Phase Winding of a Nematic Liquid Crystal by Dynamic Localized

Jul 14, 2014 - Department of Physics, Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, United States...
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Phase Winding of a Nematic Liquid Crystal by Dynamic Localized Reorientation of an Azo-Based Self-Assembled Monolayer Yue Shi,*,† Guanjiu Fang,† Matthew A. Glaser,† Joseph E. Maclennan,† Eva Korblova,‡ David M. Walba,‡ and Noel A. Clark† †

Department of Physics, Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, United States Department of Chemistry and Biochemistry, Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, United States

‡

ABSTRACT: Azobenzene-based molecules forming a selfassembled monolayer (SAM) tethered to a glass surface are highly photosensitive and readily reorient liquid crystals in contact with them when illuminated with polarized actinic light. We probe the coupling of such monolayers to nematic liquid crystal in a hybrid cell by studying the dynamics of liquid crystal reorientation in response to local orientational changes of the monolayer induced by a focused actinic laser with a rotating polarization. The steady increase in the azimuth of the mean molecular orientation of the SAM around the laser beam locally reorients the nematic, winding up an extended set of nested rings of splay-bend nematic director reorientation until the cumulative elastic torque exceeds that of the surface coupling within the beam, after which the nematic director starts to slip. Quantitative analyses of the ring dynamics allow measurements of the anchoring strength of the azo-SAM and its interaction with the nematic liquid crystal.

1. INTRODUCTION Liquid crystals show a facile response to applied fields and interfacial forces, a combination allowing the development of a variety of useful electro-optic devices such as displays. In this context, the control of liquid crystal (LC) alignment by surfaces is of key importance and has been studied extensively. The alignment of liquid crystals in devices is typically achieved by making the cell substrates anisotropic, for example by mechanical rubbing,1−3 oblique evaporation,4,5 or photoalignment.6,7 In particular, photoaligment mechanisms based on the trans−cis−trans photoisomerization cycle of azobenzene and its derivatives have been widely investigated, with the realignment of LCs over large areas achieved by azo doping of the surfaces7−10 or of the liquid crystal itself,11 generating a variety of applications, such as photoalignment, data storage, LC actuators, and photolithography.12−16 Here we investigate the dynamics of photoreorientation of a nematic liquid crystal in a surface-induced process controlled by changing the polarization direction of an actinic laser beam focused to a small spot on a high-sensitivity, azobenzene-based self-assembled monolayer (azo-SAM). The SAMs employed here are made using the derivatized methyl red azo dye dMR, shown in Figure 1, which covalently bonds to glass substrates by silane chemistry.9 In the resulting monolayers, the azobenzene group is tilted substantially from the surface normal and the alkane connection is sufficiently flexible to allow photoisomerization-induced anisotropy in the plane of the monolayer. When irradiated with ≲600 nm light, azobenzenes undergo photoisomerization,9 a reversible transformation between the trans and cis configurations.17 If the © 2014 American Chemical Society

actinic light is linearly polarized, the isomerization rate depends on the local azobenzene orientation, an angular dependence that results in the photoselection of a preferred orientation in which the long axis of the azobenzene dye is perpendicular to the incident polarization.17 Nematic LC in contact with such an azo-SAM shows planar alignment, with the nematic director n, the local average orientation of the LC molecular axes, parallel to the mean molecular long axis of the dMR.9 The dMR azoSAM system has record high photosensitivity for dynamic LC realignment, with a 90° photodriven reorientation of n achieved for a dose (intensity times time) as low as ≈6 mJ/cm2, corresponding to only ∼1.3 photons of 450 nm linearly polarized light absorbed per dMR molecule.9 Comparison of the orientational photoresponse of bare dMR azo-SAMs, made using high-precision birefringence measurements, with the induced reorientation of nematic LC in contact with the SAM, shows that the SAM−LC coupling is viscoelastic, with the LC response lagging when there are sudden changes in the direction of polarization of the incident light.18 Here we exploit the remarkable sensitivity of the dMR azo-SAM system to extend the study of SAM-induced photoreorientation to the spatiotemporal regime.

2. EXPERIMENTAL SECTION 2.1. Experimental Apparatus. These experiments employ cells with the room-temperature nematic LC E3119 in a gap with a thickness Received: May 22, 2014 Revised: July 12, 2014 Published: July 14, 2014 9560

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Figure 1. Schematic diagram of the experimental apparatus. (a) The actinic beam is a green laser (λ = 532 nm), focused by an objective lens to a small spot (a = 2.15 μm in radius) on the dMR-SAM. Polarization p is rotated using a polarizer mounted on a motor. Red light is used to visualize the nematic director field in the cell. (b) The nematic liquid crystal is sandwiched in the d = 2.53 μm gap between the dMR-SAM and the OTESAM, forming a cell with a hybrid alignment. (c) Chemical structure of dMR.

Figure 2. Concentric rings appear in the cell as the nematic director field is wound up in response to the azimuthal reorientation of the dMR-SAM by the actinic laser. (a) Schematic illustration showing the orientations of the actinic laser polarization p (angle ψ) and the LC director n (angle ϕ) with respect to the polarizer P and analyzer A used for visualizing the texture. The polarization of the actinic laser p (λ = 532 nm at 115.4 μW), indicated by a green arrow, is rotated clockwise at ω = 4.2 rad/s. The white arrows indicate the director orientation of the LC within the beam focus. (b) The actinic laser is shone on the cell, and (c) the polarization rotates, resulting in the generation of a pattern of concentric rings. A new dark ring appears whenever the polarization is rotated through an additional π/2 (second row). (d) Image sequence showing the generation of the second dark ring (top row). (e) Sketches of the corresponding LC director field for selected frames. d of 2.53 μm between two glass plates, one of which is coated by a dMR-SAM and the other by an octadecyl-triethoxysilane SAM (OTESAM). The OTE-SAM gives homeotropic orientation of the LC (n normal to the surface),20 while the dMR-SAM gives planar orientation (n parallel to the surface), stabilizing the so-called hybrid alignment characterized by splay-bend distortion of n in the plane containing n and z as indicated in Figure 1b. The local principal optic axis of the cell is along the intersection of the splay-bend plane with the glass, corresponding to the projection of n on the x−y surface. The SAM plates were prepared using the previously reported procedure,18 assembled into cells, and filled with the LC by capillarity at ∼80 °C, well in the isotropic phase. Upon cooling into the nematic phase, cells not yet exposed to actinic light exhibited a Schlieren texture, indicating

a random planar orientation of n on the SAM surface, with local but not global in-plane alignment. To study the local photoreorientation of the nematic, an actinic laser (λ = 532 nm) is focused to a small spot (4.3 μm in diameter) in a region of the LC cell with a nearly uniform director field. The actinic laser beam is initially circularly polarized using a quarter-wave plate and then passed through a linear polarizer whose orientation can be rotated at a controlled rate using a motor. The cell is illuminated with red-filtered white light (λ > 600 nm, which does not induce any additional isomerization) and observed using depolarized transmission optical microscopy, as sketched in Figure 1. This allows the visualization of the azimuthal distribution of the hybrid splay-bend plane of the nematic LC and thus of n at the SAM surface. To analyze 9561

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these reorientation dynamics, we note that the laser focal spot and the length scales of the ring patterns are large compared to the cell thickness. We therefore assume that the hybrid LC structure is locally maintained throughout the experiment and that we may describe the local LC orientation using the single azimuthal variable ϕ(r, t). 2.2. Phase Winding of the Nematic Liquid Crystal. A typical reorientation sequence is shown in Figure 2, induced by a 115.4 μW actinic beam incident on the dMR-SAM (green spot). The LC texture is viewed between crossed polarizer P and analyzer A (Figure 2a), with ψ giving the orientation of the actinic polarization (measured from P) and ϕ giving the induced director orientation at the focal spot (measured from A), which we take to be at r = 0. The initial director orientation on the as-synthesized dMR-SAM is quite uniform (Figure 2b), with n nearly parallel to A, at an angle ϕ ≈ −π/10. The laser is switched on and p rotated from ψ = 0 to ψ = π/4, giving the bright red region surrounding the green spot in Figure 2c with an intensity corresponding to the maximal probe observed light transmission T(ϕ), implying, because T(ϕ) ∝ sin2 2ϕ, an orientation of n at the origin of ϕ(r=0, t) = π/4. The bright region is bounded by a dark ring with ϕ(r) = 0. Continuous rotation of the actinic polarization then commences, with ϕ(r=0) increasing at a constant rate (in this case, with an angular frequency ω of 4.2 rad/s). Figure 2d shows the evolution of the LC orientation as the polarization is rotated from π/2 to 3π/4, during which n(r=0) also reorients through π/2. The first dark ring expands to R1 ≈ 18 μm, and a second dark ring is generated when ψ = π/2 with ϕ(r=0) = π/2, expanding in radius to R2 ≈ 14 μm. The continuous reorientation near the beam center thus generates a radial pattern of reorientation in the form of concentric, approximately ring-shaped dark bands. Four dark bands appear for each complete rotation of the polarization, with the jth dark band first appearing at r = 0 at time tj = j(T/4), where T = 2π/ω. The generation and expansion of successive dark rings, corresponding to director orientations ϕj(r, t) = (j − 1)π/2, is shown in Figure 2c. The radius of the jth dark band rj(t), measured from the origin along the radial yellow line indicated in Figure 2, is plotted in Figure 3. The first dark band (j = 1) appears at r = 0 for ψ = 0 (red open circle in Figure 3) and then expands monotonically in radius with an increasing ψ (red filled circles), out to R1 ≈ 18 μm, after which this ring expands more slowly, with oscillations in the radius. The j = 2 ring appears when ψ = π/2 and expands in a similar fashion but to a smaller saturation radius, with an oscillation in radius that is 180° out of phase with that of the j = 1 ring. The appearance and growth of the next four rings are similar, with successive rings being saturated at smaller radii, and each oscillating out of phase with its neighbors. For j < 6, the rings expand smoothly from the origin. The j = 6 ring, on the other hand, emerges and expands from the origin at ψ = 5π/2 but, when the radius reaches r = 5.43 μm, crosses the orientation of maximal torque relative to ψ and therefore slips, shrinking back to r = 0. The ring reappears half a cycle later, after which the saturation radius has increased such that the j = 6 ring can follow the behavior of the earlier rings and continue to grow without slipping. The j = 7 ring appears and slips for eight cycles before expanding, preventing the growth of the j = 8 ring. The j = 8 ring appears transiently during this time but can form only once the j = 7 ring has stopped slipping. Once it appears, the j = 8 ring continues to slip and is the last ring that light of this intensity can generate.

Figure 3. Ring radius r vs polarization azimuth of the actinic beam ψ during the ring winding experiment shown in Figure 2. The plot shows the formation and subsequent expansion of seven different dark rings (○, ring nucleation; ●, ring radius vs time). The eighth ring appears only sporadically, indicating that the torque from the azo-SAM driven by the actinic laser is not sufficient to sustain this ring. The solid magenta curves are given by the first 10 terms of the driven diffusion model curves (eq 3). The out-of-phase oscillations of the rings are evidence of SAM reorientation by off-center actinic light. The expansion of the ring pattern is limited by orientational pinning of the LC on the SAM where the dose of the light is too weak to cause reorientation. The final spacing of the rings is the equilibrium ring pattern structure (red curve in Figure 4), with squares showing the equilibrium Frank elastic ring radii.

constant in the one elastic constant approximation, and γ is the orientational viscosity. We first consider the orientation in a hollow cylinder (a < r < Rj), where the inner boundary is fixed at ϕa at r = a and the outer boundary is kept at ϕ = 0 at r = Rj, where each ring stops growing (Figure 3). With a uniform initial LC director orientation of ϕ(r,0) = 0 in the cylinder, the orientation evolves as21 ϕo(r , t ) = ϕa ∞

2

∑ e−Dαn t

ln(r /R j) ln(a /R j)

J0 2 (αnR j)[J0 (αnr )Y0(αna) − Y0(αnr )J0 (αna)] J0 2 (αna) − J0 2 (αnR j)

n=1

3. RESULTS AND DISCUSSION 3.1. Driven Diffusion Model. We begin the analysis of the ring pattern by assuming that ring growth is driven principally by photoinduced reorientation (photobuffing) of the SAM at the focus of the laser, presenting the boundary condition ϕ(a, t) = ψ(t) = ωt in the absence of slipping, and slippery anchoring off center. The radial variation of the orientation as a function of time outside this central region (r > a) is then given by the orientational diffusion equation D∇2ϕ(r,t) − ∂ϕ/∂t = 0 in cylindrical coordinates, where D = K/γ is the reorientational diffusion constant of the liquid crystal, K is the Frank elastic

+ ϕπ × a

(1)

where αn are the positive roots of J0(αna)Y0(αnRj) − Y0(αna) J0(αnRj) = 0. Now we allow the orientation at the inner boundary to increase linearly in time, as ϕa = ψ(a,t) = ωt. The response of the director field at radius r is found by integrating eq 1 in time, yielding the case in which the phase is winding up in the middle ϕ(r , t ) = ω

∫0

t

ϕo(r , t − s) ds

(2)

giving the driven diffusion model 9562

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ln(r /R j) ln(a /R j)

∞

t + ωπ ∑ n=1

2

1 − e−Dαn t × Dαn 2

⎡ J 2 (α R )[J (α r )Y (α a) − Y (α r )J (α a)] ⎤ 0 n 0 n ⎥ ⎢ 0 n j 0 n 0 n ⎥⎦ ⎢⎣ J0 2 (αna) − J0 2 (αnR j)

Γe = K

ln(r /R outer) ln(R inner /R outer)

∂r

S=K

∂ϕs(r ) ∂r

2πr

πdK Δϕ d = 2 ln(R inner /R outer)

(5)

The surface anchoring torque of the SAM is given by (3)

Γs =

The appearance of regions with constant ϕ [ϕj = (j − 1)π/ 2], corresponding to rings in the director field, may be computed using the orientational diffusion constant of the liquid crystal E31 of D ≈ 3 × 10−11 m2/s.22,23 This model which is dominated by the lowest-order terms, predicts ring formation that is slower than that observed in the experiments (magenta curves in Figure 3). The reason for this will be discussed in detail in section 3.5. 3.2. Static Ring Pattern. The asymptotic dependence of ϕ(r, t) at large values of t is described well by the static orientation field ϕs(r) of a nematic confined between two concentric cylinders. This can also be calculated by minimizing the free energy density,24 to obtain ∇2ϕs(r) = 0, which in turn yields ϕs(r ) = ϕouter + Δϕs

∂ϕs(r )

∫ ∂W∂ϕ(ϕ) dS = ∫0

a

1 Wϕ sin2[ϕ(r ) − ψ ] 2πr dr 2 (6)

where Wϕ is the surface anchoring coefficient. The surface anchoring strength at the focus of the beam can be calculated by equating the elastic and anchoring torques Γe = Γs, giving an estimate of the average surface anchoring between the dMR-SAM and E31,22 within the focus under an illumination dose of 591.8 J/cm2 per π rotation of the actinic laser Wϕ = 4.2 × 10−4 J/m2. For comparison, the anchoring energy of a weakly illuminated dMR-SAM (∼10 mJ/cm2 dose illumination 450 nm with fixed polarization) was found previously from measurements on uniformly twisted cells of 5CB to be on the order of 10−6 J/m2.9 The experiments were repeated with varying laser intensity, at a fixed rotation frequency (ω = 4.2 rad/s). The calculated surface anchoring coefficient shows a logarithmic dependence on illumination dose, as shown in Figure 5. Birefringence measurements on

(4)

where Δϕs = ϕinner − ϕouter. Figure 4 shows a fit of ϕs(r) to the experimental saturation radii, showing that this model describes the overall final structure of the concentric ring pattern well.

Figure 5. Surface anchoring strength Wϕ at the laser focus vs illumination dose JD. The polarization rotation frequency is kept at ω = 4.2 rad/s for different actinic laser powers. The surface anchoring strength depends logarithmically on the illumination dose, with a leastsquares fit giving Wϕ = 9.1 × 10−5 × log JD − 8.3 × 10−5 (red line).

Figure 4. Static state azimuth ϕs as a function of r for the final ring pattern. Each data point represents the average radius in the final steady state (around ψ = 14π in Figure 3), with the oscillation amplitude represented as an error bar. The red line is a fit to the final state based on eq 4, with the director azimuth ϕouter = 0 at Router = R1, and ϕinner = ϕs(a) fitted to be 4.38π at Rinner = a.

bare dMR-SAMs show that above the saturation illumination dose, the order parameter of the monolayer also depends logarithmically on the actinic laser dose.25 Therefore, we propose that the surface anchoring coefficient Wϕ depends linearly on the surface order parameter. The surface anchoring strength is controlled by the beam dose.18 We checked the effects of polarization rotation speed on the ring patterns. Slower rotation with the same laser intensity allows the writing of a larger and tighter ring pattern, i.e., the generation of more rings before slipping begins, and results in stronger anchoring strength at the focus of the beam as expected. In the limit that the polarization direction of the incident beam is fixed during irradiation, the diameter of a ring will increase to some large but finite value and stop, the expansion of the ring pattern being limited by an orientational pinning effect (long-term collective interaction) of the LC on the SAM which will be discussed later.

3.3. Torque and Surface Anchoring. As more and more rings are generated near the middle, the torque from the elastic distortions increases until it becomes comparable to the torque that can be sustained by the surface anchoring provided by the SAM at the center. The maximal number of rings is achieved when the newest ring in the center slips (for example, the j = 8 ring in Figure 3). Assuming the director reorientation distribution along z is linear, the hybrid LC cell with cell gap d can be treated approximately as a uniform cell with gap d/2. The elastic torque due to the radial distortion of the LC director field can be expressed as 9563

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3.4. Oscillating Rings and the Effect of Off-Center Light. In the picture presented so far, the assumption that the actinic light is confined to the focal spot on the dMR-SAM is convenient and leads to a reasonable description of the overall behavior presented above. However, this simplification ignores the fact that there is off-center light. The laser has a Gaussian profile convoluted with the diffraction due to the objective aperture, which truncates the incident actinic laser before focusing it onto the sample, resulting in photo-induced reorientation effects away from the beam center. The SAM reorientation at larger radii contributes to the finite ring growth. Once the polarization is rotated to π/2, the first ring, which has an orientation of ϕ = 0, is not favored and stops growing. When the polarization is rotated beyond π/2, for example, π/2 + δ, the LC molecules in the first ring experience a negative torque and the ring shrinks instead of growing further. However, the intensity away from the central spot is not high enough to overcome the continual reorientation near the beam center, so that the ring does not disappear. The fluence is sufficient, however, to reorient the azo-SAM locally enough to perturb the ring structure, causing oscillation of the ring radii. When the optical polarization favors the orientation halfway between two adjacent rings, say j and j + 1, the distance between these two rings increases. At the same time, the orientation in the gap between neighboring pairs, (j − 1)/j, and (j + 1)/(j + 2), is not preferred and the distance between these pairs decreases. In other words, alternating gaps expand and shrink. The surface anchoring in the vicinity of the jth ring can be estimated on the basis of the amplitude of the undulations as follows. The director orientation in the region containing the jth ring varies approximately as ϕ A = ϕs(a) j

⎛ r − Rj ⎞ ln(r /R1) ⎟ + Aj cos⎜⎜π ln(a /R1) Lj ⎟⎠ ⎝

∂F ∂F ∂F = e + w =0 ∂Aj ∂Aj ∂Aj

Analysis of the oscillation amplitude of the rings shown in Figure 3 yields W2 = 3.5 × 10−6 J/m2 at R2 = 15.71 μm, W3 = 4.9 × 10−6 J/m2 at R3 = 12.22 μm, W4 = 1.12 × 10−5 J/m2 at R4 = 10.28 μm, W5 = 1.8 × 10−5 J/m2 at R5 = 7.57 μm, W6 = 3.7 × 10−5 J/m2 at R6 = 6.79 μm, and W7 = 1.0 × 10−4 J/m2 at R7 = 3.30 μm. These estimates confirm that the azimuthal anchoring strength of the photobuffed azo-SAM becomes weaker further from the beam center. 3.5. Ring Expansion Dynamics and the Effect of OffCenter Light. On the basis of the idea that the ring patterns are driven by the local torque at the origin and pinned at their outer radii, we may use the driven diffusion model (eq 3) to calculate the radial dependence of the director reorientation at a series of times [tj = j(T/4)] in the expanding ring pattern, where ϕ(r, t) is fixed at ϕ(R1, t) = 0 at the outer boundary but increases linearly over time at r = a. The results are the magenta curves shown in Figure 6. These curves become asymptotic to

(7)

where ϕs(a) ln(r/R1)/ln(a/R1) is the static orientation within this region given by eq 4, ϕj is the orientation of the director field in the jth ring, Lj is the distance between the ϕj − π/4 and ϕj + π/4 contours, and Aj is the oscillation amplitude. The elastic free energy density is ⎛ ⎞2 K ⎜ ∂ϕ Aj ⎟ fe = ⎜ 2 ⎝ ∂r ⎟⎠

Figure 6. LC azimuth distribution vs radius at different times during ring winding. The experimental data are shown as dots. For example, the green dots show the orientation at t2 when ψ = π/2 and the second ring starts to appear; the purple dots show the director azimuth at t3 when ψ = π and the third ring starts to appear. The solid magenta lines are calculations of ϕ(r,tj) vs r based on eq 3. The black solid curve is a fit of the steady state using eq 4 at the time when ψ = 3π. The vertical dashed lines indicate the average radii of the observed rings at early times. The inset shows the static state solution ϕs as a function of r for the ring pattern. Data points and the red curve are the same as in Figure 4 for the final steady state (around ψ = 14π). The black curve is the same fit as in the main figure at the time when ψ = 3π.

(8)

and thus the total elastic free energy of this annulus is Fe =

d 2

R j + Lj/2

∫R −L /2 j

fe 2πr dr

j

(9)

the static ring pattern ϕs(r) (eq 4, black curve in Figure 6) as time increases. At the beam edge (r = a), the orientation ϕ(a) is pinned to ψ(a, t) = ωt by the light, with the increase in ϕ at larger radii driven by its positive curvature (ϕrr > 0). However, the experimental azimuthal profiles at selected times (symbols in Figure 6), derived from the red light intensity variation of the corresponding ring patterns (Figure 2), show a very different picture in which ϕ(r) increases homogeneously over almost the entire area inside the ring pattern (area S) with ϕrr < 0. ϕ(r) is nearly independent of r near the center, with ϕ(r) ≈ ψ(a) for r > a out to the radius where the rings form, with an asymptotic static shape comparable to ϕs(r). The data indicate that polarized laser light outside the main beam reorients the dMR-

The surface anchoring energy density is given by ⎛ (2j − 1)π ⎞ sin 2⎜ϕ A − fw = ⎟ ⎝ j ⎠ 2 4 Wj

(10)

and the total surface anchoring energy in this annulus is Fw =

R j + Lj /2

∫R −L /2 j

j

fw 2πr dr

(12)

(11)

This integral can be evaluated from Rj − Lj/2 to Rj and then from Rj to Rj + Lj/2 using the small-angle approximation. The total energy F = Fe + Fw may be minimized with respect to the oscillation amplitude Aj as 9564

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SAM out to a radius of ∼20 μm. The optically induced surface torque is being applied not only at r ≤ a but over a much larger region surrounding the central spot, winding up rings at the outer edge of the uniform region and giving the rapid ring growth evident in Figure 3. As more rings wind up, S decreases and eventually no new rings can be created, the off-center lightinduced anchoring then causing only local oscillations of the rings, as discussed in section 3.4. Concentric ring patterns have previously been observed and studied in freely-suspended smectic-C LC films, where they can be created mechanically using a rotating rod inserted through the middle of the film,26 or by an in-plane, rotating electric field.27 In the former case, the torque is applied only at the center of the film and the rings are wound up with dynamics that are probably described well by the driven diffusion model. In the latter case, the electric torque is applied to the whole film, with the director pinned at the outer boundary, resulting in the formation of rings at the outer boundary with a relatively uniform orientation in the center. Our photobuffed hybrid azoSAM cell shows dynamics that are like a combination of these two scenarios but more complicated, with strong anchoring at the center, surrounded by a region with weaker and radially decreasing anchoring at larger radii. 3.6. Long-Term Collective Interaction. The concentric ring patterns can be maintained by keeping the actinic laser turned on with a fixed polarization direction after the patterns are formed or can be unwound by reversing the direction of rotation of the polarization. If instead the laser is turned off, most of the ring pattern remains unchanged but the very innermost rings, which were slipping during the winding process, may disappear. The remaining rings do not disappear even after many weeks at room temperature, in strong contrast with the behavior of bare dMR-SAMs, for which the azimuthal orientation of the molecules is randomized by thermal diffusion within just a few minutes or hours after the actinic laser is turned off.18 This is also in contrast with the film experiments, in which the rings relax rapidly after the driving torques are removed.26,27 The orientational stability of the azo-SAM in contact with LC has been reported previously9,18 and is ascribed to the long-term collective interaction between the orientationally ordered SAM and the director field of the LC, which prevents the SAM molecules from relaxing because of the local ordering of the LC molecules. In addition to forming concentric ring patterns, when adjacent rings are close enough together they may break during the winding process, leading to the formation of a disclination pair (s = ±1), an effect previously observed in freely-suspended films.26 Such defects usually are annihilated if the actinic laser is left on, even if the polarization direction is fixed, by traveling in opposite directions around the pattern center. Thus, the surface energy well created by the actinic light does serve to fluidize the surface, allowing defect mobility.25 If the laser is turned off, the disclination pair is frozen in space and is not annihilated, similar to the stable ring pattern in the absence of actinic light. This long-term collective interaction also contributes to the finite ring growth as mentioned in previous sections. The director field in the area outside the ring pattern is pinned by the pre-existing alignment of the nematic LC where there is not enough light, limiting the ring growth and preventing its expansion into the rest of the cell. 3.7. Additional Observations and Discussion. At small doses, the birefringence of the dMR-SAM increases almost

linearly with dose, up to doses of 20 mJ/cm2,25 at which the dMR-SAM birefringence is on the order of 30% of the saturation value. The doses in our experiments were much larger and in the saturation region (Figure 5). This means that an increase in the beam area at a constant total laser power in the saturation region would wind larger and tighter ring patterns, because more area contributes to the torque. We also tested the response of the cell of E31 sandwiched between dMR-SAM and rubbed nylon, a surface which favors planar anchoring. The cell appeared homogeneous before being exposed to the actinic light. When exposed to actinic light with rotating polarization, the LC only reorients by a small amount before flipping back and no ring patterns are formed in this cell.

4. CONCLUSIONS In conclusion, we have described the photoreorientation dynamics of nematic LCs coupled to an azo-SAM monolayer. Rotating the polarization of a focused beam of actinic light gives a pattern of concentric rings in the cell. The number of rings grows until the elastic restoring torque due to the accumulated radial distortion of the nematic director field exceeds the anchoring strength of the photobuffed azo-SAM. The spatiotemporal evolution of the director field at early times can be modeled by a driven diffusion model. The off-center actinic light causes out-of-phase oscillations in the rings, while the central part of the beam produces an almost uniform LC orientation distribution. The observed long-term stability of the induced patterns in the absence of actinic light at room temperature is attributed to the same collective interaction between the LC and the azo-SAM molecules that limits the spatial extent of the ring patterns.

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AUTHOR INFORMATION

Corresponding Author

*Department of Physics, University of Colorado, 2000 Colorado Ave., Boulder, CO 80309-0390. E-mail: yue.shi@ colorado.edu. Funding Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Youngwoo Yi for valuable advice on making SAMs and Arthur Klittnick for his technical help. This research was supported by National Science Foundation MRSEC Grant DMR-0820579.

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REFERENCES

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dx.doi.org/10.1021/la501983u | Langmuir 2014, 30, 9560−9566