A SUPPLEMENTARY NOTE ON A THERMODYNAMIC MEASURE OF POLYMERIZATION BY M. M. GARVER
In a former paper' t o which this note is merely supplementary, I gave an exposition of what seemed to be sufficient theoretical grounds for a thermodynamic theory of polymerization. The principal arguments were drawn from an interpretation of the following equation which will be referred t o as equation (A) :
'
For the origin and significance of the equation the previous papers may be consulted. The conclusions drawn from this equation, no doubt, appeared rather speculative and were not entirely satisfactory as a basis for a thermodynamic theorem; but the applications of the theory gave surprisingly consistent and satisfactory results. The results of the theory tended to support the theory which might be regarded as not quite established but as one which might ultimately be established. There was left in my mind, and no doubt also in that of others, a question as t o the significance of the ratio p/m; as t o whether it had the same significance independent of polymerization. So long as this remained in doubt, the exact law of force could not be definitely determined; and for thermodynamic purposes this is all-important. We must know the law of force before we can determine the heat equivalent oE the work due to the forces. All ambiguity may, however, be removed by an entirely different derivation of the above equation (A), so that the exact law of force is shown and the whole theory put upon a simple, indisputable, experimental, foundation. The basis of the new treatment may be found in a fact t o which I had previously called particular attention' but Jour. Phys. Chem., 16,454 (1912). LOC.cit., p. 245.
680
M . M . Garvey
which was unaccountably overlooked in the former paper. If this proof had occurred t o me a t that time the treatment of the subject would have been quite different, for we may entirely ignore the significance of E as the “range of molecular action ” and proceed experimentally as follows : . Suppose we measure the two ratios.y/p and U / O experimentally, and call their product 7, thus:
. . . . . . . .(B) Since the ratios are experimentally observed values we may substitute for u/w another experimentally observed value in terms of m and RT so that m = RT X U/W. Thus m becomes an experimentally determined molecular weight. Since all the quantities entering into the equation (A) are now either directly observed, or are simple relations of observed quantities, there can be no doubt or ambiguity as t o their meanings. Hence also any effects due to polymerization are eliminated because included in the observations for both liquid and vapor. We see also that exactly similar equations can be found for every liquid and its vapor entirely independently of whether it is polymerized or not. No change in the form of the equation or change in the meaning of the symbols can result from the fact that one liquid, or vapor, is polymerized and another is not. The observed values are required. Hence equation (A) with the above meanings of the symbols is entirely independent of polymerization, for it applies t o every liquid whether polymcrized or not. Although the quantity 7 has a perfectly definite numerical value it remains to ‘determine its physical significance. This we may readily do from equation (B) above, which may be written y/z = ( p / u ) X W . From the theory of dimensions of physical quantities we find that z is an area; for since p and u both represent densities their ratio is a pure number and cancels out. Therefore, T/T is of the same dimensions as o, or is a force per unit area. Since y represents an attraction, the last equation may be expressed in words as follows:
Thermodynamic Measure of Polymerization
68 I
The ratio of the attraction per unit area of cross-section in a liquid film to the pressure per unit area exerted by the saturated vapor is equal to the ratio of the liquid density to the vapor density. Thus without any recourse t o the kinetic theory or to any theory of the molecule ; without any assumptions or hypotheses beyond a simple application of the theory of dimensions used t o establish the physical significance of T, we have established on purely experimental grounds the law of force in liquids and its relation t o the law of force in vapors. Since exactly the same law, except as to sign, is found to apply to both the liquid and vapor phases of a substance, we may safely assume that it applies also t o the change of phase, or, that the attractive forces which are assumed to produce a decrease in the pressure of a vapor must be numerically equal to any decrease in pressure produced by the forces. We have then, it seems to me, a reliable, experimental basis for determining the heat equivalent of the forces acting during an isothermal change in phase; and hence that we have also a secure foundation upon which to build a thermodynamic theory of the degree of polymerization of liquid substances. 1
State College,
AzLg.
Pa.,
12, 1912
