Characterization of thermo‐reversible gels by means of sedimentation equilibria

Abstract

This paper describes the deformation of gels in a centrifugal field leading to a continuous equilibrium. A gel is considered to be a binary mixture of crosslinked polymer and solvent and is assumed to remain isotropic during the deformation. From the equation for the osmotically effective pressure, called swelling pressure, the thermodynamic properties of a gel can be calculated. For highly swollen gels the expression of Svedberg and Pedersen is obtained. It is shown that the complete concentration dependence of the swelling pressure in the concentration range of the maximally swollen gel up to that at the cell bottom can be measured in a single equilibrium experiment. The homogeneity of weakly crosslinked gels can be examined by means of the method described. Soluble parts which are not incorporated into the polymer network can also be detected if they are present. From the swelling pressure-concentration curves it is possible to derive the thermodynamic properties of the physically crosslinked gelatidwater gels that were investigated. These gels can be described by means of a slightly modified Flory-Huggins equation with an interaction parameter xw in the weight fraction scale, which depends linearly on concentration. The interaction parameters show a dependence on concentration which is explained by an increased branching and crosslinking of the polymer with increasing initial polymer concentration of the gels. At low initial polymer concentration, the primary chains have to aggregate to build up relatively long chains between the network junctions. The static shear modulus G which can be calculated from the network term has the same order of magnitude as the real part of the complex shear modulus which is measured at low frequency.

Analytical Ultracentrifuge Technologies for the Characterization of Biopolymer Gels and Microgels

“…With a rather high assumed molar mass of about 500,000 glmol for the primary chain ofK-carrageenan, the number of crosslinking points per polymer chain could be estimated to be at least jive, probably much higher. This result is clearly different from that for gelatin gels where for some gels less than two crosslinking points have been observed per chain (Borchard and Colfen, 1992).…”

“…For a given system, the dynamic values obtianed have been always higher {indeed, for the system gelatin/water at low polymer concentrations even by factor of ten (Borchard and Colfen, 1992) due to the viscous part of the dynamic shear modulus}. In a creep experiment, it could be stated that the shear modulus decreased by a factor of two after 24 hours experimental duration (COlfen and Borchard, 1992). Furthermore, it is known that the slope of the regression lines in double logarithmic shear modulus vs. polymer concentration plots are always higher for the static shear moduli than they are for the dynamic ones for concentrations beyond the glass transition (COIfen, 1993).…”

“…Furthennore, it could be established from the previous studies that the shear modulus as determined by the ultracentrifuge is a static value due to its equilibrium nature whereas for example in torsional oscillation experiments, dynamic values are obtained. For a given system, the dynamic values obtianed have been always higher {indeed, for the system gelatin/water at low polymer concentrations even by factor of ten (Borchard and Colfen, 1992) due to the viscous part of the dynamic shear modulus}. In a creep experiment, it could be stated that the shear modulus decreased by a factor of two after 24 hours experimental duration (COlfen and Borchard, 1992).…”

“…In a publication of Borchard and Colfen (1992), the findings of the previous 'trilogy of papers' have been presented in a comprehensive way with the addition of some interesting new results which will be presented here:…”

Measuring Osmotic Pressure of Poly(ethylene glycol) Solutions by Sedimentation Equilibrium Ultracentrifugation

“…We chose analytical ultracentrifugation (AUC) because it allows for osmotic pressure determination with straightforward control of temperature. Others have used this technique for similar measurements involving the osmotic pressure of DNA and the swelling pressure equilibria of gels. − It also allows us to measure osmotic pressures well above the capabilities of VPO without any complications. The osmolyte concentration gradient created within the AUC cell is typically smaller than the overall concentration range of interest.…”