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Effect of residual interactions on polymer properties near the theta point
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20.The calculations of Martin yield the results where is Avogodro’s number, M is the molecular weight, is the binary cluster integral, is the traditional binary z parameter, and φ is a conveniently chosen dimensionless parameter proportional to the width of the intermolecular potential (analogous to the cut‐off parameter in our calculations). An important constraint on the magnitude of φ, namely, follows from (d) by the requirement that if Substituting this into (b) and (c) yields a minimum value of of Thus, to within experimental uncertainty, the Martin model predicts no observable change in or, very likely, in any other ratio of theta observables. The contributions considered by Martin involve corrections due to the range of the binary interactions which are irrelevant to the description of large length scale theta point polymer properties, a conclusion readily established by the theoretical arguments in Sec. II. Also the existence of correction seems to violate the scaling arguments of Sec. II A. These small contributions are associated with the factorization approximation (see Ref. 18) which was implicit in our scaling argument.
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