Optical Properties

1. Optical Properties

2. Introduction Optical properties such as color, opacity, brightness and gloss are important to users of paper and board grades. High opacity of printing papers is essential to printing papers, but glassine paper must be nearly transparent. The actual "whiteness" of paper determines how color inks will appear when printed. The papermaker must understand how sheet structure and composition determine the optical properties.

3. Experimental Characterization • Properties such as opacity and brightness, transmittance, gloss and color characterize the optical properties of paper. • Color depends primarily on the chemical compounds in paper. • Transmittance is not usually measured separately, but is calculated from reflectance values. • Sometimes a direct measurement is necessary. • Normal or diffuse illumination may be employed.

4. Reflectance, Brightness and Opacity • When light strikes a paper surface, some light is spectrally reflected and the remainder enters the sheet. • The light multiply scatters in all directions. • Some light returns vertically from the surface and the remainder in transmitted or absorbed. • Reflectance measurements can determine the reflected, transmitted and absorbed intensity.

5. Standards specify the procedures for reflectance measurements, including the spectral characteristics of the incident light. • Reflectance is usually measured using diffuse illumination and normal angle of detection as shown in Figure 1. • Opacity and brightness are the most important optical properties of paper. • Opacity measures the ability of the paper to conceal text on the other side of the sheet.

6. Brightness for papermakers is measured using the reflectance of blue light. • Blue light is used because even bleached fibers have a yellowish color, so that a “bluer” is generally interpreted as “more white”. • Color scientists use other colored light to measure brightness. • Some methods employ “white light” to determine brightness, while others are based on reflection of an idealized green light. • We can understand these better if we review some color theory.

7. The “Brightness”, or reflection factor R¥ is measured by adding sheets to a pile until there is no change to the intensity of reflected light at a wavelength of 457 nm. • R¥ is measured relative to a perfectly reflecting diffuser. • Opacity is determined by measuring the amount of light reflected by a single sheet, R0, when the sheet is backed by a perfect black background. • The opacity is then defined as the ratio R0/R¥. • Opacity could also be measured directly using a transmission densitometer.

8. Gloss • High print gloss generally needs a high gloss on the paper. • Uneven gloss, or gloss mottle, is often more noticeable than print gloss itself. • The apparent gloss of printed paper depends on both the illumination and the detection angle. • Thus, different angles may be used for gloss measurement. • At any given angle, gloss is defined as the ratio of specularly reflected light to incident.

9. Gloss depends significantly of the surface smoothness or roughness of the surface. • For goniophotometric measurements, the direction of incident and reflected light can be varied independently. • A sample reflectioncurve for 45° incidentlight is shown inFigure 2. • The nominal angle for paper gloss is 75° incident light, with very glossy papers measured at 20° while the nominal print gloss angle is 60°.

10. Papers have to be coated to achieve high gloss. • Higher coat weight givers higher gloss up to some saturation coat weight, where the gloss remains constant. • The average particle size and size distribution of the coating pigment is more important than actual shape of pigment particles. • Gloss for mixtures of two dissimilarpigments is shown in Figure 3.

11. Colloidal interactions and drying shrinkage of the coating may influence the packing disorder in the coating layer and its gloss. • The coupling between high gloss and low surface roughness explains the effect of coating on gloss. • Coating pigment particles are an order of magnitude smaller than fiber width or thickness. • Thus, they fill the surface crevices in the base paper. • The microroughness in coated paper is smaller than in uncoated paper.

12. Kubelka-Munk Coefficients • Consider a homogeneous sheet of material as shown in Figure 4. • The sheet contains particles that scatter and absorb light. • Specular reflection is ignored. • The particles are much smaller than the layer itself. • The light entering the sheet is assumed to be diffuse.

13. Kubelka and Munk one dimensional streams of light intensity, it and ir. • In any differential layer, dz, we have dir=-(S+K)irdz+Sitdz -dit=-(S+K)itdz+Sirdz where K is the absorption coefficient and S is the scattering coefficient. • Dividing the top equation by ir and the bottom equation by it yields dir/ir-dit/it=dlnir/it=-2(S+K)dz+S(it/ir+ir/it)dz

14. Setting r=ir/it, this becomes dr/[r2-2r(S+K)/S+1]=Sdz • We set z=b/r, absorb a factor of 1/r into K and S and integrate to obtain R0=(eSb(1/R¥-R¥)-1)/(1/R¥eSb(1/R¥-R¥)-R¥) where R¥ is given, by setting dr/dz=0, as R¥=1+K/S-(K2/S2+2K/S).5 The effective absorption coefficient (usually reported in m2/kg) is generally much smaller than the scattering coefficient, S, for most bleached paper grades.

15. K is typically smaller than 4 m2/kg, while S is often greater than 40 m2/kg. • The exact values depend on paper grade. • For K<<S, the equation for R¥ reduces to R¥=1-(2K/S).5 • From this it clear the the brightness is less than 100% only if the absorption coefficient K is nonzero. • The transmittance is given by a similar expression T=(1-R¥)2eSb(1/R¥-R¥)/[1-R¥2eSb(1/R¥-R¥)]

16. In practice, one doesn't measure the Kubelka-Munk coefficients. • Instead, the reflectances R0 and R¥ are measured and the coefficients S and K are calculated. • These are given by: S=ln[(1-R0R¥)/(1-R0/R¥)]/b(1/R¥-R¥) and K/S=(1-R¥)2/(2R¥) to slide 32

17. Multi layer Papers and Boards • The optical properties of multilayer papers are usually interpreted in terms of the Stokes equations. • These are, as illustrated in Figure 5 Tn+1=T1Tn/R1Rn Rn+1=R1+T12/(1-R1Rn) • The reflectance of the added layer can be different on different sides.

18. Physics of Light Scattering in Paper • The Kubelka-Munk theory is phenomenological and, thus gives no information about the actual physical light scattering in paper. • The physical description starts with the scattering and absorption of single particles, such as fibers, fines and fillers. • This includes light scattering at free particle surfaces and their interfaces. • Light scattering in paper is a multiple scattering process, because of the closely packed structure of paper.

19. Scattering from a Single Particle • Electromagnetic waves of light interact with all matter, because of electric charges at the molecular level. • The oscillating electromagnetic field of the incident light induces oscillations in the charges. • Depending on the frequency of the if the incident light, the oscillation occurs in electrons or nuclei. • The oscillating charges radiate electromagnetic energy in all directions.

20. Some of the oscillations may transfer the incident energy into other forms, such as thermal energy. • This corresponds to part of the light absorption. • The scattering properties of a material are described in terms of the complex index of refraction. n=n'+in" • The real part n' corresponds to the ordinary ray optics index of refraction that determines the deflection of light at interfaces according to Snell's law.

21. The imaginary part n" describes absorption. • In general n is a function of frequency. • The scattering field of a single particle is defined by Maxwell's equations that describe all of classical electromagnetic theory. • The Mie theory describes the exact solution for scattering from a single spherical particle. • A dimensionless particle size, x, is defined as x=pd/l where d is the diameter of the sphere and l is the wavelength of light.

22. The Mie theory employs two parameters, the albedo w and an asymmetry parameter g. • 1-w gives fraction that is removed from the incident beam and g is the average direction cosine of scattering. • Examples are given in Figures 6 and 7 for different values of the imaginary part n".

23. w is less than 1 for large values of n" and is depressed more for large x. • Even though (bleached) paper absorbs little light, so that w»1 for multiple scattering, a slight decrease from w=1 causes the brightness of a thick paper sheet to decrease. • Figure 7 shows that the asymmetry parameter decreases with increasing real part of the refractive index and decreasing size. • A decrease in g corresponds to a decrease in the Kubelka-Munk Scattering coefficient as we see on the next slide.

24. To calculate the Kubelka-Munk coefficients, we use the probabilities for forward and backward scattering respectively: p=.5w(1+g) q=.5w(1-g) • These equations hold for a one dimensional treatment, like the Kubelka-Munk theory. • The Kubelka-Munk coefficients then are S=q/c K=(1-p-q)/c where c (mass/area) depends on choice of units.

25. Note that the Kubelka-Munk theory considers one-dimensional light propagation. • The Mie theory allows light scattering in all directions. • The Kubelka-Munk theory defines all scattering as backscattering doesn't allow forward scattering. • Thus, the phenomenological Kubelka-Munk light scattering coefficient, S, is coupled with the absorption coefficient.

26. Multiple Scattering • Linear superposition can describe multiple scattering if the particles are sufficiently separated to treat them as independent scatters. • This is not true for paper and interference effects should be included. • The interference effects can be estimated from Maxwell's equations or using radiative transfer theory. • Maxwell's equations are intractable for paper, but radiative transfer theory yields simple solutions.

27. Paper Structure and Composition • The Kubelka-Munk theory does not explain how reflectance relates to optical properties of the constituent particles and packing structure. • For a sheet of pulp fibers, the Kubelka-Munk scattering coefficient reflects both single fiber scattering and bonding degree. • It is often useful to interpret the changes in scattering and absorption by explaining how papermaking variables control number of voids, surface area of scattering, number of small particles and total number of absorbing particles.

28. Fiber NetworkFiber Properties • The light scattering coefficient of unbonded fibers arises from the specific surface area, or surface area per unit mass. • Figure 8 shows that the light scattering coefficient, Sp, of chemical pulp fibers is high for small cell wall thicknesses, such as for springwood fibers.

29. Mechanical pulp fibers scatter less then chemical pulp fibers, because of their lower specific surface area. • However, the more porous and bulky sheet structure of mechanical pulp fibers counteracts this difference. • Mechanical pulp fines are often coarse and stiff compared with chemical fines. • The apparent density of a sheet made entirely of chemical pulp fines can be more than 1200kg/m3. • Mechanical fines give a density of approximately 500 kg/m3.

30. The fines fraction of mechanical pulp has a strong effect on light scattering because the fines retain some open structure. • The light scattering coefficient, Sf, of unbonded mechanical pulp fines can be > 100 m2/kg. • Fines from chemical pulps bond almost completely and Sf can be as low as 5m2/kg. • The density of paper increases when adding chemical pulp fines, but the light scattering coefficient changes very little. • Addition of mechanical pulp fines has a similar, but smaller effect on density.

31. At high fines content, the density becomes constant for mechanical pulps. • The light scattering coefficient increases systematically at high mechanical pulp fines as shown in Figure 9. • The Kubelka-Munk absorption coefficient depends mainly on the degree of bleaching.

32. For high yield pulps, K increases with yellowing. • The concentration of yellowed compound has nearly linear relationship with the absorption coefficient. • The same is not true for brightness, because R¥ is a nonlinear, but explicit function of K. • When adding dye to a paper, brightness decreases considerably more when the original brightness is 90% than when it is 75%. • This effect can be seen from the equation for K in terms of R¥.

33. Beating and Wet Pressing • Increased beating of chemical pulp or wet pressing reduces the free surface area, so the light scattering coefficient decreases. • Paper density and bonding decrease simultaneously. • Figure 10 illustrates this for high yield chemical pulps with different degrees of delignification.

34. For a typical chemical pulp, with low lignin content. the data for beating and wet pressing fall almost on a single curve, except for high beating levels. • For high yield, high lignin, chemical pulps, the effects of beating and wet pressing are not the same. • Beating and wet pressing still increase density as expected, but at a low level of wet pressing, the light scattering coefficient increases with beating. • At a high level of wet pressing, the increase in fines content from beating has no effect on scattering.

35. The effect of cell wall thickness on light scattering may almost disappear in paper made from beaten pulp as suggested in Figure 11. • Another issue is fiber collapse that reduces the light scattering coefficient more for paper made of thin walled fibers than in paper made of thick-walled fibers. • The relationship between bonding, surface area and light scattering coefficient has been used to determine the RBA. • This calculation uses plots of S against tensile strength to find S for unbonded fibers.

36. Pulp Mixtures • We assume the Kubelka-Munk coefficients satisfy a linear mixing rule S=SfiSi K=SfiKi where fi is the mass fraction of pulp i. • This reasonably accurate for K, but not necessarily for S. n i=1 n i=1

37. Fillers • The main purpose of adding fillers to paper is to improve optical properties. • The light scattering surface of paper increases as bonding degree decreases. • Filler particles have higher specific surface area than fibers. • Filler to fiber interfaces scatter little light because the n' for most fillers is very near that of fibers (~1.55). • Some specialty pigments, such as TiO2 have a high refractive index (n'=2.55).

38. The shape and size of particles and their degree of packing and aggregation have a complicated effect on light scattering. • The most common fillers are clay and calcium carbonate. • Calcium carbonate gives higher brightness and more opacity than clay because of higher light scattering coefficient. • Common forms of calcium carbonate are refined limestone and precipitated (PCC). • Talc is also used as a filler.

39. The average particle size of fillers varies from from .2m to a few m. • They are much smaller than fibers and fines. • Small particle size and large specific surface area give good opacity. • A narrow particle size distribution and low degree of agglomeration promotes light scattering. • Microvoids inside of filler particles have a similar effect. • PCC and TiO2 have small absorption coefficients and brightness near 100%.

40. Clay, talc and refined CaCO3 have a brightness of about 80%. • Talc particles have a planar shape that increases gloss of calendered paper more than other fillers. • The effect of filler on light scattering can be determined two ways. • One utilizes a layer of filler particles on a glass plate. • The other utilizes the linear mixing rules for light scattering coefficient and absorption.

41. The calculations are repeated for different filler contents, because the result depends on filler content. • This is due to two phenomena. • First, the filler causes some fiber debonding that contributes to the light scattering of the filled sheet. • Second, with increasing filler content, the filler particles aggregate. • This makes the fibers less effective in light scattering as shown in Figure 13.

42. Coating • Paper and board grades are coated primarily to improve printing properties. • Coating improves printing because it increases opacity, brightness and gloss. • The coating weight, pigment type and binders control the properties of the coating layer. • Mixtures of different pigments are often used. • The average size and size distribution of particles, particle shape and amount and type of filler are important.

43. Applying coating to polyester film allows study of the light scattering properties of films of coating films themselves. • As shown in Figure 14, the scattering coefficient can be more than 220 m2/kg. • The scattering coefficient correlates with porosity and pore size distribution. • When pigment particles become smaller and their number increases, the number of voids, the specific area and the light scattering coefficient increases.

44. The light scattering coefficient depends on wavelength of light used if there is a large number of voids whose size is comparable to the wavelength of light. • Figure 15 shows the importance of the particle packing. • The figure also shows the breakdown of the linear mixing rule for light scattering coefficient.

45. Gloss and Roughness • Glossy paper has a high specular reflectance. • Gloss results from a combination of micro roughness and optical roughness. • A very smooth, but dull paper can be made if the micro roughness is small, but the coating particles are large. • The coating particles give high optical roughness and hence diffuse reflection.

46. Micro roughness influences gloss because tilted surface facets reflect light in different directions, as illustrated in Figure 16. • A narrow distribution of surface gradients gives high gloss, while a wide distribution gives very diffuse reflection. • Micro roughness also causes anisotropy in gloss, because light incident in CD encounters more titled fiber edges than light in MD, as illustrated in Figure 17.

47. The scale of optical roughness is the same order of magnitude as the wavelength of light. • Optical roughness causes light diffraction. • The total reflection of light from a surface of normally distributed height is RF=R0exp[-(4ps)2/l2]+ 32R0/m2(ps/l)4(Dq)2 where l is the wavelength s is the RMS roughness m is the mean gradient of the surface R0 is the reflectivity of fibers or coating and Dq is the solid angle of measurement. • The 1st term is specular and the 2nd is diffuse.