Kuhn segment length

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... 

Table 1. Molecular-weight averages, monomer lengths (/) and estimated upper value of the Kuhn segment lengths (/k) of the poly[2]catenanes 48, 49, and 59, and the poly[2]catenands 51, 56.

Beyond that, we succeeded in extracting unperturbed dimensions of NaPA chains under both solvent conditions. Expressed in terms of the Kuhn segment length, a value of l = 4.2 nm could be established for both solvent conditions [54]. Having thus available a constant value for 4 for inert salt levels... 

The position of the secondary minimum of the total free energy plus the thickness of a platelet (1 nm) was considered as the equilibrium separation between layers. The surface charge density was assumed to be constant. The Kuhn segment length was evaluated using the expression... 

It does not affect the exponents in the equation (i.e.. the dependence of on N), however, but simply introduces a prefactor. This suggests a different approach, where we consider the number of adjacent bonds whose combinations of allowed rotations essentially behave like a freely jointed unit when taken collectively. We would then have Nx effective segments each of length lp known as the Kuhn segment length (Figure 8-36), defined in Equation 8-12 ... 

A modification of the lattice model to account for semi-rigid polymers replaces the contour length, L, in the axial ratio with the Kuhn segmental length (34,35) i.e., x is replaced with xk = 2q/d... 

Figure 11.18. Effects of crosslinking on the brittle fracture stress of styrene-divinylbenzene copolymers. Note the catastrophic embrittlement at very high crosslink densities (i.e., at an average number of repeat units between crosslinks less than the Kuhn segment length of 8 repeat units). The data point (not shown) for the uncrosslinked limit (polystyrene) is at (°°,41).

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... 

FIGURE 15 The dependence of Kuhn segment length A on sulfone fragments contents... 

FIGURE 16 The dependence of macromolecular coil fractal dimension on Kuhn segment length for PESF. 

FIGURE 17 The dependence of glass transition temperature T on Kuhn segment length T for PESF. 

TABLE 10 The comparison of Kuhn segment length values, obtained by different methods. 

FIGURE 23 The dependences of macromolecular coil fiactal dimension on Kuhn segment length A for aromatic polyamides (1,2) and other polymers according to the data of chapters [5,57,61 ] (3). The values A for aromatic polyamides were accepted according to the data of chapters [58] (1) and [59] (2). 

Thus, the corrections performed above allowed making more precisely the carried out earlier estimations of Kuhn segment length for aromatic polyamides. The comparison of the corrected and estimated in Ref [58] A values has shown, that the proposed in the last chapter the estimation A mode results in understated about in 2-3 times magnitudes. The correspondence of mean values of range, cited in literature, and corrected by... 

FIGURE 24 The dependence of Kuhn segment length on macromolecular coil fiactal dimension for flexible-chain polymers. The straight line—calculation according to the Eq. (54), points— the data of Ref [65]. 

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