2 Sample Preparation and Electrical Characterization of SSFLC
2.5 Electrical Properties of SSFLC with and without nc-ZnO
We shall focus in this section on the electrical properties of SSFLC test cells doped with nc-ZnO powder and the pure SSFLC. We shall apply the effective electronic circuit presented in section 2-4, to deduce the relation of the FLC capacitance with the applied voltage. All C-V curves were measured with the HP4284A LCR meter at room temperature. The cell gap and the area of our SSFLC test cells are 2 μm and 180 mm2, respectively. The FLC FELIX -017/100 mixture has a spontaneous polarization of 48.2 nC/cm2 at room temperature.
The measured CV curves of pure FLC at four different frequencies of 100 Hz, 1K, 10K and 100KHz respectively are shown in the Figure 2-16(a), and the Figure 2-16(b) is an expanded view of the curves at the high frequencies of 10 K and 100 KHz. In general, the profiles of the C-V hysteretic loops vary with frequency. The peak values of the capacitances decrease with an increase of frequency and the voltage with maximum capacitance also changes. All the C-V curves are symmetric with respect to the 0V point.
-10 -5 0 5 10 0.00E+000
4.00E-009 8.00E-009 1.20E-008
SSFLC 100Hz 1KHz 10KHz 100KHz
Capacitance CCell (F)
Bias Voltage (v)
a.
-10 -5 0 5 10
8.50E-010 8.75E-010 9.00E-010 9.25E-010
b. SSFLC
10KHz 100KHz
Capacitance CCell (F)
Bias Voltage (v)
Figure 2-16 The capacitance (CLC) versus the applied voltage on the pure SSFLC cell without doping at four different frequencies: (a) at 100Hz, 1KHz, 10KHz, and
100KHz; (b) An expanded view of the curves at the two highest frequencies 10KHz and 100KHz.
The Figure 2-17(a) shows the CV characteristic curves of the nc-ZnO doped SSFLC cell at four different frequencies of 100, 1K, 10K and 100KHz, respectively.
These CV curves are similar to those of the pure FLC with some minor differences.
Such as the C-V hysteresis loops exhibit a reversal behavior at 10K and 100KHz. In the following we shall apply the Preisach model to yield more detailed information about the doping effect of ZnO nanocrystals.
-10 -5 0 5 10 0.00E+000
5.00E-009 1.00E-008 1.50E-008
a. SSFLC with nc-ZnO doping
100Hz
b. SSFLC with nc-ZnO doping
10KHz 100KHz
Capacitance CCell (F)
Bias Voltage (v)
Figure 2-17 The capacitance (CLC) versus the applied voltage on the nc-ZnO doped SSFLC cell at four different frequencies: (a) at 100Hz, 1KHz, 10KHz, and 100KHz;
(b) An expanded view of the curves at the two highest frequencies 10KHz and 100KHz.
From the measured data, we found that the pure SSFLC can not be fitted with single Preisach model. It is considering that the FLC material FELIX 017-100 is a mixture and that it may possess several FLC dipole species with different responses at various field strength and frequencies. We therefore propose the Preisach model to have
with
Figure 2-18 presents the measured data (empty squares) and the fitting curve to Eq.
(2-14) (black solid line) of the pure SSFLC at 100Hz. We need four linear Preisach terms to achieve a good fit to the data as indicated in Figure 2-19(a). The resulting fitting parameters δ, Vc±, and FPs, as described by Eq.(2-14) are summarized in Table 2-1.
The results of SSFLC with nc-ZnO doping are presented in Figure 2-18, with the measured data (empty triangle symbol), the fitting curve (black solid line) at 100Hz.
Two linear Preisach terms are needed to yield a good fit of the data to Eq. (2-14) as shown in Figure 2-19(b). The resulting fitting parameters δ, Vc±, and FPs, as described by Eq. (2-14) are summarized in Table 2-2. At 100Hz, we found that the SSFLC with nc-ZnO doping has a higher capacitance peak and lower coercive voltage (the peak position) than the pure SSFLC.
-10 -5 0 5 10
SSFLC with nc-ZnO doping
Figure 2-18 The experimental C-V curves (open symbols) and the fitting curves (solid lines) of the SSFLC test cells without and with nc-ZnO doping cells at 100Hz.
-10 -5 0 5 10
Figure 2-19 The fitting results of the measured data of (a) the SSFLC cell, and (b) the SSFLC cell with nc-ZnO doping at 100Hz. The solid lines are the fitting curve and the symbols are the measured data. (a) The four curves with dash, dot, dash-dot and dash-dot-dot, respectively, represent the corresponding Preisach terms involved. (b) The dash and dot lines represent the corresponding Preisach terms involved in the nc-ZnO doped SSFLC cell.
In Figure 2-19, the experimental data can be synthesized with several Preisach terms because the molecules of FLC FELIX 017-100 may possess several FLC dipole species. Because the polarization of the FLC couples directly to the external electric field, these molecular dipole species may exhibit different responses at various field strength and frequencies. At the frequency 100Hz, the ZnO nano dots can effectively
“glue” their surrounding FLC dipoles together and yield an improved alignment as shown in the imaging polarimetric investigation. This novel effect is possible in view that these nc-ZnO possess fairly large dipole moments and could affect the FLC molecules via dipolar interaction, which simplifies the Preisach terms needed at 100 Hz from four to two with nc-ZnO doping. It is also interesting to point out that the peak positions (i.e., the coercive voltage) of the Preisach terms with the dashed and the dotted curves are similar for the two cells but the SSFLC cell with nc-ZnO doping yields a higher peak height. The SSFLC cell with nc-ZnO doping does not exhibit another two Preisach terms (the dash-dott and dash-dot-dot lines), which are present in the pure SSFLC. This appears to affirm that ZnO nanocrystals could effectively
connect the FLC dipole species and simplify the field-induced responses.
Table 2-1 The fitting parameters of the pure SSFLC cell to Eq. (2-14) at different frequencies.
100Hz 1KHz 10KHz 100KHz
δ1 0.36642 -0.36642
1
VC±(V) ±7.0354 ±5.38644 ±3.64075 ±5.590
(FPs)1 (C/mt2) 1.277×10-10 7.297×10-11 3.458×10-13 1.480×10-12
δ2 0.191199 -0.191199
2
VC± (V) ±2.24519 ±1.7003 ±0.355235 ±1.98496
(FPs)2 (C/mt2) 1.473×10-10 8.547×10-11 1.617×10-12 1.614×10-12
δ3 0.885003 -0.885003
3
VC±(V) ∓ 6.82148 ∓ 7.38824 ∓ 10.7792 ∓ 11.2531 (FPs)3 (C/mt2) 5.589×10-10 2.322×10-10 2.866×10-12 7.564×10-12
δ4 1.6201
4
VC± (V) ±8.4126 (FPs)4 (C/mt2) 7.257×10-12
From the Table 2-1, the pure SSFLC cell requires four linear Preisach terms model was used to fit its measured at 100Hz, but only three are needed for 1KHz and 100KHz. Both the switchable polarization (FPs) and the coercive voltage (VC±) decrease with an increase of frequency. The parameters δ1,δ2, δ3, and δ4 are positive at frequencies below 100KHz. At 100KHz, the C-V curve exhibits a reversal phenomenon. The parameter δ1,δ2 and δ3 became negative with magnitudes similar to their positive values.
Table 2-2 presents the fitting parameters of the SSFLC cell with nc-ZnO doping cell. Only two linear Preisach terms are needed at 100Hz, and it is reduced to one at 1K, 10K, and 100KHz. The δ1 andδ2 of the SSFLC with nc-ZnO doping cell are different from the corresponding values in the pure SSFLC cell. The reversal of C-V curve occurs at 10KHz and the δ parameters change sign from positive to negative. It is to know that the FLC molecules naturally try to align with the largest permittivity component along the external field. If the frequency of the electric field is so high that it cannot couple with the spontaneous polarization. Therefore, the FLC molecules will remain in (or return to) the almost fully switched state and do not contribute to the nonlinear part of the capacitance. For the reason, the inversion of the C-V curve is associated to the inversion of the dielectric δε. When the spontaneous polarization is proportion to the dielectric biaxiality, the C-V hysteresis loop will show an inversion at higher frequencies [30]. The switchable polarization (FPs) decreases with an increase of frequency from 100 Hz to 1 KHz, but becomes increase with frequency from 10KHz to 100KHz. But the coercive voltage always decreases with an increase of frequency. At higher frequency the applied field changes direction before the FLC molecules reach their final position for the applied field magnitude, so that the contribution of the molecules to the dielectric constant decrease [30]. Hence, the switchable polarization (FPs) decreases with an increase of frequency. However, after the C-V hysteresis loop shows an inversion, the behavior of the switchable polarization (FPs) may also inverse.
Table 2-2 The fitting parameters of the SSFLC cell with nc-ZnO doping to Eq. (2-14) at different frequencies
100Hz 1KHz 10KHz 100KHz
δ1 0.509512 -0.509512
1
VC±(V) ±5.11285 ±2.5093 ±3.55682 ±2.50275
(FPs)1 (C/mt2) 1.889×10-10 6.083×10-11 8.376×10-13 1.245×10-12
δ2 0.29875
2
VC± (V) ±1.84602 (FPs)2 (C/mt2) 3.319×10-10
Figure 2-20 shows the measured data of the pure SSFLC (open squares) and the SSFLC with nc-ZnO doping (open triangles) at 1KHz and their corresponding fitting curves (solid lines) to Eq. (2-14). Figure 2-21 displays the linear Preisach terms involved in the pure SSFLC and SSFLC doped nc-ZnO at 1KHz. Clearly, the pure SSFLC cell requires three Preisach terms to successfully synthesize the experimental curve, but for the SSFLC with nc-ZnO doping only one is needed at the same frequency 1KHz. The coercive voltage of the SSFLC with nc-ZnO doping is about the averaged value of the two coercive voltages of the Preisach terms (the dash and dot lines) used in the pure SSFLC. This again affirms that ZnO nanocrystals could effectively connect the FLC dipole species and simplify the field-induced responses.
-12 -6 0 6 12 0.00
1.50x10-9 3.00x10-9 4.50x10-9
6.00x10-9 CV characteristics @1 kHz SSFLC
SSFLC with nc-ZnO doping
Capacitance CCell (F)
Applied Voltage (Volt)
Figure 2-20 The experimental C-V curves (empty symbols) and their fitting results (solid lines) of the SSFLC cells without and with nc-ZnO doping at 1 kHz.
-10 -5 0 5 10
Figure 2-21 The fitting curves to Eq. (2-14) of (a) the SSFLC cell and (b) the SSFLC cell with nc-ZnO doping at 1 kHz. The symbols are the measured data. In (a) the three curves with dash, dot, and dash-dot, respectively, represent the Preisach terms involved and the solid line is the summation of all the three terms. (b) The solid line is the fit to the single-component Preisach model.
Figures 2-22 and 2-23 present the measured data of the pure SSFLC (open squares) and the SSFLC cell with nc-ZnO doping (open triangles) and the corresponding fitting curves (solid lines) at 10KHz and 100KHz, respectively. At 10 kHz, the SSFLC cell doped with nc-ZnO cell exhibits a reversal C-V hysteretic curve, however the pure SSFLC cell displays similar CV reveal behavior at 100 kHz. The experimental data of the pure SSFLC cell require a good fit to Eq. (2-14) with three linear Preisach terms at 10K, and at 100 kHz but the SSFLC cell doped with nc-ZnO
only one term is sufficient. The capacitance of the SSFLC cell with nz-ZnO doping is larger than the pure SSFLC cell at 10KHz, but at 100KHz the situation is reversed.
According to the above mentioned reason about the inversion of C-V curve, when the FLC molecules cannot couple with the spontaneous polarization, the FLC molecules will remain in (or return to) the almost fully switched state and do not contribute to the nonlinear part of the capacitance [30]. It is considered that after FLC molecules doped with nc-ZnO, the spontaneous polarization of FLC doped with nc-ZnO may produce some change which is not equal to the pure FLC. Even at the same frequency of 10KHz, the spontaneous polarization of FLC with nc-ZnO doping cannot couple the electric field. Comparing the Figure 2-16(b) and 2-17(b), the linear capacitance of the SSFLC seems almost the same value but the linear capacitance of the SSFLC with nc-ZnO doping shift to lower value with the increase of frequencies. In a word, with the increase of frequencies, the decreasing rate of SSFLC doped with nc-ZnO is faster than that of SSFLC. It might be the nc-ZnO make the FLC molecules become more sensitive to the external frequencies. Therefore, the capacitance of the SSFLC cell with nz-ZnO doping is larger than the pure SSFLC cell at 10KHz, but at 100KHz the situation is reversed.
-10 -5 0 5 10
8.50E-010 9.00E-010 9.50E-010 1.00E-009
10KHz SSFLC
SSFLC with nc-ZnO doping
Capacitance CCell (F)
Bias Voltage (v)
Figure 2-22 The experimental C-V curves (open symbols) and the fitting curves (solid lines) of the SSFLC cells without (square) and with (triangle) nc-ZnO doping at 10 kHz.
-10 -5 0 5 10 6.75E-010
7.50E-010 8.25E-010 9.00E-010
10KHz SSFLC
SSFLC with nc-ZnO doping
Capacitance CCell (F)
Bias Voltage (v)
Figure 2-23 The experimental C-V curves (open symbols) and the fitting curves (solid lines) of the SSFLC cells without (square) and with (triangle) nc-ZnO doping at 100 kHz.
In summary, both the SSFLC cells with and without nc-ZnO doping exhibit symmetric CV hysteretic curves with respect to 0V. By fitting the measured data to the Preisach model, different numbers of linear Preisach terms are required at different frequencies, indicating that the SSFLC used possesses several FLC dipolar species with different responses to the applied voltage and frequencies. At higher frequencies the external driving field changes its direction before the FLC molecules can settle down to their final orientations [29]. Therefore, both the maximum capacitances and the amount of the switchable polarization (FPs) decrease with an accompany of decreasing coercive voltage (VC±) as the applied frequency is increased.
The maximum capacitance in the C-V curves for the ferroelectric material reflects beginning of polarization reversal rather than maximum molecular density near the coercive voltage [31]. The dipoles of the ZnO nanocrystal can effectively tie up the surrounding FLC species to perform a collective switching under an external driving field. The FLC doped with ZnO nanocrystals exhibits a lower coercive voltage. The difference between the maximum and minimum of the C-V curves of the SSFLC cell doped with nc-ZnO is lager than that of the pure SSFLC cell. Based on these results,
doping with ZnO nanocrystals appears to be a simple while effective approach to improve the application properties of existing FLC materials.
Chapter 3
Electro-Optical Switching Dynamics of SSFLC Cells with and without nc-ZnO Doping
3.1 Model of Electro-Optical Response of a SSFLC Cell
Figure 3-1 Schematic diagram showing the time-resolved electro-optical characterizing apparatus used in this study.
Figure 3-1 presents the schematic diagram of the time-resolved electro-optical characterizing apparatus used in this study. This system includes a light source, a polarizer, a rotation stage for sample cell, an analyzer, a function generator, a photo detector, and a oscilloscope. A laser diode with a wavelength 670 nm was used as the light source and the propagation direction was set to along the z-axis. A SSFLC test cell was mounted on the rotation stage to be rotated about the z-axis. The fast axis of the polarizer is along to the x-axis. The function generator applies a waveform of square-wave on the SSFLC cell. The light beam transmitting through the SSFLC cell
was analyzed with the analyzer, which was set to cross with the polarizer, and then was detected with a photo detector. An oscilloscope was used to record the waveforms of signal from photo detector and the driving field from the function generator. The rubbing direction K of SSFLC cell was initially along the X-axis of the laboratory coordinate system. The sample cell can be rotated about the Z-axis with an angle of Φ.
The optic axis of the FLC film projects onto the substrate surface (K-N plane) to yield an azimuthal angle of ω relative to the rubbing direction K.
By applying Jones’ calculus, an expression of the optical field incident on a photo-detector can be derived
'
The SSFLC cell is oriented with its optic axis pointing to a direction with a polar angle of α relative to the beam propagation direction (Z-axis). The geometry is depicted in the molecular frame shown in Figure 3-2.
Figure 3-2 Schematic diagram showing the orientational relationship between the molecular frame (ξ, η, ζ) and the sample frame (K, N, Z)
The SSLFC cell behaves like a wave-retarder with an optical retardance Γ(α) given by [15].
2 2
where d is the thickness of the SSFLC cell, and λ is the wavelength of light source used. By using Eq. (3.1), the irradiance on the detector can be expresses as
( ) time-resolved optical transmission signal can be sampled and recorded with the oscilloscope at each Φ. Eq. (3-3) suggests that the resulting time-resolved angular pattern of the optical irradiance on the detector can be expressed as
( ) ( )
( )cos 22 (( )
)I Φ =b t c t+ ⎡⎣ Φ+ω t ⎤⎦, (3.4) where b(t) denotes an isotropic part of the dynamic alignment of SSFLC, c(t)=0.5Iosin2(Γ/2) represents the angularly aligned component of the SSFLC film, and ω(t) is the azimuthal angle of the optic axis projected onto the cell substrate. We recorded a total of 37 angular patterns from Φ=0o to 360 o at each specific time instant.
The measured patterns (see the black squares in Figure 3-3) can be fitted to Eq. (3-4) (the solid line) to deduce the parameters a(t), b(t), and Φ(t). Notice that upon the reversal of the sign of an applied field, all the molecules in the ferroelectric phase switch by rotation about a tilt cone. Due to the conic motion, c(t) varies with polar angle α. The detailed information about the conic motion of SSFLC can be deduced by analyzing the dynamic EO response patterns.
0 60 120 180 240 300 360 0.0
0.3 0.6 0.9 1.2
SSFLC with 10 V at 0 μm
the data of the time-resolved optical irradiance
Normalized Transmission (a.u)
Angle (degree)
b 0.13031±0.00949 c 1.01063±0.01536 w 13.06432±0.21624
Figure 3-3 Time-resolved angular pattern (symbols) of optical transmission through a SSFLC cell with 10 V at 0 μsec and the corresponding fitting curve (solid line) to Eq.
(3-4).
3.2 Time-Resolved Electro-Optical Response of SSFLC Cell
3.2.1 SSFLC cell with a driving voltage of 10V
According to section 3.1, the isotropic contribution, angular alignment term, and the projected angle of the optic axis of a SSFLC cell can be deduced from the fitting procedure. In Figure 3-4, we present the time-resolved electro-optical azimuthal patterns of an undoped SSFLC cell. The transmission intensity at each time instant had been normalized to the maximum transmission of the SSFLC cell at zero driving field, which is indicates by the solid curve in Figure 3-4. The other lines with symbols represent the azimuthal patterns recorded at five different delay times of the SSLC cell driven with an amplitude +10V (Figure 3-4(a)) and -10V (Figure 3-4(b)) of square wave form. The high dichotic ratio of the patterns indicated the SSFLC cells used in this study to have high alignment quality. It is interesting to notice that at the very beginning of the field-on period at 0 μsec the transmission intensity is larger than
that without driving field and the direction of the FLC molecule is rotated about 30 degrees. The symmetry axis of the azimuthal patterns rotates rapidly with an accompany of a reduction of modulation depth. When the electric field is applied for an extended period, the amplitude of the azimuthal pattern becomes larger than the initial value while the orientation of the azimuthal pattern does not change significantly. Similar behavior occurs in the negative field-on period shown in Figure 3-4(b).
a. Positive edge trigger delay time (μs)
0.0
b. Negative edge trigger delay time (μs) Figure 3-4 The transient electro-optical azimuthal patterns of a SSFLC cell recorded at five different delay times. The driving field is (a) +10V, (b) -10V square waveform with a field-on duration of 800μs.
These time-resolved azimuthal patterns can be fitted to Eq. (3-4) to deduce the parameters b(t), c(t), and ω(t), which are presented in Figure 3-5. The switching time course of the SSFLC director shown in Figure 3-5(b) appeared to be symmetric in both the positively and negatively driven cycles. The contrast ratio of the optical transmission decreased during the field-on period, as shown by a rapid increase of the isotropic component b(t). The isotropic component then slowly decreased with an accompanying increase of c(t). The angularly aligned component c(t) can be increased dynamically to about 1.4 times of its zero-field case.
0 1000 2000 3000 4000
0 1000 2000 3000 4000
-20
Figure 3-5 (a) Fitting parameters (symbols) of the time-resolved EO azimuthal patterns and the applied voltage (solid line) are plotted as a function of time. (b) The deduced orientation angle of the optic axis of FLC film is shown. The rubbing direction of the FLC cell with is along the 0 degree.
As shown in Figure 3-5(b), the projected angle was found to increase first and then reverses rapidly to the other direction. Similar behavior occurs in the negative driving cycle. The C-V curve at 100 Hz shown in Figure 2-16 indicates that the capacitance of the FLC film first increases gradually from 0V to +5V (or -5V). The FLC capacitance rapidly increases to a peak at a voltage about 6V and then decreases when the applied voltage increases further. Therefore when the applied voltage is switched on from 0 to 10V, the FLC molecules will experience a field strength depending on the dynamic film capacitance. When the transient applied field strength on the film crosses 6V, a reversal behavior will be observed. The response time of ω(t) can be estimated to be τ10-90=200 μsec. Notice that the electro-optical response time can be calculated with τ =γ PsE⊥. Here γ denotes the rotational viscosity, P the spontaneous polarization of FLC and E⊥ the applied electric field. By using the
available material parameters of Felix 017/100:
5 2
4.8 10 N sec cm
4.8 10 N sec cm