A contribution to the study of random degradation of chain polymers

A uniform rigorous mathematical treatment is presented for the random degradation of chain polymers, including the three fundamental initial states, viz., (a)a finite single chain (b)a number of chains of equal length, and (c)a number of chains of varying lengths. Limiting expressions are derived for the number fraction and weight fraction of chains of a given degree of polymerization, theoretically obtainable for a given degree of degradation in all three cases. The stochastic approach is employed for the derivation of the mathematical expression for the degree of degradation as function of time. It is assumed in the derivation that the probability P that a given bond still unbroken at the time t will break in the time interval between t and t + Δt is of the form P = φ(t)Δt, where φ(t)is not necessarily a constant. Instead of the well known formula α(t)= 1 − exp { − kt} an empirical formula α(t)= 1 − exp { − ktm} is proposed; this formula includes the former as' a special case (when φ(t)= const.), and is shown to better fit the experimental results obtained in studies on the degradation of cellulose and of polystyrene solutions.