The concept of pore size distribution is incorporated into the Clark model of enzyme immobilization in the present study. This refined model predicted that in the case of small harmonic pore radius with the same surface area and porosity of the support, more enzyme could be loaded in a support with nonuniform pores than that with uniform pores. In comparing the enzyme loading efficiency of the support with two different pore size distributions, the one with Gaussian distribution had the greater amount of enzyme immobilized than the other one with Rajagopalan's distribution. Furthermore, more enzyme could be loaded in a support with wider Gaussian pore size distribution than that with narrower distribution. The immobilized enzyme profile in the solid support with pore size distribution displayed a stepwise pattern which differed appreciably from the sigmoidal profile predicted for the support with uniform pore size. This stepwise enzyme distribution profile became sigmoidal with decreasing h(T) or increasing k. The new model could be used for designing protocols for an enzyme immobilization process.

Clark et al. (1985) recently formulated a kinetic model for coupling restricted diffusion and immobilized reaction of enzyme molecules in a cylindrical pore using the concept of "pore central core restricted diffusion." This model takes into consideration the increase of diffusion resistance by the reduction of available cross-sectional area during the enzyme immobilization process. It successfully predicts the results of nonuniform enzyme distribution in porous supports as observed in some experiments.Clark's model assumes that supports have uniform pore size. This is in contrast to the fact that pore size distribution exists in almost all porous solids. Treating pores of various diameters as uniform in size (e-g., average pore diameter) tends to underestimate the plugging effect of small pores by enzyme molecules during the immobilization process, especially for porous solids with broad or bimodal pore size distributions. This might result in significant deviations of the predicted values of the amount of the enzyme loaded.The objective of this study is to improve Clark's model by incorporating a pore size distribution into the pore central core restricted diffusion model. By using a refined equation for the void cross-sectional area of pore, we recalculate the amount of enzyme immobilized vs. time on stream. In addition, a real pore size distribution of silica supports is measured to investigate the deviation of the loaded amount of enzyme predicted by Clark's model. Mathematical ModelClark et al. (1985) proposed a quasisteady-state model to simulate the enzyme immobilization process within a cylindrical Correspondence concerning this paper should be addressed to C. L. Chiang pore. By using the dimensionless concentrations, the total amount of immobilized enzyme within a cylindrical pore can be determined by evaluating the following integral:Here we consider a spherical particle with a pore volume density function, Pv(rp). In order to incorporate the effect of pore size distribution into Clark's model, some modifications have been made. The first one is to consider the hydrodynamic drag effects. According to Clark's model, the restricted diffusion coefficient is related to the bulk diffusion coefficient of enzyme by a hydrodynamic drag factor, K,(X), i.e.,where X is the ratio of enzyme to effective pore diameter, which is a function of the axial coordinate, z . Equation 3, proposed by Pappenheimer et al. (1951), is suitable only for X < 0.4. Because a batch of commercial support preparation might contain a significant proportion of smaller pores, X larger than 0.4 should be considered for the realistic application of Clark's model. Hence, Eq. 3 no longer applies, and a table of K,(X) with a wider range of X(0-0.9), developed by Paine and Scherr (l975), is used to calculate K,(X) in the present work.On the other hand, the void cross-sectional area at position z, with local immobilized enzyme concentration, e,(z), is given by (4)