Environ. Sci. Techno/. 1994,28, 2360-2365
Clay Swelling and Regular Solution Theory Ellen R. Graber’ and Uri Mlngelgrln
Institute of Soils and Water, The Volcani Center, Agricultural Research Organization, P.O. Box 6, Bet Dagan 50250, Israel
Expansion and contraction of clays in contact with solvents have been often attributed to the influence exerted by the dielectric constant (E)of the solvent on the equilibrium distance between clay plates. None of the models based on this assumption offers a universal treatment of the relationship between solvent properties and swelling. It is suggested that the swelling of clays may be described by an extension of the regular solution theory. Of 11solvents tested, swelling of a mixed layer illite/smectite was greatest in N-methylformamide but that of a Na-montmorillonite was greatest in water, contradicting the assertion that swelling is correlated with solvent e . Permeability of beads of spray-dried Cu-montmorillonite (r = 3.5 km) to hexane2-propano1, 2-propanol-methanol, and methanol-water mixtures was measured by pumping the solvents at a rate of 1 mL/min through an HPLC column. The highest intrinsic permeability (k)was observed in 2-propanol with lower k values in mixtures of both higher and lower E .
Introduction
Until recently, landfills and surface impoundments were constructed with compacted clay liners engineered to yield cm/s. In a number hydraulic conductivities lower than of instances, organic fluids leaked through shrinkage cracks which developed in the clay liners and escaped into the subsurface ( I ) . Effective porosity and permeability of the porous solid medium itself when in contact with nonaqueous solvents can also be affected by swelling and shrinkage. Solvent mobility thus may be considerably different from that anticipated on the basis of a given hydraulic conductivity measurement. The ability to predict swelling or shrinkage of expandable components in porous media can become an important tool for forecasting and remediating contamination by nonaqueous fluids. This study is aimed at understanding the relationship between clay swelling and solvent properties and was motivated by the need to define the conditions under which clay liners in contact with organic fluids may fail. Swelling and contraction of expandable clays in contact with solvents are commonly explained by the diffuse double-layer theory (DDL), which predicts an increase in the equilibrium distance between clay plates as pore fluid dielectric constant (E)increases (e.g., refs 2-7). Changes in plate separation result in macroscopic fabric modifications and concomitant changes in permeability. The various models based on the DDL theory suggest simple functional relationships between plate separation and E such as square root (81, linear (61, or S-shaped (7). However, none of these models universally expIains available swelling data. Several studies reported no swelling below a threshold E and considerable swelling above it (7, 9, I O ) , or a maximum in swelling at some intermediate E (5, 7, 10-13). Similarly, intrinsic permeability measurements often yielded conflicting results that
* Corresponding author; e-mail address: VWGRABERaVOLCANI.AGRI.GOV.IL. 2360
Envlron. Sci. Technol., Vol. 28, No. 13, 1994
could not be reconciled easily with the expected €-swelling relationship (e.g., refs 14 and 15). An alternative model to the DDL theory and its numerous variants is needed to explain the observed relationship between swelling and solvent properties, particularly in concentrated clay-liquid systems. As early as 1948, MacEwan (16)suggested that crystalline swelling (o
1.2 1.o
1.o 10
20
30
40
50
0
50
6 (MPa1’2)
100
150
200
E
Flgure 1. Volumetric swelling of a mixed-layer clay in different organic solvents and water as a function of (A) solvent solubility parameter and (B) solvent dielectric constant (e). The connecting line is an empirical fit.
2.2 2.0
07
1.8
.-C
1.6 v)
.-0 1.4
=E >o
1.2 1.o 0.8
10
20
30
40
50
6 (MPa1’2)
0
50
100
15Q
200
E
Flgure 2. Volumetric swelling of Na-montmorillonite in different organic solvents and water as a function of (A) solvent solubility parameter (6) and (B) solvent dielectric constant (e). The connecting line is an empirical fit.
spray-dried from aqueous suspension to form quasispherical aggregates of 3.5 pm mean radius (26). The aggregates were packed in hexane into a stainless steel HPLC column (0.46 cm i.d., 10 cm length), which was connected to a constant flow pump. A total of 13 hexane2-propanol, 2-propanol-methanol, and methanol-water mixtures (Table 2) were pumped through the column a t a flow rate (Q) of 1mL/min, and the pressure (P)a t the inlet of the column was recorded. The pressure at the outlet was atmospheric. Intrinsic permeability ( k ) for the solvent mixtures was calculated as follows: h = P/pg
(3)
K = -(&IA )All A h
(4)
k = Kdpg
(5)
where h is the head, p is the fluid density, K is the fluid 2362
Environ. Sci. Technoi., Vol. 28, No. 13, 1994
conductivity, A is the cross-sectional area of the column, Ah is the head difference between the inlet and outlet of the column, A1 is the length of column, p is the viscosity, and g is the gravitational constant. The results are reported in Table 2 and Figure 3. Results and Discussion
Swelling Experiments. Figure 1A displays the volumetric swelling spectrum of the mixed-layer clay, with a swelling maximum immediately apparent at a 6 = 33 (Nmethylformamide). Figure 1B depicts the same swelling results plotted against fluid dielectric constant. Swelling was very weakly dependent on E up to e = 110, followed by a sharp increase at E = 182 (N-methylformarnide) and was not as predicted by the DDL theory. Swelling of the Na-montmorillonite increased monotonically with 6, fitting a sigmoid curve and exhibiting the greatest swelling in water (Figure 2A). The Na-mont-
Table 2. Intrinsic Permeability of Spray-Dried Cu-Montmorillonites solvent mixture 6 (MPa1I2) € density (g/cm3) viscosity (cP)
14.9 16.3 17.9 20.1 23.5 23.8 25.8 27.6 29.6 29.6 29.7 31.0 32.5
hex100 hex80iso20 hex6Oiso40 hex25iso75 is0100 iso95meth5 iso60meth40 iso30rneth70 methlOO meth99.9wat0.1 meth99watl meth90wat10 meth80wat20
0.67 0.69
1.9 3.0 4.7 10.4 18.3 18.8 23.1 27.4 32.6 32.6 32.9 35.6 38.9
0.32 0.36 0.57 1.23 2.27 2.07
0.71
0.75 0.78 0.78 0.78 0.79 0.79 0.79 0.79 0.82 0.85
1.22
0.84 0.59 0.59 0.61 0.86 1.13
pressure (psi) 400 450 600 1100
1900 1800 1100 900 650 750 800 1100 3000
intrinsic permeability (~10-10cm? 1.21 1.22 1.42 1.65 1.75 1.69 1.64 1.38 1.35 1.17 1.13 1.10 0.55
a Solvent mixtures are reported as solventlFlsolvent2F2, where Fi is the percentage of solvent i in the mixture. Hex, iso, meth, and wat denote hexane, 2-propanol, methanol, and water, respectively. Viscosity and density were measured; 6 and B were taken as the weighted geometric means of 6 and B of the component fluids.
1
1.8~10’~
14
16
18
20
22
24
26
28
30
32
6 (MPa1I2) Flgure 3. Intrlnsic permeabllity of spraydried Cu-montmorillonite to mixturesof hexane-2-propanol and 2-propanol-methanol as a functlon of solvent solubility parameter (6).The connecting line is an empirlcal fit.
morillonite studied by Olejnik et al. (5) also displayed sigmoidal dependence of swelling on 6 with the highest swelling in water. The solubility parameters of these clays are apparently larger than or equal to that of the examined solvent with the highest 6 (water), and their swellingspectra are thus necessarily asymmetric. Swelling of the investigated montmorillonite plotted versus fluid 6 displays a steady increase up to e = 78 (water) and thereafter a decrease with increasing e (Figure 2B) in an obvious departure from the DDL theory. Specific interactions between certain solvents and the clay surface can result in peaks in swelling spectra which are not predicted by the regular solution theory. In the investigated systems, however, the experimental data suggest that the effect of specific interactions on swelling was minimal. Swelling of the Na-montmorillonite increased gradually with 6 (Figure 21, whereas swelling due to specific interactions would dictate a sudden increase in swelling in the interacting solvent. Swelling of the mixed layer clay was also gradual, even though a very sharp increase in N-methylformamide was observed (Figure 1). The likelihood of a stronger specific interaction of the clay with N-methylformamide than with the less sterically
hindered formamide, however, is low, particularly as swelling of both Na-montmorillonite and the Cs-montmorillonite studied by Olejnik et al. (5) was considerably greater in formamide than in N-methylformamide. The small peak observed in acetone (Figure 1)may indeed be an example of swelling due to specific interactions. Intrinsic Permeability Experiments. The intrinsic permeability tests allow for the repeated exposure of a single solid sample to a number of solvents ensuring reversibility and reproducibility. The procedure is faster and more sensitive to swelling and shrinkage of the stationary phase than the above swelling tests. Permeability can either increase or decrease as a result of swelling, depending on the composition and structure the porous medium. For example, in a system of uniform spheres with a radius R, intrinsic permeability is proportional to R2. As R increases, intrinsic permeability also increases. If interstices between the spheres are filled with cuboids (e.g., a mixture of glass beads and clay), and the volume of each cuboid increases (e.g., by swelling), the intrinsic permeability of the system will decrease. The Cu-montmorillonite exhibited an intrinsic permeability (eq 5) maximum in 2-propanol and lower permeabilities in mixtures of 2-propanol and solvents having both higher and lower solubility parameters (Table 2, Figure 3). A sharp decrease was then observed in the k of the Cu-montmorillonite beads in methanol-water mixtures when water content exceeded 10% (Table 2). The investigated solid phase was composed of porous, quasi-spherical beads, each consisting of montmorillonite tactoids in an edge-to-face arrangement (27).The values of essand e,fshould be different for the intertactoid (edgeto-face) and intratactoid (face-to-face) bonds, and one could anticipate two distinct swelling peaks for this system. Multiple swelling maxima were observed in other clay systems (e.g., ref 12). Intratactoid swelling of montmorillonites is expected to be greatest in solvents with high 6 values (e.g., water; Figure 2A) and rather small in hexane2-propanol-methanol mixtures. Swellingdue to expansion a t the weaker edge-to-face bonds on the other hand may be considerable in these mixtures. Although the edgeto-face expansion is a t the expense of the interbead pore volume due to the fixed total volume of the column, it can result in an increase in permeability (Appendix). Accordingly, the data presented in Table 2 and Figure 3 are interpreted to indicate a maximum in swelling a t interEnvlron. Scl. Technol., Vol. 28, No. 13,1994 2363
tactoid bonds in nearly pure 2-propanol. The sharp reduction in k in the methanol-water mixtures was the expected outcome of swelling a t face-to-face bonds which caused a decrease in total effective porosity (pore volume available for fluid transport). Qualifications. Regular solution theory is a formalization of the age-old adage "like dissolves like." The higher solubility or dispersion of nonpolar solids in nonpolar solvents and of polar solids in polar solvents is thus intuitively obvious. Yet regular solution theory should be applied with care to clay swelling and dispersion. For example, the heterogeneous nature of the clay surface implies that various types of clay-solvent interactions may take place simultaneously. Hence, swelling spectra of clay systems may display a number of peaks such as observed in the Cu-montmorillonite bead system. Size exclusion effects (e.g., ref 28) may also complicate solvent-solid interactions. The interlayer spaces of smectites, for example, may be less accessible to bulky solvents while being freely accessible to smaller molecules. This may cause the dependence of the observed swelling on solvent 6 to deviate from that predicted by the regular solution theory. Steric factors other than size exclusion may hinder the interaction between surfaces and sorbate molecules more than they are likely to affect small molecule-small molecule interactions (29). Any ionizable solvent may undergo specific interactions with a charged surface such as that of clay, particularly in anhydrous systems. Thus, the basic nature of carbonyl or amino-containing solvent molecules may cause the interaction of the solvent with the surface to deviate from that assumed by the regular solution theory. This theory does not allow for exothermic surface interactions characteristic of ionizable species. Attempts to account for such specific interactions were to date only partially successful (23). The 6 value of solvent mixtures is taken as the weighted geometric mean of the solubility parameters of the components (23). This may be an oversimplification for many systems due to, for example, preferential interaction between certain components of the mixture and the clay surface (23, 24). Finally, the nature of the surface changes as solvation progresses. The various solvation shells (or layers) may have different solvation energies (e,f),thus complicating the relationship between swelling and solvent properties. Similarly, the degree of hydration of a clay may strongly affect nonaqueous fluid-surface interactions and, hence, the phenomenologically defined 6 of the clay. Watermiscible solvents may, furthermore, compete with and partially replace sorbed water molecules.
when fluid-fluid and solid-solid interaction energy densities are similar to each other, namely, in a solvent whose 6 equals that of the polymer. By analogy, clays are expected to display swelling maxima in solvents with 6 values similar to their own. A mixed layer illite/smectite clay exhibited maximum swelling in N-methylformamide (6 = 33), while the volumetric swelling of a Na-montmorillonite increased monotonically with increasing solvent 6. The 6 value of the Na-montmorillonite was evidently higher than or equal to that of water, which has the highest solubility parameter of any of the investigated solvents. A number of peaks may be present in the swelling spectrum of a clay. The observed maximum in the intrinsic permeability of a spray-dried Cu-montmorillonite a t 6 x 23 was assigned to swelling at edge-to-face bonds. Expansion a t the face-to-face bonds of this system occurred in a solvent mixture with a considerably higher solubility parameter. Regular solution theory is more successful in describing the experimental observations and predicting swelling of clay systems than is the DDL theory, in agreement with the suggestion that swelling is controlled by solvation (e.g., refs 16-21). Regular solution theory is particularly effective in treating nonionizable solvents and concentrated clay-liquid systems. Refinements of the regular solution theory that account for specific (exothermic) interactions may improve its applicability to clay swelling in ionizable solvents. Appendix
The development below demonstrates that a simultaneous increase in edge-to-face swelling and permeability in systems similar to the investigated Cu-montmorillonite is feasible. Following Poiseuille (321, volume flow per unit time through a cylindrical pore at a given pressure gradient is proportional to the fourth power of the radius of the pore. Accordingly, the intrinsic permeability (k)of a rigid, noninteracting porous medium with an effective pore radius of r was shown to be
where f ( u ) is a function of the shape of the pores and f ( 0 ) is the porosity factor, bothdimensionless (33). In the more general case of a nonrigid, interacting (e.g., swelling)porous medium in an approximately fixed volume, f ( u ) and f ( 0 ) both may be dependent on r. It is then possible to resolve f ( u ) f ( 0 ) into the product of C (a shape constant whose magnitude and dimensions are system dependent), n (the number of pores in the fixed volume), and an r-dependent term. Hence, k may be approximated by
Summary and Conclusions Models of clay swelling that are based on the effect of pore fluid dielectric constant on the distance between clay plates do not successfully account for the observed expansion and shrinkage in clay systems. Swelling of clays in nonionizable solvents can be described in terms of the extended regular solution theory by analogy to the swelling of organic polymers. Swelling maxima are often observed in clay systems immersed in a solvent of an intermediate 6 value in agreement with that theory. According to the extended regular solution theory, maximum swelling (solubility) of a polymer should occur 2384
Environ. Sci. Technol., Vol. 28, No. 13, 1994
k = Cnr'
(2A)
For the Cu-montmorillonite bead system which contains two types of pores
where A represents the larger (interbead) pores and B represents the smaller (intertactoid) pores. The volume (v) that each set of pores occupies can be approximated by
Norrish, K. Discuss. Faraday SOC.1954, 18, 120. Sridharan, A.; Venkatappa Rao, G. Geotechnique 1973,23, 359. Olejnik, S.; Posner, A. M.; Quirk, J. P. Clays Clay Miner. 1974, 22, 361. Murray, R. S.; Quirk, J. P. Soil Sci. SOC.Am. J . 1982,46, 865. Brown, K. W.; Thomas, J. C. Soil Sci. SOC.Am. J. 1987,51, 1451. van Olphen, H. A n Introduction to Clay Colloid Chemistry; Interscience: New York, 1963; p 251-255. Chen, S.; Low, P. F.; Cushman, J. H.; Roth, C. B. Soil Sci. SOC.Am. J . 1987 51 , 1444. Brindley, G. W. Clays Clay Minerals 1980,28,369. Brindley, G. W.; Wiewiora, K., Wiewiora, A. Am. Mineral. 1969,54, 1635. Berkheiser, V.; Mortland, M. M. Clays Clay Miner. 1975, 23, 404. Moore, C. A.; Mitchell, J. K. Geotechnique 1974,24, 627. Green, W. J.; Lee, G. F.; Jones, A. J.Water Pollut. Control Fed. 1981,53, 1347. Schramm, M.; Warrick, A. W.; Fuller, W. H. Hazard Waste Hazard Mater. 1986, 3, 21. MacEwan, D. M. C. Nature 1948, 162, 935. Low, P. F.; Margheim, J. F. Soil Sci. SOC.Am. J. 1979,43, 473. Low, P. F. Soil Sci. SOC.Am. J. 1980,44, 667. Low, P. F. Soil Sci. SOC.Am. J. 1981, 45, 1074. Viani, B. E.; Low, P. F.; Roth, C. B. J. Colloid Interface Sci. 1983, 96, 229. Viani, B. E.; Roth, C. B.; Low, P. F. Clays Clay Miner. 1985, 33, 244. Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions; Van NostrandReinhold New York, 1970. Barton, A. F. M. Handbook of Solubility Parameters and Other Cohesion Parameters; CRC Press, Inc.: Boca Raton, FL, 1983. Bagley, E. B.; Scigliano, J. M. In Solutions and Solubilities; Dack, M. R. J., Ed.; Wiley Interscience: New York, 1976; pp 437-485. Mark, H. F.; Tobolsky, A. V. Physical Chemistry of High Polymeric Systems; Interscience: New York, 1950,Chapter 8. Tsvetkov, F.; Heller-Kallai, L.; Mingelgrin, U. Clays Clay Miner. 1993,41, 527. Mingelgrin, U.; Tsvetkov, F. Clays Clay Miner. 1985, 33, 285. Lyon, W. G.; Rhodes, D. E. Environ. Toxicol. Chem. 1992, 12, 1405. Tsvetkov, F.; Mingelgrin, U.; Lahav, N. Clays Clay Miner. 1990, 38, 380. Weast, R. C., Ed. Handbook of Chemistry and Physics, 58th ed.; CRC Press: Boca Raton, FL, 1978. Windholz, M.; Budavari, S.; Blumetti, R, Otterbein, E. S. The Merck Index, lOthed.; Merckand Co.: Cleveland, 1983. Moore, W. J. Physical Chemistry; Prentice-Hail, Inc.: Englewood Cliffs, NJ, 1962; pp 223-224. Bear, J. Dynamics of Fluids in Porous Media; Elsevier Publishing Co.: New York, 1972.
and
where S is a constant defined by the three-dimensional pore shape. As the volume of the column is fixed
d VA = -d VB
(64
Differentiating eqs 4A and 5A with respect to r gives
and dVB = ~ S B ~ BdrB (~B)~
(8A)
The total differential of k (eq 3A) with respect to rB and rA is
Using eqs 6A-8A, eq 9A reduces to dk = bCBnB(rB) (b-l) drB [(1 - a CAsB(rB)(3-b))/ (bcBsA(r~)‘3”’)1 (10A) Expansion of the smaller (intertactoid) pores constrains drB to be positive, so if
dk
>0
(12A)
Equation 10A demonstrates that in a fixed volume permeability can increase upon swelling in a nonrigid, interacting porous medium comprised of two sets of pores. The conditions for an increase in k are that one set of conducting pores expands in the swelling process and that the quotient defined in eq 11A is smaller than unity. This quotient is dependent upon the geometry and characteristic dimensions (r) of the pores of type A and B. Since rB < rA, eq 11A has a high probability of being satisfied if both a and b are smaller than 3. Acknowledgments The authors wish to thank W. Lyon of RSKERL for suggesting the possibility that regular solution theory can describe clay swelling. L. Kliger is thanked for her dedicated technical assistance. Literature Cited (1) Daniel, D. E. Civ. Eng. N.Y. 1985, 55, 48. (2) Barshad, I. Soil Sci. SOC.Am. J. 1952, 16, 176.
Received for review April 8,1994. Revised manuscript received August 3, 1994. Accepted August 5, 1994.” Abstract published in Advance ACS Abstracts, September 1, 1994.
Environ. Sci. Technol., Vol. 28, No. 13, 1994
2385
