MAURICE L. HUGGWS Kodak Research Laboratories, Rochester, N. Y.
Methods for the estimation of molecular weights of high polymers from data on properties of their dilute solutions are critically discussed. Specific recommendations are made regarding future procedure.
T
against CZshow an approximately rectilinear relation (Figure 1). Such graphs are useful, therefore, in extrapolating to CZ = 0 to obtain limiting values of n/C2 (or S/C,) which can properly be substituted into Equation 1 (or into the corresponding equation relating the freezing point depression to the molecular weight).
HE molecular weights of small molecules can readily be determined, either from measurements of certain of their properties in the gaseous state or from measurements of certain properties (osmotic pressure, freezing point depression, etc.) of their dilute solutions. The molecular weights of very large molecules, however, cannot be determined from gaseous state data because of their very low vapor pressures. Moreover, the application of the usual equations relating osmotic pressure and similar properties of a solution to the determination of molecular weights of very large solute molecules leads, in general, to large errors. These equations are, theoretically and experimentally, truly applicable only to infinitely dilute solutions. If they are incorrectly used for solutions of finite concentration, an error is introduced, both for small-molecule and for large-molecule solutes. Comparing measurements for two solutes which are similar except for their size, in the same solvent and a t the same concentration and temperature, the magnitude of the error in the calculated reciprocal of the molecular weight (l/M*) is about the same in the two cases. This leads to a much greater error in the molecular weight in the case of a macromolecular solute than in the case of a small-molecule solute. This may be illustrated by Figure 1, which shows the relation between osmotic pressure (II, in atmospheres) and concentration ((72, in grams of solute per cc. of solution), for solutions in dioxane of two fractions of chlorinated polyvinyl chloride. The equation, II RT
G
=
z
A THEOmTICAL
explanation for the approximate rectilinear relation between II/CZ (or 8/C,) and Ct was furnished by the statistical treatment of the thermodynamic properties of long-chain molecules, developed independently This theoreb by Flory (6, 6) and the writer (7,8,9,18,16). ical treatment also explains the different slopes of the limes obtained for different systems in terms of molecular p r o p erties and accounts for the deviations from the straight-line relation which occur at higher concentrations. The new theoretical equation, for the osmotic pressure case, may be written
where dl, & = densities of solvent and solute, respectively M I , M2 = molecular weights of solvent and solute, respectively pi = a constant depending on nature of solvent and solute, but not on molecular weight of the latter The second term on the left in Equation 2 is negligible for many osmotic pressure studies. This is also true of the terms involving higher powers of CZ,represented in the equation by dots. Inclusion of this second term would lower the points a t highest C2values (Figure 1) only about 0,004, approximately the width of the straight lines in the graph.
2
where R = gas constant, cc. atm./degree mole T = absolute temperature is thermodynamically correct a t infinite dilution. Extrapolation of the experimental data, plotted in Figure 1, to infinite dilution (Cz = 0) gives intercepts indicating, according to Equation 1, molecular weights of 48,000 and 242,000 for the two fractions. If, however, one (incorrectly) substitutes the observed II/C2 values into Equation 1, “molecular weights” ranging from 35,000 to 49,000 for one sample and from 82,000 to 172,000 for the other are deduced. The error resulting from the use of Equation 1for solutions of finite concentration (in the usual experimental range) is thus far from negligible and is greater, the larger the molecular weight (other things being equal). The diflkulty is aggravated by the fact that accurately measurable values of thexosmotic pressure of high polymer solutions are not readily obtained in very dilute solutions. Although still neglected by some workers (17, 18, 19) these facts have been recognized by others (24,@‘I. It has been found empirically that graphs of II/C2 (or 8 / C 2 , if the data are measurements of freezing point depressions, 8)
:
: OJ
OO
0.002
0.004
0.006
CZ
OPOS
0.010
OPIZ
%/CC.
-
Figure 1. Dependence of Osmotic Pressure on Concentration for Solutions of Two Fractions of Chlorinated Polyvinyl Chloride (Per Cent C1 66) in Dioxane at 27 C. Datn by Staudinger and Sahneiders (33);
980
pi
-
0.38
INDUSTRIAL AND ENGINEERING CHEMISTRY
September, 1943
981
mains constant) without the introduction of additional terms. ~1 directly, as the slope of the straight line obtained. Once plis known for a given polymersolvent combination, a single good osmotic pressure or cryoscopic measurement suffices to determine the molecular weight of the solute. (Of course one must not assum2 the same value of p1 for two copolymers consisting of the same monomeric units but in different proportions. or for two polymers which are otherwise chemically different.) The apparent slight variation of p~with average molecular :e;ht, (Figure 6) for polymethylmethacrylate fractions in aeetone is probably the result of slight chemical Werences between the average molecules of the different fractions or of the presence of small amounts of impurities, rather than a true dependence on the molecular weight of the polymer.
It also give13the conatant
AMPLE8 of high polymers, as normally obtained, are
c
gflO0Cc.
Figure 2. Dependence of Osmotic Pressure on Concentration for Solutions of Polyisobutylene in Cyclohexane at 25O C. p a "r;."" (4). T h e ordlnnta IM n/c for the aued a i d e . ,
