Stationary state criterion for free radical initiated polymerization

Autor: Matatiahu T. Gehatia
Rok vydání: 1965
Předmět:
Zdroj: Kolloid-Zeitschrift & Zeitschrift für Polymere. 201:116-123
ISSN: 1435-1536
0303-402X
DOI: 10.1007/bf01520494
Popis: The conditions necessary for the valid assumption of the stationary state during polymerization by free radical initiators have been considered mathematically. A differential equation characterizing the sum of the concentrations of all free radicals appearing in such a system has been solved. A function F derived from this solution approaches unity if a stationary state treatment is justified. A mathematical analysis shows that the stationary state can be achieved only if the arguments of F are large in comparison to unity. Under such conditions, F=1 -1/N, where N is a large number indicating the error limits caused by the deviation of F from unity. Within the limits defined by N, the assumption of stationary state is validif 8(kt/I0/kd)1/2 ⩾ N+ ln 2N, where k d and k t are the kinetic rate constants for initiator decomposition and termination respectively, I 0 is the initial concentration of initiator and f the efficiency factor. Denoting the minimum value of I0 which fulfills the conditions of stationary state as I0, min, and setting I, the actual initiator concentration, to I 0 =n2I0, min, where n > 1 is a stability factor, the assumption of stationary state is justified within the time interval τ ⩽ t ⩽ θ, where τ ≈ 2 ln (2 N)/kdn(N + ln 2 N) and θ=(2/kd− ln [n (N + ln 2 n)/N]. With the aid of the proposed criterion one can determine: (1) if the assumptions of the stationary state are justified under the actual experimental conditions; (2) what the time limit is for which the assumption is valid; and (3) how to achieve the proper conditions to assume validity of stationary state within any given desired limits of time and maximum error.
Databáze: OpenAIRE
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