Continuous waveform drive in multicolor electrophoretic displays

Abstract

Provided are continuous waveforms for driving a four-particle electrophoretic medium comprising four different types of particles, e.g., one set of scattering particles and three sets of subtractive particles. Methods of identifying preferred waveforms for a target color state or target transition when using a continuous or quasi-continuous voltage driver / controller.

Description

[0001] Related applications

[0002] This application claims priority to U.S. Provisional Patent Application No. 63 / 147,465, filed February 29, 2021. The entire contents of all patents and publications disclosed herein are incorporated herein by reference. Background Technology

[0003] Electrophoretic displays (EPDs) change color by modifying the position of charged colored particles relative to a light-transmitting viewing surface. Because the resulting display has high contrast and is readable in sunlight, much like ink on paper, it is often called "electronic paper" or "ePaper." Electrophoretic displays are already widely used in e-readers such as the Amazon Kindle® because they provide a book-like reading experience, consume less power, and allow users to carry libraries of hundreds of books in a lightweight handheld device.

[0004] For many years, electrophoretic displays have only included charged color particles of two types: black and white. (Of course, the term "color" as used herein includes both black and white). White particles are typically light-scattering and include, for example, titanium dioxide, while black particles are absorbent in the visible spectrum and can include carbon black or absorbing metal oxides (such as copper chromite). In its simplest sense, a monochrome electrophoretic display only requires a transparent electrode at the observation surface, a back electrode, and an electrophoretic medium comprising white and black particles with opposite charges. When a voltage of one polarity is applied, the white particles move to the observation surface, and when a voltage of the opposite polarity is applied, the black particles move to the observation surface. If the back electrode comprises controllable regions (pixels)—an active matrix of segmented electrodes or pixel electrodes controlled by transistors—a pattern can be electronically rendered on the observation surface. This pattern can be, for example, text in a book.

[0005] Recently, multiple color options have become commercially feasible for electrophoretic displays, including tri-color displays (black, white, and red; black, white, and yellow) and quad-color displays (black, white, red, and yellow). Similar to the operation of a monochrome electrophoretic display, the operation of an electrophoretic display with three or four reflective pigments is analogous to a simple monochrome display, as the desired color particles are driven onto the observation surface. This driving scheme is far more complex than that of a simple monochrome display, but the final optical function of the particles is the same. It is also worth noting that such a display can only show one color at a time, i.e., the color of the group of particles that have been driven onto the observation surface.

[0006] Advanced Color Electronic Paper (ACeP™) also includes four types of particles, but the cyan, yellow, and magenta particles are subtractive rather than reflective, thus allowing for thousands of colors to be produced at each pixel. This color processing is functionally equivalent to the printing methods long used in offset and inkjet printing. A given color is produced by using the appropriate proportions of cyan, yellow, and magenta on a bright white paper background. In ACeP, for example, the relative positions of the cyan, yellow, magenta, and white particles relative to the viewing surface determine the color of each pixel. Although this type of electrophoretic display allows for thousands of colors to be displayed at each pixel, careful control of the position of each pigment (50-500 nanometers in size) within a working space approximately 10-20 micrometers thick is crucial. Clearly, variations in pigment position will result in incorrect color display at a given pixel. Therefore, this system requires precise voltage control. Further details of the system can be found in the following U.S. patents: U.S. Patent Nos. 9,361,836, 9,921,451, 10,276,109, 10,353,266, 10,467,984, and 10,593,272, the entire contents of which are incorporated herein by reference.

[0007] In most cases, the electrophoretic medium, as described above, is designed to be driven by a low-voltage square wave, which is generated, for example, by a driving circuit from a thin-film transistor backplane. Such driving circuits can be mass-produced inexpensively because they are closely related to driving circuits and manufacturing methods used to produce liquid crystal display panels, for example, found in smartphones, laptop displays, and televisions. In the past, even when the electrophoretic medium was driven directly via isolation electrodes (e.g., segmented electrodes), the driving pulse was delivered in the form of a square wave with a large amplitude and a long duration. See, for example, U.S. Patent 7,012,600, the entire contents of which are incorporated herein by reference. Using this form of driving, the electrical impulse (i.e., the amount of time a charged particle is exposed to a field of a given intensity) determines the final “state” observed at the observation surface.

[0008] The term "gray state" is used here in its conventional meaning in the imaging field, referring to a state between two extreme optical states of a pixel, but not necessarily a black-and-white transition between those two extremes. For example, several patents and publications of IENK, discussed below, describe electrophoretic displays where the extreme states are white and dark blue, making the intermediate "gray state" actually a pale blue. In fact, as already mentioned, a change in optical state may not be a change in color at all. The terms "black" and "white" may be used below to refer to the two extreme optical states of a display, and should be understood to generally include extreme optical states that are not strictly black and white, such as the white and dark blue states mentioned above.

[0009] The terms “bistable” and “bistable” are used herein in their conventional sense in the art, referring to a display comprising display elements having first and second display states, at least one optical characteristic of which differs such that, after any given element is driven to present its first or second display state using an addressing pulse of finite duration, the state will persist for at least several times (e.g., at least four times) the minimum duration of the addressing pulse required to change the state of the display element after the addressing pulse terminates. As shown in U.S. Patent No. 7,170,670, some particle-based electrophoretic displays supporting grayscale are stable not only in their extreme black and white states but also in intermediate gray states, as are some other types of electro-optical displays. This type of display is aptly referred to as “multistable” rather than bistable, but for convenience, the term “bistable” may be used herein to encompass both bistable and multistable displays.

[0010] When used to refer to driving an electrophoretic display, the term "impulse" refers to the integral of the voltage applied during the driving period of the display with respect to time. When used to refer to driving an electrophoretic display, the term "waveform" describes the sequence or pattern of voltages supplied to the electrophoretic medium within a given time period (second, frame, etc.) to produce the desired optical effect in the electrophoretic medium.

[0011] Particles that absorb, scatter, or reflect broadband or selected wavelengths of light are referred to herein as colored or pigment particles. Various materials other than pigments (the term strictly refers to insoluble colored materials) that absorb or reflect light, such as dyes or photonic crystals, can also be used in the electrophoretic media and displays of the present invention.

[0012] Numerous patents and applications transferred to or in the name of MIT and Einkel describe various techniques for encapsulating electrophoretic and other electro-optic media. Such encapsulated media comprise a plurality of small capsules, each capsule itself comprising an inner phase and a capsule wall surrounding the inner phase, wherein the inner phase contains electrophoretically mobile particles in a fluid medium. Typically, the capsules themselves are held in a polymer binder to form a coherent layer located between two electrodes. The techniques described in these patents and applications include:

[0013] (a) Electrophoretic particles, fluids, and fluid additives; see, for example, U.S. Patent Nos. 7,002,728 and 7,679,814;

[0014] (b) Encapsulation, adhesives, and encapsulation processes; see, for example, U.S. Patent Nos. 6,922,276 and 7,411,719;

[0015] (c) Microunit structures, wall materials, and methods of forming microunits; see, for example, U.S. Patent Nos. 7,072,095 and 9,279,906;

[0016] (d) Methods for filling and sealing microcells; see, for example, U.S. Patent Nos. 7,144,942 and 7,715,088;

[0017] (e) Thin films and sub-assemblies containing electro-optic materials; see, for example, U.S. Patent Nos. 6,982,178 and 7,839,564;

[0018] (f) Backplanes, adhesive layers and other auxiliary layers for use in displays, and methods thereof; see, for example, U.S. Patent Nos. 7,116,318 and 7,535,624;

[0019] (g) Color formation and color adjustment; see, for example, U.S. Patent Nos. 6,017,584; 6,545,797; 6,664,944; 6,788,452; 6,864,875; 6,914,714; 6,972,893; 7,038,656; 7,038,670; 7,046,228; 7,052,571; 7,075,502; 7,167,155; 7,385,751; 7,492,505; 7,667,684; 7,684,108; 7,791,789; 7,800,813; 7,821,702; 7,839,564; 7,910,175; 7,952,790; 7,956,841; 7,982,941; 8,040,594; 8,054,526; 8,098,418; 8,159,636; 8,213,076; 8,363,299; 8,422,116; 8,441,714; 8,441,716; 8,466,852; 8,503,063; 8,576,470; 8,576,475; 8,593,721; 8,605,354; 8,649,084; 8,670,174; 8,704,756; 8,717,664; 8,786,935; 8,797,634; 8,810,899; 8,830,559; 8,873,129; 8,902,153; 8,902,491; 8,917,439; 8,964,282; 9,013,783; 9,116,412; 9,146,439; 9,164,207; 9,170,467; 9,170,468; 9,182,646; 9,195,111; 9,199,441; 9,268,191; 9,285,649; 9,293,511; 9,341,916; 9,360,733; 9,361,836; 9,383,623; and 9,423,666; and U.S. Patent Application Publication No.2008 / 0043318; 2008 / 0048970; 2009 / 0225398; 2010 / 0156780; 2011 / 0043543; 2012 / 0326957; 2013 / 0242378; 2013 / 0278995; 2014 / 0055840; 2014 / 0078576; 2014 / 0340430; 2014 / 0340736; 2014 / 0362213; 2015 / 0103394; 2015 / 0118390; 2015 / 0124345; 2015 / 0198858; 2015 / 0234250; 2015 / 0268531; 2015 / 0301246; 2016 / 0011484; 2016 / 0026062; 2016 / 0048054; 2016 / 0116816; 2016 / 0116818; and 2016 / 0140909;

[0020] (h) A method for driving a display; see, for example, U.S. Patent Nos. 5,930,026; 6,445,489; 6,504,524; 6,512,354; 6,531,997; 6,753,999; 6,825,970; 6,900,851; 6,995,550; 7,012,600; 7,023,420; 7,034,783; 7,061,166; 7,061,662; 7,116,466; 7,119,772; 7,177,066; 7,193,625; 7,202,847; 7,242,514; 7,259,744; 7,304,787; 7,312,794; 7,327,511; 7,408,699; 7,453,445; 7,492,339; 7,528,822; 7,545,358; 7,583,251; 7,602,374; 7,612,760; 7,679,599; 7,679,813; 7,683,606; 7,688,297; 7,729,039; 7,733,311; 7,733,335; 7,787,169; 7,859,742; 7,952,557; 7,956,841; 7,982,479; 7,999,787; 8,077,141; 8,125,501; 8,139,050; 8,174,490; 8,243,013; 8,274,472; 8,289,250; 8,300,006; 8,305,341; 8,314,784; 8,373,649; 8,384,658; 8,456,414; 8,462,102; 8,514,168; 8,537,105; 8,558,783; 8,558,785; 8,558,786; 8,558,855; 8,576,164; 8,576,259; 8,593,396; 8,605,032; 8,643,595; 8,665,206; 8,681,191; 8,730,153; 8,810,525; 8,928,562; 8,928,641; 8,976,444; 9,013,394; 9,019,197; 9,019,198; 9,019,318; 9,082,352; 9,171,508; 9,218,773; 9,224,338; 9,224,342; 9,224,344; 9,230,492;9,251,736; 9,262,973; 9,269,311; 9,299,294; 9,373,289; 9,390,066; 9,390,661; and 9,412,314; and U.S. Patent Application Publication Nos. 2003 / 0102858; 2004 / 0246562; 2005 / 0253777; 2007 / 0091418; 2007 / 0103427; 2007 / 0176912; 2008 / 0024429; 2008 / 0024482; 2008 / 0136774; 2008 / 0291129; 2008 / 0303780; 2009 / 0174651; 2009 / 0195568; 2009 / 0322721; 2010 / 0194733; 2010 / 0194789; 2010 / 0220121; 2010 / 0265561; 2010 / 0283804; 2011 / 0063314; 2011 / 0175875; 2011 / 0193840; 2011 / 0193841; 2011 / 0199671; 2011 / 0221740; 2012 / 0001957; 2012 / 0098740; 2013 / 0063333; 2013 / 0194250; 2013 / 0249782; 2013 / 0321278; 2014 / 0009817; 2014 / 0085355; 2014 / 0204012; 2014 / 0218277; 2014 / 0240210; 2014 / 0240373; 2014 / 0253425; 2014 / 0292830; 2014 / 0293398; 2014 / 0333685; 2014 / 0340734; 2015 / 0070744; 2015 / 0097877; 2015 / 0109283; 2015 / 0213749; 2015 / 0213765; 2015 / 0221257; 2015 / 0262255; 2015 / 0262551; 2016 / 0071465; 2016 / 0078820; 2016 / 0093253; 2016 / 0140910; and 2016 / 0180777;

[0021] (i) Applications of displays; see, for example, U.S. Patent Nos. 7,312,784 and 8,009,348; and

[0022] (j) Non-electrophoretic displays, as described in U.S. Patent No. 6,241,921 and U.S. Patent Application Publication No. 2015 / 0277160; and U.S. Patent Application Publication Nos. 2015 / 0005720 and 2016 / 0012710.

[0023] Many of the aforementioned patents and applications recognize that the walls surrounding discrete microcapsules in an encapsulated electrophoretic medium can be replaced by a continuous phase, thereby producing a so-called polymer dispersion electrophoretic display, wherein the electrophoretic medium comprises a plurality of discrete droplets of electrophoretic fluid and a continuous phase of polymeric material, and the discrete droplets of electrophoretic fluid within such a polymer dispersion electrophoretic display can be considered as capsules or microcapsules, even without a discrete capsule film associated with each individual droplet; see, for example, U.S. Patent No. 6,866,760. Therefore, for the purposes of this application, such polymer dispersion electrophoretic media are considered a subclass of encapsulated electrophoretic media.

[0024] One related type of electrophoretic display is the so-called "microcell electrophoretic display." In a microcell electrophoretic display, charged particles and fluids are not encapsulated within microcapsules, but rather held within multiple cavities formed within a carrier medium (typically a polymer film). See, for example, U.S. Patent Nos. 6,672,921 and 6,788,449.

[0025] While electrophoretic media are typically opaque (because, for example, in many electrophoretic media, particles essentially block visible light from passing through the display) and operate in reflective mode, many electrophoretic displays can be fabricated to operate in a so-called "shutter mode," in which one display state is substantially opaque and the other is transmissive. See, for example, U.S. Patent Nos. 5,872,552; 6,130,774; 6,144,361; 6,172,798; 6,271,823; 6,225,971; and 6,184,856. Dielectrophoretic displays, similar to electrophoretic displays but dependent on changes in electric field strength, can operate in a similar mode; see U.S. Patent No. 4,418,346. Other types of electro-optic displays are also capable of operating in shutter mode. Electro-optic media operating in shutter mode can be used in multilayer structures of full-color displays; in such structures, at least one layer adjacent to the viewing surface of the display operates in shutter mode to expose or hide a second layer further away from the viewing surface.

[0026] Encapsulated electrophoretic displays are generally free from the aggregation and sedimentation failure modes of conventional electrophoretic apparatus and offer more beneficial effects, such as the ability to print or coat displays on a variety of flexible and rigid substrates. (The term "printing" is used to include all forms of printing and coating, including but not limited to: pre-metering coating such as patch die coating, slot or extrusion coating, slide or stack coating, curtain coating; roller coating such as roller blade coating, forward and reverse roller coating; concave coating; dip coating; spraying; meniscus coating; spin coating; brush coating; air knife coating; screen printing; electrostatic printing; thermal printing; inkjet printing; electrophoretic deposition (see U.S. Patent No. 7,339,715); and other similar techniques.) Therefore, the resulting display can be flexible. Furthermore, because the display medium can be printed (using a variety of methods), the display itself can be manufactured inexpensively. Furthermore, as described in U.S. Patent Application Serial 17 / 088,762, the encapsulated electrophoretic medium can be incorporated into a non-planar surface, which in turn is incorporated into an everyday object. Therefore, when a suitable electric field is provided, the surface of products, building materials, etc., can be engineered to change color. Summary of the Invention

[0027] This paper discloses an improved method for driving an electrophoretic medium comprising at least four types of particles, each having different optical properties and each type of particle having a different combination of charge polarity and charge quantity. One embodiment of this electrophoretic medium is commercially known as Advanced Color Electronic Paper or ACEP®, but other suitable electrophoretic media are described herein, and the described method is generally applicable to four-particle (or more) electrophoretic systems. In one aspect, the method includes providing a continuous driving waveform for at least 500 ms, wherein the continuous driving waveform has at least 16 unique voltage levels within the 500 ms. The waveform result obtained during transitions is less “flash” or less noticeably glaring to the observer. The resulting waveform also allows for controlled transitions, which can be, for example, abrupt, smooth, ramp, or pulse / oscillation. In one embodiment, the waveform has a rate of change of no more than 3 V / ms within at least 500 ms, while the rate of change (second derivative) changes within -1 V / ms. 2 and 1V / ms 2Between. In one embodiment, the waveform includes at least 32 unique voltage levels within 500 ms. In one embodiment, the continuously driven waveform lasts for at least 1 second. In one embodiment, the at least four types of particles include two particles of a first polarity and two particles of a second polarity. In one embodiment, the at least four types of particles include three particles of a first polarity and one particle of a second polarity. In one embodiment, the optical property is color, the color being selected from the group consisting of white, red, magenta, orange, yellow, green, cyan, blue, purple, and black. In one embodiment, at least two types of particles include surface polymers, and each of the two types of particles has a different kind of surface polymer.

[0028] On the other hand, a method for driving an electrophoretic medium comprising at least four types of particles, wherein each particle has different optical properties and each type of particle has a different combination of charge polarity and charge quantity. The method includes providing a continuous driving waveform for at least 500 ms, wherein the continuous driving waveform as a function of time takes the form:

[0029]

[0030] Throughout the waveform, V(t) is the waveform voltage as a function of time, x is a representative value of time, and the waveform includes at least three voltage levels. In one embodiment, the continuously driven waveform lasts for at least 1 second. In one embodiment, the at least four types of particles include two particles of a first polarity and two particles of a second polarity. In one embodiment, the at least four types of particles include three particles of a first polarity and one particle of a second polarity. In one embodiment, the optical property is color, selected from the group consisting of white, red, magenta, orange, yellow, green, cyan, blue, purple, and black. In one embodiment, at least two types of particles include surface polymers, and each of the two types of particles has a different type of surface polymer.

[0031] On the other hand, a display system includes: a first transparent electrode; an electrophoretic medium comprising at least four types of particles, each particle having different optical properties and each type of particle having a different combination of charge polarity and charge amount; a second electrode, wherein the electrophoretic medium is disposed between the first transparent electrode and the second electrode; a controller; and a power supply operatively connected to the first transparent electrode and the second electrode and configured to provide at least 16 unique voltage levels, wherein the controller provides at least three unique voltage levels between the first transparent electrode and the second electrode when the electrophoretic medium changes from a first display state to a second display state. In one embodiment, the power supply provides at least two voltage levels differing by more than 20 volts. In one embodiment, the at least four types of particles comprise two particles of a first polarity and two particles of a second polarity. In another embodiment, the at least four types of particles comprise three particles of a first polarity and one particle of a second polarity. In one embodiment, the optical property is color, and the color is selected from the group consisting of white, red, magenta, orange, yellow, green, cyan, blue, purple, and black.

[0032] On the other hand, a method for determining a continuous waveform for driving an electrophoretic medium disposed between a first transparent electrode and a second electrode, the electrophoretic medium comprising at least four types of particles, wherein each type of particle has different optical properties and each type of particle has a different combination of charge polarity and charge quantity, the method comprising: determining a first optical state of the electrophoretic medium; determining a second optical state of the electrophoretic medium; backpropagating an iterative driving voltage of a frame width over a desired time span from the second optical state to the first optical state, while minimizing a cost function based on a differentiable substitution model of the electrophoretic medium between the first transparent electrode and the second electrode; and combining the iterative driving voltage of the frame width to generate a continuous waveform. In some embodiments, the cost function is:

[0033]

[0034] In some embodiments, the desired time span is at least 500ms, and the frame width is less than 50ms.

[0035] On the other hand, a method for determining a continuous waveform for driving an electrophoretic medium disposed between a first transparent electrode and a second electrode, the electrophoretic medium comprising at least four types of particles, wherein each type of particle has different optical properties and each type of particle has a different combination of charge polarity and charge quantity, the method comprising: determining a first optical state of the electrophoretic medium; determining a second optical state of the electrophoretic medium; backpropagating an iterative driving voltage of a frame width over a desired time span from the second optical state to the first optical state, wherein the transition between frames does not involve a voltage change greater than ±40V; and combining the iterative driving voltage to generate a continuous waveform. In one embodiment, the continuous waveform between the first optical state and the second optical state does not have a value less than -1V / ms. 2 or greater than 1V / ms 2 The change in the rate of change of voltage as a function of time. Attached Figure Description

[0036] Figure 1A This is a representative cross-section of a four-particle electrophoretic display, in which the electrophoretic medium is encapsulated in a capsule.

[0037] Figure 1B This is a representative cross-section of a four-particle electrophoretic display, in which the electrophoretic medium is encapsulated in microcells.

[0038] Figure 2A An exemplary equivalent circuit for a single pixel of an electrophoretic display using an active matrix backplane with storage capacitors is shown.

[0039] Figure 2B An exemplary equivalent circuit of a simplified electrophoretic display of the present invention is shown, wherein the power supply is configured to provide a number of voltage levels.

[0040] Figure 3A The preferred positions of each of the four groups of particles that produce eight standard colors in a white-cyan-magenta-yellow (WCMY) four-particle electrophoretic display are shown, where the white particles are reflective and the cyan, magenta and yellow particles are absorptive.

[0041] Figure 3B The preferred positions of each of the four groups of particles that produce eight standard colors in a black-red-yellow-blue (KRYB) four-particle electrophoretic display are shown, where the black particles are absorptive and the red, yellow and blue particles are reflective.

[0042] Figures 4A and 4B show simple push-pull waveforms (of the prior art) that can be used to achieve a specific color in an EPD system that includes one reflective (white) particle and three subtractive (cyan, yellow, magenta) particles.

[0043] Figure 5A The diagram illustrates the color space that can be defined for a four-particle electrophoresis system, and how the transition from the first color to the second color can proceed along more than one path.

[0044] Figure 5B It shows how a waveform can be iteratively backpropagated from a second optical state to a first optical state and then combined to produce a preferred waveform.

[0045] Figure 6A The diagram illustrates the predicted color transition from a first color state to a second color state as a function of continuous voltages transmitted across multiple frames in a WCMY EPD system, and... Figure 6B The experimental results of providing the predicted waveform to the system are shown.

[0046] Figure 7A The diagram illustrates the predicted color transition from a first color state to a second color state as a function of continuous voltages transmitted across multiple frames in a WCMY EPD system, and... Figure 7B The experimental results of providing the predicted waveform to the system are shown.

[0047] Figure 8A The diagram illustrates the predicted color transition from a first color state to a second color state as a function of continuous voltages transmitted across multiple frames in a WCMY EPD system, and... Figure 8B The experimental results of providing the predicted waveform to the system are shown. Detailed Implementation

[0048] This invention details a method for identifying enhanced continuous waveforms driving a multi-particle color electrophoretic medium having at least four different groups of electrophoretic particles, for example, where at least three groups of particles are colored and subtractive, and at least one particle is scattering / reflecting, or when at least three groups of particles are colored and reflective, and at least one particle is subtractive. Typically, such systems include reflective white particles and subtractive primary color particles of cyan, yellow, and magenta, or reflective red, yellow, and blue particles and absorbing black particles. Of course, optional color selection can be used by choosing appropriate primary colors. Furthermore, the method for developing continuous waveforms for driving such multi-particle systems can be applied to electrophoretic display systems that include more types of particles, such as five-particle, six-particle, seven-particle, and eight-particle systems.

[0049] Continuous voltage waveforms possess a unique property of tunable transition appearance not found in traditional push-pull or square pulse-based waveforms. This is particularly important for applications where the controller has many available voltage levels (high bit depth) and where the transition appearance and final color are extremely critical. Access to trace colors within the model allows for the combination of complex, differentiable costs associated with color states.

[0050] Methods for fabricating electrophoretic displays comprising four (or more) particles have been discussed in the prior art. Electrophoretic fluid can be encapsulated in microcapsules or incorporated into a microcell structure subsequently sealed with a polymer layer. The microcapsules or microcell layers can be coated or laminated onto a plastic substrate or film with a transparent coating of a conductive material. Alternatively, microcapsules can be coated onto a transparent substrate or other electrode material using a spraying technique. (See U.S. Patent No. 9,835,925, which is incorporated herein by reference). The resulting assembly can be laminated to a backplane carrying pixel electrodes using a conductive adhesive. Alternatively, the assembly can be attached to one or more segmented electrodes on the backplane, wherein the segmented electrodes are directly driven. In another embodiment, an assembly comprising a non-planar transparent electrode material can be sprayed with a capsule and then covered with a back electrode material. (See U.S. Patent Application Serial No. 17 / 088,762). Alternatively, electrophoretic fluid can be directly dispensed onto a thin, open-cell grid already arranged on a backplane comprising an active matrix of pixel electrodes. The filled grid can then be top-sealed using an integrated protective sheet / transparent electrode.

[0051] Electrophoretic displays typically comprise an electrophoretic material layer and at least two other layers disposed on opposite sides of the electrophoretic material, one of which is an electrode layer. In most such displays, both layers are electrode layers, and one or both of the electrode layers are patterned to define pixels in the display. For example, one electrode layer may be patterned as elongated row electrodes, while the other electrode layer may be patterned as elongated column electrodes extending perpendicularly to the row electrodes, with pixels defined by the intersections of the row and column electrodes. Alternatively, and more commonly, one electrode layer may have the form of a single continuous electrode, while the other electrode layer is patterned as a matrix of pixel electrodes, each pixel electrode defining one pixel of the display. In another type of electrophoretic display, intended for use with movable electrodes separate from the display, such as styluses, printheads, or similar devices, only one layer adjacent to the electrophoretic layer includes electrodes, and the layers on opposite sides of the electrophoretic layer are typically protective layers to prevent damage to the electrophoretic layer by the movable electrodes.

[0052] The electrophoretic medium used herein includes charged particles that vary in color, reflectance or absorption properties, charge density, and mobility (measured as electromotive force) in an electric field. Particles that absorb, scatter, or reflect light over a broad band or at selected wavelengths are referred to herein as colored or pigment particles. Various materials other than light-absorbing or light-reflecting pigments (the term strictly refers to insoluble colored materials), such as dyes or photonic crystals, can also be used in the electrophoretic medium and display of the present invention. For example, the electrophoretic medium may include a fluid, a plurality of first particles and a plurality of second particles dispersed in the fluid, the first and second particles carrying opposite charges, the first particles being light-scattering particles, the second particles having one of the subtractive primary colors, and a plurality of third particles and a plurality of fourth particles dispersed in the fluid, the third and fourth particles carrying opposite charges, each having a subtractive primary color different from and different from that of the second particles, wherein the electric field required to separate aggregates formed by the third and fourth particles is greater than the electric field required to separate aggregates formed by any other two types of particles.

[0053] The electrophoretic medium of the present invention may contain any additives used in prior art electrophoretic media, such as those described in the aforementioned patents and applications of Einkel and MIT. Thus, for example, the electrophoretic medium of the present invention typically includes at least one charge control agent to control the charge on various particles, and the fluid may have a polymer dissolved or dispersed therein, the polymer having a number-average molecular weight greater than about 20,000, and the polymer being substantially non-adsorbed onto the particles to improve the bistability of the display, as described in the aforementioned U.S. Patent No. 7,170,670.

[0054] In one embodiment, the present invention uses one light-scattering particle (typically white) and three substantially non-light-scattering particles. Of course, there are no completely light-scattering particles or completely non-light-scattering particles, and the minimum light scattering level of the light-scattering particles used in the electrophoresis of the present invention, as well as the maximum permissible light scattering level in the substantially non-light-scattering particles, can vary depending on several factors, such as the exact pigments used, their colors, and the user's or application's tolerance for certain deviations from the desired color. The scattering and absorption properties of the pigments can be evaluated by measuring the diffuse reflectance of a pigment sample dispersed in a suitable matrix or liquid against white and dark backgrounds. The results from these measurements can be interpreted according to several models known in the art, such as the one-dimensional Kubelka-Munk process. In the present invention, when the pigment is approximately isotropically distributed at 15% volume in a 1µm thick layer comprising the pigment and a liquid with a refractive index less than 1.55, the white pigment preferably exhibits at least 5% diffuse reflectance measured against a black background at 550 nm. Preferably, under the same conditions, yellow, magenta, and cyan pigments exhibit diffuse reflectance of less than 2.5% measured against a black background at 650, 650, and 450 nm, respectively. (The wavelengths selected above for measuring yellow, magenta, and cyan pigments correspond to the spectral regions of minimum absorption for these pigments). Colored pigments that meet these criteria are referred to below as “non-scattering” or “substantially non-light-scattering.” Specific examples of suitable particles are disclosed in U.S. Patent No. 9,921,451, which is incorporated herein by reference.

[0055] Alternative particle groups may also be used, comprising four groups of reflective particles, or an absorbing particle having three or four different groups of reflective particles, i.e., as described in U.S. Patents 922,603 ​​and 10,032,419, which are incorporated herein by reference. For example, white particles may be formed from inorganic pigments such as TiO2, ZrO2, ZnO, Al2O3, Sb2O3, BaSO4, PbSO4, etc., while black particles may be formed from CI Pigment Black 26 or 28, etc. (e.g., manganese ferrite black spinel or copper chromite black spinel) or carbon black. The third / fourth / fifth type particles may be colors such as red, green, blue, magenta, cyan, or yellow. Pigments of this type of particle can include, but are not limited to, CI pigments PR254, PR122, PR149, PG36, PG58, PG7, PB28, PB15:3, PY138, PY150, PY155, or PY20. Specific examples include Clariant Hostaperm Red D3G 70-EDS, Hostaperm Pink E-EDS, PV fast red D3G, Hostapermred D3G 70, Hostaperm Blue B2G-EDS, Hostaperm Yellow H4G-EDS, Hostaperm Green GNX, BASF Irgazine red L 3630, Cinquasia Red L 4100 HD, and Irgazin Red L 3660HD; Sun Chemical Phthalocyanine Blue, Phthalocyanine Green, Diaryl Yellow, or Diaryl AAOT Yellow.

[0056] like Figure 1A and Figure 1BAs shown, electrophoretic displays (101, 102) typically include a top transparent electrode 110, an electrophoretic medium 120, and a bottom electrode 130, the bottom electrode 130 typically being a pixel electrode of an active matrix of pixels controlled by thin-film transistors (TFTs). However, and particularly for the displays of the present invention, the bottom electrode 130 may be a single, larger electrode, such as a graphite backing, a PET / ITO film, a metallized film, or a conductive coating. In the electrophoretic medium 120 described herein, there are four different types of particles 121, 122, 123, and 124, but more particle groups may be used with the methods and displays described herein. The electrophoretic medium 120 is typically separated by the walls of microcapsules 126 or microcells 127. An optional adhesive layer 140 may be disposed adjacent to any layer; however, it is typically adjacent to the electrode layers (110 or 130). In a given electrophoretic display (105, 106), there may be more than one adhesive layer 140, but a single layer is more common. The entire display stack is typically disposed on a substrate 150, which may be rigid or flexible. The displays (101, 102) typically also include a protective layer 160, which may simply protect the top electrode 110 from damage, or it may enclose the entire display (101, 102) to prevent water ingress, etc. The electrophoretic displays (101, 102) may also include a sealing layer 180 if necessary. In some embodiments, the adhesive layer 140 may include a primer component to improve adhesion to the electrode layer 110, or a separate primer layer may be used ( Figure 1B (Not shown in the image). The structure and components of the electrophoretic display, pigments, binders, electrode materials, etc., are described in numerous patents and patent applications published by Einkel, such as US 6,922,276; 7,002,728; 7,072,095; 7,116,318; 7,715,088; and 7839564, the entire contents of which are incorporated herein by reference.

[0057] In some embodiments, such as Figure 1AAs shown, an electrophoretic display may consist only of a first transparent electrode, an electrophoretic medium, and a second (back) electrode, which may also be transparent. However, to produce a high-resolution display, for example, for displaying images, individual pixels are used to control the colors on the image. Of course, each pixel must be addressable and unaffected by neighboring pixels to faithfully reproduce the image file in the display. One way to achieve this is to provide an array of nonlinear elements, such as transistors or diodes, having at least one nonlinear element associated with each pixel to produce an "active matrix" display. The addressing or pixel electrode of a pixel is connected to a suitable voltage source via the associated nonlinear element. Typically, when the nonlinear element is a transistor, the pixel electrode is connected to the drain of the transistor, and this arrangement will be assumed in the following description, although it is essentially arbitrary, and the pixel electrode may be connected to the source of the transistor. Typically, in a high-resolution array, pixels are arranged in a two-dimensional array of rows and columns such that any particular pixel is uniquely defined by the intersection of a particular row and a particular column. The sources of all transistors in each column are connected to a single column electrode, while the gates of all transistors in each row are connected to a single row electrode; similarly, the source-to-row and gate-to-column assignments are conventional but essentially arbitrary and can be reversed if needed. Row electrodes are connected to row drivers, which essentially ensures that only one row is selected at any given time; that is, a selection voltage is applied to the selected row electrode to ensure that all transistors in the selected row are turned on, while a non-selection voltage is applied to all other rows to ensure that all transistors in these non-selected rows remain off. Column electrodes are connected to column drivers, which apply selected voltages to different column electrodes to drive the pixels in the selected row to their desired optical state. (The aforementioned voltages are relative to a common front electrode typically set on the side of the electro-optic medium opposite to the nonlinear array and extending across the entire display). After a preselection interval called the “line address time,” the selected row is deselected, the next row is selected, and the voltage on the column driver is changed to write the next row to the display. This process is repeated so that the entire display is written line by line. The time between addressing in the display is called a “frame.” Therefore, a display that updates at 60Hz has a frame rate of 16 milliseconds.

[0058] However, frames are not limited to use with active matrix backplanes, and many of the drive waveforms described herein are described using frames as the unit of time. While the electrophoretic medium can be driven with analog voltage signals generated, for example, by power supplies and potentiometers, the use of digital controllers discretizes the waveforms into blocks typically on the order of 10 ms, but shorter or longer frame widths are possible. For example, frames can be 0.5 ms or longer, such as 1 ms, 5 ms, 10 ms, 15 ms, 20 ms, 30 ms, or 50 ms. In most cases, frames are less than 100 ms, such as 250 ms, 200 ms, 150 ms, or 100 ms. In most applications described herein, frame widths are between 10 ms and 30 ms. Suitable controllers are available from suppliers such as Digi-Key and other electronic component vendors.

[0059] In conventional electrophoretic displays using an active matrix backplane, each pixel electrode has an associated capacitor electrode (storage capacitor), such that the pixel electrode and the capacitor electrode form a capacitor; see, for example, International Patent Application WO01 / 07961. In some embodiments, N-type semiconductors (e.g., amorphous silicon) can be used to form transistors, and the “select” and “non-select” voltages applied to the gate electrode can be positive and negative voltages, respectively.

[0060] The attached diagram Figure 2A An exemplary equivalent circuit for a single pixel of an electrophoretic display is shown. As shown, the circuit includes a capacitor 10 formed between a pixel electrode and a capacitor electrode. The electrophoretic dielectric 20 is represented as a capacitor and a resistor connected in parallel. In some cases, the direct or indirect coupling capacitance 30 between the gate of the transistor associated with the pixel and the pixel electrode (often referred to as "parasitic capacitance") can introduce unwanted noise into the display. Typically, the parasitic capacitance 30 is much smaller than the capacitance of the storage capacitor 10, and when a pixel row of the display is selected or deselected, the parasitic capacitance 30 can cause a small negative offset voltage, also known as a "recoil voltage," to be generated at the pixel electrode, which is typically less than 2 volts. [In some embodiments, to compensate for the unwanted "recoil voltage," a common potential V can be used.] com Provided to the top-plane electrode and capacitor electrode associated with each pixel, so that when V com Set to the reverse voltage (V) KBWhen the values ​​are equal, each voltage supplied to the display can be offset by the same amount and will not experience a net DC imbalance. It has been found that classifying the pigments of a four-particle system into suitable configurations to produce the driving waveforms for these colors requires at least five voltage levels (high positive, low positive, zero, low negative, high negative). For more details, see U.S. Patent Application Serial No. 17 / 088,762. However, as described below, a wider range of colors and variations of color transitions can be achieved when using a continuous range of voltage levels (or approximations) to drive such a four-particle system.

[0061] Figure 2A The equivalent circuit represents the "typical" way to drive a four-particle electrophoresis system, especially when used to display high-resolution images such as photographs and text. However, simpler methods are also possible. Figure 2B The equivalent circuit shown drives the electrophoretic medium. This simple circuit simply represents a voltage source coupled to a first electrode adjacent to the electrophoretic medium and a second electrode grounded on the other side of the electrophoretic medium. If the voltage source can provide any arbitrary voltage waveform, this simple circuit can produce any possible display color, and any possible transitions between display colors. Figure 2A Similarly, the electrophoretic dielectric 20 itself can be represented as a capacitor and resistor connected in parallel. Of course, the second electrode itself does not need to be grounded; rather, it can be set at any voltage level. Appropriate voltages capable of providing arbitrary waveforms can be obtained from Tektronix, but in many cases, combining the power supply with a digital controller is more economical and efficient.

[0062] like Figure 3A As shown, in an example of a four-particle system comprising subtractive cyan, yellow, and magenta particles paired with reflective white particles, each of the eight primary colors (red, green, blue, cyan, magenta, yellow, black, and white) corresponds to a different arrangement of the four pigments. For example, for an advanced color electronic paper (ACeP) display, the three particles providing the three subtractive primary colors can be substantially non-scattering (“SNLS”). The use of SNLS particles allows for color mixing and provides more color results than the same number of scattering particles could achieve. These thresholds must be sufficiently separated relative to the voltage drive level to avoid crosstalk between particles, and this separation requires the use of high addressing voltages for certain colors. Furthermore, addressing the colored particle with the highest threshold also moves all other colored particles, which must then be switched to their desired positions at lower voltages.

[0063] like Figure 3A As shown, this system is, in principle, similar to printing on bright white paper, because the observer only sees the colored pigments on the observation side of the white pigment (i.e., the pigments that only scatter light). Figure 3AIn this embodiment, it is assumed that the viewing surface of the display is at the top (as shown in the figure), i.e., the user views the display from that direction, and light is incident from that direction. As already noted, in a preferred embodiment, only one of the four particles used in the electrophoretic medium of the invention substantially scatters light, and... Figure 3A It is assumed that the particle is a white pigment. The light scattering of the white particle forms a white reflector, and any particles above the white particle (such as...) Figure 3A All of the light (as shown) can be seen through this white reflector. Light entering the viewing surface of the display passes through these particles, is reflected from the white particles, returns through these particles, and exits from the display. Therefore, the particles above the white particles can absorb various colors, and the color presented to the user is the color produced by the combination of the particles above the white particles. Any particles arranged below the white particles (behind them from the user's perspective) are obscured by the white particles and do not affect the displayed color. Because the second, third, and fourth particles are essentially non-light-scattering, their order or arrangement relative to each other is not important, but for the reasons already noted, their order or arrangement relative to the white (light-scattering) particles is crucial.

[0064] More specifically, when cyan, magenta, and yellow particles are located below white particles ( Figure 3A In case [A], there are no particles above the white particles, and the pixels simply display white. When a single particle is above a white particle, the color of that single particle is... Figure 3A In cases [B], [D], and [F], the colors are yellow, magenta, and cyan, respectively. When two particles are positioned above a white particle, the displayed color is a combination of the colors of those two particles; Figure 3A In case [C], magenta and yellow particles appear red; in case [E], cyan and magenta particles appear blue; and in case [G], yellow and cyan particles appear green. Finally, when all three colored particles are above a white particle ( Figure 3A In the case of [H], all incident light is absorbed by the three subtractive primary color particles, and the pixel displays black.

[0065] exist Figure 3B The image shows an optional particle group using reflective color particles. Figure 3B In this embodiment, the reflective particles are red, yellow, and blue; however, optional color groups can be used if the color combination appropriately spans the useful color spectrum. Figure 3B In this system, the color observed on the surface is due to the direct reflection of colored particles, and an absorbing black layer is typically placed between the displayed and undisplayed particles to preserve color accuracy as much as possible. Because the observer is viewing light that primarily interacts with only one pigment surface, the color is perceived as... Figure 3BThe system produces images that appear more saturated. However, using... Figure 3B The overall color gamut of the system is reduced because it becomes difficult to achieve fine control over the amount of specific particles that are mixed together to produce secondary colors (such as orange, green, and purple). In applications such as digital signage, saturation is often more important than color gamut, and many users are satisfied with a set of eight "standard" colors.

[0066] Different combinations of light-scattering and light-absorbing particle groups are also possible. For example, a subtractive primary color can be represented by particles that scatter light, such that the display would include two types of light-scattering particles, one of which would be white and the other colored. However, in this case, the position of the light-scattering colored particles relative to other colored particles covering the white particles will be important. For example, when displaying black (when all three colored particles are above the white particles), the scattering colored particles cannot be above the non-scattering colored particles (otherwise they would be partially or completely hidden behind the scattering particles, and the color displayed would be the color of the scattering colored particles, not black). Of course, if more than one type of colored particle scatters light without the presence of absorbing black particles, it is not easy to render the color as black.

[0067] Figure 3A and 3B This illustrates the ideal situation where the color is not contaminated (i.e., the light-scattering white particles completely cover the area). Figure 3A Any particle located behind a white particle, or obscured by light-absorbing black particles. Figure 3B (Light scattering particles that should not be visible in the light). In reality, the masking of white particles may be imperfect; therefore, particles that would ideally be completely blocked may absorb a small amount of light. This contamination typically reduces the brightness and chromaticity of the presented colors. Figure 3B In some cases, the presence of light-absorbing particles often makes the overall image appear darker due to the incomplete scattering by reflective particles. Furthermore, because it is difficult to design pigments with precisely equidistant spacing across the color spectrum, Figure 3B Combinations of colors, such as orange, green, and purple, may not achieve the desired color. This is particularly problematic for green, as the human eye is highly sensitive to different shades of green, while different shades of red are less noticeable. In some embodiments, this can be corrected by including additional particles with different spatial or charge properties (e.g., green scattering particles), but the addition of these particles complicates the driving scheme and may require a wider range of driving voltages. Clearly, in the electrophoretic media described herein, this color contamination should be minimized to the extent that the resulting color is comparable to industry standards for color reproduction. A particularly advantageous standard is SNAP (the standard for newspaper advertising production), which specifies the values ​​of L*, a*, and b* for each of the eight primary colors mentioned above.

[0068] The waveforms used to drive the four-particle electrophoretic medium have been described previously, but they differ significantly from the waveforms of this invention. A set of waveforms for driving a color electrophoretic display with four particles is described in U.S. Patent No. 9,921,451, which is incorporated herein by reference. Most commercial electrophoretic displays use amorphous silicon-based thin-film transistors (TFTs) in the construction of an active matrix backplane (202 / 024) due to the wider availability of manufacturing equipment and the cost of various raw materials. Amorphous silicon TFTs become unstable when a gate voltage that would allow switching above approximately + / - 15V is provided. Therefore, as described in previous patents / applications for such systems, improved performance is achieved by additionally changing the bias voltage of the top transparent electrode relative to the bias voltage on the backplane pixel electrodes—a known top-side switching technique. Thus, if a voltage of +30V (relative to the backplane) is required, the top surface can be switched to -15V while the appropriate backplane pixel is switched to +15V. A method for driving a four-particle electrophoresis system with top-side switching is described in more detail, for example, in U.S. Patent No. 9,921,451.

[0069] In previous embodiments of Advanced Color Electronic Paper (ACeP), waveforms (voltage versus time curves) of the pixel electrodes applied to the backplane of the display of the present invention were described and plotted, assuming the front electrode is grounded (i.e., at zero potential). Of course, the electric field experienced by the electrophoretic medium is determined by the potential difference between the backplane and the front electrode and the distance separating them. Displays are typically observed through their front electrode, such that particles adjacent to the front electrode control the colors displayed by the pixels, and the optical transitions involved are sometimes easier to understand if the potential of the front electrode relative to the backplane is taken into account; this can be achieved by simply reversing the waveforms discussed below. Two exemplary waveforms of this type are shown in Figures 4A and 4B, which correspond to U.S. Patent No. 9,921,451. Figure 7A and 7B It is worth noting that, according to the general mathematical definition of continuity, these types of "push-pull" waveforms are not continuous. That is, when the waveform flips from push to pull (see the dashed circle), the waveform does not satisfy the expression of Equation 1:

[0070] (1)

[0071] Where V(t) is the waveform voltage as a function of time, and x is a representative value of time. Since a frame is a unit of time, the time axis can be replaced by the number of frames, as shown in Figures 4A and 4B. To some extent, the shape of the push-pull waveform is an artifact of the physical structure used to drive the electrophoretic dielectric. That is, because AM-TFTs only provide a limited range of driving voltages, the waveform must be constructed within those constraints. Although considerable effort has been made to optimize such waveforms, they often exhibit noticeable jitter due to the abrupt switching of voltage polarity.

[0072] In theory, there is no need to use discontinuous drive waveforms. Especially when the voltage across the dielectric is controlled independently (see...). Figure 2A Furthermore, there are fewer restrictions on the number of voltage levels and the length of updates, resulting in virtually an infinite number of different ways to transition from the first color to the second. Therefore, specific transition "styles" can be selected; for example, very slow transitions, very sharp transitions, or transitions that oscillate between colors or establish a transition for a specific color. Figure 5A As shown, the full color space can be obtained using a four-particle system comprising reflective white particles and subtractive particles of cyan, yellow, and magenta. For normalization, corresponding to... Figure 3A The vertices of the color space are labeled with commonly used RGB values, namely [255, 0, 0], [0, 255, 0], [0, 0, 255], [0, 255, 255], [255, 0, 255], [255, 255, 0], [255, 255, 255], and [0, 0, 0]. Therefore, any color transition from the first color to the second color can be visualized as a series of paths from beginning to end within that color space, i.e., as shown below. Figure 5A As shown.

[0073] The voltage response of a display ultimately depends on the type of electrophoretic dielectric, the capacitance and resistance of the electrophoretic layers (see [link]). Figure 2A ) and various other external functions (such as ambient temperature and the spectrum of incident light) If the color space is entirely composed of The description suggests that a new waveform can be constructed along one or more paths between the first and second color states, such as... Figure 5A As shown. Furthermore, as... Figure 5B As shown, you can query The derivative of the target color is used to derive the continuous voltage waveform by backpropagating from the target color back to the starting color. This step can be mathematically described by the following problem statement:

[0074] (2)

[0075] Of course, there are many solutions to equation (2), some of which are very expensive (due to the time required for system updates or wear), and some do not reflect the physical reality of the final display. The goal is to identify the waveform that achieves the target optical state with an acceptable number of flickers, duration, etc. This is a difficult optimization problem because the inversion process is asymmetric; for each V(t), there exists a unique optical state, but for each optical state, there exists a multiple / infinite list of input voltages. The inverse problem is described here in the context of a continuous voltage waveform, i.e., from the desired optical state to the voltage list (i.e., the waveform).

[0076] (3)

[0077] (4)

[0078] The cost function of equation (4) represents the target color and model as a function of the input voltage list V(t) in any high-dimensional space. Let be the Euclidean distance between the output colors, where i is the output dimension. This can be used to calculate the partial derivative, as follows:

[0079] (5)

[0080] (6)

[0081] in This represents the partial derivative with respect to the i-th frame in the list. This partial derivative can be used to calculate iteratively. The voltage is updated until convergence. This process leads to local minima of the waveform utilizing any voltage within a certain range. Boundary conditions can be used to prevent the voltage from being updated beyond a predefined range. or To apply. As described in this article, in to The swing between values ​​is typically 50V, but it can be higher. As with any misalignment inversion problem that requires inverting a many-to-one mapping, this initial condition becomes a sensitivity point. Therefore, the process is parallel, starting from many different random initial positions (in this case, different v(t)) and applying gradient descent to each of these signals to generate many candidate waveforms for downstream manual or algorithmic downselection.

[0082] Finally, the waveform needs to be parsed into frames for digital storage and execution, such as by a voltage controller. While the waveform can be of arbitrary length, it is typically on the order of 500 milliseconds to 5 seconds, for example, 1 second. The frame size can be appropriately adjusted depending on the time frame required for the transition. For use on a controller, these voltages can be discretized to match the available bit depth, although this method is practically suitable for applications where the provided bit depth is sufficient to remove large quantization artifacts (i.e., greater than 8 bits). However, in most cases, a 4-bit depth (16 voltage levels) is sufficient, while 32 or more voltage levels improve the correlation between the calculated final color state and the actual final color state. When the current through the device is... Given a current output, the controller should be able to support the frequency required by the waveform of the driven display. For most applications, a rate of change of less than 3V / ms is sufficient. Furthermore, to achieve a smooth transition, the rate of change of the update rate (i.e., the second derivative of the function) is preferably within -1V / ms. 2 and 1V / ms 2 Between, i.e., not less than -1V / ms 2 and not greater than 1V / ms 2 .

[0083] The preferred way to establish the color space function is to use a differential model, which is an alternative model to represent the final display structure. A specific electrophoretic display structure can be represented by a transfer function, in its simplest form:

[0084] O (7)

[0085] in The optical state is a function of time, and f is a function of time of the voltage applied to the display, given some initial states of the system at t=0. Additional inputs can be specified here, including but not limited to temperature, relative humidity, and incident spectrum. The function f can be estimated using various methods, such as an "ab initio" model built from component measurements. Suitable models can be constructed relatively inexpensively; however, the accuracy of the function will depend on the ability to account for nonlinear interactions between particle groups and vesicle-or micro-unit-wall-particle interactions. In some embodiments, illumination using a simulated spectrum from the sun to select arbitrary operating conditions, such as 20°C and 50% relative humidity, is sufficient. However, the value of the model decreases when the application of the electrophoretic medium deviates from such ideal conditions. Furthermore, for an alternative model to be differentiable, it must be a continuous (and reversible) function of voltage and time. However, hysteresis has been found in some four-particle systems, but if the hysteresis is not too severe, averaging only the backward and forward paths is sufficient to realize the function f.

[0086] Example

[0087] Examples of continuous voltage waveforms are in Figure 6A , 6B As shown in 7A, 7B, 8A, and 8B. A microencapsulated electrophoretic medium comprising reflective white particles and three subtractive (C, M, Y) particles is disposed between a PET-ITO layer and a graphite backing plate on glass. Top and bottom electrodes are coupled to a dedicated controller (LUCY™ controller from Einck Corporation), which is computer-programmable and generates at least 256 unique voltage levels between 0 and 50V. The display is mounted on the stage of a spectrophotometric optical measurement apparatus of the type described in the literature. (See D. Hertel, “Application of the Optical Measurement Methodologies of IEC and ISO Standards to Reflective E-Paper Displays,” Society for Information Display, International Symposium Digest of Technical Papers, Volume 49, issue 1, pages 161-164 (May 2018), which is incorporated herein by reference). Figure 6A , 7A As shown in Figure 8A, a series of measurements are used to build a training model, and the final training model is sufficient to predict the display color of a specific waveform. Figure 6A , 6B The image-driven panels of 7A, 7B, 8A, and 8B roughly show the color state observed at each frame. Figure 6B , 7B The waveform (frames 0 and 8B) and the progression from the first state (frame 0) to the second state (frame 85) as a function of the frame number. Since the total waveform is 2 seconds, each frame is approximately 20µs. The actual waveform is represented by black lines. Figure 6B In the diagram, the cyan, magenta, and yellow lines represent the relative positions of these colored particle groups with respect to the viewing side of the display (see [reference]). Figure 3A In reality, the "voltage" values ​​of the cyan, magenta, and yellow lines represent the relative positions between the top (observation) electrode and the opposing electrode below the electrophoretic medium. Larger positive voltages are closer to the observation surface, while larger negative voltages are furthest from it. The cyan, magenta, and yellow lines are not waveforms.

[0088] As shown in measurement tracks 6B, 7B, and 8B, when the predicted waveform is executed on the actual display, the final state is (approximately) reached in each case, and the entire transition is very close to the predicted value. Figure 6BIt exhibits a sharp optical transition. Figure 7B It shows a smooth optical transition, and Figure 8B The waveform exhibits an oscillating transition with an irregular period. Therefore, this new waveform structure at least performs a standard push-pull drive, with the advantage of a different transition appearance, which may be considered more pleasant or desirable for a particular application.

[0089] Several aspects and embodiments of the technology described in this application have been described. It should be understood that various changes, modifications, and improvements will readily occur to those skilled in the art. These changes, modifications, and improvements are intended to fall within the spirit and scope of the technology described herein. For example, various other means and / or structures for performing functions and / or obtaining results and / or one or more advantages described herein will readily occur to those skilled in the art, and each such change and / or modification is considered to be within the scope of the embodiments described herein. Those skilled in the art will recognize or be able to determine many equivalents of the specific embodiments described herein using only conventional experimentation. Therefore, it should be understood that the foregoing embodiments are presented by way of example only, and embodiments of the invention may be practiced in ways other than those specifically described within the scope of the appended claims and their equivalents. Furthermore, any combination of two or more features, systems, articles, materials, kits, and / or methods described herein, provided that such features, systems, articles, materials, kits, and / or methods do not contradict each other, is included within the scope of this disclosure.

Claims

1. A method for driving an electrophoretic medium comprising at least four types of particles, wherein, Each particle possesses distinct optical properties, and each type of particle has a distinct combination of charge polarity and charge quantity. The method includes: Provide a continuous voltage drive waveform of at least 500 ms, wherein the continuous voltage drive waveform has at least 16 unique voltage levels within the 500 ms, the continuous voltage drive waveform has a rate of change of no more than 3 V / ms within the at least 500 ms, and the rate of change is within -1 V / ms over time. 2 and 1V / ms 2 The changes between them.

2. The method according to claim 1, wherein, The continuous voltage drive waveform includes at least 32 unique voltage levels within 500ms.

3. The method according to claim 1, wherein, The at least four types of particles include two types of particles with a first polarity and two types of particles with a second polarity.

4. The method according to claim 1, wherein, The at least four types of particles include three particles of first polarity and one particle of second polarity.

5. The method according to claim 1, wherein, The optical property is color, and the color is selected from the group consisting of white, red, magenta, orange, yellow, green, cyan, blue, purple and black.

6. The method according to claim 1, wherein, At least two types of particles include surface polymers, and each of the two types of particles has a different kind of surface polymer.

7. A method for driving an electrophoretic medium comprising at least four types of particles, wherein, Each particle possesses distinct optical properties, and each type of particle has a distinct combination of charge polarity and charge quantity. The method includes: Provide a continuous voltage drive waveform of at least 500 ms, wherein the continuous voltage drive waveform, as a function of time, has the following form: ， Throughout the entire duration of the continuous voltage drive waveform, where V(t) is the waveform voltage as a function of time, x is a representative value of time, and where the continuous voltage drive waveform comprises at least three voltage levels, the continuous voltage drive waveform has a rate of change of no more than 3V / ms over at least 500ms, and the rate of change varies with time at -1V / ms 2 and 1V / ms 2 The changes between them.

8. The method according to claim 7, wherein, The continuous voltage drive waveform lasts for at least 1 second.

9. A display system, comprising: First transparent electrode; An electrophoretic medium comprising at least four types of particles, wherein each type of particle has different optical properties from one another, and each type of particle has a different combination of charge polarity and charge quantity from one another; The second electrode, wherein the electrophoretic medium is disposed between the first transparent electrode and the second electrode; A controller is configured to provide a continuous voltage drive waveform for at least 500 ms, wherein the continuous voltage drive waveform has at least 16 unique voltage levels within the 500 ms, the continuous voltage drive waveform has a rate of change of no more than 3 V / ms within the at least 500 ms, and the rate of change is within -1 V / ms over time. 2 and 1V / ms 2 Changes between; and A power supply, operably connected to the first light-transmitting electrode and the second electrode and configured to provide at least 16 unique voltage levels, wherein the controller provides at least three of the unique voltage levels between the first light-transmitting electrode and the second electrode when the electrophoretic medium changes from a first display state to a second display state.

10. The display system according to claim 9, wherein, It is configured to provide at least 32 unique voltage levels.

11. The display system according to claim 9, wherein, The power supply provides at least two voltage levels that are more than 20 volts apart.

12. The display system according to claim 9, wherein, The at least four types of particles include two types of particles with a first polarity and two types of particles with a second polarity.

13. The display system according to claim 9, wherein, The at least four types of particles include three particles of first polarity and one particle of second polarity.

14. The display system according to claim 9, wherein, The optical property is color, and the color is selected from the group consisting of white, red, magenta, orange, yellow, green, cyan, blue, purple and black.

15. A method for determining a continuous voltage waveform for driving an electrophoretic medium disposed between a first transparent electrode and a second electrode, said electrophoretic medium comprising at least four types of particles, wherein, Each type of particle has different optical properties and each type of particle has a different combination of charge polarity and charge quantity. The method includes: Determine the first optical state of the electrophoretic medium; Determine the second optical state of the electrophoretic medium; An iterative driving voltage of the frame width is backpropagated over a desired time span from the second optical state to the first optical state, while minimizing the cost function based on a differentiable substitution model of the electrophoretic medium between the first and second electrodes; and The iterative drive voltages, combined with the frame width, are used to generate a continuous voltage waveform.

16. The method according to claim 15, wherein, The cost function is: ， Among them, the cost function Represents a list of input voltages in any high-dimensional space. and initial optical state Differentiable substitution model of function Output color and target color The Euclidean distance between them, of which Indicates the output dimension. For time The function, and In order to be in The initial optical state of the electrophoretic medium.

17. The method according to claim 15, wherein, The desired time span is at least 500ms, and the frame width is less than 50ms.

18. A method for determining a continuous voltage waveform for driving an electrophoretic medium disposed between a first transparent electrode and a second electrode, the electrophoretic medium comprising at least four types of particles, wherein, Each type of particle has different optical properties and each type of particle has a different combination of charge polarity and charge quantity. The method includes: Determine the first optical state of the electrophoretic medium; Determine the second optical state of the electrophoretic medium; An iterative drive voltage of the frame width is backpropagated over a desired time span from the second optical state to the first optical state, wherein the transition between frames does not involve a voltage change greater than ±40V; and The iterative driving voltages are combined over a desired time span between the first optical state and the second optical state to generate a continuous voltage waveform, wherein the desired time span is at least 500 ms and the continuous voltage waveform has a rate of change of no more than 3 V / ms over at least 500 ms.

19. The method according to claim 18, wherein, The continuous voltage waveform between the first optical state and the second optical state does not have a value less than -1V / ms. 2 or greater than 1V / ms 2 The change in the rate of change of voltage as a function of time.

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