Theoretical Derivation of the [q]-M-Relationship in Diluted Solutions of Ring-shaped Polymer ChainsAs W. Kuhn') has shown, the properties of coiled linear macromolecules and the resulting behaviour of diluted polymer solutions can be described by the random flight statistics: -h2 = 2 . A ' mo 71) fl 2 A , 2 . A , = P . I , , , = L,, = total length of the polymer chain = mean square end-to-end distance of a random coil chain (radius of gyration: r z = = number of chain segments of a random coil chain = mean length of a chain segment P = degree of polymerization I , , , = length of the monomeric unit h i / 6 ) If we replace written as follows (with Frq10 = d e q . [ s l / m ) : by deq,[ql, the diameter of an equivalent sphere, Eq. (1) can be the molecular weight dependence of the mean equivalent coil density peq,[ql is2): Combining Eq. (4) with Einstein's viscosity law3) [tll = 2,5/6eq.[q] (5) leads to the known [q]-M-relationship for ideal diluted polymer solutions l): [g] = (2,5/Kj[,,l) . MO*' = KO [*I . Mos5

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In order to explain the difference in theta temperatures between ring-shaped polymers and their corresponding linear polymers, the Huggins parameter x of ring-shaped polymers is assumed to obey the dependence x = x1 (1 + 0 Q2) on local segment concentration as expressed by the volume fraction of the polymer @ 2 , and 0 being a constant. A comparison between theoretical results and light scattering measurements of Roovers and ourselves is satisfactory.

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Glucoamylase was immobilized onto novel porous polymer supports. The properties of immobilized glucoamylase and the relationship between the activity of immobilized enzyme and the properties of porous polymer supports were investigated. Compared with the native enzyme, the temperature profile of immobilized glucoamylase was widened, and the optimum pH was also changed. The optimum substrate concentration of immobilized glucoamylase was higher than that of native enzyme. After storage for 23 d, the immobilized glucoamylase still maintained about 84% of its initial activity, whereas the native enzyme only maintained about 58% of the initial activity. Moreover, after using repeatedly seven times, the immobilized enzyme maintained about 85% of its initial activity. Furthermore, the properties of porous polymer supports had an effect on the activity of the immobilized glucoamylase.