Single and multiple random walks on random lattices: Excitation trapping and annihilation simulations

The spectrally resolved rime-evolution of free and trapped singlet c&tons was ohtsincd II liquid-helium temperature for ternary cestals of perdeuteronaphthalene/naphrhalene/betamsth\-Inaphthalrms (host/_eue~r/supsr:rsp). The nsphthalenc guest (donor) concentration varied between 0.30 and 0.99 mole fraction. while the supertrap (acceptor1 concentrations were lO-'-lO-5. AI the lower guest concentrations (0.50 and below) the naphthalene-esciton decay time approaches the natural lifetime (= 122 ns). At higher concentrations. the decay is much shorter and sxtremcl\-non-exponentid. This behavior is inconsistent with simple homogeneous kinetics schemes that use a time-independent rate consrant for energy transport. Above the percolation concentration (0.60 naphthalens) we fitted the esperimental results with a random-flight-kinetic model. incorporating correlated random walks on the percolating guest cluster. The best fit was obtained for a-coherence length" (mean free path) of = 10' lattice units. These results are in good agrscmcm \vith previous srccdy-s~ste studies on the same samples, and seem to indicate a partial coherence of the exiton transport in holh pure and substitutionally disordered crystals at these low temperatures.

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“…thus enhancing the fusion/ trapping ratio. The collision rate constant for this process should be an interesting topic of study [46].…”

Section: Resultsmentioning

confidence: 99%

Dynamics of energy transport in ternary molecular solids. II. Time evolution of naphthalene fluorescence

Argyrakis

Kopelman

1983

Chemical Physics

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“…(8) and, similarly, the average three-particle density function F(r,r',z) = < ( ", ) g(r"+r',z) ( •"+ /+ , )> » (9) The definition of higher order averages is obvious but will not be needed. The subscripted brackets indicate an average over configuration space: <F(rO>r. = ±/dr'F(r') (10) The two-particle function by definition satisfies the identity </(r,Z)>r = dr Ar,Z) = 2( ) (11) For a random distribution of point particles/(r,z) = 2( ) because the densities at different points are uncorrelated and hence the average of the product in (8) becomes simply the product of the averages. The three-particle density function satisfies the identities ±fdr'F(r',r",t) = Q(t)j{r",t) ±fdr"F(r',r",t) = Q(t)f{r',t) dr'/ dr" F(r',r",z) = 3( ) (12) For a random distribution fir,r',t) = 3( ).…”

Section: Reaction-diffusion Modelmentioning

confidence: 99%

Reaction-Diffusion Model for A + A Reaction

Lindenberg¹,

Argyrakis²,

Kopelman³

1995

J. Phys. Chem.

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“…Brownian motion 17 and bacterial motion 18 are examples of continuous-time, continuous-step random walks, where the walker takes a step at random points in time in a random direction. Time and space can also be discretized, giving the discrete-time, discretespace random walk model, which is useful for modelling lattices [19][20][21] and is uniquely accessible by cellular automata modelling techniques. 22 Most random walks are Markovian (and can be modelled as Markovian chains) because they are memoryless, i.e.…”

Section: Introductionmentioning

confidence: 99%

Combining random walk and regression models to understand solvation in multi-component solvent systems

Gale

Johns

Wirawan

et al. 2017

Phys. Chem. Chem. Phys.

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Polysaccharides, such as cellulose, are often processed by dissolution in solvent mixtures, e.g. an ionic liquid (IL) combined with a dipolar aprotic co-solvent (CS) that the polymer does not dissolve in. A multi-walker, discrete-time, discrete-space 1-dimensional random walk can be applied to model solvation of a polymer in a multi-component solvent mixture. The number of IL pairs in a solvent mixture and the number of solvent shells formable, x, is associated with n, the model time-step, and N, the number of random walkers. The mean number of distinct sites visited is proportional to the amount of polymer soluble in a solution. By also fitting a polynomial regression model to the data, we can associate the random walk terms with chemical interactions between components and probe where the system deviates from a 1-D random walk. The 'frustration' between solvents shells is given as ln x in the random walk model and as a negative IL:IL interaction term in the regression model. This frustration appears in regime II of the random walk model (high volume fractions of IL) where walkers interfere with each other, and the system tends to its limiting behaviour. In the low concentration regime, (regime I) the solvent shells do not interact, and the system depends only on IL and CS terms. In both models (and both regimes), the system is almost entirely controlled by the volume available to solvation shells, and thus is a counting/space-filling problem, where the molar volume of the CS is important. Small deviations are observed when there is an IL-CS interaction. The use of two models, built on separate approaches, confirm these findings, demonstrating that this is a real effect and offering a route to identifying such systems. Specifically, the majority of CSs - such as dimethylformide - follow the random walk model, whilst 1-methylimidazole, dimethyl sulfoxide, 1,3-dimethyl-2-imidazolidinone and tetramethylurea offer a CS-mediated improvement and propylene carbonate results in a CS-mediated hindrance. It is shown here that systems, which are very complex at a molecular level, may, nonetheless, be effectively modelled as a simple random walk in phase-space. The 1-D random walk model allows prediction of the ability of solvent mixtures to dissolve cellulose based on only two dissolution measurements (one in neat IL) and molar volume.

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Single and multiple random walks on random lattices: Excitation trapping and annihilation simulations

Cited by 22 publications

References 12 publications

Dynamics of energy transport in ternary molecular solids. II. Time evolution of naphthalene fluorescence

Dynamics of energy transport in ternary molecular solids. II. Time evolution of naphthalene fluorescence

Reaction-Diffusion Model for A + A Reaction

Combining random walk and regression models to understand solvation in multi-component solvent systems

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