KINETICS OF A SEQUENCE OF FIRST-ORDER REACTIONS

Solutions are obtained for the finite set of coupled rate equations ∂Ci/∂t=αi, i-1C i-1+αi, iCi+α i, i+1Ci+1 (i=0, N), where αi, j are given in general as αi, i-1 = A, αi, i+1=B, αi, i= -(A+B), except that α0, 0 = -α1,0= - α, αNN= - αN-1, N= - b, α0, -1 =αN, N+1 =0. Asymptotic expressions are given for the approach to equilibrium as a function of the various rate parameters and the chain length N. For large N, we find that if A < B, the eigenvalue spectrum approaches a continuum, and the approach to equilibrium is described by a simple relaxation time λ1≃(A 1/2-B1/2)2. However, if A (1 -α/A) 2>B, the system exhibits a peculiar eigenvalue spectrum, and the relaxation is characterized by two distinct and well-separated relaxation times, λ1 and λ2 = - α{l-B[A(1-α/A) 2]-1.