## 1 Introduction  
Due to the growing awareness of environmental issues in recent years, water-based sinks are increasing their market share. In particular, digital printing such as inkjet printing is growing steadily, due to the growing demand from mass production to on-demand production. Since organic pigments, which are typical colorants, are hydrophobic, they cannot be dispersed in water; therefore, the use of dispersants is essential. Polymeric dispersants are generally used under various requirements such as maintaining stability with the long-term use of ink and fixing it after printing on paper. It has been proposed that block polymers and comb-type polymers are advantageous for developing dispersion functions [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. Research on dispersion stabilization using block polymers comprising cationic and non-ionic hydrophilic domains has been actively conducted [2; 3; 4], where adsorption by ionic interaction with the particle surface, including inorganic nanoparticles, has been carried out. When using hydrophobic and organic pigments, particularly, amphiphilic block copolymers, which have a segregated hydrophilic and hydrophobic domain, inherently form a distinct core-shell structure, and thus they are more beneficial as ink dispersants. For example, [PERSON] et al., reported the dispersion effect on hydrophobic dye of block co-polymers comprising a cationic 4-vinyl pyridines domain and a hydrophobic acrylates domain [5], showing the dispersion performances were indeed influenced by the polymer properties. The variation in block copolymers has increased, owing to the remarkable progress of synthesis technology as shown in the above. As described above, organic pigments are hydrophobic. The adsorption of block copolymers on dispersed pigments under an aqueous milieu is basically determined based on the hydrophobic interaction; the larger hydrophobicity would give the better loading capacity for pigments. On the other hand, the ideal is for the block copolymer to have good water solubility as a dispersant to create inks homogeneously. Thus, there is a dilemma in designing the amphiphilic block copolymer between increasing hydrophilicity and hydrophobicity. Despite the dilemma, the amphiphilic block co-polymers with increased hydrophobicity are preferably selected, considering the advantage of the high loading-capacity of the pigments. When the water solubility of the block copolymer is too low, the water-soluble organic solvents are feasibly applied to dissolve the polymer. Although the organic-solvent amount should be within the range where mixing with the ink is acceptable, it can be effective for ink design. Using this method, polymeric dispersants were dissolved in organic solvents and transferred into water. For example, a method of preparing a dispersed polymer in methyl-ethyl-ketone (MEK), i.e., a pre-solution, and then suspending it in a large amount of water is well known [11; 12; 13]. However, in this method the polymers are not necessarily dissolved in water, but dispersed as particles, appearing as a cloudy solution, of a sub-micron scale in size. Although the adsorption of polymers on pigments would occur at the molecular level by mechanical methods of the inking process, including forcibly stirring, it is assumed that the homogeneity of ink, which is strongly related to the property and application of ink, can be further improved by promoting the molecular dispersion of the polymer to self-assemble before and during the ink-manufacturing process. Note that the behavior of the amphiphilic block copolymers in water would often have hysteresis of state before dispersing, i.e., the kinetics for dispersing the polymers in water is important for determining the behavior. Thus, in this study, we focused on the process of transferring pre-solutions from the solvent to the water phase, and estimated the parameters to obtain the unimodal polymer solution in water.