Bindemittelnachfragekurven und Motling-Schwellen für Pigmentpapierbeschichtungen

Binder demand curves for pigmented paper coatings are generated from systematic variation of the binder-to-pigment mass ratio in a fixed pigment blend, with dry binder content expressed in pph and the resulting dry coating tested for surface strength, porosity, optical scattering, and print uniformity. The curve is not a single material property but an operational response function that depends on the packed bed void fraction of the pigment, the particle size distribution of the latex, the dispersant demand of the pigment surface, and the drying and consolidation history. In traditional offset formulations, the curve is anchored by drawdowns made with wire-wound rods on polyester or coated paper substrates, followed by conditioning at 23 °C and 50 % RH in accordance with ISO 187:2022. At binder contents below the void-saturation requirement, pick strength measured by ISO 3783:2006 decreases steeply because the binder is discontinuous in the packed pigment layer; above the saturation requirement, the excess latex coalesces into films that fill interstitial voids and reduce the optical scattering coefficient. The motling threshold is the region of the binder demand curve where the coefficient of variation of full-tone print reflectance begins to rise above the tolerance limit of the end-use printing process.

The geometric void-filling calculation for a pigment cake begins with the void fraction ε of the dry pigment consolidated under standardized pressure. If the pigment cake has a void fraction of 0.30, the binder volume needed to fill the interstitial space is ε/(1−ε), or 0.43 cm³/cm³ of solid pigment. For a latex with density 1.0 g/cm³ and a calcium carbonate pigment with density 2.7 g/cm³, the mass ratio is therefore 0.16 g/g, equivalent to 16 pph. This void-filling calculation represents the geometric lower bound; additional binder is consumed by adsorption on the pigment surface, absorption into pore structures, coalescence shrinkage, and migration into the base sheet. The measured critical binder demand of a ground calcium carbonate coating may therefore lie between 12 pph and 18 pph depending on the particle size distribution: a steep distribution with a median diameter of 0.8 µm and a broad size range packs more efficiently than a narrow distribution, lowering ε and reducing geometric demand. The same calculation for a platy kaolin pigment with an oil absorption of 40 g/100 g under ISO 787-5 typically yields a demand above 20 pph because the plate-like particles create high-aspect-ratio voids and because the pigment surface adsorbs dispersant and binder.

What Limits Oil Absorption as a Binder Demand Proxy?

Oil absorption values determined by ISO 787-5 or ASTM D281 are widely used as a rapid proxy for binder demand, but the correlation is non-linear and breaks down when the latex particle diameter approaches the modal pore throat diameter of the pigment packing. The oil absorption endpoint is defined by the torque rise during mixing of linseed oil into a dry pigment at controlled rate, and it reports a practical balance between capillary saturation and cohesive paste formation. That balance does not capture the film-forming response of a latex with a glass transition temperature between −5 °C and 25 °C, nor does it capture the effect of carboxylated latex surface charge on calcium carbonate dispersions. The consequence is that two pigments with identical oil absorption may differ in actual binder demand by 3 pph to 6 pph when one pigment contains high-aspect-ratio plates and the other contains low-aspect-ratio rhombohedral particles.

The discrepancy between geometric demand and oil absorption is amplified for plate-like pigments because the platy particles produce oriented microvoids that are not filled by linseed oil under low-shear mixing but are filled by latex under blade pressure and drying capillary force. Further divergence originates in the specific surface area measured by ISO 9277. A ground calcium carbonate with a nitrogen adsorption surface area of 10 m²/g may require less adsorbed binder than a fine delaminated kaolin with 15 m²/g, even if both have similar oil absorption. Therefore, a robust binder demand curve must be built from direct functional tests rather than from single-point oil absorption values. The direct tests include dry and wet pick strength under ISO 3783:2006, porosity by mercury intrusion under ISO 15901-1:2016, and print gloss under ISO 8254-1:2009. Each of these responses is plotted against binder content to identify the point at which additional binder no longer improves cohesion but begins to degrade optical uniformity.

Production-scale experience from short-dwell blade coaters demonstrates that the binder demand curve shifts upward when coating color solids are increased from 60 % to 68 %. The increase in solids reduces the water available for dispersion expansion, compresses the pigment packing under the blade, and changes the immobilization point. Coaters running at 1,000 m/min with blade dwell times below 5 ms frequently encounter a sharp rise in blade pressure variability when the binder level is within 1 pph of the geometric demand limit. The practical operational boundary is therefore not the geometric void-filling point but a higher critical binder level that compensates for binder migration into the base sheet and for the viscosity gradient that develops near the blade tip. Published data for this specific high-speed short-dwell configuration is limited; individual mills typically establish internal control limits with repeated IGT pick series and print mottle trials.

When Latex Binder Flocculation Shifts the Immobilization Point

The immobilization point is the time or position during coating consolidation at which the wet coating ceases to flow under shear and begins to retain particle contacts. In a short-dwell applicator, immobilization occurs within 50 ms to 200 ms after the blade, depending on base paper absorbency, coating solids, and binder chemistry. A carboxylated styrene-butadiene latex with a particle diameter of 120 nm can flocculate in the presence of dissolved calcium ions leached from ground calcium carbonate at pH above 8.5. When the flocculation initiated by residence time in the recirculation loop or high-shear zone raises the yield stress of the coating color, the immobilization point moves earlier and the binder demand curve shifts upward. The result is a coating structure in which binder-rich domains and binder-poor domains coexist, and print mottle appears at higher average binder levels than expected from the geometric calculation.

Temperature and pH control are therefore critical when binder demand curves are transferred from laboratory drawdowns to production trials. A laboratory color mixed at 22 °C may show a critical binder level of 14 pph, whereas the same color at 38 °C in a production circulation system may require 17 pph because of accelerated calcium ion release and latex destabilization. The dispersion demand of the pigment also modifies the immobilization point: an anionic polyacrylate dispersant added at 0.20 pph to 0.35 pph on dry pigment can maintain electrostatic repulsion and delay flocculation, but overdosage is known to increase water sensitivity and lower wet pick strength. The binder demand curve must therefore be constructed at controlled pH between 8.0 and 9.0, with soluble calcium concentration measured by conductivity or ion-selective electrode, because calcium levels above 150 ppm in the aqueous phase may invalidate the correlation between oil absorption and binder demand.

Motling Threshold Methodology and Surface Strength Differentials

Print mottle in coated paper is evaluated by scanning a printed full-tone or mid-tone area and calculating the coefficient of variation of reflectance after image segmentation. The method defined in ISO 13660:2001 is used to derive a mottle index that separates low-frequency non-uniformity from graininess, which is a higher-frequency defect. The motling threshold on a binder demand curve is the binder content below which the mottle index rises by more than 0.5 % to 1.0 % coefficient of variation relative to the same formulation above the threshold. No single standardized acceptance limit exists for all printing processes, because heat-set web offset, sheetfed offset, and rotogravure impose different ink rheologies and solvent demands. Individual mill specifications frequently set an upper mottle index limit between 1.0 % and 2.0 % for the mid-tone of a four-color offset print.

The motling threshold is commonly lower in heat-set web offset than in sheetfed offset because the high-temperature drying stage accelerates binder migration and redistributes latex toward the coating surface. A heat-set formulation with 12 pph binder may exhibit acceptable pick strength but unacceptable mottle because the binder content is insufficient to maintain uniform holdout after solvent penetration and rapid drying. The relationship between surface strength differential and motling threshold is measured by comparing IGT dry pick at the top and bottom of the coating in a split-tape procedure. When the surface pick strength drops by more than 0.3 m/s to 0.5 m/s across the coating thickness, the formulation is operating below the motling threshold even if the average pick value remains acceptable.

The choice of pigment blend modifies the motling threshold by changing the void size distribution and the tortuosity of the conductive pathways that carry water and binder during drying. A blend of 70 parts ground calcium carbonate and 30 parts delaminated kaolin may exhibit a motling threshold near 14 pph in laboratory drawdowns, while a blend of 50 parts GCC and 50 parts platy talc may shift the threshold upward by 2 pph to 4 pph because the platy talc creates a more tortuous network that traps binder in the lower coating layer. Published data for this specific pigment combination is limited, and the effect must be verified through a binder ladder on the target base paper using the precise base sheet absorbency and roughness conditions of the production machine.

Dewatering Rate Under Blade Pressure Controls the Practical Binder Window

Dewatering rate is the variable that most directly controls whether the practical binder window is wider or narrower than the geometric window. The water retention of coating colors is measured under pressure by TAPPI T 701 or by the Åbo Akademi gravimetric water retention device, and values in the range of 80 g/m² to 120 g/m² are typical for blade coating at high solids. When the water retention value increases, the coating remains mobile longer after the blade, allowing the pigment particles to rearrange into a denser packing before immobilization. That densification reduces the geometric binder demand and can lower the motling threshold, but it also increases the risk of binder migration because the aqueous phase remains free for a longer drying interval.

Operational boundaries on a production blade coater are therefore never fixed solely by the binder content in the formulation. They depend on blade angle, blade pressure, backing roll hardness, base sheet absorbency, drying temperature profile, and coating color temperature. Blade pressures between 150 kPa and 400 kPa produce different consolidation zones and different immobilization points, and the same formulation may show a motling threshold of 13 pph at 150 kPa and 16 pph at 300 kPa because higher pressure drives more dewatering into the base sheet. A coating color containing calcium ions from ground calcium carbonate should not be combined with amine-based pH adjustment additives that can accelerate latex destabilization and shift the binder demand curve upward. The practical binder window must therefore be re-established whenever the blade pressure, solids content, base sheet grade, or recirculation temperature changes by more than ±1 pph on the binder axis.