Benjamin P. Lee

Renormalization group study of theA+B→⊘ diffusion-limited reaction

AbstractTheA+B→⊘ diffusion-limited reaction, with equal initial densitiesa(0)=b(0)=n0, is studied by means of a field-theoretic renormalization group formulation of the problem. For dimensiond>2 an effective theory is derived, from which the density and correlation functions call be calculated. We find the density decays in time as

Critique of primitive model electrolyte theories

a,b \sim C\sqrt \Delta (Dt)^{ - d/4}

Persistence, Poisoning, and Autocorrelations in Dilute Coarsening

ford<4, with Δ=n0−C′n0d/2+..., whereC is a universal constant andC′ is nonuniversal. The calculation is extended to the case of unequal diffusion constantsDA≠DB, resulting in a new amplitude but the same exponent. Ford⩽2 a controlled calculation is not possible, but a heuristic argument is presented that the results above give at least the leading term in an ε=2−d expansion. Finally, we address reaction zones formed in the steady state by opposing currents ofA andB particles, and derive scaling properties.

Erratum: Renormalization group study of the A+B→Φ diffusion-limited reaction

To understand the range of close-to-classical critical behavior seen in various electrolytes, generalized Debye-Huckel theories (that yield density correlation functions) are applied to the restricted primitive model of equisized hard spheres. The results yield a Landau-Ginzburg free-energy functional for which the Ginzburg criterion can be explicitly evaluated. The predicted scale of crossover from classical to Ising character is found to be similar in magnitude to that derived for simple fluids in comparable fashion. The consequences in relation to experiments are discussed briefly. [S0031-9007(96)01424-X]

Fluctuation effects in steric reaction-diffusion systems

Approximate theories for the restricted primitive model electrolyte are compared in the light of Totsujis lower bound for the energy ~an improvement over Onsagers !, Gillans upper bound for the free energy, and thermal stability requirements. Theories based on the Debye-Huckel ~DH! approach and the mean spherical approximation ~MSA!, including extensions due to Bjerrum, Ebeling, Fisher, and Levin, and Stell, Zhou, and Yeh ~PMSA1, 2, 3! are tested. In the range T*5kBTDa/q 2 &10Tc.0.5, all DH-based theories satisfy Tot- sujis bound, while the MSA possesses a significant region of violation. Both DH and MSA theories violate Gillans bound in the critical region and below unless ion pairing and the consequent free-ion depletion are incorporated. However, the PMSA theories, which recognize pairing but not depletion, fail to meet the bound. The inclusion of excluded-volume terms has only small effects in this respect. Finally, all the pairing theories exhibit negative constant-volume specific heats whenT**2T c.0.1; this is attributable to the treatment of the association constant. @S1063-651X~97!03212-1#

Electrolyte Criticality and Generalized Debye-Hückel Theory

We study reaction zones in three different versions of the A+B->0 system. For a steady state formed by opposing currents of A and B particles we derive scaling behavior via renormalization group analysis. By use of a previously developed analogy, these results are extended to the time-dependent case of an initially segregated system. We also consider an initially mixed system, which forms reaction zones for dimension d<4. In this case an extension of the steady-state analogy gives scaling results characterized by new exponents.

Phase ordering in one-dimensional systems with long-range interactions.

We calculate the exact autocorrelation exponent lambda and persistence exponent theta, and also amplitudes, in the dilute limit of phase ordering for dimensions d >= 2. In the Lifshitz-Slyozov-Wagner limit of conserved order parameter dynamics we find theta = gamma_d*epsilon, a universal constant times the volume fraction. For autocorrelations, lambda = d at intermediate times, with a late time crossover to lambda >= d/2 + 2. We also derive lambda and theta for globally conserved dynamics and relate these to the q->infinity -state Potts model and soap froths, proposing new poisoning exponents.

Phase separation of ultrathin polymer-blend films on patterned substrates

A recent argument of Oerding shows that our calculation of the quantity Δ, which determines the amplitude of the asymptotic decay of the particle density in 2<d<4, was in error. Instead it is simply given by Δ=n0, the initial density, for uncorrelated initial conditions.