Number- and Weight-Average Chain Lengths

Solution The number and weight average chain lengths for a self-condensing polymerization are obtained from Equation (13.18) and (13.19) by setting Sab= E ... 

Number- and Weight-Average Chain Length of the Primary Molecules which Belong to the Sol Fraction. 

To clarify the unique characteristics of the MWD of emulsion polymers, one of the simplest and most common cases [264], where neither chain transfer (Cf=0) nor radical desorption ((5=0) occurs, is considered here. The magnitude of bimolecular termination ( ) is changed with a constant radical entry frequency (c=2xl0 ). Figure 10 shows the calculated number- and weight-average chain lengths and the polydispersity index (PDI= as a func-... 

Fig. 10 Calculated number- and weight-average chain lengths as a function of the average number of radicals in a polymer particle, n, with c=2xl0" and Cf=S=0...

According to the FS theory, the number and weight-average chain lengths of the new polymer CLD will be given by [4] ... 

Figure 15.10 Effect of the operating pressure, P, on (a) polymerization rate, (b) number- and weight-average chain lengths, (c) gel fraction, and (d) crosslink density. Source Reprinted with permission from Quintero-Ortega lA, Vivaldo-Lima E, Luna-B cenas G, Alvarado JEJ, Louvier-Hernandez JF, Sanchez IC. Ind Eng Chem Res 2005 44 2823 [44]. Copyright 2005 American Chemical Society.

From Eq. (2.21) it follows that the number- and weight-average chain lengths Xn and Xw are expressed by... 

For polymers made with multiple-site catalysts, the instantaneous number- and weight-average chain lengths are given by Eqs. (25) and (26). 

The number- and weight-average chain lengths, as well as the polydispersity, of the instantaneous polymer population can be derived from eqn [61]... 

The zeroth and first moments have clear physical meanings. Qj (=[P"j) and Qo are the radical and dead polymer chain concentrations, respectively. Q" and Qi (=[M]ox) are their monomeric unit concentrations. The number- and weight-average chain lengths of radical chains are thus... 

Flgwe 18 (a) Conversion versus time of sol, gel, and total polymers and (b) number- and weight-average chain lengths versus conversion, as well as gel development in bulk radical copolymerization of MMA/EGDMA at 70 °C with 0.3 wt.% ethylene glycol dimethacrylate (EGDMA) and 0.3 wt. 

FIGURE 9.6 Instantaneous and cumulative number- and weight-average chain lengths and the cumulative polydispersity index for an isothermal, free-radical, batch polymerization (Example 9.12). 

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