Soft Matter
View Article Online

Published on 10 November 2015. Downloaded by University of Hyderabad on 28/01/2016 13:33:23.

PAPER

Cite this: Soft Matter, 2016,
12, 1324

View Journal | View Issue

Experimental studies on the rheology of cubic
blue phases†
Rasmita Sahoo,a O. Chojnowska,b R. Dabrowskib and Surajit Dhara*a
We report detailed experimental studies on the rheology of cubic blue phases. We observe several flow

Received 11th September 2015,
Accepted 10th November 2015
DOI: 10.1039/c5sm02299aregimes within each blue phase from rheomicroscopy and small angle light scattering experiments. Both the
cubic blue phases exhibit solid-like response while the cholesteric phase shows gel-like behavior. The elastic
modulus of BP-I is larger than that of BP-II. The shear induced yield transition occurs at a higher strain in
BP-II than BP-I. Both the blue phases show stress relaxation through periodic modulation in step-strain
experiments. Our results show that the rheological responses of these two phases are significantly diﬀerent

www.rsc.org/softmatterowing to the distinct networks of defect-disclinations.

I. Introduction
In cholesteric liquid crystals the director (the average orientation direction of the molecules) spontaneously twists around asingle helical axis of fixed orientation. In highly chiral systems,
close to the isotropic transition, the orientation of the local
director can twist around two perpendicular axes and thecorresponding deformed structure is termed a ‘‘double-twist
cylinder’’.1 Blue phases are special cases in which double twist
cylinders fill up the volume by stabilizing a lattice of defectdisclinations.2,3 Depending on the arrangement of the defect lines
they are classified into three types namely, BP-I (body-centeredcubic structure), BP-II (simple cubic) and BP-III (amorphous). The
schematic diagrams of BP-I and BP-II which are the subject matterof investigation of this paper are shown in Fig. 1 The discovery ofpolymer stabilized blue phases with a wide temperature range hascreated a lot of interest owing to their possible applications.4–12
Significant progress has also been made in various applications ofblue phases. Nevertheless many fundamental aspects of these
exotic phases are still unexplored. For example, recently several
predictions were made on the rheological properties and the
dynamics of the disinclination networks of BP-I and BP-II.13–15
However experimentally very little is known about the rheologyof these phases.16–18 In this paper, we report first detailed
experimental studies on the rheology of cubic blue phases.
Our results show that different rheological responses of BP-II
and BP-I are connected to their structures and the dynamics ofthe defect networks.

aSchool of Physics, University of Hyderabad, Hyderabad-500046, India.
E-mail: sdsp@uohyd.ernet.inbInstitute of Chemistry, Military University of Technology, 00-908 Warsaw, Poland† Electronic supplementary information (ESI) available. See DOI: 10.1039/
c5sm02299a1324 | Soft Matter, 2016, 12, 1324--1329

Fig. 1 Schematic diagrams of the BP-II and BP-I. (a and c) Spatial
arrangements of double twisted cylinders in unit cells. (b) Simple cubic
unit cell of the disinclination lattice in BP-II. (d) Body centered cubic unit
cell of the disinclination lattice in BP-I. The black lines in (b) and (d) are thedefect-disinclinations.

II. Experimental
The blue phase liquid crystal used in this study is a mixtureof four fluorinated compounds and a highly chiral dopant.
These compounds were synthesized in our laboratory. They arechemically stable and exhibit high resistivity.19 The detailsof the molecular structure and their wt% are given in the
supplementary.20 It exhibits following phase transitions: I
46.4 1C BP-II 41.4 1C BP-I 36.6 1C N*. Rheological measurements
were performed using a controlled strain Rheometer (MCR 501,
Anton Paar) with a cone–plate measuring system having a plate
diameter of 25 mm and a cone angle of 11. The temperature of
the sample was controlled with an accuracy of 0.1 1C using aPeltier temperature controller. All the measurements were madeupon cooling the sample from the isotropic phase.

This journal is © The Royal Society of Chemistry 2016

View Article Online

Published on 10 November 2015. Downloaded by University of Hyderabad on 28/01/2016 13:33:23.

Paper

Soft Matter

Fig. 2 Schematic diagram of the polarized light rheomicroscopy setup.
The setup was attached under the bottom plate. The images are taken in
the reflection mode.

We attached a microscope and a camera to the rheometerfor optical rheo-microscopy. A schematic diagram of the setup
is shown in Fig. 2. The rheomicroscopy setup consists of a CCD
camera (monochrome), a microscope tube and a long working
distance objective (NA = 0.4, 20, Nikon). We used parallel
plate geometry of diameter 43 mm and the thickness of thebottom glass-plate is 6 mm. The sample was illuminated byusing a polarized light through the objective from the bottom.
An analyzer was placed in the microscope tube before the CCD
camera. The microscope tube is adjustable in the y and z direction
for focusing. The details of the small angle light scattering setup
are given in ref. 21. The gap between two parallel glass plates inrheomicroscopy was 0.075 mm.

III. Results and discussion
The bulk sample was mounted on the rheometer without any
surface treatment of the measuring plates and the measurements were made while cooling the sample from the isotropic
phase at 0.1 1C min1. To identify the phase transition temperatures in the rheometer we first measured the temperature dependent shear stress at a fixed shear rate (Fig. 3). The isotropic (I) to

Fig. 3 Temperature dependent shear stress at a constant shear rate of 10 s1.
Three diﬀerent phase transitions are marked by vertically dotted lines.

This journal is © The Royal Society of Chemistry 2016

Fig. 4 Optical rheomicroscopy images taken during the measurement of
temperature vs. shear stress at a constant shear rate of 10 s1 in three
diﬀerent phases. The direction of shear is shown by an arrow. P and A
indicate crossed polarizers.

BP-II phase transition is marked by a rapid increase of thestress and the BP-I to cholesteric phase (N*) transition ismarked by a sudden fall of the same. A small kink is observedat the BP-II to BP-I phase transition. The temperature range of
BP-II and BP-I is 5 1C and 4.8 1C, respectively. The stress in
the N* is almost comparable to that of the isotropic phase
except a gradual increase due to the decrease of temperature.
It is observed that the shear stress of BP-I is larger than that of
the BP-II and N* phase.
Fig. 4 shows some representative rheomicroscopy images
taken during the measurement of temperature dependentshear stress at a constant shear rate. In BP-II, the Grandjeancano lines are observed which are oriented perpendicular to theshear direction (Fig. 4(a)). It suggests that the director isaligned parallel to the shear direction. The increase of stresscompared to the isotropic phase is due to the motion of theseGrandjean-cano lines. As the temperature is reduced, somefilamentary structures appear in BP-I (Fig. 4(b)) and the stressalso increased compared to BP-II. These filamentary structures
are continuously broken and rejoined during the steady shear.
The cholesteric phase shows a typical texture (Fig. 4(c) and (d))
similar to that usually observed under planar degeneratesurface anchoring conditions.
The shear rate dependent viscosity and the corresponding
rheomicroscopy images are shown in Fig. 5 and 6, respectively.
We observe that the N* phase exhibits a typical shear thinningbehavior (Fig. 5(a)). The viscosity of BP-II and BP-I phases ismuch larger than that of the N* phase in the low shear rate
regime (0.01 to 1 s1). For example, at g_ = 0.01 s1, ZN* = 1.2 Pa s,
ZBP-II = 17 Pa s and ZBP-I = 52 Pa s. BP-I and BP-II show multiple
shear thinning and finally the viscosity of BP-II at the highest
shear rate is lower than that of the N* phase. Thus BP-II shows
stronger shear thinning behavior than the other two phases.
The corresponding variation of shear stresses of three phases isSoft Matter, 2016, 12, 1324--1329 | 1325

View Article Online

Published on 10 November 2015. Downloaded by University of Hyderabad on 28/01/2016 13:33:23.

Soft Matter

Fig. 5 Shear rate dependent (a) viscosity and (b) stress at three diﬀerent
temperatures. (inset) Red lines are best fits to the power law: t = ag_ a.

also shown in Fig. 5(b). Further we have also estimated theEricksen number (Er) of the three phases. The range of EricksenPapernumbers of the N* phase is 30 o Er o 9  104 where the shear
rate varies from 0.01 to 1000 s1. Similarly for the BP-II and
BP-I, the ranges of Ericksen number are 50 o Er o 7  104 and300 o Er o 1.2  105, respectively.
Shear stress of BP-II shows three distinct regimes namely
BP-II(1): g_ = 0.01–0.3 s1; BP-II(2): g_ = 0.3–2 s1 and BP-II(3):g_ = 2–1000 s1. A power law fit t = a_ga describes the data to avery good approximation. The fit parameters are: a = 0.87 anda = 0.33 in BP-II(1); a = 0.42 and a = 0.35 in BP-II(2); a = 0.12 anda = 0.87 in BP-II(3). Some representative rheomicroscopy
images in these regimes are also shown in Fig. 6. We observethat in BP-II(1), the Grandjean-cano lines flow parallel to theshear direction (downward green arrows in Fig. 6). In BP-II(2),the Grandjean-cano lines are broken and in BP-II(3) the texture
appears like a flow aligned nematic phase. In BP-I, there arealso several regimes but they are not distinctly separable as
those of BP-II. Nevertheless it is clear that the multiple shear
thinning is due to the breaking of texture at different shear
rates (BP-I in Fig. 6). The cholesteric phase shows uniform
shear thinning behavior and there is no significant change inthe textures up to the shear rate of 10 s1. Beyond this shear
rate the helix uncoils and leaves a flow induced nematic phaseand hence the viscosity decreases. In the case of BP-II and BP-I,
the flow induced nematic state appears at shear rates above 126
and 200 s1, respectively. Recently, Henrich et al. studied therheology of cubic blue phases by numerical simulation.14
Depending on the shear rate and the Ericksen number various
flow regimes have been identified in both BP-I and BP-II. So our
results qualitatively agree with their predictions.

Fig. 6 Rheomicroscopy images taken during the measurement of shear rate dependent viscosity in three phases. The direction of shear is shown by anarrow on the right side. The downward green arrows in BP-II show the motion of the Grandjean-cano lines. See ESI† (Video S1).

1326 | Soft Matter, 2016, 12, 1324--1329

This journal is © The Royal Society of Chemistry 2016

View Article Online

Published on 10 November 2015. Downloaded by University of Hyderabad on 28/01/2016 13:33:23.

Paper

Soft Matter

Fig. 7 Small angle light scattering (SALS) images taken in the HV polarisation configuration at three diﬀerent temperatures and various shear rates. The
direction of shear is shown by an arrow. The insets are contour plots with false colours.

We also performed small angle light scattering (SALS)
experiments. The details of the experimental setup werereported in ref. 21. The images of HV scattering at various shear
rates are shown in Fig. 7. We observe that the SALS patterns of
all the phases at the lowest shear rate (0.011) are mostly
circular with the largest diameter in the N* phase. It suggeststhat the orientational fluctuations are stronger in the N* phasecompared to the other two phases. Interestingly at higher shear
rates (40–126 s1) BP-II shows obscure butterfly patterns. The
butterfly patterns are prominently observed in contour plots(insets of Fig. 7). These kinds of SALS patterns are typicallyobserved in complex fluids including polymer solutions, polymer mixtures, micellar surfactants and lyotropic lamellar
phases due to the density or concentration fluctuations thatare moderately coupled to the flow.22,23 However we did notobserve any special feature in rheomicroscopy at the sameshear rates. It suggests that the characteristic time of flow isfaster than the breaking and reforming of the microstructures.

This journal is © The Royal Society of Chemistry 2016

At a shear rate of 40 s1, BP-I shows multiple scattering patterns(Fig. 7, BP-I) which are very different from BP-II. This is due tothe stronger orientational fluctuations caused by larger microstructures observed (Fig. 6, BP-I) in rheomicoscopy. At a shearof rate 40 s1, N* shows an anisotropic scattering pattern thatis elongated perpendicular to the shear direction. At a very
high shear rate (e.g., 631 s1), the scattering patterns of both
BP-II and N* phases are highly elongated perpendicular tothe shear direction. Since the images are in the q-space, theoverall alignment of the director is along the shear direction.
The scattering intensity at a higher shear rate (for example, at
631 s1) in BP-I is almost zero and this could be due to the very
low birefringence and ceasing of orientational fluctuations dueto the large elastic modulus.
Fig. 8 shows the strain dependent storage (G 0 ) and the loss00
(G ) moduli of all the phases. It is observed that in the N*
phase, in the low strain regime (g r 1%), G 0 C G00 . In the highstrain regime (g 4 1%), G00 is larger than G 0 and it shows aSoft Matter, 2016, 12, 1324--1329 | 1327

View Article Online

Published on 10 November 2015. Downloaded by University of Hyderabad on 28/01/2016 13:33:23.

Soft Matter

Paper

Fig. 8 The strain dependence of the storage G 0 and the loss G00 moduli of
the sample at three diﬀerent temperatures where o = 1 rad s1.

typical fluid-like behavior. G 0 of both the blue phases is higher
than that of the N* phase and G 0 of BP-I is around 5 times larger
than that of BP-II. The linear viscoelastic (LVE) range of boththe cubic phases is almost comparable (i.e., gc = 4%). In BP-I,
the strain induced fluidization or the yield transition (G 0 = G00 )occurs at g = 16% whereas in BP-II it occurs at a higher strain
value (g = 20%) than that of BP-I. This could be due to the factthat the defect lines in BP-II are intersecting and larger strain isneeded to break the intersection and as a result its criticalstrain amplitude is higher than that of the BP-I.
To obtain more insight into the rheological response of thedefect networks we performed step-strain measurements. Fig. 9shows the stress response under applied step-strain. Here thestrain value is changed from 0.3% (within LVE) to 30% (above
LVE range). There are three regions in the time dependentshear stress. Initially (region-I) the strain is below the LVE range
and constant for 600 s. Then the strain is increased above the
LVE range (region-II) and constant for 600 s and again it isdecreased to 0.3% (region-III). The N* phase shows expectedstress response under applied step-strain in all the regions. In

Fig. 9 Time dependent shear stress at three diﬀerent temperatures.
(inset) The periodic modulation in the BP-I, in region-III.

1328 | Soft Matter, 2016, 12, 1324--1329

Fig. 10 The frequency dependence of the storage G 0 (o) and the loss
G00 (o) moduli of the sample at three diﬀerent temperatures. The strain
amplitude g = 1%.

region-II of BP-II there is a gradual decrease of stress with timeand it could be due to the breaking of defect nodes under highstrain followed by a continuous bulk flow. In the same region of
BP-I the stress is constant where the system undergoes a flowaligned state. In this case there is no breaking of defectnetworks, as they do not intersect. In region-III both BP-I and
BP-II show sinusoidal stress oscillations that decay with time.
The amplitude of oscillation is more in BP-I than that of BP-II.
Under a large strain the defects of BP-I are displaced from theequilibrium positions consequently the network is distorted
and they tend to reorganize upon removal of the strain and this
could lead to a periodic stress oscillation that decays with time.
The small oscillation in region-III in BP-II could be due tothe reconnection of some defects. We conjecture that the stepstrain experiment clearly displays the diﬀerent dynamical
responses of BP-I and BP-II under large strain which are dueto the diﬀerent network structure of the defects.
Finally we have measured the frequency response of G 0 and
00
G of three phases (Fig. 10). The cholesteric phase exhibitsa behavior very similar to that of a gel.24 At low frequency(o o 0.2), G 0 reaches a plateau where G0 = 0.1 Pa, and theelastic modulus is higher than the loss modulus. At higher
frequency (o Z 0.2), a fluid like behavior is observed withThis journal is © The Royal Society of Chemistry 2016

View Article Online

Paper

G00 being greater than G 0 . Thus there is a crossover at a criticalfrequency o = 0.2 rad s1, from a solid-like regime whereG 0 4 G00 and a fluid-like regime where G00 4 G 0 . In the caseof BP-II and BP-I, G 0 is always greater than G00 and a plateau
signifies a solid-like behavior of the two phases.

Published on 10 November 2015. Downloaded by University of Hyderabad on 28/01/2016 13:33:23.

IV. Conclusions
In conclusion, we have experimentally studied the rheologicalproperties of cubic blue phases. Our experiment reveals several
flow regimes with characteristic microstructures within eachblue phase. At a high shear-rate regime all the phases exhibit aflow aligned nematic state. The measured apparent viscosity
is larger in BP-I than in BP-II. In the step strain measurements
BP-I exhibits decaying stress oscillation with time which is connected to the diﬀerent dynamical response of the defect networks
under large strain. The amplitude of the sinusoidal oscillations of
BP-I in the step-strain experiment is larger than that of BP-II. These
results are qualitatively in agreement with recent simulation. Both
BP-II and BP-I exhibit a solid-like behavior while the cholestericphase shows a gel-like behavior and the elastic modulus of BP-I islarger than that of BP-II. The larger critical strain for yield transitionin BP-II is due to the breaking of defect nodes.

Acknowledgements
We gratefully acknowledge the support of the CSIR (03(1207)/
12/EMR-II). R. S. acknowledges UGC for the BSR fellowship. We
acknowledge Dr Henrich for useful discussions and Dr
J. Ananthaiah for help in setting SALS experiments. OC and
RD acknowledge POIG (No. 01.03.01-14-016/08).

References
1 P. G. de Gennes and J. Prost, The Physics of Liquid crystals,
Oxford University Press, London, 2nd edn, 1993.
2 H. Grebel, R. M. Hornreich and S. Shtrikman, Phys. Rev. A:
At., Mol., Opt. Phys., 1984, 30, 3264.
3 D. C. Wright and N. D. Mermin, Rev. Mod. Phys., 1989, 61, 385.

This journal is © The Royal Society of Chemistry 2016

Soft Matter

4 H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang and T. Kajiyama,Nat. Mater., 2002, 1, 64.
5 H. J. Coles and M. N. Pivnenko, Nature, 2005, 436, 997.
6 K. M. Chen, S. Gauza, H. Q. Xianyu and S. T. Wu, J. Disp.
Technol., 2010, 6, 49.
7 D. P. Resler, D. S. Hobbs, R. C. Sharp, L. J. Friedman and
T. A. Dorschner, Opt. Lett., 1996, 21, 689.
8 Y. H. Lin, H. S. Chen, H. C. Lin, Y. S. Tsou, H. K. Hsu and
W. Y. Li, Appl. Phys. Lett., 2010, 96, 113505.
9 J. Yan, Y. Li and S. T. Wu, Opt. Lett., 2011, 36, 1404.
10 M. Mori, T. Hatada, K. Ishikawa, T. Saishouji, O. Wada,J. Nakamura and N. Terashima, J. Soc. Inf. Dispaly, 1999, 7, 257.
11 J. Yan and S. T. Wu, Opt. Mater. Express, 2011, 1, 1527.
12 Y. Li, Y. Chen, J. Sun, S. T. Wu, S. H. Liu, P. J. Hsieh, K. L.
Cheng and J. W. Shiu, Appl. Phys. Lett., 2011, 99, 181126.
13 O. Henrich, K. Stratford, D. Marenduzzo, P. V. Coveney and
M. E. Cates, J. Phys.: Condens. Matter, 2012, 24, 284127.
14 O. Henrich, K. Stratford, P. V. Coveney, M. E. Cates and
D. Marenduzzoc, Soft Matter, 2013, 9, 10243.
15 A. Dupuis, D. Marenduzzo, E. Orlandini and J. M. Yeomans,
Phys. Rev. Lett., 2005, 95, 097801.
16 R. N. Kleiman, D. J. Bishop, R. Pindak and P. Taborek, Phys.
Rev. Lett., 1984, 53, 2137.
17 N. A. Clark, S. T. Vohra and M. A. Handschy, Phys. Rev. Lett.,
1984, 52, 57.
18 M. Rajeswari, J. Ananthaiah, R. Dabrowski, V. S. S. Sastry,
S. Dhara and B. K. Sadashiva, Mol. Cryst. Liq. Cryst., 2011,
547, 39.
19 O. Chojnowska, R. Dabrowski, J. Yan, Y. Chen and S. T. Wu,
J. Appl. Phys., 2014, 116, 213505.
20 Supplementary materials at for the chemical structures of
the compounds and the video (ESI†).
21 J. Ananthaiah, M. Rajeswari, V. S. S. Sastry, R. Dabrowski
and S. Dhara, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys.,2012, 86, 011710.
22 E. K. Wheeler, P. Izu and G. G. Fuller, Rheol. Acta, 1996,
35, 139.
23 B. Belzung, F. Lequeux, J. Vermant and J. Mewis, J. Colloid
Interface Sci., 2000, 224, 179.
24 L. Ramos, M. Zapotocky, T. C. Lubensky and D. A. Weitz, Phys.
Rev. E: Stat., Nonlinear, Soft Matter Phys., 2002, 66, 031711.

Soft Matter, 2016, 12, 1324--1329 | 1329