Correction for particle-wall interactions in the separation of colloids by flow field-flow fractionation

In the characterization of materials by field-flow fractionation (FFF), the experienced analyst understands the importance of incorporating additives in the carrier liquid that minimize or eliminate interactions between the analyte and accumulation wall, particularly in aqueous systems. However, as FFF is applied to more difficult samples, such as those with high surface energies, it is increasingly difficult to find additives that completely eliminate particle-wall interactions. Furthermore, the analyst may wish to use specific conditions that preserve the high surface energy of particles, to study their interaction with other materials through their behavior in the FFF channel. With this in mind, Williams and co-workers developed a model that quantifies the effect of particle-wall interactions in FFF using an empirically determined interaction parameter. In this work, the model is evaluated for the application of flow FFF in carrier liquids of low ionic strength, where particle-wall interactions are magnified. The retention of particles ranging in size from 64 to 1000 nm is measured using a wide range of field strengths and retention levels. The model is found to be generally valid over the entire range, except for minor discrepancies at lower levels of retention. Although retention levels are dramatically affected by particle-wall interactions, the point of steric inversion (500 nm), where the size-based elution order reverses, is not affected. When particle-wall interactions are not accounted for, they lead to a bias in particle sizes calculated from standard retention theory of up to 70%. The model can also be used to refine the measurement of channel thickness, which is important for the accurate conversion of retention parameters to particle sizes. In this work, for example, errors in channel thickness led to systematic errors on the order of 10% in particle diameter.     

Bayesian analysis for weighted mean‐squared error in dual response surface optimization

Dual response surface optimization considers the mean and the variation simultaneously. The minimization of mean‐squared error (MSE) is an effective approach in dual response surface optimization. Weighted MSE (WMSE) is formed by imposing the relative weights, (λ, 1?λ), on the squared bias and variance components of MSE. To date, a few methods have been proposed for determining λ. The resulting λ from these methods is either a single value or an interval. This paper aims at developing a systematic method to choose a λ value when an interval of λ is given. Specifically, this paper proposes a Bayesian approach to construct a probability distribution of λ. Once the distribution of λ is constructed, the expected value of λ can be used to form WMSE. Copyright © 2009 John Wiley & Sons, Ltd.     

Influence of operating parameters on the retention of chromatographic particles by thermal field-flow fractionation

We have investigated the retention behavior of chromatographic particles in thermal field-flow fractionation (FFF). Retention time is found to increase with increasing temperature drop across the channel thickness, as expected for species exhibiting a thermophoretic mobility. Experiments have been performed with a vertically oriented channel rather than by using the classical horizontal configuration as this leads to much more reproducible retention data. In acetonitrile, silica-based particles are more retained than octadecyl-bonded silica particles, which confirms our previous finding, by means of a different method, that the thermophoretic mobility of the latter is smaller than that of the former. Whatever the type of particles and the nature of the carrier liquid, the relative retention time is observed to decrease with increasing carrier flow rate. This indicates that a hydrodynamic lift force acts on particles to move them away from the accumulation wall, as is usually observed in all FFF experiments with micrometer-sized particles. However, upward and downward flow directions in the vertical channel lead to similar retention data, indicating that inertial lift forces have a minor influence on retention. In addition, the relative retention time steadily decreases with increasing sample concentration, suggesting that the hydrodynamic lift force increases significantly with sample concentration. Accordingly, we speculate that a new transport phenomenon, called shear-induced hydrodynamic diffusion, not previously accounted for in the modeling of retention in FFF, is controlling the migration of the particles in the FFF channel. Implications of the influence of this phenomenon in other FFF experiments are discussed.     

Colloid characterization by sedimentation field-flow fractionation: correction for particle-wall interaction

The effect of particle-wall interaction on retention ratios in sedimentation field-flow fractionation (FFF) is shown to be describable in terms of a semiempirical parameter δ(w) having units of length. A method of experimentally determining the value of this parameter for a given system is presented. It requires the determination of retention ratios for a set of particle standards over a range of field strengths. The value of δ(w) is simply obtained from the slope of a certain straight line plot of the retention data. Once determined, this parameter may be incorporated into the procedure for the determination of particle diameters from measured retention times to take account of the effects of particle-wall interaction. In principle, δ(w) is independent of field strength and is the same for different FFF instruments providing they employ the same carrier liquid and channel wall material. Therefore, δ(w) values have the potential to be universal system constants transferable from one instrument to another.     

Scene-based nonuniformity correction algorithm based on interframe registration

In this paper, we present a simple and effective scene-based nonuniformity correction (NUC) method for infrared focal plane arrays based on interframe registration. This method estimates the global translation between two adjacent frames and minimizes the mean square error between the two properly registered images to make any two detectors with the same scene produce the same output value. In this way, the accumulation of the registration error can be avoided and the NUC can be achieved. The advantages of the proposed algorithm lie in its low computational complexity and storage requirements and ability to capture temporal drifts in the nonuniformity parameters. The performance of the proposed technique is thoroughly studied with infrared image sequences with simulated nonuniformity and infrared imagery with real nonuniformity. It shows a significantly fast and reliable fixed-pattern noise reduction and obtains an effective frame-by-frame adaptive estimation of each detector's gain and offset.     

Working without accumulation membrane in flow field-flow fractionation

Nonideal interaction of sample with the separation device is a difficulty found in chromatographic methods as well as in field-flow fractionation. However, in field-flow fractionation (FFF), greater flexibility in the choice of carrier solution composition is possible, thus reducing the need of a wide choice of surface chemistry when nonideal sample interaction is to be minimized. The use of an ultrafiltration membrane as the surface for the accumulation wall is common practice in flow field-flow fractionation. Typical membranes in use are laminates of a skin membrane onto a backing material such as woven polyester. At this point, only a limited choice of membrane chemistries is available. Many membranes have been developed for protein applications as membranes are widely used in the pharmaceutical industries. While these membranes work well for protein applications, flow field-flow fractionation is applicable to polymeric particulate as well as protein samples. Thus, sample interaction with the membrane surface is possible with nonprotein applications and these interactions can induce significant secondary effects on retention ratio and affect instrumental reliability. Also, the woven texture of membranes may detrimentally affect the FFF separation. For these reasons, the study of flow field-flow fractionation using a flat, smooth surface of controlled chemistry is of relevance. We present here the results of a new, membraneless channel that uses a bare frit as the accumulation wall and that is intended for analysis of micrometer-sized particles only. Selectivity results are comparable to those obtained with the membrane, while relative sample recovery indicates that the best quantitative performance can be obtained without the membrane. Moreover, neither sample immobilization nor losses through the frit occur when operating membraneless. On the other hand, first experimental evidence of a certain level of frit surface activity suggests that optimization of experimental conditions is required.     

On the motion of superparamagnetic particles in magnetic drug targeting

A stochastic ODE model is developed for the motion of a superparamagnetic cluster suspended in a Hagen-Poiseuille flow and guided by an external magnet to travel to a target. The specific application is magnetic drug targeting, with clusters in the range of 10–200 nm radii. As a first approximation, we use a magnetic dipole model for the external magnet and focus on a venule of 10⁻⁴ m radius close to the surface of the skin as the pathway for the clusters. The time of arrival at the target is calculated numerically. Variations in release position, background flow, magnetic field strength, number of clusters, and stochastic effects are assessed. The capture rate is found to depend weakly on variations in the velocity profile, and strongly on the cluster size, the magnetic moment, and the distance between the magnet and the blood vessel wall. A useful condition is derived for the optimal capture rate. The case of simultaneous release of many clusters is investigated. Their accumulation in a neighborhood of the target at the venule wall follows a normal distribution with the standard deviation roughly half of the distance between the magnet and the target. Ideally, this deviation should equal the tumor radius, and the magnet should be beneath the center of the tumor. The optimal injection site for a cluster is found to be just prior to arrival at the target. Two separate mechanisms for capturing a cluster are the magnetic force and, for radii smaller than 20 nm, Brownian motion. For the latter case, the capture rate is enhanced by Brownian motion when the cluster is released near the wall.     

Analysis of beam properties in the neighbourhood of a double-heterostructure laser source

Abstract

The power density distribution and beam characteristics of double-heterostructure lasers with very thin active layers in the neighbourhood of the light source are evaluated by using a plane wave spectrum approach and a second-moment order theory for diffracted scalar light beams. It is shown that the evanescent waves contribute to shape the power density when the distance is smaller than the emission wavelength λ or of the order of λ. It should be noted that the optical fields deeply penetrate into the cladding layers when the thickness of the active layer is much smaller than the emission wavelength λ.     

Particle size distribution by sedimentation/steric field-flow fractionation: development of a calibration procedure based on density compensation

Because of the important but mathematically complex role played by hydrodynamic lift forces in sedimentation/steric FFF, applied generally to particles greater than 1 micron in diameter, retention cannot readily be related to particle diameter on the basis of simple theory. Consequently, empirical calibration is needed. Unfortunately, retention is based on particle density as well as size so that a purely size-based calibration (e.g., with polystyrene latex standards) is not generally valid. By examining the balance between driving and lift forces, it is concluded that equal retention will be observed for equal size particles subject to equal driving forces irrespective of particle density. Therefore by adjusting the rotation rate to exactly compensate for density, retention can be brought in line with that of standards, a conclusion verified by microscopy. Linear calibration plots of log (retention time) versus log (diameter) can then be used. This approach is applied to two glass bead samples (5-30 and 5-50 microns) using both a conventional and a pinched inlet channel. The resulting size distribution curves are self consistent and in good agreement with results obtained independently.     

Reduction of end effect-induced zone broadening in field-flow fractionation channels

A channel configuration for the elimination of end effects in field-flow fractionation (FFF) channels is simulated and demonstrated for a microfabricated FFF system. In field-flow fractionation, the carrier liquid and sample particles are transferred from a point injection to the full breadth of the rectangular channel using a triangular end piece at the inlet. The nonuniformity in streamline length generated by this end piece results in an increased instrument-related plate height. An additional contribution from the end piece at the outlet of the channel further increases the total band broadening. This paper presents a novel approach to minimize end-effect contributions to plate height by fabricating microstructures in the channel end sections to redistribute the flow streams and force streamline lengths to be more uniform. Numerical analysis of the flow profile and sample dispersion (including spreading of particles due to diffusion and advection) is carried out to investigate the optimized microstructure column size, shape, and placement in the end pieces. The configuration obtained from the numerical simulation results is used to design a prototype device. Experimental measurement of the plate heights for this prototype with an on-chip impedance-based detector shows marked improvement in performance due to the presence of the microstructures in comparison to conventional FFF channel geometry with an average 50% reduction in plate height. The redesigned inlet triangle results in a uniform transition of the point-injected sample into a thin and straight band across the width of the channel at the start of the rectangular section of the fractionation channel.     

Size determination of diesel soot particles using flow and sedimentation field-flow fractionation

The applicability of field-flow fractionation (FFF) was investigated for determination of size and size distribution of diesel soot particles. A sample preparation procedure was developed for FFF analysis where soot particles are recovered from filters in an ethanol bath sonicator, and then they are dispersed in water containing 0.05% Triton X-100 and 0.02% NaN(3). Mean diameters obtained from sedimentation FFF (SdFFF) and flow FFF (FlFFF) agree well with each other and are in good agreement with diameters obtained from photon correlation spectroscopy (PCS) and scanning electron microscopy. The relative error was less than 11%. Data show diesel soot particles have broad size distributions ranging from 0.05 up to ～0.5 μm with the mean diameters between 0.1 and 0.2 μm. The use of FlFFF is more convenient as FlFFF fractograms can be converted directly to size distributions, while the conversion of the SdFFF fractogram needs the particle density information. The density needed for SdFFF analysis was obtained by combining the SdFFF retention data with the PCS size data. For samples whose density is known, SdFFF may be more useful as SdFFF provides a wider dynamic range than FlFFF under constant field strength.     

Hollow-Fiber flow field-flow fractionation of synthetic polymers in organic solvents

A modified polyacrylonitrile (PAN) hollow-fiber membrane from a commercial source has been applied as the separation channel in flow field-flow fractionation (FFF). With the PAN membrane fiber, the application range of flow FFF could be extended to synthetic polymers that are soluble in a variety of organic solvents. The PAN membrane was shown to be resistant to hydrophobic solvents, such as dichloromethane (DCM), tetrahydrofuran (THF), ethyl acetate, and methyl ethyl ketone (MEK), as was illustrated by the successful fractionation of different polymer standards in these solvents. The system performance was assessed using polystyrene (PS) standards with ethyl acetate as the solvent. For a 100 kDa PS standard, the average recoverywas 57%, but for standards with a molar mass of 400 kDa and higher, 100% recovery was obtained. A linear relationship between peak area and injected mass was found. The run-to-run and fiber-to-fiber repeatability was determined using 100- and 400 kDa PS standards. The repeatability appeared to be satisfactory, with relative standard deviations < 2% for the retention times and < 5% for the recoveries of the standards. Plate numbers for the 400 kDa standard on different fibers were in the order of 110. From measurements on the fractionation of ferritin aggregates, it is concluded that the instrumental band-broadening is negligible. For an accurate determination of diffusion coefficients and molecular sizes based on retention times, calibration of the channel with standards appeared to be necessary. However, it was shown that the FFF system could be coupled to a multiangle light scattering (MALS) detector, thus providing an alternative on-line method for calibration. Expressions for the maximum obtainable plate number per unit of time have been derived for a hollow-fiber flow FFF system. It is shown that an increase in the system performance can be expected from a scaling down of the fiber diameter.     

A method for eigenvalues of sparse λ-matrices

The matrix N(λ) whose elements are functions of a parameter λ is called the λ-matrix. Those values of λ that make the matrix singular are of great interest in many applied fields. An efficient method for those eigenvalues of a λ-matrix is presented. A simple explicit convergence criterion is given, as well as the algorithm and two numerical examples.     

GradH‐Correction: guaranteed sizing gradation in multi‐patch parametric surface meshing

In this paper a new method, called GradH‐Correction, for the generation of multi‐patch parametric surface meshes with controlled sizing gradation is presented. Such gradation is obtained performing a correction on the size values located on the vertices of the background mesh used to define the control space that governs the meshing process. In the presence of a multi‐patch surface, like shells of BREP solids, the proposed algorithm manages the whole composite surface simultaneously and as a unique entity. Sizing information can spread from a patch to its adjacent ones and the resulting size gradation is independent from the surface partitioning. Theoretical considerations lead to the assertion that, given a parameter λ, after performing a GradH‐Correction of level λ over the control space, the unit mesh constructed using the corrected control space is a mesh of gradation λ in the real space (target space). This means that the length ratio of any two adjacent edges of the mesh is bounded between 1/λ and λ. Numerical results show that meshes generated from corrected control spaces are of high quality and good gradation also when the background mesh has poor quality. However, due to mesh generator imprecision and theoretical limitations, guaranteed gradation is achieved only for the sizing specifications and not for the generated mesh. Copyright © 2004 John Wiley & Sons, Ltd.     

熔盐法合成金属氯化物-石墨插层化合物的判据

研究了熔融盐状态下金属氯化物-石墨层间化合物的合成判据.根据插层反应热动力学及化学键理论,选取元素的电负性和离子势作为键参数,并设计键参数函数λ为客体材料的遴选判据.基于键参数函数图对金属氯化物发生插层反应的难易程度和产物稳定性进行理论预估.研究结果表明:键参数函数图中λ≤1.2区域内的金属氯化物在700℃以下即可发生插层反应,且所得产物较为稳定;在1.2≤λ≤1.8区域内相应的客体材料在低温下很难单独插入石墨层间,常与低熔点氯化物形成共熔体后一起插入石墨层间;在λ≥1.8区域内大多为碱金属氯化物和碱土金属氯化物,理论分析认为这类物质的插层反应不适宜采用熔盐法.     

Determination of mean diameter and particle size distribution of acrylate latex using flow field-flow fractionation, photon correlation spectroscopy, and electron microscopy

Flow field-flow fractionation (flow FFF) was employed to determine the mean diameter and the size distribution of acrylate latex materials having diameters ranging from 0.05 to 1 μm. Mean diameters of the samples determined by flow FFF are in good agreement with those obtained from photon correlation spectroscopy (PCS). Scanning electron microscopy (SEM) yielded a mean diameter that is about 20% lower than those obtained from flow FFF or PCS, probably due to the shrinkage of particles during sample drying and high-vacuum measurements. It was found that flow FFF is particularly useful for the determination of particle size distributions of latex materials having broad size distributions. Flow FFF separates particles according to their sizes and yields an elution curve that directly represents the particle size distribution of the sample. In PCS, measurements had to be repeated at more than one scattering angle to obtain an accurate mean diameter for the latex having a broad size distribution. Flow FFF was fast (less than 12 min of run time) and showed an excellent repeatability in measuring the mean diameter with ±5% relative error.     

Hydrodynamic relaxation and sample concentration in field-flow fractionation using permeable wall elements

The advantages of hydrodynamic relaxation in field-flow fractionation, in which an injected sample is driven rapidly toward its equilibrium distribution by flow, are described relative to conventional field-driven relaxation. A new concept for achieving hydrodynamic relaxation, based on the use of permeable wall elements (or frit elements) embedded in the channel walls, is introduced. Here an auxiliary substream of carrier fluid, permeating uniformly into the FFF channel near the inlet, drives the sample, entrained in its own substream, close to its equilibrium configuration. Such frit elements can also be used to enrich the sample at the outlet. Equations are derived and plots are provided for the position of the splitting plane dividing the two substreams; this position defines the strength of the hydrodynamic relaxation. Variations in shear through these frit-modified end regions are also formulated and plotted. The effects of frit elements on band broadening are discussed. It is concluded that permeable wall elements in many configurations may be broadly applicable to FFF and related methods for improved sample introduction, increased separation speed, reduced risk of sample adhesion to the wall, improved flow stability, and sample enrichment.     

Analysis of whole bacterial cells by flow field-flow fractionation and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

The purpose of this study is to develop a novel bacterial analysis method by coupling the flow field-flow fractionation (flow FFF) separation technique with detection by matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometry. The composition of carrier liquid used for flow FFF was selected based on retention of bacterial cells and compatibility with the MALDI process. The coupling of flow FFF and MALDI-TOF MS was demonstrated for P. putida and E. coli. Fractions of the whole cells were collected after separation by FFF and further analyzed by MALDI-MS. Each fraction, collected over different time intervals, corresponded to different sizes and possibly different growth stages of bacteria. The bacterial analysis by flow FFF/MALDI-TOF MS was completed within 1 h with only preliminary optimization of the process.     

A method for solving high-order real symmetric eigenvalue problems

A new method for solving structural dynamics problems has been proposed by the author in a separate paper.¹ This method of solution produces a high order real symmetric eigenvalue problem of the form ( A ? λ B ? λ² C ? λ³ D …) U = 0. An algorithm for solving such an eigenvalue problem using simultaneous iteration is presented in this paper. Methods of accelerating the convergence and reducing the amount of computation are also described. A numerical example is given in which the algorithm is used to calculate the eigenvalues and eigenvectors of a framed structure.     

Surface scattering effects in CdS thin films

A method, based upon the careful investigation of the dependence of the Hall coefficient on thickness, to determine the value of the mean surface scattering length λ is presented. Hall data presented for slowly deposited cadmium sulphide thin films indicate the relationship between λ and the carrier concentration. Data are also presented to exhibit the critical dependence of λ upon substrate temperature and deposition rate. The temperature dependence of the parameter λ/μ_b indicates the predicted $\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ relationship.