Kinetic performance limits of constant pressure versus constant flow rate gradient elution separations. Part II: experimental

We report on a first series of experiments comparing the selectivity and the kinetic performance of constant flow rate and constant pressure mode gradient elution separations. Both water-methanol and water-acetonitrile mobile phase mixtures have been considered, as well as different samples and gradient programs. Instrument pressures up to 1200 bar have been used. Neglecting some small possible deviations caused by viscous heating effects, the experiments could confirm the theoretical expectation that both operation modes should lead to identical separation selectivities provided the same mobile phase gradient program is run in reduced volumetric coordinates. Also in agreement with the theoretical expectations, the cP-mode led to a gain in analysis time amounting up to some 17% for linear gradients running from 5 to 95% of organic modifier at ultra-high pressures. Gains of over 25% were obtained for segmented gradients, at least when the flat portions of the gradient program were situated in regions where the gradient composition was the least viscous. Detailed plate height measurements showed that the single difference between the constant flow rate and the constant pressure mode is a (small) difference in efficiency caused by the difference in average flow rate, in turn leading to a different intrinsic band broadening. Separating a phenone sample with a 20-95% water-acetonitrile gradient, the cP-mode leads to gradient plate heights that are some 20-40% smaller than in the cF-mode in the B-term dominated regime, while they are some 5-10% larger in the C-term dominated regime. Considering a separation with sub 2-μm particles on a 350 mm long coupled column, switching to the constant pressure mode allowed to finish the run in 29 instead of in 35 min, while also a larger peak capacity is obtained (going from 334 in the cF-mode to 339 in the cP-mode) and the mutual selectivity between the different peaks is fully retained.     

Simultaneous determination of nine trace mono- and di-chlorophenols in water by ion chromatography atmospheric pressure chemical ionization mass spectrometry

A novel analytical method was proposed for the rapidly simultaneous determination of nine mono-chlorophenols (MCPs) and di-chlorophenols (DCPs) in water samples using eluent generator ion chromatography (IC) coupled with an atmospheric pressure chemical ionization mass spectrometry (APCI-MS) in the negative mode. The IC separation was carried out on an IonPac^® AS11 analytical column (250 mm × 4.0 mm) using gradient KOH containing 15% acetonitrile as organic modifier at a constant flow rate of 1.0 mL/min. The molecular ions m/z [M − H]⁻ 127 and 161 were selected for the quantification in selected ion monitoring (SIM) mode for MCPs and DCPs, respectively. The average recoveries were between 80.6% and 92.6%. Within-day and day-to-day relative standard deviations were less than 12.1% and 13.3%, respectively. The method allowed the nine objective compounds in water samples to be determined at μg/L levels. It was confirmed that this method could be used in routine analysis.     

Some solutions to obtain very efficient separations in isocratic and gradient modes using small particles size and ultra-high pressure

The UHPLC strategy which combines sub-2 μm porous particles and ultra-high pressure (>1000 bar) was investigated considering very high resolution criteria in both isocratic and gradient modes, with mobile phase temperatures between 30 and 90 °C. In isocratic mode, experimental conditions to reach the maximal efficiency were determined using the kinetic plot representation for ΔP_max = 1000 bar. It has been first confirmed that the molecular weight of the compounds (MW) was a critical parameter which should be considered in the construction of such curves. With a MW around 1000 g mol⁻¹, efficiencies as high as 300,000 plates could be theoretically attained using UHPLC at 30 °C. By limiting the column length to 450 mm, the maximal plate count was around 100,000. In gradient mode, the longest column does not provide the maximal peak capacity for a given analysis time in UHPLC. This was attributed to the fact that peak capacity is not only related to the plate number but also to column dead time. Therefore, a compromise should be found and a 150 mm column should be preferentially selected for gradient lengths up to 60 min at 30 °C, while the columns coupled in series (3× 150 mm) were attractive only for t_grad > 250 min. Compared to 30 °C, peak capacities were increased by about 20–30% for a constant gradient length at 90 °C and gradient time decreased by 2-fold for an identical peak capacity.     

Axial dispersion coefficient in high-speed counter-current chromatography

Experimental measurements of axial dispersion coefficients in high-speed counter-current chromatography have been carried out in the single-phase and two-phase modes. Axial dispersion coefficients were calculated from the residence time distribution curve (or the elution profile). The experimental data obtained were used to develop a model involving Peclet number Pe, Reynolds number and the ratio of flow velocity u to linear angular velocity u_θ for predicting the axial dispersion coefficient. Furthermore, the models obtained from the single-phase and two-phase modes were compared, and a counterintuitive phenomenon was found in that the effects of the flow rate and the rotation speed on the axial dispersion coefficients are inconsistent: the axial dispersion coefficient decreases with the rotation speed and increases with the flow rate in the single-phase mode, but increases with rotation speed and decreases slightly with the flow rate in the two-phase mode.     

Kinetics of sodium ethylenediaminetetraacetate mineralization by cerium(IV) in nitric acid medium

The process of sodium ethylenediaminetetraacetate (EDTA) mineralization by cerium(IV) in nitric acid medium was studied in batch and continuous feeding modes. In the batch mode EDTA solution was fed into the reactor in one stroke and in the continuous mode it was fed with a constant flow rate during a definite time interval. Cerium(IV) concentration was kept at high and constant level by selecting correct relation between cerium(IV) production in the electrochemical cell and the EDTA added. During the organic mineralization process cerium(IV) is reduced to cerium(III). The process was carried out at different temperatures, concentrations of nitric acid and cerium(IV). To obtain the limiting factors in the batch mode reaction, the dependence of CO₂ evolution with time and carrier gas blowing rate was studied. Application of the model previously developed by us to the continuous process gave us the possibility to calculate pseudo first order kinetic constant on the basis of CO₂ evolution data of both EDTA destruction regimes during feeding mode and after stopping organic addition. The efficiency of organic destruction estimated on the basis of CO₂ evolved was in the range 75–95% and on the basis of liquid phase residual organic carbon analysis 95–99%.     

Investigation into the kinetics of pressurized steam gasification of chars with different coal ranks

The steam gasification of coal chars derived from three different ranks of typical Chinese coals was studied in a pressurized fixed-bed differential reactor at elevated pressure (up to 2.0 MPa). Three mathematical models [volumetric model (VM), grain model (GM), and random pore model (RPM)] for the gasification kinetics of different chars were validated, through which the kinetic parameters were obtained and discussed. The results show that the evolution trend of the coal char gasification rate with carbon conversion differs from coal ranks and has little change with pressure and temperature. The pressurized gasification process of the Shenmu sub-bituminous coal char (SM char) and the Jingcheng anthracite char (JC char) can be well-predicted by the RPM, while that of the Huolinhe lignite char can be better described by the VM. The pressure has little effect on the options of the reaction kinetic models for the three chars. The kinetic parameter E is almost a constant independent of pressure, while k ₀ changes with pressure, and it seems that k ₀ would be almost a constant over 1.0 MPa for SM and JC chars. The reaction order decreases with increasing the total system pressure and differs from different coal types.     

Some insights on the description of gradient elution in reversed‐phase liquid chromatography

The so‐called “fundamental equation for gradient elution” has been used for modeling the retention in gradient elution. In this approach, the instantaneous retention factor (k) is expressed as a function of the change in the modifier content (φ(t_s)), t_s being the time the solute has spent in the stationary phase. This approach can only be applied at constant flow rate and with gradients where the elution strength depends on the column length following a f(t?l/u) function, u being the linear mobile phase flow rate, and l the distance from the column inlet to the location where the solute is at time t measured from the beginning of the gradient. These limitations can be solved by using the here called “general equation for gradient elution”, where k is expressed as a function of φ(t,l). However, this approach is more complex. In this work, a method that facilitates the integration of the “general equation” is described, which allows an approximate analytical solution with the quadratic retention model, improving the predictions offered by the “linear solvent strength model.” It also offers direct information about the changes in the instantaneous modifier content and retention factor, and gives a meaning to the gradient retention factor.     

Molecular dynamics at constant pressure and temperature

Methods are discussed for generating by molecular dynamics isobaric-isoenthalpic, NPH, isochoric-isothermal, NVT, and isobaric-isothermal, NPT, ensembles. Andersen's constant-pressure method is reformulated so that the ensemble rather than the scaled system is directly calculated. Four constant-temperature schemes were considered. Two involve the addition of a stochastic collision term to the molecular trajectories. The Andersen method and a stochastic dynamics approach were examined. The latter employed a velocity damping term in addition to the random force. Two other methods employed uniform velocity scaling applied to all molecules. The NPT algorithm induces a transition to the dilute phase for a Lennard-Jones fluid in the spinodal region (p^* = 0.5, T^* = 1.28) of the phase diagram. The thermodynamic equivalence of the ensembles is demonstrated by long calculations of the chemical potential of Lennard-Jones states by the particle insertion method. The internal energy, pressure, constant volume and pressure specific heats, adiabatic compressibilities, pair radial distribution functions and self-diffusion coefficients are also evaluated. Only for second-order thermodynamic quantities is there evidence of an ensemble dependence.     

The Raman active internal vibrational modes of potassium nitrate

The Raman active internal vibrational modes of single crystal orthorhombic potassium nitrate have been studied in various polarizations. The full multiplet structure predicted by factor group analysis for the v₂ and v₃ regions has been observed for the first time. The expected site group splitting of the v₄ mode was not observed and can be assumed to be less than 0.5 cm^?1.     

Electrochemical behaviour of isatin at a glassy carbon electrode

A rapid, reliable and simple capillary zone electrophoresis method for the determination of organic acids in beverages was developed. The complete separation of oxalic, formic, tartaric, malic, succinic, maleic, glutaric, pyruvic, acetic, lactic, citric, butyric, benzoic, sorbic, ascorbic and gluconic acids can be achieved in less than 3.5 min with a simple electrolyte composed by phosphate as the carrier buffer (7.5 mM NaH₂PO₄ and 2.5 mM Na₂HPO₄), 2.5 mM TTAOH as electroosmotic flow modifier and 0.24 mM CaCl₂ as selectivity modifier, adjusting the pH at 6.40 constant value. Injection was performed in hydrodynamic mode (30 s) and the detection mode was UV direct at 185 nm. The running voltage was −25 kV at thermostated temperature of 25 °C. The method developed has been applied to several beverage samples with only a simple dilution and filtration treatment of the sample. The proposed method is fast because the separation time decrease two, four or, even, six times the separation times of the previous reported CZE methods. It is also simple and cheap due to a low consumption of chemicals and samples. These reasons permit it to be considered adequate for routine analysis of organic acids in beverage samples.     

Mechanism of atomization at constant temperature in capacitive discharge graphite furnace atomic absorption spectrometry

At constant temperature (isothermal) maintained throughout in the capacitive discharge technique, the measured absorbance at any time t due to concentration of analyte atoms can be given by: absorbance = p[A]₀{k₁/(k₁?k₂)}[exp(?k₂t)-exp(?k₁t)], where p is a function of the oscillator strength (a constant) and the efficiency with which the analyte atoms are produced, [A]₀ is the initial concentration of the analyte atoms, k₁ and k₂ are first-order rate constants for formation and decay of analyte atoms, respectively. This technique yields k₁?k₂ and k₁t?k₂t; and so the above equation reduces to: absorbance ?p[A]₀, resulting in large enhancement in sensitivity. In the case of lead, the immediate precursor of the gaseous lead monomer is the gaseous lead dimer, which is partly lost by diffusion of the lead dimer with a first-order rate constant, k₃. The kinetic parameters k₁, k₂ and k₃ have been evaluated, and the values of k₁ at different temperatures used to draw the Arrhenius plots, from which activation energies of the rate-determining steps have been determined. The activation energies have been used to elucidate atomization mechanisms by extensive correlation of the experimental energy values with the literature values.     

Absolute rate constant for the reaction of OH with thiophene between 293 and 473 K

The rate parameters of the OH + C₄H₄S (thiophene) reaction were measured at a pressure of 0.5 Torr in the temperature range 293–473 K by the discharge flow EPR method. The reaction was found to exhibit a negative temperature dependence. The data fit the Arrhenius expression k = (1.3 ± 0.8) × 10^?13 exp[(1750 ± 200)/T] cm³ molecule^?1 s^?1. The rate constant of (5 ± 0.4) × 10^?11 at room temperature corresponds to a short lifetime of C₄H₄S in the atmosphere.     

The pressure dependence of the rate constant for the reaction: HO + CO → H + CO2

Relative rate measurements of the reactions of the HO-radical with CO [HO + CO → H + CO₂ (1)] and with isobutane [HO + iso-C₄H₁₀ → H₂O + t-(or iso-)C₄H₉ (3)] have been made through the photolysis of dilute mixtures of HONO with CO, iso-C₄H₁₀, NO₂, and NO in simulated air at 700 and 100 torr pressure and 25 ± 2°C. In situ, long path, FT-IR analysis of the reactants and products provided essentially continuous monitoring of the reactions during the course of the experiments. The kinetic analysis of the data coupled with Greiner's estimate of k₃ give new estimates of k₁ = 439 ± 24 ppm^?1 min^?1 in air at 700 torr and k₁ = 203 ± 29 ppm^?1 in air at 100 torr. The results confirm the recent conclusions of Cox and Sie and their co-workers that the rate constant for reaction (1) is pressure dependent. Modeliers of the chemical changes which occur in the troposphere should adopt a new value for the rate constant k₁ which is about a factor of two larger than that in current use by most groups.     

Thermal decomposition of vinylacetylene in shock waves: Rate constant of initiation reaction

The thermal decomposition of vinylacetylene was studied behind incident shock waves over the temperature range 1200–1750 K and over the pressure range 0.3–0.6 atm by tracing the time variation of absorption at 230 nm. The initiation reaction and the rate constant in the thermal decomposition of vinylacetylene were determined from the initial slope of the absorption curve as C₄H₄ → h₁, C₄H₃+H, k₁ = 6.1 × 10¹³ exp (−80 kcal/RT) s⁻¹.     

Retention modeling under organic modifier gradient conditions in ion-pair reversed-phase chromatography. Application to the separation of a set of underivatized amino acids

The combined effect of the ion-pairing reagent concentration, C _ipr, and organic modifier content, φ, on the retention under φ-gradient conditions at different constant C _ipr was treated in this study by using two approaches. In the first approach, the prediction of the retention time of a sample solute is based on a direct fitting procedure of a proper retention model to 3-D φ-gradient retention data obtained under the same φ-linear variation but with different slope and time duration of the initial isocratic part and in the presence of various constant C _ipr values in the eluent. The second approach is based on a retention model describing the combined effect of C _ipr and φ on the retention of solutes in isocratic mode and consequently analyzes isocratic data obtained in mobile phases containing different C _ipr values. The effectiveness of the above approaches was tested in the retention prediction of a mixture of 16 underivatized amino acids using mobile phases containing acetonitrile as organic modifier and sodium dodecyl sulfate as ion-pairing reagent. From these approaches, only the first one gives satisfactory predictions and can be successfully used in optimization of ion-pair chromatographic separations under gradient conditions. The failure of the second approach to predict the retention of solutes in the gradient elution mode in the presence of different C _ipr values was attributed to slow changes in the distribution equilibrium of ion-pairing reagents caused by φ-variation.     

The effects of errors in measurements of absorbance and time on the calculated value of a pseudo-first-order rate constant

When data on the variation with time of the absorbance of a reactant or product are used to evaluate the rate constant of a first- or pseudo-first-order reaction, the precision of the result depends on the precisions with which both the time and the absorbance are measured. The natures of the dependences, and the ways in which they are affected by both constant and linearly varying background absorbances, are examined. If the standard error σ_t of a measurement of time is below about 0.005 t_{$\text{1}\text{2}$}, the standard error of the rate constant is virtually identical for an experiment in which the concentration of the reactant is followed as for one in which the concentration of the product is followed, but for larger values of σ_t it is better to follow the concentration of the reactant. In any event, errors in the measurements of time are much more likely to be significant than they are usually assumed to be. Other sources of error in such experiments, including constant and time-dependent background absorbances, are examined more briefly, with emphasis on the requirements that should be satisfied in work of the highest quality.     

Kinetic measurements of the gas phase HO2+CH3O2 cross-disproportionation reaction at 298 K

Flash photolysis kinetic absorption spectroscopy was used to investigate the gas phase reaction between hydroperoxy (HO₂) and methylperoxy (CH₃O₂) radicals at 298 K. Due to the large difference between the self-reactivities of the two radicals, first- or second-order kinetic conditions could not be maintained for either species. Thus, the rate constant for the cross reaction was determined from computer-modeled fits of the radical absorption decay curves, at wavelengths between 215 and 280 nm. This procedure yielded k = 2.9 × 10⁻¹² cm³ molecule⁻¹ s⁻¹ independent of total pressure (using N₂) between 25 and 600 Torr, and of the partial pressure of water vapor (up to 11.6 Torr). There was also no effect of water vapor on the rate constant for the self-reaction of methylperoxy radicals.     

Addition of modifier in supercritical fluid chromatography using a microbore reciprocating pump

Summary Solubilities of polar analytes in supercritical CO₂ can be enhanced by the addition of polar modifiers. The addition of modifier into an SFC system using a low cost reciprocating pump has been studied. Two different mixing chambers were evaluated for mixing the supercritical CO₂ with modifier. It appeared that a mixing chamber with a packed bed was enough to reduce baseline noise from the modifier pump. Results from the effect of pressure and temperature with various modifier flow rates were obtained. High percentages of modifier (>15%) at a low CO₂ pressure (2000 psi) caused baseline instability. In addition, different I.D. columns were tested with the system and the effect of modifier compressiblity on detector noise was also studied. Several pharmaceutical compounds were separated to demonstrate system performance.     

Method for Gradient Elution in Micro-Flow Liquid Chromatography

This paper describes a new method for gradient elution at low flow rate. By adjusting the solvent composition flowing into a dynamic mixer, we can program the concentration of solvent, B, inside a dynamic mixer to form a time-resolved solvent gradient delivered to the column. The input gradient is related to the output gradient by the equation, B_in = B_out + τ × dB_out/dt, in which τ is the gradient response time constant at specified flow rate, and B_in and B_out are input and output concentration of solvent B, respectively.     

Rate constant and a detailed error analysis for C2H3 + H reaction

The production and reactions of vinyl radicals and hydrogen atoms from the photolysis of vinyl iodide (C₂H₃I) at 193 nm have been examined employing laser photolysis coupled to kinetic-absorption spectroscopic and gas chromatographic product analysis techniques. The time history of vinyl radicals in the presence of hydrogen atoms was monitored using the 1,3-butadiene (the vinyl radical combination product) absorption at 210 nm. By employing kinetic modeling procedures a rate constant of 1.8 × 10^?10 cm² molecule^?1 s^?1 for the reaction C₂H₃ + H has been determined at 298 K and 27 KPa (200 torr) pressure. A detailed error analysis for determination of the C₂H₃ + H reaction rate constant, the initial C₂H₃ and H concentrations are performed. A combined uncertainty of ±0.43 × 10^?10 cm² molecule^?1 s^?1 for the above measured rate constant has been evaluated by combining the contribution of the random errors and the systematic errors (biases) due to uncertainties of each known parameter used in the modeling. © 1995 John Wiley & Sons, Inc.