Characterization of C18-bonded liquid chromatographic stationary phases by Raman spectroscopy: the effect of temperature

This study represents the first time that both the mobile phase composition and the temperature are simultaneously controlled to examine silica-bonded octadecylsilyl (C18) ligands spectroscopically at typical liquid chromatographic (LC) mobile phase flow-rates and back-pressures. Raman spectroscopy is used to characterize the behavior of the C18 bonded ligands equilibrated at temperatures from 45 to 2 degrees C in neat, single-component, mobile phase solvents including: water, acetonitrile, methanol, and chloroform. In addition, the effect of stationary phase ligand bonding density is examined by using two different monomeric reversed-phase liquid chromatographic (RPLC) stationary phases, a 2.34 and a 3.52 micromol m(-2) Microporasil C18 stationary phase, under identical conditions. The direct, on-column, spectroscopic analysis used in this study allows direct evaluation of the temperature-dependent behavior of the bonded C18 ligands. The temperature-dependent ordering of the stationary phase ligands is examined to determine if the ligands undergo a phase transition from a less-ordered "liquid-like" state at higher temperatures to a more-ordered "solid-like" state at lower temperatures. A discrete phase transition was not observed, but rather a continual ordering as temperature was lowered.     

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.     

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.     

Influence of synthetic routes on the conformational order and mobility of C18 and C30 stationary phases

Silica gels modified with n-alkyl chains (n = 18, 30) are prepared by two different synthetic routes and are examined by variable temperature FTIR and solid-state NMR spectroscopy. HPLC measurements of SRM 869, cis/trans ss-carotene isomers and xanthophylls isomers confirm the dependence of the separation mechanism on the alkyl chain length and the synthetic routes. The determination of the silane functionality and degree of cross-linking of silane ligands on the silica surface is achieved by 29Si CP/MAS NMR measurements. The structural order and mobility of the alkyl chains are investigated by means of variable temperature 13C CP/MAS NMR measurements. Variable temperature FTIR studies are performed where conformational order and flexibility of the alkyl chains in C18 and C30 phases are monitored through conformational sensitive CH2 symmetric, anti-symmetric stretching and wagging modes. In addition, the chromatographic properties of the C18 and C30 phases are determined. The results derived from the FTIR, NMR and HPLC measurements are discussed in the context of the applied synthetic routes and alkyl chain lengths.     

Evaluating the surface charge of C18 stationary phases

The surface charge of four C18 stationary phases was investigated by measuring the flow induced streaming potential, a well known electrokinetic property of charged surfaces. Three of the stationary phases (Symmetry, Gemini, and Xterra-MS) had significantly positive streaming potentials at both pH 3 and 4.5. The fourth (Zorbax-SB) appeared to be essentially neutral at pH 3 and became negative at pH 4.5. Apparent zeta potentials ranged from approximately +16 to -4 mV. The retention behavior was also investigated using chloride as model anion and glycinamide (in its protonated form) as model cation. When the retention factor (k) of glycinamide was subtracted from k of chloride anion, the resulting delta k values showed very similar trends as apparent zeta potential values, suggesting that the simple chromatographic method could be used to estimate zeta potential values, or that the zeta potential values could be useful for ranking columns according to ion exchange or exclusion behavior. The anion exchange capacity of the Symmetry and Gemini columns was also estimated, using a published chromatographic procedure, and the results suggest about 2 microEq. capacity per gram of packing.     

A chromatographic estimate of the degree of surface heterogeneity of reversed-phase liquid chromatography packing materials. II-Endcapped monomeric C18-bonded stationary phase

In a previous report, the heterogeneity of a non-endcapped C30-bonded stationary phase was investigated, based on the results of the measurements of the adsorption isotherms of two neutral compounds (phenol and caffeine) and two ionizable compounds (sodium naphthalene sulfonate and propranololium chloride) by frontal analysis (FA). The same method is applied here for the characterization of the surface heterogeneity of two new brands of endcapped C18-bonded stationary phases (Gemini and Sunfire). The adsorption isotherms of the same four chemicals were measured by FA and the results confirmed by the independent calculation of the adsorption energy distribution (AED), using the expectation-maximization (EM) method. The effect of the length of the bonded alkyl chain was investigated. Shorter alkyl-bonded-chains (C18 versus C30) and the end-capping of the silica surface contribute to decrease the surface heterogeneity under the same experimental conditions (30% methanol, 25 mM NaCl). The AEDs of phenol and caffeine are bimodal with the C18-bonded columns while they are trimodal and quadrimodal, respectively, with a non-endcapped C30-bonded column. The "supersites" (adsorption energy > 20 kJ/mol) found on the C30-Prontosil column and attributed to a cation exchange mechanism completely disappear on the C18-Gemini and C18-Sunfire, probably because the end-capping of the silica surface eliminates most if not all the ionic interactions.     

Influence of surface carbon coverage of C1 (TMS) stationary phases on the separation of nonylphenol ethoxylate ethoxymers

The determination of surfactants in surface waters is required owing to their toxicity to aquatic micro-organisms and potential as endocrine disrupters. We have previously reported a method for the simultaneous separation of linear alkyl benzene sulfonates (LAS) and nonylphenol ethoxylates (NPEO) by high-performance liquid chromatography using a C1 (TMS) column. In this earlier work we discussed some problems with the resolution of individual ethoxymers from NPEO using C1 columns from different manufacturers. Here, we postulate that this phenomenon may be linked to carbon coverage of the C1 (TMS) stationary phases and study this utilising both elemental (bulk) analyses and surface specific analyses by X-ray photoelectron spectroscopy. Data obtained indicate that for the simultaneous separation of the LAS homologues and ethoxymers of NPEO, the stationary phase must have some trimethylsilyl groups bound to the surface of the silica in order to achieve separation of the LAS homologues, however the degree of surface coverage must not be greater than ca. 0.5 micromol/m2 in order to achieve adequate resolution of the NPEO ethoxymers. These data support earlier evidence for a "pseudo" reversed-phase mechanism for this separation.     

Retention behavior of resorcinarene‐based cavitands on C8 and C18 stationary phases

The understanding of the retention behavior of large molecules is an area of interest in liquid chromatography. Resorcinarene‐based cavitands are cavity‐shaped cyclic oligomers that can create host–guest interactions. We have investigated the chromatographic behavior of two types of cyclic tetramers as analytes in high‐performance liquid chromatography. The experiments were performed at four different temperatures (15, 25, 35, 45°C) on two types of reversed stationary phases (C₈ and C₁₈) from two different manufacturers. We have found a huge difference between the retention of resorcinarenes and cavitands. In some cases, the retention factor of cavitands was even a hundred times larger than the retention factor of resorcinarenes. The retention of methylated derivates was two to four times larger compared to that of demethylated compounds on every column. The opposite retention behavior of the resorcinarenes and cavitands on the two types of stationary phases showed well the difference of the selectivity of the XTerra and BDS Hypersil columns. The retention mechanism was studied by the thermodynamic parameters calculated from the van't Hoff equation.     

Separation of 9,10-anthraquinone derivatives: evaluation of C18 stationary phases

Chromatographic study of natural products helps to determine their molecular composition and to identify their sources (biological, geographical, etc.). However, identifying anthraquinoids is still a challenge because this chemical family is composed of more than half a thousand molecules. In the present work, a series of C18 stationary phases were systematically studied to evaluate their separation potential for these compounds in high performance reversed phase liquid chromatography (RPLC). The stationary phases with various physicochemical properties were evaluated with respect to the separation of 30 standards. Selectivity of the studied stationary phases and symmetry of the obtained peaks were chosen as the evaluation criteria. Calculations of symmetry and separation capacity parameters have been proposed. These parameters are not dependent on the dimensions of the columns and were used for the classifications of phases. In conclusion, this study is intended to be a guide as to which stationary phases analysts can use for resolving separation of a complex mixture of anthraquinoids.     

Adsorption mechanism in reversed-phase liquid chromatography. Effect of the surface coverage of a monomeric C18-silica stationary phase

The effect of the bonding density of the octadecyl chains onto the same silica on the adsorption and retention properties of low molecular weight compounds (phenol, caffeine, and sodium 2-naphthalene sulfonate) was investigated. The same mobile phase (methanol:water, 20:80, v/v) and temperature (T = 298 K) were applied and two duplicate columns (A and B) from each batch of packing material (neat silica, simply endcapped or C1 phase, 0.42, 1.01, 2.03, and 3.15 micromol/m2 of C18 alkyl chains) were tested. Adsorption data of the three compounds were acquired by frontal analysis (FA) and the adsorption energy distributions (AEDs) were calculated using the expectation-maximization method. Results confirmed earlier findings in linear chromatography of a retention maximum at an intermediate bonding density. From a general point of view, the saturation capacity of the adsorbent tends to decrease with increasing bonding density, due to the vanishing space intercalated between the C18 bonded chains and to the decrease of the specific surface area of the stationary phase. The equilibrium constants are maximum for an intermediary bonding density (approximately 2 micromol/m2). An enthalpy-entropy compensation was found for the thermodynamic parameters of the isotherm data. Weak equilibrium constants (small deltaH) and high saturation capacities (large deltaS) were observed at low bonding densities, higher equilibrium constants and lower saturation capacities at high bonding densities, the combinations leading to similar apparent retention in RPLC. The use of a low surface coverage column is recommended for preparative purposes.     

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.     

Study of the thermodynamics and mass transfer kinetics of two enantiomers on a polymeric imprinted stationary phase

The adsorption isotherms of

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- and

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-phenylalanine anilide (PA) on an

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-phenylalanine anilide imprinted stationary phase have been determined using staircase frontal analysis. An aqueous buffer–organic solvent mixture has been used as mobile phase. The measurements were done at temperatures of 40, 50, 60 and 70°C for sample concentrations ranging between 5·10⁻⁴ to 1 g/l. It was found that the adsorption data fit well to both the Freundlich and the Bi-Langmuir isotherm models. Examination of the best values of the numerical coefficients of the Bi-Langmuir model shows that the site class representing the binding sites with the highest binding energy exhibits a very low saturation capacity for the non-imprinted enantiomer, indicating a high selectivity for the imprinted

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-enantiomer. The low energy site class also shows some selectivity for the

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-enantiomer. Mass transfer rate coefficients were obtained for each single breakthrough curve by using the transport model of chromatography. It was found that the mass transfer coefficient of

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-PA increases very rapidly with the sample concentration while there is only a slight increase for the other enantiomer.     

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.     

Comparison of the mass transfer in totally porous and superficially porous stationary phases in liquid chromatography

The characterization of mass-transfer processes in a chromatographic column during a separation process is essential, since the influence of the mass-transfer kinetics on the shape of the chromatographic band profiles and on the efficiency of the separation is crucial. Several sources of mass transfer in a chromatographic bed have been identified and studied: the axial dispersion in the stream of mobile phase, the external mass-transfer resistance, intraparticle diffusion, and the kinetics of adsorption–desorption. We measured and compared the characteristics and performance of a new brand of shell particles and those of a conventional brand of totally porous silica particles. The shell stationary phase was made of 2.7-μm superficially porous particles (a 1.7-μm solid core is covered with a 0.5-μm-thick shell of porous silica). The other material consisted of totally porous particles of conventional 3.5-μm commercial silica. We measured the first and second central moments of the peaks of human insulin over a wide range of mobile phase velocities (from 0.02 to 1.3 mL/min) at 20°C. The plate height equations were constructed and the axial dispersion, external mass transfer, as well as the intraparticle diffusion coefficients were calculated for the two stationary phases.     

A study of mass transfer kinetics of alanyl-alanine on a chiral crown ether stationary phase

The mass transfer kinetics of alanyl-alanine enantiomers in a column packed with a chiral stationary phase (CSP) ChiroSil RCA(+) was studied by means of the moment method. Methanol-water solutions acidified with sulphuric acid were used as the mobile phase. It was shown that the spreading of peaks in the column was strongly affected by abnormal eddy diffusion. This effect was well described within the framework of the Giddings coupling theory. The comprehensive four-term Giddings equation for eddy diffusion was applied, considering simultaneous contribution of the trans-column, trans-channel, short-range inter-channel, and long-range inter-channel dispersion factors. Through these calculations, a predominant importance of the trans-column flow velocity bias was revealed. Besides eddy diffusion, the adsorption kinetic resistance to mass transfer plays a noticeable role in band broadening, all the other contributions (from longitudinal molecular diffusion, external and intraparticle mass transfer) being of minor significance. A relative importance of the mass transfer kinetics increases correlatively with a growth of the retention factor. Both the retention and kinetics of the adsorption of alanyl-alanine on the CSP in study are enantioselective. The influence of the column pressure on retention as well as corrections required because of this influence are also discussed.     

Two dimensional reversed-phase-reversed-phase separations isomeric separations incorporating C18 and carbon clad zirconia stationary phases

Informational theory and a geometric approach to factor analysis were employed to evaluate the degree of orthogonality of a two-dimensional reversed-phase-reversed-phase chromatographic system. The system incorporated a C18 column as one dimension and a carbon clad zirconia column as the second dimension. In order to study the resolving power of this system, the separation of a sample matrix containing an artificial mix of 32 isomers (structural and diastereoisomers) was evaluated. Using this system, between 25 and 28 of the 32 isomers could be separated, depending on the mobile phase combinations--with resolution that could not possibly be achieved in a single one dimensional separation. The results from this study indicate that in order to fully evaluate the resolving power of a 2D system multiple methods of analysis are most appropriate. This becomes increasingly important when the sample contains components that are very closely related and the retention of solutes is clustered in one quadrant of the 2D space. Ultimately, the usefulness of the 2D separation is determined by the goals of analyst.     

Influence of the charge distribution on the stationary phases zeta potential

A set of seven home‐made silica based bonded phases with different functional groups was investigated. Their zeta potential data in methanol and acetonitrile as well as in methanol/water and acetonitrile/water solution were obtained by using a Zetasizer. The influence of polar functional groups on a zeta potential was investigated. The results show that the amines incorporated in the structure of chemically bonded phases of reversed‐phase materials are protonated during chromatographic analysis, resulting in changes of the zeta potential from negative to positive values. Acetonitrile causes more negative values and methanol provides positive (or less negative) values of the zeta potential.     

Surface diffusion in reversed-phase liquid chromatography using silica gel stationary phases of different C1 and C18 ligand densities

Surface diffusion phenomena were studied from kinetic and thermodynamic points of view. The existence of a linear free energy relationship between surface diffusion and the retention equilibrium suggests that the mechanism of surface diffusion is the same irrespective of the density of C(1) and C(18) ligands. Surface diffusion coefficient (D(s)) of weakly retained compounds seems to be of the same order of magnitude with corresponding molecular diffusivity. There would be an intimate correlation between surface diffusion and molecular diffusion. The value of D(s) decreases with increasing retention strength. The magnitude of the restriction for surface diffusion is comparable to about one third the enthalpy change due to the sample retention. This means that it is necessary for sample molecules adsorbed to be partially desorbed from the stationary phase surface when they migrate by surface diffusion. The results of this study provide the fundamental information for developing an appropriate model of surface diffusion, which explains some intrinsic characteristics and mechanism of surface diffusion.     

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.     

A kinetic parameter concerning mass transfer in silica monolithic and particulate stationary phases measured by the peak-parking and slow-elution methods

Mass transfer in monolithic C18-silica stationary phases and C18-silica gel particles was studied. A traditional kinetic parameter, gamma(s)D(s), which is a diffusion coefficient of solute molecules in the stationary phase, was measured by two unusual approaches, i.e., peak-parking and slow-elution methods. The correlation between the ratio of gamma(s)D(s) to molecular diffusivity (Dm) and the retention factor (k) was represented by one common curve, irrespective of the RPLC conditions. A similar curved profile was also observed between another kinetic parameter (D(Ls)), which is related to the axial diffusive molecular migration in the stationary phase, and the retention equilibrium constant (Ka). The values of D(Ls) and Ka were calculated from those of gamma(s)D(s) and k, respectively. The ratio of D(Ls)/Dm increases with decreasing Ka and seems to approach around unity when Ka is infinitely small. The dependence of D(Ls) on Ka was also studied from extra-thermodynamic points of view. The linear correlation between In D(Ls) and In Ka suggests the existence of a kind of linear free energy relationship between the mass transfer in the stationary phase and the retention equilibrium. Because these characteristics of D(Ls) are similar to those of the surface diffusion coefficient (D(sur)), D(Ls) seems to correspond to D(sur).