A model is developed in the form of one or two partial differential equations (master Smoluchowski-like equations) that describe evolution of the size distribution of polymer species formed in a step-growth polymerization of an AB 2 monomer. Groups B react with a substitution effect; i.e., they are initially equally reactive, but the reactivity of the second B group changes as the first has reacted. One master equation is sufficient to model formation of branched molecules only. Two are needed to take into account intramolecular cyclization. Monte Carlo simulations of the same process are used to verify the results of applying the kinetic model. The model can be applied to calculate various molecular parameters in polymerizing systems, including various average degrees of polymerization, size distribution of acyclic and cycle-containing polymer molecules, degree of branching, etc. Explicit formulas describing the dependence of some of these quantities on time or conversion degree are derived for the random system, i.e., the system reacting without substitution effect.

Two new rigid bi-aromatic linkers for synthesis of peptide arrays by SPOT methodology were obtained from cellulose treated with 2,4-dichloro-6-methoxy-1,3,5-triazine. Reaction with m-phenylenediamine gave non-cleavable TYPE I linker which enabled attachment of the peptides via resistant to harsh reaction conditions amide, ether, and amine bonds. Reaction with 3-Fmoc-aminobenzoic acid followed by thermal isomerization of the intermediate "superactive" ester producing an amide-like bond gave TYPE II linker that was very stable during peptide synthesis. However, the peptide was cleavable, with fragment of the linker, in the presence of 1 M LiOH solution. The uniform loading of the cellulose and efficient synthesis of the peptide array was achieved by using N-(4,6-dimethoxy-1,3,5-triazin-1-yl)-N-methylmorpholinium 4-toluenesulfonate as the coupling reagent.

A kinetic model of hyperbranched polymerization is presented where an AB2 monomer reacts with up to 10% of a B3 one (A and B are functional groups) to yield a hyperbranched polymer. The model consists of two compact rate equations for entire distributions of two kinds of molecules that are formed in the system. Changes in reactivity of B groups in the form of the so-called first shell substitution effect are taken into account. Molecular parameters, namely the number and weight averages of polymerization degree as well as the average degree of branching of hyperbranched molecules, are extracted out from the rate equations and plotted against conversion.

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