| dc.description.abstract | Polymers are simulated with a bead-spring model, with a short-ranged repulsive interaction between the beads. For a large number $N$ of beads, the mean end-to-end length, $\left\langle\vec{r}_e^2(N)\right\rangle$ scales as $N^{2\nu}$, For a finite number beads, the range of our simulations, there are corrections to this scaling law of the form $N^{2\nu_{\text{eff}}}=N^{2\nu}(a_0+a_1/N^{\Delta})$. Determining the growth exponent by simulations is troubled by these corrections. In this thesis simulations with various interactions between the beads are done in order to minimize these finite-size corrections. This is done by tuning the parameters of the potentials such that the effective growth exponent converges towards a region of $[\nu-0.02,\nu+0.02]$. The potentials that are used are the hard sphere, Lennard Jones, and the Gaussian potential. The simulations are done in both two and three dimensions. The hard sphere potential, with diameters $\sigma_{2D}=2.86$ and $\sigma_{3D}=2.05$, was the best potential according to our criterion. For the Gaussian potential we found parameters that give approximately the same results as the hard sphere potential in both two and three dimensions, but it did not significantly improve upon them. | |
