Association rates of diffusion-controlled reactions in two dimensions

1985 ◽  
Vol 4 (2-3) ◽  
pp. 139-155 ◽  
Author(s):  
Alberto Gandolfi ◽  
Anna Gerardi ◽  
Federico Marchetti
Keyword(s):  
Two Dimensions ◽  
Diffusion Controlled

The Anomalous Diffusion-limited Reaction Kinetics of a Phototrapping Reaction

1996 ◽  
Vol 464 ◽  
Author(s):  
Eric Monson ◽  
Anna L. Lin ◽  
Raoul Kopelman
Keyword(s):  
Laser Beam ◽  
Two Dimensions ◽  
One Dimensional ◽  
Rate Laws ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Diffusion Controlled ◽  
Kinetics Of ◽  
Diffusion Limited Reaction ◽  
Classical Constant

AbstractA focused laser beam acts as both a “phototrap”, bleaching fluorophore molecules which diffuse into the beam path, and as a confocal probe, detecting the excited, unbleached fluorophore molecules still present in the trap. With this focused laser beam, we observe anomalous asymptotic rate laws similar to those predicted for a diffusion-controlled elementary trapping reaction, A + T → T, in one and two dimensions. One dimensional diffusion-limited trapping kinetics are approached in capillaries with 10 μm diameters while two dimensional diffusion limited trapping kinetics are observed with unstirred samples having a quasi 2-D geometry. In the presence of stirring, the 2-D samplesexhibit the classical, constant trapping rate over time.

Time-dependent reactivity for diffusion-controlled annihilation and coagulation in two dimensions

1994 ◽  
Vol 50 (5) ◽  
pp. 3646-3655 ◽  
Author(s):  
P. A. Alemany ◽  
D. H. Zanette ◽  
H. S. Wio
Keyword(s):  
Two Dimensions ◽  
Time Dependent ◽  
Diffusion Controlled

Association Rates of Diffusion-Controlled Reactions in Two Dimensions

1985 ◽  
pp. 139-155
Author(s):  
Alberto Gandolfi ◽  
Anna Gerardi ◽  
Federico Marchetti
Keyword(s):  
Two Dimensions ◽  
Diffusion Controlled

Diffusion-controlled growth

1989 ◽  
Vol 423 (1864) ◽  
pp. 123-132 ◽  
Keyword(s):  
Growth Rate ◽  
Cone Angle ◽  
High Growth ◽  
High Growth Rate ◽  
Two Dimensions ◽  
Flow Diagram ◽  
Equivalent Model ◽  
Controlled Growth ◽  
Diffusion Controlled ◽  
Tip Radius

The conditions of diffusion-controlled growth are outlined and the observed importance of anisotropy is discussed through a tentative flow diagram. A crucial role is played by the forwardmost tips, which lead to growth. The nature of the singularity in their growth rate determines the overall fractal dimension. This has been estimated in two dimensions from effective cone-angle models, which work well for the most extreme anisotropic growth and can be augmented into a self-consistent approximation for the isotropic fractal case. The way in which the tip growth rate singularity is limited by finite tip radius is also a key ingredient. For diffusion-limited solidification where it is set by competition with surface tension, this significantly changes the form of the equivalent model with a fixed (e. g. lattice spacing) imposed tip scale. The full distribution of growth rates everywhere provides a much richer problem. We show new data and examine the consistency of how sites can evolve from the regions of high growth rate where they are born, into well-screened regions devoid of further growth.

The tangled web of agency

2018 ◽  
Vol 41 ◽  
Author(s):  
Alain Pe-Curto ◽  
Julien A. Deonna ◽  
David Sander
Keyword(s):  
Two Dimensions ◽  
Bad Company

AbstractWe characterize Doris's anti-reflectivist, collaborativist, valuational theory along two dimensions. The first dimension is socialentanglement, according to which cognition, agency, and selves are socially embedded. The second dimension isdisentanglement, the valuational element of the theory that licenses the anchoring of agency and responsibility in distinct actors. We then present an issue for the account: theproblem of bad company.

A TEM investigation of a hyper-eutectic lead-tin alloy

1988 ◽  
Vol 46 ◽  
pp. 562-563
Author(s):  
John A. Sutliff
Keyword(s):  
Volume Diffusion ◽  
Eutectic Mixture ◽  
Precipitation Reaction ◽  
Directionally Solidified ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Diffusion Controlled ◽  
Discontinuous Precipitation Reaction ◽  
Controlled Precipitation

Near-eutectic Pb-Sn alloys are important solders used by the electronics industry. In these solders, the eutectic mixture, which solidifies last, is the important microstructural consituent. The orientation relation (OR) between the eutectic phases has previously been determined for directionally solidified (DS) eutectic alloys using x-ray diffraction or electron chanelling techniques. In the present investigation the microstructure of a conventionally cast, hyper-eutectic Pb-Sn alloy was examined by transmission electron microscopy (TEM) and the OR between the eutectic phases was determined by electron diffraction. Precipitates of Sn in Pb were also observed and the OR determined. The same OR was found in both the eutectic and precipitation reacted materials. While the precipitation of Sn in Pb was previously shown to occur by a discontinuous precipitation reaction,3 the present work confirms a recent finding that volume diffusion controlled precipitation can also occur.Samples that are representative of the solder's cast microstructure are difficult to prepare for TEM because the alloy is multiphase and the phases are soft.

A transmission electron microscopic study of structural transitions in fast ionic conductors

1987 ◽  
Vol 45 ◽  
pp. 156-157
Author(s):  
R. B. Queenan ◽  
P. K. Davies
Keyword(s):  
Optical Properties ◽  
Ionic Conduction ◽  
Recent Observation ◽  
Ionic Conductivities ◽  
Sodium Aluminate ◽  
Two Dimensions ◽  
Ionic Conductors ◽  
Electron Microscopic ◽  
Transmission Electron ◽  
Trivalent Cations

Na ß“-alumina (Na1.67Mg67Al10.33O17) is a non-stoichiometric sodium aluminate which exhibits fast ionic conduction of the Na+ ions in two dimensions. The Na+ ions can be exchanged with a variety of mono-, di-, and trivalent cations. The resulting exchanged materials also show high ionic conductivities.Considerable interest in the Na+-Nd3+-ß“-aluminas has been generated as a result of the recent observation of lasing in the pulsed and cw modes. A recent TEM investigation on a 100% exchanged Nd ß“-alumina sample found evidence for the intergrowth of two different structure types. Microdiffraction revealed an ordered phase coexisting with an apparently disordered phase, in which the cations are completely randomized in two dimensions. If an order-disorder transition is present then the cooling rates would be expected to affect the microstructures of these materials which may in turn affect the optical properties. The purpose of this work was to investigate the affect of thermal treatments upon the micro-structural and optical properties of these materials.

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