Rotational Diffusion Processes in Segmented Polymers. Theory and Computer Simulations
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- Institutt for fysikk 
All biological macromolecules (DNA, RNA, proteins, polysaccarids) are polymers. These are extremely complex systems, with thousands or millions of atomic degrees of freedom. However, a range of important properties of such systems do not depend on the detailed atomic structure, but on geometrical structure on a much larger length scale. Rheological properties [1, 2, 3] as well as properties related to rotational diffusion [4, 5, 6, 7, 8, 9] of whole molecules are important examples. This justifies the use of coarse graining models, where exible coils with a continous stiffness distribution , chains of beads [1, 11, 2, 12] or chains of stiff segments [13, 14, 15, 16, 17] are used to represent the molecule. While simple compared to a model with detailed descriptions of positions and motions of individual atoms of a molecule, the mathematical complexity of these models is still significant, and only a few special cases can be solved analytically . Numerical simulation techniques are thus important tools in the study of polymer systems . This introduction first presents a general background and motivation for Brownian dynamics (BD) simulations of polymer systems (Sections 2-3). Then an overview of BD algorithms for the bead-spring and bead-rod polymer models are given (Section 4). While the resulting algorithms presented are equal to those presented in the literature [18, 19], a slightly different path is followed while deriving the algorithms. Finally an overview of the nuggetspring chain and nugget chain models is given (Section 5). Aspects of these algorithms are covered in detail elsewhere in this thesis, but for completeness and comparation with the bead chain models, an overview is given here.