1. Introduction
Liquid crystal materials offer many opportunities for applications such as data storage [1], image processing [2], or optical modulators [3] calling for media that are sensitive to external stimuli. Today, they are considered to have great potential for the realization of so called "smart materials" through micro- to nano-scale patterning techniques. One interesting material in the flourishing group of smart materials is the Liquid Crystal Elastomer (LCE) which combines the properties of liquid crystals and polymers. An elastomer is formed by a weakly crosslinked network of polymers, which confers it a high elasticity. The polymer network has maximum entropy in his undistorted state, and as a result, it resists deformation [4]. As for liquid crystals, these are materials which present phases intermediate between crystalline and isotropic called mesophases, the molecules responsible for this property are named mesogens.
In this chapter, we will present our results on the optical microstructuring of a LCE and the monitoring of its elastic properties. The liquid crystal based elastomer can be considered as an artificial muscle material. The designation of artificial muscle is attributed to soft actuators which can have muscle like behavior. A muscle is in reality an energy converter which converts chemical energy to mechanical motion. The actuators are converters which accept different types of energy and deliver a mechanical quantity like a displacement, a tension,
The LCE used in this study is a nematic thermotropic (sensitive to thermal stimuli) elastomer. A nematic elastomer can be described as crosslinked polymer chains with incorporated mesogens corresponding to rigid rod-like units which can order nematically. The average shape of the material is coupled to the molecular orientation order [4][9]: the nematic-isotropic phase transition results in the change of shape of the macroscopic sample. When the elastomer is judiciously prepared to obtain a monodomain sample [10], meaning that all the mesogens are oriented uniformly, the sample is elongated in the nematic phase where all the mesogens are parallel to each other, and has a contracted shape in the isotropic phase where the nematic order is lost.
First, we will show that advantage can be taken of the crosslinking properties of the material to inscribe refractive index modulations by optical means as in a common photoresist [11]. We present two approaches based respectively on one- and two-photon photopolymerization, that can be implemented using an optical microscopy setup. Such a method provides an accurate way to locally modify the properties of the material. Compared to its one-photon relative, the two-photon excitation mode will yield finer patterns because of its higher intrinsic spatial resolution. This technique relies on the fact that the simultaneous absorption of two low energy photons is equivalent to the absorption of a high energy photon with an energy equal to the sum of these two photons energy. The two-photon absorption (TPA) process is a quadratic phenomenon: the probability of the simultaneous absorption of two photon is not proportional to the photon flux as in the case for the linear absorption, but to the square of the flux. TPA is then significant only for high incident fluences. Thus, the use of ultra-short pulse lasers combined with microscopy techniques allows light-matter interaction to be confined within a micrometric volume around the focal point.
After the presentation of the microstructuring process, we will describe how the contractile properties of the material can be measured by detecting the thermally induced step size changes of an inscribed grating. Finally, these results will be interpreted with the help of Molecular Dynamics (MD) simulations. MD is a powerful tool to elucidate the structure and the behavior of the molecules. It has been used to simulate the behavior of polymers [12] and has proved its efficiency to describe the liquid crystalline phases [13], thus it also allows the description of elastomer behavior [14]. MD consists of a computational method which calculates time dependent atomic motions by applying the laws of classical mechanics. We have used a combination of Lennard-Jones and Gay-Berne potentials to represent the anisotropic mesogens and the calculations have been carried out in the Parrinello-Rahman-Nosé-Hoover ensemble.
2. Materials
2.1. Photopolymerizable liquid crystals
LCE are materials combining the elastic properties of the elastomers and the anisotropic properties of liquid crystals. They are formed by reticulated liquid crystalline polymers, which, in general, at low reticulation degrees, conserve the mesomorphic properties of the polymer before reticulation as well as the nature of the phases and the transition temperatures. These elastomers, when subjected to external stimuli like temperature or electromagnetic fields, can mimic the actions of muscles (contraction/extension). They are, thereby, considered as artificial muscle materials. Different types of actuators have been developed using polymers as parent material, like for example polymer gels [15] [16] [17], conductive polymers [18] [19] [20], carbon nanotubes [21] [22] [23] [24] or dielectric elastomers [25]. Soft and highly flexible, the polymers are well adapted to be used as artificial muscle materials due to their high strength, deformation capabilities, and their capacity to keep intact their properties after several operating cycles. Recently, LCE took over the field of artificial muscles. They are robust and don’t need any solvent to operate (unlike the gels or conductive polymers). The concept of LCE was proposed by P. G. de Gennes in 1975 [9]. In his studies on reticulated liquid crystal polymers, he mentioned the possibility of the material deformation without constraint. In 1981 Frinkelmann
Indeed, according to the insertion topology of the mesogen (liquid crystal phase-forming unit) in the elastomer, there exist two main families of LCEs: side-chain and main-chain elastomers. In the case of main-chain elastomers, the mesogens are directly integrated in the polymer chain, while in the case of side-chain elastomers, they are laterally attached to the polymer chain, either orthogonal to the chain, attached by one end (end on), or parallel to the chain, attached by the side (side on), as shown in figure 1.
Since the monomer used in this study is thermotropic, we will study the contraction properties of the resulting elastomer as a function of temperature. The studied elastomer is a nematic elastomer. The nematic phase is favored by the side-chain conformation. In nematic crystals, the mesogens have a random position but an orientational order: they are, on average, parallel to each other. This behavior is encouraged by the elongated form of these units.
For a nematic crystal, the amount of order can be characterized by the order parameter
where
In the case of the elastomer, the mesomorphic properties (as the nature of phases of the initial monomers) are conserved. The mesogens attached to the sides of the main chain are free to move. During the nematic-isotropic phase transition the mesogens are disoriented and the main chain drag behind them. These microscopic form changes are transferred to the macroscopic sample. The destruction of the nematic order thus generates a contraction of the system along the mesogens alignment direction and an extension in the orthogonal directions as schematized in figure 3.
2.2. Elastomer thin film preparation
The precursor of the LCE used in this study is a mixture of three compounds: a liquid crystalline acrylate monomer, a crosslinker and an ultraviolet (UV) photoinitiator. The monomer whose structure is represented in figure 4 is the 4’-acryloyloxybutyl 2,5-(4’-butyloxybenzoyloxy)benzoate [29]. The part containing the aromatic chains is the rigid part of the monomer and the attached carbon chains correspond to soft parts. The photoinitiator is the 2-benzyl-2-(dimethylamine)-4’ morpholinobutyrophenone (Irgacure 369) added at a concentration of 1 mol %, the crosslinker is the 1,6-hexanediol diacrylate at a concentration of 10 mol %. The elastomer is obtained by the photopolymerization of the monomers and the crosslinking of the polymeric chains.
Let us recall that in the case of a thermotropic nematic elastomer, the destruction of the nematic order by an increase in temperature will cause the contraction of the material along the nematic director. For the contraction to be maximum, the initial order parameter of the sample should be high. The samples were prepared in several micrometer thick glass cells filled by capillarity with the material in its isotropic phase (above 81.5
3. Experimental setup
Two different light sources were used to photo-structure the elastomers. We have used 365 nm UV light from an Argon Ion (Ar
From the Rayleigh criterion, in optimal conditions, the radial resolution of a conventional microscope is given by the radius of the Airy disc:
In the case of two-photon microscopy, Webb
The excitation is given by:
The experimental setup used for the microstructurating and the realization of the elastomers is based on a confocal microscope. The cell containing the elastomer precursor mixture is placed on a heating plate mounted on a motorized stage that can execute computer-controlled 3D translations along the X, Y, and Z axes. The observation is done by reflection with a CCD camera. The sample is illuminated in transmission with a white light lamp; a filter is used to stop any UV photons. The sample is also placed between polarizers allowing the monitoring of isotropic and nematic zones through the polarization of transmitted light induced by the mesogen alignment. The photo-patterning of the desired structures is realized in the nematic phase by moving the sample under the focus of the objective with the translation stage.
4. Experimental results
4.1. Photostructuration of the material
We have first studied the creation of a patterned elastomer by photopolymerization initiated by linear or two-photon absorption. Different sets of experiments have been performed depending on the sample alignment state (using treated or untreated glass cells) and the excitation source (UV or IR light). The first set of experiments was made using UV excitation (Argon laser,
4.2. Obtaining the thermo-active elastomer
In order to stabilize the patterns, a post-photopolymerization of the whole sample can be performed using UV light of weak intensity. Under these conditions, the pattern written by photopolymerization using a high intensity beam is preserved as it can be seen on figure 9. The resulting rubber-like film is then removed from the cell and placed on a heating plate to observe the shape changes as a function of temperature. Figure 10 represents the heating of an elastomer with an inscribed grating of 170
An elastomer with a circular pattern was also produced to highlight the uniaxial contraction and the reversible aspect of the phenomenon as can be seen in figure 11.
5. Discussion
5.1. Contraction properties
Direct observation of the micropatterned elastomer’s contraction can be readily achieved by optical microscopy. Figure 12 shows the temperature dependent deformation of the concentric pattern inscribed in a 13
5.2. Diffraction properties
The contraction of the material can be monitored indirectly by the observation of the diffraction pattern proceeding from a grating inscribed in the elastomer. Temperature induced contraction of the material will result in a change in the grating period which will modify the diffraction pattern. We present the study of the diffraction pattern obtained for a 13
Before testing the properties of the obtained gratings, we have examined the surface of the elastomer with a profilometer. In some cases when the sample is removed from the cell, its surface exhibits ridges corresponding to the grating. Such observations are commonly made in photopolymerization experiments [31]. The surface corrugation comes from the relaxation of the mechanical stresses introduced by the cross-linking process and which have been maintained by the glass plates. These ondulations are not observed in two-photon photopolymerized samples where the patterns are much thinner and inscribed inside the volume of the elastomer. In the cases where inscribed gratings led to surface ridges, we have checked that the addition of a compensating liquid did not modify the diffraction properties. Thus we may pretend that we are dealing with refractive index gratings. Index inhomogeneity stems from spatial variations in material density between parts that have been strongly polimerized and the remainder of the sample which has only been subjected to a light post-polymerization. The diffraction regime is indicated by the Klein-Cook parameter
It clearly demonstrates the decrease of the grating step with the temperature rise stemming from the unidirectional contraction accompanying the nematic/isotropic transition. In figure 15, the black dots correspond to measurements of the diffraction angle, while the red dots represent values calculated following the diffraction grating formula from the data shown in figure 13 for the 13
Since we work with a cross-linked polymer, the contraction/extension process will affect all three directions in space. The initial homogeneous nematic order makes the film behave as a biaxial material with an optical axis oriented along the nematic director. Thus, the material may change the polarization state of the light upon diffraction. To illustrate the birefringence properties of the gratings, we have measured the diffraction efficiency dependence on the orientation of the incident linear polarization. The resulting angular distribution for the polarization of the diffracted light is presented in figure 16b. Here, the simplest configuration is adopted: the incident beam is normal to the surface and its polarization is linear. As one can see in figure 16a, the diffraction efficiency is higher when the direction of the polarization of the incident beam and the grating vector are parallel. The diffracted light intensity has been fitted by :
where the angle
In the case of figure 16b the incident beam polarization is at 45
5.3. Molecular dynamics simulations
Molecular dynamics (MD) simulations are a powerful tool for understanding the properties of a sample in terms of molecular collective phenomena. We used classical MD method to simulate the contraction of the elastomer. First, the monomer molecules composed of 95 atoms was fully optimized by the density functional theory (DFT). The chosen functional was B3LYP, a hybrid functional obtained by linear combination of exchange-correlation energy functionals (Local-density approximations LDA, Generalized gradient approximations GGA) and the Hatree-Fock exchange [32]. The orbital basis set was the contracted Gaussian 6-311** set. All calculations were carried out with NWChem [33], executed on the IBM Power 6 at the "Institut du Développement et des Ressources en Informatique Scientifique" of Orsay. The obtained minimum energy configuration is represented in figure 17.
This model presents a dipole localized on the mesogen corresponding to the aromatic core. This will allow dipole-dipole interactions between the monomers. Then to simulate the contraction of the elastomer resulting from the collective behavior of the monomers the interaction between pairs of anisotropic rigid mesogenic sites was modeled using Gay-Berne (GB) potential. The Gay-Berne potential corresponds to a modified form of Lennard-Jones potential which can be easily adjusted to modify the shape of the studied system [34]. In that sense it has proven its efficiency to model mesogenic systems [35] [36] [37].
The force field modeling intra and inter-molecular contribution to the interaction energy is given by the following expression:
where
For a separation distance of
where
where
with
We have considered the molecular dynamics in a modified isothermal-isobaric (NPT) ensemble to allow an anisotropic deformation of the simulation cell. The ensemble used is the Parrinello-Rahman-Nosé-Hoover ensemble based on the
with
where
The forces acting on the system are obtained by deriving the field U. The system’s deformations are obtained by integrating the equations of motion using Beeman’s algorithme [44]:
An autocoherent process is necessary to calculate the conjugated moments. The time derivatives of the moments are calculated with the Parrinello-Rahman-Nosé-Hoover Hamiltonian.
Calculations have been carried out for 100 molecules and for simulation times up to
The bonding of the molecules (the polymerization) takes place in such a way to produce a form of sheathing around the principal chain. Crosslinking between principal chains was modeled by resorting to alkyne chains.
To measure the contraction of the simulated system we have monitored the obtained dimensions of the simulation cell vectors
Figure 22 represents the behavior of the order parameter obtained by polarized Fourier transform spectroscopy (FTIR) in the case of the same elastomer [45]. If we compare the simulation curve with figure 22 we can see that they have the same apparence. This similarity was to be expected, in fact it is the decrease of the order parameter which generates the contraction of the material. But differences between the behavior of the order parameter and the contraction can be identified: the contraction is not immediate, it starts above a given temperature which is higher than the phase transition temperature. In reality a sufficient contraction force should be achieved before observing the phenomena and these contraction forces should also exceed the friction forces with the glass plate. The fact that the simulation curve looks like the order parameter curve more than the contraction curve encourages us to consider external mechanical forces acting on the elastomer in the future.
6. Conclusion
We have demonstrated that one photon "UV" photopolymerization as well as two-photon "IR" photopolymerization can be used to microstructure artificial muscle materials made of nematic liquid crystalline elastomers without losing the contraction/extension properties. We have shown that the use of two-photon absorption allows to achieve 65 % greater spatial resolutions. A major advantage of the TPA consists in creating shape-changing volume objects, a property particularly interesting for the domain of microfluidics. We have established the possibility of generating a grating design in the sample which can be used as a step changing grating when subject to a temperature increase. We have shown that the contraction induced by the temperature is easily monitored by the widening of the diffraction figure. We can then consider the use of this kind of grating for temperature adjusted feedback devices. In addition, the birefringence properties of the gratings can open the path for polarization dependent diffractive elements.
Molecular dynamics simulations have been used to describe the contraction of the elastomer as a function of temperature. The proposed model allows the simulation of anisotropic molecules made from a combination of Gay-Berne potentials, representing the rigid mesogenic parts, and Lennard-Jones sites representing the alkyne groups of the flexible chains. Even if experimental and numerical contractions behave somewhat differently as functions of the temperature, a fact that may be attributed in part to the neglect of external mechanical forces, a rather good agreement between the behavior of the simulation curve and the order parameter has been achieved and a reasonable agreement with the contraction curve has been obtained.
References
- 1.
Ikeda T. Tsutsumi O. 1995 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers 268 1873 1875 - 2.
Lagerwall S. T. 1999 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Wiley-VCH. - 3.
Drzaic P. S. 1999 Liquid Crystal Dispersions.World Scientific. - 4.
Warner M. Terentjev E. M. 2003 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Oxford University Press, USA. - 5.
de Gennes P. G. 1997 A semi-fast artificial muscle. CR Acad. Sci. Ser. II B324 343 348 - 6.
Yu Y. Ikeda T. 2006 Two-Photon Excitation in CaF2Eu2+. Phys. Rev. Lett.45 5416 5418 - 7.
Naciri J. Srinivasan A. Jeon H. Nikolov N. Keller P. Ratna B. R. 2003 Nematic elastomer fiber actuator. Macromolecules36 8499 8505 - 8.
Ikeda Y. Yu T. Mamiya J. 2007 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Angaw. Chem. Int. Ed, 46: 506. - 9.
De Gennes, P.G(1975 Réflexionssurun type de polymèresnématiques. ACR Acad. Sci. Paris, Ser. B,46 101 103 - 10.
Kupfer J. Finkelmann H. 1991 Nematic liquid single crystal elastomers. Makromol Chem., Rapid Commun.12 717 726 - 11.
Lessard R. A. Gurusamy M. 1995 Photoreactive Polymers in Advance Applications. Chapman and Hall, New York. - 12.
Mc Cammon J. A. Gelin B. R. Karplus M. 1977 Dynamics of folded proteins. Nature.267 585 590 - 13.
Allen M. P. Warren M. A. Wilson M. R. Sauron A. Smith W. 1996 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers J. Chem. Phys.105 2850 2858 - 14.
Darinskii A. A. Zarembo A. Balabaev N. K. 2007 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers 252 101 109 - 15.
Osada Y. Okuzaki H. Hori H. 1992 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers 355 242 244 - 16.
Osada Y. De Rossi D. E. (200 2000 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Springer Berlin. - 17.
Osada Y. Khokhlov A. R. (200 2002 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Marcel Dekker, Inc, 270 Madison Avenue, New York, NY 10016, USA,1 381 - 18.
Osada Y. Khokhlov A. R. (199 1996 Conducting polymer artificial muscles. Synth. Met.78 339 354 - 19.
and Fadeev, A.G. and Qi, B. and Smela, E. and Mattes, B.R. and Ding, J. and Spinks, G.M. and Mazurkiewicz, J. and Zhou, D. andWallace, G.G. and others (Lu W. Fadeev A. G. Qi B. Smela E. Mattes B. R. Ding J. Spinks G. M. Mazurkiewicz J. Zhou D. and Wallace. G. 2002 Use of ionic liquids for pi-conjugated polymer electrochemical devices. Science 297: 983. - 20.
Pyo M. Bohn C. C. Smela E. Reynolds J. R. Brennan A. B. (200 2003 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Chem. Mater.15 916 922 - 21.
and Cui, C. and Zakhidov, A.A. and Iqbal, Z. and Barisci, J.N. and Spinks, G.M. and Wallace, G.G. and Mazzoldi, A. and De Rossi, D. and Rinzler, A.G. and others(Baughman R. H. Cui C. Zakhidov A. A. Iqbal Z. Barisci J. N. Spinks G. M. Wallace G. G. Mazzoldi A. De Rossi D. Rinzler A. 1999 Carbon nanotube actuators. Science 284: 1340. - 22.
Kim P. Lieber C. M. (199 1999 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers 2148 EOF - 23.
Zhang Y. Iijima S. 1999 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Phys. Rev. Lett.82 3472 3475 - 24.
Spinks G. M. Wallace G. G. Fifield L. S. Dalton L. R. Mazzoldi A. De Rossi D. Khayrullin I. I. Baughman R. H. 2002 Pneumatic carbon nanotube actuators. Adv. Mater.14 1728 1732 - 25.
Pelrine K. R. Kornbluh R. Pei Q. Joseph J. (200 2000 High-speed electrically actuated elastomers with strain greater than 100%. Science 287: 836. - 26.
Finkelmann H. Kock H. J. Rehage G. (198 1981 Investigations on liquid crystalline polysiloxanes 3. Liquid crystalline elastomers-a new type of liquid crystalline material. Makromol. Chem., Rapid Commun.2 317 322 - 27.
Bergmann G. H. F. Finkelmann H. Percec V. Zhao M. 1997 Liquid-crystalline main-chain elastomers. Macromol. Rapid Commun.18 353 360 - 28.
Zannoni C. 1979 The molecular physics of liquid crystals. Rijeka: G. R. Luckhurst and G. W. Gray. - 29.
Thomsen D. L. Keller P. Naciri J. Pink R. Jeon H. Shenoy D. Ratna B. R. (200 2001 Liquid crystal elastomers with mechanical properties of a muscle. Macromolecules34 5868 5875 - 30.
Zipfel W. R. Williams R. M. Webb W. W. (200 2003 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers 21 1369 1377 - 31.
Zipfel Naydenova. I. Mihaylova E. Martin S. Toal V. 2005 Holographic patterning of acrylamide-based photopolymer surface. Opt. Express13 4878 4889 - 32.
(Becke A. D. (199 1993 )Density-functional thermochemistry. III. The role of exact exchange. Chem. Phys.98 5648 5652 . - 33.
Valiev M. Bylaska E. J. Govind N. Kowalski K. Straatsma T. P. van Dam H. J. J. Wang D. Nieplocha J. Apra E. Windus T. L. de Jong W. A. 2010 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Comput. Phys. Commun. 181: 1477. - 34.
Gay J. G. Berne B. J. 1981 Modification of the overlap potential to mimic a linear site-site potential. J. Chem. Phys. 74: 3316. - 35.
Miguel E. Rull L. F. Chalam M. K. Gubbins K. E. Van Swol F. 1991 Location of the isotropic-nematic transition in the Gay-Berne model. Mol. Phys.72 593 605 - 36.
Luckhurst G. R. Stephens R. A. Phippen R. W. 1990 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers XIX. Mesophases formed by the Gay-Berne model mesogen. Liq. Cryst. 8: 451. - 37.
Smith(Allen M. P. Warren M. A. Wilson M. R. Sauraon A. w. 1996 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers em. Phys.105 2850 2858 - 38.
Rappe, AK and Casewit, CJ and Colwell, KS and Goddard Iii, WA and Skiff, WM (1999 ) UFF, UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. JOSA114 10024 10035 . - 39.
Smith(Allen M. P. Warren M. A. Wilson M. R. Sauraon A. w. 1985 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Phys. 55: 549. - 40.
Cleaver D. J. Care C. M. Allen M. P. Neal M. P. 1996 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Phys. Rev. E54 559 567 - 41.
Parrinello M. Rahman A. 1981 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers J. Appl. Phys. 52:7182 EOF 7190 EOF - 42.
Nose S. 1984 A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81: 511. - 43.
Hoover W. G. 1985 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Rev. A31 1695 1697 - 44.
Beeman D. 1976 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers J. Comput. Phys. 20:130 EOF 139 EOF - 45.
Li M. H. Keller P. Li B. and Wang. X. Brunet M. 2003 Monitoring the Contractile Properties of Optically Patterned Liquid Crystal Based Elastomers Adv. Mater. E15 5569 572