長鎖モノオレフィンの二重結合分布の理論的計算方法

抄録

Theoretical double bond distribution in the positional isomerization of higher straight chain monoolefins (carbon number n+1) has been investigated by considering the formation of j (=1, 2, …, n) -isomer of which double bond being located between j-th and j+1-th carbon to be in conformity with a stochastic process. The molar fraction of j-isomer at reaction time t can be considered as a probability x (j/t) having parameter t (≥0). The probability mass function x (j/t) is basically expressed as follows;
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of which initial conditions to be given by
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where u (k/t) is a probability of being positionally isomerized k (=0, 1, …, ∞) times for the reaction time t and v (j/k) is a probability of the formation of j-isomer after being positionally isomerized k times. The u (k/t) is given by the probability of Poisson process of which parameter is λ. The v (j/k) depends upon the mechanism of positional isomerization, and it is given by the probability of binomial distribution in case of the mechanism via half-hydrogenated state as well as via π-allylic state. The probability mass function x (j/t) is finally deduced to
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The function shows that the stochastic process of the double bond distribution is one of the compound Poisson processes. The mean of j at reaction time t : <j>t is equal to that at reaction time 0 : <j>0;
<j>t=νx (ν/0) +ξx (ξ/0) +…+ρx (ρ/0) =<j>0
and the variance of j at reaction time t : σjt2 is given by
σjt²=1/2λt+σj0²
σj0²= (ν-<j>0) ²x (ν/0) + (ξ-<j>0) ²x (ξ/0) +…+ (ρ-<j>0) ²x (ρ/0),
where σj02 is the variance of j at reaction time 0. Hence using the experimental data of σjt2 and σj02, the parameter λ which is considered to be a first order reaction rate constant of the double bond distribution is determined by the following equation;
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Theoretical results of the double bond distribution were in good agreement with experimental data presented by Shiina, Subbaram, and Knegtel.