Patent Publication Number: US-2022236655-A1

Title: External additive for toner and toner

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present disclosure relates to an external additive for toner, and a toner suitable for an electrophotographic method that uses the external additive for toner. 
     Description of the Related Art 
     In recent years, with the widespread use of electrophotographic full-color copiers, there is an increasing demand for electrophotographic toners suitable for high-speed printing and having environmental stability and long service life. Conventionally, silica is widely known as an external additive used for toners. In general, examples have been reported in which silica obtained by a dry method or a wet method (sol-gel method) is subjected to surface treatment to increase hydrophobicity. For example, Japanese Patent Application Publication No. 2007-099582 includes an example in which highly hydrophobic spherical sol-gel silica fine particles are added to a toner base particle to improve the charge stability of the toner. 
     However, when an image is output in a high-temperature and high-humidity environment for a long period of time, silica present on the toner surface is easily affected by moisture in an image output device body, which can change a toner surface state. As a result, the charging performance of the toner changes and the image density varies. Further, when an image is output after transition from a high-temperature and high-humidity environment to a low-humidity environment or a normal temperature and humidity environment, the silica present on the toner surface is also affected by the humidity change, and the image density varies. Thus, there is still room for improvement from the viewpoint of toner charge stability in different image output environments. 
     Meanwhile, WO 2015/107961 and Japanese Patent Application Publication No. 2018-004949 describe examples in which polyalkylsilsesquioxane fine particles are added to a toner base particle to improve the fluidity and charge stability of the toner. Further, Japanese Patent Application Publication No. 2008-189545 describes an example of silica in which the number of highly hydrophilic silanol groups is reduced. 
     SUMMARY OF THE INVENTION 
     However, it was found that none of the techniques described in the aforementioned patent literature is sufficient to suppress a change in the hygroscopicity of an external additive when an image is output in a high-temperature and high-humidity environment, or when an image is output under conditions where humidity changes. Therefore, there is room for improvement in terms of toner charge stability, image density stability, and environmental stability. 
     The present disclosure provides an external additive for toner that has charge stability and can suppress fluctuations in image density even when an image is output in a high-temperature and high-humidity environment or when an image is output under conditions where humidity changes, and also to provide a toner comprising the external additive. 
     The present disclosure relates to an external additive for toner comprising a particle of a silicon polymer having a siloxane bond and a Si—R 1  bond, wherein 
     the R 1  represents an alkyl group having from 1 to 6 carbon atoms 
     in a chart obtained by  29 Si-NMR measurement of the external additive, where a total peak area attributed to the external additive is denoted by A, and a peak area attributed to the Si—R 1  bond is denoted by B, the A and the B satisfy a following formula (1), and 
     in the chart obtained by  29 Si-NMR measurement of the external additive, where a total peak area attributed to the silicon polymer is denoted by SA, and a peak area attributed to a T unit structure is denoted by S3, the SA and the S3 satisfy a following formula (2). 
     
       
         
           
             
               
                 
                   
                     
                       0 
                       . 
                       2 
                     
                     ⁢ 
                     6 
                     ⁢ 
                     0 
                   
                   ≤ 
                   
                     B 
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                     .450 
                   
                 
               
               
                 
                   ( 
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                   ≤ 
                   
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                       5 
                     
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     The present disclosure can provide an external additive for toner that has charge stability and can suppress fluctuations in image density even when an image is output in a high-temperature and high-humidity environment or when an image is output under conditions where humidity changes, and also to provide a toner comprising the external additive. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments. 
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     In the present disclosure, the notations “from XX to YY” and “XX to YY” representing a numerical value range denote, unless otherwise stated, a numerical value range that includes the lower limit and the upper limit thereof, as endpoints. In a case where numerical value ranges are described in stages, the upper limits and the lower limits of the respective numerical value ranges can be combined arbitrarily. 
     The present inventors consider that the above effects are exhibited according to the following mechanism. A typical sol-gel silica particle that has been conventionally used as an external additive for toner includes a siloxane bond (Si—O—Si) as a main component. Normally, since silanol groups are present at the ends of a sol-gel silica particle, unreacted residual silanol groups are present on the surface and inside of the silica particle. Even if the residual silanol group is trimethylsilylated by coupling reaction with a silane compound or the like to improve the hydrophobicity, it is not sufficient to suppress a change in charging performance in long-term use in a high-temperature and high-humidity environment. 
     As a result of diligent studies by the present inventors, it was found that the above problems can be solved by optimizing the abundance of Si—R 1  (Si to which an alkyl group is bonded) inside an external additive particle in an external additive having a silicon polymer having a siloxane bond and a Si—R 1  bond. 
     Regarding the mechanism thereof, it is conceivable that the introduction of an alkyl group such as SiCH 3  into an external additive particle increases the hydrophobicity of the external additive particle itself and stabilizes the surface charge. It is presumed that as a result, a change in the toner charge quantity in a high-temperature and high-humidity environment and a change in the toner charge quantity due to a change in humidity can be suppressed. 
     The present disclosure relates to an external additive for toner comprising a particle of a silicon polymer having a siloxane bond and a Si—R 1  bond, wherein 
     the R 1  represents an alkyl group having from 1 to 6 carbon atoms, 
     in a chart obtained by  29 Si—NMR measurement of the external additive for toner, where a total peak area attributed to the external additive for toner is denoted by A, and a peak area attributed to the Si—R 1  bond is denoted by B, the A and the B satisfy a following formula (1), and 
     in the chart obtained by  29 Si—NMR measurement of the external additive for toner, where a total peak area attributed to the silicon polymer is denoted by SA, and a peak area attributed to a T unit structure is denoted by S3, the SA and the S3 satisfy a following formula (2). 
     
       
         
           
             
               
                 
                   
                     
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                     6 
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                     B 
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     In  29 Si—NMR, peaks are detected in different shift regions depending on the structure of the functional group bonded to Si of the constituent compound of the silicon polymer. By specifying each peak position by using a standard sample, the structure bonded to Si can be specified. Further, the abundance ratio of each constituent compound can be calculated from the obtained peak area. The ratio of the peak area of the M unit structure (S1), D unit structure (S2), T unit structure (S3), and Q unit structure (S4) to the total peak area can be obtained by calculation. 
     
       
         
         
             
             
         
       
     
     Ra, Rb, Rc, Rd, Re, and Rf each independently represent an alkyl group having from 1 to 6 (preferably from 1 to 3, more preferably 1 or 2, and even more preferably 1) carbon atoms. Further, the ratio (B/A) of the peak area B attributed to the Si—R 1  bond to the total peak area A is the abundance ratio of Si—R 1  inside the external additive particle. By satisfying the formula (1), the amount of alkyl groups present inside the external additive particle is optimized, and the environmental stability and charge stability of the toner can be improved. 
     
       
         
           
             
               
                 
                   
                     
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                       2 
                     
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     In Si—R 1 , R 1  represents an alkyl group having from 1 to 6 (preferably from 1 to 3, more preferably 1 or 2, still more preferably 1) carbon atoms. 
     When the B/A is less than 0.260, the amount of alkyl groups present inside the external additive particle is too small, so that the effect of improving the environmental stability and the charge stability is not exhibited. Further, when the B/A exceeds 0.450, the abundance of siloxane bonds inside the external additive particle is relatively small, so that the robustness and stability of the particles are lowered. 
     Preferably, 0.280≤B/A≤0.450, more preferably 0.300≤B/A≤0.400, and further preferably 0.300≤B/A≤0.330. Within these ranges, the environmental stability and charge stability of the toner are further improved. 
     A method for producing the external additive for toner, which is the particle of the silicon polymer, is not particularly limited, but it is preferable to form the particles through hydrolysis and polycondensation reaction of a silicon compound (silane monomer) obtained by a sol-gel method. Specifically, particles are preferably formed by polymerizing a mixture of a bifunctional silane having two siloxane bonds and a tetrafunctional silane having four siloxane bonds by hydrolysis and a polycondensation reaction. Silane monomers such as bifunctional silanes and tetrafunctional silanes will be described hereinbelow. 
     That is, the silicon polymer is preferably a polycondensation polymer of at least one silicon compound selected from the group consisting of bifunctional silanes and at least one silicon compound selected from the group consisting of tetrafunctional silanes. The proportion of bifunctional silane is preferably from 50 mol % to 70 mol %, and more preferably from 61 mol % to 65 mol %. The proportion of tetrafunctional silane is preferably from 30 mol % to 50 mol %, and more preferably from 35 mol % to 39 mol %. 
     The present inventors have found that the abovementioned effect is exerted by adjusting the mixing ratio of the monomers, the solvent temperature during hydrolysis and condensation reaction, the type of catalyst, the stirring time, the pH of the solution, and the like in the method for producing the external additive for toner. 
     For example, a method of increasing the mixing ratio of bifunctional silane, lowering the temperature during the condensation reaction, shortening the stirring time, lowering the pH of the solution, and lowering the temperature during hydrolysis can be used to increase the B/A. A method of increasing the mixing ratio of tetrafunctional silane, raising the temperature during the condensation reaction, extending the stirring time, raising the pH of the solution, and raising the temperature during hydrolysis can be used to decrease the B/A. 
     The external additive for toner has a particle of a silicon polymer having a siloxane bond. The particle of the silicon polymer preferably contains the silicon polymer at 90% by mass or more, and more preferably at 95% by mass or more. 
     The method for producing the silicon polymer particles is not particularly limited, and for instance the silicon polymer particles may be obtained through dropping of a silane compound onto water, to elicit hydrolysis and a condensation reaction mediated by a catalyst, followed by filtration and drying of the obtained suspension. Particle diameter can be controlled on the basis of for instance the type of the catalyst, the compounding ratio, the reaction start temperature and the dropping time. Examples of the catalyst include, although not limited thereto, acidic catalysts such as hydrochloric acid, hydrofluoric acid, sulfuric acid and nitric acid, and basic catalysts such as aqueous ammonia, sodium hydroxide and potassium hydroxide. 
     The silicon polymer particles are preferably produced in accordance with the method below. Specifically, the method preferably includes a first step of obtaining a hydrolysis product of a silicon compound; a second step of mixing the resulting hydrolysis product and an alkaline aqueous medium, to elicit a polycondensation reaction of the hydrolysis product; and a third step of mixing the polycondensation reaction product and an aqueous solution, to elicit particle formation. In some cases, hydrophobicized spherical silicon polymer particles may be obtained by further mixing a hydrophobic agent into a dispersion of spherical silicon polymer particles. 
     In the first step, the silicon compound and a catalyst are brought into contact with each other by a method such as stirring or mixing in an aqueous solution in which an acidic or alkaline substance serving as a catalyst is dissolved in water. As the catalyst, a known catalyst can be preferably used. Specifically, examples of suitable acidic catalysts include acetic acid, hydrochloric acid, hydrofluoric acid, sulfuric acid, nitric acid, and the like, and examples of suitable basic catalysts include aqueous ammonia, sodium hydroxide, potassium hydroxide, and the like. 
     The amount of the catalyst used may be adjusted, as appropriate, depending on the silicon compound and the type of catalyst. Preferably, the amount of the catalyst used is selected in the range of from 1×10 −3  part by mass to 1 part by mass with respect to 100 parts by mass of water used when hydrolyzing the silicon compound. 
     Where the amount of the catalyst used is 1×10 −3  parts by mass or more, the reaction proceeds sufficiently. Meanwhile, where the amount of the catalyst used is 1 part by mass or less, the concentration of impurities remaining in the fine particles becomes low, and hydrolysis becomes easy. The amount of water used is preferably from 2 mol to 15 mol with respect to 1 mol of the silicon compound. When the amount of water is 2 mol or more, the hydrolysis reaction proceeds sufficiently, and when the amount of water is 15 mol or less, the productivity is improved. 
     The reaction temperature is not particularly limited, and the reaction may be conducted at normal temperature or in a heated state, but preferably the reaction is conducted in a state where the temperature is held at from 10 to 60° C., since in that case the hydrolysis product is obtained in a short time and partial condensation reactions of the generated hydrolysis product can be suppressed. The reaction time is not particularly limited, and may be selected as appropriate taking into consideration the reactivity of the silicon compound that is used, the composition of the reaction solution resulting from formulating the silicon compound, the acid and water, and productivity. 
     In the method for producing the silicon polymer particles, the second step involves mixing the starting solution obtained in the first step and an alkaline aqueous medium, to elicit a polycondensation reaction of a particle precursor. A polycondensation reaction solution is obtained as a result. The alkaline aqueous medium is a solution obtained by mixing an alkaline component, water and, as needed, an organic solvent or the like. 
     The alkaline component used in the alkaline aqueous medium exhibits basicity, and acts as a neutralizer of the catalyst used in the first step, and as a catalyst of the polycondensation reaction in the second step. Examples of such alkaline components include alkali metal hydroxides such as lithium hydroxide, sodium hydroxide and potassium hydroxide; ammonia; and organic amines such as monomethylamine and dimethylamine. 
     The use amount of the alkaline component is an amount such that the alkaline component neutralizes an acid and effectively acts as a catalyst of the polycondensation reaction; in a case for instance where ammonia is used as the alkaline component, the amount of the alkaline component may ordinarily be selected within the range from 0.01 mass % to 12.5 mass % relative to 100 parts by mass of the mixture with water and the organic solvent. 
     In the second step, an organic solvent may be further used in addition to the alkaline component and water, in order to prepare the alkaline aqueous medium. The organic solvent is not particularly limited, so long as it is compatible with water, but an organic solvent is preferable herein that dissolves 10 g or more of water per 100 g at normal temperature and a normal pressure. 
     Specific examples of the organic solvent include alcohols such as methanol, ethanol, n-propanol, 2-propanol and butanol; polyhydric alcohols such as ethylene glycol, diethylene glycol, propylene glycol, glycerine, trimethylolpropane and hexanetriol; ethers such as ethylene glycol monoethyl ether, acetone, diethyl ether, tetrahydrofuran and diacetone alcohol; and amide compounds such as dimethylformamide, dimethylacetamide and N-methylpyrrolidone. 
     Alcohol solvents such as methanol, ethanol, 2-propanol or butanol are preferable among the organic solvents enumerated above. In terms of hydrolysis and a dehydration condensation reaction, it is more preferable to select, as the organic solvent, the same alcohol as the alcohol that is eliminated. 
     The third step involves mixing the polycondensation reaction product obtained in the second step with an aqueous solution, to elicit formation of particles. Water (tap water, pure water or the like) can be suitably used herein as the aqueous solution, but components that are compatible with water, such as salts, acids, alkalis, organic solvents, surfactants or water-soluble polymers may be further added to the water. The temperatures of the polycondensation reaction solution and of the aqueous solution at the time of mixing are not particularly limited, and herein a range from 5 to 70° C. is suitably selected taking into consideration for instance the composition of the solutions, and productivity. 
     A known method may be adopted, without particular limitations, as the method for recovering the silicon polymer particles. For instance a floating powder may be scooped or filtered, but filtration is preferable since the operation involved is simple and convenient. The filtration method is not particularly limited, and a known apparatus for vacuum filtration, centrifugal filtration, pressure filtration or the like may be selected herein. The filter paper, filter, filter cloth or the like used for filtration are not particularly limited so long these are industrially available, and may be selected as appropriate depending on the apparatus that is used. 
     The hydrophobicity of the silicon polymer particles may be adjusted by treating the surface of the silicon polymer particles using a known means such as a silane coupling agent or silicone oil. 
     The monomers used can be selected, as appropriate, depending on the compatibility with the solvent and the catalyst, hydrolyzability, etc., but the tetrafunctional silane is preferably tetraethoxysilane. The bifunctional silane is preferably dimethyldimethoxysilane. 
     The silicon polymer is preferably a polycondensation polymer of at least one silicon compound selected from the group consisting of silicon compounds having a structure represented by a following formula (2). 
     
       
         
         
             
             
         
       
     
     In the formula (2), R 2 , R 3 , R 4  and R 5  independently represent an alkyl group having from 1 to 6 (preferably from 1 to 3, and more preferably 1 or 2) carbon atoms, a phenyl group or a reactive group (for example, a halogen atom, a hydroxy group, an acetoxy group, or an alkoxy group (preferably having from 1 to 6 carbon atoms, and more preferably from 1 to 3 carbon atoms). At least one of R 2 , R 3 , R 4  and R 5  is the reactive group. 
     R 2 , R 3 , R 4  and R 5  are independently preferably an alkyl group having from 1 to 6 carbon atoms (preferably from 1 to 3 carbon atoms, and more preferably 1 or 2 carbon atoms) or an alkoxy group (preferably having from 1 to 6 carbon atoms, and more preferably from 1 to 3 carbon atoms). 
     In order to obtain the silicon polymer particles, it is possible to use a silicon compound (tetrafunctional silane) having four reactive groups in one molecule of the formula (2), an organosilicon compound (trifunctional silane) in which R 2  in the formula (2) is an alkyl group or a phenyl group and which has three reactive groups (R 3 , R 4 , R 5 ), an organosilicon compound (bifunctional silane) in which R 2  and R 3  in the formula (2) are each an alkyl group or a phenyl group and which has two reactive groups (R 4 , R 5 ), and an organosilicon compound (monofunctional silane) in which R 2 , R 3 , R 4  in the formula (2) are each an alkyl group or a phenyl group and which has one reactive group (R 5 ). 
     These reactive groups are hydrolyzed, addition polymerized and condensation polymerized to form a crosslinked structure, and silicon polymer particles can be obtained. Hydrolysis, addition polymerization and condensation polymerization of R 3 , R 4  and R 5  can be controlled by reaction temperature, reaction time, reaction solvent and pH. 
     The tetrafunctional silane can be exemplified by tetramethoxysilane, tetraethoxysilane, and tetraisocyanatosilane. 
     The trifunctional silane can be exemplified by methyltrimethoxysilane, methyltriethoxysilane, methyldiethoxymethoxysilane, methylethoxydimethoxysilane, methyltrichlorosilane, methylmethoxydichlorosilane, methylethoxydichlorosilane, methyldimethoxychlorosilane, methylmethoxyethoxychlorosilane, methyldiethoxychlorosilane, methyltriacetoxysilane, methyldiacetoxymethoxysilane, methyldiacetoxyethoxysilane, methylacetoxydimethoxysilane, methylacetoxymethoxyethoxysilane, methylacetoxydiethoxysilane, methyltrihydroxysilane, methylmethoxydihydroxysilane, methylethoxydihydroxysilane, methyldimethoxyhydroxysilane, methylethoxymethoxyhydroxysilane, methyldiethoxyhydroxysilane, ethyltrimethoxysilane, ethyltriethoxysilane, ethyltrichlorosilane, ethyltriacetoxysilane, ethyltrihydroxysilane, propyltrimethoxysilane, propyltriethoxysilane, propyltrichlorosilane, propyltriacetoxysilane, propyltrihydroxysilane, butyltrimethoxysilane, butyltriethoxysilane, butyltrichlorosilane, butyltriacetoxysilane, butyltrihydroxysilane, hexyltrimethoxysilane, hexyltriethoxysilane, hexyltrichlorosilane, hexyltriacetoxysilane, hexyltrihydroxysilane, phenyltrimethoxysilane, phenyltriethoxysilane, phenyltrichlorosilane, phenyltriacetoxysilane, and phenyltrihydroxysilane. 
     The difunctional silane can be exemplified by di-tert-butyldichlorosilane, di-tert-butyldimethoxysilane, di-tert-butyldiethoxysilane, dibutyldichlorosilane, dibutyldimethoxysilane, dibutyldiethoxysilane, dichlorodecylmethylsilane, dimethoxydecylmethylsilane, diethoxydecylmethylsilane, dichlorodimethylsilane, dimethyldimethoxysilane, diethoxydimethylsilane, and diethyldimethoxysilane. 
     The monofunctional silane can be exemplified by t-butyldimethylchlorosilane, t-butyldimethylmethoxysilane, t-butyldimethylethoxysilane, t-butyldiphenylchlorosilane, t-butyldiphenylmethoxysilane, t-butyldiphenylethoxysilane, chlorodimethylphenylsilane, methoxydimethylphenylsilane, ethoxydimethylphenylsilane, chlorotrimethylsilane, trimethylmethoxysilane, ethoxytrimethylsilane, triethylmethoxysilane, triethylethoxysilane, tripropylmethoxysilane, tributylmethoxysilane, tripentylmethoxysilane, triphenylchlorosilane, triphenylmethoxysilane, and triphenylethoxysilane. 
     The silicon polymer contained in the external additive for toner preferably has the siloxane bond, a Si—R 1  bond, and a Si—OR 2  bond. In a chart obtained by  29 Si—NMR measurement of the external additive for toner, where a peak area attributed to Si—OR 2  is denoted by C, it is preferable that a following formula (3) is satisfied. 
     
       
         
           
             
               
                 
                   
                     
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                       . 
                       0 
                     
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     R 2  represents an alkyl group having from 1 to 6 carbon atoms or a hydrogen atom. 
     Within the above range, the abundance ratio of the hydrophobic Si—R 1  and the hydrophilic silanol group inside the external additive particles is optimized, and the charge-up suppressing effect in a low-humidity environment is exhibited. That is, this range is preferable from the viewpoint of environmental stability and charge stability of the toner. More preferably, 0.060≤(C/A)/(B/A)≤0.150, and even more preferably 0.075≤(C/A)/(B/A)≤0.085. 
     (C/A)/(B/A) can be controlled by the selection of the silicon compound, the mixing ratio of the silicon compound, and the hydrolysis and condensation conditions. For example, a method of increasing the mixing ratio of tetrafunctional silane, lowering the temperature during the condensation reaction, lowering the temperature during hydrolysis, and the like can be used to increase (C/A)/(B/A), and a method of increasing the mixing ratio of bifunctional silane, raising the temperature during the condensation reaction, extending the stirring time, increasing the pH of the solution, raising the temperature during hydrolysis, and the like can be used to decrease (C/A)/(B/A). 
     The number-average particle diameter of primary particles of the external additive for toner is preferably from 0.02 μm to 0.30 μm. When the number-average particle diameter of the primary particles is within the above range, it becomes easy to uniformly cover the toner particle with the external additive. Further, since the stress on the toner can be suppressed, the effect of charge stability can be easily obtained. 
     When the number-average particle diameter of primary particles of the external additive for toner is 0.02 μm or more, the stress on the toner is reduced even if a large amount of images with a low print density are output for a long time in a harsh environment such as a high-temperature and high-humidity environment, so that the external additive particles are less likely to be embedded in the surface of the toner particle. Further, where the number-average particle diameter is 0.30 μm or less, it becomes difficult for the external additive particles to be separated from the toner particle surface. The number-average particle diameter of primary particles of the external additive for toner is more preferably from 0.05 μm to 0.25 μm, and further preferably from 0.08 μm to 0.18 μm. 
     It is preferable that the surface of the external additive for toner be treated with a hydrophobizing agent. That is, particles of the external additive for toner are preferably silicon polymer particles surface-treated with a hydrophobizing agent. The hydrophobizing agent is not particularly limited, but is preferably an organosilicon compound. 
     The hydrophobizing agent can be exemplified by an alkylsilazane compound such as hexamethyldisilazane, an alkylalkoxysilane compound such as diethyldiethoxysilane, trimethylmethoxysilane, methyltrimethoxysilane, and butyltrimethoxysilane, a fluoroalkylsilane compound such as trifluoropropyltrimethoxysilane, a chlorosilane compound such as dimethyldichlorosilane and trimethylchlorosilane, a siloxane compound such as octamethylcyclotetrasiloxane, a silicone oil, a silicone varnish, and the like. 
     By hydrophobizing the surface of the external additive particles, it is possible to further suppress changes in the charge quantity of the toner in a high-temperature and high-humidity environment. The external additive for toner is preferably surface-treated with at least one compound selected from the group consisting of an alkylsilazane compound, an alkylalkoxysilane compound, a chlorosilane compound, a siloxane compound and a silicone oil. Further, from the viewpoint of environmental stability and charge stability, it is more preferable that the external additive for toner be surface-treated with an alkylsilazane compound. 
     From the viewpoint of charge stability, the degree of hydrophobization of the external additive for toner that is obtained by the methanol titration method is preferably from 40% to 80%, more preferably from 50% to 60%, and further preferably from 50% to 55%. 
     In the chart obtained by  29 Si—NMR measurement of the external additive for toner, 0.00≤S3/SA≤0.50, where SA is a total peak area attributed to the silicon polymer, and S3 is a peak area attributed to a T unit structure. Within the above range, the abundance ratio of Si—R 1  and the silanol group inside the external additive particle becomes optimum, and the environmental stability and charge stability of the toner are further improved. Further, 0.00≤S3/SA≤0.40 is preferable, and 0.00≤S3/SA≤0.20 is more preferable. 
     In the chart obtained by  29 Si—NMR measurement of the external additive for toner, where the total peak area attributed to the silicon polymer is denoted by SA, the peak area attributed to the Q unit structure is denoted by S4, the peak area attributed to the T unit structure is denoted by S3, and the peak area attributed to the D unit structure is denoted by S2, it is preferable that the following formulas (I) to (III) be satisfied. 
     
       
         
           
             
               
                 
                   
                     
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                       2 
                     
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                   ( 
                   I 
                   ) 
                 
               
             
             
               
                 
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                   ≤ 
                   
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                   II 
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                   ≤ 
                   
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     Where the formulas (I) to (III) are satisfied, when the toner is stressed by a member such as a carrier, it is possible to prevent the external additive particles from being embedded in the toner particle surface and prevent the fracture of the external additive particles themselves. 
     Further, it is more preferable that 0.30≤S4/SA≤0.50, 0≤S3/SA≤0.10, and 0.50≤S2/SA≤0.70. Within these ranges, the abundance ratio of Si—R 1  such as Si—CH 3  and the silanol group inside the external additive particle is optimal, which is more preferable from the viewpoint of the environmental stability and charge stability of the toner. S4/SA, S3/SA, and S2/SA can be controlled by the selection of the silicon compound, the mixing ratio of the silicon compound, and the hydrolysis and condensation conditions. 
     The ratio of the peak area attributed to the siloxane bond in the total peak area attributed to the silicon polymer, which is calculated from the chart obtained by  29 Si—NMR measurement of the external additive for toner, is preferably from 60.0% to 85.0%, and more preferably from 63.0% to 68.0%. When the ratio is within the above range, the abundance ratio of Si—R 1  such as Si—CH 3  and the silanol group inside the external additive particle is optimal, and the charging performance in a high humidity environment is improved, which is preferable. The area ratio can be controlled by the selection of the silicon compound, the mixing ratio of the silicon compound, and the hydrolysis and condensation conditions. 
     From the viewpoint of durability stability and charge stability of the toner, the average circularity of the external additive for toner is preferably from 0.85 to 0.95, and more preferably from 0.88 to 0.93. The average circularity can be controlled by the mixing ratio of the monomers and the condensation conditions. 
     The toner comprises a toner particle including a binder resin and an external additive for toner, and the external additive for toner is the abovementioned external additive for toner. From the viewpoint of charge stability, the content of the external additive for toner in the toner is preferably from 0.1 part by mass to 20.0 parts by mass with respect to 100 parts by mass of the toner particles. The range of from 0.5 parts by mass to 15.0 parts by mass is more preferable, and the range of from 1.0 parts by mass to 10.0 parts by mass is further preferable. 
     Where the content of the external additive for toner is 0.1 parts by mass or more, even when a large amount of images with a low print density are output for a long time in a harsh environment such as a high-temperature and high-humidity environment, stress applied to toner can be suppressed, and durability stability and charge stability are improved. Further, when the content of the external additive for toner is 20.0 parts by mass or less, even when an image having a high print density is output for a long time, filming of the external additive particles on the carrier or the photosensitive member can be suppressed. 
     Binder Resin 
     The binder resin used in the toner is not particularly limited, and for instance the following polymers can be used. For example monopolymers of styrene and substituted styrene, such as polystyrene, poly-p-chlorostyrene and polyvinyltoluene; styrene copolymers such as styrene-p-chlorostyrene copolymer, styrene-vinyltoluene copolymer, styrene-vinylnaphthalene copolymer, styrene-acrylate ester copolymers, styrene-methacrylate ester copolymers, styrene-a-chloromethyl methacrylate copolymer, styrene-acrylonitrile copolymer, styrene-vinyl methyl ether copolymer, styrene-vinyl ethyl ether copolymer, styrene-vinyl methyl ketone copolymer and styrene-acrylonitrile-indene copolymer; and polyvinyl chloride, phenol resin, natural resin-modified phenol resin, natural resin-modified maleic acid resin, acrylic resin, methacrylic resin, polyvinyl acetate, silicone resin, polyester resin, polyurethane resin, polyamide resin, furan resin, epoxy resin, xylene resin, polyvinylbutyral resin, terpene resin, coumarone-indene resin and petroleum-based resin may be used. Preferred among the foregoing are polyester resins, from the viewpoint of durability stability and charging stability. 
     Further, from the viewpoint of environmental stability and charge stability, it is preferable that the acid value of the polyester resin be from 0.5 mg KOH/g to 40 mg KOH/g. The functional group that generates the acid value in the polyester resin and Si—R 1  in the external additive interact with each other, and the toner charging performance in a high-humidity environment can be further improved. The acid value is more preferably from 1 mg KOH/g to 20 mg KOH/g, and even more preferably from 1 mg KOH/g to 15 mg KOH/g. 
     Colorant 
     A colorant may be used in the toner particle. The colorant may also be contained in the toner particle. The following are examples of colorants. Examples of black colorants include carbon black, and blacks obtained by color adjustment of blending yellow, magenta and cyan colorants. A pigment may be used alone as the colorant, but from the standpoint of image quality with full-color images, preferably a dye and a pigment are used together to improve the color clarity. 
     Examples of magenta pigments include C.I. Pigment Red 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 30, 31, 32, 37, 38, 39, 40, 41, 48:2, 48:3, 48:4, 49, 50, 51, 52, 53, 54, 55, 57:1, 58, 60, 63, 64, 68, 81:1, 83, 87, 88, 89, 90, 112, 114, 122, 123, 146, 147, 150, 163, 184, 202, 206, 207, 209, 238, 269 and 282; C.I. Pigment Violet 19; and C.I. Vat Red 1, 2, 10, 13, 15, 23, 29 and 35. 
     Examples of magenta dyes include C.I. Solvent Red 1, 3, 8, 23, 24, 25, 27, 30, 49, 81, 82, 83, 84, 100, 109 and 121; C.I. Disperse Red 9; C.I. Solvent Violet 8, 13, 14, 21 and 27; oil-soluble dyes such as C.I. Disperse Violet 1; and basic dyes such as C.I. Basic Red 1, 2, 9, 12, 13, 14, 15, 17, 18, 22, 23, 24, 27, 29, 32, 34, 35, 36, 37, 38, 39 and 40 and C.I. Basic Violet 1, 3, 7, 10, 14, 15, 21, 25, 26, 27 and 28. 
     Examples of cyan pigments include C.I. Pigment Blue 2, 3, 15:2, 15:3, 15:4, 16 and 17; C.I. Vat Blue 6; C.I. Acid Blue 45, and copper phthalocyanine pigments having 1 to 5 phthalimidomethyl groups substituted on a phthalocyanine skeleton. Examples of cyan dyes include C.I. Solvent Blue 70. 
     Examples of yellow pigments include C.I. Pigment Yellow 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 23, 62, 65, 73, 74, 83, 93, 94, 95, 97, 109, 110, 111, 120, 127, 128, 129, 147, 151, 154, 155, 168, 174, 175, 176, 180, 181 and 185; and C.I. Vat Yellow 1, 3, and 20. Examples of yellow dyes include C.I. Solvent Yellow 162. The content of the colorant is preferably from 0.1 to 30 mass parts per 100 mass parts of the binder resin. 
     Wax 
     Wax may be used in the toner particle. Examples of waxes include the following. Examples of the wax include the following: hydrocarbon waxes such as low molecular weight polyethylene, low molecular weight polypropylene, alkylene copolymer, microcrystalline wax, paraffin wax and Fischer-Tropsch wax; hydrocarbon wax oxides such as polyethylene oxide wax, and block copolymers of these; waxes consisting primarily of fatty acid esters, such as carnauba wax; and partially or fully deoxidized fatty acid esters, such as deoxidized carnauba wax. 
     Other examples include the following: saturated linear fatty acids such as palmitic acid, stearic acid and montanic acid; unsaturated fatty acids such as brassidic acid, eleostearic acid and parinaric acid; saturated alcohols such as stearyl alcohol, aralkyl alcohol, behenyl alcohol, carnaubyl alcohol, seryl alcohol and melissyl alcohol; polyvalent alcohols such as sorbitol; esters of fatty acids such as palmitic acid, stearic acid, behenic acid and montanic acid with alcohols such as stearyl alcohol, aralkyl alcohol, behenyl alcohol, carnaubyl alcohol, seryl alcohol and mellisyl alcohol; fatty acid amides such as linoleamide, oleamide and lauramide; saturated fatty acid bisamides such as methylenebis stearamide, ethylenebis capramide, ethylenebis lauramide and hexamethylenebis stearamide; unsaturated fatty acid amides such as ethylenebis oleamide, hexamethylenebis oleamide, N,N′-dioleyladipamide and N,N′-dioleylsebacamide; aromatic bisamides such as m-xylenebis stearamide and N,N′-distearylisophthalamide; fatty acid metal salts (commonly called metal soaps) such as calcium stearate, calcium laurate, zinc stearate and magnesium stearate; aliphatic hydrocarbon waxes grafted with vinyl monomers such as styrene or acrylic acid; partially esterified products of fatty acids and polyvalent alcohols, such as behenic acid monoglyceride; and methyl ester compounds with hydroxyl groups obtained by hydrogenation of plant-based oils and fats. The content of the wax is preferably from 2.0 parts by mass to 30.0 parts by mass, relative to 100 parts by mass of the binder resin. 
     Charge Control Agent 
     The toner particle may comprises a charge control agent as necessary. A known charge control agent may be used, but a metal compound of an aromatic carboxylic acid is especially desirable because it is colorless and yields a toner particle that has a rapid charging speed and can stably maintain a fixed charge quantity. 
     Examples of negatively-charging charge control agents include salicylic acid metal compounds, naphthoic acid metal compounds, dicarboxylic acid metal compounds, polymeric compounds having sulfonic acids or carboxylic acids in the side chains, polymeric compounds having sulfonic acid salts or sulfonic acid esters in the side chains, polymeric compounds having carboxylic acid salts or carboxylic acid esters in the side chains, and boron compounds, urea compounds, silicon compounds and calixarenes. 
     Examples of the positive charge control agent include a quaternary ammonium salt, a polymer compound having the quaternary ammonium salt in a side chain, a guanidine compound, and an imidazole compound. The charge control agent may be added internally or externally to the toner particle. The amount of the charge control agent added is preferably from 0.2 parts by mass to 10 parts by mass with respect to 100 parts by mass of the binder resin. 
     &lt;Inorganic Fine Particles&gt; 
     The toner may include, if necessary, other inorganic fine particles in addition to the above-mentioned external additive for toner. The inorganic fine particles may be internally added to the toner particle, or may be mixed with the toner particle as an external additive. When contained as an external additive, inorganic fine particles such as silica fine particles, titanium oxide fine particles, and aluminum oxide fine particles are preferable. The inorganic fine particles are preferably hydrophobized with a hydrophobizing agent such as a silane compound, a silicone oil or a mixture thereof. 
     As the external additive for improving the flowability, inorganic fine particles having a specific surface area of from 50 m 2 /g to 400 m 2 /g or less are preferable. Inorganic fine particles having a specific surface area in the above range may be used in combination with an external additive for toner in order to achieve both improvement in flowability and stabilization of durability. 
     The inorganic fine particles are preferably used in an amount of from 0.1 parts by mass to 10.0 parts by mass with respect to 100 parts by mass of the toner particle. When the above range is satisfied, the effect of charge stability can be easily obtained. The content of the above-mentioned external additive for toner is preferably from 50% by mass to 100% by mass, more preferably from 80% by mass to 100% by mass, and still more preferably from 90% by mass to 100% by mass, based on the total amount of the external additive. 
     &lt;Developer&gt; 
     A toner can be used as a one-component developer, but it can also be mixed with a magnetic carrier and used as a two-component developer in order to further improve dot reproducibility and to supply a stable image for a long time. That is, in a two-component developer containing a toner and a magnetic carrier, the toner is preferably the abovementioned toner. 
     Generally well-known substances such as, for example, iron oxide, unoxidized iron powder; metal particles such as particles of iron, lithium, calcium, magnesium, nickel, copper, zinc, cobalt, manganese, chromium, and rare earths, particles of alloys thereof, and particles of oxides thereof; a magnetic substance such as a ferrite; a magnetic substance-dispersed resin carrier (so-called resin carrier) including the magnetic substance and a binder resin that holds the magnetic substance in a dispersed state can be used as the magnetic carrier. The mixing ratio of the magnetic carrier and the toner is preferably such that the toner concentration in the two-component developer is from 2% by mass to 15% by mass, and more preferably from 4% by mass to 13% by mass. 
     Method for Producing a Toner Particle 
     The method for producing the toner particle is not particularly limited, and a known production method such as suspension polymerization, emulsification aggregation, melt-kneading or dissolution suspension can be resorted to. A toner can then be obtained by mixing the above toner external additive, and other external additives as needed, with the obtained toner particle. 
     Mixing of the toner particle and the external additive can be accomplished using a mixing device such as a double-cone mixer, a V-type mixer, a drum-type mixer, a super mixer, a Henschel mixer, a Nauta mixer, Mechano Hybrid (by Nippon Coke &amp; Engineering Co., Ltd.) or Nobilta (by Hosokawa Micron Corporation). 
     The measurement methods for various physical properties will be explained below. 
     &lt;Separation of External Additive Particles and Toner Particles from Toner&gt; 
     It is also possible to measure each physical property by using the external additive separated from the toner by using the following method. A total of 200 g of sucrose (manufactured by Kishida Chemical Co., Ltd.) is added to 100 mL of ion-exchanged water and dissolved in a hot water bath to prepare a sucrose concentrate. A total of 31 g of the sucrose concentrate and 6 mL of Contaminone N (a 10% by mass aqueous solution of a neutral detergent for cleaning precision measuring instruments; has pH 7 and includes a nonionic surfactant, an anionic surfactant, and an organic builder; manufactured by Wako Pure Chemical Industries, Ltd.) are placed in a centrifuge tube to prepare a dispersion liquid. A total of 1 g of toner is added to the dispersion liquid, and the toner lumps are loosened with a spatula or the like. 
     The centrifuge tube is shaken with a shaker (“KM Shaker” (model: V.SX), manufactured by Iwaki Sangyo Co., Ltd.) for 20 min under the condition of 350 reciprocations per minute. After shaking, the solution is transferred to a glass tube for a swing rotor (50 mL), and centrifugation is performed at 3500 rpm for 30 min with a centrifuge. 
     In the glass tube after centrifugation, the toner is present in the uppermost layer, and the external additive for toner is present on the aqueous solution side of the lower layer. The aqueous solution of the lower layer is collected and centrifuged to separate the sucrose and the external additive for toner, and the external additive for toner is collected. If necessary, centrifugation is repeated, and after sufficient separation, the dispersion liquid is dried and an external additive for toner is collected. When a plurality of external additives for toner are added, the external additives for toner can be sorted by using a centrifugation method or the like. 
     &lt;Method for Measuring Number-Average Particle Diameter of Primary Particles of External Additive Particles for Toner&gt; 
     The number-average particle diameter of primary particles of external additive particles for toner is measured in accordance with a centrifugal sedimentation method. Specifically, 0.01 g of dried external additive particles are placed in a 25 ml glass vial, and 0.2 g of a 5% Triton solution and 19.8 g of RO water are added thereto, to produce a solution. Next, the probe (the tip within the leading end) of an ultrasonic disperser is immersed in that solution, to elicit ultrasonic dispersion at an output of 20 W for 15 minutes, and obtain a dispersion as a result. The number-average particle diameter of primary particles is measured next, using this dispersion, with the help of a centrifugal sedimentation particle size distribution measuring device DC24000 by CPS Instruments Inc. Disc rotational speed is set to 18000 rpm, and true density is set to 1.3 g/cm 3 . Prior to measurement, the device is calibrated using polyvinyl chloride particles having an average particle diameter of 0.476 μm. 
     &lt;Method for Measuring Acid Value of Resin&gt; 
     The acid value is the number of mg of potassium hydroxide required to neutralize acid components such as free fatty acids and resin acids contained in 1 g of a sample. The acid value is measured in the following manner according to JIS-K0070-1992. 
     (1) Reagent 
     A total of 1.0 g of phenolphthalein is dissolved in 90 mL of ethyl alcohol (95% by volume) and ion-exchanged water is added to make 100 mL and obtain a phenolphthalein solution. 
     A total of 7 g of special grade potassium hydroxide is dissolved in 5 mL of water and ethyl alcohol (95% by volume) is added to make 1 L. The solution is put in an alkali-resistant container so as to avoid contact with carbon dioxide, allowed to stay for 3 days, and then filtered to obtain a potassium hydroxide solution. The obtained potassium hydroxide solution is stored in an alkali-resistant container. A total of 25 mL of 0.1 mol/L hydrochloric acid is placed in a triangular flask, a few drops of the phenolphthalein solution are added, titration is performed with the potassium hydroxide solution, and a factor of the potassium hydroxide solution is obtained from the amount of the potassium hydroxide solution required for neutralization. The 0.1 mol/L hydrochloric acid used is prepared according to JIS K 8001-1998. 
     (2) Operation 
     (A) Main Test 
     A total of 2.0 g of the crushed sample is accurately weighed into a 200 mL Erlenmeyer flask, 100 mL of a mixed solution of toluene/ethanol (2:1) is added, and dissolution is performed over 5 h. Then, a few drops of the phenolphthalein solution are added as an indicator, and titration is performed using the potassium hydroxide solution. The end point of the titration is when the light red color of the indicator continues for about 30 sec. 
     (B) Blank Test 
     The same titration as in the above operation is performed, except that no sample is used (that is, only a mixed solution of toluene/ethanol (2:1) is used). 
     (3) The obtained result is substituted into the following formula to calculate the acid value. 
     
       
         
           
             A 
             = 
             
               
                 [ 
                 
                   
                     ( 
                     
                       C 
                       - 
                       B 
                     
                     ) 
                   
                   × 
                   f 
                   × 
                   5.61 
                 
                 ] 
               
               / 
               S 
             
           
         
       
     
     Here, A: acid value (mg KOH/g), B: addition amount of potassium hydroxide solution in the blank test (mL), C: addition amount of potassium hydroxide solution in the main test (mL), f: potassium hydroxide solution factor, and S: mass (g) of the sample. 
     &lt;Measurement of Acid Value of Polyester Resin from Toner&gt; 
     The following method can be used for measuring the acid value of the polyester resin in the toner. The polyester resin is separated from the toner by the following method, and the acid value is measured. The toner is dissolved in tetrahydrofuran (THF), and the solvent is distilled off under reduced pressure from the obtained soluble fraction to obtain a tetrahydrofuran (THF)-soluble component of the toner. The obtained tetrahydrofuran (THF)-soluble component of the toner is dissolved in chloroform to prepare a sample solution having a concentration of 25 mg/ml. A total of 3.5 ml of the obtained sample solution is injected into the following apparatus, and the component with a molecular weight of 2000 or more is separated as a resin component under the following conditions. 
     Preparative GPC equipment: preparative HPLC LC-980 manufactured by Nippon Analytical Industry Co., Ltd.
 
Sorting columns: JAIGEL 3H, JAIGEL 5H (manufactured by Nippon Analytical Industry Co., Ltd.)
 
Eluent: chloroform
 
Flow velocity: 3.5 ml/min
 
     After separating the high-molecular-weight component derived from the resin, the solvent is distilled off under reduced pressure, followed by drying in an atmosphere of 90° C. under reduced pressure for 24 h. The above operation is repeated until about 2.0 g of the resin component is obtained. Using the obtained sample, the acid value is measured according to the above procedure. 
     Method for Measuring the Weight-Average Particle Diameter (D4) of the Toner Particle 
     The weight-average particle diameter (D4) of the toner particle is determined by carrying out the measurements in 25,000 channels for the number of effective measurement channels and performing analysis of the measurement data, using a “Coulter Counter Multisizer 3” (registered trademark, Beckman Coulter, Inc.), a precision particle size distribution measurement instrument operating on the pore electrical resistance method and equipped with a 100-μm aperture tube, and using the accompanying dedicated software, i.e., “Beckman Coulter Multisizer 3 Version 3.51” (Beckman Coulter, Inc.), to set the measurement conditions and analyze the measurement data. 
     The aqueous electrolyte solution used for the measurements is prepared by dissolving special-grade sodium chloride in deionized water to provide a concentration of approximately 1 mass % and, for example, “ISOTON II” (Beckman Coulter, Inc.) can be used. The dedicated software is configured as follows prior to measurement and analysis. 
     In the “modify the standard operating method (SOM)” screen in the dedicated software, the total count number in the control mode is set to 50000 particles; the number of measurements is set to 1 time; and the Kd value is set to the value obtained using “standard particle 10.0 μm” (Beckman Coulter, Inc.). The threshold value and noise level are automatically set by pressing the threshold value/noise level measurement button. In addition, the current is set to 1,600 μA; the gain is set to 2; the electrolyte solution is set to ISOTON II; and a check is entered for the post-measurement aperture tube flush. 
     In the “setting conversion from pulses to particle diameter” screen of the dedicated software, the bin interval is set to logarithmic particle diameter; the particle diameter bin is set to 256 particle diameter bins; and the particle diameter range is set to from 2 μm to 60 μm. The specific measurement procedure is as follows. 
     (1) Approximately 200 mL of the above-described aqueous electrolyte solution is introduced into a 250-mL roundbottom glass beaker intended for use with the Multisizer 3 and this is placed in the sample stand and counterclockwise stirring with the stirrer rod is carried out at 24 rotations per second. Contamination and air bubbles within the aperture tube are preliminarily removed by the “aperture tube flush” function of the dedicated software.
 
(2) Approximately 30 mL of the aqueous electrolyte solution is introduced into a 100-mL flatbottom glass beaker. To this is added approximately 0.3 mL of the dilution prepared by the three-fold (mass) dilution with deionized water of “Contaminon N” (a 10 mass % aqueous solution of a neutral pH 7 detergent for cleaning precision measurement instrumentation, comprising a nonionic surfactant, anionic surfactant, and organic builder, from Wako Pure Chemical Industries, Ltd.) as a dispersing agent.
 
(3) A prescribed amount of deionized water is introduced into the water tank of the ultrasound disperser “Ultrasonic Dispersion System Tetora 150” (Nikkaki Bios Co., Ltd.), which has an electrical output of 120 W and is equipped with two oscillators (oscillation frequency=50 kHz) disposed such that the phases are displaced by 180°, and approximately 2 mL of Contaminon N is added to this water tank.
 
(4) The beaker described in (2) is set into the beaker holder opening on the ultrasound disperser and the ultrasound disperser is started. The vertical position of the beaker is adjusted in such a manner that the resonance condition of the surface of the aqueous electrolyte solution within the beaker is at a maximum.
 
(5) While the aqueous electrolyte solution within the beaker set up according to (4) is being irradiated with ultrasound, approximately 10 mg of the toner particle is added to the aqueous electrolyte solution in small aliquots and dispersion is carried out. The ultrasound dispersion treatment is continued for an additional 60 seconds. The water temperature in the water tank is controlled as appropriate during ultrasound dispersion to be from 10° C. to 40° C.
 
(6) Using a pipette, the dispersed toner-containing aqueous electrolyte solution prepared in (5) is dripped into the roundbottom beaker set in the sample stand as described in (1) with adjustment to provide a measurement concentration of approximately 5%. Measurement is then performed until the number of measured particles reaches 50000.
 
(7) The measurement data is analyzed by the dedicated software provided with the instrument and the weight-average particle diameter (D4) is calculated. When set to graph/volume % with the dedicated software, the “average diameter” on the analysis/volume statistical value (arithmetic average) screen is the weight-average particle diameter (D4).
 
     &lt;Method for Measuring Average Circularity of Particles of External Additive for Toner, Toner Particles, and Toner&gt; 
     The average circularity is used as a simple method for quantitatively representing the shape of particles. Particles in the range of from 0.01 μm to 400 μm in equivalent circle diameter are measured using a flow-type particle image analyzer FPIA-3000 manufactured by Sysmex Corporation, the circularity of the measured particles is determined by the following formula, and the value obtained by dividing the total circularity by the total number of particles is defined as the average circularity. The number of particles to be measured is 5000. 
     
       
         
           
             
               Circularity 
               ⁢ 
               
                   
               
               ⁢ 
               a 
             
             = 
             
               L 
               ⁢ 
               
                   
               
               ⁢ 
               
                 0 
                 / 
                 
                   L 
                   . 
                 
               
             
           
         
       
     
     (in the formula, L0 indicates the peripheral length of a circle having the same projected area as the particle image, and L indicates the peripheral length of the particle projected image when image processing is performed at an image processing resolution of 512×512 (pixels of 0.3 μm×0.3 μm)). 
     &lt;Method for Measuring Degree of Hydrophobicity of External Additive for Toner&gt; 
     The degree of hydrophobicity of particles of the external additive for toner is calculated by a methanol titration method. Specifically, the degree of hydrophobicity is measured by the following procedure. Methanol is added dropwise from a burette to a mixture obtained by adding 0.5 g of particles of the external additive for toner to 50 ml of RO until the entire amount of the external additive for toner is wetted. The dropwise addition is performed while stirring the mixture. 
     Whether the entire amount is wetted is determined by whether the entire external additive for toner that was floating on the water surface is submerged in the liquid and suspended in the liquid. At this time, the value of the volume percentage of methanol in the total amount of the methanol that was dropwise added and the mixed solution at the end of dropwise addition is taken as the degree of hydrophobicity. The higher the value of the degree of hydrophobicity, the higher the hydrophobicity. 
     &lt;Method for Measuring the Abundance Ratio of Constituent Compounds of External Additive for Toner, B/A and (C/A)/(B/A) by Solid-State  29 Si—NMR&gt; 
     In solid-state  29 Si—NMR, peaks are detected in shift regions that differ depending on the structure of the functional group bonded to Si of the constituent compound of the external additive for toner. By specifying each peak position using a standard sample, the structure bonded to Si can be specified. Further, the abundance ratio of each constituent compound can be calculated from the obtained peak area. The ratio of the peak area of the Q unit structure, the T unit structure, and the D unit structure to the total peak area can be obtained by calculation. 
     Specifically, the measurement conditions for solid-state  29 Si—NMR are as follows. 
     Equipment: JNM-ECX5002 (JEOL RESONANCE) 
     Temperature: room temperature
 
Measurement method: DDMAS method  29 Si 45°
 
Sample tube: zirconia, 3.2 mm in diameter
 
Sample: filled in powder form in the sample tube
 
Sample rotation speed: 10 kHz
 
Relaxation delay: 180 s
 
     Scan: 2000 
     After the measurement, peaks are separated for the M unit structure, D unit structure, T unit structure, and Q unit structure by curve fitting a plurality of silane components having different substituents and bonding groups of the sample or external additive for toner, and the area of each peak is calculated. 
     Curve fitting is performed using EXcalibur for Windows (registered trademark) version 4.2 (EX series), which is software for JNM-EX400 manufactured by JEOL Ltd. Measurement data are read by clicking “1D Pro” from a menu icon. Next, “Curve fitting function” is selected from “Command” on a menu bar, and curve fitting is performed. Curve fitting for each component is performed so that the difference (combined peak difference) between the combined peak obtained by combining the peaks obtained by curve fitting and the peak of the measurement result is the smallest. 
       M unit structure: (Ra)(Rb)(Rc)SiO 1/2   (S1)
 
       D unit structure: (Rd)(Re)Si(O 1/2 ) 2   (S2)
 
       T unit structure: RfSi(O 1/2 ) 3   (S3)
 
       Q unit structure: Si(O 1/2 ) 4   (S4)
 
     
       
         
           
             
               ( 
               
                 
                   S 
                   ⁢ 
                   1 
                 
                 + 
                 
                   S 
                   ⁢ 
                   2 
                 
                 + 
                 
                   S 
                   ⁢ 
                   3 
                 
                 + 
                 
                   S 
                   ⁢ 
                   4 
                 
               
               ) 
             
             = 
             
               S 
               ⁢ 
               
                 A 
                 . 
               
             
           
         
       
     
     Ra, Rb, Rc, Rd, Re and Rf in the formulas (S1), (S2) and (S3) are each an organic group such as a hydrocarbon group having from 1 to 6 carbon atoms (for example, an alkyl group) or a halogen atom bonded to silicon. When it is necessary to confirm the structure in more detail, the measurement results of  13 C—NMR and  1 H-NMR may be identified together with the measurement results of  29 Si—NMR. S2/SA, S3/SA and S4/SA are calculated from SA, S2, S3 and S4 thus obtained. 
     (B/A Calculation Method) 
     From the chart obtained by solid-state  29 Si—NMR, the peak area of (Si—R 1 ) in each unit structure at the following positions is calculated. R 1  is as described above and represents an alkyl group having from 1 to 6 carbon atoms. 
     The peak area of the Q4 unit structure having (Si—R 1 ) is denoted by S44, the peak area of the Q3 unit structure having (Si—R 1 ) is denoted by S43, the peak area of the Q2 unit structure having (Si—R 1 ) is denoted by S42, and the peak area of the Q1 unit structure having (Si—R 1 ) is denoted by S41. 
     The peak area of the T3 unit structure having (Si—R 1 ) is denoted by S33, the peak area of the T2 unit structure having (Si—R 1 ) is denoted by S32, and the peak area of the T1 unit structure having (Si—R 1 ) is denoted by S31. 
     The peak area of the D2 unit structure having (Si—R 1 ) is denoted by S22, and the peak area of the D1 unit structure having (Si—R 1 ) is denoted by S21. 
     The peak area of the M1 unit structure having (Si—R 1 ) is denoted by S11. 
     At this time, the peak area ratio of Si—R 1  in each unit structure is calculated as follows. 
     
       
         
           
             
               Peak 
               ⁢ 
               
                   
               
               ⁢ 
               area 
               ⁢ 
               
                   
               
               ⁢ 
               ratio 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               Si 
               ⁢ 
               
                 - 
               
               ⁢ 
               
                 R 
                 1 
               
               ⁢ 
               
                   
               
               ⁢ 
               attributed 
               ⁢ 
               
                   
               
               ⁢ 
               to 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               Q 
               ⁢ 
               
                   
               
               ⁢ 
               unit 
               ⁢ 
               
                   
               
               ⁢ 
               structure 
               ⁢ 
               
                   
               
               ⁢ 
               QB 
             
             = 
             
               
                 
                   ( 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       44 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
                 × 
                 0 
               
               + 
               
                 
                   ( 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       43 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
                 × 
                 0 
               
               + 
               
                 
                   ( 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       42 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
                 × 
                 0 
               
               + 
               
                 
                   ( 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       41 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
                 × 
                 0 
               
             
           
         
       
       
         
           
             
               Peak 
               ⁢ 
               
                   
               
               ⁢ 
               area 
               ⁢ 
               
                   
               
               ⁢ 
               ratio 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               Si 
               ⁢ 
               
                 - 
               
               ⁢ 
               
                 R 
                 1 
               
               ⁢ 
               
                   
               
               ⁢ 
               attributed 
               ⁢ 
               
                   
               
               ⁢ 
               to 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               T 
               ⁢ 
               
                   
               
               ⁢ 
               unit 
               ⁢ 
               
                   
               
               ⁢ 
               structure 
               ⁢ 
               
                   
               
               ⁢ 
               TB 
             
             = 
             
               
                 
                   ( 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       33 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
                 × 
                 
                   1 
                   / 
                   4 
                 
               
               + 
               
                 
                   ( 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       32 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
                 × 
                 
                   1 
                   / 
                   4 
                 
               
               + 
               
                 
                   ( 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       31 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
                 × 
                 
                   1 
                   / 
                   4 
                 
               
             
           
         
       
       
         
           
             
               Peak 
               ⁢ 
               
                   
               
               ⁢ 
               area 
               ⁢ 
               
                   
               
               ⁢ 
               ratio 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               Si 
               ⁢ 
               
                 - 
               
               ⁢ 
               
                 R 
                 1 
               
               ⁢ 
               
                   
               
               ⁢ 
               attributed 
               ⁢ 
               
                   
               
               ⁢ 
               to 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               D 
               ⁢ 
               
                   
               
               ⁢ 
               unit 
               ⁢ 
               
                   
               
               ⁢ 
               structure 
               ⁢ 
               
                   
               
               ⁢ 
               DB 
             
             = 
             
               
                 
                   ( 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       22 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
                 × 
                 
                   1 
                   / 
                   2 
                 
               
               + 
               
                 
                   ( 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       21 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
                 × 
                 
                   1 
                   / 
                   2 
                 
               
             
           
         
       
       
         
           
             
               Peak 
               ⁢ 
               
                   
               
               ⁢ 
               area 
               ⁢ 
               
                   
               
               ⁢ 
               ratio 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               Si 
               ⁢ 
               
                 - 
               
               ⁢ 
               
                 R 
                 1 
               
               ⁢ 
               
                   
               
               ⁢ 
               attributed 
               ⁢ 
               
                   
               
               ⁢ 
               to 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               M 
               ⁢ 
               
                   
               
               ⁢ 
               unit 
               ⁢ 
               
                   
               
               ⁢ 
               structure 
               ⁢ 
               
                   
               
               ⁢ 
               MB 
             
             = 
             
               S 
               ⁢ 
               
                   
               
               ⁢ 
               
                 11 
                 / 
                 S 
               
               ⁢ 
               
                   
               
               ⁢ 
               1 
               × 
               
                 3 
                 / 
                 4 
               
             
           
         
       
     
     The structural units of the silicon polymer are classified into M units (monofunctional), D units (bifunctional), T units (trifunctional), and Q units (tetrafunctional) according to the number of functional groups. In the present disclosure, the difference in the degree of condensation in each unit is represented as a D1 unit, a D2 unit, a Ti unit, a T2 unit, a T3 unit, and the like by the number of crosslinked oxygen atoms. That is, the number following the alphabet letter such as D and T indicates the number of crosslinked oxygen atoms forming a siloxane bond. For example, the T3 unit indicates that all three functional groups are condensed to participate in the siloxane bond. Further, the T2 unit indicates that two of the three functional groups are condensed to participate in the siloxane bond, and one functional group is not condensed. 
     Q unit structure
 
Q4: from −105 ppm to −115 ppm
 
Q3: from −95 ppm to −104 ppm
 
Q2: from −85 ppm to −94 ppm
 
Q1: from −75 ppm to −84 ppm
 
T unit structure
 
T3: from −60 ppm to −70 ppm
 
T2: from −50 ppm to −59 ppm
 
T1: from −40 ppm to −49 ppm
 
D unit structure
 
D2: from −15 ppm to −25 ppm
 
D1: from −10 ppm to −14 ppm
 
M unit structure
 
M1: from −5 ppm to −9 ppm
 
       B/A=QB+TB+DB+MB 
     is calculated from the above formula. 
     (C/A and (C/A)/(B/A) Calculation Method) 
     The peak area of the unreacted group (Si—OR 2 ) in each unit structure at the following position is calculated from the chart obtained by solid-state  29 Si—NMR. R 2  represents an alkyl group having from 1 to 6 carbon atoms or a hydrogen atom. 
     The peak area of the Q4 unit structure having an unreacted group (Si—OR 2 ) is denoted by S44, the peak area of the Q3 unit structure having an unreacted group (Si—OR 2 ) is denoted by S43, the peak area of the Q2 unit structure having an unreacted group (Si—OR 2 ) is denoted by S42, and the peak area of the Q1 unit structure having an unreacted group (Si—OR 2 ) is denoted by S41. 
     The peak area of the T3 unit structure having an unreacted group (Si—OR 2 ) is denoted by S33, the peak area of the T2 unit structure having an unreacted group (Si—OR 2 ) is denoted by S32, and the peak area of the T1 unit structure having an unreacted group (Si—OR 2 ) is denoted by S31. 
     The peak area of the D2 unit structure having an unreacted group (Si—OR 2 ) is denoted by S22, and the peak area of the D1 unit structure having an unreacted group (Si—OR 2 ) is denoted by S21. 
     The peak area of the M1 unit structure having an unreacted group (Si—OR 2 ) is denoted by S11. 
     At this time, the peak area ratio of Si—OR 2  in each unit structure is calculated as follows. 
     
       
         
           
             
               
                 Peak 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 area 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 ratio 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 Si 
                 ⁢ 
                 
                   - 
                 
                 ⁢ 
                 
                   OR 
                   2 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 attributed 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 to 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 Q 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 unit 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 structure 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 QC 
               
               = 
               
                 
                   
                     ( 
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         44 
                         / 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                     ) 
                   
                   × 
                   0 
                 
                 + 
                 
                   
                     ( 
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         43 
                         / 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                     ) 
                   
                   × 
                   
                     1 
                     / 
                     4 
                   
                 
                 + 
                 
                   
                     ( 
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         42 
                         / 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                     ) 
                   
                   × 
                   
                     1 
                     / 
                     2 
                   
                 
                 + 
                 
                   
                     ( 
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         41 
                         / 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       4 
                     
                     ) 
                   
                   × 
                   
                     3 
                     / 
                     4 
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 Peak 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 area 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 ratio 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 Si 
                 ⁢ 
                 
                   - 
                 
                 ⁢ 
                 
                   OR 
                   2 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 attributed 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 to 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 T 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 unit 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 structure 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 TC 
               
               = 
               
                 
                   
                     ( 
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         33 
                         / 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                     ) 
                   
                   × 
                   0 
                 
                 + 
                 
                   
                     ( 
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         32 
                         / 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                     ) 
                   
                   × 
                   
                     1 
                     / 
                     4 
                   
                 
                 + 
                 
                   
                     ( 
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         31 
                         / 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3 
                     
                     ) 
                   
                   × 
                   
                     1 
                     / 
                     2 
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 Peak 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 area 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 ratio 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 Si 
                 ⁢ 
                 
                   - 
                 
                 ⁢ 
                 
                   OR 
                   2 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 attributed 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 to 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 D 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 unit 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 structure 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 D 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 C 
               
               = 
               
                 
                   
                     ( 
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         22 
                         / 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                     ) 
                   
                   × 
                   0 
                 
                 + 
                 
                   
                     ( 
                     
                       S 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         21 
                         / 
                         S 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                     ) 
                   
                   × 
                   
                     1 
                     / 
                     4 
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 Peak 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 area 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 ratio 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 of 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 Si 
                 ⁢ 
                 
                   - 
                 
                 ⁢ 
                 
                   OR 
                   2 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 attributed 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 to 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 the 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 M 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 unit 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 structure 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 MC 
               
               = 
               
                 S 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   11 
                   / 
                   S 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 1 
                 × 
                 0 
               
             
           
         
       
     
     Q unit structure
 
Q4: from −105 ppm to −115 ppm
 
Q3: from −95 ppm to −104 ppm
 
Q2: from −85 ppm to −94 ppm
 
Q1: from −75 ppm to −84 ppm
 
T unit structure
 
T3: from −60 ppm to −70 ppm
 
T2: from −50 ppm to −59 ppm
 
T1: from −40 ppm to −49 ppm
 
D unit structure
 
D2: from −15 ppm to −25 ppm
 
D1: from −10 ppm to −14 ppm
 
M unit structure
 
M1: from −5 ppm to −9 ppm
 
       C/A=QC+TC+DC+MC 
     is calculated from the above formula. Further, (C/A)/(B/A) is calculated from B/A calculated above. 
     (Ratio of Peak Area Attributed to Siloxane Bond) 
     From the chart obtained by solid-state  29 Si—NMR, the ratio of the peak area attributed to the siloxane bond in the total peak area attributed to the silicon polymer is calculated by the following method. 
     The peak area attributed to the Q4 unit structure having a siloxane bond is denoted by p44, the peak area attributed to the Q3 unit structure having a siloxane bond is denoted by p43, the peak area attributed to the Q2 unit structure having a siloxane bond is denoted by p42, and the peak area attributed to the Q1 unit structure having a siloxane bond is denoted by p41. 
     The peak area attributed to the T3 unit structure having a siloxane bond is denoted by p33, the peak area attributed to the T2 unit structure having a siloxane bond is denoted by p32, and the peak area attributed to the T1 unit structure having a siloxane bond is denoted by p31. 
     The peak area attributed to the D2 unit structure having a siloxane bond is denoted by p22, and the peak area attributed to the D1 unit structure having a siloxane bond is denoted by p21. 
     The peak area attributed to the M1 unit structure having a siloxane bond is denoted by p11. 
     At this time, the peak area ratio attributed to the siloxane bond in each unit structure is calculated as follows. 
     
       
         
           
             
               Peak 
               ⁢ 
               
                   
               
               ⁢ 
               area 
               ⁢ 
               
                   
               
               ⁢ 
               ratio 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               siloxane 
               ⁢ 
               
                   
               
               ⁢ 
               bond 
               ⁢ 
               
                   
               
               ⁢ 
               attributed 
               ⁢ 
               
                   
               
               ⁢ 
               to 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               Q 
               ⁢ 
               
                   
               
               ⁢ 
               unit 
               ⁢ 
               
                   
               
               ⁢ 
               structure 
               ⁢ 
               
                   
               
               ⁢ 
               Qp 
             
             = 
             
               
                 ( 
                 
                   p 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     44 
                     / 
                     S 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
                 ) 
               
               + 
               
                 
                   ( 
                   
                     p 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       43 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
                 × 
                 
                   3 
                   / 
                   4 
                 
               
               + 
               
                 
                   ( 
                   
                     p 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       42 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
                 × 
                 
                   1 
                   / 
                   2 
                 
               
               + 
               
                 
                   ( 
                   
                     p 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       41 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
                 × 
                 
                   1 
                   / 
                   4 
                 
               
             
           
         
       
       
         
           
             
               Peak 
               ⁢ 
               
                   
               
               ⁢ 
               area 
               ⁢ 
               
                   
               
               ⁢ 
               ratio 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               siloxane 
               ⁢ 
               
                   
               
               ⁢ 
               bond 
               ⁢ 
               
                   
               
               ⁢ 
               attributed 
               ⁢ 
               
                   
               
               ⁢ 
               to 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               T 
               ⁢ 
               
                   
               
               ⁢ 
               unit 
               ⁢ 
               
                   
               
               ⁢ 
               structure 
               ⁢ 
               
                   
               
               ⁢ 
               Tp 
             
             = 
             
               
                 
                   ( 
                   
                     p 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       33 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
                 × 
                 
                   3 
                   / 
                   4 
                 
               
               + 
               
                 
                   ( 
                   
                     p 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       32 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
                 × 
                 
                   1 
                   / 
                   2 
                 
               
               + 
               
                 
                   ( 
                   
                     p 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       31 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
                 × 
                 
                   1 
                   / 
                   4 
                 
               
             
           
         
       
       
         
           
             
               Peak 
               ⁢ 
               
                   
               
               ⁢ 
               area 
               ⁢ 
               
                   
               
               ⁢ 
               ratio 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               siloxane 
               ⁢ 
               
                   
               
               ⁢ 
               bond 
               ⁢ 
               
                   
               
               ⁢ 
               attributed 
               ⁢ 
               
                   
               
               ⁢ 
               to 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               D 
               ⁢ 
               
                   
               
               ⁢ 
               unit 
               ⁢ 
               
                   
               
               ⁢ 
               structure 
               ⁢ 
               
                   
               
               ⁢ 
               Dp 
             
             = 
             
               
                 
                   ( 
                   
                     p 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       22 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
                 × 
                 
                   1 
                   / 
                   2 
                 
               
               + 
               
                 
                   ( 
                   
                     p 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       21 
                       / 
                       S 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
                 × 
                 
                   1 
                   / 
                   2 
                 
               
             
           
         
       
       
         
           
             
               Peak 
               ⁢ 
               
                   
               
               ⁢ 
               area 
               ⁢ 
               
                   
               
               ⁢ 
               ratio 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               siloxane 
               ⁢ 
               
                   
               
               ⁢ 
               bond 
               ⁢ 
               
                   
               
               ⁢ 
               attributed 
               ⁢ 
               
                   
               
               ⁢ 
               to 
               ⁢ 
               
                   
               
               ⁢ 
               the 
               ⁢ 
               
                   
               
               ⁢ 
               M 
               ⁢ 
               
                   
               
               ⁢ 
               unit 
               ⁢ 
               
                   
               
               ⁢ 
               structure 
               ⁢ 
               
                   
               
               ⁢ 
               Mp 
             
             = 
             
               p 
               ⁢ 
               
                   
               
               ⁢ 
               
                 11 
                 / 
                 S 
               
               ⁢ 
               
                   
               
               ⁢ 
               1 
               × 
               
                 1 
                 / 
                 4 
               
             
           
         
       
     
     From the above, the area ratio of the peak attributed to the siloxane bond=Qp+Tp+Dp+Mp is calculated. 
     &lt;Method for Measuring the Surface Treatment Agent for External Additive for Toner&gt; 
     The surface treatment agent for the external additive for toner is analyzed by pyrolysis-GC-MS (gas chromatography−mass spectrometry). Specifically, the measurement conditions are as follows. 
     Equipment: GC6890A (manufactured by Agilent Technologies, Inc.), pyrolyzer (manufactured by Japan Analytical Industry Co., Ltd.) 
     Column: HP-5 ms 30 m 
     Pyrolysis temperature: 590° C. 
     By specifying each peak position of the profile obtained by the measurement using a standard sample, the surface treatment agent for the external additive for toner is specified. 
     EXAMPLES 
     The present invention will be described in more concrete terms with reference to the examples illustrated below. However, these examples are not meant to limit the present invention in any way. Unless otherwise stated, the language “parts” in the formulations below refers to parts by mass in all instances. 
     &lt;Production Example of External Additive Particles 1 for Toner&gt; 
     1. Hydrolysis Step 
     A total of 43.2 g of RO water and 0.008 g of acetic acid as a catalyst were put in a 200 ml beaker and stirred at 45° C. To this, 27.2 g of tetraethoxysilane and 27.2 g of dimethyldimethoxysilane were added, followed by stirring for 1.5 h to obtain a raw material solution. 
     2. Polycondensation Step 
     A total of 68.8 g of RO water, 340.0 g of methanol, and 2.0 g of 25% ammonia water were put into a 1000 ml beaker and stirred at 30° C. to prepare an alkaline aqueous medium. The raw material solution obtained in “1. Hydrolysis step” was added dropwise over 1 min to this alkaline aqueous medium. The mixed solution after the dropwise addition of the raw material solution was stirred as it was at 30° C. for 1.5 h to advance the polycondensation reaction and obtain a polycondensation reaction solution. 
     3. Particle Formation Step 
     A total of 1000 g of RO water was put in a 2000 ml beaker followed by stirring at 25° C. The polycondensation reaction solution obtained in “2. Polycondensation step” was added dropwise over 10 min. As soon as the polycondensation reaction liquid was mixed with water, it became cloudy, and a dispersion liquid including silicon polymer particles having a siloxane bond was obtained. 
     4. Hydrophobization Step 
     A total of 27.1 g of hexamethyldisilazane as a hydrophobizing agent was added to the dispersion liquid including silicon polymer particles having a siloxane bond that was obtained in “3. Particle formation step”, followed by stirring at 60° C. for 2.5 h. After the dispersion liquid was allowed to stand for 5 min, the powder precipitated in the lower part of the solution was collected by suction filtration and dried under reduced pressure at 120° C. for 24 h to obtain external additive particles 1 for toner. The number-average particle diameter of primary particles of the obtained external additive particles 1 for toner was 0.12 μm. Table 1 shows the physical characteristics of the external additive particles 1 for toner. 
     &lt;Production Example of External Additive Particles 2 for Toner&gt; 
     External additive particles 2 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the amount of hexamethyldisilazane used in the hydrophobization step was changed to 16.3 g. Table 1 shows the physical characteristics of the obtained external additive particles 2 for toner. 
     &lt;Production Example of External Additive Particles 3 for Toner&gt; 
     External additive particles 3 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the amount of hexamethyldisilazane used in the hydrophobization step was changed to 37.9 g. Table 1 shows the physical characteristics of the obtained external additive particles 3 for toner. 
     &lt;Production Example of External Additive Particles 4 for Toner&gt; 
     External additive particles 4 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the stirring temperature in the hydrolysis step was changed to 50° C., and the amount of 25% aqueous ammonia used in the polycondensation step was changed to 1.5 g. Table 1 shows the physical characteristics of the obtained external additive particles 4 for toner. 
     &lt;Production Example of External Additive Particles 5 for Toner&gt; 
     External additive particles 5 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the stirring temperature in the hydrolysis step was changed to 40° C., and the amount of 25% aqueous ammonia used in the polycondensation step was changed to 2.3 g. Table 1 shows the physical characteristics of the obtained external additive particles 5 for toner. 
     &lt;Production Example of External Additive Particles 6 for Toner&gt; 
     External additive particles 6 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the stirring temperature in the hydrolysis step was changed to 50° C., and in the polycondensation step, the amount of RO water was changed to 98.8 g, the amount of methanol was changed to 310.0 g, and the amount of 25% aqueous ammonia was changed to 1.5 g. Table 1 shows the physical characteristics of the obtained external additive particles 6 for toner. 
     &lt;Production Example of External Additive Particles 7 for Toner&gt; 
     External additive particles 7 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the stirring temperature in the hydrolysis step was changed to 40° C., and in the polycondensation step, the amount of RO water was changed to 58.8 g, the amount of methanol was changed to 350.0 g, and the amount of 25% aqueous ammonia was changed to 2.5 g. Table 1 shows the physical characteristics of the obtained external additive particles 7 for toner. 
     &lt;Production Example of External Additive Particles 8 for Toner&gt; 
     External additive particles 8 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the stirring time of the mixed solution after dropwise addition of the raw material solution in the polycondensation step was changed to 1.0 h. Table 1 shows the physical characteristics of the obtained external additive particles 8 for toner. 
     &lt;Production Example of External Additive Particles 9 for Toner&gt; 
     External additive particles 9 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the stirring time of the mixed solution after dropwise addition of the raw material solution in the polycondensation step was changed to 2.0 h. Table 1 shows the physical characteristics of the obtained external additive particles 9 for toner. 
     &lt;Production Example of External Additive Particles 10 for Toner&gt; 
     External additive particles 10 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the stirring time in the hydrolysis step was changed to 1.0 h, and the stirring time of the mixed solution after dropwise addition of the raw material solution in the polycondensation step was changed to 1.0 h. Table 1 shows the physical characteristics of the obtained external additive particles 10 for toner. 
     &lt;Production Example of External Additive Particles 11 for Toner&gt; 
     External additive particles 11 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the stirring time in the hydrolysis step was changed to 2.0 h, and the stirring time of the mixed solution after dropwise addition of the raw material solution in the polycondensation step was changed to 2.0 h. Table 1 shows the physical characteristics of the obtained external additive particles 11 for toner. 
     &lt;Production Example of External Additive Particles 12 for Toner&gt; 
     External additive particles 12 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the hydrophobizing agent used in the hydrophobization step was changed to octamethylcyclotetrasiloxane. Table 1 shows the physical characteristics of the obtained external additive particles 12 for toner. 
     &lt;Production Example of External Additive Particles 13 for Toner&gt; 
     External additive particles 13 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the hydrophobizing agent used in the hydrophobization step was changed to chlorotrimethylsilane. Table 1 shows the physical characteristics of the obtained external additive particles 13 for toner. 
     &lt;Production Example of External Additive Particles 14 for Toner&gt; 
     External additive particles 14 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the hydrophobizing agent used in the hydrophobization step was changed to trifluoropropyltrimethoxysilane. Table 1 shows the physical characteristics of the obtained external additive particles 14 for toner. 
     &lt;Production Example of External Additive Particles 15 for Toner&gt; 
     External additive particles 15 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the hydrophobizing agent used in the hydrophobization step was changed to dimethyl silicone oil. Table 1 shows the physical characteristics of the obtained external additive particles 15 for toner. 
     &lt;Production Example of External Additive Particles 16 for Toner&gt; 
     External additive particles 16 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that no hydrophobizing agent was added in the hydrophobization step. Table 1 shows the physical characteristics of the obtained external additive particles 16 for toner. 
     &lt;Production Example of External Additive Particles 17 for Toner&gt; 
     External additive particles 17 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that in the hydrolysis step, the amount of tetraethoxysilane was changed to 30.1 g and the amount of dimethyldimethoxysilane was changed to 24.3 g. Table 1 shows the physical characteristics of the obtained external additive particles 17 for toner. 
     &lt;Production Example of External Additive Particles 18 for Toner&gt; 
     External additive particles 18 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that in the hydrolysis step, the amount of tetraethoxysilane was changed to 23.5 g and the amount of dimethyldimethoxysilane was changed to 30.9 g. Table 1 shows the physical characteristics of the obtained external additive particles 18 for toner. 
     &lt;Production Example of External Additive Particles 19 for Toner&gt; 
     External additive particles 19 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that in the hydrolysis step, the amount of tetraethoxysilane was changed to 33.8 g and the amount of dimethyldimethoxysilane was changed to 20.6 g. Table 1 shows the physical characteristics of the obtained external additive particles 19 for toner. 
     &lt;Production Example of External Additive Particles 20 for Toner&gt; 
     External additive particles 20 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the stirring time in the hydrolysis step was changed to 2.0 h, and the stirring time of the mixed solution after dropwise addition of the raw material solution in the polycondensation step was changed to 2.5 h. Table 1 shows the physical characteristics of the obtained external additive particles 20 for toner. 
     &lt;Production Example of External Additive Particles 21 for Toner&gt; 
     External additive particles 21 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that the stirring temperature and stirring time in the hydrolysis step were changed to 35° C. and 1.0 h, respectively, and the stirring time of the mixed solution after dropwise addition of the raw material solution in the polycondensation step was changed to 1.0 h. Table 1 shows the physical characteristics of the obtained external additive particles 21 for toner. 
     &lt;Production Example of External Additive Particles 22 for Toner&gt; 
     External additive particles 22 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that in the hydrolysis step, the amount of tetraethoxysilane was changed to 16.9 g, the amount of dimethyldimethoxysilane was changed to 18.6 g, 18.9 g of trimethoxymethylsilane was further added, the stirring temperature was changed to 30° C., and the stirring time was changed to 0.5 h. Table 1 shows the physical characteristics of the obtained external additive particles 22 for toner. 
     &lt;Production Example of External Additive Particles 23 for Toner&gt; 
     External additive particles 23 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that in the hydrolysis step, the amount of tetraethoxysilane was changed to 22.1 g, the amount of dimethyldimethoxysilane was changed to 21.6 g, and 10.7 g of trimethylsilanol was further added. Table 1 shows the physical characteristics of the obtained external additive particles 23 for toner. 
     &lt;Production Example of External Additive Particles 24 for Toner&gt; 
     External additive particles 24 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that in the hydrolysis step, tetraethoxysilane was not added, 45.2 g of trimethoxymethylsilane and 9.2 g of dimethyldimethoxysilane were added there instead, the stirring temperature was changed to 30° C., and the stirring time was changed to 0.5 h. Table 1 shows the physical characteristics of the obtained external additive particles 24 for toner. 
     &lt;Production Example of External Additive Particles 25 for Toner&gt; 
     External additive particles 25 for toner were obtained in the same manner as in the production example of external additive particles 18 for toner, except that in the production example of external additive particles 18 for toner, in the hydrolysis step, the stirring temperature was set to 50° C. and the stirring time was set to 1.0 h, and in the polycondensation step, the stirring time of the mixed liquid after the dropwise addition of the raw material solution was changed to 1.0 h. Table 1 shows the physical characteristics of the obtained external additive particles 25 for toner. 
     &lt;Production Example of External Additive Particles 26 for Toner&gt; 
     External additive particles 26 for toner were obtained in the same manner as in the production example of external additive particles 18 for toner, except that in the production example of external additive particles 18 for toner, in the hydrolysis step, the amount of tetraethoxysilane was changed to 22.1 g, the amount of dimethyldimethoxysilane was changed to 32.3 g, the stirring temperature was set to 50° C., and the stirring time was set to 1.0 h, and in the polycondensation step, the stirring time of the mixed liquid after the dropwise addition of the raw material solution was changed to 1.0 h. Table 1 shows the physical characteristics of the obtained external additive particles 26 for toner. 
     &lt;Production Example of External Additive Particles 27 for Toner&gt; 
     External additive particles 27 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that in the hydrolysis step, tetraethoxysilane and dimethyldimethoxysilane were not added, 54.4 g of trimethoxymethylsilane was added there instead, the stirring temperature was changed to 30° C., and the stirring time was changed to 0.5 h. Table 1 shows the physical characteristics of the obtained external additive particles 27 for toner. 
     &lt;Production Example of External Additive Particles 28 for Toner&gt; 
     External additive particles 28 for toner were obtained in the same manner as in the production example of external additive particles 27 for toner, except that in the production example of external additive particles 27 for toner, the amount of trimethoxymethylsilane was changed to 50.6 g and 3.8 g of tetraethoxysilane was added. Table 1 shows the physical characteristics of the obtained external additive particles 28 for toner. 
     &lt;Production Example of External Additive Particles 29 for Toner&gt; 
     External additive particles 29 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that in the hydrolysis step, the amount of tetraethoxysilane was changed to 30.1 g, the amount of dimethyldimethoxysilane was changed to 8.2 g, 16.1 g of trimethoxymethylsilane was further added, the stirring temperature was changed to 30° C., and the stirring time was changed to 0.5 h. Table 1 shows the physical characteristics of the obtained external additive particles 29 for toner. 
     &lt;Production Example of External Additive Particles 30 for Toner&gt; 
     External additive particles 30 for toner were obtained in the same manner as in the production example of external additive particles 1 for toner, except that in the hydrolysis step, the amount of tetraethoxysilane was changed to 15.4 g, the amount of dimethyldimethoxysilane was changed to 8.2 g, 30.8 g of trimethoxymethylsilane was further added, the stirring temperature was changed to 30° C., and the stirring time was changed to 0.5 h. Table 1 shows the physical characteristics of the obtained external additive particles 30 for toner. 
     &lt;Production Example of External Additive Particles 31 for Toner&gt; 
     A total of 124.0 g of ethanol, 24.0 g of RO water, and 10.0 g of 28% ammonia water were added in a 2000 ml beaker, the solution was adjusted to 70° C., and 232.0 g of tetraethoxysilane and 84.0 g of 5.4% aqueous ammonia were together dropwise added over 0.5 h while stirring. After the dropwise addition was completed, the mixture was further stirred for 0.5 h and hydrolyzed to obtain a dispersion liquid of silicon polymer particles having a siloxane bond. 
     After adding 95.0 g of hexamethyldisilazane to the dispersion liquid of silicon polymer particles having a siloxane bond, which was obtained in the above step, at room temperature, the dispersion was heated to from 50° C. to 60° C. and stirred for 3.0 h. Then, the powder in the dispersion liquid was collected by suction filtration and dried under reduced pressure at 120° C. for 24 h to obtain external additive particles 31 for toner. Table 1 shows the physical characteristics of the obtained external additive particles 31 for toner. 
     &lt;Production Example of External Additive Particles 32 for Toner&gt; 
     External additive particles 32 for toner were obtained in the same manner as in the production example of external additive particles 31 for toner, except that the amount of tetraethoxysilane was changed to 208.8 g and 23.2 g of trimethoxymethylsilane was added. Table 1 shows the physical characteristics of the obtained external additive particles 32 for toner. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 External 
                 Monomer 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 additive 
                 configuration mol % 
                   29 Si-NMR 
                   
                   
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 No. for 
                 Q 
                 T 
                 D 
                 M 
                   
                 (C/A)/ 
                 Si—O—Si  
                   
                   
                   
                 Hydrophobizing agent 
                 DH  
                 PD 
                   
               
               
                 toner 
                 Unit 
                 Unit 
                 Unit 
                 Unit 
                 B/A 
                 (B/A) 
                 % 
                 S4/SA 
                 S3/SA 
                 S2/SA 
                 for surface treatment 
                 % 
                 μm 
                 AC 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 53 
                 0.12 
                 0.89 
               
               
                 2 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 47 
                 0.12 
                 0.89 
               
               
                 3 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 55 
                 0.12 
                 0.89 
               
               
                 4 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 53 
                 0.05 
                 0.89 
               
               
                 5 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 53 
                 0.20 
                 0.89 
               
               
                 6 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 53 
                 0.01 
                 0.89 
               
               
                 7 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 53 
                 0.35 
                 0.89 
               
               
                 8 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 53 
                 0.12 
                 0.86 
               
               
                 9 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 53 
                 0.12 
                 0.94 
               
               
                 10 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 53 
                 0.12 
                 0.84 
               
               
                 11 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 53 
                 0.12 
                 0.96 
               
               
                 12 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Octamethyl 
                 47 
                 0.12 
                 0.89 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 cyclotetrasiloxane 
                   
                   
                   
               
               
                 13 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Chlorotrimethylsilane 
                 43 
                 0.12 
                 0.89 
               
               
                 14 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Trifluoropropyl 
                 45 
                 0.12 
                 0.89 
               
               
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                 trimethoxysilane 
                   
                   
                   
               
               
                 15 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 Dimethyl silicone oil  
                 35 
                 0.12 
                 0.89 
               
               
                 16 
                 37 
                 — 
                 63 
                 — 
                 0.317 
                 0.079 
                 65.8 
                 0.37 
                 0.00 
                 0.63 
                 None 
                 45 
                 0.12 
                 0.89 
               
               
                 17 
                 41 
                 — 
                 59 
                 — 
                 0.295 
                 0.090 
                 67.9 
                 0.41 
                 0.00 
                 0.59 
                 Hexamethyldisilazane 
                 53 
                 0.12 
                 0.89 
               
               
                 18 
                 32 
                 — 
                 68 
                 — 
                 0.340 
                 0.068 
                 63.7 
                 0.32 
                 0.00 
                 0.68 
                 Hexamethyldisilazane 
                 53 
                 0.12 
                 0.89 
               
               
                 19 
                 46 
                 — 
                 54 
                 — 
                 0.270 
                 0.105 
                 70.2 
                 0.46 
                 0.00 
                 0.54 
                 Hexamethyldisilazane 
                 53 
                 0.12 
                 0.89 
               
               
                 20 
                 37 
                 — 
                 63 
                 — 
                 0.305 
                 0.197 
                 63.5 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 53 
                 0.12 
                 0.96 
               
               
                 21 
                 37 
                 — 
                 63 
                 — 
                 0.305 
                 0.336 
                 59.3 
                 0.37 
                 0.00 
                 0.63 
                 Hexamethyldisilazane 
                 53 
                 0.12 
                 0.89 
               
               
                 22 
                 23 
                 34 
                 43 
                 — 
                 0.300 
                 0.193 
                 64.2 
                 0.23 
                 0.34 
                 0.43 
                 Hexamethyldisilazane 
                 43 
                 0.12 
                 0.89 
               
               
                 23 
                 30 
                 — 
                 50 
                 20 
                 0.400 
                 0.259 
                 49.7 
                 0.30 
                 0.00 
                 0.50 
                 Hexamethyldisilazane 
                 48 
                 0.12 
                 0.89 
               
               
                 24 
                 — 
                 83 
                 17 
                 — 
                 0.293 
                 0.159 
                 66.1 
                 0.00 
                 0.83 
                 0.17 
                 Hexamethyldisilazane 
                 40 
                 0.13 
                 0.89 
               
               
                 25 
                 32 
                 — 
                 68 
                 — 
                 0.350 
                 0.055 
                 62.7 
                 0.32 
                 0.00 
                 0.68 
                 Hexamethyldisilazane 
                 54 
                 0.12 
                 0.89 
               
               
                 26 
                 30 
                 — 
                 70 
                 — 
                 0.358 
                 0.048 
                 61.9 
                 0.30 
                 0.00 
                 0.70 
                 Hexamethyldisilazane 
                 56 
                 0.12 
                 0.89 
               
               
                 27 
                 — 
                 100 
                 — 
                 — 
                 0.250 
                 0.200 
                 71.2 
                 0.00 
                 1.00 
                 0.00 
                 Hexamethyldisilazane 
                 35 
                 0.11 
                 0.91 
               
               
                 28 
                 7 
                 93 
                 — 
                 — 
                 0.233 
                 0.230 
                 71.4 
                 0.07 
                 0.93 
                 0.00 
                 Hexamethyldisilazane 
                 34 
                 0.12 
                 0.89 
               
               
                 29 
                 41 
                 40 
                 19 
                 — 
                 0.195 
                 0.312 
                 74.4 
                 0.41 
                 0.40 
                 0.19 
                 Hexamethyldisilazane 
                 43 
                 0.12 
                 0.89 
               
               
                 30 
                 21 
                 60 
                 19 
                 — 
                 0.245 
                 0.216 
                 70.2 
                 0.21 
                 0.60 
                 0.19 
                 Hexamethyldisilazane 
                 43 
                 0.12 
                 0.89 
               
               
                 31 
                 100 
                 — 
                 — 
                 — 
                 0.000 
                 — 
                 99.0 
                 1.00 
                 0.00 
                 0.00 
                 Hexamethyldisilazane 
                 45 
                 0.11 
                 0.93 
               
               
                 32 
                 90 
                 10 
                 — 
                 — 
                 0.025 
                 1.500 
                 93.8 
                 0.90 
                 0.10 
                 0.00 
                 Hexamethyldisilazane 
                 44 
                 0.11 
                 0.92 
               
               
                   
               
            
           
         
       
     
     In the table, Si—O—Si % is the ratio of the peak area attributed to the siloxane bond to the total peak area attributed to the silicon polymer. “DH” is degree of hydrophobization. “PD” is the number-average particle diameter of primary particles, and “AC” is the average circularity. 
     &lt;Production Example of Polyester Resin A1&gt; 
     
       
         
           
               
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Polyoxypropylene(2.2)-2,2-bis(4- 
                 76.9 parts 
                 (0.167 mol parts) 
               
               
                   
                 hydroxyphenyl)propane 
               
               
                   
                 Terephthalic acid (TPA) 
                 25.0 parts 
                 (0.145 mol parts) 
               
               
                   
                 Adipic acid 
                 8.0 parts 
                 (0.054 mol parts) 
               
            
           
           
               
               
               
            
               
                   
                 Titanium tetrabutoxide 
                 0.5 parts 
               
               
                   
                   
               
            
           
         
       
     
     The above materials were placed in a 4-liter glass four-necked flask, a thermometer, a stirring rod, a condenser and a nitrogen introduction tube were attached to the flask, and the flask with the attachments was placed in a mantle heater. Next, the inside of the flask was replaced with nitrogen gas, the temperature was gradually raised while stirring, and the reaction was carried out for 4 h while stirring at a temperature of 200° C. (first reaction step). After that, 1.2 parts (0.006 mol parts) of trimellitic anhydride (TMA) was added and reacted at 180° C. for 1 h (second reaction step) to obtain a polyester resin A1. The acid value of the polyester resin A1 was 5 mg KOH/g. 
     &lt;Production Example of Polyester Resin A2&gt; 
     
       
         
           
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Polyoxypropylene(2.2)-2,2-bis(4- 
                 71.3 parts (0.155 mol parts) 
               
               
                   
                 hydroxyphenyl) propane 
               
               
                   
                 Terephthalic acid 
                 24.1 parts (0.145 mol parts) 
               
               
                   
                 Titanium tetrabutoxide 
                 0.6 parts 
               
               
                   
                   
               
            
           
         
       
     
     The above materials were placed in a 4-liter glass four-necked flask, a thermometer, a stirring rod, a condenser and a nitrogen introduction tube were attached to the flask, and the flask with the attachments was placed in a mantle heater. Next, the inside of the flask was replaced with nitrogen gas, the temperature was gradually raised while stirring, and the reaction was carried out for 2 h while stirring at a temperature of 200° C. After that, 5.8 parts (0.030 mol parts) of trimellitic anhydride was added and reacted at 180° C. for 10 h to obtain a polyester resin A2. The acid value of the polyester resin A2 was 10 mg KOH/g. 
     &lt;Production Example of Polyester Resin A3&gt; 
     
       
         
           
               
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Polyoxypropylene(2.2)-2,2-bis(4- 
                 73.4 parts 
                 (0.186 mol parts) 
               
               
                   
                 hydroxyphenyl)propane 
               
               
                   
                 Terephthalic acid (TPA) 
                 11.6 parts 
                 (0.070 mol parts) 
               
               
                   
                 Adipic acid 
                 6.8 parts 
                 (0.047 mol parts) 
               
            
           
           
               
               
               
            
               
                   
                 Tin(II) 2-ethylhexanoate 
                 0.5 parts 
               
               
                   
                   
               
            
           
         
       
     
     The above materials were placed in a 4-liter glass four-necked flask, a thermometer, a stirring rod, a condenser and a nitrogen introduction tube were attached to the flask, and the flask with the attachments was placed in a mantle heater. Next, the inside of the flask was replaced with nitrogen gas, the temperature was gradually raised while stirring, and the reaction was carried out for 2 h while stirring at a temperature of 200° C. After that, 8.2 parts (0.039 mol parts) of trimellitic anhydride (TMA) was added and reacted at 160° C. for 15 h to obtain a polyester resin A3. The acid value of the polyester resin A3 was 20 mg KOH/g. 
     &lt;Production Example of Polyester Resin A4&gt; 
     
       
         
           
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Polyoxypropylene(2.2)-2,2-bis(4- 
                 76.9 parts (0.167 mol parts) 
               
               
                   
                 hydroxyphenyl)propane 
               
               
                   
                 Terephthalic acid (TPA) 
                 24.1 parts (0.140 mol parts) 
               
               
                   
                 Titanium tetrabutoxide 
                 0.5 parts 
               
               
                   
                   
               
            
           
         
       
     
     The above materials were placed in a 4-liter glass four-necked flask, a thermometer, a stirring rod, a condenser and a nitrogen introduction tube were attached to the flask, and the flask with the attachments was placed in a mantle heater. Next, the inside of the flask was replaced with nitrogen gas, the temperature was gradually raised while stirring, and the reaction was carried out for 4 h while stirring at a temperature of 200° C. After that, 5.3 parts (0.024 mol parts) of trimellitic anhydride (TMA) was added and reacted at 180° C. for 1 h to obtain a polyester resin A4. The acid value of the polyester resin A4 was 25 mg KOH/g. 
     Production Example of Toner Particle 1 
     
       
         
           
               
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Polyester Resin A1 
                 70.0 
                 parts 
               
               
                   
                 Polyester Resin A2 
                 30.0 
                 parts 
               
               
                   
                 Fischer-Tropsch wax (peak temperature of 78° C. of 
                 5.0 
                 parts 
               
               
                   
                 maximum endothermic peak) 
               
               
                   
                 C. I. Pigment blue 15:3 
                 5.0 
                 parts 
               
               
                   
                 Aluminum 3,5-di-t-butyl salicylate compound 
                 0.1 
                 part 
               
               
                   
                   
               
            
           
         
       
     
     The starting materials in the above formulation were mixed using a Henschel mixer (FM-75 model, by Nippon Coke &amp; Engineering Co., Ltd.) at a rotational speed of 20 s −1  and for a rotation time of 5 min, followed by kneading using a twin-screw kneader (PCM-30 model, by Ikegai Corp.) set to a temperature of 125° C. and a rotational speed of 300 rpm. The obtained kneaded product was cooled and coarsely pulverized with a hammer mill to a diameter of 1 mm or less, to obtain a coarsely pulverized product. The obtained coarsely pulverized product was finely pulverized using a mechanical crusher (T-250, by Freund Turbo Corporation). 
     Further, a rotary classifier (200 TSP, by Hosokawa Micron Corporation) was used for classification, to obtain Toner particle 1. The operating conditions of the rotary classifier (200 TSP, by Hosokawa Micron Corporation) involved herein classification performed at a rotational speed of 50.0 s −1  of the classification rotor. The obtained Toner particle 1 had a weight-average particle diameter (D4) of 5.9 μm. 
     &lt;Production Example of Toner Particles 2&gt; 
     Toner particles 2 were obtained in the same manner as in the production example of toner particles 1, except that in the production example of toner particles 1, the polyester resin A1 was changed to the polyester resin A3. The obtained toner particles 2 had a weight-average particle diameter (D4) of 5.9 
     &lt;Production Example of Toner Particles 3&gt; 
     Toner particles 3 were obtained in the same manner as in the production example of toner particles 1, except that in the production example of toner particles 1, the polyester resin A1 was changed to the polyester resin A4. The obtained toner particles 3 had a weight-average particle diameter (D4) of 5.9 μm. 
     &lt;Production Example of Toner 1&gt; 
     
       
         
           
               
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Toner particles 1 
                 100 
                 parts 
               
               
                   
                 External additive particles 1 for toner 
                 6.0 
                 parts 
               
               
                   
                   
               
            
           
         
       
     
     The above materials were mixed with a Henschel mixer FM-10C type (manufactured by Mitsui Miike Machinery Co., Ltd.) at a rotation speed of 30 s −1  for a rotation time of 10 min to obtain toner 1. 
     &lt;Production Examples of Toners 2 to 34&gt; 
     Toners 2 to 34 were obtained in the same manner as in the production example of toner 1, except that the toner particles and the external additive for toner were changed to those shown in Table 2. 
     
       
         
           
               
               
             
               
                   
                 TABLE 2 
               
             
            
               
                   
                   
               
               
                   
                 External additive 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 External additive No. for 
                 Amount 
               
               
                 Toner No. 
                 Toner particle No. 
                 toner 
                 added 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 Toner 1 
                 Toner particle 1 
                 External additive particle 1 
                 6.0 
               
               
                 Toner 2 
                 Toner particle 1 
                 External additive particle 2 
                 6.0 
               
               
                 Toner 3 
                 Toner particle 1 
                 External additive particle 3 
                 6.0 
               
               
                 Toner 4 
                 Toner particle 1 
                 External additive particle 4 
                 6.0 
               
               
                 Toner 5 
                 Toner particle 1 
                 External additive particle 5 
                 6.0 
               
               
                 Toner 6 
                 Toner particle 1 
                 External additive particle 6 
                 6.0 
               
               
                 Toner 7 
                 Toner particle 1 
                 External additive particle 7 
                 6.0 
               
               
                 Toner 8 
                 Toner particle 1 
                 External additive particle 8 
                 6.0 
               
               
                 Toner 9 
                 Toner particle 1 
                 External additive particle 9 
                 6.0 
               
               
                 Toner 10 
                 Toner particle 1 
                 External additive particle 10 
                 6.0 
               
               
                 Toner 11 
                 Toner particle 1 
                 External additive particle 11 
                 6.0 
               
               
                 Toner 12 
                 Toner particle 1 
                 External additive particle 12 
                 6.0 
               
               
                 Toner 13 
                 Toner particle 1 
                 External additive particle 13 
                 6.0 
               
               
                 Toner 14 
                 Toner particle 1 
                 External additive particle 14 
                 6.0 
               
               
                 Toner 15 
                 Toner particle 1 
                 External additive particle 15 
                 6.0 
               
               
                 Toner 16 
                 Toner particle 1 
                 External additive particle 16 
                 6.0 
               
               
                 Toner 17 
                 Toner particle 1 
                 External additive particle 17 
                 6.0 
               
               
                 Toner 18 
                 Toner particle 1 
                 External additive particle 18 
                 6.0 
               
               
                 Toner 19 
                 Toner particle 1 
                 External additive particle 19 
                 6.0 
               
               
                 Toner 20 
                 Toner particle 1 
                 External additive particle 20 
                 6.0 
               
               
                 Toner 21 
                 Toner particle 1 
                 External additive particle 21 
                 6.0 
               
               
                 Toner 22 
                 Toner particle 1 
                 External additive particle 22 
                 6.0 
               
               
                 Toner 23 
                 Toner particle 1 
                 External additive particle 23 
                 6.0 
               
               
                 Toner 24 
                 Toner particle 2 
                 External additive particle 16 
                 6.0 
               
               
                 Toner 25 
                 Toner particle 3 
                 External additive particle 16 
                 6.0 
               
               
                 Toner 26 
                 Toner particle 1 
                 External additive particle 25 
                 6.0 
               
               
                 Toner 27 
                 Toner particle 1 
                 External additive particle 26 
                 6.0 
               
               
                 Toner 28 
                 Toner particle 1 
                 External additive particle 27 
                 6.0 
               
               
                 Toner 29 
                 Toner particle 1 
                 External additive particle 28 
                 6.0 
               
               
                 Toner 30 
                 Toner particle 1 
                 External additive particle 29 
                 6.0 
               
               
                 Toner 31 
                 Toner particle 1 
                 External additive particle 30 
                 6.0 
               
               
                 Toner 32 
                 Toner particle 1 
                 External additive particle 31 
                 6.0 
               
               
                 Toner 33 
                 Toner particle 1 
                 External additive particle 32 
                 6.0 
               
               
                 Toner 34 
                 Toner particle 1 
                 External additive particle 24 
                 6.0 
               
               
                   
               
            
           
         
       
     
     In the table, the amount added is the number of parts per 100 parts of toner particles. 
     Production Example of Carrier 1
         Magnetite 1 (intensity of magnetization of 65 Am 2 /kg in a 1000/4π (kA/m) magnetic field), having a number-average particle diameter of 0.30 μm.   Magnetite 2 (intensity of magnetization of 65 Am 2 /kg in a 1000/4π (kA/m) magnetic field), having a number-average particle diameter of 0.50 μm.       

     Herein 4.0 parts of a silane compound (3-(2-aminoethylaminopropyl) trimethoxysilane) were added to 100 parts of each of the above materials, with high-speed mixing and stirring at 100° C. or above, inside the vessel, to treat the respective fine particles.
         Phenol: 10 mass %   Formaldehyde solution: 6 mass % (formaldehyde 40 mass %, methanol 10 mass %, water 50 mass %)   Magnetite 1 treated with the above silane compound: 58 mass %   Magnetite 2 treated with the above silane compound: 26 mass %       

     Then 100 parts of the above materials, 5 parts of a 28 mass % aqueous ammonia solution, and 20 parts of water were charged into a flask, the temperature was raised to 85° C. over 30 minutes while under mixing by stirring, and a polymerization reaction was conducted by holding that temperature for 3 hours, to cure the generated phenolic resin. The cured phenolic resin was then cooled down to 30° C., followed by further addition of water, after which the supernatant was removed, and the precipitate was washed with water and was subsequently air-dried. Next, the resulting product was dried under reduced pressure (5 mmHg or lower) at a temperature of 60° C., to yield a spherical Carrier 1 of magnetic body-dispersed type. The volume-basis 50% particle diameter (D50) of Carrier 1 was 34.2 μm. 
     Production Example of Two-Component Developer 1 
     Herein 8.0 parts of Toner 1 were added to 92.0 parts of Carrier 1, with mixing using a V-type mixer (V-20, by Seishin Enterprise Co., Ltd.), to obtain Two-component developer 1. 
     Production Example of Two-Component Developers 2 to 34 
     Two-component developers 2 to 34 were produced in the same way as in the production example of Two-component developer 1, but herein the toner was modified as given in Table 3. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 Two-component developer No. 
                 Toner No. 
                 Carrier No. 
               
               
                   
                   
               
             
            
               
                   
                 Two-component developer 1 
                 Toner 1 
                 Carrier 1 
               
               
                   
                 Two-component developer 2 
                 Toner 2 
                 Carrier 1 
               
               
                   
                 Two-component developer 3 
                 Toner 3 
                 Carrier 1 
               
               
                   
                 Two-component developer 4 
                 Toner 4 
                 Carrier 1 
               
               
                   
                 Two-component developer 5 
                 Toner 5 
                 Carrier 1 
               
               
                   
                 Two-component developer 6 
                 Toner 6 
                 Carrier 1 
               
               
                   
                 Two-component developer 7 
                 Toner 7 
                 Carrier 1 
               
               
                   
                 Two-component developer 8 
                 Toner 8 
                 Carrier 1 
               
               
                   
                 Two-component developer 9 
                 Toner 9 
                 Carrier 1 
               
               
                   
                 Two-component developer 10 
                 Toner 10 
                 Carrier 1 
               
               
                   
                 Two-component developer 11 
                 Toner 11 
                 Carrier 1 
               
               
                   
                 Two-component developer 12 
                 Toner 12 
                 Carrier 1 
               
               
                   
                 Two-component developer 13 
                 Toner 13 
                 Carrier 1 
               
               
                   
                 Two-component developer 14 
                 Toner 14 
                 Carrier 1 
               
               
                   
                 Two-component developer 15 
                 Toner 15 
                 Carrier 1 
               
               
                   
                 Two-component developer 16 
                 Toner 16 
                 Carrier 1 
               
               
                   
                 Two-component developer 17 
                 Toner 17 
                 Carrier 1 
               
               
                   
                 Two-component developer 18 
                 Toner 18 
                 Carrier 1 
               
               
                   
                 Two-component developer 19 
                 Toner 19 
                 Carrier 1 
               
               
                   
                 Two-component developer 20 
                 Toner 20 
                 Carrier 1 
               
               
                   
                 Two-component developer 21 
                 Toner 21 
                 Carrier 1 
               
               
                   
                 Two-component developer 22 
                 Toner 22 
                 Carrier 1 
               
               
                   
                 Two-component developer 23 
                 Toner 23 
                 Carrier 1 
               
               
                   
                 Two-component developer 24 
                 Toner 24 
                 Carrier 1 
               
               
                   
                 Two-component developer 25 
                 Toner 25 
                 Carrier 1 
               
               
                   
                 Two-component developer 26 
                 Toner 26 
                 Carrier 1 
               
               
                   
                 Two-component developer 27 
                 Toner 27 
                 Carrier 1 
               
               
                   
                 Two-component developer 28 
                 Toner 28 
                 Carrier 1 
               
               
                   
                 Two-component developer 29 
                 Toner 29 
                 Carrier 1 
               
               
                   
                 Two-component developer 30 
                 Toner 30 
                 Carrier 1 
               
               
                   
                 Two-component developer 31 
                 Toner 31 
                 Carrier 1 
               
               
                   
                 Two-component developer 32 
                 Toner 32 
                 Carrier 1 
               
               
                   
                 Two-component developer 33 
                 Toner 33 
                 Carrier 1 
               
               
                   
                 Two-component developer 34 
                 Toner 34 
                 Carrier 1 
               
               
                   
                   
               
            
           
         
       
     
     &lt;Toner Evaluation Method&gt; 
     (1) Measurement of Change in Image Density 
     A Canon full-color copier imagePress C800 was used as an image forming apparatus, the two-component developer was placed in a cyan developing device of the image forming apparatus, and the toner was placed in a cyan toner container to perform the below-described evaluation. The apparatus was modified by detaching a mechanism for discharging the excess magnetic carrier contained inside the developing device from the developing device. As the evaluation paper, plain paper GF-0081 (A4, basis weight 81.4 g/m 2 , sold by Canon Marketing Japan Inc.) was used. 
     The toner laid-on level on the paper in a FFh image (solid image) was adjusted to 0.45 mg/cm 2 . FFh is a value obtained by displaying 256 gradations in hexadecimal, 00 h is the first gradation gradations (white background portion) of 256, and FF is the 256th gradation (solid portion) of 256 gradations. First, an image output test of 1000 images was performed with an image ratio of 1%. During the continuous passing of 1000 sheets, the sheets were passed under the same development conditions and transfer conditions (without calibration) as those of the first sheet. 
     After that, an image output test of 1000 images was performed with an image ratio of 80%. During the continuous passing of 1000 sheets, the sheets were passed under the same development conditions and transfer conditions (without calibration) as those of the first sheet. The density of the 1000-th image in printing at an image ratio of 1% was taken as the initial density, and the density of the 1000-th image in printing at an image ratio of 80% was measured and evaluated. 
     The above test was performed in a normal temperature and normal humidity environment (N/N; temperature 25° C., relative humidity 55%), in a high-temperature and high-humidity environment (H/H; temperature 30° C., relative humidity 80%), and in a normal temperature and low-humidity environment (N/L; temperature 23° C., relative humidity 5%). An X-Rite color reflection densitometer (500 series: manufactured by X-Rite, Inc.) was used, the initial density and the density of the 1000-th image in printing at an image ratio of 80% were measured, and ranking was performed according to the following criteria by using the difference A therebetween. 
     (Evaluation Criteria: Image Density Difference A) 
     A: less than 0.02
 
B: 0.02 or more and less than 0.05
 
C: 0.05 or more and less than 0.10
 
D: 0.10 or more and less than 0.15
 
E: 0.15 or more
 
     (2) Method for Evaluating Fogging on Non-Image Area (White Background Area) after Durability 
     A modified Canon&#39;s full-color copier image RUNNER ADVANCE C5255 was used, and the two-component developer 1 was put into the developing device of the cyan station for evaluation. The toner laid-on level on the paper in the FFh image (solid image) was adjusted to 0.45 mg/cm 2 . The evaluation environments were N/N, H/H, and N/L environments, and the evaluation paper was plain paper for copying GFC-081 (A4, basis weight 81.4 g/m 2 , sold by Canon Marketing Japan Inc.). In each environment, a 1 cm×1 cm FFh image was output in the center of the A4 paper, and fogging on a white background was measured after outputting 50000 sheets. 
     The reflectance Dr (%) of the evaluation paper before imaging was measured by a reflectometer (“REFLECTOMETER MODEL TC-6DS” manufactured by Tokyo Denshoku Co., Ltd.). The reflectance Ds (%) of the OOH image area (white background area) was measured after the durability (50001-st sheet). From the obtained Dr and Ds, fogging (%) was calculated using the following formula. 
     
       
         
           
             
               Fogging 
               ⁢ 
               
                   
               
               ⁢ 
               
                 ( 
                 % 
                 ) 
               
             
             = 
             
               
                 Dr 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   % 
                   ) 
                 
               
               - 
               
                 Ds 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   % 
                   ) 
                 
               
             
           
         
       
     
     The evaluation results were ranked according to the following criteria. 
     (Evaluation criteria: fogging (%))
 
A: less than 1.0%
 
B: 1.0% or more and less than 1.5%
 
C: 1.5% or more and less than 2.0%
 
D: 2.0% or more and less than 2.5%
 
E: 2.5% or more
 
     (3) Method for Evaluating Charge Stability 
     The triboelectric charge quantity of the toner was calculated by sucking and collecting the toner on the electrostatic latent image bearing member by using a metal cylindrical tube and a cylindrical filter. Specifically, the triboelectric charge quantity of the toner on the electrostatic latent image bearing member was measured by a Faraday cage. The Faraday cage is a coaxial double cylinder, and the inner cylinder and outer cylinder are insulated. Where a charged body having a charge quantity of Q is placed in the inner cylinder, it is as if a metal cylinder having a charge quantity Q is present due to electrostatic induction. This induced charge quantity was measured with an electrometer (Keithley 6517A, manufactured by Keithley Co., Ltd.), and (Q/M) obtained by dividing the charge quantity Q (mC) by the toner mass M (kg) in the inner cylinder was taken as the triboelectric charge quantity of the toner. 
     
       
         
           
             
               Triboelectric 
               ⁢ 
               
                   
               
               ⁢ 
               charge 
               ⁢ 
               
                   
               
               ⁢ 
               quantity 
               ⁢ 
               
                   
               
               ⁢ 
               of 
               ⁢ 
               
                   
               
               ⁢ 
               toner 
               ⁢ 
               
                   
               
               ⁢ 
               
                 ( 
                 
                   mC 
                   / 
                   kg 
                 
                 ) 
               
             
             = 
             
               Q 
               / 
               M 
             
           
         
       
     
     Evaluation image: a 2 cm×5 cm FFh image is placed in the center of A4 paper 
     First, the evaluation image was formed on the electrostatic latent image bearing member, the rotation of the electrostatic latent image bearing member was stopped before the image was transferred to the intermediate transfer body, the toner on the electrostatic latent image bearing member was sucked and collected with a cylindrical tube and a cylindrical filter, and [Initial Q/M] was measured. Subsequently, the evaluation machine with the developing device arranged therein was stored for 2 weeks in the N/N, H/H and N/L environments, and then the same operation as before the storage was performed, and the charge quantity Q/M (mC/kg) per unit mass on the electrostatic latent image bearing member after the storage was measured. A change ratio Q/M after the storage ([Initial Q/M]−[Q/M after storage in each environment])×100/[Initial Q/M] was calculated from the initial Q/M per unit mass on the electrostatic latent image bearing member and the Q/M per unit mass on the electrostatic latent image bearing member after the storage and evaluated according to the following criteria. 
     (Evaluation criteria)
 
A: change ratio is less than 2%
 
B: change ratio is 2% or more and less than 5%
 
C: change ratio is 5% or more and less than 10%
 
D: change ratio is 10% or more and less than 15%
 
E: change ratio is 15% or more
 
     &lt;Evaluation Results of Examples 1 to 27&gt; 
     Table 4 shows the evaluation results of Examples 1 to 27. 
     &lt;Evaluation Results of Comparative Examples 1 to 7&gt; 
     Table 4 shows the evaluation results of Comparative Examples 1 to 7. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                   
                 Two- 
                   
                   
                   
                   
                   
                   
                 Fogging after durability 
                 Charge stability 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 component 
                 Image density change 
                 HH 
                 NN 
                 NL 
                 HH 
                 NN 
                 NL 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Example 
                 developer 
                 HH 
                 NN 
                 NL 
                 FV 
                   
                 FV 
                   
                 FV 
                   
                 CR 
                   
                 CR 
                   
                 CR 
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 No. 
                 No. 
                 Δ 
                 Rank 
                 Δ 
                 Rank 
                 Δ 
                 Rank 
                 % 
                 Rank 
                 % 
                 Rank 
                 % 
                 Rank 
                 % 
                 Rank 
                 % 
                 Rank 
                 % 
                 Rank 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 1 
                 1 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.2 
                 A 
                 0.2 
                 A 
                 0.3 
                 A 
                 0 
                 A 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 2 
                 2 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.1 
                 B 
                 0.2 
                 A 
                 0.4 
                 A 
                 1 
                 A 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 3 
                 3 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.3 
                 A 
                 0.2 
                 A 
                 0.4 
                 A 
                 1 
                 A 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 4 
                 4 
                 0.03 
                 B 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.5 
                 A 
                 0.2 
                 A 
                 0.4 
                 A 
                 1 
                 A 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 5 
                 5 
                 0.04 
                 B 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.6 
                 A 
                 0.2 
                 A 
                 0.4 
                 A 
                 1 
                 A 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 6 
                 6 
                 0.02 
                 B 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.3 
                 B 
                 0.2 
                 A 
                 0.4 
                 A 
                 3 
                 B 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 7 
                 7 
                 0.02 
                 B 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.1 
                 B 
                 0.2 
                 A 
                 0.4 
                 A 
                 2 
                 B 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 8 
                 8 
                 0.03 
                 B 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.1 
                 B 
                 0.2 
                 A 
                 1.0 
                 B 
                 3 
                 B 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 9 
                 9 
                 0.03 
                 B 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.3 
                 B 
                 0.2 
                 A 
                 1.1 
                 B 
                 4 
                 B 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 10 
                 10 
                 0.04 
                 B 
                 0.01 
                 A 
                 0.03 
                 B 
                 1.2 
                 B 
                 0.2 
                 A 
                 1.3 
                 B 
                 3 
                 B 
                 1.0 
                 A 
                 2 
                 B 
               
               
                 11 
                 11 
                 0.03 
                 B 
                 0.01 
                 A 
                 0.02 
                 B 
                 1.0 
                 B 
                 0.2 
                 A 
                 1.2 
                 B 
                 4 
                 B 
                 1.0 
                 A 
                 3 
                 B 
               
               
                 12 
                 12 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.3 
                 B 
                 0.2 
                 A 
                 0.4 
                 A 
                 1 
                 A 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 13 
                 13 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.2 
                 B 
                 0.2 
                 A 
                 0.7 
                 A 
                 1 
                 A 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 14 
                 14 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.3 
                 B 
                 0.2 
                 A 
                 0.3 
                 A 
                 1 
                 A 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 15 
                 15 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.3 
                 B 
                 0.2 
                 A 
                 0.7 
                 A 
                 1 
                 A 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 16 
                 16 
                 0.03 
                 B 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.4 
                 B 
                 0.2 
                 A 
                 0.8 
                 A 
                 3 
                 B 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 17 
                 17 
                 0.04 
                 B 
                 0.01 
                 A 
                 0.04 
                 B 
                 1.1 
                 B 
                 0.2 
                 A 
                 1.4 
                 B 
                 4 
                 B 
                 1.0 
                 A 
                 3 
                 B 
               
               
                 18 
                 18 
                 0.03 
                 B 
                 0.01 
                 A 
                 0.04 
                 B 
                 1.3 
                 B 
                 0.2 
                 A 
                 1.3 
                 B 
                 4 
                 B 
                 1.0 
                 A 
                 4 
                 B 
               
               
                 19 
                 19 
                 0.08 
                 C 
                 0.03 
                 B 
                 0.04 
                 B 
                 1.2 
                 B 
                 0.2 
                 A 
                 1.4 
                 B 
                 4 
                 B 
                 1.0 
                 A 
                 3 
                 B 
               
               
                 20 
                 20 
                 0.03 
                 B 
                 0.01 
                 A 
                 0.09 
                 C 
                 1.1 
                 B 
                 0.2 
                 A 
                 1.8 
                 C 
                 3 
                 B 
                 1.0 
                 A 
                 8 
                 C 
               
               
                 21 
                 21 
                 0.08 
                 C 
                 0.03 
                 B 
                 0.08 
                 C 
                 1.8 
                 C 
                 0.2 
                 A 
                 1.9 
                 C 
                 7 
                 C 
                 1.0 
                 A 
                 9 
                 C 
               
               
                 22 
                 22 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.03 
                 B 
                 0.4 
                 A 
                 0.2 
                 A 
                 1.2 
                 B 
                 1 
                 A 
                 1.0 
                 A 
                 4 
                 B 
               
               
                 23 
                 23 
                 0.01 
                 A 
                 0.01 
                 A 
                 0.04 
                 B 
                 1.3 
                 B 
                 0.2 
                 A 
                 1.2 
                 B 
                 4 
                 B 
                 1.0 
                 A 
                 3 
                 B 
               
               
                 24 
                 24 
                 0.03 
                 B 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.5 
                 C 
                 1.1 
                 B 
                 0.5 
                 A 
                 3 
                 B 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 25 
                 25 
                 0.03 
                 B 
                 0.01 
                 A 
                 0.01 
                 A 
                 1.6 
                 C 
                 1.1 
                 B 
                 0.3 
                 A 
                 7 
                 C 
                 1.0 
                 A 
                 1 
                 A 
               
               
                 26 
                 26 
                 0.03 
                 B 
                 0.03 
                 B 
                 0.08 
                 C 
                 1.3 
                 B 
                 0.2 
                 A 
                 1.6 
                 C 
                 3 
                 B 
                 1.0 
                 A 
                 5 
                 C 
               
               
                 27 
                 27 
                 0.04 
                 B 
                 0.03 
                 B 
                 0.12 
                 D 
                 1.4 
                 B 
                 0.2 
                 A 
                 2.1 
                 D 
                 6 
                 C 
                 3.0 
                 B 
                 10 
                 D 
               
               
                 C.E. 1 
                 28 
                 0.14 
                 D 
                 0.07 
                 C 
                 0.15 
                 E 
                 2.5 
                 E 
                 1.6 
                 C 
                 2.3 
                 D 
                 13 
                 D 
                 7.0 
                 C 
                 11 
                 D 
               
               
                 C.E. 2 
                 29 
                 0.15 
                 E 
                 .012 
                 D 
                 0.14 
                 D 
                 2.6 
                 E 
                 1.6 
                 C 
                 2.5 
                 E 
                 12 
                 D 
                 7.0 
                 C 
                 10 
                 D 
               
               
                 C.E. 3 
                 30 
                 0.13 
                 D 
                 0.08 
                 C 
                 0.15 
                 E 
                 2.5 
                 E 
                 1.6 
                 C 
                 2.2 
                 D 
                 13 
                 D 
                 7.0 
                 C 
                 16 
                 E 
               
               
                 C.E. 4 
                 31 
                 0.14 
                 D 
                 0.08 
                 C 
                 0.15 
                 E 
                 2.5 
                 E 
                 2.1 
                 D 
                 2.3 
                 D 
                 13 
                 D 
                 7.0 
                 C 
                 11 
                 D 
               
               
                 C.E. 5 
                 32 
                 0.16 
                 E 
                 0.08 
                 C 
                 0.14 
                 D 
                 2.5 
                 E 
                 2.1 
                 D 
                 2.5 
                 E 
                 16 
                 E 
                 7.0 
                 C 
                 13 
                 D 
               
               
                 C.E. 6 
                 33 
                 0.17 
                 E 
                 0.12 
                 D 
                 0.15 
                 E 
                 2.4 
                 D 
                 1.6 
                 C 
                 2.3 
                 D 
                 17 
                 E 
                 12.0 
                 D 
                 16 
                 E 
               
               
                 C.E. 7 
                 34 
                 0.11 
                 D 
                 0.08 
                 C 
                 0.09 
                 C 
                 1.4 
                 B 
                 0.2 
                 A 
                 1.8 
                 C 
                 3 
                 B 
                 1.0 
                 A 
                 8 
                 C 
               
               
                   
               
            
           
         
       
     
     In the Table, “C.E.” denotes “Comparative example”, “FV” denotes “Fogging value”, and “CR” denotes “Change ratio”. 
     &lt;Production Examples of Toners 35 to 39&gt; 
     Toners 35 to 39 were obtained by performing production in the same manner as in the production example of toner 1, except that the toner particles and the external additive for toner were changed to those shown in Table 5. 
     
       
         
           
               
               
             
               
                   
                 TABLE 5 
               
             
            
               
                   
                   
               
               
                   
                 External additive 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 External additive No. for 
                 Amount 
               
               
                 Toner No. 
                 Toner particle No. 
                 toner 
                 added 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 Toner 35 
                 Toner particle 1 
                 External additive particle 16 
                 3.0 
               
               
                 Toner 36 
                 Toner particle 1 
                 External additive particle 16 
                 0.2 
               
               
                 Toner 37 
                 Toner particle 1 
                 External additive particle 16 
                 18.0 
               
               
                 Toner 38 
                 Toner particle 1 
                 External additive particle 16 
                 0.1 
               
               
                 Toner 39 
                 Toner particle 1 
                 External additive particle 16 
                 21.0 
               
               
                   
               
            
           
         
       
     
     &lt;Production Example of Two-Component Developers 35 to 39&gt; 
     Two-component developers 35 to 39 were obtained by performing production in the same manner as in the production example of two-component developer 1, except that the toner was changed as shown in Table 6. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                 Two-component developer No. 
                 Toner No. 
                 Carrier No. 
               
               
                   
                   
               
             
            
               
                   
                 Two-component developer 35 
                 Toner 35 
                 Carrier 1 
               
               
                   
                 Two-component developer 36 
                 Toner 36 
                 Carrier 1 
               
               
                   
                 Two-component developer 37 
                 Toner 37 
                 Carrier 1 
               
               
                   
                 Two-component developer 38 
                 Toner 38 
                 Carrier 1 
               
               
                   
                 Two-component developer 39 
                 Toner 39 
                 Carrier 1 
               
               
                   
                   
               
            
           
         
       
     
     &lt;Evaluation Results of Examples 28 to 32&gt; 
     Table 7 shows the evaluation results of Examples 28 to 32. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                   
                 Two- 
                   
                   
                   
                   
                   
                   
                 Fogging after durability 
                 Charge stability 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 component 
                 Image density change 
                 HH 
                 NN 
                 NL 
                 HH 
                 NN 
                 NL 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 developer 
                 HH 
                 NN 
                 NL 
                 FV 
                   
                 FV 
                   
                 FV 
                   
                 CR 
                   
                 CR 
                   
                 CR 
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 No. 
                 Δ 
                 Rank 
                 Δ 
                 Rank 
                 Δ 
                 Rank 
                 % 
                 Rank 
                 % 
                 Rank 
                 % 
                 Rank 
                 % 
                 Rank 
                 % 
                 Rank 
                 % 
                 Rank 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Example 
                 35 
                 0.04 
                 B 
                 0.01 
                 A 
                 0.02 
                 B 
                 1.6 
                 C 
                 1.1 
                 B 
                 1.3 
                 B 
                 4 
                 B 
                 1.0 
                 A 
                 3 
                 B 
               
               
                 28 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 Example 
                 36 
                 0.06 
                 C 
                 0.03 
                 B 
                 0.04 
                 B 
                 1.8 
                 C 
                 1.1 
                 B 
                 1.4 
                 B 
                 6 
                 C 
                 3.0 
                 B 
                 4 
                 B 
               
               
                 29 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 Example 
                 37 
                 0.07 
                 C 
                 0.03 
                 B 
                 0.05 
                 C 
                 1.8 
                 C 
                 1.1 
                 B 
                 1.6 
                 C 
                 8 
                 C 
                 3.0 
                 B 
                 4 
                 B 
               
               
                 30 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 Example 
                 38 
                 0.08 
                 C 
                 0.03 
                 B 
                 0.07 
                 C 
                 2.1 
                 D 
                 1.1 
                 B 
                 1.9 
                 C 
                 7 
                 C 
                 3.0 
                 B 
                 6 
                 C 
               
               
                 31 
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 Example 
                 39 
                 0.12 
                 D 
                 0.03 
                 B 
                 0.08 
                 C 
                 1.7 
                 C 
                 1.1 
                 B 
                 1.8 
                 C 
                 7 
                 C 
                 3.0 
                 B 
                 5 
                 C 
               
               
                 32 
               
               
                   
               
            
           
         
       
     
     In the Table, “FV” denotes “Fogging value”, and “CR” denotes “Change ratio”. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. This application claims the benefit of Japanese Patent Application No. 2021-009603, filed Jan. 25, 2021, and Japanese Patent Application No. 2021-196672, filed Dec. 3, 2021, which are hereby incorporated by reference herein in their entirety.