Kuhn statistical segment length

ATBN - amine terminated nitrile rubber X - Flory Huggins interaction parameter CPE - carboxylated polyethylene d - width at half height of the copolymer profile given by Kuhn statistical segment length DMAE - dimethyl amino ethanol r - interfacial tension reduction d - particle size reduction DSC - differential scanning calorimetry EMA - ethylene methyl acrylate copolymer ENR - epoxidized natural rubber EOR - ethylene olefin rubber EPDM - ethylene propylene diene monomer EPM - ethylene propylene monomer rubber EPR - ethylene propylene rubber EPR-g-SA - succinic anhydride grafted ethylene propylene rubber... 

Here we have chosen the Kuhn statistical segment length (=2q) as the unit for measuring length. The partition function Z of the total chain is given by... 

When all lengths associated with polymers are measured in units of the Kuhn statistical segment length 2q, the thermodynamic functions AF, II, and g, given by Eqs. (19)-(21), contain two molecular parameters N = L/2q and d s d/2q and two state variables c = (2q)3 c and a. Thus, numerical solution to Eqs. (23) and (31) provides ci, cA, and a as functions of N and d. The results for the phase boundary concentrations have been found to be represented to a good approximation by the following empirical expressions ... 

Unperturbed Dimenaons.—The most fundamental model of the statistics of a polymer in solution is the linear Gaussian chain, which exhibits the Markovian property that the mean square end-to-end distance o is directly proportional to the number of chain segments i.e. ounperturbed dimensions , and b is the (Kuhn) statistical segment length. 

The interfacial tension increment. Ay = y yo, was linear with the copolymer volume fraction, calculated for low concentration of the copolymer additive as suggested by theory for concentrations below the CMC. The slope of the fitted line was —37.0, and thus d was estimated to be 38 nm, or 63.5b when the geometric mean of the Kuhn statistical segment lengths of the two segments was used as 0.6 nm. This value of d ( 63.5 monomer units) was about 24% of the contour length of the copolymer chains and, thus, indicated an extended configuration of the copolymer chains. 

Here y N is the degree of incompatibility of the species, k-g, is the Boltzmann constant, T is the absolute temperature, 4> is the average copolymer volume fraction, and b is the Kuhn statistical segment length. Formally, the same expression for yo would be obtained if there were no copolymer chains in the system. 

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