Diffusion in three and four component microemulsions containing nonionic surfactant studied by pulsed field gradient nuclear magnetic resonance and quasi-elastic light scattering

Diffusion studies were performed with various methods to obtain some insight into the structure and the dynamical processes of three and four component microemulsions containing p-nonylphenol ethylene oxide adducts which were mixtures of highly branched p-nonyl isomers with well defined distributions of the ethylene oxide chain length.Diffusion coefficients were determined by pulsed field gradient and pulsed field gradient Fourier transform¹ H NMR as well as by quasi-elastic light scattering.The combined application of pulsed field gradient NMR and quasi-elastic light scattering gives information about the critical behaviour of the systems whereas pulsed field gradient Fourier transform NMR allows the determination of the diffusion coefficients of the individual constituents.The results suggest that the very complex three and four component microemulsions studied undergo critical concentration fluctuations in a large temperature region from about 15 °C below the lower critical solution temperatures. The deduced critical exponents are in good agreement with theoretical predictions. The aggregates in the three and four component microemulsions show differences in the self diffusion behaviour of their constituents.     

Photopolymerized diffusion-defined polyacrylamide gradient gels for on-chip protein sizing

We report on a facile diffusion-based photopatterning technique for generating linear and non-linear decreasing pore-size gradients in cross-linked polyacrylamide gels. Diffusion of low viscosity polymer precursor solutions and a two-step photopatterning process were used to define the decreasing pore-size gradient gels in a microfluidic format, thus eliminating the need for controlled mixing and delivery of polymer precursor solutions. We present an analytical model of the non-steady state diffusion process and numerically evaluate that model for direct comparison with empirical characterizations of the gradient gels. We show that the analytical model provides an effective means to predict the steepness and linearity of a desired gradient gel prior to fabrication. To assess electrophoretic assay performance in the microfluidic gradient gels, on-chip sizing of protein samples (20-116 kDa) was investigated. Baseline resolution of six proteins was demonstrated in 4 s using 3.5% to 10% polyacrylamide gradient gels. The demonstrated ability to conduct efficient protein sizing in ultra-short separation lengths (0.3 cm) means low applied electric potentials are needed to achieve the electric field strengths required for protein separations. The low required electric potentials relax operating constraints on electrical components, as is especially important for translation of the assay into pre-clinical and clinical settings. The gradient gel fabrication method reported is amenable to adaptation to non-sizing protein assays, as well as integration with upstream sample preparation steps and subsequent orthogonal downstream assays.     

Fluorescence correlation spectroscopy analysis of diffusion in a laser gradient field: a numerical approach

Fluorescence correlation spectroscopy (FCS) is widely used in biological systems. When the laser is intense enough, such as in two-photon experiments, the trapping force due to the laser gradient field can change the diffusion behavior of the fluorescent particles and induce error in the FCS measurements. Previous studies on biased FCS are qualitative. In this article, a numerical approach is proposed to treat the problem quantitatively. By assumption of a "spherical symmetry", biased FCS curves can be calculated numerically and fitted to the experimental data to retrieve the unbiased particle number, diffusion time, and polarizability of the fluorescent particles as well as the strength of the gradient field. It has been proven using simulated FCS data that the discrepancy caused by the spherical symmetry approximation is independent of the gradient field strength; therefore it can be eliminated by a calibration.     

Pivotal steps towards quantification of molecular diffusion coefficients by NMR.

Using nuclear magnetic resonance (NMR) spectroscopy with a pair of pulsed field gradients (PFGs), Stajeskal and Tanner successfully measured molecular diffusion coefficients in solution in 1965. This method has since been used extensively in various applications, especially after the PFG was implemented in commercial NMR probes. Due to the nonuniformity of the PFG and radio frequency (RF) fields, molecules distributed throughout the sample experience different PFG and RF fields and contribute unevenly to the measured diffusion coefficients, resulting in considerable errors in conventional NMR diffusion experiments. By selective excitation of a central sample region with an offset-independent adiabatic inversion pulse and a PFG, a uniform RF field can be assumed, and the PFG can be represented as a linear approximation. Under these conditions, the molecules diffuse as if they were all experiencing the same effective gradient g(e), leading to a Gaussian signal decay as a function of the PFG strength. Quantitative measurement of molecular diffusion coefficients is therefore made possible. From the diffusion coefficient of a 90 % H(2)O/10 % D(2)O sample, it is convenient to calibrate g(e) with a Java program. In a similar way the nonlinearity of the PFG can be corrected.     

Identification of partially disordered peptide intermediates through residue-specific NMR diffusion measurements

It is technically challenging to detect low-population partially disordered species that are in equilibrium with the folded and unfolded states. Residue-specific translational diffusion experiments measured by pulsed field gradient NMR have been used to detect the presence, and define the conformation, of such equilibrium intermediates. The experiment is demonstrated for equilibrium solutions of related triple helical peptides that model a small region of type I collagen with and without a mutation known to cause osteogenesis imperfecta. The data show that residue-specific diffusion coefficients of an interconverting trimer to monomer system can allow discrimination between a simple two-state model and more complex multistate models involving partially disordered intermediates.     

Electric field gradient focusing

Electric field gradient focusing (EFGF) is a relatively new separation technique with promising attributes, particularly for protein analysis. The fundamental fractionation mechanism in EFGF involves a gradient in electric field along the length of a separation column. The electrophoretic force that drives charged analytes in a region of changing electric field is opposed by a constant, pressure-driven bulk fluid flow. When the electrophoretic velocity of a particular moiety is equal and opposite to the velocity of the fluid flow, the analyte focuses into a stationary band. Thus, EFGF can both concentrate and separate charged species according to electrophoretic mobility. To date, the electric field gradients needed for EFGF have been established using a number of different approaches, including channels having changing cross-sectional areas, conductivity gradients caused by the diffusion of buffer ions across a membrane, electrode arrays, and temperature gradients in buffers whose conductivities change as a function of temperature. EFGF has proven particularly effective for sample enrichment, with concentration factors of 10,000 reported. In this article we review advances in EFGF technology and discuss prospects for further improving EFGF for chemical analysis.     

Diffusion of free radicals as studied by tomography

A linear magnetic field gradient superimposed on the main static field was used to study one-dimensional diffusion of perchlorotriphenylmethyl radicals in decalin and of oxygen molecules in polytetrafluoroethylene. A simple method is developed for deducing diffusion coefficients from both time-dependent and single-scan experiments provided that the natural linewidth is small relative to the field change over the diffusion distance.     

Influence of varying electroosmotic flow on the effective diffusion in electric field gradient separations

Recently the use electric field gradient focusing (EFGF) to enhance focusing of proteins has been proposed and explored to provide significant improvement in separation resolution. The objective of EFGF is to focus proteins of specific electrophoretic mobilities at distinct stationary locations in a column or channel. This can be accomplished in a capillary by allowing the electric potential to vary in the streamwise direction. Because the electric field is varying, so also is the electrokinetic force exerted on the proteins and the electroosmotic velocity of the buffer solution. Due to the varying electric field, the Taylor diffusion characteristics will also vary along the column, causing a degradation of peak widths of some proteins, dependent on their equilibrium positions and local velocity distributions. The focus of this paper is an analysis that allows characterization of the local Taylor diffusion and resulting protein band peak width as a function of the local magnitude of the EOF relative to the average fluid velocity for both cylindrical and rectangular channels. In general the analysis shows that as the ratio of the local electroosmotic velocity to the average velocity deviates from unity, the effective diffusion increases significantly. The effectiveness of EFGF devices over a range of protein diffusivities, capillary diameters, flow velocities, and electric field gradient is discussed.     

Polymer capture by electro-osmotic flow of oppositely charged nanopores

The authors have addressed theoretically the hydrodynamic effect on the translocation of DNA through nanopores. They consider the cases of nanopore surface charge being opposite to the charge of the translocating polymer. The authors show that, because of the high electric field across the nanopore in DNA translocation experiments, electro-osmotic flow is able to create an absorbing region comparable to the size of the polymer around the nanopore. Within this capturing region, the velocity gradient of the fluid flow is high enough for the polymer to undergo coil-stretch transition. The stretched conformation reduces the entropic barrier of translocation. The diffusion limited translocation rate is found to be proportional to the applied voltage. In the authors' theory, many experimental variables (electric field, surface potential, pore radius, dielectric constant, temperature, and salt concentration) appear through a single universal parameter. They have made quantitative predictions on the size of the adsorption region near the pore for the polymer and on the rate of translocation.     

Transport in polymer-gel composites: response to a bulk concentration gradient

This paper examines the response of electrolyte-saturated polymer gels, embedded with charged spherical inclusions, to a weak gradient of electrolyte concentration. An electrokinetic model was presented in an earlier publication, and the response of homogeneous composites to a weak electric field was calculated. In this work, the influence of the inclusions on bulk ion fluxes and the strength of an electric field (or membrane diffusion potential) induced by the bulk electrolyte concentration gradient are computed. Effective ion diffusion coefficients are significantly altered by the inclusions, so-depending on the inclusion surface charge or zeta potential-asymmetric electrolytes can behave as symmetrical electrolytes and vice versa. The theory also quantifies the strength of flow driven by concentration-gradient-induced perturbations to the equilibrium diffuse double layers. Similarly to diffusiophoresis, the flow may be either up or down the applied concentration gradient.     

Reverse nonequilibrium molecular-dynamics calculation of the Soret coefficient in liquid benzene/cyclohexane mixtures

Reverse nonequilibrium molecular dynamics is the method applied here for the investigation of thermal diffusion in realistic molecular fluids. The Soret coefficients of benzene/cyclohexane mixtures are calculated using an all-atom model. The autocorrelation functions indicate that the mole fraction gradient converges much slower than the temperature gradient. Compared to experimental data, the results show the same tendency of the Soret coefficient variation versus the mole fraction. Although a systematic error exists for the magnitude of the Soret coefficient, a meanwhile systematic error for both the mutual diffusion and thermal diffusion coefficients provides some explanation of it; and the calculation with different force field parameters indicates a possibility to annihilate the systematic error. The influences of algorithm variables such as cutoff lengths and perturbation intensities are tested. Furthermore the temperature dependence of the Soret effect is observed, yielding the same trend as previous studies.     

Static and pulsed field gradient nuclear magnetic resonance studies of water diffusion in protein matrices

Static field gradient and pulsed field gradient NMR are used to study the temperature dependence of water diffusion in myoglobin and lysozyme matrices for low hydration levels of about 0.3?g/g. We show that in order to determine reliable self-diffusion coefficients D in a broad temperature range, it is very important to consider an exchange of magnetization between water and protein protons, often denoted as cross relaxation. Specifically, upon cooling, the observed stimulated-echo decays, which reflect water diffusion near ambient temperature, become more and more governed by cross relaxation. We demonstrate that comparison of experimental results for inhomogeneous and homogeneous magnetic fields enables successful separation of diffusion and relaxation contributions to the stimulated-echo decays. Making use of this possibility, we find that in the temperature range 230-300?K, the temperature-dependent diffusivities D exhibit a Vogel-Fulcher-Tammann behavior, where water diffusion in the studied protein matrices is substantially slower than in the bulk. By comparing present and previous data, we discuss relations between translational and rotational motions and between short-range and long-range water dynamics in protein matrices. In addition, we critically examine the significance of results from previous applications of NMR diffusometry to the temperature-dependent water diffusion in protein matrices.     

Anisotropic diffusion of water in perfluorosulfonic acid membrane and hydrocarbon membranes

Polymer electrolyte membranes that are applied for polymer electrolyte fuel cell (PEFC) retain water in their three-dimensional network structure. Diffusion behavior of water in the membranes was analyzed by pulsed field gradient (PFG)-NMR method to estimate diffusion coefficient of proton species as water or hydronium ion. The membrane samples were put in a sample tube vertically or horizontally toward to the field gradient axis under determined temperature and humidity conditions. As the results, anisotropic diffusion behavior of water in the membranes was indicated. Anisotropic properties depended on the sample type, preparation conditions of the wet membranes, and measurement conditions. A perfluorosulfonic acid membrane tended to have smaller anisotropy while hydrocarbon membranes showed greater anisotropy.     

Application of pulsed field gradient NMR with high gradient strength for studies of self-diffusion in lipid membranes on the nanoscale

This work demonstrates the feasibility of noninvasive studies of lipid self-diffusion in model lipid membranes on the nanoscale using proton pulsed field gradient (PFG) NMR spectroscopy with high (up to 35 T/m) gradient amplitudes. Application of high gradients affords for the use of sufficiently small diffusion times under the conditions when the width of the gradient pulses is much smaller than the diffusion time. As a result, PFG NMR studies of partially restricted or anomalous diffusion in lipid bilayers become possible over length scales as small as 100 nm. This length scale is important because it is comparable to the size of membrane domains, or lipid rafts, which are believed to exist in biomembranes. In this work, high-gradient PFG NMR has been applied to study lipid self-diffusion in three-component planar-supported multibilayers (1,2-dioleoyl- sn-glycerol-3-phosphocholine/sphingomyelin/cholesterol). The degree of lipid orientation in the bilayers was determined with (31)P NMR. A special insert was designed to mechanically align the multibilayer stack at the magic angle with respect to the direction of the constant magnetic field to address the detrimental effects of proton dipole-dipole interactions on the NMR signal. This insert is an alternative to the conventional method of magic angle orientation of lipid membranes, the goniometer probe, which is not compatible with commercial high-gradient coils because of the lack of space in the magnet bore. Macroscopic orientation of the multibilayer stacks using the insert was confirmed with (1)H NMR spectroscopic studies and the comparison of results obtained from identical experiments using a goniometer probe for orientation. Diffusion studies were carried out at three different constant magnetic field strengths ( B 0) over a range of temperatures and diffusion times. The measured diffusivities were found to be in agreement with the data obtained previously by techniques that are limited to much larger length scales of diffusion observation than high-gradient PFG NMR.     

Computational simulation of polymerization-induced phase separation under a temperature gradient

Polymerization-induced phase separation (PIPS) via spinodal decomposition (SD) under a temperature gradient for the case of a monomer polymerizing in the presence of a non-reactive polymer is studied using high performance computational methods. An initial polymer (A)/monomer (B) one-phase mixture, which has an upper critical solution temperature (UCST) and is maintained under a temperature gradient, phase-separates and evolves to form spatially inhomogeneous microstructures. The space-dependence of the phase-separated structures under the temperature gradient field is determined and characterized using quantitative visualization methods. It is found that a droplet-type phase-separated structure is formed in the high-temperature region, corresponding to the intermediate stage of SD. On the other hand, lamella or interconnected cylinder type of phase-separated structure is observed in the low-temperature region, corresponding to the early stage of SD structure, in the large or small temperature gradient field, respectively. The kinetics of the morphological evolution depends on the magnitude of the temperature gradient field. The non-uniform morphology induced by the temperature gradient is characterized using novel morphological techniques, such as the intensity and scale of segregation. It is found that significant non-uniform structures are formed in a temperature gradient in contrast to the uniform morphology formed under constant temperature.     

Generation of stable complex gradients across two-dimensional surfaces and three-dimensional gels

Many chemical and biological processes are dependent on molecular gradients. We describe a new microfluidic approach that can be used to produce spatiotemporal gradients across two-dimensional surfaces and three-dimensional gels under flow-free conditions. Free diffusion between dynamically replenished flow channels acting as a sink and source is utilized to give rise to stable steady-state gradient profiles. The gradient profile is dictated by the engineered design of the device's gradient-generating region. Different designs can yield both linear and non-linear gradients of varying profiles. More complex gradients can be made by juxtaposing different designs within a single gradient-generating region. By fabricating an array of designs along the gradient-generating region, different gradient profiles can be generated simultaneously, allowing for parallel analysis. Additionally, simple methods of localizing gels into microdevices are demonstrated. The device was characterized by experimentally obtained gradient profiles of fluorescent molecules that corroborated closely with a simulated finite element model.     

Restricted diffusion in silica particles measured by pulsed field gradient NMR

The restricted diffusion coefficient of water through porous silica is measured by pulsed field gradient (PFG) NMR as a function of loading in order to develop a model for self-diffusion at full pore filling in sol-gel-made porous silica particles. This model describes the pore or intraparticle diffusion coefficient as a function of particle porosity, tortuosity, and the steric hindrance applied on the molecules by the pore space. The particle morphology is characterized by nitrogen adsorption and an appropriate tortuosity model is chosen in comparison with literature data. To characterize the material, NMR relaxation and diffusion studies at different degrees of pore filling were carried out in relation to the silica/water adsorption isotherm.     

Diffusive diffraction phenomenon in a porous polymer material observed by NMR using radio-frequency field gradients

Pulsed field gradient NMR diffusion experiments can, in principle, lead to the "diffusive diffraction" phenomenon. In practice, its observation by gradients of the static magnetic field is difficult in real systems because they involve internal gradients due to the static magnetic field (necessary for polarizing nuclear spins). This latter drawback can be circumvented by using gradients of the radio-frequency (rf) field (the other magnetic field used in any NMR experiment). For the first time, by means of rf gradients, a so-called diffusive diffraction peak has been observed in a real porous system and its position provides a value of the mean distance between pores; this can be further complemented by the mean pore size determined from the dependence of the apparent diffusion coefficient with respect to the diffusion interval.     

Fluid self-diffusion in Scots pine sapwood tracheid cells

The self-diffusion coefficients of water and toluene in Scots pine sapwood was measured using low field pulsed field gradient nuclear magnetic resonance (PFG-NMR). Wood chips of 8 mm diameter were saturated with the respective liquids, and liquid self-diffusion was then traced in one dimension orthogonal to the tracheid cell walls in the wood's radial direction. The experimental echo attenuation curves were exponential, and characteristic self-diffusion coefficients were produced for diffusion times spanning from very short times to times on the order of magnitude of seconds. Observed self-diffusion coefficients were decaying asymptotically as a function of diffusion time, an effect which was ascribed to the cell walls' restriction on confined liquid diffusion. The observed self-diffusion behavior in Scots pine sapwood was compared to self-diffusion coefficients obtained from simulations of diffusion in a square. Principles of molecular displacements in confined geometries were used for elucidating the wood's cellular structure from the observed diffusion coefficients. The results were compared with a mathematical model for diffusion between parallel planes.     

Existing condition and migration property of ions in lithium electrolytes with ionic liquid solvent

Ionization conditions of each ionic species in lithium ionic liquid electrolytes, LiTFSI/BMI-TFSI and LiTFSI/BDMI-TFSI, were confirmed based on the diffusion coefficients of the species measured by the pulsed gradient spin-echo (PGSE) NMR technique. We found that the diffusion coefficient ratios of the cation and anion species D(Li)(obs)/D(F)(obs) of the lithium salt and D(H)(obs)/D(F)(obs) of the ionic liquid solvent were effective guides to evaluate the ionization condition responsible for their mobility. Lithium ions were found to be stabilized, forming the solvated species as Li(TFSI)3(2-). TFSI- anion coordination could be relaxed by the dispersion of silica to form a gel electrolyte, LiTFSI/BDMI-TFSI/silica. It is expected that the oxygen sites on the silica directly attract Li+, releasing the TFSI- coordination. The lithium species, loosing TFSI- anions, kept a random walk feature in the gel without the diffusion restriction attributed from the strong chemical and morphological effect as that in the gel with the polymer. We can conclude that the silica dispersion is a significant approach to provide the appropriate lithium ion condition as a charge-transporting species in the ionic liquid electrolytes.