Observation of New States of Liquid Crystal 8CB under Nonlinear

Feb 16, 2011 - We assume the structure to be stabilized by defects that pin the new 6-fold phase. .... was achieved by drilling holes in the insulatin...
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Observation of New States of Liquid Crystal 8CB under Nonlinear Shear Conditions as Observed via a Novel and Unique Rheology/ Small-Angle X-ray Scattering Combination Bernd Struth,*,† Kyu Hyun,† Efim Kats,‡,^ Thomas Meins,§ Michael Walther,† Manfred Wilhelm,§ and Gerhard Gr€ubel† †

DESY, Notkestrasse 85, D-22607 Hamburg, Germany Institut Laue-Langevin, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9, France § Institut fuer Technische und Polymerchemie, Abteilung Polymerchemie, Karlsruher Institut f€ur Technologie, Engesserstrasse 18, 76128 Karlsruhe, Germany ^ L.D.Landau Institute for Theoretical Physics, Kosygin str. 2, 117940 GSP-1, Moscow, Russia ‡

bS Supporting Information ABSTRACT: New stable states of liquid crystal 8CB could be induced by nonlinear shear conditions and observed by a newly developed rheology/X-ray scattering setup using synchrotron X-ray radiation. Nonlinear oscillatory shear created a distorted sixth order orientational structure. Even when oscillatory shear is switched off, the induced structure remains stable and can be removed only by heating the system into the isotropic state. We assume the structure to be stabilized by defects that pin the new 6-fold phase.

’ INTRODUCTION Liquid crystals belong to the wide class of complex fluids, a class of materials easily deformable by external stresses.1 Applying a shear field to liquid crystalline phases is one of the most successful methods employed to deform and orient anisotropic phases. When a shear field is applied, the system is transferred from the equilibrium into a nonequilibrium state. The transfer causes orientation that arises from the complex interplay between structure and flow.2-4 Only little is known about the nature of the nonequilibrium state and its consequences that are reflected in the viscoelastic and anisotropic properties of a material. By designing a completely new experimental setup, we found (for a simple model system) that shear in the nonlinear regime can induce states not known for any existing equilibrium phase. In the present work we studied the influence of steady and oscillatory shear on the time evolution of the microstructure of 4-cyano-40 -octylbiphenyl (8CB) in the lamellar smectic A phase. The spacing of the lamellae is 3.4 nm in this case. X-ray scattering is the only technique that allows for direct access to such small order parameters in the nanometer or sub-nanometer regime. 8CB undergoes the following sequence of transitions as a function of temperature: crystalline (C) f smectic A (SA) f nematic (N) f isotropic (I) at TC-S = 21.5 C, TS-N = 33.6 C, and TN-I = 40.5 C. The 8CB molecule possesses an elongated ellipsoidal shape, which, together with its molecular interactions, is responsible for its special physical characteristics, e.g., complex flow behavior and anisotropy. While the nematic phase of 8CB is characterized by orientational order only, the smectic A phase exhibits a one-dimensional translational mass density modulation along the unique orientation of the molecules. The translational mass density modulation generates the characteristic r 2011 American Chemical Society

lamella structure with the molecules filling the gaps of the lamellae. The molecular long axis is perpendicular to the lamellae plane in this case and parallel to the director n. The director n also points perpendicular to the lamellae plane and defines the general orientation of the ensemble (Figure 1). This special molecular arrangement describes a state of order. Local molecular orientation in liquid crystals, exhibiting singular behavior along lines, points, or walls, is far from perfect and is characterized by a wide variety of defects, leading, e.g., to order parameter discontinuities and dislocations.5 Besides many other aspects, there seems to be no general consensus on the description of stable states of systems and their influence on order parameters or order discontinuities with dissipation far from thermodynamic equilibrium. An experimental approach to obtain insight into nonequilibrium states of liquid crystalline phases was shown by Safinya and co-workers.6 They combined steady shear flow with synchrotron radiation and recorded snapshots of 8CB mesophases as a function of temperature. As a shear cell they used the Couette geometry that consists of two vertical concentric cylinders where the outer cylinder rotates and the inner is fixed. The X-ray beam passed horizontally through the cylinders mixing the antipodal velocity directions of the forward and backward gap of the geometry. Depending on the strain amplitude and frequency large amplitude oscillatory shear (LAOS) experiments can drive a system far from its original equilibrium state where the measurable rheological parameters show strongly nonlinear mechanical Received: September 21, 2010 Revised: January 17, 2011 Published: February 16, 2011 2880

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Figure 1. Smectic orientations of the lamellae represented by the director n and relatively to the velocity v, the velocity gradient m, and the normal direction e under shear. For our experiments, the direction of the incident X-ray beam (white block arrow) is parallel to m. Possible reflections due to X-ray scattering are indicated by black spots and are oriented in the direction of the director n. In the case of the c orientation, no constructive interference will occur, and thus no reflections are observable.

behavior. In this case, the microstructural response of the system on the external stress is not directly measurable and remains up to date subject to speculation. To our knowledge, there is no experimental or theoretical approach to measure or describe the underlying structural orientation processes on the molecular level. Nucleation or expulsion of various defects can not more than be imagined. Larson and co-workers7 performed pure rheological oscillatory measurements on 8CB in the smectic A phase. They applied LAOS to the sample using the common plate/plate geometry. The plate/plate geometry avoids some characteristic drawbacks of the Couette geometry. It consists of two parallel plates with the sample loaded in the gap. While one of the plates remains stationary, the other plate rotates or oscillates to apply the shear field to the sample. Oscillatory shear experiments allow one to determine, e.g., the viscoelastic moduli and the complex viscosity of a sample. On the basis of the results of the pure oscillatory rheological experiments, they postulated an influence of a given stress and strain on the microstructure of the system. For a strain amplitude near unity, the system was transformed in the strictly nonlinear regime. Following their rheological analysis, they suggested defects to be driven out and smectic layers to be aligned. To date, an experimental approach to quantify and characterize the correlation with the local microstructural evolvement of the system under macroscopically nonlinear mechanical conditions is missing. With conventional combined rheology and small-angle X-ray scattering (Rheo/ SAXS) experiments using horizontal X-ray beams, the predicted special arrangement of the 8CB lamellae in the plate/plate geometry of a rheometer is not accessible under shear conditions.

’ METHOD Any X-ray scattering process is based on the interaction between the incoming electromagnetic wave and electron density variations in the sample. When shear is applied in between the two plates of the rheometer geometry to the 8CB sample in the smectic A phase, the molecules have a tendency to form periodic lamellae that align perpendicular to the plates accordingly to the shear flow. The ‘a’, ‘b’ and ‘c’ orientations (Figure 1) refer to the director n. The director n pointing along the neutral direction e defines the ‘a’ configuration, while n pointing along the velocity direction v and the velocity gradient direction m defines the ‘b’ and ‘c’ orientations, respectively. An incoming

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Figure 2. Plate/plate geometry with X-ray beam passing vertically through the setup. The expected orientation of the smectic lamellae defined by the director n can be ideally observed with the above presented setup. n denotes the director, v the velocity, m the velocity gradient, and e the normal direction.

X-ray beam will produce characteristic X-ray patterns depending on the orientation of the lamellae in the sample (Figure 1). In order to simultaneously obtain information about the viscoelastic properties and the structural organization on nanoscales of 8CB, we have designed and commissioned a completely new setup allowing a synchrotron X-ray beam passing vertically through a plate/plate geometry probing the perpendicular ‘a’ orientation (Figure 2).8 The ‘a’ orientation produces a characteristic X-ray scattering pattern with two reflections separated by 180 in this case (Figure 2). The orientation of the reflections depends on the orientation of the smectic A phase lamellae in the rheometer geometry and is, in principle, parallel to the director n. An incoming wave with wavevector ki can interact with the sample with periodic electron density variation and result in constructive interference and a scattered wave with wavevector kf, when certain conditions are fulfilled. Whether constructive interference occurs depends on the dimensionality of the periodicity, the spacing of the periodicity a, the wavelength of the incoming wave λ, and the orientation ja0 of the incoming wavefront with respect to the director n, expressed in the one-dimensional Laue equation (Figure 3): ðeq. 1Þ aðcos ja - cos ja0 Þ ¼ λ For the given wavelength λ of 1.26 Å of the incoming X-ray beam of our experiment, the characteristic spacing a of 8CB (35 Å), the angle ja0 between the wavevector ki and the director n, and the angle ja between the wavevector kf and the director n, no scattered intensity can be expected for ja0 < 17 (Figure 3). Corresponding to this constraint, we have chosen an experimental configuration with the X-ray beam traveling perpendicular to the plates through the sample in the gap. Using the vertical X-ray beam setup, the ‘a’ and ‘b’ orientations are detectable in this case. According to the director of the ‘b’ configuration shifted by 90 as compared to the ‘a’ orientation, the scattering pattern will also be shifted by 90 allowing for a precise determination of the director orientation. However, the recorded scattering pattern can also give information about intermediate states mixing the ‘a’ and ‘b’ and partly the ‘c’ orientation. The scattering pattern will just change its orientation according to the orientation of the director n. Only states that contain fractions of the ‘c’ orientation 2881

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Figure 3. Laue condition for a one-dimensional periodicity as expected for 8CB under shear in a plate/plate geometry. ki is the wavevector of the incident beam, kf is that of the scattered beam, and n is the director of the smectic lamellae. The x and y axes of the graph represent the angle ja0 between ki and n and the angle ja between kf and n, respectively. The equation represents the one-dimensional Laue case. No scattered signal can be expected when there is no result for ja. The experimental configuration is an X-ray beam traveling perpendicular to the plates through the sample in the gap. For the given wavelength λ of the incoming X-ray beam of our experiment and the characteristic d-spacing of 8CB, no scattered intensity can be expected for ja0 < 17.

with ja0 < 17 (Figure 3) are definitely invisible due to Laue’s scattering condition. The plate/plate geometry consists of two parallel plates with the sample loaded in the gap (Figure 3). While in our case the upper plate remains stationary, the lower plate rotates to apply a shear field to the sample. The ideal approach to probe the ‘a’ orientation of any material in a plate/plate geometry with an X-ray beam is the incoming wavefront traveling through the sample along the velocity gradient with ki parallel to m. Consequently, the intrinsically horizontal synchrotron X-ray beam had to be deflected to vertical with its wavefront propagating parallel to the plate/plate geometry through the sample in the gap and along the direction of the velocity gradient (Figure 3). Although the plate/plate geometry appears to be the easiest to analyze, there is a practical downside. Namely, a finite hydrodynamic time is required to set a linear shear profile in the system. This time, which is inversely proportional to the shear rate, has an especially important role in the case of oscillatory shear.7 If this time is longer than the oscillation period, the linear shear profile will never reach a dynamic stationary state in the system. Since smectic A liquid crystals are hydrodynamically anisotropic systems with five rather different viscosity coefficients for the macrospically disordered state, the characteristic time to set a linear shear profile can depend essentially on the orientation of a domain under consideration.

’ EXPERIMENTAL SECTION The usual standard design of commercially available rheometers allows only for a very limited range of measuring geometries and did not allow for our projected beam configuration. Recently, Thermo Fisher has developed a unique modular rheometer design;the MARS rheometer;that allows in principle for a variety of measuring geometries in combination with scattering techniques. According to our suggestions, this design was developed further by Thermo Fisher and adapted to the special needs required for the use with vertically deflected

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synchrotron radiation. On the standard MARS design, the drive unit is mounted as usual above the rheometer geometry, in our case the plate/plate configuration. When probing the sample in the gap between the two plates with a vertical X-ray beam, the scattered signal would be blocked by the drive unit. No adequate sample-to-detector distances (ranging, depending on the material’s characteristics, from several centimeters to several meters) could be achieved in this case. For our special needs, the configuration of the MARS design was inverted by Thermo Fisher. For the inverted design, the driving unit is now placed below the plate/plate configuration (Figure 2). The specifications and functionality of the inverted design are equivalent compared to the standard design. The optical element to deflect the horizontal X-ray beam to vertical is placed in between the driving unit and the plate/plate geometry. The space above is completely unspoiled and allows in principle for any sample/detector distance. For the present setup, the sample-to-detector distance varies from 150 mm to 3000 mm. In order to deflect the incoming X-ray beam to 90, we used a diamond (004) reflection and tuned the X-ray energy to 9.85 keV. Steady shear and dynamic oscillatory shear tests were performed with a plate/plate geometry of 36 mm diameter and a gap of ∼0.8 mm. The plates were fabricated out of VESPEL (DuPont), a polyimide with special mechanical and physical characteristics providing, e.g., properties such as wear resistance, thermal resistance, low coefficient of friction, creep resistance, self-lubrication, chemical resistance, and low outgassing. Additionally, VESPEL provides sufficiently high transmission for X-rays in the applied energy regime of 9.85 keV. In the region of the plates where the X-ray beam passes through the plate/plate geometry, the material was reduced to a thickness of 0.3 mm. In this case, the transmission of the incoming X-ray beam is still 80% allowing for most scattering experiments. The temperature was controlled via a specially designed chamber using Peltier elements and tempered nitrogen flow. Here, undisturbed entrance and exit of the X-ray beam was achieved by drilling holes in the insulating housing of the chamber. As a detection system, a Pilatus 300K detector was used.8 The stripes in the X-ray patterns presented below correspond to the gaps between the modules of the detector (Figure 4 and 5). Putting all components together, our experimental setup allows for the same precision in rheological measurements as the highly developed MARS standard design but provides in addition and simultaneously the possibility to obtain static as well as time-resolved structural information during the shearing process by the use of X-ray scattering techniques. This allows for very flexible experiments since the operator can measure rheological properties and see microstructural evolvements online and can immediately react accordingly with additional series of experiments on one integrated instrument. This is a clear advantage to other setups,9 where precise rheological parameters are not directly accessible during the scattering experiment. The experimental setup was developed, and the experiments were carried out at beamline BW1 at DESY, Hamburg, Germany. Preliminary rheological experiments were carried out at the Karlsruhe Institute of Technology. Materials. 4-4-n-Octyl-cyanobiphenyl (8CB; CH3(CH2)7C6H4C6H4CN, CAS 52709-84-9) was purchased from Sigma Aldrich and was used without further purification. All experiments were carried out at 22 C, just above TC-S. For this material 8CB, neither the nematic nor isotropic liquid has measurable viscoelasticity. However, at (T - TC-S)/ TC-S , 1, deep in the smectic regime, shear viscosity of the locally ordered smectic material can be much larger than that in the vicinity of TS-N and simple fluid-like behavior disappears. Possible orientations and arrangements of the sample and corresponding X-ray patterns are presented in Figures 1-3.

’ RESULTS After loading the sample we observed a prealignment of the liquid crystalline system. For a completely unperturbed system, 2882

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Figure 4. Steady shear test: (a) snapshots before, at 20 and 40 min, and after the experiment; (b) time evolution of the X-ray pattern; (c) rheological data.

one expects a random distribution of the smectic layer normal director. Consequently an X-ray beam interacting with an unperturbed system would produce a circular scattering pattern with homogeneous intensity distribution. Instead we observed in most of the cases a circular scattering pattern with a relatively inhomogeneous intensity distribution indicating a prealignment of the sample under confinement in the plate/plate geometry of the rheometer (Figure 4a top). This regularly observed prealignment occurred due to a flow from the center to the border of the plate/plate geometry that was induced by squeezing the sample when reducing the gap to 0.8 mm during the loading process. The compression flow acts as shear in this case and aligns the smectic layers accordingly. Therefore we quenched the samples from an isotropic state to smectic A. However, even a quench from 60 to 22 C could often not completely remove the prealignment. In addition to the compression flow, the prealignment seems to also be related to nucleation and growth of crystallites and domains during the cooling process. The result is a slight variation of the initial state of the experiment. It is noteworthy that these slight variations as observed by X-ray scattering had no significant influence on the afterward measured viscoelastic parameters of the sample when performing the rheological experiments. While any mechanical action applied from the rheometer to the sample is strictly macroscopic, the X-ray beam probes the fluid sample on length scales orders of magnitude smaller in the nano or subnano regime. Since slight variations in the initial state of the experiment as observed by X-ray scattering had no influence on the general rheological

behavior of the sample, one can conclude that the system reacts differently on macroscopic and microscopic length scales when loading or quenching the sample. For the steady shear experiment, the X-ray pattern was recorded simultaneously to the rheological measurement with a frame rate of 10 s. Exposure time was 5 s. When applying steady shear, γ_ = 50 s-1, to the sample, the initial X-ray pattern with the circular intensity distribution with inhomogeneities due to prealignment changed within the first seconds of the experiment to a pattern with two distinct reflections (Figure 4b). These reflections are distributed 180 apart from each other, representing the characteristic point mirror image for an ordered sample, and are clearly oriented far from any intensity maxima that appeared after the loading process. Whatever preorientation occurred, after applying stress to the sample, the two distinct reflections appeared always and immediately at the same position. The patterns indicate a jump of the lamellae director within the first 5 s of the shearing process from a random orientation to a preferred direction. Within these 5 s, the complete sample changed its orientation and aligned as expected in the ‘a’ configuration accordingly to the shear flow direction (Figure 4b). The sample was exposed to steady shear for 60 min. During that time, the circular width of the observed reflection decreased from about 60 to 40, indicating reduced angular misorientation of the smectic layers. Even 22 h after stopping the constant shear experiment, the X-ray pattern remained unchanged, no relaxation of order parameters of the aligned smectic A phase could be observed. The simultaneously measured viscosity dropped 2883

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Figure 5. LAOS experiment at unity strain amplitude and frequency 1 Hz: (a) snapshots before, at 20 and 40 min, and immediately after the experiment; (b) time evolution of the X-ray pattern during the LAOS experiment; (c) rheological data.

slightly during the first 5 min and remained almost constant until the end of the experiment (Figure 4c). For the LAOS experiments, the same loading and quenching process was used as for the steady shear experiments. However, the presence of the nonlinear oscillatory shear flow in this situation also has less expected obvious consequences. The strain amplitude was unity (γ0 = 1) for all experiments. The frequency remained constant during the experiments. A shear frequency of 1 Hz was applied. Each LAOS experiment had a duration of 60 min aiming to record the time evolution of the viscoelastic parameters G0 and G00 as a function of deformation and frequency. To follow the structural evolution of the system, the intensity of the X-ray pattern was recorded simultaneously with a frame rate of 10 s. Exposure time was 5 s. In Figure 5b we reduced the number of frames to 30 for better visibility. In Figure 5b, a typical time evolution of the X-ray pattern of 8CB exposed to unity strain amplitude (γ0 = 1) and 1 Hz frequency is presented. Before starting the LAOS experiment, we obtained a quiet random intensity distribution after loading the rheometer and after the quenching process (Figure 5a top). During the first minutes, the intensity started to redistribute and after 20 min of oscillatory shear, three pairs of stripes clearly start to have a distinct pattern: they describe an arc of about 40, bright in the center and weaker toward the edges (Figure 5a). Each pair of stripes appears as a point mirror image. During the experiment, the intensities of the reflections increased, and the widths of the circular arcs decreased to about 30 after 1 h. This indicates a higher degree of orientation in the sample with time. The

reflections were finally clearly separated. After the experiment, the intensities of the reflections still increased. The pattern could be removed only by heating to the isotropic state. The azimuthal orientation of the first pair was 55 and 235, 90 and 270 for the second pair, and 170 and 350 for the third pair (Figure 5a). While the brightness of the last pair was strongest, the one of the second pair was weakest. The reflections inhibit equivalent radial positions during the whole experiment. It is noteworthy that the appearance of six reflections is reproducible. The azimuthal orientation can differ slightly and seems to depend (in contrast to the steady shear experiment) on the preorientation of the sample after the squeezing process. The resulting structure during and after the LAOS experiment seems to use the initial state before starting the experiment as a template. The relatively small mechanical dislocation (γ0 = 1) compared with steady shear does not destroy the initial prealignment of the sample in this case. Nevertheless, new reflections appeared in each of our experimental runs, and the initial prealignment had no influence on the general trend of the experiment. When steady shear is applied (γ_ = const), the whole sample is probed after some time on quasi-infinite length scales, and the preorientation in the sample is destroyed during the process and has consequently no further influence on the alignment of the smectic lamellae during the experiment. The time evolution of the simultaneously measured viscoelastic moduli (Figure 5c) (elastic modulus G0 and viscous modulus G00 ) during the LAOS experiments is consistent with the rheological measurements of Larson and co-workers,6 leading to the interpretaion of lamellae being 2884

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Langmuir aligned and defects driven out. Nevertheless, we observed additionally, for the first time in situ, a reorientation state representing three distinct main orientations at the nano level that cannot be observed under equilibrium conditions or under steady shear. This reorientation state no longer exhibits the three simplest smectic orientations ‘a’, ’b’, and ‘c’. The system under consideration prefers a configuration maximizing layer fluctuations and therefore minimizing the quasi-equilibrium free energy. This is at the starting point the ‘a’ configuration, but during the LAOS experiment the effects are basically at a nonequilibrium but stationary state for the nonlinear shear, and the system prefers intermediate configurations. Looking at the rheological data, the viscous modulus G00 dominates the viscoelastic behavior of the material, indicating a more viscous-like state (Figure 5c). After the LAOS experiment, a frequency sweep experiment was performed. The frequency was varied from 0.1 to 10 Hz, while the strain amplitude was fixed at 0.01 in the linear regime. Interestingly, no variation of the X-ray pattern with three pairs of reflections could be observed due to the relatively small strain amplitude. The established state of the sample remained unchanged. Also LAOS measurements at strain amplitude of γ0 = 0.1 and frequency 1 Hz did not lead to the structural changes as observed during our first series of experiments. The viscoelastic moduli displayed completely linear response in this case, and no variation with time could be observed. The observed behavior provides evidence of a highly nonlinear, most probably cooperative and complex process, which shows dependencies of the shear rate, strain amplitude, and shear oscillation frequency. These parameters are impossible to lump into a single effective shear _ rate parameter γ/ω like it is often the case for copolymer structures.10-13 Macroscopic flow behaviors are not equal to the microscopic local rheology, e.g., due to grain boundaries and structural heterogeneities. The nonlinear character of the stress response reflects the overall dynamical evolution of the domain patterns. In addition and completely different from the case of stationary shear, the average strain is zero in one period of shearing in LAOS experiments.

’ DISCUSSION At the moment, we can only speculate about the complex underlying orientation mechanisms, and therefore we will base our discussion on the little that is known and will in the following draw a merely speculative image. When (as it is the case for our LAOS observations) the shear induces a new state not related to an existing equilibrium phase, the reason for its appearance is probably based on a specific mechanical instability mechanism. For the smectic A phase of the liquid crystal 8CB, one might speculate about mechanical instabilities occurring in smectics due to a mismatch between the periodicity imposed by external conditions (shear rate in our case) and the equilibrium periodicity imposed by the bulk smectic elastic modules. In the equilibrium situation (or under stationary shear) this spatial frustration is accommodated by dislocations, which permit a change in the local number of smectic layers. The dislocations are able to move with the mean flow at sufficiently low shear rates and oscillatory shear frequencies. However, when the shear rate and frequency are too high, the dislocations cannot follow the flow, and this (depending on a particular domain orientation) gives rise to an effective dilative or compressive strain perpendicular to the layers. The distortions of the lamellar smectic structure induced by strains are well-known in the realm of

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liquid crystals (for instance, the Helfrich instability or some other kind of mechanical or thermo-mechanical instability that is related to the so-called chevron formation14,15). The distortions depend sensitively on material parameters, orientation, boundary conditions, and environment conditions. The distortions may form a square lattice of “frozen” undulations or even distorted hexagonal symmetry of undulations resembling our X-ray patterns and observations. These structures induced by mechanical strains during the shearing process are metastable. If one waits long enough, the number of layers will tend to adjust itself through the motion of dislocations. In practice, the stability depends strongly on the amplitude of the perturbation. If the perturbation is not too large (e.g., only slightly above its threshold value) the undulation lattice persists only for a short time, whereas for the large perturbation (as it is the case in our LAOS experiments) distortions are not smooth any more and new defects (e.g., focal conics) may be present, which are much harder to heal. The mechanical instabilities described above are static by their nature. One might also speculate about dynamical instabilities known for lyotropic liquid crystals, where there are, in comparison with thermotropic smectics, additional degrees of freedom, e.g., in the concentration of system components. The frictional force exerted by the shearing liquid has to be balanced by elastic stress gradients. Concentration fluctuation leads to a corresponding fluctuation in the viscous stress (through the concentration dependence of the viscosity). The resulting elastic stress opposes the chemical potential gradients. The fluctuation amplitude is increased because of the increase in lifetime. This is known in liquid or liquid crystalline mixtures as Reynolds instability.16,17 However, for macroscopically disordered thermotropic smectic liquid crystals, a similar instability may occur due to orientational dependence of the viscosity coefficients. Since at the moment very little is known about the subtle interplay between dynamic and static instability mechanisms under LAOS experimental conditions, we are at present not in the position to discuss these issues in more detail. This is also true for an exact interpretation of the X-ray patterns observed during the LAOS experiments. Nevertheless, we can present for the first time data using this unique Rheo/SAXS combination. The three pairs of reflections observed during the LAOS experiment allow for several possible arrangements that are consistent with the X-ray pattern (Figure 6). On the molecular level, a distorted herringbone-like structure can be imagined (Figure 6a). In this case, the one-dimensional arrangement of the smectic lamellae would be transferred during the LAOS experiment into a threedimensional structure with oriented periodic translation that would remain stable even after stopping the experiment. A nonoriented, consequently random orientation of the quasihexagonal molecular lattice would lead to a circular and homogeneous distribution of the scattered intensity and not to distinct spots as observed. Consequently, a quasi-single crystalline arrangement would be created when applying external oscillatory shear to the sample, which appears to be very unlikely. On longer length scales, one could imagine that the order parameter has discontinuities that destroy the full translational invariance of the planar smectic A lamellae similar to smectic C chevron defects (Figure 6b). A shear-induced local alignment of the linear discontinuities could lead to the formation of domains hosting three distinct orientations of lamella density fluctuations. Another possible scenario is crystallites or domains hosting only one orientation (Figure 6c). In this case, the lamella director and thus the crystallites or domains themselves are oriented in three 2885

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return to its initial state after stopping the experiment, even after hours. Furthermore, the system did not relax from the shearinduced nonequilibrium state to the equilibrium state. Shear of both kinds;steady and oscillatory;induced a reduction of misalignment and defects and initiated growth of the smectic grains. Growth of these grains continued for hours after the shear was stopped. We could demonstrate that shear history could not be removed by additional shear or long relaxation periods in the smectic phase. During LAOS experiments, the shear history seemed to play an important role for the structural evolution of the system. A number of questions (both from the experimental and the theory side) remain to be clarified. Nevertheless, we hope that our new observations and first very qualitative analyses are useful for gaining insight into the complex rheological behavior of smectic systems under LAOS conditions, when exact or even approximate theoretical results are currently not available. Complex fluids are by far more complex than expected, and with our experiments we just started to shed first light on completely unforeseen properties of viscoelastic materials under nonlinear mechanical conditions. Encouraged by our first results, we will start a series of experiments using our newly designed setup to determine structural as well as dynamic features of fluid materials in nonequilibrium states ranging from complex fluids to cosmetics, food, and mineral or metal melts under a huge variety of experimental conditions such as temperature, magnetic and electric fields, and other external forces.

’ ASSOCIATED CONTENT

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Supporting Information. Figure illustrating that the appearance of six reflections is reproducible during LAOS experiments. This information is available free of charge via the Internet at http://pubs.acs.org/.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Figure 6. Possible scenarios of molecular and domain arrangements as created during the LAOS experiments: (a) herringbone arrangement; (b) domains with aligned linear discontinuities; (c) domain formation with three distinct order directions.

distinct directions as a consequence of the applied oscillatory shear. Both last scenarios are possible in principle, but again we are not in the position of drawing a more conclusive image of the underlying mechanisms yet. The X-ray pattern obtained during the LAOS experiments shows in a very reproducible way three pairs of clearly separated reflections. During all experiments, peak intensities increased, and the circular width of the reflections decreased. In agreement with the suggested scenario described by Larson and co-workers,7 we observe that defects were driven out, and smectic layers were aligned. Additionally, our innovative and unique approach allowed for the observation of a complete restructuration process leading to the characteristic X-ray pattern with three pairs of reflections.

’ CONCLUSION We have measured the time evolution of the liquid crystalline system 8CB undergoing steady and oscillatory shear using X-ray scattering. During both series of experiments, the system did not

’ ACKNOWLEDGMENT The authors thank DESY, Hamburg, for access to the X-ray beam and D. Novikov and H. Schulz-Ritter for their help at beamline BW1. We thank C. K€uchenmeister and her team from Thermo Fisher scientific, Karlsruhe, for many discussions and the development and construction of the unique rheometer design. ’ REFERENCES (1) Larson, R. G. The Struture and Rheology of Complex Fluids; Oxford University Press: New York, 1999. (2) Loizou, E.; Porcar, L.; Schexnailder, P.; Schmidt, G.; Batler, P. Macromolecules 2010, 43, 1041–1049. (3) Brown, E.; Forman, N. A.; Orellana, C. S.; Zhang, H.; Maynor, B. W.; Betts, D. E.; DeSimone, J. M.; Jaeger, H. M. Nat. Mater. 2010, 9, 220–224. (4) Manneville, S. Rheol. Acta 2008, 47, 301–318. (5) Clark, N. A.; Rieker, T. P. Phys. Rev. A 1988, 37, 1053–1056. (6) Safinya, C. R.; Sirota, E. B.; Plano, R. J. Phys. Rev. Lett. 1991, 66, 1986–1989. (7) Larson, R. G.; Winey, K. I.; Patel, S. S.; Watanabe, H.; Bruinsma, R. Rheol. Acta 1993, 32, 245–253. (8) Pilatus 300K, Unrivalled Data Quality for Timeresolved Experiments, http://www.dectris.com/sites/pilatus300k.html. Accessed October 2010. 2886

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dx.doi.org/10.1021/la103786w |Langmuir 2011, 27, 2880–2887