Addition polymerization distributions

In Chaps. 5 and 6 we shall examine the distribution of molecular weights for condensation and addition polymerizations in some detail. For the present, our only concern is how such a distribution of molecular weights is described. The standard parameters used for this purpose are the mean and standard deviation of the distribution. Although these are well-known quantities, many students are familiar with them only as results provided by a calculator. Since statistical considerations play an important role in several aspects of polymer chemistry, it is appropriate to digress into a brief examination of the statistical way of describing a distribution. 

Addition polymers, which are also known as chain growth polymers, make up the bulk of polymers that we encounter in everyday life. This class includes polyethylene, polypropylene, polystyrene, and polyvinyl chloride. Addition polymers are created by the sequential addition of monomers to an active site, as shown schematically in Fig. 1.7 for polyethylene. In this example, an unpaired electron, which forms the active site at the growing end of the chain, attacks the double bond of an adjacent ethylene monomer. The ethylene unit is added to the end of the chain and a free radical is regenerated. Under the right conditions, chain extension will proceed via hundreds of such steps until the supply of monomers is exhausted, the free radical is transferred to another chain, or the active site is quenched. The products of addition polymerization can have a wide range of molecular weights, the distribution of which depends on the relative rates of chain grcnvth, chain transfer, and chain termination. 

In polyolefins, the chain is propagated by an intermediate free-radical species or by an alkyl species adsorbed onto a solid. Both the free radical and the alkyl have the possibility of termination, and this creates the possibility of growth mistakes by chain transfer and chain-termination steps that create dead polymer before all reactants are consumed. The presence of termination steps produces a broader molecular-weight distribution than does ideal addition polymerization. 

The elastically effective network chains should obey Gaussian statistics. They should therefore be long enough, and their average degree of polymerization should be known. In addition the distribution of chain-lengths is expected to be rather narrow. 

Enzyme-catalyzed polymerization reactions have an important characteristic that is not found elsewhere. Once the enzyme has added a monomeric unit to the growing chain, it can either dissociate and recombine at random with other growing termini, or it can remain attached to the same chain and add further residues. Enzymes that dissociate between each addition and distribute themselves among all the termini are termed distributive. Those that process along the same chain without dissociating are termed processive. These terms apply also to degradative enzymes such as exonucleases. 

Separation of plasma from blood can be used to remove toxic substances with high molecular weights in body fluid which is important in the treatment of many fatal diseases [Nose et al., 1983] and to collect plasma for blood banks to produce plasma fractionates [Dceda et al., 1986]. Organic polymeric membranes with a mean pore diameter finer than 0.5 pm have been employed to some extent for these purposes. However, their wide pore size distributions and protein adhesion problems make their permeate flux quickly decline and their separation efficiency low. In addition, polymeric membranes generally can not withstand sterilization by autoclaves or chemical cleaning. 

Since the process represented by reactions (4a) and (4b) is a simple addition polymerization it leads to a distribution of molecular weights of the Poisson type [2]. At any st e of the reaction the concentration of polymer molecules containing n a-amino acid units [P ] is given by... 

A factor in addition to the residence time distribution and temperature distribution that affects the molecular weight distribution is the type of the chemical reaction (e.g., step or addition polymerization). 

The Flory distribution is a random distribution useful in several modes of polymerization. This distribution results from addition polymerization reactions when the only significant processes that interrupt macromolecular growth are either or both of chain transfer (to any species but the polymer) or termination by disproportionation. Likewise, this molecular weight distribution describes linear condensation polymerization when equal reactivity is assumed for all ends only when the reaction involves an equilibrium between polymerization and depolymerization. The model describes the distribution with one parameter which is the number average molecular weight. The distribution equation is ... 

In the case of addition polymerization without termination, the number fraction distribution function (the probability that a given chain has degree of polymerization N) is given by the Poisson distribution function ... 

The weight fraction distribution function for addition polymerization... 

Many addition polymerization reactions with very low concentrations of impurities have propagation rates much faster than initiation rates and have essentially no termination. Such reactions produce narrow molar mass distributions that can be approximated by the Poisson distribution. Comparison of the polydispersity index of anionically polymerized butadiene with Eq. (1.69) is shown in Fig. 1.20. 

List the necessary conditions for formation of a narrow molar mass distribution in addition polymerization. 

Many of the polymers of industrial importance are copolymers consisting of units of more than one type of monomer in the same polymer chain, and addition polymerization is one of the major routes for copolymer formation. The properties that result depend on how the monomers are distributed along the polymer chain as well as on their concentration. 

J. Pojman, J. Willis, D. Fortenberry, V. Ilyashenko, and A. Khan, Factors affecting propagating fronts of addition polymerization velocity, front curvature, temperature profile, conversion and molecular weight distribution, J. Polym. Sci. Part A Polym Chem., 33 (1995), pp. 643-652. 

The chain length distribution of free radical addition polymerization can also be derived from simple statistics. Thus, for polymer formed at any given instant, the distribution will be the most probable and will be governed by the ratio of the rates of chain growth to chain termination. 

Descriptions of networks in terms of cross-link index and density provide no information on the internal architecture, that is, the homogeneity, of the network. Depending on how they are produced, most networks are more or less inhomogeneous, that is, the local density has a distribution. With multifunctional polycondensation, the gel point is most often reached at relatively high yields, and the network formed is quite homogeneous. In addition polymerization, the gel point occurs already at relatively low yields. The polymerization continues around the spatially fixed network structured centers, and, so, densely cross-linked centers are produced within a less densely cross-linked matrix. 

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