Estimation of <i>M</i>_<i>w</i> from dilute solution viscosity

Abstract

Abstract The viscosity‐average molecular weight, M v , of a polymer is given operationally through its limiting viscosity number [η] and the Mark‐Houwink equation [η] = KM v α , where K and α are empirical constants. If [η] is measured under different conditions, α and M v will vary for the same sample. M v α is the α‐order moment about the origin of the differential weight distribution of the polymer. Practically, the results of a series of M v measurements on the same polymer are equivalent to a cluster of fractional moments of the weight distribution, with orders between 0.55 and 0.80. It is shown that the first moment of this distribution, M w , may be estimated reliably by a straightline plot of M v against α‐extrapolated to α equals 1. This simple expedient is effective although there are probably no molecular weight distributions in which the relation is strictly linear and there are no mathematical distributions for which the αth root of the αth moment is a linear function of α for all α. The deviation from linearity is small enough, however, that the real curve can be represented by a straight line over a short range of α. Thus, M w can be measured accurately, but M n , M z , or the breadth of the distribution is not accessible by this method. Experimental and literature examples show that the precision of M w estimated by this method compares well with that of primary methods for measuring this molecular weight average. If a linear relationship is observed with reliable α values, this appears to be a sufficient condition for estimation of a valid M w .