A Comparison of Frontal and Nonfrontal Methods for Determining

Langmuir 2007, 23, 4095-4101

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A Comparison of Frontal and Nonfrontal Methods for Determining Solid-Liquid Adsorption Isotherms Using Inverse Liquid Chromatography Pirre P. Yla¨-Ma¨iha¨niemi and Daryl R. Williams* Department of Chemical Engineering, Imperial College of Science, Technology and Medicine, Prince Consort Road, South Kensington, London SW7 2AZ, United Kingdom ReceiVed NoVember 8, 2006. In Final Form: December 17, 2006 Inverse liquid chromatography (ILC) has been used to determine experimental isotherms for the equilibrium adsorption of cyclohexanone onto a silica (61.8 m2/g) from hexane using the peak maximum (PM), elution by characteristic point (ECP), frontal analysis (FA), and frontal analysis by characteristic point (FACP) methods. Isotherms obtained using these four approaches gave good internal agreement, as well as being in good agreement with classically determined isotherms. Columns were successfully packed using a dry powder packing method with 9 µm diameter silica particles, and excellent intercolumn and instrument to instrument reproducibility was obtained for PM isotherms. The theoretical background to the PM, ECP, FA, and FACP methods, as well as the practical facets of isotherm determination using these methods, is outlined in this work.

Introduction Inverse liquid chromatography (ILC) is a technique for studying solid-liquid interactions, and most specifically the determination of solute adsorption isotherms, based on the use of standard LC equipment. A wide range of problems can be addressed using such a methodology including an improved understanding of the underpinning chromatographic science, determination of the intrinsic surface physicochemical characteristics of particulate materials, or an improvement in our understanding of preparative and production-scale chromatographic processes which are usually undertaken using nonlinear chromatographic conditions. ILC is clearly analogous to inverse gas chromatography (IGC), which has attracted widespread interest during the past 25 years,1,2 especially for the characterization of polymers and, more recently, pharmaceutical solids.3 ILC offers a number of clear benefits over IGC such as the potential for studying large solute molecules whose low vapor pressure would make them unsuitable for IGC, as well as polymeric solutes which also cannot be studied using IGC. Furthermore, ILC allows the direct study of solid-liquid interactions present in many industrial processes under real work conditions including relevant concentrations, pressures, temperatures, and pH values. Though the difference between IGC and ILC simply relates to the use of a liquid versus a gaseous mobile phase for delivering the solute to the sample surface, the implications of this variation are profound. This same advantage is also the greatest complication in the practical use of ILC. All ILC measurements are a result of a real competition between the solute and the mobile phase for interacting with the stationary solid phase, unlike IGC wherein the mobile phase, such as helium, can be assumed to be virtually inactive in the gas-phase solute adsorption process. * To whom correspondence [email protected].

should

be

addressed.

E-mail:

(1) Lloyd, D. R.; Ward, T. C.; Schreiber, H. P. InVerse Gas Chromatography; ACS Symposium No. 391; American Chemical Society: Washington, DC, 1989. (2) Williams, D. R. J. Chromatogr., A 2002, 969, 1-2. (3) Heng, J. Y. Y.; Pearse, D. F.; Wilson, D. A.; Williams, D. R. Characterization of Solid State Materials using Vapor Sorption Method. Solid State Characterization of Pharmaceuticals; ASSA International: Danbury, CT, 2006.

In ILC, the retention behavior of known solutes, eluted by a liquid mobile phase through a packed column of the unknown solid material, is studied. From the resulting solute chromatograms the equilibrium solute adsorption isotherms may be derived on the basis of a pulse or frontal analysis method.4-6 For a pulse method, a known quantity of a solute is injected into a column, resulting in a pulse chromatographic peak. In frontal analysis, instead, the solute concentration in the mobile phase is changed to a new constant value, resulting in a boundary breakthrough curve. The peak maximum (PM) and the elution by characteristic point (ECP) are alternative pulse methods for isotherm determination. Similarly, there are two alternative frontal analysis methods for an isotherm determination, frontal analysis (FA) and frontal analysis by characteristic point (FACP). In the characteristic point methods (ECP and FACP), an isotherm can be derived from a single experiment, while the PM and FA methods require a number of pulse peaks or frontal breakthrough curves to construct the isotherm.6 In many reported studies, liquid chromatographic (LC) retention data have been used for determining isotherms with the intention of achieving a better fundamental understanding of analytical or preparative chromatography processes.7-10 For such studies, the surface characterization of the stationary phase was not itself the main purpose in these studies, and therefore, the work reported was conducted using commercial chromatographic stationary phases that have been designed for analytical or preparative applications. These columns were often commercially slurry packed columns, whereas in the current work the columns were prepared using a dry small-scale preparation approach. Slurry packing techniques are typically much more complicated and (4) Hayashi, J.-I.; Amamoto, S.; Kusakabe, K.; Morooka, S. Energy Fuels 1993, 7, 1112-1117. (5) Donnet, J. B.; Li, Y. J.; Wang, T. K.; Balard, H.; Burns, G. T. Rubber Chem. Technol. 2002, 75, 811-824. (6) Conder, J. R.; Young, C. L. Physicochemical Measurement by Gas Chromatography; John Wiley & Sons: Chichester, U.K., 1979. (7) Jacobson, J. M.; Frenz, J. H.; Horva´th, C. Ind. Eng. Chem. Res. 1987, 26, 43-50. (8) Guillaume, M.; Jaulmes, A.; Se´bille, B.; Thuaud, N.; Vidal-Madjar, C. J. Chromatogr., B 2001, 753, 131-138. (9) Blanco, R.; Arai, A.; Grinberg, N.; Yarmush, D. M.; Karger, B. L. J. Chromatogr. 1989, 482, 1-12. (10) Gritti, F.; Guiochon, G. J. Chromatogr., A 2004, 1028, 105-119.

10.1021/la0632631 CCC: $37.00 © 2007 American Chemical Society Published on Web 03/01/2007

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time-consuming to develop than dry packing techniques for the column preparation, though are the preferred methods when columns of high chromatographic efficiency are desired as in analytical separations. Yet the column efficiency in physicochemical liquid chromatography could be expected to be less significant than in analytical liquid chromatography where the chromatograms are known to be a result of equilibrium phenomena, as peak resolution is not a specific requirement. Therefore, dry packing techniques, being both quick and simple procedures, are essential for the potential use of ILC as a material characterization method. Very few ILC studies have been published on the physicochemical characterization of the solid-state materials or solidliquid systems/interactions. In some studies, solute adsorption isotherms have been measured and compared by different isotherm determination methods. De Jong et al.11 compared PM, FA, a perturbation, and static solution methods for the isotherm determination of phenol adsorption from dichloromethane on silica. Isotherms were only determined mainly in the linear, lower surface coverage range of the isotherms, and no detailed analysis of errors or absolute isotherm comparisons were provided. The log-log plots produced support the premise that the methods give comparable results. Jacobson et al.12 discussed the advantages and disadvantages of different dynamic isotherm determination methods, including the FA, ECP, and FACP methods. Isotherms by FA and FACP under reversed-phase conditions (p-cresol from water on octadecylsilica) were compared, and the FA isotherms were concluded as the more precise isotherms due to nonidealities in the FACP data. The adsorption and desorption behavior of a model water pollutant molecule (phenylalanine) on a heterogeneous surface (porous activated carbon) was studied by Gorner et al.13 They determined isotherms from aqueous solutions by the FA and FACP methods. Several columns were prepared to measure FA adsorption data points with a freshly packed column used to obtain each isotherm point. The FA desorption experiments were conducted with columns equilibrated with a solute solution (after an FA adsorption experiment). Gorner et al. did not observe any evidence of adsorption hysteresis but noted that reusing columns resulted in lower amounts of adsorption initially, prior to stabilizing on the third measurement. The FACP isotherms were consistent at lower solute concentrations, while at higher concentrations, the FACP isotherms predicted significantly increased solute uptake values. Donnet et al.14 conducted studies of squalene adsorption from heptane on a precipitated silica material and determined FA and FACP isotherms. Donnet et al. observed a decrease in adsorption when consecutive experiments of the same solute concentration were repeated in the same column up to the fourth repeated experiment. It was stated that the reproducibility between the isotherms based on the third and fourth runs was good. The standard deviation for monolayer capacity was less than 6% between the isotherms of the third and fourth runs, and these isotherms were consistent with static results. More significant deviations were observed between isotherms based on the first and second runs. The objective of this investigation is to systematically study isotherm determinations using the PM, FA, ECP and FACP ILC methods over a wide solute concentration range with fresh laboratory-prepared dry packed columns, rather than commercially prepared columns. These ILC isotherms would then (11) De Jong, A. W. J.; Kraak, J. C.; Poppe, H.; Nooitgedacht, F. J. Chromatogr. 1980, 193, 181-195. (12) Jacobson, J.; Frenz, J.; Horvath, C. J. Chromatogr. 1984, 316, 53-68. (13) Gorner, T.; Villie´ras, F.; Polakovicˆ, M.; de Donato, P.; Garnier, C.; PaivaCabral, M.; Luc Bersillon, J. Langmuir 2002, 18, 8546-8552. (14) Donnet, J. B.; Balard, H.; Zhang, Z. T.; Pilard, J. F. Kautsch. Gummi Kunstst. 2004, 57, 151-159.

Yla¨-Ma¨iha¨niemi and Williams

be validated by comparing them with isotherms obtained by a conventional static solution method. Such work is an essential step in the development of ILC as a method for the determination of solution adsorption isotherms.

Theory The theory for determining adsorption isotherms by means of chromatographic measurements is based on a differential dynamic mass balance equation in a chromatographic column. The basic retention equation, which describes the relationship between the retention volume and the uptake of an isotherm, is derived from this mass balance equation.6 The mass balance for a single solute adsorption system in an isothermal and radially homogeneous column, assuming a constant mobile phase flow rate and an instantaneous mass transfer,15 can be expressed by eq 1, where

δn δc dx F ) cF - (c + δc)F ) -δc F ) δt δx t

( )

(1)

n is the number of moles of solute molecules, t is the time, c is the solute concentration in the mobile phase, F is the mobile phase volumetric flow rate, x is the column length, and δc/δx is the slope of the concentration gradient in the column infinitesimally narrow cross-section. For a single solute system, the amount of moles of solute molecules in a column with an infinitesimally narrow crosssection, dx, can be separated into the amount of moles in the mobile phase, nm, and the amount of moles on the stationary phase, ns (the amount adsorbed). Thus, the accumulation can also be expressed by eq 2, in which Ac dx represents the volume

( ) ( ) ()

δnm δns δc δn ) + ) A dx + δt δt x δt x δt x c

( )

δq (1 - )Ac dx (2) δt x

of the mobile phase and (1 - )Ac dx the volume of the stationary phase.  is the void fraction in a column, Ac is the cross-sectional area of a column, and q is the solute concentration on the stationary phase (uptake). When eqs 1 and 2 are combined and divided by dx, the result is differential dynamic mass balance eq 3. Equation 3 is first

F

(δxδc) + A (δcδt ) + (1 - )A (δqδt ) ) 0 t

c

x

c

x

(3)

divided by (δc/δt)x. Applying Euler’s chain relation, the equation can be transformed to eq 4. The function x ) x(t) at fixed concentration c describes the velocity of a point on a boundary of concentration c as the boundary migrates through the column.

-

dq F + Ac + (1 - )Ac )0 dc x (δx/δt)c

( )

(4)

This point on the boundary is a solute characteristic point, and it migrates with the characteristic velocity, which depends on the slope of the isotherm at concentration c. The term (δx/δt)c in eq 4 represents the characteristic velocity; therefore, time t in (δx/ δt)c represents the retention time tr of the characteristic point at concentration c.6 Equation 4 can be integrated, resulting in retention eq 5 in which the net retention volume, Vn, is obtained by subtracting the column void volume, Vo ()Acx), from the retention volume, Vr ()Ftr). Equation 5 is based on the volume (15) Guiochon, G.; Shirazi, S. G.; Katti, A. M. Fundamentals of PreparatiVe and Nonlinear Chromatography; Academic Press: Boston, 1994.

ILC and Isotherm Determination

Vn ) Vs

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dq dc

(5)

of the stationary phase, Vs ()(1 - )Acx). However, eq 5 can also be expressed on the basis of either the mass of the stationary phase or the surface area of the stationary phase.6 As the mass of the solid material is often the easiest to measure, the retention equation with the mass of the stationary phase, m, will be employed for further derivations of the isotherm equations. Peak Maximum. At finite concentration, when the isotherm is nonlinear, dq/dc in eq 5 represents the slope of the tangent of the isotherm at the measured solute concentration.6 The isotherm can be obtained by numerical integration of the experimental retention data. The values of the net retention volume divided by the mass of the stationary phase of different solute concentrations can be plotted against the solute concentration as shown in Figure 1. The uptake values for the isotherm are then obtained from the areas of rectangles. The rectangles lie between the experimental Vm/m values, minimizing the error of the numerical integration since the area which is lost and the area which is overestimated approximately mutually compensate each other. However, the rectangle of the smallest concentration is an exception, and the overall error depends on how narrow the first rectangle is. Consequently, the smallest concentration (injection size) for the experimental data points should ideally be as small as practical. Elution by Characteristic Point. The ECP isotherm is determined from the chromatographic peak of a single solute injection assuming that peak maxima of smaller injection volumes, if injected, would lie on the diffuse profile of this largest injected peak. This concept is illustrated in Figure 2, where the rear diffuse boundary of peak h2 falls under the rear diffusion boundary of the larger injection, hmax. Thus, the retention volumes for all noninjected (virtual) peaks are obtained from the corresponding time values of the diffuse profile of the largest injected peak, hmax. Since the solute concentration for the largest peak is known, and because the height of the peak corresponds to the solute concentration, the solute concentrations for the smaller noninjected peaks can be calculated from eq 6, where cmax is the solute

cmax c2 ) hmax h2

ns cpVn cptnF (area)F ) ) ) m m m m

Figure 2. Isotherm determination in the ECP method. The solid line represents the peak injected, and the dashed line represents one of the smaller noninjected (imagined) peaks.

Figure 3. Self-sharpening boundaries in the FA method.

Figure 4. Diffuse boundaries in the FA method.

(6)

concentration of the largest peak, hmax is the height of the largest peak, c2 is the solute concentration of a smaller peak, and h2 is the height of a smaller peak. The actual ECP isotherm can be obtained on the basis of eq 5 in conjunction with the numerical integration presented in Figure 1. Frontal Analysis. The principle for determining isotherms by the FA method is shown in eq 7 and Figure 3. The number of moles of solute molecules retained by the stationary phase, ns,

q)

Figure 1. Isotherm determination by numerical integration in the PM method.

(7)

is equal to the net retention volume, Vn, multiplied by the concentration of the plateau of the frontal boundary, cp. The net retention volume can be expressed by the net retention time, tn, and the flow rate, F. On the other hand, the net retention time multiplied by the plateau concentration is equal to the shaded area in Figure 3. Hence, in frontal experiments, the uptake q of an isotherm is proportional to the area between the frontal boundaries of a nonretained component and the solute.6 In practice, frontal boundaries tend to be more diffuse in shape than those shown in Figure 3.6 Figure 4 presents the more realistic

Figure 5. Simplified area calculation in the FA method.

case in which the boundaries are diffuse, though the boundary of the breakthrough curve (adsorption) is sharper and less diffuse. In that case the uptake for the isotherm is obtained using eq 8 for adsorption and eq 9 for desorption, where ts is the time when the concentration reaches the steady state and to is the retention time of a nonretained component.

(area)F (cp(ts - to) q) ) m m

∫t t c dt)F s

o

∫t t c dt

(8)

s

(area)F q) ) m

o

m

F

(9)

Figure 5 shows a simplified calculation for the area of the adsorption and desorption experiments using the retention time of the turning point (tr, c/2) of the diffuse boundary. This method naturally causes some errors for the isotherm determination, but this approach is an attractive option if the boundary is not very diffuse.

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Figure 6. Isotherm determination in the FACP method. The solid line represents the boundary obtained by a frontal experiment, and the dashed line represents one of the smaller (imagined) boundaries assumed overlapping with the largest boundary.

Frontal Analysis by Characteristic Point. The determination of an FACP isotherm is similar to the determination of an ECP isotherm, except the calculations are based on the frontal boundary as in the FA method. In other words, a single diffuse rear boundary of a frontal analysis is analyzed, and many isotherm data points are derived from that boundary.6 Figure 6 demonstrates how a boundary of a smaller (imagined) plateau concentration (c2, h2) is assumed overlapping with the boundary achieved by a frontal experiment (cmax, hmax). As in the ECP method, the height of the plateau corresponds to the solute concentration. Consequently, provided that the x-axis value of the isotherm is expressed as the solute concentration divided by the maximum solute concentration (c/co), then the c/co values for all smaller boundaries can be obtained according to eq 10, where cmax is the solute concentration

(c/co)max (c/co)2

)

hmax h2

(10)

of the highest plateau, c2 is the solute concentration of a smaller plateau, hmax is the height of the largest plateau, and h2 is the height of a smaller plateau. The uptake values for the isotherm (y-axis values) are obtained according to eq 9 on the basis of the corresponding time values of the largest boundary. Experimental Section Adsorbent, Solute, and Solvent. Silica Exsil 300 supplied by Alltech Associates (Lancashire, U.K.) was chosen as a model solid sample (adsorbent) for the experiments. Using a Micromeritics ASAP 2000 surface area analyzer (Norcross, GA), a BET surface area of 61.8 m2/g was obtained. An average particle size for a spherical silica Exsil powder of 10 µm and a pore diameter of 300 Å were quoted by the manufacturer. A particle size distribution of 3.3-20 µm (80% of the particles 99.5%) supplied by BDH Chemicals (Poole, U.K.) as the solute molecule. All experiments were carried out by using HPLC grade hexane (ca. 95% n-hexane) supplied by Fisher Scientific UK (Leicestershire, U.K.) as the solvent. 1-Hexene (99+%, Sigma-Aldrich, Dorset, U.K.) was chosen as a nonretained component for determining the column void (empty) volume since it has a molecular structure very similar to that of hexane and is detectable by a UV detector. The retention times of cyclohexanone injections correlated strongly with the solute concentration, while the retention times for 1-hexene were virtually independent of the concentration. 1-Hexene did not exhibit strong adsorption on this solid surface (silica Exsil), and it was concluded to be an appropriate molecule for the void volume determination.16,17 Isotherm Determination by a Static Method. Isotherms of cyclohexanone adsorption from hexane on silica Exsil material were determined using a solution method. A known mass of silica (0.926 (16) Yla¨-Ma¨iha¨niemi, P. A Novel Method for Investigating Solid-Liquid Interactions: Inverse Liquid Chromatography. Ph.D. Thesis, Imperial College, London, 2006. (17) Yla¨-Ma¨iha¨niemi, P.; Williams, D. R. J. Chromatogr., A, manuscript in preparation.

g) was mixed with known amounts of hexane (4.62169 g) and cyclohexanone (0.00931 g). The mixture was shaken for 20 min and then stabilized at 25 °C for at least 1 h. Subsequently, the liquidphase cyclohexanone concentration was analyzed by a gas chromatograph (Pye Unicam) using a flame ionization detector and manual 0.2 µL liquid injection. A Supelco SPB 5 column (30 m × 0.53 mm i.d.) operating at 113 °C was used with He carrier gas. The cyclohexanone concentration in the hexane solution was determined by reference to a calibration curve which had been previously determined using a range of standard solutions. The peak areas of cyclohexanone peaks (average of three measurements, RSD < 2.5%) in the standard solutions were plotted against known cyclohexanone concentrations in the standard solutions. The cyclohexanone peak area of the sample solution was the average peak area of two analyses. Repeat measurements with a difference of