The brightness and opacity of a sheet of paper are twin measures of the paper’s ability to reflect and scatter visible light. If paper reflects all or most incident light having wavelengths in the visible range (about 400 to 700 nanometers, or nm), such that little light passes through, the paper is opaque—that is, we cannot see the image on one side from the opposite side. Brightness is related to opacity, but more specific. The human eye perceives a blue-white shade as being bright. Paper brightness is measured as the amount of light reflected at a wavelength of 457 nm, and is expressed as a percent of the incident light. Brightness and opacity can both be measured using
special instruments.
Opacity is expressed as a contrast ratio of reflectances: the ratio of the reflectance of light from a single sheet over a black background, divided by the reflectance of the same sheet backed by a standardized white body. (Reflectance is measured at a wavelength of 572 nm.) Opacity is also expressed as a percent of 100.
Improving the opacity and brightness of a given paper sheet is the principal objective of adding fillers such as precipitated calcium carbonate (PCC). Numerous studies have shown that fillers exhibit a wide range of scattering coefficients; these studies have also shown that PCC fillers provide the best optical performance in terms of scattering coefficient, which is directly related to opacity and brightness.
All this is described by the principles of a special theory for paper optics, first developed by Kubelka and Munk, and has been universally adopted by the pulp and paper industry. The basis of the theory is the assumption that two parameters, the absorption coefficient (K) and the scattering coefficient (S), govern both brightness and opacity. Absorption of light determines the darkness or lightness of a material, with pure black indicating perfect absorption of visible light and pure white indicating perfect reflectance. Since PCC fillers are extremely white, and thus exhibit both a high scattering coefficient and very low absorption coefficient, they have a dominating influence on opacity and brightness when added to paper pulp. Again according to Kubelka-Munk, the opacity and brightness of paper depends mostly on the scattering coefficient of both the pulp and the PCC filler in the paper and is expressed by the equation:
Spaper = (1 – y)Spulp + ySfiller
where y is the fraction of PCC filler in the paper. In this equation, only pulp and filler are assumed to have an appreciable effect on light scattering and overall optical performance.
Although Spulp does not vary greatly for various types of fiber, Sfiller does vary and is highest for titanium dioxide (TiO2). Prior to the ready availability of satellite PCC, TiO2 was used to impart whiteness and brightness to filled papers, particularly high quality grades. However, TiO2 is very expensive, typically more than ten times that of other filling pigments. Thus, when performance and cost are considered simultaneously, PCC will outperform all fillers, and leads not only to high values for Spaper but to desirable economics as well. The paper industry now understands this quite well and has adopted PCC as the filler of choice for most grades of paper.
The superior optical performance of PCC fillers is a byproduct of their morphology. The scalenohedral and clustered forms of PCC fillers are particularly effective at scattering visible light. This occurs because light is most efficiently scattered when two conditions are met:
- The particles scattering the light are close in size to the wavelength of the light.
- The light is passing through multiple media (air, fibers, fillers, etc.), and these media have significantly different refractive indices. (A material’s refractive index is the relative slowing of the speed at which light travels through the medium vs. the speed at which light travels through a vacuum.)
Because structurally, “clustered” morphologies contain a significant fraction of open voids, the light striking a filled sheet alternately passes countless times through void space and solid calcium carbonate. Extensive work at Specialty Minerals Inc. has shown that the small size and large void-space fraction of clustered PCC will maximize opacity and brightness in paper.
Optical physics suggests that ideal light scattering can be obtained by using a particle roughly one-half the wavelength of visible light itself. This translates to particles about 0.2-0.3 micrometers (µm) in diameter—and also creates something of a “Catch-22” for solid ground calcium carbonate (GCC) particles or other pigment materials such as chalk, kaolin, and titanium dioxide (TiO2). In the absence of significant void volume, these particles must rely solely on their intrinsic size and refractive index to scatter light. But any solid particle small enough to provide ideal reflectance also becomes vulnerable to the dynamic environment of paper making, resulting in low particle retention. Put another way, the small size that is needed for optical purposes also can be the particle’s most serious weakness in terms of survivability.
Though scalenohedral PCC fillers typically exhibit average particle diameters in the range 1 to 3 µm, the discrete crystals emanating from the central core have diameters on the order of 0.2 µm. This, as noted, is perfect for light scattering, and, in turn, perfect for maximum brightness and opacity.
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