Dependence of effective peak capacity in comprehensive two-dimensional separations on the distribution of peak capacity between the two dimensions

One of the basic tenets of comprehensive two-dimensional chromatography is that the total peak capacity is simply the product of the first- and second-dimension peak capacities. As formulated, the total peak capacity does not depend on the relative values of the individual dimensions but only on the product of the two. This concept is tested here for the experimentally realistic situation wherein the first-dimension separation is undersampled. We first propose that a relationship exists between the number of observed peaks in a two-dimensional separation and the effective peak capacity. We then show here for a range of reasonable total peak capacities (500-4000) and various contributions of peak capacity in each dimension (10-150) that the number of observed peaks is only slightly dependent on the relative contributions over a reasonable and realistic range in sampling times (equal to the first-dimension peak standard deviation, multiplied by 0.2-16). Most of this work was carried out under the assumption of totally uncorrelated retention times. For uncorrelated separations, the small deviations from the product rule are due to the "edge effect" of statistical overlap theory and a recently introduced factor that corrects for the broadening of first-dimension peaks by undersampling them. They predict that relatively more peaks will be observed when the ratio of the first- to the second-dimension peak capacity is much less than unity. Additional complications are observed when first- and second-dimension retention times show some correlation, but again the effects are small. In both cases, deviations from the product rule are measured by the relative standard deviations of the number of observed peaks, which are typically 10 or less. Thus, although the basic tenet of two-dimensional chromatography is not exact when the first dimension is undersampled, the deviations from the product rule are sufficiently small as to be unimportant in practical work. Our results show that practitioners have a high degree of flexibility in designing and optimizing experimental comprehensive two-dimensional separations.     

Fast, high peak capacity separations in gas chromatography-time-of-flight mass spectrometry

Peak capacity production (i.e., peak capacity per separation run time) is substantially improved for gas chromatography-time-of-flight mass spectrometry (GC-TOFMS) and applied to the fast separation of complex samples. The increase in peak capacity production is achieved by selecting appropriate experimental conditions based on theoretical modeling of on-column band broadening, and by reducing the injection pulse width. Modeling to estimate the on-column band broadening from experimental parameters provided insight for the potential of achieving GC separations in the absence of off-column band broadening, i.e., the additional band broadening not due to the on-column separation process. To optimize GC-TOFMS separations collected with a commercial instrumental platform, off-column band broadening from injection and detection needed to be significantly reduced. Specifically for injection, a commercially available thermal modulator is adapted and applied (referred to herein as thermal injection) to provide a narrow injection pulse, while the TOFMS provided a data collection rate of 500 Hz, initially averaged to 100 Hz for data storage. The use of long, relatively narrow open tubular capillary columns and a 30 °C/min programming rate were explored for GC-TOFMS, specifically a 20 m, 100 μm inner diameter (i.d.) capillary column with a 0.4 μm film thickness to benefit column capacity, operated slightly below the optimal average linear gas velocity (at ~2 mL/min, due to the flow rate constraint of the TOFMS). Standard autoinjection with a 1:100 split resulted in an average peak width of ~1.2 s, hence a peak capacity production of 50 peaks/min. Metabolites in the headspace of urine were sampled by solid-phase microextraction (SPME), followed by thermal injection and a ~7 min GC separation (with a ~6 min separation time window), producing ~660 ms peak widths on average, resulting in a total peak capacity of ~550 peaks (at unit resolution) and a peak capacity production of ~90 peaks/min (~2-fold improvement relative to standard autoinjection with the 1:100 split). This total peak capacity production achieved is equivalent to, or greater than, that currently utilized in metabolomics studies using GC/MS, but with much slower separations, on the order of 40 to 60 min, corresponding to a 5-fold or greater GC/MS analysis throughput rate.     

A refrigeration plant with 300 W capacity at 1.8 K

An industrial-scale helium II refrigeration plant operating at 1.8 K with a low specific energy consumption (436 kW_el for 370 W effective refrigeration) was built to cool superconducting components of particle accelerators and separators. The performance, process, control system, and important aggregates are described; the plant is compared with similar plants built previously.     

Effect of first-dimension undersampling on effective peak capacity in comprehensive two-dimensional separations

The objective of this work is to establish a means of correcting the theoretical maximum peak capacity of comprehensive two-dimensional (2D) separations to account for the deleterious effect of undersampling first-dimension peaks. Simulations of comprehensive 2D separations of hundreds of randomly distributed sample constituents were carried out, and 2D statistical overlap theory was used to calculate an effective first-dimension peak width based on the number of observed peaks in the simulated separations. The distinguishing feature of this work is the determination of the effective first-dimension peak width using the number of observed peaks in the entire 2D separation as the defining metric of performance. We find that the ratio of the average effective first-dimension peak width after sampling to its width prior to sampling (defined as ) is a simple function of the ratio of the first-dimension sampling time (t(s)) to the first-dimension peak standard deviation prior to sampling (1sigma): = square root1+0.21(t /(s)(1) sigma(2) This is valid for 2D separations of constituents having either randomly distributed or weakly correlated retention times, over the range of 0.2 on t(s)/1 sigma from this expression is in qualitative agreement with previous work based on the effect of undersampling on the effective width of a single first-dimension peak, but predicts up to 35% more broadening of first-dimension peaks than is predicted by previous models. This simple expression and accurate estimation of the effect of undersampling first-dimension peaks should be very useful in making realistic corrections to theoretical 2D peak capacities, and in guiding the optimization of 2D separations.     

Generation of ultrahigh peak capacity LC separations via elevated temperatures and high linear mobile-phase velocities

The use of a combination of ultraperformance liquid chromatography at approximately 11,000 psi on sub 2-microm particles combined with reversed-phase gradient chromatography at a temperature of 90 degrees C is described as applied to the analysis of endogenous and drug metabolites in human and animal urine. By using elevated temperatures, back pressures can be reduced while maintaining high flow rates and chromatographic efficiency, with peaks 1-3 s wide at the base. Application to urine samples provided a peak capacity of approximately 700 for a 10-min analysis and greater than approximately 1000 in 1 h. Despite the narrow nature of the peaks, good quality mass spectra were also obtained, allowing the identification of typical drug and endogenous metabolites. These ultra-high-resolution chromatograms should be ideal for the analysis of complex samples in, for example, metabolite identification, impurity identification, and metabonomic/metabolomic studies. Applications in natural product analysis and proteomics can also be envisaged.     

Peak capacity optimization of peptide separations in reversed-phase gradient elution chromatography: fixed column format

The optimization of peak capacity in gradient elution RPLC is essential for the separation of multicomponent samples such as those encountered in proteomic research. In this work, we study the effect of gradient time (tG), flow rate (F), temperature (T), and final eluent strength (phi(final)) on the peak capacity of separations of peptides that are representative of the range in peptides found in a tryptic digest. We find that there are very strong interactions between the individual variables (e.g., flow rate and gradient time) which make the optimization quite complicated. On a given column, one should first set the gradient time to the longest tolerable and then set the temperature to the highest achievable with the instrument. Next, the flow rate should be optimized using a reasonable but arbitrary value of phi(final). Last, the final eluent strength should be adjusted so that the last solute elutes as close as possible to the gradient time. We also develop an easily implemented, highly efficient, and effective Monte Carlo search strategy to simultaneously optimize all the variables. We find that gradient steepness is an important parameter that influences peak capacity and an optimum range of gradient steepness exists in which the peak capacity is maximized.     

Molar heat capacity at constant volume for air from 67 to 300 K at pressures to 35 MPa

Measurements of the molar heat capacity at constant volumeC _v for air were conducted with an adiabatic calorimeter. Temperatures ranged from 67 to 300 K, and pressures ranged up to 35 MPa. Measurements were conducted at 17 densities which ranged from gas to highly compressed liquid states. In total, 227C _v values were obtained. The air sample was prepared gravimetrically from research purity gases resulting in a mole fraction composition of 0.78112 N₂ + 0.20966 O₂ + 0.00922 Ar. The primary sources of uncertainty are the estimated temperature rise and the estimated quantity of substance in the calorimeter. Overall, the uncertainty (± 2) of theC _v values is estimated to be less than ± 2% for the gas and ±0.5% for the liquid.Nomenclature C _v Molar heat capacity at constant volume, J · mol^–1 K^–1 - C _v ⁰ Molar heat capacity in the ideal-gas state, J · mol^–1 · K^–1 - V _bomb Volume of the calorimeter containing sample, cm³ - P Pressure, MPa - P Pressure rise during a heating interval, MPa - T Temperature, K - T ₁,T ₂ Temperature at start and end of heating interval, K - T Temperature rise during a heating interval, K - Q Calorimetric heat energy input to bomb and sample, J - Q ₀ Calorimetric heat energy input to empty bomb, J - N Moles of substance in the calorimeter, mol - Fluid density, mol · dm^–3     

Contributions to the heat capacity of solid molybdenum in the range 300–2890 K

An analysis has been made of contributions to the heat capacity of Mo, with a special examination of the effect of the formation of vacancies near the melting point. Literature values of the heat capacity at constant pressure C _P were fitted to a polynomial. Using recent measurements of the velocity of sound at high temperature and literature data of the coefficient of expansion, the dilation correction was made to C _P to obtain the heat capacity at constant volume C _V . This heat capacity was taken to consist only of independent contributions from electron excitations (C _VE), harmonic lattice vibrations (C _VH), anharmonic lattice vibrations (C _VA), and the formation of vacancies (C _VV). Three models of C _VE (free electron, band theory, and electron-photon) have been used to calculate the electronic contribution, and an examination of the results indicates that the electron-phonon model is the best. C _VH is assumed to be given by the Debye model, with a single Debye temperature. Thus, the excess heat capacity C _VEX= C _V -C _VE -C _VH is taken as equal to (C _VA +C _VV ), where C _VA is linear with temperature (C _VA=A T), and we have fitted the values of C _VEX to determine the values of A and the energy and entropy of formation of vacancies which give the best fit. The anharmonic contribution is positive. The energy of vacancy formation is 100,000 J · mol^–1, in agreement with estimates by Kraftmakher from C _P data. The entropy of formation is 11.6 J · mol^–1 · K^–1. The concentration of vacancies at the melting point (2890 K) is calculated to be 6.3%.     

Heat capacity and pressure at phase separation and solidification of3He in hcp4He

We have measured heat capacity and pressure of 0.45% and 0.9%³He-⁴He mixtures at pressures between 25 bar and 33 bar and temperatures between 20 mK and 250 mK. The data show the latent heats and the pressure changes associated with the phase separation (or remixing) and with the liquification (or solidification) of the resulting droplets in the hcp matrix. Above about 31 bar, the phase separation and the liquid-solid phase transition are separately observable. From these data, as well as from the heat capacity of the liquid droplets, we conclude that the droplets are filled with almost pure³He showing bulk behavior and that only a part of the separated³He is liquified. The amount of the liquid depends on the history of the sample. The phase separation is reproducible and lasted for many hours. In the pressure range of the hcp-L₁-L₂ univariant the sample moves along the univariant for a limited temperature range.     

Heat capacity and thermodynamic functions of GaSe from 300 to 700 K

The heat capacity of ?-GaSe has been determined by differential scanning calorimetry in the temperature range 300–700 K. Smoothed heat capacity data have been used to evaluate the thermodynamic functions of gallium monoselenide (entropy, enthalpy increment, and reduced Gibbs energy).     

Effects of tryptic peptide esterification in MALDI mass spectrometry

The effect of esterification on MALDI ion yield is investigated by using alcohols having different aliphatic chain lengths. For peptides whose ionization yields increase with derivatization, more hydrophobic alcohols tend to yield greater peak enhancements. The completeness of the reaction increases from propanol to methanol. Undesired solvolysis of the amide group in the side chain of Asn or Gln leads to unexpected ester products. Ethanol is suggested as the optimal alcohol for esterification in proteomics experiments since it yields almost complete esterification without substantial solvolysis. Ethanol esterification was employed to facilitate the identification of gel-separated proteins.     

Melting of Solid 4He by Ultrasound at 1.2 K

We observed the melting of solid ⁴ He in superfluid when the sound waves were injected to its rough surface at 1.2 K. Single crystal was grown between two transducers and ultrasound pulses were applied normally to the solid-liquid interface from solid side or liquid side. Amount of melting was on the same order in both cases. We developed surface height measurement system using the sound wave itself and measured the amount of melting by changing the sound power and the number of pulses.     

Assessing the dynamic range and peak capacity of nanoflow LC-FAIMS-MS on an ion trap mass spectrometer for proteomics

Proteomics experiments on complex mixtures have benefited greatly from the advent of fast-scanning ion trap mass spectrometers. However, the complexity and dynamic range of mixtures analyzed using shotgun proteomics is still beyond what can be sampled by data-dependent acquisition. Furthermore, the total liquid chromatography-mass spectrometry (LC-MS) peak capacity is not sufficient to resolve the precursors within these mixtures, let alone acquire tandem mass spectra on all of them. Here we describe the application of a high-field asymmetric waveform ion mobility spectrometry (FAIMS) device as an interface to an ion trap mass spectrometer. The dynamic range and peak capacity of the nanoflow LC-FAIMS-MS analysis was assessed using a complex tryptic digest of S. cerevisiae proteins. By adding this relatively simple device to the front of the mass spectrometer, we obtain an increase in peak capacity >8-fold and an increase in dynamic range of >5-fold, without increasing the length of the LC-MS analysis. Thus, the addition of FAIMS to the front of a table-top mass spectrometer can obtain the peak capacity of multidimensional protein identification technology (MudPIT) while increasing the throughput by a factor of 12.     

Dynamics in He at 4 and 8 K from inelastic neutron scattering

From inelastic neutron scattering we determine the dynamic structure factor S(q, ) of fluid He at 4K (1 bar; 19.51 nm^–3) and 8K (18.7 bar; 19.46 nm^–3) as a function of frequency cofor wavenumbers 1 <q < 30 nm^–1. Forq 4 nm^–1, S(q, ) is given by the Rayleigh-Brillouin triplet of hydrodynamics. For q > 4 nm^–1 the central Rayleigh line vanishes and S(q, ) is given by the phonon Damped Harmonic Oscillator model similar as in superfluid helium. The phonons are overdamped for a small region nearq = 20 nm^–1. At 8K, helium starts to behave in a visco-elastic manner, similar as seen in classical fluids. We discuss a unifying model that connects the properties of superfluid helium to those of classical fluids.     

The solubility of4He in3He below 0.1 K

The Zharkov-Silin Fermi Liquid theory of solutions of⁴He in non-superfluid liquid³He has been applied to the recent phase separation data of Nakamura et al. At zero pressure, the difference in binding between a⁴He atom in liquid⁴He and in liquid³He is smaller than previous estimates, and the⁴He effective mass is close to the bare mass. The volume measurements of Laheurte show that the difference in binding has a minimum near 11 atm. This implies an enhanced solubility of⁴He in³He below 0.1 K at this pressure, although there is experimental evidence that the solubility at 0 K remains zero.     

Structure Properties of the 3He-4He mixture at T = 0 K

The spatial structure properties of³ He-⁴ He mixtures at T = 0 K are investigated using the hypernetted-chain formalism. The variational wave function used to describe the ground-state of the mixture is a simple generalization of the trial wave functions for pure phases and contains two- and three-body correlations. The elementary diagrams are taken into account by means of an extension of the scaling approximation to the mixtures. The two-body distribution (g(^,)(r)) and the structure functions (S(^,)(k)) together with the different spin-spin distribution functions of the ³He component in the mixture are analyzed for several concentrations of³ He. Two sum-rules, for the direct and the exchange part of the g ^{(3, 3)}(r), are used to ascertain the importance of the full treatment of the Fermi statistics in the calculation. The statistical correlations are found responsible for the main differences between the several components of the distribution function. Due to its low concentration, ³He behaves as a quasi-free Fermi gas, as far as the statistical correlations are concerned, although it is strongly correlated with the ⁴He atoms through the interatomic potential.     

Thesmal conductivity of helium at temperatures from 300 to 6000°K

Experimental data on the thermal conductivity of helium at atmospheric pressure and temperatures from 300 to 6000°K are correlated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No 3, pp. 412–417, March, 1982.