Numerical simulations of the second-order electrokinetic bias observed with the gated injection mode in chips

It is well known that sample introduction via electrokinetic mode leads to a bias in conventional CE, which is proportional to the difference of electrophoretic mobilities between species. In electrophoretic separation chips using the gated injection mode, flow distribution at the crossjunction, which is linked to the electric field strength distribution during the loading step, induces an additional contribution to species discrimination. This second-order bias has a similar effect on quantitation like usual electrokinetic bias: the higher the analyte's apparent mobility, the larger the amount injected into the separation channel. The present paper assesses by numerical simulations the influence of several parameters, namely the injected amount, the electric field distribution, and the analyte-apparent Peclet number on this second-order bias.     

Effective potentials between nanoparticles in suspension

Results of molecular dynamics simulations are presented for the pair distribution function between nanoparticles in an explicit solvent as a function of nanoparticle diameter and interaction strength between the nanoparticle and solvent. The effect of including the solvent explicitly is demonstrated by comparing the pair distribution function of nanoparticles to that in an implicit solvent. The nanoparticles are modeled as a uniform distribution of Lennard-Jones particles, while the solvent is represented by standard Lennard-Jones particles. The diameter of the nanoparticle is varied from 10 to 25 times that of the solvent for a range of nanoparticle volume fractions. As the strength of the interactions between nanoparticles and the solvent increases, the solvent layer surrounding the nanoparticle is formed which increases the effective radii of the nanoparticles. The pair distribution functions are inverted using the Ornstein-Zernike integral equation to determine an effective pair potential between the nanoparticles mediated by the introduction of an explicit solvent.     

NMR studies of molecular conformations in alpha-cyclodextrin

A new approach for analysis of NMR parameters is proposed. The experimental data set includes scalar couplings, NOEs, and residual dipolar couplings. The method, which aims at construction of the conformational distribution function, is applied to alpha-cyclodextrin in isotropic solution and dissolved in a dilute liquid crystal. An attempt to analyze the experimental data using an average molecular conformation resulted in unacceptable errors. Our approach rests on the maximum entropy method (ME), which gives the flattest possible distribution, consistent with the experimental data. Very good agreement between experimental and calculated NMR parameters was observed. In fact, two conformational states were required in order to obtain a satisfactory agreement between calculated and experimental data. In addition, good agreement with Langevin dynamics computer simulations was obtained.     

Rapid comparison of diacetylmorphine on banknotes by tandem mass spectrometry

A procedure is described for the determination of the distribution of the contamination of banknotes with controlled drugs using tandem mass spectrometry. The method is illustrated using diacetylmorphine, which is the major active component of heroin. A series of banknotes is introduced into the mass spectrometer and the intensities of two product ions (m/z 328 and 268) derived from the precursor protonated molecule (m/z 370) are recorded. A banknote is considered contaminated if it shows a significant peak for both product ions, and if the ratio of intensities of these two peaks falls within accepted limits. The distribution of diacetylmorphine on sterling banknotes taken from general circulation within the UK can be modelled by an arcsin (square root) transformation of the data or by a log transformation of the data with a higher proportion of contamination. The two models were found to be in close agreement, predicting an upper limit (at 99.9% confidence) of contamination on banknotes from general circulation between 9 and 10%. The percentage contamination in a case study was calculated and compared to the background distribution using the two models proposed. This comparison revealed that the contamination present in the case study was inconsistent with that present on banknotes in general circulation.     

Thermodynamic modelling of polymer solutions with a modified Staverman equation

A model describing the thermodynamic behaviour of polymer solutions is derived which explicitly accounts for the flexibility of the polymer chains. Based on computer simulations on various lattices it is shown that the flexibility of a polymer chain can be modelled by distinguishing different polymer conformations. Here each conformation is characterized by its corresponding number of external contact sites. The equilibrium between the different conformations is then solved for any polymer concentration and any combination of interaction energies utilizing a modified Staverman equation. The model predictions are in good agreement with the results of the computer simulations which were performed using the simple-sampling and the slithering-snake algorithm. Since the knowledge of the distribution of the conformations of a single polymer chain on an empty lattice is a prerequisite to perform the model calculations, Poisson distribution functions are fitted to the results of the corresponding computer simulations. The generalization of these distribution functions not only facilitates the use of the new model but also allows to model polymers of varying chain stiffness.     

Effect of surface hydrophobicity distribution on retention of ribonucleases in hydrophobic interaction chromatography

The effect of surface hydrophobicity distribution of proteins on retention in hydrophobic interaction chromatography (HIC) was investigated. Average surface hydrophobicity as well as hydrophobic contact area between protein and matrix were estimated using a classical thermodynamic model. The applicability of the model to predict protein retention in HIC was investigated on ribonucleases with similar average surface hydrophobicity but different surface hydrophobicity distribution. It was shown experimentally that surface hydrophobicity distribution could have an important effect on protein retention in HIC. The parameter "hydrophobic contact area," which comes from the thermodynamic model, was able to represent well the protein retention in HIC with salt gradient elution. Location and size of the hydrophobic patches can therefore have an important effect on protein retention in HIC, and the hydrophobic contact area adequately describes this.     

A new procedure for the determination of distillation temperature distribution of high-boiling petroleum products and fractions

The distribution of distillation temperatures of liquid and semi-fluid products, including petroleum fractions and products, is an important process and practical parameter. It provides information on properties of crude oil and content of particular fractions, classified on the basis of their boiling points, as well as the optimum conditions of atmospheric or vacuum distillation. At present, the distribution of distillation temperatures is often investigated by simulated distillation (SIMDIS) using capillary gas chromatography (CGC) with a short capillary column with polydimethylsiloxane as the stationary phase. This paper presents the results of investigations on the possibility of replacing currently used CGC columns for SIMDIS with a deactivated fused silica capillary tube without any stationary phase. The SIMDIS technique making use of such an empty fused silica column allows a considerable lowering of elution temperature of the analytes, which results in a decrease of the final oven temperature while ensuring a complete separation of the mixture. This eliminates the possibility of decomposition of less thermally stable mixture components and bleeding of the stationary phase which would result in an increase of the detector signal. It also improves the stability of the baseline, which is especially important in the determination of the end point of elution, which is the basis for finding the final temperature of distillation. This is the key parameter for the safety process of hydrocracking, where an excessively high final temperature of distillation of a batch can result in serious damage to an expensive catalyst bed. This paper compares the distribution of distillation temperatures of the fraction from vacuum distillation of petroleum obtained using SIMDIS with that obtained by the proposed procedure. A good agreement between the two procedures was observed. In addition, typical values of elution temperatures of n-paraffin standards obtained by the two procedures were compared. Finally, the agreement between boiling points of polar compounds determined from their retention times and actual boiling points was investigated.     

On the distribution of dye molecules in stretched poly(vinyl alcohol)

The symmetry of the orientational distribution function of dye molecules in stretched PVA films is studied using polarized fluorescence. The different symmetries are monitored by a simple experimental technique in which angle-resolved fluorescence depolarization ratios are measured. A uniaxial distribution of rhodamine 6G molecules is obtained on stretching the film at temperatures above 60°C. In contrast a biaxial distribution of trypaflavine molecules is found for stretch temperatures in the 50–115°C range. It is suggested that the hydrogen bonding between the PVA chains, and between the dye molecules and the PVA chains, influences the symmetry of the distribution upon stretching.     

Determination of cellulase colocalization on cellulose fiber with quantitative FRET measured by acceptor photobleaching and spectrally unmixing fluorescence microscopy

The determination of cellulase distribution on the surface of cellulose fiber is an important parameter to understand when determining the interaction between cellulase and cellulose and/or the cooperation of different types of cellulases during the enzymatic hydrolysis of cellulose. In this communication, a strategy is presented to quantitatively determine the cellulase colocalization using the fluorescence resonance energy transfer (FRET) methodology, which is based on acceptor photobleaching and spectrally unmixing fluorescence microscopy. FRET monitoring of cellulase colocalization was achieved by labeling cellulases with an appropriate pair of FRET dyes and by adopting an appropriate FRET model. We describe here that the adapted acceptor photobleaching FRET method can be successfully used to quantify cellulase colocalization regarding their binding to a cellulose fiber at a resolution <10 nm. This developed quantitative FRET method is promising for further studying the interactions between cellulase and cellulose and between different types of cellulases.     

Effect of interchange reactions on the molecular weight distribution of poly(ethylene terephthalate): A Monte Carlo simulation

The effect of the interchange reactions of poly(ethylene terephthalate) (PET) on its molecular weight distribution (MWD) was analyzed using a Monte Carlo simulation method. Three kinds of motions, which correspond to the direct ester(SINGLEBOND)ester interchange reaction, alcoholysis, and internal alcoholysis in polyester, were performed in this simulation: bond flip, end attack, and backbite. Two systems with two different types of nonequilibrium distribution (monodisperse and bimodal distribution) were initially prepared. The initial biases from equilibrium MWD are rapidly relaxed to an equilibrium MWD as the reaction progresses. The MWD at equilibrium is well described by the most probable MWD proposed by Flory. From the polydispersity data, it is concluded that about 0.3 interchanges per segment are sufficient to equilibrate the nonequilibrium system. For the validity of the simulation, the variation of MWD of the mixtures of two PETs having different molecular weights were monitored using gel permeation chromatography. The agreement between simulation and experiment is remarkably good. © 1996 John Wiley & Sons, Inc.     

Electron correlation effects in SCF+CI wave functions—Fermi and coulomb correlation holes in HCN

The Coulomb correlation hole distribution function has been computed with respect to various reference centers in the HCN molecule, using standard SCF +CI type wave functions. The extent to which statistical correlation between unlike-spin electrons is introduced into an SCF wave function through the inclusion of configuration interaction has been assessed by an examination of the range and depth of such holes, and compared with the behavior of analogous Fermi distribution functions. Our results show that the range of Fermi correlation is consistently longer than that of the corresponding Coulomb correlation.     

Pair interaction potentials of colloids by extrapolation of confocal microscopy measurements of collective suspension structure

A method for measuring the pair interaction potential between colloidal particles by extrapolation measurement of collective structure to infinite dilution is presented and explored using simulation and experiment. The method is particularly well suited to systems in which the colloid is fluorescent and refractive index matched with the solvent. The method involves characterizing the potential of mean force between colloidal particles in suspension by measurement of the radial distribution function using 3D direct visualization. The potentials of mean force are extrapolated to infinite dilution to yield an estimate of the pair interaction potential, U(r). We use Monte Carlo simulation to test and establish our methodology as well as to explore the effects of polydispersity on the accuracy. We use poly-12-hydroxystearic acid-stabilized poly(methyl methacrylate) particles dispersed in the solvent dioctyl phthalate to test the method and assess its accuracy for three different repulsive systems for which the range has been manipulated by addition of electrolyte.     

Partitioning behaviour in aqueous two-phase systems and fractionation by counter-current distribution of chick-embryo erythrocytes with numerical resolution of distribution curves

The partition of chick-embryo and young-chick erythrocytes in dextran-poly-(ethylene glycol) two-phase systems depends on the interfacial tension and electrical potential differences between the phases. Counter-current distribution with charged 5% dextran-poly(ethylene glycol) systems has proved to be an adequate method for the separation of primitive and definitive erythrocytes present in chick embryos when a phase settling time of 20 min is used. The computer-aided numerical resolution of experimental curves has shown the existence of subpopulations which could not have been detected by using conventional methods.     

Microfluidic light scattering as a tool to study the structure of aqueous polymer solutions

A small-angle light scattering (SALS) apparatus, coupled with a specially designed microfluidic device is shown to monitor the formation and subsequent size distribution of giant multilamellar vesicles of a diblock copolymer in aqueous solution. The closed-face design, fabricated between glass slides using a UV-curable optical adhesive, incorporates multiple inlets, a mixing system, and a viewing window to perform on-line SALS. The mixing of each component is tested using polystyrene latex microspheres. Vesicles of the block copolymer, EO6BO11 in aqueous solution are formed on the SALS chip and the pair distance distribution function determined using an inverse Fourier transformation of the scattered intensity to quantify the population and distribution for a range of vesicle sizes. These experiments provide demonstrations of how SALS on a microfluidic device can be used as a rapid screening tool to optimize processing conditions for a range of polymer solutions.     

Atomistic simulation of the growth of defect-free carbon nanotubes

Atomistic simulation of defect-free single-walled carbon nanotube (SWCNT) growth is essential for the insightful understanding of the SWCNT''s growth mechanism. Despite the extensive effort paid in the past two decades, the goal has not been completely achieved, due to the huge timescale discrepancy between atomistic simulation and the experimental synthesis of SWCNTs, as well as the lack of an accurate classical potential energy surface for large scale simulation. Here, we report atomistic simulations of defect-free SWCNT growth by using a new generation of carbon–metal potential and a hybrid method, in which a basin-hopping strategy is applied to facilitate the defect healing during the simulation. The simulations reveal a narrow diameter distribution and an even chiral angle distribution of the growth of SWCNTs from liquid catalyst, which is in agreement with most known experimental observations.     

Dose distribution verification in intraoperative radiation therapy using an N-isopropyl acrylamide-based polymer gel dosimeter

The purpose of the current study was to verify the dose distribution of an Intrabeam-50 kV IORT system using polymer gel dosimetry technique. Results of dose distribution evaluation using NIPAM polymer gel dosimetry were compared with those measured using an ionization chamber and simulated using MCNPX code. Results showed the calculated gamma index was less than 1 with 2% dose-difference/2 mm distance-to-agreement for comparison between NIPAM and ionization chamber as well as between NIPAM and MCNPX simulation. It was concluded that the NIPAM polymer gel dosimetry is useful for verifying the dose distribution of low energy X-ray IORT technique.

     

Computation of distribution of minimum resolution for log-normal distribution of chromatographic peak heights

General equations are derived for the distribution of minimum resolution between two chromatographic peaks, when peak heights in a multi-component chromatogram follow a continuous statistical distribution. The derivation draws on published theory by relating the area under the distribution of minimum resolution to the area under the distribution of the ratio of peak heights, which in turn is derived from the peak-height distribution. Two procedures are proposed for the equations' numerical solution. The procedures are applied to the log-normal distribution, which recently was reported to describe the distribution of component concentrations in three complex natural mixtures. For published statistical parameters of these mixtures, the distribution of minimum resolution is similar to that for the commonly assumed exponential distribution of peak heights used in statistical-overlap theory. However, these two distributions of minimum resolution can differ markedly, depending on the scale parameter of the log-normal distribution. Theory for the computation of the distribution of minimum resolution is extended to other cases of interest. With the log-normal distribution of peak heights as an example, the distribution of minimum resolution is computed when small peaks are lost due to noise or detection limits, and when the height of at least one peak is less than an upper limit. The distribution of minimum resolution shifts slightly to lower resolution values in the first case and to markedly larger resolution values in the second one. The theory and numerical procedure are confirmed by Monte Carlo simulation.     

Separation of poly-3-hydroxyvalerate-co-3-hydroxybutyrate through gradient polymer elution chromatography

Polyhydroxyalkanoates are biodegradable polyesters produced by bacteria that can have a wide distribution in molecular weight, composition of monomers, and functionalities. This large distribution often leads to unpredictable physical properties making commercial applications challenging. To improve polymer homogeneity and obtain samples with a clear set of physical characteristics, poly-3-hydroxyvalerate-co-3-hydroxybutyrate copolymers were fractionated using gradient polymer elution chromatography (GPEC) as opposed to extensively used bulk fractionation. Separation was achieved using a reversed-phase column with chloroform and ethanol as the solvent and non-solvent, respectively. A separation was also conducted on a normal-phase column to compare elution patterns between columns of varied polarity. The fractions were analyzed using Size Exclusion Chromatography (SEC) and NMR to determine the percentage of 3-hydroxyvalerate in the copolymer as well as its molecular weight. It was found that as the percentage of "good" solvent was increased in the mobile phase, the polymers eluted with decreasing percentage of 3-hydroxyvalerate and increasing molecular weight which indicates the importance of precipitation/redissolution in the separation. The elution pattern of the polymer remained unchanged when using both a normal- and reversed-phase column which also illustrates the dominance of precipitation/redissolution in GPEC of polyhydroxyalkanoates. As such, GPEC is shown to be an excellent choice to provide polyhydroxyalkanoate samples with a narrower distribution in composition than the original bulk copolymer sample.     

Voronoi cell volume distribution and configurational entropy of hard-spheres

The Voronoi cell volume distributions for hard-disk and hard-sphere fluids have been studied. The distribution of the Voronoi free volume vf, which is the difference between the actual cell volume and the minimal cell volume at close packing, is well described by a two-parameter (2gamma) or a three-parameter (3gamma) gamma distribution. The free parameter m in both the 2gamma and 3gamma models is identified as the "regularity factor." The regularity factor is the ratio of the square of the mean and the variance of the free volume distribution, and it increases as the cell volume distribution becomes narrower. For the thermodynamic structures, the regularity factor increases with increasing density and it increases sharply across the freezing transition, in response to the onset of order. The regularity factor also distinguishes between the dense thermodynamic structures and the dense random or quenched structures. The maximum information entropy (max-ent) formalism, when applied to the gamma distributions, shows that structures of maximum information entropy have an exponential distribution of vf. Simulations carried out using a swelling algorithm indicate that the dense random-packed states approach the distribution predicted by the max-ent formalism, though the limiting case could not be realized in simulations due to the structural inhomogeneities introduced by the dense random-packing algorithm. Using the gamma representations of the cell volume distribution, we check the numerical validity of the Cohen-Grest expression [M. H. Cohen and G. S. Grest, Phys. Rev. B 20, 1077 (1979)] for the cellular (free volume) entropy, which is a part of the configurational entropy. The expression is exact for the hard-rod system, and a correction factor equal to the dimension of the system, D, is found necessary for the hard-disk and hard-sphere systems. Thus, for the hard-disk and hard-sphere systems, the present analysis establishes a relationship between the precisely defined Voronoi free volume (information) entropy and the thermodynamic entropy. This analysis also shows that the max-ent formalism, when applied to the free volume entropy, predicts an exponential distribution which is approached by disordered states generated by a swelling algorithm in the dense random-packing limit.