Absolute Values of the Rate Constants for Individual Steps

ABSOLUTE VALUES OF THE RATE CONSTANTS FOR INDIVIDUAL STEPS 

If Ts were somehow determined at the polymerization rate Rpj the ratio 

Methods for Determining the Mean Lifetime of an Active Center—We have previously taken it for granted that experimental measurements are confined to steady-state conditions, where the rate of annihilation of radicals is almost exactly equal to the rate of their formation. Thus it was that we were able to equate Ri to Rt to obtain Eq. (10). At the very outset of the polymerization, however, the radical concentration is zero, and a finite time must be required before it reaches (or closely approaches) the steady state level. Since the rate of polymerization is proportional to the radical concentration, the interval preceding arrival at the steady state must be characterized by an acceleration in the polymerization. 

In order to formulate an answer to the obviously important question of the length of this interval of acceleration and to ascertain under what conditions it may be long enough to observe experimentally, we shall examine the non-steady-state interval from the point of view of reaction kinetics. Let us suppose, however, that the polymerization is photoinitiated, with or without the aid of a sensitizer. It is then possible to commence the generation of radicals abruptly by exposure of the polymerization cell to the active radiation (usually in the near ultraviolet), and the considerable period required for temperature equilibration in an otherwise initiated polymerization can be avoided. Then the rate of generation of radicals (see p. 114) will be 2//a s, and the rate of their destruction 2kt [M ]. Hence 

At the steady state this net rate is zero and [M ]s = flabs/kty , where 

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