Solution adsorption from liquid chromatography

Solution Adsorption from Liquid Chromatography H. L. WANG,* J. L. DUDA,* AND C. J. R A D K E t '1 *Chemical Engineering Department, The Pennsylvania State University, University Park, Pennsylvania 16802, and ?Chemical Engineering Department, University of California, Berkeley, California 94720 Received April 23, 1977; accepted February 27, 1978 The dynamic technique of frontal analysis is applied toward the measurement of binary solutionsolid adsorption utilizing a commercial liquid chromatograph. The original mathematical treatment of ideal equilibrium chromatography is reexamined. Careful analysis of the chromatographic adsorption process indicates that the absolute surface excess concentration determined from the dynamic experiment is constrained to be a volumetric reduced adsorption if the assumption of constant volumetric flow rate is made. A macroscopic approach, however, shows that this constraint can be removed if, in addition to the outlet concentration, the outlet flow rate is accurately monitored. The macroscopic approach also reveals that the dynamic technique can be applied in spite of finite mass transfer resistance and adsorption kinetics. New dynamic and static experimental results for the system n-hexane/n-hexanollsilica gel are presented and are shown to agree over the entire composition range. The advantages of the dynamic flow technique are outlined. INTRODUCTION

Traditionally, adsorption from solution is determined by contacting a known amount of liquid solution of known composition with a known amount of solid adsorbent, agitating until equilibrium is attained, and measuring the final equilibrium bulk composition. One of the major problems with this static technique is the difficulty in accurately measuring concentration changes, especially when the solution is very dilute or when the system contains only slightly adsorbing species. Accurate concentration measurements can be eliminated in a dynamic technique in which a solution step-concentration change is introduced into an adsorbent-packed column and the adsorption amount is calculated from the breakthrough time of the concentration wave. Although this dynamic or chromatographic technique has been widely used in the determination of adsorption from gases (1-4), little effort has been directed toward 1 To whom correspondence should be addressed.

liquid systems. This may be partly due to the equipment requirements associated with the dynamic technique. However, high-pressure commercial liquid chromatography has become quite common in recent years and this study demonstrates that, with only slight modifications, a commercial liquid chromatograph can be used to measure adsorption from solution. Calculation of a solution adsorption isotherm with the dynamic technique requires a quantitative description of the chromatographic process. The first mathematical description of ideal equilibrium chromatography was derived by Wilson (5) and subsequently modified by DeVault (6) using a differential material balance. The theoretical treatments of Wilson and DeVault deal more extensively with the mathematics of flow through a packed column than with the nature of the adsorption process. Equivalent derivations were given by many following authors and these early studies were reviewed by Claesson (7). Smit and Van Den Hoek (8) later pointed

153

0021-9797/78/0661-0153502.00/0 Journal of Colloid and Interface Science, Vol. 66, No. 1, August 1978

Copyright © 1978 by Academic Press, In¢. All rights of reproduction in any form reserved.

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WANG, DUDA, AND RADKE

out that, for liquid systems, "preferential" adsorption isotherms should be used in DeVault's equation and they suggested that adsorption and composition be expressed in volume units and volume fraction. This suggestion was restated by Bayl6 and Klinkenberg (9). Schay et al. (10) proposed a simplified mode of determining adsorption isotherms by frontal chromatography and made use of material balance equations' comprising the state of the chromatographic column before and after complete breakthrough of a concentration front. Recently, Sharma and Fort (11) utilized a pumpdriven liquid chromatograph in place of the traditional gravitational chromatographic column to study dilute liquid solutionsolid adsorptions based on an overall material balance. Their experiments involved the introduction of a step-concentration change from a pure solvent to a solution of desired concentration and thus required a desorption procedure for each separate concentration. Sharma and Fort do point out that the macroscopic frontal-analysis technique can apply to adsorption measurements with channeling, diffusion, and finite adsorption kinetics. Some assumptions, however, have been involved in the preceding analyses without being mentioned. For example, the assumptions of isochoric adsorption and a stationary adsorbed phase have been implicit in all previous studies. Some treatments even neglect the occupied volume of the adsorbed phase. Thus questions arise whether these assumptions put constraints on the behavior of the measured adsorption isotherm and whether the measured adsorption is identical to that obtained by the conventional static method. This work pursues the answers to these questions by a detailed mathematical analysis of the adsorption and transport occurring on the chromatographic column and by experimentally comparing the static and dynamic adsorption isotherms for the system n-hexane/n-hexanol/silica gel over the entire solution composition range. Journal of Colloid and Interface Science, Vol. 66, No. 1, August 1978

In chromatography the term "adsorption" is often referred to in an ambiguous manner. Hence, in the following theoretical development, we employ the conventions of Gibbs as summarized by the IUPAC Council (12). THEORY

The mathematical treatment of an adsorption chromatographic column is essentially a material balance incorporating the Gibbsian definition of adsorption. Two alternative approaches to the theory of chromatographic adsorption measurement are presented. The microscopic approach, which is similar to DeVault's treatment (6), deals exclusively with an isochoric ideal equilibrium chromatography. Based on a mass balance over a differential section of column, this approach is capable of describing the concentration velocity inside the column. The alternate macroscopic approach, which is based on a mass balance over the entire column, can be applied in adsorption measurements for real general cases which include the effects of volume changes, dispersion, and finite adsorption kinetics. However, the macroscopic approach is applicable only to the frontal analysis technique. Microscopic Approach Consider a liquid solution flowing through a packed column of uniform cross-sectional area, A. The mass balance equation of species i for assumed one-dimensional plug flow in the absence of longitudinal diffusion can be written as

1 __° ( p , Q ) _ A Ox

oq,+ , Ot

[1]

where Q is the volumetric flow rate, /5+ is the average mass concentration of species i in the moving stream excluding the material which is held stationary by the surface or other mechanisms, and ~bi is the mass of species i per unit volume of column at the position, x, and time, t. Equation [1] is the

SOLUTION ADSORPTION FROM LIQUID CHROMATOGRAPHY

155

basic transport equation which will be used later in the analysis of the chromatographic process. It is the species accumulation term H (O@dOt) that is associated with the adsorption phenomena occurring in the column. To show how tO~is related to adsorption of species i, consider a rectangular model --Z=Bi 2=0 of a differential section of the chromatographic column as shown in Fig. 1. The schematic column section of Fig. 1 aids in visualizing the chromatographic process, FIG. 1. Rectangular model of a differential chrobut does not limit the generality of the result- matographic column section. (Flow is in the positive ing equations. In Fig. 1, a solid adsorbent x direction.) of thickness hi and surface area W2d~ is exposed to a liquid solution of height h2. surface is chosen at the solid surface (i.e., The y - z plane corresponds to the cross sec= 0), the surface excess quantity, now tion of the column. The dimensions of this denoted as F~(°), is called the absolute idealized column section can be related to surface excess concentration (ASEC) of the actual parameters for the entire column species i. ASEC is the measured quantity in by the following identities: conventional gas-solid adsorption experiments (14). Its value is generally positive V = column volume = (W)(H)(L), for gaseous systems since the density in the A = column cross-sectional area adsorption space is always greater than that = (W)(H), [2] in the gas phase. In some high-pressure gas adsorption studies (15-17), the adsorpMas = total surface area of adsorbent tion isotherm was observed to pass through = ( L ) ( W ) , and a maximum with increasing pressure. This e = column porosity = hz/H. maximum is consistent with the " e x c e s s " When equilibrium is established in this concept. For a particular species in liquid idealized differential section, the concen- solution, the ASEC may be positive or negatration profiles of all species become func- tive, exhibiting maxima and/or minima, tions only of distance from the solid sur- because the adsorption mechanism is face. For a solution-impermeable solid mainly due to shifts in solution composisystem, Gibbs' definition of adsorption (13) tion rather than shifts in solution density. reduces to It should be emphasized that ASEC is not measured in the conventional liquid-solid F~(~) = pi(z)dz + [p~(z)- pi=Jdz, [3] adsorption experiments, rather a reduced adsorption (12) is detected. The mass of h~ ~5 species i per unit volume of column in where z is the distance from the solid surEq. [1] is defined by a volume-average face, p~ is the mass concentration of species concentration over the column volume of i, and the superscript ~ denotes the conthe section, centration far from the solid surface. The Gibbsian surface excess quantity, F~(~>, is Mas I~ ~ pi(z)dz. [4] called the surface excess concentration of ~i V hi species i with respect to the dividing surface of z = 8 for its magnitude critically depends The definition of species surface excess on the arbitrary location of 8. If the dividing concentration in Eq. [3] transforms Eq.

I

Journal of Colloid and Interface Science, Vol. 66, No. 1, August 1978

156

WANG,

DUDA, AND RADKE

[4] to

@~

Mas =

V

F( °~ + Em ~.

[5]

Thus, the column-average mass concentration is composed of an ASEC term and a bulk concentration term. To relate tk~ to a reduced adsorption, we presume that the adsorption process is isochoric demanding that no volume changes occur due to bulk mixing and no volume contractions or expansions occur near the solid surface due to changes in molecular configuration, orientation, or force fields. Then the partial specific volumes, V~, become constants which are independent of local composition and distance from the solid surface. With this isochoric restriction, application of Eq. [3] reveals that the summation of the products of partial specific volume and species surface excess concentration over all species is equal to the location of the dividing surface: rCiF(~' = 3.

[6]

i=1

Inherent in Eq. [6] is the identity ~ = i

V~p~(z > 0) = 1. Finally, combination of Eqs. [3], [4], and [6] with the identities in Eq. [2] yields the desired expression for the column-average mass concentration of species i in terms of the volumetric reduced adsorption, Fiv:

Oi -

Mas V

F~v + ePi~ (isochoric adsorption).

[7]

The volumetric reduced adsorption is defined analogously to the conventional mass or molar reduced adsorption, Fim or F~n, except that its use is confined to isochoric mixing systems (18, 19), Fiv __-

Vo

(pO _ p~)

Mas = r, -

(6r.

[8]

1=1

Journal of Colloid and Interface Science, Vol. 66, No. 1, August 1978

where the initial solution has volume V° and mass concentration pfl. Note that Eq. [7] applies only when isochoric adsorption is assumed whereas Eq. [5] is valid in all cases. We now incorporate the preceding results into the mass balance equation. If adsorption equilibrium is established instantaneously at all points of the column, Eq. [5] can be substituted for the accumulation term in Eq. [1]. For a binary liquid, the adsorption isotherm, F(°), is a function of the concentration, p1¢~, because fixing pl ~ at constant temperature and pressure totally fixes the composition. Hence, the transport equation becomes 1

0 --

A Ox

(t51 Q)

-

( M ~ dF1¢°~

dpl ~

+

e

] OPl~ ] Ot

•

[9]

To simplify the chromatographic transport problem, we specify the average concentration of each species in the moving stream to be the bulk equilibrium concentration: Pi =Pi=

i

=

1, 2.

[10]

This requirement implies that the surface excess molecules comprising the ASEC are stationary but the remaining solution molecules, including those next to the solid surface, are moving with the bulk flow in the column. The ASEC molecules, as defined by F(°), can move downstream only by exchange with the moving stream. Thus, in this work the species ASECs define the stationary phase. The remainder of the liquid solution constitutes the mobile phase. Next, we make the approximation that the volumetric flow rate of the moving stream is constant throughout the column at any instant, i.e., OQ/Ox = 0. [11] The assumption of a constant volumetric flow rate in the column is used in almost

SOLUTION ADSORPTION FROM LIQUID CHROMATOGRAPHY all chromatographic experiments. However, implicit in Eq. [11] is the subtle restriction that the adsorption process be isochoric so that the partial specific volumes of both species remain constant in both the bulk phases and interfacial layer. The fact that a position-independent volumetric flow rate can be maintained only by an isochoric adsorption process has not been previously recognized; a detailed proof is found in the Appendix. Recall now that Eq. [7] applies only when the adsorption process is isochoric. Thus, comparison of Eqs. [5] and [7] reveals that the ASEC becomes identical to the volumetric reduced adsorption when isochoric adsorption or constant volumetric flow rate is assumed. In other words, when a constant volumetric flow rate is assumed, information about the adsorption behavior of individual species is lost and only information on exchange adsorption between species can be obtained. Under the assumptions embodied in Eqs. [10] and [11], the basic transport relation, Eq. [9], reduces to

Q Opl ~ A

Ox

~ Ma~ dF1 v -

L

V

- -

dpi =

] Opl ~ +

• j

J--~'

[12]

where Fav has been used in order to emphasize the isochoric constraint on the adsorption process. Since the bulk concentration varies with column position and time, Eq. [12] rearranges to an expression for the concentration velocity:

( Ox ) - - ~ p,~ =

Q/•A Mas dF1 v I+-• V dpl ~

[13]

Equation [13] is the fundamental relation of isochoric ideal equilibrium adsorption chromatography. It prescribes the concentration velocities of a concentration boundary moving down the column. The concentration velocity depends on the slope of the adsorption isotherm at that concentration. The steeper the slope, the slower that concentration moves. Consequently,

157

the concentration gradient boundary will become sharper as it travels down the column if the adsorption isotherm is convex over the concentration gradient range. On the other hand, it will tend to broaden if the adsorption isotherm is concave over that range. DeVault has thoroughly discussed these isotherm curvature phenomena (6). To determine an adsorption isotherm from the chromatographic process, Eq. [13] is integrated along a locus of constant concentration over the column length. Since F1v is a function of pl ~ only and Q is independent of position in the isochoric case, it follows that the slope of the volumetric reduced adsorption isotherm is related to the column dead volume Vd and the retention volume Vr or time tr of the particular concentration front:

Mas

dF1 v

dpl ~

- Qtr- eAL = Vr-

Va.

[14]

The derivation of Eq. [14] completes the microscopic approach discussion in that an adsorption isotherm can now be constructed from a chromatogram. Equation [14] assumes the same form as in DeVault's work (6) except that the restriction to a volumetric reduced adsorption isotherm is now rigorously introduced by the preceding analysis. This reduced adsorption isotherm corresponds to the "preferential isotherm" of Smit and Van Den Hoek if adsorption is expressed in volume units and concentration is expressed in volume fraction (8). Before presenting the macroscopic approach, we note that other reduced adsorption isotherms may be introduced into Eq. [14]. Thus analogous treatments show that the species ASEC becomes identical to the mass reduced or the molar reduced adsorption, respectively, if, instead of an isochoric process, a constant mass density or a constant molar density adsorption process is assumed (20). However, the isochoric process is the least stringent approximation of the three. This is apparent because the assumption of an isochoric process requires Journal o f Colloid and Interface Science, Vol. 66, No. 1, August 1978

158

WANG, DUDA, AND RADKE

only constant partial specific volumes of the two components. The assumption of a constant mass (or molar) density process requires constant and equal partial specific (or molar) volumes of the two components. Macroscopic

Approach

In the macroscopic analysis we restrict our attention to the frontal analysis technique where the column is preflushed with a solution of known composition, Pl', until equilibrium is established in the column. Then a concentration-step change to Pi" is introduced into the column at t = O, and the effluent flow rate and composition are recorded as functions of time until the effluent composition becomes steady and identical to the inlet composition. At this time, denoted by t~, equilibrium has been established with the new composition in the column. Under these circumstances, the integral mass balance for species 1 over the entire column and over the experimental time, t=, is ml(t~)

- ma(O) =

ii

+

{h,iQidt-

fo +

~,oQodt,

[15]

where tSl,i and t51,o are the average inlet and outlet concentrations of species 1 in the moving stream, Qi and Qo are the inlet and outlet volumetric flow rates, and ma is the total mass of species 1 in the column. Since the column is in adsorption equilibrium at both the initial and final states, we separate the mass in the column into equilibrium bulk and surface excess amounts according to Gibbs' definition, ml(t) = pl~(t)Vd

t = 0 , t=,

AF1 (o) Mas - A p l °~ = M a s [ FI(°)(pl') ] p- lPl' rl(°)(pl') , ,

pl"Qit~ -

[16]

where again F~(°) is the ASEC of species 1 and is a function of p O~. Next we again define the stationary and mobile phases as in the microscopic approach so that the bulk and the average flowing stream concentrations become identical [i.e., p~(0) =/5~,o(0) Journal o f Colloid and Interface Science, Vol. 66, No. 1, August 1978

+

pl,oQodt

=

-

[17]

Va.

Pl" -- P l '

As/5~,o(t) and Q o ( t ) are measurable, Eq. [17] provides a relation for calculating the slopes of chords of the species absolute surface excess isotherm (i.e., the function relating ASEC to the liquid concentration). As pointed out earlier, it is impossible to measure species absolute surface excess isotherms by the conventional static method. The capability of measuring the species absolute surface excess isotherms is the first unique feature of the macroscopic approach. If the volumetric flow rate of the effluent stream is presumed constant after an inlet step-concentration change is introduced, then Eq. [17] reduces to: Mas

+ F~(°)(p~(t))mas

for

= Pl', a n d pl~(t=) = pl,o(t~) = Pi"]. Furthermore, since commercial liquid chromatographs usually employ constant flow rate reciprocating pumps, the inlet volumetric flow rate is independent of time. However, since volume changes due to mixing and adsorption can occur, the outlet volumetric flow rate is not necessarily constant and indeed may be a function of time. Therefore Eqs. [15] and [16], when combined, reduce to:

[ : ]

AFlV Api---T -

pl"t~ -

Q

+ [~i,odt

pi" - p l ' -

v,~ = Q t r -

v~.

[18]

The bracketed term in Eq. [18] is the retention time of the step-concentration gradient boundary, tr. This retention time can be located graphically by equating the shaded areas in the outlet concentration versus

159

SOLUTION ADSORPTION FROM LIQUID CHROMATOGRAPHY

time response curve as shown in Fig. 2. The volumetric reduced adsorption isotherm, F1v, is employed in Eq. [18] to emphasize again that the assumption of constant volumetric flow rate places the constraint that F1(°) = F1v on the adsorption process. In the limit of Apl = ~ 0, Eq. [18] becomes identical to Eq. [14] which was derived from the microscopic approach for isochoric ideal equilibrium chromatography. However, review of the macroscopic approach shows that the macroscopic frontal-analysis technique applies equally well to noninstantaneous equilibrium cases. Consequently, Eq. [18] is valid even if complexities due to mass transfer resistance, slow adsorption process, back mixing, channeling, and other nonequilibrium processes are present. This is the second unique feature of the macroscopic approach. Because it is not restricted to ideal and instantaneous equilibrium chromatography, we employ the macroscopic frontal-analysis technique to determine experimental adsorption from binary liquid solutions. For simplicity the column outlet flow rate is assumed to be equal to the inlet flow rate. Hence, from Eq. [18], the adsorption isotherms so obtained are interpreted to be volumetric reduced adsorption isotherms. EXPERIMENTAL

To evaluate the dynamic technique we study adsorption from n-hexane/n-hexanol

g

~o Pt j -= 8

o

I

tr Time, t

FIG. 2. Retention time determination in macroscopic frontal analysis.

Pumpll

I

, I~Go

Re lef vo,vo+ v

I

Filter

Solution

--

Reservoir II

Ga Reference Valve

Draw-Off

Recorder

Waste

FIC. 3. Modified chromatographic apparatus for adsorption experiments.

solution on silica gel. This system is chosen since the adsorption of an alcohol and an alkane should be quite different on a polar solid. The particular silica gel chosen is a wide-pore (170 ]k) gel obtained from Davison Chemical Co. (Grade 62). Details of these experimental studies are presented by Wang (20).

Dynamic Experiments The apparatus utilized in the dynamic technique is a Waters Associates liquid chromatography instrument (ALC/GPC501) with a refractive index detector. However, for quantitative adsorption detection an additional pump is required and the injection valve must be modified to facilitate immediate flow switching between the two pumps. A schematic diagram of the adsorption apparatus is shown in Fig. 3. To start an adsorption experiment, two hexane/ hexanol binary solutions (I and II) with different compositions are prepared gravimetrically. The adsorption column is placed in a constant temperature bath (25 + 0. I°C) and is first flushed with Solution I until equilibrium is attained in the column. A step-concentration change from Solution I to Solution II is then introduced by switching the selection valve. The effluent composition is continuously monitored by the differential refractive index detector until a new equilibrium state is attained in the column. The flow rate is then measured by Journal of Colloid and Interface Science, Vol. 66, No. 1, August 1978

160

WANG, DUDA, AND RADKE

collecting and weighing the effluent. The corrected retention volume, which is directly related to the slope of the chord of the adsorption isotherm, is obtained by subtracting the column void volume and the dead volume of tubing and fittings from the total retention volume. The above frontalanalysis adsorption experiment is then repeated at different compositions over the entire composition range. The complete volumetric reduced adsorption isotherm is constructed by step-by-step summation over the slope data if the step-concentration change experiments are conducted sequentially, or by numerical integration if the experiments are carried out only at discrete points over the composition range. To enhance accuracy, adsorption experiments are performed with positive and negative concentration changes to see which direction gives a sharper response curve and hence a more precise retention time. The direction of the experiment is important at dilute hexanol concentrations where a sharp response curve is obtained only when a positive concentration change i s employed. The observed sharpening or broadening effects were consistent with the shape of the adsorption isotherm. Also, the relative insensitivity of the breakthrough curves to variations in flow rate and particle size reveals that mass transfer resistances outside and inside the pores are insignificant under the present experimental conditions. Furthermore, irreversible adsorption is measured by employing both fresh silica gel unexposed to hexanol and used silica gel from which the reversible adsorption of hexanol has been removed by extensive hexane flushing. Any difference in adsorption between the fresh and the reflushed silica gel is attributed to irreversible adsorption.

Static Experiments Static adsorption experiments are performed in the usual manner with glass adJournal of Colloid and Interface Science, Vol. 66, No. 1, August 1978

sorption flasks shaken in a thermostated water bath (25 _+ 0. I°C) and the adsorption isotherm is determined from the concentration changes. To prevent volatile losses and to allow convenient supernatant sample withdrawal, the adsorption flasks are sealed with Mininert-Valves (Applied Science Laboratories, Inc.) glass blown onto the flasks. In the determination of the equilibrium solution compositions, a conventional refractometer is used except at the two extreme ends of the composition range, where instead a differential refractometer is used to improve the accuracy. Bulk compositions in different adsorption bottles of identical initial conditions are measured after different time periods to check the rate of adsorption. The results of these experiments indicate that adsorption equilibrium in the hexane/hexanol/ silica gel system is established quickly and it gives credence to the instantaneous equilibrium assumption used in the microscopic chromatographic approach. This conclusion is also consistent with the dynamic observation that the adsorption is independent of particle size and flow rate. RESULTS AND DISCUSSION

Reduced Adsorption Isotherms Volumetric reduced adsorptions are measured in the dynamic technique, but mass reduced adsorptions are measured in the static method. Therefore, in order to compare results between the two types of measurements, the volumetric reduced adsorptions are transformed to mass reduced adsorptions: F1m = rlv/p~V2.

(19)

Figure 4 shows the mass reduced adsorption isotherm of hexanol in the dilute region for the n-hexaneln-hexanollsilica gel system at 25°C. These data could be interpreted as indicating a saturated or plateau adsorption. However, since a reduced adsorption isotherm is measured, the adsorp-

161

SOLUTION ADSORPTION FROM LIQUID CHROMATOGRAPHY

tion must return to zero when the composition corresponds to pure hexanol. This reduced adsorption behavior is shown in Figure 5 which presents the adsorption results for the entire composition range. Adsorption at high concentrations of hexanol (greater than 0.6 weight fraction) could not be measured accurately by the dynamic technique due to continuous drifting of the response curve. The reasons for this drifting could not be determined. It might be due to a slow adsorption process or a mass transfer resistance because of the relatively large viscosity of concentrated hexanol solutions or some undetermined equipment problems. Experimental points from both the static and the dynamic adsorption techniques are seen to agree everywhere. The root-mean-square deviation between the results of the two methods is 0.0127 g/g which corresponds to a 7.8% error at the maximum reduced adsorption. The static adsorption data are a little larger than the dynamic adsorption data. This consistent behavior might be explained by variations in surface preparation of the silica gel which is sensitive to preheating. Also, possible experimental errors in the first concentration-step change of the dynamic measurements, which is equal to about 74% 0.20

,

,

l

~

i

~

m

~

,

i

i

i

t

l

l

D O Q D O O D D

olo

c 0.05 .£ ~:~ Irreversible Adsorption

0.0 0.0

I

r

I O.Oi

p

I

I

I

I 0()2

I

r

I

I 0.03

Weight Froction of Hexonoi,w B

FIG, 4. Mass reduced adsorption isotherm of nhexanol for the n-hexane (species A)/n-hexanol (species B)/ silica-gel (340 mS/g) system at 25°C: (©) static measurements with absolute refractometry; (A) static measurements with differential refractometry; ([]) dynamic measurements. The line represents a nonlinear regression fit of the data.

0 2 0 ~ - -

I

I

I

I

I

4

F ~ - -

o1~ O QIC 0 0 i

0.0~

"~

0 Ir revetsibte

. . . . 00. .

C3

'

'

o'6

'

'

Weight Fraction of Hexan01, ~B

FIG. 5. Mass reduced adsorption isotherm of nhexanol for the n-hexane (species A)/n-hexanol (species B)/silica gel (340 m2/g) system at 25°C: (O) static measurements with absolute refractometry; (A) static measurements with differential refractometry; (CO) dynamic measurements. The line represents a nonlinear regression fit of the data. of the maximum adsorption, could account for the observed difference. Finally, a difference between the static and the dynamic measurement techniques could emerge because the chromatographic process is hydrodynamic in nature and retention of a particular solution component can be caused by mechanisms other than adsorption. Thus if large molecules, such as polymers, are present in the solution, mechanical entrapment (24) and/or volume exclusion from small pores (25) can influence the retention. Further, the hydrodynamic chromatographic effect (26) can arise whenever there is a large size difference among the solution molecules. For the present system, these purely hydrodynamic-retention mechanisms are not significant since the molecular sizes of the two species are of the same order and both are much smaller than the pore size. Thus the observed retention is due to adsorption only. The steep rise in adsorption at infinite dilution of hexanol and the " S " shape of the isotherm as shown in Fig. 5 are characteristics of reduced adsorption isotherms for which one component (hexanol) is more Journal of Colloid and Interface Science, V o l , 66, N o . 1, A u g u s t 1978

162

WANG, DUDA, AND RADKE

Ooqb 0

0

% °0o oO0Oo o o Adsorbed Phase

?! ; ffff Molecules of Species A 0

Molecules of Species B

FIG. 6. Extension of Schay and Nagy's monolayer analysis to binary mixtures of different molecular sizes and shapes (21). The dashed line is the dividing surface of irregular shape separating the mixed monolayer from the bulk solution. strongly adsorbed than the second component (hexane) (18). Agreement of the static and dynamic adsorption data proves that a volumetric reduced adsorption isotherm (or more generally, an absolute surface e x c e s s isotherm) is measured in the dynamic method. Because the adsorption isotherm has a negative slope over the middle concentration region, the material balance equations [14] and [18] predict that a concentration wave should elute faster than a pure fluid at the same flow rate. This is o b s e r v e d e x p e r i m e n t a l l y and f u r t h e r demonstrates that reduced isotherms are detected by the dynamic technique. The amount of hexanol that is irreversibly adsorbed is about 33% of the maximum adsorption. This irreversible adsorption begins at the lowest detectable concentration (0.001243 in hexanol weight fraction) and remains constant within experimental error over the whole composition range; it corresponds to about 20% of a monolayer of hexanol molecules oriented normal to the surface. Presumably the irreversible adsorption of hexanol arises from strong bonding of the alcohol to surface silanol or siloxane groups. Individual Isotherms

The term individual isotherm is defined as the function relating, at constant temJournal of Colloid and Interface Science, Vol. 66, No. 1, August 1978

perature and pressure, the amount of a particular component in the interfacial layer per unit surface area with the composition of the liquid phase (12). This function is meaningful only when the location and the thickness of the interfacial layer have been defined. The two individual isotherms of hexanol and hexane in the present system (i.e., FAs and FBs) are resolved from the reduced adsorption isotherm based on Schay's model of mixed monolayer adsorption (21). In this model, the solution material is divided into a homogeneous bulk phase and an adsorbed monolayer. Schay emphasized (22) that the concept of a mixed monolayer cannot be given any, even approximately clear, meaning if the constituent molecules are of materially different sizes and shapes. However, this limitation is not necessary and the monolayer analysis can be extended if the dividing surface is not restricted to be parallel to the solid surface, but can assume an irregular geometry such as the dashed line in Fig. 6 (20). Values of the monolayer capacities, (FA)m and (rB)m, used in the monolayer analysis are determined from the occupied areas per molecule on the surface and the specific area of the adsorbent. Since silica gel and hexanol are both polar but hexane is nonpolar, we presume that hexanol molecules are adsorbed in a vertical configuration with their polar hydroxyl ends adjacent to the silica gel surface. Conversely, hexane molecules are assumed not to be oriented on the surface. The occupied area per hexane molecule on the surface is estimated by assuming that the adsorbed molecules have the same packing as the molecules of the liquid state (14). With these approximations, the monolayer capacities, (FA)m and (FB)m, are calculated (20) to be 3.61 x 10-4 and 9.20 × 10-4 g/m z, respectively. These monolayer capacity values combined with 340 m2/g for the nitrogen BET surface area of silica gel permit separation of the experimental reduced adsorption isotherm into

163

SOLUTION ADSORPTION FROM LIQUID CHROMATOGRAPHY

two individual isotherms, FAs and FBs, as shown in Fig. 7. The results of the monolayer model reveal that the individual isotherm of hexanol increases with concentration very rapidly and reaches, at a very low concentration of less than 0.04 weight fraction, a plateau where the molar ratio of hexanol to hexane in the adsorbed monolayer is about 3. Another noticeable feature of the monolayer model is that the plateaus of the two individual isotherms cover a wide range of composition. Several possible explanations for this behavior can be found in Kipling's monograph (18). No attempt is made here to explain the shapes of the individual isotherms nor to apply the adsorbed phase models of Everett (23). The success of the monolayer model in correlating the adsorption data indicates that monolayer adsorption may be occurring, but it does not conclusively prove this. However, the possibility of monolayer adsorption in the present system is further strengthened by Kipling's observation that not all binary reduced adsorption isotherms can be resolved with a monolayer hypothesis (18). CONCLUSIONS

The dynamic technique of frontal analysis utilizing a commercial liquid chromatograph provides a convenient and accurate means for measuring liquid solution-solid adsorption. If a constant volumetric flow rate assumption is made in interpreting the chromatographic breakthrough curves, the absolute surface excess concentration (ASEC) determined from the dynamic experiment is constrained to be a volumetric reduced adsorption. A macroscopic approach, however, shows that this constraint can be removed if, in addition to the outlet concentration, the outlet flow rate is accurately monitored. The macroscopic analysis also reveals that the dynamic technique can be applied in spite of finite mass transfer resistances, adsorption kinetics, longitudinal molecular diffusion, and concentration

0.2

0.4 0.6 Weight Frcction of Hexonol, ~B

0.8

1.0

Fio. 7. Individualadsorptionisothermsof n-hexane (species A) and n-hexanol (species B) on silica gel (340 m~/g) at 25°C by Schay and Nagy's monolayer analysis (21).

spreading due to deviations from a plug flow velocity profile, such as channeling and/or back mixing. To increase the accuracy in analyzing the breakthrough curve, the dispersion of the breakthrough curve should be minimized by careful column packing and by adjusting operating conditions such as flow rate, particle size, and direction of concentration change. The dispersion of the breakthrough curve is partly related to the adsorption kinetics, and analysis of this dispersion can provide information for a kinetics study. Adsorption at high concentrations can be obtained by a series of adsorption experiments with sequential concentration buildup from zero to the desired value. Thus, the entire adsorption isotherm can be obtained without the cumbersome desorption as in the experiments of Sharma and Fort (11). Moreover, with the dynamic technique, reversible and irreversible adsorption can be conveniently resolved since adsorption can be studied repeatedly on the same adsorbent surface. As the dynamic technique involves only determination of a corrected retention volume, the concentration determination procedure required in static adsorption experiments is eliminated and accuracy is thereby improved. However, both Journal of Colloid and Interface Science, Vol. 66, No. 1, August 1978

164

W A N G , DUDA, A N D R A D K E

the static method (which is limited by a maximum solid/liquid mass ratio from which a clear bulk solution is available for analysis) and the dynamic method (which is limited by a maximum column length for which a sufficient pressure head is available) become inaccurate when one component is only slightly preferentially adsorbed over the other. Nevertheless, the static method is subject to the more severe limitation. The adsorption data for the n-hexane/nhexanol/silica gel system from both the static and the dynamic adsorption experiments show agreement over the entire composition range. The rate of the adsorption process is fast and the mass transfer resistances are not significant under the experimental conditions. Irreversible adsorption of hexanol occurs whenever a fresh surface of silica gel is exposed to the hexanol solution. The irreversible adsorption begins at the lowest detectable concentration and remains constant over the whole composition range; it corresponds to about 20% of a monolayer of hexanol molecules oriented perpendicular to the surface. Schay and Nagy's monolayer model (21) can be extended to a liquid solution of different molecular sizes and shapes for decomposing the measured reduced adsorption isotherm into the two individual isotherms. The success of the monolayer model in correlating the adsorption data indicates that monolayer adsorption may be occurring. The monolayer model also reveals that hexanol is more strongly adsorbed than hexane for the molar ratio of hexanol to hexane in the adsorbed monolayer is about 3. APPENDIX

In this appendix we prove that the volumetric flow rate in the column is position independent (OQ/Ox = 0) only when the adsorption process is isochoric ((zi = constant). From the species continuity equation (OpJOt + V'piui = 0) and the definition of Journal of Colloid and Interface Science,

Vol. 66, No. 1, August 1978

the local volume-average velocity of a fluid e l e m e n t (u I : p l W l U l q- p2~Z2U2), the divergence of the volume-average velocity may be written as V"

Um

= p l U l " V ~/1 "4- ,02U 2 • V ~/2

- ~¢i Opl _ ¢42 0/)2 Ot ~ '

[A.I]

where ui is the local species velocity of component i. With the partial specific volume identity, pIVi + P2¢¢2 = l, Eq. [A. I] simplifiesto D~/~

V . u = = p~ ~

D~/2

+ P2 D--7- '

[A.2]

where D/Dt is the substantial derivative operator and is identical to [O/Ot + (ui'V)]. Equation [A.2] states that when the adsorption process is isochoric so that the partial specific volumes of both species remain constant in both the bulk and adsorbed phases, then the divergence of the volumeaverage velocity of a fluid element vanishes throughout the extent of the column. By the Gauss' divergence theorem, the volume integral of Eq. [A.2] over an arbitrary section of column reduces to

= Q ( x 2 , t ) -- Q ( X l , t ) ,

[1.3]

where xl and x2 are arbitrary positions along the column and V12 is the column volume between these two positions. We note that no physical assumptions have been employed so far so that Eqs. [1.2] and [A.3] are completely general. They even apply when the velocity profile in the column is not uniform. We note further that, when the adsorption process is isochoric so that Eq. [A.2] vanishes, then Eq. [1.3] demands a position-independent volumetric flow rate, Q. Conversely, if the volumetric flow rate is position independent, the process must behave such that the volume integral of the right side of Eq.

SOLUTION ADSORPTION FROM LIQUID CHROMATOGRAPHY

[A.2] over any column section vanishes. The most probable condition for this to be valid is the isochoric assumption where the partial specific volumes of both species are constant; otherwise, a highly improbable behavior of the partial specific volumes of the two species is required. Therefore, the assumption of a position-independent volumetric flow rate is equivalent to the assumption of an isochoric adsorption process. REFERENCES 1. Gilmer, H. B., and Kobayashi, R., AIChE J. 10, 797 (1964). 2. Masukawa, S., and Kobayashi, R., AIChE J. 15, 191 (1969). 3. Helfferich, F., and Klein, G., "Multicomponent Chromatography." Dekker, New York, 1970. 4. Huber, J. F. K., and Gerritse, R. G., J. Chromatogr. 58, 137 (1971). 5. Wilson, J. N.,J. Amer, Chem. Soc. 62, 1583(1940). 6. DeVault, D., J. Amer. Chem. Soc. 65, 532 (1943). 7. Claesson, S., Ark. Kemi Mineral. Geol. 23A, No. 1 (1946). 8. Smit, W. M., and Van Den Hoek, A., Rec. Trav. Chim. Pays-Bas 76, 561 (1957). 9. Bayl6, G. G., and Klinkenberg, A., Rec. Trav. Chim. Pays-Bas 76, 593 (1957). 10. Schay, G., Nagy, L. Gy., and Rficz, Gy., Acta Chim. Acad. Sci. Hung. 71, 23 (1972).

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11. Sharma, S. C., and Fort, T., J. Colloid Interface Sci. 43, 36 (1973). 12. Everett, D. H., Pure Appl. Chem. 31, 579 (1972). 13. Gibbs, J. W., "Collected Works," Vol. 1, p. 219. Longmans, New York, 1928. 14. Young, D. M., and Crowell, A. D., "Physical Adsorption of Gases." Butterworths, London, 1962. 15. Antropoff, A. v., Steinberg, F., Kalthof, F., Schmitz, L., and Schaeben, R., Z. Elektrochem. 42, 544 (1936). 16. Antropoff, A. v,, and Schaeben, L., Z. Elektrochem. 44, 586 (1938). 17. Antropoff, A. v., Kolloid-Z. 98, 249 (1942). 18. Kipling, J. J., "Adsorption from Solutions of Non-Electrolytes." Academic Press, New York, 1965. 19. Guggenheim, E. A., and Adam, N. K., Proc. Roy. Soc. London Ser. A 139, 218 (1933). 20. Wang, H. L., "Solution Adsorption from Liquid Chromatography." Masters Thesis, The Pennsylvania State University, 1976. 21. Schay, G., and Nagy, L. G., J. Chim. Phys. Physicochim. Biol. 58, 149 (1961). 22. Schay, G., in "Surface and Colloid Science" (E. Matijevic, Ed.), Vol. 2, p. 155. Wiley-Interscience, New York, 1969. 23. Everett, D. H., Trans. Faraday Soc. 60, 1803 (1964); 61, 2478 (1965). 24. Szabo, M. T., Soc. Petrol. Eng. J. 15, 323 (1975). 25. Small, H., J. Colloidlnterface Sci. 48, 147 (1974). 26. AlgeR, K. H., and Segal, L., "Gel Permeation Chromatography." Dekker, New York, 1971.

Journal of Colloid and Interface Science, Vol. 66, No. 1, August 1978