Contact hysteresis

For equilibrium systems with no contact hysteresis G = W, which is the classical Griffith criterion in fracture mechanics. For such a system, Eqs. 12 and 37 are the same. That is, the strain energy release rate is given by... 

Fig. 11. versus P data and contact hysteresis reported by Chaudhury and Whitesides [471. (a) The data for unmodified PDMS-PDMS contacts. No contact hysteresis was observed, (b) The data for and PDMS modified with alkyl siloxane monolayers, PDMS° -03Si(CH2)9CH3. A weak contact hysteresis was observed, (c) The data for PDMS modified with fluroalkyl siloxane monolayers, PDMS -03Si(CH2)2(CF2)7CF3. A large contact hysteresis was observed. In all cases, the open circles represent the loading data, and the filled circles represent the unloading data. 

Lin et al. [70, 71] have modeled the effect of surface roughness on the dependence of contact angles on drop size. Using two geometric models, concentric rings of cones and concentric conical crevices, they find that the effects of roughness may obscure the influence of line tension on the drop size variation of contact angle. Conversely, the presence of line tension may account for some of the drop size dependence of measured hysteresis. 

Surfactant-coated surfaces may also rearrange on contact with a liquid as shown by Israelachvili and co-workers [77]. This mechanism helps to explain hysteresis occurring on otherwise smooth and homogeneous surfaces. 

It is clear from our discussion of contact angle hysteresis that there is some degree of variability in reported contact angle values. The data collected in Table X-2, therefore, are intended mainly as a guide to the type of behavior to be expected. The older data comprise mainly results for refractory and relatively polar solids, while newer data are for polymeric surfaces. 

There is appreciable contact angle hysteresis for many of the systems reported in Table X-2 the customary practice of reporting advancing angles has been followed. 

Thus D(r) is given by the slope of the V versus P plot. The same distribution function can be calculated from an analysis of vapor adsorption data showing hysteresis due to capillary condensation (see Section XVII-16). Joyner and co-woikers [38] found that the two methods gave very similar results in the case of charcoal, as illustrated in Fig. XVI-2. See Refs. 36 and 39 for more recent such comparisons. There can be some question as to what the local contact angle is [31,40] an error here would shift the distribution curve. 

One other cause of hysteresis remains to be mentioned. As was pointed out earlier (p. 177) the contact angle may be different as the mercury is advancing over or receding from a solid surface, and it depends also on the chemical and physical state of the surface the mercury may even react with the surface layer of the solid to form an amalgam. A change in 9 of only a few degrees has a significant effect on the calculated value of pore radius (cf. Table 3.15). 

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