Copolymerization Near a Selectively Adsorbing Surface

From the facts presented above, it is evident that the copolymer sequences discussed here are correlated throughout their whole length. Also, it was found that any sufficiently large part of the averaged sequence has practically the same correlation properties as the entire sequence. This means that the generated sequences show scale invariance, a feature typical offractal structures. 

To gain some further insight into the discussed problem, the block length distribution functions /a( ) and were calculated, using both Monte Carlo simulations and the analytical probabilistic model [88]. 

In the oo limit, the distribution over strongly adsorbed blocks/a (f) is described by the following conditional probabibty distribution function 

For copolymer chains of a finite length N, the probabibty distribution over the length of blocks is given by [88] 

One can show that the block length distribution function /b( ) is characterized for asymptotically large l by the power-law decay of its density /bCO a ta with the exponent a = 3/2 [88]. The exponent a estimated from the simulation data (a % 1.6) is, up to the experimental uncertainty, quite close to that predicted by the exact analytical model. As has been noted above, such a power-law decay is a characteristic of the Levy probabilistic processes [36]. 

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Radical graft copolymerization near a selectively adsorbing surface... 

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