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| Hauptseite > Publikationsdatenbank > Untersuchungen zur statistischen Mechanik von linearen Polymeren unter verschiedenen physikalischen Bedingungen |
| Hauptseite > Publikationsdatenbank > Untersuchungen zur statistischen Mechanik von linearen Polymeren unter verschiedenen physikalischen Bedingungen |
| Book/Report | FZJ-2018-02261 |
1983
Kernforschungsanlage Jülich, Verlag
Jülich
Please use a persistent id in citations: http://hdl.handle.net/2128/17963
Report No.: Juel-1832
Abstract: The statistical mechanics of chain molecules is investigated for various physical conditions. As a model for such chain molecules we use the $\underline{s}$elf-$\underline{a}$voiding- $\underline{w}$alk (SAW) on a diamond lattice. Because mainly numerical methods are used, various Monte Carlo techniques are tested and analysed. First the up to now best known problem, the collapse transition of a single polymer, is investigated for the whole crossoverregion. A first scaling analysis for temperatures close to the e temperature is performed. The asymptotic innerchain density is estimated in agreement with the simulations. Using these results about the quality of the tested methods the problem of a chain on a randomly diluted lattice is investigated and a crossover is constructed for the case, that the dilution is so strong, that the SAW is placed on a critical percolating cluster. Then we investigate the adsorption transition of a single chain at a hard wall with short range attractive force. In this ca se a complete scaling analysis of the energy, the mean squared radius of gyration, the mean squared end-to-end distance and the free energy is performed. The exponents $\gamma^{1}$, $\gamma^{11}$, $\gamma^{1}_{SB}$ and the crossover exponent $\varphi$ are calculated. Even for d=2 the phase diagram is constructed by a simple real-space renormalization calculation. Using the dynamic simulation technique, which obeys the Rouse dynamics for random walks, the statics and dynamics of polymeric melts are investigated. Even for the case of small static entanglement lengths N$_{e}$ (N/N$_{e}$ > 10, N chain length) there is no onset of reptation, neither for the mean square displacements of inner monomers, nor for the time dependent structure function.
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