric gel. This paper formulates a theory of the coupled mass transport and large deformation. The free energy of the gel results from two molecular processes: stretching the network and mixing the network with the small molecules. Both the small molecules and the long polymers are taken to be incompressible, a constraint that we enforce by using a Lagrange multiplier, which coincides with the osmosis pressure or the swelling stress. The gel can undergo large deformation of two modes. The first mode results from the fast process of local rearrangement of molecules, allowing the gel to change shape but not volume. The second mode results from the slow process of long-range migration of the small molecules, allowing the gel to change both shape and volume. We assume that the local rearrangement is instantaneous, and model the long-range migration by assuming that the small molecules diffuse inside the gel. The theory is illustrated with a layer of a gel constrained in its plane and subject to a weight in the normal direction. We also predict the scaling behavior of a gel under a conical indenter.

https://imechanica.org/files/Kinetics%202007%2010%2022%20correct.pdf

A theory of coupled diffusion and large deformation in polymeric gels

The incubation of lens proteins with reducing sugars leads to the formation of fluorescent yellow pigments and cross-like similar to those reported in aging and cataractous human lenses. Called nonenzymatic browning or the Maillard reaction, this aging process also occurs in stored foods. Reducing sugars condense with the free amino group of proteins, then rearrange and dehydrate to form unsaturated pigments and cross-linked products. Although most proteins in living systems turn over with sufficient rapidity to avoid nonenzymatic browning, some, such as lens crystallins and skin collagen, are exceptionally long-lived and may be vulnerable.

https://science.sciencemag.org/content/sci/211/4481/491.full.pdf

Nonenzymatic browning in vivo: possible process for aging of long-lived proteins.

This review covers the recent advances in studies of the volume phase transition and critical phenomena of polymer gels mostly carried out in our group from 1973 to the present. We aimed here to discuss intensively (i) the basic understanding of the transition from the viewpoints of structure, dynamics, kinetics, and equilibrium thermodynamics, (ii) technological applications of the volume transition, and (iii) the relation between the phase transition and biological interactions.

Volume phase transition and related phenomena of polymer gels

We report measurements of the spectrum of light scattered from thermally excited displacement fluctuations in polyacrylamide gels. These measurements have been carried out on the polarized scattered light as a function of scattering angle and temperature for 5% and 2.5% polyacrylamide gels using the methods of optical mixing spectroscopy. We also present a theory for the amplitude and time dependence of the thermally excited longitudinal and transverse displacements of the gel fiber network. These displacements are responsible, respectively, for the polarized and depolarized scattered light. The correlation function for the displacements having wave vector q is predicted for these gels to have the form of an exponential decay: exp(− Γt). The decay rate is given by Γ = Glq2/f or Gtq2/f, where f is the frictional force per unit volume on the fiber network as it moves with unit velocity relative to the gel liquid. Gl is the longitudinal compressional modulus for longitudinal displacements and Gt is the shear...

Spectrum of light scattered from a viscoelastic gel

On the presence and mechanism of formation of heavy molecular weight aggregates in human normal and cataractous lenses

The theory of light scattering indicates that aggregation of the crystalline lens proteins can produce opacity. Furthermore, it is known that calcium increase? in the cataractous lens. We have, therefore, investigated the effectiveness of calcium ion in producmg aggregates of the soluble proteins of the bovine lens. The experimental restdts show: (1) CaCU produce's aggregates of the soluble protein of the lens; (2) the pre-a and at fraction of the lens protein are the specific targets of calcium ion even in the presence of sidfhydryl reducing reagent; (3) the aggregation can be reversed and transparency restored when calcium is removed either by dialysis or chelation; and (4) the molecular weight distribution and index of refraction of the aggregates have been measured.

Calcium-induced aggregation of bovine lens alpha crystallins.

Measurements of the diffusion coefficient of E. coli ribosomes by the technique of optical mixing spectroscopy are used to show that these ribosomes, when incubated in a 4°C cold room, undergo a slow aggregation with time. Even in the presence of this aggregation, it was possible to observe the diffusive character of the single 70s ribosome. It was found that at high (≥0.100 molar) KCl concentrations the ribosomes broke into their subunits. At moderate KCl concentrations they were relatively stable and at a very low KCl concentration (0.005 M) they were observed to dimerize. The values of the diffusion coefficients of the 50s subunits, the 70s single ribosome and the ribosome dimer determined in these measurements are consistent with currently accepted values.

Observations of self-aggregation and dissociation of E. coli ribosomes by optical mixing spectroscopy.

An intense light source, preferably of high monochromaticity, having its beam modulated at a frequency fo through a wavelength range including an absorption line of a species to be detected, energizes a chamber containing a sample of the species. The modulation frequency may also be a multiple or sub-multiple of the natural resonant accoustic frequency of the sample chamber. A microphone in the sample chamber provides an output signal proportional to the concentration of the species. The radiation beam is further incident upon a calibration chamber containing a predetermined concentration of the species. A microphone in the calibration chamber provides a calibration signal for comparison with the sample signal to determine the concentration of the species in the sample cell. Means are provided for adjusting the center of the wavelength modulation range so that it bears a known relation to the center of the species absorption line.

Lon O. Hocker

Papers

Spectrum of light scattered from a viscoelastic gel

On the presence and mechanism of formation of heavy molecular weight aggregates in human normal and cataractous lenses

Calcium-induced aggregation of bovine lens alpha crystallins.

Observations of self-aggregation and dissociation of E. coli ribosomes by optical mixing spectroscopy.

Opto-acoustic spectroscopy employing amplitude and wavelength modulation