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An annealed average over the surface randomness corresponds to an average at the partition function level. Odijk (Ref. 15) implicitly assumes that the random interactions are an annealed random variable by averaging the equations for the polymer Green function. The polymer Green function is a partition function too, albeit a restricted one, hence Odijk's equation is for the annealed case too, and the equivalence with the equation of Andelman and Joanny (Ref. 16) should not come as a suprise.
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Only in the limit of infinitely long chains the adsorption-desorption transition has the characteristics of a real phase transition.
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