Calculation of the rate constants of diffusion-controlled chemical reactions for reagents of arbitrary shape

Chekunaev, N.I.

doi:10.1016/j.chemphys.2004.02.008

Cited by 4 publications

(8 citation statements)

References 13 publications

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“…This increase by a factor of 16 is much smaller than the 133-fold increase in length as expected for diffusion-controlled reactions with long molecules. It shows the strong influence of “diffusive interaction (DI)”. ,,,, If pF 133 is regarded as 133 reactive sites spaced along a line, reaction of an electron with one of them removes that electron precluding reaction of that electron with any of the other sites. Data in Figure indicates that DI reduced the rate by a factor of 133/16 = 8.3.…”

Section: Resultsmentioning

confidence: 99%

“…Here, eq comprises the first two terms of a series that converges rapidly. While eq is known to have inherent failings at very short times and high concentrations, especially when combined with low diffusion constants, , it is the form recovered for electron transfer to small molecules ,, and for reactions of more extended objects ,, and was used in the first application to conjugated polymers . For large molecules, the form of the transient term in eq has been described as universal .…”

Section: Introductionmentioning

confidence: 99%

“…(3) Reactions with nonspherical molecules can be accommodated in the same framework with R eff representing an average reaction distance. Recent theories can compute R eff for diffusion of point particles (or spheres) to the surfaces of shapes including ellipsoids, lines, planes, and cubes of spherical reactants. ,,− The important changes to eq contributed by many theoreticians have affected the sense and utility of what might be termed the “modified Smoluchowski equation”. Although the change from R to R eff is superficially simple, the developing meaning of R eff represents a deeper evolution of our understanding.…”

Section: Introductionmentioning

confidence: 99%

“…While eq is known to have inherent failings at very short times and high concentrations, especially when combined with low diffusion constants, , it is the form recovered for electron transfer to small molecules ,, and for reactions of more extended objects ,, and was used in the first application to conjugated polymers . For large molecules, the form of the transient term in eq has been described as universal . The large values of R eff for polymeric molecules should extend the time dependence to longer times and make its shape more easily observable, but quantitative experimental tests are not yet available.…”

Section: Introductionmentioning

confidence: 99%

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Length and Time-Dependent Rates in Diffusion-Controlled Reactions with Conjugated Polymers

et al. 2009

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Rate constants for diffusion-controlled reactions of solvated electrons with conjugated fluorene oligomers (oF) and polymers (pF) were measured in liquid tetrahydrofuran (THF). Preparative gel permeation chromatography (GPC) was used to separate the polyfluorenes into fractions having narrowed distributions of lengths. Both oF and pF's were used in determinations of the attachment rate constants k(inf) as a function of length, where k(inf) refers to the rate coefficients at long times where they are indeed constant. The results find that in going from oF(1) to pF(133), k(inf) increases by a factor of 16, which is much smaller than that of the 133-fold increase in length. The extent of this increase and its change with length are in excellent agreement with published theoretical models that describe diffusion to long thin objects as either prolate spheroids or one-dimensional arrays of spheres. As the concentration of polymer was increased, the effects of large transient terms in the rate constant were observed. As predicted by the Smoluchowski diffusion equation, with modifications by more contemporary theorists, these transient effects are larger and persist to longer times for the larger molecules. For the longest molecule, pF(133), k(t) increases by more than a decade at short times. In that case, the "transient term" becomes dominant and the rate coefficient is approximately proportional to the square of the effective reaction radius in contrast to the linear dependence usual for diffusional reactions. The size of these transient effects and their quantitative confirmation are unprecedented.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Length and Time-Dependent Rates in Diffusion-Controlled Reactions with Conjugated Polymers

et al. 2009

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“…The actual shapes of the immobilized vesicles on glass are unknown, and it can be expected that they are not perfectly symmetric, so that the vesicle radius R ‘ as measured by our experiments is regarded as a mean size parameter of the vesicle. However the difference between a circular, a hemispherical, and even cylindrical object is small, and hence the corrections to the size parameter from the shape dependence are also expected to be relatively small within a reasonable range of shapes. The distributions clearly indicate the heterogeneity in the sizes of vesicles adsorbed on glass.…”

Section: Discussionmentioning

confidence: 99%

Probing Lipid Vesicles by Bimolecular Association and Dissociation Trajectories of Single Molecules

et al. 2006

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Vesicles prepared by DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) and SOPC (1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine) lipid molecules having sizes smaller than the diffraction-limited focused laser beam have been used to confine single molecules in the laser focus. The confinement of single molecules in a volume smaller than the focused laser beam leads to a Gaussian distribution of single molecule fluorescence intensity. The interactions of single Nile Red molecules with DMPC and SOPC lipid bilayers were studied by single molecule fluorescence confocal microscopy. Nile Red molecules were observed to associate with and dissociate from individual DMPC and SOPC vesicles adsorbed on a glass surface, generating on-and-off fluctuations in a fluorescence signal representing a very low noise two-state trajectory. Off-time statistics were used to investigate the mean radius of the vesicles and the size distribution functions. The means of the on-time distributions of Nile Red in DMPC and SOPC vesicles were significantly different. The association and dissociation reactions of single Nile Red molecules with a vesicle have been studied. Features of the bimolecular interaction between the probe Nile Red and the vesicle were evaluated from the uncorrelated mean on-time and vesicle radius distributions, and the linear Nile Red concentration dependence of the mean off-time. Nile Red is shown to be a useful probe of the structural fluctuations and heterogeneity of these membrane structures, and it is a useful model with which to directly study a diffusion-influenced reversible bimolecular reaction.

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A Molecular Dynamics simulation study on nitrobenzene and OH radical in supercritical water

Huang

Dong

et al. 2015

Journal of Molecular Liquids

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Calculation of the rate constants of diffusion-controlled chemical reactions for reagents of arbitrary shape

Cited by 4 publications

References 13 publications

Length and Time-Dependent Rates in Diffusion-Controlled Reactions with Conjugated Polymers

Length and Time-Dependent Rates in Diffusion-Controlled Reactions with Conjugated Polymers

Probing Lipid Vesicles by Bimolecular Association and Dissociation Trajectories of Single Molecules

A Molecular Dynamics simulation study on nitrobenzene and OH radical in supercritical water

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