On-fibre Derivatisation Research Articles

Comparison of carbonyl profiles from Czech and Spanish lagers: Traditional and modern technology

Beer is one from the most popular alcoholic beverages worldwide. For consumer acceptance, a significant factor is its flavour and taste; carbonyl compounds play an important role as indicators of the deterioration of flavour and aroma in beers. The aim of this study was to characterize differences in the carbonyl profile from Czech and Spanish beers, based on tradition and modern technology, respectively.Headspace solid-phase microextraction and gas-chromatography mass spectrometry were used to compare lager beers. The technique of on-fibre derivatization with O-(2,3,4,5,6-pentafluorobenzyl)hydroxylamine (PFBOA) was used to achieve satisfactory recovery and sensitivity.Statistical factor analysis showed three principal components, two of them explaining more than 79% of the variability and these results were related to ANOVA-significant difference analysis based on the country of origin. These two factors were related to Strecker aldehydes and Maillard products. PCA analysis scatterplot confirmed a significant difference between the Spanish and Czech beers, particularly with regard to the content of diacetyl and (E)-non-2-enal.

Reaction of OH radicals with 5-hydroxy-2-pentanone: formation yield of 4-oxopentanal and its OH radical reaction rate constant

Environmental context Alkanes, major constituents of vehicle exhausts, are emitted to the atmosphere where they react, chiefly by gas-phase reactions with the hydroxyl radical, to form products which can also react further. In laboratory experiments, we studied the further reactions of a model first-generation alkane reaction product. Understanding alkane reaction chains is important because the toxicity, secondary aerosol formation and other properties of vehicle emissions can change as new compounds are formed. Abstract 1,4-Hydroxycarbonyls are major products of the gas-phase reactions of alkanes with OH radicals, and in the atmosphere they will react with OH radicals or undergo acid-catalysed cyclisation with subsequent dehydration to form highly reactive dihydrofurans. 3-Oxobutanal (CH3C(O)CH2CHO) and 4-oxopentanal (CH3C(O)CH2CH2CHO) are first-generation products of the OH radical-initiated reaction of 5-hydroxy-2-pentanone (CH3C(O)CH2CH2CH2OH). The behaviours of 3-oxobutanal and 4-oxopentanal have been monitored during OH+5-hydroxy-2-pentanone reactions carried out in the presence of NO, using solid phase microextraction fibres coated with O-(2,3,4,5,6,-pentafluorobenzyl)hydroxyl amine (PFBHA) for on-fibre derivatisation of carbonyl compounds and an annular denuder coated with XAD resin and further coated with PFBHA. The time-concentration data for 4-oxopentanal during OH+5-hydroxy-2-pentanone reactions were independent of relative humidity (0–50%), and were consistent with a rate constant for OH+4-oxopentanal of (1.2±0.5)×10–11cm3 molecule–1s–1 at 296±2K, a factor of 2 lower than both literature rate constants for other aldehydes and that estimated using a structure-reactivity approach. The molar formation yield for 4-oxopentanal from OH+5-hydroxy-2-pentanone in the presence of NO was determined to be 17±5%, consistent with predictions based on a structure-reactivity relationship and current knowledge of the subsequent reaction mechanisms.

Determination of furfural in beers, vinegars and infant formulas by solid-phase microextraction and gas chromatography/mass spectrometry

The solid-phase microextraction (SPME) technique with on-fibre derivatisation was evaluated for the analysis of furfural in infant formulas, beers, and vinegars. The poly(dimethylsiloxane)/divinylbenzene (PDMS/DVB) fibre was used and O-2,3,4,5,6-(pentafluorobenzyl)hydroxylamine hydrochloride (PFBHA) was first loaded onto the fibre. Food sample of 2 mL was then placed in a 4 mL PTFE-capped glass vial. Headspace extraction by the SPME fibre was performed at 80°C for 20 min under 1100 rpm magnetic stirring with the addition of 40% sodium chloride. Afterwards, the SPME fibre was directly desorbed at the injection port of a gas chromatography/mass spectrometer (GC/MS), followed by the analysis of derivatives formed on-fibre. To avoid matrix interferences, standard addition method was performed. The adsorption-time profiles were examined. The precision, recovery and method detection limits (MDLs) were evaluated with spiked food samples. The relative standard deviations from different spiked samples were all less than 5% and the recoveries were 100 ± 5%. With 2 mL of food sample, MDLs were in the range of 3.09 ∼ 14.05 µg L−1. Compared with other techniques, the study shown here provided a simple, fast and reliable method for the analysis of furfural in food samples.

Headspace solid-phase microextraction and on-fibre derivatization of primary aromatic amines for their determination by pyrolysis to aryl isothiocyanates and gas chromatography-mass spectrometry

A sensitive and solvent-free procedure for the determination of aromatic amines in environmental and food samples was studied using solid-phase microextraction (SPME) for on-fibre derivatization and gas chromatography-mass spectrometry (GC-MS). The analytical procedure involved headspace impregnation of allyl isothiocyanate on the SPME fibre and then extraction/derivatization of aromatic amines by placing impregnated fibre in the headspace of the sample. The allyl thiourea derivatives were pyrolyzed in the injection port of the GC and the aryl isothiocyanates thus formed were chromatographed. SPME parameters such as selection of coating material, extraction/derivatization time and temperature were optimized. The optimum extraction was obtained using a divinylbenzene/carboxen/polydimethylsiloxane fibre placed for 20 min in the headspace of the sample heated to 70 °C. This method increased the extractability and detectability of aromatic amines from complex environmental and food samples. The calibration curves for derivatized amines were linear in the range 0.05–100 μg L−1 with correlation coefficients in the range 0.9946–0.9994 and limits of detection in the range 6–180 ng L−1. Many real samples including food colours, ice cream powder, soft drink concentrate, and industrial area sand have been analyzed and were found to contain elevated levels of aromatic amines.

Determination of carbonyl compounds in fish species samples with solid-phase microextraction with on-fibre derivatization

Headspace solid-phase microextraction (HS-SPME) with on-fibre derivatization has been applied for determining volatile carbonyl compounds in fish muscle samples associated to different species and technological treatments. o-2,3,4,5,6-(Pentafluorobenzyl)hydroxylamine hydrochloride (PFBHA) has been used as derivatization reagent and the formed oximes were determined by gas chromatography coupled to mass spectrometry (GC–MS). The method has been optimised for improving the extraction–derivatization of analytes. Factors as the type of fibre, salting-out effect, incubation temperature and time, stirring and sample volume have been evaluated. The technique combines the typical advantages of SPME (economical, solventless, minimal sample handling or suitability for routine analysis) with a very high sensitivity using low quantities of sample (only 0.5 g of muscle). The comparison with an optimised and validated SPME method without derivatization showed excellent results in terms of sensitivity and selectivity since several compounds, as those associated to technological processes were detected in the different fish samples only after carbonyl derivatization.

Determination of carbonyl compounds in beer by derivatisation and headspace solid-phase microextraction in combination with gas chromatography and mass spectrometry

Headspace solid-phase microextraction (SPME) followed by gas chromatography and mass spectrometry was applied for quantification of 41 chemically diverse carbonyl compounds in beer. Therefore, in-solution derivatisation with o-(2,3,4,5,6-pentafluorobenzyl)hydroxylamine (PFBHA) combined with SPME was optimised for fibre selection, PFBHA concentration, extraction temperature and time and ionic strength. Afterwards, the method was calibrated and validated successfully and extraction efficiency was compared to sampling with on-fibre derivatisation. In-solution derivatisation enabled the detection of several compounds that were poorly extracted with on-fibre derivatisation such as 5-hydroxymethylfurfural, acrolein, hydroxyacetone, acetoin, glyoxal and methylglyoxal. Others, especially (E)-2-nonenal, were extracted better with on-fibre derivatisation.

Determination of aliphatic aldehydes in maize and grass silages using on-fibre derivatisation with O-(2,3,4,5,6-pentafluoro)benzylhydroxylamine

Aldehydes and ketones are volatile compounds of silages which probably affect feed preference, palatability and intake. A sensitive and fast method was developed to determine aliphatic aldehydes in maize and grass silages. The method is based on the solid phase micro-extraction and on-fibre derivatisation of aldehydes with O-(2,3,4,5,6-pentafluoro)benzylhydroxylamine hydrochloride (PFBHA). The derivatisation agent was adsorbed onto divinylbenzene/poly(dimethylsiloxane) 65 μm fibre and then exposed to the aldehydes in the headspace of the silage samples. Aldehydes selectively react with PFBHA forming volatile oximes, which were desorbed in the injection port of a gas chromatograph and analysed by mass spectrometry. Using this method, eight aldehydes were detected in maize and grass silages being ethanal, propanal, butanal, 2-methylpropanal, pentanal, 3-methylbutanal, hexanal and heptanal, at levels ranging from tens to 200 mg/kg fresh matter. In two pilot laboratory experiments, contents of butanal and 3-methylbutanal decreased in silages prepared from grasses inoculated with Lactobacillus plantarum (1 × 10 5 CFU/g) or prepared from wilted forage.

Solid-phase micro-extraction procedure for the determination of 1,3-dichloro-2-propanol in water by on-fibre derivatisation with bis(trimethylsilyl)trifluoroacetamide

The headspace solid-phase micro-extraction technique with on-fibre derivatisation followed by gas chromatography-tandem mass spectrometry has been evaluated for the analysis of 1,3-dichloro-2-propanol in water. An asymmetric factorial design has been performed to study the influence of five experimental factors: extraction time and temperature, derivatisation time and temperature and pH. The best extraction performance is achieved in the headspace mode, with 5 mL stirred water samples (pH 4) containing 1.3 g of NaCl, equilibrated for 30 min at 25 degrees C, using divinylbenzene-carboxen-polydimethylsiloxane as the fibre coating. On-fibre derivatisation has been used for the first time with 50 microL of bis(trimethylsilyl)trifluoroacetamide at 25 degrees C during 15 min, leading to effective yields. The proposed method provides high sensitivity, good linearity and repeatability (relative standard deviation of 5.1% for 10 ng mL(-1) and n = 5). The limits of detection and quantification were 0.4 and 1.4 ng mL(-1), respectively. Analytical recoveries obtained for different water samples were approx. 100%.

Unsaturated dicarbonyl products from the OH-initiated photo-oxidation of furan, 2-methylfuran and 3-methylfuran

This study presents the application of O-(2,3,4,5,6)-pentafluorobenzyl-hydroxylamine hydrochloride (PFBHA) on-fibre derivatisation Solid Phase Microextraction (SPME) to the sampling and quantification of the unsaturated 1,4-dicarbonyl products obtained in the photo-oxidation of furan, 2-methylfuran and 3-methylfuran with HONO: butenedial, 4-oxo-2-pentenal and 2-methylbutenedial, respectively. The use of Proton Transfer Reaction Mass Spectrometry (PTR-MS) is also considered and the advantages of the combined use of both methodologies is discussed. The 1,4 unsaturated dicarbonyl products sampled by SPME were quantified by GC-FID. The experiments were carried out in the EUPHORE outdoor simulation chambers. The results confirm that 1,4-dicarbonyls are the main products of the OH-initiated oxidation of furan and its methylated derivatives, a fact with environmental implications. Molar yields of (1.09 ± 0.41) and (0.90 ± 0.36) were obtained in two experiments of furan photo-oxidation. The yields of 4-oxo-2-pentenal and methylbutenedial were estimated to be (0.60 ± 0.24) and (0.83 ± 0.33) respectively, assuming the same SPME response factor as for butenedial. Furthermore, the unsaturated 1,4-dicarbonyls have also been identified in the chemical characterisation of the aerosols formed in the reactions. The yield of aerosols quantified were (8.5 ± 0.8)% in the photo-oxidation of furan, (1.85 ± 0.18)% in the photo-oxidation of 2-methylfuran and (5.5 ± 0.5)% in the photo-oxidation of 3-methylfuran, at the following concentrations of their precursors: 829 ± 249 ppbV and 748 ± 224 (in two furan experiments), 633 ± 190 in the 2-methylfuran and 641 ± 192 ppbV in the 3-methylfuran experiment.

Research into conditions of quantitivity in the determination of carboniles in complex air matrices by adsorptive solid phase microextraction

This study focuses on certain aspects of the quantitivity of adsorptive solid phase microextraction when applied in the form of on-fibre derivatisation with O-(2,3,4,5,6)-pentafluorobenzyl-hydroxylamine hydrochloride (PFBHA) for the determination of carboniles in air samples of relevance in the atmosphere. The study was performed in the high-volume outdoor atmospheric simulation chambers (EUPHORE) located in Valencia (Spain). At short sampling times, the adsorption profiles obtained when only benzaldehyde was inserted in the chamber coincided with those obtained when other carbonylic compounds were also introduced at the same concentration, and this was also the case when the concentration of all the gaseous mixture components was increased considerably from one experiment to another. In a number of experiments applying different conditions, it was proven that all the extraction profiles belonged to the same regression when the fibre responses were plotted against the concentration–time product. A number of calibrations were obtained for benzaldehyde introduced in the chamber alone and in a mixture with three other carboniles at similar concentration values. A statistical test is applied to confirm that they all belonged to the same regression since they shared homogeneous variances. After these tests, the method of SPME on-fibre derivatisation for the determination of carboniles was considered to be safely applicable to quantification. Moreover, the concentration levels at which certain unwanted effects, i.e., displacement, saturation and competition, were observed are a few orders of magnitude higher than their occurrence levels in atmospheric processes.

Determination of biogenic diamines with a vaporisation derivatisation approach using solid-phase microextraction gas chromatography–mass spectrometry

A gas-phase on-fibre derivatisation method for the determination of putrescine and cadaverine by gas chromatography/mass spectrometry using trifluoroacetylacetone (TFAA) has been studied and optimised. Small amounts (2μl) of putrescine, cadaverine and TFAA standards were vaporised at high temperature in a 20cm3 closed SPME vial. The subsequent derivatives were recovered from the headspace of the vial using a PDMS/DVB fibre. The optimised mole ratio for [TFAA]/[Putrescine+Cadaverine] reaction was 22.3/1 with a derivatisation and extraction temperature of 120oC and an extraction time of 20min. The retention times for the derivatised putrescine and cadaverine were 20.5 and 22.2min, respectively on a capillary column, CP-Sil 8CB; 30m length×0.25mmi.d.×0.25μm film thickness. The correlation coefficients (R2) of calibration curves for putrescine and cadaverine were 0.999 and 0.997, respectively over a range of sample masses of 20–350ng, using nonadecane as an internal standard. Putrescine and cadaverine recoveries were determined to be 93.9% and 103.3%, respectively. The method was found to be a straightforward single step procedure that was unaffected by complex sample matrices and was successfully tested on samples of meat, vegetables and cheese.

Optimisation of a complete method for the analysis of volatiles involved in the flavour stability of beer by solid-phase microextraction in combination with gas chromatography and mass spectrometry

Headspace solid-phase microextraction combined with gas chromatography and mass spectrometry was used for the quantification of 32 volatiles which represent the typical chemical reactions that can occur during beer ageing. Detection was accomplished by employing on-fibre derivatisation using o-(2,3,4,5,6-pentafluorobenzyl)hydroxylamine (PFBHA) and normal HS-SPME extraction. The procedures were optimised for SPME fibre selection, PFBHA loading temperature and time, extraction temperature and time, and effect of salt addition. Interference of matrix effects was overcome by calibrating according to the standard addition method and by using internal standards. Afterwards, the method was validated successfully and was applied to study the flavour stability of different beer types.

Determination of aldehydes in human breath by on-fibre derivatization, solid-phase microextraction and GC–MS

A GC–MS method for the simultaneous determination of hexanal, heptanal, octanal, nonanal and decanal in exhaled breath was established and validated. The aldehydes were derivatized on PDMS/DVB fibres using O-2,2,4,5,6-(pentafluorobenzyl) hydroxylamine hydrochloride (PFBHA) as the headspace derivatization reagent. The resultant oximes were quantified by GC–MS in selected ion monitoring (SIM) mode. The method provides detection limits of 0.01–0.03 nM for the aldehydes, with a linear response in the concentration range 0.002–20 nM. Within-day precision values for the five aldehydes at 0.02–0.04 nM and 0.2–0.4 nM were in the ranges: 3–9% and 3–8%, respectively; the corresponding between-day precision values were 11–22% and 10–24%. Exhaled breath samples could be stored at −20 °C for 48 h.

Optimisation of the on-fibre derivatisation of volatile fatty acids in the simultaneous determination together with phenols and indoles in cow slurries

The on-fibre derivatisation of volatile fatty acids (VFAs) using N-(tert-butyldimethylsilyl)-N-methyltrifluoroacetamide (MTBSTFA) was optimised in the simultaneous determination of VFAs together with phenols and indoles by headspace solid-phase microextraction (SPME)-gas chromatography-mass spectrometry. Firstly, the nature of the SPME fibre was optimised and four different fibres were studied (100 microm polydimethylsiloxane, 85 microm Carboxen/polydimethylsiloxane, 5/30 microm divinylbenzene/Carboxen/polydimethylsiloxane and 85 microm polyacrylate). The optimum fibre (50/30 microm divinylbenzene/Carboxen/polydimethylsiloxane) was used to study the exposure time of the fibre to the derivatisation agent and the desorption time and temperature. Firstly, a factorial design was built but since the three variables had a significant effect, a central composite design was used to build the response surfaces. The best signals were obtained after the exposure of the fibre in the headspace of the MTBSTFA derivatisation reagent for 1 h and desorption at 300 degrees C for 9 min. The determination of underivatised phenols and indoles was not affected by the presence of the derivatisation reagent in the fibre.

Improved method for the in vitro assessment of antioxidant activity of plant extracts by headspace solid-phase microextraction and gas chromatography–electron capture detection

The simultaneous monitoring of malondialdehyde, pentanal and hexanal, final products of lipid peroxidation is reported, using a headspace solid-phase microextraction (HS-SPME) technique with on-fibre derivatisation. The aldehydes are extracted and subjected to on-sorbent derivatisation into stable hydrazones with 2,4,6-trichlorophenylhydrazine (TCPH) and analyzed. The degree of inhibition of oxidation is performed by monitoring the chlorinated hydrazones after thermal desorption, by gas chromatography–electron capture detection. The procedure was employed to evaluate in vitro the antioxidant activity of Hypericum perforatum L. extracts and of the well-known antioxidant vitamin E following induction of oxidation of sunflower oil, as a model lipid system. Prior to the measurement of antioxidant activity, the optimal process conditions, i.e. headspace volume, temperature, agitation, extraction/derivatisation time and desorption time and temperature were properly established. Aqueous extracts of H. perforatum L. exhibited the highest antioxidative effect. The method is shown to be promising for screening purposes for antioxidant substances and natural extracts.

Analysis of trace levels of pesticides in rainwater by SPME and GC-tandem mass spectrometry after derivatisation with PFFBr

Solid-phase microextraction (SPME) was used for the analysis of some pesticides (bromoxynil, chlorotoluron, diuron, isoproturon, 2,4-MCPA, MCPP and 2,4-D) in rainwater after derivatisation with PFBBr and gas chromatography-ion trap mass spectrometry. The derivatisation procedure was optimized by testing different methods: direct derivatisation in the aqueous phase followed by SPME extraction, on-fibre derivatisation and derivatisation in the injector. The best result was obtained by headspace coating the PDMS/DVB fibre with PFBBr for 10 min followed by direct SPME extraction for 60 min at 68 degrees C (pH 2 and 75% NaCl). Good detection limits were obtained for all the compounds: these ranged between 10 and 1,000 ng L-1 with a relatively high uncertainty due to the combination of derivatisation and SPME extraction steps. The optimized procedure was applied to the analysis of pesticides in rainwater and results obtained shows that this method is a fast and simple technique to assess the spatial and temporal variations of concentrations of pesticides in rainwater.

Automated analysis of 2-methyl-3-furanthiol and 3-mercaptohexyl acetate at ng L −1 level by headspace solid-phase microextracion with on-fibre derivatisation and gas chromatography–negative chemical ionization mass spectrometric determination

A fast and automated method for the analysis at ng L −1 level of aroma-powerful polyfunctional thiols has been developed and applied to wine. The sample is just poured in a 20 mL vial and its vapour extracted with a poly(dimethylsiloxane)–divinylbenzene (PDMS–DVB) solid-phase microextraction fibre (65 μm thickness) previously exposed to vapours of the reactive (pentafluorobenzyl bromide) and of an alkali (tributylamine). The derivatised compounds are subsequently desorbed in the GC system and determined by negative chemical ionization mass spectrometry. The method is fully automated by using a Combi-Pal autosampler conveniently programmed. The analysis takes 50 min, which contrasts to the long and tedious methods previously proposed. The development of an optimal procedure is constrained by the aggressive character of the reagent (towards the fibre and the chromatographic column), its volatility and the quality of the blanks that can be obtained. Therefore, a critical step was fixing in the fibre a “safe” and repetitive amount of reagent. This was achieved by exposing the fibre (5 min) to the vapours of a water:acetone (9:1) solution containing 200 mg L −1 of reagent. Under these conditions, the extraction-derivatisation of analytes improves with time and temperature, and the best working conditions are dictated by a compromise between sensitivity, speed and chromatographic performance. Although analytes studied were 2-methyl-3-furanthiol, 4-mercapto-4-methyl-2-pentanone, 3-mercaptohexanol, 2-furanmethanethiol and 3-mercaptohexyl acetate, a good analytical performance could be achieved only for these two last compounds. Both of them can be repetitively (10% < RSD < 20%) determined in wine at concentrations below 0.1 ng L −1. Other aspects considered in the method setup were the oxidation of analytes during the process, and the electron-capture detection (ECD) and MS properties of the pentafluorobenzyl derivatives of different polyfunctional thiols.

Optimisation of a solid-phase microextraction method for the determination of parabens in water samples at the low ng per litre level

A procedure for the determination of five esters of p-hydroxybenzoic acid (parabens) in water samples is presented. Analytes (methyl, ethyl, propyl, butyl and benzyl paraben) are concentrated on a solid-phase microextraction (SPME) fibre, converted on their tert-butyldimethylsilyl derivatives and selectively determined using gas chromatography in combination with tandem mass spectrometry (GC–MS/MS). Influence of different factors on the efficiency of extraction and on-fibre derivatization steps is described in detail. For all species, the highest enrichment factors were achieved using a polyacrylate (PA) fibre exposed directly to stirred water samples, containing 150 mg/ml of sodium chloride, at room temperature. Performance of the further on-fibre derivatization reaction was also maximum at room temperature, considering a short exposition period of the SPME fibre to vapours of the silylation reagent. Under optimised conditions, the proposed method achieved quantification limits from 0.001 to 0.025 ng/ml and it was free of matrix effects; therefore, external calibration can be used as the quantification technique. From our knowledge, this work describes the first application of SPME and gas chromatography to the determination of parabens in water. The analysis of a limited number of real samples revealed the presence of parabens in raw sewage water at concentrations up to 3 ng/ml.

Analysis of methylamine by solid-phase microextraction and HPLC after on-fibre derivatization with 9-fluorenylmethyl chloroformate

Analysis of methylamine by solid-phase microextraction and HPLC after on-fibre derivatization with 9-fluorenylmethyl chloroformate

Analysis of methylamine by solid-phase microextraction and HPLC after on-fibre derivatization with 9-fluorenylmethyl chloroformate

A method for the determination of methylamine (MA) in aqueous matrices is reported which uses solid-phase microextraction (SPME) for enrichment and derivatization of the analyte, and high performance liquid chromatography (HPLC). The fluorogenic reagent 9-fluorenylmethyl chloroformate (FMOC) has been used for derivatization. The SPME fibres were successively immersed in the samples and in the derivatization solutions to extract MA and FMOC, respectively. After a defined time of reaction, the derivatized analyte was desorbed into the chromatographic system, and chromatographed in a LiChrosphere 100 RP18, 125 mm×4 mm i.d., 5 μm, column under gradient elution. In order to improve the MA-FMOC peak profile, a precolumn ( 20 mm×2.1 mm i.d., packed with Hypersil C 18 phase, 30 μm) was connected on-line to the analytical column by means of a switching valve. The experimental conditions (including fibre coating, times of adsorption, reaction and desorption, and concentration of reagent) have been optimised, and the results have been compared with those achieved by using a method previously validated for aliphatic amines in which extraction and derivatization were carried into C 18 solid-phase extraction (SPE) cartridges. Although less sensitive, the SPME based method allowed the quantification of MA over the range 2.5–10.0 μg/ml with linearity, reproducibility and accuracy comparable to that of the SPE based method, the limit of detection being 0.75 μg/ml. The main advantages of the proposed SPME procedure are: sample handling involved in the extraction and derivatization steps was considerably reduced, it was free organic solvent and non-destructive. Moreover, the proposed conditions allowed the selective determination of MA in the presence of other primary and secondary short-chain aliphatic amines. The utility of the proposed procedure for the quantification of MA in different types of waters is discussed.