JP2012177811A - Method for evaluating temporal stability of electric resistance of electrophotographic belt - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for evaluating the temporal stability of electric resistance of an electrophotographic belt including a polyether ether ketone and a carbon black.SOLUTION: The method for evaluating the temporal stability of electric resistance of an electrophotographic belt including a polyether ether ketone and a carbon black dispersed in the polyether ether ketone includes a step of obtaining a number-average particle size of the carbon black observed from a cut surface of the belt, obtaining Ripley's L function in a circular range having a radius of 1.2 μm with coordinate values of a plane's center of gravity as the center, and determining a distribution pattern of the Ripley's L function.

Description

The present invention relates to a method for evaluating the stability over time of the electrical resistance of an electrophotographic belt.

2. Description of the Related Art Conventionally, an image forming apparatus of a so-called intermediate transfer method is known by an electrophotographic method or an electrostatic recording method. In the intermediate transfer type image forming apparatus, the electrostatic latent image formed on the photosensitive member as the first image carrier is developed by a developing device to form a developer image (toner image). The toner image is primarily transferred onto an intermediate transfer member that is an image carrier, and then secondarily transferred onto a recording material such as paper. As a material constituting the intermediate transfer member, polyimide resin, polycarbonate resin, polyvinylidene fluoride resin, polyether ether ketone resin, polyphenylene sulfide resin, and the like are used. As the intermediate transfer member, a so-called intermediate transfer belt in which the resin material is molded into a seamless belt shape is widely used.

Conventionally, a semiconductive film formed from a resin composition containing a polyether ether ketone resin (PEEK resin) and a conductive filler and a method for producing the same have been disclosed (Patent Document 1). However, by using a resin composition obtained by adding a conductive filler to a polyether ether ketone resin, a semiconductive film having a uniform thickness, small variation in volume resistivity depending on location, and excellent mechanical strength. It was not easy to manufacture. In Patent Document 1, the above problem is solved by strictly controlling the temperature at the time of melt extrusion of the mixed resin and cooling and solidification.

JP 2005-112942 A

However, an intermediate transfer belt containing a polyether ether ketone resin and carbon black may have a reduced volume resistivity due to continued use. This decrease in volume resistivity due to continued use is considered to be due to the following mechanism. That is, the transfer electric field at the time of primary transfer and secondary transfer is repeatedly applied to the intermediate transfer belt for a long time, resulting in partial insulation breakdown of the polyetheretherketone resin and the formation of a conductive path inside the intermediate transfer belt. This is a mechanism in which the volume resistance of the belt decreases. This phenomenon is thought to be caused by partial dielectric breakdown of the resin due to the concentration of the electric field in the vicinity of the carbon black aggregates in the polyether ether ketone resin and in the minute gaps between the large-sized aggregates. . Therefore, it is considered that evaluating the dispersibility of carbon black, which is a direct cause of dielectric breakdown, is effective for evaluating the temporal stability of electrical resistance.

Conventionally, as a method for evaluating the dispersibility of carbon black in a resin, indices such as the particle size (particle diameter) of carbon black, the distance between nearest particles, and the partition method have been used.
However, the spatial distribution of the particles is unknown because the positional information between the particles is not reflected only by the evaluation of the particle size (particle diameter). Moreover, in the evaluation of the distance between the closest particles, attention is paid only to the closest particle, and therefore the dispersibility of the whole particle cannot be accurately evaluated. In addition, a method (compartment method) is known in which the number of particles in a compartment is counted to know the distribution mode (compartment method). However, the distribution mode differs depending on how the compartments are divided (compartment size and shape), making it difficult to determine the distribution.

  Accordingly, an object of the present invention is to provide a method for more accurately determining the dispersion state of carbon black and evaluating the temporal stability of the electrical resistance of an electrophotographic belt.

As a result of intensive studies by the present inventors for the above purpose, the dispersion state of carbon black is further quantified by using Ripley's L function and Geary's C statistic in addition to the number average particle diameter of carbon black. We have found an evaluation method that shows accurate and accurate results. Ripley's L function indicates the spatial distribution pattern of carbon black particles, and Geary's C statistic indicates the spatial autocorrelation of the particle sizes of adjacent carbon blacks.
That is, the method for evaluating the stability over time of the electric resistance of the electrophotographic belt according to the present invention is an electric resistance of an electrophotographic belt containing polyether ether ketone and carbon black dispersed in the polyether ether ketone. The Ripley L function in a circular range having a radius of 1.2 μm centered on the plane barycentric coordinate value of the carbon black observed from the cut surface of the belt is obtained. The method includes a step of determining a distribution pattern.

  According to the present invention, it is possible to more objectively and quantitatively predict the temporal stability of the electrical resistance of an electrophotographic belt containing a polyether ether ketone resin and carbon black.

The figure which shows an example of Ripley's L function used for the evaluation method of this invention. The flowchart which shows the evaluation method of this invention.

  In the field of spatial statistics, the spatial distribution of points is divided into three distributions: random distribution, concentrated distribution, and regular distribution (constant interval distribution). A random distribution is a spatial distribution of points that is realized when each point is placed independently of each other and with the same probability anywhere in any region. The concentrated distribution is a spatial distribution in which points are clustered in a specific area. Further, the regular distribution (constant interval distribution) is a spatial distribution in which points are distributed while maintaining a certain distance from each other.

The Ripley L function is described below. First, Ripley's K function is defined as follows:
K (d) =
E [number of other points contained in a circle with radius d centered at a randomly selected point] / ρ
In other words, K (d), which is a K function, is a value obtained by dividing the average of other points contained in a circle with a radius d centered on a randomly selected point by the density ρ (average density) of points in all regions. is there. It is known that random distribution of points on a finite plane follows a Poisson distribution. If the points are randomly distributed according to the Poisson distribution, the expected value of the number of other points present in the circle of radius d is the value obtained by multiplying the average density ρ by the area of the circle πd ² , so that It is represented by

Here, the L function is a standardized function of the K function. L (d), which is an L function, is expressed by Equation 2.

Considering the exponent of the L function, L (d) = 0 when the points are randomly distributed regardless of the radius d. Further, L (d) takes a positive value when the spatial distribution is a concentrated distribution, and takes a negative value when the spatial distribution is a regular distribution (constant interval distribution).

Next, Geary's C statistic will be described.
There is spatial autocorrelation when attribute values distributed in space have a certain tendency based on geographical proximity (adjacency).
Geary's C statistic is expressed by Equation 3.

Here, N is the total number of particles, Xi and Xj are the particle sizes (equivalent circle diameters) of adjacent particles, and Wij is a binary weighting factor. It takes a value in the range of 0-2. When similar attribute values (for example, particle diameters) are arranged, the C statistic approaches 0, which is referred to as positive spatial autocorrelation. When different attribute values (for example, particle diameter) are juxtaposed, they approach 2 and this is called negative spatial autocorrelation. The C statistic is 1 when attribute values are randomly distributed.

By using Geary's C statistic, it is possible to accurately evaluate the spatial autocorrelation between the particle size of a particle and the particle size of a particle existing in the vicinity thereof. If the C statistic shows random, the relationship between the particle size of a certain particle and the particle size of its neighboring particles is random, so that it can be judged that the dispersibility is “good”. On the other hand, if the C statistic shows a positive autocorrelation, it is possible to detect the case where particles having similar particle diameters are close to each other, so that the dispersibility can be determined to be “bad”. If the C statistic shows a negative autocorrelation, it can be detected that there are many small sized particles in the vicinity of large sized particles and many large sized particles in the vicinity of small sized particles. Therefore, it can be determined that the dispersibility is “bad”.

EXAMPLES Hereinafter, although an Example demonstrates this invention further in detail, the technical scope of this invention is not limited to these.

Example 1
<Preparation of carbon black-containing PEEK resin pellets>
Polyetheretherketone resin pellets (VICTREX PEEK 450G, manufactured by Victrex Co., Ltd.) were freeze-machined to produce PEEK resin powder 1 having an average particle size of 200 μm. Furthermore, the polyether ether ketone resin pellets (“VICTREX PEEK 151G” manufactured by Victrex Co., Ltd.) were freeze-machined to prepare PEEK resin powder 2 having an average particle size of 200 μm.
PEEK resin powder 1 and PEEK resin powder 2 were mixed at a weight ratio of 60:40 and mixed for 5 minutes with a cylindrical rotary blender to prepare PEEK resin powder 3.
Next, using a twin screw extruder equipped with a hopper and a quantitative feeder, 100 parts by mass of PEEK resin powder 3 and carbon black (made by Denki Kagaku Kogyo, trade name “Denka Black granular product”) from the quantitative feeder into the hopper ) Was supplied in a predetermined amount as shown in Table 3 and melt-kneaded. At this time, the cylinder set temperature of the extruder was set to 330 ° C to 370 ° C. The melt-kneaded product was extruded from a strand die into a string shape, cooled in a cooling water tank, and then cut with a pelletizer to prepare carbon black-containing PEEK resin pellets having an outer diameter of about 2 mm and a length of about 3 mm.

<Repeated kneading>
The obtained carbon black-containing PEEK resin pellets were dried in a hot-air circulating dryer for 8 hours at a temperature of 120 ° C., then supplied again to the twin-screw extruder, repeatedly melt-kneaded, and the same steps as above To produce carbon black-containing PEEK resin pellets. The number of times of repeated melt-kneading was the number of times described in Table 3 (2 to 6 times).

<Preparation of seamless belt>
Using the carbon black-containing PEEK resin pellets as a molding material, a cylindrical film having a predetermined thickness shown in Table 3 was molded using a single screw extruder equipped with an annular die and a gear pump. At this time, the cylinder set temperature of the extruder was set to 350 ° C to 400 ° C.
Next, the obtained cylindrical film was cut into a predetermined width using a slitter to produce a PEEK resin seamless belt.
Furthermore, ribs made of urethane rubber (width 5 mm, height 1 mm) projecting inward and restricting the axial movement of the intermediate transfer belt (electrophotographic belt) are formed on both edge portions of the inner peripheral surface of the seamless belt. ) Was continuously attached around the inner surface.

<Measurement of volume resistivity>
The volume resistivity of the PEEK resin seamless belt is as follows: resistance meter for ultra-high resistance (made by ADC, trade name “R8340A”), measurement electrode (main electrode (outer diameter 25 mm, height 10 mm, stainless steel), guard electrode (Inner diameter 35 mm, outer diameter 40 mm, height 10 mm, made of stainless steel) and counter electrode (outer diameter 80 mm, thickness 5 mm, made of stainless steel)). The measurement conditions were an applied voltage of 100 V and a measurement time of 10 seconds (measuring atmosphere: temperature 23 ° C., relative humidity 55%).

<Durability evaluation test>
The produced seamless belt was incorporated as an intermediate transfer belt into an image forming apparatus (Canon color copier “iR-ADV C2030”).
A4 size paper (Canon CLC paper, weighing 80 g / m ² ) was used under the conditions of a temperature of 23 ° C. and a relative humidity of 10% (normal temperature / low humidity environment), and an evaluation image with an image ratio of 5% was sent in A4 horizontal feed. 200K sheets were output continuously, and the intermediate transfer belt was taken out at the end of the durability test. After lightly wiping the surface of the intermediate transfer belt with Silbon paper, the volume resistivity of the intermediate transfer belt after the durability test was measured under the same normal temperature and low humidity environment conditions as in the durability test. The volume resistivity was measured at 10 points in the circumferential direction of the intermediate transfer belt, and an average value was obtained. The volume resistivity measured under the same normal temperature and low humidity conditions before the durability test was compared with the volume resistivity of the intermediate transfer belt after the durability test, and the resistance reduction characteristics were ranked as shown in Table 1.

<Measurement of dielectric breakdown strength>
As for the dielectric breakdown strength of the intermediate transfer belt, in accordance with JIS standard C2110-1, a dielectric breakdown test device (manufactured by Tama Denso Co., Ltd., trade name “TP-516UZ”) and a spherical probe having a tip of 20 mm in outer diameter The measurement was performed in an air atmosphere at a temperature of 23 ± 1 ° C. and a relative humidity of 50 ± 5%. A DC voltage was applied in the thickness direction of the seamless belt at a constant speed at which dielectric breakdown occurred in an average of about 10 to 20 seconds, and the voltage (KV) when dielectric breakdown occurred was measured. The voltage (KV) was divided by the belt thickness (mm) to determine the dielectric breakdown strength (KV / mm).

<Observation of cross section of intermediate transfer belt>
A sample of about 5 × 5 mm was cut out from the intermediate transfer belt, embedded in an epoxy resin so that the belt cross-section became the upper surface, and then polished by a buff grinder to make the cross-section smooth. Further, the ground surface of the sample was ion milled with argon ions in a vacuum to prepare a sample for observing the cross section of the intermediate transfer belt. After vacuum-depositing platinum on the observation surface, the sample cross section was observed using an electron microscope (Hitachi High-Technologies scanning electron microscope S4800). The observation magnification was 20000 times. Further, the cross section was observed by cutting out samples from 10 locations per intermediate transfer belt.

<Calculation of number average particle diameter>
The image of the cross section obtained with the scanning electron microscope was subjected to binarization image processing using an image analysis apparatus (manufactured by Nireco, “Luzex AP”).
First, the equivalent circle diameter D of each particle was calculated from the cross-sectional area A of each particle obtained from the binarized image by the following formula.
D = √ (4A / π)
Next, a value (arithmetic average value) obtained by dividing the total of the equivalent circle diameter D of all the observed particles by the total number of observed particles was defined as the number average particle size.

<Dispersibility evaluation by Ripley's L function>
Based on the binarized image, the number average particle diameter of carbon black particles in the PEEK resin and the plane barycentric coordinate value (X coordinate, Y coordinate) of the carbon black particles were determined. Next, Ripley's L function in a circular range with a radius of 1.2 μm was obtained from the plane barycentric coordinate value (X coordinate, Y coordinate) of the carbon black particles using the package spatstat of free software “R” for numerical analysis . When the distribution pattern of the L function is “random distribution” or “regular distribution” (“constant interval distribution”), the dispersibility is good, and when the L function distribution is a concentration distribution, the dispersibility is poor.

Each distribution pattern is determined by using the random number of the free software “R” to generate the same number of point coordinates as the number of analysis particles in the same range as the observation region, and obtain the range of the random distribution. went. Specifically, uniform random numbers were tried 1000 times, L functions were calculated for each, and upper and lower limits (ranges) of the random distribution were obtained. If the L function of the observation sample falls within the upper and lower limits of the random distribution obtained from random numbers, it will be "random distribution", if it exceeds the upper limit, it will be "concentrated distribution", and if it falls below the lower limit, it will be "regular distribution" ]). An example of the L function is shown in FIG. The gray portion in the graph of FIG. 1 is a range of random distribution obtained by trying uniform random numbers 1000 times. The horizontal axis represents the distance (radius d: μm), and the vertical axis represents the L function (L (d)). Further, in the peripheral portion of the binarized image, the number of other particles existing within the radius d from the plane center-of-gravity coordinate value (X coordinate, Y coordinate) of a certain particle tends to decrease compared to the central portion of the binarized image. Therefore, Ripley's edge correction method was used as the edge correction for the calculation of the L function.

<Dispersibility evaluation by Geary's C statistic>
Further, in the above Ripley's L function calculation result, the Geary C statistic was obtained for a sample in which the result of “good” dispersibility was obtained. Geary's C statistic was calculated from the plane center of gravity coordinates (X coordinate, Y coordinate) and number average particle diameter (equivalent circle diameter) of carbon black particles using the package spdep of the numerical analysis free software “R”. . In the plane barycentric coordinate value of the carbon black particles, four particles selected in the order of approaching from a distance as viewed from any carbon black particle were defined as adjacent particles, and the C statistic was calculated. In addition, when the particle coordinates are randomly given using a uniformly distributed random number (uniform random number) without changing the position coordinates of each particle, the range of the C statistic becomes 0.85 to 1.15. The results were ranked as shown in Table 2 according to the C statistic calculated from the actual particles.

An example of an evaluation flow of the evaluation method for the intermediate transfer belt of the present invention is shown in FIG.
In the example shown in FIG. 2, first, the dielectric breakdown strength is measured to determine whether the dielectric breakdown strength is 7 KV / mm (first threshold) or more (step S11). And evaluated as defective (step S12). In the case of 7 KV / mm or more, the process proceeds to step S21.
In step S21, the number average particle diameter is measured to determine whether the number average particle diameter is 115 nm (second threshold) or less. If the number average particle diameter is less than 115 nm, it is evaluated as defective (step S22). When the number average particle diameter is 115 nm or more, the process proceeds to step S31.

  In step S31, whether the L function obtained from the intermediate transfer belt sample falls within the upper and lower limits (within range) of the L function when the same number of point coordinates as the number of analyzed particles is randomly generated using a uniform random number. The distribution pattern is determined based on the above. If the upper limit of the L function when the uniform random number is used is exceeded, it is determined as a concentrated distribution (ie, “defective”) (step S32). When a uniform random number is used and the L function is lower than the lower limit and lower than the upper limit, it is evaluated as “random distribution”. When the value is below the lower limit of the L function when uniform random numbers are used, it is evaluated as “regular distribution”. In the case of “random distribution” or “regular distribution”, the process proceeds to step S41.

In step S41, the C statistic obtained from the intermediate transfer belt sample is obtained when the particle diameter is randomly given using a uniform random number with the plane barycentric coordinate value of the carbon black particle observed from the cut surface of the belt as it is. Determine whether it falls within the range of the C statistic. If the upper limit of the C statistic when using a uniform random number is exceeded, it is evaluated as “with positive autocorrelation”. When the value is below the lower limit of the C statistic when using uniform random numbers, it is evaluated as “with negative autocorrelation”. In the case of “with positive autocorrelation” or “with negative autocorrelation”, it is determined as “good” (step S42). When the C statistic is equal to or higher than the lower limit and lower than the upper limit when using uniform random numbers, it is evaluated as “random (no autocorrelation)” and determined as “best” (step S51).
The results of the examples are shown in Table 3.

The “particles of 1 μm or more” in the table indicates the ratio (%) of particles having a number average particle diameter of 1 μm or more.

<Examples 1-2, 1-3, 1-5, 1-6, 1-8, 1-9, 1-11, 1-12>
An intermediate transfer belt satisfying all the conditions that the dielectric breakdown voltage is 7 KV / mm or more, the number average particle diameter is 115 nm or less, the L function is a random distribution, and the C statistic is random is an image durability test. The decrease in volume resistivity due to was less than half an order of magnitude.
<Examples 1-1, 1-4, 1-7, 1-10>
An intermediate transfer belt that satisfies the conditions that the dielectric breakdown voltage is 7 KV / mm or more, the number average particle diameter is 115 nm or less, and the L function is a random distribution, but the condition that the C statistic is random is not satisfied. The volume resistivity decreased by more than half digit and less than one digit.

(Comparative Example 1)
<Preparation of carbon black-containing PEEK resin pellets>
In the same manner as in Example 1, polyether ether ketone resin pellets (Victrex PEEK 450G, manufactured by Victrex) were freeze-machined to produce PEEK resin powder 1 having an average particle size of 200 μm. Similarly, polyether ether ketone resin pellets (Victrex PEEK 151G, manufactured by Victrex) were freeze-machined to produce PEEK resin powder 2 having an average particle size of 200 μm.
In the same manner as in Example 1, PEEK resin powder 1 and PEEK resin powder 2 were mixed at a weight ratio of 60:40, and mixed for 5 minutes by a cylindrical rotary blender to prepare PEEK resin powder 3.

Next, in the same manner as in Example 1, using a twin screw extruder equipped with a hopper and a quantitative feeder, the PEEK resin powder 3 and the carbon black were mixed in the hopper from the quantitative feeder into the material mixing ratio described in Table 4. The mixture was melted and kneaded. At this time, the cylinder set temperature of the extruder was set to 330 ° C to 370 ° C. The melt-kneaded product was extruded from a strand die into a string shape, cooled in a cooling water tank, and then cut with a pelletizer to prepare carbon black-containing PEEK resin pellets having an outer diameter of about 2 mm and a length of about 3 mm. In Comparative Example 1, the melt kneading by the twin screw extruder was performed once. The seamless belt was produced and evaluated in the same manner as in Example 1.
Table 4 shows the results of the comparative example.

The “particles of 1 μm or more” in the table indicates the ratio (%) of particles having a number average particle diameter of 1 μm or more.

<Comparative Examples 1-1, 1-2, 1-4>
In the intermediate transfer belt that does not satisfy the condition that the L function has a random distribution, the decrease in volume resistivity by an image durability test is one digit or more.
<Comparative Example 1-3>
Intermediate transfer not satisfying the condition that the dielectric breakdown voltage is 7 KV / mm or more, the L function is a random distribution, and the C statistic is random, but the number average particle diameter is 115 nm or less The belt also had a volume resistivity decrease of more than an order of magnitude.

Claims (2)

A method for evaluating the temporal stability of the electrical resistance of an electrophotographic belt comprising polyether ether ketone and carbon black dispersed in polyether ether ketone,
Obtain the number average particle size of the carbon black particles observed from the cut surface of the belt,
An electrophotographic belt comprising: a step of obtaining a Ripley L function in a circular range having a radius of 1.2 μm centered on a plane barycentric coordinate value of carbon black particles and determining a distribution mode of the L function. Evaluation method of electrical resistance over time. Measuring breakdown strength and determining whether the breakdown strength is greater than or equal to a first threshold;
Measuring the number average particle size and determining whether the number average particle size is less than or equal to a second threshold,
In the step of determining the distribution pattern of the L function, it is determined whether the L function is equal to or lower than the upper limit of the L function when the same number of point coordinates as the number of analyzed particles are randomly generated using a uniform random number. ,
Geary's C statistic is obtained, and this C statistic is obtained when the particle diameter is randomly given using a uniform random number while maintaining the plane barycentric coordinate value of the carbon black particle observed from the cut surface of the belt. 2. The method for evaluating stability over time of electric resistance of an electrophotographic belt according to claim 1, further comprising a step of determining whether the value falls within the range of the statistic.