Direct Quantification of Rapid and Efficient Single-Stroke Actuation by

Feb 11, 2019 - New York University Abu Dhabi , P.O. Box 129188, Abu Dhabi , United Arab Emirates. ‡ Radcliffe Institute for Advanced Study, Harvard ...
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Direct Quantification of Rapid and Efficient Single-Stroke Actuation by a Martensitic Transition in a Thermosalient Crystal Abdullah Khalil, Durga Prasad Karothu, and Pance Naumov J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 11 Feb 2019 Downloaded from http://pubs.acs.org on February 11, 2019

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Journal of the American Chemical Society

Abdullah Khalil†, Durga Prasad Karothu†, and Panče Naumov*,‡ †

New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, United Arab Emirates Radcliffe Institute for Advanced Study, Harvard University, 10 Garden St, Cambridge, MA 02138, United States

‡

Supporting Information Placeholder ABSTRACT: Molecular dynamic crystals conveniently combine flexibility required for mechanical reconfiguration, strength for effective translation of elastic energy, and long-range order of mechanically coupled molecules for rapid conversion of disordered motion (heat) or photons (light) into ordered motion (work). By direct measurement of the actuation force generated by crystals of a thermosalient solid, here we describe the first direct quantification of the work and energy conversion that can be accomplished by using dynamic crystals as supramolecular actuators. Upon reversible α-to-γ phase transition, crystals of (phenylazophenyl)palladium hexafluoroacetylacetonate of sub-millimeter to millimeter size exert forces in the range of 1‒100 mN upon longitudinal and lateral expansion, respectively. This work translates to a volumetric power density of about 2 MW m‒3 and efficiency comparable to the existing multicomponent actuators. The ever-increasing interest in miniaturized mechanical devices1–3 requires novel materials for actuators4‒11 with micrometer to millimeter size. The currently used actuators include piezoelectric,4 magnetostrictive5 and electromagnetic6 materials. Dynamic crystals12,13 are prospective actuating materials that are capable of amplifying molecular reconfiguration to macroscopic motion. The collective action of molecules coupled with long-range order in these materials can translate minute geometrical changes— common for molecular machines in solution14,15—into readily observable macroscopic motion of crystals that are effective supramolecular machines with three-dimensional order and structural anisotropy.16‒18 Herein, we report direct measurement of the force which a thermosalient (“jumping”) crystal19‒32 can exert when activated by heat, and for the first time we rigorously quantify the work it can perform. The expansion forces of the thermosalient material (phenylazophenyl)palladium hexafluoroacetylacetonate (PHA)19,27 were determined using cantilever-type force sensor. The results provide basis for direct benchmarking of thermosalient materials against other thermal expansion actuators. PHA was synthesized following a literature method19 and recrystallized as two habits (Figure 1) of identical, α phase structure (Table S1, SI).19,25 The average aspect ratio, length (l) / thickness (h), for type 1 and type 2 crystals were 2.67 and 5.45, respectively. Under polarized light, type 1 crystals showed distinct birefringence and were single crystals (Figure 1b, panels b1 and b2),33,34 while type 2 crystals had multiple crystalline domains (Figure 1b, panels b3 and b4).

Figure 1. Crystal habits and structure of form α PHA crystals. (a) Lateral (a1, a3) and cross-sectional (a2, a4) views of type 1 (a1, a2) and type 2 (a3, a4) crystals. Labels l, w and h correspond to the length, width and thickness, respectively. (b) Transmission polarized optical microscopic images of type 1 (b1, b2) and type 2 (b3, b4) crystals. The crystal contour is marked with dashed lines. ‘P’ and ‘A’ stand for the directions of the polarizer and the analyzer, respectively. (c1) Representative morphology with face indexing of type 1 crystals. (c2) Molecular structure of PHA. (c3) Unit cell expansion directions for type 1 crystals. Scale bars: a1, a2, b1, b2 = 0.1 mm; a3, a4, b3, b4 = 1 mm.

Above room temperature, PHA undergoes two phase transitions, α→γ, around 69.5‒81.3 °C, and γ→β, at 95.4 °C. 25 While the transition α→γ is thermosalient, martensitic and reversible, the transition γ→β is neither thermosalient nor reversible. Upon heating over the α→γ transition at 75 °C the crystals of both habits suddenly expand along their longitudinal direction (l). The crystals also expand slightly in the lateral direction (h), but do not expand noticeably in width (w). Heating over the second transition, γ→β (~95 °C) however, does not result in observable changes in crystal size, however the orange crystals become permanently dark red (Movies S1 and S2, SI). For the purpose of this study, the crystals were heated up to ~75‒80 °C, and thus above α→γ but below the γ→β transition, and the expansion force was meas-

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ured along the longitudinal and lateral directions. The longitudinal and lateral expansion of type 1 crystals (Figure 1, panel c1) occurs along their respective [100] and [011] crystallographic directions. The force that heated crystals of PHA generate upon expansion was measured in direct contact mode by using a cantilever-type microforce sensor that can record forces of up to 120 mN with a resolution of 1 µN (Figure 2a and Movies S3 and S4, SI).35 The deflection was converted to force by using standard equations (Eqs 4 and 5, SI).

Figure 2. Measurement of force exerted by PHA crystals undergoing a thermosalient phase transition. (a) Schematic representation of the sensor position with respect to crystal used to measure the longitudinal (a1) and lateral (a2) expansion force. The arrows denote direction of expansion against a solid surface. (b,c) Representative force-time curves for type 1 (b) and type 2 (c) crystals in the longitudinal (green) and lateral (red) directions. The insets show images of the crystal in contact with the sensor before (25 °C) and after (80 °C) the transition. The actual size of the images in the insets in panels b and c is 2  2 mm and 10  10 mm, respectively. (d) Force recorded in longitudinal direction during thermal cycling of type 1 and type 2 crystals. The crystals initially undergo thermal expansion with gradual increase of force, followed by a sharp increase in the force at the transition point (Figure 2b and 2c). Based on measurements on four type 1 crystals, the force in the longitudinal direction was found to be 6.5 ± 1.5 mN, nearly three times the force in the lateral direction (1.8 ± 0.4 mN). For three type 2 crystals, this ratio is nearly five-fold (80 ± 6 mN and 17 ± 2.5 mN, respectively). This difference is consistent with the higher aspect ratio of type 2 crystals, which brings about stronger longitudinal force. The expansion forces of PHA crystals with submillimeter dimensions were typically on the order of 1‒10 mN, whereas longer crystals of several millimeters exerted forces as high as 80 mN despite that they are polycrystalline. When type 2 crystals of PHA undergo the thermosalient transition α→γ they tend to delaminate along their longest direction (Movie S3, SI).25 Although the transition is reversible, some of the separated fragments slide out, and this results in weaker force in the following cycles. Representative longitudinal force curves of thermally cycled crystals are shown in Figure 2d (Movies S5 and S6, SI). Whereas crystals of type 1 exhibit appreciable cyclability and maintain peak force of about 5 mN after the third cycle, the force of type 2 crystals drops to nearly half the initial value

after the third cycle due to fracturing. One of the reasons for the different robustness is the different distribution of residual stresses inside the crystal whose profile across the crystal cross-section depends on the aspect ratio.12 A secondary reason is the high concentration of defects in type 2 crystals; being effective concentrators of the elastic energy, crystal defects serve as nuclei for evolution of cracks and promote disintegration.12 The smaller size and single crystal nature of type 1 crystals facilitate retention of their integrity even after repeated cycling. This result indicates that although stronger forces can be extracted from bigger crystals, smaller crystals are favored for prolonged operation.

Figure 3. Variation of the force exerted by PHA crystals with crystal size and mass. The maximum expansion force for type 1 (panels a1 and a2) and type 2 (panels b1 and b2) crystals plotted as a function of l, h and m in the longitudinal (green) and lateral (red) directions. R represents the respective linear correlation coefficients. To correlate the expansion forces to the mass (m) and size (l, h) of crystals, the force exerted by 12 crystals of each habit was recorded from samples of varying mass and dimensions. The maximum force in longitudinal and lateral directions for type 1 crystals (Figure 3a1 and a2) increases with size as a consequence of the increasing strain. The maximum expansion force for the same sample set plotted versus the mass shows improved linear correlation. Similar trend was observed for type 2 crystals where the expansion force increases almost linearly with crystal size (Figure 3b1 and b2). Although the crystals exhibit major expansion in preferred crystallographic directions, the overall expansion is a consequence of the net cooperative molecular motion in three dimensions.36 For both crystal habits and especially type 1, the strongest force is exerted in the longitudinal direction ([100]), and it is significantly stronger than that in the lateral direction ([011]) (Figure 1, panel c3). This is in line with the preferred expansion of PHA crystals during the phase transition along the crystallographic axis a. Notably, the coefficient of positive thermal expansion before the phase transition is also an order of magnitude higher relative to axes b and c.25 In the latter case, the expansion is suppressed due to the net expansion and contraction along axes b and c, respectively, along with the negative coefficient of expansion along c.25 The quantification of the expansion force provides an opportunity to explore the potential of molecular martensitic materials as thermal expansion actuators. The performance of actuators is

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Journal of the American Chemical Society usually expressed as generated power per volume (volumetric power density, VPD), and the maximum obtainable strain.37 The maximum strain is d/x, where d is the cantilever deflection upon crystal expansion and x is equal to l or h for longitudinal or lateral expansion, respectively. The VPD can be obtained as VPD = (Fd) / (tV), where F is the maximum expansion force, t is the time required for the phase transition and V is the crystal volume. The values of d and F can be obtained directly by force measurement, l and h are measured under optical microscope, and the value of V is calculated by dividing the crystal mass with its density (1.896 g cm‒3). The value of t was determined as t = l / u, where u is the speed of propagation of the habit plane along the length l. For PHA crystals, the value of u has been previously determined (0.54 m s‒1) by approximating the progression of the habit plane with linear front and averaging over three crystals.25 Using the above relations, the VPD of PHA crystals were found to be in the range of 1.3‒2.7 MW m‒3, corresponding to strain values of 0.3‒1.6  10‒2. These values are co-plotted in Figure 4 along with the respective values for other actuators. It is noteworthy that the VPD of the PHA crystals exceeds the values for some common materials such as moving coil and some shape memory actuators with comparable strain values. In comparison with the thermal expansion (100 K) actuators, the strains that can be reached with PHA crystals are an order of magnitude higher without a significant toll on the VPD. Also, based on the temperature difference between forms α and γ (50 K), the PHA crystals can be classified as ‘thermal expansion (50 K)’ actuators. Therefore, much higher strain values with similar VPD can be obtained from PHA crystals with only 50 K temperature rise relative to the existing thermal expansion actuators, which require a temperature rise of 100 K. Moreover, as discussed in the previous section, the PHA crystals can be cycled several times simply by heating and cooling and without the requirement of a mechanically coupled system to reset their original state—an important limitation with the currently used shape memory and solenoid-based actuators.38 Importantly, the PHA crystals also provide an added benefit of being lightweight actuators since their density (1.896 g cm‒3) is significantly lower than that of the conventional shape memory and bimetal-based thermal expansion (100 K) actuators (4‒8 g cm‒3).39 The impressive ability of PHA crystals to generate high strains with high VPD is also linked to their much lower elastic modulus, 3.27 GPa (SI). This value is in agreement with the elastic moduli of similar organic crystals.40 In contrast, the moduli of conventional thermal expansion actuators are 70‒300 GPa,38 resulting in significantly lower strains upon actuation. The volumetric work density (VWD) of PHA crystals given by the relation (Fd) / V was found to be 2‒15 mJ cm‒3 which is comparable to spin-crossover (SCO) complexes with VWD of ~15 mJ cm‒3.41 However, for layered metallic or polymeric composites based on SCO complex, the reported VWD values are as high as 150‒600 mJ cm‒3,42,43 indicating that hybrid actuators based on thermosalient crystals could increase their VWD and VPD several orders of magnitude. The efficiency of PHA crystals as thermal expansion actuators can be calculated using the relation (Fd) / (cmΔT), where c is the specific heat capacity of PHA crystals, 3.14 J g‒1 K‒1 (SI) and ΔT is the temperature change required for phase transformation (50 K). The calculated efficiency is in the range of 10 ‒6‒10‒4%, an order of magnitude lower compared to conventional thermal actuators (~10‒3‒10‒2%).37 This is primarily due to significantly high specific heat capacity and low forces of PHA crystals as compared to the commonly used materials for thermal expansion actuators (aluminum and silicon). Nevertheless, the high VPD, similar strain and much lower density are unique advantages that justify further research into the prospects for application of thermosalient crystals as organic-based thermal expansion actuators.

Figure 4. Volumetric power density versus strain for various actuators. The PHA crystals as thermal expansion actuators studied in this work are highlighted in blue. The plot, except for the PHA data, is reproduced with permission from ref.37

Details on the preparation and characterization, basic crystallographic data for a PHA crystal, face indices for type 1 crystal, Block-diagram of the setup used for measurement of the crystal expansion force, Typical variation in the sensor signal in idle state, ORTEP diagram of PHA. Movie S1. Phase transformation of habit type 1 PHA crystal. Movie S2. Phase transformation of habit type 2 PHA crystal. Movie S3. Longitudinal force measurement for type 2 crystal. Movie S4. Lateral force measurement for type 1 crystal. Movie S5. Cyclic force measurement for type 1 crystal. Movie S6. Cyclic force measurement for type 2 crystal.

*Corresponding author. E-mail: [email protected]

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

The authors declare no competing financial interests.

This research work was sponsored in part by New York University Abu Dhabi and was partially carried out using the optical microscopy facility at the Core Technology Platform resources at New York University Abu Dhabi. We thank Dr. Liang Li for measuring the specific heat capacity of PHA crystals and Dr. Ejaz Ahmed for his help with measurement off the elastic modulus.

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