General Theory of Polymerization

The individual steps are as follows. Later each step is considered in detail in the light of individual investigations. 

The very early formation of particles was also proposed by Vysotskii et al. (6), who studied the early stages of polymerization and similarly stated that there are two basic processes of particle growth of silica in the aqueous system  

Growth of particles at the e. pense of silicic acid in the solution from the moment of its preparation. 

Further growth of larger particles by deposition of silicic acid dissolving from the smaller particles. This is a slower process and may be negligible at low pH after the monomer has been used up. 

After the gel network has been formed, the structure becomes stronger as the necks between particles become thicker owing to solution and deposition of silica. 

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In the opinion of the author, the development of fundamental qualitative concepts should be a primary problem because without an even simplified but general understanding of the physical basis of the elementary act of polymerization, it is difficult to develop a general theory of polymerization. The process of generalised comprehension of experimental facts cannot be replaced by any most universal and detailed quantum-chemistry calculations. Their results are in many respects predetermined by the initial formulation of the problem and the... 

The general theory of polymerization should include a) the theory of chemical reactions, b) the reaction rates theory and c) the kinetic statistical theory of polymerization. 

The general theory of polymerization is first outlined. Then the details of each step are reviewed and finally the more recent work of a number of investigators is discussed. Succeeding steps in polymerization from monomer to large particles and gels or powders have been represented schematically by Her (5) as in Figure 3.1. This applies to aqueous systems, in which silica is somewhat soluble. Very little is known about the polymerization when Si(OHL is formed in nonaqueous solutions. 

A general theory of dichroism induced by strain in polymeric networks Is developed by adaptation of methods developed earlier for treating strain birefringence. It is generally applicable to dichrolc bands associated with any specified conformation involving sequences of one or more consecutive bonds. The transition dipole moment is introduced in the local framework of the skeletal bonds associated therewith. Possible differences in transition moments for various conformations and repeat units are taken into account. Numerical calculations for PE chains show gauche bonds, rather than trans, to be more favorably oriented with respect to the chain vector r. 

Helfand has presented a general theory of inhomogeneous polymeric systems and has applied it to the interface between immiscible honmpolymers and to block copolymers In order to simplify the problem of the numerical calculation of the microdomain sizes, he has derived from his general theory a narrow interface approximation The values predicted by the simplified theory for the dimensions of the lamellar block copolymer microdomains are in good agreement with the experimental results ... 

The general theory of nucleation and polymerization in aqueous systems, in which silica shows some solubility, is discussed in detail in Iler s book (3). However, very little was known at the time the book was published (1979) about the polymerization of silica when Si(OH)4 is formed in nonaqueous systems. Progress made up to 1990 in the understanding of the hydrolysis and condensation of silicon alkoxides that leads to silica gels or to silica sols of large particle diameter are lucidly discussed by Brinker and Scherer (8). Brinker s chapter in this book (Chapter 18) includes a clear explanation of the difference between hydrolysis and condensation of aqueous silicates and silicon alkoxides. 

A few words on the stability of steady states of polymerization. This question arises immediately as soon as the multiplicity of steady-state conditions spears. It is well known that three solutions are possible in the flow of reactants. The general theory of thermal instability of reactors has been developed in detail in Refe. [16-20,30,31], and the theory of kinetic instability caused by peculiarities of the kinetic schenK (self-acceleration. gel-effect, etc. in Refs. [37-40]). The instability of steady states of poly-nKiization plug reactors of a hydrodynamic nature is more interesting for the present paper. It can be assumed that the state corresponding to the negative slopes of the P(Q) curve are unstable if P = const is maintained [30, 33, 34]. At Q = const, all states are stable and realizable. The analysis of this problem in zero-dimensional formulation [41], for a reactor determined by only one value of T, p, q and a complex variable hydrodynamic resistance has shown that the slope of the curve is not an exhaustive stability criterion. 

Stress relaxation experiments involve the measurement of the force required to maintain the deformation produced initially by an applied stress as a function of time. Stress relaxation tests are not performed as often as creep tests because many investigators believe they are less readily understood. The latter point is debatable, and it may only be that the practical aspects of creep measurements are simpler. As will be shown later, all the mechanical parameters are in theory interchangeable, and so all such measurements will contribute to the understanding of viscoelastic theory. Whereas stress relaxation measurements are useful in a general study of polymeric behavior, they are particularly useful in the evaluation of antioxidants in polymers, especially elastomers, because measurements on such systems are relatively easy to perform and are sensitive to bond rupture in the network. 

JS presented a general theory of ring-chain equilibria as early as 1950. Their theory has been extensively used by polymer chemists to describe the cyclic populations of linear polymeric equilibrates in concentrated solutions... 

The performance of absolute asymmetric polymerization demands the generation of crystals with specific crystallographic motives. In the absence of a general theory of crystal packing, the discovery of crystalline motifs required to perform such reactions was achieved generally by using mix and try methods. The present authors approach to the problem comprised, first, an outline of the requirements... 

Carothers WH (1929) Studies on polymerization and ring formation I. An introduction to the general theory of condensation polymers. J Am Chem Soc 51 2548—2549... 

Harkins W.D (1946) A General Theory of Reaction Loci in Emulsion Polymerization. J. Chem. Phys.l4 47-48. 

Harkins WD. A general theory of tbe reaction loci in emulsion polymerization. J Cbem Pbys 1945 13 381-382. 

Emulsion Polymerization. Emulsion SBR was commercialised and produced in quantity while the theory of the mechanism was being debated. Harkins was among the earliest researchers to describe the mechanism (16) others were Mark (17) and Elory (18). The theory of emulsion polymerisation kinetics by Smith and Ewart is still vaUd, for the most part, within the framework of monomers of limited solubiUty (19). There is general agreement in the modem theory of emulsion polymerisation that the process proceeds in three distinct phases, as elucidated by Harkins (20) nucleation (initiation), growth (propagation), and completion (termination). 

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