September 2008

During the past decade, and in line with an increased interest in understanding superhydrophobic surfaces, the frequency with which Wenzel¹ and Cassie² are cited has increased sixfold.³ At the Sixth International Symposium on Contact Angle, Wettability and Adhesion which was held in July, no fewer than a dozen papers presented made a significant reference to the Cassie and Wenzel states. This is despite these theories being 64 and 72 years old respectively^1,2.

For those of you who may not be familiar with Wenzel and Cassie, allow me to introduce them to you. Young's equation defines the thermodynamic equilibrium between the drop (liquid phase), the solid (solid phase), and the surrounding air (gas phase) in terms of energies: the solid/gas interfacial energy (i.e., surface energy), the solid/liquid energy (defined by the three-phase contact line), and the liquid/gas energy (i.e., surface tension). For a more detailed discussion, see the "Contact Angle" article we contributed to on wikipedia.org for reference (http://en.wikipedia.org/wiki/Contact_angle). In short, Young's equation defines chemical reactions and forces.

In the case of superhydrophobicity, topography and roughness can be quantified and used to better define and predict apparent contact angle (θ*) and relative repellency.

In a Wenzel state, the liquid fills the voids below the liquid and thus occupies more surface area. The additional parameter in this case is roughness (r). Wenzel's formula states that solid surface energy (when the contact angle is greater than 90°) is a function of contact angle multiplied by factor r. Thus,

cosθ* = r cosθ

where θ* represents the apparent contact angle. The formula attempts to make an adjustment for the increase in surface area that results from the presence of a texture or roughness so long as the liquid is in contact with the surface. Thus as the roughness increases (by an increase in r), the contact angle will increase reflecting an increase in relative hydrophobicity and repellency.

In a Wenzel state, the contact angle hysteresis tends to be large. As drop volume is removed, for example, receding contact angles below 50° have been measured.

In a Cassie (a.k.a., Cassie-Baxter) state, the drop, as illustrated above, rests upon the asperities with gas left in the voids below the drop. The surface area is less than it would be for a drop of the same volume and apparent contact angle on a flat surface or a rough surface in a Wenzel state. To adjust for this reduction in surface area, we use Φs. Thus,

cosθ* = -1 + Φs (cosθ + 1)

If θ = 100°, for example, and we measure θ* at 155°, then 88% of the bottom of the drop is touching air. This helps us understand how the contact angle hysteresis in a Cassie state is low, usually under 10°. The liquid has very little interaction with the solid since only 12% of the bottom of the drop is in contact with the solid.

There are myriad examples of superhydrophobic surfaces in nature and increasingly there is a desire to understand this phenomenon in an effort to fabricate materials and coatings with greater repellency. For a more detailed discussion on superhydrophobicity and a tutorial on measuring large contact angles using a ramé-hart Contact Angle Goniometer with DROPimage software, see our April 2008 Newsletter here: http://www.ramehart.com/goniometers/newsletters/2008-04_news.htm

Not surprisingly more than one researcher has questioned the Cassie and Wenzel models. Charles Extrand⁴ at Entregris has proposed that the three-phase line dictates the contact angle, not the liquid/solid interface below the drop.⁵ More recently Gao and McCarthy³ in their boldly titled paper How Wenzel and Cassie Were Wrong conclude that contact area plays no role in understanding contact angle behavior, that the place to look to understand contact angle, advancing and receding angles, and contact angle hysteresis is the interactions of the liquid and solid at the three-phase contact line. Their study was accomplished with a legacy ramé-hart Contact Angle Goniometer. Already others⁶ are defending the classic Cassie and Wenzel theories and challenging Gao and McCarthy.

Researchers at Ariel University in Israel⁷ presented a paper at the recent Contact Angle Symposium. They are studying a condition they refer to as a "Cassie impregnated regime" wherein a Cassie state exists but the voids under the drop are partially or completely filled with drop liquid. By vibrating the drop, they claim to better understand a mixed Cassie/Wenzel state and the wetting transitions from a classic Cassie state to both a Cassie impregnating state and the classic Wenzel state.

Clearly, more research will continue to uncover the mysteries of wetting and either completely debunk the Cassie and Wenzel theories, or offer new models to better understand repellency, adhesion, and contact angle phenomena on superhydrophobic surfaces.

If you would like to learn more about How Wenzel and Cassie Were Wrong, please contact us. 

¹ Wenzel, R. N. Industrial & Engineering Chemistry 1936, 28, 988-994.
² Cassie, A. B. D.; Baxter, S. Transactions of the Faraday Society 1944, 40, 546-551.
³ Gao, L.; McCarthy, T. J. Langmuir 2007, 23, 3762-3765.
⁴ Extrand, C. W. Langmuir 2003, 19, 3793.
⁵ See US Patent 6976585 at http://tinyurl.com/6l9zjl
⁶ McHale, G. Langmuir 2007, 23, 8200-8205.
⁷ http://tinyurl.com/657joy