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. 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 > epsilonc approximately equal to 1/N(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) approximately N, the MWD's first moment and monomer concentration m relax very close to equilibrium. (2) Hole-filling (or peak decay) after tau(fill) approximately epsilon2N2. The absence or surfeit of small chains is erased. (3) Global MWD shape relaxation after tau(slow) approximately N2. By this time second and higher MWD moments have relaxed. During episodes (2) and (3) the fast variables (N, 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 < epsilonc, response remains non-linear but with a less dramatic peak or hole during episode (1). Our predictions are in agreement with viscosity measurements on the most widely studied system, alpha-methylstyrene.

Irreversible adsorption from dilute polymer solutions.

We study irreversible polymer adsorption from dilute solutions theoretically. Universal features of the resultant non-equilibrium layers are predicted. Two broad cases are considered, distinguished by the magnitude of the local monomer-surface sticking rate Q: chemisorption (very small Q) and physisorption (large Q). Early stages of layer formation entail single-chain adsorption. While single-chain physisorption times tau ads are typically micro- to milli-seconds, for chemisorbing chains of N units we find experimentally accessible times tau ads=Q(-1)N(3/5), ranging from seconds to hours. We establish 3 chemisorption universality classes, determined by a critical contact exponent: zipping, accelerated zipping and homogeneous collapse. For dilute solutions, the mechanism is accelerated zipping: zipping propagates outwards from the first attachment, accelerated by occasional formation of large loops which nucleate further zipping. This leads to a transient distribution omega(s) approximately s(-7/5) of loop lengths s up to a maximum size smax approximately (Qt)(5/3) after time t. By times of order tau ads the entire chain is adsorbed. The outcome of the single-chain adsorption episode is a monolayer of fully collapsed chains. Having only a few vacant sites to adsorb onto, late-arriving chains form a diffuse outer layer. In a simple picture we find for both chemisorption and physisorption a final loop distribution Omega(s) approximately s(-11/5) and density profile c(z) approximately z(-4/3) whose forms are the same as for equilibrium layers. In contrast to equilibrium layers, however, the statistical properties of a given chain depend on its adsorption time; the outer layer contains many classes of chain, each characterized by a different fraction of adsorbed monomers f. Consistent with strong physisorption experiments, we find the f values follow a distribution P(f) approximately f(-4/5).

Interfacial reactions: mixed order kinetics and segregation effects

We study A-B reaction kinetics at a fixed interface separating A and B bulks. Initially, the number of reactions R(t) approximately tn(infinity)(A)n(infinity)(B) is second order in the far-field densities n(infinity)(A), n(infinity)(B). First order kinetics, governed by diffusion from the dilute bulk, onset at long times: R(t) approximately x(t)n(infinity)(A), where x(t) approximately t(1/z) is the rms molecular displacement. Below a critical dimension, d0) leads to anomalous decay of interfacial densities. Numerical simulations for z = 2 support the theory.