Literature data on the average molecular weights M,, M w , M,, and/or Mu for several polymers indicated that they fell outside the continuum originally proposed to model molecular weight distribution (MWD), where the log-normal (LN) distribution, or positively valued Gex parameters m and k , define the continuum. Following the papers of Kubin, it is possible to embrace these polymers in an extended continuum by including these parameters, both negatively valued, in it.
To the extent that m 1 -1 and k < -5, the extended continuum models average molecular weights through M,+Z. The correspondence of Gex models of MWD of a polymer obtained from data on its M,, M,, and M, with that obtained from data on its M,, Mu, and M , is indicated, using published data. The numerical value of the m parameter in a Gex model is of use in polymerization kinetics; when m values are obtained for each analysis from multiple analyses upon a given polymer, their consistency indicates the concordance of the three average molecular weights from each test run.
The Gex parameters based upon M,,, M,, and Mu or M, can be used to estimate values for higher average molecular weights of linear, unimodal homopolymers. This is of use in interpreting rheological data on such polymers.