Molecular weight instantaneous average

As pointed out by Hamielec and Ouano (8), the separation of a branched polymer by size in the SEC process results in molecular species of different molecular weights eluting at the same volume. Thus, the molecular weight of these species is not monodispersed and MCV) must be replaced by the instantaneous number average molecular weight when using the universal calibration procedure for branched polymers. 

Note that the weight and Z average molecular weights so obtained are only approximate and less than the true values. This is a consequence of the universal calibration method giving the instantaneous number average molecular weight across the chromatogram. 

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-... 

Literature data for the suspension polymerization of styrene was selected for the analysi. The data, shown in Table I, Includes conversion, number and weight average molecular weights and initiator loadings (14). The empirical models selected to describe the rate and the instantaneous properties are summarized in Table II. In every case the models were shown to be adequate within the limits of the reported experimental error. The experimental and calculated Instantaneous values are summarized in Figures (1) and (2). The rate constant for the thermal decomposition of benzoyl peroxide was taken as In kd 36.68 137.48/RT kJ/(gmol) (11). 

Figure 2. Measured and calculated instantaneous and cummulative molecular weight averages. ( ) experimental cummulative values Solid lines, calculated values (Table II).

The "ideal" concept of emulsion polymerization was built on the assumption that the monomer was water insoluble and that in the absence of chain transfer, the number average degree of polymerization, Xj can be related to the rate processes of initiation and propagation by the steady-state relationship Xjj = 2 Rp/Rj. Since Ri and Rp are both constant and termination is assumed to be Instantaneous during the constant rate period described by Smith-Ewart kinetics, the above equation predicts the generation of constant molecular weight polymer. Data has been obtained which agrees with Smith-Ewart but there is... 

An equation, similar to that shown above for, was used by Fitch et al. (19) for Instantaneous viscosity average molecular weights and by Wall (20) and Robertson (21) for Instantaneous Intrinsic viscosities. 

Figure 9. Change in cumulative and instantaneous weight average molecular weights...

Recall that corresponding instantaneous values of DP and Rp are linked by Eq. (6-64). If sufficient polymer can be collected for molecular weight measurements from a polymerization that goes to only 5 or 10% conversion, the average value of [M] can be inserted into this equation with the measured DP and Rp to estimate kp kfc -1- td)- If the ratio kia/ktc is known or assumed, then k /k is available. 

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. 

Equations (17), (21), (32), (33) and those of Table 1 completely determine the instantaneous polymerization kinetics and molecular weight averages. Simple relationships are available... 

The term zero-one designates that all latex particles contain either zero or one active free radical. The entry of a radical in a particle that already contains a free radical will instantaneously cause termination. Thus, the maximum value of the average number of radicals per particle, n, is 0.5. In a zero-one system, compartmentalization plays a crucial role in the kinetic events of emulsion polymerization processes. In fact, a radical in one particle will have no access to a radical in another particle without the intervention of a phase transfer event. Two radicals in proximity will terminate rapidly however, the rate of termination will be reduced in the process because of compartmentalization, as the radicals are isolated as separate particles. Consequently, the propagation rate is higher and the molecular weight of the polymer formed is larger than in the corresponding bulk systems. Which model is more appropriate depends primarily on the particle size. Small particles tend to satisfy the zero-one model, as termination is likely to be instantaneous. ... 

Fig, IA. Number of polymer chains vs conversion. B Number average molecular weight vs conversion. C Rate of polymerization vs time. D Conversion vs time. Diagnostic plots for instantaneous initiation (At), with various chain transfers (A2a, A2b, A2c) and for slow initiations (A3a, A3b)... 

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