Kuhn statistical length

Within the framework of this model, the DNA chain is characterized by three parameters the bending rigidity, measured in terms of the persistence length, a, or the Kuhn statistical length (6 = 2a) the torsional rigidity C the DNA effective diameter, d. Numerous properties of linear and circular DNA molecules can be quantitatively understood in terms of the elastic rod model and the same set, under given ambient conditions, of the above three parameters. 

Poly- -hexylisocyanate is a semirigid chain. Samples cover from 0.8 up to 50 or 100 Kuhn statistical lengths. A phase transition out of the isotropic phase occurs... 

Figure 8.49 Plots of F versus X for AB-type diblock copolymers having the same Kuhn statistical length (// = ) for various values of block length ratio 9 (1) 1/10, (2) 1/3, (3) 1/2, (4) 2/3, and (5) 9/10. (Reprinted from Kim and Han, Macromolecules 25 271. Copyright 1992, with permission from the American Chemical Society.)...

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... 

If the persistence length Ip is much larger than the mean chain diameter, d, Yamakawa and Fujii gave limiting values for ai = - ln(d/2Ip) and = 0.1382. Freire and Garcia de la Torre [122] have considered further these coefficients. The factor 2Ip appears rather than Ip simply because 2Ip is equivalent to the statistical Kuhn segment length... 

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 ... 

To a first approximation, the maximum elongation due to stretching effects can be calculated using the statistical length L of the molecules according to Kuhn,... 

Several parameters, most of which are interrelated and can be estimated in terms of each other, are utilized to describe the conformational properties of polymer chains [1,2]. These quantities include the steric hindrance parameter a, the characteristic ratio Cx, the persistence length Ip, the statistical chain segment (or Kuhn segment) length lk, the root mean square radius of gyration Rg (often briefly referred to as simply the "radius of gyration"), and the molar... 

A measure of the stiffness of the amylose molecule in dimethyl sulfoxide can be obtained from the parameters of the various hydrodynamic theories. For example, the length of the Kuhn statistical segment. Am, calculated from Cowie s data is of the order of 95 A., corresponding to 18... 

Flory, P. J., Statistical Mechanics of Chain Molecules, Hanser Publisher, New York (1989). To express the stiffness of a chain, the worm-like chain is a useful model, which is characterized by two parameters the persistence length Ip and the contour length L. In the limit of L/lp —> oo, the Kuhn segment length as defined by Eq. (1.32) is twice the persistence length. 

This equation states that the statistical segment length L increases with increasing values of rj. Thus a stiffer chain has a larger 17, a larger L and a smaller Z. The Kuhn segment length is thus adjusted to account for chain stiffness. On the other hand, L depends on temperature since freedom of rotation, and hence, chain stiffiiess, is temperature dependent. 

Taking into account that the effects of short-range ordering, e.g., of fixed valence angles and hindrance of internal rotation [3, 4], do not change the shape of the distribution function and the correlation Rg-N but increase Ro, that can be interpreted in terms of increase of a statistical length of an equivalent Kuhn chain segment [5]. 

Values of domain size and separation were discussed in terms of Helfand s NIA theory, tacitly assuming that the two components of the block copolymer constituted a symmetric polymer pair, i.e. equality of Kuhn statistical step lengths, b, and monomer molar density. Whilst this is approximately true for values of b for styrene and isoprene, the densities are quite different. However, calculations of domain size and domain separation as a function of molecular weight for both styrene and isoprene domains show that both types have the same molecular weight dependence and moreover the difference in the values for either styrene or isoprene domains is negligible. Figure 10... 

Fig. 11. Master curve for thickness (t) dependence of Tg of thin films of pol3m(iers that have no specific interactions with the substrate (72). The equation for the curve is Tg = t /(l+t ) where Tg = Tg(t)/Tg(bulk), Tg is in Kelvin, t = tIL, and L is the statistical chain (Kuhn) segment length. By contrast, if strong specific interactions between the polymer and the substrate result in restricted interfacial region mobility, the behavior becomes very different from what is shown below and Tg may instead increase with decreasing thickness.

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. 

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