Tải bản đầy đủ - 0trang
III. Diffusion of Adsorbed Ions in Soil Clays and Clay-Type Minerals
P. H. NYE
1 , Micas and Vermiculites
The self-diffusion coefficients of ions in mica and vermiculite minerals are
shown in Table I. In these experiments the ion exchanges with its own isotope,
and the interlayer spacing does not change during the exchange. Many experiments have also been made on the release of ions from micas and vermiculites.
Although these reactions are undoubtedly controlled in part by the rate of diffusion of the interlayer ions in exchange for different ions in the surrounding
solution, the c-axis spacing changes simultaneously, and the interpretation of the
measurements is uncertain.
Clearly, the main factor influencing the diffusion coefficient is the interlayer
spacing. For the unexpanded potassium illite studied by de Haan et al. (1965),
the value of D lod2'm2/seccorresponds to a penetration of only about 0.3 nm,
or the diameter of one ion in a year. Of the different cation forms of a dioctahedral vermiculite studied by Graf et al. (1968), the Rb and Cs forms are unexpanded, and their self-diffusion coefficients were too low to measure. The Ba
and Sr forms, with a c-axis spacing of 1.24-1.23 nm, corresponding to one molecular layer of water between the sheets, yielded values of D 10-'7-10-16m 2/seC.
The Ca and Mg forms with a c-axis spacing of 1.5-1.4 nm, correspondingto two
molecular layers of water, gave values of D
10-'5-10-'6 m2/sec. For other
vermiculites containing two water layers, greater mobilities have been reported.
Keay and Wild (1961) found D = ( 1.3-4.5) x lo-" mYsec for the self-diffusion
of Ba in six different minerals, and Lai and Mortland (1968) found D = 6.1 X
m2/secfor Na vermiculite. The difference in these results may be caused by
the structure of the octahedral layer. In the trioctahedral forms the 0 - H bond near
the center of the hexagonal network of tetrahedrally coordinated silicon atoms is
directed along the c-axis. In the dioctahedral forms the direction of the 0-H
group is altered; consequently, a cation in the interlayer will be less shielded by
the proton from the negative 0 atom, and will occupy a more stable position.
Rausell-Colom et al. (1965) have offered this explanation for the relative stability of dioctahedral micas to weathering.
The interlayer .water in expanded (1.4-1.5 nm) vermiculite has an ordered
structure (Walker, 1956; Barshad, 1949; Bradley and Serratosa, 1960) in which
it surrounds the interlayer ions between the aluminosilicate layers. It is therefore
to be expected that the activation energy for diffusion will be greater than that for
ions in solution, which is about 17 M/mole. Keay and Wild (1961) determined
activation energies of 46 kJ/mole for Na self-diffusion in Na vermiculite. When
Na replaced divalent (Mg, Ca, Sr, Ba) cations, the activation energy was 37
kJ/mole, but for the reverse reaction the activation energy was 56 kJ/mole. In
both forms the spacing corresponded with two molecular layers of water, and the
difference is the increase in enthalpy in the change from the Na to the divalent
form. Walker (1959) determined an activation energy of 50 M/mole for diffusion
Self-Diffusion Coefficients of Interlayer Ions in Mica and Vermiculite
lllitic subsoil (< 2-pm
5-20 pm CEC 2.29
CEC 1.1-1.6 mq/g
(< 2 pm)
8.9 x 10-l*
1.8 x 10-1"
de Haan et a1
Graf er al.
<4 x lo-':'
2.9) x lo-''
(1.3-4.5) x lo-"
Keay and Wild
Lai and Mortland
P. H. NYE
of Sr into Mg vermiculite, during which there was a slight expansion of the
lattice from 1.45 to 1 S O nm.
2 . Montinorillonites and Kaolins
In the studies with micas and vermiculites the movement of the ion in the plane
of the aluminosilicate layers into a surrounding solution has been measured. In
the work on clay pastes, which will now be described, the particles are, as a rule,
oriented randomly, and movement through the whole mass is studied. The pathway for the movement of the ions is thus tortuous, and the observed mohility
includes a “geometry” effect. Most of the work has been done on montmorillonite,
in which the number of water molecules between the aluminosilicate layers
is greater than in vermiculite, and the surface charge density is less.
A great variety of experimental conditions have been used. In some examples
the mobility of the ions has been determined from the electrical conductivity of
the homoionic pastes, prepared in a variety of ways; in others, from the selfdiffusion of the ions, determined by a variety of methods. The proportion of clay
to solution has ranged from a dilute suspension to a stiff paste, and solutions of
varying electrolyte concentration have been used. The resulting measurements
have been interpreted in a number of ways. Table I1 attempts to order them by
comparing the apparent mobilities of the ions in “salt-free” gels with their
mobilities in solution at infinite dilution. Although many gels that are claimed to
be salt-free are in fact hydrolyzed, in all instances the mobility cited can be
attributed to the overwhelming majority of cations that are satisfying negative
charges on clay lattices rather than on free anions in solution.
In spite of the inclusion of geometry effects, all the ions have greater mobility
in the montmonillonites and kaolins than in the vermiculites. The values are also
consistent in showing that the ion with the largest unhydrated radius suffers the
greatest reduction in mobility. This is particularly well shown by Cremers (1968)
for the alkali cations on both montmorillonite and kaolinite, and by Gast (1962)
for the alkali and alkaline earth cations on montmorillonite. Large cations are
more polarized in an electric field than small ones, and they interact more strongly
with the negatively charged 0 atoms that form the clay surfaces (Bolt et al., 1967).
(See Section III,B,2.) There is some indication that the divalent ions have lower
mobility than monovalent ions of comparable unhydrated size (cf. Na+, r = 0.095
nm, and Ca2+,r = 0.099 nm), although Hoekstra (1965)found that Na and Ca had
similar mobilities in frozen Na and Ca bentonite pastes, where in each case the
unfrozen water amounted to 56%.
The mobilities of the monovalent ions on kaolinite are similar to their
mobilites on montmorillonite, in spite of the fact that the ions on kaolinite are
adsorbed on external suifaces, whereas on montmorillonite they will be mainly in
Mobility of Ions in Salt-Free Clay Gels Relative to Solution at 25°C
0.1-10 g clayllO0 ml
4-6 g clay/100 g gel
4.9-10.6 g clay/
100 g gel
3 g clay/100 ml soh
60 g clay/100 g gel
56 g clay/100 g gel
70 g clayll00 g gel
3 1-35 g clay/ 100 ml
Self-diffusion coefficients in water at
infinite dilution (m2/sec x 1 0 9
van Olphen (1957)
Lai and Mortland
Fletcher and Slabough
Cremers ( 1968)
Diffusion Coeffscients of Ions Diffusing into Water-Saturated Clay Films in Ca Form"
in free solution
x log mZ/sec
"From Ellis el a / . (1970a,b)
Ellis et al. (1970a,b) measured the diffusion of heavy metal ions into watersaturated films of Ca clay deposited on a slide. The clay particles were highly
oriented so that hindrance caused by tortuosity should be slight. Since they
measured the concentration profile of the penetrating ions by X-ray flourescence,
they were able to determine the diffusion coefficient at varying proportions of the
metal ion in the exchange complex. At low proportions nearly all the ion is in the
exchangeableform and little is in the solution, so that the correspondingdiffusion
coefficient is a measure of the mobility of the ion in the adsorbed state. Table I11
shows the values obtained.
The order of mobility was kaolinite > illite > montmorillonite > vermiculite.
In kaolinite all ions will be on external surfaces. In illite and montmorillonite
most exchangeable ions are in interlayer positions. However, when the heavy
metal ion is diffusing into the clay, it may diffuse preferentially on external
surfaces, and this may explain its greater mobility in illite than in
montmorillonite, which has a wider interlayer spacing. In vermiculite the c-axis
spacing is 1.5 nm, which accounts for the low mobility. The mobility of the
heavy metal ions is in the order Zn > Mn > Cu, which does not accord with
either their mobility in solution or their unhydrated radii.
The mobility of Fe3+ is about a fifth of that of Fez+, although it will be noted
that Fe3+has appreciable mobility. The mobility of the divalent heavy metal ions
is of the same order of magnitude as for the Ca, Sr, Ba series on kaolinite and
montmorillonite in Table 11.
The important feature of the activation energies for diffusion in clay gels
shown in Table IV is that they nearly all lie in the range 17-25 kJ/mole. In the
lower range this is close to the activation energy for diffusion in solution, and it is
DIFFUSION OF SOLUTES IN SOILS
considerably lower than the value of about 42 kJ/mole found for diffusion in the
structures having two water layers.
Davey and Low (1968) have shown that the activation energies reported for Na
bentonite may be up to 4.2 kJ/mole too high because of the formation of hydrous
aluminum oxide on the surface during preparation of the Na-saturated clay. Street
et al. (1968) and Miller and Brown (1969) also hold aluminum oxide responsible
for the variability in activation energies reported for Li, Na, and K bentonites.
These general findings have been illuminated by a number of detailed studies.
It would be expected that the mobility of ions in clays would be reduced by
geometry effects, by electrostatic attraction between the ions and the clay lattice,
and by changes in the structure of the water near the clay surfaces. These effects
will now be discussed.
B. FACTORS AFFECTING THE DIFFUSION COEFFICIENTS
1 . Geometry Effects
Cremers and Thomas (1966). Cremers and Laudelout (1965), and Thomas and
Cremers (1970) have measured the conductance of the sodium forms of
montmorillonite, illite, and kaolinite clays suspended in sodium chloride solutions. Both the proportions of clay and the concentration of electrolyte were
varied over a wide range. Figure 3 illustrates their results. They relate the
Activation Energies for Self-Diffusion or Conduction in Salt-Free Clay Gels"
Lai and Mortland ( 1962)
Street et al. (1968)
L o w (1958)
1 41 6
Values given in kilojoules per mole.
P. H. NYE
FIG.3. Electrical conductivity (mMho/cm) of Na montmorillonite gels, K,, versus conductivity
of equilibrium NaCl solutions, Kl, for various porosities. I is the isoconductivity. From top to
bottom: 0 = 1 (broken line); 0.96,0.91, 0.86, 0.80, 0.73, 0.64. After Cremers (1968).
specific conductance of the gel, KO,to the specific conductance of the solution in
the pores, K l , by the equation
K O = K&
K , is the excess specific conductance created by the mobility of the exchangeable
ions. At high electrolyte concentration K , will be small in comparison with K 1 .
The “formation factor,” 8, is then a measure of the extent to which the solid
particles reduce the specific conductance of the gel in relation to the solution by
reducing the cross section for the passage of the ions, and by increasing the
tortuosity and viscosity of their pathway.
They found that the experimental values obtained for 8 in dilute gels (porosity
of 1.O-0.65 for montmorillonites and 1.O-0.5for kaolinites) are well described
by a theoretical equation due to Fricke (1924):
8 = 1 + (1 + 0.21n)(i
( n > 10)
Here 8 is the volume fraction of the liquid, and n is the ratio of the diameter of
the particles to their thickness. A plot of 8 - 1 against (1 -8)/8 is a straight line
passing through the origin, and the slope gives the value of n (see Fig. 4). These
values of n, in the range 10-60, for six different clays, agreed very well with
independent determinations by electron microscopy or viscosity. In concentrated
DIFFUSION OF SOLUTES IN SOILS
gels Cremers (1968) found that fF: is better described by a theoretical equation due
to Bruggeman and developed by Meredith and Tobias (1962):
Q = (I/e)(l + 0.21n)
(n > 10)
The high values of Q measured for clays with high axial ratios are quite inconsistent with a cubic model of a concentrated clay gel, which has sometimes been
used to deduce geometry effects.
Turning now to the excess conductivity created by the exchangeable ions, we
see in Fig. 3 that there is an “isoconductivity” value (I) at which the specific
conductivity of the gel is the same as that of the solution-for all concentrations
of clay. Dakshinamurti (1960, 1965) had previously noticed this property in a
number of clay systems. Cremers (1968) shows that, because there is such an
isoconductivity point, the exchangeable ions may be assigned a constant “surface conductance,” and that this is governed by the same formation factor as the
FIG. 4. Formation factors versus porosity according to the Fricke equation. W-B (Wyoming
bentonite), C-B (Camp Berteau montmorillonite), K-2 (Zettlitz kaolinite), K-B (Boulvit kaolinite). n
is the axial ratio. After Cremers (1968).
ions in solution. Thus, as far as the geometry effect is concerned, the exchangeable ions behave in Fq. (3) as though they were distributed uniformly over the
adjacent pore solution-by no means an obvious result. With this knowledge of
the geometry effect for the exchangeable ions, Cremers is able to conclude that
the conductivity of the gels is “consistent with” 0.5-0.6 of the exchangeable Na
in each clay having the same mobility as in solution and the remainder being
For other cations the experimental data are less complete, but Cremers concludes tentatively that on montmorillonite the following fractions are freely
mobile: K 0.3, Cs 0.15, Ca 0.15; and on kaolinite: K 0.15, Cs 0.05.
2 . Electrostatic and Viscosity Efsects
It is difficult to distinguish experimentally between a proportion of exchangeable ions having the same mobility as in free solution with the rest having none,
and a more continuous distribution of mobilities over all the exchangeable ions.
That the activation energy for diffusion of Na in clays approximates that in water
is some indication that the observed mobility derives from freely mobile ions.
The somewhat higher activation energies for K, Rb, and Cs ions (see Table IV)
suggest that some ions with modified hydration are contributing to the observed
mobility. This problem has been analyzed further by Shainberg and Kemper
(1966a) and by van Schaik et al. (1966), who have developed the ideas of Low
(1962, 1968). He calculated the variation in electrostatic potential of an ion as it
moved parallel to the surface of a clay lattice from one position of stability to the
next. He estimated that there would be a negligible potential barrier to surmount
if the ion were more than 1.0 nm above the plane of negative charge on the
lattice. Shainberg and Kemper (1966a) calculated that if the negative charge is in
the octahedral layer (as in montmorillonite) an unhydrated ion adjacent to the
surface will require 4.8 kJ/mole more activation energy than an ion separated
from the surface by one molecular thickness of water (about 0.25 nm). This
effect alone would lead to a sixfold difference in the mobility of the ion. If, in
addition, the first molecular layer of water is more viscous than subsequent
ones-and there is much evidence for this (Low, 1961; Grim, 1968)-it is
reasonable to assume that the mobility of the unhydrated ions can be neglected.
The next step is to consider how much the mobility of the hydrated ions is
restricted by reduction in the fluidity of water near the surfaces. By measuring
the diffusion of DOH in oriented flakes of bentonite containing varying amounts
of water, Kemper er al. (1964) found that in Na bentonite the relative mobility of
water in layers one, two, and three molecular thicknesses from each bentonite
surface was 0.3, 0.6, and 0.65; in Ca bentonite the corresponding values were
0.05, 0.5, and 0.7.
DIFFUSION OF SOLUTES IN SOILS
Against this background, van Schaik et al. (1966) have measured the selfdiffusion of Na and Ca in oriented, expanded flakes of Wyoming bentonite.
Because the ions were diffusing in the plane of the flakes, the tortuosity factorthe factor by which the mobility is multiplied to allow for an increased path
length-was high, 0.55, as estimated from diffusion of DOH in similar flakes.
They were able to calculate a weighted average fluidity of the water surrounding
the hydrated ions, the weighting factors being provided by the relative concentrations of ions in each molecular layer calculated from the theory of the diffuse
double layer. The reasonable assumption was made that the relative diffusion
coefficient of DOH is a measure of the relative fluidity of water. From the
measured diffusion coefficients they concluded that 0.60-0.87 of the Na ions
and 0.15-0.47 of the Ca ions are, on a time average, hydrated.
By measurement of conductivity of Li, Na, and K bentonite pastes, Shainberg
and Kemper (1966a) have similarly estimated that the hydrated fractions are Li
0.64, Na 0.57, and K 0.39. This work was, however, done with centrifuged
pastes, pushed from a glass tube into the conductance cell; and it has been
assumed that the tortuosity factor can be taken as 0.67. If the flakes were not well
oriented, this value seems likely to be too high. A lower value would have the
effect of increasing the fractions hydrated.
Although these estimates of the fraction of hydrated ions are subject to numerous uncertainties-for example, the average fluidity depends on the accuracy of
the calculation of the distribution of ions in the diffuse double layer; and the
assumption that unhydrated ions are virtually immobile is very sensitive to the
value chosen for the dielectric constant near the surface of the lattice-they
illustrate well the difficulties that arise in arriving at an exact model of ion
movement through clays. They also agree reasonably well with the independent
calculations of Shainberg and Kemper (1966b), based on considerations of electrostatic energy, that the fractions of ions hydrated in homoionic bentonites are Li
0.82, Na 0.64, K 0.51. These calculations also are admittedly uncertain, since
they neglect terms involving the energy of water-to-water links.
Further insight into the fluidity of interlayer water is provided by neutronscattering spectroscopy, which has been applied to clays by White, Hunter, and
co-workers (Olejnick and White, 1972). Figure 5 shows a plot of log,oDH,o
against the reciprocal of the thickness of the interlayer water in Li and Na
montmorillonite and Li and Na vermiculite. The experimental values agree well
with the theoretical expression represented by the straight line in Fig. 5:
D = Dbulkexp(-26VIdRT)
where 6 = surface energy of included water plus ions;
V = molar volume of water;
d = interlayer thickness of water.
Here 26Vld is the reduction in free energy of water confined between two
' ' '
(Water layer thickness)-',d-' &I)
FIG. 5 . Variation of the diffusion coefficient of water in montmorillonite and vermiculite with
reciprocal of the interlayer spacing. After Olejnick and White (1972).
parallel plates. The reduction is equal to an increase in the activation energy of
diffusion because the water molecules jump from a lower energy level.
These measurements of water mobility are lower than those obtained from
diffusion of DOH by a factor of about 4. If correct, they indicate that the fraction
of ions hydrated is underestimated by van Schaik et al. (1966).
3 . Effect of Dehydrating Clays
The work on montmorillonite described in the previous section has been done
with clay suspensions or pastes with expanded lattices. Work has also been done
on drier montmorillonites in which only one or two molecular layers of water lie
between the sheets; in this respect it links with the studies of diffusion in vermiculites.
Mott (1967) has measured the self-diffusion coefficients of Na and Sr in
homoionic bentonite at varying degrees of hydration. Figure 6 shows his results.
He used oriented flakes in which diffusion in the plane of the flakes was very little
reduced by geometry; in fact it proceeded 300 times as fast as it did across the
plane of the flakes in specimens with two water layers between the sheets (279
mg of H20per gram of dry clay). The mobility of Na over the range 350-200 mg
of H20per gram of clay (three to two water layers) was also measured by
electrical conductivity, with satisfactory agreement between the two methods. In
drier clay the conductivity method proved unreliable because of difficulty in