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Paper Bulk and Surface

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  1. Paper Bulk and Surface

  2. Introduction We now consider macroscopic bulk and surface properties of paper. Macroscopically, the density, bulk, porosity, and thickness characterize the physical appearance of paper. At the next level we need to consider the distribution of fibers, fillers etc. We also need to consider the variation of mass density in the thickness direction. These are difficult to measure.

  3. The roughness of paper surface is very important, particularly for printing papers and boards. These are often coated to improve properties. For these, the amount of coating color depends on the roughness of the base sheet. Effects of local compressibility are also very important. Surface chemistry is the primary determiner of the friction of paper. The surface topology is not important.

  4. Bulk Properties • It is very difficult to measure the true thickness of paper because of the rough surface. • Density is important because it can be used to estimate other properties, such as tensile strength, elastic modulus, and light scattering. • These also depend on how the density was achieved from fibers, pigments and refining. • The z-directional structure and material distribution affect paper properties, including bulk, bending stiffness, optical properties and surface roughness.

  5. Definition of Density, Bulk and Porosity • The density of paper is just the ratio of basis weight and thickness = b/d • The specific volume, called bulk, is the inverse. • If we consider the paper as the mixture of two pulps, the density is given by  = (M1+M2)/(V1+V2), where Vi and Mi are the volumes and masses of the corresponding pulps.

  6. Since V1+V2=M1/1 + M2/2, the bulk is given by 1/r = x/r1+(1-x)/r2, where x=M1/(M1+M2) is the mass fraction of component 1. • This suggests a linear mixing rule for bulk. • Figure 1 shows that, in reality, either bulk or density exhibit small deviations from a linear mixing rule.

  7. The porosity, f, is used to describe solid materials that have some open volume regions. • It is the ratio of pore volume to total volume where V is the volume of the sheet, Vf is the volume of fibers, r and rf are the paper and fiber wall densities.

  8. The porosity includes the porosity of the cell wall along with that due to the uncollapsed lumen space of fibers. • Thus the fiber density is of order f= 1000 - 1100 kg/m3. • To obtain the true density of paper, it is necessary to measure the average thickness at sufficiently fine lateral resolution. • Preferably, the measurement would give the volume that excludes surface depressions, but includes the pores behind surface overhangs.

  9. This is illustrated in Figure 2. • Even this effective may not correctly characterize a homogeneous paper material such as might be sectioned from a larger 3-d body. • Thus we see that an unambiguous definition • cannot be given for the density and porosity of paper.

  10. Measurement of thickness • As indicated in the previous section, the paper thickness difficult to define unambiguously. • The most common thickness of measurements for paper are the apparent thickness, dapp the piling thickness dpile and the effective thickness deff. • The apparent thickness is the value ordinarily quoted for paper and board. • The apparent thickness is measured with a hard platen that is large compared with the fiber dimensions.

  11. To avoid sheet compression, the applied total pressure is about .1 MPa. • This is close to the maximum local thickness as shown in Figure 3. • Corresponding to this are apparent density and and apparent bulk values. • The piling thickness is used when one needs to estimate the thickness of a book if printed with a given paper.

  12. One measures a thick pad of paper with the same instrument as used for apparent thickness. • The piling thickness is always less than the apparent thickness, because the surfaces of adjacent sheets conform to one another. • The effective thickness is measured using soft rubber platens. surface profilometry or mercury displacement. • The effective thickness can also be calculated from bending stiffness Sb and tensile stiffness St.

  13. This is given by • The tensile stiffness is measured from load elongation measurements. • The corresponding elastic modulus, E, is obtained from E=St/d • The soft rubber platen method uses a standard thickness gauge equipped with rubber platens. • Calibration is an issue, because of the properties of rubber.

  14. The mercury displacement method depends on the fact that mercury doesn't penetrate paper in the absence of external pressure. • This is illustrated in Figure 4. • The method is very time consuming and is primarily used to calibrate other thickness measurements.

  15. Since the measurement methods for deff are difficult to implement, it is often necessary to use empirical methods to estimate deff from dapp or dpile. • The apparent thickness is typically 10-20% higher than the effective thickness, depending on the grade. • For very smooth papers, such as super calendered, dapp and deff are nearly equal. • The difference between the two depends on the basis weight and furnish.

  16. Figure 5 shows a basis weight series where the apparent thickness was linear in the basis weight. dapp=kb+a • The intercept a, arises from the surface roughness. • It is plausible to interpret kb=deff or k-1=reff. • For thick papers or board, we have dapp=deff.

  17. Measuring z-directional Distributions • The small thickness of paper complicates the analysis of the z-directional distribution of material in paper. • The resolution and repeatability are often lower than for in-plane properties. • Table 1 lists some measurement and sample preparation techniques. • The details are given in the references.

  18. Section block faces and thin cross sections with a light or a scanning electron microscope (SEM). • For microtome sectioning, it is necessary to cure the sample material into an embedding medium, such as an epoxy resin. • Split layers and in-plane ground surfaces give material for measurements of ash content and fines content, chemical composition, in-plane fiber orientation, etc. • Dry grinding devices remove layers from a paper or board sheet on a flat suction table.

  19. Freeze-splitting or tape-splitting splits specimens into roughly two halves. • Repeating this procedure makes possible separating possibly more than 8 layers. • This method is illustrated in Figure 6. • Optical sectioning uses a confocal laser-scanning microscope (CLSM). • The natural opacity of paper limits this method.

  20. Examples of z-distribution • The distributions of mass, fines, fillers, and size describe the z-directional structure of paper. • These distributions strongly depend on the furnish and on the forming unit and press section of the paper machine. • For multi-layered board grades, using mechanical pulp in the middle layers, and well-bonding chemical pulp in the surface layers can increase bending stiffness. • The surface layer composition can control the brightness and color.

  21. The target in papermaking is to have middle layers with low density and surface layers with high density. • This provides good smoothness, printability, and bending stiffness. • A parabolic density distribution can be obtained by wet pressing, forming or calendering. • When wet pressing employs fast high-pressure pulses, the local density increases in the direction of water removal.

  22. Slow low pressure pulses do not effect the density distribution as illustrated in Figure 7. • In the forming section, variations in drainage rate affect the density distribution. • Pronounced density profiles can be obtained with multi-ply forming. • High fines concentration at sheet surfaces improves smoothness, printability, and bending stiffness.

  23. Good print quality, low linting, and high resistance to water roughening will result. • Continuous one-sided drainage, as in a Fourdrinier, leads to a gradient of fines concentration that increase in the direction of the drainage. • For papers of high filler content, such as supercalendered printing papers, the filler in the z-direction is essential for good paper properties.

  24. An even distribution offers good mechanical, optical, and printing properties, but it may cause linting. • Examples of filler distributions are shown in Figure 9. • Fillers do not readily adhere to fiber surfaces, so the depletion effect at sheet surfaces is more important than with fines. • Retention aids are used to control the retention of fillers and fines.

  25. Sizing can be added to the stock, or applied to the web surface. • When applied to the web surface, the penetration depth depends on application technique, size viscosity, etc. • A conventional size press gives a uniform distribution. • A roll and blade application leaves the size at the surface. • This is desirable to avoid linting and other surface problems.

  26. Surface size may have a positive contribution to bending stiffness. • Iodine staining can distinguish starch size from fibers and fillers. • When inspected under a light microscope in diffuse light,starch has a dark tone, while fibers and voids are almost invisible. • This is illustrated in Figure 10. • The starch distribution is determined by image analysis.

  27. Surface Roughness • Roughness is especially significant in printing papers, graphical boards, many packaging boards. • It effects optical properties such as gloss, absorption of ink, amount of coating necessary. • A rough base paper requires more coating to cover the surface, but some roughness is also necessary for good adhesion of the coating layer.

  28. In offset printing, the paste ink transfers only where the ink film is in contact with the paper. • Surface depressions deeper than the thickness of ink remain uncovered. • Lateral variations in roughness, such as the combined effect of poor formation and calendering lead to print mottle. • In gravure printing high roughness causes missing dots because paper must absorb the ink from the ink cells. • This requires direct contact.

  29. Definitions • Roughness has three components. • Optical roughness at length scales <1 m. • Micro roughness at 1um – 100 m. • Macro roughness at 0.1-1 mm. • Optical roughness relates to the surface properties of individual pigment particles and pulp fibers. • It also affects paper gloss and absorption of fluids.

  30. Micro roughness arises primarily from the shapes and positions of fibers and fines in the network. • Macro roughness is the result of paper formation. • Micro and macro roughness affect paper gloss and its uniformity. • Printing and coating properties depend more on macro roughness than micro roughness.

  31. Root mean square (RMS) roughness is given by • RRms2 = where L is the length, z(x) is the local surface height and z0 is the mean surface height. • Other quantities of interest are defined in Figure 11. • They all measure roughness relative to a plane. To slide 36slide 37 slide 39

  32. Measurement Methods • Profilometry • Scanning surface profilometry gives the complete topology of micro roughness. • This is illustrated in Figure 12 below. • One can also useoptical distancesensors alongwith triangulationor autofocusing. • In triangulation, a narrow laser beam reflects from the surface and hits the detector at a point.

  33. The point of contact depends on the distance from the surface. • In autofocusing, the objective is moved until the surface is in focus and gives the smallest spot on the detector. • The position of the objective determines thesurface height. • These methodsare comparedin Table 2 at right.

  34. Indirect Measurements • The Bendtsen method uses a hard ring and gives a flow rate. • The ring is does not conform to the surface. • This method detects macro roughness and corresponds to hard nips such as in printing. • The Parker Print Surf (PPS) method uses a soft measuring head that partially conforms to the paper surface. • This method is primarily sensitive to micro roughness.

  35. This method measures the flow rate (ml/min) of air that is forced through the space between paper surface and the ring placed at the high points of the surface. • It gives the result of mean separation as defined in Figure 11. • The PPS roughness, G, is given by G=kQ1/3 where k is a geometric constant and Q is the air flow rate.

  36. The major disadvantage of air leak methods is that air flows not only between the measurement head and the paper, but also through the bulk of the paper. • Thus, the PPS roughness gives only a fair correlation with the profilometric roughness as shown in Figure 13. • The optical contactratio, defined inFigure 11gives another measureof roughness.

  37. The Chapman smoothness, as shown in Figure 14, determines the contact ratio with a glass prism pressed against the paper surface. • In the areas where paper does not contact the prism, the light is totally reflected. • In contact areas, light is refracted into the paper because the refractive index of glass is near that of the fiberwall material. • The reflectedlight intensity isproportional tothe contact area.

  38. The contact image can also enable measurement of the surface pit length, defined in Figure 11. • Because of the hard glass surface, the method is sensitive to the macro roughness. • For all of the indirect methods, the paper surface is under compression. • The actual compressive pressure depends on the measurement.

  39. Sheet Compressibility • Paper is very compressible in the thickness direction. • Ez = 10-50 MPa or less than 1/10 of the in-plane elastic modulus • Paper compression occurs generally in the pores of the network. • Fibers are essentially incompressible by comparison.

  40. Figure 15 shows that the surface roughness and the thickness of paper decreases under compressive pressure.

  41. The volume occupied by internal pores of paper is Vp=V-Vf where V is the total volume and Vf is the volume of fibers. • At low pressures, surface roughness decreases linearly with pore volume, as shown in Figure 16. to slide 49

  42. At low and moderate pressures, changes in pore structure and roughness of paper are reversible. • The original structure recovers when pressure is removed. • However at higher pressures, permanent deformation starts to occur. • The combined actions of heat and pressure promote permanent deformations. • Supercalendering of paper takes advantage of this fact.

  43. Effect of fiber properties • The Poisson distribution of surface suggests that in a first approximation, all fibers make the same contribution to thickness and surface height is proportional to local basis weight. • This implies the following estimate of the RMS thickness: Rrms = where N is the average number of fibers under the measured head of area A, b the basis weight of paper, deff the effective thickness of paper and mf the mass of a fiber.

  44. As seen in Figure 17, at a given weight, the roughness increases with increasing fiber mass and paper thickness. • Long fibers give high roughness because of the high mass. • Long fibers are often more coarse than short fibers • Paper thickness increases with fiber coarseness through reduced fiber flexibility.

  45. Coarse fibers yield particularly rough paper surfaces. • For chemical pulps, hardwood should give better smoothness than softwood and groundwood should be better than TMP. • Beating reduces paper roughness through the decrease of paper thickness deff.

  46. For mechanical pulping, refining increases the relative proportions of short fibers that in turn reduces roughness through the lower average mass as shown in Figure 18.

  47. Papermaking effects • Roughness of paper is controlled by calendering. • Uncalendered paper is unsuitable for most applications, especially printing. • Using a calender or supercalender can produce the smooth surface required. • Pigment sizing, or coating, reduces roughness because small particles fill voids on the base paper surface.

  48. Smaller effects arise from formation and wire marks on macro roughness and drying on micro roughness. • In calendering, surface roughness decreases proportionately more than thickness. • Surface layers have higher compressibility as shown in Figure 16. • In principle, strong calendering could remove all roughness, but this is impossible without simultaneous loss of paper thickness.

  49. Figure 19 shows how coarse latewood fibers gave higher density than earlywood fibers at the same PPS. • The opposite is true for uncalendered paper. • Beating of the latewood fibers increased the uncalendered to 430 kg/m3, with only a mild effect on the calendered density. • Thicker areas compress more and lose more porosity and opacity than thin areas, which are rougher.