Macromolecule random walk model

K. W. Foreman and K. F. Freed (1998) Lattice cluster theory of multicomponent polymer systems Chain semiflexibility and speciflc interactions. Advances in Chemical Physics 103, pp. 335-390 K. F. Freed and J. Dudowicz (1998) Lattice cluster theory for pedestrians The incompressible limit and the miscibility of polyolefin blends. Macromolecules 31, pp. 6681-6690 E. Helfand and Y. Tagami (1972) Theory of interface between immiscible polymers. 2. J. Chem. Phys. 56, p. 3592 E. Helfand (1975) Theory of inhomogeneous polymers - fundamentals of Gaussian random-walk model. J. Chem. Phys. 62, pp. 999-1005... 

The characteristic feature of a macromolecule in solution is its high degree of conformational freedom. The simplest possible model for an isolated macromolecule is the random walk (or... 

It should also be remarked that, in attempts to find the actual configurations of macromolecules, lattice models have played important roles (73). The main interest here is the investigation of self-avoiding walks on a given lattice as a model of a real chain. One tries to find, for example, the mean square length of the random walk as a... 

The study of pol5rmeric fractals in different states started directly after the publication of Mandelbrot s fractal conception [1], that is, about at the end of 70s of the last century. The cause of the indicated approach application for a pol5rmer macromolecules analysis is obvious enough it is difficult to find a more suitable object for fiuctal models application. One from the first research in this field with the experimental method of electrons spin-relaxation for proteins [2] found, out that the protein macromolecule dimension was equal to 1.65 0.04, that coincides practically exactly with the dimension of 5/3 of random walk without self-intersections, by which a polymeric macromolecule is usually simulated [3]. 

The standard model for diffusive motion in polymers is Brownian diffusion, which occurs as a series of infinitesimal reorientational steps. This model is most appropriate for intermediate-to-large sized spin probes and spin-labeled macromolecules, where the macromolecule is much larger than any solvent molecules. Because of this broad applicability, the Brownian diffusion model is the most widely used. This type of rotational diffusion is completely analogous to the one-dimensional random walk used to describe translational diffusion in standard physical chanistry texts, with the difference that the steps are described in terms of a small rotational step 59 that can occur in either the positive or negative direction. In three dimensions, rotations about each of three principal axes of the nitroxide must be taken into account. A diffusion constant may be defined for each of these rotations motions, in a way that is completely analogous to the definition of translational diffusion constant for the one-dimensional random walk. 

---