Surface roughness

Roughness refers to the uneven surface of paper or board. As already indicated, in theory, one cannot unambiguously define where the surface ends and the internal pore structure of paper begins. Roughness is especially significant in printing papers, graphical boards and many packaging boards. It affects optical properties such as gloss, the absorption of ink, and the required amount of coating. A rough base paper requires more coating to cover the surface, but some roughness is also necessary for good adhesion of the coating layer.

In offset printing, the viscous ink transfers to paper only in areas where the ink film makes contact with the paper. Surface depressions deeper than the thickness of the ink film remain uncovered. Lateral variations in roughness, such as the combined effect of poor formation and calendering, lead to print unevenness. In gravure printing, high roughness causes missing dots because paper must absorb the ink from raster cups. This is only possible with direct contact.

Definitions

Roughness is often divided into three components according to the in-plane resolution:

  • Optical roughness at length scales < 1 μm.
  • Micro roughness at 1 μm–100 μm.
  • Macro roughness at 0.1–1 mm.

Optical roughness relates to the surface properties of individual pigment particles and pulp fibres. It also affects paper gloss and absorption of fluids. Micro roughness in turn arises primarily from the shapes and positions of fibres and fines in the network structure. Macro roughness is the result of paper formation. Micro and macro roughness affect paper gloss and its uniformity. The printing and coating properties of paper depend more on macro roughness than micro roughness.

The root mean square (RMS) deviation of surface height is the most common measure of roughness. In the case of a line scan, the RMS roughness RRMS is given by

(1)

where L is the length of the measured line,
z(x) the local surface height, and
z0 the mean surface height.

Figure 1 defines other quantities characterising the topology of paper. They all measure roughness with respect to a plane and depend on the applied pressure. They have use in characterising the printing properties of paper where paper presses against a printing cylinder or plate. Paper can also acquire a flat cut-off surface in calendering.

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Figure 1. Various roughness characteristics that employ a reference plane.

The same measures are applicable even in the absence of a reference plane, but then one needs to define the local top height of the profile. For example, a tangent surface drawn through the highest peaks can define the reference level. In this way, one can, for example, determine the void volume to predict the consumption of coating colour. Definition of surface pit length can also use the mean height, in analogy to the microscale of formation. In parallel to many other cases, such as print quality characterisation, one can also use many other measures for a given surface map 1, z(x). In some cases, it might be of interest to look at the “lacunarity” of the map, of the typical size of the islands of height greater than some reference height z. Another possibility that draws analogies from the physics of interfaces is to look at the “two-point correlation function” measuring the RMS fluctuations of two points at distance y on the surface. This can also be conveniently obtained from the Fourier power spectrum of z(x).

Standardised measurement methods to characterise the surface properties of paper are described in Surface properties.

Sheet compressibility

Paper is very compressible in its thickness direction. The z-direction elastic modulus is 2 Ez= 10–50 MPa or less than one tenth of the in-plane elastic modulus. Even a small compressive pressure affects the measurement of thickness and roughness, and the measured values are valid only in applications where compression is low. For example, in a printing nip paper, thickness is smaller than the measured value.

A common belief is that paper compression occurs in the pores of the network while fibres are essentially incompressible. Figure 2 shows how both the surface roughness and the thickness of paper decrease when the compressive pressure increases. The compression therefore divides in some manner between the rough surface layers and bulk of paper.

Figure 2. PPS roughness (a) and apparent thickness of paper (b) as a function of clamping pressure using a logarithmic scale3.

The volume occupied by the internal pores of paper is Vp = V – Vf , where V is the total (apparent) volume of the sheet, and Vf is the constant volume of the fibres, measurable by immersing the sheet in a non-swelling, low-viscosity oil. Figure 3 shows that at small pressures, surface roughness decreases linearly with pore volume. At high pressures, surface pores are almost fully compressed but the compression of internal pores still increases.

Figure 3. PPS roughness vs. pore volume, V p for different pulps. Pore volume is expressed as a “void ratio”, V p / Vf where the volume occupied by fibres, Vf, is assumed constant in compression3.

At small and moderate compressive pressures, the changes in pore structure and roughness of paper are reversible. The original structure recovers when pressure is removed. At higher pressures, permanent deformations start to occur. The combined actions of heat and pressure promote permanent deformations. Supercalendering of paper makes use of this fact. Sometimes the apparently permanent compressive deformations recover because of moisture from printing or coating. This is surface roughening.