Smectic layers reorientation with stripes and heliconical structure in surface stabilised ferroelectric liquid crystal

ABSTRACT High-tilt angle ferroelectric liquid crystal material in surface stabilised geometry (SSFLC) is investigated for the smectic layer reorientation and its molecular dynamics by electro-optical and dielectric spectroscopy techniques. Smectic layer reorientation (5$^o$ o to 45$^o$ o) is obtained by controlled cooling rate and applying electric field in the vicinity of transition temperature from chiral nematic (${N^*}$N∗) to chiral smectic C ($Sm{C^*}$SmC∗) phase. After slow cooling down to room temperature, the stripe domain textures along the rubbing are observed with quasi-bistable states. Dielectric spectroscopy has revealed the unusual increment in the dielectric permittivity. A dielectric relaxation process at lower frequency than Goldstone mode with the increase in DC bias up to 2 $V$V is observed in the sample cooled without any bias. This increment is found to be originated by the heliconical structure within the stripes which is seen in the optical textures recorded at the time of dielectric scan. However, this increment is not observed in the sample cooled under DC bias. Thus, there exist different phenomena in the high tilt angle SSFLC sample cooled in different conditions of DC bias; stripe domains, smectic layers reorientation, heliconical stricture and twisted structure within stripes which are significant to explore deeply in high-tilt angle ferroelectric liquid crystals. GRAPHICAL ABSTRACT


Introduction
The discovery of ferroelectricity in liquid crystals is almost half a century old, but still, there is no practical application-based breakthrough as compared to their counterpart nematic liquid crystals.Although, ferroelectric liquid crystals (FLCs) are more advantageous than nematic liquid crystals, among which the high switching speed, memory effect and various modes of operations are the most common [1].
The probable reason for lacking the applied aspect in FLCs could be the alignment of FLC molecules as compared with the nematic liquid crystals due to the complexity of the molecular arrangements in the smectic layers which are arranged in chiral structure.Patel and Goodby in 1986 presented a technique to control the alignment by cooling the FLC sample under the electric field during a direct transition (T c ) from cholesteric to chiral smectic C (SmC � ) phase [2].Asymmetric electric field application to one of the orientations induces the reorientation of smectic layers during the cooling cycle [2][3][4].When the sample remains in the cholesteric phase, the homogeneously aligned sample has the direction of the helix perpendicular to the aligning substrate and molecules remain in the nematic phase.However, when the sample is cooled to the SmC � phase both the conditions change drastically and the helix tends to get oriented in the direction parallel to the substrate where the molecules develop strong transverse intermolecular interaction among themselves.If a controlled electric field is applied in such a condition of transition, the molecules freeze as per the electric field polarity, and transverse molecular interaction allows the smectic layers to develop in the direction not precisely perpendicular to the buffing direction but away from it, as a result, the smectic layers get reoriented and focal conic domains (FCDs) are developed in the tilted smectic layer structured.
Smectic layer reorientation is a usually observed phenomenon, particularly in the materials having cholesteric to SmC � phase transition because it has been realized that most of the SmC � features depend on the higher temperature phases [5][6][7].However, the absence of chiral smectic A (SmA) phase could induce the hightilt angle in the SmC � phase and the magnitude of the smectic layer tilting reaches equal to the magnitude of the molecular tilt angle [5,8].If it is intended to induce the smectic layer deviation in the material in which the chiral SmA (SmA � ) phase is also present at a lower temperature than the nematic phase but above the SmC � phase, the induced tilt angle magnitude must persist in SmA � phase [9].However, the layer reorientation is consistent in the FLC material where there is a SmA � phase just below the nematic phase and above the SmC � phase [4].Adding some ionic impurity to conventional FLC with SmA phase, the smectic layer reorientation has also been achieved close to the tilt angle by applying the DC bias field [10].However, the layer rotation is achieved more than the tilt angle in FLC and anti-FLC phases by applying various waveforms of the electric field [11,12].
Smectic layer reorientation under specific constraints has resulted into a particular layer arrangement in FLCs like the formation of the zig-zag stripes in surface stabilised FLC (SSFLC) under the application of electric field when cooled to SmC � phase from higher temperature phases [13][14][15][16].The stripes are parallel to the rubbing direction and possess the pattern of zig-zag induced in chevron structure by the electroclinic effect in the SmA � phase.In these stripes, the molecular tilt is different from adjacent stripes having a certain tilt angle with respect to each other.This tilt angle between the stripes increases with the increase in the applied electric field.Reversible smectic layer reorientation by confined geometry of nanopores [17], polyamide layer with waveform combination [18][19][20][21] has been investigated in detail.
But the main problem of analysis comes in high-tilt angle (45 o ) FLCs where the optical contrast ratio between the two switching states is almost negligible and the same may happen in adjacent stripes also even after the switched states.In these FLCs, the strong surface anchoring is not sufficient to align the molecules in the rubbing direction due to the absence of the smectic A (SmA) phase in the material.The absence of the SmA phase leads the materials to undergo double change while cooling from chiral nematic (N�) to the SmC � phase.The molecules of high-tilt FLC have to undergo tilting and layering simultaneously.Thus, alignment is the main issue in high-tilt FLCs due to either of the issues; therefore, very few research work have been reported in the literature three decades ago by Patel et al. and a few more groups.Although, this type of hightilt FLCs has very high potential in optical switches where the refractive index can be maximum exploited as the molecules switch from 0 o to 90 o by changing the polarity of the applied electric field.
In the present investigation, a high-tilt angle (45 o ) facilitated FLC material (CS-2004) is explored for the internal structure of stripes along with smectic layer reorientation in its surface stabilised FLC (SSFLC) state.The motive of the study is to investigate the internal structure of the stripe domains under various conditions of electric field.The irreversible reorientation process of smectic layers is achieved by cooling the sample under the influence of DC electric field.All the electric fields (DC or AC) were applied by impedance analyser.This is because we wanted to investigate the dielectric properties and electro-optical phenomenon together to map the dielectric processes with the optical textures.The twisted internal structure in stripes was observed in the cell aligned by high DC bias field, whereas the heliconical structure was seen in the cell aligned without any bias.We have shown the dynamical processes of all different structures in a single cell by dielectric spectroscopy and simultaneously captured optical textures.Since the sample cell is in SSFLC geometry, it is very difficult to observe any traces of helical structure or its related process, but it is interesting to notice the helix-based heliconical structure and its contribution to the dielectric properties.

Materials and instrumentation
Thin ready-made cells (Vin Karola Instruments, USA) of thickness 3 μ m, having inner surfaces coated with a polymer and rubbed unidirectional for planar alignment of FLC molecule, were used in the present investigation.The effective electrode area was 5 mm x 5 mm and the sheet resistance of the Indium Tin Oxide (ITO) plate was ,30 Ω/□.The cell was sealed except for the two openings available for filling the material, one was for an inlet and another was for an air outlet.The electrical contacts were taken out from the electrode for applying an electric field.
The high-tilt-angle FLC material (CS-2004: Chisso Corporation, Japan) was used to fill into the empty ready-made cell.The FLC material was kept at one of the openings of the cell.Then, the cell along with the FLC was heated at 5 o C temperature above its nematic to isotropic phase transition temperature.At this temperature, the FLC material did not have any character of a liquid crystal and the material behaved like an ordinary isotropic liquid.Then, the material crept automatically inside the cell by the capillary action.The cell was kept at this temperature for around 30 min and then it was cooled to room temperature at the rate of 0.1 o C=min.Once the FLC was inserted into the cell, two openings (inlet and outlet) were also sealed by ultra violet curable sealant (UV-sealant) to avoid any material leakage.
This FLC material at room temperature has a tilt angle of 45 o , the helical pitch value of ,15 μ m, and the P s is ,60 nC=cm 2 .The phase sequence of this FLC, CS-2004, has the following phase transition temperature ranges: Crystalline where N � stands for the chiral nematic phase.Such a sample cell was prepared and then placed in an electrically shielded sample holder where it was connected to the two electrical Bayonet Neill -Concelman or British Naval Connectors (BNCs) for the application of the electric field.The alignment of FLC molecules was seen under the polarising optical microscope (Carl Zeiss Axioskop 40A Pol, Germany).The temperature of the sample cell was controlled inside the sample holder using a temperature controller (Julabo F 25, Germany) with an accuracy of �0.1 o C. The dielectric studies were carried out at room temperature at various bias voltages in the frequency range from 20 Hz to 1 MHz using an impedance analyser (Wayne Kerr 6540A, UK, frequency range from 20 Hz to 120 MHz).

Alignment control for layer reorientation
Two alignment configurations are the main issues of this study.One of them is the alignment of FLC in a surface stabilised sample without any bias field.In another, the alignment is suppressed by applying DC bias from the nematic phase to room temperature during the cooling cycle of the sample.In the earlier one, no bias or any other field was applied and the sample was cooled slowly.Since the sample is in SSFLC configuration, the spontaneous polarisation is self-minimised by domains in the form of stripes.Such stripes are supposed to remain parallel to the buffing direction [13] and the same case is observed here also as they are strictly parallel to the smectic layer normal in case of alignment without any field.In the latter one, the sample cell was installed in the sample holder which was connected to the temperature controller through the water circulation pipes for controlling the temperature.Then the sample holder was also connected to the impedance analyser through BNC cables to apply electric field during cooling and latter at room temperature for the property analysis measurements.The sample was cooled at a prolonged rate under the application of a DC bias electric field using the impedance analyser.However, a small amplitude of measuring electric field was also applied by impedance analyser simultaneously with the DC bias field that may affect the final effective field on the dipoles at low frequencies.Generally, the dipoles can be largely affected by the electric field at frequency lower than the relaxation process.Therefore, the measuring field frequency was set at ,50 kHz by pausing the impedance analyser scan at the set frequency.The applied field was maintained asymmetric as it is preferred to get uniform alignment in such hightilt angle FLC materials [16].The alignment was good enough to study the layer reorientation along with the stripe formation in SSFLC configuration.

Measurement method
After the sample is ready for the measurements, the alignment of the FLC molecules is achieved by cooling the sample under two conditions, separately: one is without bias and another is under the DC bias.After getting a good alignment in both conditions, all the measurements were performed at room temperature one by one.Two techniques were employed for the analysis: optical and dielectric spectroscopy.Sometimes, both techniques were employed simultaneously.Simultaneous use of both techniques was adopted to trace the origin of any dipolar or surface related relaxation process causing the change in texture.

Results and discussion
It is well known that the uniform alignment of liquid crystal molecules is very important for applied and basic aspects.In almost all FLC materials where the T c is from SmA � to SmC � phase, in such FLCs when it is cooled from isotropic to nematic, first, the LC molecules align along the rubbed grooved surface, and then further cooling in SmA � phase, the layer formation in smectic phase takes place as the tilt angle in SmA � phase is zero.In SmC � phase, only the tilt formation takes place which means that the smectic layer normal is along the rubbed direction and FLC molecules are tilted with respect to the rubbed direction, resulting in the uniform alignment of molecules in such materials.However, in the FLC having a direct transition from N � to SmC � phase generates the random nucleation in SmC � [2].Therefore, slow cooling is the prerequisite condition in these FLC materials for uniform alignment, otherwise, alignment ends with an unaligned multidomain even in the thin cell.In the present investigation, the cooling rate was maintained at 0.
The slow cooling rate up to 4 o -5 o C below T c is necessary because the molecular tilt near T c temperature is soft, which becomes rigid in SmC � phase, resulting in the uniform alignment.That means the FLC molecules are aligned along the rubbed direction and smectic layers are reoriented by 45 o (tilt angle of the material) to the rubbed direction.In the present investigation, there have been two categories of the sample alignment based on the electric field applied during the cooling of the sample; one is aligned in the absence of field whereas in another it is with the DC applied field during the cooling of the sample.Besides this, both categories have been studied by dielectric spectroscopy and optical microscopy.Their corresponding optical microscopy at the time of dielectric measurements has been taken for the direct realisation of dynamical processes.First, the results of the sample aligned without DC field have been studied whereas in the latter case, the results of sample aligned with DC field.

Optical texture observation
The SSFLC sample cell is slowly cooled at the cooling rate of 0.1 o C=min without any field and the texture is formed as shown in Figure 1(a).As seen in Figure 1(a), the stripe domains are clearly visible and aligned along the rubbing direction.However, some of the domains in the sample are wider than the domains in the regular stripes.In adjacent stripes, the direction of polarization is opposite to each other to minimize the energy of the sample.Both the states are bi-stable like in conventional SSFLC sample cells [22,23].There are stripes formation inside the large domain.Therefore, here we call them the 'stripe domains'.These stripe domains are bi-stable.Furthermore, for this bi-stable cell to remain in the neutralized condition, the orientation of dipoles is pointing in the UP direction in one stripe.In another adjacent domain stripe, the dipoles are pointing in the DOWN direction.Therefore, if one stripe domain is bright, then, the chances are there that the adjacent stripe domain would be comparatively dark under the polarizing optical microscope.The same is clearly seen in Figure 1(a).The stripe domains in conducting and non-conducting regions are almost same because the sample is cooled without electric field.This means that one strip domain, which develops from the bottom rubbed surface, is UP and in the adjacent stripe domain it will be DOWN from the top rubbed surface resulting in the neutralised state in the bi-stable cells of high-tiltangle FLC materials, as seen in Figure 1(a).
The optical contrast and molecular orientation in high tilt angle SSFLC differ from those in conventional FLC-based SSFLC cells.In the conventional FLC cell, the molecular tilt angle remains around 22.5 o in which the complete switching of FLC molecule covers 45 o angle.But in high tilt angle FLC, the situation is different because the tilt angle is 45 o with which molecule covers 90 o angle in other switched state.The optical contrast in these two states remains almost the same and hence it becomes challenging to predict the state of the sample (dark or bright).The schematic diagram in Figure 1(b) shows the molecular arrangement in the strip domains developed from the bottom and top rubbed surfaces.In the gray image, there can be seen a clear stripe pattern of periodically varying intensity.In this cell configuration, both the states in the stripe domains are stable and behave like SSFLC cells.Since there is an optical contrast (transmission intensity) change in the adjacent stripe, there should be a change in the alignment orientation of the FLC molecules in these stripe domains.Based on this assumption, the schematic is drawn in the adjacent inset in Figure 1(b).In both the stripes domains, FLC molecules will rotate about the pseudo cone, acquiring the extreme position in opposite states.As seen in Figure 1(b) inset, the net dipole moment of the adjacent layers is required to be nearly zero to minimize the energy of the system.The angle formed by the alignment direction in two adjacent stripes domains is nearly 17 o as measured under the optical microscope.Half part of 17 o is distributed in each stripe, which is ,8 o .And assuming the maximum tilt angle to be 45 o , the angle of rotation between the smectic layers is around 37 o , schematic in Figure 1(b).

Dielectric spectroscopy observation
In both the strip domains, the molecules are in a stable state along the rubbed direction.In one stripe domain, the dipoles are pointing UP and in the adjacent stripe they are pointing DOWN, refer to Figure 1(b).The rubbing direction is the most favourable condition for molecular orientation in the arrangement of surface stabilised high-tilt FLC sample.The dielectric behaviour is recorded at different measuring AC voltage (Supplementary Figure S1) and positive bias field strengths, as shown in Figure 2. It is surprising to see that ε 0 increases with the increase in the bias voltage up to 2 V and then starts decreasing with the increase in bias field, as seen in Figure 2(a).This means that the molecular phase fluctuation is taking place in one of the stripe domains with a positive polarity bias field whereas, in the adjacent stripe domain, the direction of the electric field and the direction of the dipoles are in the same direction.However, in another stripe domain where the direction of the dipole is opposite to the applied electric field, they have to reorient in the direction of the applied field.Hence, the FLC molecules have to move on the hypothetical cone to the other side.This phase angle is around 90 o on the hypothetical cone at þ2 V bias and is contributing to maximum phase fluctuation, resulting in a more permittivity value.Further increase in the bias field around þ4 V, the molecules have to go to the other side of the cone (180 o ) and the dipoles in that stripe domain are in the direction of the applied electric field, resulting in the suppressed dielectric permittivity as seen in Figure 2(a).
This behaviour is also reflected in the loss-factor curves as the bias voltage is increased.The magnitude of the Goldstone mode (GM) peak increases and shifts towards the left side as seen in Figure 2(b).On the other hand, one additional hump is also observed at lower frequency than GM on increasing the bias from 0.8 to 1.5 V.This low-frequency process is similar to the surface effect-based relaxation recently observed [24][25][26].This behaviour of lower frequency process is contradictory to our previous results of conventional FLC materials and sample cell configuration where the DC biasing diminishes the process [24,27], but here, this is intensified at 2 kHz frequency up to 1.5 V.

Optical textures along with dielectric spectroscopy measurement
It will be more informative if optical texture variation could be correlated with the dielectric measurements.If the lower frequency process is due to the surface effect, then it must show changes in the optical textures at sufficiently high voltage [24].Therefore, the dielectric measurement scan with frequency and optical texture images are taken simultaneously.During the full scan of frequency for dielectric, the image was captured at 50À 60 Hz frequency.At this frequency, the dielectric permittivity value is noticeably high, which means that the dipolar relaxation process contribution is also significant and could induce molecular fluctuations at the suitable magnitude of applied bias voltage.This information can be extracted from the optical textures under cross polarized microscope, Figure 3.As seen in Figure 3(a), the field of view covers the conducting and non-conducting portions of the sample.There is no noticeable change in conducting region in comparison to non-conducting.The texture remains almost the same which means that the applied field is below the threshold field required for the complete molecular switching, therefore its corresponding dielectric permittivity value, ε 0 , at 60 Hz, Figure 2(a) of data from 0.2 V and above till 1.5 V is also low.
At 2 V bias, the heliconical texture is observed in one of the stripes during the dielectric measurement scan, Figure 3; then its corresponding permittivity value ε 0 at ,60 Hz is seen close to the maximum, as seen in Figure 2(a).However, the optical textures at lower and higher DC bias than 2 V are shown in Supplementary Figure S4.Molecular relaxation information is further inferred from tanδ plots of Figure 2(b).There can be noticed two dielectric relaxation processes in the bias range from 0.6 to 3 V; one is GM and another is surface based process [24].The higher value of the dielectric properties (ε 0 ) in the bias range (0.6 to 3 V) than at 0 V is because of the availability of large degrees of freedom to the molecular dipoles than at 0 V bias.When contributing to higher permittivity with large degrees of freedom, the molecules remain somewhere between the polariser and analyser over the hypothetical cone  where they can fluctuate more than in other states.This allows a large contribution to the dielectric properties.
At 4 V, no heliconical texture is observed because molecules have been switched thoroughly to one of the extreme states over hypothetical cone in the stripe of one type orientation.In an adjacent stripe of other type orientation, they are already in the direction of the applied field, Supplementary Figure S4(b).Dielectric permittivity corresponding to the scan of 4 V is reduced to the least value, Figure 2(a) indicating that the lower frequency molecular relaxation is suppressed largely, whereas GM is still there with a suppressed magnitude as reflected in Figure 2(b).As seen in Figure 3(c) corresponding to 4 V dielectric measurement, the dark stripe has again become dark due to the property of FLC having 45 o tilt angle.The overall molecular switching covers 90 o angle and attains almost the same angular relation with the polarizer and analyzer due to which the optical contrast is the same as it was at 0 V bias.On reversing the polarity of the bias, the behavior of the sample is same but in reverse orientation and in adjacent stripe domain.

Optical texture observation
The cell was aligned by applying 2 V positive DC bias due to which the smectic layers are rotated by ,5 o angle with respect to the rubbing direction.But at 2 V, merely ,5 o layer rotation is observed due to the low field strength to overcome the value of anchoring energy, Figure 4.However, the overall transmission is more toward the dark stripe than the bright because the difference in the transmission through the adjacent stripes.On the other hand, if the electric voltage of À 2 V was applied then this contrast would have been toward the bright side.In other words, the FLC molecules have to overcome the surface anchoring energy of rubbed surfaces due to the bias field by rotating both stripes to one side only.The application of an electric field has affected the stripe width also in field active (conducting) region in comparison to the non-active (non-conducting) region.The width of the stripe in the non-conducting region is ,2.6 μ m whereas it is ,3.6 μ m in conducting region and the ratio of two is ,0.72.The contrast ratio between the stripes is almost the same in both conducting and non-conducting regions, suggesting the molecular arrangement is not differing largely when the smectic layers are reoriented at this field value.It means there is a difference in the molecular director in adjacent stripes which may be affected by increasing the aligning applied electric field.
The layers are orientated in the opposite direction at 22 o angle by applying negative polarity of 3 V bias to the same cell and keeping the cooling rate and other parameters the same as in previous case.The texture of the same is shown in Figure 5.This means that the more dipoles are also taking part in the reorientation process than at 2 V and smectic layers start reorienting when the tilt angle is stabilized at 22 o angle with respect to the rubbing direction.The increased value of reorientation of smectic layers is due to the applied potential value must be closer to the threshold value, which allows the larger reorientation than at 2 V.The trend of the stripe width pattern in conducting and non-conducting regions is the  same as it was in the 2 V aligned sample.The stripe width in the conducting region is shorter than in the nonconducting of À 3 V aligned sample.The ratio of two adjacent stripe widths in non-conducting and conducting is 0.66.Texture color is also changing in comparison to the above two cases of 0 and 2 V suggesting the considerable change in molecular orientation along with reorientation of smectic layers.
This cell is reheated to the isotropic phase and cooled slowly after staying in the isotropic phase for 10 min, as in above cases.This time, the sample is cooled in the presence of a higher DC bias of þ10 V which is more than threshold value of 4À 5 V.The layer reorientation is observed to be 34 o , Figure 6(a).Also, when the negative polarity bias of À 10 V applied, the reorientation is again 34 o , Figure 6(b), but in opposite direction.This means that around 10 V bias, the smectic layer reorientation is stabilised around the angle 34 o with respect to the rubbing direction.It should be mentioned here that once the bias field is removed, the states in both the domain stripes are thermally stable states in all the above discussed cases.It is also worthwhile to notice that during the cooling cycle the tilt angle of the molecules gets stabilised below 2 o -3 o of T c in SmC � phase.
Again, the alignment is achieved by applying 20 V bias voltage and the layer orientation was found to be orientated 45 o degrees which is the tilt angle of the FLC material and is shown in Figure 7.This means that surface anchoring energy has to be overcome by the bias field to make the tilt angle stabilization, which is around 10 V in the present cell geometry.The main difference between conventional FLCs and FLCs without SmA � phase is in the tilting of FLC molecules and the smectic layer formation.In conventional FLCs, the phase transition is from N � to SmA � and then to SmC � phase.In this phase sequence, the smectic layer formation and tilting of molecules within smectic layer take place in SmA � and SmC � , respectively.On the other hand in high-tilt-angle FLCs, where the transition is from N � to SmC � phase, first, the tilting of molecules takes place at the T c temperature and then the formation of smectic layering.Therefore, such high tilt angle FLC materials are more difficult to align, particularly in thick and non-bi-stable cell geometries.
The stripe width in conducting region is ,3.8 μ m whereas it is , 2.3 μ m in non-conducting region.However, the stripe width distribution is not uniform in conducting region, but it has a maximum distribution of ,3.8 μ m.The stripe width ratio between the nonconducting and conducting regions is ,0.58.It has been demonstrated that the stripe width is almost proportional to the sample cell thickness [21].In our case, this finding also seems to be matching with the cell gap of ,3 μ m.However, if the concept of smectic layer compression is also considered [28], the stripe width can be correlated with smectic layer thickness.If the compression due to deformation by the electric field is large, then the smectic layer thickness is reduced.The reduction in layer thickness increases the stripe width as evident from present experimental findings.

Dielectric spectroscopy observation
The dielectric spectroscopy of the 2 V DC bias aligned sample is taken under the influence of positive and negative DC bias at room temperature.In case of positive DC bias application, the dielectric permittivity at lower frequency shows the consistently decreasing trend with bias.Data is shown in Supplementary Figure S2.
The impact of negative bias voltage in the same cell geometry is shown in Figure 8(a), the permittivity at À 4 V bias jumps to almost the value of 50 and then starts decreasing with negative polarity.This means that in one of the stripe domains, the dipole moment of the FLC molecule is in the same direction as the direction of the applied bias field, also schematically represented in Supplementary Figure S2(b).In another adjacent strip domain, the molecules tend to orient in the direction of the applied bias field.In this case, the molecules have to reorient against the favorable condition, resulting in the slow phase change over the hypothetical cone and hence more phase fluctuations, contributing to an increase in the dielectric permittivity value at a low bias field.The phase fluctuations are maximum at À 3 to À 4 V bias, suggesting the molecules are somewhere in the middle of the hypothetical cone.This effect is clearly seen in the optical micrographs also, Figure 8(b,c).At around À 4 V bias in Figure 8(a), the ε 0 is maximum and texture at this voltage is also slightly brighter than previous, Figure 8(d).Again for a higher bias field of À 10 V, the molecules in that stripe domain go to the extreme position over the hypothetical cone which is again a dark state.On the other hand, in the sample aligned by À 2 V, the results are the same but in opposite orientation.
The alignment of the stripe domains at À 20 V DC bias, which is sufficiently higher than the threshold field, is achieved and investigated by dielectric spectroscopy Supplementary Figure S3.As discussed above, the smectic layer orientation is dependent on the magnitude and polarity of the bias field.As seen in the optical textures of Figures 6 and 7, the smectic layer orientation was found about 45 o to the rubbed direction.The layer orientation is towards left with positive polarity and right with negative polarity bias field with respect to the rubbing direction.
The maximum smectic layer orientation of 45 o was observed in the sample aligned by cooling under around 20 V. The smectic layer orientation of 45 o is equivalent to the tilt angle of the FLC material, Figure 7.The layer orientation would be right to the rubbed direction with one polarity and will be left with the opposite polarity bias field.Again both the states are UP and DOWN in bi-stable states which could be due to the reason that both the favorable states are far away from each other (Figure 7).One is along the rubbed direction and another is 45 o from the rubbed direction.

Twisted domains in sample cooled under high DC bias: optical texture and corresponding dielectric spectroscopy observation
It is known that a DC bias field, above the threshold field, can switch the molecules at the extreme position of rotation in the layer and can achieve the maximum tilt angle of molecular director from layer normal.In the present study, stripes have been formed with the smectic layers reorientation in which the molecules are arranged differently in adjacent stripes.Here, there are four main cases namely ðiÞ stripe domain formation along the rubbed direction, ðiiÞ stripes reorientation away from rubbing direction, ðiiiÞ twisted domain structure in stripes, and ðivÞ appearance of periodic heliconical structure [29].
Twisted domain structure in stripes is seen in the sample aligned in the cooling cycle at a high DC bias of À 20 V, inset (lower left) of refer back to Figure 7.The stripes are reoriented along the structure memory which means the reoriented smectic layer is a permanent adjustment and cannot be reverted even by a strong DC bias of opposite polarity in SmC � phase, Figures 4-7.As seen in the inset of Figure 6(a,b), and inset (lower left) of Figure 7, the left and right-handed twists are seen in adjacent stripes.The overall color intensity variation in adjacent stripes is due to different orientations of smectic layers whereas the periodic twist pattern intensity is due to molecular rotation inside the reoriented smectic layers similar to that of the helical pattern in non-SSFLC cell.However, this periodicity is not exactly similar to the dechiralization pattern in non-SSFLC structure because the cell in the present study is SSFLC geometry.Therefore, the twisted structure is purely induced structure and not intrinsically helical formed.In another way, the twist is not uniform throughout the sample but it is affected largely by local defects and can vary from ,4 to ,8 μ m in width.
On the other hand, some stray non-uniform field is working in the non-conducting region also which is not as strong as it is in conducting region, Figure 7.Some heliconical structure is noticeable within the stripe which is depicted by enlarging the localised view of the image, inset at the right portion of the image in Figure 7. Schematic is considered for the same in Figure 1(b) because this portion is almost equivalent to the texture in Figure 1.In the bright stripe, the molecules are slightly reoriented and are aligned nearly at angle 45 o to polarizer and analyzer due to which the brighter intensity portion increases in size than the dark stripe where the molecules are aligned slightly away from 45 o , which means in the direction of analyzer.However, as per the nature of polarity of the applied field, the majority of molecules are tending to align at 45 o and the bright stripe seems wider than the dark.There would also be the reverse case, if the reverse field is applied, the dark stripe would be slightly wider than the brighter one but have non-uniform stripe width.On the other hand, there is a breakage in this continuity of stripe width.This breakage represents the restrictions of molecular rotation by opposite polarity molecules and allows the formation of heliconical structure.This is a regular structure near the electrodes only up to where the stray field is influencing.

Conclusions
In conclusion, it can be mentioned that if the FLC material possesses SmA � phase, the single process of smectic layer formation in SmA � phase and tilting of LC molecules after T c in SmC � phase takes place separately and hence easy to align unidirectional.But if the SmA phase is absent from the phase sequence and material phase changes from nematic to SmC � directly, then it is a challenge to align the FLC molecules because both the processes of smectic layer settlement and tilting of FLC molecules take place simultaneously at the same phase transition.A hightilt angle FLC (CS-2004) without the SmA � phase has been investigated for the alignment under particular conditions of DC bias application during cooling of the sample.During slow cooling at the T c temperature, there are two processes of layer formation and tilting of the molecules in competition.The anchoring energy of alignment layer is not enough to break this competition.This results in two distinct stripe domains in thin cells having UP and DOWN dipolar orientation in neighbouring stripes to minimise the FLC material energy.The smectic layer reorientation is found varying as a function of applied DC bias during cooling.The stripe domains are still persisting in the reoriented structure.Beside this, the application of DC bias during dielectric measurement has shown the twisted structure inside the stripe domains with clockwise and anticlockwise orientation.At a low field of DC bias at room temperature, the heliconical structure is observed in one type of stripe domain and has contributed remarkably to the dielectric permittivity also at this DC bias.This has been confirmed by taking the optical textures at the same time of dielectric measurements.Such types of twisted and helix based heliconical structures are interesting to explore further for the understanding of helical geometry configuration in SSFLC.

Figure 1 .
Figure 1.(Colour online) (a) Texture of the FLC sample aligned by cooling without any DC bias under cross positions of polariser and analyser and (b) processed image by image processing tool ImageJ (National Institute of Health, USA) of a small section of texture shown in the yellow square.The enlarged field illustrates the molecular arrangement of FLC within the stripe domains.Inset image shows the enlarged portion of the square portion in the main texture.

Figure 2 .
Figure 2. (Colour online) (a) Real part of complex dielectric constant (ε 0 ) and (b) loss factor (tanδ) of the sample, cooled under zero bias field, as a function of frequency at various positive DC bias.

Figure 3 .
Figure 3. (Colour online) Optical textures of the sample cooled under 0 V DC bias.Textures taken at room temperature at 2 V and showing the helix-based structure.Enlarge view of the rectangular shaped marking portion shows the clear helix based structuring within the stripe domain.

Figure 4 .
Figure 4. (Colour online) Optical texture of the sample at room temperature after aligned by cooling under the DC bias application of 2 V. Arrows indicate the direction of alignment.Scale bar is 20 μm.

Figure 5 .
Figure 5. (Colour online) Optical texture of the sample at room temperature after aligning by cooling under the application of À 3 V DC bias.Arrows indicate the direction of alignment.

Figure 6 .
Figure 6.(Colour online) Optical texture of the sample at room temperature showing the smectic layer reorientation after aligned by cooling under the DC bias application of (a) 10 V and (b) À 10 V.The enlarged inset indicates the clockwise and anti-clockwise layer twisting in both adjacent stripes.

Figure 7 .
Figure 7. (Colour online) Smectic layer reorientation at À 20 V DC bias during the cooling of the sample.Heliconical structure shown in the enlarged view on the top right side.Double headed white arrows represent the orientation of FLC molecules in stripes.Twisted layer structure in an adjacent stripes in the enlarged view of the yellow marked section, bottom left.Bottom right schematic indicates the alignment of molecules in adjacent stripes which is distinct from the alignment in the sample cooled without DC bias.

Figure 8 .
Figure 8. (Colour online) (a) Real part of dielectric constant of sample cooled under À 2 V as a function of frequency and at various magnitude of positive DC bias voltage.Optical texture of the sample at (b) 0 V DC bias, (c) À 2 V, (d) À 5 V, and (e) À 10 V.