Individual contributions of capillarity and adsorptive surface forces to the matric potential are seldom differentiated in determination of soil water characteristic (SWC) curves. Typically, capillary forces dominate at the wet end, whereas adsorptive surface forces dominate at the dry end of a SWC where water is held as thin liquid films. The amount of adsorbed soil water is intimately linked to soil specific surface area (SA) and plays an important role in various biological and transport processes in arid environments. Dominated by van der Waals adsorptive forces, surface-water interactions give rise to a nearly universal scaling relationship for SWC curves at low water contents. We demonstrate that scaling measured water content at the dry end by soil specific surface area yields remarkable similarity across a range of soil textures and is in good agreement with theoretical predictions based on van der Waals interactions. These scaling relationships are important for accurate description of SWC curves in dry soils and may provide rapid and reliable estimates of soil specific surface area from SWC measurements for matric potentials below ‒10 MPa conveniently measured with the chilled-mirror dew point technique. Surface area estimates acquired by fitting the scaling relationship to measured SWC data were in good agreement with SA data measured by standard methods. Preliminary results suggest that the proposed method could provide reliable SA estimates for natural soils with hydratable surface areas smaller than 200 m2/g.
 Progress in developing definitive models of the dry end of the SWC [Rossi and Nimmo, 1994; Ross et al., 1991] was hampered by data scarcity and experimental challenges using standard pressure plate devices with prohibitively long equilibration times at potentials lower than ‒1.5 MPa [Gee et al., 2002]. Additionally, the introduction of residual water content as a fitting parameter in most SWC models often obscures the physical representation of key processes in the low potential range.
Tuller et al.  proposed detailed pore scale models for water retention in soils that enable consideration of individual contributions of capillary and adsorptive components to soil water matric potential. A simplified form of the augmented Young-Laplace equation [Philip, 1977; Tuller et al., 1999] was used to calculate liquid-vapor interfacial configurations within angular pore space elements considering film adsorption and capillary processes. On the basis of detailed knowledge of the liquid-vapor interface and application of a statistical upscaling scheme, Or and Tuller  developed a physically based SWC model that allows separation of a SWC curve into capillary and adsorptive contributions (Figure 1). Adsorptive contributions to the SWC are attributed to van der Waals surface forces forming liquid films, whereas capillary contributions are due to liquid held in pore corners behind curved interfaces. Generally, capillary forces dominate at the wetter range of the curve, whereas adsorptive surface forces dominate at the dry end. Results of Or and Tuller  indicate that for a wide range of soil textures, capillary contributions become negligible for matric potential values lower than ‒10 MPa. We use this threshold value as a practical definition of the “dry end” of a SWC. The relationship between matric potential (ψ) in pascals, chemical potential (μ) in J/kg, and matric head (H) in meters, is given as μ = ψ/ρw = gH, where ρw is the density of water in kg/m3 and g is the acceleration of gravity in m/s2.
 The role of van der Waals forces in controlling adsorbed water film thickness leads to the postulation concerning proportionality between water content at the dry end and specific surface area of a soil. In the following we provide evidence for such scaling relationship and discuss potential applications for inferring specific surface area from measured “dry end” SWC data.
2. Evidence for General Scaling Relationships
 The “dry end” gravimetric water content (θm) may be expressed as a function of soil specific surface area (SA, in m2/kg) and the thickness of water film (h, in meters) adsorbed on mineral surfaces:
where ρw is the density of water. Such a hypothesis is supported by experimental data reported by Grismer  and by analyses of Or and Tuller [1999, Figure 5]. Grismer  found linear relationships between equilibrium water content of initially oven-dry soil samples exposed to an atmosphere with relative humidity (RH) close to 100% and soil specific surface area measured by means of ethylene glycol monoethyl ether (EGME) adsorption [Carter et al., 1965; Pennell, 2002].
 Forces other than molecular van der Waals interactions may play a role in controlling water films. These include electrostatic and hydration forces that vary with mineral and surface properties and with soil solution composition and concentration (readers are referred to Tuller et al.  for a thorough review). Neglecting contributions of capillary condensation at relatively low matric potentials (<‒10 MPa), and considering van der Waals forces on planar surfaces only (with negligible steric interactions across adjacent surfaces), yields a simple expression for equilibrium thickness (h) of an adsorbed thin water film (<100 nm) as a function of matric head according to Iwamatsu and Horii :
where Asvl [J] is the Hamaker constant for solid-vapor interactions through the intervening liquid, ψ [m] is the matric head, ρw [kg/m3] is the density of the liquid, and g [m/s2] is acceleration due to gravity. The Hamaker constant represents average interactions between macroobjects such as mineral surfaces and liquid due to short-range (<100 Å) van der Waals forces [Ackler et al., 1996; Bergström, 1997].
 The generality of scaling relationships between gravimetric water content and soil specific surface area at low potentials was further investigated using six data sets reported by Campbell and Shiozawa . These data sets with properties listed in Table 1 were chosen based on the availability of SA measurements (values in parentheses are results of repeated measurements), their wide range of textures, and availability of SWC data at low matric potentials.
Table 1. Measured Texture and Specific Surface Area of Six Soilsa
EGME Surface Area, m2/g
Values in parentheses are SA measurements obtained in this study.
97 ( )
 Dividing measured gravimetric water content at the “dry end” by soil specific surface area (Table 1) enables estimation of adsorbed film thickness as a function of matric potential. The results depicted in Figure 2 show remarkable scaling behavior and similarity among all soils except Salkum silt loam. From Table 1 it appears that the reported EGME-measured surface area for Salkum is relatively low considering its clay content of 22.5%. To reexamine the reliability of SA values, we followed the procedure outlined by Pennell  and repeated the EGME surface area measurements for L-soil, Royal, Salkum, Walla Walla, and Palouse B, using original samples from the Campbell and Shiozawa  study. The resulting repeated measurements for L-soil, Royal, Walla Walla, and Palouse B closely match reported values (Table 1, values in parentheses). Specific surface area for Salkum soil was slightly higher at 67 m2/g. Even with the higher SA, the scaled gravimetric water content for Salkum did not match the data for other soils (Figure 2). A possible explanation for the discrepancy may be traced back to sample preparation for the EGME measurement. Oxidizing organic substances and dissolving cementing materials (e.g., MnO2) with 30% hydrogen peroxide (H2O2) [Jackson, 1979] was accompanied by unusually strong reaction with the Salkum soil. The reaction did not cease even after multiple H2O2 treatments over a 4-week period. We thus conjecture that incomplete dissolution of MnO2 left some of the Salkum SA inaccessible for EGME adsorption and potentially led to underestimation of specific SA.
 In summary, the results in Figure 2 demonstrate excellent agreement between scaled dry end SWC data and theoretical predictions of film thickness due to van der Waals surface forces (equation (2)), using an effective Hamaker constant value of ‒6 × 10‒20 J.
3. Estimation of Specific Surface Area
 On the basis of findings outlined in previous sections we pursued the potential for solving the “inverse problem,” namely, the estimation of soil specific surface area from SWC data at low matric potential values. This could offer an alternative to the tedious and time-consuming EGME measurements, especially with availability of new psychrometric devices for fast and reliable measurement of matric potentials at low water contents. In essence, the method would use water as the probing molecule, thereby relaxing assumptions concerning applicability of EGME and gas adsorption for wetting processes with water (i.e., molecular size and polarity differences).
 Experiments using a temperature compensated WP4 Dewpoint PotentiaMeter (Decagon Devices Inc.) based on the chilled-mirror dew point technique [Gee et al., 1992] enable rapid determination of soil water potential in equilibrium with water vapor in a sealed chamber. At equilibrium, the relative humidity in the chamber at a given temperature is used to determine the sample water potential. We used samples of L-soil, Royal, Salkum, Walla Walla, and Palouse B, and added Millville silt loam and SAz-1 Cheto Ca2+ montmorillonite obtained from the Clay Minerals Society source clays repository (Purdue University) to test the method and extend the range of investigated surface areas.
 We prepared five 10-g oven-dry subsamples of each soil and added small amounts of water while mixing the sample. The target gravimetric water contents were established beforehand based on the soil texture (e.g., we used 0.16, 0.17, 0.18, 0.19, and 0.20 kg/kg for Ca2+ montmorillonite, and 0.01, 0.02, 0.03, 0.04, and 0.05 kg/kg for L-soil). After mixing, the samples were transferred into WP4 stainless steel sampling cups enclosed with plastic lids. To prevent evaporation losses, the cups were sealed with aluminum foil and placed into Ziploc bags. The samples were then stored for 2 days at 10°C to allow equilibration.
 Following the equilibration period, we conducted three consecutive soil water potential measurements at 24°C for each sample with the WP4 Dewpoint PotentiaMeter. Immediately after the measurements we determined the mass of the wet samples. After oven-drying, we obtained the exact gravimetric water content of each sample that corresponds to the measured water potential.
was fitted to measurements by nonlinear regression with SA as a free fitting parameter. The resulting match between measurements and model (equation (3)) are shown in Figure 3.
 Specific surface area values obtained from nonlinear regression are listed in Table 2. We also attempted to estimate surface area using the driest point only (i.e., rearranging equation (3) and solving for SA with the lowest water content). Results of this test are reported in parentheses. Although more thorough investigations with a larger number of samples and broader range of soil types are required, these results demonstrate potential usefulness of SWC psychrometric measurements for estimation of soil specific SA. The disparity between WP4 and EGME determined SA for Ca2+ montmorillonite may be attributed to differences in water and EGME adsorption isotherms, suggesting that EGME adsorption in Ca2+ saturated clays is significantly higher than water adsorption [Chiou and Rutherford, 1997].
Table 2. Comparison of Specific Surface Area Measurements Obtained With a Psychrometric Method and EGME Adsorptiona
Psychrometric Surface Area, m2/g
EGME Surface Area, m2/g
Values in parentheses represent SA estimates using a single point, driest, on the SWC curve.
 The proposed approach considers adsorptive processes only and ignores potential liquid retention due to capillary condensation on rough particle surfaces and in micropores. Theoretical analyses of Philip  and Novy et al.  demonstrate that surface roughness not only induces capillary condensation, but also modifies the adsorptive force field. The contribution of capillary condensation vanishes when the ratio between film thickness and characteristic roughness height falls below 0.1 [Philip, 1978]. For practical purposes we can select a cutoff potential around ‒10 MPa for which capillary condensation due to surface roughness becomes negligible [Or and Tuller, 2000]. Slit-shaped micropores such as between adjacent clay tactoids might give rise to steric forces and enhance potential for capillary condensation [Christenson, 1994; Derjaguin and Churaev, 1976; Evans et al., 1986; Forcada, 1993; Iwamatsu and Horii, 1996], resulting in overestimation of hydrated surface area based on equation (3). Clearly more work is required to establish relationships between clay content and the extent of liquid retention due to capillary condensation.
 The amount and type of exchangeable cations and layer charge could also affect water adsorption. The amount of adsorbed water increases with both the hydratable surface area and the layer charge [Chiou and Rutherford, 1997]. At low hydration state the increase in adsorbed water with layer charge occurs mainly on external surfaces [Laird, 1999] where cations/charge sites have significantly larger hydration numbers than charge sites located on internal (interplatelet) surfaces. This leads to formation of water molecule clusters around cations/charge sites rather than adsorption of a uniform multilayer water film. The nature of cations occupying external and internal charge sites also affects water adsorption. Dontsova et al.  and Orchiston [1955, 1959] show that clays saturated with monovalent cations absorb less water than clays saturated with divalent cations. This is attributed to an increase in surface charge density, hence an increase in water adsorption when divalent cations are occupying the surface charge sites. Larger, less hydrated cations (K+ and Ca2+) also seem to decrease water adsorption when compared with smaller cations (Na+ and Mg2+) [Dontsova et al., 2004]. Observations by Grismer , however, reveal that layer charge and cation effects are relatively unimportant in natural soils with hydratable surface areas below 200 m2/g. This is supported by the foregoing discussion that identifies the dominance of water adsorption processes on external surfaces of clay minerals, which contribute only a small portion to the total hydratable surface area [Laird, 1999].
 Finally, the value of Hamaker constant Aslv (solid-vapor interactions through intervening water film) is a critical parameter for describing the adsorption process. Typical values for Hamaker constants for soil solid-liquid-vapor systems range from ‒10‒19 to ‒10‒20 J [Watanabe and Mizoguchi, 2002]. Because of the complexity of the solid phase composed primarily of crystalline and amorphous silicates, and the complex geometry that affect van der Waals interactions (and chemistry of soil solution), it would be difficult to accurately predict a Hamaker constant value for a soil. Values from the literature were typically determined for mica or quartz surfaces and pure water based on the Lifshitz theory that considers van der Waals interactions only [Iwamatsu and Horii, 1996; Beaglehole et al., 1991; Curry and Christenson, 1996; Ackler et al., 1996]. In real soils, it is reasonable to expect a more complex picture involving additional effects such as electrostatic effects due to the diffuse double layer (DDL) and consideration of surface geometry and heterogeneity. We therefore conclude that the remarkable agreement found with the Hamaker constant of ‒6 × 10‒20 J should be seen as an effective value that lumps effects of heterogeneous surface properties, geometry, electrostatic, and van der Waals interactions.
 On the basis of the foregoing discussion, the psychrometric approach for SA determination should provide reliable values for natural soils with hydratable surface areas below 200 m2/g. As a first approximation, we recommend using SWC values for ‒10 MPa and lower (drier) with an effective Hamaker constant of ‒6 × 10‒20 J and equation (3) to predict SA values.
5. Summary and Conclusion
 We propose scaling relationships for soil water characteristic curves at low water contents and provide evidence that the “dry end” of scaled SWCs can be approximated with an adsorption isotherm based on van der Waals interactions. This simple concept can be used to infer soil specific surface area from a few SWC points measured at low water contents. This becomes particularly attractive with recent availability of advanced psychrometric methods allowing simple, rapid, and reliable measurement of water potentials down to ‒250 MPa. The proposed method offers a potential alternative to standard EGME and gas adsorption measurements requiring extensive sample preparation associated with numerous experimental challenges, and the use of probe molecules whose properties are considerably different than water. A comparison with surface area estimates obtained with the commonly applied EGME method shows considerable potential of the proposed psychrometric measurements.
 The results presented here are preliminary, awaiting additional tests with more samples covering a broader range of soil types (including specific tests for the value of the Hamaker constant). Additionally, an in-depth investigation of potential effects of capillary condensation at low water contents is needed to reduce errors in SA estimation (mostly overestimation). Capillary condensation is not expected to have large impact at the dry end where only two to three molecular layers of water are present (~‒10 MPa). Surface microroughness should extend the range of influence of capillary condensation that would impact SA determination. On the basis of observations, we recommend a conservative cutoff water potential of ‒10 MPa (approximately two to three molecular water layers [Or and Tuller, 1999, Figure 5]) for applications with unknown surface roughness. This value could probably be relaxed (less negative) for soils with low surface area to enhance accuracy of water content measurement, hence SA estimation.
 In conclusion, the dry end of the SWC shows remarkable scaling behavior due to water retention by surface adsorption as thin liquid films. The dependency on soil specific surface area is used to infer SA from relatively simple psychrometric measurements of the SWC dry end. The method enables extension of parametric SWC to the very dry end (large negative matric potential values) important for biological activity in arid environments. The scaling behavior bridges a modeling gap in representing transport processes in the transition from mass flow to vapor transport.
 The authors express their gratitude to Gaylon Campbell for providing original soil samples used by Campbell and Shiozawa . Special thanks go to Jon Drasdis (UConn) for assistance with sample preparation and WP4 measurements, and David Robinson (USU) for his insightful comments on an earlier version of the manuscript. We gratefully acknowledge support by National Research Initiative Competitive grants 2004-35107-1489 and 2001-35107-11009 from the USDA Cooperative State Research, Education, and Extension Service and by the Idaho Agricultural Experimental Station (IAES). This paper is approved as IAES journal paper 05P46.