Лако-красочные материалы — производство

We have seen how the concept of surface energy in principle relates to adhesion. The surface energy terms discussed (e. g., Eqs. (1) to (7)) are all energies per unit area. We now need to consider carefully what we mean by the interfacial area.

If the interface between phases 1 and 2 is ‘‘perfectly’’ flat, there is no problem in defining the interfacial area, A. However, this chapter is particularly concerned with rough surfaces: indeed almost all practical surfaces are, to a degree, rough. We first consider modest degrees of roughness, where a simple geometric factor may be applied. It is argued, however, that the complexity of many rough surfaces makes them different in kind, that is qualitatively different, from a flat surface. Ultimately the ascription of a numerical value to quantify roughness itself may be arbitrary, depending on the size of the probe chosen to measure it. It is concluded that the only practicable interpretation of ‘‘unit area’’ is the nominal geometric area. The consequence is that the production of a rough surface per se increases surface energy (Eq. (1)), and from this, work of adhesion and fracture energy of the joint (Eqs. (4) and (7)).

A. Roughness Factor

Where the surface roughness is not very great it might be adequately expressed by a simple Wenzel roughness factor [52],

A

ao

where A is the ‘‘true’’ surface area and Ao the nominal area. For simple ideal surfaces, r can be calculated from elementary geometric formula. Thus a surface consisting of a hemisphere would have a roughness factor of 2, one consisting of square pyramids with all sides of equal length, a roughness factor of /3. For simple real surfaces the roughness factor can be calculated from straightforward measurements, such as profilometry. In such cases we could substitute a corrected area into the definition of surface energy (Eq. (1)) and thence via Eqs. (3) and (4) evaluate the spreading coefficient and work of adhesion. Thus the spreading coefficient S’ for a rough surface becomes

S’ = r (Ksv — Ksl) — Klv (9)

Some of the effects of roughness on the spreading of a liquid can be predicted from Eqs. (2), (3), and (9), providing the liquid does not trap air as it moves over the surface. These are summarized in Table 1.

It is important to appreciate the assumption implicit in the concept of the roughness factor: chemical nature and local environment of surface molecules on the rough surface and on the smooth surface are the same.