Polymer Chains with Nonlinear Interactions: Equilibrium Properties, Thermal Fragmentation, and Force-Induced Rupture

This work intends to show how the coupled dynamics of a nonlinear polymer chain alters processes such as thermal fragmentation and force-induced rupture. For that purpose we first examine the equilibrium relaxation properties of nonlinear polymer chains which have a distinct impact on all dynamical processes in such systems. We find that in chains with nonlinear interaction potentials the relaxation properties of the end-to-end distance and the principal components are essentially those of the harmonic chain, though with shifted correlation times. Soft nonlinear potentials increase the correlation times. While these changes are not too large for the single-well potentials, for the double-well ones they can lead to the increase in the relaxation times by orders of magnitude. Thus strong internal friction may be modeled by use of the simple double-well potential with effective parameters derived from a more complex original model. The principal components, whose directions follow the normal modes of the harmonic chain, can exhibit vastly different subdiffusive kinetics. Concerning the thermally activated bond rupture in polymer chains we focus on two experimentally relevant situations. First, we consider the thermally activated fragmentation of a homopolymer chain. In our model the dynamics of the intact chain is a Rouse one until a bond breaks and bond breakdown is considered as a first passage problem over a barrier to an absorbing boundary. Using the framework of the Wilemski-Fixman approximation we calculate mean activation times of individual bonds for free and grafted chains. We show that these times crucially depend on the length of the chain and the location of the bond yielding a minimum at the free chain ends. In the Markovian limit of high activation barriers the distribution of the fragmentation location in the chain flattens since all activation times become equal. Second, we study a set up corresponding to the one found in single molecule pulling experiments. A homopolymer chain is pulled at one of its ends with a force that increases monotonically in time while the opposite end is kept fixed. In addition to the influence of non-Markovian fluctuations in the coupled system the delayed force propagation into the chain has a further impact on its overall rupture dynamics. We show that the non-Markovian fluctuations play a minor role for the scaling of rupture forces in large ensembles of breakable bonds. In contrast, they have a measurable effect on the rupture forces when there is only one breakable link in a long chain of monomers. In long chains of breakable bonds the complex interplay between the force propagation into the chain and the extreme value statistics underlying rupture causes a non-monotonic scaling of the most probable rupture force fmax as a function of the chain length N . For short chains its decrease is proportional to [ln(constN)] and it saturates at the value depending on the loading rate for very long ones. In between it can exhibit a non-monotonic behavior: The most probable rupture force attains its minimum for a certain intermediate chain length. We derive a theoretical model which reproduces the numerically observed non-monotonic scaling of the rupture force. Finally we analyze experimental data of the rupture of covalent bonds in ds-DNA loops. We calculate the intrinsic activation rate of the weakest covalent bond in the repeating unit of the DNA backbone and find that this rate is by orders of magnitude larger compared to the expected activation rate of an isolated bond. This difference is attributed to an interaction with the surface and a possible force-induced catalytic reaction. In summary, it is shown that a sensitive interplay of internal correlation times, extreme value statistics, and the timescale of external forcing can complicate the rupture kinetics even in extremely simple chain models.