Computer simulations on the structure, dynamics and deformation of polymer chains

P.D. Thesis of Markus Wittkop

Group Prof.Dr.D.Göritz

The structure, dyanmics and deformation behavior of single polymer chains at various temperatures were studied by means of computer simulations. The bond-fluctuation model was used which is a coarse-grained lattice model incorporating a dynamical Monte-Carlo process.

Investigations of the probability distribution functions of the end-to-end distance of subchains showed that three principal cases can be distinguished: the subchain is identical to the whole chain (s=0), the subchain constitutes one extremity of the whole chain (s=1), the subchain belongs to the central part of the whole chain (s=2). The distribution functions can be described by scaling functions tex2html_wrap_inline19 for small x and tex2html_wrap_inline23 for large x, x being the scaled distance. Particularly in the cases s>0 unknown values for the exponents tex2html_wrap_inline31 , tex2html_wrap_inline33 and tex2html_wrap_inline35 were determined or the precision of given values were significanltly improved.

Simulations concerning the subchain swelling delivered that the subchains are more swollen than an isolated chain containing the same number of segments. This excess swelling is most pronounced in the center of chain. The excess swelling can be described with the analytical results of Duplantier and of Schäfer and Baumgärtner.

Investigations of the deformation behavior of athermal chains showed that in the case of random walks the deformation is increasing linearly with the applied force and increasing linearly with the chain length N for small and intermediate forces. In contrast to that the deformation in the case of self-avoiding walks is linear in force but nonlinear in chain length N. In the case of intermediate forces the prediction of the concept of Pincus blobs could be confirmed. Both the logitudinal and lateral dimensions are linear functions of the chain length, but nonlinear function of the force. Analytical calculations were used to describe the intermediate regime between the linear and nonlinear force regimes.

Furthermore the collaps transition at decreasing temperatures was investigated. The critical exponents at the theta-temperature as well as the scaling behavior are in good agreement with the literature. Below the theta-temperature it was found that the chains are locally more compact than on a more global scale. For the upto now unknown dynamical behavior of chains in the collaped state deviations from the Rouse model were observed: the center of mass shows an anomalous diffusion. The relaxation times decrease according to tex2html_wrap_inline41 , d being the dimension of space.

Investigations of the deformation behavior at varying temperatures showed distinct changes of the deformation when cooling from above to below the theta-temperature. In contrast to a homogeneous deformation above the theta-temperature a coexistence of an almost undeformed globule and a highly stretched strand was found below the theta-temperature. Thus, the deformation is inhomogeneous. During the globule-strand coexistence the total force as well as the energetic and entropic part are independent of the elongation. The deformation is controlled by the energy. Depending on chain length and temperature the globule-strand system is getting unstable. The vanishing of the globule-strand system accompanied by large changes in the energetic and entropic parts of the force is the result. For large elongation the deformation is, similar to above the theta-temperature, again controlled by the entropy.