Driving methods for a variable light transmission device

11579510 · 2023-02-14

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Inventors

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Abstract

A variable light transmission device has at least one layer of electrophoretic medium comprising charged particles. Application of a an electric field having a waveform formed by a superposition of a carrier and a modulator waveform enables the switching of the device from a closed state to an open state, wherein the open state has higher light transmission than the closed state. As a result, the device enables the selection of the desired optical state by the user.

Claims

1. A method of operating a variable light transmission device, the method comprising: providing the variable light transmission device comprising at least one electrophoretic medium layer comprising a plurality of discrete droplets of electrophoretic medium comprising charged particles in a suspending fluid, each droplet being present in a polymer-dispersed medium or within capsules or within microcells, each droplet being surrounded by walls, the walls including lateral walls, wherein the electrophoretic medium layer is disposed between two electrodes; applying an electric field across the electrophoretic medium layer via application of a driving waveform that causes movement of the charged particles to the lateral walls of the droplets, resulting in aggregation of the charged particles to the lateral walls of the droplets, the variable light transmission device switching from an initial optical state to a final optical state, wherein the driving waveform is applied from a start until a completion of the application of the driving waveform, wherein the time from the start until the completion of the application of the driving waveform is a total driving time, wherein the final optical state has higher percent light transmission than the initial optical state, wherein the driving waveform is a superposition of a carrier waveform and a modulator waveform, wherein the carrier waveform has amplitude V.sub.1 and frequency ω.sub.1, wherein the modulator waveform has initial amplitude V.sub.2 and frequency ω.sub.2, wherein V.sub.1 is of from about 30 V to about 180 V, ω.sub.1 of from about 50 Hz to about 1000 Hz, wherein V.sub.2 is of from about 3 V to about 60 V, ω.sub.2 is from about 0.1 Hz to about 10 Hz, wherein V.sub.1 is greater than V.sub.2 and on is greater than ω.sub.2, and wherein the amplitude of the modulator waveform is variable and is reduced from an initial amplitude value the start of the application of the driving waveform to the variable light transmission device to a final amplitude value at the completion of the application of the of the driving waveform to the variable light transmission device.

2. The method of operating a variable light transmission device according to claim 1, wherein the final amplitude value of the modulator waveform is zero.

3. The method of operating a variable light transmission device according to claim 1, wherein the final amplitude value of the modulator waveform is from 0.1 V to 3 V.

4. The method of operating a variable light transmission device according to claim 1, wherein the driving waveform is selected from the group consisting of square, sinusoidal, trigonal, and sawtooth waveforms.

5. The method of operating a variable light transmission device according to claim 1, wherein the driving waveform is represented by Equation 1 V 1 sin ( ω 1 t ) .Math. "\[LeftBracketingBar]" sin ( ω 1 t ) .Math. "\[RightBracketingBar]" + V 2 t total - t t total sin ( ω 2 t ) .Math. "\[LeftBracketingBar]" sin ( ω 2 t ) .Math. "\[RightBracketingBar]" Equation 1 wherein t.sub.total is the total driving time of the application of the driving waveform to switch the variable light transmission device, and wherein t is time passed from the start of the application of the driving waveform.

6. The method of operating a variable light transmission device according to claim 1, wherein the driving waveform is represented by Equation 2 V 1 [ sin ( ω 1 t ) ] + V 2 t total - t t total sin ( ω 1 t ) Equation 2 wherein t is the total driving time of the application of the driving waveform to switch the variable light transmission device, and wherein t is time passed from the start of the application of the driving waveform.

7. The method of operating a variable light transmission device according to claim 1, wherein the driving waveform is represented by Equation 3 V 1 2 ω 1 π sin - 1 ( sin ( 2 π t ) ) + V 2 t total - t t total 2 ω 2 π sin - 1 ( sin ( 2 π t ) ) Equation 3 wherein t.sub.total is the total driving time of the application of the driving waveform to switch the variable light transmission device, and wherein t is time passed from the start of the application of the driving waveform.

8. The method of operating a variable light transmission device according to claim 1, wherein the driving waveform is represented by Equation 4 V 1 [ t ω 1 - floor ( t ω 1 ) ] + V 2 t total - t t total [ t ω 2 - floor ( t ω 2 ) ] Equation 4 wherein t is the total driving time of the application of the driving waveform to switch the variable light transmission device, and wherein t is time passed from the start of the application of the driving waveform.

9. The method of operating a variable light transmission device according to claim 1, wherein the modulator waveform has initial amplitude V.sub.1 of from about 80 V to about 140 V, and frequency ω.sub.1 of from about 70 Hz to about 110 Hz.

10. The method of operating a variable light transmission device according to claim 1, wherein the modulator waveform has initial amplitude V.sub.2 of from about 10 V to about 30 V, and frequency ω.sub.2 of from about 0.5 Hz to about 5 Hz.

11. The method of operating a variable light transmission device according to claim 1, wherein the charged particles of the electrophoretic medium layer of the variable light transmission device comprise titanium dioxide.

12. The method of operating a variable light transmission device according to claim 1, wherein the total driving time of the application of the driving waveform is from about 1 s to about 100 s.

13. The method of operating a variable light transmission device according to claim 1, wherein the total driving time from the start of the application of the driving waveform to the completion of the application of the driving waveform to the variable light transmission device is from about 5 s to about 90 s.

14. The method of operating a variable light transmission device according to claim 1, wherein the reduction of amplitude value of the modulator waveform from the initial amplitude value to the final amplitude value is performed in 2 or more sequential steps.

15. The method of operating a variable light transmission device according to claim 1, wherein the reduction of amplitude value of the modulator waveform from the initial amplitude value to the final amplitude value is performed in 5 or more sequential steps.

16. The method of operating a variable light transmission device according to claim 1, wherein the reduction of amplitude value of the modulator waveform from the initial amplitude value to the final amplitude value is performed in 10 or more sequential steps.

17. The method of operating a variable light transmission device according to claim 1, wherein the reduction of amplitude value of the modulator waveform from the initial amplitude value to the final amplitude value is performed in 100 or more sequential steps.

18. The method of operating a variable light transmission device according to claim 1, wherein % Total Transmittance of the final optical state of the variable light transmission device is from about 30% to about 95%.

19. The method of operating a variable light transmission device according to claim 1, wherein % Total Transmittance of the final optical state of the variable light transmission device is from about 40% to about 90%.

20. The method of operating a variable light transmission device according to claim 1, wherein % haze of the final optical state of the variable light transmission device is from about 5% to about 20%.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is an example of a graph of a linear stepwise reduction of an amplitude of the modulator waveform over time in 5 steps (from 21 V to 0 V over 30 s).

(2) FIG. 2A is a schematic illustration of a variable light transmission device at the initial optical state (closed state).

(3) FIG. 2B is a schematic illustration of a variable light transmission device at the final optical state (open state).

DETAILED DESCRIPTION

(4) Herein, the terms “final optical state”, “open state” and light-transmissive state are used interchangeably and represent the state wherein the film has higher light transmittance. The terms “initial optical state”, “closed state” and non-light-transmissive are used interchangeably and represent the state wherein the film has lower light transmittance than the open state.

(5) For convenience, the term “light” is normally be used herein, but this term should be understood in a broad sense to include electromagnetic radiation at non-visible wavelengths.

(6) In the variable light transmission device of the present invention, the transparent state (final optical state or open state) is brought about by field dependent aggregation of the electrophoretic particles; such field dependent aggregation may take the form of movement of electrophoretic particles to the lateral walls of a droplet (whether that droplet is present in a polymer-dispersed medium, or within a capsule or microcell), or “chaining”, i.e. formation of strands of electrophoretic particles within the droplet, or possibly in other ways. Regardless of the exact type of aggregation achieved, such field dependent aggregation of the electrophoretic particles causes the particles to occupy only a small proportion of the viewable area of each droplet, as seen in a direction looking perpendicular to the viewing surface through which an observer views the electrophoretic medium. Thus, in the light-transmissive state (or final optical state or open state), the major part of the viewable area of each droplet is free from electrophoretic particles and light can pass therethrough. In the case of movement of electrophoretic particles from the closed state (or initial optical state), where the electrophoretic particles are dispersed relatively uniformly across the viewing area of each droplet (see FIG. 2A), to the open state or final optical state (see FIG. 2B), where the particles are aggregated to the lateral walls of a droplet via the application of electric field, the phenomenon of induced charge electro-osmosis (ICEO) is likely involved. The phenomenon has been described in the art (see article by Squires and Bazant, “Induced-charge electro-osmosis” J. Fluid Mech. 2004, 509, 217-252).

(7) In the closed state, the relatively uniform distribution of the particles across the viewing area of the droplets of the electrophoretic device (FIG. 2A) obstructs the transmission of light through the device. On the contrary, the aggregation of the electrophoretic particles near the lateral wall of the droplets of the electrophoretic device (FIG. 2B), allows more light to pass through the device.

(8) ICEO is a second-order phenomenon that occurs when a polarizable particle experiences an electric field in the presence of an electrolyte. The induced particle motion depends upon the square of the applied voltage, but does not depend upon the polarity of the applied field, and therefore can be driven by AC fields. In this case the particle velocity is inversely dependent on the AC frequency. ICEO-mediated organization of the particles, and hence the formation of an open state, is promoted by application of relatively high frequency AC fields (typically at least 50 Hz) to the electrophoretic medium, and by the use of high voltages (typically at least about 30V). Conversely, dispersion of the electrophoretic particles into the suspending fluid, leading to the formation of a closed state, is promoted by application of low frequency fields (typically less than 50 Hz) to the electrophoretic medium. This state may be produced by normal electrophoretic particle switching or by ICEO-induced flow at these low frequencies. Normal electrophoretic particle switching does not require high voltage. Typically, voltages in the range of 5-20V are adequate.

(9) In other words, to favor the open state of the device, it is advantageous to vary both the operating voltage and the waveform, using a high frequency, high voltage waveform. On the contrary, low frequency and low voltage waveform favors the close state. These changes in waveform can be coupled with either patterned electrodes or various conductive particle materials, such as doped, metallic or semi-conductive materials, like those described in U.S. Pat. No. 7,327,511, to optimize the response in both directions.

(10) An additional concern for variable light transmission devices comprising capsules is grain. In this application, “grain” refers to visual non-uniformities caused by several factors, such as clusters of colored binder or clumps/layers of capsules, capsule packing variability, voids, thickness variations, and coating defects including pinholes. These non-uniformities reduce visibility when a user looks through the device in the open state. The term “grain” originates in film photography, where early silver films were known to have clumps of silver that made a developed picture appear “grainy.”

(11) Variable light transmission devices comprising microcapsules consist of microscopic areas that have differences in coat weight and degree of multi-layering. If these devices are driven to their darkest states, the differences in coat weight and packing can be viewed by a user as grain. One method for reducing the amount of grain in an encapsulated electrophoretic medium is by applying a driving method according to the various embodiments of the present invention.

(12) According to one embodiment of the present invention, grain can be appreciably improved for a variable light transmission device containing encapsulated electrophoretic media by utilizing a driving method comprising applying a waveform to the device having an initial optical state until the film switches to a final optical state, the initial state having a lower percent transmission than the final state.

(13) As mentioned above, the electrophoretic medium layer is capable of displaying open state and a close state, wherein the selection of the optical state is driven by the electric field applied to the electrodes. The waveform of the electric field applied on the device at the initial optical state of the film to drive the final optical state is a superposition of two simpler waveforms (a) a carrier waveform and (b) a modulator waveform, wherein the modulator waveform has an initial amplitude that is reduced over the time period of the application of the waveform on the variable light transmission device. Thus, the term “initial amplitude” of the modulator waveform are used throughout this disclosure to indicate that the value is the amplitude at the time of the initial application of the waveform to the variable light transmission device. The more general term “amplitude” of the modulator waveform is also used that may include all the amplitude values of the applied modulator waveform, and not only the initial amplitude value. The term final amplitude of the modulator waveform are used to indicate the amplitude of the modulator waveform at the time in which the application of the waveform to the variable light transmission device to bring the device to its open state is terminated.

(14) Herein, the amplitude of the carrier waveform is represented by V.sub.1 and it is expressed in volts (V). The frequency of the carrier waveform is represented by ω.sub.1 and it is expressed in Hertz (Hz). The initial amplitude of the modulator waveform is represented by V.sub.2 and it is expressed in volts (V). The frequency of the modulator waveform is represented by ω.sub.2 and it is expressed in Hertz (Hz). The total driving time of the application of the driving waveform to switch the variable light transmission device is represented by t.sub.total and it is expressed in seconds (s).

(15) The waveform applied at the initial optical state of the device to drive the final optical state can be expressed by one of the Equations 1-4, which are provided below. These equations correspond to a decrease in the amplitude of the modulator waveform over time in a linear manner from the maximum initial amplitude value to a final amplitude value. In this embodiment, the final amplitude valued is reached at the time when the waveform application on the variable light transmission device is terminated and the device is in its open state. Equations 1 corresponds to a square waveform, Equation 2 correspond to sinusoidal waveform, Equation 3 corresponds to trigonal waveform, and Equation 4 corresponds to sawtooth waveforms. Other types of waveforms can be also applied. The term “linear” as used herein to describe reduction of the amplitude of the modulator waveform over time includes any reduction over time in a stepwise (digitized) manner. As an illustration, FIG. 1 provides an example of a linear stepwise amplitude reduction over time in 5 steps.

(16) V 1 sin ( ω 1 t ) .Math. "\[LeftBracketingBar]" sin ( ω 1 t ) .Math. "\[RightBracketingBar]" + V 2 t total - t t total sin ( ω 2 t ) .Math. "\[LeftBracketingBar]" sin ( ω 2 τ ) .Math. "\[RightBracketingBar]" Equation 1 V 1 [ sin ( ω 1 t ) ] + V 2 t total - t t total sin ( ω 1 t ) Equation 2 V 1 2 ω 1 π sin - 1 ( sin ( 2 π t ) ) + V 2 t total - t t total 2 ω 2 π sin - 1 ( sin ( 2 π t ) ) Equation 3 V 1 [ t ω 1 - floor ( t ω 1 ) ] + V 2 t total - t t total [ t ω 2 - floor ( t ω 2 ) ] Equation 4

(17) The Equations 1-4 indicate that the waveforms are the result of superposition of the carrier AC waveform, represented by the first factor of the equations and the modulator AC waveform, represented by the second factor of the equations. The term t in the equations is the time passed from the initial application of the waveform, expressed in seconds (s). The expressions |sin(ω.sub.1t)| and |sin(ω.sub.2t)| correspond to absolute values of the sine values. Sin is the sine value of the number following the symbol. Floor function is the function that takes as input a real number and gives as output the greatest integer less than or equal to the real number.

(18) In one embodiment the waveform of the electric field applied at the initial optical state of the device to drive the device to the final optical state is a superposition of a carrier waveform and a modulator waveform, wherein the modulator waveform is reduced over time from an initial amplitude (at the application of the superposed waveform to the device) to a final amplitude (at the termination of the application of the superposed waveform to the device), wherein the final amplitude is zero volts. In another embodiment the final amplitude is greater than zero volts. The final amplitude value of the modulator waveform can be from about 0.01 V to about 4 V, or from about 0.1 V to about 3 V.

(19) In one embodiment, the waveform of the electric field applied at the initial optical state of the device to drive the final optical state is a superposition of a carrier waveform and a modulator waveform, wherein the modulator waveform is reduced over time from an initial amplitude (at the application of the superposed waveform to the device) to a final amplitude (at the termination of the application of the superposed waveform to the device) in a non-linear manner. The non-linear reduction of the amplitude of the modulator waveform over time can be selected to be described by any non-linear mathematical equation (amplitude versus time) such as an exponential function, power law, or any other expression. As with the linear manner, the reduction can be performed by a stepwise manner and the final amplitude of the modulator waveform (at the completion of the application of the amplitude to the device) can be zero volts or a value that is greater than zero volts. The final amplitude value of the modulator waveform can be from about 0.01 V to about 4 V, or from about 0.1 V to about 3 V.

(20) The amplitude V.sub.1 of the carrier portion of the waveform has a value of from about 30 V to about 180 V, and the frequency ω.sub.1 of the carrier waveform has a value of from about 50 Hz to about 1000 Hz. The initial amplitude V.sub.2 of the modulator portion of the waveform has a value of from about 3 V to about 60 V, and the frequency ω.sub.2 of the modulator waveform has a value of from about 0.1 Hz to about 10 Hz. The amplitude V.sub.1 of the carrier portion of the waveform may have a value of from about 50 V to about 150 V, or from about 90 V to about 140 V and the frequency ω.sub.1 of the carrier waveform may have a value of from about 60 Hz to about 500 Hz or form 70 Hz to 120 Hz. The initial amplitude V.sub.2 of the modulator waveform can be selected from about 5 V to about 50 V, or from about 10 V to about 30 V. The frequency ω.sub.2 of the modulator waveform can be selected from about 0.5 Hz to about 5 Hz, or from about 0.8 Hz to about 2 Hz. The amplitude V.sub.1 of the carrier portion of the waveform is higher than the initial amplitude V.sub.2 of the modulator portion of the waveform. The frequency ω.sub.1 of the carrier waveform is higher than the frequency ω.sub.2 of the modulator waveform. The total driving time (t.sub.total) in which the waveform is applied to the variable light transmission device to switch from the initial optical state to the final optical state may be from about is to about 100 s, from about 5 s to about 90 s, from about 10 s to about 60 s, or from about 20 s to about 40 s.

(21) Generally, the frequencies mentioned here have lower values than typically used for such switching to the open state. This contributes to less energy consumption for the device, which offers reduced operation costs and/or higher autonomy. In addition, the superposition of the carrier and modulator waveforms benefit from a shorter time required for the switch, and a higher transmission of the lower haze observed at the open state, compared to other typically used waveforms.

(22) As mentioned above, the waveform applied at an initial optical state of the variable light transmission device to drive the final optical state of the device, is a superposition of two waveforms, a carrier waveform and a modulator waveform. The amplitude of the carrier waveform V.sub.1 and the frequency of the carrier waveform ω.sub.1 are larger than the corresponding initial amplitude and the frequency of the modulator waveform V.sub.2 and ω.sub.2 respectively. The purpose of the application of the carrier square waveform portion is to shutter the pigment particles, that is, to aggregate them in the equatorial space of a capsule or a droplet of the electrophoretic fluid. The modulator waveform portion has lower amplitude and frequency than the amplitude and frequency of the carrier wave form. Thus, while not wanting to be bound to theory, it is believed that the utilization of a carrier waveform in addition to the modulator waveform may improve shuttering by facilitating ICEO motion of the particles and aggregate them in the equatorial space of a capsule or a droplet of the electrophoretic fluid. The methods according to various embodiments of the present invention may contribute to the remixing of the liquid of the capsule or the droplet, where the electrically chargeable particles reside, and enable any such particles that have been trapped in the center of the capsules or liquid droplets to move to equatorial positions. Such particles trapped in the center of the center of the cavity may reduce the light transmission and increase haze of the film in the open state. Thus, the application of a waveform that includes a modulator waveform contributes to an open state having higher transmission and lower haze.

(23) The amplitude of the modulator waveform is reduced from the initial amplitude value V.sub.2 at the time of the application of the waveform to the initial optical state of the device to a smaller final amplitude value of the modulator waveform at the time the application of the waveform is completed. The reduction of the amplitude of the modulator waveform can be selected to be linear with time or it can be exponential with time, or it can be expressed via any other mathematical equation as a function of time. In general, this reduction of the amplitude of the modulator waveform can be performed in more than 2, or more than 5 or more than 10 or more than 50 or more than 100 or more than 200 steps. The waveform that is applied to the variable light transmission device can be square, sinusoidal, trigonal, sawtooth waveform or it can be any other waveform type.

(24) It will be apparent to those skilled in the art that numerous changes and modifications can be made in the specific embodiments of the present invention described above without departing from the scope of the invention. Accordingly, the whole of the foregoing description is to be construed in an illustrative and not in a limitative sense. All of the foregoing published patents, publications, and pending applications are incorporated by reference herein in their entireties.

EXAMPLES

(25) Examples are now given, though by way of illustration only, to show details of variable light transmission devices made and evaluated according to various embodiments of the present invention.

(26) Preparation—Variable Light Transmission Device

(27) A nonaqueous internal phase was prepared by combining polyisobutylene succinimide (OLOA® 11000, supplied by Chevron), 1-limonene, Cargille® 5040 immersion fluid, Mogul L carbon black (supplied by Cabot Corp.), polystyrene, and 2-hexyldecanoic acid. The internal phase thus prepared was then encapsulated by adding the mixture to an aqueous solution of porcine gelatin/acacia followed by addition of Emperor 2000 carbon black with 5 wt % Kolliphor P188.

(28) After heating, mixing, and pH adjustment, the resulting capsules were cooled and then sorted to create a mixture of capsules with a size distribution between 20 and 60 μm diameter, with a mean diameter of 30-50 μm.

(29) The capsule slurry was centrifuged and then mixed with an aqueous binder of fish gelatin (Norland HiPure Liquid Gelatin) at a ratio of 1 part by weight binder to 7 parts by weight of capsules. A solution of colorant (10 wt % Emperor 2000 carbon black with 5 wt % Kolliphor P188 (Sigma-Aldrich 15759), was prepared in water and then added to the aqueous binder at a ratio of 1 part colorant to 49 parts binder. The resultant mixture of binder and encapsulated internal phase was bar coated on to a 125 μm thick indium-tin oxide coated polyester film. The coated film was dried to produce an electrophoretic medium approximately 23 μm thick containing essentially a single layer of capsules.

(30) The capsule-coated surfaces of the coated films were then overcoated with a urethane acrylate based adhesive. As the adhesive layer was added, a screen-printed sheet of 125 um thick indium-tin oxide coated polyester film was applied. The resulting assemblies were then cured by exposure to UV light from a CSun UV lamp. Using the techniques above, window pixels (i.e., top and bottom light-transmissive electrodes) were built.

(31) Testing—Variable Light Transmission Device

(32) The device constructed as described above was driven with waveforms of the form described above following a sequence that was designed to switch the device from the closed state to the open state. This waveform consisted of a superposition of a carrier waveform and a modulator waveform. The carrier waveform had an amplitude of 120 V and frequency of 86 Hz, whereas the modulator waveform had an amplitude of 21 V and frequency of 1 Hz. The waveform was applied to the device for 30 seconds. In Example 1, the amplitude of the modulator waveform was reduced from 21 V to zero in 5 steps over the applied period of 30 s. The applied modulator amplitude over time is provided in FIG. 1. In Example 2, the amplitude of the modulator waveform was decreased from 21V to zero V in 30 steps over the applied period of 30 s. In both examples 1 and 2, the reduction of the amplitude of the modulator waveform was performed in a linear manner. That is, in Example 1, the initial amplitude of the modulator waveform (21 V) was sequentially reduced 5 times by 4.2 V (21/5) each time every 6 s (30/5). In Example 2, the initial amplitude of the modulator waveform (21 V) was sequentially reduced 30 times by 0.70 V (21/30) each time every 1 s (30/30). On the contrary, in comparative Example A, the modulator waveform was constant for the applied period of 30 s at 21 V. After the application of the waveform, each sample was placed in front of a calibrated light source with an integrated sphere detector on the opposite side of the device. The % Total Transmission of light through the device (light transmission intensity as the percent of the intensity of the incident light) was determined. Percent haze was also determined, which is defined as the percentage of diffuse transmitted light, that is, light that is scattered as it is transmitted, compared to total transmitted light, from a normal, collimated source with an azimuthal angle of greater than 2.5°. Percent haze was determined via a calibrated chopping wheel. Table 1 below shows the results obtained from the above-mentioned evaluation of the three waveform examples.

(33) TABLE-US-00001 TABLE 1 Comparative Ex. A Ex. 1 Ex. 3 Amplitude of the 120 120 120 carrier waveform (V.sub.1) in Volts Frequency of the 86 86 86 carrier waveform (ω.sub.1) in Hz Initial amplitude of 21 21 21 the modulator waveform (V.sub.2) in Volts Frequency of the 1 1 1 modulator waveform (ω.sub.2) in Hz Total Time applied 30 30 30 (t.sub.total) in s Amplitude of the No reduction The amplitude is The amplitude is modulator over time; reduced over time reduced over time ωaveform change Constant from initial 21 V from initial 21 V over time amplitude is to final 0 V in 5 to final 0 V in 30 applied steps steps % Total 24 40 39 Transmittance of final state % Haze of final 20 17 18 state

(34) Table 1 indicates that the % Total Transmittance was increased and the percent haze was decreased when the amplitude of the modulator waveform was decreased over the time of the application of the waveform to the variable light transmission device to achieve the open state of the device. The comparative Example A, wherein a constant amplitude modulator waveform was applied, showed a lower % Total Transmittance and higher percent haze compared to Ex. 1 and Ex. 2.

(35) Although the present invention has been described with respect to square wave AC waveforms, it will be clear to one of skill in the art that other periodic forms (for example, sine waves, triangular waves, and the like) would be substituted without departing from the spirit of the invention.