A chromatographic estimate of the degree of heterogeneity of RPLC packing materials

Journal of Chromatography A, 1103 (2006) 43–56

A chromatographic estimate of the degree of heterogeneity of RPLC packing materials 1. Non-endcapped polymeric C30-bonded stationary phase Fabrice Gritti a,b , Georges Guiochon a,b,∗ a

b

Department of Chemistry, University of Tennessee, Knoxville, TN 37996-1600, USA Division of Chemical Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6120, USA Received 3 May 2005; received in revised form 23 September 2005; accepted 3 October 2005 Available online 7 December 2005

Abstract 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. © 2005 Elsevier B.V. All rights reserved. Keywords: Column reproducibility; Monolithic column; Adsorption isotherm; Band profiles; Frontal analysis; Isotherm modeling; Affinity energy distribution; Multi-Langmuir isotherm; Phenol; Caffeine

1. Introduction Separation scientists using RPLC on a daily basis complain on the unsymmetrical shape of many band profiles. The peak tailing lowers the practical efficiency of the chromatographic column and degrades the separations achieved. In order to detect the peak of a compound at constant signal-to-noise ratio, or detection sensitivity, a larger amount of this compound must be injected on real columns than would be needed on columns

∗

Corresponding author. Fax: +1 865 974 2667. E-mail address: [email protected] (G. Guiochon).

0021-9673/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2005.10.010

packed with a perfect packing material that would give symmetrical peaks. The lack of symmetry of peaks in RPLC has long been explained by the lack of surface homogeneity of the adsorbent and, more specifically, to the presence of undesired, isolated silanol groups within the bonded alkyl layer [1,2]. These silanol groups would be particularly nefarious under pH conditions leading to their ionization. Then, the ionic surface could strongly interact with basic or cationic analytes, resulting in an excessive retention and a peak tailing that impedes their satisfactory detection. The pH range within which these residual silanols are active depends on the column, essentially on the nature of the solid support, the density of the bonded chains, and the end-capping of

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the support. Column manufacturers have attempted to seize this challenge. They now offer new chromatographic supports based on either a hybridized solid support (organic–inorganic solid) or a completely organic support, the goal being to limit as much as possible the density of residual silanols on the stationary phase. The mere presence of residual silanols may not suffice to explain completely the origin of peak tailing in chromatography [3]. Many weakly basic, acidic, and neutral compounds exhibit also a degree of band tailing [4]. The interactions between silanol groups and these compounds are too weak to explain these unsymmetrical peaks and their excessive retention. Although this may still be controversial, there are strong reasons suggesting that the origin of peak tailing in RPLC is in the heterogeneity of the structure of the alkyl-bonded phase. Solutes do not simply adsorb at the interface between the bulk mobile phase and the top of the hydrophobic layer (adsorption). This alkyl-bonded layer has a finite thickness, its density is lower than that of a liquid, and the chains have lost their degrees of freedom of translation. It can be penetrated easily be analyte molecules. The area of contact between the collapsed layer and the analyte molecules is low and the equilibrium constant is rather small (the adsorption energy is of a few kJ/mol). The analyte molecules, however, can penetrate between the chains, into regions where the area of contact with these chains is much larger. This takes place particularly where the chain density is low or the chains are disordered. Under this quasi-partition configuration, the adsorption energy may increase to 20 kJ/mol. Even a very small density of such adsorption sites might affect considerably the band because it reduces drastically the concentration range within which the isotherm is linear. In some cases, the upper limit of this range may be lower than the UV detection limit [5]. Several groups have studied the structure of the layer of alkyl chains bonded to silica surfaces, using IR [6] and Raman [7] spectroscopies, small angle neutron scattering (SANS) [8], fluorescence lifetime measurements [9] and various NMR methods [10,11]. Solid state NMR spectrometry is the most powerful tool to characterize the morphology of these layers [10]. Both the conformational structure and the dynamic aspects of the immobilized alkyl chains can be probed. Recent investigations of C30 -bonded silica packing materials have demonstrated that there are regions where the chains are in the gauche and others in the trans-conformation. Regions with gauche conformations induce a degree of disorder in the local structure of the layer while trans-conformations lead rather to locally ordered regions. NMR spectroscopy revealed spots on the surface where the bonded layer is rather rigid (trans and ordered chains) and others where it is mobile (gauche and disordered chains). This description of the structure of a C30 -bonded silica explains why the shape selectivity of this packing material for stereoisomers is higher than that of C18 -bonded silica columns [10,11]. The heterogeneity of the alkyl-bonded stationary phase has not been suspected as a major cause for peak tailing. This description of the structure of alkyl-bonded silica surfaces is consistent with the conclusions reported above and derived from the results of dynamic chromatography experiments. The results of measurements by frontal analysis of the adsorption isotherm data of low molecular weight compounds

have definitely demonstrated that it is not possible to explain the retention mechanism in RPLC by assuming the presence of a single type of adsorption sites on the surface of chemically bonded alkyl silica [12]. Rather, there are different spots on the modified-surface on which analytes are either weakly or strongly adsorbed. This was shown to be the case for all commercial C18 -bonded stationary phases studied [4]. On their surfaces were found low- and high-energy adsorption sites, the former corresponding to conventional adsorption, the latter being more analogous to partition sites. This paper reports on the results of our investigations of the heterogeneity of a non-endcapped polymeric C30 -bonded silica (Prontosil-C30 ). We chose this stationary phase because previous studies seemed to demonstrate that the retention mechanism in RPLC involved adsorption sites located deep inside the hydrophobic layer. The C30 ligands being longer than the conventional C18 ones, it is likely that the distribution of the adsorption sites will differ. This study aimed at characterizing the C30 -bonded phase in the same way as the C18 phases were [4], using the adsorption isotherms of a few probe compounds. Furthermore, this polymeric C30 column used was not endcapped. Despite the high density of the chains bonded to the surface that is expected with polymeric phases, it will be possible to check whether some analyte molecules may penetrate deep in the C30 layer and strongly interact with the bare silica surface, by measuring the adsorption data of ionizable compounds. We used the same chromatographic methods as in our previous studies of the homogeneity of C18 -bonded silica materials [4]. We measured the adsorption isotherms of four different compounds that will sense the surface heterogeneity, two neutral compounds (phenol and caffeine) and two ionizable compounds (1-naphthalene sulfonate and propranololium), which have also different molecular sizes. The smallest molecules (phenol) are expected to access the largest part of the surface of the bonded material. Larger molecules are expected to be excluded from certain regions of the surface and to have access to a lower fraction of the surface area. Thus, the comparison of the values of the saturation capacity derived from the isotherm modeling should bring useful information. The comparison between the adsorption properties of two ions of opposite charges should inform on possible ion-exchange interactions with the surface, especially for this non-endcapped material. The treatment of the adsorption data with the expectation-maximization program [13] will afford the adsorption energy distribution of these compounds on the surface. The results derived from the chromatographic data will be combined with previous findings based on NMR measurements made on the same C30 -bonded silica surfaces, allowing more precise conclusions. 2. Theory 2.1. Determination of single-component isotherm data by frontal analysis and its limits The accurate measurement of the adsorption data of chemicals can be performed conveniently by frontal analysis (FA), provided that they are not too toxic nor too expensive, this condition

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is met by all the compounds used in this study, phenol, caffeine, sodium 2-naphthalene sulfonate, and propranololium chloride. Accordingly, numerous successive breakthrough curves could be recorded. The experimental details of the methodology, the mass balance equations regarding the FA method, and the procedure of derivation of the adsorption isotherm data are given elsewhere [12]. The practical limits of the concentration range within which FA data can be acquired are clear. At high concentrations, it is set by the solubility of the compound studied in the mobile phase. In practice, it is cautious not to exceed about 90% of this concentration, to avoid the risk of occlusion of some pipes. At low concentrations, other difficulties appear. The elution times of the breakthrough curves of very low concentration plateaus may become excessive. The high-energy sites that may be found on the surface of the stationary phase are responsible for this problem. It is necessary to measure the characteristics of these sites (saturation capacity, equilibrium constant). This requires knowledge of the adsorption data in the range in which the isotherm contribution of these sites varies from the linear domain to the saturation region. This is the typical situation in the case of a surface having few but very strong, high-energy sites. It is necessary to measure the isotherm data at concentrations that are within the linear range of this isotherm contribution, to obtain a good reliable estimate of its equilibrium constant. In this case, the injection of low concentration plateaus during a finite time is necessary. However, it may be that, with the standard injection band width, an equilibrium plateau is not obtained at the column outlet because a long band tailing will erode the injected low concentration plug injected. This tailing is due to the long retention and the slow mass transfer which are often prevalent on high-energy sites. A longer injection time must be applied in that case in order to be able to observe the equilibrium plateau of the breakthrough curve. Unfortunately, the retention time may be excessively long (typically beyond 60 min) which requires a long time and consumes much solvent. Then, only one breakthrough curve was recorded and the amounts adsorbed for lower concentrations are determined by using the FACP method [14,15]. This reduces somewhat the accuracy of the results.

gram converges, after a large number of iterations, toward the most expected adsorption energy distribution (AED). The major advantage of this method is that it injects no arbitrary information in the calculation, hence does not pollute the resulting AED by the consequences of arbitrary assumptions on what the AED or the isotherm should be. The number of iterations required for the program to converge depends essentially on the maximum column loading possibly reached during the measurements. Our experience in this domain tells us that the stationary phase concentration must reach at least 40% of the saturation capacity of the column. Otherwise, the density of low-energy sites (the last ones to fill up) cannot be estimated with any accuracy. The mathematical details about the expectationmaximization method are given elsewhere [13].

2.2. Calculation of the adsorption energy distributions

Da =

Because the surfaces of chromatographic packing materials are not homogeneous and because different analytes interact with a given surface through different interactions, giving different adsorption energies, the distribution of these different adsorption sites is of major importance to ascertain that the best physical isotherm model is selected. So far, we found no commercial C18 -bonded adsorbent that has a homogeneous surface. Simple analytes (e.g., phenol, caffeine) adsorb with different energies on this surface. These findings were made possible by using a mathematical method elaborated by Stanley et al. [13] and called the expectation-maximization method. Starting from the raw experimental adsorption data and assuming a certain model of local isotherm (e.g., the Langmuir, Jovanovic, Moreau or BET isotherms, which are all irreducible isotherms), the pro-

where u is the mobile phase linear velocity, L the column length, and N the number of theoretical plates or apparent efficiency of the column under linear conditions. All necessary information on the ED model and the calculation of its numerical solutions are given elsewhere [14,18–20]. The ED model was solved using the Rouchon program based on the finite difference method [20]. The boundary conditions were those of Danckwerts [21].

2.3. From the isotherm data to the isotherm model The determination of the best physical isotherm model is based on the complementary information given by the fitting of the adsorption data to various possible models and by the AED. For instance, a good fitting bi-Langmuir isotherm model cannot be selected if a tri-modal AED is calculated from the very same data nor a Toth model when the AED is bimodal. Details on the selection of the best isotherm model from the adsorption data are given elsewhere [12]. 2.4. Modeling of high-concentration band profiles The breakthrough curves were calculated using the best model of the isotherm of the compound studied and the equilibrium-dispersive model (ED) of chromatography [14,16,17]. The ED model assumes instantaneous equilibrium between the mobile and the stationary phase and a finite column efficiency originating from an apparent axial dispersion coefficient, Da , that accounts for the dispersive phenomena (molecular and eddy diffusion) and also for the non-equilibrium effects that take place in a chromatographic column. These effects are supposed to be small, otherwise the ED model is not valid. The axial dispersion coefficient is related to the experimental parameters through the following equation: uL 2N

(1)

2.5. Determination of the molecular volumes of the analytes The molecular volumes of the different analytes used in this work were generated by the SYBYL7.0 molecular modeling package [22]. First, the energy of the molecule is minimized using the Tripos force field. This is followed by the calculation

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of the volume from the surface contour option. Accordingly, the molecular volume of phenol, 2-naphthalene sulfonate sodium, caffeine, and propranololium chloride are 82.1, 128.8, 145.9, ˚ 3 , respectively. and 263.2 A 3. Experimental 3.1. Chemicals The mobile phase used in this work for the determination of the adsorption isotherm data was a mixture of methanol and water (30:70, v/v). Both solvents were HPLC grade, purchased from Fisher Scientific (Fair Lawn, NJ, USA). The mobile phase was filtered before use on a surfactant-free cellulose acetate filter membrane, 0.2 ␮m pore size (Suwan-nee, GA, USA). NaCl (25 mM) was added in the case of the adsorption study of ionizable compounds. Thiourea was chosen to measure the column hold-up volume under the experimental conditions. The presence of 25 mM of sodium chloride in the mobile phase does not affect the hold-up volume of the column. Thiourea, phenol, caffeine, and propranolol hydrochloride were obtained from Aldrich (Milwaukee, WI, USA). 2-Naphthalene sulfonate sodium was purchase from Acros Organics (Fair Lawn, NJ, USA). 3.2. Materials The 150 mm × 4.6 mm Prontosil-C30 column used in this work was purchased from MAC-MOD Analytical Inc. (Chadds Ford, PA, EU). This column is packed with a C30 -bonded, polymeric, non endcapped, porous silica. The main characteristics of the bare porous silica and of the bonding material used are summarized in Table 1, according to the manufacturer. The total porosity of the column measured with the mobile phase described in Section 3.1, at 295 K (
T = 0.651) was derived from the retention times of two consecutive injections of thiourea. 3.3. Apparatus The breakthrough curves of the chemicals were acquired using a Hewlett-Packard (Palo Alto, CA, USA) HP 1090 liquid chromatograph. This instrument includes a multi-solvent delivery system (three tanks, volume 1 L each), an auto-sampler with a 250 ␮L sample loop, a column thermostat, a diode-array UVdetector, and a data station. Compressed nitrogen and helium bottles (National Welders, Charlotte, NC, USA) are connected to the instrument to allow the continuous operations of the pump, the auto-sampler, and the solvent sparging. The extracolumn volumes are 0.035 and 0.290 mL, as measured from the auto-sampler and from the pump system, respectively, to the

column inlet. All the retention data were corrected for this contribution. The flow-rate accuracy was controlled by pumping the pure mobile phase at 22 ◦ C and 1 mL/min during 50 min, from each pump head, successively, into a volumetric glass of 50 mL. The relative error was less than 0.4%, so that we can estimate the long-term accuracy of the flow-rate at 4 ␮L/min at flow-rates around 1 mL/min. All measurements were carried out at a constant temperature of 22 ◦ C, fixed by the laboratory air-conditioner. The daily variation of the ambient temperature never exceeded ±1 ◦ C. 3.4. Frontal analysis isotherm measurements on the Prontosil-C30 column In order to make accurate measurements of adsorption isotherm data, the retention factor, k should be neither too high (which limits the number of data points that can be acquired within a reasonable period of time) nor too low (which causes a decrease in the accuracy of the data). Values of k between 3 and 6 are ideal to achieve a precise, accurate isotherm determination. This is the case for these four compounds with a 30/70 (v/v) methanol:water solution as the mobile phase, except for propranolol hydrochloride which is excessively retained. As explained in the theory section, however, FACP was used in this case instead of FA to derive the adsorption data. Prior to any isotherm measurements, the solubilities at 22 ◦ C of the compounds in the mobile phase were determined approximately by the stepwise addition of 0.5 mL of pure mobile phase into a volume of 25 mL of a saturated solution containing a small amount of undissolved compound, until complete dissolution. Accordingly, the maximum concentrations used in the FA measurements were 200, 35, 40, and 50 g/L for phenol, caffeine, propranolol hydrochloride, and 2-naphthalene sulfonate sodium, respectively. Successive master sample solutions were prepared, with decreasing concentrations, until the measurements could be made in the linear domain of the adsorption isotherm. The consecutive sequences of FA measurements were carried out (see procedure below). Together, they give an isotherm that is accurate at both low and high concentrations. At least 25 data points were recorded for each compound, depending on the number of the successive FA runs. One pump of the HPLC instrument was used to deliver a stream of the pure mobile phase to the column, the second pump a stream of the pure master sample solution. The concentration of the studied compound in the stream percolating through the column is determined by the concentration of the master sample solution and the ratio of the flow-rates delivered by the two pumps. The breakthrough curves are recorded successively, all at a flow-rate of 1 mL/min, with a sufficiently long time interval between each breakthrough curve to allow for the

Table 1 Physico-chemical properties of the polymeric C30 -bonded columns provided by the manufacturer

C30 -Prontosil

Column dimension (mm × mm)

Particle size (␮m)

Mesopore ˚ size (A)

Specific surface (m2 /g)

Bonding process

Carbon content (%)

Surface coverage (␮mol/m2 )

End-capping

150 × 4.6

5

200

200

Polymeric

18.5

n.a.

No

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re-equilibration of the column with the pure mobile phase. The injection time of each new solution was set long enough (typically between 5 and 10 min) to reach a stable plateau at the column outlet. Two overloaded band profiles (one at low, the other at high column loading) needed for the validation of the fitted isotherms were recorded at the time when the frontal analysis experiments were carried out. An isotherm is acceptable only if it accurately predicts the band profiles at both low and high column loadings. To avoid recording any UV-absorbance signal larger than 1500 mAU and the associated too large signal noise, the detection of the breakthrough curves and the overload band profiles of phenol, caffeine, 2-naphthalene sulfonate, and propranolol were carried out at different wavelengths. The detector responses for the samples were calibrated accordingly. 4. Results and discussion The adsorption isotherms of the four compounds are shown in Fig. 1A–D that encompass the whole concentration range stud-

47

ied. The best numerical estimates of the isotherm parameters are listed in Table 2. The adsorption energy distributions, calculated from the raw adsorption data, are shown in Fig. 2A–D, for phenol (A), caffeine (B), 2-naphthalene sulfonate sodium (C), and propranolol chloride (D). 4.1. Adsorption isotherm of phenol on the C30 -bonded silica column The isotherm is Langmuirian (Fig. 1). The adsorption energy distribution is obviously tri-modal (Fig. 2A). The isotherm model most consistent with these experimental results is the tri-Langmuir adsorption isotherm model. The best estimates of the isotherm parameters (see Table 2) show that 1 L of the polymeric C30 -bonded silica adsorbent may adsorb at the interface between the bulk mobile phase and the C30 chains, 3.56 mol of phenol on the lowest energy sites (type 1). However, the surface is definitely heterogeneous and prior to equilibration with type 1 sites, this volume of stationary phase will adsorb 0.69 mol

Fig. 1. Adsorption data of phenol, caffeine, 2-naphthalene sulfonate, and propranolol on the C30 -bonded Prontosil column measured by frontal analysis. The mobile phase is a mixture of methanol and water (30/70, v/v). Sodium chloride (25 mM) are added to elute the ionizable compounds (2-naphthalene sulfonate and propranolol), T = 295 K. (A) 0–50 g/L range; (B) 0–5 g/L range; (C) 0–0.1 g/L range; (D) 0–0.01 g/L range.

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Table 2 Best isotherm parameters accounted for by the adsorption of phenol, caffeine, naphthalene sulfonate, and propranololium on the RP-C30 bonded HPLC column from a mixture of methanol and water (30/70, v/v) Probe solute

Phenol (neutral)

Caffeine (neutral)

Naphthalene sulfonate (anionic −)

Propranolol (cationic +)

qS,1 (moL/L) b1 (L/moL)

3.56 (3.51) 0.42 (0.44)

0.96 (1.27) 3.02 (2.01)

1.46 (1.44) 1.02 (1.06)

0.77 (0.75) 7.28 (10.1)

qS,2 (moL/L) b2 (L/moL)

0.69 (0.66) 7.29 (7.57)

0.10 (0.12) 62.1 (51.8)

0.012 (0.013) 80.3 (121)

0.029 (0.022) 350 (802)

qS,2 /qS,1 + qS,2

16% (16%)

9.4% (8.6%)

0.8% (0.9%)

3.6% (2.8%)

b2 /b1

17 (17)

21 (26)

79 (114)

48 (79)

qS,3 (mmoL/L) b3 (L/mmoL)

2.03 (1.06) 0.24 (0.47)

2.73 (3.14) 0.83 (0.90)

6.8 (4.4) 0.48 (0.61)

7.6 (4.5) 4.8 (11.1)

qS,4 (mmoL/L) b4 (L/mmoL)

– –

0.17 (0.08) 12.8 (25.6)

– –

0.84 (0.11) 43.6 (178)

NaCl salt (25 mM) was added to measure the isotherms of the ionizable compounds. The values in parenthesis are the isotherm parameters derived from the calculation of the AED.

Fig. 2. AEDs of phenol (A), caffeine (B), 2-naphthalene sulfonate sodium (C), and propranolol chloride (D) calculated by the EM method from the raw adsorption data given in Fig. 1. The number of iteration was fixed at 10 millions, the number of energy grid points was 225 and the energy grid range was bmin = 1/10Cmax and bmax = 1/Cmax . Cmin and Cmax are the lowest and highest mobile phase concentrations used in FA.

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of phenol, with a stronger adsorption energy, on a second type of sites, which are located deeper inside the hydrophobic layer. Finally, there is a third type of sites, much less abundant on the surface, which is detected. It is saturated with only 2 mmol of phenol per liter of adsorbent. The difference between the adsorption energies on sites 2 and 1, and between those on sites 3 and 2 are 7.0 and 8.5 kJ/mol, respectively. These differences result from an increase in the surface area of contact between the analyte molecule and the hydrophobic layer. They are typical of hydrophobic or dispersive interactions [12]. The relative contributions of the saturation capacities of sites 1, 2, and 3 to the total saturation capacity of the adsorbent are ca. 84, 16, and 0.05%, respectively. To calculate the average number of phenol molecules adsorbed per C30 -bonded chains at saturation, we need an estimate of the number of ligands per unit volume of packing material in the column, since the concentration of phenol adsorbed is given in volume unit of the packing material. Such an estimate can be derived as follows. First, based on the carbon content of the packing material (i.e., 18.5% C) given by the manufacturer and on the chemical structure of the bonded moiety ( O Si (CH2 )29 CH3 ), it is possible to calculate the fractional weight of each atom in the bonded layer of the Prontosil silica. One oxygen atom is taken into account in the bonded phase because it was prepared following the polymeric route and water was added during the reaction. The fractional weights of hydrogen, silicon, and oxygen in the bonded phase are: %Oxygen = %Silicon =

%Hydrogen

16 × 18.5 = 0.8% 30 × 12

28 × 18.5 = 1.4% 30 × 12
 2×1 1 = + × 18.5 = 3.1% 12 30 × 12

The weight percentage of the whole bonded phase is then of 23.8%. Second, the density of the packing material can be estimated from the densities of the bare solid silica (2.20 g/cm3 ) and of liquid triacontane (CH3 (CH2 )28 CH3 , 0.78 g/cm3 ), assuming that the latter is the same as the density of the bonded layer: ρpacking =

1 = 1.53g/cm3 0.762/2.20 + 0.238/0.78

Accordingly, 1 g of stationary phase consists of 0.35 cm3 of bare silica and 0.30 cm3 of a C30 -bonded organic layer. The specific surface area of silica per volume of stationary phase, Spv , is: Spv = Spsilica × ρsilica × = 200 × 2.2 ×

Vsilica Vsilica + VC30

0.35 = 237m2 /mL 0.35 + 0.30

The surface concentration of triacontyl chains bonded to the silica surface (a parameter not available from the manufacturer)

49

is less straightforward to estimate because the layer is polymeric. Based on the carbon content of the packing material, the specific surface of the bare silica, Sp , the molecular weight of the triacontyl bonded chains (assuming that the unit bonded is ( O Si (CH2 )29 CH3 )) and the mole percent of carbon in the bonded moiety SC , the apparent surface coverage [MC /m2 ] of triacontylsilane (Si C30 ) chains is derived from a classical relationship [23] as: MC %C × 106 = 2 m (SC − %C)MW Sp

(2)

with SC = 77.4%, %C = 18.5%, MW = 465 g/mol, and Sp = 200 m2 /g (Table 1), it is found that the apparent surface concentration of triacontyl chains is 3.4 ␮mol/m2 . This value is similar to the one usually found for monomeric octadecyl phases (between 2 and 4 ␮mol/m2 ). The number of triacontyl chains per volume of stationary phase is then: MC MC = 2 × Spv = 3.4 × 237 = 0.81 mol/L 3 cm m Our measurements show that the maximum concentration qS of phenol adsorbed per squared meter of neat silica is qS,1 + qS,2 + qS,3 = 4.25 mol/L. Hence, an average of about 4.25/0.81 = 5.25 molecules of phenol interact with each bonded C30 chain at saturation, when the low-energy sites are filled. Similar calculations were made for various brands of monomeric C18 -bonded silicas [4] and the results are shown in Table 3. The molecular unit attached to silica is ( Si (CH2 )17 CH3 ) and the density of the bonded phase was assumed to be that of liquid octadecane (0.78 g/cm3 ). These results show that, under the same experimental conditions (methanol/water, 30/70, v/v), between one and two and a half molecules of phenol interact with one C18 chain when the low-energy sites are saturated, a value less than half the number for Prontosil. The C30 -bonded hydrophobic layer is certainly more complex than the monolayer of C18 -chains bonded to conventional RPLC monomeric materials. It is polymeric, hence extends in three dimensions. Both the longer alkyl chain length and the 3-D network of polymeric C30 chains explain the larger capacity of the low-energy sites. The equilibrium constants are also different. This constant is about twice smaller on the polymeric C30 -bonded phase than on the monomeric C18 -bonded one (about 0.5 L/mol versus 1.0 L/mol). This difference suggests that the surface area of contact between phenol and the bonded layer is smaller with the C30 than with the C18 layer. Overall, because of the compensation between a lower adsorption constant and a higher density of sites, the Henry constant, H1 , is nearly the same on these two types of phases. The second type of adsorption sites has a saturation capacity of 0.69 mol of phenol per liter of adsorbent (about 3.0 ␮mol/m2 ). These sites are located deeper in the hydrophobic layer because their adsorption energy is higher. Their density is about one per C30 chain. Surprisingly, their saturation capacity is about the same on C18 - and C30 -bonded phases and their equilibrium constants are close (ca. 10 L/mol). This is consistent with these sites of type 2 providing the same environment to the adsorbed molecule, the layer of bonded, disordered C18 or C30 chains.

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Table 3 Comparison between C18 -bonded phases and the Prontosil-C30 phase of the maximum number of molecules of phenol adsorbed per attached ligand at the column saturation Columns

Bonding process

%C

Spsilica (m2 /g)

Ligand density (␮mol/m2 )a

Ligand density (mol/L)b

NPhenol /NLigand

C30 -Prontosil C18 -Vydac C18 -Hypersil C18 -Kromasil C18 -Luna C18 -Symmetry C18 -Chromolith C18 -XTerra C18 -Sunfire C18 -Gemini C18 -Ascentis C18 -Resolve

Polym. Polym. Monom. Monom. Monom. Monom. Monom. Monom. Monom. Monom. Monom. Monom.

18.5 7.7 13.0 20.0 18.2 19.5 19.5 15.2 17.5 14.0 25.0 10.2

200 70 200 314 420 340 300 176 349 375 450 200

3.4 5.0 3.1 3.6 3.3 3.2 3.6 2.5 3.8 2.1 3.8 2.45

0.79 0.58 0.87 1.25 1.63 1.22 1.21 0.57 1.51 0.98 1.47 0.73

5.4 1.5 2.5 1.6 1.4 1.7 2.2 1.5 1.3 2.4 1.4 1.3

a b

Per squared meter of silica. Per liter of packing material.

The density of the third type of sites is extremely low, only 2 mmol/L of adsorbent, or a saturation concentration of the surface of 9 nmol/m2 . Sites of this type are usually absent for phenol on conventional C18 -bonded phases, in the presence of a mobile phase having a composition comparable to that used here. However, sites of this type were observed on some old Symmetry-C18 columns [24] and on a brand new ChromolithC18 column [25,26]. The adsorption energy on the sites of this type is 15.5 kJ/mol higher than that on the low-energy sites of type 1. This energy difference is compatible with strong classical interactions taking place in the adsorption field at the bonded layer/mobile phase interface. These additional interactions could involve either strong hydrogen-bond interactions with non-endcapped, isolated silanol groups or interactions with a large hydrophobic cavity inside the C30 hydrophobic layer. Note that the saturation capacity of the column for phenol appears to be very high (more than 4 mol/L of adsorbent). This is merely due to the relatively small volume of the molecule of ˚ 3 ). When expressed in number of moles adsorbed phenol (82.3 A per liter of adsorbent, the saturation capacity decreases with increasing molecular volumes. 4.2. Adsorption isotherm of caffeine on the C30 -bonded silica column The adsorption isotherm of caffeine (Fig. 1A–D) is also Langmuirian. The selectivity coefficient, αcaffeine/phenol = 1.93, measured from the ratio of the overall Henry constants of phenol and caffeine exceeds markedly 1, which confirms that the packing material was not endcapped, according to the test of Kimata et al. [27]. On the series of endcapped C18 monomeric materials that we tested a year ago [4], this selectivity coefficient was always between 0.4 and 0.5, except the endcapped polymeric C18 column (Vydac Grace) which has a caffeine/phenol selectivity of 0.9. The high selectivity observed for the non-endcapped C30 polymeric column is certainly due to the absence of end-capping and to the selective adsorption of caffeine on the isolated silanols located within the C30 -bonded layer.

The AED for caffeine is quadri-modal (Fig. 2B). Thus, the adsorption mechanism of caffeine involves four distinct types of adsorption sites. Adsorption isotherm data and AED are consistent with a quadri-Langmuir adsorption isotherm (coefficients in Table 2). This result contrasts with the results obtained with the different brands of monomeric and polymeric endcapped C18 columns, with which the adsorption isotherm of caffeine is properly described by the bi-Langmuir model and the AED is bimodal [4]. Again, the lack of endcapping of the silica surface and the increase of the length of the alkyl-bonded chains contribute to increase the degree of heterogeneity of the stationary phase. As shown in Table 2, the saturation capacities of the first two types of sites (i.e., the two low-energy sites that are due to the heterogeneity of the structure of the C30 -bonded layer) are significantly lower than those for phenol (see previous section). About four and six times fewer molecules of caffeine than of phenol are adsorbed at saturation per bonded chain on sites of types 1 and 2, respectively. Yet, a molecule of caffeine occupies a volume that is only about twice that of a phenol molecule ˚ 3 versus 82.1 A ˚ 3 ). This means that the access to the sites (160 A of types 1 and 2 depends on the size of the analyte molecule. The larger the compound, the larger the number of such sites from which its molecules are excluded. On the other hand, caffeine is adsorbed more strongly than phenol. The adsorption energies of caffeine on sites of types 1 and 2 are nearly seven-fold larger because the contact area between the C30 -bonded chains and the analyte molecules is larger for caffeine than for phenol. Whether for phenol or for caffeine, the difference between the adsorption energies on sites of types 2 and 1 is about the same, e.g., 7–8 kJ/mol. This value is slightly larger than the similar differences observed on the monomeric C18 -bonded phases (on which it is around 5 kJ/mol). As for phenol, there is a third, high-energy type of sites. When saturated, these sites can hold a density of about 12 nmol/m2 of caffeine. The adsorption energy of caffeine on these sites is about 14 kJ/mol higher than on the lowest energy sites, the same difference that is observed with phenol. Given the

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very small density of these sites, they could be identified either as some deeper, rare hydrophobic cages or as some rare silanol groups that would be accessible to both phenol and caffeine. The large selectivity between caffeine and phenol observed on the C30 -bonded phase (αcaffeine/phenol = 1.93) is also due in part to the contribution of the sites of a fourth type, very highenergy adsorption sites, which are not observed with phenol. Without them, the selectivity coefficient would be around 1.3 only, much closer to the one observed with the endcapped, polymeric C18 -bonded column (0.9, reference [4]). The saturation capacity of these sites for caffeine is only 0.7 nmol/m2 , but the adsorption energy is 20.5 kJ/mol higher than on sites of type 1. Definitely, such a high-energy difference is consistent with strong, highly selective analyte-surface interactions, taking place with some bare regions of the silica surface to which the caffeine molecules have access. Similar high-energy sites were also observed on the non-endcapped C18 -bonded Resolve [3] and on the endcapped Chromolith [26] adsorbents. As a conclusion, caffeine adsorbs on C30 -Prontosil much in the same way as phenol does (the sites of types 1, 2, and 3, involve probably only simple dispersive interactions). However, in addition, very strong, highly selective interactions take place between caffeine and the adsorption sites of a type 4, involving probably acid–base interactions between the non-endcapped isolated silanol groups and the weak base caffeine. To test the possibility of ion-exchange interactions between the silica surface (Si O− ) and other analytes under our experimental conditions (no buffer, pH about neutral), we investigated the adsorption of two ionizable compounds, one negatively charged, the other positively charged. 4.3. Adsorption isotherm of 2-naphthalene sulfonate on the C30 -bonded silica column 2-Naphtahlene sulfonate was dissolved in the mobile phase under its basic anionic form (as the sodium salt, M = 230.2 g/mol). Previous measurements made on two adsorbents, C18 -Symmetry and C18 -Xterra [28], have shown that, in the absence of a buffer or of supporting salts in the mobile phase, an S-shaped isotherm is observed. The best adsorption isotherm model that accounts for this behavior is the Bi-Moreau isotherm. Important adsorbate–adsorbate interactions take place under such conditions. To eliminate them, the simple addition of a supporting salt suffices. The addition of the counter-ion usually “Langmuirizes” the isotherms of organic ions [29] and the study of the adsorption mechanism of these compounds is then made possible by including the information coming from the calculation of the AED (which assumes local Langmuir adsorption, hence no adsorbate–adsorbate interactions). Accordingly, 25 mM of sodium chloride were added to the methanol/water mobile phase (30/70, v/v). This does not affect the hold-up time of the columns, as measured by the elution time of thiourea. The adsorption isotherm shown in Fig. 1A–D is clearly Langmuirian. The corresponding adsorption energy distribution is shown in Fig. 2C. It is tri-modal and the best isotherm model is the tri-Langmuir isotherm model.

51

The maximum amount of 2-naphthalene sulfonate that can be adsorbed on the sites of type 1 is 1.46 mol/L of adsorbent. This is much less than the saturation capacities of this type of sites for phenol and slightly more than for caffeine. The intermediate ˚3 ˚ 3 versus 82.1 A molecular size of this ionic compound (128.8 A 3 ˚ and 160 A for phenol and caffeine, respectively) may explain this difference. Surprisingly, however, the characteristics of the sites of type 2 for the 2-naphthalene sulfonate (saturation capacity and adsorption energy) do not match those of the sites of type 2 observed for phenol and for caffeine. In contrast, the saturation capacity (qS,2 = 0.012 mol/L or 50 nmol/m2 ) and the difference between the adsorption energies (
2 −
1  11 kJ/mol) for the anionic compound are consistent with the properties of the sites of type 3 observed for phenol and for caffeine. The third type of sites observed has physico-chemical properties that strongly suggest that this type is of a similar nature as the type 2 and the high-energy sites found for the two neutral compounds, e.g., some form of hydrophobic cages in which the analyte becomes embedded. The values of the saturation capacity, qS,3 = 6.8 mmol/L (i.e., 29 nmol/m2 ) and the increase of the adsorption energy over that of the sites of type 1,
3 −
1  15 kJ/mol are of the same order of magnitude as those found for the sites of type 3 of phenol and caffeine. It is unlikely that these sites involve ionized silanol groups because these anions would repulse the 2-naphthalene sulfonate anion. 4.4. Adsorption isotherm of propranololium on the C30 -bonded silica column The adsorption of a cation was also investigated on the polymeric C30 -bonded column, using the same mobile phase as for the anion, containing 25 mM NaCl. Propranolol was dissolved under its protonated form (as the salt propranololium chloride M = 295.8 g/mol). The adsorption isotherm could not be measured by FA in the whole range of concentration investigated because the retention of propranolol becomes excessively high at very low concentrations, which would have resulted in too high a solvent consumption. Frontal analysis by characteristic points (FACP) [14] was used instead to measure the adsorption data in the low concentration range. The final adsorption data are plotted in Fig. 1A–D. The corresponding AED is shown in Fig. 2D. It has four narrow, well resolved modes. The adsorption of propranolol is best described by a tetraLangmuir adsorption isotherm model. Propranolol has the larger molecular size of the compounds tested (molecular volume ˚ 3 ). As expected, the saturation capacity on the lowest 263.2 A adsorption energy sites, or sites of type 1, is the lowest of the four measured (0.77 mol versus 0.96, 1.46, and 3.56 mol for caffeine, 2-naphthalene sulfonate, and phenol, respectively). On the other hand, the equilibrium constants measured on the four types of adsorption sites are the largest among the four compounds studied. The density of the sites of types 2 and 3 (124 and 33 nmol/m2 , respectively) are comparable to those measured for 2-naphthalene sulfonate. The sites of types 2 and 3 are adsorption sites that show the heterogeneity of the C18 -bonded layer. The

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differences between the adsorption energies of the sites of types 2 and 3, and that of the sites of type 1 are 9.5 and 15.9 kJ/mol, respectively. The most important difference between the adsorption behaviors of the two organic ions is the fourth type of adsorption sites which has an unusually large adsorption energy, an energy so large that the thermodynamic characteristic (qS,4 and b4 ) of this type of sites could not be measured directly from the fitting of the FA adsorption data to the isotherm model. The retention at infinite dilution is so long that recording the breakthrough curves at very low concentrations would have consumed too much solvent for poorly precise data. This was not the case with the fourth site of caffeine. These results mean that an exceptionally strong interaction takes place between the propranololium cation and the surface, but that there are no such interactions with anions. It is very likely that this fourth type of sites is due to the ionized silanol groups (Si O− ) participating into ion-exchange interactions with the protonated form of propranolol. The number of these interaction sites is very small (only 4 nmol/m2 ) and it cannot be measured accurately. A significant difference is observed between the isotherm characteristics that are derived from the fitting of the FA data to the isotherm model and those that are afforded by the AED results (a factor 8 for qS,4 , 4 for b4 , see Table 2). However, the values of the Henry constant given by both methods are closer (36.6 versus 19.58). From the FA and the AED results, values of 21.3 and 24.0 kJ/mol can be derived for the differences between the adsorption energies on the sites of types 1 and 4. These very high values are consistent with the interactions with sites of type 4 being strong ion-exchange interactions. 4.5. Surface heterogeneity of the polymeric C30 -bonded phase in RPLC Fig. 3 compares the contributions to the overall Henry constant of the different types of sites that are present on the

C30 -bonded stationary phase. The very existence of these sites escapes any analysis of linear chromatographic data but is clearly demonstrated by nonlinear chromatographic data, as acquired by frontal analysis. It is striking to observe that adsorption of the compound on the adsorption sites of type 1, the lowest energy sites, sites that account for more than 80% of the total saturation capacity of the column, contributes only to a small fraction of the retention in linear chromatography. It represents only 20% of the overall Henry constant for the neutral compounds (phenol and caffeine), 25% for the anionic compound 2-naphthalene sulfonate, and 5% for the cation propranololium. The relatively high contribution of the adsorption on the sites of type 1 observed for the anionic compound is most probably explained by its repulsion from the areas of the surface where are the non-endcapped ionized silanols. In contrast, the sites of type 1 contribute poorly to the retention factor of propranolol due to the additional strong interaction of these same silanol groups and the high contribution of the sites of type 4. The major part of the retention of the analyte under linear conditions is due to its interactions with the high-energy sites, sites that account for a very small fraction of the total saturation capacity but for most of the Henry constant. Depending on the analyte, the sites of types 2, 3, and 4 account for only between 1 and 15%, 0.05 and 1%, and 0.015 and 0.1% of the total saturation capacity. Fig. 4 shows plots the saturation capacity (Fig. 4A) and of the equilibrium constant (Fig. 4B) of the sites of type 1 (each data point shown is the average of the values derived from the fitting of the FA data and from the calculation of the AED) as functions of the molecular volume of the analyte. The larger the volume of the compound, the smaller the saturation capacity of the column for this compound and the larger its adsorption energy on the sites of type 1. This observation is mostly explained by the surface area of contact between the analyte and the C30 chains increasing with increasing molecular size of the compound, an effect typical of retention mechanisms in RPLC. The molecular surface area increases with increasing molecular volume and

Fig. 3. Contribution of each type of adsorption sites (qS,i bi ) to the overall retention of the compounds in linear conditions. For each compound, the comparison between the Henry constants found from the best fitting parameters (left rectangles) of the adsorption data and the calculated AED (right rectangles) is given.

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Fig. 4. Relationship between the thermodynamic parameters found for sites 1, b1 (A) and qS,1 (B), and the molecular volume of the analyte. Note that the equilibrium constant increases and that the saturation capacity decreases when the size of the compound increases, typical of hydrophobic interactions and of a surface roughness.

weight, and the saturation capacity in mol/L decreases in the same time. Also, the geometry of the solute (e.g., the deviation of its structure from a planar or a rod-like shape, as characterized by the relative value of its lowest or two lowest moments of inertia) as well as its polarity affect the values of the saturation capacities and the equilibrium constant found. This justifies the only relative correlation shown in Fig. 4. As aforementioned, the retention volumes of the analytes under linear conditions on the non-endcapped C30 -bonded column are essentially governed by their interaction with the highenergy adsorption sites of types 2, 3, and 4. The number of these sites depends on the nature of the analyte, e.g., essentially on its molecular volume and its charge. The relative abundance of the sites of types 2 and 1 exhibit some obvious trend (Table 2). In the absence of repulsion of an anion by ionized silanol groups, the larger the molecular size of the analyte, the smaller the relative number of sites of type 2. The proportion of the surface area of the adsorbent covered by type 2 sites drops down from 16 to 9.4% and to 3.6% of the saturation capacity of the pack˚3 ing material when the molecular volume increases from 82 A 3 3 ˚ (caffeine) and to 263 A ˚ (propranolol). The (phenol) to 146 A effect of the negative charge of the anion naphthyl sulfonate is

53

Fig. 5. Same as in Fig. 4, except the type of sites 2.

˚ 3 ), drastic and, despite its rather small molecular volume (129 A the relative abundance of the sites of type 2 to those of sites of type 1 becomes less than 1%. As for the adsorption sites of type 1, the logarithm of the equilibrium constant b2 of the sites of type 2 increases with increasing molecular volume of the analyte while the density of these sites decreases (Fig. 5). This phenomenon is also typical of retention mechanisms in RPLC, which seems to confirm that the nature of these sites is the same as that of the sites of type 1, but that they are located deeper in the C30 -bonded layer, closer to the silica surface and that they provide a larger surface area of contact between the analyte and the bonded chains. Note that the data point for naphthalene sulfonate is an outlier in this figure. Fig. 6 shows the same plots as Figs. 4 and 5 but for the sites of type 3. In contrast with the plots for the sites of types 1 and 2, there is no obvious correlation between the molecular size of the analyte and the density of the sites of type 3. On the average, there are about 5 mmol/L of these sites, corresponding to an average ˚ However, the density is distance between sites of type 3 of 115 A. about three times higher for the organic ions than for the neutral compounds. For the sake of comparison, the average distances ˚ for phenol, between sites of type 1 are 4.3, 6.7, 8.3, and 9.3 A naphthalene sulfonate, caffeine, and propranolol, respectively,

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Fig. 7. Difference between the adsorption energies on sites 4, 3, and 2 and sites 1 for the different compounds studied. Note the similarity for all the compounds.

Fig. 6. Same as in Fig. 4, except the type of sites 3.

˚ and for the sites of type 2, they are 9.8, 74, 25.8, and 47.8 A, respectively. As the other equilibrium constants, b3 increases with increasing molecular size of the analyte. This means that the intensity of the interactions with the sites of type 3 depends also on the surface of contact between the analyte and the surface of the C30 -bonded silica. The natures of the sites of types 1, 2, and 3 are probably similar and they all involve dispersive interactions. Fig. 7 compares the values of the differences between the adsorption energies on the sites of types 2 and 1 (left), 3 and 1 (center), and 4 and 1 (right). The average values of these differences are 8 kJ/mol between sites of types 2 and 1, 15 kJ/mol between sites of types 3 and 1, and 21 kJ/mol between sites of types 4 and 1. These differences are nearly independent of the analyte studied. The origin of the nature of the fourth type of sites is arguable. It is unclear whether these sites are related to interactions of the solute with some isolated silanol groups or rather are due to adsorption in hydrophobic cages located deep inside the bonded layer, or possibly to both since isolated, ionizable silanol groups can be buried under the bonded alkyl layer. Different mechanisms may be involved, according to the nature of the solute but some conclusions are obvious. First the adsorption energy on these sites is at least 20 kJ/mol higher than that on the sites

of type 1. This makes the adsorption energy compatible with strong ion-exchange interactions between ionizable compounds and ionized silanol groups Si O− . Undoubtedly, this is what happens with propranololium, as confirmed by the observation of a very long tail for the breakthrough curves at extremely low concentrations (tail explained by the overloading of the sites of type 4 and of their Langmuir isotherm). The total desorption of propranolol takes place only after 100 min for a 14 min injection of a 200 ␮mol/L solution of propranolol chloride. This is a typical thermodynamic tailing. Second, the density of the sites of type 4 is very small (2 nmol/m2 , which represent one ˚ This density is compatible with the analyte site every 281 A). interacting with non-endcapped residual silanol groups trapped in the polymeric network of the O Si C30 bonded chains. On the other hand, it seems that caffeine also interacts with the sites of type 4 and the interpretation of the adsorption mechanism in this case is less clear. Caffeine is not charged when dissolved in the mobile phase used. Hence, as stated elsewhere [3], it seems hasty to identify the sites of type 4 as due to ion-exchange interactions. Other strong interactions, e.g., hydrogen-bond interactions between the nitrogen atoms of caffeine and isolated silanol groups could take place. It is surprising, however, that phenol, which is twice smaller than caffeine, has easier access to surface heterogeneities, and participates easily to hydrogen-bond interactions, both as a donor and as an acceptor, does not interact with the sites of type 4. Accordingly, at this point, it cannot be concluded how caffeine interacts strongly with the packing material studied [3]. It must be noted that the mechanism of adsorption is specific both of the adsorbent surface and of the adsorbate. There are probably many types of sites on an adsorbent and they interact differently with different compounds. 5. Conclusion This work confirms our previous conclusions that actual RPLC packing materials are heterogenous by nature. Similar conclusions regarding the same C30 -bonded Prontosil stationary phase have been reached independently by authors using

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a different method, the cross polarization/magic angle spinning nuclear magnetic resonance (CP/MAS NMR) [11,30–32]. Still, from a chromatographic perspective, numerous important details regarding the nature of the heterogeneity of the alkylbonded silica adsorbents are missing. More systematic investigations are necessary. They include the accurate measurements of the adsorption isotherms of many analytes of different molecular sizes, polarities, and structures. CP/MAS NMR measurements have showed that the chemically bonded alkyl chains have two different types of conformations. One fraction of the chains is disordered and mostly in the gauche conformation. The other fraction is ordered, the chains being parallel and mostly in the trans-conformation. Chromatographic measurements, mostly acquired by FA and by the thermodynamic interpretation of the data, have shown that, when eluted by methanol/water solutions (with a salt in the case of ionic compounds), all the compounds studied have a Langmuirian adsorption isotherm (i.e., an isotherm convex upward) that can be modeled by a tri-Langmuir equation, consistent with a tri-modal AED, and the existence of at least three different types of adsorption sites. Some compounds interact with the surface through four different sites. Obviously, it is difficult to compare the results of chromatographic and NMR measurements. On the one hand, chromatographic measurements affords quantitative information regarding the adsorption parameters of one compound on the surface and these parameters (number, adsorption energy, and density of the different adsorption sites) depend both on the nature of the compound (e.g., its molecular volume, its hydrophobicity, its polarity, its charge) and on the characteristics of the adsorbent surface (degree of coverage, density, and acidity of the underivatized silanol groups). On the other hand, no probe is used in the NMR measurements, so the quantitative information derived from the data is limited to the structure and the dynamics of the C30 -alkyl chains bonded to the silica surface. Chromatographic measurements shed some light on the different possible interactions that could be involved between the analyte-probe and the adsorbent surface, whether onto, into the hydrophobic layer or onto the silica surface. Not surprisingly, chromatographic data give a richer amount of information on this matter than NMR data. Despite the fundamental differences in the approaches of the two methods, the results are consistent and NMR identified positively the coexistence of domains in which the chains are rigidly arranged and of others in which they exhibit a high degree of flexibility and disorder. This conclusion comforts the chromatographic results. It is expected that local heterogeneities exist in the disordered regions of the hydrophobic layer where the analyte molecules interact with the stationary phase in ways that are different from those in which they interact with the ordered parts. The analyte molecules can squeeze between disordered chains where their interaction energies with the stationary phase are higher than when they interact with the tip of the bonded chains in regions where these chains are well ordered and rigid. It is reasonable to think that the former case includes the sites of types 2, 3, and probably 4 for certain compounds while the latter corresponds essentially to the sites of type 1.

55

In addition to a method of examining the heterogenous structure of the C30 -bonded phase, the FA measurements provide a good test of evaluation of the consequences of an absence of endcapping of the material packing and of the presence of ionized silanols on its surface. The use of a non-buffered mobile phase such as the one selected for this work, which had a pH close to neutral, leads to the partial ionization of the silanol groups on conventional porous silicas [33]. Then, obvious differences are observed between the adsorption models of a positively and a negatively charged compound. In the latter case, only three different types of adsorption sites are observed while those of four types of sites are found in the former case. The fourth type of sites must be attributed to strong ion-exchange interactions that cannot take place between the ionized silanol groups and an anionic compound. The choice of phenol, caffeine, sodium 2-naphthalene sulfonate, and propranololium chloride as test probes for FA measurements made possible to demonstrate the surface heterogeneity of the RPLC packing material. First, these compounds have all convex upward Langmuirian adsorption isotherms and no adsorbate–adsorbate interactions take place. Their overall isotherms can be resolved into the sum of a few local Langmuir isotherms, each describing the adsorption of the probe on a particular type of adsorption sites. Second, the differences in ˚ 3 ) permits the study of their molecular sizes (from 82 to 263 A the relationship between this size and the characteristics of the adsorption on the different types of sites. This indicates whether the type of interactions between the analyte and the surface is of dispersive origin (in which case, ln b increases linearly with increasing molecular volume). We will use this test for a systematic characterization of other types of RPLC adsorbents like those used in new commercial columns, which are supposed to exhibit fewer “active” sites than traditional ones. Acknowledgments This work was supported in part by grant CHE-00-70548 of the National Science Foundation and by the cooperative agreement between the University of Tennessee and the Oak Ridge National Laboratory. We thank Ryam Kafrim from the Department of Chemistry at the University of Tennessee for the calculation of the molecular volumes of the different compounds used in this study and the precious discussion about the simulation program Sybyl7.0. References [1] U.D. Neue, D.J. Phillips, T.H. Walter, M. Capparella, B. Alden, R.P. Fisk, LC–GC 12 (6) (1994) 468. [2] D.V. McCalley, Anal. Chem. 75 (2003) 3404. [3] F. Gritti, G. Guiochon, J. Chromatogr. A 1028 (2004) 75. [4] F. Gritti, G. Guiochon, Anal. Chem. 75 (2003) 5726. [5] F. Gritti, G. Guiochon, Anal. Chem. 77 (2005) 1020. [6] L.C. Sander, J.B. Callis, L.R. Field, Anal. Chem. 55 (1983) 1068. [7] M. Ho, M. Cai, J.E. Pemberton, Anal. Chem. 69 (1997) 2613. [8] L.C. Sander, C.J. Glinka, S.A. Wise, Anal. Chem. 62 (1990) 1099. [9] M. Pursch, L.C. Sander, H.-J. Egelhaaf, M. raitza, S.A. Wise, D. Oelkrug, K. Albert, J. Am. Chem. Soc. 121 (1999) 3201.

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