A mathematical model for hydrodynamic and size exclusion chromatography of polymers on porous particles

When packed columns filled with porous particles are used for the separation of macromolecules, either size exclusion chromatography (SEC), hydrodynamic chromatography (HDC), or a combination of both determine the macromolecule retention mechanism. This paper develops a simple mathematical model to describe a molecular weight calibration graph, which includes both HDC and SEC. There is a transition between the HDC calibration region at higher molecular weights to an SEC region at lower molecular weights. The degree to which SEC and HDC are mixed depends on the particle diameter, the relative size of the pores, and the macromolecule size. In addition, using fractal considerations, the fractal character of the apparent selectivity between two adjacent peaks on the chromatogram is shown. This model constitutes an attractive tool to enhance the expansion of these two chromatographic techniques for the separation of biological or synthetical macromolecules.     

Polymeric porogens used in the preparation of novel monodispersed macroporous polymeric separation media for high-performance liquid chromatography.

A novel approach to monosized macroporous polymeric separation media with vastly enhanced pore size distributions and chromatographic properties has been developed. Key to this approach is the combined use of monodispersed polymeric particles and suitable solvents as porogens in the copolymerization of styrene and divinylbenzene. Following polymerization, the polymeric porogen is dissolved, leaving behind the monosized beads with a controlled pore structure. The exact pore size and pore size distribution of the final beads are largely controlled by the amount of soluble polymer in the polymerizing mixture: the larger the proportion of soluble polymer in the system, the larger the pores. The uniformly sized macroporous beads prepared with an optimized ratio of polymeric and low molecular weight porogens proved to be very efficient even in short columns for the separation of polystyrene standards in the SEC mode and the separation of proteins in the reversed-phase mode. The relationship between pore size and specific surface area, on one hand, and chromatographic properties of the stationary phase, on the other, have been clearly documented.     

The effect of stationary-phase pore size on retention behavior in micellar liquid chromatography

One of the limitations that has restricted the applicability of micellar liquid chromatography (MLC) is the weak eluting power of micellar mobile phases compared to conventional hydro-organic mobile phases used in reversed-phase liquid chromatography. This may be the result of Donnan or steric exclusion of the micelles from the pores of the stationary phase, within which nearly all (> or = 99%) of the stationary phase resides and the analytes spend most of their time. To determine whether wide-pore stationary phases would overcome this limitation in MLC, several C8 and C18 stationary phases ranging from 100 to 4000 A were investigated using a diverse set of test solutes and micellar solutions of anionic, neutral, and cationic surfactants as mobile phases. With the larger pore size stationary phases, the eluting power of the MLC mobile phases was enhanced with all surfactant types, the greatest effect being with the neutral surfactant. Differences in retention behavior were observed between various solute types and between the C8 and C18 stationary phases. These differences appear to be related to the relative hydrophobicity of the solutes and to differences in the surfactant-modified stationary phases. Partitioning behavior of representative solutes on the large-pore C8 and C18 columns was shown to follow the three-phase partitioning model for MLC. Methylene group selectivity data showed only minor differences in the stationary-phase characteristics between the small- and large-pore size C18 columns. The true eluting power of micellar mobile phases was revealed with wide-pore stationary phases and was demonstrated by the separation and elution of an extended series of alkylphenones on C18 columns.     

Nonaqueous capillary electrochromatographic separation of synthetic neutral polymers by size exclusion chromatography using polymeric stationary phases

In this paper, we report the separations of large, neutral, synthetic polymers using primarily a nonaqueous mobile phase without the use of a supporting electrolyte. The size- exclusion-based mechanism for separation was achieved on sulfonated polystyrene/divinylbenzene stationary phases. The effect of water, voltage, stationary phase exchange capacity, and pore size were investigated. The stationary phase and solvent interactions were studied by attenuated total reflectance Fourier transform infrared spectroscopy (ATR FT-IR) and a possible mechanism for the generation of EOF in the THF/water system is provided. Linear calibration curves were obtained for polystyrenes ranging in MW from 5K to 2M, for columns made using a combination of high capacity ion exchanger and a neutral polystyrene/divinylbenzene material of varied pore sizes. Analysis of polyurethane, polystyrene, and other polymer samples using CEC correlated well with results obtained by conventional HPLC. The size exclusion CEC separations provide an alternative mode for determining the relative molecular weights of polymers, with reduced solvent consumption.     

Quantitative LC-MS of polymers: determining accurate molecular weight distributions by combined size exclusion chromatography and electrospray mass spectrometry with maximum entropy data processing

We report on the successful application of size exclusion chromatography (SEC) combined with electrospray ionization mass spectrometry (ESI-MS) and refractive index (RI) detection for the determination of accurate molecular weight distributions of synthetic polymers, corrected for chromatographic band broadening. The presented method makes use of the ability of ESI-MS to accurately depict the peak profiles and retention volumes of individual oligomers eluting from the SEC column, whereas quantitative information on the absolute concentration of oligomers is obtained from the RI-detector only. A sophisticated computational algorithm based on the maximum entropy principle is used to process the data gained by both detectors, yielding an accurate molecular weight distribution, corrected for chromatographic band broadening. Poly(methyl methacrylate) standards with molecular weights up to 10 kDa serve as model compounds. Molecular weight distributions (MWDs) obtained by the maximum entropy procedure are compared to MWDs, which were calculated by a conventional calibration of the SEC-retention time axis with peak retention data obtained from the mass spectrometer. Comparison showed that for the employed chromatographic system, distributions below 7 kDa were only weakly influenced by chromatographic band broadening. However, the maximum entropy algorithm could successfully correct the MWD of a 10 kDa standard for band broadening effects. Molecular weight averages were between 5 and 14% lower than the manufacturer stated data obtained by classical means of calibration. The presented method demonstrates a consistent approach for analyzing data obtained by coupling mass spectrometric detectors and concentration sensitive detectors to polymer liquid chromatography.     

Overloading study of bases using polymeric RP-HPLC columns as an aid to rationalization of overloading on silica-ODS phases

The separation of ionized bases by reversed-phase liquid chromatography with alkyl silica columns often leads to severely tailed bands that are highly detrimental. Band shape and its dependence on sample mass are notably different when mobile-phase pH is changed, and this behavior has not been previously explained. Ionized silanols present in the stationary phase have been credited with a role in determining peak shape. In the present study, separations on two different polymer columns were compared with those previously obtained on alkyl silica phases. Because silanols are absent from polymer columns, this comparison enabled us to assess the role of silanols in separations on alkyl silica phases and to offer an explanation of why band shape changes with sample size and mobile-phase pH for both polymer and silica-based phases.     

Reconciliation between experimental and Monte Carlo-based simulation of the pore size distribution in mesoporous silicon

It is demonstrated for the first time that mesoporous PS structures obtained by the electrochemical etching of p(+)(100) oriented silicon wafers might assume the peculiarity of invariance of the first peak positions in their pore size distribution curves, albeit for current densities far from the electropolishing region and at constant electrolyte composition. A new Monte Carlo-based simulation model is presented that predicts reasonably the pore size distribution of the PS layers and the observed invariance of peak position with respect to changes in current density. The main highlight of the new model is the introduction of a 'light avalanche breakdown' process in a mathematical fashion. The model is also able to predict an absolute value of 4.23?? for the smallest pore created experimentally. It is discussed that the latter value has an exact physical meaning: it corresponds with great accuracy to the width of a void created on the surface due to the exclusion of one Si atom.     

High-aspect-ratio, silicon oxide-enclosed pillar structures in microfluidic liquid chromatography

The present paper discusses the ability to separate chemical species using high-aspect-ratio, silicon oxide-enclosed pillar arrays. These miniaturized chromatographic systems require smaller sample volumes, experience less flow resistance, and generate superior separation efficiency over traditional packed bed liquid chromatographic columns, improvements controlled by the increased order and decreased pore size of the systems. In our distinctive fabrication sequence, plasma-enhanced chemical vapor deposition (PECVD) of silicon oxide is used to alter the surface and structural properties of the pillars for facile surface modification while improving the pillar mechanical stability and increasing surface area. The separation behavior of model compounds within our pillar systems indicated an unexpected hydrophobic-like separation mechanism. The effects of organic modifier, ionic concentration, and pressure-driven flow rate were studied. A decrease in the organic content of the mobile phase increased peak resolution while detrimentally effecting peak shape. A resolution of 4.7 (RSD = 3.7%) was obtained for nearly perfect Gaussian shaped peaks, exhibiting plate heights as low as 1.1 and 1.8 μm for fluorescein and sulforhodamine B, respectively. Contact angle measurements and DART mass spectrometry analysis indicate that our employed elastomeric soft bonding technique modifies pillar properties, creating a fortuitous stationary phase. This discovery provides evidence supporting the ability to easily functionalize PECVD oxide surfaces by gas-phase reactions.     

Principle of two-dimensional characterization of copolymers

Two-dimensional polymer characterization is used for a simultaneous analysis of molar masses and chemical heterogeneities (e.g., end groups, copolymer composition, etc.). This principle is based on coupling of two different chromatographic modes. Liquid adsorption chromatography at critical conditions (LACCC) is applied for a separation according to the chemical heterogeneity, whereas in the second-dimension fractions are analyzed with regard to their molar mass distribution by means of size exclusion chromatography (SEC). Because appropriate standards for a calibration of the SEC are seldom available, matrix-assisted laser desorption/ionization-time-of-flight mass spectrometry (MALDI-TOF MS) was used to substitute the SEC. The LACCC-MALDI MS coupling enables acquiring additional structural information on copolymer composition, which can considerably enhance the performance of this coupled method.     

Effects of pore flow on the separation efficiency in capillary electrochromatography with porous particles

The effect of pore flow on the separation efficiency of capillary electrochromatography (CEC) has been studied using columns packed with particles with different pore sizes. A previously developed model was used to predict the (relative) pore flow velocity in these columns under various experimental conditions. Equations are derived describing the effect of pore flow on peak broadening in CEC. The theory has been compared with practice in the reversed-phase CEC separation of various polyaromatic hydrocarbons. It is shown, by theory and experimentally, that the mass-transfer resistance contribution to peak dispersion can be effectively eliminated when using porous particles with a high (> or =50 nm) average pore diameter. Moreover, at high pore-to-interstitial flow ratios the flow inhomogeneity contribution (the A term in the plate height equation) is also shown to decrease. Under optimal conditions, a reduced plate height of 0.3 for the nonretained compound could be obtained. It is argued that fully perfusive porous particles can be a more efficient separation medium in CEC than nonporous particles.     

Polar polymeric stationary phases for normal-phase HPLC based on monodisperse macroporous poly(2,3-dihydroxypropyl methacrylate-co-ethylene dimethacrylate) beads

The effect of variables such as shape template size, porogen composition and percentage, content of cross-linking monomer, and polymerization temperature on the properties of uniformly sized 3-microm porous poly(glycidyl methacrylate-co-ethylene dimethacrylate) beads prepared by the staged templated suspension polymerization technique has been studied. The porous properties of the beads including surface morphology, pore size distribution, and specific surface area have been optimized to obtain highly efficient stationary phases for normal-phase HPLC. A column packed with diol stationary phase obtained by hydrolysis of poly(glycidyl methacrylate-co-ethylene dimethacrylate) beads affords an efficiency of 67,000 plates/m for toluene using THF as the mobile phase. The retention properties and selectivity of the diol beads are easily modulated by changes in the composition of the mobile phase. The performance of these beads is demonstrated with the separations of a variety of polar compounds including positional isomers, aniline derivatives, and basic tricyclic antidepressant drugs.     

High-resolution length sorting and purification of DNA-wrapped carbon nanotubes by size-exclusion chromatography

We report a size-exclusion chromatography (SEC) process to purify DNA-wrapped carbon nanotubes (DNA-CNT) and to sort them into fractions of uniform length. A type of silica-based column resin was identified that shows minimum adsorption of DNA-CNT. Three such columns in series with pore sizes of 2000, 1000, and 300 A were found to separate DNA-CNT into fractions of very narrow length distribution, as measured directly by atomic force microscopy. The average length decreases monotonically from > 500 nm in the early fractions to < 100 nm in the late fractions, with length variation < or = 10% in each of the measured fractions. Using UV-vis-NIR spectroscopy, we showed that SEC is very effective in removing graphitic impurities that contribute to the spectral baseline and a broad absorption peak at approximately 270 nm. This result highlights the importance of CNT purification in the study of optical properties of CNT.     

Colloid-imprinted carbons as stationary phases for reversed-phase liquid chromatography

A novel colloid-imprinting method is employed for the preparation of carbonaceous stationary phases for reversed-phase liquid chromatography (RPLC). This colloid-imprinting method combined with oxidative stabilization treatment affords carbons with a porous shell/nonporous core structure. The particle morphology, pore size, pore shape, and Brunauer-Emmett-Teller surface area of these carbons can be finely tuned by selecting proper experimental conditions. Although their surface area and pore volume decrease noticeably after graphitization, their primary pore structure is maintained. In addition, the graphitization process eliminates the high-energy sites and substantially reduces structural heterogeneity, making colloid-imprinted carbons attractive stationary phases for reversed-phase liquid chromatography. The colloid-imprinted graphitic carbons with surface mesoporosity appeared to be attractive for chromatographic separations of alkylbenzenes under reversed-phase conditions.     

Influence of surface charge on ingress of chloride ion in hardened pastes

The amount of free chloride content in concrete is one of major factors in initiating the corrosion process. The material and environmental factors play a key role in diffusing the chloride ion through the cover concrete to reinforcement. Thus, the electrochemical study is indispensable to understand the mechanism of chloride ingress into concrete. Determination of surface charge and its influence on diffusion of chloride ion into cement matrix of concrete are researched for Ordinary Portland Cement (OPC) paste and cement paste containing Ground Granulated Blastfurnace Slag (GGBS). Different kinds of experiments such as measurement of membrane potential, determination of porosity and pore size distribution, determination of pore solution concentration, and steady state diffusion coefficient of chloride and sodium ions are employed to understand the mechanism of chloride ingress. The obtained results show that the positive surface charge on the pore walls of hardened paste regardless of GGBS’s presents. The surface charge of hardened paste mainly depends on pore solution concentration and cement composition. The physiochemical characteristics of the pores are affecting on transporting ions through it. Hardened paste has greater resistance to diffusing sodium ions than chloride ions. Moreover, there is a strong interaction between transport of chloride ion and surface charge in matured hardened paste.     

Pore structure and function of synthetic nanopores with fixed charges: tip shape and rectification properties

We present a complete theoretical study of the relationship between the structure (tip shape and dimensions) and function (selectivity and rectification) of asymmetric nanopores on the basis of previous experimental studies. The theoretical model uses a continuum approach based on the Nernst-Planck equations. According to our results, the nanopore transport properties, such as current-voltage (I-V) characteristics, conductance, rectification ratio, and selectivity, are dictated mainly by the shape of the pore tip (we have distinguished bullet-like, conical, trumpet-like, and hybrid shapes) and the concentration of pore surface charges. As a consequence, the nanopore performance in practical applications will depend not only on the base and tip openings but also on the pore shape. In particular, we show that the pore opening dimensions estimated from the pore conductance can be very different, depending on the pore shape assumed. The results obtained can also be of practical relevance for the design of nanopores, nanopipettes, and nanoelectrodes, where the electrical interactions between the charges attached to the nanostructure and the mobile charges confined in the reduced volume of the inside solution dictate the device performance in practical applications. Because single tracks are the elementary building blocks for nanoporous membranes, the understanding and control of their individual properties should also be crucial in protein separation, water desalination, and bio-molecule detection using arrays of identical nanopores.     

Single-particle fritting technology for capillary electrochromatography

Large perfusive silica beads (particle size 110 microm, through pore approximately 2 microm) held in place by the keystone effect were used as single-particle frits for the manufacture of particulate packed capillary columns. High-quality capillary electrochromatographic separations of a standard test mixture of alkylbenzenes were obtained over the full voltage range of 5-30 kV, with no requirement for pressurization. Excellent robustness was demonstrated by the reproducibility of migration times, peak efficiencies, and resolution during 100 consecutive runs at the highest voltage (30 kV) without thermostating and pressurization. Superior performance relative to traditional sinter-fritted columns is ascribed to the heat-free fritting process and short frit length of approximately 110 microm.     

Comparative study of hydrocarbon, fluorocarbon, and aromatic bonded RP-HPLC stationary phases by linear solvation energy relationships.

The retention properties of eight alkyl, aromatic, and fluorinated reversed-phase high-performance liquid chromatography bonded phases were characterized through the use of linear solvation energy relationships (LSERs). The stationary phases were investigated in a series of methanol/water mobile phases. LSER results show that solute molecular size and hydrogen bond acceptor basicity under all conditions are the two dominant retention controlling factors and that these two factors are linearly correlated when either different stationary phases at a fixed mobile-phase composition or different mobile-phase compositions at a fixed stationary phase are considered. The large variation in the dependence of retention on solute molecular volume as only the stationary phase is changed indicates that the dispersive interactions between nonpolar solutes and the stationary phase are quite significant relative to the energy of the mobile-phase cavity formation process. PCA results indicate that one PCA factor is required to explain the data when stationary phases of the same chemical nature (alkyl, aromatic, and fluoroalkyl phases) are individually considered. However, three PCA factors are not quite sufficient to explain the whole data set for the three classes of stationary phases. Despite this, the average standard deviation obtained by the use of these principal component factors are significantly smaller than the average standard deviation obtained by the LSER approach. In addition, selectivities predicted through the LSER equation are not in complete agreement with experimental results. These results show that the LSER model does not properly account for all molecular interactions involved in RP-HPLC. The failure could reside in the V2 solute parameter used to account for both dispersive and cohesive interactions since "shape selectivity" predictions for a pair of structural isomers are very bad.     

钢筋混凝土柱纯扭破坏尺寸效应数值分析

在地震作用下,钢筋混凝土柱时常会受到扭矩的作用,而扭矩的存在会改变钢筋混凝土柱的破坏模式。为探究钢筋混凝土柱纯扭破坏的尺寸效应行为,采用三维细观数值模拟方法,考虑了混凝土细观组分的非均质性及钢筋与混凝土间的粘结滑移作用,建立了钢筋混凝土柱的纯扭作用数值模型。模拟分析了结构尺寸、纵筋率、配箍率和截面形状对钢筋混凝土柱抗扭破坏的影响。结果表明:钢筋混凝土柱扭转破坏表现为脆性特征,名义抗扭强度表现出明显的尺寸效应;纵向配筋对扭转强度尺寸效应影响不大;方形截面柱比圆形截面柱具有更强的尺寸效应;箍筋可以提高扭转强度,且可以削弱名义抗扭强度的尺寸效应。最后,修正了Ba?ant尺寸效应律,建立了全结构尺寸范围内的名义抗扭强度预测公式。     

Fabrication of graphene oxide nanosheets incorporated monolithic column via one-step room temperature polymerization for capillary electrochromatography

Graphene oxide (GO) has received great interest for its unique properties and potential diverse applications. Here, we show the fabrication of GO nanosheets incorporated monolithic column via one-step room temperature polymerization for capillary electrochromatography (CEC). GO is attractive as the stationary phase for CEC because it provides not only ionized oxygen-containing functional groups to modify electroendoosmotic flow (EOF) but also aromatic macromolecule to give hydrophobicity and π-π electrostatic stacking property. Incorporation of GO into monolithic column greatly increased the interactions between the tested neutral analytes (alkyl benzenes and polycyclic aromatics) and the stationary phase and significantly improved their CEC separation. Baseline separation of the tested neutral analytes on the GO incorporated monolithic column was achieved on the basis of typical reversed-phase separation mechanism. The precision (relative standard deviation (RSD), n = 3) of EOF was 0.3%, while the precision of retention time, peak area, and peak height for the tested neutral analytes were in the range of 0.4-3.0%, 0.8-4.0%, and 0.8-4.9%, respectively. In addition, a set of anilines were well separated on the GO incorporated monolith. The GO incorporated monolithic columns are promising for CEC separation.     

Automated instrumentation for comprehensive two-dimensional high-performance liquid chromatography of proteins

A comprehensive two-dimensional (2-D) liquid chromatographic separation system is presented. The system uses a microbore cation exchange column, operated under gradient conditions, as the first dimension separation. Effluent from this first column alternately fills one of two loops on a computer-controlled eight-port valve. A second pump then forces loop material onto a second column, a size exclusion column. UV detection is used, and the system is applied to the separation of protein standards and serum proteins. The 2-D system has a higher resolving power and peak capacity than either of the two columns used alone. The entire first column effluent is analyzed on the second column in virtually the same time it takes to complete the first column separation, without the use of stopped flow methods. The entire system is automated and operated under computer control. Three-dimensional (3-D) data representation provides a means of viewing peak profiles in either separation dimension and contour mapping of the 3-D data provides a more reliable means of peak identification from run to run than that provided by single-column elution times.