Diffusion-limited exciton fusion reaction in one-dimensional tetramethylammonium manganese trichloride (TMMC)

Kroon, Ron; Fleurent, Hilde; Sprik, R.

doi:10.1103/physreve.47.2462

Cited by 82 publications

(97 citation statements)

References 42 publications

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“…We therefore expect that our results are relevant for a range of experimental systems and theoretical models and believe they will encourage further work on the fundamental implications of fluctuations on nonequilibrium processes. The strong impact of fluctuation on the coagulation process below the critical dimension has already been probed by experimental studies on effectively one-dimensional exciton dynamics [52,53]. Similar experiments on excitons which disperse in all three spacial directions [54] may be suitable for analysis of our predictions of a violation of the LMA in three dimensions.…”

Section: Discussionmentioning

confidence: 81%

Long-range and many-body effects in coagulation processes

Winkler

Frey

2013

Phys. Rev. E

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We study the problem of diffusing particles which coalesce upon contact. With the aid of a nonperturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply anomalously slow decay. Above two dimensions, the long-time, low-density behavior is known to conform with the law of mass action. For this case, we establish an exact mapping between the physics at the microscopic scale (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. In addition, we identify a term violating this classical law. It originates in long-range and many-particle fluctuations and is a simple, universal function of the macroscopic decay rate.

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Section: Discussionmentioning

confidence: 81%

Long-range and many-body effects in coagulation processes

Winkler

Frey

2013

Phys. Rev. E

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“…Unfortunately, experiments investigating fluctuations in reaction-diffusion systems are deplorably rare. Three notable exceptions are: (i) the unambiguous observation of a t −1/2 density decay (in an intermediate time window) for the diffusion-limited fusion process A + A → A, as realized in the kinetics of laserinduced excitons in quasi one-dimensional N(CH 3 ) 4 MnCl 3 (TMMC) polymer chains [13]; (ii) the demonstration of non-classical A + B → C kinetics, with an asymptotic t −3/4 density decay in three dimensions in a calcium / fluorophore system [14]; and (iii) the identification of directed percolation critical exponents in studies of spatio-temporal intermittency in ferrofluidic spikes [15].…”

Section: Introductionmentioning

confidence: 99%

Applications of field-theoretic renormalization group methods to reaction–diffusion problems

Täuber¹,

Howard²,

Vollmayr-Lee³

2005

J. Phys. A: Math. Gen.

278

506

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Abstract. We review the application of field-theoretic renormalization group (RG) methods to the study of fluctuations in reaction-diffusion problems. We first investigate the physical origin of universality in these systems, before comparing RG methods to other available analytic techniques, including exact solutions and Smoluchowski-type approximations. Starting from the microscopic reaction-diffusion master equation, we then pedagogically detail the mapping to a field theory for the single-species reaction kA → ℓA (ℓ < k). We employ this particularly simple but non-trivial system to introduce the field-theoretic RG tools, including the diagrammatic perturbation expansion, renormalization, and Callan-Symanzik RG flow equation. We demonstrate how these techniques permit the calculation of universal quantities such as density decay exponents and amplitudes via perturbative ǫ = d c − d expansions with respect to the upper critical dimension d c . With these basics established, we then provide an overview of more sophisticated applications to multiple species reactions, disorder effects, Lévy flights, persistence problems, and the influence of spatial boundaries. We also analyze field-theoretic approaches to nonequilibrium phase transitions separating active from absorbing states. We focus particularly on the generic directed percolation universality class, as well as on the most prominent exception to this class: evenoffspring branching and annihilating random walks. Finally, we summarize the state of the field and present our perspective on outstanding problems for the future.

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“…Thus, experiments probing the exciton kinetics in semiconducting polymers promise to provide an excellent testing ground for a wide variety of nonequilibrium statistical models. Indeed, the dynamics of laser-induced excitons in N(CH 3 ) 4 MnCl 3 (TMMC) polymer chains appears to be the best experimental realization to date for diffusion-limited fusion processes A + A → A, where (in an intermediate time window) the predicted power law for the particle density n ∼ t −1/2 has actually been observed unambiguously [20].…”

Section: Introductionmentioning

confidence: 99%

Random walks with imperfect trapping in the decoupled-ring approximation

Aspelmeier¹,

Magnin²,

Graupner³

et al. 2002

Eur. Phys. J. B

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Abstract. We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical simulations reveal this solution, which is exact in the limit of perfect traps, to be remarkably robust with respect to a significant lowering of the trapping probability. We demonstrate that for randomly distributed traps, the long-time asymptotics of our result recovers the known stretched exponential decay. We also study an anisotropic three-dimensional version of our model, where for sufficiently large transverse diffusion the system is described by the mean-field kinetics. We discuss possible applications of some of our findings to the decay of excitons in semiconducting organic polymer materials, and emphasize the crucial influence of the spatial trap distribution on the kinetics.

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Diffusion-limited exciton fusion reaction in one-dimensional tetramethylammonium manganese trichloride (TMMC)

Abstract: Diffusion-limited exciton fusion reaction in one-dimensional tetramethylammonium manganese trichloride (Tmmc) Kroon, R.; Fleurent, H.; Sprik, R.

Cited by 82 publications

References 42 publications

Long-range and many-body effects in coagulation processes

Long-range and many-body effects in coagulation processes

Applications of field-theoretic renormalization group methods to reaction–diffusion problems

Random walks with imperfect trapping in the decoupled-ring approximation

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