Process chain particulate system

We can develop a stochastic model for two-phase polymerization by following the changes in the number and size of the growing polymers (or radicals) with time in an arbitrary particle of a system. [For a more general discussion of probability methods in particulate systems see Ref. 7.] Let us say that at some time t the particle contains m radicals of sizes Xi, x2,. . . xm (in order of their appearance) with probability density pm (xu x2,. .. Xm t). Since a polymer chain is usually long, we take the chain length or polymer size to be a continuous variable. Now, we assume that in a short time interval [t, t + t] changes in the particle occur by these processes ... 

The evidence for this mode of chain extension comes chiefly from the studies of Robbins etal (1967), who used pulse-chase labelling to show that a mutant of S. typhimurium that could not synthesise a complete core structure would assemble oligosaccharide chains in which the most recently inserted residues were near the reducing end. A similar mechanism could be shown both in cell-free particulate systems and the intact organisms. The individual steps in this process have not been separated in vitro and the intermediates with longer saccharide chains cannot readily be isolated without degradation. 

The term sol-gel is used broadly to describe the preparation of ceramic materials by a process that involves the preparation of a sol, the gelation of the sol, and the removal of the liquid. A sol is a suspension of colloidal particles in a liquid or a solution of polymer molecules. The term gel refers to the semirigid mass formed when the colloidal particles are linked to form a network or when the polymer molecules are cross-linked or interlinked. Two different sol-gel processing routes are commonly distinguished the particulate (or colloidal) gel route in which the sol consists of dense colloidal particles (1 to 1000 nm) and the polymeric gel route in which the sol consists of polyma- chains but has no dense particles >1 nm. In many cases, particularly when the particle size approaches the lower limit of the colloidal size range, the distinction between a particulate and a polymeric system may not be very clear. 

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