Post-gel relations

It may be noted that the curves in Fig. 5.10 representing the weight fractions of various species calculated from Eq. (5.83) continue through the gel point (or = 0.5) without discontinuity. This would be expected as the derivations of the distribution equations (5.81)-(5.83) place no restriction on or or p except that it be in the physically real range from zero to unity. These equations are vahd only for finite species beyond the gel point. If Eq. (5.83) for Wx is summed over all values of X, the weight fraction of sol (w ) would result. When the units are trifunctional (/ = 3), this yields (Flory, 1953)  

Since the sum of the weight fractions of gel Wg and sol Ws must be unity, we obtain an expression for the gel fraction as 

Problem 5.30 A mixture of equivalent amounts of glycerol and 1,2,3-propanetricarboxy-lic acid is condensed to the extent of 65% conversion. Assuming equal reactivity of functional groups, calculate (a) weight fractions of sol and gel in the mixture, and (b) weight fractions of the monomer and the dimer in the sol fraction. 

Problem 5.31 Stoichiometric polymerization of 1,3,5-benzenetriacetic acid with 1,10-decanediol was conducted beyond the gel point to measure the mass fraction of sol at different extents of reaction p, yielding the following data (Argyropoulos et. al., 1987)  

Calculate the sol fraction by Flory s equation to compare with the experimental values. Answer  

Problem 5.31 Stoichiometric polymerization of l,3,Sbenzenetriacetic acid with 1,10-decanediol was con- 

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Fig. 4. Schematic representation for the relation of T vs (O for three states of pre-gel, critical gel, post-gel, and the definition of the characteristic frequency, of, eo of the pre-gel and the post-gel respectively.

Hydrolysis and Polycondensation. As shown in Figure 1, at gel time (step C), events related to the growth of polymeric chains and interaction between coUoids slow down considerably and the stmcture of the material is frozen. Post-gelation treatments, ie, steps D—G (aging, drying, stabilization, and densification), alter the stmcture of the original gel but the resultant stmctures aU depend on the initial stmcture. Relative rates, of hydrolysis, (eq. 2), and condensation, (eq. 3), determine the stmcture of the gel. Many factors influence the kinetics of hydrolysis and... 

In this communication a study of the catalytic behavior of the immobilized Rhizomucor miehei lipase in the transesterification reaction to biodiesel production has been reported. The main drawbacks associated to the current biodiesel production by basic homogeneous catalysis could be overcome by using immobilized lipases. Immobilization by adsorption and entrapment have been used as methods to prepare the heterogeneous biocatalyst. Zeolites and related materials have been used as inorganic lipase supports. To promote the enzyme adsorption, the surface of the supports have been functionalized by synthesis procedures or by post-treatments. While, the enzyme entrapping procedure has been carried out by sol-gel method in order to obtain the biocatalyst protected by a mesoporous matrix and to reduce its leaching after several catalytic uses. 

Further densification of C-S-H phase and transformation to the type HI and also IV, in the form of compact gel, leads to the significant reaction rate decrease. The formation of inner C-S-H begins. This is also the consequence of lower content both of anhydrous phases and of the liquid phase. The further growth of Ca(OH)2 crystals is observed. Finally, one can conclude that there is less experimental data relating to the post-induction period. 

Ascorbic acid, dehydroascorbic acid, dlketogluconic acid, and glucose have been determined down to nanogram levels by h.p.l.c. on a hydrophilic, polyvinylalcohol gel, post-column derivatization with benzamldine, and fluorlmetric detection. The method was applied to ascorbic acid in fruit Juice.Ascorbic acid, its 2-sulphate, 2-phosphate, 2-0-methyl, and 6-bromo-6-deoxy derivatives, and a related non-enzymic browning product, 5-methyl-3,4-dihydroxy-... 

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