Mechanical manipulation of molecular lattice parameters in smectic elastomers

Abstract

Smectic liquid crystalline elastomers (SLCE) represent unique materials that combine a 1-D molecular lattice arrangement and orientational order with rubber-elasticity mediated by a polymer network. Such materials may exhibit large thermo-mechanical, opto-mechanical and electro-mechanical effects, due to the coupling of macroscopic sample geometry and microscopic structural features. It is shown that the molecular layer dimensions in the smectic phases can be influenced reversibly by macroscopic strain of the material. We present a microscopic model on the basis of experimental results obtained by mechanical dilatation measurements, optical interferometry, X-ray scattering, ¹³C NMR, FTIR and polarizing microscopy data. The model gives an explanation of the controversial results obtained in different types of smectic elastomers.

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1. Introduction

SLCE exhibit a variety of unique mechanical effects as a consequence of their coupling of mesogenic orientational order on a microscopic scale with the anisotropy of the polymeric backbone structure and macroscopic sample dimensions and shape.^1–42 Reviews on research activities in the field can be found, for example, in ref. 43–45.

Physical properties of liquid crystal elastomer samples can be manipulated, for example, thermally,¹ optically,² or electrically.^3–6 Consequently, these materials represent potential candidates for thermo-mechanical, electro-mechanical or even opto-mechanical actuators. For example, heating of liquid crystal elastomers above the clearing temperature may lead to dramatic changes of sample dimensions. This has motivated the proposition to employ such materials in artificial muscles.^1,7

Another interesting aspect is the inverse phenomenon, the change of mesogenic order and orientation by means of macroscopic mechanical deformations of the samples. Since the elastic network of the polymer backbone in nematic or smectic elastomers is coupled to the orientation of the mesogenic units (Fig. 1a), one may expect that a sufficiently strong mechanical strain can effect e.g. the reorientation of the director (optic axis), an induction of a spontaneous polar order and electrical polarization (during a mechanically induced smectic A-smectic C* transition), or a change of the molecular lattice parameters (like smectic layer spacings). So far, little is known about these effects in smectic elastomers. In cholesteric samples, a control of the cholesteric structure by mechanical stretching has been proposed²⁹ and exploited in the fabrication of tunable photonic crystals.^30,31 Among the mechanically induced microscopic effects, the phenomenon of soft elasticity observed in nematic elastomers is probably the most extensively investigated, and controversely discussed one.^43,44 Experimental evidence for mechano-electrical effects, like the induction of a spontaneous electric polarization, has not been reported so far. Interactions of the mechanical strain with the smectic order and lattice parameters have been described,^8–13 but observations on different materials appear somewhat contradictory. In this study, we will focus particularly on the interplay of macroscopic deformations and smectic structure when SLCE films are exerted to uniaxial in-plane stress. We compare experimental observations in different materials, and discuss microscopic models of the mechanical behaviour.

Fig. 1 (a) Sketch of the microscopic structure of a typical smectic LC elastomer, containing a siloxane backbone and mesogenic side chain substituents. (b) The bottom graph shows the chemical structure of the precursor polymer used here. Approximately 28% of the siloxane backbone units are substituted by mesogenic groups, a few percent of them serve as cross linkers. The material described here has a cross linker content of x = 0.05. The phase sequence of the non-crosslinked material is SmX 65 °C SmC* 95–96 °C SmA 125 °C Iso.

2. Experimental

Since experiments reported by Nishikawa and coworkers a couple of years ago,^8,9 it has become clear that the existence of a layer structure in smectic LC elastomers can have an important impact on the mechanical properties of macroscopic samples. When such a film is exerted to uniaxial stress normal to the smectic layers, the relatively large (enthalpic) compression modulus of the smectic layers, as compared to the lower entropy elasticity of the elastomers network, is responsible for a very small strain. On the other hand, comparable uniaxial stress in the plane of smectic layers produces much larger deformations. Whereas in isotropic rubbers, volume conservation is related to a Poisson ratio of 1/2, the smectic elastomers investigated by Nishikawa et al. compensate strain in stretching direction almost completely by a lateral contraction within the smectic layer plane. The dimension normal to the smectic layers remains practically unchanged. Such materials, when prepared as single crystals, may represent anisotropic rubbers with amazing properties. When stretched uniaxially in the smectic layer plane, they show a comparably low effective elastic modulus. If, however, stress is uniform in all directions in the layer plane, such a material will respond hard. For an SLCE membrane with layers stacked parallel to its surfaces, isotropic stretching in the plane is coupled by the large bulk modulus to a compression of the layers, which involves the large layer compression modulus. When the membrane is heated to a temperature above the phase transition into the isotropic or nematic phase, this modulus vanishes and the membrane becomes soft. A rubber balloon of such material would be much harder to inflate in the smectic than in the isotropic state where only the entropy elasticity is effective. One could change the effective elasticity of such a balloon by more that one order of magnitude by heating or cooling across the clearing point.

In contrast to the observations in ref. 8 and 9, experiments with different SLCE did not show any peculiarities of the elastic behaviour at the clearing point.^10,15,16 The chemical composition of these samples is shown in Fig. 1b. Elasticity measurements on smectic elastomer balloons showed that the effective elastic modulus is rather unaffected by the transition into the isotropic state.^15,16 Moreover, experiments with thin films under uniaxial stress have revealed that in the same material, the compensation of uniaxial strain is achieved by a Poisson ratio very close to 1/2.¹⁰ It has been shown that thin free standing SLCE films exposed to uniaxial stress in the film plane change their thickness, they shrink normal to the smectic layers. Several mechanisms can be proposed to explain this behaviour. Before we describe them, we recollect in short experimental results from earlier work:

(a) SLCE films of a few hundred nanometer thickness, with lateral extensions of several millimeters, can be prepared by a technique described in ref. 10: Polymer films are drawn on a metal frame and then cross linked by UV irradiation in the smectic A phase (with a 250 W Panacol-Elosol UV point source UV-P 280). The smectic layers in these films are oriented perfectly parallel to the surfaces. The films can be stretched at least up to 90% elongation (strain ε ≈ 0.9). Under such deformation, the film thickness changes by up to 30%.¹⁰ The deformations are almost completely reversible. Even when the material had been stretched to almost twice its length, there is usually only a small residual strain of a few percent.^10,13

(b) The stretched SLCE films in smectic A remain almost black when viewed under crossed polarizers normal to the smectic layers (in reflection as well as in transmission). A representative example is shown in Fig. 2. It shows images that have been taken with crossed polarizers when the stretching axis is parallel to one of the polarizers (c) and diagonal to the polarizers (d), respectively. In both cases, there is almost complete extinction in the film plane. Only the borders of the film appear bright because disordered smectic material is collected there from the preparation technique. It shows that even under large uniaxial strain, the observable birefringence of the films is very weak. It can be attributed entirely to an induced anisotropic network deformation. The mesogenic groups remain in the preferential direction normal to the layers, the optic axis stays normal to the film, along the observation direction (or has only a negligibly small tilt). This holds even in the smectic C* temperature range. Moreover, the optical tilt angle in the smectic C* phase of the elastomer samples is obviously much weaker than expected from values of the non-crosslinked precursor material, when the films have been cross linked in smectic A.

Fig. 2 Reflection microscopy images of a SmA elastomer film stretched between two clamps. From the reflection colors, an original film thickness (a) between 300 nm (yellow/orange region Y on the bottom) to 470 nm (green region G in the center) can be determined. After stretching by 43% (b), the film thickness decreases by almost 20%. Images (c) and (d) are taken with crossed polarizers. It is obvious that apart from the film edges where disordered excess smectic material is present, the planar film shows practically no birefringence under strain.

(c) Another experimental result is derived from NMR experiments of the non-crosslinked precursor polymer. NMR data indicate that the average projection of the molecular long axes on the direction of the optical axis is almost the same in the smectic A and C* phases.¹² Details are described below.

(d) Furthermore, FTIR measurements have been performed on free standing SLCE films in order to confirm the molecular orientation during stretching.⁴² The preliminary results agree with the NMR findings. The average mesogen orientation is nearly uninfluenced by in-plane strain of the films at deformations at least up to 50%.

(e) Finally, after the mesogenic configuration under the influence of uniaxial stress has been confirmed by several independent methods, X-ray reflectivity measurements have been performed in order to determine whether the observed film thickness compression is related to a smectic layer compression.¹³ The Poisson ratio of approximately 1/2 found in the stretching experiments suggests that the deformations have a direct impact on the smectic layer structure.

Thin films (thickness approximately 0.5 μm, lateral extensions 1 × 3 mm) have been prepared and stretched in several steps up to a maximum strain of 90%. Optical and X-ray reflectivity data have been recorded at every step. Results of the X-ray measurement are shown in Fig. 3. The image shows X-ray reflectivity curves at different deformation states. The strain ε = δx/x gives the relative elongation of the film in stretching direction. After the experiment, the stress was released and the reversibility of the sample deformation has been checked.

Fig. 3 X-Ray reflectivity of the elastomer material shown in Fig. 1, measured in the geometry of a mechanically stretched planar film (5% cross linkers of the total number of mesogenic substituents). In addition to bulk signals (1, 2) from the meniscus material, the film peak (1′) is observed. It shifts with increasing strain, indicating a layer compression up to 30%. The insert enlarges the region of the film peak in the reflectivity curves. The number of acquisitions of the 90% stretched sample was twice as large as for the other three measurements.

The X-ray spectrum in the small angle region shown in Fig. 3 consists of the Bragg peaks originating from the smectic layer structure, with the scattering vector normal to the film plane. The positions of the individual peaks reflect the layer spacing in different parts of the sample. In particular, the reflectivity curves consist of relatively small signals from the film (1′) and additional parasitic peaks (1, 2) from SLCE material in the meniscus and on the clamps holding the film. The layers in the bulk material at the holder are randomly disordered, and the Bragg condition is always fulfilled for a certain small portion of this material, which is still much larger than the material contained in the micrometer thick film. These additional signals cannot be avoided in the setup used here, since the dimensions of the non-stretched film are smaller than the footprint of the X-ray beam. A certain benefit of this situation is that it allows direct comparison of the shifted layer peak of the deformed film material with the original signal from undeformed layers in the meniscus. At very large deformations of the films, the two clamps that hold the film are separated wide enough, so that the footprint of the X-ray beam is completely on the film, and the parasitic peaks are absent. The insert in Fig. 3 focuses on the film signals. From Bragg’s law, d = λ/(2sinΘ), the smectic layer thickness d can be determined using the positions Θ of the (1′) peaks and the X-ray wave length λ = 0.15406 nm (Cu Kα₁). Data presented in Fig. 4 show that the compression of the lattice constant d amounts to a remarkable magnitude of about 30%.

Fig. 4 Smectic layer thickness derived from the film peaks in Fig. 3 as a function of lateral strain. The solid line symbolizes the theoretical isotropic rubber model. The vertical bars indicate the distribution of layer spacings that is sufficient to explain the broadening of the X-ray reflexes (see text).

Summarizing, the smectic layer spacing in the deformed elastomers decreases with increasing strain so that it compensates the lateral elongation of the films, with a Poisson ratio close to 1/2. This is obviously a unique observation in solid matter, even if one takes into account that the smectic A liquid crystal is a soft material: The molecular lattice structure is changed by about 1/3 by mechanical stretching. The explanation for such unexpected behaviour can be sought in different models, which have to be evaluated on the basis of the experimental data.

3. Models

The decreasing smectic layer spacing can, in principle, be achieved by one of the following mechanisms (Fig. 5):

Fig. 5 Possible molecular mechanisms that may lead to a reduction of the smectic layer thickness during a mechanical stress of the sample. From the experimental observations, the first three mechanisms can be practically excluded, the interpenetration mechanism provides the main contribution to the geometrical changes.

(a) Compression of layers might be caused by an induced tilt of the mesogens (Fig. 5 top). If one assumes in crude approximation that the layer thickness d is connected to an average mesogenic tilt angle θ and the mesogen length d₀ by the relation d = d₀cosθ, then induced tilt angles up to more than 40° would be required, in order to account for the compression magnitudes observed in the experiment. This induced tilt must be oriented preferentially in the direction of the stretching axis. Another problem with this model is that in such a situation, the optical properties of the LC elastomers must change. The optic axis would not remain normal to the film plane. Either a tilt of the optical axis from the layer normal, with an angle comparable to the induced molecular tilt, would be expected, or a biaxially anisotropic structure (since the tilt in the plane of layer normal and stretching axis is twofold degenerate). In both cases, the films should acquire a strong birefringence when they are stretched. This is in clear contradiction with the optical observations under crossed polarizers (Fig. 2c and d). In fact, the preliminary FTIR data⁴² indicate that there is some very weak induced mesogenic tilt in the stretched materials, but the effect is far too small to account for the observed compression magnitudes. Moreover, layer thickness reduction by induced tilt is a nonlinear effect, and one would expect a threshold behaviour that is not detected experimentally.

(b) Another possible model, the destruction of the smectic layer structure by rupture of layers (second image in Fig. 5), may be ruled out on the basis of the observation that the deformations are reversibile. If the smectic layers would reorganize during stretching, it is highly unlikely that the original layer structure is restored after relaxation of the stress. Moreover, the X-ray reflexes would remain at the original positions and simply broaden out.

(c) One may further assume that in the particular material investigated in ref. 10, 15 and 16, the smectic A phase is tilted already in the stress-free films. Smectic phases with the optical axis normal to the layers but an average molecular tilt respective to the layer normal have been designated as de Vries smectic A phases. There are several arguments in favour of that model.¹¹ Since a microphase segregation is known in these side chain substituted siloxane polymers, the tilt between adjacent smectic layers may not be correlated and the tilt azimuth may be randomly distributed along the direction normal to the layers. If such a material is forced to compress its layers, the mesogens may simply change their tilt angle. Nevertheless, since the deformation is not isotropic in the layer plane, the increased tilt should be accompanied by an induced azimuthal ordering. The optical properties are expected to change, in particular, the optic axis should not remain normal to the layers. This model therefore represents an unlikely explanation of the layer compression mechanism as well.

(d) Compression along the layer normal could also be achieved if the orientational order parameter of the mesogens is considerably reduced and finally a transition into the isotropic phase takes place. We exclude the latter effect from energy considerations as well as from the persistence of the smectic layer reflex at large strain.

(e) Finally, there is the possibility that the mesogenic units in adjacent smectic layers interpenetrate (Fig. 5 bottom), or at least the mesogens interpenetrate the backbone and spacer layers. In ordinary smectics such a process would require a substantial energy, expressed in layer compression moduli of the order of 10⁷ N. It seems, however, that this interpretation is the only model that explains all experimental observations satisfactorily. We conclude that the material has, in contrast to the samples investigated in Nishikawa’s work,^8,9 an extremely low layer compression modulus. This makes the entropic parts of the elasticity dominant over the enthalpic parts.

4. Discussion and summary

It is so far not completely understood why the SLCE presented here behave qualitatively different to the materials studied e.g. in ref. 8 and 9. We propose an explanation, which has to be tested in detailed experimental comparison of both types of SLCE. A reasonable hypothesis is that the principal differences in sample preparation lead to completely different microscopic structures. SLCE studied by Finkelmann and coworkers, e.g.ref. 8 and 9, are prepared in a two step cross linking procedure. During the comparably slow formation of the elastomers in the cross linking reaction, one may expect that a certain segregation of smaller and larger pieces of the forming network takes place, so that the density of crosslinks is not necessarily homogeneous on the molecular level. While the average cross linking density may be comparable to the samples prepared in our photo crosslinking reaction,^10,13 the network is expected to be more heterogeneous on a microscale. This will result in relatively large compartments with an intact, defect free smectic layer structure, accompanied by regions with higher local cross link concentration. In contrast, the photo crosslinking of short chain precursor polymers in thin free standing films is much faster and will lead to a relatively homogeneous distribution of cross links even on a microscopic level. The average separation between these interlayer connections is but a few mesogens. The coupling of the two subsystems of elastic network and liquid crystalline order may be much stronger in that case. The cross links will act as lattice defects under a deformation of the material. This results in a strong influence on the smectic layer structure, in particular when the sample is stretched.

It has been shown in earlier theoretical work,^46,47 that the induction of defects in a smectic layer structure considerably softens such a material. In smectic elastomers, there is the competition between the processes of the stabilization of the smectic structure by suppression of fluctuations⁴⁸ and destabilization by the induction of defects.⁴⁹ This may explain the considerable difference in the layer compression modulus (a reduction by at least one order of magnitude), like it has been predicted for other smectic systems with quenched disorder.⁴⁶

The question whether the smectic order is changed during sample deformation cannot be answered unambiguously regarding the present experimental data. In the X-ray graphs shown in Fig. 2a, it is obvious that the scattering peaks broaden considerably when the film is stretched. This could be connected with a loss of correlation in the smectic structure (homogeneous broadening). However, the samples studied here do not deform exactly uniformly in the film plane.^10,13 Strain is larger in the center of the films than near the clamps holding them, and the X-ray signal is average over the film area. Since the strain is not completely uniform in the sensitive area, slightly different compressions in different film areas will lead to a distribution of smectic layer spacings in different regions of the film. The broadening of X-ray peaks may be, at least in part, related to the latter process (heterogeneous broadening). In Fig. 4, the vertical bars mark the width of the layer spacing distribution that would be sufficient to explain the broadening of the X-ray peak 1′. In view of the inhomogeneity of the film thickness across the sample (cf. Fig. 2a), such a distribution is reasonable.

Another aspect of the X-ray spectra is the decreasing intensity of the film peak with increasing strain (inset of Fig. 3). A quantitative comparison of the intensities of the film peak is very difficult, since the sample has to be removed from and re-inserted into the X-ray setup for each stretching experiment, but it is evident that the intensity of the signal that corresponds to the film material (area under the (1′) curve) in the 34% stretched film is only half as large as in the 21% stretched film, whereas the bulk signal (1) remains roughly unchanged. Such a loss of intensity may indicate (a) a decreased smectic layer order in the film or (b) a lower amount of material in the spot. A rough estimate shows that the latter effect, through thinning of the film, is expected to be much smaller than the observed signal loss. Therefore, it may be appropriate to speculate about a decreasing smectic order parameter with increasing strain. Unfortunately, in the non-stretched film the (1′) peak is indistinguishable from the bulk signal, so we cannot determine its intensity in the original sample. The peak in the 90% stretched film is too much smeared out as to be useable for quantitative intensity analysis, but the trend seems to be preserved. The detailed study of the influence of the mechanical deformation on the smectic order parameter may be a fruitful task for future experiments.

As shown above, the elastomers studied here are unique in that molecular lattice constants can be reversibly influenced by macroscopic deformation of monodomain samples. The observed phenomenon is in some respect comparable to the mechanical manipulation of the helical pitch in cholesteric elastomers which, as mentioned above, has been demonstrated earlier,³⁰ but the cholesteric twist structure is of course much softer than smectic layer spacings.

Summarizing, our model suggests that two types of SLCE can be distinguished, which, owing to differences in their microstructure and the relative influences of smectic layer distortions induced by the cross links, may behave qualitatively differently under in-plane uniaxial strain. For both types of elastomers, possible technical applications might be envisaged, and a detailed study of mechanical properties of SLCE with controlled distributions of cross links will be required to clarify the physical consequences of this structural feature. On the basis of our model, one may propose the following strategies for the controlled preparation of ordered single crystal SLCE with special mechanical properties: for materials with incompressible layers, it is necessary to obtain a microscopically inhomogeneous structure, with sufficiently large undisturbed smectic compartments (probably of the order of 10⁻⁸ m). This can be achieved either by an appropriate precursor material or by a sufficiently slow (two-step) cross linking process. On the contrary, if smectic elastomers with isotropic rubber properties are sought, the cross linking density has to be microscopically homogeneous, which is achieved by a fast cross linking process of (random) precursor copolymers with appropriate cross linker distribution.

Acknowledgements

This study was supported by the Deutsche Forschungsgemeinschaft within project STA 425/14.

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