## 1 Introduction  
The utilization of crosslinkers in polymer chemistry has profoundly impacted the development and performance of various materials. Among these, zirconium-based crosslinkers have garnered significant attention due to their unique chemical properties and their ability to enhance the structural integrity and functionality of polymers [1; 2; 3]. Crosslinking, a process that involves linking polymer chains through chemical bonds, can dramatically alter the physical properties of materials, making them more suitable for a wide range of applications, from coatings and adhesives to biomedical devices [4; 5] and enhanced oil recovery [6; 7]. Crosslinkers are essential in the formulation of paper pigment coatings, where they play a critical role in improving the durability, gloss, water resistance, and printability of coated papers [8; 9; 10; 11]. Various types of crosslinkers have been employed in this domain, each offering distinct advantages and limitations. Formaldehyde-based crosslinkers such as urea-formaldehyde(UF) and melamine-formaldehyde(MF) resins were widely used until the advent of methylated MF and UF in the 1970s in paper pigment coating. These resins contain functional methoxymethyl (=NCH\({}_{2}\)OCH\({}_{3}\)) groups that react with hydroxyl groups of starch and polyvinyl alcohol (PVA) and carboxyl groups of latex, forming methylene and dimethylene ether linkages. These resins are sensitive to temperature and pH because they undergo acid-catalyzed condensation reactions [12; 13]. However, due to environmental and health concerns arising from formaldehyde emissions, regulatory restrictions and consumer demand for safer alternatives have significantly reduced their usage [14; 15; 16]. Conventional crosslinkers like glyoxal face significant challenges, including limited efficacy for synthetic water-soluble binders and ineffectiveness at higher pH levels, specifically above pH 8.5 [12; 17]. These limitations restrict their versatility and applicability across different binder systems. Additionally, glyoxal and its derivatives tend to increase the viscosity of wet formulations due to their reaction with hydroxyl groups in the binder, complicating the coating process and affecting the final product quality [18; 19; 20]. Environmental and health concerns are also prominent, as glyoxal is a known irritant and poses risks during handling and application [21; 22; 23]. Moreover, due to their specific chemical interactions with the binder, conventional crosslinkers can negatively impact the physical properties of coated paper, such as flexibility, printability, and adhesion [24]. These challenges underscore the need for more effective and environmentally friendly alternatives in paper coating applications. A commonly used form of zirconium crosslinker is ammonium zirconium carbonate (AZC), a soluble alkaline salt of zirconium available as an aqueous solution known for its insolubilization properties since the early 1960s [25; 26]. Among zirconium-based crosslinkers, AZC and potassium zirconium carbonate (KZC) are notable for their capability to insolubilize coatings. KZC was chosen for this study due to its broader operational pH range (3 to 8) and its effective crosslinking mechanism, which does not involve the evaporation of ammonia like AZC [27; 28]. The ammonia in AZC can react with clay dispersion, causing an undesirable increase in viscosity during storage times. As KZC is new on the market compared to AZC, it offers more excellent stability and ease of handling, making it more versatile and efficient in a wider range of coating formulations. Despite the growing interest in zirconium-based crosslinkers, there remains a gap in the comprehensive understanding of how varying the zirconium content affects the final properties of crosslinked materials. Zirconium content is a critical parameter in the formulation of these crosslinkers, influencing the viscosity, reactivity, and overall performance of the crosslinked network [29; 30; 31].