A new mathematical model based on Michaelis Menten (MM) kinetics is developed to predict the changes in molecular weight distribution (MWD) during the enzymatic depolymerization of guar galactomannan. The model accounts for the effect of branching by considering the guar molecule as a substrate having three types of bonds with different MM kinetic parameters. The overall kinetics of the enzymatic reactions then can be represented in terms of composite kinetic parameters that are functions of the MM parameters for the individual bonds. The depolymerization is assumed to follow a random scission mechanism, in which an enzyme randomly attacks the substrate molecule at any one of the three types of bonds, and leaves the substrate on cleavage of the bond. Expressions for the variation in molecular weights during depolymerization are developed by applying moment generating techniques to the kinetic model. The model is evaluated against the complete MWD obtained using gel permeation chromatography. During the initial stages of depolymerization, the enzymatic reaction is in the zero-order regime of MM kinetics and the polydispersity index (PDI) increases with time. Subsequently, the PDI decreases as the depolymerization tends to follow first order kinetics. We also show that for a zero-order, random or nonrandom scission, the variation of PDI with time can exhibit a maximum. These analyses confirm that an increase in PDI during the depolymerization is not necessarily due to nonrandom scission, as previously concluded.

We develop a new rheology-based method to study the complexation of cyclodextrins with hydrophobes in hydrophobically modified associative polymer solutions. The associative polymers have comb-like structure with hydrophobic groups randomly attached to the polymer backbone. Intermolecular interactions between the hydrophobic groups form a transient network resulting in thickening of the polymer solutions. On addition of cyclodextrins (CD) to the solution, the hydrophobes are encapsulated within the hydrophobic cavity of the cyclodextrins. This reduces viscoelastic properties of the polymer solution by several orders of magnitude. We exploit the existence of a dynamic equilibrium between CD adsorbed to the hydrophobes and free CD in the solution, to develop a rheology-based Langmuir-type adsorption isotherm for estimating the binding constant for molecular complexation. The model is based on the assumption that the amount of CD adsorbed is proportional to the reduction in elastic modulus of the polymer solution due to the encapsulation of the network junctions by CD. The effects of temperature on binding constant are studied to estimate the enthalpy and entropy of complexation. Experiments are conducted with both a-and b-CD at different polymer concentrations and temperatures to estimate the relative strength of binding of the CDs. At a given temperature and a polymer concentration, a-CD has a lower binding constant compared to that of b-CD, indicating higher affinity of a-CD to adsorb onto the hydrophobes. Since a-CDs have a smaller ring size, they can snugly fit to the hydrophobes and the association leads to higher enthalpy and entropy change.

Guar galactomannan, a naturally occurring polysaccharide, is susceptible to hydrolysis by three enzymes: beta-mannosidase, beta-mannanase, and alpha-galactosidase. The beta-mannosidase cleaves a single mannose unit from the nonreducing end of the guar molecule, the beta-mannanase cleaves interior glycosidic bonds between adjacent mannose units, and the alpha-galactosidase cleaves the galactose side branches off the guar. In this study, hydrolysis of guar solutions using hyperthermopilic versions of these enzymes together in different proportions and combinations are examined. The enzymatic reactions are carried out in situ in a rheometer, and the progress of the reaction is monitored through measuring the variation in zero shear viscosity. We find the presence of alpha-galactosidase to affect the action of both beta-mannanase and beta-mannosidase with respect to solution rheology. However, this effect is more pronounced when the alpha-galactosidase and beta-mannanase or beta-mannosidase enzymes were added sequentially rather than simultaneously. This likely is the result of debranching of the guar, which facilitates attack on beta-1,4-linkages by both the beta-mannanase and the beta-mannosidase enzymes and increases hydrolytic rates by the individual enzymes. A rheology-based kinetic model is developed to estimate the reaction rate constants and interpret synergistic effects of multiple enzyme contributions. The model fits the experimental data well and reveals that both the native and the debranched guar have the same activation energy for beta-mannanase action, although debranching considerably increases the frequency of enzyme-guar interactions.

We examine a new approach to reversibly modulate hydrophobic interactions in associative polymers using cyclodextrins (CD) and enzymes that cause scission of the a-1, 4 linkages in cyclodextrins. The associative polymers have a comb-like structure with pendant hydrophobic groups randomly attached to the polymer backbone. The intermolecular interaction between hydrophobic groups forms a transient network resulting in thickening of solutions containing the polymer. The CDs, doughnutshaped cyclic polysaccharides, encapsulate the hydrophobes within their hydrophobic cavity and eliminate hydrophobic interactions. This results in several orders of magnitude reduction in solution viscosity and other viscoelastic properties. Subsequent degradation of the CDs by enzymes restores the hydrophobic interactions and the original rheological properties. A rheokinetic model is developed to describe the kinetics of the enzymatic reactions. The model accounts for equilibrium between the CD bound to the hydrophobes and free CD in solution and assumes the enzyme hydrolyzes only the free CD in the solution, which causes the release of the bound CDs in order to maintain equilibrium. The reaction is assumed to follow Michaelis Menten kinetics and the kinetic parameters are determined by tracking the changes in the viscoelastic properties of the polymer solution during the enzymatic scission of CD. The effects of enzyme concentration, polymer concentration and temperature on the rate of recovery of the original rheological properties are experimentally determined, and used to validate the trends of the rheokinetic model.