Effect of short-chain alcohols on surfactant-mediated reversed-phase liquid chromatographic systems

The behaviour of β-blockers in a reversed-phase liquid chromatographic (RPLC) column with mobile phases containing a short-chain alcohol (methanol, ethanol or 1-propanol), with and without the surfactant sodium dodecyl sulphate (SDS), was explored. Two surfactant-mediated RPLC modes were studied, where the mobile phases contained either micelles or only surfactant monomers at high concentration. Acetonitrile was also considered for comparison purposes. A correlation was found between the effects of the organic solvent on micelle formation (monitored by the drop weight procedure) and on the nature of the chromatographic system (as revealed by the retention, elution strength and peak shape of β-blockers). When SDS is added to the mobile phase, the free surfactant monomers bind the C18 bonded chains on the stationary phase, forming an anionic layer, which attracts strongly the cationic β-blockers. The retention is modified as a consequence of the solving power of the organic solvent, micelles and surfactant monomers. The molecules of organic solvent bind the micelles, modify their shape, and may avoid their formation. They also bind the monomers of surfactant, desorbing them from the stationary phase, which affects the retention. The remaining surfactant covers the free silanols on the siliceous support, avoiding the interaction with the cationic solutes. The retention of β-blockers results from a combination of electrostatic and hydrophobic interactions, the latter being weaker compared to the hydro-organic system. The peak efficiencies and asymmetries are excellent tools to probe the surfactant layer on the stationary phase in an SDS/organic solvent system. The peaks will be nearly symmetrical wherever enough surfactant coats the stationary phase (up to 60% methanol, 40% ethanol, 35% 1-propanol, and 50% acetonitrile).     

Peak half-width plots to study the effect of organic solvents on the peak performance of basic drugs in micellar liquid chromatography

The addition of the anionic surfactant sodium dodecyl sulphate (SDS) to hydro-organic mixtures of methanol, ethanol, propanol or acetonitrile with water yielded enhanced peak shape (i.e. increased efficiencies and symmetrical peaks) for a group of basic drugs (β-blockers) chromatographed with a Kromasil C18 column. The effect can be explained by the thin layer of surfactant associated to the hydrocarbon chain on the stationary phase in the presence of the organic solvents, which covers the free silanols on the siliceous support avoiding their interaction with the cationic basic drugs. These instead interact with the anionic head of the surfactant increasing their retention and allowing a more facile mass transfer. The peak shape behaviour with the four organic solvents (methanol, ethanol, propanol and acetonitrile) was checked in the presence and absence of SDS. The changes in peak broadening rate and symmetry inside the chromatographic column were assessed through the construction of peak half-width plots (linear relationships between the left and right half-widths at 10% peak height versus the retention time). The examination of the behaviour for a wide range of compositions indicated that the effect of acetonitrile in the presence of SDS is different from ethanol and propanol, which behave similarly. Acetonitrile seems to be superior to the alcohols in terms of peak shape, which can be interpreted by the larger reduction in the adsorbed surfactant layer on the C18 column. However, the decreased efficiencies observed at increasing surfactant concentration in the mobile phase should be explained by the reduction in retention times, more than by a change in the stationary phase nature.     

Comparison of the performance of non-ionic and anionic surfactants as mobile phase additives in the RPLC analysis of basic drugs

Surfactants added to the mobile phases in reversed-phase liquid chromatography (RPLC) give rise to a modified stationary phase, due to the adsorption of surfactant monomers. Depending on the surfactant nature (ionic or non-ionic), the coated stationary phase can exhibit a positive net charge, or just change its polarity remaining neutral. Also, micelles in the mobile phase introduce new sites for solute interaction. This affects the chromatographic behavior, especially in the case of basic compounds. Two surfactants of different nature, the non-ionic Brij-35 and the anionic sodium dodecyl sulfate (SDS) added to water or aqueous-organic mixtures, are here compared in the separation of basic compounds (β-blockers and tricyclic antidepressants). The reversible/irreversible adsorption of the monomers of both surfactants on the stationary phase was examined. The changes in the nature of the chromatographic system using different columns and chromatographic conditions were followed based on the changes in retention and peak shape. The study revealed that Brij-35 is suitable for analyzing basic compounds of intermediate polarity, using "green chemistry", since the addition of an organic solvent is not needed and Brij-35 is a biodegradable surfactant. In contrast, RPLC with hydro-organic mixtures or mobile phases containing SDS required high concentrations of organic solvents.     

Submicellar and micellar reversed-phase liquid chromatographic modes applied to the separation of β-blockers

The behaviour of a reversed-phase liquid chromatographic (RPLC) system (i.e. elution order, resolution and analysis time), used in the analysis of β-blockers with acetonitrile–water mobile phases, changes drastically upon addition of an anionic surfactant (sodium dodecyl sulphate, SDS). Surfactant monomers cover the alkyl-bonded phase in different extent depending on the concentration of both modifiers, in the ranges 1 × 10⁻³–0.15 M SDS and 5–50% acetonitrile. Meanwhile, the surfactant is dissolved in the mobile phase as free monomers, associated in small clusters or forming micelles. Four characteristic RPLC modes are yielded, with transition regions between them: hydro-organic, micellar, and low and high submicellar. The mobile phases in the two latter modes contain a concentration of SDS below or well above the critical micellar concentration (CMC) in water (i.e. 8 × 10⁻³ M), and more than 30% acetonitrile. High submicellar RPLC appeared as the most promising mode, as it allowed full resolution of the β-blockers in practical times, while these were unresolved or highly retained in the other RPLC modes. The strong attraction of the cationic solutes to the anionic SDS makes a direct transfer mechanism between surfactant molecules in the stationary and mobile phases likely.     

Chromatographic Behavior of Aromatic Diamines in Hydro-Organic, Micellar and Submicellar Reversed Phase Liquid Chromatographic Modes

The chromatographic behavior (retention, elution strength, efficiency, peak asymmetry and selectivity) of some aromatic diamines in the presence of methanol with or without anionic surfactant SDS in the four different reversed phased liquid chromatographic (RPLC) modes, i.e., hydro-organic, micellar (MLC), low submicellar (LSC) and high submicellar (HSC), was investigated. In the three surfactant-mediated modes, the surfactant monomers coat the stationary phase even up to 70 % methanol; this results in the suppression of peak tailing (by masking the silanol groups on the stationary phase). In MLC and HSC, the solute retention decreases by increasing the surfactant concentration, while this situation was reversed in LSC. In the region between MLC and HSC modes (25–50 % methanol), retention of late eluting solutes was increased by increasing methanol content which is seemingly due to disaggregation of SDS micelles. Changes in selectivity were observed after changing the concentrations of SDS and methanol, in a greater extent when concentration of SDS was changed. Among the four studied RPLC modes, HSC showed the best efficiency with nearly symmetrical peaks. Prediction of retention of solutes in HSC based on a mechanistic retention model combined with Pareto-optimality method allowed the full resolution of target diamines in practical analysis times.     

Retention mechanisms in micellar liquid chromatography

Micellar liquid chromatography (MLC) is a reversed-phase liquid chromatographic (RPLC) mode with mobile phases containing a surfactant (ionic or non-ionic) above its critical micellar concentration (CMC). In these conditions, the stationary phase is modified with an approximately constant amount of surfactant monomers, and the solubilising capability of the mobile phase is altered by the presence of micelles, giving rise to diverse interactions (hydrophobic, ionic and steric) with major implications in retention and selectivity. From its beginnings in 1980, the technique has evolved up to becoming a real alternative in some instances (and a complement in others) to classical RPLC with hydro-organic mixtures, owing to its peculiar features and unique advantages. This review is aimed to describe the retention mechanisms (i.e. solute interactions with both stationary and mobile phases) in an MLC system, revealed in diverse reports where the retention behaviour of solutes of different nature (ionic or neutral exhibiting a wide range of polarities) has been studied in a variety of conditions (with ionic and non-ionic surfactants, added salt and organic solvent, and varying pH). The theory is supported by several mechanistic models that describe satisfactorily the retention behaviour, and allow the measurement of the strength of solute-stationary phase and solute-micelle interactions. Suppression of silanol activity, steric effects in the packing pores, anti-binding behaviour, retention of ionisable compounds, compensating effect on polarity differences among solutes, and the contribution of the solvation parameter model to elucidate the interactions in MLC, are commented.     

Characterization of C18-bonded liquid chromatographic stationary phases by Raman spectroscopy: the effect of mobile phase composition

Raman spectroscopy is used to examine the effect of mobile phase composition on the orientation of octadecyl-bonded silica-based reversed-phase liquid chromatographic (RPLC) stationary phase ligands. The effect of ligand bonding density is also investigated. The present experimental set-up utilizes a direct, noninvasive, on-column approach to examine the solvent dependent conformational behavior of the bonded ligands under flow-rate and back pressure conditions similar to those used during conventional RPLC measurements. Neat, single-component, mobile phase solvents including water, acetonitrile, methanol and chloroform are used to investigate the hypothesized collapsing and extension of stationary phase ligands with changes in mobile phase composition. No evidence of phase collapse was observed upon changing the mobile phase composition from an organic to an aqueous content. Also, Raman spectroscopic measurements allowed the differentiation between associated and free acetonitrile solvent.     

Performance of short-chain alcohols versus acetonitrile in the surfactant-mediated reversed-phase liquid chromatographic separation of β-blockers

Organic solvents are traditionally added to micellar mobile phases to achieve adequate retention times and peak profiles, in a chromatographic mode which has been called micellar liquid chromatography (MLC). The organic solvent content is limited to preserve the formation of micelles. However, at increasing organic solvent contents, the transition to a situation where micelles do not exist is gradual. Also, there is no reason to neglect the potentiality of mobile phases containing only surfactant monomers instead of micelles (high submicellar chromatography, HSC). This is demonstrated here for the analysis of β-blockers. The performance of four organic solvents (methanol, ethanol, 1-propanol, and acetonitrile) was compared in mobile phases containing the anionic surfactant sodium dodecyl sulphate in the MLC and HSC modes. The association of the organic solvent molecules with micelles gives rise to a significant loss in the elution strength of the organic solvent; whereas upon disruption of micelles, it tends to that observed in the hydro-organic mode. The elution behaviour of the β-blockers was modelled to predict the retention times. This allowed the detailed exploration of the selectivity and resolution of the chromatographic systems in relatively wide ranges of concentration of surfactant and organic solvent. The best performance in terms of resolution and analysis time was achieved using HSC with acetonitrile, being able to base-line resolve a mixture of eight β-blockers. Ethanol also provided a good separation performance, significantly improved with respect to methanol and 1-propanol. In contrast, the hydro-organic mode using acetonitrile or any of the short-chain alcohols could not succeed with the separation of the β-blockers, owing to the poorer selectivity and wider peaks.     

Chromatographic behavior of new deazapurine ribonucleosides in hydrophilic interaction liquid chromatography

The chromatographic behavior of new biogenic purine nucleosides in hydrophilic interaction liquid chromatography was examined on three different stationary phases, namely bare silica, and amide‐ and cyclofructan‐based stationary phases. The effects of buffer concentration, pH and acetonitrile‐to‐aqueous‐part ratio in the mobile phase on retention and peak shape were assessed. The retention coefficients and peak symmetry values substantially differed with respect to analytes´ structures, stationary phase properties and mobile phase composition. The bare silica column was unsuitable for these compounds under the chromatographic conditions tested due to very broad and asymmetrical peaks. Furthermore, the cyclofructan‐based stationary phase provided almost Gaussian peak shapes of all deazapurine nucleosides under most conditions tested. Therefore, the cyclofructan‐based stationary phase is the most suitable choice for the chromatographic analysis of nucleosides.     

Adsorption of the anionic surfactant sodium dodecyl sulfate on a C18 column under micellar and high submicellar conditions in reversed‐phase liquid chromatography

Micellar liquid chromatography makes use of aqueous solutions or aqueous‐organic solutions containing a surfactant, at a concentration above its critical micelle concentration. In the mobile phase, the surfactant monomers aggregate to form micelles, whereas on the surface of the nonpolar alkyl‐bonded stationary phases they are significantly adsorbed. If the mobile phase contains a high concentration of organic solvent, micelles break down, and the amount of surfactant adsorbed on the stationary phase is reduced, giving rise to another chromatographic mode named high submicellar liquid chromatography. The presence of a thinner coating of surfactant enhances the selectivity and peak shape, especially for basic compounds. However, the risk of full desorption of surfactant is the main limitation in the high submicellar mode. This study examines the adsorption of the anionic surfactant sodium dodecyl sulfate under micellar and high submicellar conditions on a C₁₈ column, applying two methods. One of them uses a refractive index detector to obtain direct measurements of the adsorbed amount of sodium dodecyl sulfate, whereas the second method is based on the retention and peak shape for a set of cationic basic compounds that indirectly reveal the presence of adsorbed monomers of surfactant on the stationary phase.     

Characterization of micellar mobile phases for reversed-phase chromatography

Cationic, anionic, and nonionic surfactants are characterized for their usefulness as micellar mobile phases in reversed-phase chromatography. Conditions found previously to provide optimum chromatographic efficiency for sodium dodecyl sulfate also provide high efficiency for the cationic and nonionic surfactants studied. The use of 3% n-propanol in the micellar mobile phase and column temperatures of 40°C appear to offer a broadly applicable solution to the low efficiency previously reported for micellar mobile phases. A chromatographic method for the determination of critical micelle concentrations is reported; it compares favorably with literature methods. Micellar mobile phases are shown to mimic ion-pairing mobile phases, allowing the separation of neutral solutes as well as solutes charged oppositely to the surfactant and offer a more rugged method of analysis than hydro-organic ion-pairing methods.     

Efficiency enhancements in micellar liquid chromatography through selection of stationary phase and alcohol modifier

Micellar liquid chromatography (MLC) remains hindered by reduced chromatographic efficiency compared to reversed phase liquid chromatography (RPLC) using hydro-organic mobile phases. The reduced efficiency has been partially explained by the adsorption of surfactant monomers onto the stationary phase, resulting in a slow mass transfer of the analyte within the interfacial region of the mobile phase and stationary phase. Using an array of 12 columns, the effects of various bonded stationary phases and silica pore sizes, including large-pore short alkyl chain, non-porous, superficially porous and perfluorinated, were evaluated to determine their impact on efficiency in MLC. Additionally, each stationary phase was evaluated using 1-propanol and 1-butanol as separate micellar mobile phase alcohol additives, with several columns also evaluated using 1-pentanol. A simplified equation for calculation of A' and C' terms from reduced plate height (h) versus reduced velocity (nu) plots was used to compare the efficiency data obtained with the different columns and mobile phases. Analyte diffusion coefficients needed for the h versus nu plots were determined by the Taylor-Aris dispersion technique. The use of a short alkyl chain, wide-pore silica column, specifically, Nucleosil C4, 1000A, was shown to have the most improved efficiency when using a micellar mobile phase compared to a hydro-organic mobile phase for all columns evaluated. The use of 1-propanol was also shown to provide improved efficiency over 1-butanol or 1-pentanol in most cases. In a second series of experiments, column temperatures were varied from 40 to 70 degrees C to determine the effect of temperature on efficiency for a subset of the stationary phases. Efficiency improvements ranging from 9% for a Chromegabond C8 column to 58% for a Zorbax ODS column were observed over the temperature range. Based on these observed improvements, higher column temperatures may often yield significant gains in column efficiency, assuming the column is thermally stable.     

Use of a three-factor interpretive optimisation strategy in the development of an isocratic chromatographic procedure for the screening of diuretics in urine samples using micellar mobile phases

Screening of diuretics in urine is feasible through direct injection of the samples into the chromatographic system and isocratic reversed-phase liquid chromatography (RPLC) with micellar-organic mobile phases of sodium dodecyl sulfate (SDS) and 1-propanol. The surfactant coverage of the chromatographic column makes the addition of organic competing amines less necessary than in conventional aqueous-organic RPLC to achieve well-shaped peaks. Also, the range of elution strengths of micellar mobile phases required to elute mixtures of hydrophobic and hydrophilic diuretics is smaller. This allows the isocratic separation of the diuretics within adequate analysis times. An interpretive methodology is applied to optimise the resolution of a mixture of 15 diuretics of diverse polarity and acid-base behaviour (althiazide, amiloride, bendroflumethiazide, benzthiazide, bumetanide, canrenoic acid, chlorthalidone, ethacrynic acid, furosemide, piretanide, probenecid, torasemide, triamterene, trichloromethiazide and xipamide), using pH and concentrations of surfactant and organic modifier in the mobile phase as separation factors. Twelve diuretics were resolved in 25 min using 0.055 M SDS-6.0% 1-propanol at pH 3.0. The mixture of 15 diuretics was also resolved with two mobile phases showing complementary behaviour: 0.05 M SDS-5.6% 1-propanol at pH 5.4 and 0.11 M SDS-5.4% 1-propanol at pH 4.2. The results were applied to the analysis of urine samples with limits of detection similar to those usually reported for aqueous-organic RPLC, taking into account that the samples were injected without any previous treatment to separate or preconcentrate the analytes.     

Chromatographic behaviour of steroidal saponins studied by high-performance liquid chromatography-mass spectrometry

The chromatographic behaviour of steroidal saponins found in Anemarrhena asphodeloides, Asparagus officinalis, Convallaria majalis, Digitalis purpurea and Ruscus aculeatus was studied by HPLC-MS using a C-18 reversed-phase column and aqueous acetonitrile or aqueous methanol mobile phase gradients, with or without the addition of 1% acetic acid. The behaviour was compared to that of triterpene saponins found in Aesculus hippocastanum, Centella asiatica, Panax notoginseng and Potentilla tormentilla. Inclusion of methanol in the mobile phase under acidic conditions was found to cause furostanol saponins hydroxylated at C-22 to chromatograph as broad peaks, whereas the peak shapes of the spirostanol saponins and triterpene saponins studied remained acceptable. In aqueous methanol mobile phases without the addition of acid, furostanol saponins chromatographed with good peak shape, but each C-22 hydroxylated furostanol saponin was accompanied by a second chromatographic peak identified as its C-22 methyl ether. Methanolic extracts analysed in non-acidified aqueous acetonitrile mobile phases also resolved pairs of C-22 hydroxy and C-22 methoxy furostanol saponins. The C-22 methyl ether of deglucoruscoside was found to convert to deglucoruscoside during chromatography in acidified aqueous acetonitrile, or by dissolving in water. Poor chromatography of furostanol saponins in acidified aqueous methanol is due to the interconversion of the C-22 hydroxy and C-22 methoxy forms. It is recommended that initial analysis of saponins by HPLC-MS using a C-18 stationary phase is performed using acidified aqueous acetonitrile mobile phase gradients. The existence of naturally-occurring furostanol saponins methoxylated at C-22 can be investigated with aqueous acetonitrile mobile phases and avoiding methanol in the extraction solvent.     

Measurement of the elution strength and peak shape enhancement at increasing modifier concentration and temperature in RPLC

Two approaches are proposed to measure the effect of different experimental factors (such as the modifier concentration and temperature) on the elution strength and peak shape in reversed-phase liquid chromatography, which quantify the percentage change in the retention factor and peak width (referred to the weakest conditions) per unit change in the experimental factor. The approaches were applied to the separation of a set of flavonoids with aqueous micellar mobile phases of the surfactant Brij-35 (polyoxyethylene(23)dodecanol), in comparison with acetonitrile–water mixtures, using an Eclipse XDB-C18 column. The particular interaction of each flavonoid with the oxyethylene chains of Brij-35 molecules (adsorbed on the stationary phase or forming micelles) changed the elution window, distribution of chromatographic peaks and partitioning kinetics, depending on the hydroxyl substitution in the aromatic rings of flavonoids. At 25?°C, peak shape with Brij-35 mobile phases was significantly poorer with regard to acetonitrile–water mixtures. At increasing temperature, the efficiency of Brij-35 increased, approaching at 80?°C the values obtained at equilibrium conditions, already reached with acetonitrile at 25?°C.     

Separation of Tetracycline Antibiotics by Hydrophilic Interaction Chromatography Using an Amino-Propyl Stationary Phase

In this work the potential of hydrophilic interaction chromatography (HILIC) is explored for the analysis of tetracycline antibiotics. The choice of the polar stationary phase is first discussed and it is demonstrated that aminopropyl stationary phases lead to higher efficiencies and peak symmetry than bare silica ones. The influence of the composition of the mobile phase is studied next : the concentration of the weaker solvent (acetonitrile), the nature and concentration of the more polar solvent (water or methanol), pH, the nature and ionic strength of the buffer. It is shown that high efficiencies are reached only with a citrate buffer that impairs the interactions with the residual silanol groups whatever the mobile phase pH is. We demonstrate that the citrate buffer strongly interacts with the cationic moiety of the aminopropyl stationary phase and thus reduces the accessibility of silanols. The separation of oxytetracycline, tetracycline and chlortetracycline is achieved in a few minutes at pH 3.5 or 5, with no peak tailing as usually observed in reversed phase liquid chromatography with an opposite elution order when compared with reversed phase liquid chromatography.     

Prediction of peak shape as a function of retention in reversed-phase liquid chromatography

Optimisation of the resolution of multicomponent samples in HPLC is usually carried out by changing the elution conditions and considering the variation in retention of the analytes, to which a standard peak shape is assigned. However, the change in peak shape with the composition of the mobile phase can ruin the optimisation process, yielding unexpected overlaps in the experimental chromatograms for the predicted optimum, especially for complex mixtures. The possibility of modelling peak shape, in addition to peak position, is therefore attractive. A simple modified-Gaussian model with a parabolic variance, which is a function of conventional experimental parameters: retention time (tR), peak height (H0), standard deviation at the peak maximum (sigma0), and left (A) and right (B) halfwidths, is proposed. The model is a simplification of a previous equation proposed in our laboratory. Linear and parabolic relationships were found between the peak shape parameters (sigma0), A and B) and tR, with a mean relative error of 1-5% in most cases. This error was partially due to variations in peak position and shape among injections, which in some cases were above 2%. Correlations between (sigma0, A and B) and the retention time, which is easily modelled as a function of mobile phase composition, allowed a simple and reliable prediction of chromatographic peaks. A parameter that depends on the slopes of the linear relationships for A and B versus tR is also proposed to evaluate column efficiency. The modified-Gaussian model was used to describe the peaks of six diuretics of diverse acid-base behaviour and polarity, which were eluted with 15 mobile phases where the composition was varied between 30 and 50% (v/v) acetonitrile and the pH between 3 and 7.     

The role of the dual nature of ionic liquids in the reversed-phase liquid chromatographic separation of basic drugs

The cationic nature of basic drugs gives rise to broad asymmetrical chromatographic peaks with conventional C18 columns and hydro-organic mixtures, due to the ionic interaction of the positively charged solutes with the free silanol groups on the alkyl-bonded reversed-phase packing. Ionic liquids (ILs) have recently attracted some attention to reduce this undesirable silanol activity. ILs are dual modifiers (with a cationic and anionic character), which means that both cation and anion can be adsorbed on the stationary phase, giving rise to interesting interactions with the anionic free silanols and the cationic basic drugs. A comparative study of the performance of four imidazolium-based ILs as modifiers of the chromatographic behaviour of a group of β-blockers is shown. The ILs differed in the adsorption capability of the cation and anion on C18 columns. Mobile phases without additive and containing a cationic (triethylamine, TEA) or anionic (sodium dodecyl sulphate, SDS) additive were used as references for the interpretation of the behaviours. The changes in the nature of the chromatographic system, at increasing concentration of the additives, were followed based on the changes in retention and peak shape of the β-blockers. The silanol suppressing potency of the additives, and the association constants between the solutes and modified stationary phase or additive in the mobile phase, were estimated. The study revealed that SDS and the ionic liquid 1-hexyl-3-methylimidazolium tetrafluoroborate are the best enhancers of chromatographic peak shape among those studied.     

A reversed-phase/hydrophilic interaction mixed-mode C18-Diol stationary phase for multiple applications

A mixed-mode chromatographic packing material, C18 and diol groups modified silica (C18-Diol), was prepared with controllable hydrophobicity and hydrophilicity. It demonstrated excellent aqueous compatibility and stability in aqueous mobile phase; compared to the traditional C18 column, improved peak shape of basic analytes was also obtained. Additionally, it exhibited both reversed-phase liquid chromatographic (RPLC) and hydrophilic interaction chromatographic (HILIC) performance; the analyte separation scope was thus enlarged, demonstrated by simultaneous separation of twenty acids, bases and neutrals. More interestingly, a novel on-line two-dimensional liquid chromatography on the single column (2D-LC-1C) was established by modifying the high performance liquid chromatographic instrument only with the addition of an extra six-port two-position valve. The early co-eluted components of the extract of Lonicera japonica on the 1st-dimension (RPLC) were collected for the online re-injection to the 2nd-dimension (HILIC) by conveniently varying the mobile phase components. Six more peaks were obtained. The established system was simple, easy operation and low cost, which had advantages in analyzing complicated samples.