Light scattering from mixtures of interacting, nonionic micelles with hydrophobic solutes.

Model equations for the Rayleigh ratio and the electric field autocorrelation function are derived using thermodynamic fluctuation theory applied to crowded solute-containing micellar solutions and microemulsions with negligible molecular species and polydispersity. This theory invokes non-equilibrium thermodynamics and enforces local equilibrium between molecular solute, surfactant, and the various micellar species, in order to elucidate the influence of self-assembly on light scattering correlation functions. We find that self-assembly driven variations in the average micelle radius and aggregation number along gradients in concentration, which were previously shown to drive strong multicomponent diffusion effects expressed via the ternary diffusivity matrix [D], do not affect the scattering functions in the limit of zero local polydispersity. Hence, theoretical predictions for the Rayleigh ratio and the field autocorrelation function for ternary mixtures of solute-containing, locally monodisperse micellar solutions are identical to those developed for binary mixtures of monodisperse, colloidal hard spheres. However, self-assembly driven multicomponent diffusion phenomena are predicted to influence the thermodynamic driving forces for diffusion in these mixtures. In support of our theoretical results, measurements for the Rayleigh ratio and the field autocorrelation function for ternary aqueous solutions of decaethylene glycol monododecyl ether (C12E10) with either decane or limonene solute were performed for several molar ratios and volume fractions up to ϕ ≈ 0.25, and for binary mixtures of C12E10/water up to ϕ ≈ 0.5. Excellent agreement between our light scattering theory and experimental data is achieved for low to moderate volume fractions (ϕ < 0.3), and at higher concentrations when our theoretical results are corrected to account for micelle dehydration.

Xylem network connectivity and embolism spread in grapevine(Vitis vinifera L.).

Xylem networks are vulnerable to the formation and spread of gas embolisms that reduce water transport. Embolisms spread through interconduit pits, but the three-dimensional (3D) complexity and scale of xylem networks means that the functional implications of intervessel connections are not well understood. Here, xylem networks of grapevine (Vitis vinifera L.) were reconstructed from 3D high-resolution X-ray micro-computed tomography (microCT) images. Xylem network performance was then modeled to simulate loss of hydraulic conductivity under increasingly negative xylem sap pressure simulating drought stress conditions. We also considered the sensitivity of xylem network performance to changes in key network parameters. We found that the mean pit area per intervessel connection was constant across 10 networks from three, 1.5-m stem segments, but short (0.5 cm) segments fail to capture complete network connectivity. Simulations showed that network organization imparted additional resistance to embolism spread beyond the air-seeding threshold of pit membranes. Xylem network vulnerability to embolism spread was most sensitive to variation in the number and location of vessels that were initially embolized and pit membrane vulnerability. Our results show that xylem network organization can increase stem resistance to embolism spread by 40% (0.66 MPa) and challenge the notion that a single embolism can spread rapidly throughout an entire xylem network.

Multicomponent diffusion of interacting, nonionic micelles with hydrophobic solutes.

Ternary diffusion coefficient matrices [D] were measured using the Taylor dispersion method, for crowded aqueous solutions of decaethylene glycol monododecyl ether (C12E10) with either decane or limonene solute. The matrix [D], for both systems, was found to be highly non-diagonal, and concentration dependent, over a broad domain of solute to surfactant molar ratios and micelle volume fractions. A recently developed theoretical model, based on Batchelor's theory for gradient diffusion in dilute, polydisperse mixtures of interacting spheres, was simplified by neglecting local polydispersity, and effectively used to predict [D] with no adjustable parameters. Even though the model originates from dilute theory, the theoretical results were in surprisingly good agreement with experimental data for concentrated mixtures, with volume fractions up to φ≈ 0.47. In addition, the theory predicts eigenvalues D- and D+ that correspond to long-time self and gradient diffusion coefficients, respectively, for monodisperse spheres, in reasonable agreement with experimental data.

Multicomponent Diffusion in Aqueous Solutions of Nonionic Micelles and Decane.

Taylor dispersion and dynamic light scattering techniques were used to measure the ternary diffusivity matrix [D] and the micelle gradient diffusion coefficient, respectively, in crowded aqueous solutions of decaethylene glycol monododecyl ether (C12E10) and decane. The results indicate that C12E10 diffused down its own gradient with the micelle gradient diffusivity while decane diffused down a decane gradient at a much slower rate. Furthermore, strong diffusion coupling, comprising decane diffusion down a surfactant gradient and surfactant diffusion up a decane gradient, was also observed with cross diffusivities that were on the order of or larger than the main diffusivities. Measurements of the micelle aggregation number, hydration index, and the hydrodynamic radius, obtained using both static and dynamic light scattering methods, indicate that decane-containing micelles interacted as hard spheres and had radii and aggregation numbers that increased linearly with the molar ratio of solute to surfactant. A theoretical model, developed using Batchelor's theory for gradient diffusion in a polydisperse system of interacting hard spheres, was effectively used to predict [D] with no adjustable parameters. A comparison with the theory indicates that decane diffused down its own gradient by micelle self-diffusion while surfactant diffused down a surfactant gradient by micelle gradient diffusion. It is also shown that intermicellar interactions drove decane diffusion down a C12E10 gradient by a volume exclusion effect while an increase in the micelle aggregation number and hydrodynamic radius with decane was necessary to drive surfactant diffusion up a decane gradient.

Multicomponent diffusion in solute-containing micelle and microemulsion solutions.

Holographic interferometry was used to obtain new results for the four coefficients that determine rates of multicomponent diffusion of hydrophobic solutes and surfactants in microemulsions. The three solutes pentanol, octanol, and heptane were examined in microemulsions formed from decaethylene glycol monododecyl ether (C12E10) and sodium dodecyl sulfate (SDS). These coefficients are compared with relevant binary and effective binary diffusion coefficients, and also with ternary diffusion coefficients reported in the literature. It is shown that a strong coupling exists between the diffusion of hydrophobic solutes and surfactant in solute-containing microemulsions. In particular, the presence of a gradient in the concentration of the solute can induce a surprisingly large flux of surfactant either up or down the solute gradient. Within the framework of irreversible thermodynamics, these results indicate that hydrophobic solute molecules significantly alter the chemical potential of the surfactant in microemulsions. These effects are present to a comparable degree for both the nonionic C12E10 and ionic SDS microemulsions.

Analysis of HRCT-derived xylem network reveals reverse flow in some vessels.

Long distance water and nutrient transport in plants is dependent on the proper functioning of xylem networks, a series of interconnected pipe-like cells that are vulnerable to hydraulic dysfunction as a result of drought-induced embolism and/or xylem-dwelling pathogens. Here, flow in xylem vessels was modeled to determine the role of vessel connectivity by using three dimensional xylem networks derived from High Resolution Computed Tomography (HRCT) images of grapevine (Vitis vinifera cv. 'Chardonnay') stems. Flow in 4-27% of the vessel segments (i.e. any section of vessel elements between connection points associated with intervessel pits) was found to be oriented in the direction opposite to the bulk flow under normal transpiration conditions. In order for the flow in a segment to be in the reverse direction, specific requirements were determined for the location of connections, distribution of vessel endings, diameters of the connected vessels, and the conductivity of the connections. Increasing connectivity and decreasing vessel length yielded increasing numbers of reverse flow segments until a maximum value was reached, after which more interconnected networks and smaller average vessel lengths yielded a decrease in the number of reverse flow segments. Xylem vessel relays also encouraged the formation of reverse flow segments. Based on the calculated flow rates in the xylem network, the downward spread of Xylella fastidiosa bacteria in grape stems was modeled, and reverse flow was shown to be an additional mechanism for the movement of bacteria to the trunk of grapevine.

Automated analysis of three-dimensional xylem networks using high-resolution computed tomography.

Connections between xylem vessels represent important links in the vascular network, but the complexity of three-dimensional (3D) organization has been difficult to access. This study describes the development of a custom software package called TANAX (Tomography-derived Automated Network Analysis of Xylem) that automatically extracts vessel dimensions and the distribution of intervessel connections from high-resolution computed tomography scans of grapevine (Vitis vinifera) stems, although the method could be applied to other species. Manual and automated analyses of vessel networks yielded similar results, with the automated method generating orders of magnitude more data in a fraction of the time. In 4.5-mm-long internode sections, all vessels and all intervessel connections among 115 vessels were located, and the connections were analyzed for their radial distribution, orientation, and predicted shared wall area. Intervessel connections were more frequent in lateral than in dorsal/ventral zones. The TANAX-reconstructed network, in combination with commercial software, was used to visualize vessel networks in 3D. The 3D volume renderings of vessel networks were freely rotated for observation from any angle, and the 4.5 µm virtual serial sections were capable of being viewed in any plane, revealing aspects of vessel organization not possible with traditional serial sections.

Diffusion of sodium dodecyl sulfate micelles in agarose gels.

The gradient diffusion of ionic sodium dodecyl sulfate micelles in agarose gel was investigated at moderate concentrations above the CMC. Of particular interest were the effects of micelle, gel, and sodium chloride concentration on the micelle diffusivity. Holographic interferometry was used to measure the gradient diffusion coefficient at three sodium chloride concentrations (0, 0.03, 0.10 M), three gel concentrations (0, 1, 2 wt%), and several surfactant concentrations. Time-resolved fluorescence quenching was used to measure aggregation numbers both in solution and gel. The micelle diffusivity increased linearly with surfactant concentration at the two larger sodium chloride concentrations and all gel concentrations. In general, the strength of this effect increased with decreasing sodium chloride concentration and increased with gel concentration. This behavior is evidence of decreasing micelle-micelle electrostatic interactions with increasing sodium chloride concentrations, and increasing excluded volume effects and hydrodynamic screening with increasing gel concentration, respectively. The only exception was at 0.1M sodium chloride and 2 wt% agarose, which showed a slight reduction in the slope compared to 1 wt% agarose. It was found that the concentration effect is quite strong for charged solutes: at a NaCl concentration of 0.03 M in a 2% agarose gel, in a solution with 3% SDS micelles by volume, the micelle diffusion coefficient is doubled relative to its value in the same gel at infinite dilution. The extrapolated, infinite-dilution diffusion coefficients and the rate at which the micelle diffusivity increased with surfactant concentration were compared with predictions of previously published theories in which the micelles are treated as charged, colloidal spheres and the gel as a Brinkman medium. The experimental data and theoretical predictions were in good agreement.

Effect of emulsion drop-size distribution upon coalescence in simple shear flow: a population balance study.

A population balance is used to examine the effect of the shape of the initial drop-size distribution of an emulsion upon its short and long-time evolution in simple shear flow. Initial distributions that are monodisperse, multidisperse, lognormal, bimodal, multimodal, and step functions are considered. At short times, it is shown that the rate of coalescence decreases by up to 25% for step distributions and up to 75% for lognormal distributions as the width of the distribution increases. Bimodal, multidisperse and multimodal distributions show intermediate decreases in the rate of coalescence, between these two values, with increases in the distribution width. Furthermore, it is found that the initial rate of coalescence is strongly dependent upon the presence of large drops. As the number fraction of large droplets within the distribution increases, the rate of coalescence also increases. At long times, all distributions move toward an asymptotic distribution shape in which the frequency of drops decreases algebraically with drop diameter at small drop diameters, and decreases exponentially with drop diameter at large drop diameters. Though portions of each distribution showed the expected asymptotic scaling behavior at long times, each asymptotic distribution nevertheless retains 'fingerprints' of the respective initial distribution. Overall, the rate of coalescence for a system is bounded by the initial rate, which is a function of the initial distribution shape, and the asymptotic rate, which is dependent upon the long-time scaling behavior. Finally, it is shown that the resolution with which the drop-size distribution of an emulsion is experimentally measured can have a significant effect upon predicted rates of coalescence.

The effect of surface charge distribution on hindered diffusion in pores.

An analytic solution is derived for the hindered diffusion of charged, small solutes in charged, cylindrical pores in which the pore wall potential consists of the sum of an average and an oscillatory component. When the oscillatory contribution is absent, the effect of electrostatic interactions on diffusion is negligible. However, when the wall potential or surface charge density varies axially, electrostatic interactions hinder the rate of diffusion significantly, and can stop it completely if "choke points" develop where the solute concentration becomes zero. The degree of hindrance is generally weaker when the electrostatic charge on the pore wall and the charge on the solute have the same signs, leading to a repulsion, than it is in the presence of an attraction. The electrostatic hindrance is also affected by the length scale of the axial variation along the pore wall, becoming stronger as that length grows, until an asymptotic value is reached. The theory for the effect of variations of the electrostatic potential on rates of diffusion is shown to be in good agreement with experimental data taken from the literature. The results here are obtained by using generalized Taylor dispersion theory, and are therefore rigorous predictions of what occurs over times long enough that the solute diffuses through a tube many times longer than a single periodic cell. The electrostatic interactions are calculated using the linear Poisson-Boltzmann equation.

The Effect of Solute Concentration on Equilibrium Partitioning in Polymeric Gels.

The effect of solute concentration on the equilibrium partitioning of sphere-like, colloidal solutes in stiff polymer hydrogels is examined theoretically and experimentally. The theoretical development is a statistical mechanics approach, and allows quantitative calculations to be performed to determine the concentration-dependent partition coefficient correct to first order in solute concentration at specific surface charge densities. The theory predicts that repulsive steric and/or electrostatic solute-fiber interactions exclude solute from the gel phase, but that repulsive solute-solute interactions cause partitioning into the gel to increase with increasing solute concentration. These trends are enhanced for larger solutes, increased fiber volume fractions, or stronger electrostatic repulsion. Partition coefficients have also been measured for two proteins, bovine serum albumin (BSA) and alpha-lactalbumin (ALA), in a system consisting of a salt solution and cubes of agarose hydrogel. To investigate the effect of electrostatic interactions, the experiments were performed at 0.15 M KCl and 0.01 M KCl. The theory underpredicts the strong electrostatic repulsion between BSA macromolecules at the lower ionic strength. The experimental results for ALA show the influence of an attractive interaction between the protein macromolecules, in addition to hard-sphere repulsive and electrostatic interactions. Copyright 2001 Academic Press.