Contact angle Wenzel state

The effect of roughness on the wettability of an idealized sinusoidal surface has been studied with a digital computer. The equations of Wenzel and of Cassie and Baxter are discussed in relation to the model. The heights of the energy barriers between metastable states of a drop are seen to be of utmost importance in determining the magnitude of contact angle hysteresis. 

The theoretical discussion of contact angle and wetting to this point has assumed implicitly that the solid surface in question is a smooth, ideal plane. In fact, of course, very few solid surfaces even begin to approach such a state. The finest polished glass surface, for example, will usually have asperities of 5 nm or more. Commonly encountered polished surfaces, will be much rougher by factors of 10-1000. The earliest, and still most useful, quantitative attempt to correlate the observed contact angle of a liquid on a solid with the surface roughness is the Wenzel relationship which proposes a thermodynamic relationship such that... 

Wenzel case. This indicates a contact angle of 0° in the Wenzel state. Figure 6 also shows the experimental values of Abdelsalam et al. [15]. Their results in the context of our theory will be discussed in the following section. 

The term super-hydrophobicity designates the enhancement of the natural nonwettability of a flat substrate, as characterized by its contact angle 0fiat, by the vmderlying surface roughness while 6 for water on any flat material never exceeds 120°, its contact angle on micro- or nano-textured materials can reach values close to 180° [18], This super-hydrophobic effect can be obtained through two different situations, the so-called Wenzel [19] and Cassie [20] states. 

The Cassie-Baxter-Wenzel theory [44, 47,48] defines the critical contact angle value on the smooth surface above this value, the Cassie-Baxter model is more stable wetting state and below this value the Wenzel model is the most stable wetting state. If the measured contact angle on a smooth surface is lower than this critical value and if the superhydrophobic behaviour is observed, the transition between the two models should be possible like, for example, with the LDPE surface treated in both plasmas. In this case, the roughness factor is 1.043, the contact angle on the dried surface reaches a value of 171° and the contact angle on the same surface partially wetted with water vapour or dipped in water is only 140°. 

The contact angle of the liquid with air is 180° and so an increasing air area underneath the drop changes the Cassie-Baxter contact angle (0cb) to higher values. The hysteresis values for such surfaces is much smaller than in the Wenzel case which makes the two states distinguishable even when it is not detectable if the spaces between the structures are filled or not. The smaller the hysteresis, the easier the drop can roll off such surface. 

In the Wenzel (W) state the topographic properties of the surface are descrihed hy a roughness factor r [4], which gives the ratio of the effective area of actual, rough surface to the ideal flat surface, i.e. r 1. The apparent contact angle is given by... 

SLA, the LLR functionalized with a pure CHj-terminated SAM shows extremely high dynamic and static contact angles, an indication of Cassie-type wetting. The papillae are able to support the drop, even in the absence of the tubular wax of the original leaf. As soon as there is a hydrophilic contribution present in the SAM, Wenzel-type wetting occurs. Note the high standard deviations, which arise from the fact that in some measurements, the Cassie state still persisted, whereas in others, the drop penetrated into the structures. Both types of behavior were sometimes even observed on the same sample, which is an indication of the presence of metastable states. An explanation for this metastable Cassie regime... 

---