Polymer molecular weight distribution statistics

The molecular weight properties of both polymers are presented in Table III. Figure 5 is the experimental cloud-point curve. The system was particularly sluggish because of reduced mobility of the components in the lower temperature range, so precision is somewhat diminished. According to the molecular weight distribution statistics and computational results like those shown in Figure 1, the critical point should be shifted approximately 10% up the... 

As early as 1952, Flory [5, 6] pointed out that the polycondensation of AB -type monomers will result in soluble highly branched polymers and he calculated the molecular weight distribution (MWD) and its averages using a statistical derivation. Ill-defined branched polycondensates were reported even earlier [7,8]. In 1972, Baker et al. reported the polycondensation of polyhydrox-ymonocarboxylic acids, (OH)nR-COOH, where n is an integer from two to six [ 9]. In 1982, Kricheldorf et al. [ 10] pubhshed the cocondensation of AB and AB2 monomers to form branched polyesters. However, only after Kim and Webster published the synthesis of pure hyperbranched polyarylenes from an AB2 monomer in 1988 [11-13], this class of polymers became a topic of intensive research by many groups. A multitude of hyperbranched polymers synthesized via polycondensation of AB2 monomers have been reported, and many reviews have been published [1,2,14-16]. 

Scarcely had the covalent chain concept of the structure of high polymers found root when theoretical chemists began to invade the field. In 1930 Kuhn o published the first application of the methods of statistics to a polymer problem he derived formulas expressing the molecular weight distribution in degraded cellulose on the assumption that splitting of interunit bonds occurs at random. 

At present, however, the determination of the Molecular weight distribution curve is rather difficult. Hence, in polymer chemistry, the so-called Molecular weight of a polymer is merely a statistical average. 

Random hyperbranched polymers are generally produced by the one-pot polymerization of ABX monomers or macromonomers involving polycondensation, ring opening or polyaddition reactions hence the products usually consist of broad statistical molecular weight distributions. 

In agreement with Flory s predictions, hyperbranched polymers based on A,jB monomers reported in the literature exhibit a broad molecular weight distribution (typically 2-5 or more). The polydispersity of a hyperbranched polymer is due to the statistical growth process. A strategy to overcome this disadvantage is to add a By-functional core molecule, or a chain terminator, which Hmits the polydispersity and also provides a tool to control the molecular weight of the final polymer. The concept of copolymerizing an A2B monomer with a B3 functional core molecule was first introduced by Hult et al. [62] and more recently also utilized by Feast and Stainton [63] and Moore and Bharathi [64]. 

The product of a polymerization is a mixture of polymer molecules of different molecular weights. For theoretical and practical reasons it is of interest to discuss the distribution of molecular weights in a polymerization. The molecular weight distribution (MWD) has been derived by Flory by a statistical approach based on the concept of equal reactivity of functional groups [Flory, 1953 Howard, 1961 Peebles, 1971]. The derivation that follows is essentially that of Flory and applies equally to A—B and stoichiometric A—A plus B—B types of step polymerizations. 

In ideal random crosslinking polymerization or crosslinking of existing chains, the reactivity of a group is not influenced by the state of other groups all free functionalities, whether attached or unattached to the tree, are assumed to be of the same reactivity. For example, the molecular weight distribution in a branched polymer does not depend on the ratio of rate constants for formation and scission of bonds, but only on the extent of reaction. Combinatorial statistics can be applied in this case, but use of the p.g.f. simplifies the mathematics considerably. 

A second and distinct era in the development of branched macromolecular architecture encompasses the time between 1940 to 1978, or approximately the next four decades. Kuhn 151 published the first report of the use of statistical methods for analysis of a polymer problem in 1930. Equations were derived for molecular weight distributions of degraded cellulose. Thereafter, mathematical analyses of polymer properties and interactions flourished. Perhaps no single person has affected linear and non-linear polymer chemistry as profoundly as P. J. Flory. His contributions were rewarded by receipt of the Nobel Prize for Chemistry in 1974. 

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