Random rods model

For thin rods of length /, it can be shown that L = 112 [27]. Estimate K for fibrinogen, which can be approximated as a thin rod of length 700 A, partitioning into a porous solid with s = 0.012/A. What does K change to if all pore dimensions are exactly doubled in size Assume the applicability of the random-plane model of pore space. 

The kink-jump technique applies random local rotational jumps along the chain. An algorithm for the bead-rod model would have, for example, the following steps ... 

Fig. 9.— Double Log Plots of (a) Intrinsic Viscosity, (b) the Reciprocal of the Diffiision Coefficient, and (c) Sedimentation Coefficient Data versus Molecular Weight for Human Cervical Mucins. [Key and O, whole mucins and , subunits and A, T-domains. Molecular weights determined from Zimm plots (filled symbols) or the Svedbeig equation using QLS (open symbols). Values for the slopes are in all cases consistent with a random-coil model and not with a rigid sphere or a rod.]...

Fig. 25 Agarwal and Mashelkar s modified bead-rod model for grafted chain in elongational flow [209]. The backbone has p uniformly distributed side chains. Each side chain is modeled as a random coil and has g beads with bead size 2c. The hydrodynamic force exerted on the coils adds additional force to the backbone so the force along the linear backbone consists of two part

Ever since Hermann Staudinger developed the macromolecular hypothesis in the 1920s (41), polymer scientists have wondered about the spatial arrangement of polymer chains, both in dilute solution and in the bulk. The earliest models included both rods and bedspring-like coils. X-ray and mechanical studies led to the development of the random coil model. In this model the polymer chains are permitted to wander about in a space-fiUing way as long as they do not pass through themselves or another chain (excluded-volume theory). 

In the limit of zero scattering angle the rod model and the random orientation correlation approach can formally be connected. At small angles can be expanded as a series in h (18,17, ), yielding... 

Many investigators have used the Ogston model and its fundamental idea as a basis for their models. Most recently, Johansson and Elvingson [182] obtained the probability distribution g(r) for spaces in a random suspension of fibers i.e., the probability that a randomly chosen point in a network of fibers is found at a radial distance r to the fiber of closest approach. For a cylindrical cell (CC) model, which consists of an infinite cylindrical cell, containing solvent and polymer, with the polymer represented as a rod centered in the cell, they obtained g(r) for one cylindrical cell as... 

Existing SEC retention theories have been independently developed for each of the molecular-shape models shown in Figure 1. The deep hollow cyclin-drical pore in the figure (A, B, and C) illustrates the SEC exclusion effect on three types of solute molecules, hard-sphere, rigid-rod, and random-coil, respectively. The individual theories and their bases of commonality are now reviewed briefly. 

Note 1 The model describes the whole spectrum of chains with different degrees of chain stiffness from rigid rods to random coils, and is particularly useful for representing stiff chains. 

Model simulating the hydrodynamic properties of a chain macromolecule consisting of a sequence of beads, each of which offers hydrodynamic resistance to the flow of the surrounding medium and is connected to the next bead by a rigid rod which does not. The mutual orientation of the rods is random. 

By using a model of the gel phase in which the gel matrix was assumed to consist of straight, rigid rods that were infinitely long and randomly distributed, Laurent and Killander54 derived the equation... 

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