Simulations of polymer cyclization by Brownian dynamics

The dynamic characteristics of polymers in dilute solution, such as the end-to-end distance relaxation time, tau(m), and the time of diffusion-controlled cyclization, tau(a), were studied using Brownian dynamics simulations. The major goal was to estimate the effect of the impenetrability of the chain backbone on the dynamic properties. We compared several models of polymer chains: phantom ones with and without excluded volume and a nonphantom model with excluded volume. The hydrodynamic interaction between chain segments was not taken into account. The impenetrability of a chain is found to have a small effect on the magnitude of tau(m). For sufficiently long chains, tau(m) exceeded the value for phantom chains by factor of 1.5. The ratio tau(a)/tau(m) remained the same for the phantom and nonphantom models. On the other hand, the excluded volume effect changed the dependence of tau(m) on the chain contour length, in accordance with the known theoretical conclusions. In addition, the presence of excluded volume caused a a-fold increase of the scaling factor between tau(a) and tau(m) for sufficiently long chains. This scaling factor and, consequently, tau(a) appeared to be reciprocally proportional to the reaction radius R. When the reaction radius is close to the statistical segment length l, tau(a) was estimated as tau(a) = zeta(l/R)tau(m), where the coefficient zeta is equal to 1.3 +/- 0.2 and 2.6 +/- 0.3 for chains without and with excluded volume, respectively.