Evaluation of a microfabricated thermal modulator for comprehensive two-dimensional microscale gas chromatography

A microfabricated thermal modulator (μTM) designed for ultimate use in a comprehensive two-dimensional microscale gas chromatography (μGC × μGC) system is evaluated. The 2-stage device measures 13 mm (l) × 6 mm (w) × 0.5 mm (h) and consists of two interconnected serpentine etched-Si microchannels suspended from a thin Pyrex cap and wall-coated with PDMS (polydimethylsiloxane). The chip is mounted within a few tens of micrometers of a thermoelectric cooler that maintains both stages at a baseline temperature between -35 and -20 °C in order to focus analytes eluting from an upstream separation column. Each stage is heated to 210 °C sequentially at a rate as high as 2400 °C/s by independent thin-film resistors to inject the analytes in consecutive fractions to a downstream column, and then cooled at a rate as high as -168 °C/s. The average power dissipation is only ～10 W for heating and 21 W for cooling without using consumable materials. In this study, the outlet of the μTM is connected directly to a flame ionization detector to assess its performance. Following a demonstration of basic operation, the modulated peak amplitude enhancement (PAE) and full-width-at-half-maximum (fwhm) are evaluated for members of a series of n-alkanes (C(6)-C(10)) as a function of the rim and stage temperatures; modulation period, phase, and offset; analyte concentration; and carrier-gas flow rate. A PAE as high as 50 and a fwhm as narrow as 90 ms are achieved for n-octane under optimized conditions.     

Improving peak capacity in fast online comprehensive two-dimensional liquid chromatography with post-first-dimension flow splitting

The use of flow splitters between the two dimensions in online comprehensive two-dimensional (2D) liquid chromatography (LC × LC) has not received very much attention, in comparison with their use in 2D gas chromatography (GC × GC), where they are quite common. In principle, splitting the flow after the first dimension column and performing online LC × LC on this constant fraction of the first dimension effluent should allow the two dimensions to be optimized almost independently. When there is no flow splitting, any change in the first-dimension flow rate has an immediate impact on the second dimension. With a flow splitter, one could, for example, double the flow rate into the first dimension column and perform a 1:1 flow split without changing the sample loop size or the sampler's collection time. Of course, the sensitivity would be diminished, but this can be partially compensated through the use of a larger injection; this will likely only amount to a small price to pay for this increased resolving power and system flexibility. Among other benefits, we found a 2-fold increase in the corrected 2D peak capacity and the number of observed peaks for a 15-min analysis time, using a post-first-dimension flow splitter. At a fixed analysis time, this improvement results primarily from an increase in the gradient time, resulting from the reduced system re-equilibration time, and, to a smaller extent, it is due to the increased peak capacity achieved by full optimization of the first dimension.     

Off-line coupling of subcritical water extraction with subcritical water chromatography via a sorbent trap and thermal desorption

In this study, the off-line coupling of subcritical water extraction (SBWE) with subcritical water chromatography (SBWC) was achieved using a sorbent trap and thermal desorption. The sorbent trap was employed to collect the extracted analytes during subcritical water extraction. After the extraction, the trap was connected to the subcritical water chromatography system, and thermal desorption of the trapped analytes was performed before the SBWC run. The thermally desorbed analytes were then introduced into the subcritical water separation column and detected by a UV detector. Anilines and phenols were extracted from sand and analyzed using this off-line coupling technique. Subcritical water extraction of flavones from orange peel followed by subcritical water chromatographic separation was also investigated. The effects of water volume and extraction temperature on flavone recovery were determined. Because a sorbent trap was used to collect the extracted analytes, the sensitivity of this technique was greatly enhanced as compared to that of subcritical water extraction with solvent trapping. Since no organic solvent-water extractions were necessary prior to analysis, this technique eliminated any use of organic solvents in both extraction and chromatography processes.     

Targeted multidimensional gas chromatography using microswitching and cryogenic modulation

A new method is described that allows fast target analysis in multidimensional gas chromatography by using a microswitching valve between two GC columns, with cryogenic trapping and rapid re-injection of trapped solutes in the second dimension. The essence of the procedure is that heart-cut fractions from the first column (1D) can be selectively transferred to column 2 (2D), where a moveable cryogenic trap first focuses the transferred solute(s) at the head of the second column and then permits their facile rapid analysis on 2D. Since 2D is a short narrow-bore column, which exhibits very fast analysis (on the order of a few seconds elution), peak responses (heights) are significantly enhanced (by up to 40-fold). Additionally, by using a 2D phase of a selectivity different from that used for 1D, it is possible to also separate components that are not resolved on the first column and to increase the resolution for other compounds. The heart-cut valve isolates the section(s) of solutes of interest from the first column separation, and this provides a considerable simplification to the chromatogram-in addition to the separation and sensitivity advantages. By using this method, multidimensional gas chromatography with multiple heart-cuts can be completed within the same time as the primary column separation. Since the described method permits non-heart-cut fractions to be transferred to a monitor detector, normal detection of these fractions is still permitted. By modulation of the cryotrap, it is also possible to achieve comprehensive two-dimensional gas chromatography for the heart-cut fractions; however, only those compounds passed to the second, separation column, which passes through the cryotrap, will be subjected to GC x GC analysis. The technique and the various modes of operation are described in this paper.     

A simple, robust orthogonal background correction method for two-dimensional liquid chromatography

Background correction is a very important step that must be performed before peak detection or any quantification procedure. When successful, this step greatly simplifies such procedures and enhances the accuracy of quantification. In the past, much effort has been invested to correct drifting baseline in one-dimensional chromatography. In fast online comprehensive two-dimensional liquid chromatography (LC×LC) coupled with a diode array detector (DAD), the change in the refractive index (RI) of the mobile phase in very fast gradients causes extremely serious baseline disturbances. The method reported here is based on the use of various existing baseline correction methods of one-dimensional (1D) liquid chromatography to correct the two-dimensional (2D) background in LC×LC. When such methods are applied orthogonally to the second dimension ((2)D), background correction is dramatically improved. The method gives an almost zero mean background level and it provides better background correction than does simple subtraction of a blank. Indeed, the method proposed does not require running a blank sample.     

Longitudinally modulated cryogenic system. A generally applicable approach to solute trapping and mobilization in gas chromatography

This paper describes a novel approach to solute trapping and remobilization. It involves the use of a subambient trap, with a narrow capillary column passing through the cooled region. A mechanism allows for longitudinal movement of the trap relative to the chromatographic column or narrow transfer line through which analytes travel. Either the trap or the column can be moved, and the frequency or manner of relative movement determines the type of result obtained. A series of preliminary studies are described that define the general approach to using this device and demonstrate the unique benefits that may arise from the modulation movement. Significant improvement (reduction) in peak width occurs if the device is placed immediately prior to the detection system, and consequently a great increase in detection limits results. With a 25 cm length of capillary column between the trap and detector, it is calculated that the plate height of dodecane is 0.082 mm, equivalent to 12?100 plates/m. This was found to be much greater than that for dodecane analyzed on a 25 m column. By slow displacement of the column through the trap, it is demonstrated that the solute is trapped in the first 1 cm (or less) of the column located in the cold trap.     

Fast comprehensive two-dimensional gas chromatography with cryogenic modulation

The fast separation of a mixture of 29 compounds by using comprehensive two-dimensional gas chromatography is reported. Capillary column sets with shorter lengths and smaller inner diameter in both the first and second dimensions have been tested, for both fast chiral and achiral separations. Fast chiral separations, which included enantiomer separations of limonene, linalool, citronellol, and alpha-isomethylionone, were achieved within 23 min, which corresponds to approximately 2-fold faster than analyses under conditions previously considered as normal. Fast achiral separations, which do not have the restriction of requiring a minimum quality of chiral resolution, were obtained within 5 min, which is markedly faster than separations on the normal column set under conditions more commonly employed. The achiral fast GC x GC method used a 5 m x 0.1 mm i.d. first dimension column, interfaced to a 0.3 m x 0.05 mm i.d. second column, with temperature program rate of 35 degrees C.min-1; a modulation period of 1 s was employed. Peak widths at baseline on the first column were a little over 1 s, while modulated peak widths at half-height recorded with a flame ionization detector operating at 200 Hz were approximately 30 ms. The benefits and limitations of GC x GC for fast chiral and achiral separations are reported and discussed.     

Partial modulation method via pulsed flow modulator for comprehensive two-dimensional gas chromatography

A partial modulation method by using a pulsed-flow modulator for comprehensive two-dimensional gas chromatography is proposed. The method is based on the fact that when a pulsed flow of inert gas is introduced into the conjunction between a primary and a secondary column, the concentration of analyte is disturbed, and a plug of higher or lower concentration is created. The plug, which forms a spike signal coupled to the primary GC signal, is then separated in a secondary column, creating a new dimension of GC information. The modulation is partial because only a fraction of the primary signal is modulated and converted into the secondary signal; the remaining primary signal stays unchanged. Therefore, this method yields a comprehensive two-dimensional chromatogram and a primary one-dimensional chromatogram in a single GC run. In this study, the modulation mode, modulation index, and modulation percentage are discussed and the reproducibility of peak areas and retention time are investigated. With a 5.8% modulation percentage and a primary peak half-width 1.7 times wider than the modulation time, the standard deviation for the peak areas are 0.15% for the primary and 0.78% for the secondary chromatograms. Chromatograms of laboratory-mixed hydrocarbons and of high-temperature fuel oil no. 6 standard are demonstrated.     

Adaptive two-dimensional microgas chromatography

We proposed and investigated a novel adaptive two-dimensional (2-D) microgas chromatography system, which consists of one 1st-dimensional column, multiple parallel 2nd-dimensional columns, and a decision-making module. The decision-making module, installed between the 1st- and 2nd-dimensional columns, normally comprises an on-column nondestructive vapor detector, a flow routing system, and a computer that monitors the detection signal from the detector and sends out the trigger signal to the flow routing system. During the operation, effluents from the 1st-dimensional column are first detected by the detector and, then, depending on the signal generated by the detector, routed to one of the 2nd-dimensional columns sequentially for further separation. As compared to conventional 2-D GC systems, the proposed adaptive GC scheme has a number of unique and advantageous features. First and foremost, the multiple parallel columns are independent of each other. Therefore, their length, stationary phase, flow rate, and temperature can be optimized for best separation and maximal versatility. In addition, the adaptive GC significantly lowers the thermal modulator modulation frequency and hence power consumption. Finally, it greatly simplifies the postdata analysis process required to reconstruct the 2-D chromatogram. In this paper, the underlying working principle and data analysis of the adaptive GC was first discussed. Then, separation of a mixture of 20 analytes with various volatilities and polarities was demonstrated using an adaptive GC system with a single 2nd-dimensional column. Finally, an adaptive GC system with dual 2nd-dimensional columns was employed, in conjunction with temperature ramping, in a practical application to separate a mixture of plant emitted volatile organic compounds with significantly shortened analysis time.     

Modulator design for comprehensive two-dimensional gas chromatography: quantitative analysis of polyaromatic hydrocarbons and polychlorinated biphenyls

A novel cryogenic modulator was constructed for comprehensive two-dimensional gas chromatography (GC x GC). The modulator is based on two-step cryogenic trapping with CO2 and thermal desorption with electric heating. The GC x GC system included a nonpolar first-dimension column and two semipolar second-dimension columns, one connected to a flame ionization detector and the other one to a electron capture detector. A Matlab-based program, which allowed determination of peak heights and volumes, was written for the data analysis. The GC x GC system was applied for the analysis of polyaromatic hydrocarbons and polychlorinated biphenyls. The functioning of the modulator and the quantitativity of the method were studied with both peak volumes and peak heights from a three-dimensional plot. The separate peak areas from the modulated chromatogram were calculated as a comparison. The quantitative results were compared with those obtained with the same system but without the thermal modulation. The method was found to be repeatable and linear with use of peak volumes as well as peak heights. There was also good agreement with the results obtained by integration of separate peak areas. The developed GC x GC method was applied to the analysis of a Soxhlet extract of a certified sediment sample. The results were compared with the certified values.     

Dual-injection system with multiple injections for determining bidimensional retention indexes in comprehensive two-dimensional gas chromatography

A new instrumental approach for collection of retention index data in the first (1D) and second (2D) dimensions of a comprehensive two-dimensional (2D) gas chromatography (GCxGC) experiment has been developed. First-dimension indexes were determined under conventional linear programmed temperature conditions (Van den Dool indexes). To remove the effect that the short secondary column imposes on derived 1D indexes, as well as to avoid handling of pulsed GCxGC peaks, the proposed approach uses a flow splitter to divert part of the primary column flow to a supplementary detector to simultaneously generate a conventional 1D chromatogram, along with the GCxGC chromatogram. The critical 2D indexes (KovAts indexes) are based upon isovolatility curves of normal alkanes in 2D space, providing a reference scale against which to correlate each individual target peak throughout the entire GCxGC run. This requires the alkanes to bracket the analytes in order to allow retention interpolation. Exponential curves produced in the 2D separation space require a novel approach for delivery of alkane standards into the 2D column by using careful solvent-free solid-phase microextraction (SPME) sampling. Sequential introduction of alkane mixtures during GCxGC runs was performed by thermal desorption in a second injector which was directly coupled through a short transfer line to the entrance of the secondary column, just prior to the modulator so that they do not have to travel through the 1D column. Thus, each alkane mixture injection was quantitatively focused by the cryogenic trap, then launched at predetermined times onto the 2D column. The system permitted construction of an alkane retention map upon which bidimensional indexes of a 25-perfume ingredient mixture could be derived. Comparison of results with indexes determined in temperature-variable one-dimensional (1D) GC showed good correlation. Plotting of the separation power in the second dimension was possible by mapping Trennzahl values throughout the 2D space. The methodology was applied to the separation of a standard mixture composed of 25 analytes (very diverse in polarity and structure) suspected to be allergens in perfume samples. The method will allow straightforward determination of temperature-variable retention indexes of target analytes.     

Design for on-line coupling of supercritical fluid extraction with liquid chromatography: quantitative analysis of polynuclear aromatic hydrocarbons in a solid matrix

Supercritical fluid extraction (SFE) was directly coupled with high-performance liquid chromatography (LC) via the simplest interface--only one six-port injection valve. By using water to eliminate decompressed CO2 gas in the solid-phase octadecylsilica trap, high extraction recovery (> or = 95%) of polynuclear aromatic hydrocarbons (PAHs) from a sand matrix was achieved under optimized conditions. The volume of rinse water had little influence on the recovery, due to the very low solubility of PAHs in water and the sorption properties of the C-18 trap. Different amounts of sand matrix with a fixed mass of analytes have also been tested. No decrease in recovery was found when the matrix (sand) increased from 1 to 10 g. Methanol and acetone were used as a CO2 modifier to enhance the extraction efficiency. Finally, PAHs in naturally contaminated soil were successfully extracted and quantitatively determined by this hyphenated system. Compared to the EPA method (Soxhlet extraction following by GC/MS), on-line SFE-LC gave precise results in a much shorter time.     

Comprehensive three-dimensional gas chromatography with parallel factor analysis

Development of a comprehensive, three-dimensional gas chromatograph (GC3) instrument is described. The instrument utilizes two six-port diaphragm valves as the interfaces between three, in-series capillary columns housed in a standard Agilent 6890 gas chromatograph fitted with a high data acquisition rate flame ionization detector. The modulation periods for sampling column one by column two and column two by column three are set so that a minimum of three slices (more commonly four or five) are acquired by the subsequent dimension resulting in both comprehensive and quantitative data. A 26-component test mixture and quantitative standards are analyzed using the GC3 instrument. A useful methodology for three-dimensional (3D) data analysis is evaluated, based on the chemometric technique parallel factor analysis (PARAFAC). Since the GC3 instrument produces trilinear data, we are able to use this powerful chemometric technique, which is better known for the analysis of two-dimensional (2D) separations with multichannel detection (e.g., GC x GC-TOFMS) or multiple samples (or replicates) of 2D data. Using PARAFAC, we mathematically separate (deconvolute) the 3D data "volume" for overlapped analytes (i.e., ellipsoids), provided there is sufficient chromatographic resolution in each of the three separation dimensions. Additionally, PARAFAC is applied to quantify analyte standards. For the quantitative analysis, it is demonstrated that PARAFAC may provide a 10-fold improvement in the signal-to-noise ratio relative to a traditional integration method applied to the raw, baseline-corrected data. The GC3 instrument obtains a 3D peak capacity of 3500 at a chromatographic resolution of one in each separation dimension. Furthermore, PARAFAC deconvolution provides a considerable enhancement in the effective 3D peak capacity.     

Comprehensive two-dimensional gas chromatographic separations with a microfabricated thermal modulator

Rapid, comprehensive two-dimensional gas chromatographic (GC × GC) separations by use of a microfabricated midpoint thermal modulator (μTM) are demonstrated, and the effects of various μTM design and operating parameters on performance are characterized. The two-stage μTM chip consists of two interconnected spiral etched-Si microchannels (4.2 and 2.8 cm long) with a cross section of 250 × 140 μm(2), an anodically bonded Pyrex cap, and a cross-linked wall coating of poly(dimethylsiloxane) (PDMS). Integrated heaters provide rapid, sequential heating of each μTM stage, while a proximate, underlying thermoelectric cooler provides continual cooling. The first-dimension column used for GC × GC separations was a 6 m long, 250 μm i.d. capillary with a PDMS stationary phase, and the second-dimension column was a 0.5 m long, 100 μm i.d. capillary with a poly(ethylene glycol) phase. Using sets of five to seven volatile test compounds (boiling point ≤174 °C), the effects of the minimum (T(min)) and maximum (T(max)) modulation temperature, stage heating lag/offset (O(s)), modulation period (P(M)), and volumetric flow rate (F) on the quality of the separations were evaluated with respect to several performance metrics. Best results were obtained with a T(min) = -20 °C, T(max) = 210 °C, O(s) = 600 ms, P(M) = 6 s, and F = 0.9 mL/min. Replicate modulated peak areas and retention times were reproducible to <5%. A structured nine-component GC × GC chromatogram was produced, and a 21 component separation was achieved in <3 min. The potential for creating portable μGC × μGC systems is discussed.     

Exploring the possibilities of cryogenic cooling in liquid chromatography for biological applications: a proof of principle

The possibilities to use cryogenic cooling to trap components in liquid chromatography was investigated. In a first step, van 't Hoff plots were measured with a reversed-phase column using the temperature control unit of a conventional high performance liquid chromatography (HPLC) system to gain insight in the retention behavior of proteins at low temperatures. It was estimated that retention factors in the range of k = 10(4) could be achieved at T = -20 °C for lysozyme, indicating that temperature is a usable parameter to trap components in LC. In a next step, trapping experiments were carried out on a nano-LC system, equipped with a UV-detector, using a commercial reversed-phase column. An in-house built setup, allowing cooling of a segment of the column down to temperatures below T = -20 °C, was used to trap components. Experiments were conducted under isocratic and gradient conditions with methanol as organic solvent. It is demonstrated that, by thermally trapping and elution of components, an enhanced S/N ratio and decreased peak widths can be obtained. At the same time, a significant increase in pressure drop occurs during the cooling process. Limitations and benefits of the technique are further discussed.     

Experimental study of the quantitative precision for valve-based comprehensive two-dimensional gas chromatography

For complex sample analysis, there is a need for multidimensional chromatographic instrumentation to be able to separate more compounds, often in shorter time frames. This has led to the development of comprehensive two-dimensional chromatographic instrumentation, such as comprehensive two-dimensional gas chromatography (GC × GC). Lately, much of the focus in this field has been on decreasing peak widths and, therefore, increasing peak capacity and peak capacity production. All of these advancements make it possible to analyze more compounds in a shorter amount of time, but the data still need to remain quantitative to address the needs of most applications. In this report, the relationship among the modulation ratio (M(R)), peak sampling phase (φ), retention time variation (Δt(R)), and how these parameters relate to quantitative analysis precision via the relative standard deviation (RSD) was studied experimentally using a valve-based GC × GC instrument. A wide range of the number of modulations across the first dimension peak width, that is, a M(R) range from ~1 to 10, was examined through maintaining an average first dimension peak width at the base, (1)w(b) of ~3 s and varying the second dimension separation run time from 300 to 2900 ms. An average RSD of 2.1% was experimentally observed at an average M(R) of 2, with a corresponding peak capacity production of ~1200 peaks/min possible. Below this M(R) the RSD quickly increased. In a long-term study of the quantitative precision at a M(R) of 2.5, using 126 replicate injections of a test mixture spanning ~35 h, the RSD averaged 3.0%. The findings have significant implications for optimizing peak capacity production by allowing the use of the longest second dimension run time, while maintaining quantitative precision.     

Applications of Hadamard transform to gas chromatography/mass spectrometry and liquid chromatography/mass spectrometry

Successful application of the Hadamard transform (HT) technique to gas chromatography/mass spectrometry (GC/MS) and liquid chromatography/mass spectrometry (LC/MS) is described. Novel sample injection devices were developed to achieve multiple sample injections in both GC and LC instruments. Air pressure was controlled by an electromagnetic valve in GC, while a syringe pump and Tee connector were employed for the injection device in LC. Two well-known, abused drugs, 3,4-methylenedioxy-N-methylamphetamine (MDMA) and N, N-dimethyltryptamine (DMT), were employed as model samples. Both of the injection devices permitted precise successive injections, resulting in clearly modulated chromatograms encoded by Hadamard matrices. After inverse Hadamard transformation of the encoded chromatogram, the signal-to-noise (S/N) ratios of the signals were substantially improved compared with those expected from theoretical values. The S/N ratios were enhanced approximately 10-fold in HT-GC/MS and 6.8 in HT-LC/MS, using the matrices of 1023 and 511, respectively. The HT-GC/MS was successfully applied to the determination of MDMA in the urine sample of a suspect.     

General strategy for performing temperature programming in high performance liquid chromatography: prediction of linear temperature gradients

This paper describes how an empirical retention model is transferred from temperature-programmed gas chromatography (GC) to high temperature liquid chromatography (HT-HPLC). In order to evaluate the retention prediction, a temperature range from 50 to 180 °C was investigated using two test mixtures consisting of steroids and polycyclic aromatic hydrocarbons. In this temperature range, heating rates from 1.5 °C min(-1) up to 30 °C min(-1) were applied using four different high temperature stable HPLC columns with inner diameters of 1.0, 2.1, 3.0, and 4.6 mm. Temperature lag phenomena in the HPLC column as well as in the column oven are discussed, and it is shown that the linear elution strength (LES) model can be applied without any mathematical extension in order to take a temperature-dependent delay time into account. On the basis of this approximation, it is possible to perform a systematic method development using linear temperature gradients in liquid chromatography. Furthermore, it is shown that only two initial temperature gradient runs are necessary to predict the retention times of the analytes with a maximal relative error of less than 2%.     

Comprehensive two-dimensional gas chromatography with fast enantioseparation

The development of fast chiral analysis for use in comprehensive two-dimensional gas chromatography in which a short second dimension enantioselective capillary column provides a route to precise measurement of chiral ratios of enantiomers is described. Retention times as short as 8 s are reported for (+/-)-limonene, with adequate enantioseparation maintained (Rs approximately 1.0) on a 1-m cyclodextrin derivative-coated capillary column. Sufficiently fast elution on the second column was achieved by using GC/ MS in which the subambient pressure (vacuum outlet) conditions promote increased diffusion coefficients and higher component volatility; a 4-fold reduction of second-dimension retention time was observed, as compared with ambient pressure outlet conditions. The enantiomeric distribution of several monoterpene compounds in bergamot essential oil is reported as a demonstration of the method. Total analysis time of the target components was approximately 8.5 min.     

Limits of detection and quantification in comprehensive multidimensional separations. 1. A theoretical look

Comprehensive multidimensional separations (e.g., GC×GC, LC×LC, etc.) are increasingly popular tools for the analysis of complex samples, due to their many advantages, such as vastly increased peak capacity, and improvements in sensitivity. The most well-established of these techniques, GC×GC, has revolutionized analytical separations in fields as diverse as petroleum, environmental research, food and flavors, and metabolic profiling. Using multidimensional approaches, analytes can be quantified at levels substantially lower than those possible by one-dimensional techniques. However, it has also been shown that the modulation process introduces a new source of error to the measurement. In this work, we present the results of a study into the limits of quantification and detection (LOQ and LOD) in comprehensive multidimensional separations using GC×GC and the more popular "two-step" integration algorithm as an example. Simulation of chromatographic data permits precise control of relevant parameters of peak geometry and modulation phase. Results are expressed in terms of the dimensionless parameter of signal-to-noise ratio of the base peak (S/N(BP)) making them transportable to any result where quantification is performed using a two-step algorithm. Based on these results, the LOD is found to depend upon the modulation ratio used for the experiment and vary between a S/N(BP) of 10-17, while the LOQ depends on both the modulation ratio and the phase of the modulation for the peak and ranges from a S/N(BP) of 10 to 50, depending on the circumstances.