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.

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.

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.

Kinetics of light-induced ordering and deformation in LC azobenzene-containing materials.

Azobenzene-containing smart materials are able to transform the energy of light into directional mechanical stress. We develop a theory of time-dependent light-induced ordering and deformation in azobenzene materials starting from the kinetic equations of photoisomerization. The liquid crystalline (LC) interactions between rod-like trans-isomers are taken into account. Angular selectivity of the photoisomerization known as an "angular hole burning" or the Weigert effect leads to the light-induced ordering and deformation of the azobenzene materials. The time evolution of ordering and deformation is found as a function of intensity of light depending on the opto-mechanical characteristics of the materials, such as probabilities of the optical excitation of trans- and cis-isomers, angular jump during the single isomerization event, viscosity of the materials, strength of the LC interactions in both the isotropic and LC materials, and the angular distribution of chromophores in polymer chains. Established structural-property relationships are in agreement with a number of experiments and can be used for the construction of light-controllable smart materials for practical applications.

Elongated micro-structures in magneto-sensitive elastomers: a dipolar mean field model.

Based on a dipole model for the mutual magnetic interactions among the magnetizable micro-particles in magneto-sensitive elastomers we develop a mean field approach to describe the arrangement of these particles into elongated micro-structures. If these micro-structures are oriented parallel to an external magnetic field the present approach provides an efficient calculation of the behavior of such samples, which is a result of the interplay between micro-structure and shape effects. Accordingly, we are able to draw comprehensive phase diagrams for the resultant deformation and predict for very oblate samples a discontinuous shape change in the presence of a homogeneous external field.

Light-induced deformation of polymer networks containing azobenzene chromophores and liquid crystalline mesogens.

Two-component polymer networks containing liquid crystalline (LC) mesogens and azobenzene chromophores belong to a class of smart materials which combine uniquely the orientation order of liquid crystals and light-induced deformation of photosensitive polymers. In the present study we develop a theory of light-induced deformation of azobenzene-containing LC networks. It is shown that preferential reorientation of chromophores perpendicular to the polarization direction of the light E leads to the reorientation of the mesogens due to LC interactions between the components. Reorientation of the chromophores and mesogens results in the light-induced deformation of the polymer network. The sign of deformation (expansion/contraction with respect to the vector E) depends on the orientation distribution of the mesogens and chromophores inside the network strands. The magnitude of deformation increases with increase of the volume fraction of chromophores and the strength of LC interactions between the components. The influence of the dilution of azobenzene-containing networks by the bent cis-isomers of the chromophores on the light-induced deformation is discussed.

Dynamic moduli of magneto-sensitive elastomers: a coarse-grained network model.

The viscoelastic properties of magneto-sensitive elastomers (MSEs) in a low-frequency regime are studied using a coarse-grained network model. The proposed model takes into account the mechanical coupling between magnetic particles included in a whole network structure and magnetic interactions between them. We show that the application of a constant uniform magnetic field leads to the splitting of the relaxation spectrum into two branches for the motions of the particles parallel and perpendicular to the field. The shear dynamic moduli G' and G'' of MSEs are calculated as a function of frequency. The values of G' and G'' are shown to depend on the direction of the shear deformation with respect to the magnetic field. For instance, both G' and G'' decrease if the magnetic field is applied parallel to the shear velocity (D-geometry) and increase if it is applied along the shear gradient (G-geometry). The latter prediction is in a qualitative agreement with existing experimental data. The theory allows us to analyse experimental data and to extract the structural characteristics of MSEs.

Mechanical properties of magneto-sensitive elastomers: unification of the continuum-mechanics and microscopic theoretical approaches.

A new theoretical formalism is developed for the study of the mechanical behaviour of magneto-sensitive elastomers (MSEs) under a uniform external magnetic field. This formalism allows us to combine macroscopic continuum-mechanics and microscopic approaches for complex analysis of MSEs with different shapes and with different particle distributions. It is shown that starting from a model based on an explicit discrete particle distribution one can separate the magnetic field inside the MSE into two contributions: one which depends on the shape of the sample with finite size and the other, which depends on the local spatial particle distribution. The magneto-induced deformation and the change of elastic modulus are found to be either positive or negative, their dependences on the magnetic field being determined by a non-trivial interplay between these two contributions. Mechanical properties are studied for two opposite types of coupling between the particle distribution and the magneto-induced deformation: absence of elastic coupling and presence of strong affine coupling. Predictions of a new formalism are in a qualitative agreement with existing experimental data.

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.

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.

Photoisomerization Kinetics and Mechanical Stress in Azobenzene-Containing Materials.

Kinetics of photoisomerization and time evolution of ordering in azobenzene-containing materials are studied theoretically and by using computer simulations. Starting from kinetic equations of photoisomerization, we show that the influence of light is equivalent to the action of the effective potential, which reorients chromophores perpendicularly to polarization direction. The strength of the potential is defined by optical and viscous characteristics of the material. The potential generates photomechanical stress of giant values ∼GPa, in accordance with recent experimental findings for azobenzene materials deep in a glassy state. The proposed approach has a great predictive strength for deeper understanding and further development of the photocontrollable smart compounds.

Theory of light-induced deformation of azobenzene elastomers: effects of the liquid-crystalline interactions and biaxiality.

We study light-induced deformation of azobenzene elastomers which can display liquid-crystalline (LC) order. It is shown that photomechanical behavior of azobenzene elastomers is determined by the strength of the LC interactions, which is proportional to the density of rodlike azobenzene chromophores. At weak LC interactions, a uniaxial order and uniaxial deformation of azobenzene elastomers along the polarization vector of the light E is observed. At strong LC interactions, the light is able to induce a phase transition from the uniaxial to the biaxial state, with two axes being related to the vector E and to a preferable alignment of the chromophores in the plane perpendicular to E. The phase transition can be of either the first or the second order. Azobenzene elastomers can demonstrate elongation or contraction along the polarization vector E, depending on the orientation distribution of chromophores around the main chains of network strands. The results of the theory are in a qualitative agreement with experiments and computer simulations, which demonstrate biaxial ordering in azo-containing polymers.