Dynamic diffusion

This result comes from the idea of a variational rate theory for a diffusive dynamics. If the dynamics of the reactive system is overdamped and the effective friction is spatially isotropic, the time required to pass from the reactant to the product state is expected to be proportional to the integral over the path of the inverse Boltzmann probability. 

The simple pore structure shown in Figure 2.69 allows the use of some simplified models for mass transfer in the porous medium coupled with chemical reaction kinetics. An overview of corresponding modeling approaches is given in [194]. The reaction-diffusion dynamics inside a pore can be approximated by a one-dimensional equation... 

For an artificial lipid bilayer of any size scale, it is a general feature that the bilayer acts as a two-dimensional fluid due to the presence of the water cushionlayer between the bilayer and the substrate. Due to this fluidic nature, molecules incorporated in the lipid bilayer show two-dimensional free diffusion. By applying any bias for controlling the diffusion dynamics, we can manipulate only the desired molecule within the artificial lipid bilayer, which leads to the development of a molecular separation system. 

The most intriguing aspect of the self-spreading lipid bilayer is that any molecule in the bilayer can be transported without any external bias. The unique characteristic of the spreading layer offers the chance to manipulate molecules without applying any external biases. This concept leads to a completely non-biased molecular manipulation system in a microfluidic device. For this purpose, the use of nano-space, which occasionally offers the possibility of controlling molecular diffusion dynamics, would be a promising approach. 

This power law decay is captured in MPC dynamics simulations of the reacting system. The rate coefficient kf t) can be computed from — dnA t)/dt)/nA t), which can be determined directly from the simulation. Figure 18 plots kf t) versus t and confirms the power law decay arising from diffusive dynamics [17]. Comparison with the theoretical estimate shows that the diffusion equation approach with the radiation boundary condition provides a good approximation to the simulation results. 

Dahan, M., Levi, S., Luccardini, C., Rostaing, P., Riveau, B., and Trillcr, A. (2003) Diffusion dynamics of glycine receptors revealed by single-quantum dot tracking. Science 302, 442 145. 

Shortly thereafter came reports of integrated three-pulse photon echoes, especially using the echo peak shift to provide information about spectral diffusion [21, 23]. In one experiment [10, 23] the peak shift shows an intriguing oscillation at short times with a period of about 180 fs, followed by a slower relaxation with a decay time of 1.4 ps. The three-pulse echo amplitude can also be heterodyned, leading to 2DIR experiments [24 26]. The latter experiments provide a wealth of information, and there are several ways to extract the desired spectral diffusion dynamics [149]. 

We have described our most recent efforts to calculate vibrational line shapes for liquid water and its isotopic variants under ambient conditions, as well as to calculate ultrafast observables capable of shedding light on spectral diffusion dynamics, and we have endeavored to interpret line shapes and spectral diffusion in terms of hydrogen bonding in the liquid. Our approach uses conventional classical effective two-body simulation potentials, coupled with more sophisticated quantum chemistry-based techniques for obtaining transition frequencies, transition dipoles and polarizabilities, and intramolecular and intermolecular couplings. In addition, we have used the recently developed time-averaging approximation to calculate Raman and IR line shapes for H20 (which involves... 

Constraints may be introduced either into the classical mechanical equations of motion (i.e., Newton s or Hamilton s equations, or the corresponding inertial Langevin equations), which attempt to resolve the ballistic motion observed over short time scales, or into a theory of Brownian motion, which describes only the diffusive motion observed over longer time scales. We focus here on the latter case, in which constraints are introduced directly into the theory of Brownian motion, as described by either a diffusion equation or an inertialess stochastic differential equation. Although the analysis given here is phrased in quite general terms, it is motivated primarily by the use of constrained mechanical models to describe the dynamics of polymers in solution, for which the slowest internal motions are accurately described by a purely diffusive dynamical model. 

In fact, in this picture, the relaxation time X is dominated by the disappearance of the last few layers, where W becomes of order L. For surface diffusion dynamics, Rettori and Villain (see also Ozdemir and Zangwill, 1990) showed that. 

Aging behavior observed in the mean square displacement, (Ax ), as a function of time for different ages. The colloidal system reorganizes slower as it becomes older, (c) y = (Ax )/3 (upper curve) and (Ax ) (lower curve) as a function of the age measured over a fixed time window At = 10 min. For a diffusive dynamics both curves should coincide, however these measurements show deviations from diffusive dynamics as well as intermittent behavior. Panels (a) and (b) from http // www.physics.emory.edu/ weeks/lab/aging.html and Panel (c) from Refill. 

Beyond imaging, the combination of CRS microscopy with spectroscopic techniques has been used to obtain the full wealth of the chemical and the physical structure information of submicron-sized samples. In the frequency domain, multiplex CRS microspectroscopy allows the chemical identification of molecules on the basis of their characteristic Raman spectra and the extraction of their physical properties, e.g., their thermodynamic state. In the time domain, time-resolved CRS microscopy allows the recording of the localized Raman free induction decay occurring on the femtosecond and picosecond time scales. CRS correlation spectroscopy can probe three-dimensional diffusion dynamics with chemical selectivity. 

Pyranine has been used to study the proton dissociation and diffusion dynamics in the aqueous layer of multilamellar phospholipid vesicles [101], There are 3-10 water layers interspacing between the phospholipid membranes of a multilamellar vesicle, and their width gets adjusted by osmotic pressure [102], Pyranine dissolved in these thin layers of DPPC and DPPC+cholesterol multilamellar vesicles were used as a probe for the study. Before the photoreleased proton escapes from the coulombic cage, the probability of a proton excited-anion recombination was found to be higher than in bulk. This was attributed to the diminished water activity in the thin layer. It was found that the effect of local forces on proton diffusion at the timescale of physiological processes is negligible. 

While these models match experimental data reasonably well at lower fields, recent experiments at higher magnetic fields of 3.4 and 9.2 T show enhancement values that are much higher than predicted with the currently employed theory.41,72,79 At these higher fields, the timescale of molecular interactions that give rise to Overhauser DNP effects is much shorter (sub-picoseconds to picoseconds) and thus should be more sensitive to the rotational diffusion dynamics of water, closely related to the atomistic details of the radical and solvent, instead of translational diffusion dynamics. These atomistic details are not accurately represented in the FFHS or rotational models (Equations (13) and (15)), implying that further work needs to be done to develop more accurate models. 

Aqueous phase (2.7 mm3) was placed in the thin lower compartment of the microcell and the Dil dodecane solution (63 mm3) was added on top of the aqueous layer. Fluorescence of the interfacial Dil was observed in the range of 571-575 nm. The influence of two kinds of surfactants, sodium dodecyl sulfate (SDS) and dimyristoyl phosphatidylcholine (DMPC), on the lateral diffusion dynamics of single molecules at the interface was investigated. DMPC was dissolved in chloroform, and the solution was mixed with pure diethyl ether at a ratio of 1 19 (chloroform diethyl ether) by volume. Pure water was placed in the lower container, and the DMPC solution was subsequently (5 mm3) spread carefully on the water. After evaporation of chloroform and diethyl ether, the Dil dodecane solution was added on the DMPC layer. Since Dil has a high... 

Unfortunately, very little is known about dephasing in high-viscosity liquids. Aside from some recent work by Fayer s group (37,141,142), there are almost no experimental studies available. As discussed in Section II.C, the available dephasing theories do not explicitly consider this regime or distinguish between inertial and diffusive dynamics. 

In pure liquids, short-range repulsive forces are responsible for most of the dephasing. The viscoelastic theory describes the interaction of these forces with the diffusive dynamics of the liquid (Section IV.D). The resulting frequency modulation is in the fast limit in low-viscosity liquids but can reach the slow-modulation limit at higher viscosities. This type of dephasing was seen in supercooled toluene (Section IV.C). 

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