Polymer continued distribution

The methods described above give continuous distributions of relaxation times. However, the molecular theories of Viscoelasticity of polymers as... 

Umpleby II RJ, Bode M, Shimizu KD. Measurement of the continuous distribution of binding sites in molecularly imprinted polymers. Analyst 2000 125 1261-1265. 

The proportionality factor G may depend on many characteristics of the solute polymer,but since D is the only polymer-dependent variable in Eq. (2.5), it is reasonable here to treat G as a function of D only for a homologues series of polymers. Thus, for a polydisperse polymer sample with a continuous distribution of molecular weight M, Eq. (2.5) may be generalized as... 

Tn emulsion polymerization and in some suspension polymerizations, free radicals are generated in a continuous phase and diffuse into a dis-persed-phase particle or droplet where polymerization takes place (5). The molecular weight distributions or, equivalently, the polymer size distributions of these systems depend on the relative rates of radical arrival and termination. Frequently in emulsion polymerization the radicals are terminated so quickly that each particle in the dispersed phase... 

Two-phase polymerization is modeled here as a Markov process with random arrival of radicals, continuous polymer (radical) growth, and random termination of radicals by pair-wise combination. The basic equations give the joint probability density of the number and size of the growing polymers in a particle (or droplet). From these equations, suitably averaged, one can obtain the mean polymer size distribution. 

If a mixture contains more than two fractions the treatment can easily be generalized. For example, a trimodal mixture gives four linear isotherm sections ). The Increasing part of fig. 5.29 is replaced by two sections of different slope in the first the lowest molecular weight is displaced from the surface, in the second the middle fraction. For a continuous distribution of molecular weights a rounded isotherm is obtained the adsorption fractionation varies smoothly with the polymer dose. 

Fig. 25. Relationship between functions f(s) and f(r) for different cell distribution patterns in foamed polymer (1) uniform size cells (2) continuous distribution (3) decreasing distribution (4) increasing distribution (5) triangular distribution here, b is the maximum cell diameter...

The fraction of growing polymer chains that continues propagating after gelation can be estimated from the relative areas of the high and low molecular weight polymer fractions in each distribution. From this analysis, it is concluded that about A0% of the polymer continues to propagate under these conditions, as shown in Table VI. 

Most cocatalysts continue to influence the polymer MW distribution even after the optimum ratio of cocatalyst to chromium (maximum activity) has been reached. This behavior indicates that some of the lower pathways in Scheme 45 also contribute. Either sites are changed, or even destroyed, by attack on the Cr-O-Si bonds, or the alkyl exchange reaction occurs. This latter pathway tends to enhance the low-MW side of the MW distribution by introducing another chain transfer mechanism. Only some very specific, perhaps the most acidic, sites are probably involved, such as those sites producing low-MW polymer on Cr/silica-titania or Cr/AIPO4. These sites already have a tendency to produce low-MW polymer [52,332,681],... 

Results obtained with different initial concentrations have not been reported, but, evidently, such data could be normalized if first-order kinetics are obeyed for each decay curve. This first-order decay implies that a definite population can be isolated in a given temperature interval, while in the case of radicals and ions, there is a continuous distribution of pairs. The difference between these two cases is thus not very great. Heating induces in the polymer molecular motions which correspond to destruction of the traps with activation energies of the order of a few kcal mole-1. 

The photostabilization of polymers continues to be a rapidly advancing area of scientific and technological interest. Carlsson and Wileshave written several reviews on photostabilizing mechanisms in polymers, while Swasey has given an updated guide to stabilization, and Reid has discussed the effects of stabilizers in vinyl polymers. Nemzek and Mayo have predicted the service life of polypropylene, and Bredereck has reviewed the photostabilization of PVC. Several comprehensive review articles have appeared. Pospisil has reviewed in considerable depth the photo-oxidation mechanisms of phenolic anti-oxidants, Shlyapintokh has reviewed the kinetics of stabilizer distribution, Vink has... 

These cut-off values are nominal values (N.M.W C O ) and are therefore not always precise enough to be used as an exact parameter when fractioning continuously distributed polymers However ultra-filtration from nano filtration could have a scale of 100-lmil Dalton, Fig 3 illustrates a typical example of the membrane range... 

Very large micelles may also form in binary surfactant systems. These are long wormlike micelles that become entangled at higher concentrations, giving rise to rheological properties similar to those in polymer solutions. Such systems have been examined by H band shape analysis [52,53]. The protons of the surfactant hydrocarbon chain form a very large dipolar coupled spin system with an essentially continuous distribution of transverse relaxation rates. The distribution of relaxation rates is related to the distribution of order... 

The molar mass distributiMi for two polymers. The first polymer (continuous trace) follows the Flory-Schulz MMD with Mn = 40000 Mw is the double, i.e., Mw = 80000). The second polymer (dotted trace) follows the Schulz-Zimm MMD with Mn = 40000 and Mw = 120000. The molar mass distribution is diplayed as the molar fraction (a) and weight fraction (b) vs. mass. 

Synthetic polymers are polydisperse, i.e., they feature a continuous distribution of molecular chains with different molar masses. A well-known example of a mono-disperse polymer is the naturally occurring substance insulin. 

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