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Gas diffusion in polycrystalline silicalite membranes investigated by 1H pulse field-gradient NMR.

1H pulse field-gradient (PFG) spin-echo NMR was performed to measure the diffusivity of methane in a polycrystalline MFI-type silicalite membrane. Measured diffusivities decreased with an increase in the diffusion distance and converged to the constant value. This result suggests the presence of a transport barrier in the membrane. The long-time diffusivity in the membrane was 3.7 x 10(-9) m2/s, which was a factor of 3 smaller than reported values in a single crystal. The distance between the transport barriers was estimated to be much larger than 6 mum from the relationship of diffusivity with displacement. It should be noted that the estimated distances were larger than the smallest dimension of the crystals appearing in the membrane surface. Gas permeation and pervaporation tests were carried out on the same sample for which NMR measurements were taken. The estimated methane flux using measured long-time diffusivity by the permeation theory overestimated the experimental value, although it is closer to the experimental value than the value estimated using the short-time diffusivity. These results mean that the methane diffusivity in a silicalite membrane is much smaller than that in a single crystal.

Journal Article↗

Distribution and diffusivity of a hydrophobic probe molecule in the interior of a membrane: theory and simulation.

We propose a simple model for the distribution of position and orientation and the diffusion of a hydrophobic probe molecule embedded in a membrane. The molecule experiences both a Maier-Saupe orienting potential as well as an enclosing potential of repulsion from the membrane walls. A statistical thermodynamics treatment of the model provides predictions of the location and orientation of the molecule within the membrane. In particular, we evaluate the order parameter of the molecule in terms of the model constants. The diffusivity of the probe is studied by Brownian dynamics simulation. For rotational diffusion, we check an available analytical approximate treatment that allows for the prediction of the dynamics in terms of equilibrium quantities. We also pay attention to quantities related to the initial and mean reorientational rate of the probe. For translational diffusion, we use the simulation results to analyze some general aspects of lateral and transversal diffusion.

Algorithms↗

Diffusion imaging for evaluation of tumor therapies in preclinical animal models.

The increasing development of novel targeted therapies for treating solid tumors has necessitated the development of technology to determine their efficacy in preclinical animal models. One such technology that can non-invasively quantify early changes in tumor cellularity as a result of an efficacious therapy is diffusion MRI. In this overview we present some theories as to the origin of diffusion changes as a result of tumor therapy, a robust methodology for acquisition of apparent diffusion coefficient maps and some applications of determining therapeutic efficacy in a variety therapeutic regimens and animal models.

Animals↗

Ultrafast dynamics for electron photodetachment from aqueous hydroxide.

Charge-transfer-to-solvent reactions of hydroxide induced by 200 nm monophotonic or 337 and 389 nm biphotonic excitation of this anion in aqueous solution have been studied by means of pump-probe ultrafast laser spectroscopy. Transient absorption kinetics of the hydrated electron, e(aq) (-), have been observed, from a few hundred femtoseconds out to 600 ps, and studied as function of hydroxide concentration and temperature. The geminate decay kinetics are bimodal, with a fast exponential component ( approximately 13 ps) and a slower power "tail" due to the diffusional escape of the electrons. For the biphotonic excitation, the extrapolated fraction of escaped electrons is 1.8 times higher than for the monophotonic 200 nm excitation (31% versus 17.5% at 25 degrees C, respectively), due to the broadening of the electron distribution. The biphotonic electron detachment is very inefficient; the corresponding absorption coefficient at 400 nm is <4 cm TW(-1) M(-1) (assuming unity quantum efficiency for the photodetachment). For [OH(-)] between 10 mM and 10 M, almost no concentration dependence of the time profiles of solvated electron kinetics was observed. At higher temperature, the escape fraction of the electrons increases with a slope of 3x10(-3) K(-1) and the recombination and diffusion-controlled dissociation of the close pairs become faster. Activation energies of 8.3 and 22.3 kJ/mol for these two processes were obtained. The semianalytical theory of Shushin for diffusion controlled reactions in the central force field was used to model the geminate dynamics. The implications of these results for photoionization of water are discussed.

Journal Article↗

Studies on optical properties of two commercial visible-light-cured composite resins by diffuse reflectance measurements.

Two commercial visible-light (VL)-cured composite resins were examined for their optical properties by diffuse reflectance measurements in VL spectrum and Kubelka-Munk's theory. Cured Silux Plus displayed diffuse reflectance similar to that of cured Z100, although uncured Silux Plus showed diffuse reflectance less than that of uncured Z100. By Kubelka-Munk's analyses, two optical constants of the composites at eight wavelengths such as absorption and scattering coefficients were calculated using the difference in diffuse reflectance of the composites backed between white and black standards. Upon curing, the two optical constants of the composites significantly altered especially in the shorter wavelengths. By lowering the wavelength, two optical constants of the composites tended to increase, giving rise to less light reflection and transmission. The theoretical optical transmittance of the composites was expressed in terms of hyperbolic functions of thickness of the composites at eight wavelengths in VL, dependent upon the two optical constants. The actual optical transmittance of 1 mm composites were fairly comparative with the theoretical values at 1 mm. The depth of cure of the two composites matched well with the thickness of the uncured composites which yielded the minimum theoretical optical transmittance in the wavelength region of 400-500 nm.

Composite Resins↗

Reduction-of-dimensionality kinetics at reaction-limited cell surface receptors.

It has been suggested for several years that reactions between ligands and cell surface receptors can be speeded up by nonspecific adsorption of the ligand to the cell surface followed by two-dimensional surface diffusion to the receptor, a mechanism referred to as "reduction-of-dimensionality" (RD) rate enhancement. Most of the theoretical treatments of this and related problems have assumed that the receptor is an irreversibly absorbing perfect sink. Such receptors induce a depletion zone of ligand probability density around themselves. The reaction rate in this case (called "diffusion-limited") is limited only by the time required for ligands to diffuse through this depletion zone. In some cases, however, the receptor may be far from "perfect" such that a collision with a ligand only rarely leads to binding. Receptors then do not create significant local depletion zones of ligand probability density, and the reaction rate becomes strongly affected by the (small) probability of reaction success per diffusive encounter (the "reaction-limited" case). This article presents a simple theory of RD rate enhancement for reaction-limited receptors that are either reversible or irreversible binders. In contrast to the diffusion-limited theories, the reaction-limited theory presented here: (a) differs quantitatively from diffusion-limited models; (b) is simple and algebraic in closed form; (c) exhibits significant rate enhancement in some realistic cases; (d) depends strongly on the actual Brownian rather than pure diffusive nature of the ligand's motion; (e) depends (for irreversibly binding receptors only) on the kinetic rates (not just equilibria) of reversible adsorption to nontarget regions, in contrast to some previous approximate theories of reduction of dimensionality; and (f) is applicable to actual ligand/receptor systems with binding success probabilities at the opposite extreme from the perfect sink/diffusion-limited models.

Adsorption↗

Increased oxygen consumption following activation of brain: theoretical footnotes using spectroscopic data from barrel cortex.

Optical imaging spectroscopy (OIS) and laser Doppler flowmetry (LDF) data sequences from anesthetized rats were used to determine the relationship between changes in oxy-and deoxygenated hemoglobin concentration and changes in blood volume and flow in the presence and absence of stimulation. The data from Jones et al. (accompanying paper) were used to explore the differences between two theoretical models of flow activation coupling. The essential difference between the two models is the extension of the model of Buxton and Frank by Hyder et al. (1998, J. Appl. Physiol. 85: 554--564) to incorporate change in capillary diffusivity coupled to flow. In both models activation-increased flow changes increase oxygen transport from the capillary; however, in Hyder et al.'s model the diffusivity of the capillary itself is increased. Hyder et al. proposed a parameter (Omega), a scaling "constant" linking increased blood flow and oxygen "diffusivity" in the capillary bed. Thus, in Buxton and Frank's theory, Omega = 0; i.e., there are no changes in diffusivity. In Hyder et al.'s theory, 0 < Omega < 1, and changes in diffusivity are assumed to be linearly related to flow changes. We elaborate the theoretical position of both models to show that, in principle, the different predictions from the two theories can be evaluated using optical imaging spectroscopy data. We find that both theoretical positions have limitations when applied to data from brief stimulation and when applied to data from mild hypercapnia. In summary, the analysis showed that although Hyder et al.'s proposal that diffusivity increased during activation did occur; it was shown to arise from an implementation of Buxton and Frank's theory under episodes of brief stimulation. The results also showed that the scaling parameter Omega is not a constant as the Hyder et al. model entails but in fact varies over the time course of the flow changes. Data from experiments in which mild hypercapnia was administered also indicated changes in the diffusivity of the capillary bed, but in this case the changes were negative; i.e., oxygen transport from the capillary decreased relative to baseline under hypercapnia. Neither of the models could account for the differences between the hypercapnia and activation data when matched for equivalent flow changes. A modification to the models to allow non-null tissue oxygen concentrations that can be moderated by changes due to increased metabolic demand following increased neural activity is proposed. This modification would allow modulation of oxygen transport from the capillary bed (e.g., changes in diffusivity) by tissue oxygen tension and would allow a degree of decoupling of flow and oxygen delivery, which can encompass both the data from stimulation and from hypercapnia.

Animals↗

Heterogeneous Nucleation of n-Butanol Vapor on Submicrometer Charged and Neutral Particles of Lactose and Monosodium Glutamate.

Condensation of a supersaturated vapor of n-butanol on monodisperse submicrometer particles of lactose and monosodium glutamate is investigated in a flow cloud chamber (FCC). The dependence of critical supersaturation S(cr) on the particle size in the range 30 to 90 nm is experimentally examined. The results show that the size dependence of S(cr) qualitatively agrees with that predicted by the Fletcher version of the Volmer theory of heterogeneous nucleation, but to a lesser degree. The experimental S(cr) is smaller than the theoretical prediction even with the line tension and surface diffusion taken into account, and they induce heterogeneous nucleation better than perfectly wetted particles. The discrepancy can not be fully accounted for by the effects of line tension and surface diffusion and the existing theory concerning the curvature-dependent surface tension. The condensation on single positive-charged particles of diameter 30, 60, and 90 nm is also examined. A lowering of S(cr) at an efficiency much larger than the prediction by Volmer's theory for ion-induced nucleation is observed, and the charge effect fades away as particle size increases. Copyright 2000 Academic Press.

Journal Article↗

Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.

The technique of fluorescence recovery after photobleaching is used to perform an extensive study of the lateral diffusion of a phospholipid probe in the binary mixture dimyristoylphosphatidylcholine/cholesterol, above the melting temperature of the phospholipid. In the regions of the phase diagram where a single liquid phase exists, diffusion can be quantitatively described by free volume theory, using a modified Macedo-Litovitz hybrid equation. In the liquid-liquid immiscibility region, the temperature dependence of the diffusion coefficient is in excellent agreement with current theories of generalized diffusivities in composite two-phase media. A consistent interpretation of the diffusion data can be provided based essentially on the idea that the primary effect of cholesterol addition to the bilayer is to occupy free volume. On this basis, a general interpretation of the phase behavior of this mixture is also proposed.

Cholesterol↗

Determination of optical properties of turbid media using pulsed photothermal radiometry.

Pulsed photothermal radiometry (PPTR) measures blackbody radiation emitted by a sample after absorption of an optical pulse. Three techniques for obtaining the absorption coefficient of absorbing-only, semi-infinite samples are examined and shown to give comparable results. An analytic theory for the time dependence of the PPTR signal in semi-infinite scattering and absorbing media has been derived and tested in a series of controlled gel phantoms. This theory, based on the diffusion approximation of the radiative transport equation, is shown to model the time course of the detected signal accurately. Furthermore, when the incident fluence is known, the theory can be used in a non-linear, two-parameter fitting algorithm to determine the absorption and reduced scattering coefficients of a turbid sample with an accuracy of 10-15% for transport albedos ranging from 0.42-0.88.

Algorithms↗

Diffusion and microstructural properties of solutions of charged nanosized proteins: experiment versus theory.

We have reanalyzed our former static small-angle x-ray scattering and photon correlation spectroscopy results on dense solutions of charged spherical apoferritin proteins using theories recently developed for studies of colloids. The static structure factors S(q), and the small-wave-number collective diffusion coefficient D(c) determined from those experiments are interpreted now in terms of a theoretical scheme based on a Derjaguin-Landau-Verwey-Overbeek-type continuum model of charged colloidal spheres. This scheme accounts, in an approximate way, for many-body hydrodynamic interactions. Stokesian dynamics computer simulations of the hydrodynamic function have been performed for the first time for dense charge-stabilized dispersions to assess the accuracy of the theoretical scheme. We show that the continuum model allows for a consistent description of all experimental results, and that the effective particle charge is dependent upon the protein concentration relative to the added salt concentration. In addition, we discuss the consequences of small ions dynamics for the collective protein diffusion within the framework of the coupled-mode theory.

Journal Article↗

Delay-time statistics for diffuse waves.

We formulate a theory for the statistics of the dynamics of a classical wave propagating in random media by analyzing the frequency derivative of the phase under the assumption of a Gaussian process. We calculate frequency correlations and probability distribution functions of dynamical quantities, as well the first non-Gaussian C2 correction. In A. Z. Genack, P. Sebbah, M. Stoytchev, and B. A. van Tiggelen, Phys. Rev. Lett. 82, 715 (1999), microwave measurements have been performed to which this theory applies.

Journal Article↗

Temporal chaos versus spatial mixing in reaction-advection-diffusion systems.

We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time-independent flows and equal Pe clet numbers of different components, is demonstrated to work accurately for time-dependent flows and different Pe clet numbers.

Journal Article↗

Effects of near-neighbor correlations on the diffuse scattering from a one-dimensional paracrystal.

The one-dimensional paracrystal model is generalized by folding the lattice sites with objects whose scattering lengths or sizes and separation display a spatial correlation from cell to cell. A general theory to calculate the diffuse scattering and the scattering-length autocorrelation function is developed. The investigated models of coupling along the paracrystalline chain are the correlations between (i) the sizes of the scatterers, (ii) the sizes of scatterers and their separations, and (iii) the sizes of scatterers and the fluctuation of their separation distances. In the first case (i), the size of a scatterer is, on average, linked to that of its neighbors. As a result, a continuous transition from the total lack of size correlation (known as decoupling approximation or DA) to the scattering from monodisperse domains (local monodisperse approximation or LMA) is obtained. In the second case of correlation (ii), the mean interobject distance is assumed to depend on the respective sizes of nearest neighbors. Depending on the introduced correlation parameter, aggregation or hard-core-type effects can be accounted for. Surprisingly, in some cases, it is possible to find a peak in the scattering curve without any structure in the total interference function. The size-separation correlations may also dramatically reduce the scattering intensity close to the origin compared to the completely uncorrelated case. The last model (iii) foresees a coupling between the sizes of neighboring objects and the variance of the separation between neighbors. Within this model, on average along the chain, the fluctuations of distances between scatterers become dependent on the respective sizes of neighbors, while the mean distance between objects remains constant.

Journal Article↗

Dielectrophoresis of DNA: time- and frequency-dependent collections on microelectrodes.

This paper reports measurements that characterize the collection of DNA onto interdigitated microelectrodes by high-frequency dielectrophoresis. Measurements of time-dependent collection of 12 kilobase pair plasmid DNA onto microelectrodes by dielectrophoresis show significant reduction in the response as the frequency increases from 100 kHz to 20 MHz. Collection time profiles are quantitatively measured using fluorescence microscopy over the range 100 kHz to 5 MHz and are represented in terms of two parameters: the initial dielectrophoretic collection rate, and the initial to steady-state collection transition. Measured values for both parameters are consistent with trends in the frequency-dependent real part of the effective polarizability measured for the same plasmid DNA using dielectric spectroscopy. The experimentally measured parameters are qualitatively compared with trends predicted by theory that takes into account dielectrophoretic particle movement and diffusion. The differences between experiment and theory are discussed with suggested improvements to theoretical models, for example, including the effects of electrohydrodynamically driven fluid motion.

Computer Simulation↗

Parametric dependence of conduction speed for a diffusive model of a myelinated axon.

A simple model of a myelinated axon, using ideas from cable theory and accounting for the diffusion of potential across the internode, is formulated and solved to obtain transcendental expressions relating conduction velocity and various model parameters. Numerical simulations are performed to obtain graphs of several parameter relationships.

Action Potentials↗

Analysis of fluorophore diffusion by continuous distributions of diffusion coefficients: application to photobleaching measurements of multicomponent and anomalous diffusion.

Fluorescence recovery after photobleaching (FRAP) is widely used to measure fluorophore diffusion in artificial solutions and cellular compartments. Two new strategies to analyze FRAP data were investigated theoretically and applied to complex systems with anomalous diffusion or multiple diffusing species: 1) continuous distributions of diffusion coefficients, alpha(D), and 2) time-dependent diffusion coefficients, D(t). A regression procedure utilizing the maximum entropy method was developed to resolve alpha(D) from fluorescence recovery curves, F(t). The recovery of multi-component alpha(D) from simulated F(t) with random noise was demonstrated and limitations of the method were defined. Single narrow Gaussian alpha(D) were recovered for FRAP measurements of thin films of fluorescein and size-fractionated FITC-dextrans and Ficolls, and multi-component alpha(D) were recovered for defined fluorophore mixtures. Single Gaussian alpha(D) were also recovered for solute diffusion in viscous media containing high dextran concentrations. To identify anomalous diffusion from FRAP data, a theory was developed to compute F(t) and alpha(D) for anomalous diffusion models defined by arbitrary nonlinear mean-squared displacement versus time relations. Several characteristic alpha(D) profiles for anomalous diffusion were found, including broad alpha(D) for subdiffusion, and alpha(D) with negative amplitudes for superdiffusion. A method to deduce apparent D(t) from F(t) was also developed and shown to provide useful complementary information to alpha(D). alpha(D) and D(t) were determined from photobleaching measurements of systems with apparent anomalous subdiffusion (nonuniform solution layer) and superdiffusion (moving fluid layer). The results establish a practical strategy to characterize complex diffusive phenomena from photobleaching recovery measurements.

Biophysical Phenomena↗

Peritoneal transport physiology: insights from basic research.

Clinical uses of the peritoneal cavity, such as i.p. chemotherapy or peritoneal dialysis, depend on underlying physiological mechanisms of transport between the blood and the peritoneal cavity. Clinical models of peritoneal transport have focused on an idealized "peritoneal membrane." However, such a membrane does not physically exist. Transport actually occurs between the peritoneal cavity and blood which is contained in discrete capillaries distributed in the tissue interstitium surrounding the cavity. To integrate the properties of the capillaries and the interstitium, the "distributed model" approach couples pore theory, which simulates transendothelial transport, with diffusion and convection within the tissue space. The distributed theory can explain why the peritoneal membrane, when compared with the artificial kidney, appears tight to urea but leaky to protein. The additional resistance to urea transport has been attributed to "unstirred layers" adjacent to the peritoneal membrane. These can now be defined physiologically by examining diffusion in the tissue space. Absolute rates of convection into and out of the cavity cannot yet be accurately predicted, but the physiological forces can be specified. Net "ultrafiltration" during dialysis results from not only high osmotic pressure in the peritoneal dialysate but also from a small but significant hydrostatic pressure which drives convection in the opposite direction. Recent implications from protein absorption studies that lymphatics are the cause of the decrease in net ultrafiltration are only partly true. Analysis of data from the tissue space has shown that the deposition of protein occurs from the cavity into the tissue interstitium with a slow uptake into lymphatics.

Animals↗