Numerical determination of the adsorption isotherms of tryptophan at different temperatures and mobile phase compositions

Single-component adsorption isotherm data were acquired by frontal analysis (FA) for tryptophan on a C(18)-Kromasil packed column, using acetonitrile-water solutions of various compositions (2.5, 5, and 7.5% ACN+1% acetic acid) and at five different temperatures between 25 and 65 degrees C. The adsorption isotherm model accounting best for these data is the bi-Moreau model, showing that two types of adsorption sites coexist on the surface and that strong adsorbate-adsorbate interactions take place. Large concentration band profiles of tryptophan were obtained for the three mobile phase compositions, at five different temperatures and the best values of the adsorption isotherm coefficients were determined by the inverse method (IM) of chromatography. The advantages and drawbacks of using the FA and the IM for determining the coefficients of the adsorption isotherm of tryptophan under the experimental conditions selected are discussed. The results of the FA and IM measurements are in good agreement. Both indicate that the retention time of tryptophan decreases rapidly with increasing acetonitrile concentration in the mobile phase as well as the saturation capacities of the two types of adsorption sites, with the highest values of the two saturation capacities being found for the lowest ACN content and the lowest temperature. The adsorption constant on the low-energy sites decreases with increasing acetonitrile content and temperature. In contrast, the adsorption constant on the high-energy sites increases with increasing ACN content of the mobile phase but decreases with increasing temperature. The solute-solute interaction parameters for the low and the high-energy adsorption sites increase rapidly with increasing ACN concentration in the mobile phase and with increasing temperature.     

Effect of the mobile phase composition on the isotherm parameters and the high concentration band profiles in reversed-phase liquid chromatography

Single-component adsorption isotherm data were acquired by frontal analysis for phenol on a C18-Kromasil packed column, under reversed-phase liquid chromatography conditions, using various methanol-water solutions (30-60%, v/v, methanol). The isotherm model accounting best for these data was the biLangmuir model. With increasing methanol content, the two saturation capacities decrease, particularly that of the high-energy sites, the adsorption constant of the low-energy sites decreases significantly and that of the high-energy sites decreases strongly. These results allow a quantitative investigation of the properties of the high-energy sites (which are not necessarily the so-called active sites), a feature rarely discussed yet. The band profiles calculated with the numerical values of the isotherm model parameters derived by fitting the frontal analysis data to the model and using the equilibrium-dispersive model agree very well with the experimental band profiles in the whole concentration range.     

Effect of the ionic strength of salts on retention and overloading behavior of ionizable compounds in reversed-phase liquid chromatography II. Symmetry-C18

In a companion paper, we describe the influence of the concentration and the nature of salts dissolved in the mobile phase (methanol:water, 40:60, v/v) on the adsorption behavior of propranolol (R'-NH2+ -R, Cl-) on XTerra-C18. The same experiments were repeated on a Symmetry-C18 column to compare the adsorption mechanisms of this ionic compound on these two very different RPLC systems. Frontal analysis (FA) measurements were first carried out to determine the best isotherm model accounting for the adsorption behavior of propranolol hydrochloride on Symmetry with a mobile phase without salt (and only 25% methanol to compensate for the low retention in the absence of salt). The adsorption data were best modeled by the bi-Moreau model. Large concentration band profiles of propranolol were recorded with mobile phases having increasing KCl concentrations (0, 0.002, 0.005, 0.01, 0.05, 0.1 and 0.2 M) and the best values of the isotherm coefficients were determined by the inverse method (IM) of chromatography. The general effect of a dissociated salt in the mobile phase was the same as the one observed earlier with XTerra-C18. Increasing the salt concentration increases the two saturation capacities of the adsorbent and the adsorption constant on the low-energy sites. The adsorption constant on the high-energy sites decreases and the adsorbate-adsorbate interactions tend to vanish with increasing salt concentration of the mobile phase. The saturation capacities decrease with increasing radius of the monovalent cation (Na+, K+, Cs+, etc.). Using sulfate as a bivalent anion (Na2SO4) affects markedly the adsorption equilibrium: the saturation capacities are drastically reduced, the high-energy sites nearly disappear while the adsorption constant and the adsorbate-adsorbate interactions on the low-energy sites increase strongly. The complexity of the thermodynamics in solution might explain the different influences of these salts on the adsorption behavior.     

Adsorption isotherms of the fullerenes C60 and C70 on a tetraphenylporphyrin-bonded silica

The single-component adsorption isotherms of the C60 (from 0 to 15 g/L) and C70 (from 0 to 8 g/L) buckminsterfullerenes on a tetraphenylporphyrin-bonded silica were acquired by frontal analysis, using a solution of toluene-1-methylnaphthalene (40:60, v/v) as the mobile phase. The best isotherm model derived from the fitting of these adsorption data was the bi-Langmuir model, a choice supported by the bimodal affinity energy distribution (AED) obtained for C60. The isotherm parameters derived from the inverse method (IM) of isotherm determination (by fitting calculated profiles to experimental overloaded band profiles of C60 and C70) are in very good agreement with those derived from the FA data. According to the isotherm parameters found by these three methods (FA, AED, IM), the tetraphenylporphyrin-bonded silica can adsorb 54 and 42 mmol/L of C60 and C70 fullerenes, respectively, a result that is consistent with the relative molecular size of these two compounds. The 20% lower surface accessibility for C70 is compensated by a three times higher equilibrium constant on the low-energy sites, giving a selectivity alpha(C70/C60) = 3.6. Large volumes (0.2, 0.8 and 1.7 mL) of mixtures of C60 (3.2 g/L) and C70 (1.3 g/L) were injected and their elution profiles compared to those calculated from the competitive bi-Langmuir model derived from the single-component isotherm data. A good agreement is obtained between calculated and experimental profiles, which supports the two-site adsorption mechanism derived from the single-component adsorption data. The measurements of the influence of the pressure on the retention of C60 and C70 demonstrate that the partial molar volumes of the two buckminsterfullerenes are 12 mL/mol larger in the stationary than in the mobile phase.     

Effect of temperature on the adsorption behavior of tryptophan in reversed-phase liquid chromatography

Single-component adsorption isotherm data of l-tryptophan on a C(18)-bonded silica column were acquired by frontal analysis (FA), with aqueous mobile phases containing 5% of acetonitrile at five different temperatures between 23 and 62 degrees C. The non-linear fitting of these data provided the bi-Moreau model for all temperatures as the best isotherm model. The inverse method (IM) was used to derive the parameters at these temperatures from the parameters of the 25 degrees C isotherm. The adsorption constants and the saturation capacities of the low and high-energy sites decreases by increasing the temperature, while the adsorbate-adsorbate parameters of both sites increase. An excellent agreement was found between the experimental and calculated overloaded band profiles at all the temperatures used. The breakthrough curves obtained and the overloaded band profiles obtained were found to have different shapes according to the range of concentration studied and the temperatures. At low concentration 0.05-0.5 g/L the breakthrough curves and the overloaded band profiles have a front shock and diffuse rear, which indicates langmuirian behavior, but at intermediate 1-2 g/L and high concentration 8 g/L they start to have diffuse fronts and shocks at the rear or more than one shock at the rear which indicates non-langmuirian behavior. At 23 degrees C the isotherm has another langmuirian part, which appears at high concentration. The behavior of the breakthrough curves is explained by the shape of the isotherm in which all of the isotherms have a langmuirian part (the isotherm is concave upward) and an antilangmuirian part (the isotherm is concave downward). The temperature affected the breakthrough curves by decreasing the time of the appearance of the fronts for all concentration ranges studied, and by decreasing the time difference between the highest concentration and lowest concentration of the fronts, especially the low concentration range at 0.5 g/L. The fronts of the breakthrough curves at high concentration seems to be the most affected by temperature.     

The adsorption mechanism of nortryptiline on C18-bonded Discovery

The adsorption isotherms of an ionizable compound, nortriptyline, were accurately measured by frontal analysis (FA) on a C(18)-Discovery column, first without buffer (in an aqueous solution of acetonitrile at 15%, v/v of ACN), then with a buffer (in 28%, v/v ACN solution). The buffers were aqueous solutions containing 20 mM of formic acid or a phosphate buffer at pH 2.70. The linear range of the isotherm could not be reached with the non-buffered mobile phase using a dynamic range larger than 40,000 (from 1.2 x 10(-3) g/L to 50 g/L). With a 20 mM buffer in the liquid phase, the isotherm is linear for concentrations of nortriptyline inferior to 10(-3) g/L (or 3 micromol/L). The adsorption energy distribution (AED) was calculated to determine the heterogeneity of the adsorption process. AED and FA were consistent and lead to a trimodal distribution. A tri-Moreau and a tri-Langmuir isotherm models accounted the best for the adsorption of nortriptyline without and with buffer, respectively. The nature of the buffer affects significantly the middle-energy sites while the properties of the lowest and highest of the three types of energy sites are almost unchanged. The desorption profiles of nortriptyline show some anomalies in relation with the formation of a complex multilayer adsorbed phase of acetonitrile whose excess isotherm was measured by the minor disturbance method. The C(18)-Discovery column has about the same total saturation capacity, around 200 g of nortriptyline per liter of adsorbent (or 116 mg/g), with or without buffer. About 98-99% of the available surface consists in low energy sites. The coexistence of these different types of sites on the surface solves the McCalley's enigma, that the column efficiency begins to drop rapidly when the analyte concentration reaches values that are almost one hundred times lower than those that could be predicted from the isotherm data acquired under the same experimental conditions. Due to the presence of some relatively rare high energy sites, the largest part of the saturation capacity is not practically useful.     

Separation mechanism of nortriptyline and amytriptyline in RPLC

The single and the competitive equilibrium isotherms of nortriptyline and amytriptyline were acquired by frontal analysis (FA) on the C18- bonded discovery column, using a 28/72 (v/v) mixture of acetonitrile and water buffered with phosphate (20 mM, pH 2.70). The adsorption energy distributions (AED) of each compound were calculated from the raw adsorption data. Both the fitting of the adsorption data using multi-linear regression analysis and the AEDs are consistent with a trimodal isotherm model. The single-component isotherm data fit well to the tri-Langmuir isotherm model. The extension to a competitive two-component tri-Langmuir isotherm model based on the best parameters of the single-component isotherms does not account well for the breakthrough curves nor for the overloaded band profiles measured for mixtures of nortriptyline and amytriptyline. However, it was possible to derive adjusted parameters of a competitive tri-Langmuir model based on the fitting of the adsorption data obtained for these mixtures. A very good agreement was then found between the calculated and the experimental overloaded band profiles of all the mixtures injected.     

Calculations of the energy distribution from perturbation peak data--a new tool for characterization of chromatographic phases

The calculation of the adsorption energy distribution (AED) was recently introduced as an important tool for the chromatographic community for characterization of modern phases. The AED-calculations, provides model-independent information about the numbers of different adsorption sites and their respective energy-levels, prior to the selection of an adsorption isotherm model which narrows the number of possible rival models. The selection of a proper model for the fitting of the determined raw data is crucial; if the wrong model is selected misleading information about the retention mechanism may be drawn. The AED-calculations require raw adsorption isotherm data (i.e. data points) which is unfortunately not obtained by the newly validated perturbation peak method. In this study, we developed mathematical expression allowing the use of the raw tangential slope provided by the perturbation peak method for AED calculations. The approach worked excellently and was verified against both computer-generated adsorption isotherm data as well as experimentally determined data, using three different experimental systems. It was found that the calculations of the AED, as based on perturbation peak data, converts faster and are not more sensitive to experimental noise as compared to the classical AED calculations using raw adsorption isotherm data.     

Accuracy and precision of adsorption isotherm parameters measured by dynamic HPLC methods

The fluctuations of the column temperature, the composition and the flow rate of the mobile phase affect the accuracy and precision of the adsorption isotherm parameters measured by dynamic HPLC methods. Experimental data were acquired by frontal analysis (FA) for phenol in equilibrium between C18-bonded Symmetry and a methanol:water mixture (20:80, v/v), at 303 K and a flow rate of 1 mL/min. The fluctuations of the experimental parameters were 0.1 K for the temperature, 0.1% for the mobile phase composition and 0.001 mL/min for the flow rate. The best isotherm model was shown to be the tri-Langmuir isotherm. Random errors were calculated and shown to agree with experimental results. Overloaded band profiles of phenol were acquired at low (sample size, 100 microL, concentration 3 g/L) and high (same sample size, concentration 60 g/L) loadings, at seven temperatures (298, 300, 302, 303, 304, 306, and 308 K), for seven mobile phase compositions (methanol 16, 18, 19, 20, 21, 22, and 24%), and with seven mobile phase flow rates (0.95, 0.97, 0.99, 1.00, 1.01, 1.03, and 1.05 mL/min), always keeping two experimental parameters at the values selected for the FA runs. Assuming that the isotherm model stays the same, the inverse method (IM) was used to derive the isotherm parameters in each case. Temperature affects the equilibrium constants according to Van't Hoff law. A temperature change of 1 K around 303 K causes a relative variation of 1.5% of the high-energy adsorption constant b3 and of 0.6% of the saturation capacity q3. The isotherm parameters are very sensitive to the mobile phase composition, especially the highest energy mode. Both adsorption constants b2 and b3 follow the linear strength solvent model (LSSM). A methanol volume fraction change of 1% causes a relative decrease of 3.2 and 5.0% of b2 and b3, respectively and a 2% decrease of the saturation capacity q3. Finally, flow rate changes affect only the saturation capacities. A flow rate change of 1 % causes a 2% change in the saturation capacity parameters.     

A chromatographic estimate of the degree of heterogeneity of RPLC packing materials. 1. Non-endcapped polymeric C30-bonded stationary phase

A new chromatographic method estimating the degree of heterogeneity of RPLC packing materials is based on the results of systematic measurements of the adsorption data in a wide concentration range for selected probe compounds. These data are acquired by frontal analysis (FA), modeled, and used for the calculation of the adsorption energy distribution (AED). Four compounds were used, two neutral compounds of different molecular sizes (caffeine and phenol) and two ionizable compounds of opposite charges, 2-naphthalene sulfonate, an anion, and propranololium, a cation. This work was done on a C30-bonded silica stationary phase (Prontosil-C30), using the same aqueous mobile phase (30% methanol, v/v) for all compounds, except that sodium chloride (25 mM) was added to elute the ionizable compounds. All four adsorption isotherms have Langmuirian behavior. The AEDs are tri-modal for phenol, quadri-modal for caffeine. The total saturation capacity of the stationary phase is four-fold lower for caffeine than for phenol, due in part to its larger molecular size. The equilibrium constants on the low-energy sites of types 1 and 2 are eight-fold larger. These two types of sites characterize the heterogeneity of the bonded layer itself. The density of the high-energy sites of types 3 and 4 is higher for caffeine, suggesting that caffeine molecules can be accommodated in some hydrophobic cages into which smaller molecules like phenol cannot. These high-energy types of sites characterize the heterogeneity of the whole stationary phase (silica support included). The ionizable compounds have larger molecules than the neutral ones and, accordingly, a lower relative density of sites of type 2 to sites of type 1. A tri-modal and a quadri-modal energy distributions were observed for the 2-naphthalene sulfonate anion and the propranololium cation, respectively. The fourth types of sites measured and its unusually high equilibrium constant are most probably due to ion-exchange interactions between the non-endcapped ionized silanols and the propranololium ion. No such strong interactions are observed with the anionic compound.     

Effect of the mobile phase composition on the adsorption behavior of tryptophan in reversed-phase liquid chromatography

Single-component adsorption isotherm data of l-tryptophan on a C18-bonded silica column were acquired by frontal analysis (FA), with aqueous mobile phases containing 2.5, 5, and 7.5% of acetonitrile (ACN) or 7, 10, 15, and 20% of methanol (MeOH). Most of these isotherms have two inflection points and three different parts. The low and the high concentration parts exhibit langmuirian behavior. The intermediate part exhibits anti-langmuirian behavior. The inflection points shift toward higher concentrations with increasing mobile phase concentration in ACN or MeOH, which causes the differences in the isotherm profiles. The nature of the organic modifier and its concentration affect only the isotherm profile and the numerical values of its parameters, not the nature of the best model, which is the bi-Moreau model in all cases. The isotherm profiles depend on the experimental conditions because they affect the intensity of the adsorbate-adsorbate interactions. Overloaded band profiles of tryptophan were recorded with the seven mobile phase compositions. They were used to determine the best values of the isotherm coefficients by the inverse method (IM) of chromatography. There is an excellent agreement between the values of these parameters obtained by FA and by IM. Increasing the concentration of either ACN or MeOH in the mobile phase causes a slight decrease in the saturation capacities of the low and the high energy sites, and in the adsorption constant of the low energy sites. The adsorption constant of the high energy sites increases with increasing concentration of either solvent or is little affected. The adsorbate-adsorbate interaction constants of both low and high energy sites increase for both solvents. Saturation capacities of the high energy sites are higher for ACN than for MeOH.     

Effect of the flow rate on the measurement of adsorption data by dynamic frontal analysis

The adsorption data of propyl benzoate were acquired by frontal analysis (FA) on a Symmetry-C18 column, using a mixture of methanol (65%, v/v) and water as the mobile phase, at three different flow rates, 0.5, 1.0 and 2.0 mL/min. The exact flow rates Fv were measured by collecting the mobile phase in volumetric glasses (deltaFv / Fv < or = 0.2%). The extra-column volumes and the column hold-up volume were accurately measured at each flow rate by tracer injections. The detailed effect of the flow rate on the value of the amount adsorbed was investigated. The best isotherm model accounting for the adsorption data was the same BET isotherm model at all three flow rates. Only slight differences (always less than 5%) were found between the three different sets of isotherm parameters (saturation capacity, q(s), equilibrium constant on the adsorbent, b(s) and equilibrium constant on successive layers of propyl benzoate, bL). The reproducibility of the same isotherm parameters measured by the inverse method (IM) is less satisfactory, leading to R.S.D.s of up to 10%. A flow rate increase is systematically accompanied by a slight increase of the amount adsorbed. This phenomenon is consistent with the influence of the pressure on the equilibrium constant of adsorption due to the difference between the partial molar volumes of the solute and the adsorbate. The larger average pressure along the column that is required to achieve a larger flow rate causes a larger amount of solute to be adsorbed on the column at equilibrium. This result comforts the high sensitivity and versatility of the FA method for isotherm determination under any kind of situation.     

Thermodynamic characterization of separations on alkaline-stable silica-based C18 columns: why basic solutes may have better capacity and peak performance at higher pH

A systematic study was made to explain the large improvements in separation performance and capacity of basic compounds at alkaline conditions. The adsorption of three probe components was investigated on four alkaline-stable silica-based C18 columns at three different pH-levels: 3, 7 and 11. The probes were 3-phenyl-1-propanol (neutral), 2-phenylbutyric acid (acidic) and metoprolol (basic). Adsorption isotherms were acquired over a broad concentration range, in order to detect both high and low energy sites. Before the choice of the proper adsorption isotherm model, the adsorption energy distribution (AED) was calculated yielding the number of different kinds of interaction sites between the solute and the stationary phase. The neutral probe was entirely unaffected by pH and its AED was unimodal (one site) indicating homogenous adsorption. For the acidic probe the interactions were unimodal at pH 3 where the probe is uncharged and at least bimodal (two sites) at pH 7 and 11 where the probe is charged. For the basic probe, the interactions were heterogeneous at both pH 3 and 11. The equilibrium constants of the high and low energy sites were different by a factor of 55-100 at pH 3 and only 6-7 at pH 11. The difference in saturation capacities between the two sites was much smaller at pH 11 where 20% of the total capacity is from the high energy site, as compared to pH 3 where the high energy site was only 2-5% of the total capacity. This explains why peaks of amines (basic solutes) tail at low pH while their peaks are symmetrical at alkaline pH. The Langmuir model fit the unimodal data and the bi-Langmuir model fit the bimodal AED data. The calculated band profiles based on these parameters agreed excellently with the experimental data. The electrostatic-modified Langmuir, on the other hand, did not describe this adsorption process well.     

Adsorption mechanism of acids and bases in reversed-phase liquid chromatography in weak buffered mobile phases designed for liquid chromatography/mass spectrometry

The overloaded band profiles of five acido-basic compounds were measured, using weakly buffered mobile phases. Low buffer concentrations were selected to provide a better understanding of the band profiles recorded in LC/MS analyses, which are often carried out at low buffer concentrations. In this work, 10 microL samples of a 50 mM probe solution were injected into C(18)-bonded columns using a series of five buffered mobile phases at (SW)pH between 2 and 12. The retention times and the shapes of the bands were analyzed based on thermodynamic arguments. A new adsorption model that takes into account the simultaneous adsorption of the acidic and the basic species onto the endcapped adsorbent, predicts accurately the complex experimental profiles recorded. The adsorption mechanism of acido-basic compounds onto RPLC phases seems to be consistent with the following microscopic model. No matter whether the acid or the base is the neutral or the basic species, the neutral species adsorbs onto a large number of weak adsorption sites (their saturation capacity is several tens g/L and their equilibrium constant of the order of 0.1 L/g). In contrast, the ionic species adsorbs strongly onto fewer active sites (their saturation capacity is about 1g/L and their equilibrium constant of the order of a few L/g). From a microscopic point of view and in agreement with the adsorption isotherm of the compound measured by frontal analysis (FA) and with the results of Monte-Carlo calculations performed by Schure et al., the first type of adsorption sites are most likely located in between C(18)-bonded chains and the second type of adsorption sites are located deeper in contact with the silica surface. The injected concentration (50 mM) was too low to probe the weakest adsorption sites (saturation capacity of a few hundreds g/L with an equilibrium constant of one hundredth of L/g) that are located at the very interface between the C(18)-bonded layer and the bulk phase.     

Physical origin of peak tailing on C18-bonded silica in reversed-phase liquid chromatography

Single component isotherm data of caffeine and phenol were acquired on two different stationary phases for RPLC, using a methanol/water solution (25%, v/v, methanol) as the mobile phase. The columns were the non-endcapped Waters Resolve-C18, and the Waters XTerra MS C18. Both columns exhibit similar C18 -chain densities (2.45 and 2.50 micromol/m2) and differ essentially by the nature of the underivatized solid support (a conventional, highly polar silica made from water glass, hence containing metal impurities, versus a silica-methylsilane hybrid surface with a lower density of less acidic free silanols). Thirty-two adsorption data points were acquired by FA, for caffeine, between 10(-3) and 24 g/l, a dynamic range of 24,000. Twenty-eigth adsorption data points were acquired for phenol, from 0.025 to 75 g/l, a dynamic range of 3000. The expectation-maximization procedure was used to derive the affinity energy distribution (AED) from the raw FA data points, assuming a local Langmuir isotherm. For caffeine, the AEDs converge to a bimodal and a quadrimodal distribution on XTerra MS-C18 and Resolve-C18, respectively. The values of the saturation capacity (q(s,1) approximately equal to 0.80 mol/l and q(s,2) approximately equal to 0.10 mol/l) and the adsorption constant (b1 approximately equal to 3.11/mol and b2 approximately equal to 29.1 l/mol) measured on the two columns for the lowest two energy modes 1 and 2, are comparable. These data are consistent with those previously measured on an endcapped Kromasil-C18 in a 30/70 (v/v), methanol/water solution (q(s,1) = 0.9 mol/l and q(s,2) = 0.10 mol/l, b1 = 2.4 l/mol and b2 = 16.1 l/mol). The presence of two higher energy modes on the Waters Resolve-C18 column (q(s,3) approximately equal to 0.013 mol/l and q(s,4) approximately equal to 2.6 10(-4) mol/l, b3 approximately equal to 252 l/mol and b4 = 13,200 l/mol) and the strong peak tailing of caffeine are explained by the existence of adsorption sites buried inside the C18-bonded layer. It is demonstrated that strong interactions between caffeine and the water protected bare silica surface cannot explain these high-energy sites because the retention of caffeine on an underivatized Resolve silica column is almost zero. Possible hydrogen-bond interactions between caffeine and the non-protected isolated silanol groups remaining after synthesis amidst the C18-chain network cannot explain these high energy interactions because, then, the smaller phenol molecule should exhibit similarly strong interactions with these isolated silanols on the same Resolve-C18 column and, yet, the consequences of such interactions are not observed. These sites are more consistent with the heterogeneity of the local structure of the C18-bonded layer. Regarding the adsorption of phenol, no matter whether the column is endcapped or not, its molecular interactions with the bare silica were negligible. For both columns, the best adsorption isotherm was the Bilangmuir model (with q(s,1) approximately equal to 2 and q(s,2) approximately equal to 0.67 mol/l, b1 0.61 and b2 approximately equal to 10.3 l/mol). These parameters are consistent with those measured previously on an endcapped Kromasil-C18 column under the same conditions (q(s,1) = 1.5 and q(s,2) = 0.71 mol/l, b1 = 1.4 l/mol and b2 = 11.3 l/mol). As for caffeine, the high-energy sites are definitely located within the C18-bonded layer, not on the bare surface of the adsorbent.     

Determination of single component isotherms and affinity energy distribution by chromatography

Adsorption isotherm data were acquired by frontal analysis (FA) and large sample-size band profiles were recorded for phenol and caffeine. For both compounds, the isotherm data fit well to the Langmuir, Toth, and Bi-Langmuir models of adsorption. The Langmuir model must be dismissed because it does not predict accurately the overloaded band profiles. However, profiles calculated using the unimodal Toth and the bimodal Bi-Langmuir models are indistinguishable. The expectation-maximization procedure was used to calculate directly the affinity energy distribution (AED) from the raw FA data points. For both compounds, the AED converges to a bimodal distribution at high numbers of iterations. This result, which shows the high sensitivity of the EM method, suggest that the Bi-Langmuir model makes better physical sense than the Toth model. This model also permits a detailed investigation of the properties of active sites, a feature often evoked in chromatography but so far rarely the topic of a quantitative investigation.     

Systematic errors in the measurement of adsorption isotherms by frontal analysis Impact of the choice of column hold-up volume, range and density of the data points

Besides the accuracy and the precision of the measurements of the data points, several important parameters affect the accuracy of the adsorption isotherms that are derived from the data acquired by frontal analysis (FA). The influence of these parameters is discussed. First, the effects of the width of the concentration range within which the adsorption data are measured and of the distribution of the data points in this range are investigated. Systematic elimination of parts of the data points before the calculation of the nonlinear regression of the data to the model illustrates the importance of the numbers of data points (1) within the linear range and (2) at high concentrations. The influence of the inaccuracy of the estimate of the column hold-up volume on each adsorption data point, on the selection of the isotherm model, and on the best estimates of the adsorption isotherm parameters is also stressed. Depending on the method used to measure it, the hold-up time can vary by more than 10%. The high concentration part of the adsorption isotherm is particularly sensitive to errors made on t(0,exp) and as a result, when the isotherm follows bi-Langmuir isotherm behavior, the equilibrium constant of the low-energy sites may change by a factor 2. This study shows that the agreement between calculated and experimental overloaded band profiles is a necessary condition to validate the choice of an adsorption model and the calculation of its numerical parameters but that this condition is not sufficient.     

Characterization of an unusual adsorption behavior of racemic methyl-mandelate on a tris-(3,5-dimethylphenyl) carbamoyl cellulose chiral stationary phase

An interesting adsorption behavior of racemic methyl mandelate on a tris-(3,5-dimethylphenyl)carbamoyl cellulose chiral stationary phase was theoretically and experimentally investigated. The overloaded band of the more retained enantiomer had a peculiar shape indicating a type V adsorption isotherm whereas the overloaded band of the less retained enantiomer had a normal shape indicating a type I adsorption behavior. For a closer characterization of this separation, adsorption isotherms were determined and analyzed using an approach were Scatchard plots and adsorption energy distribution (AED) calculations are combined for a deeper analysis. It was found that the less retained enantiomer was best described by a Tóth adsorption isotherm while the second one was best described with a bi-Moreau adsorption isotherm. The latter model comprises non-ideal adsorbate-adsorbate interactions, providing an explanation to the non-ideal adsorption of the more retained enantiomer. Furthermore, the possibility of using the Moreau model as a local model for adsorption in AED calculations was evaluated using synthetically generated raw adsorption slope data. It was found that the AED accurately could predict the number of adsorption sites for the generated data. The adsorption behavior of both enantiomers was also studied at several different temperatures and found to be exothermic; i.e. the adsorbate-adsorbate interaction strength decreases with increasing temperature. Stochastic analysis of the adsorption process revealed that the average amount of adsorption/desorption events increases and the sojourn time decreases with increasing temperature.     

Effect of the pH, the concentration and the nature of the buffer on the adsorption mechanism of an ionic compound in reversed-phase liquid chromatography. II. Analytical and overloaded band profiles on Symmetry-C18 and Xterra-C18

In a previous report, the influence of the pH, the concentration, and the nature of the buffer on the retention and overloading behavior of propranolol (pKa = 9.45) was studied on Kromasil-C18 at 2.75 < pH < 6.75, using four buffers (phosphate, acetate, phthalate, and succinate), at three concentrations, 6, 20, and 60 mM. The results showed that the propranolol cation was eluted as an ion-pair with the buffer counter-anion. A similar study was carried out with Symmetry-C18 and Xterra-C18. Two additional buffers, formate and citrate, were also used. Propranolol elution band profiles were recorded for a small (less than 1 microg) and a large (375 microg) sample size. The results are similar to those obtained with Kromasil and confirm earlier conclusions. The buffer concentration, not its pH, controls the retention time of propranolol, in agreement with the chaotropic model. The retention factor depends also on the nature of the buffer, particularly on its valence, and on the hydrophobicity of the basic anion. With the monovalent anions HCOO- (pH 3.75), H2PO4- (pH 2.75), HOOC-Ph-COO- (pH 2.75), HOOC-CH2-CH2-COO- (pH 4.16), CH3COO- (pH 4.75) and HOOC-CHCOOH-COO- (pH 3.14), at moderate loadings, and for the two larger buffer concentrations, the band profiles are well accounted for by a simple bi-Langmuir isotherm model (no adsorbate-adsorbate interactions). By contrast, these profiles are accounted for by a bi-Moreau isotherm model (i.e., with significant adsorbate-adsorbate interactions) with the bivalent anions -OOC-Ph-COO- (pH 4.75), -OOC-CH2-CH2-COO- (pH 5.61), HPO4(2-) (pH 6.75), and HOOC-CHCOO(-)-COO- (pH 4.77) and with the trivalent anion -OOC-CHCOO(-)-COO- (pH 6.39). The best values of the isotherm parameters were determined using the inverse method. The saturation capacity and the equilibrium constant on the low-energy sites increase with increasing buffer concentration, a result consistent with the formation in the mobile phase of a hydrophobic complex between the propranolol cation and the buffer anion. With bivalent and trivalent anions, adsorbate-adsorbate interactions are strong on the low-energy sites but they remain negligible on the high-energy sites. The density of the high energy sites is lower and the equilibrium constant on the low-energy sites are both higher with the bivalent and the trivalent buffer anions than with the univalent buffer anions. These results are consistent with the formation of a 2:1 and a 3:1 propranolol-buffer complex with the bivalent and the trivalent anions, respectively.