Stochastic dynamics of hairballs in single-polymer growth

Real-time monitoring of the single-chain growth of synthetic polymers shows that their end-to-end extension during polymerization in living conditions does not increase continuously. Instead, it remains in a non-equilibrium state, exhibiting stochastic wait-and-jump events when one end of the polymer is subjected to a constant force and the other end is clamped. This wait-and-jump observation was attributed to the stochastic formation and unwinding of conformational entanglements, referred to as hairballs, which result from intrachain and non-bonded interactions within the polymer. In this work, we propose a new theoretical approach to investigate the microscopic dynamics of a single hairball formation and unravelling process during single-chain polymerisation. A discrete state stochastic approach is adopted to analyse the respective wait-and-jump events, which provides fully analytical solutions for all dynamic properties under non-equilibrium conditions. Our theory suggests that dynamic conformation fluctuations of the hairball may be responsible for the experimentally observed complex non-exponential behaviour in the waiting times. Excellent quantitative agreements with existing experimental data provide strong support for our theory. Further, using a Monte Carlo simulation approach, we analysed the correlations between the waiting time and extension of polymer in a single jump, which indicates the possibility of more complex dynamics of polymer growth.