Dynamics of living polymers

We study theoretically the dynamics of living polymers which can add and subtract monomer units at their live chain ends. The classic example is ionic living polymerization. In equilibrium, a delicate balance is maintained in which each initiated chain has a very small negative average growth rate (velocity) just sufficient to negate the effect of growth rate fluctuations. This leads to an exponential molecular weight distribution (MWD) with mean (N) over bar. After a small perturbation of relative amplitude epsilon, e.g. a small temperature jump, this balance is destroyed: the velocity acquires a boost greatly exceeding its tiny equilibrium value. For epsilon>epsilon(c)approximate to1/(N) over bar (1/2) the response has 3 stages: (1) Coherent chain growth or shrinkage, leaving a highly non-linear hole or peak in the MWD at small chain lengths. During this episode, lasting time tau(fast)similar to(N) over bar, the MWD's first moment and monomer concentration m relax very close to equilibrium. (2) Hole-filling (or peak decay) after tau(fill)similar toepsilon(2)(N) over bar (2). The absence or surfeit of small chains is erased. (3) Global MWD shape relaxation after tau(slow)similar to(N) over bar (2). By this time second and higher MWD moments have relaxed. During episodes (2) and (3) the fast variables ((N) over bar ,m) are enslaved to the slowly varying number of free initiators (chains of zero length). Thus fast variables are quasi-statically fine-tuned to equilibrium. The outstanding feature of these dynamics is their ultrasensitivity: despite the perturbation's linearity, the response is non-linear until the late episode (3). For very small perturbations, epsilon