JP7552065B2 - Method for producing aqueous pigment dispersion and aqueous ink, and method for designing aqueous pigment dispersion and aqueous ink - Google Patents

Description

The present invention relates to a method for producing an aqueous pigment dispersion and an aqueous ink, and a method for designing an aqueous pigment dispersion and an aqueous ink.

In recent years, water-based inks have been replacing organic solvent-based inks in a wide range of fields due to their safety and low environmental impact. In particular, water-based inks have almost no odor, so there is an increasing demand for them as inks that can be used in closed spaces such as offices.

Water-based inks are used in a variety of printing methods, including offset printing, gravure printing, and inkjet recording. Among these, the inkjet recording method allows on-demand printing, and is currently being studied extensively as an alternative to the electrophotographic (toner) method used in offices, etc.

Water-based inks are produced, for example, by supplying and mixing a binder resin, an aqueous medium, etc., as necessary, to an aqueous pigment dispersion obtained by dispersing a pigment in an aqueous medium in advance using a pigment dispersant. Therefore, when using water-based inks in inkjet recording methods, in order to provide good ejection stability, it is important to use an aqueous pigment dispersion that can reduce the generation of coarse particles, for example, caused by the pigment, which can cause clogging of the aqueous ink ejection nozzle, and can prevent the pigment from settling over time.

In order to control the aggregation and sedimentation of pigments in an aqueous pigment dispersion and obtain an aqueous pigment dispersion having high pigment dispersion stability, it is important to quantify the interactions between the pigment, the pigment dispersant, and the aqueous medium (in other words, the phenomena occurring near the pigment interface). However, these interactions are dynamic behaviors, and it is difficult to quantify them by direct observation.
Therefore, currently, the phenomena occurring near the pigment interface can only be qualitatively explained by combining multiple analytical methods.

In light of this situation, a method has been proposed to quantify the phenomena occurring near the pigment interface in an aqueous pigment dispersion by combining the results of small-angle X-ray scattering of ink using a large synchrotron radiation facility (SPring 8) with the easily measurable physical properties of the aqueous pigment dispersion (viscosity, particle size, etc.) (see Non-Patent Document 1). This method is praised for successfully quantifying the interactions between the pigment, pigment dispersant, and aqueous medium, as well as the dispersion state of the pigment. However, since measurements must be made at the large synchrotron radiation facility (SPring 8), which is the only one in Japan and is both extremely large and extremely expensive, it is difficult to use it every time during product development or when dealing with problems.

On the other hand, a storage test is generally conducted as a simple method for evaluating the pigment dispersion stability of an aqueous pigment dispersion. However, even if the storage test is accelerated by applying a temperature load of, for example, 60°C, the evaluation of the pigment dispersion stability may usually require a period of one month or more. Therefore, conventional storage tests have been a factor in lengthening the product development period.

J. Jpn. SOC. Color Mater. , 92 213 (2019)

Therefore, an object of the present invention is to provide a method for producing an aqueous pigment dispersion that does not require large-scale equipment and that can produce an aqueous pigment dispersion having high pigment dispersion stability in a short period of time, and a method for producing an aqueous ink using the aqueous pigment dispersion.
Another object of the present invention is to provide a method for designing an aqueous pigment dispersion, which can design an aqueous pigment dispersion having high pigment dispersion stability in a short period of time without requiring large-scale equipment, and a method for designing an aqueous ink using the design method.

As a result of intensive research into solving the above problems, the inventors found that the above problems could be solved by using pulse NMR measurement to determine an index of hydrophilicity and an index of the total surface area of the particles for a pigment dispersion for evaluation containing a pigment, a pigment dispersant, and an aqueous medium, and using these indices to determine the composition ratio of the pigment and pigment dispersant in an aqueous pigment dispersion containing a pigment, a pigment dispersant, and an aqueous medium that have solubility parameters that are close to those of the pigment, pigment dispersant, and aqueous medium in the pigment dispersion for evaluation, respectively, thereby completing the present invention.

前記式（１）中、Ｒ_ａｖは、前記１つの評価用水分散体の前記Ｔ２緩和時間の逆数を表し、Ｒ_ｂは、前記ブランク溶液の前記Ｔ２緩和時間の逆数を表す。
［３］ 前記粒子の総表面積の指標が、前記粒子の体積平均粒径の逆数と正比例する値である前記［１］～［２］のいずれかに記載の水性顔料分散体の製造方法。
［４］ 前記粒子の総表面積の指標を得る工程が、前記粒子の体積平均粒径から、下記式（２）により、前記粒子の総表面積の指標である粒子の総表面積値（ＴＳＡ）を得ることを、前記複数の評価用分散体のそれぞれについて行う処理を含む、
前記［１］～［３］のいずれかに記載の水性顔料分散体の製造方法。

前記式（２）中、Ｍ_ｖは、前記粒子の体積平均粒径を表す。
前記式（２）中、Ψ_ｐは、粒子体積比を意味し、下記式（３）で表される。

前記式（２）及び式（３）中、ρ_ｐは、前記第１の顔料の密度を表す。
前記式（３）中、Ｃ_ｐは、前記評価用分散体における前記第１の顔料の濃度を表す。
前記式（３）中、ρ_ｗは、前記第１の水性媒体の密度を表す。
［５］ 前記［１］～［４］のいずれかに記載の水性顔料分散体の製造方法により水性顔料分散体を製造する工程と、
前記水性顔料分散体と、バインダー樹脂と、第３の水性媒体とを混合する工程と、
を含むことを特徴とする水性インクの製造方法。
［６］ 第２の顔料と第２の顔料分散剤と第２の水性媒体とを含有する水性顔料分散体における前記第２の顔料と前記第２の顔料分散剤と前記第２の水性媒体との組成比率を決定する水性顔料分散体の設計方法であって、
第１の顔料と第１の顔料分散剤としてのポリビニルピロリドンと第１の水性媒体とを含有し、前記第１の顔料に対する前記第１の顔料分散剤の組成比率が異なる複数の評価用分散体を用意する工程と、
前記複数の評価用分散体のそれぞれについて、パルスＮＭＲ測定によりＴ２緩和時間を求め、前記Ｔ２緩和時間の逆数に基づいて親水化度の指標を得る工程と、
前記複数の評価用分散体のそれぞれについて、粒子の体積平均粒径の測定を行い、前記粒子の総表面積の指標を得る工程と、
前記親水化度の指標を横軸とし、前記粒子の総表面積の指標を縦軸としたときの、前記親水化度の指標、前記粒子の総表面積の指標、及び前記組成比率の関係を示すグラフにおいて前記粒子の総表面積の指標が極大値をとるときの、前記第１の顔料に対する前記第１の顔料分散剤の組成質量比率（Ｒ／Ｐ）の±０．２以下の範囲を、前記水性顔料分散体における前記第２の顔料に対する前記第２の顔料分散剤の組成質量比率として決定する第１の工程と、
前記決定した組成質量比率に従って前記水性顔料分散体における前記第２の顔料と前記第２の顔料分散剤と前記第２の水性媒体との組成比率を決定する第２の工程と、
を含み、
前記第２の顔料のハンセン溶解度パラメータが、前記第１の顔料のハンセン溶解度パラメータの±３（Ｊ／ｃｍ^３）^１／２以下であり、
前記第２の顔料分散剤のハンセン溶解度パラメータが、前記第１の顔料分散剤のハンセン溶解度パラメータの±１０（Ｊ／ｃｍ^３）^１／２以下であり、
前記第２の水性媒体のハンセン溶解度パラメータが、前記第１の水性媒体のハンセン溶解度パラメータの±３（Ｊ／ｃｍ^３）^１／２以下である、
ことを特徴とする水性顔料分散体の設計方法。
［７］ 前記［６］に記載の水性顔料分散体の設計方法を用いて前記第２の顔料と前記第２の顔料分散剤と前記第２の水性媒体とを含有する水性顔料分散体を設計する工程と、
前記設計された水性顔料分散体と、バインダー樹脂と、第３の水性媒体との組成比率を決定する工程と、
を含むことを特徴とする水性インクの設計方法。 That is, the present invention includes the following aspects.
[1] A method for producing an aqueous pigment dispersion containing a second pigment, a second pigment dispersant, and a second aqueous medium, comprising the steps of:
preparing a plurality of evaluation dispersions each containing a first pigment, polyvinylpyrrolidone as a first pigment dispersant, and a first aqueous medium, the plurality of evaluation dispersions each having a different composition ratio of the first pigment dispersant to the first pigment;
determining a T2 relaxation time for each of the plurality of evaluation dispersions by pulse NMR measurement, and obtaining an index of hydrophilicity based on the reciprocal of the T2 relaxation time;
measuring the volume average particle size of the particles for each of the plurality of evaluation dispersions to obtain an index of the total surface area of the particles;
determining, as a composition mass ratio of the second pigment dispersant to the second pigment in the aqueous pigment dispersion, a range of ±0.2 or less of a composition mass ratio (R/P) of the first pigment dispersant to the first pigment when the index of the total surface area of the particles takes a maximum value in a graph showing the relationship between the index of the hydrophilicity degree, the index of the total surface area of the particles, and the composition ratios, with the index of the hydrophilicity degree being plotted on the horizontal axis and the index of the total surface area of the particles being plotted on the vertical axis;
mixing the second pigment, the second pigment dispersant, and the second aqueous medium in accordance with the determined composition mass ratio;
Including,
the Hansen solubility parameter of the second pigment is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment;
the Hansen solubility parameter of the second pigment dispersant is within ±10 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment dispersant;
The Hansen solubility parameter of the second aqueous medium is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first aqueous medium;
A method for producing an aqueous pigment dispersion comprising the steps of:
[2] The step of obtaining the index of hydrophilicity includes a process of determining a T2 relaxation time by the pulse NMR measurement for a blank solution having the same composition ratio of the first pigment dispersant and the first aqueous medium in one of the plurality of evaluation dispersions and not containing the first pigment, and obtaining an index of hydrophilicity (R sp ), which is an index of the hydrophilicity, from the reciprocal of the T2 relaxation time of the one evaluation aqueous dispersion and the reciprocal of the T2 relaxation time of the blank solution according to the following formula ( ₁ ), for each of the plurality of evaluation dispersions.
A method for producing the aqueous pigment dispersion described in [1] above.

In the formula (1), R _av represents the reciprocal of the T2 relaxation time of one of the aqueous dispersions for evaluation, and R _b represents the reciprocal of the T2 relaxation time of the blank solution.
[3] The method for producing an aqueous pigment dispersion according to any one of [1] to [2] above, wherein the index of the total surface area of the particles is a value that is directly proportional to the reciprocal of the volume average particle size of the particles.
[4] The step of obtaining an index of the total surface area of the particles includes a process of obtaining a total particle surface area value (TSA), which is an index of the total surface area of the particles, from the volume average particle size of the particles by the following formula (2), for each of the plurality of evaluation dispersions,
The method for producing the aqueous pigment dispersion according to any one of items [1] to [3] above.

In the formula (2), _Mv represents the volume average particle size of the particles.
In the above formula (2), Ψ _p means a particle volume ratio and is represented by the following formula (3).

In the formulas (2) and (3), ρ _p represents the density of the first pigment.
In the formula (3), _Cp represents the concentration of the first pigment in the dispersion for evaluation.
In the formula (3), _ρw represents the density of the first aqueous medium.
[5] A step of producing an aqueous pigment dispersion by the method for producing an aqueous pigment dispersion according to any one of [1] to [4] above;
mixing the aqueous pigment dispersion, a binder resin, and a third aqueous medium;
A method for producing an aqueous ink, comprising:
[6] A method for designing an aqueous pigment dispersion, the method comprising determining a composition ratio of a second pigment, a second pigment dispersant, and a second aqueous medium in an aqueous pigment dispersion containing the second pigment, the second pigment dispersant, and the second aqueous medium, the method comprising the steps of:
preparing a plurality of evaluation dispersions each containing a first pigment, polyvinylpyrrolidone as a first pigment dispersant, and a first aqueous medium, the dispersions having different composition ratios of the first pigment dispersant to the first pigment;
determining a T2 relaxation time for each of the plurality of evaluation dispersions by pulse NMR measurement, and obtaining an index of hydrophilicity based on the reciprocal of the T2 relaxation time;
measuring the volume average particle size of the particles for each of the plurality of evaluation dispersions to obtain an index of the total surface area of the particles;
a first step of determining, as a composition mass ratio of the second pigment dispersant to the second pigment in the aqueous pigment dispersion, a range of ±0.2 or less of a composition mass ratio (R/P) of the first pigment dispersant to the first pigment when the index of the total surface area of the particles takes a maximum value in a graph showing the relationship between the index of the hydrophilicity degree, the index of the total surface area of the particles, and the composition ratio, with the index of the hydrophilicity degree being plotted on the horizontal axis and the index of the total surface area of the particles being plotted on the vertical axis;
a second step of determining a composition ratio of the second pigment, the second pigment dispersant, and the second aqueous medium in the aqueous pigment dispersion according to the determined composition mass ratio;
Including,
the Hansen solubility parameter of the second pigment is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment;
the Hansen solubility parameter of the second pigment dispersant is within ±10 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment dispersant;
The Hansen solubility parameter of the second aqueous medium is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first aqueous medium;
A method for designing an aqueous pigment dispersion comprising the steps of:
[7] A step of designing an aqueous pigment dispersion containing the second pigment, the second pigment dispersant, and the second aqueous medium by using the method for designing an aqueous pigment dispersion described in [6] above;
determining a composition ratio of the designed aqueous pigment dispersion, a binder resin, and a third aqueous medium;
A method for designing an aqueous ink, comprising:

According to the present invention, it is possible to provide a method for producing an aqueous pigment dispersion that does not require large-scale equipment and that can produce an aqueous pigment dispersion having high pigment dispersion stability in a short period of time, and a method for producing an aqueous ink using the aqueous pigment dispersion.
Furthermore, according to the present invention, it is possible to provide a method for designing an aqueous pigment dispersion, which can design an aqueous pigment dispersion having high pigment dispersion stability in a short period of time without requiring large-scale equipment, and a method for designing an aqueous ink using the design method.

FIG. 1 is a plot of _Rsp vs. TSA for evaluation dispersions with different ratios of pigment to pigment dispersant. FIG. 1 is a plot of K _a vs. TSA for evaluation dispersions with different ratios of pigment to pigment dispersant.

The manufacturing method of the aqueous pigment dispersion and aqueous ink of the present invention, and the design method of the aqueous pigment dispersion and aqueous ink are described in detail below. However, the explanation of the constituent elements described below is one example of one embodiment of the present invention, and is not limited to these contents.

(Method of Producing Aqueous Pigment Dispersion and Method of Designing Aqueous Pigment Dispersion)
The method for producing an aqueous pigment dispersion of the present invention includes a step of preparing a plurality of dispersions for evaluation, a step of obtaining an index of the degree of hydrophilicity, a step of obtaining an index of the total surface area of the particles, a determining step, and a mixing step, and further includes other steps as necessary.
The method for producing an aqueous pigment dispersion is a method for producing an aqueous pigment dispersion containing a second pigment, a second pigment dispersant, and a second aqueous medium.
The second pigment, the second pigment dispersant, and the second aqueous medium will be described in detail later.
The method for designing an aqueous pigment dispersion of the present invention includes a step of preparing a plurality of dispersions for evaluation, a step of obtaining an index of the degree of hydrophilicity, a step of obtaining an index of the total surface area of the particles, a first determining step, and a second determining step, and further includes other steps as necessary.

The present inventors have conducted extensive research with the aim of providing a method for producing an aqueous pigment dispersion that does not require large-scale equipment and that can produce an aqueous pigment dispersion having high pigment dispersion stability in a short period of time, and a method for producing an aqueous ink using the aqueous pigment dispersion.
The present inventors have also conducted intensive research with the aim of providing a method for designing an aqueous pigment dispersion, which can produce an aqueous pigment dispersion having high pigment dispersion stability in a short period of time without requiring large-scale equipment, and a method for designing an aqueous ink using the design method.
From the index of hydrophilicity obtained by pulse NMR measurement of the aqueous pigment dispersion and the index of the total surface area of the particles, it was possible to find a ratio of pigment and pigment dispersant effective for pigment dispersion stability in the aqueous pigment dispersion. It was also found that the ratio can be applied to pigments, pigment dispersants, and aqueous media having Hansen solubility parameters similar to those of the pigments, pigment dispersants, and aqueous media used in the measurement.
As a result, the inventors found that the problems of the present invention can be solved by determining an index of the degree of hydrophilicity using pulse NMR measurement for a pigment dispersion for evaluation containing a pigment, a pigment dispersant, and an aqueous medium, and also determining an index of the total surface area of the particles, and using these determined indices to determine the composition ratios of the pigment and pigment dispersant in an aqueous pigment dispersion containing a pigment, a pigment dispersant, and an aqueous medium having solubility parameters approximate to those of the pigment, pigment dispersant, and aqueous medium in the dispersion for evaluation, respectively, thereby completing the present invention.
Specifically, the inventors have found that when the composition ratio of the pigment dispersant to the pigment is plotted on a graph with the hydrophilicity index determined for the evaluation dispersion on the horizontal axis and the total surface area index of the particles on the vertical axis, the composition ratio that gives the maximum value is the composition ratio that provides excellent pigment dispersion stability.

<Step of preparing multiple dispersions for evaluation>
The step of preparing a plurality of dispersions for evaluation is not particularly limited as long as it is a step of preparing a plurality of dispersions for evaluation containing a first pigment, polyvinylpyrrolidone as a first pigment dispersant, and a first aqueous medium, and having different composition ratios of the first pigment dispersant to the first pigment. The dispersions for evaluation are usually obtained by mixing the first pigment, the first pigment dispersant, and the first aqueous medium.

The first pigment dispersant is preferably polyvinylpyrrolidone, since it has a simple composition, is a standard pigment dispersant, and has high affinity for a wide range of pigments. However, other pigment dispersants may be used as the first pigment dispersant.
The molecular weight of polyvinylpyrrolidone is not particularly limited, but a weight average molecular weight of 80,000 to 120,000 is preferred in view of the standard molecular weight for a pigment dispersant.
The first pigment, the other first pigment dispersants, and the first aqueous medium will be described in detail below.

The concentration (content) of the first pigment in the dispersion for evaluation is not particularly limited, but may be, for example, 1 to 40 mass %, 5 to 30 mass %, or 10 to 25 mass %.
The content of the first aqueous medium in the dispersion for evaluation is not particularly limited, but may be, for example, 50 to 99 mass %, 60 to 95 mass %, or 75 to 90 mass %.
The composition mass ratio of the first pigment dispersant to the first pigment in the multiple dispersions for evaluation is not particularly limited, but may be, for example, 0.01 to 0.99, 0.05 to 0.80, or 0.10 to 0.70.
However, the total content of the first pigment, the first pigment dispersant, and the first aqueous medium in the dispersion for evaluation does not exceed 100% by mass.

When preparing multiple dispersions for evaluation, the difference in the composition mass ratio of the first pigment dispersant to the first pigment is not particularly limited, but may be changed in increments of 0.05 or 0.1, for example.

The dispersion for evaluation can be produced, for example, by the following method.
(1) A method of preparing a dispersion for evaluation by adding a first pigment to a mixture containing a first pigment dispersant and a first aqueous medium, and then dispersing the first pigment in the mixture using a stirring and dispersing device.
(2) A method in which a first pigment and a first pigment dispersant are kneaded using a kneading machine such as a two-roll mill or a mixer, the resulting kneaded mixture is added to a first aqueous medium, and a dispersion for evaluation is prepared using a stirring and dispersing device.
(3) A method in which a first pigment is added to a solution obtained by dissolving a first pigment dispersant in an organic solvent compatible with water, such as methyl ethyl ketone, tetrahydrofuran, etc., and then the first pigment is dispersed in the organic solution using a stirring and dispersing device, and then phase inversion emulsification is carried out using an aqueous medium, and the organic solvent is then distilled off to prepare a dispersion for evaluation.

The kneading machine is not particularly limited, but examples include a Henschel mixer, a pressure kneader, a Banbury mixer, an intensive mixer, a planetary mixer, and a butterfly mixer.

As stirring and dispersing devices, for example, ultrasonic homogenizers, high-pressure homogenizers, paint shakers, ball mills, roll mills, sand mills, sand grinders, Dyno Mills, Dispermats, SC Mills, Nanomizers, etc. can be used alone or in combination of two or more types.

<Step of Obtaining an Index of Hydrophilicity>
The step of obtaining an index of the hydrophilicity is not particularly limited as long as it is a step of determining the T2 relaxation time for each of a plurality of dispersions for evaluation by pulse NMR measurement and obtaining an index of the hydrophilicity based on the reciprocal of the T2 relaxation time.

Pulsed NMR (Nuclear Magnetic Resonance) is a technique specialized for obtaining the relaxation time (spin-lattice relaxation time: T1 relaxation time) and spin-spin relaxation time (T2 relaxation time) of 1H nuclei, which are indexes for evaluating molecular mobility.
The pulsed NMR measurement has the following features.
・Very sensitive to sample conditions (hardness of solid materials, molecular motion of liquid samples, etc.) ・No need for pretreatment such as drying or degassing ・Upper concentration limit is fundamentally unlimited, lower concentration limit is 1% to 2%
・Measurement time is only about 5 minutes from start to finish ・Good reproducibility

In general, the movement of liquid molecules adsorbed to particle surfaces is restricted, but liquid molecules in the bulk liquid can move freely. As a result, the NMR relaxation time (T2 relaxation time) of liquid molecules adsorbed to particle surfaces is shorter than the T2 relaxation time of molecules in the bulk liquid, and can differ by several orders of magnitude. The inverse of the T2 relaxation time is related to the degree of hydrophilicity of particles in the particle dispersion.

The pulsed NMR measurement can be carried out, for example, under the following conditions.
Measurement device: Acron Area (manufactured by XiGo Nanotools)
Pulse sequence: CPMG method Resonance frequency: 13 MHz
Measurement temperature: 30°C
Measurement sample: 1.0 ^cm3

式（１）中、Ｒ_ａｖは、１つの評価用水分散体のＴ２緩和時間の逆数を表し、Ｒ_ｂは、ブランク溶液のＴ２緩和時間の逆数を表す。
ただし、本発明において、式（１）は、本発明の効果を阻害しない範囲で、変形がされていてもよい。例えば、式（１）の右辺に、右辺の（Ｒ_ａｖ－Ｒ_ｂ）／Ｒ_ｂを整数倍するような係数ａが付されていてもよい。その場合、求められるＲ_ｓｐは、係数ａがない場合と比べてａ倍大きい値である。しかし、粒子の総表面積の指標と組み合わせて顔料と顔料分散剤との組成比率の最適範囲を求める際には、その値の変化は、求められる最適範囲には、影響しない。そのような変形された式（１）も前記式（１）に含まれる。 The index of hydrophilicity is preferably calculated from the reciprocal of the T2 relaxation time of the dispersion for evaluation and the reciprocal of the T2 relaxation time of the blank solution.
That is, the step of obtaining an index of the hydrophilicity preferably includes a process of determining the T2 relaxation time by pulse NMR measurement for a blank solution having the same composition ratio of the first pigment dispersant and the first aqueous medium in one of the plurality of evaluation dispersions and not containing the first pigment, and obtaining an index of the hydrophilicity (Rsp), which is an index of the hydrophilicity, from the reciprocal of the T2 relaxation time of one of the evaluation aqueous dispersions and the reciprocal of the T2 relaxation time of the blank solution according to the following formula (1), for each of the plurality of evaluation dispersions.

In formula (1), R _av represents the reciprocal of the T2 relaxation time of one aqueous dispersion for evaluation, and R _b represents the reciprocal of the T2 relaxation time of the blank solution.
However, in the present invention, formula (1) may be modified within a range that does not impair the effects of the present invention. For example, a coefficient a may be added to the right side of formula (1) such that (R _av -R _b )/R _b on the right side is multiplied by an integer. In that case, the R _sp obtained is a value a times larger than when there is no coefficient a. However, when determining the optimum range of the composition ratio of the pigment and the pigment dispersant in combination with an index of the total surface area of the particles, a change in this value does not affect the optimum range that is obtained. Such modified formula (1) is also included in the above formula (1).

<Step of obtaining an index of total surface area of particles>
The step of obtaining an index of the total surface area of the particles is not particularly limited as long as it is a step of measuring the volume average particle size of the particles for each of a plurality of dispersions for evaluation and obtaining an index of the total surface area of the particles.

The volume average particle size of the particles can be measured, for example, under the following conditions.
Measuring device: Microtrac MT3000II (manufactured by Microtrac Bell)
Measurement solvent: water Solvent refractive index: 1.333
Abundance ratio: volume basis Particle transmittance: transmittance Particle shape: non-spherical Particle refractive index: 1.81
・Analysis mode: Rosin-Rammler distribution (±2σ) (Software included with the device: DMS ver. 11.0.0-246V)

式（２）中、Ｍ_ｖは、粒子の体積平均粒径を表す。
式（２）中、Ψ_ｐは、粒子体積比を意味し、下記式（３）で表される。

式（２）及び式（３）中、ρ_ｐは、第１の顔料の密度を表す。
式（３）中、Ｃ_ｐは、評価用分散体における第１の顔料の濃度を表す。
式（３）中、ρ_ｗは、第１の水性媒体の密度を表す。
なお、本発明において、式（２）は、本発明の効果を阻害しない範囲で、変形がされていてもよい。例えば、式（２）の右辺に、右辺の〔６／（ρ_ｐ×Ｍ_ｖ）〕×Ψ_ｐを整数倍するような係数ｂが付されていてもよい。その場合、求められるＴＳＡは、係数ｂがない場合と比べてｂ倍大きい値である。しかし、親水化度の指標と組み合わせて顔料と顔料分散剤との組成比率の最適範囲を求める際には、その値の変化は、求められる最適範囲には、影響しない。そのような変形された式（２）も前記式（２）に含まれる。 The index of the total surface area of the particles is preferably a value that is directly proportional to the reciprocal of the volume average particle size of the particles.
Furthermore, the step of obtaining an index of the total surface area of the particles preferably includes a process of obtaining a total particle surface area value (TSA), which is an index of the total surface area of the particles, from the volume average particle size of the particles using the following formula (2), for each of the multiple evaluation dispersions.

In formula (2), _Mv represents the volume average particle size of the particles.
In formula (2), Ψ _p means a particle volume ratio and is represented by the following formula (3).

In formulas (2) and (3), ρ _p represents the density of the first pigment.
In formula (3), _Cp represents the concentration of the first pigment in the dispersion for evaluation.
In formula (3), ρ _w represents the density of the first aqueous medium.
In the present invention, formula (2) may be modified within a range that does not impair the effects of the present invention. For example, a coefficient b may be added to the right side of formula (2) such that [6/(ρ _p ×M _v )] × Ψ _p on the right side is multiplied by an integer. In this case, the TSA obtained is a value b times larger than when there is no coefficient b. However, when determining the optimal range of the composition ratio of the pigment and the pigment dispersant in combination with the hydrophilicity index, the change in this value does not affect the optimal range obtained. Such modified formula (2) is also included in the above formula (2).

<Determining (first) step>
The step of determining the composition mass ratios in the manufacturing method of an aqueous pigment dispersion, and the first step of determining the composition mass ratios in the design method of an aqueous pigment dispersion are not particularly limited as long as they are steps of determining, as the composition mass ratio of the second pigment dispersant to the second pigment in the aqueous pigment dispersion, a range of ±0.2 or less of the composition mass ratio (R/P) of the first pigment dispersant to the first pigment when the index of the total surface area of the particles takes a maximum value in a graph showing the relationship between the index of the hydrophilicity degree, the index of the total surface area of the particles, and the composition ratios, with the index of the hydrophilicity degree on the horizontal axis and the index of the total surface area of the particles on the vertical axis.
The pigment dispersion stability of the dispersion for evaluation is most stable at the maximum value in the graph. If the index of the total surface area of the particles is within ±0.2 of the composition mass ratio (R/P) at the maximum value in the graph, the pigment dispersion stability is superior to other ranges.
The reason why the local maximum value was adopted instead of the maximum value is as follows. The pigment surface has a wide distribution in terms of interface chemistry, and even if a pigment dispersion is uniform when viewed macroscopically, it is expected that the pigment surface is likely to have non-uniform adsorption of the solvent or resin when viewed microscopically. Furthermore, the interface chemistry distribution may also have multiple peaks depending on the pigment type. For this reason, if the maximum value instead of the local maximum value is adopted in the graph, there is a concern that the optimal value will be overlooked.

The range of the composition mass ratio (R/P) within ±0.2 is further preferably within ±10% of the TSA at the maximum value and within ±5% of the R _sp at the maximum value.

<Mixing step>
The mixing step is not particularly limited as long as it is a step of mixing the second pigment, the second pigment dispersant, and the second aqueous medium in accordance with the determined composition mass ratio.
Here, when the second pigment, the second pigment dispersant, and the second aqueous medium are mixed according to the determined composition mass ratio, the composition mass ratio may be exactly the same as the determined composition mass ratio, or the composition mass ratio may be slightly changed within a range that does not impair the pigment dispersion stability. For example, the concentration of the second pigment in the aqueous pigment dispersion to be produced may differ by ±2 mass% from the concentration of the second pigment in the aqueous pigment dispersion at the determined composition mass ratio. For example, the concentration of the second pigment dispersant in the aqueous pigment dispersion to be produced may differ by ±2 mass% from the concentration of the second pigment dispersant in the aqueous pigment dispersion at the determined composition mass ratio. For example, the concentration of the second aqueous medium in the aqueous pigment dispersion to be produced may differ by ±2 mass% from the concentration of the second aqueous medium in the aqueous pigment dispersion at the determined composition mass ratio.

The mixing method may be, for example, the following method.
(1) A method for preparing an aqueous pigment dispersion by adding a second pigment to a mixture containing a second pigment dispersant and a second aqueous medium, and then dispersing the second pigment in the mixture using a stirring and dispersing device.
(2) A method in which a second pigment and a second pigment dispersant are kneaded using a kneading machine such as a two-roll mill or a mixer, the resulting kneaded mixture is added to a second aqueous medium, and an aqueous pigment dispersion is prepared using a stirring and dispersing device.
(3) A method in which a second pigment is added to a solution obtained by dissolving a second pigment dispersant in an organic solvent compatible with water, such as methyl ethyl ketone, tetrahydrofuran, etc., and then the second pigment is dispersed in the organic solution using a stirring and dispersing device. Next, phase inversion emulsification is performed using an aqueous medium, and then the organic solvent is distilled off to prepare an aqueous pigment dispersion.

Examples of the kneading machine and stirring/dispersing device include the kneading machine and stirring/dispersing device mentioned in the manufacturing method of the dispersion for evaluation described above.

<Second step of determining>
The second determining step in the method for designing an aqueous pigment dispersion is not particularly limited, so long as it is a step of determining the compositional ratio of the second pigment, the second pigment dispersant, and the second aqueous medium in the aqueous pigment dispersion in accordance with the determined compositional mass ratio.
Here, when determining the composition ratio of the second pigment, the second pigment dispersant, and the second aqueous medium according to the determined composition mass ratio, the composition ratio may be exactly the same as the determined composition mass ratio, or may be slightly changed within a range that does not impair the pigment dispersion stability. For example, the concentration of the second pigment in the designed aqueous pigment dispersion may be different from the concentration of the second pigment in the aqueous pigment dispersion at the determined composition mass ratio by ±2% by mass. For example, the concentration of the second pigment dispersant in the designed aqueous pigment dispersion may be different from the concentration of the second pigment dispersant in the aqueous pigment dispersion at the determined composition mass ratio by ±2% by mass. For example, the concentration of the second aqueous medium in the designed aqueous pigment dispersion may be different from the concentration of the second aqueous medium in the aqueous pigment dispersion at the determined composition mass ratio by ±2% by mass.

The Hansen solubility parameter of the second pigment is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment.
The Hansen solubility parameter of the second pigment dispersant is within ±10 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment dispersant.
The Hansen solubility parameter of the second aqueous medium is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first aqueous medium.
Hansen solubility parameters (HSP) are values used to predict the solubility of a substance. HSP is based on the idea that two substances with similar intermolecular interactions tend to dissolve in each other. HSP (unit: (J/cm ³ ) ^1/2 ) is composed of the following three parameters:
・δd: Energy due to dispersion forces between molecules ・δp: Energy due to dipole interactions between molecules ・δh: Energy due to hydrogen bonds between molecules These three parameters can be considered as coordinates in a three-dimensional space (Hansen space). When the HSPs of two substances are placed in Hansen space, the closer the distance between the two points, the easier it is to dissolve in each other. In other words, the difference in the Hansen solubility parameters of two substances indicates that the hydrophilic and hydrophobic states of the two substances are similar.

If the Hansen solubility parameter of the second pigment is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment, the two pigments can be said to have similar hydrophilic and hydrophobic states from the viewpoint of pigment dispersion stability.
If the Hansen solubility parameter of the second pigment dispersant is within ±10 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment dispersant, the two pigment dispersants can be said to have similar hydrophilic and hydrophobic states from the viewpoint of pigment dispersion stability.
If the Hansen solubility parameter of the second aqueous medium is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first aqueous medium, the two aqueous media can be said to have similar hydrophilic and hydrophobic states from the viewpoint of pigment dispersion stability.
Therefore, within these ranges, even if the composition ratio of the pigment to the pigment dispersant with excellent pigment dispersion stability obtained in the evaluation dispersion is applied to the composition ratio of the pigment to the pigment dispersant in the aqueous pigment dispersion, an aqueous pigment dispersion with excellent pigment dispersion stability can be obtained.
The first pigment and the second pigment may be the same. The first pigment dispersant and the second pigment dispersant may be the same. The first aqueous medium and the second aqueous medium may be the same.

The Hansen solubility parameter of the second pigment is preferably within ±2.5 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment, more preferably within ±2 (J/cm ³ ) ^1/2 , and even more preferably within ±1.5 (J/cm ³ ) ^1/2 .
The Hansen solubility parameter of the second pigment dispersant is preferably within ±8 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment dispersant, more preferably within ±5 (J/cm ³ ) ^1/2 , and even more preferably within ±3 (J/cm ³ ) ^1/2 .
The Hansen solubility parameter of the second aqueous medium is preferably within ±2.5 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first aqueous medium, more preferably within ±2 (J/cm ³ ) ^1/2 , and even more preferably within ±1.5 (J/cm ³ ) ^1/2 .

The Hansen solubility parameter of a pigment can be determined, for example, by the following method.
10 mg (0.01 g) of the pigment to be measured and 9.99 g of organic solvent (pigment concentration: 0.1% by mass) were placed in a transparent screw cap bottle (screw cap bottle, volume: 20 ^cm3 ), and the mixture was shaken and mixed for 30 minutes using a high-speed shaker (Cute Mixer), and then centrifuged for 30 minutes at 4000 rpm (25°C) using a LUMiSizer, a multi-sample particle size distribution measurement device for evaluating dispersibility. If the amount of transmitted light is less than 20%, the pigment dispersibility is deemed good and the organic solvent is judged to be a "good solvent", and if the amount of transmitted light is 20% or more, the organic solvent is judged to be a "poor solvent".
The organic solvent and the corresponding judgment result of "good solvent" or "poor solvent" are input into computer software Hansen Solubility Parameters in Practice 4th Edition 4.1.07 (HSPiP) to calculate the Hansen solubility parameter of the pigment to be measured.
As the Hansen solubility parameters of the organic solvents used, the values recorded in the above-mentioned computer software Hansen Solubility Parameters in Practice 4th Edition 4.1.07 (HSPiP) can be used as they are.

The Hansen solubility parameter of a pigment dispersant can be determined, for example, by the following method.
50 mg (0.05 g) of the pigment dispersant to be measured and 9.95 g of organic solvent (pigment dispersant concentration: 0.5 mass%) were placed in a transparent screw cap bottle (screw cap bottle, capacity: 20 ^cm3 ), and the mixture was shaken and mixed for 30 minutes using a high-speed shaker (cute mixer), and then allowed to stand for 24 hours in an environment at 25°C.
If it is confirmed by visual observation after leaving the organic solvent to stand for 24 hours that the entire amount of the pigment dispersant has been dissolved, the organic solvent is judged to be a "good solvent." If it is not confirmed that the entire amount of the pigment dispersant has been dissolved, for example, because some of the pigment dispersant remains dissolved, the organic solvent is judged to be a "poor solvent."
The organic solvent and the corresponding judgment result "good solvent" or "poor solvent" are input into computer software Hansen Solubility Parameters in Practice 4th Edition 4.1.07 (HSPiP) to calculate the Hansen solubility parameter of the pigment dispersant to be measured.
As the Hansen solubility parameters of the organic solvents used, the values recorded in the above-mentioned computer software Hansen Solubility Parameters in Practice 4th Edition 4.1.07 (HSPiP) can be used as they are.

For the Hansen solubility parameters of the aqueous medium, the values recorded in the above Hansen Solubility Parameters in Practice 4th Edition 4.1.07 (HSPiP) can be used as is. Also, for the Hansen solubility parameters of the aqueous medium, known values may be used. The Hansen solubility parameters of an example of an aqueous medium are known as follows:

<Pigments>
The first pigment and the second pigment (hereinafter, sometimes simply referred to as "pigments") are not particularly limited, and for example, an organic pigment or an inorganic pigment that is usually used in conventional screen printing or aqueous inkjet recording inks can be used.

In addition, the pigment may be either a non-acid-treated pigment or an acid-treated pigment, and may be in either a dry powder or wet cake form.

Examples of inorganic pigments that can be used include iron oxide and carbon black produced by the contact method, furnace method, or thermal method.

Examples of organic pigments that can be used include azo pigments (including azo lakes, insoluble azo pigments, condensed azo pigments, chelate azo pigments, etc.), polycyclic pigments (such as phthalocyanine pigments, perylene pigments, perinone pigments, anthraquinone pigments, quinacridone pigments, dioxazine pigments, thioindigo pigments, isoindolinone pigments, quinophthalone pigments, etc.), lake pigments (such as basic dye-type chelates, acid dye-type chelates, etc.), nitro pigments, nitroso pigments, aniline black, etc.

Specific examples of pigments used in black inks include Mitsubishi Chemical Corporation's No. 2300, No. 2200B, No. 900, No. 980, No. 960, No. 33, No. 40, No. 45, No. 45L, and No. 52, HCF88, MCF88, MA7, MA8, MA100, etc. manufactured by Columbia Corporation; Raven 5750, Raven 5250, Raven 5000, Raven 3500, Raven 1255, Raven 700, etc. manufactured by Cabot Corporation; Regal 400R, Regal 330R, Regal 660R, Mogul L, Mogul 700, Monarch 800, Monarch 880, Monarch 900, Monarch 1000, Monarch 1100, Monarch 1300, Monarch 1400, etc. manufactured by Degussa Corporation; Color Black Carbon blacks such as FW1, FW2, FW2V, FW18, FW200, S150, S160, S170, Printex 35, U, V, 1400U, Special Black 6, 5, 4, 4A, NIPEX150, NIPEX160, NIPEX170, and NIPEX180 can be used.

Specific examples of pigments used in yellow ink include C.I. Pigment Yellow 1, 2, 12, 13, 14, 16, 17, 73, 74, 75, 83, 93, 95, 97, 98, 109, 110, 114, 120, 128, 129, 138, 150, 151, 154, 155, 174, 180, and 185.

Specific examples of pigments used in magenta ink include C.I. Pigment Violet 19, C.I. Pigment Red 5, 7, 12, 48 (Ca), 48 (Mn), 57 (Ca), 57:1, 112, 122, 123, 146, 168, 176, 184, 185, 202, 209, and mixtures or solid solutions of at least two or more pigments selected from these pigments.

Specific examples of pigments used in cyan ink include C.I. Pigment Blue 1, 2, 3, 15, 15:3, 15:4, 15:6, 16, 22, 60, 63, 66, etc.

Specific examples of pigments used in red ink include one or more selected from the group consisting of C.I. Pigment Red 17, 49:2, 112, 149, 150, 177, 178, 179, 188, 254, 255, and 264.

Specific examples of pigments used in orange ink include C.I. Pigment Orange 1, 2, 5, 7, 13, 14, 15, 16, 24, 34, 36, 38, 40, 43, 63, 64, 71, 73, and 81.

Specific examples of pigments used in green ink include C.I. Pigment Green 7, 10, 36, 58, and 59.

Specific examples of pigments used in violet inks include C.I. Pigment Violet 19, 23, 32, 33, 36, 38, 43, and 50.

Specific examples of pigments that can be used in white ink include alkaline earth metal sulfates, carbonates, finely powdered silicic acid, synthetic silicates, and other silicates, calcium silicate, alumina, alumina hydrate, titanium oxide, zinc oxide, talc, clay, and the like. These may be surface-treated.

The pigments mentioned above can be used alone or in combination of two or more types.

<Pigment dispersant>
Examples of the first pigment dispersant and the second pigment dispersant (hereinafter, sometimes simply referred to as "pigment dispersant") include polyvinyl alcohols; polyvinylpyrrolidones; acrylic resins such as acrylic acid-acrylic acid ester copolymers; styrene-acrylic resins such as styrene-acrylic acid copolymers, styrene-methacrylic acid copolymers, styrene-methacrylic acid-acrylic acid ester copolymers, styrene-α-methylstyrene-acrylic acid copolymers, and styrene-α-methylstyrene-acrylic acid-acrylic acid ester copolymers; aqueous resins such as styrene-maleic acid copolymers, styrene-maleic anhydride copolymers, and vinylnaphthalene-acrylic acid copolymers, and salts of aqueous resins. Examples of the pigment dispersant that can be used include the Ajisper PB series from Ajinomoto Fine-Techno Co., Ltd., the Disperbyk series from BYK Japan Co., Ltd., the EFKA series and JONCRYL series from BASF, the SOLSPERSE series from Lubrizol Japan Co., Ltd., and the TEGO series from Evonik.

As a pigment dispersant, it is preferable to use the polymer (G) described below, which can significantly reduce coarse particles and, as a result, impart the good ejection stability required when ejecting the ink by an inkjet method.

As the polymer (G), a polymer having an anionic group can be used. In particular, it is preferable to use a polymer having a number average molecular weight in the range of 500 to 30,000, which has a solubility in water of 0.1 g/100 mL or less and is capable of forming fine particles in water when the neutralization rate of the anionic group with a basic compound is 100%.

As the anionic group, for example, a carboxyl group, a carboxylate group, a sulfonic acid group, a sulfonate group, etc. can be used. Among them, it is preferable to use a carboxylate group or a sulfonate group in which a part or all of the carboxyl group or the sulfonic acid group is neutralized with a basic compound or the like in order to impart good water dispersion stability.

Such polymers having anionic groups may be produced by known methods, or commercially available products may be used. Specific examples of commercially available products include Acrydic WML-542 (manufactured by DIC Corporation) and Unidic EMG-1015 (manufactured by DIC Corporation).

The solubility of polymer (G) in water was defined as follows. That is, 0.5 g of polymer (E), whose particle size was adjusted to the range of 250 μm to 90 μm using sieves with 250 μm and 90 μm openings, was sealed in a bag made of processed 400 mesh wire mesh, immersed in 50 mL of water, and left to stand for 24 hours at 25°C with gentle stirring. After immersion for 24 hours, the 400 mesh wire mesh containing polymer (E) was dried for 2 hours in a dryer set at 110°C. The change in weight of the 400 mesh wire mesh containing polymer (E) before and after immersion in water was measured, and the solubility was calculated using the following formula.

In the present invention, whether or not fine particles are formed in water when the neutralization rate of the anionic group with the basic compound is 100% is judged as follows.
(1) The acid value of the polymer (G) is measured in advance by an acid value measurement method based on JIS test method K 0070-1992. Specifically, 0.5 g of the polymer (G) is dissolved in tetrahydrofuran, and the acid value is determined by titration with a 0.1 M alcoholic solution of potassium hydroxide using phenolphthalein as an indicator.
(2) 1 g of polymer (G) is added to 50 mL of water, and then a 0.1 mol/L aqueous potassium hydroxide solution sufficient to neutralize the resulting acid value by 100% is added to the mixture to achieve 100% neutralization.
(3) The 100% neutralized liquid is irradiated with ultrasonic waves in an ultrasonic cleaner (SND Corporation ultrasonic cleaner US-102, 38 kHz self-oscillation) at a temperature of 25° C. for 2 hours, and then left at room temperature for 24 hours.

After leaving it for 24 hours, a sample of the liquid 2 cm deep from the liquid surface is taken and a dynamic light scattering particle size distribution analyzer (Nikkiso Co., Ltd., dynamic light scattering particle size analyzer "Microtrac Particle Size Distribution Analyzer UPA-ST150") is used to determine whether light scattering information due to the formation of fine particles is obtained, thereby confirming the presence of fine particles.

To further improve the stability of the fine particles formed by polymer (G) in water, the particle diameter of the fine particles is preferably in the range of 5 nm to 1000 nm, more preferably in the range of 7 nm to 700 nm, and most preferably in the range of 10 nm to 500 nm. Furthermore, the narrower the particle size distribution of the fine particles, the better the dispersion stability tends to be, but even if the particle size distribution is broad, it is possible to obtain an ink with better dispersion stability than before. Note that the particle diameter and particle size distribution were measured using a dynamic light scattering particle size distribution measuring device (Microtrac Particle Size Distribution Meter UPA-ST150, dynamic light scattering particle size measuring device manufactured by Nikkiso Co., Ltd.), in the same manner as in the measurement method for the fine particles.

The number average molecular weight of the polymer (G) is preferably in the range of 500 to 30,000, more preferably 1,000 to 6,000, even more preferably 1,300 to 5,000, and particularly preferably 1,500 to 4,500, which can effectively suppress pigment aggregation in the aqueous medium (C) and is particularly preferred for obtaining an ink with good pigment dispersion stability.

The number average molecular weight is a polystyrene-equivalent value measured by GPC (gel permeation chromatography), specifically, under the following conditions:

(Method of measuring number average molecular weight (Mn))
Measurement was performed by gel permeation chromatography (GPC) under the following conditions.
Measurement device: High-speed GPC device ("HLC-8220GPC" manufactured by Tosoh Corporation)
Column: The following columns manufactured by Tosoh Corporation were used, connected in series.

"TSKgel G5000" (7.8mm I.D. x 30cm) x 1 "TSKgel G4000" (7.8mm I.D. x 30cm) x 1 "TSKgel G3000" (7.8mm I.D. x 30cm) x 1 "TSKgel G2000" (7.8mm I.D. x 30cm) x 1 Detector: RI (differential refractometer)
Column temperature: 40°C
Eluent: tetrahydrofuran Flow rate: 1.0 mL/min Injection amount: 100 μL (sample concentration 0.4% by mass in tetrahydrofuran solution)
Standard sample: A calibration curve was prepared using the following standard polystyrene.
(Standard polystyrene)
"TSKgel Standard Polystyrene A-500" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene A-1000" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene A-2500" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene A-5000" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene F-1" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene F-2" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene F-4" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene F-10" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene F-20" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene F-40" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene F-80" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene F-128" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene F-288" manufactured by Tosoh Corporation
"TSKgel Standard Polystyrene F-550" manufactured by Tosoh Corporation

The surface tension of the ink containing polymer (G) is preferably 30 dyn/cm or more, more preferably 40 dyn/cm or more, and particularly preferably 65 dyn/cm to 75 dyn/cm, which is close to the surface tension of water. The surface tension is measured by adding 1 g of polymer (G) to water, then adding a 0.1 mol/L aqueous potassium hydroxide solution sufficient to neutralize the resulting acid value by 100%, and then 100% neutralizing the polymer solution.

The neutralization rate of polymer (G) was determined by the following formula:

The acid value of the polymer (G) was measured based on JIS test method K 0070-1992. Specifically, 0.5 g of a sample was dissolved in tetrahydrofuran, and titrated with a 0.1 M alcoholic solution of potassium hydroxide using phenolphthalein as an indicator.
The method for measuring the acid value of other polymers in this specification also complies with JIS test method K 0070-1992.

The acid value of the polymer (G) is preferably in the range of 20 mgKOH/g to 400 mgKOH/g, more preferably 30 mgKOH/g to 300 mgKOH/g, and even more preferably 40 mgKOH/g to 190 mgKOH/g, which can effectively suppress pigment aggregation in the aqueous medium (C) and is even more preferable for obtaining an ink with good pigment dispersion stability.

As the polymer (G), a polymer that is insoluble or poorly soluble in water when not neutralized and forms fine particles when 100% neutralized can be used, and there is no particular limitation so long as it is a polymer that has hydrophobic groups in one molecule in addition to anionic groups, which are hydrophilic groups.

Such polymers include block polymers having a polymer block with a hydrophobic group and a polymer block with an anionic group. In polymer (G), the number of anionic groups and the solubility in water are not necessarily determined by the acid value or the number of anionic groups at the time of polymer design. For example, even if the polymer has the same acid value, those with lower molecular weights tend to have higher solubility in water, and those with higher molecular weights tend to have lower solubility in water.

The polymer (G) may be a homopolymer, but is preferably a copolymer, and may be a random polymer, a block polymer, or an alternating polymer, but is preferably a block polymer. The polymer may also be a branched polymer, but is preferably a linear polymer.

In addition, polymer (G) is preferably a vinyl polymer from the viewpoint of design freedom, and in the present invention, a vinyl polymer having the desired molecular weight and solubility characteristics is preferably produced by using "living polymerization" such as living radical polymerization, living cationic polymerization, or living anionic polymerization.

Among these, polymer (G) is preferably a vinyl polymer produced using a (meth)acrylate monomer as one of the raw materials, and the method for producing such a vinyl polymer is preferably living radical polymerization or living anionic polymerization, and further preferably living anionic polymerization from the viewpoint of being able to more precisely design the molecular weight of the block polymer and each segment.

<Aqueous medium>
As the first aqueous medium and the second aqueous medium (hereinafter sometimes simply referred to as the “aqueous medium” or the “aqueous medium (C)”), water alone or a mixed solvent of water and an organic solvent (F) described later can be used.

Specific examples of water that can be used include pure water or ultrapure water such as ion-exchanged water, ultrafiltered water, reverse osmosis water, and distilled water.

Examples of the organic solvent (F) include ketones such as acetone, methyl ethyl ketone, methyl butyl ketone, and methyl isobutyl ketone; alcohols such as methanol, ethanol, 2-propanol, 2-methyl-1-propanol, 1-butanol, and 2-methoxyethanol; ethers such as tetrahydrofuran, 1,4-dioxane, and 1,2-dimethoxyethane; glycols such as dimethylformamide, N-methylpyrrolidone, ethylene glycol, diethylene glycol, triethylene glycol, tetraethylene glycol, propylene glycol, polyethylene glycol, and polypropylene glycol; diols such as butanediol, pentanediol, hexanediol, and diols of the same group; and prolaurate. Glycol esters such as pyrene glycol; glycol ethers such as diethylene glycol monoethyl, diethylene glycol monobutyl ether, diethylene glycol monohexyl ether, propylene glycol ether, dipropylene glycol ether, and cellosolve including triethylene glycol ether; alcohols such as methanol, ethanol, isopropyl alcohol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, and other butyl alcohols, pentyl alcohol, and alcohols of the same family; sulfolane; lactones such as γ-butyrolactone; lactams such as N-(2-hydroxyethyl)pyrrolidone; and the like can be used alone or in combination of two or more kinds.

In addition to the above, the organic solvent (F) is preferably a water-soluble organic solvent (f1) having a boiling point of 100°C or more and 200°C or less and a vapor pressure of 0.5 hPa or more at 20°C, in order to obtain a quick-drying effect in which the ejected droplets dry quickly on the recording medium after landing on the surface of the recording medium.

Examples of the water-soluble organic solvent (f1) include 3-methoxy-1-butanol, 3-methyl-3-methoxy-1-butanol, 3-methoxy-3-methyl-1-butyl acetate, ethylene glycol monomethyl ether, ethylene glycol monoethyl ether, ethylene glycol monopropyl ether, ethylene glycol monobutyl ether, ethylene glycol monoisobutyl ether, ethylene glycol-t-butyl ether, propylene glycol monomethyl ether, propylene glycol monoethyl ether, propylene glycol monopropyl ether, propylene glycol monomethyl ether acetate, diethylene glycol dimethyl ether, diethylene glycol methyl ethyl ether, diethylene glycol diethyl ether, dipropylene glycol dimethyl ether, 4-methoxy-4-methyl-2-pentanone, and ethyl lactate, and two or more of these can be used in combination.

Among these, it is preferable to use a water-soluble organic solvent (f1) having a hydrogen bond term δH of HSP (Hansen solubility parameter) in the range of 6 to 20 in order to maintain good dispersion stability of the ink and to suppress deterioration of, for example, the ink ejection nozzle of an inkjet device due to the influence of the solvent contained in the ink.

Specific examples of water-soluble organic solvents having hydrogen bond terms of HSP within the above range include 3-methoxy-1-butanol, 3-methyl-3-methoxy-1-butanol, ethylene glycol monomethyl ether, ethylene glycol monoethyl ether, ethylene glycol monopropyl ether, ethylene glycol monobutyl ether, ethylene glycol monoisobutyl ether, ethylene glycol-t-butyl ether, propylene glycol monomethyl ether, propylene glycol monoethyl ether, and propylene glycol monopropyl ether, and more preferably 3-methoxy-1-butanol and 3-methyl-3-methoxy-1-butanol.

As an organic solvent that can be used in combination with the aqueous medium (C), in addition to the water-soluble organic solvent (f1) described above, or together with the water-soluble organic solvent (f1), it is preferable to use propylene glycol (f2) in combination with one or more organic solvents (f3) selected from the group consisting of glycerin, glycerin derivatives, diglycerin, and diglycerin derivatives, in order to achieve both the effect of quick-drying the ink on the recording medium and the effect of preventing the ink from drying or solidifying at the ink ejection port.

As the organic solvent (f3), for example, glycerin, diglycerin, polyglycerin, diglycerin fatty acid ester, polyoxypropylene (n) polyglyceryl ether represented by the following general formula (1), polyoxyethylene (n) polyglyceryl ether represented by the following general formula (2), etc. can be used alone or in combination of two or more kinds.

Among these, it is particularly preferable to use glycerin and polyoxypropylene (n) polyglyceryl ether (n=8-15) as the organic solvent (f3), as these have excellent setting properties for printed matter and are effective in preventing the ink from drying or solidifying at the ink ejection port.

In general formula (1) and general formula (2), m, n, o, and p each independently represent an integer from 1 to 10.

The organic solvent (F) is preferably used in the range of 0.5% to 30% by mass relative to the total amount of the aqueous pigment dispersion, and is particularly preferably used in the range of 5% to 20% by mass, since this prevents the aqueous ink obtained from the aqueous pigment dispersion from having a low image density and also prevents a decrease in the dispersion stability of the pigment.

(Method of manufacturing water-based ink and method of designing water-based ink)
The method for producing an aqueous ink of the present invention includes a step of producing an aqueous pigment dispersion and a mixing step, and further includes other steps as necessary.
The method for designing an aqueous ink of the present invention includes a step of designing an aqueous pigment dispersion and a step of determining the composition ratio, and further includes other steps as necessary.
The step of producing an aqueous pigment dispersion is a step of producing an aqueous pigment dispersion by the method for producing an aqueous pigment dispersion of the present invention.
The step of designing an aqueous pigment dispersion is a step of designing an aqueous pigment dispersion by the method of designing an aqueous pigment dispersion of the present invention.

<Mixing step>
The mixing step is not particularly limited as long as it is a step of mixing the aqueous pigment dispersion, the binder resin, and the third aqueous medium, and a mixing method typically used in producing aqueous inks can be used.

<Step of determining composition ratio>
The step of determining the composition ratio is not particularly limited as long as it is a step of determining the composition ratio of the designed aqueous pigment dispersion, binder resin, and third aqueous medium.

<Water-based ink>
The aqueous ink produced in the present invention contains the aqueous pigment dispersion produced by the method for producing an aqueous pigment dispersion of the present invention, a binder resin, and a third aqueous medium.
The water-based ink may further contain additives.

<<Binder resin>>
The binder resin (A) serves, for example, to fix the pigment onto the recording medium.

Examples of the binder resin (A) include urethane resins, polyvinyl alcohols, polyvinylpyrrolidones, polyacrylic acids, acrylic acid-acrylonitrile copolymers, potassium acrylate-acrylonitrile copolymers, vinyl acetate-acrylic acid ester copolymers, acrylic acid-alkyl acrylate copolymers, and other acrylic copolymers, styrene-acrylic acid copolymers, styrene-methacrylic acid copolymers, styrene-methacrylic acid-acrylic acid alkyl ester copolymers, styrene-α-methylstyrene-acrylic acid copolymers, styrene-α-methylstyrene-acrylic acid-acrylic acid alkyl ester copolymers, and other styrene-acrylic acid resins, styrene-maleic acid, styrene-maleic anhydride, vinylnaphthalene-acrylic acid copolymers, vinylnaphthalene-maleic acid copolymers, vinyl acetate-ethylene copolymers, vinyl acetate-fatty acid vinylethylene copolymers, vinyl acetate-maleic acid ester copolymers, vinyl acetate-crotonic acid copolymers, vinyl acetate-acrylic acid copolymers, and other vinyl acetate-based copolymers and salts thereof.

Among these, it is preferable to use urethane resin or acrylic resin as the binder resin, as these are easy to obtain and improve the abrasion resistance of the printed matter.

Examples of urethane resins include urethane resins obtained by reacting one or more polyols selected from the group consisting of polyether polyols, polyester polyols, and polycarbonate polyols with a polyol having a hydrophilic group that is an anionic group, a cationic group, a polyoxyethylene group, or a polyoxyethylene-polyoxypropylene group, and a polyisocyanate.

The weight average molecular weight of the urethane resin is not particularly limited, but to further improve the abrasion resistance of the printed matter, it is preferable to use one with a weight average molecular weight of 5,000 to 200,000, and more preferably 20,000 to 150,000.

A crosslinking agent can be used in the ink to further improve the abrasion resistance. When using a crosslinking agent, it is preferable to use a urethane resin that has a functional group that can undergo a crosslinking reaction with the functional group of the crosslinking agent.

Examples of functional groups include carboxyl groups and carboxylate groups that can be used as hydrophilic groups. Carboxyl groups and the like contribute to the stability of the aqueous dispersion of the urethane resin in an aqueous medium, and when they undergo a crosslinking reaction, they also act as functional groups and can partially crosslink with the crosslinking agent.

Examples of crosslinking agents that can be used include polyisocyanate crosslinking agents, epoxy crosslinking agents, and melamine crosslinking agents. These crosslinking agents may be used alone or in combination of two or more. Among these, it is preferable to use a polyisocyanate crosslinking agent, since it reacts with the hydroxyl groups of the urethane resin to form three-dimensional crosslinks, thereby providing good mechanical strength, conformability to uneven surfaces, adhesion to substrates, sheet retention, and stain resistance.

The amount of crosslinking agent used is preferably in the range of 0.01 to 20 parts by mass per 100 parts by mass of urethane resin (solid content), more preferably in the range of 0.05 to 15 parts by mass, and even more preferably in the range of 0.1 to 10 parts by mass, in order to achieve high levels of conformability to unevenness, adhesion to substrates, and sheet retention.

Urethane resins can be produced, for example, by reacting a polyol with a polyisocyanate and, if necessary, a chain extender.

As chain extenders, polyamines and other compounds containing active hydrogen atoms can be used.

The chain extender is preferably used in such a range that the equivalent of the amino group and active hydrogen atom-containing group of the chain extender is 1.9 or less (equivalent ratio) relative to the equivalent of the isocyanate group of the urethane prepolymer obtained by reacting the polyol with the polyisocyanate, more preferably in the range of 0.0 to 1.0 (equivalent ratio), and even more preferably at 0.5% by mass.

The chain extender can be used when reacting the polyol with the polyisocyanate or after the reaction. The chain extender can also be used when dispersing the resulting urethane resin in an aqueous medium to make it aqueous.

There are no particular limitations on the acrylic resin that can be used for the binder resin (A), and examples include homopolymerized or copolymerized (meth)acrylate resins, and resins copolymerized with vinyl monomers that can copolymerize with (meth)acrylate. In the present invention, "(meth)acrylic acid" refers to methacrylic acid or acrylic acid, "(meth)acrylate" refers to methacrylate or acrylate, and "(meth)acryloyl" refers to methacryloyl or acryloyl.

Examples of (meth)acrylates and vinyl monomers that can be copolymerized with (meth)acrylates include alkyl (meth)acrylates such as methyl (meth)acrylate, ethyl (meth)acrylate, n-butyl (meth)acrylate, sec-butyl (meth)acrylate, t-butyl (meth)acrylate, isopropyl (meth)acrylate, and isobutyl (meth)acrylate; aromatic (meth)acrylates such as benzyl (meth)acrylate; hydroxyl group-containing monomers such as 2-hydroxyethyl (meth)acrylate and 2-hydroxypropyl (meth)acrylate; methoxypolyethylene glycol mono(meth)acrylate; p) acrylates, alkyl polyalkylene glycol mono(meth)acrylates such as methoxy polypropylene glycol mono(meth)acrylate; fluorine-based (meth)acrylates such as perfluoroalkylethyl (meth)acrylate; styrene, styrene derivatives (p-dimethylsilylstyrene, (p-vinylphenyl)methyl sulfide, p-hexynylstyrene, p-methoxystyrene, p-tert-butyldimethylsiloxystyrene, o-methylstyrene, p-methylstyrene, p-tert-butylstyrene, α-methylstyrene, etc.), vinylnaphthalene, vinylanthracene, 1,1-diphenyl aromatic vinyl compounds such as acylethylene; glycidyl (meth)acrylate, epoxy (meth)acrylate, ethylene glycol di(meth)acrylate, diethylene glycol di(meth)acrylate, trimethylolpropane tri(meth)acrylate, tetramethylene glycol tetra(meth)acrylate, 2-hydroxy-1,3-diacryloxypropane, 2,2-bis[4-(acryloxymethoxy)phenyl]propane, 2,2-bis[4-(acryloxyethoxy)phenyl]propane, dicyclopentenyl (meth)acrylate, tricyclodecanyl (meth)acrylate, tris(acryloxy)phenyl, (meth)acrylate compounds such as (dimethylaminoethyl) isocyanurate and urethane (meth)acrylate; (meth)acrylates having an alkylamino group such as dimethylaminoethyl (meth)acrylate, diethylaminoethyl (meth)acrylate and dimethylaminopropyl (meth)acrylate; vinylpyridine compounds such as 2-vinylpyridine, 4-vinylpyridine and naphthylvinylpyridine; conjugated dienes such as 1,3-butadiene, 2-methyl-1,3-butadiene, 2,3-dimethyl-1,3-butadiene, 1,3-pentadiene, 1,3-hexadiene and 1,3-cyclohexadiene. These monomers can be used alone or in combination of two or more.

In order to improve the texture of the printed matter, it is preferable to use an acrylic resin obtained by copolymerizing the above-mentioned monomers with a monomer having a specific functional group. Examples of monomers having such functional groups include monomers having a carboxyl group, monomers having an epoxy group, monomers having a hydrolyzable silyl group, and monomers having an amide group.

Examples of monomers having a carboxyl group that can be used include (meth)acrylic acid, itaconic acid, crotonic acid, fumaric acid, maleic anhydride, and citraconic acid.

Examples of monomers having a hydrolyzable silyl group include vinyl silane compounds such as vinyl methyl dimethoxy silane, vinyl trimethoxy silane, vinyl triethoxy silane, and vinyl tris (2-methoxyethoxy) silane; and (meth)acryloyloxy alkyl silane compounds such as 3- (meth) acryloyloxy propyl trimethoxy silane, 3- (meth) acryloyloxy propyl methyl dimethoxy silane, 3- (meth) acryloyloxy propyl triethoxy silane, and 3- (meth) acryloyloxy propyl methyl diethoxy silane. These monomers can be used alone or in combination of two or more.

Examples of monomers having an amide group that can be used include acrylamide compounds such as (meth)acrylamide, N,N-dimethylacrylamide, isopropylacrylamide, and diacetoneacrylamide.

The form of dispersion of the acrylic resin in water is not particularly limited, and examples include emulsions forcibly emulsified with an emulsifier, and dispersions containing nonionic groups or neutralized ionic groups in the resin. In particular, the above-mentioned acrylic resin is preferably a dispersion obtained by neutralizing an acrylic resin having a carboxyl group with a basic compound. The basic compound may be the same as the basic compounds exemplified as those usable for neutralizing the carboxyl groups of urethane resins.

<<Aqueous medium>>
The third aqueous medium may be the aqueous medium mentioned in the description of the aqueous pigment dispersion.

The third aqueous medium is preferably used in the range of 1% to 50% by mass relative to the total amount of ink, and is particularly preferably used in the range of 10% to 30% by mass in order to obtain an ink that has the high ejection stability required when ejecting using an inkjet method and can produce clear printed matter.

The organic solvent (F) is preferably used in the range of 1% to 30% by mass relative to the total amount of ink, and is particularly preferably used in the range of 5% to 25% by mass, as this provides excellent setting properties for printed matter and is effective in preventing the ink from drying or solidifying at the ink ejection port.

The water-soluble organic solvent (f1), propylene glycol (f2), and organic solvent (f3) are preferably used in a mass ratio [water-soluble solvent (f1)/propylene glycol (f2)] in the range of 1/25 to 1/1, and using them in the range of 1/20 to 1/1 is particularly preferred in terms of providing excellent setting properties for printed matter and preventing the ink from drying or solidifying at the ink ejection ports.

The water-soluble organic solvent (f1), propylene glycol (f2), and organic solvent (f3) are preferably used in a mass ratio [propylene glycol (f2)/organic solvent (f3)] in the range of 1/4 to 8/1, and using them in the range of 1/2 to 5/1 is particularly preferred in terms of providing excellent setting properties for printed matter and preventing the ink from drying or solidifying at the ink ejection ports.

<<Additives>>
Examples of the additives include surfactants (E), sugars, preservatives, viscosity adjusters, pH adjusters, chelating agents, antioxidants, and ultraviolet absorbers.

Surfactant (E) can be used to improve the leveling properties of the ink by, for example, lowering the surface tension of the ink. Furthermore, surfactant (E) can prevent streaks from appearing on the printed matter by allowing the ink ejected from the nozzles of the inkjet head to wet and spread well on the surface after landing on the recording medium.

As the surfactant (E), various anionic surfactants, nonionic surfactants, cationic surfactants, amphoteric surfactants, etc. can be used, and it is preferable to use an anionic surfactant or a nonionic surfactant.

As the surfactant (E), it is preferable to use one with an HLB in the range of 4 to 20 in order to stably maintain the state in which the surfactant (E) is dissolved in the ink, which has water as the main solvent.

Surfactant (E) is preferably used in the range of 0.001% to 2% by mass, more preferably 0.001% to 1.5% by mass, and even more preferably 0.5% to 1.5% by mass, relative to the total amount of ink. An inkjet ink containing surfactant (E) in the above range has good wettability of the ejected droplets on the surface of the recording medium, has sufficient wetting and spreading on the recording medium, and is preferable in terms of preventing streaks in the printed matter. Furthermore, an ink containing surfactant (E) in the above range has the effect of improving wettability and leveling on the recording medium.

The pH of the aqueous ink is preferably 7.0 or more, more preferably 7.5 or more, and even more preferably 8.0 or more, in order to improve the storage stability and ejection stability of the ink, and to improve the wetting spread, print density, and waterfastness when printed on a fabric that is easily or poorly ink-absorbent. The upper limit of the pH of the ink is preferably 11.0 or less, more preferably 10.0 or less, and even more preferably 9.5 or less, in order to suppress deterioration of the components that constitute the ink application or ejection device (e.g., ink ejection port, ink flow path, etc.) and to reduce the effects of the ink adhering to the skin.

The present invention will be described in further detail below with reference to examples, but the scope of the present invention is not limited to these examples.

(Preparation of Pigment Dispersion for Evaluation)
The following raw materials were used to prepare pigment dispersions for evaluation:

<Ingredients>
Pigment: Mitsubishi Carbon Black "#960" (product name, Mitsubishi Chemical Corporation)
Pigment dispersant: Polyvinylpyrrolidone (PVP) "K-30" (product name, manufactured by Nippon Shokubai Co., Ltd.)
・Aqueous medium: "Ion-exchanged water"

The above pigment, pigment dispersant, and aqueous medium were mixed in the formulation shown in Table 2 below, and then dispersed to obtain a pigment dispersion for evaluation.
Specifically, a 50 mL polyethylene sealed container was charged with a given amount of pigment, pigment dispersant, and aqueous medium according to the blending composition (g) in Table 2, and then 10 g of Zr beads YTZ-0.5 (product name, manufactured by Nikkato Corporation) with a diameter of 0.5 mm was further added, followed by dispersion using a paint conditioner. The dispersion time was uniformly set to 2 hours.
The numerical values of the compounding composition (g) in Table 2 are the actual amounts (g) charged.
The total amount of materials charged for No. 1-1 to No. 1-9 (pigment concentration 10% by mass) was 10.00 g
The total amount of materials charged for No. 2-1 to No. 2-9 (pigment concentration 15% by mass) was 6.67 g
The total amount of materials charged for No. 3-1 to No. 3-9 (pigment concentration 20% by mass) was 5.00 g

(Measurement of Volume Average Particle Size)
The volume average particle size of the obtained pigment dispersion for evaluation was measured by the following method. The results are shown in Table 2.
Measuring device: Microtrac MT3000II (manufactured by Microtrac Bell)
Measurement solvent: water Solvent refractive index: 1.333
Abundance ratio: volume basis Particle transmittance: transmittance Particle shape: non-spherical Particle refractive index: 1.81
・Analysis mode: Rosin-Rammler distribution (±2σ) (Software included with the device: DMS ver. 11.0.0-246V)

式（２）中、Ｍ_ｖは、粒子の体積平均粒径を表す。
式（２）中、Ψ_ｐは、粒子体積比を意味し、下記式（３）で表される。

式（２）及び式（３）中、ρ_ｐは、第１の顔料の密度（三菱カーボンブラック「＃９６０」の場合、１．８ｇ／ｃｍ^３）を表す。
式（３）中、Ｃ_ｐは、評価用分散体における第１の顔料の濃度を表す。
式（３）中、ρ_ｗは、第１の水性媒体の密度（イオン交換水の場合、１．０ｇ／ｃｍ^３）を表す。 Calculation of Total Surface Area (TSA) of Particles
Using the volume average particle diameter thus obtained, the total surface area (TSA) of the particles was calculated according to the following formula (2). The results are shown in Table 2.

In formula (2), _Mv represents the volume average particle size of the particles.
In formula (2), Ψ _p means a particle volume ratio and is represented by the following formula (3).

In formulas (2) and (3), _ρp represents the density of the first pigment (1.8 g/cm ³ in the case of Mitsubishi carbon black “#960”).
In formula (3), _Cp represents the concentration of the first pigment in the dispersion for evaluation.
In formula (3), ρ _w represents the density of the first aqueous medium (1.0 g/cm ³ in the case of ion-exchanged water).

<Pulsed NMR Measurement and Calculation of _Rsp >
Pulse NMR measurement was carried out on the obtained pigment dispersion for evaluation under the following conditions. _Rsp was calculated by the following formula (1). The results are shown in Table 2.

<<Pulse NMR measurement conditions>>
Measurement device: Acron Area (manufactured by XiGo Nanotools)
Pulse sequence: CPMG method Resonance frequency: 13 MHz
Measurement temperature: 30°C
Measurement sample: 1.0 ^cm3

式（１）中、Ｒ_ａｖは、１つの評価用水分散体のＴ２緩和時間の逆数を表し、Ｒ_ｂは、ブランク溶液のＴ２緩和時間の逆数を表す。
ここで、顔料を含有しないブランク溶液は、以下の方法で調製した。
以下の表２に記載の配合組成で顔料分散剤と水性媒体とを混合し、顔料分散剤を水性媒体に溶解させることで、顔料を含有しないブランク溶液を得た。

In formula (1), R _av represents the reciprocal of the T2 relaxation time of one aqueous dispersion for evaluation, and R _b represents the reciprocal of the T2 relaxation time of the blank solution.
Here, a blank solution containing no pigment was prepared in the following manner.
A pigment dispersant and an aqueous medium were mixed according to the formulation shown in Table 2 below, and the pigment dispersant was dissolved in the aqueous medium to obtain a blank solution not containing a pigment.

The dispersibility index K _{a ,} which is an index of the thickness of the hydration layer, was calculated by the following formula: The results are shown in Table 2.

A graph was prepared for each pigment concentration, with _Rsp on the horizontal axis and TSA on the vertical axis, and the graph is shown in FIG.
From the results in Table 2 and Figure 1, at a pigment concentration of 10% by mass, TSA showed a maximum value when the composition mass ratio (R/P) was 0.3. At a pigment concentration of 15% by mass, TSA showed a maximum value when the composition mass ratio (R/P) was 0.3. At a pigment concentration of 20% by mass, TSA showed a maximum value when the composition mass ratio (R/P) was 0.4.

Meanwhile, a graph was prepared for each pigment concentration, with _Ka on the horizontal axis and TSA on the vertical axis, and the graph is shown in FIG.
In Fig. 2, no mountain-shaped curve was obtained as in Fig. 1. This confirmed that it is appropriate to use the index of hydrophilicity and the index of the total surface area of the particles when determining the composition mass ratio.

<Evaluation of pigment dispersion stability>
The pigment dispersion stability of the evaluation dispersion was evaluated by the following evaluation method. The results are shown in Table 3.
The test sample was sealed in a polyethylene container and stored in an atmosphere at 60° C. for 30 days, and the average particle size (D50) before and after storage was measured according to the following average particle size measurement method. Similarly, the viscosity of the evaluation dispersion before and after storage was measured according to the following viscosity measurement method.

The viscosity was measured (sample temperature 25° C.) using a Viscometer TV-20 (manufactured by Toki Sangyo Co., Ltd.).
Measurements were performed (sample temperature 25° C.) using a dynamic light scattering Nanotrac particle size analyzer UPA-150EX (manufactured by Nikkiso Co., Ltd.) The particle size values used were the volume average particle size (Mv) and the 50% particle size (D50).

The change in viscosity was calculated using the following formula:
Ratio of change before and after storage (= (measured value after storage)/(measured value before storage)×100(%))

The evaluation was performed according to the following criteria. The results are shown in Table 3.
<<Evaluation criteria>>
◯: The change in the average particle size (D50) and viscosity before and after storage is less than 20% for both. ×: At least one of the changes in the average particle size (D50) and viscosity before and after storage is 20% or more.

(Hansen solubility parameters)
The Hansen solubility parameters of the following materials were determined using the method described herein, and the results are shown in Table 4.
<Ingredients>
Pigment: Mitsubishi Carbon Black "#960" (product name, Mitsubishi Chemical Corporation)
Pigment: Mitsubishi Carbon Black R (product name, Mitsubishi Chemical Corporation)
Pigment dispersant: Polyvinylpyrrolidone (PVP) "K-30" (product name, manufactured by Nippon Shokubai Co., Ltd.)
Pigment dispersant: Acrydic WML542 (product name, DIC Corporation, styrene acrylic resin, acid value = 170 mg KOH/g)
・Pigment dispersant: ARFON UH-2170 (product name, Toagosei Co., Ltd.)

(Preparation of Aqueous Pigment Dispersion 1)
An aqueous pigment dispersion was prepared using the following raw materials:

<Ingredients>
Pigment: Mitsubishi Carbon Black "#960" (product name, Mitsubishi Chemical Corporation)
Pigment dispersant: Acrydic WML542 (product name, DIC Corporation, styrene acrylic resin, acid value = 170 mgKOH/g) theoretical value 100% neutralized (neutralizing agent: potassium hydroxide)
・Aqueous medium: "Ion-exchanged water"

The above pigment, pigment dispersant, and aqueous medium were mixed in the formulation shown in Table 5 below, and then dispersed to obtain an aqueous pigment dispersion.
Specifically, a 50 mL polyethylene sealed container was charged with a given amount of pigment, pigment dispersant, and aqueous medium according to the blending composition (g) in Table 5, and then 10 g of Zr beads YTZ-0.5 (product name, manufactured by Nikkato Corporation) having a diameter of 0.5 mm was further added, followed by dispersion using a paint conditioner. The dispersion time was uniformly set to 2 hours.

The volume average particle size and pigment dispersion stability of the resulting aqueous pigment dispersion were evaluated using the methods described above. The results are shown in Table 5.

From Tables 2, 3, and Figure 1, when the pigment concentration is 20.0 mass%, the optimal range for the mass ratio (R/P) is 0.4. Therefore, the optimal range for the mass ratio (R/P) in the aqueous pigment dispersion prepared above is 0.2 to 0.6. The results in Table 5 correspond to these results.

(Preparation of Aqueous Pigment Dispersion 2)
An attempt was made to prepare an aqueous pigment dispersion using the following raw materials in the same manner as in Preparation 1 of Aqueous Pigment Dispersion, but no dispersion was obtained due to poor dispersion.

<Ingredients>
Pigment: Mitsubishi Carbon Black R (product name, Mitsubishi Chemical Corporation)
・Pigment dispersant: ARFON UH-2170 (product name, Toagosei Co., Ltd.)
・Aqueous medium: "Ion-exchanged water"

Claims (7)

A method for producing an aqueous pigment dispersion containing a second pigment, a second pigment dispersant, and a second aqueous medium, comprising the steps of:
preparing a plurality of evaluation dispersions each containing a first pigment, polyvinylpyrrolidone as a first pigment dispersant, and a first aqueous medium, the plurality of evaluation dispersions each having a different composition ratio of the first pigment dispersant to the first pigment;
determining a T2 relaxation time for each of the plurality of evaluation dispersions by pulse NMR measurement, and obtaining an index of hydrophilicity based on the reciprocal of the T2 relaxation time;
measuring the volume average particle size of the particles for each of the plurality of evaluation dispersions to obtain an index of the total surface area of the particles;
determining, as a composition mass ratio of the second pigment dispersant to the second pigment in the aqueous pigment dispersion, a range of ±0.2 or less of a composition mass ratio (R/P) of the first pigment dispersant to the first pigment when the index of the total surface area of the particles takes a maximum value in a graph showing the relationship between the index of the hydrophilicity degree, the index of the total surface area of the particles, and the composition ratios, with the index of the hydrophilicity degree being plotted on the horizontal axis and the index of the total surface area of the particles being plotted on the vertical axis;
mixing the second pigment, the second pigment dispersant, and the second aqueous medium in accordance with the determined composition mass ratio;
Including,
the Hansen solubility parameter of the second pigment is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment;
the Hansen solubility parameter of the second pigment dispersant is within ± 5 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment dispersant;
The Hansen solubility parameter of the second aqueous medium is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first aqueous medium ;
the second pigment dispersant is different from the first pigment dispersant,
The second aqueous medium and the first aqueous medium are the same ;
A method for producing an aqueous pigment dispersion comprising the steps of: the step of obtaining the index of hydrophilicity includes a process of determining a T2 relaxation time by the pulse NMR measurement for a blank solution having the same composition ratio of the first pigment dispersant and the first aqueous medium in one of the plurality of evaluation dispersions and not containing the first pigment, and obtaining an index of hydrophilicity (R sp ), which is an index of the hydrophilicity, from the reciprocal of the T2 relaxation time of the one evaluation aqueous dispersion and the reciprocal of the T2 relaxation time of the blank solution according to the following formula ( ₁ ), for each of the plurality of evaluation dispersions;
A method for producing the aqueous pigment dispersion according to claim 1.

In the formula (1), R _av represents the reciprocal of the T2 relaxation time of one of the aqueous dispersions for evaluation, and R _b represents the reciprocal of the T2 relaxation time of the blank solution. The method for producing an aqueous pigment dispersion according to any one of claims 1 to 2, wherein the index of the total surface area of the particles is a value that is directly proportional to the reciprocal of the volume average particle size of the particles. the step of obtaining an index of the total surface area of the particles includes a process of obtaining a total particle surface area value (TSA), which is an index of the total surface area of the particles, from the volume average particle size of the particles by the following formula (2), for each of the plurality of evaluation dispersions;
A method for producing the aqueous pigment dispersion according to any one of claims 1 to 3.

In the formula (2), _Mv represents the volume average particle size of the particles.
In the above formula (2), Ψ _p means a particle volume ratio and is represented by the following formula (3).

In the formulas (2) and (3), ρ _p represents the density of the first pigment.
In the formula (3), _Cp represents the concentration of the first pigment in the dispersion for evaluation.
In the formula (3), _ρw represents the density of the first aqueous medium. A step of producing an aqueous pigment dispersion by the method for producing an aqueous pigment dispersion according to any one of claims 1 to 4;
mixing the aqueous pigment dispersion, a binder resin, and a third aqueous medium;
A method for producing an aqueous ink, comprising: A method for designing an aqueous pigment dispersion, the method comprising determining a composition ratio of a second pigment, a second pigment dispersant, and a second aqueous medium in an aqueous pigment dispersion containing the second pigment, the second pigment dispersant, and the second aqueous medium, the method comprising the steps of:
preparing a plurality of evaluation dispersions each containing a first pigment, polyvinylpyrrolidone as a first pigment dispersant, and a first aqueous medium, the plurality of evaluation dispersions each having a different composition ratio of the first pigment dispersant to the first pigment;
determining a T2 relaxation time for each of the plurality of evaluation dispersions by pulse NMR measurement, and obtaining an index of hydrophilicity based on the reciprocal of the T2 relaxation time;
measuring the volume average particle size of the particles for each of the plurality of evaluation dispersions to obtain an index of the total surface area of the particles;
a first step of determining, as a composition mass ratio of the second pigment dispersant to the second pigment in the aqueous pigment dispersion, a range of ±0.2 or less of a composition mass ratio (R/P) of the first pigment dispersant to the first pigment when the index of the total surface area of the particles takes a maximum value in a graph showing the relationship between the index of the hydrophilicity degree, the index of the total surface area of the particles, and the composition ratio, with the index of the hydrophilicity degree being plotted on the horizontal axis and the index of the total surface area of the particles being plotted on the vertical axis;
a second step of determining a composition ratio of the second pigment, the second pigment dispersant, and the second aqueous medium in the aqueous pigment dispersion according to the determined composition mass ratio;
Including,
the Hansen solubility parameter of the second pigment is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment;
The Hansen solubility parameter of the second pigment dispersant is within ± 5 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first pigment dispersant;
The Hansen solubility parameter of the second aqueous medium is within ±3 (J/cm ³ ) ^1/2 of the Hansen solubility parameter of the first aqueous medium ;
the second pigment dispersant is different from the first pigment dispersant,
The second aqueous medium and the first aqueous medium are the same ;
A method for designing an aqueous pigment dispersion comprising the steps of: A step of designing an aqueous pigment dispersion containing the second pigment, the second pigment dispersant, and the second aqueous medium by using the method for designing an aqueous pigment dispersion according to claim 6;
determining a composition ratio of the designed aqueous pigment dispersion, a binder resin, and a third aqueous medium;
A method for designing an aqueous ink, comprising:

Images