JP4809593B2 - Design method for two-component developer - Google Patents

Description

The present invention relates to a developer designing method for use in electrophotographic copying machines, printers, facsimiles, and the like .

  In an image forming apparatus such as an electrophotographic copying machine or a printer, the surface of the photoconductor is uniformly charged, and then the photoconductor surface is exposed with, for example, a laser beam in accordance with image data. A charge distribution corresponding to the image pattern is formed. Furthermore, a toner image is formed by developing the toner in accordance with the charge distribution pattern by a developing device, and then the toner image is transferred to a recording paper and fixed on the recording paper by thermal fixing, thereby Form.

  As the developing method in the above developing device, toner which is colored particles of resin powder having a particle size of about 5 to 10 micrometers, and magnetism having an average particle diameter of 30 to 100 micrometers such as ferrite, magnetite and iron powder. There are a two-component development method using a two-component developer mixed with a carrier which is particles, and a one-component development method using only a toner and no carrier.

  In general, an electrophotographic apparatus using a two-component developer includes one or a plurality of developing rolls having a magnet roll inside a cylindrical sleeve roll, and the photosensitive roll and the developing roll are opposed to each other by the developing roll. The toner and the carrier are mixed and supplied to the space to be developed, and the toner is developed on the photoreceptor.

  In order to attach the toner according to the charge distribution formed on the surface of the photoreceptor, it is necessary to charge the toner. However, in the case of a two-component developer, the toner is removed by friction generated between the toner and the carrier when they are mixed. It is charged. In this case, in order to form an image with an appropriate density, it is important to give the toner an appropriate charge amount and a stable charge amount.

  However, there is a problem that the charge amount of toner is greatly affected by environmental conditions, particularly humidity. That is, at low humidity, the toner is well charged and the toner charge amount is large. At high humidity, the toner is difficult to be charged and the toner charge amount is small. Since the amount of toner adhering to the surface of the photoreceptor has a characteristic inversely proportional to the toner charge amount, if the toner charge amount becomes unstable due to fluctuations in humidity, the toner adhesion amount also fluctuates, causing a problem that the image density is not stable. .

  In order to solve such problems, the present inventor has proposed a new image forming method disclosed in Patent Document 1. This method obtains a condition such that the relationship between the charge amount Q / M per unit weight of toner and the toner / carrier weight mixing ratio T / C satisfies a predetermined formula, and the mixing ratio T / C satisfying the condition is obtained. In this case, a developer is used, and there is an excellent effect that a stable and high-definition image can be formed.

Japanese Patent Laid-Open No. 8-248672

JP 2002-278168 A Atsumi Kondo: Mechanism of tribocharging with powder toner: 43rd meeting of the Electrophotographic Society, pp. 26-30 (1979) Ryuji Kurita: Saturation charge of one-component and two-component developers: Journal of Electrophotographic Society, 26, 2, pp. 126-129 (1987) Yamazaki et al. 4: Triboelectric charging and toner surface charge density in a two-component development system: Journal of Electrophotographic Society, 31, 2, pp. 113-123 (1992) L. H. Lee: A Surface Interaction Model for Triboselection on Toner-Carrier Pair: Photo. Sci. Eng. 22, no. 4, pp. 228-231 (1978) Hisao Okada: Simulation of developer charging: 74th Electrophotographic Society of Japan Research Meeting, pp. 37-40 (1994) Masatoshi Nakayama: Electrostatic induction: pp. 88-90, Kyoritsu Publishing (1983) Nobuyoshi Hoshi, Masaho Anzai, Effective carrier coverage of two-component developer, Journal of Electrophotographic Society, Vol. 25, No. 4 (1986) Corona, Fundamentals and Applications of Electrophotographic Technology, 1988

  However, the developer used in the image forming method proposed in Patent Document 1 must satisfy a predetermined conditional expression. For this purpose, several hundreds of combinations of toner and carrier are repeatedly evaluated. There is a problem that it requires a lot of labor.

SUMMARY OF THE INVENTION An object of the present invention is to theoretically investigate the mechanism of toner charging in order to reduce such labor, and to provide a developer design method having excellent toner charge amount stability.

One of the features of the present invention is a two-component developer design method in which a toner that is colored particles and a carrier that is magnetic particles are mixed, and the particle size, true density, and dielectric constant of the toner particles are set to r, ρ, respectively. _t, and epsilon _t, the particle size of the carrier particles, respectively the true density R, [rho _c, the dielectric constant of the surface of the carrier particles when the epsilon _c, with _{L ch = Rρ c ε c /} rρ t ε t A step of determining the constant _Lch , Q / M for the toner charge- mass ratio, T / C for the toner / carrier weight mixing ratio, and Q / M for Q / M when T / C is zero. When (0)
Q / M = Q / M (0) / (1 + L _ch × T / C)
And a method of designing a two-component developer including a step of selecting a toner and a carrier so as to satisfy the relationship of ε _c > ε _t .

According to the present invention, it is possible to stabilize the charge amount of the toner regardless of environmental fluctuations such as humidity. Therefore, it is possible to provide a developer design method capable of forming a high-quality image having a stable printing density. It becomes possible.

  Before describing a specific embodiment of the present invention, a toner charging mechanism investigated by the present inventor will be described.

  The models relating to the toner charging mechanism that the inventors have paid attention to are the equilibrium contact electric field model and the surface state model. For the same charging phenomenon, we found that there was an inconvenience in physical interpretation in the comparison result between the two, and proposed a new model that solved this inconvenience.

  Non-Patent Documents 1, 2, and 3 disclose balanced contact electric field models in which the saturation charge amount is determined so that the contact electric field between the toner and the carrier is constant. When the charge amount-toner density characteristic equation of this model is converted into the characteristic equation of the surface state model of Non-Patent Document 4, the surface state model requires that the effective surface state density of the toner and carrier be equal, which is inconvenient for physical interpretation. It is pointed out in Non-Patent Documents 1 and 3 that this occurs.

  As a result of well analyzing this equilibrium contact electric field model, it was found that the contact part was not well modeled. In dielectric contact, both dielectric constants should affect the contact electric field, but the balanced contact field model only considers the dielectric constant of the vacuum. In this balanced contact electric field model, it is assumed that charges are distributed on the surface. However, if it is distributed on the surface, if the toner and the carrier come into contact with each other, the positive and negative charges are neutralized, and no electrostatic capacity should be formed at the contact portion. There is also the idea that capacitance is formed in the gap around the contact part, but the gap spacing is not uniquely determined, and there remains a contradiction that the contact electric field becomes zero due to charge neutralization at the contact part. . Therefore, when viewed on a microscopic scale, it is appropriate to consider that the contact portion between the toner and the carrier is in contact with no gap, and the center of the charge distribution exists at a small distance from the contact surface. It is.

  By the way, when considering the source of charge of toner and carrier, it means that the balance between the negative charge of electrons and the positive charge of nuclei has collapsed, resulting in a state where electrons on the electron orbit of atoms and molecules are excessive or insufficient. it can. That orbit is a level. Therefore, the electric field formed by the electrons existing at this level and the atoms or molecules lacking the electrons should reflect the dielectric properties of the molecules or atoms, that is, the toner or carrier. Also, if the charge of electrons and nuclei is the charge of toner and carrier, it should be present at a small distance.

  The present inventor believes that the fact that the physical quantity of the material that determines the toner charge amount cannot be clearly indicated is the biggest cause that the two-component developer excellent in charge amount stability cannot be developed in a short period of time. For this reason, the inventor tried to solve the problem of inconvenience of physical interpretation pointed out in the above non-patent literature.

  Next, a new balanced contact electric field model according to the present invention that eliminates the conventional theoretical deficiencies will be described.

FIG. 1 shows a model of a contact portion between a toner and a carrier. In the figure, it is assumed that electric charges are uniformly distributed at a slightly deeper position from the contact surface between the toner and the carrier (this will be called a surface in the present invention). The contact electric field is calculated by applying Gauss's law to the minute part where the toner and the carrier are in contact. The dielectric constant of the toner is ε _t and the dielectric constant of the carrier is ε _c . The toner is a sphere having a density ρ _t and a radius r, and the carrier is a sphere having a density ρ _c and a radius R. Further, the number of adhered toner per unit surface area of the carrier is n. These notations are the same as in Non-Patent Document 2.

  First, the electric field inside the toner is derived from Gauss's law.

If the average electric field inside the toner is E _t ′, the above equation can replace the integral with the product,

  It becomes. Similarly for carriers,

It becomes. Therefore, the electric field E _{k of the} contact portion is careful of the direction of the electric field,

  It becomes.

Next, the relationship between q _t and q _c is derived from the continuity of the electric flux density. Assuming that the electric field on the toner side at the contact surface is E _t ″ and the electric field on the carrier side is E _c ″, since the electric flux density at the contact surface is continuous, the following equation is established.

Consider the continuity of the electric flux inside each toner and carrier. The passage area of the electric flux at the interface and S _i, and passes therethrough the electric flux flowing out of the carrier charge, when the flow into the toner charge, the following equation holds.

  From Equation 2, Equation 3, Equation 5, Equation 6, and Equation 7,

Is obtained. In addition, since charges are uniformly distributed on the surface, the absolute values of q _t and q _c are inversely proportional to the total surface area ratio.

  It becomes. Therefore,

  It becomes. Solving this for qt, we get

  Further, a relational expression of the weight mixing ratio T / C of n, toner and carrier,

  Is used, the charge mass ratio Q / M of the toner is

  It becomes. This formula is equivalent to the formulas of Non-Patent Document 1 and Non-Patent Document 2, except that it includes the dielectric constants of toner and carrier.

  Next, the relationship between the dielectric constant and the surface state density of the surface state model will be considered.

  If the contact portion has a capacitance, the amount of charge that can be accumulated is proportional to the dielectric constant. The place where charges are accumulated in the dielectric is the electron capture level or emission level of toner or carrier, and therefore the amount of charge that can be accumulated is considered to be proportional to the number of levels. These levels are surface levels in the surface state model. Therefore, it is considered that there is a proportional relationship between the dielectric constant ε and the surface state density N.

Using this relationship, the dielectric constant of Equation 13 can be replaced with the surface state density. In accordance with the description of Non-Patent Document 5 analyzed by the inventor in the same manner as the theory of Non-Patent Document 4, when the surface state densities b _t and b _c per unit weight are used,

  Is obtained. Therefore, Equation 13 is

  It becomes. This Q / M-T / C characteristic equation is the following characteristic equation disclosed in Non-Patent Document 5 derived from the surface state model:

And the format is exactly the same. It can be seen that kE _k = e (W _c −W _t ) is the relationship between the two characteristic formulas, and the contact electric field E _k is proportional to the work function difference.

  As described above, when the dielectric constants of both the toner and the carrier are taken into consideration, it has been found that the equation of the saturation charge amount derived from the equilibrium contact electric field model coincides with the equation derived from the surface state model.

  Here, the relationship between the dielectric constant and the surface state density will be described.

  From Non-Patent Document 6, the static (DC) dielectric constant ε of the dielectric is

It is represented by ω _p is the plasma frequency, and ω ₀ is a restoring force coefficient that suppresses charge transfer in a finite manner. Further, ω _p is obtained by using the electron density n, the absolute value e of the electron charge, and the electron mass m.

  It is expressed. Therefore,

It becomes. The electron density n is considered to be proportional to the surface state density N (proportional coefficient is s) when considering the vicinity of the surface. Also, since the term of ε _{0 in} the above equation is irrelevant to the presence or absence of electrons,

  Get.

  That is, it has been found that the physical quantity called the dielectric constant of the material appearing in the formula of the new equilibrium contact electric field model shown in the present invention is related to the surface state density in the surface state model. In Patent Document 1 previously proposed by the present inventor, the relationship between the number of surface states of the toner and the carrier determines the relationship between the toner charge amount and the weight mixing ratio of the toner and carrier, and the toner charge amount is less than the environment. It has been elucidated that a desirable and stable developer has a characteristic that the toner charge amount is little changed with respect to the weight mixing ratio of the toner and the carrier. Such a developer is a case where the number of surface states of the carrier is larger than the number of surface states of the toner, and it has been found that the number of surface states corresponds to the dielectric constant as described above. In designing the toner and the carrier, it can be derived that the dielectric constant of the carrier should be designed larger than the dielectric constant of the toner. And since the dielectric constant of this carrier is a dielectric constant in the vicinity of the carrier surface that contributes to charging, it is considered that it is the dielectric constant of the resin coating layer covering the carrier surface, that is, the resin coating material. As a result, it was concluded that the dielectric constant should be selected to be larger than that of the toner.

  Next, an embodiment of the image forming apparatus according to the present invention will be described with reference to FIG.

  In FIG. 2, reference numeral 1 denotes a photosensitive member, around which a charger 2, an exposure device 3, and a developing device 4 are arranged. The surface of the photoreceptor 1 rotating in the clockwise direction is uniformly charged by the charger 2. The exposure device 3 generates a light beam corresponding to the image data and irradiates the surface of the photoreceptor 1 with this light. On the photosensitive member 1, the portion irradiated with light becomes conductive and the surface charge disappears.

  In the present embodiment, a two-component developer composed of toner and carrier is used for the developing device 4. The developer is transported to a space area where the photosensitive member 1 and the developing roll 41 face each other as the developing roller 41 having a magnet therein rotates. A developing bias power supply 48 is connected to the developing roll 41, and a developing bias voltage in which alternating current is superimposed on direct current is applied from the power supply 48. With the above structure, the toner having the same charging polarity as that of the photosensitive member 1 adheres to the place where the charge on the surface of the photosensitive member 1 disappears due to the action of the electric field between the photosensitive member 1 and the developing roll 41. The toner image formed on the photoreceptor 1 by development is transferred to the paper 7 by the transfer device 5. The toner image transferred to the paper 7 is melted by heating with a fixing device (not shown), and fixed on the paper 7 to form an image. The toner remaining on the photosensitive member 1 is removed by the cleaning device 6. The toner removed by the cleaner 6 is collected by the toner hopper 42 and used again for development.

  When the toner is consumed by the development, the toner concentration in the developer of the developing machine 4 is lowered and the output value of the toner concentration sensor 44 is changed. The detection signal of the toner density sensor 44 is compared with a reference value by the control unit 46. When it is detected that the toner density has fallen below a predetermined value, the toner replenishing roller 43 is driven to supply toner from the toner hopper 42 into the developing device 4. Replenish. When the output of the toner density sensor 44 reaches a value corresponding to a predetermined toner density, the control unit 46 stops the supply roller 43 so that the toner density in the developing device 4 does not become excessive.

  A space area where the photoconductor 1 and the developing roll 41 are opposed to each other is a portion where development is performed, and an interval between the photoconductor 1 and the developing roll 41 is referred to as a developing gap. Further, the ratio of the moving speed of the peripheral surface of the photoreceptor 1 and the moving speed of the peripheral surface of the developing roll 41 is referred to as a peripheral speed ratio.

  In the embodiment of the present invention, as the two-component developer supplied to the development gap, a developer having a larger dielectric constant on the surface of the carrier than that of the toner is used. A specific example for increasing the dielectric constant of the carrier surface will be described below.

First, an example in which the above dielectric constant relationship is realized by coating the carrier surface will be described. Silicone resin and acrylic resin were coated with magnesium ferrite having a volume average particle size of 55 μm as a core material. As a method for increasing the dielectric constant of the coating film on the carrier surface, carbon black, which is a conductive material, was added to the coating resin. Since the conductive material has a high dielectric constant, it is considered that the dielectric constant of a resin having a relative dielectric constant of about 2 to 2.9 can be increased by adding it to the coating film. The carbon black used is non-aggregating carbon black having an average particle size of about 0.03 μm.
The prototype carriers (1), (2), and (3) are shown below.
(Carrier 1)
Symbol name: D-1
Coat resin: Silicone Coat film thickness: 0.9 μm
Conductive agent: Carbon black having an average particle size of 0.03 μm is added at 10% of the coating resin weight (carrier 2)
Symbol name: D-2
Coat resin: Silicone Coat film thickness: 0.6 μm
Conductive agent: Carbon black having an average particle size of 0.03 μm is added at 10% of the weight of the coating resin (carrier 3)
Symbol name: D-3
Coat resin: Acrylic Coat film thickness: 0.9 μm
Conductive agent: Carbon black having an average particle size of 0.03 μm added at 3% of the weight of the coating resin These carriers are cyan polyester toner and the toner / carrier weight ratio T / C is 0.053, 0.075, 0 Each 10 g was mixed in a 10 cc polyethylene container so as to be .111, and then mixed for 10 minutes at a rotation speed of 42 rpm with a stirring mixer called Turbler mixer T2C type (manufactured by Willy Bachofen Manufacturing Engineers). Thereafter, the toner charge amount Q / M was measured with a 210HS type charge amount measuring device (manufactured by Trek Japan). FIG. 3 shows the relationship between the toner charge amount Q / M and the mixing ratio T / C. The measurement result was applied to the following Equation 23 described in Patent Document 1, and the value of the parameter Lch was obtained as follows.

(Carrier 1)
Lch = 35
(Carrier 2)
Lch = 23
(Carrier 3)
Lch = 69
A developer prepared by mixing these carriers and cyan polyester toner at a mixing ratio of 0.05 was subjected to printing evaluation by a printer DDP92 (manufactured by Hitachi Printing Solutions). As a result, the developers using the carriers D-1 and D-2 were relatively stable in both the mixing ratio and the toner charge amount when continuous printing was performed. However, it has been found that with the developer using the carrier D-3, a slight fog is generated on the white background portion after the toner is replenished. Carriers D-1 and D-2 satisfy the parameter Lch value of Equation 23 of 50 or less, and are considered to have excellent stability for the reason described in Patent Document 1. In addition, in the carriers D-1 and D-2, the value of the Lch is smaller in the D-2, and although it is slight, the variation in the charge amount is also less when the carrier D-2 is used. . The current print quality standard is higher than when the patent document 1 was filed. From this experimental result, the developer using the carrier D-1 is not sufficient, and the development using the carrier D-2 is not sufficient. The agent was judged to be at an acceptable level.

  Next, the dielectric constants of the films coated on these carriers were confirmed. The carrier is as small as 55 μm, and the dielectric constant of the coating film on the surface cannot be measured. Accordingly, Equations 15, 16, and 17 and Equation 23 described in Patent Document 1 are compared, and the following Equation 24 is obtained.

Therefore, the dielectric constant of the carrier was derived from this equation. The dielectric constant of the toner was measured by using a dielectric loss measuring device TRS-10T (manufactured by Ando Electric Co., Ltd.) after molding the toner into a pellet. The relative dielectric constant ε _t / ε ₀ (where ε ₀ is the dielectric constant of vacuum) of the polyester toner was 3.0.

In Equation 24, R = 55 μm, r = 8.5 μm, ε _t = 3ε ₀ (ε ₀ is the dielectric constant of vacuum) ρ _c = 5 g / cubic cm, ρ _t = 1.1 g / cubic cm The result was obtained.
(Carrier 1)
ε _c = 2.5ε ₀
(Carrier 2)
ε _c = 3.8ε ₀
(Carrier 3)
ε _c = 1.3ε ₀
From the above analysis, the dielectric constant (= 3.8) of the surface coat film of the carrier D-2 that has passed the current print quality standard is larger than the dielectric constant (= 3.0) of the toner. It was found to be in good agreement with the elucidation. Carriers D-1 and D-2 have the same weight ratio of the conductive agent added to the coating resin, but carrier D-2 has a higher dielectric constant. This is because the resin coating on the carrier surface is carried out by dissolving the resin in a solvent and mixing it with the carrier, and then volatilizing the solvent of the resin by baking, but when the coat film is thin like carrier D-2 It is presumed that the shrinkage of the coating film at the time of baking increased and the density of the conductive agent in the coated film after baking increased.

  The experiment described above is performed when carbon black having an average particle size of 0.03 μm is added. However, the experiment was also performed when the particle size of carbon black as a conductive agent added to the coating film was changed. In the same manner as in Example 1, the ferrite carrier surface was coated with a silicone resin added with cohesive carbon black having an average particle size of 0.06 μm. This was mixed with a red polyester toner, and printing evaluation was performed with a continuous paper printer L160 (manufactured by Hitachi Printing Solutions). As a result, the red color became slightly darker as it was printed. Furthermore, when printing was continued, the blackness decreased again and returned to a bright red color. However, the charge amount has increased. When this carrier was observed with a scanning electron microscope (SEM), a minute portion that appeared black in the coating film, which was considered to be an aggregate of carbon black, was observed, and the coating film also appeared uneven. In the case of carbon black having a relatively large particle size, which is agglomerated, the carbon black is unevenly distributed in the coating film, and the carbon black falls off the carrier surface together with the coating film, contaminates red toner and becomes blackish. It is thought that it has been. In addition, carbon black drops off due to the poor affinity between carbon black and resin, so as printing continues, the amount of charge increases and the carbon that falls off disappears. It is thought that it became.

  As a result of these experiments, it was found that it is desirable to add carbon black having a particle diameter of 0.05 μm or less to the silicone resin as the carrier coating film. On the other hand, when the average particle size is 0.001 μm or less, the yield is low and the production cost is extremely high. Therefore, it is desirable that the carbon black used has a particle size in the range of 0.001 to 0.05 μm. A fluororesin may be used instead of the silicone resin.

  On the other hand, it has been found that the addition amount of carbon black is desirably 5% to 15% by weight with respect to the silicone resin. That is, if the added amount of carbon black is less than 5% by weight, the effect of stabilizing the charge amount is insufficient, and if it is more than 15%, the coating uniformity is poor and the coating film is liable to peel off.

  Next, the core material of the carrier will be described. In the above-described experiment, ferrite formed by adding magnesium oxide as an accessory component to iron oxide was used as the core material. Such a magnesium ferrite carrier has an electrical resistance that is 4 to 5 orders of magnitude higher than that of the magnetite carrier, and the electrical resistance of the carrier can be maintained high even when a conductive agent is added to the carrier coating film. Therefore, even if alternating current is superimposed on the developing bias applied to the developing roll of the two-component developing device, dielectric breakdown does not occur, and carrier skipping and image defects are unlikely to occur.

  In FIG. 4, the horizontal axis shows the gradation area ratio (number of dots per unit area) corresponding to the original density, and the vertical axis shows the gradation density characteristics taking the density of the obtained image, and only the DC bias voltage is shown. In this case, the gradation characteristic has a small density change as shown by the curve 81. However, when alternating current is superimposed, the density change range ranges from a bright low density image to a dark high density image as shown by the curve 82. A spread image can be obtained. Therefore, by using magnesium ferrite as the carrier core material and adopting a developing bias method in which direct current and alternating current are superimposed, gradation characteristics with a wide density change range can be obtained.

FIG. 6 is a diagram illustrating an analysis model for toner charging according to the present invention. 1 is a configuration diagram showing a first embodiment of an image forming apparatus according to the present invention. FIG. 4 is a relationship diagram between a toner charge amount and a toner / carrier mixture ratio of a two-component developer according to the present invention. FIG. 6 is a gradation characteristic diagram of the two-component developing device according to the present invention.

Explanation of symbols

1 is a photosensitive member, 2 is a charger, 3 is an exposure unit, 4 is a developing unit, 5 is a transfer unit, 6 is a cleaning unit, 7 is paper, 41 is a developing roll, 42 is a toner hopper, and 43 is a toner supply roller. , 44 is a toner concentration sensor, 45 is a stirring screw, 47 is a developer regulating member, 48 is a developing bias power supply, and 53 is a transfer power supply.

Claims (1)

In a method for designing a two-component developer in which a toner that is colored particles and a carrier that is magnetic particles are mixed,
The particle size, true density, and dielectric constant of the toner particles are r, ρ _t , and ε _t , respectively, the particle size and true density of the carrier particles are R, ρ _c , and the dielectric constant of the surface of the carrier particles is ε _c , respectively. When
Determining a constant L _ch represented by L _ch = Rρ _c ε _c / rρ _t ε _t ;
When the charge mass ratio of the toner is Q / M, the weight mixing ratio of the toner and the carrier is T / C, and the value of Q / M when the T / C is zero is Q / M (0),
Q / M = Q / M (0) / (1 + L _ch × T / C) (1)
A method for designing a two-component developer, comprising a step of selecting a toner and a carrier so as to satisfy the formula (1) and satisfy a relationship of ε _c > ε _t .

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