Visualisation, Modeling and Image Analysis ofCoated Paper Microstructure:

Particle Shape − Microstructure InterrelationsJANET PRESTON*1, MARTTI TOIVAKKA2, PETER HEARD3

1Imerys Minerals Ltd., Par Moor Centre, Par Moor Rd., Par, Cornwall, UK2Laboratory of Paper Coating and Converting,

Center for Functional Materials, Abo Akademi University, Finland3Interface Analysis Centre, University of Bristol, UK

*Corresponding Author's Email: Janet.Preston@imerys.com

ABSTRACT

Most physical and functional properties of pigment coated papers are influenced by coating layer structure at a micro-scopic level. For example, number and size of micro voids contribute to macroscopic properties such as brightness,light scattering efficiency, opacity and the printability of paper. In this paper high resolution Focused Ion Beam (FIB)sectioning and imaging is combined with a novel advanced image analysis technique, to produce new information aboutthe microscopic properties of paper coatings. These observations are compared with computer-generated numericalmodel structures.

Distinctly different coating structures were created using different morphology coating pigments in an attempt to in-terrelate the particle shapes and the corresponding microscopic pore structures. Three paper coatings were preparedcontaining a narrow particle size distribution ground calcium carbonate (GCC), a precipitated calcium carbonate (PCC)and kaolin respectively as the sole pigments. After being applied to a woodfree basepaper, the coatings were charac-terised using mercury porosimetry, reflectometry and standard paper tests. The pore structure was then where possiblefilled with a varnish and the pore space within the coating layer imaged by means of a FIB sectioning technique.

An image analysis technique called "Maximal Inscribed Sphere" (MIS) algorithm was used to characterise the experi-mental 2-D sections. The technique partitions a void space of porous material into an unambiguously defined collectionof individual pores and throats connecting them. The results show differences in the pore structure as created by the dif-ferent pigment particle geometries. A semi-quantitative agreement with the numerical model structures was observed.The approach produces useful new information concerning the microscopic properties of paper coatings including dis-tributions of pore size, pore surface area, pore connectivity, pore surface-to-volume ratio, throat-to-surface area ratioas well as fractal structural parameters.

This fundamental knowledge can be used to improve our mechanistic understanding of the link between pigments,coating structure and paper/ printing performance.

Keywords: pigment coating; coating structure; image analysis; microstructure; computer simulation

INTRODUCTION

Controlling the porosity of a paper coating layer is vitalfor the performance of that coating. There has been ex-tensive work conducted in this area, for example optimi-sation of the pore structure for optimum light scatteringand paper brightness and opacity. The packing togetherof different morphology minerals has also been stud-ied by means of computer simulation and experiments,for optimised rheology and coater runnability [1]. Thevoid structure also affects flow of liquids and gases in acoating; absorption of inks and fountain solutions duringprinting is controlled by the pore space structure at and

near the coating surface. Problems such as blistering inheatset web-offset printing are related to gas permeabil-ity of a coating. Parameters such as the rate of consolida-tion of the ink film, the print gloss and ink requirement toachieve a target colour density are all impacted by coat-ing structure.

Although coating and pore structures are commonly dis-cussed in context of coated paper performance, the ac-tual microscopic structure and the geometry of void spacestill remains largely unknown. The meanings of terms"coating structure" and "structuring" are quite broadly in-

terpreted, while the correct meanings should refer to the"spatial arrangement of coating color components on pa-per surface and its control." In the context of coating pig-ments, particle size distributions are commonly quotedsince they are measurable. Besides a large number ofexperimental work in this field [2], several theoreticalworks outline the use of particle packing simulations tostudy the interrelations between particle size and shapeand coating properties [2--9]. However, for the end useperformance a more important aspect is the void spacethat is created by the packed pigment particles, not theparticles themselves. In practice, it is difficult to predictthe kind of pore space that is created by a certain particleshape and size distribution.

Macroscopic properties related to the pore space such asporosity, specific surface area and permeability can eas-ily be measured experimentally, but often these do notprovide the necessary level of detail to increase our un-derstanding of the pore structure - performance relation-ships. Local variations in a pore structure generate physi-cal effects, e.g.mottle, that cannot be explained with sim-ple macroscopic measurements. It is, therefore, of inter-est to try to measure and characterize the microstructuresin detail.

Much of the early work on the effect of pigments andcoating structure and its effect on fluid absorption hasbeen reviewed and reported by Lepoutre in 1976 [3].Mathematical models are being developed to generatethree dimensional simulations of paper coating struc-tures. Pan et al. have used a cubic lattice type structurewith the sites linked by pores [4]. There is a high con-nectivity between the sites (with six throats per pore) andthe size distribution of the pores follows a Rayleigh dis-tribution. This model has proved successful in predictingthe effect of coating unevenness and substrate porosityon soluble binder migration. The applications of numer-ical simulation to model pigment coating structures arereviewed by Vidal [8].

Toivakka and Nyfors investigated pore shapes in modelcoating structures using an image analysis techniquebased on morphological operations [10]. The resultsshow that even the most simple particle geometries,monodispersed spheres, create complex pore structureswhose properties cannot be predicted from the particlegeometry alone. The topographical model generated bythe image analysis technique was used by Bousfield et al.in liquid flow simulations [11]. This approach gavea good approximation of flow into a simple system ofpacked spheres, for example, plastic pigment coatings ata range of different latex levels.

Mechanical properties of paper coatings modeled aspacking structures were numerically investigated byToivakka and Bousfield. The results could explain quali-tatively the changes in mechanical properties of coatingsat different pigment volume concentrations [12].

The effect of pore shape in more complex structures was

studied experimentally by Senden et al. [13]. They pre-pared a series of etched porous networks to give a widerange of pore morphologies and studied the absorptionand spreading of iso-propanol (with and without surfac-tant) into these structures. They concluded that changesin the equilibrium contact angle of the fluids used, re-sulted in a larger variation in flow rate than would be pre-dicted by the Lucas Washburn equation. This was mainlydue to 'snap off' events occurring at discontinuities withinthe structures. These were the rate determining stagewhich was slower by an order of magnitude than the otherflow events. The spreading of the droplet on the surfacewas associated with this time lag and the fluid having thelowest contact angle spread furthest and covered a largernumber of pores. The pore morphology, and the ratio ofvertical pores to the horizontal pores also played a largepart in the absorption rate. When there were only 20%vertical pores and 80% horizontal pores, the fluid did notpenetrate very far, whereas when there were 60% verticalpores, the fluid penetrated significantly faster. It was alsosuggested that this was due to the number of interfacesincreasing by an order of magnitude. In all the systemsstudied, sub surface spreading of the fluid occurred andwas attributed to the fact that flow within the pore struc-ture was more favourable than spreading at the surface.

Kent and Lyne studied the effect of pore shape on fluidimbibition [14]. They suggest that liquid accelerates intoa converging pore, and this is why water with an ini-tial contact angle of greater than 90 can penetrate intoa cellulose fibre network (which generally has converg-ing pores). Diverging pores cause deceleration of capil-lary penetration. The behaviour becomes more complexwhen fluids encounter discontinuities and dislocations inthe pore wall. The fluid can stick at such discontinuitiesand hinge around the dislocation. Lyne states that in min-eral coatings and filled papers, the frequency of these dis-locations and divergent pore geometries are more impor-tant in determining penetration rate than pore size [15].

Matthews et al. have developed the Pore-Cor model togive a three dimensional structure which has similar per-colation characteristics to the experimental structure asmeasured with mercury porosimetry [16]. Pore-Cor isa network simulator which simulates the void structure ofporous materials. The model consists of unit cells whichhave 1000 pores in a 10 x 10 x 10 array, linked with 3000throats and maximum pore connectivity of 6. Schoelkopfincorporated a wetting algorithm and inertial effects de-scribed by the Bosanquet equation into the Pore-Corprogram [17]. Advancements in the program are tak-ing into account the anisotropic nature of the pores andthroats in the coating structure, and double conical throatsare being introduced [18, 19].

Recently, focused ion beam (FIB) cross-sections havebeen used to visualise the penetration of ink into thepaper. The more conductive nature of the ink usedhere compared with the coating gave high contrast be-tween them, allowing easy assessment of the penetrationand the microscopic structure into which the penetration

Table 1. The particle size distributions and specific sur-face areas of the pigments.

Kaolin GCC PCC2.0µm 88 93 931.0µm 66 69 740.50µm 39 30 300.25µm 15 10 60.10µm 6 4

SA m2/g 11.8 11.6 7.4

has occurred. This method has been used to visualiserotogravure, sheet-fed offset and UV cured offset inkswithin coated paper surface layers [20, 21]. The prepara-tion of thin sections of paper using the focused ion beam(FIB) technique has been published by Uchimura et al.[22]. These authors showed that it was possible to obtaina thin section of printed paper that could subsequentlybe analysed by the EDX attachment on a SEM, withoutany structural changes or artefacts associated with resinembedment. Tomutsa and Radmilovic have used 0.1µmFIB sections to reconstruct a 3-D image of epoxy impreg-nated North Sea chalk [23]. Okayasu et al. carried out asimilar study in which porosity obtained using FIB sec-tioning was compared to mercury intrusion porosimetrydata [24]. They concluded that the FIB technique was su-perior to a microtome method for sample sectioning, asit did not result in sample chipping. There was also nothermal damage to binder samples observed.

While a large amount of work has been devoted to under-standing the pigment coating structure, the detailed mi-crostructure still remains largely unknown. The funda-mental understanding of relationships between pigmentparticle shapes, the coating structure created by the var-ious shapes and the resulting physical and functionalproperties of coated paper is limited today. The currentwork aims to measure and characterize the coating mi-crostructures in detail with a novel combination of highresolution FIB imaging and an advanced image analysistechnique.

MATERIALS

Three model coatings were prepared using kaolin, narrowPSD GCC and an experimental PCC as sole pigments.These pigments were selected as they had relatively sim-ilar particle sizes, but different morphologies. The par-ticle size distributions and specific surface areas of thepigments are given in table 1. The pigments were formu-lated with 5pph Dow 920 binder and 1pph CMC Finn-Fix 5. The coating solids were adjusted to 1% lower thanthe maximum runnable solids and applied to a 50g/m2

woodfree basepaper using a Helicoater at 600m/min. Atarget coat weight of 13g/m2 was sought. The coatingswere laboratory calendered using a Perkins Supercalen-der for 10 nips at 65C, 70bar pressure at 36m/min.

Varnishing of SamplesPortions of the model coatings were filled with a fluidUV varnish, which was left to penetrate into the coatingpores. It was originally envisaged that the varnish wouldbe applied to the coated papers using a laboratory print-ing unit whereby the pressure in the printing nip wouldhelp the penetration of varnish into the pores. Howeverlaboratory offset printing was not possible with the lowviscosity UV varnish (Wessco 3032) as the IGT rollersand printing disc slipped. The amount of varnish appliedwas also insufficient with this method.

As an alternative application method, blade coating of theUV varnish was carried out using a bench coater. Threecoatings were applied to ensure that the pores were filledwith varnish and then cured after standing using a Mini-cure unit, to immobilise the varnish in the pores. A fur-ther coat was applied and immediately cured to leave amirror like glossy surface. The varnished samples weresectioned directly using a FIB microscope without fur-ther preparation.

Computer Generated Numerical ModelStructuresNumerical 3-D model structures corresponding to theexperimental samples were generated using RASP-software [7]. The particle size and shape distributionswere taken from table 1, and one decade of particle sizesfrom 0.2 to 2 microns was considered. The GCC wasmodeled as 8-faced frustums, PCC as hexagonal needle-like particles, and kaolin as hexagonal plates. No binderwas included in the simulations, since FIB imaging is notable to detect it. There are several uncertainties in pa-rameters when modeling coating structures, e.g., the trueshape distributions of pigments with aspect ratios largerthan unity are difficult to estimate, and the influence ofthe base paper structure on coating structure is not welldefined. The present work aims only to demonstrate thepossibilities provided by the computer-based tools, and,therefore, a thorough numerical analysis was not done.The computer-generated numerical model structures areshown in Fig. 1.

METHODSFocused Ion BeamAn FEI FIB201 gallium focused ion beam instrumentwas used for sectioning and high-resolution imaging.The instrument is capable of producing a gallium ionbeam of between 7nm (at 1pA beam current) and 300nm(at 12nA) in diameter at 30keV energy. A platinumorganometallic gas injector allows ion beam assisted de-position of platinum over selected areas of the sample.This facility was used prior to the sectioning shown herein order to protect the top surface of the sample duringion milling. For sample sectioning, a large ion currentwas used initially to remove a staircase-shaped trench. Afiner beam of lower current was then used to 'polish' thelarger vertical face of the trench by scanning the beam in

Fig. 1. The computer-generated numerical model structures for PCC (LEFT), GCC (CENTER), and kaolin (RIGHT).The top images are the 3-D structures, the middle images show the surface structure, and the bottom images cross--sections in X- and Z-directions (pigment is black).

a line and moving it progressively up to remove furthermaterial. The sample was then tilted to 45 and the pol-ished face imaged using the same ion beam, generally ata much lower beam current to achieve high resolution.

The Fig. 2 shows the geometry of the FIB 'trench' andthe images in the results section are taken from the rearwall of this trench, viewed from above at an angle of 45.In the examples shown in this work, the samples havebeen cut and polished and then imaged without coatingof the polished cut face with a platinum film. It has beenfound that 'organic rich' components such as the ink ab-sorb the gallium rendering them more conductive, so theyare easily imaged in this technique. However the coatinglayer does not absorb the beam to any great extent andthe particles are not imaged without a conductive coat-ing. Hence an organic layer such as an ink or a varnishcan be seen, but the particles in the coating layer are notvisible [20]. The images were captured using the ion-induced secondary electrons whose energy distributionpeaks at a few electron volts. If the potential of the sam-ple rises by a few volts, then this signal is severely cur-tailed and the image will appear dark. For the potentialof the sample to rise by a few volts as a result of a 4-10pAion current impinging upon it, the resistance of the sam-ple to ground must be > 1010Ω. It appears that this wasthe case for the coating material, while for the varnish

Fig. 2. FIB methodology for sectioning coated papersamples.

the resistance was less than this, and its appearance waslight. After this image has been collected, the cut sectionis coated with a layer of Pt, which allows visualisation ofthe particles as well as the ink layer.

Paper Testing

The coated papers were conditioned at 50% relative hu-midity and 23C for at least 24 hours before standardlaboratory paper testing was performed. A DataColorElrepho 3300 was used to measure the optical charac-teristics of the papers using D65 illumination with the

Table 2. The standard paper properties for the coated pa-pers.

Kaolin GCC PCCTappi Gloss 75 / % 75 58 65PPS 1000 kPa/µm 0.55 0.80 0.75Bendsten porosity ml/min 8.5 20 20Opacity (D65 -400nm) 86.7 86.8 87Brightness (D65 -400nm) 82.5 88.1 88.1Imaging reflectometry

Effective RI 1.425 1.250 1.158Macro-roughness/ 0.7 1.3 1.1Reflectometer gloss/% 51 32 32

400nm UV cut off filter in place; paper brightness (D65),opacity (DIN). TAPPI 75 gloss on Hunterlab and PPSat 1000 kPa on PrintSurf were determined. A Surfopticimaging reflectometer was used to determine the micro,macro-roughness and effective refractive index of the pa-per surfaces. The instrument uses imaging technology tomap the 3-D angular distribution of light forward scat-tered from surfaces in the range 10 about an angle ofincidence of 75. The macro-roughness can be derivedfrom the width of this angular distribution and is desig-nated FWHM. It also uses polarized light at two wave-lengths to determine the refractive index (RI) and opti-cal micro-roughness (roughness features ≤ wavelengthof light) [25].

Coating pore size distributions were determined by mer-cury porosimetry. Measurements were made using aPASCAL 140/440 Porosimeter (Thermo Electron S.p.A.,Italy). Coated paper samples of approximately 20cm2

and portions of pigment tablet were evacuated for 10minutes before being measured. Corrections for the com-pression of mercury, glassware and oil phase were takeninto account by running a blank experiment. Curve fit-ting programs were used in order to separate the contribu-tion of the basepaper from the coating component. Thisallowed the average pore size and volume of the coatinglayers alone to be determined.

Paper samples were embedded in an Epoxy resin andsectioned using an ultra-microtome. A Jeol 6700F fieldemission scanning electron microscope was used to ob-tain micrographs of the coating surfaces and sections.

The Image Analysis Technique to Characterizethe Pore Space

Porous structure of a pigment coating is a complicatednetwork of interconnected voids of various sizes. Inthe current work, the pore space is divided into its con-stituent pores by an image analysis technique called"Maximal Inscribed Sphere" algorithm (MIS). The tech-nique, which can be applied to both experimental and nu-merical model coating structures, partitions a void spaceof porous material into unambiguously defined collec-tion of individual pores. The algorithm works on digi-tized data, either with pixels in two dimensions, or withcorresponding small cubic volumes, called voxels, if 3-

Fig. 3. Pore size, pore volume and effective refractiveindex of coated paper samples.

D data if available. A maximal inscribed sphere (circlein 2-D) is calculated for each voxel (pixel in 2-D) in thevoid space, which allows one to identify the pore centersas largest spheres, and throats connecting the pore cen-ters as the smallest spheres. The end result is a collectionof pores that are separated from each other by the nar-row throats that correspond to the minimum in hydraulicradii, when moving from one pore to another. This poredescription is useful, since it is based on a criterium witha clear physical meaning. The throats, or the minima inhydraulic radii control, e.g., the flow resistance through aporous structure. While the pore definition is the same asused in [26], the current algorithm is superior to the pre-vious ones by eliminating problems related to so-calleddirectional erosion and false pore centers. The detailsof the MIS algorithm are described in [5--7]. While inthe current work, the image analysis technique is appliedto FIB images and computer-generated numerical modelstructures, it can with ease also be used when analysingother imaging data, e.g., SEM or TEM cross-sections andX-ray computed microtomography 3-D images.

RESULTSThe paper coating properties were interpolated at a coatweight of 13g/m2 and are included in table 2. As wouldbe expected the kaolin coatings had higher sheet gloss,lower roughness and lower brightness in comparison tothe carbonates. The Bendtsen porosity was also muchlower indicating a considerably more closed coating.This was also seen in the effective refractive index (RI)of the surfaces, which was higher (less air) than the car-bonate coatings.

The pore size and volume of the coated papers were mea-sured using mercury porosimetry. The results and theeffective refractive index of the coatings are shown inFig. 3. The PCC has the highest pore volume, pore sizeand a low effective RI (bubble size), which is indicativeof surface porosity. The kaolin coating has the small-est pores, the lowest pore volume and a high effectiveRI. While the samples present model surfaces with thedifferent pore structures, the differences are smaller thanexpected. This could be partly caused by the similar par-ticle size distributions of GCC and PCC.

Fig. 4. Surface (top row) and cross-sectional (center and bottom rows) micrographs of PCC (LEFT), GCC (MIDDLE)and kaolin (RIGHT) coatings. PPC shows random orientation of the needle-type geometry of the pigment with a poroussurface. Overlapping fine kaolin platelets provide a low surface porosity.

When the pore volume is expressed as a volume %, thepore volumes are calculated to be, 25.1% for the kaolin,27.2% for the GCC and 32.7% for the PCC, using a den-sity of 2.58 for kaolin, 2.7 for the carbonates, 1.0 for thelatex and 1.5 for the CMC.

For comparison with the FIB sections a further 12.7%should be added to these values, to allow for the factthat the FIB will not differentiate between pore spaceand binder present. This gives a volume % porosity of37.8% for the kaolin, 39.9% for the GCC and 45.5% forthe PCC.

Electron MicroscopyElectron microscope images of the coating surface andsections through the coating layers are shown in Fig. 4.The needle like PCC structure can clearly be seen in thePCC coating (top-left in Fig. 4). The needles appear to berandomly orientated and do not seem to be aligned to anygreat extent in the machine direction, despite the fact thatthey have been applied with a blade coater. In the top-middle of the Fig. 4, the GCC coating surface is shownand in top-right, the kaolin coating, showing the plateyparticles. The higher porosity of GCC and PCC coat-

ings, when compared to the kaolin coating is evident fromthe sections. The kaolin particles appear almost fused to-gether, or perhaps have been smeared during the cuttingprocess.

Fig. 5 is a section through a varnished paper coating,where the excess varnish is clearly visible on the coat-ing surface. The secondary electron image produced inthe SEM, does not show the degree of varnish penetrationinto the coating pores.

Fig. 5. SEM image of a varnished coating, showing theexcess varnish on the surface.

Fig. 6. FIB section through the GCC coating. Pigmentsare in dark grey/black.

Fig. 7. FIB section through the PCC coating. Pigmentare in dark grey/black.

FIB SectionsThe FIB was used to first section through and then scanthe surface of the cut face. As the FIB beam scannedthe surface the varnish absorbed the gallium ions and al-lowed the surface to become conducting, and hence bevisualised. In Fig. 6, a section through the GCC coatingcan be seen. The angular calcite crystals have been out-lined with the varnish allowing good visualistion of thepores.

The sectioned PCC coating is shown in Fig. 7. It can beseen that the coating was sectioned in the cross-machinedirection, and that the majority of the needle like parti-cles are sticking out of the plane of the FIB section, andappear as spheres rather than as needles. Sectioning thepaper in the machine direction would have resulted in alarger proportion of rod like needles. However, lookingat the surface of the coating (Fig. 4) the needles are notparticularly well orientated in the machine direction.

Problem of Kaolin SectioningWith the 100% kaolin sample, problems were experi-enced in imaging within the coating layer. It appearsthat the varnish was unable to penetrate into the tightlypacked pores within the calendered coating. Anotherpossibility is that the penetrating fluid has 'snapped off'at the edges of the kaolin platelets, breaking the conduct-

Fig. 8. Only the surface pores are accessible and visiblewith the kaolin coating.

Fig. 9. After coating the cut edge with Pt, the particlesand pores are visible.

ing pathway and preventing the pore structure from be-ing clearly seen. The closed packed structure of plateykaolin can be expected to have very small throats con-necting the pores, which results in high flow resistancethrough the pore network. Only the surface pores can beseen in Fig. 8. After coating with a Pt spray, the tightlypacked kaolin particles are evident (Fig. 9). In order totry and enhance the conductive nature of the sections,and to force a fluid into the coating pores, a conductingfluid (5% Polypyrrole aq.solution) was introduced to thekaolin coating, under vacuum to remove excess air. Thesamples were then placed in an ultrasonic bath to ensurethat the conductive polymer had penetrated as much aspossible. These samples were then analysed using theFIB sectioning technique. However, once again no pen-etration of the polypyrrole polymer between the particleswas observed.

Image Analysis of the FIB cross-sections

Below, the cross-sectional images of the GCC and PCCcoatings (from FIB imaging) and the model structures(from computer generate packings) are analyzed with theMIS algorithm. The Kaolin coating could not be an-alyzed due to experimental problems described above.Prior to the analysis the FIB images were scaled hori-zontally by a factor of 1/

√2 to compensate for the 45

tilting angle used in imaging.

(a) The original FIB-image,

(b) the masked and thresholded image,

(c) the porespace divided into its constituentpores using the MIS algorithm,

(d) the connection paths (skeleton) for the porespace.

Fig. 10. An example of MIS analysis of a PCC coatingcross-section. The images are scaled horizontally by afactor of 1/

√2 to compensate for the 45 tilting angle

used in imaging.

(a) The original FIB image,

(b) the masked and thresholded image,

(c) the porespace divided into its constituentpores using the MIS algorithm,

(d) the connection paths (skeleton) for the porespace.

Fig. 11. An example of a MIS analysis of a GCC coatingcross-section. The images are scaled horizontally by afactor of 1/

√2 to compensate for the 45 tilting angle

used in imaging.

Figs. 10 and 11 show examples of FIB images and theresults of the MIS analysis. The corresponding imagesfor all the cross-sections are in the appendix. Figs. 10band 11b show the pore space (pores are white, pigmentis black) after thresholding. Usually the choice of thegreyscale level used in thresholding influences the poros-ity calculation. However, FIB images are not as sensitiveto this problem as SEM images, because pore edges seemto gather charge and provide good contrast for the thresh-olding operation. Note that the base paper fibers (e.g.,bottom of the Fig. 10a) and some of the pore space thathas poor image quality (bottom right in Fig. 11a) has beenremoved with masking. This will not influence the anal-ysis, only the total area that is analyzed is reduced. Afterthresholding, it is trivial to calculate porosities in eachof the FIB slices, as is shown in Fig. 12. The porositiesare surprisingly high, on the average 47% for PCC and48% for GCC. The high values in comparison to the ex-perimental ones in Fig. 3, can be explained by the factthat in FIB imaging the binder and the thickener can-not be separated from the pore space. When these areexcluded and the densities of the coating materials aretaken into account, the true volume porosities from mer-cury porosimetry are 45.5% for the PCC and 39.9% forthe GCC. These values are in reasonable agreement withthe FIB porosities from the image analysis. It is some-what surprising that there is hardly any difference be-tween PCC and GCC porosities, but this may be due tothe fact that the particle size distributions for the pig-ments are quite similar. The average porosities in thenumerical model structures compare well to the exper-imental ones as shown in Fig. 12.

Figs. 10c and 11c show the individual pores with randomcolors as isolated with the MIS analysis. The pores areseparated from each other by minima in hydraulic radii,which are called throats. From 20 FIB cross-sectionseach, 3990 pores for PCC, and 2636 pores GCC wereidentified. The lower value of GCC is caused by itssmaller total analyzed area as is seen in the masked im-ages in Appendix. The pore density calculated by di-viding the number of pores with the total analyzed areain the FIB images was 4.29 pores/µm2 for PCC and4.23 pores/µm2 for GCC. Once a collection of pores isidentified, one can generate various statistics based onindividual pore characteristics. Figs. 13 and 14 showthe frequency and by area distributions of the equivalentpore areas in all the cross-sections. Again, only minimaldifferences between the coatings prepared with differentpigments can be identified. The average pore sizes byfrequency are 0.324µm(PCC) and 0.333µm(GCC) andby area 0.457µm(PCC) and 0.471µm(GCC). The valuesfor the numerical model structures were slightly higher,0.502µm (PCC) and 0.518µm (GCC). The difference canbe partly explained by calendering effects and the pig-ment particle size cut-off of 0.2µm used in the simula-tions.

When comparing the pore sizes to mercury porosimeterresults, a more appropriate statistic could be the throatsize, which is the size of the connection between neigh-

boring pores. The narrow constrictions, i.e., the throats,control the flow resistance into and through the pores.The average throat sizes as calculated from the MIS-segmented images were 0.145µm (PCC) and 0.146µm(GCC), which are reasonably close to the experimentallymeasured values in Fig. 3. The throat size can also be ex-pressed as a relative quantity, which then indicates whatfraction of a pore is connected to the neighboring pores.For the samples in this work, the 2-D connected area isvery high; an average of 40% of the pores are in contactwith their neighbors as shown in Fig. 15.

Another measure of connectivity is the coordinationnumber distribution for the pore space, which shows amaximum at three connected neighbors for both the PCCand GCC (Figs. 16a and b). Very similar values wereobtained for the numerical model structures as shown inFigs. 16c and d. Note also that there are a number of poreswith very high connectivities up to 10, and even somedead-end pores with connectivity of one. However, oneshould avoid drawing too far-reaching conclusions fromthe two dimensional analysis, since our initial work with3-D structures show significant differences to two dimen-sions, especially for the connectivity, which seems to bemuch higher in three dimensions than in two. A graphicalillustration of the connectivity is shown in Figs. 10d and11d, which draw connection path skeletons. The skele-ton in combination with flow resistances derived from thepore and throat data could be used to predict the perme-abilities of microstructrures.

The anisotropy of a coating structure can be quantifiedwith, e.g., pore shape statistics. Here a simple approachwas used, where a number of random positions in the porespace were chosen, and in each position the maximal linesegments in horizontal and vertical directions were cal-culated. For isotropic material the ratio of the lengthsof y- and x-directional line segments, pore-shape-factor,should be one on the average. In FIB images the poreswere slightly elongated in x/y plane. The pore-shape-factor was estimated for PCC and GCC as 1.18±0.05 and1.06±0.06, respectively. The higher anisotropy for thePCC is probably due to its anisotropic particle shape. Theanisotropy of the pores in the GCC coating is explainedeither by scatter in experimental data, or it could alsobe caused by calendering, which compresses the coat-ing structure in z-direction. For the numerical modelstructure of GCC, in which calendering is not consid-ered, the pore-shape-factor was calculated to be for GCC1.01±0.08, as is expected. The poreshapes for the othernumerical model structures were: PCC 1.06±0.07, andkaolin 4.79±0.53. Both values can be explained by theanisotropic particle shape. Especially noteworthy is thehigh value of kaolin caused by the oriented high aspectratio particles.

An attempt was made to use fractal dimension as a wayof differentiating the microscopic pore structures fromeach other. Fig. 17 shows the fractal dimension estima-tion which is based on pore circumference and pore area.When plotting the former against the square root of the

Fig. 12. Left: Porosities in FIB cross-sections for PCC and GCC coatings. The interslice separation is ca. 100nm.Right: Porosities in numerical model coating structures. Interslice separation is 50nm.

Fig. 13. The frequency distribution of the equivalent circular poresizes for PCC (left) and GCC coatings (right)

Fig. 14. The area distribution of the equivalent circular poresizes for PCC (left) and GCC coatings (right)

Fig. 15. The frequency distribution of relative connected areas for PCC (left) and GCC coatings (right)

Fig. 16. The coordination number distribution by frequency for PCC (topleft) and GCC coatings (topright) as well asfor the corresponding numerical model structures: PCC (bottomleft), GCC(bottomright)

Fig. 17. The fractal dimensions based on pore circumference and pore area for PCC (left) and GCC coatings (right)

latter on a log-log scale, data for an euclidian system fallson a line with a slope of one. From the figure it can beconcluded that the coating structures seem to be fractal.The fractal dimensions are similar, 1.08 for PCC and 1.09for GCC. For the numerical model structures the fractaldimensions were slightly higher: PCC 1.16, GCC 1.15,and kaolin 1.08. Further studies into this area is needed toclarify whether fractal dimension could be a useful statis-tic.

There is almost unlimited number of statistics that canbe calculated from the MIS analysis. The current workhas tried to illustrate the possibilities that the presentedapproach provides. The challenge that remains, is thatof tying the statistics with some physical and functionalproperties of interest and then identifiying the most use-ful ones. Some interrelations are already known, e.g., theporosity and poresize contribute to light scattering prop-erties such as brightness, opacity and gloss. Throat sizecontrols the flow resistance of a coating and, thus, e.g.blistering tendency. Prediction of ink-setting is one areain which further understanding of microstructure mightbe useful. There the pore and throat sizes in combina-tion with the pore connectivity play an important role. Inthe present work, the low amount of binder did not allowtesting of the printability of the coated papers.

CONCLUDING REMARKSIn this work three model coatings were prepared withvery different pore structures and corresponding numeri-cal model structures were constructed. The experimentalcoatings were prepared with a minimum level of binder(5pph) to maximise the effects of pigment shape on coat-ing microstructure. This amount of binder would be suf-ficient for rotogravure printing, but would most probablybe insufficient to withstand the forces prevalent in offsetprinting. The PCC coating was the most porous as deter-mined with the Bendsten porosity and the effective RI,and the calendered 100% kaolin coating the least. How-ever, there was less difference than expected between theporosities of the PCC and GCC coatings.

Varnish was applied to the surface of the coatings andallowed to penetrate the coating structure. In the caseof the 100% calendered kaolin coating it was extremelydifficult to get the varnish to penetrate into the centre ofthe coating layer. This may be due to the `snap off' of thefluid as it passes around the edges of the kaolin particles,which create a tortuous pore network. This would agreewith the findings of Senden, who found that penetrationwas slow in the z direction if there were not many verticalpores [13].

The focused ion beam instrument was suitable for ob-taining sections through the varnished coating. Repeatedscanning of the gallium beam allowed the varnish in thepores to form a conductive pathway and to be imaged.Slices through the coating were made at approximately100nm spacing. This step interval was found to be a lit-tle too large to get a good 3-D representation of the pore

structure using the fine coating pigments.

An advanced image analysis technique, MIS algorithm,was used to analyze the detailed microstructures bothin experimental and computer-generated images. Thestatistics obtained indicated smaller than expected differ-ences between the coating structures. This was in partcontributed to the similar particle size distributions ofGCC and PCC, and the lack of particle orientation forthe latter.

The statistics calculated for the numerical coating struc-tures was found to be in good agreement with that of theexperimental data. This encourages further developmentof the presented approach in order to predict coating mi-crostructures based on pigment particle size and shapedistributions. The currently available numerical tools al-low for simulation of coating layers consisting a largenumber of arbitrary shaped particles with inclusion offilm-forming binder. The possibility to investigate boththe 3-D and 2-D structures of the same numerical samplein combination with recent successes in predicting opti-cal and mass transfer properties through numerical sim-ulation [27, 28] should lead to valuable insight into thecoating structure in future. Related to modeling, on theexperimental side, one challenge remaining is the charac-terization of particle shape distributions. No satisfactoryequation exists to calculate particle shape for needle-likeparticles from particle size analysis data based on sedi-mentation.

With further research efforts on both experimental andtheoretical fronts, the reality of virtual experimentationof paper coating that ties together the pigment particleproperties, the detailed characterization of the coatingstructure and the physical and functional properties of thecoating, i.e., performance of the pigment coated paper,could be possible in future. The increased understandingof microscopic pore structures through the approach pro-posed in present work, enables pigment manufacturers todesign new, better pigment geometries and sizes, and pa-permakers to improve and optimize coating formulationswhen using existing pigments.

ACKNOWLEDGEMENTSThanks are expressed to John Parsons, Ian Soper,Matthew Cheeseman and Thomas Byholm for help withthe sample preparation and data analysis. Tony Hiorns isalso thanked for helpful discussions.

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APPENDIX 1. The FIB cross-section data and the corresponding MIS analysis data

PCC

GCC

APPENDIX 2. Examples of cross-sections and MIS analysis data for the numerical model coating structures.

PCC model structure

GCC model structure

Kaolin model structure