ELECTRIC FIELD DEPENDENCE OF DIFFUSION AND TRAPPING IN POLYDIACETYLENE

ELECTRIC FIELD DEPENDENCE OF DIFFUSION AND TRAPPING IN POLYDIACETYLENE 

Transport in low-dimensional systems exhibits a rich variety of novel features. This manifests itself in unusual electric field and time dependences of drift velocities, Onsager generation rates, and survival fractions in the presence of deep traps. These features are indeed observed in the polydiacetylenes which are expected to be ideal quasi-one-dimensional substances. 

Once a free carrier has been created, we then encounter a further class of fascinating transport phenomena associated with the low dimensionality of the system and this is where we want now to focus our attention upon. Let us first consider the diffusion of carriers along a one-dimensional chain. A realistic view of the polymer backbone in PDA is of course not one of perfect order but every now and again we must expect a defect which leads to the formation of a trap (or anti-trap) with probability s [5]. In addition, carriers will also eventually reach recombination centres which lead to the total annihilation of the charge [6]. Depending on the time temperature domain, an ordinary trap may be indistinguishable from a recombination centre. We therefore 

The photocurrent measured experimentally j(t) can be more conveniently analysed in the space of the Laplace variable p 

The field and frequency dependence of the drift velocity Vd(P n) in a 1-d system has been analysed in great detail in references [5,9] using mean field theory and scaling theory. The disorder was described by allowing a subset of the diffusion or jump rates W to differ and follow a distribution function p(W). We shall not repeat all the details here but only recall the main conclusions [9] the linear response relationship between and the diffusivity D in the low field limit n l given by 

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