Instantaneous Molecular Weight Distribution

For one of the samples, PVAc - Lot 1, the number average molecular weight distribution is plotted in Figure 2. Also shown is the instantaneous number average number of LCB points per molecule, plotted as a function of number average molecular weight. Note that increased rapidly with increasing num-... 

This can be accumulated in a similar manner to that of instantaneous molecular weight distributions (11, 8) ... 

Another sampling effect which deserves mention is that since the molecular weight distribution shifl towards higher molecular weights with conversion, a slice will not in general contain proportionate amounts of polymer from all conversions. This dufting can be accounted for in the theoretical predictions by incorporating it into cumulation of the instantaneous property distributions (e.g. Equation 8). 

The mechanism of the polymerization of this monomer has been studied in far greater detail than any other. It is clear from the outset that a much more complex mechanism is involved than is the case for olefins. A large proportion of the initiator is used to form polymer whose molecular weight is only a few hundreds and the overall molecular weight distribution is so broad as to be rivalled only by those found in polyethylene produced by the high pressure process (19, 39). The initiator disappears almost instantaneously on mixing the reactants (19, 38). Under these conditions, an almost monodisperse polymer would be expected if chain transfer or termination processes are absent. 

The instantaneous differential molecular weight distribution is given by ... 

Polymerization rate represents the instantaneous status of reaction locus, but the whole history of polymerization is engraved within the molecular weight distribution (MWD). Recently, a new simulation tool that uses the Monte Carlo (MC) method to estimate the whole reaction history, for both hnear [263-265] and nonlinear polymerization [266-273], has been proposed. So far, this technique has been applied to investigate the kinetic behavior after the nucleation period, where the overall picture of the kinetics is well imderstood. However, the versatility of the MC method could be used to solve the complex problems of nucleation kinetics. 

Chains with monodisperse molecular weight distribution (Mw/Mn = 1.00) can occur in idealized conditions when all polymerizing centers initiate instantaneously and chain termination is absent. In these cases the catalyst is actually an initiator. These living polymerizations are quite rare among transition metal catalysts. More often, random chain termination leads to many chains formed per metal atom. A Schulz-Flory most probable distribution of polyalkene molecular weights (Mw/Mn = 2.00) is the result. In cases when more than one type of active site is present, bimodal or multimodal distributions of molecular weights result (Mw/Mn > 2.00). 

The opposite of the large diameter pipeline with little axial or radial mixing is the perfect backmixed reactor with instantaneous mixing and uniformity. For polystyrene reactors with several hours of residence time, complete mixing in 1-2 min is usually adequate to satisfy a practical definition of perfectly mixed. The probability of exit of any fluid element from this type of reactor is independent of when it entered. The residence time distribution is exponential and the molecular weight distribution in the case of no termination is Mw/Mn = 2.0, which will spread out to 2.3 when chain transfer controls. If product requirements necessitate a narrower residence time distribution, one can utilize several of these reactors in series. This becomes necessary to control the grafting distribution in rubber modified polystyrene. 

Pig. 9. (B) Plots of componantE of instantaneous molecular weight distribution S... 

For the calculation of molecular weights in CSTR emulsion reactors, a vsefnl classification comes to mind. This includes those monomer systems whose molecular weight and branching development depends on particle size and those that do not. Styrene falls into the former class and vinyl chloride and vinyl acetate into the latter class. Thus, in vinyl chloride emulsion polymerization where LCB is neglected, the instantaneous molecular weight distribution is given by... 

In ideal size-exclusion chromatography (SEC), fractionation is exclusively by hydrodynamic volume. Due to axial dispersion, however, a whole distribution of hydrodynamic volumes (and, therefore, of molecular weights) is instantaneously present in the detector cell. Under these conditions, it is assumed that the mass chromatogram w(V) (i.e., the instantaneous mass w versus the elution time or elution volume V) is a broadened version of a true (or corrected) mass chromatogram w V), as follows [1] ... 

A digital-computer program was written to solve the equations and calculate the conversion at any time in a batch polymerization. Polymerization rates, instantaneous and cumulative molecular-weight distributions, and molecular-weight averages are also calculated at this time. 

It is doubtful, however, that a true living system without termination or transfer exists in these polymerizations instead we believe that the narrow distributions may result from a combination of essentially instantaneous initiation, relatively long kinetic lifetime, and kinetic termination without transfer. H. Morawetz has derived an equation relating the molecular weight distribution to the relative rates of propagation and termination and the concentration of active species for such a case ( ). The equation accounts for the possible occurrence of narrow distributions, and we are presently experimentally investigating these calculations and predictions for the polymerization of the p-isopropyl monomer. 

Fig. 37. Simulation of the instantaneous molecular weight distribution of PE during pyrolysis, expressed in term of repeated units n heating rate 10°C/min, pressure 1 atm. Panel (a) Total mass fraction of chains nearby the border range of evaporable compounds at different temperature levels panel (b) temperature profiles of components in the gas and the nearest liquid phase.

Living polymers resulting from an instantaneously initiated but non-terminated polymerization, have a nearly Poisson molecular weight distribution, provided that Mo > Me. The polymerization seems to cease as the concentration of the residual monomer attains its equilibrium value - no further conversion of the monomer into polymer could be detected at that stage of the reaction. Nevertheless, the system is not yet in its ultimate equilibrium state. 

Various factors are important in determining the composition and molecular weight distribution of multicomponent copolymers e.g. monomer reactivity ratios, reaction conditions). Stockmaycr was one of the first to report on the problem and presented formulae for calculating the instantaneous copolymer composition as a function of chain length. Othershave examined the variation in copolymer composition with chain length by computer simulation. One method of ensuring a functionality of at least one is to use a functional initiator or transfer agent. 

A polydispersity of about 2 is typical of high molecular weight condensation polymers. A polydispersity of 1.5-2.0 is typical of the instantaneous molecular weight distribution of a free-radical polymer, but the composite distribution from a moderate- to high-conversion reactor will often be broader than this due to thermal inhomogeneities. Coordination catalysis produces very broad distributions, while some low-temperature, ionic polymerizations can give nearly monodisperse polymers (see Peebles [1] for a comprehensive treatment of molecular weight distributions). 

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