Role of dimensionality and spatial extent in influencing intramicellar kinetic processes

Hatlee, Michael D.; Kozak, John J.; Rothenberger, Guido; Infelta, Pierre P.; Gräetzel, Michael

doi:10.1021/j100449a017

Cited by 101 publications

(44 citation statements)

References 3 publications

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“…3. Our numerical results could be fitted quite well by a sum of two exponentials K T,ro(7)=KT,,,(0)(a, e-r/r1+a2 e-7/72), (28) with a, +az= 1.…”

Section: Spin-dipolar Relasatlon Hal Translational Dl_ffuslon: Adaptimentioning

confidence: 65%

Electron spin relaxation of photobiochemically generated radical pairs diffusing in micellar supercages

Steiner¹,

Wu²

1992

Chemical Physics

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A kmettc analysts of prevtous experrmental data [T. Ulrtch and U.E. Sterner. Chem. Phys. Letters I I2 ( 1984) 3651 on the magnettc-field dependent recombmatton kmetrcs of radtcal pans photochemtcally produced wtth trtplet spm correlatron m waterIn-otl mtcroemulsion droplets of vartable stze ( rM) provtded the I~-and field-dependence of the rate constant k, of the T, =S. T0 spm relaxatron process. It was found Independent of rM at low fields. but strongly decreasmg wtth mcreasmg lhl at fields Z 100 G. The latter behavtour was attrtbuted to the mechamsm of electron-spm dtpolar Interactton. Quantttattve treatments of thts relaxatton mechamsm are provtded (I) by adapting Torrey's analyttcal result for homogeneous solutton to the sttuatton of one radtcal patr m a mrcellar supercage and (n) by Monte Carlo calculatton of the autocorrelatton functron of the perttnent perturbatton matrtx element, consrdermg diffuston tn the %olume or on the surface of the supercage. The electron-spur dtpolar relaxatton mechamsm can quantttattvely account for the expertmental data on k, at fields 2 100 G.

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“…3. Our numerical results could be fitted quite well by a sum of two exponentials K T,ro(7)=KT,,,(0)(a, e-r/r1+a2 e-7/72), (28) with a, +az= 1.…”

Section: Spin-dipolar Relasatlon Hal Translational Dl_ffuslon: Adaptimentioning

confidence: 65%

Electron spin relaxation of photobiochemically generated radical pairs diffusing in micellar supercages

Steiner¹,

Wu²

1992

Chemical Physics

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“…As documented in Carslaw and Jaeger (22) and utilized recently in ref. 6, the time dependence of C(6, t) is given formally by…”

Section: Section 3 Correspondence With Calculations On Planar Latticesmentioning

confidence: 99%

“…There exists an extensive literature on this general class of problems, ranging from the classic review of Noyes (1) in 1961 to the more recent monographs of Aris (2), Nicolis and Prigogine (3), and Haken (4). The specific study of Bloomfield and Prager (5) was the motivation, in part, of subsequent work on the role of dimensionality and spatial extent in influencing intramicellar kinetic processes (6).…”

Section: Section 1 Introductionmentioning

confidence: 99%

Surface site diffusion and reaction on molecular “organizates” and colloidal catalysts: A geometrical perspective

Politowicz¹,

Kozak²

1987

Proc. Natl. Acad. Sci. U.S.A.

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We study surface-mediated, diffusion-controlled reactive processes on particles whose overall geometry is homeomorphic to a sphere. Rather than assuming that a coreactant can diffuse freely over the surface of the particle to a target site (reaction center), we consider the case where the coreactant can migrate only among N -1 satellite sites that are networked to the reaction site by means of a number of pathways or reaction channels. Five distinct lattice topologies are considered and we study the reaction efficiency both for the case where the satellite sites are passive and for the case where reaction may occur with rinite probability at these sites. The results obtained for this class ofsurface problems are compared with those obtained by assuming that the reaction-diffusion process takes place on a planar, two-dimensional surface (lattice). The applicability of our results to surface-mediated processes on "organizates" (cells, vesicles, micelles) and on colloidally dispersed catalyst particles is brought out in the Introduction, and the correspondence between the latticebased, Markovian approach developed here and Fickian models of surface diffusion, particularly with regard to the exponentiality of the decay, is discussed in the concluding section. Section 1. IntroductionTheoretical efforts to understand diffusion-controlled reactive events on the surface of cellular, vesicular, or micellar systems or on the surface of catalyst particles dispersed in a fluid phase have usually invoked reaction-diffusion models solved by assuming that one reactant can diffuse freely over the surface of the system. In a typical application, a rotational diffusion equation is written down and solved for a concentration variable C(0, t)-namely,at sinO aO ae (where 0 is an angle defined with respect to an underlying spherical polar coordinate system and D is an associated rotational diffusion coefficient)-subject to a variety ofinitial and boundary conditions, C(0, t = 0) and C(0 = 00, t), respectively. There exists an extensive literature on this general class of problems, ranging from the classic review of Noyes (1) in 1961 to the more recent monographs of Aris (2), Nicolis and Prigogine (3), and Haken (4). The specific study of Bloomfield and Prager (5) was the motivation, in part, of subsequent work on the role of dimensionality and spatial extent in influencing intramicellar kinetic processes (6).The particular problem we should like to address derives from the observation that in many diffusion-reaction problems in which the reactants are confined to the surface of a particle, the species are not free to diffuse freely over the surface of the system. In cellular systems, for example, whereas it is known that lateral diffusion on the surface of the encompassing membrane may be quite free, a diffusing species must nonetheless negotiate transmembrane (and other) proteins whose presence bifurcates the surface into channels and breaks the rotational symmetry of the problem [for a recent review here, see Sackmann (7)]....

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“…One thinks immediately of such problems as morphogenesis in biology (1-3), kinetic processes in organized molecular assemblies in chemistry (see, for example, ref. 4), and the catalyst pellet in reactor engineering (5). Recently, we have studied the dynamics of elementary reactions in a confined space by Monte Carlo simulation (6).…”

mentioning

confidence: 99%

“…By carrying through this program for each side of the unit polygon, one generates a new figure of fractal dimension (11): InN D= ln(l/r). [4] This procedure can be repeated over and over again and, as Mandelbrot has illustrated, the sth generation will produce a figure considerably different in structure from the original unit polygon.…”

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confidence: 99%

Stochastic flows in integral and fractal dimensions and morphogenesis

Hatlee

Kozak

1981

Proc. Natl. Acad. Sci. U.S.A.

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The effect of dimensionality and spatial extent on the dynamics of an irreversible reaction confined to a finite system was studied by a Monte Carlo simulation. Stochastic flows on surfaces of integral and fractal dimensions and the consequences of reducing the dimensionality of the reaction space are described. As regards the timing and efficiency of chemical reactions in small systems, our simulations show that placing the reactive site at a central location may be favored at an early stage of growth but, as the system evolves in size, a location on the boundary becomes favored.The possible relevance of these calculations to the problem of morphogenesis is brought out.The role of boundaries and the effect of system size in influencing the dynamics of chemically reacting systems in the farfrom-equilibrium regime is a problem of widespread experimental and theoretical interest. One thinks immediately of such problems as morphogenesis in biology (1-3), kinetic processes in organized molecular assemblies in chemistry (see, for example, ref. 4), and the catalyst pellet in reactor engineering (5). Recently, we have studied the dynamics of elementary reactions in a confined space by Monte Carlo simulation (6). We consider both reactants and products to be confined to a reaction volume (a lattice) subject to finite boundary conditions and then use the Monte Carlo algorithm to study the influence of spatial extent and dimension on the evolution of the system. In this paper, we focus attention on a single, irreversible reaction: A + B + C, where A is the migrating species ( a single molecule undergoing random displacements on a given lattice) and B is the fixed trap (a target molecule or reactive site, positioned at some point in the host lattice). We then compute the average number, (n), of steps required for trapping (walk length), subject to a variety of constraints on the migrating molecule as it encounters the (finite) boundaries of the system. The results of our simulations cast light on the advantages of reducing the (integral or fractal) dimension of the diffusion space and demonstrate quantitatively how this effect depends on the spatial extent of the system. The Monte Carlo simulations reported here were carried out as described in section II of ref. 6 and the results obtained were subject to the same convergence criteria.Description of the boundary conditions In this paper, as in our earlier work, the emphasis is on the role of boundaries and, in particular, the interplay between dimensionality and spatial extent in influencing dynamical processes on finite lattices. Three types of finite boundary conditions are considered. The first, referred to as the confining boundary condition, is implemented by imposing the restriction that if the walker attempts to step onto the boundary, it must return to the lattice site from whence it started. The second type of boundary condition, referred to as the reflecting boundary condition, is implemented by the restriction that if the walker attempts to step onto th...

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Role of dimensionality and spatial extent in influencing intramicellar kinetic processes

Cited by 101 publications

References 3 publications

Electron spin relaxation of photobiochemically generated radical pairs diffusing in micellar supercages

Electron spin relaxation of photobiochemically generated radical pairs diffusing in micellar supercages

Surface site diffusion and reaction on molecular “organizates” and colloidal catalysts: A geometrical perspective

Stochastic flows in integral and fractal dimensions and morphogenesis

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