An exact truncation theorem is proved for the expansion, in terms of moments of the molecular weight distribution, of the Gibbs spinodal determinants of a wide class of generalized mean-field Flory-Huggins models for polydisperse polymer solutions. A similar truncation theorem for the critical-point determinants is derived on the assumption that an expansion in a finite number of moments exists. These truncations have been exploited elsewhere through the relative economy they confer on computations involved in the testing and refinement of such theoretical models by fitting them to experimental data. A much simplified general and explicit expression is found for the relevant spinodal determinants of the mean-field models. If the relevant free energy of mixing is assumed to depend on the moments
M
0
,
M
1
, . . . ,
M
n
of the molecular weight distribution, this expression shows the spinodal to be a function of
M
0
,
M
1
, . . ,
M
2
n
+1
. The critical point is a function of
M
0
,
M
1
, . . . ,
M
3
n
+2
. The truncations at
M
2
n
+1
and
M
3
n
+2
betoken a collapse to a small subspace of the formal Hilbert-space representation of the composition space of the solution. The mathematical proof follows the pathway of the classical routes to the rigorous theory of function spaces opened up by von Koch and Fredholm, and the spinodal expression bears the imprint of a classical solution of Stieltje’s moment problem. In addition, modern operational methods of combinatorial theory are relevant to future extensions of the present work. Theoreticians may, therefore, be interested to come to the aid of experimentalists struggling with the analysis of data of much practical import.
