Number and weight averages

ISO viscosity number. Table 12.1 compares typical correlations between number and weight average molecular weights with ISO numbers, AT-values and ASTM viscosity measurements. 

The instantaneous number and weight average degrees of polymerization are given by... 

The average values of for each seed were determined by averaging the values of ( )j) required to match the experimental number and weight average degrees of polymerization. The value of (j)j for each run was found by solving the equation for in... 

Polymerization Dynamics. Relationships presented were utilized for the simulation of monomer concentration, number and weight average molecular weights, and population density distributions for two experimental observations. Experimental values of these variables are in reasonable proximity of calculated values. 

Number and weight average molecular weight transients are siammarized in Figure 7. The more viscous conditions of Run 4 resulted in an overdamped response whereas, the less viscous conditions of Run 5 resulted in overshoot. The simulation was more damped and delayed than the experimental response. 

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 ... 

If the "polymer" component is a random copolymer, the number and weight average molecular weights is entered (lines 870 and 890). The mole fraction and monomer weight of the reactive monomer in the polymer is also entered (lines 910 and 960). The calculations assume that the reactive and nonreactive monomers have the same weight. 

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

The broadening of the distribution as the reaction proceeds toward completion is shown also by the expressions for the number and weight average degrees of polymerization. Both go to infinity as a— ac, of course, but Xw gets there faster—so much so that the ratio of Xw/xn goes to infinity also (see Eq. 29). 

The number and weight average values of y in the sol fraction are, respectively, ... 

Fig. 72.—Number and weight average degrees of polymerization prior to gelation and for the sol after gelation vs. the over-all degree of cross-linking (p) for the rectangular distribution. ...

Number of segments in species i (Chap. XII et seq,) Number and weight average number of units, or segments. 

NUMBER AND WEIGHT AVERAGE DIAMETERS CALCULATED USING MIE SCATTERING... 

Number and weight average molecular weights for Polysciences Standards and McMaster Standard B, calculated from raw chromatograms using the molecular weight calibration curve M(V) = 0.20 X 10 exp(-0.341 V - 0.006 V ) with V in counts (1 count = 5 ml). 2... 

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). 

Ziegler-Natta catalysts are used commercially for the production of stereoregular polymers, especially isotactic polypropylene and high-density linear polyethylene. The resultant polymers have number and weight average molecular weights (Mn and Mw, respectively) that are defined as... 

The number- and weight-average molecular weights are given by the following equations ... 

Many number- and weight-average molecular weight correlations are available in the literature [106] however, the //-values are greatly influenced by the molecular weight distribution (MWD) of the sample and therefore caution should... 

In evaluation of the parameters Aj and Bj, Timm and Ra-chow ( ) utilized number and weight average molecular weights coupled with the observed, normalized chromatogram for that standard. Specifically,... 

The broadening of the distribution with increasing a can also be noted by the XwfXn value. Equations 2-167 and 2-169 show that the difference between the number- and weight-average degrees of polymerization increases very rapidly with increasing extent of reaction. At the gel point the breadth of the distribution Xw/Xn is enormous, since Xw is infinite, while X has a finite value of 4 (Fig. 2-19). Past the gel point the value of Xw/Xn for the sol fraction decreases. Finally, at a = p — 1, the whole system has been converted to gel (i.e., one giant molecule) and Xw/Xn equals 1. 

Fig. 2-19 Number- and weight-average degrees of polymerization as a function of a for a trifunctional polymerization. The portions of the plots after the gel point (a = 5) are for the sol fraction only. After Flory [1946] (by permission of American Chemical Society, Washington, DC).

Using the same approach as in Secs. 2-7a and 2-7b, the following equations are derived for the weight-fraction distribution, number- and weight-average degrees of polymerization,... 

Recall also from Section 3.3.1.1 that we introduced the extent of reaction, p, which is related to the degree of polymerization, x . From Eq. (7.91), we can derive the following expressions for the number- and weight-average molecular weights in terms of the extent of reaction ... 

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