Kratky-Porod chain

The vector field entirely and uniquely determines the stream lines and their properties. As we focus our attention on the mesoscopic properties of stream lines, assuming that they can resemble a polymer-like amorphous packing of chain backbones, we have to consider in greater detail their intrinsic properties. As shown in the next section, Santos and Suter [98] elaborated a model for generating packing structures of Porod-Kratky chains. 

Note 2 In the literature this chain is sometimes referred to as Porod-Kratky chain. 

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... 

The quantity a is called the persistence length and is a measure of chain stiffiiess. The wormlike chain model (sometimes called the Porod-Kratky chain) is a special continuous curvature limit of the freely rotating chain, such that the bond length I goes to zero and the number of bonds n goes to infinity, but the contour length of the chain L = nl and the persistance length a are kept constant. In this limit... 

Nagai K. Theory of light scattering by an isotropic system composed of anisotropic units with application to the Porod-Kratky chain. Polym J 1972 3 67-83. 

ILS experiments indicate a semi-rigid behavior for the PDA chains. Therefore we can expect to observe the form factor of the Porod-Kratky chain. More precisely, the q scattering behavior of a rod like molecule should be measured since the normalize form factor P( of an infinitely long worm-like chain has the asymptotic form ... 

The most austere representation of a polymer backbone considers continuous space curves with a persistence in their tangent direction. The Porod-Kratky model [99,100] for a chain molecule incorporates the concept of constant curvature c0 everywhere on the chain skeleton c0 being dependent on the chemical structure of the polymer. It is frequently referred to as the wormlike chain, and detailed studies of this model have already appeared in the literature [101-103], In his model, Santos accounts for the polymer-like behavior of stream lines by enforcing this property of constant curvature. 

A comparison is presented between the behavior of unperturbed stars of finite size whose configurational statistics are evaluated by R1S theory and the Kratky-Porod wormlike chain model. Emphasis Is placed on the initial slopes of the characteristic ratio, C, or g when plotted as a function of the reciprocal of the number of bonds, n. 

The Kratky-Porod wormlike chain model [20,21] is widely used for describing conformational characteristics of less flexible chains. The polymer is viewed as a semi-flexible string (or worm) of overall contour length L with a continuous curvature. The chain is subdivided into N segments of length AL, which are linked at a supplementary angle r. The persistence length q (Fig. 1) is defined as... 

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)... 

The structures of linear PS chains as well as of generated RIS backbone chains are discussed in the light satisfactorily by the theory of Kratky and Porod, if the system is under 9 conditions. 

Finally, it should be mentioned that an interesting interpretation of the third eq. (5.4) is obtained by introducing the model of the worm-like chain, as developed by Kratky and Porod (153, 154). As is well-known the characteristic quantity of this model is the persistence length, i.e. the projection of the end-to-end distance of an infinitely long coiled worm... 

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