Light-Induced Deformation of Azobenzene-Containing Colloidal

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Light Induced Deformation of Azobenzene Containing Colloidal Spheres: Calculation and Measurement of Opto-Mechanical Stresses Sarah Loebner, Nino Lomadze, Alexey Kopyshev, Markus Koch, Olga Guskova, Marina Grenzer Saphiannikova, and Svetlana A. Santer J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b11644 • Publication Date (Web): 16 Jan 2018 Downloaded from http://pubs.acs.org on January 16, 2018

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Light induced deformation of azobenzene containing colloidal spheres: calculation and measurement of opto-mechanical stresses Sarah Loebner,1 Nino Lomadze,1 Alexey Kopyshev,1 Markus Koch,2 Olga Guskova,2 Marina Saphiannikova,2* Svetlana Santer1* 1

Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany 2

[*]

Leibniz Institute of Polymer Research Dresden, 01069 Dresden, Germany

Prof. Svetlana Santer, e-mail: [email protected] PD Dr. Marina Saphiannikova, e-mail: [email protected]

Keywords: azobenzene containing polymers, colloidal particles, opto-mechanical stress, effective orientation potential

Abstract We report on light induced deformation of colloidal spheres consisting of azobenzene containing polymers. The colloids of the size between 60nm and 2µm 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. Based on recently proposed theory [V. Toshchevikov et al. J. Phys. Chem. Lett. 2017], we calculated the opto-mechanical stresses (ca. 100 MPa) needed for such giant deformations and compared them with the experimental results. 1 ACS Paragon Plus Environment

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Introduction The opto-mechanical deformation of azobenzene containing polymer films has already been known for more than two decades.1,2 Azobenzene groups undergo photo-isomerization reaction from trans- to cis-state when exposed to UV irradiation and from cis- to trans on irradiation at longer wavelength.3 Irradiation at the wavelengths around 500nm induces cyclic trans–cis–trans isomerization which results in the preferred orientation of the trans/cis chromophores perpendicular/parallel to the light polarization. 4 When azobenzenes are incorporated into a polymer matrix, the photo-isomerization is transduced to global mechanical deformation of the whole polymer material. The irradiation field acts only on the photo-responsive azobenzenes, which are typically attached to the polymer backbones as side chains via covalent or non-covalent bonds. Depending on the irradiation field applied, one can achieve different deformations within the polymer material. For instance, when a thin polymer film is exposed to illumination with an interference pattern, the formation of surface relief grating (SRG) takes place.5 Here the polymer topography deforms following the local distribution of the electrical field vector. The topography pattern then simply mimics the interference pattern and forms a sinus shaped feature of periodicity equal to the optical periodicity. 6,7,8 ,9,10,11 This is true for both types of spatially modulated illumination: far field (external EM field) 12 , 13 , 14 , 15 and near field (surface plasmon EM field).16,17,18,19,20,21,22 The only exception here is the irradiation with SP interference pattern when the topography has two times smaller periodicity than the optical one.

23,24,25

When applying

alternating light of homogeneous intensity distribution, but different wavelength, one can get reversible change in the thickness and roughness of the polymer film.26,27,28,29,30 Irradiation of free standing azobenzene elastomers results even in reversible bending/stretching of the macroscopic piece of the polymer material.31,32 Under irradiation with linearly polarized light, the polymer 2 ACS Paragon Plus Environment


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material stretches in the direction of light polarization.33,34 This occurs in polymer film either supported by solid or fluid surface, i.e. freely floating. 35 Applying irradiation with linearly polarized light to colloids made of azobenzene containing polymers results in significant elongation of these objects along the electrical field vector.36,37 The mechanism of the photo-mechanical deformation is related to the generation of internal opto-mechanical stress. The process on the molecular level can be viewed as following: under irradiation inducing cyclic trans-cis-trans isomerization, the azobenzene molecules rotate and orient perpendicularly to the electrical field vector. This re-distribution of the azobenzenes causes a re-orientation of the polymer backbones to which the azobenzenes are attached, and thus the macroscopic deformation of a sample due to strong mechanical coupling between the two phases: active azobenzene molecules and a passive polymer matrix.38,39,40,41,42 Based on this molecular mechanism, the group of Saphiannikova has recently developed a theory describing the light induced mechanical stress in azobenzene containing materials, where the stresses from 100 MPa up to ~ 1 GPa were predicted for the azobenzene polymers deep in a glassy state.43 This theoretical prediction is also supported by several experimental results where metal films or graphene sheets were utilized as nanoscopic mechanical sensors to probe stresses generated during SRG formation. Here metal 44 , 45 or graphene layers 46 were deposited on photosensitive polymer films and irradiated with interference pattern. During SRG formation the process of metal/graphene layer deformation was recorded in-situ using AFM and Raman microscopy. These observations were then utilized to recalculate opto-mechanical stresses. The stresses as high as 1 GPa were estimated.47 In this paper, theoretical and experimental efforts were combined for the first time in order to study the stresses needed for deformation of photosensitive colloidal particles under irradiation with linearly polarized light. For this, the colloids of different sizes starting from 60nm up to ca. 2µm 3 ACS Paragon Plus Environment

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were prepared using precipitation procedure and deposited on a glass surface. Under irradiation with linearly polarized light, the colloids deform along the electrical field vector up to ca. 6 times of their initial size. Applying the newly developed theory, we calculated the stress needed for the colloid deformation to be as high as ca. 100MPa. To measure this stress we construct the following experimental system. The colloidal particles were immersed in a PDMS layer of known mechanical properties. Under irradiation with linearly polarized light, the particles deform despite the PDMS constrain, resulting in a local compression of the PDMS matrix. Analysing the extent of the PDMS compression, we calculated the stress which a colloidal particle has to exert on the PDMS in order to induce corresponding deformations. This stress can be as high as 37MPa which is in good agreement with the theoretically predicted value.

Experimental Part Materials. Preparation of colloidal particles. Photoresponsive colloidal spheres consisting of poly[(methyl methacrylate)-co-(Disperse Red 1 acrylate)] poly(MMA-co-DR1A) (Tg = 102°C provided by Sigma Aldrich) have been prepared through hydrophobic aggregation of the polymer chains in tetrahydrofuran (THF). Milli-Q water was added dropwise to the THF solution of poly(MMA-co-DR1A) (c=1mg/ml) resulting in formation of colloidal spheres. Then a large amount of water was added to quench the structures formed.48 During this procedure the colloids of the size ranging between 400nm and 800nm in diameter are mostly formed with a small fraction of nano- (several tens of nanometers) and micro-particles (several micrometers). The colloidal spheres were drop casted on a glass surface. The glass substrate (1870, Roth, Germany) was cleaned first by sonication in acetone and isopropanol for 10 minutes each, then by treatment with Helmanex during 2h followed by rinsing thoroughly with water and drying with nitrogen. 4 ACS Paragon Plus Environment


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Preparation of PDMS layer. The PDMS films with incorporated colloidal spheres were prepared by cast moulding using Sylgard 184 (Dow Corning). The mixture of elastomer and curing agent (10:1 ratio) was poured onto the polymer colloidal spheres adsorbed on a glass surface and cured for 24 hours at room temperature. The films were then detached from the substrate and deposited backwards on the glass slides. Methods. The irradiation of the sample was performed from the colloidal particles side with the linearly polarized light of λ= 491nm and I=100mW/cm² (Cobalt, Germany). AFM measurements were conducted using tapping mode AFM (Nanoscope V, Brucker, Germany) and commercial tips (NanoSensors) with a resonance frequency of 300 kHz and a spring constant of ~50 N/m. The experiments were carried out in air, at room temperature. Optical micrographs were recorded using Olympus BX51 (Olympus, Japan). Setup of molecular modelling and the definition of L, p, n and α parameters for the theory. The optimisation of the molecular geometry of DR1A was performed with Gaussian09 Revision C.01 suite of programs49 using density functional theory and B3LYP/6-31G(d,p) functional with a tight self-consistent field convergence threshold (10-8-10-10 a.u.), as described in our recent publication.50 From these calculations the DR1A side chain geometrical parameters were defined: Lazo=1.28nm, dazo=0.44nm, hazo=0.30nm and the average aspect ratio p=3.45. One chain of poly((MMA)3-co-DR1A)25 (molecular weight was chosen to be close to experimental one) was constructed in Polymer builder of BIOVIA Materials Studio® software (Version 9.0).51 In the MD simulations, the polymer consistent force field was employed.52 All azobenzenes of the DR1A side chains adopted the trans-isomerization state. The partial charges on atoms of poly((MMA)3-co-DR1A)25 were assigned corresponding to the polymer consistent force field, and the net charge of the molecule was set to zero. 5 ACS Paragon Plus Environment

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After geometry optimization of poly((MMA)3-co-DR1A)25 in gas phase using SMART algorithm with the ultra-fine quality settings (convergence threshold for energy is 2·10-5 kcal·mol-1), the simulation box was constructed in Amorphous Cell module. The initial density of the system was set to 0.8 g·cm-3 in a cubic simulation box with the edge length of 3.3 nm. For this density, 1000 structures were generated and their energy was minimized. The structure with the lowest potential energy was chosen for the molecular dynamics (MD) simulations. The MD simulations for density calculations were performed for 10 ns with 0.5 fs integration step in Forcite module applying NPT ensemble with the Nose thermostat (Q ratio 0.01, T=298 K) and the Berendsen barostat (decay constant of 0.1 ps). The final density of the system was evaluated as 1.2 g·cm-3, which is close to the density of pure PMMA at 20oC.53 Knowing the size of the simulation box after the NPT calculations and the number of the azobenzene moieties in this volume, the azobenzene number density n=1.0302·1021 for the volume of 1 cm3 was recalculated. Also from these calculations, the parameters of the rigid main-chain segment were defined: L=3.516nm, d=0.602nm and the aspect ratio L/d=5.84 (see Supporting Information Figure S1). They are used together with n for the analytical assessment of the mechanical properties (strength of the light-induced potential, viscosity of plastic flow and light-induced stress) following Eqs. (9), (14) and (15). The angle α in the shape factor q was defined as the torsion angle between the vector connecting nitrogen atoms of the nitro and amino substituents of DR1A side chain and the backbone carbon atoms of the same monomeric DR1A unit (see Supporting Information Figure S1). The averaging was performed for all azo side chains for the trajectory of 10 ns. For these calculations, the NVT MD simulation of an isolated poly((MMA)3-co-DR1A)25 chain at ambient conditions was performed. The mean radius of gyration of the chain was found to be 5.17±0.13 nm, and the most probable orientation angle of the side azobenzene chain with respect to the polymer backbone was α = 70o and =0.121±0.081 (see Supporting Information Figure S1). 6 ACS Paragon Plus Environment


Results and Discussion Colloids consisting of azobenzene containing polymer poly(MMA-co-DR1A) were deposited on a glass surface from a water solution using drop casting (see Experimental Part). The size distribution of the particles is broad ranging from ca. 60nm up to 2µm in diameter as shown in Figures 1a,c,e representing some characteristic areas on a glass surface.

Figure 1. Representative AFM micrographs of the photosensitive colloids before (left column: a, c, e) and after (right column: b, d, f) irradiation. The colloids were adsorbed on a glass surface (a, c, e) followed by irradiation with a single-beam laser of λ= 491nm (I=100 mW/cm²) during (b) 4 7 ACS Paragon Plus Environment

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minutes, (d) 30 minutes, (f) 90 minutes. The direction of polarization is depicted by white arrows.

The particles are solid like and are not deformed by adhesion forces, i.e. their height is equal to their diameter. After irradiation of the sample with linearly polarized light (λ=491nm, I=100mW/cm2) the colloids deform along the electrical field vector (white arrow in Figures 1b, d, f tirr=4, 30 or 90min, respectively) forming an ellipsoid like shape. The extent of deformation depends strongly on the size of the particle and irradiation time (at all other parameters fixed). At fixed particle size, the deformation increases with irradiation time and reaches its saturation at a certain irradiation point. For instance, for the particles of the diameter in the range of few hundreds nanometers, 90 minutes irradiation time is enough in order to induce maximal deformation, while for the larger colloids to achieve saturation in the deformation, the irradiation time has to be extended up to 6 hours. Under deformation the height and length of the smaller ellipsoid axis of the particle decreases indicating that the deformation is closer to the uniaxial one. The calculation of the particles volume before and after irradiation reveals volume conservation process. Figure 2a shows the size dependence of the particle deformation, calculated as a ratio between the length of the ellipsoid main axis after irradiation, Dirr, and the diameter of the particle before irradiation, D0. The irradiation time here was chosen to induce maximal deformation. With increasing the particle size the extent of the maximal deformation increases. Thus, for the smallest colloid of 60nm in diameter, the increase in the size is 1.3, while for the 400nm colloid one gets already 3.5 times increase (Figure 2a). For larger colloids such as one shown in Figure 2b with a diameter of 1.15µm the deformation can be already as large as 4.5 times. The maximal particle deformation measured was 6.25 times for the colloid of 1.60µm in diameter. The error bars in Figure 2 correspond to the uncertainness of the AFM measurements.

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Figure 2. (a) Dependence of the particle deformation on their diameter calculated as the ratio of the longer axis of the spheroids after irradiation, Dirr, and the initial diameter of the colloids, D0. The chemical structure of the photosensitive polymer is inserted in the right lower corner(b) Several AFM microcgraphs of selected particles shown before (left column) and after irradiation (right column).

The size dependence of the particle deformation could result from several aspects. Most probably size dependence could be related to the forces opposing the deformation, that are acting on the adsorbed colloidal spheres, such as the adhesion and the surface tension. Moreover, the colloidal 9 ACS Paragon Plus Environment

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spheres were prepared using the gradual hydrophobic aggregation, which could lead to a non-uniform distribution of the components of the colloidal particle,47,54 with easily precipitated longer polymer chains in the core of the colloids and the components with lower molecular weight on their shells. Therefore, smaller colloids could be stiffer showing less pronounced deformation, and vice versa larger spheres could be easily driven by light. Another explanation, coming from the computer simulations of the size-dependent mechanical response of nanoscale polymer particles,55 is based on so-called densification of the polymer layer at the rim of the sphere. Since the thickness of this layer was found to be ca. 1 nm regardless the sphere diameter, the smaller particles are less deformed under the same applied stimulus, as compared to larger objects. Additionally, the microlens effect causing the non-uniform light intensity in the colloids, and therefore their inhomogeneous deformation, has correlations to the size of the colloids. 56 Finally, the photochemical trans-cis interconversion of azobenzenes in the polymer spheres could be also related to different light-propagation depth in nm- and µm-range particles. The question arising here is whether small colloids could also be stretched to larger extent? We have found that under long time irradiation (6 hours) with high intensity light of 200 mW/cm2 small particles deform also up to ca. (5.5±0.5) times (Figure 3). Moreover, under these irradiation conditions the deformation extent does not depend on the particle size (at least in the range between 100nm and 600nm) (Figure3). It is obvious, that under irradiation with larger intensity one generates larger opto-mechanical stresses. Most probably, the above described factors inhibiting deformation of the solid spheres can be overcome at larger irradiation intensity.



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Figure 3. Dependence of the deformation extent on diameter of the particles after irradiation with linearly polarized light (λ=491nm) at intensity of 200mW/cm2 during 6 hours.

Indeed, we were able to verify how the adhesion force alters the deformation process. In order to exclude adhesion forces, we put colloids in water where they can freely float. The irradiation with linearly polarized light (λ=355nm, I=100mW/cm2) results in the colloid deformation as well (see video Figure S2 in Supporting Information). However, the deformation extent does not depend in this case on particle size being ca. 2 for particles of diameter ranging between 2µm and 10µm. It was not possible to detect the size changes of smaller particles using optical microscope due to resolution limit. We cannot directly compare particle deformation in air and in water, since the irradiation wavelength differs for both experiments (491nm and 355nm, respectively). However, these results show that the adhesion alters significantly the deformation process. As can be seen, eliminating the adhesion or increasing the irradiation intensity both result in size independent deformation of the colloids. The above described experiments also show that the particle deformation depends on irradiation wavelength. This topic is out of the scope of the present work. 11 ACS Paragon Plus Environment

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However, we can speculate at this stage, the difference in the deformation extent of the colloids irradiated at 355nm (maximal 2 times) and 491nm (ca. 6 times) is most probably related to the isomerization process of the azobenzene group. At 491nm irradiation, both isomers trans and cis can be pumped and interconverted simultaneously, since the π-π* is overlapping the n-π* transition. 57 This results in a continuous cyclic photo-isomerisation process accompanied by rotation of the azobenzene groups towards orthogonal position to the electrical field vector. In case of 355nm irradiation only cis-isomers can be pumped effectively meaning that less fraction of the azobenzene can rotate in order to align perpendicularly to the light polarization. Thus, one expects less opto-mechanical stress within the polymer under irradiation with 355nm than in case of 491nm. To estimate the mechanical stress needed for deformation of a polymer sphere, Nunzi et al. applied Hertz theory to calculate uniaxial compression of a sphere exposed to an external force, F.37 According to this approach a force needed for the deformation of the sphere of diameter, D, to an extent of ε is related in a simple way: F=4/3ED2ε 1.5, where E is the Young modulus of the sphere, and ε is δL/D (L is the elongated length) being a strain of deformation. In this way, the authors reported on a pressure of 3.5GPa assuming the modulus E=1GPa. However, since the Young modulus of the solid particles under irradiation is un-known and can even differ for the particles with different initial sizes, as discussed above, we decided to use another approach. Moreover, under irradiation the sphere is deformed not “passively” under externally applied forces, but represents an active system where the deformation is driven by internal stresses arising from the light-induced orientation of azobenzenes and polymer backbones. To measure the stress that should be exerted on the particle to induce corresponding deformation, we have constructed the following experiment. Photosensitive particles were embedded into a thin PDMS film as shown in Figures 4a-c. The PDMS was poured on the adsorbed spheres, cured at 12 ACS Paragon Plus Environment


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room temperature during 24 hours (Figure 4b), followed by the removal of the film from the glass surface (Figure 4c). Afterwards the PDMS surface with immersed colloids was characterized with AFM and optical microscopy (Figure 5a).

Figure 4. (a-c) Scheme of the procedure applied to integrate photosensitive particles (red balls) into a PDMS film (blue colour). The spheres on glass (a) are covered with a layer of PDMS (b). (c) The PDMS film is peeled off the glass, taking the spheres with it. (d) Scheme of the embedded particles deformed during irradiation with linearly polarized light (λ=491 nm, I= 100mW/cm²) from the particle side. The electrical field vector points in horizontal direction (c). (e) Scheme of the geometrical parameters used for calculation of the opto-mechanical stress exerted by deformed particle on PDMS film. D0 is the initial diameter of the particle (1µm), Dirr is the particle length after irradiation, h0 is the particle protrusion before irradiation, h1 is PDMS protrusion after irradiation and h2 is the depth of the holes after irradiation. All parameters were inferred from the AFM measurements.

Particles are well visible as red points in the optical micrograph, while on the AFM image one can see that a small part of the particles is protruded from the PDMS film (depicted schematically as h0 in Figure 4b). Depending on the particle size, different heights are measured ranging from 20nm to 30nm. The particles are immersed in the PDMS as depicted schematically in Figure 4b. Several particles were not removed with the PDMS film and left behind empty holes (Figure 5a). After 13 ACS Paragon Plus Environment

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irradiation with linearly polarized light (λ= 491nm, I=100mW/cm², tirr= 15minutes) the particles are stretched along the electrical field vector (schematically shown as a red ellipse in Figures 4d and e). The particle deformation results in compression of the PDMS in the direction of elongation and as a consequence protrusion of the adjoining PDMS material at the PDMS/air interface. This is visible as raised areas near the holes (Figure 5b) and schematically depicted in Figure 4e as a red profile with the h1 height of the extrusions. The particles height decreases during elongation, so that now they appear as holes in the PDMS film (Figure 5b). The acquiring of Figure 5b was performed by scanning the sample with AFM tip from top to bottom while simultaneously irradiating the sample with linearly polarized light. In this way the micrograph represents time evolution of the topography change, i.e. the upper colloids/holes are shown at the early stage of irradiation than the lower particles. Therefore, the two colloids at the right upper corner appear still as elevated particles, while the colloids down are already deformed and appear as holes. As a consequence, the extent of PDMS deformation increases also from top to bottom as can be seen from the cross-sectional analysis shown in Figure 5d. The strain field around the deformed colloidal particle in the PDMS matrix is highly inhomogeneous. It is not possible to access the strain values near the ends of ellipsoidal particles, where the field would be maximal. Therefore, the macroscopic compression strain ε=h1/h2 along the vertical axis has been used as the second best choice. Taking advantage of the well-known mechanical properties of the PDMS films58 namely using the compression modulus of the PDMS 186.9MPa,54 the stress needed for the PDMS deformation was calculated to be ~37MPa: σ=E.ε= 186.9MPa.(30nm/150nm)=37.4MPa. This value can be considered as a lower estimate of the opto-mechanical stress, as the latter contains also a contribution from the yield stress necessary to plasticise the glassy colloid.42 Thus, we use in this experiment the PDMS as a nano-probe to sense a contribution into the opto-mechanical stress, which exceeds the yield stress. 14 ACS Paragon Plus Environment


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Figure 5. (a, b) AFM micrographs of the PDMS film with embedded particles (a) before and (b) during irradiation. It is scanned from top to bottom while irradiating with λ= 491nm (I=100 mW/cm²). The scanning direction is indicated by the black arrow. (d) Cross sections recorded along the lines 1 and 2 from (b) represent different PDMS deformations: cross section 1(black line) corresponds to early stage of irradiation than the cross section 2 (blue line). h1 is shown schematically in Figure 4e. (c) Optical micrograph depicts embedded spheres (red points) and empty holes (grey spots) before irradiation.

To theoretically calculate the opto-mechanical stress needed for the deformation of a colloidal particle under irradiation with linearly polarized light we applied the concept of effective orientation potential published recently.43 The internal stress of the ensemble of rod-like particles in the presence of external potential Ueff was calculated by S. Prager in 1957, see Table 14.3-1 15 ACS Paragon Plus Environment

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(A) in the text book of R.B. Bird:59

τ = −3nkT uu + nkTδ − n u Here

n

∂ Ueff ∂u

(1)

is the number density of particles, each characterized by the unit orientation vector

u.

The angular brackets describe averaging over the ensemble of particles and δ is the unit tensor. The time evolution of 2nd order orientation tensor uu , which describes an average orientation state of the particle ensemble, is given by Eq. (14.2-14.11) from the same book:59

∂ ∂ 1 1 1 uu = δ − uu − u Ueff , ∂t 3λ λ 3kTλ ∂u

(2)

where λ is the rotational relaxation time. Let us assume that initial orientation of the rod-like molecules is isotropic: uu = δ / 3 . Then, the internal stress

τ

is equal to 0 in the absence of

external potential. The effective orientation potential, acting on the azo-polymers with different architecture, was introduced in Refs. 42 and 43. If we consider the azo-polymer to be built from a number of rigid Kuhn segments each containing

m

azobenzenes, then the light-induced potential acting on the

Kuhn segment becomes U eff = qmV0 cos 2 θ . Here

V0 is the potential strength, θ is the angle

between the light polarization vector E and orientation of the Kuhn segment

u.

The shape

factor q = [3〈 cos 2 α 〉 − 1] / 2 takes into account the orientation distribution of azobenzenes around the main chain, i.e. around the long axis of Kuhn segment with long axis of azobenzene and

α

being the angle between the

u.

It is shown in the experiment that an azo-polymer sphere elongates along the polarization direction E || x under homogeneous illumination. The stress causing this elongation can be calculated from

Eq. (1) as 16 ACS Paragon Plus Environment


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[

τ xx = −3nkT u x2 + nkT − 2qmV0 n u x2 − u x4

]

(3a)

τ yy = τ zz = −τ xx / 2 2 where the time evolution of ux

(3b)

is defined by Eq. (2) as

[

∂ 2 1 1 2 2 qmV 0 − u x2 − u x4 ux = ux − ∂t 3λ λ 3kT λ

]

(4)

In above equations to eliminate u x4 , it is necessary to use the closure approximation. To simplify the calculations, we use a linear closure which approximates the branch of positive order parameters S = [3〈ux2 〉 −1] / 2 ≥ 0 : u x4 =

6 2 1 ux − . 5 5

(5)

Let us first solve Eq. (4) using the approximation (5):

τ 1 u x2 (t ) = exp( −t / τ e ) + e [1 − exp( −t / τ e )] 3 τ0 with τ e =

λ 1 − Vr

and τ 0 =

λ 1 / 3 − Vr

, where the reduced potential is introduced: Vr =

(6) 2qmV0 . 15kT

This solution provides the isotropic orientation at t = 0 , that is in the dark, and the stationary orientation at t → ∞ : u x2

It is nicely seen that u x2

st

st

=

τ e 1 / 3 − Vr . = 1 − Vr τ0

(7)

= 1 / 3 at Vr = 0 , that is the stationary state is isotropic in the absence of

light. When the light-induced potential becomes very large, Vr → ∞ , the stationary state is a perfect uniaxial orientation along E || x . Now using Eqs. (3) and (6) we can write the time-dependent stress:


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[

]

τ xx (t ) = 3nkT 1 / 3 − Vr − (1 − Vr ) u x2 (t ) .

(8)

Neglecting an instantaneous elastic deformation, we assume that this stress induces a plastic deformation of the azo-polymer sphere:

τ xx (t ) = 2ηε&xx (t )

(9)

where η is the viscosity of plastic flow and ε&xx is the instantaneous elongation rate. Note that the plastic deformation is caused by a part of the stress which exceeds the yield stress, σ Y . Typical values of σ Y for glassy polymers are about tens of MPa.42 Thus, Eq. (9) provides a lower estimate of the light-induced stress. The elongation itself can be obtained by integrating

ε&xx over

time: Dirr / D 0 = exp [ε xx (t ) ] with

t

ε xx (t ) = ∫ ε&xx (t′)dt ′ . As a final result we obtain the time-dependent Hencky strain: 0

ε xx (t ) =

 τ  3nkT λ [exp( −t / τ e ) − 1]1 / 3 − e  . 2η τ0  

(10)

with the stationary value at t → ∞ :

ε st = nkT

λ Vr . η Vr − 1

(11)

Using the last expression, it is possible to estimate the light-induced potential

V0 acting on an

azobenzene chromophore. For that let us first express the rotational time of the rod-like particles via the viscosity of plastic flow, see Eqs. (6-32b) and (6-42) from the text book of R.G. Larson:60 λ=

where

Dr 0

is

the

rotation

πη L3 1 = 6 Dr 0 18 kT (ln L / d + C )

diffusivity

of

,

the

(12) particle

and

the

constant

C = −0.662 + 0.917 /( L / d ) − 0.05 /( L / d ) 2 takes into account the end-effect terms for short rods.61 18 ACS Paragon Plus Environment


Page 20 of 27

Thus, the reduced potential V r is defined by 18 ln L / d + C Vr = ε st Vr − 1 π nL3

(13)

The value of stationary Hencky strain can be obtained from the experiment as ε st = ln Dirr / D0 . In our simplified calculations, we do not take into account the adhesion force which acts as an inhibiting process of colloid deformation. Smaller spheres experience stronger adhesion to the substrate surface and as a result noticeably smaller elongation ratios: Dirr / D0 ~ 1.5 are measured for the smaller spheres with D0 ~ 100 nm compared to Dirr / D0 ~ 5 for the larger spheres with D0 ~ 1 µ m , see Figure 2. Therefore, to allow for a better comparison of the experimental data with the theory, that neglects the adhesion effects, we chose the large spheres with

D 0 = 1000 ± 300

nm, the stationary elongation of which reaches the values of

D irr / D 0 = 5 . 0 ± 0 . 3 . This gives the Hencky strain of about ε st = 1 . 61 ± 0 . 06 . The Kuhn segment has the length of L = 3.516 nm calculated as described in Experimental Part and the diameter d = 0 .602 nm; thus L / d = 5 .84 . The number of azobenzenes in the Kuhn segment is equal m = 3 .5 . Hence, the number density of the segments is 3.5 smaller than the number density of azobenzenes: n = 0.294⋅1021 cm−3 . For the stationary elongation Dirr / D0 = 5.0 we obtain Vr = 0.907 , from which follows V r = − 9 . 789 . Vr − 1

The MD simulations provide the most probable orientation of the DR1A side chains with α=70o and =0.121±0.081 and thus the shape factor q=−0.319. The strength of the light-induced potential acting on the Kuhn segment is estimated to be V0 =

15 kT Vr = 2.70 ⋅ 10 −19 J. 2 qm

(14)


Page 21 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


The viscosity of plastic flow can be calculated from the rotation time in the presence of light as

τe =

λ 1 − Vr

. For a rough estimate we can use τ e = 60 min . Then the rotation time in the absence

of light λ = 648 min and

η=

18 kT (ln L / d + C ) λ = 26 .4 GPa ⋅ s πL3

(15)

We can also estimate the stress. At t = 0 the tensile stress has the largest value:

τ tens = τ xx ( 0 ) − τ yy ( 0 ) = − 3nkTV r = −

2 qmnV 0 . 5

(16)

This results in the opto-mechanical stress needed for the deformation of the large colloidal particle ca. τ tens = 35.5 MPa at Dirr / D0 = 5.0 that corresponds very well with the experimentally estimated stress of ca. 37 MPa. Also we estimated the tensile stress of τ tens = 24 .8 MPa for the smaller deformation

D irr / D 0 = 4 . 7

and

τtens = 57.0 MPa for the larger deformation

Dirr / D0 = 5.3 . This provides the average value of τ tens = (40 ± 16) MPa . For small particles shown in Figure 3 irradiated at larger intensity with half-time of inscription of 180min, the estimated tensile stress is τ tens = (140 ± 50) MPa for Dirr / D0 = 5.6 ± 0.1 As we mentioned above, both . the experimentally and theoretically estimated values of the opto-mechanical stress provide its lower estimates, as the yield stress of about 10-50 MPa should be added to these estimates.42 The magnitude of the observed light induced mechanical stress is closer to the lower limit of the values from recently proposed theory,43 ranging from 100MPa up to giant values of ~1 GPa for different azobenzene containing glassy polymer systems.

Conclusions 20 ACS Paragon Plus Environment


Page 22 of 27

We report on light induced deformation of photosensitive particles under irradiation with linearly polarized light. Theoretical and experimental investigations have been performed to estimate the magnitude of opto-mechanical stresses needed for deformation. The colloids were prepared using precipitation procedure which generates particles of different sizes starting from ca. 60nm up to few micrometres. The particles, adsorbed on a glass surface and exposed to light irradiation (λ=491nm, I=100mW/cm2), were stretched along the electrical field vector. The maximal deformation was measured to be up to 6 times, i.e. the particle of 1.6µm in diameter was elongated to an ellipsoid of the length ca. 10µm. Theoretical calculations of the photo-mechanical deformation related to the generation of internal opto-mechanical stress reveal, that the stress needed for such huge elongation is about 100 MPa. The theoretical approach is based on the orientation model, in which under irradiation the azobenzene molecules rotate and orient perpendicularly to the electrical field vector resulting in re-orientation of polymer backbones to which the azobenzenes are attached. In this way, the macroscopic deformation of a sample takes place due to strong mechanical coupling between the two components: active azobenzene molecules and a passive polymer matrix. Experimentally we measured stress which solid particles exert on a PDMS matrix during deformation. For this, the particles were immersed in a PDMS layer of known mechanical modulus. During irradiation with linearly polarized light and corresponding deformation of the particles, the PDMS material was compressed in the directions of elongation. The compression stress was estimated to be 37MPa which is in good agreement with theoretically predicted value.


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ACKNOWLEDGMENTS. This research is supported by the German Research Council (DFG) (GU 1510/3-1 and SA 1657/13-1). SL and SS thank Helmholtz Graduate School on Macromolecular Bioscience (Teltow, Germany) for financial support.



Page 24 of 27

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Light-Induced Deformation of Azobenzene-Containing Colloidal

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