New Insights into Coating Uniformity and Base Sheet Structures

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MATERIALS AND INTERFACES New Insights into Coating Uniformity and Base Sheet Structures Christina Dahlstro¨m* and Tetsu Uesaka Department of Natural Sciences, Engineering and Mathematics, Fibre Science and Communication Network, Mid Sweden UniVersity, Holmgatan 10, 851 70 SundsVall, Sweden

Base sheet structures, such as surface roughness and mass density distribution (formation), have been known to affect coating uniformity. However, the literature is not necessarily consistent in determining which structure controls coating uniformity. This study employed scanning electron microscopy (SEM) and image analysis, combined with autocorrelation and frequency analyses, to investigate the fundamental mechanisms of coating and to resolve some of the controversies in the literature regarding the base sheet effects. The results showed that coating thickness variation resembles a process of random deposition with leveling. At small length scales (in the size of fiber width), leveling causes a very strong dependence of coating thickness variations on the surface profile of the base sheet, whereas at larger length scales, coating thickness variation diminishes in its intensity by the same leveling effect, but still retains a significant correlation with base sheet structure, particularly formation. Frequency analyses clearly showed that the discrepancies in the results for the base sheet effects in the literature are due to the length scales used in the experiments, that is, the sampling area and the resolution of the measurements. 1. Introduction In paper coating, base sheet is coated with pigment slurry to reduce surface roughness and enhance optical properties and print performance. Print quality demands for coated papers are steadily growing, and achieving coating uniformity is crucial for high image sharpness, color fidelity, and print uniformity.1,2 The coating uniformity includes both the uniformity in coating thickness and the uniformity in internal coating structures, including chemical composition (Figure 1). Although this distinction may seem trivial, it becomes important when one investigates the basic mechanisms of coating uniformity, as discussed later. In this Article, we focus our discussions only on coating thickness (or mass) uniformity. The coating uniformity is generally governed by, for example, the coating methods, base sheet properties, coating rheology, and the drying methods.3,4 The base sheet is one important factor, and it is often believed that the coating uniformity is controlled by fiber mass distributions (so-called “formation”) of base sheet. However, a close examination of the literature shows that the direct data supporting the above statement are surprisingly scarce and sometimes inconsistent. Huang and Lepoutre used the burnout test to evaluate the coating uniformity using two base sheets with different formation.5 The burnout test is a practical method to evaluate coating thickness uniformity at a glance, particularly at a large scale.6 The sheets with worse formation showed greater coat weight variations at a coat weight of 12 g/m2, whereas at the lower coat weight of 8 g/m2 there was no clear effect of formation. Huang and Lepoutre also compared smooth, dense base sheets with rough, porous base sheets, both of which were blade-coated with approximately 8 g/m2 coat weight.7 Coat weight distributions were again measured by using the burnout test at length scales larger than 500 µm. It was found that coating uniformity was superior for smooth and dense sheets. * To whom correspondence should be addressed. Tel.: +46 (0)60 14 88 13. Fax: +46 (0)60 14 88 20. E-mail: christina.dahlstrom@ miun.se.

Tomimasu et al. used an electrograph method, in which electrons transmitted through the paper sample are detected on an electron microscope film, and a surface profilometer to examine the effects of base sheet structures on coat weight distribution.8 Four commercial newsprints made on different formers were coated, and electrographs were taken before and after coating. Local coat weight correlated to local basis weight of the base sheet at large length scales (a resolution of 800 µm). At small length scales (a resolution of 100 µm), however, it was the base sheet roughness that correlated with coat weight distribution. Matsubayashi and co-workers used spectrophotometer equipped with a scanning X-Y stage to study the relationship between base paper formation and coat weight distribution (resolution >1 mm).9 The method enabled measurements of coat weight distribution and sheet formation at the same area. High coat weight appeared to occur in areas of low basis weight (correlation ∼50%). Gane et al. introduced Walsh analysis, using profilometer and optical imaging data, as a tool to investigate how the base sheet surface profile affects coating thickness distribution.10 The total sampling length used to perform Walsh analysis was only 128 µm, but can easily be extended for larger length scale analyses.

Figure 1. These images were obtained using a scanning electron microscope (SEM), and they represent cross sections of a coated paper. The left image illustrates the coating thickness, and the right image shows the internal coating structure. The base sheet was made from chemical and mechanical pulp, and the coating pigments were clay and calcium carbonate.

10.1021/ie900819c CCC: $40.75  2009 American Chemical Society Published on Web 10/05/2009

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Figure 2. The left image represents level coating, and the right image corresponds to contour coating. Note that the wavelengths of the base sheet surface profile are different between the left and right figures.

Zou et al. used SEM, combined with image analysis, to perform direct local mapping of coating thickness and base sheet structures (e.g., mass density, surface height, and porosity).11 Among the measured base sheet structure parameters, the local coating thickness showed the strongest correlation to the base sheet surface profile (i.e., surface height), explaining about 50% of the coating thickness variations. The mass density (formation) and porosity, however, had much weaker correlation to coating thickness than the surface height. (In this analysis, the base sheet surface profile was measured using a reference line defined for each SEM image of 300 µm in length. Therefore, variations greater than 300 µm were not captured.) Dahlstro¨m et al. further analyzed the local correlations between coating thickness and base sheet structures using a similar SEM/image analysis technique with band-pass filtering.12 They showed that, at small length scales in the order of fiber width, the coating mechanism was “level coating” (sometimes called void filling), and thus surface height had a very high correlation with coating thickness. At larger length scales, however, the coating mechanism became almost “contour coating”, that is, resulting in uniform coating thickness (Figure 2). Wiltsche and co-workers extended a similar cross-sectionanalysis concept into 3D by using an automated serial sectioning method in combination with light microscopy.13 They found that the blade-coated sample showed an almost ideal levelcoating behavior. However, in that study, the samples chosen were calendered, and the base sheet surface profile and the coating thickness variations may have been altered in that process. These results clearly suggest that, depending on the measurement methods and length scales captured, the conclusions are different. The burnout test, for example, is not a direct measurement of coating thickness but a reflectance measurement, which is influenced by the optical properties of the coating layer, such as coat weight and scattering coefficient, and of underlying charred base sheets. In addition, it cannot detect small-scale variations, for example, less than 500 µm where most of the coating thickness variations occur.8,11,12 On the other hand, the SEM/image analysis technique directly determines the coating thickness variations, together with other structural variables of the base sheet, with much less than 1 µm resolution. It is, however, time-consuming to determine the large length scale variations of more than say 6 mm, even with an automated image analysis system. This limitation may be critical if the large-scale, coating thickness variations control end-use performance. Engstro¨m et al. showed a good correlation between the coefficient of variation of coating mass measured by a soft X-ray technique and print mottle in the 2-4 mm range.4 The comprehensive reviews of coating uniformity and base sheet effects and the measurement methods are given by Engstro¨m.3,14 Although the literature is pointing toward base sheet surface roughness as one of the controlling factors of coating uniformity, the results for the effects of formation are not consistent and need to be examined in a systematic manner. There still remains the question of what controls coating uniformity in the larger length scales. (Here, we define a small length scale as the scale

Figure 3. SEM image of a paper cross section (top) and the corresponding binary image (bottom) of the coating layer. The measurements are done pointwise along the x-axis on the binary image.

of the order of fiber width, and a “large” length scale as the scale much larger than the fiber width. “Large” length scale may often refer to the size of fiber flocs. However, fiber flocs are a subjective entity whose length scale in reality spans continuously from less than one millimeter to a few centimeters. It is difficult to pinpoint a specific length scale, unless one takes into account the sensitivity function of human visual system to spatial frequencies.15 We, therefore, avoid using the floc size to define the “large” length scale.) In this Article, coating thickness variations are revisited from the point of the stochastic nature of the process, and the objective is to find base sheet properties that control coating uniformity. 2. Materials and Methods 2.1. Scanning Electron Microscopy and Image Analysis. Characterization of the paper structures was made by scanning electron microscopy (SEM). Paper samples for cross section analyses were cut in 1 × 2 cm2 pieces at two random positions from the original sheet. The paper samples were placed vertically in spring holders and immersed into a mold.16 The samples were embedded with a low viscosity resin and cured overnight in an oven at 68-70 °C. The cured block was dryground by hand with 320, 500, 1200, and 4000 grit SiC-paper and then etched for 15 s with an etching solution17,18 to smooth the surface for image analysis. The block was finally carboncoated to obtain an electrically conducting surface. Digital images of the paper cross sections were obtained using the scanning electron microscope LEO 1450EP. Backscatter images were generated using 10 kV accelerating voltage and 8 mm working distance. A number of images were taken in a sequence giving a total length of approximately 6 mm for each sample, with a resolution of 0.155 µm (image width ∼40 000 pixels). The results presented are averages of the two images for each coat weight. The digital images were stitched together using ImageJ software. The local structure parameters measured were coating thickness, coating surface profile, base sheet thickness, base sheet surface profile, mass length, and pore length according to the method developed by Allem.19 (This method was later extended and further developed by other researchers.20-22) Figure 3 shows a typical SEM image of a paper cross section and the corresponding binary image of the coating layer. The measurements are done pointwise along the x-axis of the binary image. An advantage with this method is that one can not only determine coating thickness variations, but also precisely map the local coating thickness onto the underlying base sheet structures. One deviation in the procedure from the previous work19 is the pointwise measurements, and also that the coating thickness was computed by subtracting the coordinates of the interface between the coating and the base sheet from the surface coordinates of the coating layer. The first pixel with value 255

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Figure 5. The left plot shows the shot noise process, that is, random deposition process, and the right plot is its corresponding autocorrelation function.

Figure 4. A typical power spectrum of coating thickness variations. The two data series correspond to the paper sample with coat weight 22 g/m2.

(white), that is, the base sheet adjacent to the coating, determines the interface between the coating layer and the base sheet. 2.2. Samples. The base sheets used in this study were obtained from a LWC paper mill and were produced from 40% kraft and 60% groundwood (GWD), with a basis weight of 40 g/m2. The base sheet was coated on one side only (felt side) with a GCC coating color using a cylindrical laboratory coater (CLC-6000) at a speed of 800 m/min. The coating formulation was made from 100% GCC (96 wt % of less than 2 µm particles) and 8 pph SBR latex (Dow CP-692 NA). Solids content of the coating color was 60%, and the coat weights were 12 and 22 g/m2. Viscosity was 210 mPa s (Brookfield at 100 rpm), and the pH was adjusted to 8. The same coating formulation was used for both coat weights, only the blade pressure was varied to obtain the different coat weights. Figure 4 shows a typical power spectrum of coating thickness variations, and the data series correspond to the two samples analyzed with coat weight 22 g/m2. In the longer wavelengths, there is a difference between the two samples due to some wrinkles and coating streaks, which were revealed after visual inspection of the sample and inspection of its burnout images.23 2.3. Data Analysis. Each data set is approximately 6 mm in length, and the wavelength components larger than the data length were filtered out. Finite sample length sometimes creates artifacts in the longer correlation lengths. To avoid the effects of finite sample length, a reflection image of the original data set was added at both ends of the original data set. Autocorrelation Functions. The variations of many of the paper structures are often of random, rather than periodic, nature.11 It is, therefore, appropriate to characterize the variations in terms of the autocorrelation function RXX(ξ), as defined by eqs 1 and 2:24 RXX(ξ) ) E[X(x)X(x + ξ)] ) N-ξ-1

1/(N - |ξ|)

∑

XnXn+ξ ξ g 0

Figure 7. The autocorrelation function for the LWC paper sample with coat weight of 12 g/m2 (left) and the magnified function in the neighborhood of ξ ) 0 (right).

subsequent redeposition of the particles toward the lower height area, that is, “levelling”. The mountain-shape response function of each shot noise in Figure 5 represents the probability of redeposition.25 Suppose an “imaginary particle” randomly deposits with the average frequency λ (the number of deposition per length) and the leveling takes place with an equal probability within the distance ω and the height h0, the autocorrelation function is given by eqs 3 and 4.25 Figure 6 shows an example of the autocorrelation function of a shot noise process, where the response function has a box shape. R(ξ) ) h20λ2ω2 + h20λ(ω - |ξ|) |ξ| e ω

(3)

R(ξ) ) h20λ2ω2 |ξ|>ω

(4)

(1)

n)0

RXX(ξ) ) RXX(-ξ) ξ < 0

Figure 6. An example of the autocorrelation function of a shot noise process, where the response function has a box shape.

(2)

E[] denotes the expectation (mean operator) of the random process X, ξ is the lag, x is the position, and N is the length of vector X. Different classes of random processes show unique signatures in the autocorrelation function. Figure 5 shows an example of autocorrelation function of the shot noise process, whose signal is the accumulation of shot noises that occur randomly on the time axis.25 As will be discussed later, this example is particularly interesting from the point of coating. Coating may be regarded as the random deposition of coating color (pigments) and the

3. Results and Discussion 3.1. Nature of the Variations of Coating Thickness and Base Sheet Structures. Figure 7 shows a typical autocorrelation function for coating thickness variations of the LWC paper sample of coat weight 12 g/m2. Comparing this autocorrelation function with that of Figure 5, we find that the coating process closely resembles the shot noise process, that is, a random deposition process. Further, a close examination of the peak (the right plot of Figure 7) reveals that there is a finite correlation length, which is easily resolvable by the present method. Suppose we approximate

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Figure 8. The autocorrelation functions for the LWC paper samples with coat weights of 12 and 22 g/m2.

Figure 9. The top images show the leveling mechanism on a rough surface, where the particles are redistributed toward the lower height areas. The corresponding mechanism on a smooth surface is illustrated in the bottom images, where the redistribution of particles smooths the surface. Table 1. Different Parameters Obtained from the Autocorrelation Function sample 2

LWC, coat weight 12 g/m LWC, coat weight 22 g/m2

λ (m-1)

ω (µm)

h0 (µm)

h0ωλ (µm)

92 000 224 000

21.4 27.9

2.76 1.91

5.43 11.9

the peak shape as a triangle, we can estimate the parameters, ω, h0, and λ in eq 3 from Figure 8, as listed in Table 1. First, the correlation lengths ω (21.4 and 27.9 µm) are in the order of fiber width, which is understandable because most of the leveling of coating suspensions, that is, lateral flow from the peaks down to the valleys during the consolidation (Figure 9), occurs in this length scale. For the higher coat weight (22 g/m2), ω was longer and h0 was lower. This result may be explained by the fact that for the higher coat weight there is more time available for leveling before consolidation. The average number of deposition, λ, increased with coat weight, as expected. Figure 8 shows the autocorrelation functions for the paper samples with coat weights of 12 and 22 g/m2. The heights of the plateaus in the autocorrelation functions for coating thickness are given by h02ω2λ2 (Figure 6), where h0ωλ is the average coating thickness. Kartovaara26 determined the coat weight variations by β-radiography (a resolution of 1 mm) and noted that the standard deviation of coat weight increases with average coat weight, but reaches a plateau at around coat weight 13-15 g/m2. This observation is consistent with the fundamental properties of the random deposition process with local leveling. For example, Baraba´si and Stanley showed that random deposition with “surface relaxation” (or redeposition, i.e., leveling) yields a plateau value of the standard deviation of the thickness variation as the total number of depositions increases.27 Although leveling or surface relaxation is a local effect, it can propagate in a longer distance, depending on the system size, as the total number of deposition increases.

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Figure 10. The autocorrelation function is shown for the base sheet surface profile, LWC paper sample with coat weight of 12 g/m2.

If the coating process is described as the random deposition with surface relaxation, the effect of leveling may be observed mainly in the small length scales, and in large length scales with a much smaller magnitude. The same phenomenon is explained by the surface-tension-driven leveling mechanism.28 For instance, surface tension is proportional to surface curvature. Surface curvature tends to be higher at smaller length scales than at larger length scales because of the presence of surface voids. Therefore, the surface tension, and thus leveling effect, are more evident in smaller length scales, but leave a trace in larger length scales. This will be further discussed in the subsequent section. The autocorrelation functions were also determined for the base sheet structure parameters. The mass length variations (i.e., the formation) were found to follow the shot noise process, as expected from the basic mechanism of paper making (random deposition of fibers). The base sheet thickness and pore length had the same stochastic property, that is, random deposition process, as the mass length. The fact that the coating thickness variations and the mass density variations (formation) share the same stochastic properties has an important implication. Like formation, coating thickness variations have a long tail in a long wavelength range in their power spectrum and will exhibit “flocs”-like structures macroscopically29 (e.g., in burnout tests). The surface profile of the base sheet, on the other hand, gave a different functional form, as shown in Figure 10. It is characterized by a signature from a large-scale periodic variation (∼3 mm wavelength) and a peak near ξ ) 0 with the correlation length of the same length scale of a typical fiber width (∼30 µm). Visual inspection of the sample showed that the former originated from macroscopic paper distortions (called “cockling”) and the latter was related to microscale roughness caused by individual fibers. In summary, coating thickness variations closely resemble the process of random deposition, with a leveling effect. Therefore, if there is any effect of base sheet structures, it should be through this leveling effect. In the next section, we will discuss whether these explanations are consistent with the results reported in the literature. 3.2. Correlation between Coating Thickness Variation and Base Sheet Structures. Two of the important differences in the experiments reported in the literature are (1) the sample length of the measurements and (2) the spatial resolution for determining coating thickness variations and base sheet structure variations. Both factors influence the correlations between coating thickness and base sheet structure variations. To examine the effects of sample size, we first used highpass filters to eliminate longer wavelength components from

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Figure 11. The correlations between coating thickness and base sheet structure variations are plotted as a function of the cutoff wavelength of the high-pass filter. The left plot represents the paper sample with coat weight of 12 g/m2, and the right plot corresponds to 22 g/m2. The legend applies for both plots. The pore (or mass) length is defined as the total length of the base sheet pores (or fibers) that is measured at every position on the x-axis, as seen in Figure 3.

Figure 12. The correlations between coating thickness and base sheet structure variations are plotted as a function of the cutoff wavelength of the low-pass filter. The left plot represents the paper sample with coat weight of 12 g/m2, and the right corresponds to coat weight of 22 g/m2. The legend applies for both plots. The pore (or mass) length is defined as the total length of the base sheet pores (or fibers) that is measured at every position on the x-axis, as seen in Figure 3.

Figure 13. The contribution to the total coating thickness variation from the base sheet properties, for high- and low-pass filtering, respectively, with cutoff wavelength of 300 µm. The left plot represents the paper sample with coat weight of 12 g/m2, and the right corresponds to 22 g/m2.

the coating thickness and base sheet variations. This procedure corresponds to removal of the “waviness” components (e.g., removing “cockles” from the base sheet surface profile), and also this is essentially the same as a reduction of the sample size. In this investigation, we used different cutoff wavelengths to examine the effect of sample size. In Figure 11, the high-pass-filtered coating thickness variations are correlated with the corresponding base sheet structures at different cutoff wavelengths, and the R2 values are plotted. As the cutoff wavelength decreases (i.e., as shorter and shorter wavelength components are removed), the correlations increased between the (filtered) coating thickness variations and the corresponding base sheet parameters. All correlation coefficients reported in Figures 11 and 12 are negative; for example, the higher the base sheet parameter, the thinner the coating thickness. Particularly, the surface profile of the base sheet shows an extremely high correlation at shorter cutoff wavelengths. This result is in agreement with Dahlstro¨m et al.12 and is a manifestation of the leveling/surface filling effect. However,

as the cutoff wavelength increases (i.e., as the sample length becomes larger so that increasingly longer wavelength components are included in the measurements), the correlation between the base sheet surface profile and coating thickness variations decreased. Low-pass filters eliminate the smaller length scale components. Therefore, the results from low-pass filtering emulate the result obtained from methods with limited resolution (e.g., the burnout method). Figure 12 shows the results from the correlation analysis using a low-pass filter, instead of a highpass filter. Interestingly, as the cutoff wavelength increases (i.e., as the resolution of the measurements decreases), the mass length and base sheet thickness emerged as the key parameters controlling the coating thickness variations, particularly at the lower coat weight of 12 g/m2. At the higher coat weight of 22 g/m2, however, the correlation is rather modest, as will be discussed later. Because the correlation is negative, the result indicates, again, the leveling effect: the lower is the mass density, the higher is the coating thickness.

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The behavior observed for low- and high-pass filtration, respectively, explains the seemingly contradictory results reported in the literature for different measurements methods. For example, using the SEM method with limited image size (say 300 µm),11 it was found that the base sheet surface profile has the highest correlation with coating thickness variation, whereas formation showed very little correlation. However, using the burnout test with limited resolution (length scales larger than 500 µm),7 the formation appeared to be the most important base sheet structure parameter. Therefore, it is evident that the resolution of the measurements and the sample size have a significant effect on the correlations observed. Although the results in Figures 11 and 12 consistently explain the different experimental results in the literature, there is one important point to be noted: the correlations shown in Figures 11 and 12 are between the “filtered” data. In other words, although the correlation between the mass and coating thickness variations was very high (R2 ≈ 1) at more than 1 mm cutoff wavelength (Figure 12), the variance of “filtered” coating thickness makes up only a small proportion of the “total” variance of original coating thickness. This situation is illustrated in a typical power spectrum of coating thickness variations, as shown in Figure 4. It is seen that most of the coating thickness variations exist at the length scales smaller than around 400 µm; as the wavelength increases, the variance diminishes. (Note that bin size is increased as wavelength increases in Figure 4.) To see the overall contribution of the filtered component of each base sheet structure parameter to the total coating thickness variations, R2 has been renormalized. This was done by multiplying R2 by the relative share of the filtered coating thickness variance, that is, filtered coating thickness variance (σ2CT, filt) divided by total coating thickness variance (σ2CT, filt). Figure 13 shows the results for both coat weights at a cutoff wavelength of 300 µm. For smallscale variations (high-pass), the base sheet surface profile explained more than 50% of the total coating thickness variations. At length scales larger than 300 µm (low-pass), the base sheet structures contribute very little to the total coating thickness variations. This is the case even for the formation parameter (mass length). This implies that in the larger scale, the uniformity may be affected more by coating flow instabilities and macro-defects of base sheet, such as wrinkles, than by the base sheet structures. 4. Conclusions Autocorrelation analyses showed that coating thickness variations are a process of random deposition with local leveling. Therefore, at small length scales, in the order of fiber width, leveling (surface filling) occurs so that coating thickness variations are essentially determined by the surface profile at the corresponding length scale. At larger length scales, the same leveling suppresses the inherent coating thickness variations (random deposition), leaving only a trace of the effect of base sheet structures, creating contour-coating. The controversies in the literature were explained in terms of the sample size and resolution and the fundamental mechanism of coating. For lower resolution and larger sample size measurements, formation (mass distributions) and base sheet thickness variations appear as the key properties controlling coating thickness variations. For higher resolution and smaller sample size measurements, however, the surface profile of the base sheet becomes a prominent parameter that controls coating thickness variations.

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This Article only concerns coating thickness variations. To relate the discussions to print mottles, another important coating uniformity, the “within-coating structure” variations (Figure 1), must be investigated. We will report the results in future work. Acknowledgment We would like to thank Xuejun Zou at FPInnovationsPaprican for valuable discussions and also for providing us with paper samples prepared under controlled conditions. We also would like to thank Boel Nilsson and Staffan Palovaara at SCA R&D Centre for valuable assistance with the microscope and Stefan Lindstro¨m at Mid Sweden University for helpful discussions regarding frequency analyses. Financial support from Nutek and Imerys is gratefully acknowledged. Literature Cited (1) Ozaki, Y.; Bousfield, D. W.; Shaler, S. M. Characterization of coating layer structural and chemical uniformity for samples with backtrap mottle. Nord. Pulp Pap. Res. J. 2008, 23, 8–13. (2) Xiang, Y.; Bousfield, D. W. Effect of coat weight and drying condition on coating structure and ink setting. Proceedings of the AdVanced Coating Fundamentals Symposium; San Diego, CA, 2001; pp 51-61. (3) Engstro¨m, G. Forming and consolidation of coating layers and their impact on coating and print uniformity - an overview. Proceedings of the 2nd International Papermaking & EnVironment Conference; Tianjin, China, 2008; pp 84-102. (4) Engstro¨m, G.; Johansson, P.-Å.; Rigdahl, M. Factors in the blade coating process which influences the coating mass distribution. Proceedings of the Ninth Fundamental Research Symposium; Cambridge, 1989; pp 921-950. (5) Huang, T.; Lepoutre, P. Coating-paper interactions - the effect of basestock roughness, absorbency and formation on coated paper properties. Pap. Puu-Pap. Tim. 1995, 77, 484–490. (6) Engstro¨m, G.; Lafaye, J. F. Precalendering and its effect on papercoating interaction. Tappi J. 1992, 75, 117–122. (7) Huang, T.; Lepoutre, P. Effect of basestock surface structure and chemistry on coating holdout and coated paper properties. Tappi J. 1998, 81, 145–152. (8) Tomimasu, H.; Luner, P.; Suzuki, K.; Ogura, T. The effect of basestock structure on coating weight distribution. Tappi J. 1990, 73, 179–187. (9) Matsubayashi, H.; Takagishi, Y.; Kataoka, Y.; Saito, Y.; Miyamoto, K. The influence of coating structure on paper quality. Proceedings of the TAPPI Coating Conference; Orlando, 1992; pp 161-171. (10) Gane, P. A. C.; Hooper, J. J.; Baumeister, M. The influence of furnish content on formation and basesheet profile stability during coating. Tappi J. 1991, 74, 193–201. (11) Zou, X.; Allem, R.; Uesaka, T. Relationship between coating uniformity and basestock structures. Part 1: Lightweight coated papers. Pap. Technol. 2001, 42, 27–37. (12) Dahlstro¨m, C.; Uesaka, T.; Norgren, M. Base sheet structures that control coating uniformity: Effects of length scale. Proceedings of the TAPPI AdVanced Coating Fundamentals Symposium; Montre´al, Canada, 2008; pp 124-133. (13) Wiltsche, M.; Bauer, W.; Donoser, M. Coating application method and calendering influence on the spatial coating layer formation obtained by an automated serial sectioning method. Proceedings of the TAPPI AdVanced Coating Fundamentals Symposium; Atlanta, GA, 2006. (14) Engstro¨m, G. Coating coverage-definition and measuring techniques. Proceedings of the International Symposium on Paper Coating CoVerage: Visions for Coating DeVelopment; Helsinki, Finland, 1999; 178 pp. (15) Fahlcrantz, C.-M. On the evaluation of print mottle. Ph.D. Thesis, Royal Institute of Technology, Stockholm, 2005; p 191. (16) Chinga, G.; Helle, T. Staining with OsO4 in the study of coated paper structure. Pap. Puu-Pap. Tim. 2003, 85, 44–48. (17) Williams, G. J.; Drummond, J. G. Preparation of large sections for the microscopical study of paper structure. Proceedings of the TAPPI Papermakers Conference; San Francisco, CA, 1994; pp 517-523. (18) Nanko, H. Personal communication, 2006. (19) Allem, R. Characterization of paper coatings by scanning electron microscopy and image analysis. J. Pulp Pap. Sci. 1998, 24, 329–336. (20) Dickson, A. R. Quantitative analysis of paper cross-sections. Appita J. 2000, 53 (4), 292–295. (21) Chinga, G.; Helle, T. Structure characterisation of pigment coating layer on paper by scanning electron microscopy and image analysis. Nord. Pulp Pap. Res. J. 2002, 17 (3), 307–312. (22) Klein, R.; Schulze, U. Metrology-related evaluation of graphic paper and board cross sections by digital image analysis. Int. Papierwirtschaft 2006, 48–58.

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(23) Dobson, R. L. Burnout, a Coat Weight Determination Test ReExamined. Proceedings of the TAPPI Coating Conference; Chicago, IL, 1975; pp 123-131. (24) Vaseghi, S. V. AdVanced Digital Signal Processing and Noise Reduction, 3rd ed.; John Wiley & Sons Ltd: Chichester, 2006; pp 39-91. (25) Papoulis, A.; Unnikrishna Pillai, S. Probability, Random Variables and Stochastic Processes, 4th ed.; McGraw-Hill: New York, 2002; pp 435-463. (26) Kartovaara, I. Coatweight distribution and coating coverage in blade coating. Pap. Puu-Pap. Tim. 1989, 71, 1033–1042. (27) Baraba´si, A. L.; Stanley, H. E. Fractal Concepts in Surface Growth; Cambridge University Press: Cambridge, 1995; pp 38-54.

(28) Bousfield, D. W. A model to predict the leveling of coating defects. Tappi J. 1991, 74, 163–170. (29) Haglund, L.; Norman, B.; Wahren, D. Mass-distribution in random sheets - theoretical evaluation and comparison with real sheets. SVensk Papperstidning-Nordisk Cellulosa 1974, 77, 362.

ReceiVed for reView May 19, 2009 ReVised manuscript receiVed September 14, 2009 Accepted September 14, 2009 IE900819C