First- and second-approximation calculations in the relaxation function of high-sugar/polysaccharide systems

The distribution function of Maxwellian relaxation times (phi) was derived from the small- deformation dynamic properties of high-sugar/agarose, /deacylated gellan and /high-methoxy pectin mixtures. First-approximation calculations of phi employed the time derivative of the experimentally measured storage and viscous moduli, with the two traces converging at the theoretically predicted slope of - 0.5. Second-approximation calculations were based on phi, as derived by the first approximation, being a simple power function of relaxation times (tau(-m)). The slope m was measured at various points and used to derive correction factors for shifting the relaxation function to the second approximation. Thus, values of phi calculated from G' and G" were brought into satisfactory agreement, particularly in the recorded portion of the glass transition region. Once the function phi is accurately determined, it can be readily used for calculations of other viscoelastic properties.