Kratky-Porod equation

In the rod limit, Le = L, and de = d. On the other hand, in the coil limit, Le - V6de, if we assume the chain to be in the unperturbed state. It is to be noted that the axial ratio of the fuzzy cylinder is greater than unity even in the coil limit. At intermediate N, L and the axial ratio Le/de may be calculated, respectively, from the Kratky-Porod equation [102,103] for the (unperturbed)... 

Lumpkin, D jardin and Zimm38 used Eq.(13) to study the effect of a pore size distribution, but did not assume that . a- for each pore. Instead, they calculated -(a.) for each pore size a. by solving the Kratky-Porod equation l. However, as explained above, one cannot obtain Eq.(13) from the very general Eq.(lO) in this case therefore, their results, which showed that the pore size distribution has a strong effect on the electrophoretic mobility, are not reliable for quantitative comparisons. 

Fig. 3.20. Form function H(q) of a Kratky-Porod chain in the infinite limit, according to ref. 20. Here fp is the persistence length and Nlp the length of the curve. The product y = N(qlp)2 H (q) is a function of (qlp) and the asymptot represented by a dashed line is given by the equation y=n(qlp) + 2/3.

Equation (8.173) indicates the analogy between the change of (.y) of the Kratky-Porod model and the time evolution of u(i) in rotational Brownian motion both processes are Gaussian with the constraint 1,2 = 1,35 pjqjj gqn (g.i74) it can be shown that for small s... 

From their light-scattering measurements Holtzer, Benoit, and Doty (126) concluded that the short-range interactions control the dimensions of cellulose nitrate chains, and they discussed their results in terms of the worm-like chain model of Kratky and Porod (142), obtaining a persistence length of about 34.7 A. In Fig. 21 these data are shown as a plot of (S yjMw against Mw. The open circles are the experimental points and the broken curve is that calculated from the equations for the worm-like chain model. The theoretical curve is claimed to reproduce the data to within the probable experimental error in all but two cases. 

The two regimes can be easily seen with a Kratky plot, q2g(q) = f(q), suggested by Kratky and Porod (14) see figure 4. The plot shows the transition between the gaussian coil behavior and the rod conformation, l e location of die intersection between the two regimes depends on the local rigidity of the chain. With equation 3-29 and 3-36 we obtain the point intersection between the two asynqitotos... 

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