Fundamentals of Inorganic Membrane Science and Technology Edited by A.]. Burggraaf and L. Cot

�9 1996, Elsevier Science B.V. All rights reserved

Chapter 3

Adsorption phenomena in membrane systems

Yi Hua Ma

Department of Chemical Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 1609, USA

3.1 INTRODUCTION

In a gas solid system, some adsorbate species are generally distributed between a solid surface and a gas phase. This is due to the fact that below critical temperature, all gases tend to be adsorbed on a solid as a result of the van der Waals interactions with the solid surface. This type of adsorption is ~ called physical adsorption (physisorption). In this case, the important factors affecting adsorption include the magnitude and nature of adsorbent-adsorbate and adsorbate-adsorbate interactions. The degree of surface heterogeneity and the translational and internal degrees of freedom which the adsorbed molecules

possess can also be important. A certain distribution of the adsorbate between the gas and solid phases

exists in a gas-solid system. The distribution depends on temperature and pressure and is customarily expressed as the moles or weight adsorbed per unit weight of solid either as a function of pressure at a constant temperature (isotherm) or as a function of temperature at a constant pressure (isobar). Thermo- dynamic treatments can be used to develop adsorption models to describe the distribution of the species between the gas and solid phases. Some of the more commonly used adsorption models will be discussed in the following sections.

Experimentally, adsorption isotherms are usually determined to describe the amount adsorbed, n, as a function of pressure, p. The measurements are nor- mally carried out for several temperatures. The data can be alternatively plotted

35

3 6 3 - - ADSORPTION P H E N O M E N A IN M E M B R A N E SYSTEMS

as n versus temperature, T, at constant pressure (isobars) or as p versus T at constant n (isosteres). Adsorption models are then used to fit the experimental data. However, it should be cautioned that such a fit is not sufficient for the theoretical verification of the adsorption model. A consideration of the vari- ation of the energy and entropy of adsorption is a more reliable way of testing the models.

A second type of adsorption is called chemisorption. In this case, the adsorp- tion energy is comparable to the chemical bond energies and adsorbate mole- cules have the tendency to be localized at particular sites even though surface diffusion or some molecular mobility may still occur. Due to the chemical nature of the interactions between the gas and the solid surface, the equilibrium gas pressure in the adsorption system can be extremely low. This enables one to study the adsorbent-adsorbate system under high vacuum using diffraction and spectroscopic techniques for the identification of the actual species pre- sented on the surface and the determination of their packing and chemical state.

Although there exists a large amount of adsorption data in the literature on adsorbents such as activated alumina and silica, adsorption data on inorganic membranes relating adsorption phenomena to membrane permeation are scarce. The importance of having a better understanding of the adsorption phenomena in interpreting permeation data has been demonstrated by the recent work of Ma and his co-workers [1-4] on the theoretical analysis and experimental investigation of adsorption and diffusion in silica membranes.

The objective of this chapter is to present the fundamental theories of adsorp- tion followed by the description and discussion of experimental techniques for the measurements of adsorption isotherms and for the determination of surface area and pore size distribution. The adsorption of gases on microporous mem- branes and the inter-relation between adsorption and permeation are then discussed. The adsorption in liquid phase is briefly presented. The chapter concludes with a brief summary.

3.2 A D S O R P T I O N I S O T H E R M S

3.2.1 Types of Isotherms

As discussed in the previous section, the distribution between the adsorbate phase and the adsorbed phase can be described by an adsorption model, known as adsorption isotherms. Based on experimental data reported in the literature, Brunauer et al. [5] divided adsorption isotherms into five different types which are shown in Fig. 3.1 (BDDT classification). The first two types are by far the most frequently encountered in adsorption systems. The Type I isotherm is the well-known Langmuir isotherm which will be discussed in the next section. The

3 - - ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS 37

l,,, o r,~ "0 r

= o

I

f 1 , , ]

0 1.0 0 1.0

III

1

0 1.0

Relative pressure, p/pO

o

/ i

IV

I < 0 ~0

V /

,, , ]

1.0

Relative pressure, p/pO

Fig. 3.1. The BDDT classification of the five types of adsorpt ion isotherm.

Langmuir isotherm assumes a monolayer coverage while the Type II isotherm deals with multilayer adsorption followed by capillary condensation. Types II and III are closely related-to Types IV and V. The only significant difference between Types II, III and Types IV, V is that a maximum adsorption is reached for the latter case while for the former case, the adsorption increases as the adsorbate gas approaches its vapour pressure.

3.2.2 The Langmuir Isotherm

The Langmuir isotherm was first developed by Langmuir in 1915 [6] to describe monolayer adsorption. Since then, a number of different approaches have appeared in the literature for the derivation of the Langmuir adsorption isotherm. For example, the statistical thermodynamic derivation was given by Adamson [7]. The following kinetic derivation is essentially similar to that given by Langmuir [8]. It is assumed that the surface consists of a certain number of adsorption sites, So. The number of sites already occupied by the adsorbate molecules is designated as $2. The number of unoccupied sites is equal to $1 = So- $2. If we assume that the rate of adsorption is proportional to the number of unoccupied sites and the gas pressure, p, while the rate of desorption is proportional to the number of sites already occupied by the

38 3 -- ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS

adsorbate molecules and at equilibrium, the rate of adsorption is equal to that of desorption, then

kl $1 p = kl p(So- $2) = k2 S 1 (3.1)

Dividing Eq. (3.1) by So and recognizing that the fraction of surface covered, 0, equals $2/So, then we have the conventional Langmuir equation

0= bp (3.2) l + p b

where

kl b = ~

k2

and is called the Langmuir constant. 0 can also be expressed as n/no, where n denotes the kg-moles adsorbed per kg of adsorbent and no is the saturation capacity or the amount adsorbed at the saturation monolayer coverage. The Langmuir isotherm then becomes

nobp n - (3.4)

l + b p

Typical Langmuir isotherms are shown in Fig. 3.2(a) for several gases on a microporous silica membrane [1]. It is interesting to note that at low pressures, Eq. (3.4) reduces to a linear isotherm

n = nobp (3.5)

while at high pressures, n approaches the saturation value of no. Equation (3.5) is sometimes called Henry's law or Henry's equation [9].

One conventional way to test the experimental data for the Langmuir iso- therm is to rearrange Eq. (3.4) in the following linear form

p 1 p - = ~ + ~ (3.6) n bno no

A plot of p / n versus p gives a straight line (shown in Fig. 3.2(b)) with the slope of l /n0 and the intercept of 1/bn0, from which no and b can be determined.

The rate constants kl and k2 can be related to the concepts of adsorption time, which is the average time an adsorbed molecule spent on the surface, and the Langmuir constant b can then be expressed as

b = bo e -Q/RT (3.7)

and

(3.3)

No o ~ ~o bo = (3.8)

~/2nMRT

3 -- ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS 39

(a) 2.s

2.0

1.5

O

1.0

0.5

0.0 I

0.0

T=30 ~ .... Dubinin-Radushkevich

CO 2

C2H 4

CH 4

N2

0.4 0.8 1.2 1.6

p, [MPa]

(b)

g~

1.2

0.8

0.4

_

0.0

0.0

&

T=30 ~

CO 2

0.4 0.8 1.2 1.6

p, [MPa]

Fig. 3.2. Adsorp t ion isotherms of gases on the microporous silica membranes: (a) the isotherms; (b) the plot of Eq. (3.6). The solid lines in (a) are also the Langmuir isotherm fits.

4 0 3 - - ADSORPTION P H E N O M E N A IN MEMBRANE SYSTEMS

where No is the number of elementary sites each with a site area of G ~ Q is the energy of adsorption and t0 can be approximated by the molecular vibration time. From the assumption of one molecule per site, the total number of adsorbed molecules cannot exceed No. In fact, at monolayer coverage, No is equal to the saturation value at high pressures.

The Langmuir isotherm can be extended to multicomponent adsorption systems by the following expression

nobiPi Yli = l

where J is the total number of species in the multicomponent system.

(3.9)

3.2.3 The BET Iso therms

Brunauer et al. [10] derived an isotherm equation for multilayer adsorption of gases which includes both Type I and Type II isotherm. A more generalized form of the isotherm was later derived by Brunauer et al. [5] to include all five types of the isotherm. Assuming that the Langmuir equation applies to each layer, Brunauer et al. [5] made the following additional assumptions: (1) The heat of adsorption for the first layer has a distinct value while that of the second and succeeding layers is equal to the heat of condensation of the liquid adsor- bate. (2) Adsorption and desorption can only occur at the exposed layer. Based on these assumptions and applying the similar approach used in the derivation of the Langmuir equation, the following equation known as BET isotherm is obtained

Yl CX - ( 3 . 1 0 )

no (1 - x) [1 + (c- 1) x]

where x is the relative pressure equal to p/pO with p being the pressure of the adsorbate and p0 being the vapour pressure of the adsorbate and c ~ e a Q / R T with AQ equal to the difference between the heat of adsorption and the latent heat of condensation. Physically, c may be interpreted as the ratio of the adsorption time of the molecules in the first layer and the adsorption time of the molecules in the second and subsequent layers.

Like the Langmuir isotherm, Eq. (3.10) can be rearranged to give

x 1 (c - 1)x ~ = ~ + ~ (3.11) n (1 -x ) cno cno

Again, a plot of x/[n(1 - x)] versus x gives a straight line and c and no can be obtained from the slope and the intercept of the line.

3 --ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS 41

The BET equation has been used as the general method for the determination of surface area from adsorption data because experimentally it is relatively easy to apply. This will be discussed in detail in Section 3.3.2.

In addition to Types I and II isotherm, the BET equation also appears to cover the Type III isotherm. For large values of c, i.e., large AQ which is equivalent to cases where the heat of adsorption is much larger than the latent heat of condensation, the BET equation reduces to the Langmuir isotherm. For small values of c, the BET equation follows Type III behaviour. For the intermediate values of c (e.g., --100 for the adsorption of permanent gases such as nitrogen and argon on polar surface), the BET equation corresponds to the Type II isotherm. In this case, the following approximate form of the BET equation can be used

n 1

no 1 - x (3.12)

Equation (3.12) can fit well in the usual region of the BET equation and has been used to estimate surface area with a single point [ 11]. This one point method has been incorporated into commercial equipment for rapid surface area determi- nations.

3.2.4 Isotherms Derived from the Equation of State

The use of an equation of state to derive isotherms is based on the assumption that the adsorbed layer can be treated as a two-dimensional phase~ Inthis case, the fundamental equations in classical thermodynamics can be applied. Thus, at constant temperature, the Gibbs adsorption isotherm becomes

Ad~ = nd~t (3.13)

where A is the surface area, ~ is the spreading pressure, n is the number of moles adsorbed per unit mass of adsorbent and ~t is the chemical potential of the adsorbate. If we assume that the gas phase can be treated as an ideal gas, then, at thermodynamic equilibrium and constant temperature

d~t = RTd lnp (3.14)

The combination of Eqs. (3.13) and (3.14) gives

d~ n - RT (3.15)

dlnp A

Equation (3.15) forms the basis for the derivation of adsorption isotherms from equations of state. Alternatively, it can also be used to obtain equations of state from adsorption isotherms. For example, for a linear isotherm, n / p is constant and the integration of Eq. (3.15) gives

4 2 3 - - ADSORPTION P H E N O M E N A IN MEMBRANE SYSTEMS

~ = RT (3.16)

where o is the area occupied by an adsorbed molecule. A simple modification of Eq. (3.16) is to include a co-volume term to give

~(c~- b)= RT (3.17)

Substitution of Eq. (3.17) into Eq. (3.15) and integration give the isotherm

kp = ~ 0 e~176 (3.18) 1 - 0

A large number of equations of state has been used to derive adsorption isotherms. Some of the isotherms and their corresponding equations of state have been presented by Adamson [7].

3.2.5 The Potential Theory

Polanyi [12] took a somewhat different approach to multilayer adsorption by assuming that dispersion forces play the determining role in adsorption, result- ing in the existence of a potential field in the vicinity of the adsorbent surface. The adsorbed layer has the highest density at the solid surface and its density decreases as the distance from the surface increases. Thus, it is possible to draw equipotential surfaces as shown in Fig. 3.3. The space between each adjacent potential surface represents a definite adsorption volume which is a function of the potential field. Mathematically, it can be represented as

W =fie) (3.19)

where W is the adsorbed volume above the surface with potential energy field ~. Equation (3.19) is called the characteristic curve which is characteristic of a

Gas

I1211 .................... i

Fig. 3.3. Equipotential contours according to the Polanyi potential theory.

3 - - ADSORPTION P H E N O M E N A IN MEMBRANE SYSTEMS 4 3

particular gas-solid system although its form is unspecified. Since the charac- teristic curve is temperature independent, for a given adsorption system all isotherms should result in the same characteristic curve. In theory, this allows one to predict adsorption isotherms at any temperature from measurements carried out at one single temperature. The isotherm derived from the potential theory is particularly useful in interpreting capillary condensation or pore filling. Thus, it is most appropriate to be used to describe the adsorption in microporous solids.

One way of plotting the characteristic curve can be obtained by considering the work required to transport molecules from the solid surface to the gas phase. Since at the adsorption equilibrium, the change of free energy of the system must be zero. The removal of gas molecules from the surface must, therefore, be compensated by the compression work on the surface. Thus

0 P 0

- ] v @ - RTh P

P

(3.20)

where p0 is the vapour pressure of the adsorbate. Based on the theory of dispersion interaction, the ratio of the forces of

attraction of different molecules is equal to that of polarizability of the mole- cules of the vapours. This ratio is called an affinity coefficient ~ and is intro- duced into the potential function [13]. Furthermore, a parameter K, reflecting the function of the size distribution of volume of the pores, is also included in the equation. Thus, the form of the characteristic curve can be written as [13]

2 -C

- K ~2 W = W0 e (3.21)

where W0 is the limiting volume of the adsorbent sites that represent the volume of the micropores of the adsorbent. Equation (3.21) is called the Dubinin- Radushkevich or DR equation. From Eq. (3.21), a plot of In W v e r s u s 1~ 2 should yield a straight line. A plot for CO2 and H20 on microporous silica membranes is shown in Fig. 3.4 [1].

3.3 EXPERIMENTAL TECHNIQUES

3.3.1 Determination of Adsorption Isotherms

Both volumetric and gravimetric techniques have been used for the determi- nation of adsorption isotherms of gases on solids. The volumetric technique is one of the widely used methods for the adsorption isotherm determination and is based on the measurement of the pressure-volume relation to determine the

44 3 ~ ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS

-2

-.3

i

N

CO 2 T=30~

Wo=0.11 cm3/g

-5

-6

7i

A CO 2 T=30~

A CO 2 T=70~

CO 2 T=70~

H20 T=70~

Glass M e m b r a n e

J,i ~ i , ~ , l , , J" ~ ' " l ~ ' " ' l " ~ l ' ' ' l t ' ' ' ' l ' ' ' ' ' " " 5 10 15 20 25

e 2 / 10 6 , [cal 2 / m o l 2]

Fig. 3.4. Dubin in-Radushkevich plot for the microporous silica membranes .

amount of adsorbate gas on a adsorbent at different relative pressures (p/p~ It requires an accurate calibration of the dead volume in the system. The gravi- metric method was first developed by McBain and Bakr [14]. The early version of the gravimetric technique makes use of a delicate spiral quartz spring. The adsorbent weight gained during adsorption is determined by measuring the extension of the spring which is pre-calibrated with known weights. The mod- ern gravimetric unit, however, uses electromicrobalances or transducers. The progress of adsorption can be followed by continuously recording the weight gain as a function of time. This makes it possible for the technique to be used for the measurement of the kinetics of adsorption and the determination of diffusion coefficients.

Typical gravimetric units for both sub-atmosphere and high pressure meas- urements of equilibrium adsorption isotherms are shown schematically in Fig. 3.5 [1,15]. The all-glass sub-atmosphere ulxit is housed in an insulated constant temperature box free from any kind of disturbance, either mechanical or ther- mal. The unit contains a Cahn 2000 electrobalance with sensitivity of 10 -7 g for

3 m A D S O R P T I O N P H E N O M E N A IN M E M B R A N E SYSTEMS 45

(a) 7Data acquistion

(b)

2 :

- 7 - - - - ' 4 j [

11 Roughing pump

Insuiated Box

..." ..."

.. 8,dence mmmbly ...."

Oma ~ q u i ~ k ~ Sy.tom

,

..' " . . . . . . .

....... i,i:.-.~..

Transducer

l

Antivilxation -... Stamcl ...

"..

Tom;~rturo Controller

Cold Trap

'--V V__ G~ Vacuum Cytk~m' Pump

Fig. 3.5. Schematic of the gravimetric units. (a) Sub-atmosphere unit (0-100 kPa): 1.Balance assembly. 2. Controlled heaters. 3. Sample. 4. Thermocouple. 5. Gas reservoir. 6. Pressure sensors. 7. Injection assembly. 8. Zeolite trap. 9. Cold trap. 10. Turbomolecular pump. 11. Insulated box. (b)

High pressure unit (0-5 MPa)

we igh t measurements . The sys tem can be evacuated to h igh v a c u u m by an

oil-free tu rbo-molecular p u m p in conjunct ion wi th a rough ing p u m p . The h igh v a c u u m is needed for sample act ivation at e levated t empera tu res before ad-

46 3 -- ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS

,e--high vocuum line ,~--nitrogen

F

Fig. 3.6. Schematic of the volumetric unit. (A) Gas burette filled with mercury; (B) diffusion pump; (C) adsorption vessel; (D) vessel containing some pure condensed nitrogen; (E) capillary differential

manometer; (F,G) manometer; (H) vacuum and pressure chamber [16].

sorption measurements. The use of an oil-free turbo-molecular pump instead of the conventional oil diffusion pump is to avoid the possible contamination of the sample by the oil vapour. During the adsorption experiment, the pressure is measured by capacitance pressure gauges. Temperature control and meas- urements are accomplished by digital controllers. The weight change during the adsorption measurement is recorded by a data acquisition system equipped with a personal computer. The high pressure unit shown in Fig. 3.5(b) is similar to the sub-atmosphere unit except it is constructed of 316 stainless steel capable of operation up to 3 MPa.

The volumetric unit shown in Fig. 3.6 is typically used for the determination of the BET surface area. The major parts of the unit are shown in the figure. Detailed description of the operation of the volumetric unit can be found in Lippens et al. [16].

3.3.2 Surface Area Determinations

A detailed physical chemical interpretation of permeation mechanisms in microporous membranes is possible if the specific surface of the membrane is determined. Such a determination is mostly done by measuring gas adsorption in the solid although microscopic techniques such as scanning electron micros-

3 w ADSORI~ION PHENOMENA IN MEMBRANE SYSTEMS 47

copy can also be used. We shall restrict our discussion to the adsorption techniques for the surface area determinations.

Since the definition of surface area can sometimes be ambiguous, it is impor- tant to recognize that the macroscopic determination of surface area generally involves the measurement of a certain property of the solid (e.g., equilibrium adsorption capacity) which can be a qualitative measure of the development of the surface. This property can then be related to the actual surface area through an appropriate theory (e.g., BET isotherm). Therefore, one should not be sur- prised that the results from different models may give different values of the surface area.

The BET equation (Eq. (3.11)) can be written in terms of volume adsorbed

x 1 ( c - 1)x - + ~ (3.22)

Va(1 - x) VmC Vmc

where Va is the volume of gas adsorbed and Vm is the volume of gas at the monolayer coverage. As previously discussed, a plot of x~ {Va(1 - x)} versus x will, in most cases, give a straight line between a relative pressure of 0.05 and 0.25. Vm can be calculated from the slope and intercept of the straight line and can be used for the determination of the specific surface area when the area occupied by a molecule in the monolayer is known. In addition to the assump- tion that the liquid structure could be modeled as the closest packing of spheres, Emmet and Brunauer [17] also assumed that the density of the multilayer adsorbed molecules is equal to that of the liquid at the same temperature. With these assumptions, the area of a nitrogen molecule is found to be 16.27 A2. Using this value, the BET surface area of a solid substance can be determined from

SBE w -- 4.371 Vm (3.23)

where SBET is in m2/g and Vm is in cm 3 (at STP) per gram of adsorbent. By assuming the thickness of a monolayer coverage being equal to the

diameter of a nitrogen molecule, Shull [18] demonstrated that by plotting V a / V m versus the relative pressure, a number of non-porous solids could be represented by a single curve. The value of 4.3 A for a nitrogen molecule used by Shull corresponds to the closest packing of spheres, which appears to be inconsistent with the assumption that each molecule of the subsequent layer in a multilayer adsorption is simply situated on top of a nitrogen molecule of the previous layer. In order to calculate the t-value, it is, therefore, necessary to assume that the density of the adsorbed layer is the same as the density of the normal liquid nitrogen. Thus, for nitrogen, we have

Va t= 15.47 (3.24)

SBET

where t is the statistical thickness of the adsorbed layer and is in A. SBE TiS the

4 8 3 E ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS

BET surface area determined by Eq. (3.23). Substitution of Eq. (3.23) into Eq. (3.24) gives

Wa t = 3.54 (3.25)

Vm

Eq. (3.25) gives t - 3.54 ~ for a monolayer coverage which is considerably different from the value of 4.3 ~ used by Shull. Linsen [19] showed that a number of solids could be represented by a single t-curve up to a relative pressure of 0.75. Above this value, deviations from the single curve were observed due to capillary condensation. The thickness of the adsorbed layer is not very much affected by the nature of the solid surface for most adsorbents. Deviations from a single t-curve, however, have been observed for certain adsorbents at a relative pressure considerably less than the value of 0.75 al- though the effect of the nature of the solid surface is still negligible. For example, for Aerosil (SiO2) , t-values for relative pressures less than 0.15 are essentially identical to the common t-curve [19]. For certain adsorbents, notably graphitized carbon blacks, the t-values calculated from Eq. (3.25) using the Vm values determined from the BET isotherm (Eq. (3.22)) do not fall on the common t-curve. On the other hand, a plot of Va versus t for these materials gives a straight line whose slope gives the surface area St (Eq. (3.24)) which is greater than the BET surface area SBET. For a detailed discussion of common t-curves, the reader is referred to Linsen [19].

As previously discussed, SBET c a n be replaced by St to give

W a

S t -- 15.47 t (3.26)

In some cases, St obtained from Eq. (3.26) is greater than SBET. However, in the range of low relative pressures, the Va versus t plot gives a straight line passing through the origin in almost all the cases. St obtained from the slope of the straight line in this range is generally in good agreement with the BET surface area, SBET.

At high relative pressures, deviations from the straight line may exist. The three possible cases of the Va versus t plot are shown in Fig. 3.7 [16]. The shape of these curves can provide considerable insight concerning the shape and dimension of the pore.

Curve I shows a straight line passing through the origin for the entire range of the relative pressures. This is an indication that the surface is freely accessible to the adsorbate molecules up to high relative pressures. Multilayer formation is unhindered on all parts of the surface.

Curve 2 indicates that above a certain relative pressure, negative deviation from the straight line occurs. The straight line portion of the curve is an indication of unhindered multilayer adsorption. As the adsorption continues,

3 m ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS 49

o

S u

o

u

o

a l

f

f

/

J

3 1

- , t , Layer thickness

Fig. 3.7. To t a l a d s o r b e d v o l u m e as a f u n c t i o n of t he l a y e r th ickness .

the space in the pores available for adsorption decreases due to the formation of adsorbed layers. In the large holes of the solid, pore filling can only be accomplished by capillary condensation at relative pressures close to unity. On the other hand, for a slit-shaped pore, adsorption takes place on both parallel walls of the slit until they are completely filled at a certain relative pressure, above which the surface area becomes inaccessible to the adsorbate molecules. With no capillary condensation taking place in a slit-shaped pore, the negative deviation from the straight line corresponds to a smaller slope-which represents the surface area still accessible to adsorbate molecules.

The positive deviation from the straight line shown by curve 3 signifies larger adsorption than simple multilayer adsorption due, primarily, to capillary con- densation, which can take place in pores with a certain shape and dimension. The increased slope of the Va versus t curve represents this increased adsorption.

An important modification of the de Boer t-plot has been proposed by Sing and his co-workers [20], who introduced the concept of "standard isotherm" for each adsorbent system. The standard isotherm is defined for a non-porous adsorbent with a similar composition to that of the porous one being investi- gated. He further introduced a quantity, C~s = (n/nx)s, where nx is the amount adsorbed on the non-porous reference material, to be used for the correction of pore radii for multilayer adsorption.

3.3.3 Pore Size Distribution

Historically, the calculation of pore size distributions in porous materials has been primarily based on various forms and modifications of capillary theory

5 0 3 - - ADSORPTION P H E N O M E N A IN MEMBRANE SYSTEMS

using carefully measured complete nitrogen adsorption isotherms. The most general characteristics of adsorbents having a wide range of pore size distribu- tion is the presence of a hysteresis loop, i.e., the adsorption branch does not coincide with the desorption branch in a certain range of relative pressures. Although no single mechanism has been put forward to explain all the experi- mentally observed hysteresis phenomena, capillary condensation remains the most commonly cited explanation for this complicated phenomenon. In this case, the pores are generally modelled as a bundle of capillaries with different sizes and the radius of the pores is related to the relative pressure through the Kelvin equation

p yV (3.27) RT ln p ~ r

where y is the surface tension and r is the radius of the pore. Equation (3.27) can be applied to both adsorption and desorption branches

of the isotherm. For the model of a bundle of capillary tubes, it is more appropriate to use the desorption branch of the isotherm for the determination of the pore size distribution. The basic idea is that the effective meniscus radius is the difference between the capillary radius and the thickness of the multilayer adsorption at p/pO, which can be obtained from de Boer's t-plot. In practice, at each desorption pressure, Pd, the capillary radius can be calculated from Eq. (3.27). The actual pore radius is then the sum of the calculated capillary radius and the estimated thickness of the multilayer. The exposed pore volume and surface area can be obtained from the volume desorbed at that specific desorp- tion pressure. This step can be repeated at different desorption pressures. Except for the first desorption step, the desorbed volume should be corrected for the multilayer thinning on the sum of the area of the previously exposed pores. The pore size distribution can then be determined from the slope of the cumulative volume versus r curve.

A severe limitation of the bundle of capillaries model is that it can give erroneous readings for materials with "ink-bottle" pores. In this case, the pores are emptied at the capillary pressure of the neck followed by the discharge of the large cavity, resulting in a large reading of the desorbed volume at the capillary pressure of the "ink-bottle" neck.

Brunauer and co-workers [21,22] used the following general thermodynamic relation [23] to obtain the pore size distribution (referred to as the "modelless" method)

7dS = A~tdn (3.28)

where S is the surface area covered by the adsorbate during pore filling due to capillary condensation and A~t = RT ln(p/p ~ is the change in chemical potential during adsorption. Equation (3.28) can be integrated to give

3 m A D S O R I ~ I O N P H E N O M E N A IN M E M B R A N E SYSTEMS 51

n s

RT P dn (3.29) S - - ~ ~ ln p

Yl h

A hydraulic radius can be defined as

V rh - S (3.30)

where V is the volume in the pores and S is the corresponding surface area. The procedure for the determination of the pore size distribution is the same as before. In this case, both the volume and the surface area (determined by Eq. (3.29)) are determined by the change in n through the desorption branch. A way to check the pore size distribution is to compare the area determined by Eq. (3.29) with the BET area determined by the adsorption branch before the hysteresis loop.

For meso- and macro-pore materials, the Laplace [24] equation has also been applied for the determination of pore size distribution with the assumption that the pores are cylindrical, resulting in the equality of the two radii of curvature in the Laplace equation. In practice, the penetration of a non-wetting liquid such as mercury into the pores at a specific pressure is related to the pore radius through the following equation, with the assumption that all pores are equally accessible

27 I cos0c I r > (3.31)

P

where r is the radius of the pore, 0c is the contact angle, y is the surface tension and p is the pressure.

By incrementing the pressure, the volume of mercury penetrating into the pores is also increased. This relation between the applied pressure and the penetrating mercury volume can be used to determine the pore size distribution from the slope of the V versus p plot through the following equation [7]

P(r) - p dV r dp (3.32)

where P(r) is the pore size distribution and V is the cumulating volume of the penetrating mercury into pores with radius smaller than r. This technique has the same limitation as that of adsorption isotherm described previously. For "ink-bottle" pores, a large pressure is required for the mercury to penetrate the small pore neck, but once this pressure is reached, mercury will be able to penetrate into the wide opening of the pore with ease, giving erroneously large pore volume reading for the size of the pore neck. Mercury porosimeters are commercially available and a typical V versus P plot and the pore size distribu- tion determined from a commercial instrument are shown in Fig. 3.8.

52 3 -- ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS

A 0.20

O) 0 "0 0.15

0.10

1000

0.30 -

0.25

0.05

0.00

10000 100 10 1

Radius (R#), nm

Fig. 3.8. Pore size distribution from mercury porosimeter (courtesy of Quantachrome).

The mercury porosimetry data can also be used to calculate the surface area through the following thermodynamic relation

Vt

S - - 1---L ~ pdV (3.33) 7cos0 0

where Vt is the total penetrated volume. It has been shown that agreement between the surface area determined from

Eq. (3.33) and that from the nitrogen adsorption isotherm is reasonably good [25].

For microporous materials (pore size smaller than 2 nm), no capillary con- densation occurs in the pores. During the mulfilayer adsorption, the fining of the pores is achieved by the meeting of the adsorbed layers from the opposing walls [ 1]. For this type of pore fining, the adsorption isotherm may show a steep increase in the low pressure region exhibiting the characteristics of a high c-value BET isotherm followed by a levelling off displaying the property of a Langmuir isotherm. Although the BET equation for n layers adsorption can be used to fit this type of adsorption, the Langmuir equation has also been used to fit experimental data of this type of adsorption behaviour (e.g., adsorption on zeolites). Most recently, the Dubinin-Raduschkevich (DR) equation has also been frequently used to describe the adsorption in microporous materials. For this case, the DR equation is placed in the following form

W0 - exp - B log 2 (3.34)

3 m A D S O R P T I O N P H E N O M E N A I N M E M B R A N E SYSTEMS 53

where ~ is the similarity coefficient characteristic of the adsorbate, B is an empirical constant characteristic of the adsorbent, W is the adsorbed volume at p/p0 and W0 is the adsorbed volume when the pores are completely filled.

Just like meso- and macro-pore materials, microporous materials generally consist of a range of pore sizes. As expected, there were many attempts on using adsorption isotherms for the determination of the micropore size distribution. These include the inclusion of a Gaussian distribution [26] or Gamma distribu- tion [27] in the empirical constant B in the DR equation. Because this approach introduces artificial physical constraints into the DR equation, its usefulness has been debated. An entirely different approach, generally known as the MP method, uses an extension of the t-curve method for obtaining surface area [28]. However, the method has been criticized for the fact that in the low p/pO range where the micropore filling takes place, the assumption of the validity of the t-plot in the MP method is least viable.

Everett and Powl [29] used intermolecular potential functions to describe the adsorption in the Henry's law region in slit-like and cylindrical micropores. The 12-6 Lennard-Jones potential and other forms of potential functions derived from it were used to describe the interactions between single atomic or molecu- lar species, and the interactions between single molecule and solid surfaces of different configurations. The values of the resulting potential functions were computed to illustrate the change of the shape of the potential energy curve and the adsorption potential minimum as functions of the widths of the slit or radius of the capillary and compared with those for infinite separation or infinite radius. They further proposed several methods to compute the effective pore radius, surface area and pore volume from experimental adsorption data of Ar, Kr and Xe on different activated carbons. Although in most cases, the agreement between the results calculated from different methods was generally reasonably good, some variations did exist due to the uncertainty in the values of the parameters used in the calculations. For more detailed discussion of the models and methods of the data analysis, the readers are referred to the original work of Everett and Powl.

Using the concept of Gibbs free energy for adsorption, Horvath and Kawazoe [30] extended Everett and Powl's potential function approach to describe the adsorption in microporous molecular sieve carbons. According to Horvath and Kawazoe, the Gibbs free energy for adsorption, RTln(p/p~ is the sum of the energy for adsorbate-adsorbate interactions and adsorbate-adsorbate-adsorb- ent interactions. The potential energy of interaction, r used by Horvath and Kawazoe can be expressed as

r = Kr I - /~ /4 +/~/1~ (3.35)

54 3 ~ ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS

where r is the distance between an adsorbate molecule and an atom in the surface layer, a* is the potential energy minimum and according to Everett and Powl [29], K and c~ can be expressed as

and

m

K=in nm)ln~ -m (3.36)

1

r~ = do (3.37)

where do is the arithmetic mean of the diameters of adsorbent atoms in the wall and the adsorbate atoms. As reported by Horvath and Kawazoe [30], with n = 10 and m = 4, K - 3.07 and r~ = 0.858 do.

The potential energy of one molecule between two parallel layers of distance L apart is given by

~,(r)-K~,*[-(-~14+i-~)l~176 (3.38)

Since the free energy for adsorption is expressed as the sum of the adsorbate- adsorbate and adsorbate-adsorbate-adsorbent interactions, the potential en- ergy minimum, r corresponding to these two interactions can be expressed in terms of two dispersion constants, Aa_ a and As-a, respectively, the number density of the adsorbate molecules (Na) and adsorbent atoms (Ns) per unit area

~_ c~ r (3.39) �9 /;)1~ (, )1~ 1

(3.40)

[32]. Thus, the potential function becomes

f,(r)-NaAa-a+NsAa-s[aa 4 - (~yy/4

where according to Kirkwood-Miiller

6 m e c2 ~s (Xa As_ a =

(X s (X a

Zs Za

3 m e c2 (Xa ~a a a - a -" 2 ( 3 . 4 1 )

and

where me is the mass of an electron, c is the speed of light and ~ and Z are the polarizability and magnetic susceptibility respectively with subscripts a and s indicating adsorbate and adsorbent respectively.

3 m ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS 55

Applying Eq. (3.39) and integration over the slit space [30] or applying an energy balance on the adsorbent system [31] gives the final form of the equation for the calculation of the pore size distribution

RT In P = (3.42) p0

Ns Aa-s + Na Aa_a (34 (310 (34 (310 Av (34(L - d) 3 -- 9 -- ~ q- 9

3(L-d / 9 (L -d / 3(d / 9(d)

where d = ds + da, with ds and da being the diameter of the adsorbent atom and the adsorbate molecule, respectively and Av is Avogadro's number.

Since Eq. (3.42) was derived for a slit-like pore, its application to other geometries, such as cylindrical pores, requires further consideration. Saito and Foley [31] followed the same procedure as that used by Horvath and Kawazoe to derive an equation for cylindrical pores with specific applications to the determination of pore size distribution in zeolites. In addition to using a cylindrical potential energy function, they also made the following assump- tions: (1) a perfect cylindrical pore with infinite length; (2) The formation of the inside wall of the cylinder by a single layer of atoms (oxide ions in the case of zeolites); and (3) adsorption taking place only on the inside wall of the cylinder and due, only, to the adsorbate and adsorbent interactions. The final equations derived by Saito and Foley are

o o

p 12~Av(Na Aa_ a + Ns As-a) RT In pO - d ~-~

o

[ 1 ( d;k{_~O~k 2k+1 1 - ~ 21 (~pp/10 -

for the line-averaged potential energy and

(3.43)

o o

p 12/l:Av(Na Aa_a + N s As-a) RT In pO = d ~-~ (3.44)

0

I k l l ~ p p ) ~ p p J -~k(~ppl } 1 (1-d~k{-~220~k~d~O d 4

for the area-averaged potential energy and dp is the diameter of the cylindrical pore and

(x0. 5 = F(-4.5) (3.45) F(-4.5-k) F(k + 1)

56 3 - - A D S O R P T I O N P H E N O M E N A I N M E M B R A N E SYSTEMS

TABLE 3.1

Physical parameters for micropore size distribution calculation

Parameter Adsorbent Adsorbate Adsorbent Adsorbate Carbon [30] Nitrogen [30] Oxide [31] Argon [31]

Diameter (d, nm)

Polarizability (0~, cm 3)

Magnetic susceptibility (X, cm3) Density (N, moles/cm 2)

0.34 0.3 0.276 0.336 1.02x10 -24 1.46x10 -24 2.5x10 -24 1.63x10 -24

13.5• -29 2x10 -29 1.3x10 -29 3.25x10 -29

3.845x1015 6 . 7 x 1 0 1 4 1 . 3 1 x 1 0 1 5 1.31x1015

130. 5 = F(-4.5) (3.46) F(-1 .5- k) F(k + 1)

where F() is the gamma function. To use Eqs. (3.42), (3.43) or (3.44) for the determination of pore size distribu-

tions, the physical parameters in these equations have to be estimated. The parameters used by Horvath and Kawazoe for the adsorption of nitrogen on carbons and by Saito and Foley for the adsorption of argon on zeolites are summarized in Table 3.1. Simple sensitivity analyses on the parameters per- formed by Saito and Foley [31] show that as expected, the diameter of the oxide ion has a large effect on the pore size distribution calculation due to it being raised to the higher power in the equations. The effect of the number density of the adsorbent atom per unit area and that of the adsorbate and the magnet susceptibility of the adsorbate (argon) is moderate while the effect of adsorbent ion (oxide ion) is observed to be negligible on the calculation of the pore size distribution.

j ~o Or

f

0 u.4 0.5 0.6 0.7 0.8 0.9

~iameter (rim)

Fig. 3.9. Micropore size distribution of fresh FCC catalyst [31].

3 - - A D S O R P T I O N P H E N O M E N A I N M E M B R A N E SYSTEMS 57

The procedure for using Eqs. (3.42), (3.43) and (3.44) for the determination of the pore size distribution is quite straightforward. Nitrogen is the most com- monly used gas for the experiment although argon may be preferred here and was used by Saito and Fogey [31] in their work. Once the nitrogen (or argon) adsorption isotherm is measured, appropriate values of L can be chosen to be substituted into these equations to determine the values of p/pO. The values of V/Vo corresponding to the calculated values of p/pO can then be determined from the measured adsorption isotherm. A plot of V~ Vo versus (L - ds) gives the pore size distribution. Micropore size distributions for fresh FCC catalysts determined by Saito and Foley [31] using different models are shown in Fig. 3.9.

3.4 A D S O R P T I O N O N MEMBRANES

There are relatively few studies dealing with adsorption on microporous inorganic membranes. Except the work by Ma and his co-workers and Burggraaf and his co-workers, few studies on the interrelation between adsorption and permeation have been reported. The extremely thin membrane layer on a relatively thick membrane support makes the adsorption measurement rather difficult. Neither gravimetric nor volumetric technique will provide sufficient accuracy for the measurement due to the extremely small fraction of the mem- brane layer in a supported membrane. Nevertheless, adsorption measurements can give important information on pore sizes and permeation mechanisms in microporous membranes. This section will examine the adsorption of gases on microporous membranes and of liquids on mesoporous and macroporous membranes.

3.4.1 Adsorption of Gases on Microporous Silica Membranes and Interrelation between Adsorption and Permeation

In a series of papers, Ma and his co-workers [1-4] systematically examined the interrelationship between adsorption, permeation and diffusion in micro- porous silica membranes. Both equilibrium and nonequilibrium properties of the microporous inorganic gas separation membranes were studied. Both high pressure and low pressure gravimetric units were used in their adsorption measurements.

The adsorption equilibrium isotherms of several gases (CO2, H20, C2H4, N 2, C2H5OH, and CH2C12) on the silica membrane were determined. The data could best be fitted with the Dubinin-Radushkevich (DR) equation although the Langmuir isotherm could also fit the data quite well (see Figs. 3.2 and 3.4). Such a good fit of the equilibrium adsorption data has important theoretical implica- tions on the pore size of the membrane.

5 8 3 - - ADSORPTION P H E N O M E N A IN MEMBRANE SYSTEMS

One of the most interesting aspects of their adsorption study is the determi- nation of the upper and lower bounds of the pore size of the hollow fibre silica membranes. Even though very different assumptions were made in the deriva- tion of the DR equation and the Langmuir isotherm, the physical meaning of the constants W0 in the DR equation and no in the Langmuir isotherm is quite similar. If the pores are sufficiently small and homogeneous, there will not be enough space to provide conditions for multilayer adsorption. In this case, essentially there will be no difference between the values of W0 and no. On the other hand, with increasing pore size, the value of W0 will gradually increase while no will remain the same value as-the value for monolayer coverage. When the pores are large enough, capillary condensation will take place and devia- tions from the DR equation will be observed. For the hollow fibre microporous silica membrane, the values of no and W0 reported by Bhandarkar et al. [1] are very close, implying that the pores in the membrane are small enough so that only micropore filling takes place. This assertion of micropore filling was further verified by the fact that no hysteresis was observed for the adsorption of ethanol on the hollow fibre glass membrane. Since no adsorption/desorpfion hysteresis was observed, this implied that the pores were small enough so that the phenomenon of capillary condensation did not take place in the membrane pores. Therefore, the upper limit of the size of the pores in the membrane could be estimated to be 20 ~.

The DR equation can be used to estimate the lower limit of the pore size. From the fitting of the experimental data, it is possible to obtain the limiting micropore volume filling W0. The W0 values obtained for different adsorbates in the microporous hollow fibre silica glass membrane are quite similar ranging from 0.08 to 0.15 cm3/g. The small deviations can be attributed to the error involved in the determination of the gas molar volume since the true volume of the gas adsorbed on the porous adsorbent is difficult to determine. On the other hand, for the condensible gases below their critical points, excellent agreement between the W0 values was achieved (see Fig. 3.4). Based on the fact that the values of W0 obtained for various gases with different molecular diameters were almost the same, it was concluded that the micropore volume in the membrane was accessible to all the gases regardless of their molecular diame- ter. Therefore, the lower limit for the diameter of the micropore in the hollow fibres is at least the molecular diameter of the largest gas used in the study (Kinetic diameter of CH2C12 = 4.8 A). Therefore, the pore widths in the micro- porous hollow fibre glass membrane are within the limits of 5 A < d < 20 ~.

The effect of adsorption on the separation of gaseous mixtures can be further demonstrated by the experimental results presented in Fig. 3.10 [33] which shows the effect of adsorption on the selectivity coefficient. The temperature and pressure dependency of the experimentally determined selectivity coeffi- cients are shown in Fig. 3.10. As shown in Fig. 3.2(a), the equilibrium adsorption

3 - - ADSORI~ION PHENOMENA IN MEMBRANE SYSTEMS 59

30

o m

E o

e ~

M

25

2 0 - -

15

1.0

Purge Gas: He Ak

Feed: CO2(10.4%)+H 2

Smail-OD Fiber

T-343 K

T=363 K

3.0 1.5 2.0 2.5

Feed Gas Pressure, [MPa] Fig. 3.10. Selectivity coefficient of N2--CO2 mixtures as a f tmction of t empera tu re and pressure .

capacity for C O 2 o n the microporous hollow fibre membrane is considerably higher than that of N2-At any temperature, an increase in pressure will result in an increase in the adsorption of CO2, which will make it more difficult for N 2

to permeate. This will result in an increase in the selectivity coefficient of C O 2 / N 2 as shown in the figure. On the other hand, at any pressure, an increase in temperature will reduce the CO2 adsorption and thereby, causing the selec- tivity coefficient to decrease.

The effect of adsorption on separation is only significant at low temperatures. At high temperatures, physical adsorption is negligible. The permeation through microporous membranes will probably be primarily controlled by diffusion. In this case, the size of the diffusing molecule relative to that of the pore will play an important role. Shelekhin et al. [2] show the dependence of the permeability on the kinetic diameters of several gases (see Fig. 3.11). The kinetic diameters were calculated from the minimum equilibrium cross-sectional diameter from the Lennard-Jones potential. A dramatic decrease in the permeability coefficients is observed with an increase of the penetrant kinetic diameter. Therefore, one of the most important factors controlling the permeation through microporous membranes is the restriction imposed by the molecular size of the penetrant.

60 3 u ADSORPTION P H E N O M E N A IN MEMBRANE SYSTEMS

. m

gh

1000.00 _

100.00-=_

10.00-=_

1.00---=

0.10--=

_

0.01

2.4

H 2

T=30~

CO

2OO

CH 4

i 1 1 t , l l l l l i , l t , I 1 1 1 1 1 1 ~ 1 1 ~ i l l t I l ~ l i ~ ' ' ' 2 ~ 3.2 3.6 4.0

Kinetic diameter, d, [A] Fig. 3.11. Permeability coefficients as a function of the gas kinetic diameter.

3.4.2 Adsorpt ion on Sol-Gel Derived Ceramic Membranes

Adsorption studies were performed on non-supported SiO 2 and SiO2/TiO2 (30 mol% TiO2) membrane top-layer materials by de Lange et al. [34]. The SiO 2 membrane top layer was prepared by acid catalysed hydrolysis of tetra-ethyl- ortho-silicate (TEOS) in ethanol while the SiO2/TiO2 top layer was prepared by prehydrolysis of TEOS in ethanol with an acid catalyst followed by the addition of titanium precursor Ti-(OnBu)4 in ethanol. The details of the synthesis condi- tions can be found in de Lange [35] and de Lange et al. [36]. Both volumetric and gravimetric units were used for the determination of the equilibrium isotherms. Measurements were made at both sub-atmospheric and high pres- sures over a wide range of temperatures. The equilibrium adsorption isotherms for CO2 at several temperatures are shown in Fig. 3.12. At low temperatures, the isotherms showed the Langmuir behaviour while at high temperatures, Henry's law could be applied. Other gases, such as H2, CH4 and iso-C4Hlo showed similar behaviour although some deviation from the Langmuir iso- therm for iso-C4Hlo was observed. The adsorption capacity for CO2 and iso- C4H10 on silica is relatively high at the ambient temperature while that of H2 and

3 - -ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS 61

6ol A I I-- g

,U." ~

-~ 273 K

~ 3 ' ! . o

2 ~ 305 K -~- 323 K E :~; -E- 348 K

> ~ --~ 373 K

00 " 25 " "50 " 75 100 125 473K Pressure (kPa)

Fig. 3.12. C02 adsorption isotherms on Si02 [34].

CH 4 is extremely low. This is consistent with the low isosteric heats of adsorp- tion for H 2 and CH 4 calculated from the adsorption isotherms.

De Lange et al. [34] also reported that the variation of the calculated isosteric heat of adsorption as a function of surface coverage was relatively small for all the four gases they studied, indicating low adsorbate-adsorbate interactions. The slight decrease in the isosteric heat of adsorption for iso-C4H10 as the coverage increases was attributed to be caused either by the non-Henry behav- iour of isobutane at low temperatures or the stronger interaction between the surface and the adsorbed molecules at low coverages. Finally, the effect of TiO2 on adsorption was reported to be small although only limited investigation was carried out.

It is interesting to note that their high pressure adsorption experiments for CO2 and CH 4 showed that Henry's law could be applied to pressures of about 15 and 8 bar, respectively for temperatures above 373 K. An interesting impli- cation of this linearity is that if the gas permeation is indeed linearly propor- tional to the amount adsorbed, then the Henry's law constant can be used to calculate the gas fluxes through microporous membranes at high pressures.

3.4.3 Liquid Adsorption on Membranes

One of the factors causing fouling in ultrafiltration membranes is the adsorp- tion of solutes in the membrane pores. Since fouling, in general, has been discussed in the previous chapter, the discussion presented here will be re- stricted to the adsorption phenomenon. Clark et al. [37] studied the relationship between membrane fouling and protein adsorption on alumina ultrafiltration membranes. Equilibrium adsorption of bovine serum albumin (BSA) was meas- ured by the standard static method at 7~ Their study covered the concentra- tion range between 1 and 10 g/l , pH values between 2 and 10 and NaC1

62 3 - - ADSORPTION P H E N O M E N A IN M E M B R A N E SYSTEMS

4 "1 t -

O

J3

m

O pH ,,, 4.9

p H , , 4 pH - s pH '- 10

_ p H = 2 i . . . .

0 5 I 0 15 Concentrat ion BSA ( g / l )

Fig. 3.13. BSA adsorption isotherms on 40/~ alumina membrane as a function of pH (7~ [37].

concentrations of 0, 0.1 and 0.2 M. The equilibrium adsorption isotherms are shown in Fig. 3.13 for different pH values. The adsorption of BSA showed a maximum near the isoelectric point of the protein (pH = 4.9) due, in part, to the increasing tendency for the protein to come out of the solution at the point where its net charge is zero. The similar phenomenon has been observed by others in polymeric systems [38,39]. The maximum adsorption at the isoelectric point is consistent with the minimum flux observed during filtration experi- ment when the pH of the filtrate is around 4.9. They also reported that increas- ing NaC1 concentration caused the BSA adsorption to decrease and that the increased adsorption near the isoelectric point was essentially eliminated in the presence of NaC1. The presence of salt either interferes with the electrostatic interaction between the membrane and the protein or increases the solubility of the protein at its isoelectric point.

The adsorption of tetracycline and hemoglobin on alumina membranes was also reported by Ma et al. [40] and Bansal et al. [41,42]. Both bioproducts showed the same adsorption behaviour as that of BSA. They also developed a technique, believed to be the first time, to quantitatively determine the extent of fouling (adsorption) of inorganic membranes by proteins. The technique involves the staining of the protein on the membrane with phosphotungstic acid and the use of the energy dispersive capability of an electron microscope to determine the amount of tungsten present. The calibration can be obtained by measuring known amounts of adsorbed protein from equilibrium adsorp- tion studies. The technique has been applied to the determination of the location and amount of foulant (protein) within the membrane pores from a digital X-ray map showing element constituents stained on the foulant. Typical four

3 -- ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS 63

(a)

(b)

Fig. 3.14. (a) 250x magnification X-ray map of clean 0.2 llm pore size membrane showing cross section near the membrane surface. (b) 250x magnification X-ray map showing cross section near the membrane surface of a 0.2 llm pore size membrane which had been subjected to equil ibrium

adsorotion in 1.6 ~/1 hemoglobin solution at o H 6.9 [41 l.

64 3 - - A D S O R P T I O N P H E N O M E N A I N M E M B R A N E SYSTEMS

quadrant X-ray maps of a clean membrane and a membrane surface which had been subjected to adsorption in hemoglobin solution are shown in Fig. 3.14. Figure 3.14(a) represents a control and indicates that no tungsten or phospho- rous can be seen when no protein is present. On the other hand, the presence of phosphorous and tungsten in the lower left and upper right quadrants, respec- tively shown in Figure 3.14(b), indicates protein adsorbed throughout the membrane pores.

3.5 SUMMARY

Basic adsorption isotherms have been described in this chapter. For micro- porous membranes, the use of the DR equation to describe micropore filling has been shown to be quite adequate. Techniques for the determination of surface area and pore size distribution have ben presented. The use of potential func- tions for the determination of pore size distribution in microporous materials has been described. Although the potential function techniques give consistent and satisfactory results, caution must be exerted in using these techniques for the calculation of the pore size distribution, due to the uncertainty involved in the values of the parameters used in the calculation and the simplifying as- sumptions employed in the derivation of the model equations.

Adsorption plays an important role in the separation of gaseous mixtures by microporous membranes and of liquids in ultra- and microfiltration. Adsorp- tion can either enhance or reduce the selectivity coefficient, depending, in part, on the affinity of the individual gases. Adsorption can cause membrane fouling in ultra- and microfiltration. A thorough understanding of the interrelation between adsorption and separation in microporous membranes can provide information for improvement of membrane synthesis.

REFERENCES

1. M. Bhandarkar, A.B. Shelekhin, A.G. Dixon and Y.H. Ma, Adsorption, permeation and diffusion of gases in microporous membranes. I. Adsorption of gases on microporous glass membranes. J. Membr. Sci., 75 (1992) 221.

2. A.B. Shelekhin, A.G. Dixon and Y.H. Ma, Adsorption, permeation and diffusion of gases in microporous membranes. II. Permeation of gases in microporous glass mem- branes. J. Membr. Sci., 75 (1992) 233.

3. A.B. Shelekhin, A.G. Dixon and Y.H. Ma, Adsorption, permeation and diffusion of gases in microporous membranes. III. Application of percolation theory to interpreta- tion of porosity, tortuosity, and surface area in microporous glass membranes. J. Membr. Sci., 83 (1993) 181.

4. A.B. Shelekhin, A.G. Dixon and Y.H. Ma, Theory of gas diffusion and permeation in inorganic molecular sieve membranes. AIChE J., 41 (1995) 58.

3 m ADSORPTION PHENOMENA IN MEMBRANE SYSTEMS 65

5. S. Brunauer, L.S. Deming, W.E. Deming and E.J. Teller On a theory of the van der Waals adsorption of gases. J. Am. Chem. Soc., 62 (1940) 1732.

6. I. Langmuir, Chemical reactions at low pressures. J. Am. Chem. Soc., 27 (1915) 1139. 7. A.W. Adamson, Physical Chemistry of Surfaces, 5th Edn. Wiley, New York, 1990, p. 598. 8. I. Langmuir, The adsorption of gases on plane surfaces of glass, mica and platinum. J.

Am. Chem. Soc., 40 (1918) 1361. 9. S.J. Gregg and K.S.W. Sing, Adsorption, Surface Area and Porosity. Academic Press,

London and New York, 1967. pp. 197, 221. 10. S. Brunauer, P.H. Emmett and E. Teller, Adsorption of gases in multimolecular layers.

J. Am. Chem. Soc., 60 (1938) 309. 11. K.J. Katz, An explicit function for specific surface area. Anal. Chem., 26 (1954) 734. 12. M. Polanyi, Verh. Dt. Phys. Ges., 15 (1916) 55. 13. M.M. Dubinin, The potential theory of adsorption of gases and vapours for adsorbents

with energetically nonuniform surfaces. Chem. Rev., 60 (1960) 235. 14. J.W. McBain and A.M. Bakr, A new sorption balance. J. Am. Chem. Soc., 48 (1926) 690. 15. Y.H. Ma, Weiruo Sun, M. Bhandarkar, Jinqu Wang and G.W. Miller, Adsorption and

diffusion of nitrogen, oxygen, and methane in molecular sieve carbon at elevated pressures. Sep. Techn., 1 (1991) 90.

16. B.G. Linsen, Ed., J.M.H. Fortuin, C. Okkerse and J.J. Steggerda (Eds.), Physical and Chemical Aspects of Adsorbents and Catalysts. Academic Press, London and New York, 1970.

17. P.H. Emmet and S. Brunauer, Accumulation of alkali promoters on surfaces of iron synthetic ammonia catalysts. J. Am. Chem. Soc., 59 (1937) 310.

18. C.G. Shull, The determination of pore size distribution from gas adsorption data. J. Am. Chem. Soc., 70 (1948) 1405.

19. B.G. Lisen (Ed.), Physical and Chemical Aspects of Adsorbents and Catalysts. Academic Press, New York, 1970.

20. G.D. Parfitt, K.S. Sing and D.Urwin, The analysis of the nitrogen adsorption isotherms of microporous materials. J. Colloid Interface Sci., 53 (1975) 187.

21. S. Brunauer, R.Sh. Mikhail and E.E. Bodor, Pore structure analysis without a pore shape model. J. Colloid Interface Sci., 24 (1967) 451.

22. J. Hagymassy, Jr., I. Odler, M. Yudenfreund, J. Skalny and S. Brunauer, Pore structure analysis by water vapour adsorption III. Analysis of hydrated calcium silicates and Portland cement. J. Colloid Interface Sci., 38 (1972) 20.

23. A.V. Kiselev, Usp. Khim., 14 (1945) 367. 24. P.S. de Laplace, Mechanique Celeste. Supplement to Book 10, 1806. 25. L.C. Drake and H.L. Rittrer, Ind. Eng. Chem., Anal. Ed., 17 (1945) 787. 26. H.F. Stoceckli, Generalization of the Dubinin-Radushkevich equation for the filling of

heterogeneous microporous systems. ]. Colloid Interface Sci., 59 (1977) 184. 27. M. jaroniec, R. Madey, J. Choma, B. McEnaney and T.J. Mays, Comparison of adsorp-

tion methods for characterizing the microporosity of activated carbons. Carbon, 27 (1989) 77.

28. R.Sh. Mikhail, S. Brunauer and E.E. Bodor, Investigation of a complete pore structure analysis I. Analysis of micropores. J. Colloid Interface Sci., 26 (1968) 45.

29. D.H. Everett and J.C. Powl, Adsorption in slit-like and cylindrical micropores in the Henry's law region. ]. Chem. Soc., Faraday Trans., I, 72 (1976) 619.

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