Modeling of thermal processes in very high pressure liquid chromatography for column immersed in a water bath: Application of the selected models

Currently, chromatographic analyses are carried out by operating columns packed with sub-2 μm particles under very high pressure gradients, up to 1200 bar for 5 cm long columns. This provides the high flow rates that are necessary for the achievement of high column efficiencies and short analysis times. However, operating columns at high flow rates under such high pressure gradients generate a large amount of heat due to the viscous friction of the mobile phase stream that percolates through a low permeability bed. The evacuation of this heat causes the formation of significant or even large axial and radial gradients of all the physico-chemical parameters characterizing the packing material and the mobile phase, eventually resulting in a loss of column efficiency. We previously developed and successfully applied a model combining the heat and the mass balances of a chromatographic column operated under very high pressure gradients (VHPLC). The use of this model requires accurate estimates of the dispersion coefficients at each applied mobile phase velocity. This work reports on a modification of the mass balance model such that only one measurement is now necessary to accurately predict elution peak profiles in a wide range of mobile phase velocities. The conditions under which the simple equilibrium-dispersive (ED) and transport-dispersive (TD) models are applicable in VHPLC are also discussed. This work proves that the new combination of the heat transfer and the ED model discussed in this work enables the calculation of accurate profiles for peaks eluted under extreme conditions, like when the column is thermostated in a water bath.     

Studies on external peak broadening in open-tubular liquid chromatography systems using the exponentially modified Gaussian model

Summary To optimize performance in Open-Tubular Liquid Chromatography (OTLC) it is necessary to minimize external peak broadening. To see how to reduce the external broadening an insight into its origins is required. This can be obtained by careful evaluation of experimental results with peak deconvolution methods based on the exponentially modified Gaussian model and comparison with theoretical predictions. It is assumed that the column response is Gaussian and that the responses due to the external effects are exponential.For peak deconvolution the algorithm described by Yau was used. Simulations were carried out to check the performance of the algorithm in calculating the standard deviation and the time constant. The effects of the presence of more than one time constant and of the number of data points and their position were investigated. The limits within which reliable results can be obtained are reported.Experimental results were obtained with laser-induced fluorescence and mass spectrometric detection. It is shown that the Yau algorithm can be used to obtain physically realistic estimates of the contribution to peak distortion in the various system components. By suitable design external effects can be reduced to the order of 1 nl and in some cases even lower limits can be reached.Part of this paper was presented at the 3rd Workshop on LC/MS and MS/MS, October, 24–26, 1984 in Montreux, Switzerland.     

Advances in numerical methods for the solution of population balance equations for disperse phase systems

Accurate prediction of the evolution of particle size distribution is critical to determining the dynamic flow structure of a disperse phase system. A population balance equation (PBE), a non-linear hyperbolic equation of the number density function, is usually employed to describe the micro-behavior (aggregation, breakage, growth, etc.) of a disperse phase and its effect on particle size distribution. Numerical solution is the only choice in most cases. In this paper, three different numerical methods (direct discretization methods, Monte Carlo methods, and moment methods) for the solution of a PBE are evaluated with regard to their ease of implementation, computational load and numerical accuracy. Special attention is paid to the relatively new and superior moment methods including quadrature method of moments (QMOM), direct quadrature method of moments (DQMOM), modified quadrature method of moments (M-QMOM), adaptive direct quadrature method of moments (ADQMOM), fixed pivot quadrature method of moments (FPQMOM), moving particle ensemble method (MPEM) and local fixed pivot quadrature method of moments (LFPQMOM). The prospects of these methods are discussed in the final section, based on their individual merits and current state of development of the field. Supported by the National Basic Research Program of China (Grant No. 2004CB720208), the National Natural Science Foundation of China (Grant Nos. 40675011 & 10872159), and the Key Laboratory of Mechanics on Disaster and Environment in Western China     

Simulation of nonisothermal reactive liquid chromatography using two-dimensional lumped kinetic model

A nonisothermal two-dimensional lumped kinetic model of reactive liquid chromatography is formulated and applied to simulate the separation of multicomponent mixtures in a fixed-bed cylindrical column operating under nonisothermal condition. The axial and radial variations of concentration and temperature as well as reversibility of the chemical reactions are incorporated in the model equations. The model comprises a system of convection-diffusion-reaction partial differential equations coupled with algebraic and differential equations. Due to the nonlinearity of adsorption and reaction kinetics, it is required to apply an accurate numerical scheme for solving the model equations. In this study, an efficient and accurate high-resolution flux-limiting finite-volume scheme is proposed to solve the model equations. A number of stoichiometrical reactions are numerically simulated to determine the level of coupling between the temperature and concentration profiles. Moreover, the effects of various critical parameters on the process performance are examined. The results obtained are beneficial for understanding reaction and separation processes inside a liquid chromatographic reactor and to improve its performance.     

超高效液相色谱塔板高度方程的推导

近年来,分析工作者采用超高效液相色谱(UPLC)完成了许多过去不能完成的分离分析工作。但是在阐述UPLC原理时不少人却采用了van Deemter方程。这是不对的。本文研究了UPLC色谱过程动力学,从热传导方程出发运用色谱动力学原理推导了包括考虑流动相摩擦生热影响的UPLC塔板高度方程H=2γD_m/u+((2λd_pu^1/3)/(u^1/3+ω(D_m/d_p)^1/3))+((2ku)/((1+k)²(1+κ₀)κ_d))+ ((θ(κ₀+κ₀k+k)²d_p²u)/(D_mκ₀(1+κ₀)²(1+k)²)) +(κ_i(κ₀+κ₀k+k)²d_p^5/2u^2/3)/(3κ₀Ω D_m^2/3(1+κ₀)²(1+k)²+(r₀²(κ₀+κκ₀k+k)u)/(4(1+k)D_r)·exp(-Kr₀²α)。上述方程右端最后一项代表了流动相摩擦生热对塔板高度的贡献。当流动相线速度较低时,流动相摩擦生热对塔板高度的贡献趋近于零,塔板高度方程还原成Horvath和Lin的方程;当流动相线速度较高时,由于流动相摩擦生热,柱轴心与边缘温差增加,流动相线速度径向分布差异导致柱效率降低,而柱轴心与边缘的温差与流动相线速度平方成正比。作者明确指出:UPLC的柱效率与柱内径密切相关,采用细内径柱有利于实现高效率;过高的流动相线速度将导致柱效率崩溃。     

Purification of thymine dimer from monomer solution in preparative liquid chromatography

Summary Cyclobutane pyrimidine dimers and monomers of thymine were separated on a C₁₈ reversed-phase high performance liquid chromatographic column. Using two mathematical models, the effect of the sample sizes on peak shapes in preparative liquid chromatography was investigated. One of these approaches is through a linear kinetic model, and the other is based on the non-linear adsorption isotherm. With the injection of small samples good agreement between the calculated value by the linear kinetic model and experimental, data were achieved. With increased sample size, this model is defective in its prediction of large concentration profiles of sample. However, the nonlinear model permits the accurate prediction of the location of the component band and the determination of the appropriate time to start and stop collection of the enriched fraction at higher concentrations of monomer and the lower concentrations of dimer. Therefore, extremely small amounts of dimer can be extracted from monomer solutions.     

离散相系统群体平衡模型的求解算法

准确预测离散相系统中微观粒子的尺度分布演变对系统动态流动行为的准确确定起关键性作用. 粒子的尺度分布演变以及引起尺度分布变化的离散相微观行为(聚并、破碎、长大等)由群体平衡模型来描述. 该模型是关于数值密度函数的非线性双曲型方程, 数值求解为主要手段. 本文对群体平衡方程的直接离散方法、Monte Carlo、矩方法从实现难易程度、计算机资源消耗、计算精度三方面进行了详细阐述, 并着重介绍了几种性能优越的矩方法—— 矩积分方法(QMOM)、矩直接积分方法(DQMOM)、可调节矩积分方法(M-QMOM)、自适应矩直接积分方法(ADQMOM)、定点矩积分方法(FPQMOM)、粒子游动算法(MPEM)和局部定点矩积分方法(LFPQMOM). 最后根据算法的优缺点及其当前发展状况对不同算法的未来发展做了预测.     

Investigation of endogenous corticosteroids profiles in human urine based on liquid chromatography tandem mass spectrometry

The accurate and precise measurement of endogenous corticosteroids in urine is a powerful tool to understand the biochemical state in several diseases. In this study, a rapid, accurate, and sensitive method based on liquid chromatography-tandem mass spectrometry (LC–MS/MS) for the quantification of 67 endogenous gluco- and mineralo-corticosteroids and progestins has been developed and validated. Sample preparation, chromatographic separation, and mass spectrometric detection were optimized. Urine samples (0.5 mL) were hydrolyzed with β-glucuronidase and the released analytes were extracted by liquid–liquid extraction. The chromatographic separation was performed in 20 min after redisolution of the extract. MS behavior of endogenous corticosteroids was evaluated in order to select the most specific precursor ion ([M+H]⁺, [M+NH₄]⁺, or [M+H-nH₂O]⁺) for the detection. MS/MS determination was performed under selected reaction monitoring mode using electrospray ionization in positive mode. The method was shown to be linear (r > 0.99) in the range of endogenous concentrations for all studied metabolites. Limits of detection (LOD) below 1 ng mL⁻¹ were typically obtained for analytes with a 3-oxo-4-ene structure whereas LODs below 15 ng mL⁻¹ were common for the rest of analytes. Recoveries were higher than 80% and intra-assay precisions below 20%, evaluated at three concentration levels, were found for most steroids. No significant or moderate matrix effect, ranging from 54 to 155%, was observed for most of the analytes. The applicability of the method was confirmed by analyzing 24 h urine samples collected from twenty healthy volunteers and comparing the results with previously established normal ranges. The wide coverage of corticosteroid metabolism, together with short analysis time, low sample volume, simple sample preparation, and satisfactory quantitative results make this method useful for clinical purposes.     

Numerical solution of nonlinear and non-isothermal general rate model of reactive liquid chromatography

Abstract

A nonlinear general rate model (GRM) of liquid chromatography is formulated to analyze the influence of temperature variations on the dynamics of multi-component mixtures in a thermally insulated liquid chromatographic reactor. The mathematical model is formed by a system of nonlinear convection–diffusion reaction partial differential equations (PDEs) coupled with nonlinear algebraic equations for reactions and isotherms. The model equations are solved numerically by applying a semi-discrete high-resolution finite volume scheme (HR-FVS). Several numerical case studies are conducted for two different types of reactions to demonstrate the influence of heat transfer on the retention time, separation, and reaction. It was found that the enthalpies of adsorption and reaction significantly influence the reactor performance. The ratio of density time heat capacity of solid and liquid phases significantly influences the magnitude and velocity of concentration and thermal waves. The results obtained could be very helpful for further developments in non-isothermal reactive chromatography and provide a deeper insight into the sensitivity of chromatographic reactor operating under non-isothermal conditions.     

A systematic investigation of algorithm impact in preparative chromatography with experimental verifications

Computer-assisted optimization of chromatographic separations requires finding the numerical solution of the Equilibrium-Dispersive (ED) mass balance equation. Furthermore, the competitive adsorption isotherms needed for optimization are often estimated numerically using the inverse method that also solves the ED equations. This means that the accuracy of the estimated adsorption isotherm parameters explicitly depends on the numerical accuracy of the algorithm that is used to solve the ED equations. The fast and commonly used algorithm for this purpose, the Rouchon Finite Difference (RFD) algorithm, has often been reported not to be able to accurately solve the ED equations for all practical preparative experimental conditions, but its limitations has never been completely and systematically investigated. In this study, we thoroughly investigate three different algorithms used to solve the ED equations: the RFD algorithm, the Orthogonal Collocation on Finite Elements (OCFE) method and a Central Difference Method (CDM) algorithm, both for increased theoretical understanding and for real cases of industrial interest. We identified discrepancies between the conventional RFD algorithm and the more accurate OCFE and CDM algorithms for several conditions, such as low efficiency, increasing number of simulated components and components present at different concentrations. Given high enough efficiency, we experimentally demonstrate good prediction of experimental data of a quaternary separation problem using either algorithm, but better prediction using OCFE/CDM for a binary low efficiency separation problem or separations when the compounds have different efficiency. Our conclusion is to use the RFD algorithm with caution when such conditions are present and that the rule of thumb that the number of theoretical plates should be greater than 1000 for application of the RFD algorithm is underestimated in many cases.     

Comparison between the adsorption behaviors of an organic cation and an organic anion on several reversed-phase liquid chromatography adsorbents

Adsorption data of an organic cation (propranololium chloride) and an organic anion (sodium 1-naphthalene sulfonate) were measured by frontal analysis on two RPLC adsorbents, Symmetry-C18 and XTerra-C18, with aqueous solutions of methanol as the mobile phases. The influence of supporting neutral salts on the adsorption behavior of these two ions are compared. The Henry constants are close (H approximately 5). The four sets of isotherm data are all well accounted for using the bi-Moreau model. However, the isotherms of the two ions behave differently at high concentrations. The initial behaviors of all the isotherms are antilangmuirian but remain so in a much wider concentration range for the cation than for the anion, due to its stronger adsorbate-adsorbate interactions on the low-energy adsorption sites. The retention times of both ions increase with increasing concentration of neutral salt in the mobile phase, suggesting the formation of ion-pair complexes, with Cl- for the cation and with Na+ for the anion. The adsorbate-adsorbate interactions vanish in the presence of salt and the bi-Moreau isotherm model tends toward a bi-Langmuir model. Differences in adsorption behavior are also observed between the cation and the anion when bivalent inorganic anions and cations, respectively, are dissolved in the mobile phase. High concentration band profiles of 1-naphthalene sulfonic acid are langmuirian, except in the presence of a trivalent cation, while those of propranolol are antilangmuirian under certain conditions even with uni- or divalent cations.     

Peak parking method for measurement of molecular diffusivity in liquid phase systems

The combination of series of measurements of band broadening made with the peak parking (PP) method, using successively an open capillary tube and a HPLC column, gives a convenient procedure for the measurement of the molecular diffusivity (D_m) of compounds in solutions, of their axial dispersion coefficient (D_ax,m) in chromatographic columns, and of the tortuosity or obstructive factor of the column bed. The molecular diffusivity measured for benzene in methanol was in excellent agreement with literature data. The ratio of the axial dispersion coefficient to this diffusivity gives the obstructive factor (γ_m) of the packed bed, which was 0.74 for the column used. The values of D_m in other solutions were obtained from the D_ax,m values measured by the PP method, by correcting the D_ax,m values with the γ_m value. The D_m values determined by this method were in good agreement with those previously reported or estimated using literature correlations. These results showed that the PP method is effective for the experimental measurement of D_m.     

Preparation and characterization of lauryl methacrylate-based monolithic microbore column for reversed-phase liquid chromatography

Poly(lauryl methacrylate-co-ethylene dimethacrylate) monoliths were in situ synthesized within the confines of a silicosteel tubing of 1.02 mm i.d. and 1/16" o.d. for microbore reversed-phase HPLC. In order to obtain practically useful monoliths with adequate column efficiency, low flow resistance, and good mechanical strength, some parameters such as total monomer concentration (%T), cross-linking degree (%C) and polymerization temperature were optimized. High-efficiency monoliths were successfully obtained by thermal polymerization of a monomer mixture (40%T, 10%C) with a binary porogenic solvent consisting of 1-propanol and 1,4-butandiol (7:4, v/v) at a high temperature of 90 °C. The morphology and porous structure of the resulting monoliths were assessed by scanning electron microscope (SEM) and inverse size exclusion chromatography (ISEC), while the column performance was evaluated through the separations of a series of alkylbenzenes in acetonitrile-water (50:50, v/v) eluent. At a normal flow rate of 50 μL/min (corresponding to 1.66 mm/s), the optimized monolithic columns typically exhibited theoretical plate numbers of 6000 plates/10 cm-long column for amylbenzene (k>40), and the pressure drop was always less than 1 MPa/10 cm. The monoliths, which were chemically anchored to the tube inner wall surface using a bifunctional silylation agent, exhibited adequate mechanical strength of up to 12-13 MPa, and were properly operated at 10 times higher flow rate than normal, reducing the separation time to one tenth. The lauryl methacrylate-based monolithic column was applied to a rapid and efficient separation of ten common proteins such as aprotinin, ribonuclease A, insulin, cytochrome c, trypsin, transferrin, conalbumin, myoglobin, β-amylase, and ovalbumin in the precipitation-redissolution mode. Using a linear CH(3)CN gradient elution at a flow rate of 500 μL/min (10-times higher flow rate), 10 proteins were baseline separated within 2 min.     

液相色谱塔板高度方程的统一形式

研究了色谱分离过程中物质的径向扩散和流动相发热对柱效能的影响。从热传导方程出发,运用色谱过程动力学原理推导了包括考虑流动相径向扩散、色谱柱发热影响的液相色谱塔板高度方程：

该方程概括了高效液相色谱（HPLC）、超高效液相色谱（UPLC）、毛细管电色谱（CEC）和消滞留层液相色谱（ESFLC）塔板高度与各种因素的关系。方程最后一项代表了径向扩散和柱发热对塔板高度的贡献。当流动相线速度较低且柱内径较细时,流动相摩擦生热和径向扩散对塔板高度的贡献趋近于零,塔板高度方程还原成Horvath和Lin的方程;当流动相线速度较高时,由于流动相摩擦生热,柱轴心与边缘温差增加,导致流动相线速度径向分布差异,使得柱效率降低。柱轴心与边缘的温差与流动相线速度平方成正比。该文指出,在流动相高线速度情况下,液相色谱的柱效率与柱内径密切相关,采用细内径柱有利于实现高速与高效率;过高的流动相线速度将导致色谱柱效率崩溃。     

Electrosonic spray ionization--an ideal interface for high-flow liquid chromatography applications

Electrosonic spray ionization (ESSI) has been studied as an interface between high-performance liquid chromatography (HPLC) and mass spectrometry (MS), using sample flow rates up to 3.0 ml min⁻¹. This ionization interface was compared with pneumatically assisted electrospray ionization (ESI) using mass spectrometry for detection. For experiments that did not involve direct comparison of different flow rates, the ESI experiments were performed using post column splitting to work at optimal conditions. ESSI allows the interfacing of conventional or high-resolution liquid chromatography (LC) methods to mass spectrometry without post column splitting. High sample flow rates could be handled without a significant loss of signal intensity using a nebulization gas flow rate of 5.5 L min⁻¹. Since ESI needs to be operated with lower sample flow rates, it is limited to micro/nano LC systems, or post column splitting must be used. In particular, nano LC systems have to be treated with great care and require constant maintenance. When using post-column splitting, the increased diffusion can become a problem especially when using systems with very small void volumes. In all experiments ESSI showed better signal intensities than a commercially available, pneumatically assisted ESI source. ESSI does not require heating of the nebulizer gas, which should help to preserve the original structure of thermally unstable molecules. Therefore, ESSI is presented as an alternative to the commercially available heated ESI sources of AB SCIEX, Thermo Fischer, Agilent and Waters. The observed LC-ESSI-MS ion chromatograms are shown to be very stable even when using flow rates higher than 1.0 ml min⁻¹, which could be very suitable for ultra high performance LC, where sample flow rates up to 2.0 mL min⁻¹ with backpressures up to 1200 bar are used. Also, a difference in the relative intensities of singly and doubly protonated peptide monomers and dimers was observed between the two ionization methods. The coefficients of determination for the calibration of instrument response for Val–Tyr–Val and Met-Enkephalin showed excellent linearity over a wide concentration range (0.1–100 μM), while ESI results were only linear over a much smaller range (0.1–20 μM). The observed behavior is thought to be caused by insufficient ionization efficiency of solutions above ∼20 μM by ESI, exemplifying the robustness of ESSI as an interface between LC and MS.     

Abraham model correlations for ionic liquid solvents: computational methodology for updating existing ion-specific equation coefficients

The computational methodology for updating existing values of Abraham model ion-specific equation coefficients is illustrated using published experimental solubility and partition coefficient for solutes dissolved in 1-ethyl-3-methylimidazolium trifluoroacetate, 1-butyl-3-methylimidazolium trifluoroacetate and 1-hexyl-3-methylimidazolium trifluoroacetate. The updated Abraham model ion-specific equation coefficients that are reported for the trifluoroacetate anion are based on 51 experimental values.     

Development of chemical isotope labeling liquid chromatography mass spectrometry for silkworm hemolymph metabolomics

Silkworm (Bombyx mori) is a very useful target insect for evaluation of endocrine disruptor chemicals (EDCs) due to mature breeding techniques, complete endocrine system and broad basic knowledge on developmental biology. Comparative metabolomics of silkworms with and without EDC exposure offers another dimension of studying EDCs. In this work, we report a workflow on metabolomic profiling of silkworm hemolymph based on high-performance chemical isotope labeling (CIL) liquid chromatography mass spectrometry (LC-MS) and demonstrate its application in studying the metabolic changes associated with the pesticide dichlorodiphenyltrichloroethane (DDT) exposure in silkworm. Hemolymph samples were taken from mature silkworms after growing on diet that contained DDT at four different concentrations (1, 0.1, 0.01, 0.001 ppm) as well as on diet without DDT as controls. They were subjected to differential ¹²C-/¹³C-dansyl labeling of the amine/phenol submetabolome, LC-UV quantification of the total amount of labeled metabolites for sample normalization, and LC-MS detection and relative quantification of individual metabolites in comparative samples. The total concentration of labeled metabolites did not show any significant change between four DDT-treatment groups and one control group. Multivariate statistical analysis of the metabolome data set showed that there was a distinct metabolomic separation between the five groups. Out of the 2044 detected peak pairs, 338 and 1471 metabolites have been putatively identified against the HMDB database and the EML library, respectively. 65 metabolites were identified by the dansyl library searching based on the accurate mass and retention time. Among the 65 identified metabolites, 33 positive metabolites had changes of greater than 1.20-fold or less than 0.83-fold in one or more groups with p-value of smaller than 0.05. Several useful biomarkers including serine, methionine, tryptophan, asymmetric dimethylarginine, N-Methyl-D-aspartic and tyrosine were identified. The changes of these biomarkers were likely due to the disruption of the endocrine system of silkworm by DDT. This work illustrates that the method of CIL LC-MS is useful to generate quantitative submetabolome profiles from a small volume of silkworm hemolymph with much higher coverage than conventional LC-MS methods, thereby facilitating the discovery of potential metabolite biomarkers related to EDC or other chemical exposure.     

Modelling the thermal behaviour of the low-thermal mass liquid chromatography system

We report upon the experimental investigation of the heat transfer in low thermal mass LC (LTMLC) systems, used under temperature gradient conditions. The influence of the temperature ramp, the capillary dimensions, the material selection and the chromatographic conditions on the radial temperature gradients formed when applying a temperature ramp were investigated by a numerical model and verified with experimental temperature measurements. It was found that the radial temperature gradients scale linearly with the heating rate, quadratically with the radius of the capillary and inversely to the thermal diffusivity. Because of the thermal radial gradients in the liquid zone inside the capillary lead to radial viscosity and velocity gradients, they form an additional source of dispersion for the solutes. For a temperature ramp of 1 K/s and a strong temperature dependence of the retention of small molecules, the model predicts that narrow-bore columns (i.d. 2.1 mm) can be used. For a temperature ramp of 10 K/s, the maximal inner diameter is of the order of 1 mm before a substantial increase in dispersion occurs.