Kuhn chain 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... 

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]. 

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. 

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, b denotes the Kuhn s statistical segment length. The network is represented by a huge chain internally cross-linked at cross-linking points where it touches and at the surfaces of Mf filler particles. The point-like local cross-hnk constraints are easy to handle and can be represented by the term... 

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 first model (Kuhn chain) is built up by planar segments of limited conjugation length which are separated by defects, e.g. cis double bonds. The second concept of a worm-like chain (Porod-Kratky chain) visualizes a continuous... 

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. 

Fig. 13 Above Schematics of a hairy-rod polymer consisting of a stiff backbone and flexible covalently connected side chains. N, Zk, and v are the number of segments, the segment length (the Kuhn length), and the volume of the beds of the side chains, respectively M, Zu, L, and d are the number of the repeat units, distance between grafting points (the unit length) and the length and diameter of the rod, respectively. Below. End-on schematics of (a) nematic (Nem) and (b) hexagonal (Hex) phase of hairy-rod molecules. Adapted from [24]...

Length of the i th type of bond along the shortest path across the chain backbone. Length of a statistical chain segment (Kuhn segment). 

---