Search

In this contribution, we review the recent literature relating to the measurement and modelling of all diffusion-dominated processes contributing to the efficiency of a chromatographic column. In first instance, this involves the measurement and modelling of the overall effective diffusion coefficient D eff (determining the so-called B-term band broadening). The latter manifests itself most clearly during a so-called peak parking experiment. Using effective medium theory modelling, the measured D eff -value can subsequently be decomposed into its constituent contributions, of which the intra-particle or the mesoporous zone and the surface diffusion coefficient are the most important ones. As an accurate estimation of the diffusion processes also allows computing the C-term plate height contribution terms, the review ends with some recent insights obtained when using the established B- and C-term contributions to compute the degree of eddy-dispersion in contemporary packed bed columns. [Display omitted] • Recent literature on measurement and modelling of diffusion in chromatography reviewed. • The effective medium theory modelling is explained and compared with simulations. • Measurements of microscopic diffusion parameters is discussed. • The effect of the diffusion parameters on the eddy-dispersion is considered. [ABSTRACT FROM AUTHOR]

The use of CO 2 -based mobile phases for separations, more generally referred to as supercritical fluid chromatography (SFC), allows to perform highly efficient and fast separations due to its low viscosity and high diffusivity of the solutes in the mobile phase. Nevertheless, the instrumental capabilities of current state-of-the art instrumentation in SFC is still not on the same level as that of ultra-high performance liquid chromatography. Not only is the maximum operating pressure lower, also the extra-column fluidic path is not fully optimized to exploit the possibilities of high efficiency columns packed with small particles. The effect of the strong solvent injection inherent to SFC hinders the optimal implementation of short small particle columns. The current limits in separation power in SFC are discussed and the requirements for future generation instruments are reviewed. An overview is presented of innovations in column technology, separation conditions and optimization of the instrumental design. • The low viscosity of CO 2 -based mobile phases allows high kinetic performance. • To allow the use of high modifier content, higher operating pressures are required. • Improvements in extra-column dispersion needed to enable the use of narrow ID columns. • New chiral stationary phases allow very fast (<1min) enantioseparations. • Injection solvent effects deteriorate 1D and 2D performance of SFC. [ABSTRACT FROM AUTHOR]

It is shown that all Cm and Cs expressions ever established in the literature are intrinsically fully identical and can be derived from a simple parallel plug flow model. Analytically solving this model yields Cm- and Cs-term expressions that exactly correspond to the expressions obtained via either the method of moments (general rate model) or via Giddings' nonequilibrium theory. This holds for open-tubular as well as packed and monolithic columns. From this equivalence, a set of convenient "translation" expressions could be established, enabling a swift transition between the different Cm- and Cs-term expressions that currently coexist in literature. The link with the parallel plug flow model provides a good physical insight into the assumptions underlying the general rate model (e.g., a plug flow in the flow-through pores) and in the physical meaning of the different parameters involved in it. The parallel plug flow model also allows us to illustrate the difference between the zone and the phase retention factor and between the intraparticle diffusion coefficient and the effective diffusion coefficient used in the general rate model. These differences are subtle, but as they can have a large impact, they constitute important potential sources of confusion currently obscuring the modeling of HPLC columns. [ABSTRACT FROM AUTHOR]

• A new in-column methacrylate-based polymerization procedure was developed for imaging the internal morphology of bare silica HPLC columns • Polymerization was performed in a commercial and in a home-made silica column • The obtained silica/polymeric rod can be mechanically cut allowing cross section SEM imaging • The developed procedure allows mapping of the local external porosity in packed column • The procedure could be of assistance to steer the optimization of packing processes of HPLC columns. To allow an enhanced understanding of the order in packed HPLC columns, in this work a methodology for immobilizing native polar silica particles is developed based on the polymerization of a methyl methacrylate (MMA) and ethylene glycol dimethacrylate (EGDMA) as a cross-linker in the interstitial pores of HPLC columns. Subsequent mechanical cutting then allows scanning electron microscopy (SEM) based imagery of cross-sections of the packed bed. In this way, the packing efficiency of home-made and commercial HPLC columns with 4.6 mm inner diameter and 150 mm length comprising the same packing material of 5 µm silica particles are compared. The methodology is developed for native silica used in e.g. hydrophilic interaction liquid chromatography (HILIC) and in normal phase LC. In order to confirm the feasibility of the developed methodology, the conventional methods for the evaluation of column, efficiency and porosity, are also employed. The obtained porosity information is compared and showed the same trend with the external porosity measurements obtained via inverse size exclusion approach, illustrating its potential application to study the micro-heterogeneity of packed HPLC columns and to guide the optimization of the packing process of HPLC columns. [ABSTRACT FROM AUTHOR]

• Flow segmentation can be used to measure radial dispersion coefficient (D rad) in practice. • Mass flow meter feedback can be used to correct flow rate mismatches. • Method validated by showing independence of relative central flow rate and tracer concentration. • Measured D rad -values higher than in most engineering literature reports but still within cited range. The present contribution reports on the practical implementation and validation of a new experimental method to determine the radial dispersion (D rad) in packed bed liquid chromatography columns, as well as on the results obtained with it. A first important validation was that the measured D rad -values were independent of the applied relative central flow rate (varied from 25% to 57%). The obtained D rad -values did not vary significantly when changing the concentration of the injected tracer to check potential mass overloading effects (25, 50 or 75 ppm of tracer for the acetophenone measurements; 12.5 and 25 ppm of tracer for the toluene measurements). And yet another important validation step was the observation that the D rad -values clearly converged to the value of D eff for velocities going to zero, as physically and theoretically expected. Plotting the obtained results as a plot of D rad /D mol versus the reduced velocity ν, a quasi-linear relationship is obtained. The slope of the curve (β = 0.38 and β = 0.46 for toluene and acetophenone, respectively) is significantly larger than the value that is most frequently cited in engineering literature. However, the obtained β-values and D rad /D mol -values still fall within the broad range of β- and D rad /D mol -values cited in literature. [ABSTRACT FROM AUTHOR]

• Alternative radial dispersion coefficient (D rad) measurement method is proposed. • Method is based on the use of flow segmentation frit technology. • Different D rad -determination read-out methods are possible and have been established. • Negligible effect of segmentation ring thickness proven via computational fluid dynamics. • Correction method established for flow rate mismatches between central inlet and outlet. We report on an alternative experimental method to determine the transversal or radial dispersion coefficient (D rad) in packed bed columns for liquid chromatography. The method uses a recently developed type of column end-fitting with an impermeable segmentation ring that splits the incoming flow in a central and peripheral part. Using this device and continuously sending a tracer-laden flow through the central inlet and a tracer-less flow through the peripheral inlet, a steady-state radial dispersion pattern is established which can be used to determine the degree of radial dispersion. The present part of the study lays the theoretical foundation for the method and shows the parameter sensitivity of the different possible data analysis variants. In addition, computational fluid dynamics simulations have been used to validate the established procedure (agreement between true and determined D rad -value better than 0.4%) as well as to study the effect of the most important error sources: the presence of the annular flow segmentation ring and the almost inevitable occurrence of mismatches between the central and the peripheral in- and outlet flows. In the latter case, a combined read-out method can be proposed that nearly perfectly compensates for the flow mismatch error (remaining error on the D rad -value smaller than 3%). [ABSTRACT FROM AUTHOR]

• HIC method development is demonstrated using a ternary salt system. • The ternary salt system included ammonium sulfate, sodium chloride, and phosphate buffer. • Prediction error increases with increase in gradient duration and did not exceed 12 %. • A method for optimizing ternary-gradient conditions is established using a genetic algorithm. • Application is demonstrated for critical-pair separation in a mixture of proteins. The use of a ternary mobile-phase system comprising ammonium sulphate, sodium chloride, and phosphate buffer was explored to tune retention and enhance selectivity in hydrophobic interaction chromatography. The accuracy of the linear solvent-strength model to predict protein retention with the ternary mobile-phase system based on isocratic scouting runs is limited, as the extrapolated retention factor at aqueous buffer conditions (k 0) cannot be reliably established. The Jandera retention model utilizing a salt concentration averaged retention factor (k ¯ 0) in aqueous buffer for ternary systems overcomes this bottleneck. Gradient retention factors were derived based on isocratic scouting runs after numerical integration of the isocratic Jandera model, leading to retention-time prediction errors below 11 % for linear gradients. Furthermore, an analytical expression was formulated to predict HIC retention for both linear and segmented linear gradients, considering the linear solvent-strength (LSS) model within ternary salt systems, relying on a fixed k 0. The approach involved conducting two gradient scouting runs for each of the two binary salt systems to determine model parameters. Retention-time prediction errors for linear gradients were below 12 % for lysozyme and 3 % for trypsinogen and α -chymotrypsinogen A. Finally, the analytical expression for a ternary mobile-phase system was used in combination with a genetic algorithm to tune the HIC selectivity. With an optimized segmented ternary gradient, a critical-pair separation for a mixture of 7 proteins was achieved within 15 min with retention-time prediction errors ranging between 0.7 and 15.7 %. [ABSTRACT FROM AUTHOR]

Columns for liquid chromatography produce ever narrower peaks and analysts continue to push to smaller column diameters to save solvents and have better MS responses. The combined effect of both trends is that the instrument volumes outside the separation column (=extra-column volumes of the instrument) become a significant contributor to the overall dispersion. This currently occurs to such an extent that the current state-of-the-art chromatographic columns have become too good compared to the quality of most instruments. Extra-column dispersion also becomes very critical in the now rapidly emerging multi-dimensional LC application area. The present contribution reviews past and recent studies of the experimental and theoretical work conducted thus far to measure, predict and optimize extra-column dispersion. Emphasis is put on providing some general rules that can be followed to minimize extra-column dispersion in the most efficient way (i.e., without sacrificing too much of the available pressure or detection sensitivity). • An overview is provided of past and recent studies of the extra-column dispersion. • The different methodologies to measure extra-column dispersion are discussed. • The different instrument contribution to extra-column dispersion contribution are reviewed. • Trade-offs between dispersion and pressure drop or sensitivity are presented. • General rules to minimize extra-column dispersion are provided. [ABSTRACT FROM AUTHOR]

Temperature-responsive liquid chromatography (TRLC) offers an alternative for retention and selectivity optimisation in HPLC. This approach thereby exploits temperature gradients on stimuli-responsive stationary phases and forfeits the necessity for solvent gradients, allowing analyses to be performed using aqueous mobile phases. Consequently, it can be employed as a green alternative to reversed-phase separations. However, current production to obtain temperature-responsive columns inherently require dedicated column packing processes with polymer-modified particles. To facilitate the development of temperature-responsive phases, a flow-through modification procedure was developed allowing on-column modification of aminopropyl silica columns. Three columns were manufactured using this novel flow-through approach, which achieved identical column efficiencies compared to existing TRLC column. Demonstrating the possibility of bypassing the dedicated packing processes without losing efficiency. Additionally, it was observed that flow-through produced columns yielded higher retention at elevated temperatures despite their reduced carbon load. Further investigation of the carbon load revealed the presence of stationary phase gradients, whose influence was studied via novel developed retention experiments, which revealed a negligible change reduction in retention upon a change of polymer modification from 19.8% to 14.5%. However, further decrease from 14.5% to 12.3% resulted in a larger change. Interestingly, a further enhancement in apparent plate numbers was observed when operating the column under a reversed flow, yielding an increasing stationary phase gradient. This on-column modification procedure demonstrates the potential for modification of existing (commercial) packed columns to achieve temperature-responsive phases without loss of efficiency or retention. Thus, not only facilitating accessibility to temperature-responsive phases, but also aiding with development of further generations of temperature-responsive phases by removing the need for packing optimisation. Additionally, a novel experiment was set up to easily investigate the effect of inhomogeneous stationary phases retention. [Display omitted] • Novel on-column procedure for temperature-responsive stationary phases without loss of efficiency or retention. • Flow-through modification procedure removes the need for in-house packing setups. • Presence of stationary phase gradient capable to further improve column efficiency. • Flow-through modification allows for production of temperature-responsive columns from pre-packed columns. [ABSTRACT FROM AUTHOR]

The present study reports on a computational fluid dynamics study of the band broadening occurring in injector systems frequently used in contemporary liquid chromatography instruments. The aim of this work is to determine band broadening originating purely from the injection volume in absence of any other possible contribution (e.g. band broadening due to the injection valve) and to unravel the mechanism behind it. Simulations of the dispersion process in flow through needle injectors were performed. In addition, fixed loop injectors were also simulated and comparison with flow through needle injectors was made. The results are also represented in a dimensionless form, allowing to generalize them to different experimental conditions. It was shown that two different injection regimes exist (the convection regime and the diffusion regime), both leading to narrow injection bands, while operating the injection needle in between the two regimes leads to broad injections bands. It was also found that the band broadening in the flow-through needle injector is strongly affected by the holding time between sample uptake and the actual injection. As a result, fixed, full loop injectors produced narrower injection bands compared to flow-through needle injectors operated with a realistic holding time. [ABSTRACT FROM AUTHOR]

The topic of this report is experimental verification of previously published theoretical predictions. The mixing rate ( R ϕ ) is the temporal rate of increasing a fraction of stronger solvent in the mobile phase of gradient LC. The optimal R ϕ ( R ϕ ,Opt ) is the one at which a required peak capacity ( n ) of gradient LC analysis is obtained in the shortest time. The key factors affecting R ϕ ,Opt are the sample molecular weight ( M ), the void time ( t M ), and the column pressure condition − R ϕ ,Opt in a column operating below the instrumental pressure limit is 2–3 times higher than R ϕ ,Opt in a column operating at the instrumental pressure limit. Using previously proposed speed optimization criteria, t / s i , where t , s and i are the analysis time, the separation capacity (a metric proportions to n ), and the order ( i = 2 or i = 4 for analyses operating below or at the instrumental pressure limit, respectively), parameter R ϕ ,Opt for analyses of small-molecule samples has been experimentally found. For both orders, the agreement with the theoretical prediction can be considered as very good. Base on the experimental results, we continue to recommend the earlier proposed theoretically based mixing rate of 5%/ t M as a default for all analyses of small-molecule samples (100 < M < 400), and 50 % 3 / M / t M for larger molecules. Experimental evidence is also provided to explain why earlier published less accurate equations for peak capacity and analysis time are not suitable for theoretical prediction of R ϕ ,Opt . [ABSTRACT FROM AUTHOR]

We have investigated which of the different existing peak variance read-out methods (including the effect of a deconvolution pre-treatment method) are most suited to eliminate the system contribution from the total observed band broadening observed in LC systems. Emphasis is put on the most demanding case, i.e., the measurement of non-retained component peaks, which typically are very narrow and tailed. The problem with such peaks is that the method that is generally considered to be the only mathematically correct method (i.e., the method of moments) leads to peak variance values that are so strongly dominated by the tail of the peak that they become highly exaggerated and practically meaningless (i.e., they are dominated by the peak width at 10 or 12 σ t , which corresponds to resolutions and peak purities that are so high they are never pursued in practice). Interestingly, filtering away the extra-column contribution from the entire peak shape using peak deconvolution (wherein not only the second order moment is corrected but also all other moments) produces corrected 4 σ t - and half height peak widths that are physically meaningful, i.e., the corrected values allow to make sufficiently accurate predictions of how the peak width at 4 σ t and at half height changes when the column length changes. This result now allows to navigate away from the classical method of moments to define the column plate height, and resort to plate heights based on the practically much more relevant 4 σ t - and 5 σ t -widths, provided theses are corrected via peak deconvolution. [ABSTRACT FROM AUTHOR]

• Adapted and improved set-up to measure molecular diffusion coefficient D mol in SFC. • New method to measure longitudinal effective diffusion Deff inside the column. • Unique data for D eff /D mol are presented as a function of the retention factor. • Estimation of the surface diffusion coefficient γ s D s /D mol vs. retention are made. • γ s D s /D mol is found to decrease strongly with increasing retention in SFC. The improvement of supercritical fluid chromatography (SFC) instrumentation enhanced its reliability and utility over the past decade. The further development of high speed and high resolution separations is however obstructed by the lack of accurate models for axial dispersion in SFC. This work is a first step to tackle this by developing more reliable methods to measure molecular (D mol) and longitudinal diffusion (D eff) in SFC, as these affect all aspects of separation efficiency. In the present contribution, we report on an improved method, to enable more flexible, reliable and accurate measurements of D mol in SFC using commercial instrumentation. A two-column variant of the stopped-flow experiment is proposed as an adapted set-up for measuring the effective longitudinal diffusion coefficient D eff in SFC-conditions. Using the set-ups for a number of test-compounds, it has been found that D eff , and the coefficients describing its constituent sub-processes (cf. particle diffusion D part and surface diffusion γ s D s), all vary in a linearly proportional way with the bulk diffusion coefficient D mol within a high degree of accuracy. It has also been found that D eff decreases much more sharply with increasing retention factor compared to LC. By applying the effective medium theory, it was found that the relative surface diffusion coefficient γ s D s /D mol decreases strongly with retention factor for the investigated solutes and column, in contrary to what is typically observed in reversed phase liquid chromatography. Results indicate that this might be related to a change in retention behavior of the analytes. Obviously, more analytes and conditions need to be explored to complete this picture and the extend range of applicability of these observations. [ABSTRACT FROM AUTHOR]

• Viscous heating-induced plate heights are computed up to 2500 bar operations. • Plate height contribution originating from radial gradients could be isolated (H loc,rad). • H loc,rad is independent of the axial gradients and the dispersion generated by the bed. • H loc,rad has been computed as a function of the radial dispersion and retention enthalpy. Over the past years viscous heating band broadening occurring in high pressure liquid chromatography has been studied extensively. In the present numerical study, we investigate the fine details of this band broadening contribution under extreme high-pressure conditions (2500 bar). To analyze the results, we first show that viscous heating leads to two clearly distinguishable band broadening effects, one originating from the radial differences in the species migration velocity and the other from the axial variations. It was found that the radial contribution is independent of the intrinsic band broadening of the bed (i.e. band broadening in absence of viscous heating) while it strongly depends on the radial dispersion coefficient and the retention enthalpy of the analytes. On the other hand, the axial contribution is strongly dependent on the bed intrinsic band broadening and it is found to be 4 to 5 times lower than the radial contribution. We also show the strong effect of the endfittings on the temperature gradients inside the column thus on the resulting viscous heating band broadening. [ABSTRACT FROM AUTHOR]

• Viscous heating-induced plate height contribution (H vh) is computed using CFD. • Future ultra-high-pressure conditions (2500bar) are considered. • Increase in bed conductivity needed to keep affordable H vh is determined. • Same exercise is made for decrease of wall conductivity (=alternative solution). • Effect of anisotropic wall and perfect adiabatic insulation is quantified as well. We report on a numerical simulation study of a number of potential column technology solutions to minimize the plate height contribution (H vh) originating from the use of ultra-high pressures and their concomitant viscous heating effect. Looking as far as possible into the future of UHPLC, all main results are obtained for the case of a 2500 bar pressure gradient. However, to generalize the result, a correlation is given that can be used to interpolate the results to lower pressures with some 10% accuracy. For the considered case of a 2.1mm column, a liquid flow rate of 0.45 ml/min, an analyte with retention factor k(25°C)=3 and a retention enthalpy chosen such that ΔH R /R= -1000 K, it is found that, in order to keep the global plate height as measured at the column outlet (H vh,glob,out) below 1 μm, the bed conductivity would need to be raised to λ bed =2.4 W/m•K, i.e., 4 times higher than a typical packed bed of fully-porous or core-shell silica particles. An equivalent effect on the band broadening could be obtained if it would be possible to replace the steel column wall with a low conductivity material. In this case, a wall conductivity of 0.25 W/m•K, i.e., 64 times smaller than the conductivity of steel, would be needed to keep H vh,glob,out below 1 μm. Results are also interpreted based on contour plots of the axial and radial velocity variation of a retained analyte. [ABSTRACT FROM AUTHOR]

• The separation efficiency of HIC was assessed in isocratic and gradient mode. • The optimal flow rate yielding maximum peak capacity decreases with gradient time. • Effects of particle diameter and column coupling on resolving power is demonstrated. • A peak capacity of 240 was achieved using a 10 cm column packed with 2.3 µm particles. This study reports on the assessment of the separation performance of hydrophobic interaction chromatography for intact protein analysis using non-porous butyl polymethacrylate phases. The maximum peak capacity in inverse gradient mode was reached at a volumetric flow rate which was significantly (10–20 times) higher than the flow rate yielding the minimum plate height in isocratic mode, as the gradient volume dominates the peak-capacity generation. The flow rate yielding the maximum peak capacity increased with decreasing gradient volume, i.e. , steeper gradients, and also depends on the magnitude of the mass-transfer contribution to peak dispersion (affected by particle size and molecular diffusion coefficient of proteins) at these high flow rates. The maximum peak capacity using a 100 mm long column packed with 4 µm particles for steep 7.5 min gradients was determined to be 60. Increasing the column length by coupling columns leads to better gradient performance than increasing the gradient duration for gradients of 60 min and longer. Using a coupled column system (2 × 100 mm long columns packed with 4 µm particles), the maximum peak capacity was determined to be 105, which was 33% higher compared to that of a single column while applying a similar gradient volume. Decreasing the particle size to 2.3 µm leads to higher peak capacities even though the column was operated at lower volumetric flow rate. The maximum peak capacity obtained with the 2.3 µm column was 128% higher than was obtained with the coupled column. Even at suboptimal conditions, the 2.3 µm column yields a higher peak capacity (14%) than when using two coupled columns packed with 4 µm at optimal conditions (gradient time of 120 min and a flow rate of 0.5 mL/min). [ABSTRACT FROM AUTHOR]

• The novel SFC feed injector that adds the sample to the mobile phase stream was investigated. • Optimal feed speed is a trade-off between injection solvent mismatch and sample dilution. • The overfeed volumes increases band broadening and is best replaced by an apolar solvent. • Partial sample injection can further decrease injection band broadening. The behavior of a novel type of SFC injector, the feed injector, was investigated. In SFC, the sample compounds are usually diluted in a solvent which has a higher elution strength than the mobile phase, which leads to solvent mismatch upon injection and evidently band broadening. The feed injector differs from standard injectors as the sample, contained in the sample needle or loop, is not switched in line with the mobile phase flow, but directly injected/added to the mobile phase flow (F). The subsequent mixing of sample and mobile phase flows inherently results in a dilution of the sample, thus reducing the solvent mismatch. However, for a given injection/feed flow rate F feed , the total volume in which the sample is contained increases with a factor (F feed + F)/F feed. In addition, to ensure that all of the loaded sample is injected on the column, an additional overfeed volume (V ov) needs to be injected after the sample plug. To better understand the effect of these operating parameters, a wide range of injection conditions was investigated by varying the F feed / F -ratio, V ov , overfeed solvent etc. under SFC conditions. It was found that an optimal F feed /F exists which is independent of F and decreases with increasing solvent strength dependency of the sample compound. Decreasing V ov has a beneficial effect on peak dispersion but can only be varied over a certain range to ensure the full injection of the loaded sample. On the other hand, it was found that a much larger gain could be made by switching the overfeed solvent to one more compatible with the CO 2 -based mobile phase. Further reduction of the band broadening could be achieved by applying partial sample injections. [ABSTRACT FROM AUTHOR]

• Multilevel simulation study of viscous heating effects at pressures up to 2500 bar. • Effective conductivity values calculated for the materials most commonly used in LC. • Halving radial temperature difference requires doubling the bed conductivity. • Only structures with connected enhanced conductivity cores can achieve this. • Ultra-low conductivity column walls can alleviate viscous heating effects as well. We report on a numerical study of the thermal conductivity and temperature distribution in analytical packed bed and monolithic HPLC columns to assess the feasibility of a number of potential solutions to the viscous heating problem that would normally impede high efficiency separations when moving to extreme operating pressures (e.g., 2500 bar). Computational fluid dynamic (CFD) simulations were employed to study heat transfer on three hierarchical levels of the column: meso‑pore level, through-pore level and column level. At the first level, realistic values were determined for the conductivity of the porous zone (k pz), depending on the internal structure of the porous zone and the mobile phase used (acetonitrile, water or a mixture of both). These k pz -values were in turn used at the second level to determine realistic values for the effective conductivity of the bed (k eff). It was shown that the presence of a solid core only has a minor effect on the packed bed conductivity. Using highly conducting materials as core material can be expected to maximally lead to a 60% increase in bed conductivity. Contrarily, in monolithic beds, the presence of a core material would form one continuous phase of highly conducting material, thus greatly enhancing the conductivity of the bed. At the third level, the temperature field in the entire column (bed and column housing) was resolved for three typical boundary conditions: isothermal, adiabatic and still-air oven. The effect of different physical properties (inlet pressure, mobile phase composition, bed conductivity, wall conductivity and column ID) on these temperature fields was investigated. It was shown that, theoretically, besides 1 mm ID columns also "core-shell monoliths" can provide a solution to viscous heating (by increasing the bed conductivity). Other possible solutions are proposed and discussed. [ABSTRACT FROM AUTHOR]

• Measurement of effective (D eff) and intra-particle diffusion (D p z & γ s D s) of proteins. • For the first time done under retained conditions at elevated pressure. • D eff , D p z , and γ s D s vary strongly with pressure, requiring dedicated peak parking set-up. • D p z and γ s D s correlate strongly with hydrodynamic radius. • Decrease of D p z and γ s D s with pressure suggests deeper penetration into stationary-phase. To determine the efficiency that can be obtained in a packed-bed liquid-chromatography column for a particular analyte, a correct determination of the molecular and effective diffusion coefficients (D m and D eff) of the analyte is required. The latter is usually obtained via peak parking experiments wherein the flow is stopped. As a result, the column pressure rapidly dissipates and the measurement is essentially conducted at ambient pressure. This is problematic for analytes whose retention depends on pressure, such as proteins and potentially other large (dipolar) molecules. In that case, a conventional peak parking experiment is expected to lead to large errors in D eff. To obtain a better estimate of D eff , the present study reports on the use of a set-up enabling peak parking measurements under pressurized conditions. This approach allowed us to report, for the first time, D eff for proteins at elevated pressure under retained conditions. First, D eff was determined at a (average) pressure of about 105 bar for a set of proteins with varying size, namely: bradykinin, insulin, lysozyme, β-lactoglobulin, and carbonic anhydrase in a column packed with 400 Å core-shell particles. The obtained data were then compared to those of several small analytes: acetophenone, propiophenone, benzophenone, valerophenone, and hexanophenone. A clear trend between D eff and analyte size was observed. The set-up was then used to determine D eff of bradykinin and lysozyme at variable (average) pressures ranging from 28 bar to 430 bar. These experiments showed a decrease in intra-particle and surface diffusion with pressure, which was larger for lysozyme than bradykinin. The data show that pressurized peak parking experiments are vital to correctly determine D eff when the analyte retention varies significantly with pressure. [ABSTRACT FROM AUTHOR]

• Determined experimental effective diffusion coefficients (D eff) under HILIC conditions. • Applied Effective Medium Theory to derive intra-particle diffusion (D part) from D eff. • Analyzed mesopore composition as a function of mobile phase composition. • D part / D m reaches minimum when stationary phase layer thickness is largest. • Proposed model linking mesopore composition, analyte retention and size to D part. A detailed analysis of intra-particle volumes and layer thicknesses and their effect on the diffusion of solutes in hydrophilic interaction liquid chromatography (HILIC) was made. Pycnometric measurements and the retention volume of deuterated mobile phase constituents (water and acetonitrile) were used to estimate the void volume inside the column, including not only the volume of the mobile phase but also part of the enriched water solvent acting as the stationary phase in HILIC. The mobile phase (hold-up) volume accessible to non-retained components was estimated using a homologous series approach. The joint analysis of the different approaches indicated the formation of enriched water layers on the hydrophobic silica mesopore walls with a thickness varying significantly with mobile phase composition. The maximal thickness of the enriched water layers, which corresponded to the minimum void volume accessible to unretained solutes, marked a transition in the retention behavior of the studied analytes. Discrepancies between deuterated solvent measurements and pycnometry were explained by the existence of an irreplaceable water layer adsorbed on the silica surface. Regarding the diffusion behavior in HILIC, peak parking experiments were used to interpret the influence of the acetonitrile content on the effective diffusion coefficient D eff. A systematic decrease in D eff and molecular diffusion D m was observed with decreasing acetonitrile concentration, primarily attributed to variations in mobile phase viscosity. Notably, D eff / D m remained nearly unaffected by variations in mobile phase composition. Finally, the effective medium theory was used to make a comprehensive analysis of D part / D m to study the contribution to band broadening when the solute resides in the mesopores. The obtained data unveiled a curvature with a minimum corresponding to conditions of maximum water-layer thickness and retention. For the weakly retained compounds (k ' < 0.5) the D part / D m -values were found to be relatively high (order of 0.35-0.5), which directly reflects the high γ s D s / D m -values that were observed (order 0.35-7). [ABSTRACT FROM AUTHOR]

Highlights • Columns with 4 distinct types of band broadening quality were analyzed. • Retention and peak parking measurements showed identical B-, C m -, C s -term dispersion. • Differences could be fully attributed to eddy-dispersion. • Total pore blocking confirmed packing heterogeneity as main difference between columns. Abstract We report on a systematic study involving columns with a clearly different efficiency (4 distinct quality groups) obtained by packing the columns that were C 18 bonded and endcapped with a different carbon loading. Using B-term analysis (via peak parking) and theoretical models to estimate the magnitude of the C m - and C s -term contributions, it could be concluded that the difference in efficiency among the groups was entirely due to a difference in eddy dispersion. As such, the columns provided an ideal testing ground to verify how well the total pore blocking (TPB)-method can be used to probe differences in packing heterogeneity. In agreement with earlier literature observations, it turns out the TPB-method is much more sensitive to packing heterogeneities than the eddy dispersion (H eddy)-contribution measured under open-pore conditions via B- and C- term subtraction. Typically, differences in H eddy on the order of 0.1–0.5μm translate into a difference on the order of 0.5–2μm in the TPB mode. This confirms the TPB as a powerful technique to make very sensitive measurements of the homogeneity of packed beds. [ABSTRACT FROM AUTHOR]

Highlights • Detailed calculations of the effective heat conductivity in packed beds were made. • Silica cores contribute less than previously assumed to the effective conductivity. • Even high conductivity cores can only be expected to have a minimal effect. • A physically more sound alternative for the Zarichnyak-model is proposed. • Two conceptual other strategies to enhance the effective conductivity are discussed. Abstract We report on a numerical study of the thermal conductivity of core-shell particle packed bed columns. Covering a variety of packing structures and a broad range of mobile phase and porous zone conductivities, it was in all cases found that switching to particles with a highly conducting core (e.g., with a gold or copper core instead of a silica core) would produce a much smaller increase of the effective heat conductivity of the bed (k eff) than previously expected in literature. We found maximal increases on the order of some 20–70%, which is much lower than the potential increases up to 2000% assumed in literature. The overestimation in literature could be attributed to the fact that this literature was based on an incorrect extrapolation of the Zarichnyak-model which was the heat conductivity model predominantly used up till now. On the other hand, the computed relationships between k eff and the core conductivity obtained in the present study are in good agreement with an analytical solution derived from the effective medium theory, a theory which is physically much more relevant for the case at hand than the Zarichnyak-model. The results also show that the observed increase in effective bed conductivity between fully porous and core-shell particle beds frequently observed in literature is not only due to the presence of the core, but that differences in the shell layer conductivity can play an equally important role. In addition, it could also be demonstrated that, if ways could be found to increase the conductivity of the shell layer, this would produce a much stronger increase of the overall bed conductivity than will ever be possible by increasing the conductivity of the cores. [ABSTRACT FROM AUTHOR]

A specific and sensitive capillary liquid chromatography-ultraviolet detection (cap-LC-UV) method in combination with a micro-extraction by packed sorbent (MEPS) sample clean-up procedure has been developed and validated for the simultaneous analysis of chlorpromazine, olanzapine and their flavin-containing monooxygenase (FMO) mediated N-oxides in rat brain microdialysates. Chromatographic separation was obtained on an Acclaim Pepmap RP C18 column with an ID of 300 µm. An injection volume of 20 µL was used to inject the largely aqueous samples and was shown to have no influence on the obtained peak shape of the compounds of interest. Optimal conditions for MEPS extraction were obtained on a mixed-mode M1 (80% C8, 20% SCX) cartridge after diluting microdialysate samples with phosphate buffer pH 2.5 (1:3 v/v). The method was validated and lower limits of quantification (LLOQ) were determined at 0.5 nM for all compounds. Linearity was demonstrated between the LLOQ and 1 µM for all compounds (R 2 >0.995). MEPS recoveries were between 92% and 98%, with intra- and interday variabilities below 15%. The applicability of the developed method was successfully demonstrated by analysing rat brain microdialysates. The capillary LC-UV method in combination with MEPS sample treatment provides a simple, sensitive method to quantify all compounds of interest in 45 min and can be applied for routine therapeutic monitoring and pharmacokinetic studies of olanzapine, chlorpromazine and their respective N-oxides. [ABSTRACT FROM AUTHOR]

The limits in operating pressures are extended for narrow-bore columns in gradient elution up to 2000 bar. As the required pumps for these pressures are incompatible with common chromatographic solvents and are not suitable to apply a mobile phase composition gradient, a mobile phase delivery and injection system is described and experimentally validated which allows to use any possible chromatographic solvent in isocratic and gradient elution. The mobile phase delivery and injection system also allows to perform multiple separations without the need to depressurize the column. This system consists out of 5 dual on/off valves and two large volume loops in which the gradient and equilibration volume of initial mobile phase are loaded by a commercial liquid chromatography pump. The loops are then flushed toward the column at extreme pressures. The mobile phase delivery and injection system is first evaluated in isocratic elution and shows a comparable performance to a state-of-the-art commercial flow-through-needle injector but with twice the pressure rating. Distortion of the loaded gradient by dispersion in the gradient storage loop is studied. The effect of the most important parameters (such as flow rate, pressure and gradient steepness) is experimentally investigated. Different gradient steepnesses and volumes can be applied at different flow rates and operating pressures with a good repeatability. Due to the isobaric operation of the pumps, the gradient is monitored in real-time by a mass flow meter installed at the detector outlet. The chromatograms are then converted from time to volume-base. A separation of a 19-compound sample is performed on a 300 × 2.1 mm column at 1000 bar and on a 600 × 2.1 mm column at 2000 bar. The peak capacity was found to increase from 141 to 199 and thus scales with L as is predicted by theory. This allows to conclude that the inlet pressure for narrow-bore columns in gradient elution can be increased up to 2000 bar without fundamental pressure-induced limitations. [ABSTRACT FROM AUTHOR]

When using compressible mobile phases such as fluidic CO 2 , the density, the volumetric flow rates and volumetric fractions are pressure dependent. The pressure and temperature definition of these volumetric parameters (referred to as the reference conditions) may alter between systems, manufacturers and operating conditions. A supercritical fluid chromatography system was modified to operate in two modes with different definition of the eluent delivery parameters, referred to as fixed and variable mode. For the variable mode, the volumetric parameters are defined with reference to the pump operating pressure and actual pump head temperature. These conditions may vary when, e.g. changing the column length, permeability, flow rate, etc. and are thus variable reference conditions. For the fixed mode, the reference conditions were set at 150 bar and 30 °C, resulting in a mass flow rate and mass fraction of modifier definition which is independent of the operation conditions. For the variable mode, the mass flow rate of carbon dioxide increases with system pump operating pressure, decreasing the fraction of modifier. Comparing the void times and retention factor shows that the deviation between the two modes is almost independent of modifier percentage, but depends on the operating pressure. Recalculating the set volumetric fraction of modifier to the mass fraction results in the same retention behaviour for both modes. This shows that retention in SFC can be best modelled using the mass fraction of modifier. The fixed mode also simplifies method scaling as it only requires matching average column pressure. [ABSTRACT FROM AUTHOR]

The applicability of the kinetic plot theory to temperature-programmed gas chromatography (GC) has been confirmed experimentally by measuring the efficiency of a temperature gradient separation of a simple test mixture on 15, 30, 60 and 120 m long (coupled) columns. It has been shown that the temperature-dependent data needed for the kinetic plot calculation can be obtained from isothermal experiments at the significant temperature, a temperature that characterizes the entire gradient run. Furthermore, optimal flow rates have been calculated for various combinations of column length, diameter, and operating temperature (or significant temperature). The tabulated outcome of these calculations provide good starting points for the optimization of any GC separation. [ABSTRACT FROM AUTHOR]

The interest in implementation of miniaturized ultra-high performance liquid chromatography (UHPLC) in neurochemical research is growing because of the need for faster, more selective and more sensitive neurotransmitter analyses. The instrument performance of a tailor designed microbore UHPLC system coupled to electrochemical detection (ECD) is investigated, focusing on the quantitative monoamine determination in in vivo microdialysis samples. The use of a microbore column (1.0 mm I.D.) requires miniaturization of the entire instrument, though a balance between extra-column band broadening and injection volume must be considered. This is accomplished through the user defined Performance Optimizing Injection Sequence, whereby 5 μL sample is injected on the column with a measured extra-column variance of 4.5-9.0 μL2 and only 7 μL sample uptake. Different sub-2 μm and superficially porous particle stationary phases are compared by means of the kinetic plot approach. Peak efficiencies of about 16 000-35 000 theoretical plates are obtained for the Acquity UPLC BEH C18 column within 13 min analysis time. Furthermore, the coupling to ECD is shown suitable for microbore UHPLC analysis thanks to the miniaturized flow cell design, sufficiently fast data acquisition and mathematical data filtering. Ultimately, injection of in vivo samples demonstrates the applicability of the system for microdialysis analysis. [ABSTRACT FROM AUTHOR]

Supercritical fluid chromatography, where a low-viscosity mobile phase such as carbon dioxide is used, proves to be an excellent technique for fast and efficient separations, especially when sub-2 μm particles are used. However, to achieve high velocities when using these small particles, and in order to stay within the flow rate range of current SFC-instruments, narrow columns (e.g. 2.1 mm ID) must be used. Unfortunately, state-of-the-art instrumentation is limiting the full separation power of these narrower columns due to significant extra-column band broadening effects. The present work identifies and quantifies the different contributions to extra-column band broadening in SFC such as the influence of the sample solvent, injection volume, extra-column volumes and detector cell volume/design. When matching the sample solvent to the mobile phase in terms of elution strength and polarity (e.g. using hexane/ethanol/isopropanol 85/10/5 vol%) and lowering the injection volume to 0.4 μL, the plate count can be increased from 7600 to 21,300 for a low-retaining compound ( k ′ = 2.3) on a 2.1 mm × 150 mm column (packed with 1.8 μm particles). The application of a water/acetonitrile mixture as sample solvent was also investigated. It was found that when the volumetric ratio of water/acetonitrile was optimized, only a slightly lower plate count was measured compared to the hexane-based solvent when minimizing injection and extra-column volume. This confirms earlier results that water/acetonitrile can be used if water-soluble samples are considered or when a less volatile solvent is preferred. Minimizing the ID of the connection capillaries from 250 to 65 μm, however, gives no further improvement in obtained efficiency for early-eluting compounds when a standard system configuration with optimized sample solvent was used. When switching to a state-of-the-art detector design with reduced (dispersion) volume (1.7–0.6 μL), an increase in plate count is observed (from 11,000 to 14,000 plates on a 2.1 mm × 100 mm column with 1.8 μm particles for k ′ = 3) even when 250 μm tubing was used. Using this detector cell and decreasing the ID of the tubing from 250 to 120 μm resulted in an additional increase to 17,300 plates. Further decreasing the tubing ID (e.g. 65 μm) appeared to have no observable influence on the obtained plate count. [ABSTRACT FROM AUTHOR]

Mathematical kinetic plot expressions have been established for the correct extrapolation of the kinetic performance measured in a thin-film capillary GC column with fixed length into the performance that can be expected in a longer column used at the same outlet velocity but at either the maximal inlet pressure or at the optimal inlet pressure, i.e., the one leading to an operation at the kinetic performance limit of the given capillary size. To determine this optimal pressure, analytical solutions have been established for the three roots of the corresponding cubic equation. Experimental confirmation of the kinetic plot extrapolations in GC has been obtained measuring the efficiency of a simple test mixture on 30, 60, 90 and 120 m long (coupled) columns. [ABSTRACT FROM AUTHOR]

• Commercial SFC instrument modified to measure diffusion coefficients (D mol). • Chromatographic column used to eliminate sample solvent effect. • D mol determined for variety of pharmaceutical compounds in CO 2 with 10–50% vol% MeOH. • Large difference in D mol -values observed for structurally very similar compounds. • Variation in mobile phase viscosity allows to predict d mol in investigated range of conditions. Diffusion data are essential for adequate analysis of the kinetic separation performance of any chromatographic system. Unfortunately, for Supercritical Fluid Chromatography (SFC), very little data is available of the diffusion coefficients in mobile phases typically used in contemporary methods, i.e. with a non-negligible amount of polar modifier such as methanol. In this work, a relative simple method which only requires minor modifications to a standard commercially available SFC instrument is used to determine the diffusion coefficient of an extensive set of pharmaceutical compounds in the range of 10–50 vol% of modifier (methanol) in CO 2. By using a traditional SFC column, the solute is first separated from the sample solvent plug, before entering a long capillary, where the band broadening can be linked to its diffusion coefficient using the Taylor-Aris equation. By using two UV-detectors, before and after the capillary, the effect of the dispersion in the column can be eliminated and the true volumetric flow rate determined. It was found that in the investigated range of conditions, the change in mobile phase viscosity in a first approximation allows to predict the variation in diffusion coefficient. Chemical structure and more particularly functional groups can however have a significant effect on the diffusion coefficient. [ABSTRACT FROM AUTHOR]

The limits of supercritical fluid chromatography have been experimentally explored using inlet pressures at the limits of the current commercial instrumentation (400–600 bar), as well as pressures significantly surpassing this (up to 1050 bar). It was found that efficiencies in the range of 200,000 theoretical plates can be achieved for a void time t 0 of roughly 6 min using superficially porous particles (2.7 and 4.6 μm) while remaining within the pressure limits of current commercial instrumentation and columns. If lower efficiencies are sufficient (<100, 000 plates), smaller particles (e.g. 1.8 μm) provide the best trade-off between analysis time and efficiency. Apparent efficiencies of 83,000 ( k ′ = 2.2) to 76,000 ( k ′ = 6.6) plates could be achieved for void times around 1 min by pushing the pressure limits up to 1050 bar on a column length of 500 mm. As the optimal mobile phase velocity for these small particle columns is even higher, it is required to use narrow-bore columns (2.1 mm ID) to remain within the instrument limits of flow rate. The smaller column volume however puts a strain on the separation efficiency due to extra-column band broadening, resulting in losses up to 50% for weakly retained compounds for column lengths below 250 mm. It is also illustrated that when using sub-2 μm particles, especially for separations where a significant amount of organic modifier is required, the current pressure limits of state-of-the-art instrumentation can sometimes be insufficient. For a gradient running from 4 to 40 v % methanol on a 300 mm column at the optimal flow rate the pressure increases from 420 to 810 bar. Operating SFC-columns with a large pressure gradient induces several (undesired) side effects which have been investigated as well. It has been found that, since the viscosity increases strongly with pressure in SFC, the optimal flow rate and the minimal plate height can significantly change when the column length is changed. Whereas e.g. a 3 × 150 mm column (2.7 μm particles) has an optimal flow rate of 1.5 ml/min and minimal plate height of 5.66 μm, a 3 × 1050 mm column has an optimal flow rate of 1.2 ml/min and a minimal plate height of 6.25 μm. Nevertheless, an increase in operating pressure drop in SFC results in a significant gain in kinetic performance. [ABSTRACT FROM AUTHOR]

• Filling and emptying of fraction collection loops in first-in-last-out mode studied. • Shape and variance of the peaks entering a second dimension column investigated. • Results depend on dimensionless elution time and ratio of filling and emptying flows. • Numerical model for peak variance numerically and experimentally verified. • Tightly coiled loops exhibit narrower, less tailing peaks than straight capillaries. Currently, the shape and variance of the analyte band entering the second dimension column when injected from an open loop interface in two-dimensional liquid chromatography is not fully understood. This is however important as it is connected to several other variables encountered when developing 2D-LC methods, including the first dimension flow rate, the sampling (modulation) time and the loop volume. Both numerical simulation methods and experimental measurements were used to understand and quantify the dispersion occurring in open tubular interface loops. Variables included are the analyte diffusion coefficient (D mol), loop filling and emptying rates (F fill & F empty), loop inner diameter or radius (R loop) and loop volume (V loop). For a straight loop capillary, we find that the concentration profile (as measured at the loop outlet) depends only on a single dimensionless parameter t e m p t y * = V l o o p F e m p t y · D m o l R l o o p 2 and the ratio of the filling and emptying flow rates F empty /F fill. A model depending only on these two parameters was developed to predict of the peak variance resulting from the filling and emptying of a straight capillary operated in the first-in-last-out (FILO) modulation mode. Comparison of the concentration profiles and the corresponding variances obtained by either numerical simulation or experiments with straight capillaries shows the results generally agree very well. When the straight capillary is replaced by a tightly coiled loop, significantly smaller (20-40%) peak variances are observed compared to straight capillaries. The magnitude of these decreases is not predicted as well by simulations, however the simulation results are still useful in this case, because they represent an upper boundary (i.e., worst-case scenario) on the predicted variance. [ABSTRACT FROM AUTHOR]

• Novel temperature gradient systems are evaluated for their application in TRLC. • Unravelling of the properties of temperature gradient in TRLC. • Application of temperature gradients in TRLC for the separation of a sample of polyphenols. • Temperature gradient in TRLC can offer both a significant peak refocusing and reduction in analysis time. Temperature Responsive Liquid Chromatography (TRLC) offers an alternative and environmentally friendly way to perform reversed-phase like separations. Its use of temperature responsive polymers to control retention based on column temperature, instead of the fraction of organic modifier in the mobile phase mobile, eliminates the need for solvent composition gradients and allows, for example, for purely aqueous separations. In principle this temperature induced retention should allow for gradient elutions to be performed using downward temperature gradients to control retention and refocus the analyte peaks. Yet, the unavailability of dedicated commercial temperature controlling systems allowing suitable temperature control in TRLC limits implementations thereof often to isothermal or step gradient applications. In this work we study the potential of 1) a simple yet programmable water bath and of 2) a modified HPLC system allowing column temperature programming through controlled mixing of a warm and cold mobile phase streams. The performance of both systems was evaluated under both isocratic and gradient applications, resulting in a more thorough understanding of the influence of temperature gradients in TRLC. This knowledge is then applied to a sample of phenolic solutes, illustrating that, although both systems have some flaws, both are able to impose temperature gradients in TRLC resulting in significantly reduced retention and enhanced refocusing of the analyte peak. [ABSTRACT FROM AUTHOR]

• Post-column flow splitting is commonly used for coupling fast LC analyses to MS. • Flow splitting can lead to very small volumetric variance peaks in the detector. • A framework is developed to help choose connecting capillaries when using splitting. • At high split ratio the capillary has a large effect even for larger volume columns. • Narrow capillaries are advised for high split ratios to avoid losses in efficiency. It is common practice in liquid chromatography to split the flow of the effluent exiting the analytical column into two or more parts, either to enable parallel detection (e.g., coupling the separation to two destructive detectors such as light scattering and mass spectrometry (MS)), or to accommodate flow rate limitations of a detector (e.g., electrospray ionization mass spectrometry). In these instances the user must make choices about split ratio and dimensions of connecting tubing that is used between the split point and the detector, however these details are frequently not mentioned in the literature, and rarely justified. In our own work we often split the effluent following the second dimension (2D) column in two-dimensional liquid chromatography systems coupled to MS detection, and we have frequently observed post 2D column peak broadening that is larger than we would expect to result from dispersion in the MS ionization source itself. For the present paper we describe a series of experiments aimed at understanding the impact of the split ratio and post-split connecting tubing dimensions on dispersion of peaks exiting an analytical column. We start with the simple idea – based on the principle of conservation of mass – that analyte peaks entering the split point are split into two parts such that the analyte mass (and thus peak volume) entering and exiting the split point is conserved, and directly related to the ratio of flow rates entering and exiting the split point. Measurements of peak width and variance after the split point show that this simple view of the splitting process – along with estimates of additional dispersion in the post-split tubing - is sufficient to predict peak variances at the detector with accuracy that is sufficient to guide experimental work (median error of about 10% over a wide range of conditions). We feel it is most impactful to recognize that flow splitting impacts apparent post-column dispersion not because anything unexpected happens in the splitting process, but because the split dramatically reduces the volume of the analyte peak, which then is more susceptible to dispersion in connecting tubing that would not cause significant dispersion under conditions where splitting is not implemented. These results will provide practitioners with a solid basis on which rational decisions about split ratios and dimensions of post-split tubing can be made. [ABSTRACT FROM AUTHOR]

• Sample breakthrough from modulation loops used for 2D-LC was simulated. • Universal breakthrough curves were found that only depend on a dimensionless t* factor. • The maximum loop filling for a given level of analyte loss was determined as a function of t*. • Very good agreement was found between experimental and simulation results for straight loop capillaries. • Coiling of the loop capillary enhances radial mixing/suppresses analyte loss. Two-dimensional liquid chromatography is increasingly being used to address challenging separations in fields ranging from pharmaceutical analysis to the food industry. A significant impediment to development of more methods is the lack of a complete theoretical foundation upon which sound development decisions can be made. One parameter that is currently not fully understood is the extent of filling of sampling loops in the case where effluent from the first dimension separation is transferred to the second dimension separation through this type of open loop interface. This is a highly important parameter because it is connected to several other variables in a 2D-LC system, including the first dimension flow rate, the sampling (modulation) time, and the loop volume. In this study we have used both numerical simulation methods and experimental measurements to understand the extent to which sampling loops can be filled before a significant fraction of the analyte is lost from the end of the loop. Variables included in the study are the analyte diffusion coefficient (D mol), loop filling rate (F fill), loop inner diameter or radius (R loop) and loop volume (V loop). For a straight loop capillary we find that analyte breakthrough curves (as measured at the loop outlet) depend only on a single the dimensionless parameter t * = V l o o p F f i l l · D m o l R l o o p 2 . As a function of this parameter, the fraction of analyte lost from the loop outlet for different extents of loop filling could be calculated, allowing to develop guidelines for the maximum permissible extent of filling before a specified level of analyte loss is reached. Breakthrough measurements using a coiled loop capillary show that less breakthrough is observed compared to the straight capillary at high filling flow rates, presumably due to secondary flows that increase radial dispersion. These measurements enabled the calculation of apparent radial diffusion coefficients for use with coiled capillaries such that the same relation for t* can be used to predict analyte loss due to breakthrough. These results should be very useful to practitioners of 2D-LC, enabling them to make rational decisions about the extent of loop filling on the basis of experimental conditions and analyte type. [ABSTRACT FROM AUTHOR]

It is well known that high-speed/high-efficiency separations in nano-flow liquid chromatography (LC) are very sensitive to the quality of the connections between the column and the rest of the instrument. In the present study, two types of connection errors (capillary misalignment and the occurrence of an inter-capillary gap) have been investigated using computational fluid dynamics. Interestingly, it has been found that large degrees of capillary misalignment (assuming an otherwise perfect contact between the capillary end-faces) can be afforded without introducing any significant dispersion over the entire range of investigated relative misalignment errors (0 ≤ ε/ d cap ≤ 75%), even at the largest flow rates considered in nano-LC. On the other hand, when an inter-capillary gap is present, the dispersion very rapidly increases with the radial width D c of this gap (extra variance ∼ D c n with n even reaching values above 4). The dependency on the gap length L c is however much smaller. Results show that, when D c ≤ 30 μm and L c ≤ 200 μm, dispersion losses can be limited to the order of 1 nL 2 at a flow of 1.5 μL/min, which is generally very small compared to the dispersion in the capillaries (20 μm i.d.) themselves. This result also reconfirms that zero-dead volume connectors with a sufficiently narrow bore can in theory be used without compromising peak dispersion in nano-LC, at least when the capillaries can be matched perfectly to the connector in- and outlet faces. The results are also indicative of the extra dispersion occurring inside microfluidic chips or in the connections between a microfluidic chip and the outer world.

We report on a Computational Fluid Dynamics (CFD) study of the extra dispersion caused by the change in diameter when coupling two pieces of capillary tubing with different diameter. In this first investigation into the problem, the focus is on the typical flow rates (0.25≤F≤2μL/min) and diameters (d≤40μm) used in nano-LC, considering both the case of either a doubling or halving of the diameter. The CFD simulations allow to study the problem from a fundamental point of view, i.e., under otherwise perfect conditions (perfect alignment, zero dead-volume). Flow rates, capillary diameters, diffusion coefficients and liquid viscosities have been varied over a range relevant for nano-LC (Reynolds-numbers Re ≤ 1), with also an excursion made towards high-temperature nano-LC conditions (Re ≥ 10 and more). The extra dispersion caused by the change in diameter has been quantified via a volumetric variance σ 2 conn , defined in such a way that the overall dispersion across the entire capillary system can be easily reconstructed from the known analytical solutions in the individual segments. When the two capillaries are longer than their diffusion entry length, covering most of the practical cases, σ 2 conn converges to a limiting value σ 2 conn,∞ which varies to a close approximation with the square of flow rate. Under the investigated nano-LC conditions, the σ 2 conn,∞ -values are surprisingly small (e.g., on the order of 0.01 to 0.15 nL 2 in a 20 to 40μm connection) compared to the dispersion occurring in the remainder of the capillaries., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier B.V. All rights reserved.)

Separation performance in chromatography has been extensively studied since the dawn of the technique. Although the basic principles of band broadening and the resulting separation performance in isocratic elution are in general well known and understood, this is much less the case for gradient separations. In this tutorial, first the basic principles, concepts and parameters that determine separation performance, peak width and variance and analysis time in isocratic separations are reviewed. This is subsequently used to discuss the parameters that affect peak width in gradient elution, together with the concepts of plate count and plate height in this elution mode. In addition, the effect of peak compression in gradient elution is elaborated. Finally, the effect of extra-column dispersion on separation performance in gradient elution is discussed, and an overview of how these contributions can be experimentally evaluated is given., (Copyright © 2022 Elsevier B.V. All rights reserved.)