Fibonacci Ratio in a Thermodynamical Case

FIBONACCI RATIO IN A THERMODYNAMICAL CASE 239 the three results occurring at the end of Section 3, it is possible to deduce the coefficient of x k ~ 1 when k is even. The coefficient is k L 3(k-2) 3* 5(fe-2)(k-4) k-1\ 2(k-3) 2 • 4(fc-3)(&-5) 3-5-liX-2)(k-4)(fe-6)) 2 • 4 • 6(fc-3)(fc-5)(k-7) + " J ' the expression within the brackets terminating, since k is even. Consider the thermodynamics of an infinite chain of alternately spaced IE molecules of donors and acceptors (N-> • °°) , and assume there is an average of one mobile electron per molecule (as is quite common for some one-dimensional organic crystals [1, 2]). Each molecule may contain a maximum of two such electrons and as the temperature is raised two electrons may jump onto the same molecule. Because electrons repel each other,, it costs an energy U D or U A to put two electrons on a molecule type D or type A, respectively5 a common situation is that U D » U A. Under these conditions, it can cost almost no energy to have sites A doubly occupied, while double occupancy of sites D is effectively eliminated.