Mechanochromic Detection for Soft Opto-Magnetic Actuators

New multi-stimuli responsive materials are required in smart systems applications to overcome current limitations in remote actuation and to achieve versatile operation in inaccessible environments. The incorporation of detection mechanisms to quantify in real time the response to external stimuli is crucial for the development of automated systems. Here, we present the first wireless opto-magnetic actuator with mechanochromic response. The device, based on a nanostructured-iron (Fe) layer transferred onto suspended elastomer structures with a periodically corrugated backside, can be actuated both optically (in a broadband spectral range) and magnetically. The combined opto-magnetic stimulus can accurately modulate the mechanical response (strength and direction) of the device. The structural coloration generated at the corrugated back surface enables to easily map and quantify, in 2D, the mechanical deflections by analyzing in real time the hue changes of images taken using a conventional RGB smartphone camera, with a precision of 0.05°. We demonstrate the independent and synergetic optical and magnetic actuation and detection with a detection limit of 1.8 mW·cm–2 and 0.34 mT, respectively. The simple operation, versatility, and cost-effectiveness of the wireless multiactuated device with highly sensitive mechanochromic mapping paves the way to a new generation of wirelessly controlled smart systems.


Equation of the radius of curvature for bimorph cantilevers.
When bimorph cantilevers are heated, the difference in the thermal expansion coefficients () generate a differential stress, inducing a cantilever deflection. For a bi-material system, the temperature induced bending can be estimated using its radius of curvature, r, which depends on the stress from the temperature change (ΔT) and the residual stress that may be present in the material layers. It can be estimated by: 2 + ( 2 2 2 ) 2 + 2 1 2 1 2 (2 1 2 + 3 1 2 + 2 2 2 )] [6 1 2 1 2 ( 1 + 2 )( 1 -2 )∆ ] (1) where t i (I = 1 and 2) is the layer thickness of each layer (1 = PDMS and 2 = nanostructured-Fe), and E i is the Young's modulus of the ith layer. As the thickness of the nanostructured-Fe layer is much smaller than that of PDMS, t 1 ≫t 2 , equation (1) can be simplified to = 1 1 2 Thus, r decreases as t 1 and E 1 decrease. Furthermore, r decreases as the difference in the thermal expansion coefficients and temperature change (ΔT) increase.

Equations for the magnetic actuation.
A magnetic material of volume V experiences a magnetic torque under an external magnetic field due to the misalignment of the magnetization of the material ( in respect to the applied ) magnetic field ( , which tends to the alignment of both vectors. It can be expressed as: )

= ×
The magnetic torque ( is orthogonal to both vectors, and it is maximized when and ) are perpendicular to each other.
In addition, in the presence of a magnetic field gradient, magnetic materials experience a force that pulls the material upward the magnetic field gradient, which is proportional to the magnetization and the magnetic field strength: In this case, the force is maximized when the magnetic moment is parallel to the external magnetic field.
= 0 ∇( · ) Figure S1. A) Open source software for color analysis in regions of interest (ROI) of a video source. B) Relation between the wavelength and associated the Hue value.  (1) and for a 235.4 mW/cm 2 illumination using the 1470 nm laser. B) Correlation between the light generated temperature changes and the induced color changes produced by the curvature variation. On the right, the thermal pictures in the absence of illumination and with 82.2 mW/cm 2 light intensity are shown. C) Dynamic thermal change generated by a 808 nm pulsed laser (frequency 0.1 Hz, intensity 70.3 mW/cm 2 ) acquired with a Thermal FLIR camera from a region of interest located at the tip of the cantilever.

Explanation of the magnetic actuation for different directions and orientation of the magnetic field with respect to the cantilever:
"For example, for the case where the magnet moves along the cantilever (Fig. 4C):

M H
In this case H and M are parallel to each other, thus the cross-product results in HM = 0. Consequently, in this case we expect no torque. Moreover, the field gradient is in the same direction as M and since the cantilever is clamped on one side, no bending of the cantilever should take place. Hence, in first approximation, the response of the cantilever to the magnetic field should be negligible, as observed experimentally (Fig. 4C). Note that the weak response observed experimentally is probably due to the fact that the cantilevers are slightly bent in the as made state. (ii)

M H
In this case M and H are perpendicular to each other. Consequently, the cross-product MH is maximized, which leads to a strong response of the cantilever to the applied field, as observed experimentally. Namely, as the magnet gets closer, the cantilever feels a stronger magnetic field, consequently the torque will be larger. Moreover, in this case since M and H are at 90º, no effect of the field gradient is expected (since it is proportional to the dot product between M and H, MH = 0). However, since the cantilever bends with increasing applied fields as a result of the torque, some effect of the field gradient is also expected, which should further strengthen the response of the cantilever. Figure S6. Plot of the long-term optical actuation with the 808 nm laser during 10000 cycles with an actuation frequency of 0.1 Hz and an intensity of 204 mW/cm 2 .