Linear peak capacity of a comprehensive multi-dimensional separation

In order to resolve (quantifiably and identifiably separate) the same number of peaks in the analysis of the same mixture yielding statistically uniform peak distribution, a comprehensive 2-D separation needs a two times larger peak capacity than a 1-D separation does. Each additional dimension further reduces the utilization of the peak capacity of comprehensive multi-dimensional (MD) separation by a factor of two per dimension. As a result, the same peak capacity means different things for separations with different dimensionalities. This complicates the use of the peak capacity for comparison of the potential separation performance of the separations with different dimensionalities. To facilitate the comparison, a concept of a linear peak capacity has been proposed. The linear peak capacity of an MD separation is the peak capacity of a 1-D separation that, in the analysis of the same mixture, is statistically expected to resolve the same number of peaks as the MD separation is. There are other factors that differently affect the performance of the separations that have different dimensionalities. Peak capacity of a 2-D separation with a rectangular separation space is 27% larger than the product of the peak capacities of its first and second dimension. This advantage of a 2-D separation is essentially nullified by the fact that the peak capacity of the first dimension of an optimized 2-D separation cannot be higher than 80% of the peak capacity of its first dimension standing alone. All in all, the incremental peak capacity gained from addition of a second dimension will not exceed 50% of the peak capacity of the added second dimension. All results are valid for arbitrarily shaped (not necessarily Gaussian) peaks.     

Properties and analytical applications of the heteropolymolybdates of phosphorus, arsenic, silicon and germanium-III Examination of two- and three-component systems without separation

By taking advantage of the possible variations in acid and molybdenum concentration, wavelength of measurement, alpha- and beta-modifications, and media, P, As, Si and Ge can be determined spectrophotometrically as the heteropolymolybdates without separation. Rapid procedures are proposed for the analysis of two- and three-component mixtures of these elements.     

Using Clar sextets for two- and three-dimensional aromatic systems

After a brief history of the aromaticity concept, the use of Clar sextet circles is reviewed for explaining various aspects of planar aromatic systems (benzenoids, heterocycles) and of tridimensional carbon aggregates. When folding a graphene sheet for obtaining nanotubes, nanotori, or nanocones, the congruence of Clar sextet circles allows the classification of all such aggregates into two classes (congruent or incongruent) with marked differences in properties; this is in agreement with the well-known condition h - k ≡ 0 (mod 3), equivalent to congruence, in terms of the chiral vectors h and k for graphene sheets.     

Protein proteolysis and the multi-dimensional electrochromatographic separation of histidine-containing peptide fragments on a chip

This paper reports a system for three-dimensional electrochromatography in a chip format. The steps involved included trypsin digestion, copper(II)-immobilized metal affinity chromatography [Cu(II)-IMAC] selection of histidine-containing peptides, and reversed-phase capillary electrochromatography of the selected peptides. Trypsin digestion and affinity chromatography were achieved in particle-based columns with a microfabricated frit whereas reversed-phase separations were executed on a column of collocated monolithic support structures. Column frits were designed to maintain constant cross sectional area and path length in all channels and to retain particles down to a size of 3 microm. Cu(II)-IMAC selection of histidine-containing peptides from standard peptide mixtures and protein digests followed by reversed-phase chromatography of the selected peptides was demonstrated in the electrochromatography mode. The possibility to run a comprehensive proteomic analysis by combining trypsin digestion, affinity selection, and a reversed-phase separation on chips was shown using fluorescein isothiocyanate-labeled bovine serum albumin as an example.     

On the caging number of two- and three-dimensional hard spheres

Local structural arrest in random packings of colloidal or granular spheres is quantified by a caging number, defined as the average minimum number of randomly placed spheres on a single sphere that immobilize all its translations. We present an analytic solution for the caging number for two-dimensional hard disks immobilized by neighbor disks which are placed at random positions under the constraint of a nonoverlap condition. Immobilization of a disk with radius r = 1 by arbitrary larger neighbor disks with radius r > or = 1 is solved analytically, whereas for contacting neighbors with radius 0 < r < 1, the caging number can be evaluated accurately with an approximate excluded volume model that also applies to spheres in higher Euclidean dimension. Comparison of our exact two-dimensional caging number with studies on random disk packing indicates that it relates to the average coordination number of random loose packing, whereas the parking number is more indicative for coordination in random dense packing of disks.     

Wetting transitions in two-, three-, and four-phase systems

We discuss wetting of rough surfaces with two-phase (solid-liquid), three-phase (solid-water-air and solid-oil-water), and four-phase (solid-oil-water-air) interfaces mimicking fish scales. We extend the traditional Wenzel and Cassie-Baxter models to these cases. We further present experimental observations of two-, three-, and four-phase systems in the case of metal-matrix composite solid surfaces immersed in water and in contact with oil. Experimental observations show that wetting transitions can occur in underwater oleophobic systems. We also discuss wetting transitions as phase transitions using the phase-field approach and show that a phenomenological gradient coefficient is responsible for wetting transition, energy barriers, and wetting/dewetting asymmetry (hysteresis).     

Recent progress on adsorption and membrane separation for organic contaminants on multi-dimensional graphene

Graphene, a two-dimensional (2D) layered nanomaterial, which has attracted great attention in the environmental field due to its excellent physical and chemical properties, including easily modified surface characteristics, tunable structure, and excellent stability. However, the inherent problems of nanomaterials, such as serious aggregation, difficulty in recycling, and potential ecological risks, have severely hindered the large-scale application of graphene. Therefore, immobilization of nanomaterials into macroscopic structures is one of the most feasible strategies to solve these problems, which is of great significance to promote the progress of nano-water treatment chemistry and technology. With the deepening of related studies, diverse dimensional graphene materials with large specific surface area, internal interconnected porous network and novel functionalities have been successively developed. Herein, we review the structural characteristics and synthesis methods of multi-dimensional graphene materials and highlight some examples with impressive and unique properties. Furthermore, we specifically emphasize their removal performance and mechanisms for organic contaminants in adsorption and membrane separation. Finally, the future outlooks, research directions and foreseeable challenges in this filed are summarized and prospected as concluding remarks based on our understanding.     

Comprehensive multi-dimensional liquid chromatographic separation in biomedical and pharmaceutical analysis: a review

'Multi-dimensional' liquid separations have a history almost as long as chromatography. In multi-dimensional chromatography the sample is subjected to more than one separation mechanism; each mechanism is considered an independent separation dimension. The separations can be carried out either offline via fraction collection, or directly coupled online. Early multi-dimensional separations using combinations of paper chromatography, electrophoresis and gels, in both planar and columnar modes are reviewed. Developments in HPLC have increased the number of measurable analytes in ever more complex matrices, and this has led to the concept of 'global metabolite profiling'. This review focuses on the theory and practice of modern 'comprehensive' multi-dimensional liquid chromatography when applied to biomedical and pharmaceutical analysis.     

A refinement of the terpolymer equation and its simple extension to two- and four-component systems

Terpolymer composition estimation with an established equation has been found to give results that vary with the feed monomer ratio substitution pattern used. A new copolymer equation has been derived that overcomes this difficulty to give the same composition results regardless of the order of monomer substitution. The new equation also gives comparable or better agreement with experimentally determined copolymer compositions than obtained by use of the established Alfrey-Goldfinger terpolymer equation. In addition, this new terpolymer equation demonstrates a versatility not shown by the present terpolymer equations in that it can be readily adapted by inspection to enable estimation of copolymer compositions for two- or for four-component polymer systems. It is also readily adaptable for copolymers with more than four components, and may also be valid for composition estimation of these because of the derivation method used, although it has not as yet been possible to test this possibility. © 1996 John Wiley & Sons, Inc.     

Correlations between chemical structure and chain packing in two- and three-dimensional systems

Phosphatidylcholines (PCs) containing a branched chain fatty acid at the sn-1 position of the glycerol backbone were characterized by calorimetric and X-ray diffraction studies with bilayers as well as by thermodynamic studies with monolayers. Branching leads to altered thermal properties which are connected with a modified structural polymorphism. Gel phases with interdigitated chains or nonbilayer liquid-crystalline phases could be found in dependence on the length of the side branches. The pressure-area isotherms of the monobranched PCs were measured over a wide range of temperature. The critical temperatures T_c of the transition between the liquid-expanded and condensed films were estimated and compared with the main transition temperatures T_m of the bulk phase. T_c was found to be either lower or higher or equal to T_m. The correlations between T_c and T_m are discussed in terms of chain packing in the two- and threedimensional systems.     

Comprehensive multi-dimensional chromatographic studies on the separation of saturated hydrocarbon ring structures in petrochemical samples

Characterization of complex petrochemical samples has been a classical subject of comprehensive two-dimensional (2D) gas chromatography (GC x GC). Macroscopic properties of these samples can be described accurately by separation of compounds in classes of identical molecular functionality. Ring structures in the carbon backbone of these compounds, which can be divided in saturated and unsaturated, are amongst the foremost functionalities affecting samples properties. Unfortunately, GC x GC tuned for separation of both saturated and unsaturated ring structures is likely to result in convoluted chromatograms when a distribution of both molecular properties is present in the sample. An independent liquid chromatographic (LC) separation preceding GC x GC could be used to resolve the mixture based on unsaturated rings, allowing saturated rings to be resolved separately in the GC x GC separation. This three-dimensional separation (abbreviated LC-GC x GC) was performed after rigorous evaluation of LC as part of a multidimensional separation using LC x GC. Group-type separation was achieved using this separation for components with either saturated or unsaturated rings. Results of this separation were used to compare information obtained by GC x GC with LC-GC x GC.     

On the impact and the separation approximations in the theory of multiphoton interactions ivith thermally perturbed systems

Criteria are provided for the factorization of thermal averages incuring in the calculation of cross-sections for several-photon processes, into produc     

Rapid sequential separation of essential oil compounds using continuous heart-cut multi-dimensional gas chromatography-mass spectrometry

A method for separation and identification of peaks in essential oil samples based on rapid repetitive heart-cutting using multidimensional gas chromatography (MDGC)-mass spectrometry (MS) coupled with a cryotrapping interface is described. Lavender essential oil is analyzed by employing repetitive heart-cut intervals of 1.00 and 1.50 min, achieved in a parallel MDGC-MS/GC-FID experiment. The number of peaks that were detected in 1D GC operation above a given response threshold more than tripled when MDGC-MS employing the cryotrapping module method was used. In addition, MDGC-MS enabled detection of peaks that were not individually evident in 1D GC-MS, owing to effective deconvolution in time of previously overlapped peaks in 1D GC. Thus separation using the cryomodulation approach, without recourse to using deconvolution software, was possible. Peaks widths decreased by about 5-7-fold with the described method, peak capacity increased from about 9 per min to 60 per min, and greater sensitivity results. Repeatability of retention times for replicate analyses in the multidimensional mode was better than 0.02% RSD. The present study suggests that the described heart-cutting technique using MDGC-MS can be used for general improvement in separation and identification of volatile compounds.     

Study on the feasibility of obtaining highly enriched Carbon-13 in one- and two- stage modes of laser separation process

The feasibility of obtaining highly enriched (¹³C & 80%) carbon-13 by isotope-selective IR multiphoton dissociation (MPD) of Freon 22 (CF₂HCl) molecules in one- and two-stage modes of the process in an apparatus with the intracavity arrangement of the separation reactor, which resembled current technological facilities in its basic characteristics, was studied. The one-stage separation scheme was realized using the selective MPD of Freon 22 by which¹³C is concentrated in the dissociation product tetrafluoroethylene (C²F⁴). Carbon-13 concentrations in the product and MPD yields were measured depending on the laser radiation frequency and Freon 22 and bath gas (nitrogen) pressure. At the chosen irradiation geometry and a laser pulse repetition rate of 30 Hz,¹³C concentrations of 83 and 89% in the final product with the production rate of ∼36 and ∼7 mg¹³C/h were attained. The two-stage separation scheme was furnished on the basis of isotopically selective dissociation of the intermediate product CF²HI enriched in¹³C by its buildup process upon irradiation of a CF²HCl mixture with HI. The final product in this case was CF²H² having a¹³C concentration of 98 ± 1.5%. The production rate of the two-stage laser separation process was ∼22 mg¹³C/h.     

Application of the Hill determinant approach to several forms of potentials in two- and three-dimensional quantum systems

Energy levels of the Schrödinger equation are calculated for several forms of potentials in two- and three-dimensional space and over a wide range of values of the perturbation parameters by means of the Hill determinant approach. The obtained numerical results are compared with those previously reported by other methods.     

Formation and decay of methylviologen radical cation dimers on the surface of colloidal CdS: separation of two- and three-dimensional relaxation

Methylviologen molecules adsorbed to CdS particles can be reduced to radical cations in situ by optical excitation of the semiconductor. Confinement of the viologen to the surface results in a dramatic increase in the rate of radical cation dimer formation, compared with the bulk solution reaction, arising from the reduction of dimensionality of the reaction space. Subsequently, the dimers are destroyed via reoxidation by unreduced viologen from the bulk solution.     

Average local electrostatic potential and the core-valency separation in atoms

The average local electrostatic potential function, V(r)/ ρ(r), is calculated for 87 atoms, Li-Ac, in the ground state using the nonrelativistic average-over-configuration numerical Hartree-Fock density. It is found empirically that in a given atom the shell boundaries are expressed as the successively increasing maxima in V(r)/ ρ(r) and the outermost maximum presents good approximate estimates of the core-valence separation in atoms. The likeness in behavior of V(r)/ ρ(r) at each shell boundary with the maximum hardness principle is discussed. The single-exponent-fit parameters for the electron density in the valency region are provided for all atoms. © 1995 John Wiley & Sons, Inc.     

Structure-type separation of diesel fuels by solid phase extraction and identification of the two- and three-ring aromatics by capillary GC-mass spectrometry

A simple and effective solid phase extraction (SPE) method using silica gel micro glass columns has been developed for the separation of diesel fuel into groups of aliphatic, and mono-, di- and polyaromatic hydrocarbons. It is based on a stepwise gradient of dichloromethane in n-pentane. The resulting fractions were analyzed by capillary gas chromatography with a flame ionization detector and coupled gas chromatography-mass spectrometry. Commercially available standards, and retention indices and mass spectra were used for identification of individual aromatic compounds. The principal polycyclic aromatic hydrocarbons (PAHs) in diesel fuel are naphthalene, biphenyl, fluorene, phen-anthrene and their alkylated derivatives. Sulfur-containing PAHs are mainly represented by methyl-substituted dibenzo-thiophenes.