The determination of the lifetime of active polymeric molecules

In all homogeneous reactions the velocity is determined by the concentration of active or activated molecules which participate in the ratedetermining step. If the nature and reactivity of such molecules are determined it may be said that the mechanism of the reaction is completely established. With one or two exceptions, however, this state of affairs is yet to be reached in chemical kinetics. Polymeric reactions are in this respect even in a less advanced stage of development. As with ordinary chain reactions the expression for the overall velocity contains at least three characteristic coefficients relating to the three main processes controlling the rate. By a straightforward kinetic analysis, no matter how accurate and detailed it may be, it is not possible to determine the individual values of such coefficients. In some of the photochemical reactions it has been practicable to find independently the rate of starting of polymerization or the chain length which means in effect that the ratio of the propagation and termination coefficients may be computed. But there is no way in which the individual value of either of these coefficients may be measured. It is the purpose of this paper to suggest one method how this general problem in polymerization may be approached. In the simplest possible way the velocity of polymerization (R ) is given by the equationR =∑k p (P )(M ), whereP is the active molecule which reacts with the monomer to make the next highest polymer in the series,k p is the corresponding velocity coefficient, and∑ means that all possible kinds ofP molecules must be taken into account. A first approximation in the study of these reactions thus consists in determining∑ (P ). There are, however, no reactions whichP may undergo which could be compared with the polymerization reaction itself in order that the value of (P ) may be computed. Thus the method so useful when hydrogen atoms are involved, namely the measurement of the simultaneous conversion of para-hydrogen, cannot be employed. The value of (P ) may, however, be defined in another way, namelyd (P )/dt = (P )/ז , whereז is the mean lifetime of (P ) andd (P )/dt is the rate of production. If this latter quantity can be determined then (P ) may be computed if some method of measuringז is available.d (P )/dt is not easy to determine, but in some sufficiently simple photo-polymerizations in the gas phase its value may be calculated from the number of quanta absorbed by the system and the efficiency of the primary process in starting off polymerization. As in many photo-reactions the lifetime of the active species is too short to attempt to measureז directly by observing the rate of polymerization when the light or source of primary activation is suddenly removed. A method of integrating a large number of such decay periods can be devised if a rotating sector is interposed between reaction vessel and source of light. This in itself is not sufficient. But if the decrease in the value of the concentration ofP is due to reaction involving twoP molecules, as, for example, in the combination of free radicals, then it can easily be shown that the velocity of polymerization will depend on the sector speed. A transition between two extreme velocities (in which the ratio is √2 : 1) occurs within a comparatively small speed interval which gives almost directly the lifetime ofP (Melville 1937). This method has of course the disability that it will only work providedP disappears at a rate proportional to (P )2 . Another disadvantage of the rotating sector method is that it is confined to a comparatively limited range of measurements,ca . 10-4 to 10-1 sec. The former limit is obviously fixed by mechanical considerations but in any case such short lived molecules are rarely encountered in kinetics. The upper limit is not so seriously handicapped.