Kuhn segment persistence length

Since the memory stretches in both directions, the Kuhn segment of length must be roughly twice as big as the persistence length /. This is indeed true. Moreover, the relationship = 2/ is exact for a worm-like polymer chain (see Section 2.3) it is also valid for other models, although only approximately. 

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... 

Kuhn was the first to point out that the dimensions of a chain with given persistence p may always be described as if it were completely flexible (see (5.1.1)) by grouping a number of monomer units together into statistical chain elements (s.c.e.) or Kuhn segments. The number a of bonds in such an s.c.e. is the larger the stlffer the chain. The basic idea is that such s.c.e. s may be considered as orlentatlonally independent they are then independent subsystems as defined in sec. 1.3.6. The real chain of N bonds is now modelled as an equivalent ideal chain of = N/a s.c.e. s and the Kuhn length becomes bt (where a > 1, b > 1). Then (r ) = vdilch equals = 6pN(, provided that a... 

For EC, Bheda, Fellers and White find Vp/Vp = 1.43 in dichlordacetic acid and 1.18 in acetic acid. For HPC, they report v /vp = 1.29 to 1.37 in four different solvents. These results are compatible with the theory for monodisperse rods. It is to be noted that polydispersity of segment lengths should be unimportant if the chains are uniform in structure and composition or, more generally, if dissipation of directional persistence over the span of a Kuhn segment is the result of a number of restricted changes in chain direction. Hence, corrections for polydispersity should not be required for chains conforming to the representation here adopted. 

The rigidity of a chain is characterized by the statistical segment A introduced by Kuhn For long chains the Kuhn segment is equal to the doubled persistence length (A = 2a). 

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... 

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. 

In principle, the persistence length should vary with temperature. The higher the temperature of a chain, the more it bends, and hence, the shorter its persistence length and Kuhn segment. However, in most cases this dependence is not important, since the range of temperatures where polymers may even exist is not that wide. 

Correiations of Bond Orientations of an ideai Chain the Persistence Length the Kuhn Segment... 

Kawaguchi et al. 1998). Hence, one may conclude that the process of repetition at the PS-PS interfaces is controlled by an elementary act of a-relaxation (conformational transitiorrs in the chain backbone), and the persistence length of this kinetic rmit is eqtral to statistical Kuhn s segment. Second, both the values of E (D) at the interface and of E ( )"" are smaller than those of E (D) in the brrlk (Jou, 1986) and E (a) " (Bershtein et al., 1994) by a factor of 2. It indicates that the decrease in at flee polymer... 

Let us consider a polymer chain which contains N monomer links with persistence length I (Kuhn length 21) and width d. The free energy in a polymer can be written as the summation from the contributions of elastic energy, interacting energy between links (or segments), osmotic term (translational entropy of the counter ion) and Coulomb interaction. 

Recalling from Eq. (2) that each Kuhn segment equals two persistence lengths [53], we find that for a wormlike chain a minimum of... 

---