Study of the mass transfer kinetics in a monolithic column

The purpose of this work is to investigate the mass transfer kinetics of butylbenzoate on a monolithic RPLC column, with methanol-water (65:35, v/v) as the mobile phase. We used the perturbation method, measuring the height equivalent to a theoretical plate (HETP) of the peaks obtained as the response to small pulses of solute injected on a concentration plateau. The equilibrium isotherm of butylbenzoate was previously determined by frontal analysis. It is well accounted for by a liquid-solid extended multilayer BET isotherm model. The equilibrium data derived from the pulse method are in excellent agreement with those of frontal analysis in the accessible concentration range of 0 to 8 g/dm3. Plots of the HETP of small pulses. injected on eight different plateau concentrations, were acquired in a wide range of mobile phase flow velocities. The axial dispersion and the mass transfer kinetic coefficients were derived from these data. The validity of these measurements is discussed. The mass kinetics of butylbenzoate depends strongly on the plateau concentration. Processes involving adsorptive interactions between the solute and the stationary phase, e.g. surface diffusion and adsorption-desorption kinetics, combine in series to the external mass transfer kinetics and to effective pore diffusivity.     

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

The influence of the salt concentration (potassium chloride) on the retention and overloading behavior of the propranolol cation (R'-NH2+ -R) on an XTerra-C18 column, in a methanol:water solution, was investigated. The adsorption isotherm data were first determined by frontal analysis (FA) for a mobile phase without salt (25% methanol, v/v). It was shown that the adsorption energy distribution calculated from these raw adsorption data is bimodal and that the isotherm model that best accounts for these data is the bi-Moreau model. Assuming that the addition of a salt into the mobile phase changes the numerical values of the parameters of the isotherm model, not its mathematical form, we used the inverse method (IM) of chromatography to determine the isotherm with seven salt concentrations in the mobile phase (40% methanol, v/v; 0, 0.002, 0.005, 0.01, 0.05, 0.1 and 0.2 M). The saturation capacities of the model increase, q(s,1) by a factor two and q(s,2) by a factor four, with increasing salt concentration in the range studied while the adsorption constant b1 increases four times and b2 decreases four times. Adsorbate-adsorbate interactions vanish in the presence of salt, consistent with results obtained previously on a C18-Kromasil column. Finally, besides the ionic strength of the solution, the size, valence, and nature of the salt ions affect the thermodynamic as well as the mass transfer kinetics of the adsorption mechanism of propranolol on the XTerra column.     

Adsorption behavior and prediction of the band profiles of the enantiomers of 3-chloro-1-phenyl-1-propanol. Influence of the mass transfer kinetics

The single-component and competitive adsorption isotherms of the enantiomers of 3-chloro-1-phenyl-1-propanol were measured by frontal analysis. The stationary phase was a cellulose tribenzoate coated on silica, the mobile phase an n-hexane-ethyl acetate (95:5) solution. The adsorption data measured fitted well to the Langmuir isotherm model. The band profiles of single components and of their mixtures were calculated using the equilibrium-dispersive model. These profiles were found to match quite satisfactorily the experimental band profiles. However, the agreement between calculated and experimental band profiles was significantly improved when a more complex model taking into account the mass transfer kinetics was used. The mass transfer rate coefficients, k(f), for both single components were determined by using the transport-dispersive model of chromatography. The coefficients obtained were used to predict the band profiles of mixtures of the two enantiomers to good agreement.     

Adsorption-desorption isotherm hysteresis of phenol on a C18-bonded surface

Single component adsorption and desorption isotherms of phenol were measured on a high-efficiency Kromasil-C18 column (N = 15000 theoretical plates) with pure water as the mobile phase. Adsorption isotherm data were acquired by frontal analysis (FA) for seven plateau concentrations distributed over the whole accessible range of phenol concentration in pure water (5, 10, 15, 20, 25, 40, and 60 g/l). Desorption isotherm data were derived from the corresponding rear boundaries, using frontal analysis by characteristic points (FACP). A strong adsorption hysteresis was observed. The adsorption of phenol is apparently modeled by a S-shaped isotherm of the first kind while the desorption isotherm is described by a convex upward isotherm. The adsorption breakthrough curves could not be modeled correctly using the adsorption isotherm because of a strong dependence of the accessible free column volume on the phenol concentration in the mobile phase. It seems that retention in water depends on the extent to which the surface is wetted by the mobile phase, extent which is a function of the phenol concentration, and of the local pressure rate, which varies along the column, and on the initial state of the column. By contrast, the desorption profiles agree well with those calculated with the desorption isotherms using the ideal model, due to the high column efficiency. The isotherm model accounting best for the desorption isotherm data and the desorption profiles is the bi-Langmuir model. Its coefficients were calculated using appropriate weights in the fitting procedure. The evolution of the bi-Langmuir isotherm parameters with the initial equilibrium plateau concentration of phenol is discussed. The FACP results reported here are fully consistent with the adsorption data of phenol previously reported and measured by FA with various aqueous solutions of methanol as the mobile phase. They provide a general, empirical adsorption model of phenol that is valid between 0 and 65% of methanol in water.     

Effect of the ionic strength of the solution and the nature of its ions on the adsorption mechanism of ionic species in RPLC III. Equilibrium isotherms and overloaded band profiles on Kromasil-C18

In two companion papers, we have described the influence of the concentration and the nature of completely dissociated 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 and on Symmetry-C18. The same experiments were repeated on a Kromasil-C18 column to compare the adsorption behavior of this ionic compound on these three different RPLC systems. The adsorption data of propranolol hydrochloride were first measured by frontal analysis (FA) using a mobile phase without salt. These data fit best to the Bi-Moreau model. Large concentration band profiles of propranolol were recorded with mobile phases containing 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 using the numerical solution of the inverse problem of chromatography. The general effect of a dissociated salt in the mobile phase was the same as the one observed earlier with XTerra-C18 and Symmetry-C18. However, obvious differences were observed for the shape of the band profiles recorded at low column loading (1.5 g/L, 250 microL injected). A long shoulder is visible at all salt concentrations and the band broadening is maximum at low salt concentrations. A slow mass transfer kinetics on the high-energy sites of the bi-Moreau model might explain this original shape. Five other salts (NaCl, CsCl, KNO3, CaCl2 and Na2SO4) were also used at the same ionic strength (J = 0.2 M). As many different band profiles were observed, suggesting that specific solute-salt interactions take place in the adsorbed phase.     

Comparison of the adsorption equilibrium of a few low-molecular mass compounds on a monolithic and a packed column in reversed-phase liquid chromatography

Adsorption isotherm data were acquired by frontal analysis for several low-molecular mass compounds (3-phenyl 1-propanol, 4-tert.-butylphenol, butylbenzene, and butyl benzoate) on a classical packed column and a monolithic column using methanol-water RP-HPLC conditions. These columns have similar characteristics (C18-bonded silica, close specific surface areas and bonding densities). In each case, the isotherm model best accounting for the data was the same on both columns. The solute polarity determines the class of this model. For the two -OH compounds it was a Langmuirian adsorption isotherm. The hydrocarbon data were best modeled by an anti-Langmuir convex-downward isotherm model. The adsorption data for the aromatic ester exhibited a nearly linear behavior, depending on the methanol concentration of the mobile phase. A slightly convex downward isotherm was obtained at high methanol concentrations while the best fitting was obtained with a liquid-solid extended multilayer B.E.T. isotherm model at low concentrations. The validation of these models is discussed in detail. In all cases, similar values of the adsorption-desorption constants were found, underlining the closeness of the adsorption energies on both columns. By contrast, the adsorption capacity of the monolithic column was found to be approximately 1.4 greater than that of the packed column in spite of the close values of the surface areas of the silica in both columns.     

Modeling of overloaded gradient elution of nociceptin/orphanin FQ in reversed-phase liquid chromatography

The Reversed-phase (RP) gradient elution chromatography of nociceptin/orphanin FQ (N/OFQ), a neuropeptide with many biological effects, has been modeled under linear and non-linear conditions. In order to do this, the chromatographic behavior has been studied under both linear and nonliner conditions under isocratic mode at different mobile phase compositions--ranging from 16 to 19% (v/v) acetonitrile (ACN) in aqueous trifluoracetic acid (TFA) 0.1% (v/v)-on a C-8 column. Although the range of mobile phase compositions investigated was quite narrow, the retention factor of this relatively small polypeptide (N/OFQ is a heptadecapeptide) has been found to change by more than 400%. In these conditions, gradient operation resulted thus to be the optimum approach for non-linear elution. As the available amount of N/OFQ was extremely reduced (only a few milligrams), the adsorption isotherms of the peptide, at the different mobile phase compositions examined, have been measured through the so-called inverse method (IM) on a 5 cm long column. The adsorption data at different mobile phase compositions have been fitted to several models of adsorption. The dependence of the isotherm parameters on the mobile phase composition was modeled by using the linear solvent strength (LSS) model and a generalized Langmuir isotherm that includes the mobile phase composition dependence. The overloaded gradient separation of N/OFQ has been modeled by numerically solving the equilibrium-dispersive (ED) model of chromatography under a selected gradient elution mode, on the basis of the previously determined generalized Langmuir isotherm. The agreement between theoretical calculations and experimental overloaded band profiles appeared reasonably accurate.     

Reproducibility of low and high concentration data in reversed-phase liquid chromatography. II. Overloaded band profiles on Chromolith-C18

Single-component adsorption isotherm data were acquired by frontal analysis (FA) for six low molecular weight compounds (phenol, aniline, caffeine, o-toluidine, p-toluidine and propylbenzoate) on one Chromolith-C18 column (#30, Merck, Darmstadt, Germany), using different methanol:water solutions (composition between 60/40 and 15/85 v/v, depending on the solute) as the mobile phase. These data were modeled for best agreement between the experimental data points and the adsorption isotherm model. The adsorption-energy distributions were also derived and used for the selection of the best isotherm model. Widely different models were obtained for these six compounds, four being convex upward (i.e., Langmuirian) and two having at least one inflection point. Overloaded band profiles corresponding to two different sample sizes (a low and a high loading factor) were recorded on six monolithic columns (#30-35) belonging to the same manufactured lot. These experimental band profiles were compared to the profiles calculated from the isotherm measured by FA on the first column, using the equilibrium-dispersive (ED) model of chromatography. For four of the six columns (#30, #32, #33, and #35), the reproducibility was better than 5 and 2.5% for the low and the high concentration profiles, respectively. On the other two columns (#31 and #34), the bands showed significant and systematic retention time shifts for all six compounds (with nearly identical band shapes), the relative adsorption being between 6 and 15% stronger on column #31 or between 2 and 7% lower on column #34. These differences seem to be correlated with the differences in the total porosities of these columns, which differ by 3% from columns #31 to #34, the higher porosity column giving the stronger adsorption.     

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.     

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.     

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.     

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.     

Application of the general rate model and the generalized Maxwell-Stefan equation to the study of the mass transfer kinetics of a pair of enantiomers

The general rate model of chromatography can be coupled with the generalized Maxwell-Stefan equation that describes the surface diffusion flux. The resulting model is useful to describe the behavior of two enantiomers during their separation on chiral phases, cases in which the mass transfer kinetics is known to be sluggish. A case in point is the modeling of the elution profiles of the racemic mixture of the two enantiomers of 1-phenyl-1-propanol on cellulose tribenzoate coated on silica, a popular chiral stationary phase. The competitive equilibrium isotherm behavior of the two enantiomers on the chiral stationary phase was described using the competitive Tóth isotherm model. An excellent agreement between the experimental and the calculated profiles was observed in the whole range of experimental conditions investigated, at low and high column loadings.     

Influence of microwave irradiation on the intraparticle diffusion of an insulin variant in reversed-phase liquid chromatography under linear conditions

The influence of microwave irradiation on the mass transfer kinetics of an insulin variant in reversed-phase liquid chromatography (RPLC) was investigated. The elution band profiles of insulin were obtained by the pulse-response method, under linear conditions. The RPLC column was placed in a microwave oven and the incremental change in the temperature of the column effluent stream at various microwave energies and mobile phase flow rates were measured. The microwave energy dissipated in the column was set at 15 and 30 W and the mobile phase flow rate was varied from 1.0 to 2.5 mL/min at a mobile phase composition of acetonitrile, water, and trifloroacetic acid (31:69:0.1, v/v/v). The experimental data were analyzed using the conventional method of moment analysis and the lumped pore diffusion model. Regardless of mobile flow rates, the effluent temperatures measured at 15 and 30 W microwave power input were 25+/-1 and 30+/-1 degrees C, respectively. The effect of microwave irradiation on the mass transfer of the variant insulin was determined by comparing the band profiles obtained under the same experimental conditions, at the same column temperature, with and without irradiation. The calculated intraparticle diffusion coefficient, D(e), at 30 W (30+/-1 degrees C) microwave irradiation was ca. 20% higher than without irradiation at 30+/-1 degrees C. These preliminary results suggest that microwave irradiation may have a significant influence on the intraparticle diffusion of insulin in RPLC.     

Numerical determination of competitive adsorption isotherm of mandelic acid enantiomers on cellulose-based chiral stationary phase

The use of inverse method for the determination of competitive adsorption isotherm of mandelic acid enantiomers on cellulose tris(3,5-diethylphenyl carbamate) stationary phase is proposed in this work. Non-dominated sorting genetic algorithm with jumping genes (NSGA-II-JG) was applied to acquire the isotherm parameters by minimizing the sum of square deviations of the model predictions from the measured elution profiles. Three different competitive isotherm models, i.e., Langmuir, biLangmuir and Tóth, combined with transport-dispersive chromatographic model were used in predicting the elution profiles. Orthogonal collocation on finite element (OCFE) method was applied to obtain the calculated elution profiles. Results indicate that biLangmuir isotherm and Tóth isotherm give remarkably similar equilibrium isotherms within the investigated liquid concentration range. Band profiles calculated from both isotherm models are in good agreement with the experimental data. The validity of the determined parameters was verified by comparing the model predictions with experimental elution profiles at various experimental conditions.     

Repeatability and reproducibility of high concentration data in reversed-phase liquid chromatography. I. Overloaded band profiles on Kromasil-C18

Single-component adsorption-isotherm data were acquired by frontal analysis (FA) for six low-molecular-mass compounds (phenol, aniline, caffeine, theophylline, ethylbenzene and propranolol) on one Kromasil-C18 column, using water-methanol solutions (between 70:30 and 20:80, v/v) as the mobile phase. Propranolol data were also acquired using an acetate buffer (0.2 M) instead of water. The data were modeled for best agreement between calculated and experimental overloaded band profiles. The adsorption energy distribution was also derived and used for the selection of the best isotherm model. Widely different isotherm models were found to model best the data obtained for these compounds, convex upward (i.e. Langmuirian), convex downward (i.e. anti-Langmuirian), and S-shaped isotherms. Using the same sample size for all columns (loading factor, Lf approximately 10%), overloaded band profiles were recorded on four different columns packed with the same batch of Kromasil-C18 and five other columns packed with different batches of Kromasil-C18. These experimental band profiles were compared to the profile calculated from the isotherm measured by FA on the first column. The repeatability as well as the column-to-column and the batch-to-batch reproducibilities of the band profiles are better than 4%.     

New thermodynamically consistent competitive adsorption isotherm in RPLC

A new equation of competitive isotherms was derived in the framework of the ideal adsorbed solution (IAS) that predicts multisolute adsorption isotherms from single-solute isotherms. The IAS theory makes this new isotherm thermodynamically consistent, whatever the saturation capacities of these single-component isotherms. On a Kromasil-C(18) column, with methanol-water (80/20 v/v) as the mobile phase, the best single-solute adsorption isotherm of both toluene and ethylbenzene is the liquid-solid extended multilayer BET isotherm. Despite a significant difference between the monolayer capacities of toluene (370 g/l) and ethylbenzene (170 g/l), the experimental adsorption data fit very well to single-component isotherms exhibiting the same capacities (200 g/l). The new competitive model was used for the modeling of the elution band profiles of mixtures of the two compounds. Excellent agreement between experimental and calculated profiles was observed, suggesting that the behavior of the toluene-ethylbenzene adsorbed phase on the stationary phase is close to ideal. For example, the concentrations measured for the intermediate plateau obtained in frontal analysis differ by less than 2% from those predicted by the IAS model.     

Numerical modeling of the elution peak profiles of retained solutes in supercritical fluid chromatography

In supercritical fluid chromatography (SFC), the significant expansion of the mobile phase along the column causes the formation of axial and radial gradients of temperature. Due to these gradients, the mobile phase density, its viscosity, its velocity, its diffusion coefficients, etc. are not constant throughout the column. This results in a nonuniform flow velocity distribution, itself causing a loss of column efficiency in certain cases, even at low flow rates, as they do in HPLC. At high flow rates, an important deformation of the elution profiles of the sample components may occur. The model previously used to account satisfactorily for the retention of an unsorbed solute in SFC is applied to the modeling of the elution peak profiles of retained compounds. The numerical solution of the combined heat and mass balance equations provides the temperature and the pressure profiles inside the column and values of the retention time and the band profiles of retained compounds that are in excellent agreement with independent experimental data for large value of mobile phase reduced density. At low reduced densities, the band profiles can strongly depend on the column axial distribution of porosity.     

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.     

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.