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Adsorption from solution and gas adsorption
1
J. Rouquerol and K.S.W. Sing (Editors) Adsorption at the gas-rsolid and liquid-solid interface © 1982 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
ADSORPTION FROM SOLUTION AND GAS ADSORPTION DOUGLAS H. EVERETT Department of Physical Chemistry, School of Chemistry, University of Bristol, U.K.
INTRODUCTION An important step in the unification of theories of adsorption is that of establishing links, both theoretical and experimental, between the adsorption of single gases, mixed gases and the components of a liquid mixture.
Purely
thermodynamic arguments can establish general relationships between single gas and solution adsorption, but to derive detailed solution adsorption isotherms from gas adsorption data recourse must be had to theoretical models such as the surface phase model or the Polanyi potential theory. these are applicable only to ideal systems.
In their simplest forms,
Alternatively, solution adsorption
may be regarded as the limit to which mixed gas adsorption tends as vapour saturation and bulk condensation conditions are approached.
This paper reviews
these theoretical approaches and attempts to assess their relative merits and achievements in accounting for experimental observations.
Attention is drawn
to several important fundamental problems, and to the need for more accurate and extensive experimental data. THERMODYNAMIC APPROACH The problem of discussing equilibrium between a liquid mixture in the bulk and adsorbed states may be looked upon as a special case of the general problem of physico-chemical equilibrium.
The conventional procedure is to establish an
expression for an appropriately defined equilibrium constant (K) which is then related through thermodynamic arguments to a corresponding standard free energy difference (~GiT):
~Gf7
we seek to express the problem in terms of the equation
= - RT In K.
(1)
In bulk thermodynamics, except in the case of ideal systems, the definition of K involves consideration of the deviations from ideality expressed in terms either of vi rial coefficients, for gas phases, or activity coefficients, for liquid mixtures: we shall expect to meet the same problems in the case of adsorption equilibrium.
On the other hand, ~GiT
is a function only of the properties of
2
pure reactants and products and can be defined unambiguously. We shall first assess the extent to which an analogous strategy can be employed in the case of adsorption from solution, and begin with the problem of defining an appropriate standard free energy difference.
This can be done without rhe
need to invoke any theoretical model of adsorption: the subsequent discussion of the adsorption equilibrium constant requires, however, the introduction of a model. The thermodynamic description of surface layers can be developed in a wide variety of ways
[t].
One
general treatment [ZJ, which is independent of
any molecular model, defines the excess thermodynamic properties of the interface with respect to a Gibbs dividing surface placed so that the surface excess of one component (usually chosen as component 1) is zero: the surface excess of component Z per unit area is called the areal relative adsorption of Z with respect to 1, and
.
i
(l)t
s denoted by FZ .
However, in the case of adsorption in solid/liquid systems the most conveniently measured quantity is the change, ~x;, in the mole fraction of component Z, from o 9, h f l ' (0) . " i a 1 mo1 e f r ac t i' on X 0 ,i s cqu i'1'i. b rate d X to x ' w en an amount; 0 so ut i.on n of arn.t
z
z
with a mass m of solid.
The quantity
z
nO~x;/m
is called the specific reduced
adsorption of component Z. If the specific surface area (a ) of the solid is known, then the areal reduced adsorption f
(n)
0
9,
s
= n ~xZ/m as' can be calculated. Z The relative and reduced adsorptions are related, for a binary mixture, by
(Z) Standard thermodynamic arguments lead to the Gibbs adsorption equation, which at constant temperature, is - da
(3)
Here a is the 'interfacial or surface tension' of the liquid mixture/solid
a/8A)T a. s ,no
interface defined as the differential surface excess free energy, (8G
In the case of liquid/solid interfaces the operational interpretation of a in mechanical terms involves a number of complex problems.
through equation (3), a clear thermodynamic meaning. (3) is that
d~;
~
Nevertheless it has,
The importance of equation
is related to the mole fraction x; and activity coefficient
t For the definition of r~l) without the direct introduction of the concept of a dividing surface see F.C. Goodrich in Surface and Colloid Science, E. Matijvic (ed.), Vol.l, 1-38; G. Schay, ibid., Vol.Z, l55-Zll.
3
y; through (4)
so that r(n) da
2
- RT
Thus when
~
x lx2Y2
r~n)
£ £ d (x y 2 ) . 2
(5)
has been measured as a function of composition, and if
y; is
known, differences in a can be calculated by integration of (5): x
a* 2 - a
£ 2
I
RT
r(n) 2 ~
x
Y lx 2 2
2 2
d (x y ) , 2 2
(6)
x£=l 2
or if the limits of integration correspond to the two pure components:
RT
(7)
where a * is the surface tension of the interface between pure liquid i and the i solid. The adsorption characteristics of the system can be derived if the
- a) and its temperature dependence is known [3J. Fig. 1 illustrates function (a * 2 £ . (n) £ £ £ . £ 2 * the functlon r /x agalnst x , and (a - a) as a function of x 2 2' for lx 2Y2 2Y2 2 a typical system. It is important to stress that the reliability of calculated
values of 0, and of O* - a * is heavily dependent on precise adsorption 2 l, measurements especially at the two ends of the concentration range. Clearly if it were possible to derive a as a function of x; from other types of measurement then the surface excess isotherm could be constructed.
At the moment
no successful general method of doing this has been developed.
On the other hand it is possible in principle to derive values of (a 2* - a * l) from vapour adsorption measurements using the single vapours. Thus for the
adsorption n~,
1
of a pure component from the vapour phase, the Gibbs adsorption
isotherm takes the form
4
.1
.2
.4
.3
x
.7
.6
.5
.8
.9
7
JI,
2
6
(b)
L
5
o - 02*
4
~ mJm
3
2
.1 .
(n)
.2 JI, Q, Q,
.4
.3 •
.5 Q, JI,
.7
.6
*
.8
.9
· Q, F1g. 1. (a)f 2 !(x1 x2Y2) as funct10n of x2Y2' and (b) (02 - 0) as f unct10n of x2' for the system [cyc1ohexane(l) + benzene(2)] /Graphon at 298.15K.
5
r.1
da
=
d\l.
1
(8)
where Pi is the pressure of i and Pi* its saturation vapour pressure. the solid surface is clean and has a surface tension a~
RT
o
a.1 - as
As
At
n?1
o
so that
J>ji a
* n. d In (p./p.). 1
1
(9)
1
p.=O 1
[-(a. - aO)J tS often called the spreading pressure of the adsorbed
The quantity
1
layer, n.
s
Integration of (9) to the saturation vapour pressure thus gives n
the spreading pressure of pure component i when the adsorbed layer is in
*
i,
equilibrium with saturated vapour: Pi=Pi*
RT
n.*
A
1
s
J
a * n i d In (Pi/Pi)'
(10)
p.=O 1
A typical graph illustrating this integration is shown in Fig. 2:(a): again the importance of measurements both at very low pressures and close to saturation is evident.
An important fundamental question concerns the interpretation of the limit to
* which the integral tends as p .... p.. 1*
Some authors [4J take the view that as
1
this limit is approached a ... 0i and-n Larionov ~
* i
= a
*
i al. [5J,[6J distinguish two cases.
0
- as'
On the other hand
On an open surface at the
saturation vapour pressure a condensed multilayer is formed which exposes a liquid/vapour interface and makes a liquid/solid interface with the substrate: the physical situation is that of a duplex film (Fig. 3 (a».
-
Then
*
(11)
'IT. 1
where a
*£/s 1S . what was denoted by a * in equation (7). In this instance the i i
difference in equation (7) is related to vapour adsorption through the e9uation:
*
aI'
£/v
),(open surface).
(12)
On the other hand, if the adsorbent is porous, the final state is one in which the internal solid surface is completely wetted, while the liquid/vapour interface consists only of' the external area of the pore entrances which is usually negligible compared with that of the internal solid/liquid interface (Fig. 3 (b».
6
o
o
~
~
I
o
~
I
Fig. 2 (a) f. as function of RT In p./p.* for adsorption of neo-pentane by Graphon at 273.l5K; tb) Schematic curve of RT lA p./p~ as function of f i to illustrate "~~"integral in equ.(9),)')')')' integral i~ equ.(l4) taken up to monolayer coverage f . m
7
£/v VAPOUR
s/l
(a)
(b)
Fig. 3 (a) Duplex film at saturation v.p. on plane surface having both a liquid/ solid and liquid/vapour interface. (b) Saturation adsorption in porous solid where area of £/v interface is negligible compared with the £/s interface.
In this case,therefore, it is concluded that to a good approximation
* - TI *2), (porous solid). (TIl
(13)
Attempts to confirm equations (12) and (13) face a number of difficulties.
It
has already been commented that as illustrated in Fig. 2 integration of equation (10) faces difficulties both at low pressures and in the extrapolation to Pi/Pi*
+
1.
Larionovet to n~
=00, l/n~
Fig. 4.
One method of making this extrapolation is suggested by al. [7J who advocate using a graph of TI/n~
= 0 at the saturation vapour pressure.
In some instances (e.g. Fig. 4 (b»
1
againstTIto extrapolate This is illustrated in
a linear extrapolation seems
a
satisfactory, in others (e.g. Fig.4(a»
curvature as TI/n + 0 leads to uncertainty. Z It would appear from their papers (although this is not clearly explained) that
they regard the curvature as caused by 'capillary condensation' at the points of contact between non-porous carbon particles, and take the linear extrapolation (ignoring the curvature) as giving TI * "corrected for capillary condensation". Z' It often happens that adsorption data are not available up to saturation and
in this case for porous adsorbents Larionov et approximate procedure.
al.
[6J
suggest an alternative
They suggest in effect that the total integral (10)
should be taken in two parts (Fig. 2 (b».
The first, which they denote by A sv
and call the 'integral work of adsorption in the monolayer' is
8
(a)
....
....
'0. ,
7fA /RT s
1TA IRT s
Fig. 4 1TA /n~ (b) iso-o~tane
RT as function of 1TA /RT for adsorption of (a) benzene vapour and vapour by Graphitisea carbon black (redrawn from ref. [7]).
r n
RT
As v
A
s
a
* dna, 1n (P/Pi)
(14)
0
where nO is the monolayer capacity, and A the area of the solid surface. m s They then write, for the spreading pressure 1T
*
A
sv
(15)
which implies that the second part of the integral is
a
R-v
cose
RT A
S
[ n
* dna. 1n (p./p.) 1
(16)
1
m
Now it is known [8J, [9J that, subject to certain conditions (e g , absence of v
hysteresis, not too small pores),when
capillary condensation occurs in a
porous medium the following equation applies:
9
00
RT (J£vcos 6
A s
j
* dn(J, In (P/Pi)
(17)
a
Ib where ~
is the adsorption at which capillary condensation begins.
suggested as a means of obtaining the surface area of mesopores. (16) does is to identify ~ with n~,
This has been What equation
when (16) and (17) become identical.
The
suggested procedure is thus to calculate A from experimental data using * sv £ IT from (15) using the bulk value of cr v and an
equation (14), and to find
estimate of 6. It is to be noted that as shown in Fig. 2 (b) A # cr (monolayer) o sv cr o • The application of this method requires a knowledge of n m, which is s
apparently obtained using the BET equation.
A comparison of these various methods of calculating the surface tension difference is given in Table 1. TABLE 1 Adsorption
£l. graphitised
carbon black o*,s/£ _ o*,s/ £ 2 1 mJ m- 2
r------------------,
vapour ads.
I
vapour ads.
I I
benzene + CCl4 CC14 + isooctane benzene + isooctane benzene + ethanol
-2.9 +1.2 -4.1 +4.5
:
isooctane + ethanol
+8.59
L _ ~4 ...~7
Adsorption
£l. aerosil
benzene + CC14 CC14 + isooctane benzene + isooctane Adsorption
£l. porous
I I
I
r----.,
I 12.43 I
14.22 13.93 28.15
I
6.13 , I 18.56 II ...
silica
a
s
*2
-
( 1T
10
3
vapour adsorption benzene + CC14 CC14 + isooctane isooctane + benzene
-0.3 +6.63 +6.33 +10.9
2.07 0.94 -3.01
1T
solution ads ••
-0.023 +6.95 +6.68 +12.27 (+10.0) .:~:.3. :. 8~
r----'
I I
IL
12.73 , 6.07 I 17.81 .JI
*l ) / RT
mol g
-1
desorption 2.20 1.44 -3.64
solution ads. 1. 97 1.17 -3.12
• I
I I I
I
J
10
* In the case of adsorption by graphitised carbon black the values of (TI * - TIl) Z calculated from vapour adsorption and corrected for the difference between the £/v surface tensions, agree well with the surface tension differences calculated from solution adsorption.
In the case of aerosil, however, which is also non-
* without any allowance for the porous, it appears in sharp contrast that (TI * - TIl)' Z
£/v surface tension, agrees with the solution adsorption figures.
It is possible
that since the aerosil was used in the form of compacted pellets it behaved as a porous solid, but then hysteresis in the vapour adsorption would be expected but is not reported.
Experiments on porous silica, where hysteresis was
* depends on observed, lead to ambiguous results since the value of (TI* - TIl) which branch of the isotherm is considered.
Z
In two cases the solution adsorption
figure lies between those derived from the adsorption and desorption branches. The values obtained using equations (14) and (15) tend to be too
low.
Further
careful experimental study of these problems is needed. SURFACE PHASE MODEL So far the analysis has been model-free and enables a link to be made between the overall integrated results of solution and vapour adsorption data.
To
proceed further and derive an equation of the form (1) one has to make use of a model of the adsorbed layer.
We shall first investigate the use of a
'surface phase' model in which the concentration profile in a real system is replaced by a step function (Fig.
5).
In this case it can be shown
[1OJ
that
the chemical potential of component i in the surface layer can be written o )li
)l~'£
+ RT In
~
x~y~ ~
~
(o~
+
~
.
- o)a; ,
(18)
where a. is the partial molar area of component i, and x~ i.
and y~
~
are, respectively,
~
the mole fraction and activity coefficient of i in the surface layer.
The
justification for taking the standard chemical potential as equal to that in the bulk pure liquid is that as x , ->-1, i.
y~ ->- 1, ~
0
->-
o~ i. and )l? ->- )l~'oi.; ~
pure liquid bulk and surface regions are in equilibrium
and since in the
)l~'o ~
)l~'£ ~
To use this equation it is necessary to be able to calculate x? from adsorption ~
measurements, and for this purpose some estimate of the thickness of the adsorbed layer is needed.
If the layer is t molecular layers thick then x~
is given by
[9J. (19)
where a? is the cross-sectional area of the molecule (in molar units) and is ~
related to a
i
by
11
Fig. 5
.
profile of X as z function of distance from surface z and step function approximation used in 'surface phase' model.
Concentrat~on
t z
t t
Xz--
xR-
z
(ZO)
a.
~
Thus a
o
dx~/dX~ ~
and a
0
are needed as well as t. For simple systems it is usual to Z assume a monolayer model, unless application of the criteria [12J x~ < 1 and l
~
~
> 0 indicates that a monolayer model is thermodynamically unacceptable.
In this case the minimum integral value of t needed to achieve thermodynamic consistency is often
c~osen.
This model clearly involves some rather drastic assumptions and its application requires the selection of a number of parameters whose values are not easily derived from independent data.
However, it serves
a~
a useful basis for a
preliminary discussion. Since the solid surface is supposed to remain filled, it follows that adsorption equilibrium is associated with the exchange process (Zl) where (1)0 denotes a molecule of 1 on the surface, etc.; area.
~
Alternatively, chosing a
a~ is a chosen standard
aI' (ZZ)
where r
=
aZ/a
l•
At equilibrium
12 (23) which on insertion of (18) and the corresponding expressions for
~l
£ and
~2
£ leads
to (24)
Since the right hand side of (24) is a property of the two pure components, an adsorption equilibrium constant can be defined as
(25)
* and a standard free energy change defined as (02* - 02)a -e-
t.G
l
leading to
- RT In K •
a ds
(26)
a
Since, according to (12) or (13) the standard free energy change can in principle at least be obtained from vapour adsorption data for the single components, so can K • We a are now left with the problem of obtaining x
°2 and
(n)
from K and 2 a, as shown by (25) this will depend on a knowledge of the bulk and surface activity coefficients. no problem.
hence f
It might be supposed that those in the bulk phase posed
In fact accurate data are often missing for many systems of interest
in adsorption work:
But the main difficulty arises from the lack of independent
information regarding the activity coefficients in the interfacial layer. For relatively simple systems it may be adequate to assume that both bulk and interfacial regions behave ideally and that, as a rough approximation, the molecules are of equal size: a mole fraction of 2 is given by
l
= a 2 = a and r = 1.
In this case the surface
(27)
and the reduced adsorption by
~ l-X~X~(Ka
-
l~
l+(K a - l)X;J
(28 )
13 It has sometimes been suggested [13J that surface layers are more nearly ideal than the bulk liquid mixture and that as a second approximation one can set Y~'
Y~'
Y~
Yi.
1 (or at least Y~/Y~
=
=
1), and use the experimental values of
However, this is not a general rule since some systems which are nearly
ideal in the bulk exhibit substantial deviations from ideality in the surface [3J. More sophisticated, though still rather crude, theoretical treatments assume that the surface layer can be represented in terms of a regular solution model [10 bJ or as a mixture of molecules of different size following Flory-Huggins statistics [10 b, l4J and taking account of thermal contributions to the activity coefficients. Thus the activity coefficients can be written as the product of an'athermal' and a 'thermal' term [15, l6J : In y~
ath,a th,a + In y. In y.
(29)
~
~
~
¢l
ath,a In Yl
In
ath,a In Y 2
¢2 In - - (r - 1)¢2 a x 2
0+
(l
1
(30)
- -;::)¢l
Xl
where ¢l' ¢2 are the fractional coverages (area fractions)of 1 and 2.
In
[y~
ath,a Yl
1/: :g] In
and equation (24) becomes
II<
~
] - (1 - 1:.)
::
(31)
r '
[SJ
l/r exp
Here y~h,a
Thus
[-
(0
*2
+ (1 -
1:.} rlJ-
(32)
may be estimated using the Flory-Huggins x-parameter derived from the
bulk properties [10~.
However, in their analysis Larionov et al. have considered d ata Yth,a Yth,a =1, an d h ave use d gas a d sorpt~on . t h e athermal case were h 2 l together with equation (32) to calculate adsorption isotherms from solution.
[16J Typical results are shown in Fig. 6 for the systems (CC1 + iso-C 8H18) 4 and (C + iso-C phitised carbon [17J. While agreement in the first case 6Ho 8H18)/gra is good, that for the second is only moderate. While the surface phase model provides a reasonable approximate basis for the correlation of vapour and solution adsorption, it must be emphasized that it
14
(b)
(a)
n~(n)/m nnno1g
n -1
o(n)/m 2
-1
TIDIlo1g
o o
0.4
o
o
Fig. 6 Comparison of experimental results (full lines) and calculated isotherms
for (a) (iso-octane + CC14)/graphitised carbon and (b) (iso-octane + C6H6)/ aerosil Filled points, calculated with yih,o= YZh,o= 1; open clrcles, assuming y~ = yr and layer thickness of ten monolayers. (redrawn from refs. 16,17.
depends not only on the assumptions of the model but also requires the assignment of values to a number of parameters including the molar surface areas of the adsorbed molecules, the surface area of the solid and the thickness of the adsorbed layer.
In any self consistent analysis the same values should be used
for the molar areas. The agreement achieved by Larionov ~ a1. [SJ was obtained 2 using 0.50 nm for the molecular area of benzene when deriving the surface area of the solid from a BET plot of benzene vapour adsorption, while a value of 2 0.40 nm was employed in analysing the solution adsorption data. Furthermore, the molecular area of CC1 was taken as 0.29 nm in reference [~ , but 0.537 nm 4 when analysing adsorption on silica gel [6J. It is not known how sensitive the agreement between experiment and theory is to variations in these parameters, but clearly if it is necessary to take different values for different systems in order to get this agreement, then the situation is far from satisfactory.
15 POLANYI POTENTIAL THEORY It vou1d clearly be preferable if one could break away from the simple monolayer or adscrbed phase model and represent the system in terms of a smooth concentration profile, and in principle this might be possible using the basic concepts of the polanyi.potential theory.
Attempts to correlate vapour and solution adsorption
using this approach have been made by, among others ,Hansen and Fackler
[}.81
and
more recently by Siskova, Erdos and Kadlec [19J. We first recall that the chemical potential of a component of a liquid mixture subjected to a pressure p has the general form ~i
JI,
= ~i
t JI, JI, t (T,p) + RT In xiY i + (p - p)v.~
t&
(33)
where pt is a reference pressure; v. is the partial molar volume of i (strictly ~ t the mean value over the pressure range p ~ p). Under ordinary conditions the last term can be neglected.
However, liquid close to an adsorbing surface is
subjected to an anisotropic stress of such a magnitude that a contribution of the same nature as the last term becomes important.
A full analysis in terms of
the local stress conditions is complex, but for the present purpose it is convenient to represent this excess chemical potential by E • Since the stress condition i varies with distance from the surface, E. will vary continuously from some maximum
a
~
value of E
close to the suface to zero far from the surface. In a layer of i liquid distant A from the surface the chemical potential can thus be written (34)
At equilibrium the distribution of matter must be such that successive layers are at equilibrium with one another and with the bulk, i.e. there must be equilibrium in all exchange processes of the type
where r is now the ratio of molecular volumes.
This leads to
l/r , (all A),
RT
Since the
E~
~
A vary with A, so will K and, in principle, if a
(36)
E~
~
A is known K can a
be calculated:the composition of the layers will change smoothly from A (x;,x;) far from the surface where K = 1, to (x~,x~) in the layer adjacent to the surface.
The assumption is now made that the value of E
i
at some surface A
16
which encloses a volume ¢ of adsorption space is equal to the Po1anyi adsorption potential at that degree of filling in adsorption of i from the vapour A
e.
(37)
~
or in terms of the volume of adsorption space filled (38)
where
p~
~
=
p.(¢) is the pressure at which,in vapour adsorption, the adsorption ~
space up to layer A, of volume ¢, is filled. Thus if the vapour adsorption isotherms are known
~
1 (¢)
Z (¢ ) -
E:
E:
and K
A a
= RT ~
In
~ j
~ PI*
PZ(¢) 11r
*
= K (¢) =
--
a
{p;/p~¢)}-
In
j
{p~/PI
(¢)}]
(39)
(40)
--
p (¢)
Pz
1
Further progress is again hindered by lack of knowledge of the dependence of activity coefficients on the stress conditions near the surface. known then
If these were
A could be calculated from KA and the contribution of the layer z a
X
between A and A + dA (or the volume element ¢ to ¢ + d¢) to the total surface excess obtained (ref.l(a), equ.96)
n~(n)(A)
where v
=
A
A,tiv; V
A
1
dA
(41)
A
(4Z)
1X1 + vzx z
is the mean molar volume in the element considered. The total surface excess would then be obtained by integration
j
o
dA
1
As
j
d¢
(43)
o
If we make the simple assumption of ideal systems, then these equations become
17
(44)
Insertion of equation (40) into (44) leads to equations essentially similar to those derived for ideal systems using the surface phase model. Hansen and Fackler
[18J
attempted to use this method to calculate the adsorption
of propan-l-ol and butan-l-ol from aqueous solution by Spheron 6, but found only rough agreement between observed and calculated isotherms.
This is perhaps not
surprising since the Polanyi characteristic curves for the alcohols and water are of different shapes and the activity coefficients are not expected to be unity.
Siskova, Erdos and Kadlec
[19J
studied six systems: their results are
shown in Fig. 7. The observed and calculated curves are in moderate agreement, although in most cases the observed maximum in the surface excess of component 2 lies at lower values of x; than predicted. While this approach has the apparent merit of avoiding the surface phase concept, its weakness lies in the assumption that £~
~
is determined solely by
interaction with the solid surface and so can be derived from the adsorption isotherm of the pure substance from the vapour phase.
However, in adsorption
from solution a given molecule at A will be surrounded by molecules of both kinds, while in vapour adsorption up to the A-surface, molecules at this surface interact only with molecules of the same kind, and then only with those in the layers closer to the surface. Further study of the potential approach is certainly called for to examine its possible usefulness more carefully. ADSORPTION OF MIXED GASES We consider finally the question of whether theories of the adsorption of mixed gases can be adapted to adsorption from liquid mixtures.
Many treatments
of mixed gas adsorption have been developed, the objective being to predict mixed gas adsorption isotherms from those of the single gases. ideal behaviour of both vapour and adsorbed states.
Most assume
The concept of 'ideal
surface solutions' having a defined spreading pressure is often employed and used to discuss adsorption from solution by extrapolation to the saturation vapour pressure of the surface solution
[20J .
For ideal systems the results
bear a close resemblance to those already discussed.
A more sophisticated
approach has been developed by Bering, Serpinski and Surinova
[21J
who extend
their earlier method of calculating mixed gas adsorption from the single gas isotherms [22J to solution isotherms. This involves the assumption that as . • approached n°b ecomes a linear funct~on • fO saturat10n ~s 0 n h w en t h e compos~t~on . . l 2
18
o
0.2
0.4
xf
0.6
1.0
0.8
0.2
0.4
~
x2
0.6
0.8
1.0
Fig. 7 Comparison of calculated (full lines) and experimental (points) adsorption isotherms using equ. (44) (a) CC14 + benzene (b) CC14 + toluene (c) chlorobenzene + benzene (d) chlorobenzene + toluene (e) CC14 + chlorobenzene (f) toluene + benzene, adsorbed by silica gel. Redrawn from ref. 18.
of the gas mixture (x~)
is held constant.
In addition it is assumed that the
activity coefficients of the 'surface solution' tends towards thbse of the'bulk solution as saturation is approached.
This method has been tested for the systems
(benzene + iso-octane), (CCI4 + iso-octane) and (ethanol + benzene)/graphitised carbon black.
Only for the first system have
d~tailed
results been published
showing excellent agreement between the calculated and experimental curves.
No
curves have been published for the latter two systems so that one cannot comment on the general applicability of this method of calculation. It seems doubtful whether even in principle methods based on the adsorption isotherms of the single gases can prove useful where substantial deviations from ideality occur: a fuller understanding of activity coefficients in surface layers is essential before further progress can be made. The question therefore arises whether experimental data on mixed vapour adsorption can be extrapolated to saturation conditions. problems.
This faces two major
First, there is no proven theory of multilayer adsorption of mixed
gases which could be used as a basis of an extrapolation technique, and secondly there are currently few data available on mixed vapour adsorption over a
19 sufficiently wide range of conditions, including the approach to saturation, to guide the development of a theory.
This is an area which needs much further
study.
CONCLUSIONS In this review inter-relations have been sought between the adsorption of single vapours by solids and that of the components of liquid mixtures.
It must be
concluded that although general thermodynamic relations can be developed between certain integrals derived from experimental data from these two sources, the problem of using single vapour adsorption isotherms to calculate surface excess isotherms for mixtures cannot be solved without much more detailed theories of adsorption from solution.
Thus although there are several reasonably useful
techniques when the systems concerned exhibit ideal behaviour, there is no generally applicable solution for non-ideal systems.
The situation is in fact
no worse than that faced in the analogous problem of the calculation of the equilibrium of chemical reactions where again the solution depends ultimately on the ability to predict activity coefficients.
20
REFERENCES 1 For reviews see e.g. Specialist Periodical Reports, Colloid Science, Chemical Society London, D.H. Everett (ed) (a) Vol. 1 (1973), Chapter 2;(b) Vol. 2 (1975), Chapter 2; (c) Vol. 3 (1979), Chapter 2. 2 G. Schay, J.Co11.Interface Sci., 42(1973)478-485; Pure and App1.Chem., 48(1976) 393-400; D.H. Everett, Pure and App1.Chem.S3(1981)2181-2198. 3 e.g. D.H. Everett and R.T. Podo11,J.Co11.Interface Sci. 82(1981)14-24; D.H. Everett, J.Phys.Chem. 85 (1981)in press. 4 A.L. Myers and S. Sircar, J.Phys.Chem. 76(1972)3415-3419. 5 O.G. Larionov,K.V.Chmutov and M.D. Yudi1evich,Zhur.Fiz.Khim.,41(1967)2616(Russ.J.Phys.Chem.41(1967)1417-1420). 6 S.A. Kazaryan, O.G. Larionov and K.V. Chmutov, Zhur.Fiz.Khim.S1(1977)188-191 (Russ.J.Phys.Chem.S1(1977)103-10S). 7 Yu.F.Berezkina,S.A. Kazaryan,E.Kurbanbekov, O.G. Larionov and K.V. Chmutov, Zhur.Fiz.Khim.46(1972),S45,1242,1694(Russ.J.Phys.Chem.46(1972)318,1242,1694. 8 S.S. Kist1er,E.A. Fischer and I.R. Freeman, J.Amer.Chem.Soc. 65(1943)1909-1919. 9 c f.D.H. Everett and J.M. Haynes,J.Co11.Interface Sci.,38(1972)12S-137;D.H.Everett in Characterisation of Porous Solids,S.J. Gregg,K.S.W.Sing 2nd H.F. Stoeck1i (eds.) Soc.Chem.lnd.London,1979,229-2S1. 10 D.H. Everett (a) Trans.Faraday Soc., 60(1964)1803-1813; (b) ibid.,61(196S) 2478-2495. . ----11 C.E. Brown, D.H. Everett and C.J. Morgan,J.Chem.Soc.Faraclay Trans.I, 17(1975) 883;c f. ref.1(a) equ.(9) and (63). 12 A.I. Rusanov, Phase Equilibrium and Surface Phenomena,Chimia,Leningrad 1967 (in Russian), Chap.VI; c f. ref.1(a),p.66. 13 A.A. Zhukhovitskii,Zhur.Fiz.Khim., 18(1944)214-233; 19(1945)337; A.V. Kise1ev and L.F. Pav1ova,Izvestia Akad.Nauk.S.S.R., Ser.Khim •. 1965,18-27 (Bu1l.Acad. Sci.U.S.S.R,Chem.Ser.,196S,lS-23) and ear1ier.work. 14 S.G. Ash, D.H. Everett and G.H. Findenegg,Trans.•Faraday Soc.64 (l968) 2639-2644. 15 e.g. A.J.Ashworth and D.H. Everett,Trans.Faraday Soc., 56 (,l960)l609-1618. 16 S.A. Kazaryan,E.Kurbanbekov, O.G. Larionov and ,K.V.Chmutov,Zhur.Fiz.Khim., 49(1975)1247-1251 (Russ.J.Phys.Chem.49(197S)728-730). 17 S.A. Kazaryan,E.Kurbanbekov,O.G.Larionov and K.V. Chmutov,Zhur Fiz.Khim.,49 (1975)1243-1247 (Russ.J.Phys.Chem.,49(197S)72S-728) 18 R.S. Hansen and W.V. Fack1er,J.Phys.Chem.,S7(19S3)634-637. 19 M. Siskova, E. Erdos and O.Kadlec, ColI. Czech. Chem. Comm., 39 (1974)1.954-1964. 20 S. Sircar and A.L. Myers, A.I.Ch.E. Journal 19 (1973)lS9-166;c f. ref l(b), p.64:S.Sircar and A.L. Myers,Chem.Eng.Sci., 28(1973)489-499. 21 B.P. Fering and V.V. Serpinskii,Izvest.Acad.Nauk.S.S.R., Ser.Khim., 1972, 166-168(Bu11.Acad.Sci.U.S.S.R.,Chem.Ser.,1972,152-1S4). 22 B.P. Bering, V.V. Serpinkii and S.I. Surinova, Izvest.Acad.Nauk.S.S.R.Ser. Khim. 22 (1973) 3-6 (Bull.Acad. Sci. U. S. S.R. ,Chern.Ser. 220"97.5)1-4) •
J. Rouquerol and K.S.W. Sing (Editors) Adsorption at the gas-rsolid and liquid-solid interface © 1982 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
ADSORPTION FROM SOLUTION AND GAS ADSORPTION DOUGLAS H. EVERETT Department of Physical Chemistry, School of Chemistry, University of Bristol, U.K.
INTRODUCTION An important step in the unification of theories of adsorption is that of establishing links, both theoretical and experimental, between the adsorption of single gases, mixed gases and the components of a liquid mixture.
Purely
thermodynamic arguments can establish general relationships between single gas and solution adsorption, but to derive detailed solution adsorption isotherms from gas adsorption data recourse must be had to theoretical models such as the surface phase model or the Polanyi potential theory. these are applicable only to ideal systems.
In their simplest forms,
Alternatively, solution adsorption
may be regarded as the limit to which mixed gas adsorption tends as vapour saturation and bulk condensation conditions are approached.
This paper reviews
these theoretical approaches and attempts to assess their relative merits and achievements in accounting for experimental observations.
Attention is drawn
to several important fundamental problems, and to the need for more accurate and extensive experimental data. THERMODYNAMIC APPROACH The problem of discussing equilibrium between a liquid mixture in the bulk and adsorbed states may be looked upon as a special case of the general problem of physico-chemical equilibrium.
The conventional procedure is to establish an
expression for an appropriately defined equilibrium constant (K) which is then related through thermodynamic arguments to a corresponding standard free energy difference (~GiT):
~Gf7
we seek to express the problem in terms of the equation
= - RT In K.
(1)
In bulk thermodynamics, except in the case of ideal systems, the definition of K involves consideration of the deviations from ideality expressed in terms either of vi rial coefficients, for gas phases, or activity coefficients, for liquid mixtures: we shall expect to meet the same problems in the case of adsorption equilibrium.
On the other hand, ~GiT
is a function only of the properties of
2
pure reactants and products and can be defined unambiguously. We shall first assess the extent to which an analogous strategy can be employed in the case of adsorption from solution, and begin with the problem of defining an appropriate standard free energy difference.
This can be done without rhe
need to invoke any theoretical model of adsorption: the subsequent discussion of the adsorption equilibrium constant requires, however, the introduction of a model. The thermodynamic description of surface layers can be developed in a wide variety of ways
[t].
One
general treatment [ZJ, which is independent of
any molecular model, defines the excess thermodynamic properties of the interface with respect to a Gibbs dividing surface placed so that the surface excess of one component (usually chosen as component 1) is zero: the surface excess of component Z per unit area is called the areal relative adsorption of Z with respect to 1, and
.
i
(l)t
s denoted by FZ .
However, in the case of adsorption in solid/liquid systems the most conveniently measured quantity is the change, ~x;, in the mole fraction of component Z, from o 9, h f l ' (0) . " i a 1 mo1 e f r ac t i' on X 0 ,i s cqu i'1'i. b rate d X to x ' w en an amount; 0 so ut i.on n of arn.t
z
z
with a mass m of solid.
The quantity
z
nO~x;/m
is called the specific reduced
adsorption of component Z. If the specific surface area (a ) of the solid is known, then the areal reduced adsorption f
(n)
0
9,
s
= n ~xZ/m as' can be calculated. Z The relative and reduced adsorptions are related, for a binary mixture, by
(Z) Standard thermodynamic arguments lead to the Gibbs adsorption equation, which at constant temperature, is - da
(3)
Here a is the 'interfacial or surface tension' of the liquid mixture/solid
a/8A)T a. s ,no
interface defined as the differential surface excess free energy, (8G
In the case of liquid/solid interfaces the operational interpretation of a in mechanical terms involves a number of complex problems.
through equation (3), a clear thermodynamic meaning. (3) is that
d~;
~
Nevertheless it has,
The importance of equation
is related to the mole fraction x; and activity coefficient
t For the definition of r~l) without the direct introduction of the concept of a dividing surface see F.C. Goodrich in Surface and Colloid Science, E. Matijvic (ed.), Vol.l, 1-38; G. Schay, ibid., Vol.Z, l55-Zll.
3
y; through (4)
so that r(n) da
2
- RT
Thus when
~
x lx2Y2
r~n)
£ £ d (x y 2 ) . 2
(5)
has been measured as a function of composition, and if
y; is
known, differences in a can be calculated by integration of (5): x
a* 2 - a
£ 2
I
RT
r(n) 2 ~
x
Y lx 2 2
2 2
d (x y ) , 2 2
(6)
x£=l 2
or if the limits of integration correspond to the two pure components:
RT
(7)
where a * is the surface tension of the interface between pure liquid i and the i solid. The adsorption characteristics of the system can be derived if the
- a) and its temperature dependence is known [3J. Fig. 1 illustrates function (a * 2 £ . (n) £ £ £ . £ 2 * the functlon r /x agalnst x , and (a - a) as a function of x 2 2' for lx 2Y2 2Y2 2 a typical system. It is important to stress that the reliability of calculated
values of 0, and of O* - a * is heavily dependent on precise adsorption 2 l, measurements especially at the two ends of the concentration range. Clearly if it were possible to derive a as a function of x; from other types of measurement then the surface excess isotherm could be constructed.
At the moment
no successful general method of doing this has been developed.
On the other hand it is possible in principle to derive values of (a 2* - a * l) from vapour adsorption measurements using the single vapours. Thus for the
adsorption n~,
1
of a pure component from the vapour phase, the Gibbs adsorption
isotherm takes the form
4
.1
.2
.4
.3
x
.7
.6
.5
.8
.9
7
JI,
2
6
(b)
L
5
o - 02*
4
~ mJm
3
2
.1 .
(n)
.2 JI, Q, Q,
.4
.3 •
.5 Q, JI,
.7
.6
*
.8
.9
· Q, F1g. 1. (a)f 2 !(x1 x2Y2) as funct10n of x2Y2' and (b) (02 - 0) as f unct10n of x2' for the system [cyc1ohexane(l) + benzene(2)] /Graphon at 298.15K.
5
r.1
da
=
d\l.
1
(8)
where Pi is the pressure of i and Pi* its saturation vapour pressure. the solid surface is clean and has a surface tension a~
RT
o
a.1 - as
As
At
n?1
o
so that
J>ji a
* n. d In (p./p.). 1
1
(9)
1
p.=O 1
[-(a. - aO)J tS often called the spreading pressure of the adsorbed
The quantity
1
layer, n.
s
Integration of (9) to the saturation vapour pressure thus gives n
the spreading pressure of pure component i when the adsorbed layer is in
*
i,
equilibrium with saturated vapour: Pi=Pi*
RT
n.*
A
1
s
J
a * n i d In (Pi/Pi)'
(10)
p.=O 1
A typical graph illustrating this integration is shown in Fig. 2:(a): again the importance of measurements both at very low pressures and close to saturation is evident.
An important fundamental question concerns the interpretation of the limit to
* which the integral tends as p .... p.. 1*
Some authors [4J take the view that as
1
this limit is approached a ... 0i and-n Larionov ~
* i
= a
*
i al. [5J,[6J distinguish two cases.
0
- as'
On the other hand
On an open surface at the
saturation vapour pressure a condensed multilayer is formed which exposes a liquid/vapour interface and makes a liquid/solid interface with the substrate: the physical situation is that of a duplex film (Fig. 3 (a».
-
Then
*
(11)
'IT. 1
where a
*£/s 1S . what was denoted by a * in equation (7). In this instance the i i
difference in equation (7) is related to vapour adsorption through the e9uation:
*
aI'
£/v
),(open surface).
(12)
On the other hand, if the adsorbent is porous, the final state is one in which the internal solid surface is completely wetted, while the liquid/vapour interface consists only of' the external area of the pore entrances which is usually negligible compared with that of the internal solid/liquid interface (Fig. 3 (b».
6
o
o
~
~
I
o
~
I
Fig. 2 (a) f. as function of RT In p./p.* for adsorption of neo-pentane by Graphon at 273.l5K; tb) Schematic curve of RT lA p./p~ as function of f i to illustrate "~~"integral in equ.(9),)')')')' integral i~ equ.(l4) taken up to monolayer coverage f . m
7
£/v VAPOUR
s/l
(a)
(b)
Fig. 3 (a) Duplex film at saturation v.p. on plane surface having both a liquid/ solid and liquid/vapour interface. (b) Saturation adsorption in porous solid where area of £/v interface is negligible compared with the £/s interface.
In this case,therefore, it is concluded that to a good approximation
* - TI *2), (porous solid). (TIl
(13)
Attempts to confirm equations (12) and (13) face a number of difficulties.
It
has already been commented that as illustrated in Fig. 2 integration of equation (10) faces difficulties both at low pressures and in the extrapolation to Pi/Pi*
+
1.
Larionovet to n~
=00, l/n~
Fig. 4.
One method of making this extrapolation is suggested by al. [7J who advocate using a graph of TI/n~
= 0 at the saturation vapour pressure.
In some instances (e.g. Fig. 4 (b»
1
againstTIto extrapolate This is illustrated in
a linear extrapolation seems
a
satisfactory, in others (e.g. Fig.4(a»
curvature as TI/n + 0 leads to uncertainty. Z It would appear from their papers (although this is not clearly explained) that
they regard the curvature as caused by 'capillary condensation' at the points of contact between non-porous carbon particles, and take the linear extrapolation (ignoring the curvature) as giving TI * "corrected for capillary condensation". Z' It often happens that adsorption data are not available up to saturation and
in this case for porous adsorbents Larionov et approximate procedure.
al.
[6J
suggest an alternative
They suggest in effect that the total integral (10)
should be taken in two parts (Fig. 2 (b».
The first, which they denote by A sv
and call the 'integral work of adsorption in the monolayer' is
8
(a)
....
....
'0. ,
7fA /RT s
1TA IRT s
Fig. 4 1TA /n~ (b) iso-o~tane
RT as function of 1TA /RT for adsorption of (a) benzene vapour and vapour by Graphitisea carbon black (redrawn from ref. [7]).
r n
RT
As v
A
s
a
* dna, 1n (P/Pi)
(14)
0
where nO is the monolayer capacity, and A the area of the solid surface. m s They then write, for the spreading pressure 1T
*
A
sv
(15)
which implies that the second part of the integral is
a
R-v
cose
RT A
S
[ n
* dna. 1n (p./p.) 1
(16)
1
m
Now it is known [8J, [9J that, subject to certain conditions (e g , absence of v
hysteresis, not too small pores),when
capillary condensation occurs in a
porous medium the following equation applies:
9
00
RT (J£vcos 6
A s
j
* dn(J, In (P/Pi)
(17)
a
Ib where ~
is the adsorption at which capillary condensation begins.
suggested as a means of obtaining the surface area of mesopores. (16) does is to identify ~ with n~,
This has been What equation
when (16) and (17) become identical.
The
suggested procedure is thus to calculate A from experimental data using * sv £ IT from (15) using the bulk value of cr v and an
equation (14), and to find
estimate of 6. It is to be noted that as shown in Fig. 2 (b) A # cr (monolayer) o sv cr o • The application of this method requires a knowledge of n m, which is s
apparently obtained using the BET equation.
A comparison of these various methods of calculating the surface tension difference is given in Table 1. TABLE 1 Adsorption
£l. graphitised
carbon black o*,s/£ _ o*,s/ £ 2 1 mJ m- 2
r------------------,
vapour ads.
I
vapour ads.
I I
benzene + CCl4 CC14 + isooctane benzene + isooctane benzene + ethanol
-2.9 +1.2 -4.1 +4.5
:
isooctane + ethanol
+8.59
L _ ~4 ...~7
Adsorption
£l. aerosil
benzene + CC14 CC14 + isooctane benzene + isooctane Adsorption
£l. porous
I I
I
r----.,
I 12.43 I
14.22 13.93 28.15
I
6.13 , I 18.56 II ...
silica
a
s
*2
-
( 1T
10
3
vapour adsorption benzene + CC14 CC14 + isooctane isooctane + benzene
-0.3 +6.63 +6.33 +10.9
2.07 0.94 -3.01
1T
solution ads ••
-0.023 +6.95 +6.68 +12.27 (+10.0) .:~:.3. :. 8~
r----'
I I
IL
12.73 , 6.07 I 17.81 .JI
*l ) / RT
mol g
-1
desorption 2.20 1.44 -3.64
solution ads. 1. 97 1.17 -3.12
• I
I I I
I
J
10
* In the case of adsorption by graphitised carbon black the values of (TI * - TIl) Z calculated from vapour adsorption and corrected for the difference between the £/v surface tensions, agree well with the surface tension differences calculated from solution adsorption.
In the case of aerosil, however, which is also non-
* without any allowance for the porous, it appears in sharp contrast that (TI * - TIl)' Z
£/v surface tension, agrees with the solution adsorption figures.
It is possible
that since the aerosil was used in the form of compacted pellets it behaved as a porous solid, but then hysteresis in the vapour adsorption would be expected but is not reported.
Experiments on porous silica, where hysteresis was
* depends on observed, lead to ambiguous results since the value of (TI* - TIl) which branch of the isotherm is considered.
Z
In two cases the solution adsorption
figure lies between those derived from the adsorption and desorption branches. The values obtained using equations (14) and (15) tend to be too
low.
Further
careful experimental study of these problems is needed. SURFACE PHASE MODEL So far the analysis has been model-free and enables a link to be made between the overall integrated results of solution and vapour adsorption data.
To
proceed further and derive an equation of the form (1) one has to make use of a model of the adsorbed layer.
We shall first investigate the use of a
'surface phase' model in which the concentration profile in a real system is replaced by a step function (Fig.
5).
In this case it can be shown
[1OJ
that
the chemical potential of component i in the surface layer can be written o )li
)l~'£
+ RT In
~
x~y~ ~
~
(o~
+
~
.
- o)a; ,
(18)
where a. is the partial molar area of component i, and x~ i.
and y~
~
are, respectively,
~
the mole fraction and activity coefficient of i in the surface layer.
The
justification for taking the standard chemical potential as equal to that in the bulk pure liquid is that as x , ->-1, i.
y~ ->- 1, ~
0
->-
o~ i. and )l? ->- )l~'oi.; ~
pure liquid bulk and surface regions are in equilibrium
and since in the
)l~'o ~
)l~'£ ~
To use this equation it is necessary to be able to calculate x? from adsorption ~
measurements, and for this purpose some estimate of the thickness of the adsorbed layer is needed.
If the layer is t molecular layers thick then x~
is given by
[9J. (19)
where a? is the cross-sectional area of the molecule (in molar units) and is ~
related to a
i
by
11
Fig. 5
.
profile of X as z function of distance from surface z and step function approximation used in 'surface phase' model.
Concentrat~on
t z
t t
Xz--
xR-
z
(ZO)
a.
~
Thus a
o
dx~/dX~ ~
and a
0
are needed as well as t. For simple systems it is usual to Z assume a monolayer model, unless application of the criteria [12J x~ < 1 and l
~
~
> 0 indicates that a monolayer model is thermodynamically unacceptable.
In this case the minimum integral value of t needed to achieve thermodynamic consistency is often
c~osen.
This model clearly involves some rather drastic assumptions and its application requires the selection of a number of parameters whose values are not easily derived from independent data.
However, it serves
a~
a useful basis for a
preliminary discussion. Since the solid surface is supposed to remain filled, it follows that adsorption equilibrium is associated with the exchange process (Zl) where (1)0 denotes a molecule of 1 on the surface, etc.; area.
~
Alternatively, chosing a
a~ is a chosen standard
aI' (ZZ)
where r
=
aZ/a
l•
At equilibrium
12 (23) which on insertion of (18) and the corresponding expressions for
~l
£ and
~2
£ leads
to (24)
Since the right hand side of (24) is a property of the two pure components, an adsorption equilibrium constant can be defined as
(25)
* and a standard free energy change defined as (02* - 02)a -e-
t.G
l
leading to
- RT In K •
a ds
(26)
a
Since, according to (12) or (13) the standard free energy change can in principle at least be obtained from vapour adsorption data for the single components, so can K • We a are now left with the problem of obtaining x
°2 and
(n)
from K and 2 a, as shown by (25) this will depend on a knowledge of the bulk and surface activity coefficients. no problem.
hence f
It might be supposed that those in the bulk phase posed
In fact accurate data are often missing for many systems of interest
in adsorption work:
But the main difficulty arises from the lack of independent
information regarding the activity coefficients in the interfacial layer. For relatively simple systems it may be adequate to assume that both bulk and interfacial regions behave ideally and that, as a rough approximation, the molecules are of equal size: a mole fraction of 2 is given by
l
= a 2 = a and r = 1.
In this case the surface
(27)
and the reduced adsorption by
~ l-X~X~(Ka
-
l~
l+(K a - l)X;J
(28 )
13 It has sometimes been suggested [13J that surface layers are more nearly ideal than the bulk liquid mixture and that as a second approximation one can set Y~'
Y~'
Y~
Yi.
1 (or at least Y~/Y~
=
=
1), and use the experimental values of
However, this is not a general rule since some systems which are nearly
ideal in the bulk exhibit substantial deviations from ideality in the surface [3J. More sophisticated, though still rather crude, theoretical treatments assume that the surface layer can be represented in terms of a regular solution model [10 bJ or as a mixture of molecules of different size following Flory-Huggins statistics [10 b, l4J and taking account of thermal contributions to the activity coefficients. Thus the activity coefficients can be written as the product of an'athermal' and a 'thermal' term [15, l6J : In y~
ath,a th,a + In y. In y.
(29)
~
~
~
¢l
ath,a In Yl
In
ath,a In Y 2
¢2 In - - (r - 1)¢2 a x 2
0+
(l
1
(30)
- -;::)¢l
Xl
where ¢l' ¢2 are the fractional coverages (area fractions)of 1 and 2.
In
[y~
ath,a Yl
1/: :g] In
and equation (24) becomes
II<
~
] - (1 - 1:.)
::
(31)
r '
[SJ
l/r exp
Here y~h,a
Thus
[-
(0
*2
+ (1 -
1:.} rlJ-
(32)
may be estimated using the Flory-Huggins x-parameter derived from the
bulk properties [10~.
However, in their analysis Larionov et al. have considered d ata Yth,a Yth,a =1, an d h ave use d gas a d sorpt~on . t h e athermal case were h 2 l together with equation (32) to calculate adsorption isotherms from solution.
[16J Typical results are shown in Fig. 6 for the systems (CC1 + iso-C 8H18) 4 and (C + iso-C phitised carbon [17J. While agreement in the first case 6Ho 8H18)/gra is good, that for the second is only moderate. While the surface phase model provides a reasonable approximate basis for the correlation of vapour and solution adsorption, it must be emphasized that it
14
(b)
(a)
n~(n)/m nnno1g
n -1
o(n)/m 2
-1
TIDIlo1g
o o
0.4
o
o
Fig. 6 Comparison of experimental results (full lines) and calculated isotherms
for (a) (iso-octane + CC14)/graphitised carbon and (b) (iso-octane + C6H6)/ aerosil Filled points, calculated with yih,o= YZh,o= 1; open clrcles, assuming y~ = yr and layer thickness of ten monolayers. (redrawn from refs. 16,17.
depends not only on the assumptions of the model but also requires the assignment of values to a number of parameters including the molar surface areas of the adsorbed molecules, the surface area of the solid and the thickness of the adsorbed layer.
In any self consistent analysis the same values should be used
for the molar areas. The agreement achieved by Larionov ~ a1. [SJ was obtained 2 using 0.50 nm for the molecular area of benzene when deriving the surface area of the solid from a BET plot of benzene vapour adsorption, while a value of 2 0.40 nm was employed in analysing the solution adsorption data. Furthermore, the molecular area of CC1 was taken as 0.29 nm in reference [~ , but 0.537 nm 4 when analysing adsorption on silica gel [6J. It is not known how sensitive the agreement between experiment and theory is to variations in these parameters, but clearly if it is necessary to take different values for different systems in order to get this agreement, then the situation is far from satisfactory.
15 POLANYI POTENTIAL THEORY It vou1d clearly be preferable if one could break away from the simple monolayer or adscrbed phase model and represent the system in terms of a smooth concentration profile, and in principle this might be possible using the basic concepts of the polanyi.potential theory.
Attempts to correlate vapour and solution adsorption
using this approach have been made by, among others ,Hansen and Fackler
[}.81
and
more recently by Siskova, Erdos and Kadlec [19J. We first recall that the chemical potential of a component of a liquid mixture subjected to a pressure p has the general form ~i
JI,
= ~i
t JI, JI, t (T,p) + RT In xiY i + (p - p)v.~
t&
(33)
where pt is a reference pressure; v. is the partial molar volume of i (strictly ~ t the mean value over the pressure range p ~ p). Under ordinary conditions the last term can be neglected.
However, liquid close to an adsorbing surface is
subjected to an anisotropic stress of such a magnitude that a contribution of the same nature as the last term becomes important.
A full analysis in terms of
the local stress conditions is complex, but for the present purpose it is convenient to represent this excess chemical potential by E • Since the stress condition i varies with distance from the surface, E. will vary continuously from some maximum
a
~
value of E
close to the suface to zero far from the surface. In a layer of i liquid distant A from the surface the chemical potential can thus be written (34)
At equilibrium the distribution of matter must be such that successive layers are at equilibrium with one another and with the bulk, i.e. there must be equilibrium in all exchange processes of the type
where r is now the ratio of molecular volumes.
This leads to
l/r , (all A),
RT
Since the
E~
~
A vary with A, so will K and, in principle, if a
(36)
E~
~
A is known K can a
be calculated:the composition of the layers will change smoothly from A (x;,x;) far from the surface where K = 1, to (x~,x~) in the layer adjacent to the surface.
The assumption is now made that the value of E
i
at some surface A
16
which encloses a volume ¢ of adsorption space is equal to the Po1anyi adsorption potential at that degree of filling in adsorption of i from the vapour A
e.
(37)
~
or in terms of the volume of adsorption space filled (38)
where
p~
~
=
p.(¢) is the pressure at which,in vapour adsorption, the adsorption ~
space up to layer A, of volume ¢, is filled. Thus if the vapour adsorption isotherms are known
~
1 (¢)
Z (¢ ) -
E:
E:
and K
A a
= RT ~
In
~ j
~ PI*
PZ(¢) 11r
*
= K (¢) =
--
a
{p;/p~¢)}-
In
j
{p~/PI
(¢)}]
(39)
(40)
--
p (¢)
Pz
1
Further progress is again hindered by lack of knowledge of the dependence of activity coefficients on the stress conditions near the surface. known then
If these were
A could be calculated from KA and the contribution of the layer z a
X
between A and A + dA (or the volume element ¢ to ¢ + d¢) to the total surface excess obtained (ref.l(a), equ.96)
n~(n)(A)
where v
=
A
A,tiv; V
A
1
dA
(41)
A
(4Z)
1X1 + vzx z
is the mean molar volume in the element considered. The total surface excess would then be obtained by integration
j
o
dA
1
As
j
d¢
(43)
o
If we make the simple assumption of ideal systems, then these equations become
17
(44)
Insertion of equation (40) into (44) leads to equations essentially similar to those derived for ideal systems using the surface phase model. Hansen and Fackler
[18J
attempted to use this method to calculate the adsorption
of propan-l-ol and butan-l-ol from aqueous solution by Spheron 6, but found only rough agreement between observed and calculated isotherms.
This is perhaps not
surprising since the Polanyi characteristic curves for the alcohols and water are of different shapes and the activity coefficients are not expected to be unity.
Siskova, Erdos and Kadlec
[19J
studied six systems: their results are
shown in Fig. 7. The observed and calculated curves are in moderate agreement, although in most cases the observed maximum in the surface excess of component 2 lies at lower values of x; than predicted. While this approach has the apparent merit of avoiding the surface phase concept, its weakness lies in the assumption that £~
~
is determined solely by
interaction with the solid surface and so can be derived from the adsorption isotherm of the pure substance from the vapour phase.
However, in adsorption
from solution a given molecule at A will be surrounded by molecules of both kinds, while in vapour adsorption up to the A-surface, molecules at this surface interact only with molecules of the same kind, and then only with those in the layers closer to the surface. Further study of the potential approach is certainly called for to examine its possible usefulness more carefully. ADSORPTION OF MIXED GASES We consider finally the question of whether theories of the adsorption of mixed gases can be adapted to adsorption from liquid mixtures.
Many treatments
of mixed gas adsorption have been developed, the objective being to predict mixed gas adsorption isotherms from those of the single gases. ideal behaviour of both vapour and adsorbed states.
Most assume
The concept of 'ideal
surface solutions' having a defined spreading pressure is often employed and used to discuss adsorption from solution by extrapolation to the saturation vapour pressure of the surface solution
[20J .
For ideal systems the results
bear a close resemblance to those already discussed.
A more sophisticated
approach has been developed by Bering, Serpinski and Surinova
[21J
who extend
their earlier method of calculating mixed gas adsorption from the single gas isotherms [22J to solution isotherms. This involves the assumption that as . • approached n°b ecomes a linear funct~on • fO saturat10n ~s 0 n h w en t h e compos~t~on . . l 2
18
o
0.2
0.4
xf
0.6
1.0
0.8
0.2
0.4
~
x2
0.6
0.8
1.0
Fig. 7 Comparison of calculated (full lines) and experimental (points) adsorption isotherms using equ. (44) (a) CC14 + benzene (b) CC14 + toluene (c) chlorobenzene + benzene (d) chlorobenzene + toluene (e) CC14 + chlorobenzene (f) toluene + benzene, adsorbed by silica gel. Redrawn from ref. 18.
of the gas mixture (x~)
is held constant.
In addition it is assumed that the
activity coefficients of the 'surface solution' tends towards thbse of the'bulk solution as saturation is approached.
This method has been tested for the systems
(benzene + iso-octane), (CCI4 + iso-octane) and (ethanol + benzene)/graphitised carbon black.
Only for the first system have
d~tailed
results been published
showing excellent agreement between the calculated and experimental curves.
No
curves have been published for the latter two systems so that one cannot comment on the general applicability of this method of calculation. It seems doubtful whether even in principle methods based on the adsorption isotherms of the single gases can prove useful where substantial deviations from ideality occur: a fuller understanding of activity coefficients in surface layers is essential before further progress can be made. The question therefore arises whether experimental data on mixed vapour adsorption can be extrapolated to saturation conditions. problems.
This faces two major
First, there is no proven theory of multilayer adsorption of mixed
gases which could be used as a basis of an extrapolation technique, and secondly there are currently few data available on mixed vapour adsorption over a
19 sufficiently wide range of conditions, including the approach to saturation, to guide the development of a theory.
This is an area which needs much further
study.
CONCLUSIONS In this review inter-relations have been sought between the adsorption of single vapours by solids and that of the components of liquid mixtures.
It must be
concluded that although general thermodynamic relations can be developed between certain integrals derived from experimental data from these two sources, the problem of using single vapour adsorption isotherms to calculate surface excess isotherms for mixtures cannot be solved without much more detailed theories of adsorption from solution.
Thus although there are several reasonably useful
techniques when the systems concerned exhibit ideal behaviour, there is no generally applicable solution for non-ideal systems.
The situation is in fact
no worse than that faced in the analogous problem of the calculation of the equilibrium of chemical reactions where again the solution depends ultimately on the ability to predict activity coefficients.
20
REFERENCES 1 For reviews see e.g. Specialist Periodical Reports, Colloid Science, Chemical Society London, D.H. Everett (ed) (a) Vol. 1 (1973), Chapter 2;(b) Vol. 2 (1975), Chapter 2; (c) Vol. 3 (1979), Chapter 2. 2 G. Schay, J.Co11.Interface Sci., 42(1973)478-485; Pure and App1.Chem., 48(1976) 393-400; D.H. Everett, Pure and App1.Chem.S3(1981)2181-2198. 3 e.g. D.H. Everett and R.T. Podo11,J.Co11.Interface Sci. 82(1981)14-24; D.H. Everett, J.Phys.Chem. 85 (1981)in press. 4 A.L. Myers and S. Sircar, J.Phys.Chem. 76(1972)3415-3419. 5 O.G. Larionov,K.V.Chmutov and M.D. Yudi1evich,Zhur.Fiz.Khim.,41(1967)2616(Russ.J.Phys.Chem.41(1967)1417-1420). 6 S.A. Kazaryan, O.G. Larionov and K.V. Chmutov, Zhur.Fiz.Khim.S1(1977)188-191 (Russ.J.Phys.Chem.S1(1977)103-10S). 7 Yu.F.Berezkina,S.A. Kazaryan,E.Kurbanbekov, O.G. Larionov and K.V. Chmutov, Zhur.Fiz.Khim.46(1972),S45,1242,1694(Russ.J.Phys.Chem.46(1972)318,1242,1694. 8 S.S. Kist1er,E.A. Fischer and I.R. Freeman, J.Amer.Chem.Soc. 65(1943)1909-1919. 9 c f.D.H. Everett and J.M. Haynes,J.Co11.Interface Sci.,38(1972)12S-137;D.H.Everett in Characterisation of Porous Solids,S.J. Gregg,K.S.W.Sing 2nd H.F. Stoeck1i (eds.) Soc.Chem.lnd.London,1979,229-2S1. 10 D.H. Everett (a) Trans.Faraday Soc., 60(1964)1803-1813; (b) ibid.,61(196S) 2478-2495. . ----11 C.E. Brown, D.H. Everett and C.J. Morgan,J.Chem.Soc.Faraclay Trans.I, 17(1975) 883;c f. ref.1(a) equ.(9) and (63). 12 A.I. Rusanov, Phase Equilibrium and Surface Phenomena,Chimia,Leningrad 1967 (in Russian), Chap.VI; c f. ref.1(a),p.66. 13 A.A. Zhukhovitskii,Zhur.Fiz.Khim., 18(1944)214-233; 19(1945)337; A.V. Kise1ev and L.F. Pav1ova,Izvestia Akad.Nauk.S.S.R., Ser.Khim •. 1965,18-27 (Bu1l.Acad. Sci.U.S.S.R,Chem.Ser.,196S,lS-23) and ear1ier.work. 14 S.G. Ash, D.H. Everett and G.H. Findenegg,Trans.•Faraday Soc.64 (l968) 2639-2644. 15 e.g. A.J.Ashworth and D.H. Everett,Trans.Faraday Soc., 56 (,l960)l609-1618. 16 S.A. Kazaryan,E.Kurbanbekov, O.G. Larionov and ,K.V.Chmutov,Zhur.Fiz.Khim., 49(1975)1247-1251 (Russ.J.Phys.Chem.49(197S)728-730). 17 S.A. Kazaryan,E.Kurbanbekov,O.G.Larionov and K.V. Chmutov,Zhur Fiz.Khim.,49 (1975)1243-1247 (Russ.J.Phys.Chem.,49(197S)72S-728) 18 R.S. Hansen and W.V. Fack1er,J.Phys.Chem.,S7(19S3)634-637. 19 M. Siskova, E. Erdos and O.Kadlec, ColI. Czech. Chem. Comm., 39 (1974)1.954-1964. 20 S. Sircar and A.L. Myers, A.I.Ch.E. Journal 19 (1973)lS9-166;c f. ref l(b), p.64:S.Sircar and A.L. Myers,Chem.Eng.Sci., 28(1973)489-499. 21 B.P. Fering and V.V. Serpinskii,Izvest.Acad.Nauk.S.S.R., Ser.Khim., 1972, 166-168(Bu11.Acad.Sci.U.S.S.R.,Chem.Ser.,1972,152-1S4). 22 B.P. Bering, V.V. Serpinkii and S.I. Surinova, Izvest.Acad.Nauk.S.S.R.Ser. Khim. 22 (1973) 3-6 (Bull.Acad. Sci. U. S. S.R. ,Chern.Ser. 220"97.5)1-4) •