Лако-красочные материалы — производство

It may not be possible, even in principle, to ascribe a unique ‘‘surface area’’ to a surface. It has long been recognized from work on gas adsorption on porous solids that the surface area measured depends on the size of the probe molecule. A small probe can enter finer surface features and therefore may give a larger value. The surface area is, as Rideal [59] recognized in 1930, in a sense arbitrary, not absolute. More recently evidence has been produced suggesting that many engineering surfaces and many fracture surfaces are fractal in nature [60,61]. For a fractal surface, the area depends on the size of the ‘‘tile’’ used to measure it, the actual relationship depending on the fractal dimension of the surface. The area of such a surface tends to infinity as the tile size tends to zero.

The roughness factor may be calculated for a fractal surface. As demonstrated below, its value varies according to the probe size and the fractal dimension [62].

Consider the adsorption of probe molecules of various sizes (cross-sectional area a)[1] on a fractal surface [63,64]. Let n be the number of molecules required to form a mono­layer. If log n(a) is plotted against log a, a straight line with negative slope is obtained which can be represented as

log n(a)=(-Dj log a + C (10)

where D is the fractal dimension of the surface and C is a constant. Therefore

n(a) = Pa-D/2 (11)

where p is another constant. (For an ideal plane surface (D = 2), this equation reduces to the trivial relationship that the number of probes required to cover a given surface is inversely proportional to the probe area.)

The area (in dimensionless form) can be expressed as

For a fractal surface D >2, and usually D < 3. In simple terms the larger D, the rougher the surface. The intuitive concept of surface area has no meaning when applied to a fractal surface. An ‘‘area’’ can be computed, but its value depends on both the fractal dimension and the size of the probe used to measure it. The area of such a surface tends to infinity, as the probe size tends to zero.

Obviously the roughness factor is similarly arbitrary, but it is of interest to use Eq. (14) to compute its value for some trial values of D and a. This is done in Table 2. In order to map the surface features even crudely, the probe needs to be small. It can be seen that high apparent roughness factors are readily obtained once the fractal dimension exceeds two, its value for an ideal plane.

The roughness factor concept may be useful for surfaces which exhibit modest departures from flatness. Beyond this, it is misleading as changes in the local molecular environment make the rough surface qualitatively different from a flat one. In many cases it is not meaningful to talk of the area of a rough surface as if it had, in principle, a unique

value. What area, then, should be used for a rough surface in the context of surface energy and work of adhesion, Eqs. (1) to (7)? It seems inescapable when we refer to the surface area A that we must use the ideal, formal area, i. e., macroscopic area of the interface. This has important implications for the effect of surface roughness on adhesive joint strength. Surface energy is defined in Eq. (1) as the excess energy per unit area, and it is now clear that this area is the ‘‘nominal’’ area, i. e., the macroscopic area of the interface. The production of a rough surface raises the energy of the molecules in the surface, as dis­cussed above. This raised energy is still normalized by reference to the same nominal, macroscopic area as before. Consequently, the production of a rough surface per se increases surface energy (per unit nominal area, Eq. (1), and consequently increases the work of adhesion and fracture energy of the joint (Eqs. (4) and (7)).