Molecular sieves vol 1 5 karge weitkamp vol 3 post synthesis modification i 2003

Preface to Volume 3

For many purposes, zeolites and related materials are not utilized in the as-synthesized form. Rather, they are only employed after an appropriate post-synthesis modification.
Undoubtedly, the classic procedure of zeolite treatment after synthesis is that
of ion exchange achieved through treatment of a suspension of the as-synthesized (or natural) zeolite powder (usually in the sodium or potassium form) in
an aqueous solution of a salt containing the cations to be introduced. Starting in
the 1930s, this type of ion exchange has been extensively studied, not only as a
method of preparation, but also with respect to thermodynamics and kinetics.
Application on an industrial scale is well developed and, because of its importance, ion exchange in zeolites has been reviewed several times. Thus, the
first chapter of Volume 3 of the series “Molecular Sieves – Science and Technology”, which was contributed by R.P. Townsend and R. Harjula, was able to focus
on the developments and advances made during the last decade. It emphasizes
the need for improvement of theoretical approaches, utilization of the rapidly
growing computational power, and the importance of acquiring reliable data as
the bases for progress in fundamental studies on conventional ion exchange.
The more recent development of solid-state ion exchange and related modification techniques such as reactive ion exchange between solid zeolite powders
and solid or gaseous compounds containing the cations we wish to introduce is
rather exhaustively dealt with in the subsequent chapter written by H.G. Karge
and H.K. Beyer. The concept of solid-state ion exchange is explained and contrasted to the conventional exchange process. Experimental procedures as well
as techniques for monitoring the solid-state modification of zeolites are described in great detail and illustrated by a large number of investigated systems.
Related methods of post-synthesis modification, possible mechanisms, and first
approaches to study the kinetics of solid-state ion exchange are discussed.
Post-synthesis modification of zeolites via alteration of the aluminum content of the framework became a most important topic of zeolite chemistry when,
in the mid 1960s, the effect of stabilization through dealumination was discovered. In Chapter 3, H.K. Beyer contributes a systematic review on techniques
for the dealumination of zeolites by hydrothermal treatment or isomorphous
substitution amended by a section on the reverse process, i.e., introduction of
aluminum into and removal of silicon from the framework.
Methods of post-synthesis modification essentially different from those discussed in the first three chapters are based on the generation of extra-frame-


X

Preface to Volume 3

work aggregates of metals (as presented in the chapter by P. Gallezot), ionic clusters (as described in the contribution by P.A. Anderson), and oxides and sulfides (treated in the last chapter written by J. Weitkamp et al.). One of the main
motivations for studying the generation of such clusters inside the void volume
of zeolite structures originates, of course, from possible applications in catalysis.
This is most evident in the case of metal cluster/zeolite systems which are successfully employed in heterogeneous catalysis of hydrogenation, hydrocracking,
hydroisomerization, etc. However, both ionic clusters and oxidic and sulfidic
clusters hosted by the frameworks of zeolites are interestring candidates as catalysts for base-catalyzed, redox, photocatalyzed and perhaps other reactions. In
view of cluster formation with zeolites as hosts, questions of size, location, distribution, interaction with the framework, and stabilization of the active aggregates play a decisive role. Thus, in all three contributions on clusters in zeolites,
methods of their preparation as well as problems of their characterization and
utilization as catalysts and photosensitive materials, as sensors, in optics, and
electronics are extensively dealt with. These areas are still challenging for future
resarch and promising in view of potential applications.
However, not all important phenomena of post-synthesis modification are
covered with the present six chapters of Volume 3 of the series ‘Molecular Sieves
– Science and Technology’. Topics such as, for instance, ‘Incorporation of Dyes
into Molecular Sieves’, ‘Preparation of Ship-in-the-Bottle Systems’, ‘Secondary
Synthesis in Zeolites’, ‘Pore Size Engineering’, ‘Modification of Mesoporous
Materials’ are equally important and, to a large extent, presently subject to very
active research and development. Therefore, such topics will be dealt with in one
of the subsequent volumes under the title ‘Post-Synthesis Modification II’.
September 2001

Hellmut G. Karge
Jens Weitkamp


Ion Exchange in Molecular Sieves
by Conventional Techniques
Rodney P. Townsend 1, Risto Harjula 2

1
2

Scientific Affairs, Royal Society of Chemistry, Burlington House, Piccadilly,
London W1J 0BA, UK; e-mail:
Laboratory of Radiochemistry, PO Box 55, 00014 University of Helsinki, Finland;
e-mail:

Dedicated to Professor Gerhard Ertl on the occasion of his 65th birthday

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

Introduction

1.1
1.2

The Importance of Ion Exchange Phenomena in Molecular Sieves
Origin and Nature of Ion Exchange Behaviour in Molecular Sieves

2

The Importance and Utility of Theoretical Approaches

2
5

. . . . . . .

2.1
2.2
2.3

Preference, Uptake and Selectivity . . . . . . . . . . . . . . .
Batch and Column Exchange Operations . . . . . . . . . . . .
Thermodynamic Parameters, Non-Ideality and the Prediction
of Exchange Compositions . . . . . . . . . . . . . . . . . . .
2.4 Kinetic Processes and the Prediction of Rates of Exchange . .
2.4.1 Hierarchical Model of Zeolite Particle or Pellet . . . . . . . .
2.4.2 Intraparticular Exchange Rate Processes . . . . . . . . . . . .
2.5 Trace Ion Exchange . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Column Models . . . . . . . . . . . . . . . . . . . . . . . . . .

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Experimental Approaches . . . . . . . . . . . . . . . . . . . . . . . . 29

3.1
3.2
3.2.1
3.2.2
3.2.3

Practical Experiments . . . . . . .
Pitfalls . . . . . . . . . . . . . . . .
Selectivity Reversal and Ion Sieving
Zeolite Hydrolysis Effects . . . . .
Colloidal Solids in Suspension . .

4

Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Molecular Sieves, Vol. 3
© Springer-Verlag Berlin Heidelberg 2002


2

R.P. Townsend · R. Harjula

1
Introduction
1.1
The Importance of Ion Exchange Phenomena in Molecular Sieves

Throughout the 1990s there was a decline in the number of fundamental studies
carried out on the ion exchange properties of zeolites and related materials. One
has only to examine the content of published conference proceedings on the
subject over the last 20 years to observe this trend: the situation has moved from
one where whole sessions were devoted to ion exchange studies, to one where
the subject is subsumed into sessions covering other areas. Part of this decline is
to be expected, as increased attention has been rightly paid to the intriguing
possibilities that can arise through the exploitation of newer alternative postsynthesis methodologies, many of which are discussed elsewhere in this volume.
Nevertheless, the fact remains that conventional ion exchange techniques
continue to be used routinely for post-synthesis modification during the preparation of molecular sieves for major industrial applications. Also, there are now
areas where molecular sieves find major application directly as ion exchangers

per se. In this respect the situation has changed markedly since the early 1960s,
when Helfferich, in his classic book on ion exchange, could justifiably describe
zeolites “as ion exchangers they are of little practical importance” [1]. These
direct applications are especially detergency [2–7] and also the removal of
nuclear waste [8–13] or other environmental pollutants [3]. However, it is
generally a combination of properties of a particular zeolite in addition to its
ion exchange capability that has tipped the balance in favour of its use, rather
than any intrinsic superiority per se, which the zeolite may possess as an ion
exchanger.
If, therefore, conventional ion exchange remains an important post-synthesis
preparative technique, and the materials have in addition major direct applications as ion exchangers, why have the number of fundamental studies decreased?
It is certainly not because ion exchange behaviour of molecular sieves is sufficiently well understood and predictable to render further fundamental research
studies unnecessary. Two causes are suggested to explain this decline:
1. Many theoretical treatments of the ion exchange reaction within zeolites
(both equilibrium and kinetic) are obscure and complicated. This has without doubt rendered inaccessible the real value of the work to those many
workers who have a practical need to predict and control ion exchange behaviour during the industrial exploitation of molecular sieves. Although
theoretical understanding is important, it is easy to forget that the end purpose of such work should be to provide information and tools that the
chemical engineer or other user of the molecular sieve can apply simply and
effectively. Obscurities in theoretical treatments mean that users often do not
appreciate how basic theory can be used, not just to simplify the number of
measurements which need to be made, but also to predict and control behaviour during application. The theory should not be an end in itself!


Ion Exchange in Molecular Sieves by Conventional Techniques

3

2. The second cause is related to the first. Even where the value of theory for the
prediction and control of the behaviour of these materials has been recognised, the utility of these approaches has often been greatly reduced because
of the experimental methods which have been employed or by the poor

experimental data which have been available, or both. Indeed, it is only comparatively recently that a proper recognition has arisen concerning the number of potential pitfalls and difficulties that can militate against the acquisition of meaningful and accurate experimental data.
A good example of this is the frequently studied Na/Ca-zeolite A system, which
has received much attention because of its importance in detergency applications. Careful and detailed experimental studies over a period spanning some
20 years by different sets of workers [14–20] resulted in calculated values of the
standard free energy of exchange (kJ equiv–1*) which ranged from –0.59 [14] to
–3.09 [17]. Plots of the corrected selectivity coefficient (defined below; see

E
Fig. 1. Plots of the logarithm of the corrected selectivity coefficient ln KG [cf. KA/B
in
–
Eq. (7b)] as determined by different workers for the Na/Ca exchange in zeolite A. ECa is the
equivalent fraction of calcium in the zeolite [(Eq. (3b)]. BRW Barrer, Rees and Ward [14];
A Ames [15]; WF Wolf and Furtig [16]; SW Sherry and Walton [17]; BR Barri and Rees [18];
WGC Wiers, Grosse and Cilley [19]; FT Franklin and Townsend [20]. Taken from [8]

* Throughout this paper the term “equiv” denotes 1 mol of unit negative or positive charges.


4

R.P. Townsend · R. Harjula

Eq. 7b) naturally show a similar diversity but also differ from each other in curve
shape and trends (Fig. 1). These marked differences (particularly at the extrema
of the plots) were variously ascribed to experimental error [20], to variable
quantities of non-exchangeable sodium in the materials employed [20] (the
materials differed in their source and in their method of preparation [14–20])
or to variable levels of hydronium exchange depending on the pH and other conditions used [20, 21].
Thus, even for this very important example, not only is some of the published

theoretical work difficult to interpret, but also experimental data from different
studies are frequently incompatible and incomplete.
It is essential therefore that a critical review of advances over the last decade
should look at the developments in the context of the field as a whole. This is our
intention here. After a discussion of the origin, ubiquity and nature of ion
exchange behaviour in molecular sieves, recent advances in the application of
thermodynamic and kinetic descriptions of the ion exchange process will
be described. This will demonstrate some of the shortcomings of current
approaches, together with the relative paucity of reliable literature data that
can be applied easily and practically. This whole topic has particular relevance to those industrial applications where zeolites are used directly as ion
exchange materials and this will be exemplified throughout the chapter using
two main examples. The first of these is the application of A- and P-type zeolites
as detergent builders, where the approach is to use a batch exchange approach
to remove hardness ions (especially calcium) as fast as is practicable before
the indigenous water hardness harms the wash performance of the detergent
product. The second concerns the treatment of nuclear waste, where a variety
of higher silica zeolites have been employed using a continuous (column)
process to remove, and subsequently store, high concentrations of monovalent
and divalent radionuclides such as caesium and strontium. For both these
major applications, in addition to selectivity, it is noteworthy that the systems
are normally multicomponent, that the kinetics of exchange are all important and that the morphology of the exchanger material must be controlled
carefully.
Post-synthesis modification comes into its own when preparing molecular
sieves with desirable and exploitable properties other than those of ion exchange, be they optical, magnetic, catalytic or adsorptive. Here it is not directly
the thermodynamic and kinetic ion exchange properties that are of prime
importance but rather which experimental, preparative methods are most commonly used. Thus it is important to assess what are the most appropriate experimental methods of preparation, as well as to review the many pitfalls one can
fall into which can subsequently give rise to very inaccurate and inadequate
experimental data. These experimental problems can include framework
hydrolysis, hydronium exchange, dealumination, the presence of key trace impurities, dissolution phenomena, carbonate and bicarbonate interference, colloidal
phenomena, metal ion complex formation and cation hydrolysis.

Having thus reviewed developments and advances over the last decade, the
chapter concludes with some recommendations on directions and topics for this
area of research in the future.


Ion Exchange in Molecular Sieves by Conventional Techniques

5

1.2
Origin and Nature of Ion Exchange Behaviour in Molecular Sieves

Ion exchange is a characteristic property manifested by most molecular sieves.
In essence, whenever isomorphous replacement of one cation by another of different charge occurs within an initially neutral crystalline framework such as a
pure silica molecular sieve, then a net electrical charge remains dispersed over
that framework. This is neutralised through the presence, within the microporous channels, of cations of opposite charge (often referred to as counterions).
An example of this is seen in the introduction by direct synthesis of small quantities of aluminium into the silicalite framework to give the material ZSM-5.
Silicalite, the pure silica analogue of ZSM-5, is then seen to be just the end-member of a set of isomorphous microporous molecular sieves that exhibit ion
exchange properties which are a function of the quantity and distribution of
aluminium atoms within the structurally similar frameworks. In addition, since
one can prepare, through post-synthesis modification of the framework composition, a variety of other isomorphous metallosilicates and metal aluminosilicates, it is obvious that zeolites possessing ion exchange capabilities are a
common occurrence.
Pure aluminium phosphate molecular sieves are probably more common
than are pure silica analogues of zeolites. They resemble pure silica zeolites in
that they possess frameworks that are electrically neutral, but there is a significant difference between these two classes of inorganic solids. In topological
terms both are 4:2 connected nets of T:O atoms (“T” denoting tetrahedral
framework and “O” denoting oxygen). From this it is obvious that it is only
required for the T ion to have a charge of +4 for the connectivity of the net to
give rise naturally to a neutral framework in concert with the oxide anions. This
is fulfilled for pure silicalite. In the case of ALPO molecular sieves the requirement is also fulfilled, but the 4:2 T:O net now comprises two types of strictly

alternating T-cations (aluminium and phosphorus, possessing respectively formal positive charges of 3 and 5). Providing the cations alternate strictly throughout the framework, the 4:2 Al,P:O net holds no overall charge; however, in
contrast to a pure silica zeolite, where the formal charge at every atomic centre
is zero, within a pure AlPO the formal charge is not dispersed homogeneously,
but changes from –1 at each aluminium to +1 at each phosphorus. This greater
heterogeneity of charge distribution may in part explain the experimental
observation that ALPOs frequently exhibit poorer thermal stability than do pure
silica zeolites.
For a particular ALPO molecular sieve to possess an ion exchange capacity as
an intrinsic property, it is necessary to prepare a material where some of the aluminium and/or phosphorus framework atoms have been replaced by other
atoms of different charge. This can occur using for example silicon, to form the
so-called SAPO materials, or with metals in addition or not to silicon, to form
respectively the so-called MeAPSO and MeAPO analogues. However, it is important to note that although silicon could in principle replace either aluminium or
phosphorus to give rise to positively or negatively charged SAPO molecular
sieves, respectively, in practice only the latter process seems to occur, or another


6

R.P. Townsend · R. Harjula

process in which two silicons replace one of each of aluminium and phosphorus,
which gives rise to no net change in framework charge [22]. In MeAPSOs, divalent or trivalent metal ions replace the aluminiums in the framework. In this way
the charge imbalance is minimised as these isomorphous substitutions either
make no difference to the overall framework charge (T3+ for Al3+) or only
increase it by one negative charge per substitution (e.g. Mg2+ for Al3+), a process
analogous to when aluminium replaces silicon in aluminosilicates [22].
Overall therefore, and in common with aluminosilicate zeolites, the norm is
for MeAPSOs and MeAPOs to possess cation exchange properties rather than
the reverse. In this respect, zeolites and ALPOs resemble many other classes of
ion exchangers that are mineralogical in origin, such as the clay minerals. These

are layered materials where a cation exchange property can arise primarily from
isomorphous replacement of trivalent cations by divalent, or tetravalent cations
by trivalent ones, within the layers [23]. However, there is a major exception:
these anionic exchangers are the double metal hydroxides, which are also layered structures but which exhibit a net positive charge across the lattice. The
“parent” material here is the mixed Mg,Al hydroxide, commonly referred to as
hydrotalcite. It would be intriguing to understand better the conditions (if any)
under which one might expect to synthesise microporous three-dimensional
framework structures which similarly have a net positive charge dispersed over
the lattice and hence an anion exchange capacity coupled with a molecular sieve
capability.
It is important to note that, up to this point, we have been considering the zeolite, ALPO, SAPO, etc., as being described adequately as a 4:2 T:O net. This topological description, which in general terms is, as Smith points out [24], nothing
more than a mathematical construct of the human brain, does nevertheless
allow us to appreciate both the origin and magnitude of an ion exchange capacity arising from T-atoms being replaced by others of different charge. However,
this description is not sufficient to cover the observed differences in ion
exchange properties (i.e. selectivity, kinetic rate, level of exchange) that may be
seen between various molecular sieves having similar exchange capacities. To
understand these differences, one must not only examine more closely the topological properties of the nets but also bring to bear structural considerations.
Considering these topological properties in more detail, it is adequate at this
point to take as read that all the T-atoms within the microporous net are joined
to each other by bridging oxygens. One can therefore concentrate on the Tatoms only and describe molecular sieves in terms of four-connected threedimensional (4-conn.3D) nets of T-atoms [25] that, in turn, can be derived from
appropriate 3-conn.2D nets [26]. Considering the latter nets first, these differ
from one another in the ways the nodes (T-atoms) link to each other via networks of polygons. Any node can then be described by its “vertex symbol”, viz.
by its surrounding polygons with the number of each type of similar polygon
surrounding the node being denoted by a superscript [26]. Thus the simplest
example of a 3-conn.2D network (the hexagonal net) becomes a 63-net; a more
complicated example could be the 4.6.12-net which forms the basis for the
gmelinite structure [26]. Note that all the nodes within each of these two separate examples are topologically equivalent. This need not be the case. For exam-


Ion Exchange in Molecular Sieves by Conventional Techniques

7

Fig. 2. Structure of mordenite viewed along the main 8-ring and 12-ring channels parallel to
the c-axis. Four topologically distinct types of T-atoms are observed within the 3-conn.2D
(4.5.8)1 (4.5.12)1 (5212)1 (5.8.12)1 net

ple, consider the case of mordenite (Fig. 2), which is derived from a (4.5.8)1
(4.5.12)1 (5212)1 (5.8.12)1-net containing four topologically distinct types of Tatoms [24].
Similar considerations apply when one considers the 4-conn.3D nets that
constitute molecular sieves. Here it is often convenient to describe the structure
in terms of polyhedral units or cages, with the polyhedra described topologically in terms of face symbols [25] (not to be confused with vertex symbols defined
above). Thus the face symbol for the familiar sodalite unit, which is geometrically a truncated octahedron, is 4668 with all vertices geometrically and topologically equivalent. If these units are then linked together, for example either
through their 4-windows or half their 6-windows, one forms respectively the
zeolite A and faujasitic structures. Both these structures possess cubic symmetry, with each structure comprising 26-hedral cages connected to each other
throughout the microporous zeolite framework, but the vertices of the sodalite
units are no longer all topologically equivalent. For zeolite A the sodalite units
enclose a cage which is the great rhombicuboctahedron (4126886) [25] whereas
for faujasite the cage is the so-called 26-hedron type II, denoted by the face symbol 4641264124 [25].
Why are these matters significant when one considers the ion exchange properties of molecular sieves? The answer is that these topologically non-equivalent
T-atoms combined with the overall structural properties of the three-dimensional microporous framework often give rise to several very different types of
local environments which repeat themselves regularly throughout the crystalline structure. These different local environments, evidenced by solid state
NMR combined with X-ray crystallography [27], are distinct in themselves, differing from each other sterically and electronically, and these differences will be


8

R.P. Townsend · R. Harjula

manifested not only through their characteristic adsorptive and catalytic behaviour, but also through their ion exchange properties. Formally, therefore, zeolites

may be regarded as comprising a set of crystallographically distinct sublattices,
each having characteristic selectivities for different exchanging cations, depending on these local environments [28]. The overall ion exchange behaviour of a
molecular sieve can therefore be a subtle function of the structural and topological properties combined. An important combination of structural and topological properties concerns the ordering of isomorphously substituted framework atoms [29]: this determines what fraction of the overall framework charge
is found on each sublattice. Other significant structural properties can be losses
in symmetry through restricted rotation [27], and whether the sites are accessible to exchanging cations (i.e. the sizes of the micropore channels allowing
ingress and egress of exchanging cations plus water).
A further point is worth emphasising: since site heterogeneity in a particular
zeolite is manifested through such a set of crystallographically distinct sublattices, zeolites differ in this respect significantly from some other common classes of ion exchangers, such as the clay minerals or the resins. Whereas in zeolites
well-defined sites are repeated regularly through the crystalline matrix, in clay
minerals and resins site heterogeneity is often manifested in terms of patches, or
regions of the surface where the sorption energies are approximately constant
[30]. Thus a statistical thermodynamic model of ion exchange for clay minerals
and resins [30] can differ markedly in character from ones developed for zeolites
[31, 32].
As a consequence of all these factors combined, both the equilibrium and
kinetic aspects of selectivity and uptake of ions within molecular sieves can
rarely be understood in a straightforward manner. Phenomena which have
received either considerable attention in recent years or deserve further study
include the so-called “ion sieve effect”, behaviour of high silica materials, the
effects that framework flexibility can have on selectivity and rates of exchange,
multicomponent ion exchange, prediction of exchange equilibria, and the possibility of inducing phase transitions within zeolites through ion exchange. Many
of these are considered further below.
So far we have considered topological and internal structural factors which
give the molecular sieve particular ion exchange properties. However, an ion
exchange capacity can also be manifested which is not an intrinsic property of
the material. The source of this property is unsatisfied valencies occurring at the
termination of the crystal edges and faces, or at faults within the crystalline
structure. In formal terms, the origin of this is topological, in that this incidental and secondary property arises from disruptions in the net at interfaces, surfaces and faults, but the nature and extent of this incidental property depends
essentially on structural and morphological characteristics. For the former, we
can take as an example an ion exchange capacity arising either from the presence of silanol groups [33, 34], or from hydroxyl groups attached to aluminium

atoms situated at the surface [35]. In clay minerals, as much as a fifth of the total
exchange capacity may arise from such sources whereas in the case of zeolites
the contribution of such incidental (or secondary) ion exchange properties is
usually small compared to the intrinsic, or primary source. The exception here


Ion Exchange in Molecular Sieves by Conventional Techniques

9

can be high silica zeolites [35, 36], whose overall ion exchange properties have
received considerable attention over the last decade [37–42].
Interestingly, the external morphology can also be an important factor in
determining ion exchange behaviour of molecular sieves. The crystal habit, the
average crystallite size, the distribution of crystallite sizes and the properties of
aggregates of crystallites can all affect the magnitude of secondary ion exchange
characteristics, since these can alter significantly the surface to volume aspect
ratio and hence the number of external surface sites available [35]. Also, the
kinetic properties may depend on these morphological characteristics, as
instanced by recent studies on a highly aluminous form of zeolite P [6, 7].

2
The Importance and Utility of Theoretical Approaches
When a zeolite in (say) the sodium-exchanged form is suspended in a solution
comprising a mixture of different cations and anions, two properties of the
material are brought into sharp focus. The first of these concerns which types of
cations are “preferred” over sodium or each other by the zeolite. This property is
commonly referred to as the selectivity of a given form of zeolite for another
cation, but there are so many definitions of “selectivity” that the term “preference” may be better used for the present. The second key property to which one’s
attention is drawn, and which is separate from selectivity (however defined), is

the rate at which the mixture of cations achieves its equilibrium distribution
between the exchanging phases (viz., the electrolyte solution and the sublattices
within the zeolite).
2.1
Preference, Uptake and Selectivity

The preference manifested by a molecular sieve for a particular cation is strongly dependent not only on the character of the material under examination, but
also on the conditions of the system as a whole (viz., temperature, perhaps pressure, composition of exchanger and solution phases, pH, nature of solvent, etc.).
Given a comprehensive definition of these conditions, the preference of a given
form of zeolite for a given cation will then be invariant for that set of conditions
because it is essentially an equilibrium property of the system. However, it is
important to define clearly what is meant by “preference”. There are numerous
selectivity coefficients defined in the literature and, on occasion, “selectivity
coefficient” is confused with “separation factor”, a function whose value does
depend strongly on the total ion concentration in solution. Similarly,“uptake” or
“loading” is often confused with “capacity”. To distinguish these terms, a few
basic definitions are required.
Considering as an example a binary exchange involving cations A (valency
zA) and B (valency zB), the reaction equation is usually written as:
–
–
(1)
zA B zB + zB AzA = zA BzB + zB AzA


10

R.P. Townsend · R. Harjula

where the overbars denote the exchanger phase. The preference displayed by the

zeolite for one ion over another is then described by a selectivity coefficient,
which is just a mass action quotient. According to the choice of concentration
units, a series of these selectivity coefficients may be defined which differ
numerically from one another:
–
–x zB c zA
EAzB cBzA
c–AzB cBzA
A B
x
E
kA/B = 0
≠ kA/B = 01
(2)
–
–x zAc zB ≠ k A/B = 01
cAzB c–BzA
EBzA cAzB
B A
where cA , cB are the cation concentrations in solution (mol dm–3) and the corresponding concentrations in the molecular sieve are indicated with an overbar
(equiv kg–1 dry exchanger). The definition of kA/B is consistent with IUPAC recommendations [43] but is not very convenient for zeolites because of the signifX and k E are selectivity coefficients in which the zeolite
icant water content. kA/B
A/B
phase cation concentrations are defined in terms of the mole fraction and equivalent fraction E, respectively:
––
(3a)
X A = c–A / Si c–i .
–
(3b)
E = z c– / S z c– .

A

A A

i i i

When zA = zB = zi , then equivalent and mole fractions are numerically identical
E . Otherwise, these functions are not numerically identical. In pracand k XA/B = kA/B
E
tice, kA/B has been used most extensively for studies on zeolites.
The selectivity coefficients given in Eq. (2) can be used to derive more fundamental equilibrium properties of the system, such as the standard thermodynamic functions describing the exchange reaction (viz. DGq, DHq, DSq), provided
one has information on the nature and extent of all activity corrections for nonideality. However, the key point to note is that having defined the reference
states, by contrast with a selectivity coefficient, these standard thermodynamic
functions are independent of exchanger composition since they refer by definition to a reaction between components which move from one set of specific,
defined standard states to another. The magnitudes and signs of these standard
functions therefore give no immediate information whatsoever on the actual
preference which a zeolite may display for a particular ion under a given set of
experimental conditions. This point, obvious to the thermodynamicist, has
often been missed, and effort has been invested uselessly in attempting to relate
calculated values of standard thermodynamic functions to mechanistic theories
of exchange under real conditions. This has resulted in work being published
that is of little practical utility, if not plainly wrong. The issue of misunderstanding and consequently misusing thermodynamic data in this manner is
expanded elegantly by McGlashan [44].
The selectivity of a particular molecular sieve for a given ion as a function of
exchanger composition is normally measured from an ion exchange isotherm,
which is an isonormal [45], isothermal and reversible plot of equilibrium distributions of ions between the solution and zeolite phases. It is emphasised that it
is only valid to calculate selectivity coefficients, and derived thermodynamic
data, from isotherms which are reversible (that is, the forward and reverse
isotherms coincide within experimental uncertainty). The types of isotherms,

Ion Exchange in Molecular Sieves by Conventional Techniques

11

Fig. 3. Examples of ion exchange isotherms exhibiting both unselective and selective behaviour towards the incoming ion A (curves are respectively convex and concave with respect to
the ordinate). Clear limits to exchange are also observed which are lower than those expected
on the basis of the theoretical exchange capacity of the zeolite. The arrows depict reversible
behaviour

Fig. 4. Example of an ion exchange isotherm showing non-reversibility of exchange within a
plateau region, characteristic of phase separation and coexistence of two phases over the composition range corresponding to hysteretic behaviour

and the causes for the shapes observed, are discussed elsewhere [45]. However,
two isotherm types, which are particularly characteristic of molecular sieves
(although not uniquely so), are shown in Figs. 3 and 4.
Figure 3 shows isotherms for which only partial exchange for the incoming
cation occurs. The isotherm plots enable one to distinguish clearly various
basic definitions. Taking, for example, a constant level of exchange or uptake for
–
an incoming ion (e.g. EA = 0.5, then for this given uptake, the selectivity coefficient can vary from low to high values (cf. the two depicted curves). The abscis–
sa of the isotherm ranges from EA = 0 to EA = 1; values of EA are determined
by dividing the uptake by the ion exchange capacity, which is the number of
exchange sites of unit charge per unit quantity of exchanger (defined as con-


12

R.P. Townsend · R. Harjula

venient – see comments on this above). However, Fig. 3 shows curves which are
–
asymptotic to values of EA < 1, demonstrating that the maximum uptake (or
loading) under specified experimental conditions for the incoming cation can
be less than what would be expected from the value of the ion exchange capacity. The cause of this may be due to inadequate experimental rigour, especially
during batch exchange experiments (see Sects. 2.2 and 3.2.1 for further discussion); however, genuine “ion sieve” or “volume steric” effects can also operate as
a consequence of the crystalline and microporous nature of molecular sieves.
Ion sieving, known for a long time and commonly observed in zeolites, arises
when part of the microporous channel network within the molecular sieve is
inaccessible to the incoming exchanging cations simply because their ionic
diameters exceed the free diameters of the windows through which they must
pass [46]. The “volume steric” effect is less common, and arises when the
cations have free access to the microporous voids and channels within the
crystal but nevertheless the size of the incoming ions is such that the channels
are completely filled before 100% exchange for the incoming ion can be
achieved [47].
Over the last decade, during a series of studies on high silica zeolites including ZSM-5, ZSM-11 and EU1-1, another possible cause for partial exchange has
been identified. Although full exchange of hydronium ion for sodium was
observed by Chu and Dwyer for a range of high silica zeolites [37], and ion sieve
effects were identified by the same workers to explain partial exchange with
some organic-substituted ammonium cations in ZSM-5 [39], Matthews and Rees
found more complex behaviour with alkaline earth and rare earth cations in
ZSM-5 [38]. Univalent cations exchanged to 100% but this was not the case for
multivalent cations. Part of the explanation for the significantly lower maximum
loadings found with multivalent cations (especially Ca2+ and La3+) was ascribed
to the distribution of the relatively low number of aluminium atoms in the
framework, which could make it difficult for multivalent cations to neutralise
effectively widely spaced negative charges on the framework [38]. To test this
hypothesis, McAleer, Rees and Nowak [40] carried out a series of Monte-Carlo
simulations which implied that the charge on divalent cations could only be satisfied adequately by aluminium atoms within the framework which were spaced

apart by < 0.12 nm. More recently, similar experimental and theoretical studies
were carried out on zeolite EU-1, where analogous behaviour to ZSM-5 was
observed, although cut-off values for exchange were much higher in EU-1 [41].
Topological and structural differences between ZSM-5 and EU-1 were proposed
as explanations for this different behaviour [41] (see the earlier discussion in
Sect. 1.2).
Figure 4 shows a type of isotherm shape that is seen with crystalline ion
exchangers such as molecular sieves and clay minerals, but is nevertheless relatively uncommon. The shape resembles the type II vapour adsorption isotherm
of the Brunauer classification, having a clear “plateau” region and inflexion
point. An example is the Na/K exchange in zeolite P [48] that was found to be
reversible over the whole range of equivalent fraction of potassium in the crys–
tal (EK ). Zeolite P has the gismondine-type structure (GIS [49]). More commonly, isotherms of this type are found to be partially irreversible in the plateau


Ion Exchange in Molecular Sieves by Conventional Techniques

13

region, resulting in a hysteresis loop between the forward and reverse isotherms
(Fig. 4). Examples of such hysteretic behaviour include the Na/K and Na/Li
exchanges in zeolite K-F [50], which is a framework structure isotype of edingtonite EDI [49], and the Sr/Na exchange in zeolite X [51]. Isotherms of this type
(whether fully reversible or not) are characteristic of systems where the process
of exchanging one cation for another induces structural distortions and changes
in the molecular sieve framework, resulting in the end-members of the exchange
–
–
(EA = 0 and EA = 1, respectively) being different phases. If the framework is flexible and consequently the required structural transformation can occur readily,
the plateau region (where the two phases coexist) will be reversible. This is the
situation observed for the Na/K exchange in zeolite P [48] which has long been
recognised as a material which exists as several structural varieties [52] depending on ion exchange form and level of hydration [53] and which is recognised as

having an unusually flexible framework [49, 52].
When a hysteresis loop occurs, this corresponds to a situation where the endmembers of the exchange exhibit limited mutual solid solubility; in other words,
over this region of the isotherm two separate phases coexist. Barrer and Klinowski considered the conditions under which phase separation may be expected to occur in a statistical thermodynamic treatment involving an interaction
energy for entering ions wAA/kT [31]. When this term is sufficiently negative, so
that the cations segregate rather than form a homogeneous phase, they showed
that conditions could arise under which a physical mixture of two A- and B-type
crystals has a lower free energy than the homogeneous A/B phase [31]. If in
addition the nuclei of the A-rich phase grow within the B-rich “parent” phase
matrix then two positive free energy terms are involved in the exchange process.
These are a strain free energy resulting from the misfit between the new growing phase within the old, and an interfacial free energy. These tend “to delay the
appearance of the new phase beyond the true equilibrium points for forward
and reverse reactions” [31]. This is the proposed explanation for the hysteretic
behaviour seen in systems such as the Na/K and Na/Li exchanges in K-F [50] or
the Sr/Na exchange in X [51], and contrasts with P [48, 53]. This has significance
for the use of a high aluminium analogue of P in detergency [6, 7]. This material, named “maximum aluminium P” (MAP), has the gismondine framework
structure of zeolite P but with a Si/Al ratio of unity [6]. The unusually flexible
framework [49, 52] is reported to lead to cooperative calcium binding, as well as
to unusual water adsorption/desorption properties that enhance bleach stability
[6, 7]. These properties, combined with superior kinetic behaviour, result in a
material that reduces water hardness much more effectively than zeolite A (sic,
[6, 7, 45]).
2.2
Batch and Column Exchange Operations

Practically all industrial ion exchange applications, except the use of zeolites in
detergency, involve column operations (e.g. the removal of radionuclides from
nuclear waste effluents). However, basic studies of ion exchange equilibria are
usually carried out using the batch method.

14

R.P. Townsend · R. Harjula

It is instructive at this point to compare these two techniques by considering
the conversion of a zeolite from one ionic form (B) to another (A) as shown in
Eq. (1) and using the selectivity coefficient kA/B defined in Eq. (2).
In batch ion exchange, a given amount m of zeolite in the B-form is contacted with a given volume v of a salt solution of ion A. At equilibrium, the ions are
distributed between the solid and solution phase according to:
cAzB
c–AzB
=
k
.
(4)
5
A/B 5
cBzA
c–BzA
The progress of the reaction is illustrated in Fig. 5 for two univalent cations
(zA = zB = 1) assuming a constant selectivity coefficient kA/B = 10 and an ion
exchange capacity of 4 mequiv g–1. It is clear that it is difficult to obtain a high
degree of conversion by a single batch equilibration. In this example, 430 cm3 of
0.1 equiv dm–3 solution of ion A is required for 99% conversion. This is almost
an 11-fold excess even though the exchange equilibrium operates in favour of
ions A.
In zeolites strong selectivity reversals are often observed and this makes it
very difficult to obtain a high conversion to the required ionic form. This problem is discussed in more detail in Sect. 3.2.1. Here, conversion will be discussed
in qualitative terms. The solution concentrations of A and B [Eq. (4)] can be
written as:

–
(5)
cB = c–A /(V/m) = EAQ/(V/m)
and
–
cA = cA(o) – cB = cA(o) – EAQ/(V/m)

(6)

Loading (meq/g)

Solution concentration (N)

where Q is the ion exchange capacity (equiv kg–1), V/m is the solution volume
(dm3) to zeolite mass (kg) ratio in the batch equilibration and cA(o) is the initial

Solution volume (ml)

Fig. 5. Batch exchange: loading of ion A in zeolite (solid curve) and concentration of A in solution (broken curve) as a function of solution volume when contacting 1 g of zeolite in B-form
batchwise with 0.1 g equiv–1 solution of A. Selectivity coefficient kA/B and exchange capacity Q
have been given values of 10 and 4.0 mequiv g–1, respectively


15
Outlet concentration (N)

Average loading (meq/g)

Ion Exchange in Molecular Sieves by Conventional Techniques

Effluent volume (ml)

Fig. 6. Column exchange: average loading of ion A in zeolite (solid curve) and concentration
of A in outlet solution (broken curve) as a function of solution volume passed through the
column. Mass of zeolite bed 1 g, inlet solution pure A at 0.1 equiv dm–3 concentration. kA/B and
Q as in Fig. 5

concentration of A (equiv dm–3) in the solution. To obtain a high conversion to
the A-form in a single equilibration, kA/B and cA must be high and cB must be low.
cB can be made low by using a large volume of solution per unit mass of zeolite
(maximum value of cB = Q/(V/m)) (Eq. 5). cA can be made large by using a high
initial concentration of A and large V/m ratios (Eq. 6).
In column exchange, a solution of ion A is passed through a column that contains a given quantity (m) of zeolite. This process is illustrated in Fig. 6 using the
same parameters as in Fig. 5 for the batch exchange. In column exchange, the
conversion to the A-form proceeds much more easily, as ion B is constantly
removed from the system. However, ion A is not homogeneously distributed in
the bed, but is first taken up by material near the column inlet and the conversion proceeds in the direction of solution flow. When most of the zeolite has
been converted to the A-form, ion A starts to emerge from the column and cA
tends to the value of the feed concentration, when the column has become completely exhausted.
The important point to note is that by contrast with batch exchange, far less
solution is needed for full conversion. In the example of Fig. 6, only 50 cm3 of
0.1 equiv dm–3 solution is required for every gram of zeolite to achieve 99% conversion. This is only a 25% excess.
Figures 5 and 6 represent highly idealised cases and serve here only to
describe qualitatively the differences between batch and column exchanges. In
realistic situations, the selectivity coefficient decreases with increasing loading
of A in the zeolite (see Fig. 1). This means that an even higher excess of A must
be used under real conditions. In addition, in column exchange, the rate of
exchange reaction often tends to decrease at high loadings, which lowers the
gradients of the loading and concentration curves (Fig. 5) and increases the
solution volume needed for full conversion.

Pure synthetic zeolites are fine powders that are usually unsuitable for column operation. Therefore, batch methods are used for the study of ion exchange


16

R.P. Townsend · R. Harjula

equilibria. Granular zeolite exchangers that are suitable for column work are
manufactured by using suitable binders (e.g. clay, silica, alumina) and care must
be taken in extrapolating data obtained from batch experiments to column
operation.
2.3
Thermodynamic Parameters, Non-Ideality and the Prediction
of Exchange Compositions

To derive thermodynamic parameters of ion exchange, the normal procedure is
to correct for solution phase non-ideality first by deriving a corrected selectivity
coefficient in which concentrations within the external solution are replaced by
activities. The means by which this may be done, for binary or multicomponent
systems, is described elsewhere [54, 55]. The corrected selectivity coefficients
E are then:
corresponding to k XA/B and kA/B
––
XAzB aBzA
KXA/B = 92
,
(7a)
––
XBzA aAzB
–

E zB a zA
E = A B .
KA/B
(7b)
–
92
EBzA aAzB
E is identical to the function K shown in Fig. 1 and taken from [20].
K A/B
G
The thermodynamic equilibrium constant Ka is then obtained by integrating
the appropriate form of the Gibbs-Duhem equation to give as corresponding
expressions for Eqs. (7a) and (7b), respectively, the following:
1

–
X dE
lnKa – D = Ú lnKA/B
A,
0

(8a)

1

–
E dE
lnKa – D = (zB – zA) + Ú lnKA/B
A,

(8b)

0

where D is the water activity term [56, 57]. D is normally ignored on the assumption its magnitude is small; however, it should be noted that for the most commonly employed formulation, corresponding to Eq. (8b) and after Gaines and
Thomas [58], D π 0 when the system is behaving ideally if zA π zB but rather
equates to (zA – zB) [56, 59]. This must follow since, when the system is behaving
ideally, the values of all the activity coefficients are by definition unity for all
E = constant [56, 57] since
compositions and hence Ka = K XA/B = KA/B
–
g–AzB
f AzB
x
E
Ka = KA/B
=
K
(9)
–
5
A/B 5
g–BzA
f BzA
where fi , gi are the appropriate rational activity coefficients for cations in the
exchanger phase in association with their equivalents of anionic charge.
Equations (8a) and (8b) provide the starting point for the prediction of ion
exchange equilibria in molecular sieves, an activity which has received a significant level of attention over the last decade or so. The basis for prediction comes

Ion Exchange in Molecular Sieves by Conventional Techniques

17

from a principle put forward some time ago [60], viz., that because D is small and
changes little with zeolite composition, and providing salt imbibition is negligible (which is true for relatively dilute electrolyte solutions [61]), then for a given zeolite composition, the ratios of activity coefficients fi ,gi will hardly change
in value as the total concentration of electrolyte in the external solution is
changed [56, 60, 62]. Providing these assumptions hold, then taking as an example a binary exchange process, from Eqs. (8b) and (9), it follows that [62]:
1

–
– zB – – zA –
E – = (z – z ) + lnK E dE
lnKA/B(E
Ú
B
A
A – ln (g A(EA)/g B(EA))
A/B
A)
0

(10)

–
where the subscripted EA in parentheses indicates that the values of the corrected selectivity coefficient and the rational activity coefficients refer to a particu– –
lar composition EB , EA and must be invariant since all the terms of the righthand side are constant or hardly change when the total concentration of the
external electrolyte solution is changed. The details of the methods which must
be employed to predict selectivity trends are described elsewhere [62]; the
important point to note is that if the above assumptions hold then for successful

predictions it is only required to evaluate the appropriate corrected selectivity
coefficient as a function of zeolite phase composition and to have an accurate
knowledge of the solution phase activity coefficient g [54, 55, 62]. For binary
exchanges, this approach has been used to test a variety of systems over the last
decade, including exchanges involving Pb/Na, Pb/NH4 , Cd/Na and Cd/NH4
equilibria in clinoptilolite, ferrierite and mordenite [63–65] using different coanions (chloride, nitrate and perchlorate [62, 66]) as well as the Cd/Na-X and
Cd/K-X systems [67], with a high level of predictive success [62, 67]. Recently, a
related model has been used with good accuracy for the prediction of K/Na and
Ca/Na equilibria over a wide range of total ionic concentrations in solution for
natural clinoptilolite [68]. Successful predictions were also achieved for the
Ca/Na, Ca/Mg and Mg/Na systems in zeolite A [18, 20, 69]; however, for Mg/Na
and Mg/NH4 exchanges in a range of faujasites [70], predictions failed badly in
some cases. The failures were attributed at the time to salt imbibition, but further detailed experimental studies involving hydronium exchange in the Ca/NaX, Ca/Na-Y, Cs/Na-MOR and Cs/K-MOR systems [71–75] have shown that the
situation is in reality much less straightforward. Failures in predictive methods,
particularly at trace levels of exchange, cannot be attributed simply to hydrolysis, hydronium exchange or salt imbibition despite earlier suggestions to this
effect [70, 76]. An important factor appears to be the presence of colloid-size
zeolite particles [74]. These matters are discussed further in Sect. 3.2.3.
To apply the same prediction procedure as that described above for ternary
or multicomponent exchanges, it is helpful to derive analogous equations to
those shown in Eqs. (8), (9) and (10) for binary exchange. For ternary exchange,
this was done by Fletcher and Townsend [77] and this approach was used to
predict compositions for Na/Ca/Mg-A [20, 69], Na/K/Cd-X [67] and Na/NH4/
Mg-X,Y ternary equilibria [70]. For the first two of these systems, ternary
exchange equilibria were predicted successfully but for the Na/NH4/Mg-X,Y systems, the procedure failed for the higher silica Y materials, as for the corresponding conjugate binary exchanges [70]. In parallel with these studies, the


18

R.P. Townsend · R. Harjula

model of ternary ion exchange in zeolites [77] was compared with other models
published in the literature for clay minerals and resins [78, 79] and a further
detailed study [80] came to the conclusion that these other approaches were
appropriate under certain specified conditions [80] for the prediction of exchange equilibria in zeolites.
A recent criticism of the ternary exchange model [81], on the basis that the
equations could have simply been built up from the conjugate binary systems
(obviously true), overlooks the main point. If one uses the conjugate binary systems it is necessary to use a model-based approach to predict activity coefficients for the multicomponent exchange equilibrium in the zeolite and the presence of sublattices within the zeolite framework can make this more difficult to
do than for clay minerals and resins (Sect. 1.2) [80]. The ternary exchange model of Fletcher and Townsend [77] does not require one to measure at all the activity coefficients, let alone predict them for multicomponent systems from binary
data, using some model. All that is required is knowledge of the ternary corrected selectivity coefficients that are obtained by integrating the appropriate
Gibbs-Duhem equations over the ternary composition surface [77] in analogy
with the binary approach pioneered by Gaines and Thomas [58]. However,
acquiring sufficient data for a ternary system is a difficult and time-consuming
exercise [20, 67, 70, 82] and simpler approaches can prove quite adequate provided one validates some of the predictions made [83]. Thus, another model,
developed originally for clay minerals [84], has been shown after minor revision
to work well for ternary anion [85] and cation [86] exchanges in organic resins
and has even been extended successfully to a five-component zeolitic system
(Sr/Cs/Ca/Mg/Na equilibria in chabazite) [87]. This system is very important in
the field of nuclear waste treatment [87].
Accurate prediction is similarly much needed for detergent applications [2, 7,
18, 69]. The level and nature of “hardness” in household water varies extensively from one location to another, as do the conditions under which consumers
expect effective laundering to occur (e.g. temperature). Thus accurate selectivity
data (i.e. isotherms and selectivity plots as a function of loading), and reliable
predictive models that are simple to use, are important, since it would clearly be
impossible to measure directly the performance of a given “builder” zeolite for
all conceivable situations. Successful predictions have been achieved for the
binary Na/Ca-A, Na/Mg-A and Ca/Mg-A systems [2, 18, 69] as well as for the corresponding ternary system [2, 69]. Similar successful predictions were recently
achieved also for zeolite MAP [7] once the original iterative procedures of
Franklin and Townsend [69] had been modified appropriately. Figures 7 and 8
show examples of such successful predictions in A, for both the binary and
ternary cases.

Occasionally, isotherms of binary and multicomponent exchanges are
described using various empirical adsorption equations. These cannot be used
for the prediction of multicomponent equilibria [88]. In fact, a closer inspection
of these equations reveals that they have no in-built facility for true prediction
(i.e. for the calculation of equilibria over ranges of different total solution
concentrations for heterovalent exchanges). Thus these equations are useful
in describing the observed isotherm in a mathematical form but the only pre-


Ion Exchange in Molecular Sieves by Conventional Techniques

19

a

b
Fig. 7a, b. Predicted isotherms and experimental points for a the Na/Ca-A system and b the
Na/Mg-A system. Solid lines are predicted isotherms; experimental points are measured at
normalities of 0.025, 0.10 and 0.4 equiv dm–3, shown respectively as solid triangles, circles and
squares. Taken from [69]


20

R.P. Townsend · R. Harjula

Fig. 8. Ternary experimental and predicted points for the Na/Ca/Mg-A system at a normality
of 0.4 equiv dm–3. Measured solution and zeolite phase equilibrium compositions are shown
as unfilled stars and filled squares, respectively. The predicted zeolite phase at 0.4 equiv dm–3
is shown as an unfilled circle while the filled circle represents experimental validations at

0.4 equiv dm–3. Taken from [69]

diction these equations can give is the interpolation of the isotherm under
one given set of experimental conditions. With such limited utility, these empirical approaches are not recommended for the “prediction” of ion exchange equilibria.
2.4
Kinetic Processes and the Prediction of Rates of Exchange

In direct applications involving zeolites as ion exchangers, it is not normally the
case that the system is allowed to reach equilibrium. In batch operations (e.g. in
detergency) the time available may be such that the exchange process is interrupted long before equilibrium is reached. Similarly, in column operations (e.g.
effluent purification), when the system is operating under steady-state conditions, the balance between throughput of liquid and time of exchange means


Ion Exchange in Molecular Sieves by Conventional Techniques

21

that the system is frequently operating under non-equilibrium conditions.
Knowledge of the kinetics of the multicomponent exchange processes (i.e. all of
the reaction rates, diffusive mechanisms and hydrodynamic processes which
contribute to the overall rates of exchange of all of the different types of ions
involved) is therefore of key importance if one is to be able to predict and control behaviour. Unfortunately, this is easier said than done. The kinetics of ion
exchange processes in zeolites are extremely complicated even when one focuses on just one mechanistic process [45]; only recently, it was rightly stated that
the “picture presented in the literature for diffusion in zeolites is confusing, conflicting and/or inconsistent with theory” [89]. Space permits only a brief
overview of the current state of affairs and this is presented here using a hierarchical model [90] for the zeolite particle or pellet. Much more detail is given elsewhere [45].
2.4.1
Hierarchical Model of Zeolite Particle or Pellet

Whether one is considering an agglomerate of aggregated zeolite crystallites, or
a pellet, a hierarchical model [89, 90] allows one to distinguish the different

transport and/or rate processes which operate at different length scales.
The highest level is concerned with the macroparticle or pellet itself; and the
key issue here is whether transport of ions through the fluid film which encompasses the macroparticle is rate-controlling or not. That this process can be ratecontrolling has been recognised for a long time, being favoured by a low concentration of exchanging ions in solution and a small mean particle size; however, it is known that the hydrodynamic regime pertaining can affect its influence markedly, with high levels of agitation (such as are achieved at high
impeller speeds in a batch reactor [89]) rendering relatively insignificant any
mass transfer resistance through the boundary film. The mechanical integrity of
the macroparticle can also be very important. Taking detergent powder particles
as an example [which can comprise agglomerates of (primary) zeolite crystalline particles held together by means of adhesive, viscoelastic surfactant
bridges], these are designed to break up under shear and/or other hydrodynamic regimes that are imposed as part of the wash cycle. On breaking up and dispersing, some of these dispersed smaller particles may find themselves in
regions of low agitation and consequently the rate of removal of hardness ions
from the wash liquor can be slower than desired due to the onset of film diffusion control.
Generally, however, the aim is to avoid conditions leading to film diffusion
control. This means that the focus is shifted towards transport processes that
occur at the intermediate level (that is, in the mesopores and macropores within the macroparticle or pellet itself) and those which occur at the smallest
dimensional level (viz., in the very micropores of the molecular sieve) [45,
89]. Within the mesopores and macropores between the primary zeolite crystallites transport will be dominated by molecular and ionic intercrystalline diffusion possibly coupled to surface diffusion processes, while, in the zeolite
micropores themselves, intracrystalline diffusion occurs, also possibly coupled


22

R.P. Townsend · R. Harjula

with specific exchange rates associated with the different zeolite sublattices
[91, 92].
The overall observed kinetics of exchange is of course the result of all the
above-described mechanisms working in concert [45, 89]. To cope with the complexities of the system, a simple approach one may adopt is the homogeneous
diffusion model, which assumes that the behaviour of each distinct diffusing
species within the macroparticle may be described in terms of a single solidphase “effective diffusivity” [89]. More sophisticated approaches include the
heterogeneous diffusion models, where the macropore and micropore diffusion
processes are described separately and are then assumed in different mathematical treatments either to occur in series or in parallel [45, 89].

In practice, to date, most research activity has focused on the intraparticular
diffusion which takes place in the zeolite micropores themselves, on the questionable assumption that these processes are normally the rate-controlling ones.
2.4.2
Intraparticular Exchange Rate Processes

Our understanding of the processes which govern the rates of ion exchange
within the micropores of molecular sieves has advanced little over the last
decade, yet the imperative to be able to control and manipulate these rates
remains as strong as ever. To summarise the current situation it is necessary first
to emphasise some basic principles and then to define certain terms and coefficients.
To begin, it is important to distinguish the intrinsic dynamic nature of the
system from the kinetic processes we actually observe during an ion exchange
reaction. An obvious yet important point to remember is that even after
exchange equilibrium has been attained, the equilibrium is a dynamic one. Thus
transport of all exchangeable cations and of the solvent molecules continues but
after equilibrium has been reached there are no net changes in the relative distribution of species between, and hence concentrations in, phases with time.
This dynamic character is readily verified by adding to the equilibrated system
a trace amount of a radioactive isotope of one of the cation types into (say) the
solution phase of the system and then observing the rate at which isotopic
exchange between the two phases takes place. The isotopic exchange process
may include as a rate-determining step an intracrystalline exchange process [91,
92] but it is also certainly a transport process, which is described in terms of a
self-diffusion coefficient D*AA [93]. Self-diffusion coefficients D*AA and D*BB ,
which can change markedly with temperature [45] or as the equilibrium concentrations of different cations within the zeolite are altered [45, 94], should be
sharply distinguished from the exchange diffusion coefficient DAB [95]. DAB
describes the kinetics of the A/B exchange process, that is, the observed rates of
change of concentrations of ions A and B within each phase as a function of time
and as the system moves to equilibrium.
Consider therefore a binary A/B exchange between the zeolite and external
solution, which is not initially at equilibrium. On mixing the two phases, the A

and B cations, which will almost certainly possess different ionic radii and pos-


Ion Exchange in Molecular Sieves by Conventional Techniques

23

sibly charge, will begin to move in their respective directions of negative chemical potential gradient in order to equalise their respective chemical potentials
within all phases in the system. However, the mobilities of the two cation types
A and B are likely to be different, which means that the more mobile cation type
will tend to build its concentration, and hence lower its concentration gradient,
faster than the other. If this process were to continue unchecked, charge separation within each phase and between the phases would occur, with a concomitant
electrical potential gradient. In practice, of course, the electrical potential gradient that forms as charge separation takes place does not build, but rather acts to
slow the faster moving cations and speed the slower ones. Thus it is not adequate
to consider only the chemical potential gradients. The net flux JA of (say) the Aexchanging species is actually described by:
(11)
J = – D [grad c– – (z c– F/RT) grad V]
A

AB

A

A A

where F is the Faraday constant and V the electrical potential. An expression for
DAB has been derived by Barrer and Rees using an irreversible thermodynamic
approach. The form of this is complicated but, if cross-coefficients other
than those due to the electrical potential gradient are assumed to be negligible,
then [96]:

– 2
–
–
– 2
–
–
D*
AA D*
BB [c Az A(∂ ln a B / ∂ ln c B) + c B z B (∂ ln a A/ ∂ ln c A)]
DAB = 00000000
(12)
0.
– 2
– 2
D*
AAc AzA + D*
BBc BzB
Two points should be noted from Eq. (12). First, the magnitude of DAB depends
strongly on the composition of the exchanger not only because it is a direct function of ionic concentrations, but also because it is a function of both D*AA and
D*
BB, which we have already noted vary with exchanger composition [45]. Secondly, DAB is a function of the non-ideality of the zeolite [data for which can be
obtained, as we saw earlier, from the activity coefficients described in Eq. (10)].
One may expect therefore that to describe adequately the kinetic behaviour of
even a binary exchange process in a molecular sieve would be a very complicated task.
To validate this and other similar models, it is necessary to solve, using appropriate boundary conditions, the differential equations describing overall the
transient diffusion process for each ion, of the general form:
(13)
(∂ c– /∂ t) = div D gradc–
i

AB

i

which for spherical symmetry (a good approximation for most primary zeolite
particles) becomes [95]:
∂ c–i 1 ∂ 2
∂ c–i
r
D
(14)
=
6 42 5
AB 6 .
∂t
r ∂r
∂r

΂

΃

As an example of the above approach, Brooke and Rees [95] studied the Sr/Cachabazite system. Figure 9 shows their computed time-dependent concentration
profiles within the zeolite particles both before and after non-ideal behaviour
was taken into account. The effect on DAB of taking non-ideality into account was
even more dramatic, with a discontinuity appearing in the plot of ∂DAB / ∂ c–A