Optical deformations of azobenzene polymers: orientation approach vs. other concepts.

It has been 30 years since the discovery of surface restructuring in thin azopolymer films by two independent research groups. A wide variety of topographical structures have been created by the application of two-/four-beam interference patterns, space light modulators and even helical beams. There are a number of comprehensive reviews which describe in detail the advances in superficial photopatterning of azopolymer films and macroscopic deformations of azonetworks. The theoretical approaches are only briefly touched on in these reviews and often are accompanied by the remark that the phenomenon is far from being understood. In this review, we would like to present the polymer theoretist's point of view on this intriguing problem. We begin by describing a multitude of theoretical approaches and commenting on the pluses and drawbacks of each. Importantly, we show that in most cases the presence of an azopolymer matrix is either ignored or limited to a specific class of azopolymers (liquid-crystalline or elastomeric). We then move to early orientation approaches based on the hypothesis that reorientation of azo-chromophores by modulated polarized light is the sole cause of superficial patterning. At the end of the review a modern orientation approach, as proposed by our own group, is presented. This approach has high predictive power because it can explain a large pool of experimental data for different classes of azopolymers including glassy and liquid-crystalline materials. This is made possible by taking into account both the light-induced orientation process and the change of anisotropic interactions between the chromophores upon their isomerization. Last but not least, this is the only approach that provides an estimate of the light-induced stress large enough to cause plastic deformations of glassy azopolymers. Recent finite element modeling results show remarkable similarity to real patterns and even time-dependent data are well explained. With this, we claim that the puzzle is finally understood and the orientation approach is ready for its implementation for major azopolymer classes.

Effect of microstructure evolution on the mechanical behavior of magneto-active elastomers with different matrix stiffness.

Evolution of microstructure in magneto-active elastomers (MAEs) which can be caused by an applied magnetic field is a fascinating phenomenon with a significant impact on the mechanical behavior of the composite. To gain insight into the underlying mechanisms of this phenomenon, it is essential to create a model that can appropriately describe the field induced change in the particle distribution and its mechanical implications. The magneto-mechanical coupling is driven by magnetic interactions between the particles in the applied field. These magnetic interactions can result in macroscopic deformation of the sample and also in rearrangement of the microstructure, i.e. the local positions of the particles. In the case of initially isotropic MAEs made with a sufficiently soft matrix, this leads to the formation of chains of magnetized particles, creating a significant increase in the mechanical moduli along the field direction. In this paper, we implement a transversely isotropic Neo-Hookean material model to account for such anisotropic elastic behavior. A dipolar mean field approach is used to describe magnetic interactions between the particles. A penalty term is introduced to compensate for the micro-mechanical elastic energy required to move the particles inside the cross-linked elastomer. The resulting model can predict the huge magneto-rheological effects observed in experiments, and improves our understanding of how microstructure evolution affects magnetically induced deformation and stiffness of MAEs.

Viscoplastic Modeling of Surface Relief Grating Growth on Isotropic and Preoriented Azopolymer Films.

We report on solving of two intriguing issues concerning the inscription of surface relief gratings within azopolymer thin films under irradiation with SS, PP and RL interference patterns. For this, we utilize the orientation approach and viscoplastic modeling in combination with experimental results, where the change in surface topography is acquired in situ during irradiation with modulated light. First, the initial orientation state of polymer backbones is proved to be responsible for the contradictory experimental reports on the efficiency of the SS interference pattern. Different orientation states can influence not only the phase of SS grating but also its height, which is experimentally confirmed by using special pretreatments. Second, the faster growth of gratings inscribed by the RL interference pattern is shown to be promoted by a weak photosoftening effect. Overall, the modeled results are in good agreement with the order of relative growth efficiency: RL-PP-SS.

Magneto-Mechanical Enhancement of Elastic Moduli in Magnetoactive Elastomers with Anisotropic Microstructures.

Magnetoactive elastomers (MAEs) have gained significant attention in recent years due to their wide range of engineering applications. This paper investigates the important interplay between the particle microstructure and the sample shape of MAEs. A simple analytical expression is derived based on geometrical arguments to describe the particle distribution inside MAEs. In particular, smeared microstructures are considered instead of a discrete particle distribution. As a consequence of considering structured particle arrangements, the elastic free energy is anisotropic. It is formulated with the help of the rule of mixtures. We show that the enhancement of elastic moduli arises not only from the induced dipole-dipole interactions in the presence of an external magnetic field but also considerably from the change in the particle microstructure.

Columnar Aggregates of Azobenzene Stars: Exploring Intermolecular Interactions, Structure, and Stability in Atomistic Simulations.

We present a simulation study of supramolecular aggregates formed by three-arm azobenzene (Azo) stars with a benzene-1,3,5-tricarboxamide (BTA) core in water. Previous experimental works by other research groups demonstrate that such Azo stars assemble into needle-like structures with light-responsive properties. Disregarding the response to light, we intend to characterize the equilibrium state of this system on the molecular scale. In particular, we aim to develop a thorough understanding of the binding mechanism between the molecules and analyze the structural properties of columnar stacks of Azo stars. Our study employs fully atomistic molecular dynamics (MD) simulations to model pre-assembled aggregates with various sizes and arrangements in water. In our detailed approach, we decompose the binding energies of the aggregates into the contributions due to the different types of non-covalent interactions and the contributions of the functional groups in the Azo stars. Initially, we investigate the origin and strength of the non-covalent interactions within a stacked dimer. Based on these findings, three arrangements of longer columnar stacks are prepared and equilibrated. We confirm that the binding energies of the stacks are mainly composed of π-π interactions between the conjugated parts of the molecules and hydrogen bonds formed between the stacked BTA cores. Our study quantifies the strength of these interactions and shows that the π-π interactions, especially between the Azo moieties, dominate the binding energies. We clarify that hydrogen bonds, which are predominant in BTA stacks, have only secondary energetic contributions in stacks of Azo stars but remain necessary stabilizers. Both types of interactions, π-π stacking and H-bonds, are required to maintain the columnar arrangement of the aggregates.

Cyclic Photoisomerization of Azobenzene in Atomistic Simulations: Modeling the Effect of Light on Columnar Aggregates of Azo Stars.

This computational study investigates the influence of light on supramolecular aggregates of three-arm azobenzene stars. Every star contains three azobenzene (azo) moieties, each able to undergo reversible photoisomerization. In solution, the azo stars build column-shaped supramolecular aggregates. Previous experimental works report severe morphological changes of these aggregates under UV-Vis light. However, the underlying molecular mechanisms are still debated. Here we aim to elucidate how light affects the structure and stability of the columnar stacks on the molecular scale. The system is investigated using fully atomistic molecular dynamics (MD) simulations. To implement the effects of light, we first developed a stochastic model of the cyclic photoisomerization of azobenzene. This model reproduces the collective photoisomerization kinetics of the azo stars in good agreement with theory and previous experiments. We then apply light of various intensities and wavelengths on an equilibrated columnar stack of azo stars in water. The simulations indicate that the aggregate does not break into separate fragments upon light irradiation. Instead, the stack develops defects in the form of molecular shifts and reorientations and, as a result, it eventually loses its columnar shape. The mechanism and driving forces behind this order-disorder structural transition are clarified based on the simulations. In the end, we provide a new interpretation of the experimentally observed morphological changes.

Field-Induced Transversely Isotropic Shear Response of Ellipsoidal Magnetoactive Elastomers.

Magnetoactive elastomers (MAEs) claim a vital place in the class of field-controllable materials due to their tunable stiffness and the ability to change their macroscopic shape in the presence of an external magnetic field. In the present work, three principal geometries of shear deformation were investigated with respect to the applied magnetic field. The physical model that considers dipole-dipole interactions between magnetized particles was used to study the stress-strain behavior of ellipsoidal MAEs. The magneto-rheological effect for different shapes of the MAE sample ranging from disc-like (highly oblate) to rod-like (highly prolate) samples was investigated along and transverse to the field direction. The rotation of the MAE during the shear deformation leads to a non-symmetric Cauchy stress tensor due to a field-induced magnetic torque. We show that the external magnetic field induces a mechanical anisotropy along the field direction by determining the distinct magneto-mechanical behavior of MAEs with respect to the orientation of the magnetic field to shear deformation.

Modeling of Nonlinear Optical Phenomena in Host-Guest Systems Using Bond Fluctuation Monte Carlo Model: A Review.

We review the results of Monte Carlo studies of chosen nonlinear optical effects in host-guest systems, using methods based on the bond-fluctuation model (BFM) for a polymer matrix. In particular, we simulate the inscription of various types of diffraction gratings in degenerate two wave mixing (DTWM) experiments (surface relief gratings (SRG), gratings in polymers doped with azo-dye molecules and gratings in biopolymers), poling effects (electric field poling of dipolar molecules and all-optical poling) and photomechanical effect. All these processes are characterized in terms of parameters measured in experiments, such as diffraction efficiency, nonlinear susceptibilities, density profiles or loading parameters. Local free volume in the BFM matrix, characterized by probabilistic distributions and correlation functions, displays a complex mosaic-like structure of scale-free clusters, which are thought to be responsible for heterogeneous dynamics of nonlinear optical processes. The photoinduced dynamics of single azopolymer chains, studied in two and three dimensions, displays complex sub-diffusive, diffusive and super-diffusive dynamical regimes. A directly related mathematical model of SRG inscription, based on the continuous time random walk (CTRW) formalism, is formulated and studied. Theoretical part of the review is devoted to the justification of the a priori assumptions made in the BFM modeling of photoinduced motion of the azo-polymer chains.

A Cascading Mean-Field Approach to the Calculation of Magnetization Fields in Magnetoactive Elastomers.

We consider magnetoactive elastomer samples based on the elastic matrix and magnetizable particle inclusions. The application of an external magnetic field to such composite samples causes the magnetization of particles, which start to interact with each other. This interaction is determined by the magnetization field, generated not only by the external magnetic field but also by the magnetic fields arising in the surroundings of interacting particles. Due to the scale invariance of magnetic interactions (O(r-3) in d=3 dimensions), a comprehensive description of the local as well as of the global effects requires a knowledge about the magnetization fields within individual particles and in mesoscopic portions of the composite material. Accordingly, any precise calculation becomes technically infeasible for a specimen comprising billions of particles arranged within macroscopic sample boundaries. Here, we show a way out of this problem by presenting a greatly simplified, but accurate approximation approach for the computation of magnetization fields in the composite samples. Based on the dipole model to magnetic interactions, we introduce the cascading mean-field description of the magnetization field by separating it into three contributions on the micro-, meso-, and macroscale. It is revealed that the contributions are nested into each other, as in the Matryoshka's toy. Such a description accompanied by an appropriate linearization scheme allows for an efficient and transparent analysis of magnetoactive elastomers under rather general conditions.

Magneto-Mechanical Coupling in Magneto-Active Elastomers.

In the present work, the magneto-mechanical coupling in magneto-active elastomers is investigated from two different modeling perspectives: a micro-continuum and a particle-interaction approach. Since both strategies differ significantly in their basic assumptions and the resolution of the problem under investigation, they are introduced in a concise manner and their capabilities are illustrated by means of representative examples. To motivate the application of these strategies within a hybrid multiscale framework for magneto-active elastomers, their interchangeability is then examined in a systematic comparison of the model predictions with regard to the magneto-deformation of chain-like helical structures in an elastomer surrounding. The presented results show a remarkable agreement of both modeling approaches and help to provide an improved understanding of the interactions in magneto-active elastomers with chain-like microstructures.

Giant Extensional Strain of Magnetoactive Elastomeric Cylinders in Uniform Magnetic Fields.

Elongations of magnetoactive elastomers (MAEs) under ascending-descending uniform magnetic fields were studied experimentally using a laboratory apparatus specifically designed to measure large extensional strains (up to 20%) in compliant MAEs. In the literature, such a phenomenon is usually denoted as giant magnetostriction. The synthesized cylindrical MAE samples were based on polydimethylsiloxane matrices filled with micrometer-sized particles of carbonyl iron. The impact of both the macroscopic shape factor of the samples and their magneto-mechanical characteristics were evaluated. For this purpose, the aspect ratio of the MAE cylindrical samples, the concentration of magnetic particles in MAEs and the effective shear modulus were systematically varied. It was shown that the magnetically induced elongation of MAE cylinders in the maximum magnetic field of about 400 kA/m, applied along the cylinder axis, grew with the increasing aspect ratio. The effect of the sample composition is discussed in terms of magnetic filler rearrangements in magnetic fields and the observed experimental tendencies are rationalized by simple theoretical estimates. The obtained results can be used for the design of new smart materials with magnetic-field-controlled deformation properties, e.g., for soft robotics.

Modeling of Stripe Patterns in Photosensitive Azopolymers.

Placed at interfaces, azobenzene-containing materials show extraordinary phenomena when subjected to external light sources. Here we model the surface changes induced by one-dimensional Gaussian light fields in thin azopolymer films. Such fields can be produced in a quickly moving film irradiated with a strongly focused laser beam or illuminating the sample through a cylindrical lens. To explain the appearance of stripe patterns, we first calculate the unbalanced mechanical stresses induced by one-dimensional Gaussian fields in the interior of the film. In accordance with our orientation approach, the light-induced stress originates from the reorientation of azobenzenes that causes orientation of rigid backbone segments along the light polarization. The resulting volume forces have different signs and amplitude for light polarization directed perpendicular and parallel to the moving direction. Accordingly, the grooves are produced by the stretching forces and elongated protrusions by the compressive forces. Implementation into a viscoplastic model in a finite element software predicts a considerably weaker effect for the light polarized along the moving direction, in accordance with the experimental observations. The maximum value in the distribution of light-induced stresses becomes in this case very close to the yield stress which results in smaller surface deformations of the glassy azopolymer.

Stacks of Azobenzene Stars: Self-Assembly Scenario and Stabilising Forces Quantified in Computer Modelling.

In this paper, the columnar supramolecular aggregates of photosensitive star-shaped azobenzenes with benzene-1,3,5-tricarboxamide core and azobenzene arms are analyzed theoretically by applying a combination of computer simulation techniques. Without a light stimulus, the azobenzene arms adopt the trans-state and build one-dimensional columns of stacked molecules during the first stage of the noncovalent association. These columnar aggregates represent the structural elements of more complex experimentally observed morphologies-fibers, spheres, gels, and others. Here, we determine the most favorable mutual orientations of the trans-stars in the stack in terms of (i) the π - π distance between the cores lengthwise the aggregate, (ii) the lateral displacements due to slippage and (iii) the rotation promoting the helical twist and chirality of the aggregate. To this end, we calculate the binding energy diagrams using density functional theory. The model predictions are further compared with available experimental data. The intermolecular forces responsible for the stability of the stacks in crystals are quantified using Hirshfeld surface analysis. Finally, to characterize the self-assembly mechanism of the stars in solution, we calculate the hydrogen bond lengths, the normalized dipole moments and the binding energies as functions of the columnar length. For this, molecular dynamics trajectories are analyzed. Finally, we conclude about the cooperative nature of the self-assembly of star-shaped azobenzenes with benzene-1,3,5-tricarboxamide core in aqueous solution.

Modeling of the photo-induced stress in azobenzene polymers by combining theory and computer simulations.

It has been shown recently that the photo-induced deformations in azobenzene-containing polymers of a side-chain architecture can be explained by means of the so-called orientational approach. The explanation is based on the following sequence of steps: (i) reorientation of azobenzenes under illumination, (ii) reorientation of the polymer backbones coupled mechanically to azobenzenes, and (iii) development of large stress in a material. Step (i) is based on the angle selective absorption of the azobenzene chromophore, which is a well established fact. Step (iii) has been validated in a series of recent theoretic studies in an infinite coupling limit. Concerning step (ii), in a real material, the backbone-azobenzene coupling will be always finite, resulting in a decrease of the effective torque sensed by the backbones and in a time delay in their reorientation. To study the relevance of these effects in detail, we perform coarse-grained molecular dynamics simulations of side-chain azobenzene-containing oligomers in bulk at conditions close to the glassy state. The focus is on the dynamical properties of such a system and on its response to the illumination, with the latter modeled either as an orientation potential applied to the azobenzenes or via their stochastic photo-isomerization. By matching the amount of light-induced stress evaluated in both cases, we obtained the equivalent orientation potential as a function of the illumination intensity and the system density.

Do Columns of Azobenzene Stars Disassemble under Light Illumination?

The clustering properties of star-shaped molecules comprising three photochromic azobenzene-containing arms are investigated with specific focus on the influence of light on these structures. Previous experimental works report self-assembly of azobenzene stars in aqueous solution into long columnar clusters that are detectable using optical microscopy. These clusters appear to vanish under UV irradiation, which is known to induce trans-to-cis photoisomerization of the azobenzene groups. We have performed MD simulations, density functional theory, and density functional tight binding calculations to determine conformational properties and binding energies of these clusters. Our simulation data suggest that the binding strength of the clusters is large enough to prevent a breaking along their main axis. We conclude that very likely other mechanisms lead to the apparent disappearance of the clusters.

All-Optical Reversible Azo-Based Wrinkling Patterns with High Aspect Ratio and Polarization-Independent Orientation for Light-Responsive Soft Photonics.

Azobenzene-containing polymers (azopolymers) can serve as building blocks for an emerging class of soft photonics. Using their photoresponses for the micro/nanofabrication of smart surface is a key but still a challenging step. Here, we report a simple visible-light-illumination strategy to trigger diverse configurations of surface wrinkling on azopolymer-based film/substrate systems, which can be switched between flat and wrinkled states by controlling the intensity of the incident light. Different photoresponsive characteristics of azobenzene are involved in driving the wrinkling/dewrinkling switch. For the first time, we achieve the controlled wrinkling with an unexpected high aspect ratio and surprisingly polarization-independent ordered orientation by exploiting the unique photosoftening effect of azobenzene. Theoretical analysis reveals that an in situ photoinduced reversible soft/hard-contrast boundary determines the wrinkling orientation, which is used to fabricate diverse on-demand hierarchical wrinkles. These photoresponsive systems find broad photonic applications that are not easily accessible to other systems, e.g., optically reversible smart display, information security, and well-regulated optical devices.

Effects of local rearrangement of magnetic particles on deformation in magneto-sensitive elastomers.

Based on the dipole-dipole approach for magnetic interactions we present a comprehensive analysis of spatial rearrangement of magnetic particles under a magnetic field and its effect on the magneto-induced deformation of magneto-sensitive elastomers. The presented formalism allows analyzing non-affine displacements of magnetic particles in a general way and reveals how the local rearrangement of particles under a magnetic field affects the magneto-induced deformation. The formalism includes two contributions: (1) displacements due to elastic coupling with a deformed matrix and (2) rearrangements on the background of the deformed matrix due to magnetic interactions between the particles. We show that in the linear response regime the sign of deformation is defined by the first contribution and the second one amplifies the magnitude of deformation. The sign and magnitude of deformation depend on the factors cos2 θ and cos4 θ, where averaging is over mutual pairs of particles and θ is the angle between the vector connecting the particles and the direction of the magnetic field. We test the new formalism on isotropic-like lattice distributions with cos2 θ = 1/3 and show that the difference in the sign of their deformation is defined by the difference in the factor cos4 θ. The results are compared for 3-dimensional and 2-dimensional systems, which are shown to have a similar behavior as a function of the aspect ratio of a sample.

Orientation Approach to Directional Photodeformations in Glassy Side-Chain Azopolymers.

To make a polymer-based material photosensitive, it is usually modified by inclusion of azobenzene (azo) chromophores. Their interaction with the light leads to conversion of absorbed energy into mechanical work. The wavelengths ∼500 nm induce cyclic trans-cis isomerization, which results in preferred orientation of the trans-isomers perpendicular to light polarization. This causes reorientation of the polymer backbones to which the azos are attached and appearance of the light-induced stress that dictates a direction of the macroscopic deformation. The directional photodeformations can be explained by an orientation approach, in which the reorientation of azos is described by the effective orientation potential. Here, we show how to calculate the time-dependent orientation state of the polymer backbones and the light-induced stress tensor. For side-chain azopolymers, a tensile stress in the direction of light polarization is predicted. Implementing the stress in a viscoplastic material model of the finite element software ANSYS, we show that a square azopolymer post elongates along the electric field vector for the linearly polarized light and contracts along the propagation direction for the circularly polarized light. These results of viscoplastic material modeling are in accordance with the experiments on light-induced reshaping of microscaled square and cylinder posts. Hence, the orientation approach works rather well for homogeneous illumination. We discuss how this approach can be used to describe surface deformations induced by complex light interference patterns.

Light-Induced Deformation of Azobenzene-Containing Colloidal Spheres: Calculation and Measurement of Opto-Mechanical Stresses.

We report on light-induced deformation of colloidal spheres consisting of azobenzene-containing polymers. The colloids of the size between 60 nm and 2 µm in diameter were drop casted on a glass surface and irradiated with linearly polarized light. It was found that colloidal particles can be deformed up to ca. 6 times of their initial diameter. The maximum degree of deformation depends on the irradiation wavelength and intensity, as well as on colloidal particles size. On the basis of recently proposed theory by Toshchevikov et al. [ J. Phys. Chem. Lett. 2017 , 8 , 1094 ], we calculated the opto-mechanical stresses (ca. 100 MPa) needed for such giant deformations and compared them with the experimental results.

Kinetics of Ordering and Deformation in Photosensitive Azobenzene LC Networks.

Azobenzene-containing polymer networks are unique compounds that are able to change their shape in response to light, which makes them prospective materials for photocontrollable nano-templates, sensors, microrobots, artificial muscles, etc. In present work, we study the kinetics of light-induced ordering and deformation in two-component polymer networks containing optically inert liquid crystalline (LC) mesogens and azobenzene chromophores. By this, we generalize our previous theory [J. Phys. Chem. Lett. 2017, 8, 1094⁻1098] devoted to the kinetics of photoizomerization in one-component azo-polymers without mesogenic inclusions. The kinetic equations of photoisomerization are used, taking into account the angular selectivity of the photoisomerization with respect to the polarization direction of the light E. After multiple trans-cis-trans photoisomerization cycles, the azobenzenes are reoriented preferably perpendicular to the vector E. This changes the ordering of the mesogens due to the orientational LC interactions between the components. The light-induced reordering is accompanied by network deformation. Time evolution of ordering and deformation is found as a function of the intensity of light and structural parameters of the LC azo-networks, which define the viscosity, the strength of the LC interactions between the components, the volume fraction of the azobenzene moieties, and the angular distribution of azobenzenes in polymer chains. Established structure-property relationships are in agreement with a number of experimental data.