Highly sensitive two-dimensional ion chromatography mass spectrometry method for nitrite determination in hydroxypropyl methylcellulose.

Due to their potential adverse health effects, some N-nitrosamines in drug products are strictly regulated with very low maximum daily intake limits. Nitrosamines can be formed from the reaction of nitrite and secondary or tertiary amines when both species co-exist in the drug synthesis or formulation process. One key strategy to mitigate nitrosamine risk in drugs is to select low-nitrite containing pharma excipients for formulation. It is necessary to develop a sensitive method for trace nitrite determination in pharma excipients as it enables drug producers to study nitrosamine formation kinetics and select excipient suppliers. This study details the development and validation of a two-dimensional ion chromatography mass spectrometry (2D-IC/MS) method for trace nitrite determination in hydroxypropyl methylcellulose (HPMC), one of the most important pharmaceutical excipients used in many drug formulations. The 2D-IC system was operated in heart-cutting mode with a concentrator column coupling the two dimensions. A standard bore anion-exchange column was used in the first dimension (1D) to enable a large volume injection for increased sensitivity and provide improved resolution between nitrite and the interfering chloride peak. A high efficiency microbore anion-exchange column with different selectivity was used in the second dimension (2D) to resolve nitrite from other interfering species. The use of 2D-IC resulted in significantly improved resolution, solving the sensitivity loss issue due to ion suppression from an otherwise 1D separation. MS detection with selective ion monitoring and isotope labeled nitrite internal standard further improve the method specificity, accuracy, and ruggedness, as compared with conductivity detection. For trace determination, it is also extremely important to have a clean blank. For this purpose, a novel cleaning procedure using a strong anion wash was developed to remove nitrite contamination from labware. The optimized method was validated with linearity of nitrite in the concentration range of 18.5-5005.8 ng/g having a regression coefficient of >0.9999, precision with RSD at 3.5-10.1 % and recovery of 90.5-102.4 %. The limit of detection and limit of quantitation were 8.9 and 29.6 ng/g relative to the HPMC sample, or equivalent to 89 and 296 pg/g in the sample solution, respectively.

Evaluation of multi-solvent size exclusion chromatography columns packed with sub-2 µm particles for the characterization of synthetic polymers.

With the recent development of small particle stationary-phases and dedicated instrumentation, the combination of size-exclusion chromatography (SEC) with ultra-high performance liquid chromatography (UHPLC) technology has been realized. It opened up a new polymer analysis technique called UHP-SEC. Although high resolution and fast analysis can be achieved, the multi-solvent suitability for a given column was limited to either organic or aqueous eluents. In this work, the capability of novel SEC columns (AdvanceBio SEC columns) packed with 1.9 µm particles for the characterization of synthetic polymers in organic solvents as well as the multi-solvent compatibility for organic and aqueous eluents have been demonstrated. About six times faster separation for both polystyrene (PS) and polyethylene glycol (PEG) with good peak shape and repeatability were achieved in comparison with standard SEC columns at comparable resolution. Especially for PEG, in contrast to other SEC columns, this column could provide close-to-accurate determination of molecular weights with tetrahydrofuran (THF) as mobile phase. Good reproducibility was obtained after switching several times from water to THF and vice versa with RSD% in retention times less than 0.5 %. Different samples such as polyols, isocyanates and additives can also be analyzed for molecular weight and distribution or composition determination. Volume overload, especially with injection volumes higher than 10 µL needs to be considered. This new column offers a powerful choice for oligomer and polymer analysis with both aqueous and organic mobile phase. Ultimately, hyphenating SEC columns to various detectors can enable more information regarding chemical composition, molecular weight, concentration, and structure.

Minimize Precolumn Band Broadening with Immiscible Solvent Sandwich Injection.

We investigated the possibility of reducing the effect of precolumn band broadening (PreCBB) by sandwiching the sample between two small plugs of an immiscible liquid. It has been found that in cases of severe PreCBB, improvements in peak efficiency can amount up to 20 times for the early-eluting compounds. For smaller degrees of PreCBB, the gain on the efficiency of early-eluting compounds is smaller (order of 50%), yet it is still significant. It has been verified that the presence of the immiscible fluid sandwich does not affect the repeatability of the analysis nor the linearity of the calibration curves used for analyte quantitation. It is also shown that the main effect of the two sandwich plugs is the minimization of the dispersion in the precolumn transfer tubing itself, which makes the method fundamentally different from pure on-column focusing methods such as the performance optimizing injection sequence (POISe) method. It is further demonstrated that both halves of the sandwich are needed, since the beneficial effect is clearly much smaller when only one plug is present. A drawback of the method is that some of the late-eluting peaks are slightly adversely affected by the presence of the sandwich liquid in the case where 127 µm i.d. tubing was used. The mechanism for this peak deterioration effect is at present still unclear but only occurs under gradient conditions and is clearly linked to the size of the sandwich plugs (the smaller the plugs, the smaller the adverse effect) and the internal diameter of the tubing used between the injection valve and the column.

Investigation of the effects of solvent-mismatch and immiscibility in normal-phase × aqueous reversed-phase liquid chromatography.

Comprehensive two-dimensional liquid chromatography (LC × LC) is an attractive separation technique that allows achieving high peak capacities and information on chemical correlations. Unfortunately, its application in industrial practice is still not widespread due to limiting factors such as complex method development, tedious method optimization and solvent-incompatibility (such as solvent-strength mismatch or immiscibility experienced during fraction transfer). A severe case of solvent-incompatibility is encountered in the comprehensive coupling of normal-phase LC and reversed-phase LC (NPLC × RPLC). NPLC × RPLC is considered a desirable LC × LC system, especially for the characterization of synthetic polymers, due to the high orthogonality of the two retention mechanisms. However, its experimental realization often suffers from solvent-injection effects in the RPLC dimension, such as peak-deformation, peak-splitting, or even unretained elution ("breakthrough") of sample components. Such a decrease in performance or loss of retention is highly dependent on the types of solvents used. To explore the boundaries of solvent compatibility, we applied large-volume injections (LVI) of reference analytes (e.g. alkyl benzenes; ethoxylate and propoxylate polymers) dissolved in water-immiscible sample solvents, such as dichloromethane, n-hexane, and isooctane in fast water-based gradient RPLC separations (using methanol or acetonitrile as eluent). It was found that, when using highly aqueous initial gradient conditions, hydrophobic sample diluents were retained and eluted during the applied gradient. Depending on the relative retention of the retained diluent and the sample analytes, good chromatograms for LVI of immiscible solvents were obtained, comparable with injections under ideal conditions. The conclusions from injection experiments in aqueous RPLC were verified by coupling an NPLC system with a gradient from isooctane to tetrahydrofuran and an RPLC system with a gradient from water to acetonitrile in an online comprehensive NPLC × RPLC separation of a mixture of propoxylate polymers. The separation provided separation of the polymers based on their number of hydroxyl end-groups (NPLC) and oligomer chain-length (RPLC), without suffering from significant band-broadening effects due to solvent-mismatch upon injection in the second-dimension RPLC system.

Fast determination of functionality-type × molecular-weight distribution of propoxylates with varying numbers of hydroxyl end-groups using gradient-normal-phase liquid chromatography × ultra-high pressure size-exclusion chromatography.

Understanding the relation between chemical characteristics and properties of synthetic polymers is one of the challenges faced by analytical chemists in industry. This is a complex task, as polymers are not synthesized as single molecule, but are populations of chemically similar compounds with distributions over several properties. The latter include, for example, molecular weight, nature of end-groups (functionality), and chemical composition. In this paper, comprehensive two-dimensional liquid chromatography was used to determine the combined functionality-type and molecular-weight distributions of hydroxy­functionalized propoxylates. Propoxylates derived from different initiators (one up to eight terminal hydroxyl groups) were separated in the first dimension using a gradient normal-phase LC separation (NPLC). In the second dimension ultra-high pressure size-exclusion chromatography separation (UHPSEC), further speciating distributions based on molecular size. The developed NPLC × SEC method with evaporative light-scattering detection can be used for the fast screening (< 30 min) of mutually dependent functionality-type and molecular-weight distributions of unknown propoxylates.

A multi-location peak parking approach for calculation of second dimensional retention indices for improved volatile compound identification with cryogen-free comprehensive heart-cut two-dimensional gas chromatography.

Comprehensive heart-cut multidimensional gas chromatography (CH/C MDGC) without a cryogenic trapping device was developed with an established approach for calculation of first and second dimensional retention indices (1I and 2I) for improved compound identification. A first dimensional (1D) DB-1MS column (60 m) and a second dimensional (2D) DB-WAX column (60 m) were applied with a Deans switch (DS) using a constant H/C window of 0.2 min and a periodic multiple heartcut strategy comprising 225H/C throughout the CH/C. 1I was calculated based on comparison of the middle of the heartcut time with the alkane retention times on the 1D column. A multi-location peak parking approach using sixteen sets of automated injections of alkane references was also established with the least square curve fitting method for construction of the alkane isovolatility curves which were applied for 2I calculation. The untargeted compound analysis of a perfume sample was then performed according to comparison with the libraries of mass spectra, 1I and 2I. The CH/C MDGC system with a 25 h analysis time showed a peak capacity (nc) of 9198 and 128 separated peaks with 71 compounds successfully identified according to MS, 1I and 2I library match under the established error approximation criteria. Furthermore, relationship between the analysis time and number of separated peaks was proposed based on the set of 84 identifiable compounds. With the compensation of lower separation performance and greater I errors, the analysis time could be reduced by applying a 2.5 min H/C window with a total analysis time of 2 h and nc of 1134.

Strategies towards simpler configuration and higher peak capacity with comprehensive multidimensional gas chromatography.

Experimental and data analysis approaches in multidimensional gas chromatography (MDGC) comprising comprehensive multiple heart-cut (H/C) and comprehensive two dimensional GC (GC × GC) were developed with an example application illustrated for analysis of a technical glycol precursor sample. The GC × GC system employed a long 1D (30 m) and a short 2D (5 m) column with a flow modulator and a Deans switch (DS) as a splitter; meanwhile. The H/C system was applied solely as a DS located between long 1D (30 m) and 2D (60 m) columns without use of cryogenic trapping devices. The effects of injection time and 2D column flow in GC × GC and the impacts of H/C window and number of injections (total analysis time) in H/C analysis were investigated. The analysis performance for each condition was evaluated according to peak capacity and number of separated compounds. The continuum between the two techniques was then established via the relationship between analysis time and analysis performance. The separation performances were improved with longer analysis time so that the suitable condition was selected within this compromise. Under the selected conditions, volatile compounds in the technical glycol precursor sample were identified according to the match between the experimental MS spectra and first dimensional retention indices (1 I) with that from the NIST2014 database and literature. An hour analysis with GC × GC resulted in a total peak capacity of 798, number of separated peaks of 61 and average MS match score of 887 ± 35; meanwhile, the corresponding numbers were improved to be 9198, 107 and 898 ± 24, respectively, with the 25 h comprehensive H/C analysis.

Maximizing two-dimensional liquid chromatography peak capacity for the separation of complex industrial samples.

We report on a study on the use of 2D-LC in industry wherein we maximized the peak capacity by serially coupling up to six 15 cm long columns in the 1st dimension. For the considered aromatic amine oligomer sample, the combination of reverse phase pentafluorophenyl column providing selectivity based on π-π interaction in the 1st and a more retaining reverse phase polymeric C18 column in the 2nd dimension proved to give the highest orthogonality, calculated to be 0.82. Whereas a 1D run on a single column revealed around 120 compounds, the optimized 2D-LC system revealed around 940 compounds. To achieve this, flow splitting to improve the peak capacity in the 1st dimension and shifting gradients in the 2nd dimension were used. The overall peak capacity of the system was calculated to be 11,000 with correction for orthogonality and undersampling. The total analysis time with the 6-column system was around 20 h.

Two-dimensional liquid chromatography with active solvent modulation for studying monomer incorporation in copolymer dispersants.

A pseudo-comprehensive two-dimensional liquid chromatography approach with size exclusion chromatography in the first dimension and gradient reversed-phase liquid chromatography in the second dimension was successfully developed for the characterization of vinyl acetate/acrylic acid copolymers and vinyl acetate/itaconic acid/acrylic acid terpolymers. Active solvent modulation was exploited to prevent the polymer breakthrough in the second dimension separation caused by the strong solvent used in the first dimension. The conditions of the active solvent modulation valve were optimized to achieve sufficient on-line dilution and to completely prevent polymer breakthrough without adding excessive time to the modulation cycle. Using this approach, copolymers made with different monomer ratios and processes were studied. Heterogeneous composition distribution due to insufficient monomer incorporation was detected in some of the copolymer samples. We demonstrated that with active solvent modulation, the two-dimensional liquid chromatography approach is no longer limited to water-soluble polymers and can be used for a broader range of polymers and copolymers.

Characterization of complex polyether polyols using comprehensive two-dimensional liquid chromatography hyphenated to high-resolution mass spectrometry.

Polyether polyols are often used in formulated systems, but their complete characterization is challenging, because of simultaneous heterogeneities in chemical composition, molecular weight and functionality. One-dimensional liquid chromatography-mass spectrometry is commonly used to characterize polyether polyols. However, the separation power of this technique is not sufficient to resolve the complexity of such samples entirely. In this study, comprehensive two-dimensional liquid chromatography hyphenated with high-resolution mass spectrometry (LC × LC-HRMS) was used for the characterization of (i) castor oil ethoxylates (COEs) reacted with different mole equivalents of ethylene oxide and (ii) a blended formulation consisting of glycerol ethoxylate, glycerol propoxylate and glycerol ethoxylate-random-propoxylate copolymers. Retention in the first (hydrophilic-interaction-chromatography) dimension was mainly governed by degree of ethoxylation, while the second reversed-phase dimension resolved the samples based on degree of propoxylation (blended formulation) or alkyl chain length (COEs). For different COE samples, we observed the separation of isomer distributions of various di-, tri- and tetra-esters, and such positional isomers were studied by tandem mass spectrometry (LC-MS/MS). This revealed characteristic fragmentation patterns, which allowed discrimination of the isomers based on terminal or internal positioning of the fatty-acid moieties and provided insight in the LC × LC retention behavior of such species.

Evaluation of active solvent modulation to enhance two-dimensional liquid chromatography for target analysis in polymeric matrices.

A new methodology is presented for two-dimensional liquid chromatography (2D-LC) separations of polymers. Active solvent modulation (ASM) was evaluated in its effectiveness to enhance solvent compatibility for both separation dimensions. As an example the determination of target compounds in epoxy resins was used. Ultra-high pressure size-exclusion chromatography was applied in the first dimension using THF as the solvent. The second dimension separation was operated in reversed-phase mode using an acetonitrile/water gradient. ASM prevents sample breakthrough in the second dimension and produces chromatograms that are of great peak shape and high resolution. It enables very sensitive determination of target components down to the low ppm level. The resulting high-speed 2D-LC method (10 min analysis time) showed good linearity (R2 > 0.9995) and reproducibility (as low as 0.3-0.7% peak area RSD). ASM was also applied in comprehensive 2D-LC (SECxLC) mode for characterization of molecular weight and chemical composition distribution of a polymer blend consisting of epoxy novolac and phenol novolac. The SECxLC separation was executed at short run times (20 min). ASM technology can markedly enhance productivity in 2D-LC analysis for many complex sample matrices.

Positive Temperature Coefficient Compensating Heating for Analytical Devices.

Positive temperature coefficient thermistors acting as heating devices are quickly growing in popularity and are being adapted into critical applications in many sectors from medical to space discovery. Positive temperature coefficient heating offers substantial benefits for miniaturized and portable analytical devices in key aspects such as energy efficiency, safety in overheating, size, scalability, and in discovering new thermal management strategies. These heaters can reach 230 °C without additional requirements for regulating electronics. By incorporating positive temperature coefficient technology into a commercial diode array photometric detector, the detector is made suitable for coupling with gas chromatography. The detector cartridge flow cell is heated to a specific target temperature within the range of 70 to 150 °C without impacting the detector's construction material or imparting any negative effect to the surrounding detector system electronics. Applying a temperature of 150 °C to the cell permits analysis of volatile and semivolatile compounds with a boiling point equivalent to that of n-hexadecene (285 °C). Model compounds of alkene homologues from C8 to C16 showed a maximum peak asymmetry of 1.10 with the heated cell design. A high degree of repeatability was observed with RSD of less than 0.01% in retention time and 3% in peak area ( n = 10).

Elimination of N,O-bis(trimethylsilyl)trifluoroacetamide interference by base treatment in derivatization gas chromatography mass spectrometry determination of parts per billion of alcohols in a food additive.

A novel base treatment followed by liquid-liquid extraction was developed to remove the interference of excess derivatization reagent BSTFA [N,O-Bis(trimethylsilyl)trifluoroacetamide] and its byproducts for trace determination of 1-chloro-2-propanol and 2-chloro-1-propanol in a food additive. The corresponding trimethylsilyl derivatives were analyzed by gas chromatography mass spectrometry (GC/MS) detection in selective ion monitoring mode. Due to a large volume splitless injection needed for achieving the required sensitivity, excess BSTFA in the derivatization sample solution interfered with the trimethylsilyl derivatives of the analytes of interest, making their quantitation not attainable. Efforts were made to decompose BSTFA while keeping the trimethylsilyl derivatives intact. Water or aqueous sulfuric acid treatment converted BSTFA into mainly N-trimethylsilyltrifluoroacetamide, which partitions between aqueous and organic layers. In contrast, aqueous sodium hydroxide decomposed BSTFA into trifluoroacetic acid, which went entirely into the aqueous layer. No BSTFA or its byproduct N-trimethylsilyltrifluoroacetamide or trifluroacetamide was found in the organic layer where the derivatized alcohols existed, which in turn completely eliminated their interference, enabling accurate and precise determination of parts per billion of the short-chain alcohols in the food additive. Contrary to the conventional wisdom that a trimethylsilyl derivative is susceptible to hydrolysis, the derivatized short-chain alcohols were found stable even in the presence of 0.17N aqueous sodium hydroxide as the improved GC/MS method was validated successfully, with a satisfactory linearity response in the concentration range of 10-400ng/g (regression coefficient greater than 0.999), good method precision (<4%), good recovery (90-98%), and excellent limit of detection (3ng/g) and limit of quantitation (10ng/g).

Using the column wall itself as resistive heater for fast temperature gradients in liquid chromatography.

A new system is proposed for applying fast temperature gradients in liquid chromatography. It consists of a 0.7 mm × 150 mm fused-silica column coated with a 50 µm Nickel-layer, which is connecting with a power source and a temperature control system to perform fast and reproducible temperature gradients using the column wall itself as a resistive heater. Applying a current of 4A and passive cooling results in a maximal heating and cooling rate of, respectively, 71 and -21 °C/min. Multi-segment temperature gradients were superimposed on mobile phase gradients to enhance the selectivity for three sets of mixtures (pharmaceutical compounds, a highly complex mixture and an insecticide sample). This resulted in a higher peak count or better selectivities for the various mixtures.

Hydrophilic interaction liquid chromatography for the separation of acidic agricultural compounds.

Organic acids with very low pKa require extremely low pH conditions to achieve adequate retention in reversed-phase liquid chromatography, but an extremely low pH mobile phase can cause instrument reliability problems and limit the choice of columns. Hydrophilic interaction chromatography is a potential alternative to reversed-phase liquid chromatography for the separation of organic acids using more moderate conditions. However, the hydrophilic interaction chromatography separation mechanism is known to be very complex and involves multiple competing mechanisms. In the present study, a hydrophilic interaction chromatography column packed with bare silica core-shell particles was used as the separation column and six agricultural organic acids were used as model analytes to evaluate the effects of buffer concentration, buffer pH, and temperature on sample loading capacity, selectivity, retention, and repeatability. It was found that using a higher concentration of buffer can lead to a significant improvement in the overall performance and reproducibility of the separation. Investigation of column equilibration time revealed that a very long equilibration time is needed when changing mobile phase conditions in between runs. This limitation needs to be acknowledged in hydrophilic interaction chromatography method development and sufficient equilibration time needs to be allowed in method scouting.

Loop-based multiple heart-cutting two-dimensional liquid chromatography for target analysis in complex matrices.

Loop-based multiple heart-cutting (MHC) two-dimensional liquid chromatography (2D-LC) is presented as a solution to quantify target components in complex matrices, such as additives in polymers, at very high chromatographic resolution. The determination of hexabromocyclododecane (HBCD) in polystyrene (PS) is described. One dimensional ((1)D) LC analysis with UV detection did not allow quantitation of the main isomers of HBCD due to peak overlap with polymer components. MHC 2D-LC analysis provided the separation power, accuracy, and repeatability needed for quantitative analysis of the additives of interest. Heart-cuts from peaks of the (1)D-chromatogram or entire regions of interest are sampled into loops, where they remain parked until their sequential reinjection onto the second dimension ((2)D) column. A column set consisting of phenyl ((1)D) and C18 ((2)D) stationary phases gave baseline separation in (2)D between HBCD and PS background. Linearity for spiked polymer samples was achieved over a range of 0.02-1.00 wt % HBCD relative to the amount of polymer. The limit of quantitation was estimated at 0.01 wt % HBCD in PS. A peak area RSD of 0.7% obtained for ten replicates of a real sample demonstrated excellent repeatability of the analysis. MHC 2D-LC is an elegant solution for quantitative analyses of difficult-to-separate samples when conventional (1)D separation fails.

Selectivity tuning via temperature pulsing using low thermal mass liquid chromatography and monolithic columns.

Low thermal mass LC was applied to the capillary LC separation of a complex insecticide mixture by increasing temperature and decreasing gradients, as well as fast selected temperature pulses to increase resolution of overlapped components. The technology was applied using a new generation of capillary monolithic stationary phases. Considerable peak shifts and selectivity changes were observed for given temperature conditions. The concept of temperature pulsing during an elution profile shows promise for increasing resolution in difficult separations and can provide a relatively simple means to solve coelution problems.

Practical comparison of LC columns packed with different superficially porous particles for the separation of small molecules and medium size natural products.

Commercial C(18) columns packed with superficially porous particles of different sizes and shell thicknesses (Ascentis Express, Kinetex, and Poroshell 120) or sub-2-µm totally porous particles (Acquity BEH) were systematically compared using a small molecule mixture and a complex natural product mixture as text probes. Significant efficiency loss was observed on 2.1-mm id columns even with a low dispersion ultra-high pressure liquid chromatography system. The Kinetex 4.6-mm id column packed with 2.6-µm particles exhibited the best overall efficiency for small molecule separations and the Poroshell 120 column showed better performance for mid-size natural product analytes. The Kinetex 2.1-mm id column packed with 1.7-µm particles did not deliver the expected performance and the possible reasons besides extra column effect have been proved to be frictional heating effect and poor column packing quality. Different column retentivities and selectivities have been observed on the four C(18) columns of different brands for the natural product separation. Column batch-to-batch variability that has been previously observed on the Ascentis Express column was also observed on the Kinetex and Poroshell 120 column.

Thermal modulation for multidimensional liquid chromatography separations using low-thermal-mass liquid chromatography (LC).

We report on a proof-of-principle experiment with a novel thermal modulation device with potential use in two-dimensional liquid chromatography (LC × LC) systems. It is based on the thermal desorption concept used in two-dimensional gas chromatography (GC × GC) systems. Preconcentration of neutral analytes eluting from the first dimension column is performed in a capillary "trap" column packed with highly retentive porous graphitic carbon particles, placed in an aluminum low-thermal-mass LC heating sleeve. Remobilization of the trapped analytes is achieved by rapidly heating the trap column, by applying temperature ramps up to +1200 °C/min. Compared to the nonmodulated signal, the presented thermal modulator yielded narrow peaks, and a concentration enhancement factor up to 18 was achieved. With a thermally modulated LC separation of an epoxy resin, it is shown that when the thermal modulation is applied periodically, the trapped and concentrated molecules can be released periodically and that the modulating interface can both serve as a preconcentration device and as an injector for the second dimension column of an LC × LC setup. Because of the thermal modulation, a high-molecular-weight epoxy resin could be adequately separated and the different fractions were identified with a GPC analysis, as well as an offline second dimension LC analysis.

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.