Research Article www.acsami.org
Isotropic Negative Thermal Expansion Metamaterials Lingling Wu,† Bo Li,‡ and Ji Zhou*,† †
State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China ‡ Advanced Materials Institute, Shenzhen Graduate School, Tsinghua University, Shenzhen, 518055, China S Supporting Information *
ABSTRACT: Negative thermal expansion materials are important and desirable in science and engineering applications. However, natural materials with isotropic negative thermal expansion are rare and usually unsatisfied in performance. Here, we propose a novel method to achieve two- and three-dimensional negative thermal expansion metamaterials via antichiral structures. The two-dimensional metamaterial is constructed with unit cells that combine bimaterial strips and antichiral structures, while the threedimensional metamaterial is fabricated by a multimaterial 3D printing process. Both experimental and simulation results display isotropic negative thermal expansion property of the samples. The effective coefficient of negative thermal expansion of the proposed models is demonstrated to be dependent on the difference between the thermal expansion coefficient of the component materials, as well as on the circular node radius and the ligament length in the antichiral structures. The measured value of the linear negative thermal expansion coefficient of the threedimensional sample is among the largest achieved in experiments to date. Our findings provide an easy and practical approach to obtaining materials with tunable negative thermal expansion on any scale. KEYWORDS: negative thermal expansion, antichiral, bimaterial, 3D printing, metamaterial
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INTRODUCTION Negative thermal expansion materials are highly desired in infrastructure engineering and precision instrument manufacturing.1−6 An important related research is to design composite materials with a coefficient of thermal expansion (CTE) of zero by combining materials with negative- and positive-CTE in an appropriate ratio.7,8 Extensive use of zero-CTE materials could be found in various fields,9 such as optics10,11 and electronics.12 However, only a few materials naturally exhibit negative thermal expansion characteristics because the phenomenon is derived from abnormal mechanisms such as phase transitions,13 shortening of bond lengths,14 rigid unit modes,15 electronic effects,16 and magnetostriction.17 Although several natural negative thermal expansion materials such as perovskite, NaZn13-type La(Fe,Si,Co)13 compounds,18 Ag3[Co(CN)6],19 (Hf, Mg)(WO4)3,20 and the well-known ZrW2O8 family of materials4,21 exist, few are widely used because of their narrow temperature range of negative thermal expansion, low thermal expansion coefficient value, anisotropy of thermal response,22−24 and low design freedom. In the past decade, metamaterials have offered an entirely new route to construct artificial materials with abnormal properties not present in the component materials. Several approaches have been proposed to achieve negative thermal expansion structures.10,25−28 However, because most of the negative thermal expansion cells in these models are © XXXX American Chemical Society
asymmetric, i.e., their thermal expansion property is tailored in only one particular direction, few exhibit isotropic negative thermal expansion. In 2015, a two-dimensional lattice with a large negative CTE was fabricated from bimetallic strips by Ha based on the chiral structure.29 However, the relationship between the effective coefficient of thermal expansion of the model and its size parameters remains uninvestigated. Furthermore, three-dimensional negative thermal expansion metamaterials have not been constructed so far. In this paper, a novel model with an isotropic negative thermal expansion is proposed and demonstrated through the use of two- and three-dimensional antichiral structures. The metamaterials are also demonstrated to possess significant negative thermal expansion coefficients. Both simulation and experimental results show that tailored negative thermal expansion could be achieved by changing the component materials and size parameters of the model. Because the auxetic properties are independent of scale, we believe that the proposed structures could be applied at the macro-, micro-, or even nanoscale.30 Modeling Procedure and Simulation. The unit cell of the model is designed on the basis of antichiral structurea Received: May 12, 2016 Accepted: June 22, 2016
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DOI: 10.1021/acsami.6b05717 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
Figure 1. (A) Existing two- and three-dimensional systems of antichiral models. (B) Deformation schematic of the anti-tetrachiral model under thermal stress. (C) Deformation schematic of the anti-trichiral model under thermal stress.
Figure 2. (A) Diagram of the two-dimensional bimaterial anti-tetrachiral element and the anti-trichiral element. (B) Relationship between the circular node radius (r) and the effective CTE of antichiral elements with different lengths of ligament (l). (C) Relationship between the ligament length (l) and the effective CTE of antichiral elements with different node radii (r). (D) Simulated deformation of a two-dimensional anti-tetrachiral element with r = 40 mm, t = 1 mm, and l = 100 mm. (E) Simulated deformation of a two-dimensional anti-trichiral element with r = 40 mm, l = 100 mm, and t = 1 mm. (F) Relationship between the effective CTE of antichiral elements and the difference in CTE of their component materials. In the simulation of (F), l = 100 mm, r = 25 mm, t = 1 mm, α1 = 1.85 × 10−5 1/K, and α2 varies from 1.85 × 10−5 to 9.25 × 10−5 1/K in increments of 1.85 × 10−6 1/K. In the simulation of (B) and (C), r changes from 20 to 40 mm in increments of 5 mm and l varies from 100 to 140 mm in increments of 10 mm.
fact, the antichiral structures contain a series of similar systems when the number of attached ligaments (henceforth denoted as N) changes.36 The unit cell is rotationally symmetrical of order N, where N has been demonstrated to be restricted to only 3 (anti-trichiral) or 4 (anti-tetrachiral) in two-dimensional
well-established mechanical structure with an isotropic negative Poisson’s ratio.31−33 As proposed by Wojciechowski34 and initially realized by Lakes and Sigmound,31,35 the antichiral structure is constructed as a central point (henceforth referred to as a “node”) with several tangentially attached ligaments. In B
DOI: 10.1021/acsami.6b05717 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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Figure 3. (A) Simulated deformation of a three-dimensional anti-tetrachiral element with r = 25 mm, l = 100 mm and t = 2 mm. (B) Relationship curves between the effective CTE along three orthogonal directions and the node radius for the three-dimensional anti-tetrachiral element.
systems.37 In a three-dimensional mechanism, only an antitetrachiral system can be constructed because a threedimensional anti-trichiral structure does not geometrically exist.38 The existing patterns of antichiral systems are shown in Figure 1A. To obtain a negative thermal expansion effect, we introduced bimaterial strips into the above antichiral structures. Previous research has demonstrated by finite elements that bimaterial elements in anti-tetrachiral honeycombs presented negative thermal properties.33 In this paper, the linear coefficient of thermal expansion αL was used to define the thermal expansion of the model, which is calculated by the following equation αL =
1 ∂L · L ∂T
varied from 20 to 40 mm in increments of 5 mm. The twodimensional anti-tetrachiral and anti-trichiral models are shown in Figure 2A. To study the relationship between the effective CTE of the elements and the CTE of the component materials, we set the CTE of material 1 (α1) to 1.85 × 10−5 1/K and increased the CTE of material 2 (α2) from 1.85 × 10−5 to 9.25 × 10−5 1/K in increments of 1.85 × 10−6 1/K. The simulated temperature range was 303.15−773.15 K. The simulated relationship curves between the effective CTEs of the antichiral models and their size parameters are plotted in Figure 2B,C, which show that, for both the antitrichiral and anti-tetrachiral structures, the effective CTE is proportional to the node radius r and ligament length l. The deformation of the two-dimensional antichiral structures with the temperature increasing are shown in Figure 2D,E. As evident in these figures, when the temperature was increased from 303.15 to 773.15 K, both structures shrank isotopically. The curve in Figure 2F indicates that the effective CTE of the bimaterial antichiral structures is proportional to the difference between the CTEs of the component materials. Furthermore, the relationship curves for the two-dimensional anti-trichiral and anti-tetrachiral structures are exactly the same when the circular node radius (r) and ligament length (l) are constant. The simulated results indicate that tunable negative thermal expansion can be achieved by carefully selecting the component materials and adjusting the geometrical parameters of the bimaterial antichiral models. The simulated deformation of a three-dimensional anti-tetrachiral element with r = 25 mm, l = 100 mm, and t = 2 mm is shown in Figure 3A, and the relationship curves between the effective CTE along three orthogonal directions and the node radius for the threedimensional anti-tetrachiral element are plotted in Figure 3B, which shows an isotropic negative thermal expansion of the model. The complete simulation results for the two-and threedimensional antichiral models are presented in the Supporting Information (Figure S1).
(1)
where L is the length of the unit cell along the studied direction, and T is the temperature. A bimaterial structure composed of two materials with different CTEs has been demonstrated to bend with a curvature of 1/ρ under a thermal stress proportional to the difference of the CTEs of the component materials39
1 ∝ (α2 − α1) ρ
(2)
where α1 and α2 are the CTEs of the component materials. Combining the bimaterial strips with the antichiral structures results in new negative thermal expansion metamaterials. Equation 2 is known to be valid for bimaterial strips made from thin ligaments where the end effects are neglected,40 and both thermal stress and applied loading stress can cause material deformation. Therefore, the bending of ligaments in the models due to thermal stress will result in a shortening of the node−node distance and a tendency to contract the structure in both in-plane principal directions, as shown in Figure 1B,C. As a result, the entire system will exhibit isotropic negative thermal expansion. To verify this hypothesis, theoretical simulation work was performed using the Solid Mechanics module in COMSOL Multiphysics commercial software. Models with two-dimensional anti-tetrachiral and anti-trichiral structures and a threedimensional anti-tetrachiral structure constructed with two materials with different CTEs were considered. To simplify the simulation work, the thickness of both component materials (t) was set to 1 mm, the ligament length (l) was varied from 100 to 140 mm in increments of 10 mm, and the node radius (r) was
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METHODS Preparation of the Two-Dimensional Antichiral Samples. To experimentally verify the negative thermal expansion property of the models, we first fabricated twodimensional samples of bimetal antichiral metamaterials with a ligament length l of 100 mm and a variable node radius r. The model requires two component materials with different thermal expansion coefficients. We selected a bimetal plate with C
DOI: 10.1021/acsami.6b05717 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
Figure 4. Two-dimensional measurement setup. (A) View of the measurement setup. (B) Fabricated anti-tetrachiral sample placed on the heating platform. (C) Fabricated parts for the two-dimensional antichiral samples.
Figure 5. Three-dimensional experiment. (A) Measured relationship between the CTE of the component materials of the three-dimensional antitetrachiral samples and the temperature. (B) Measured relationship between node radius and the effective CTE of the three-dimensional antitetrachiral samples. (C) Sample with r = 20 mm placed in a vacuum drying oven and the measured lengths of the sample. (D) Deformation of the tested sample with r = 20 mm after the increasing of temperature.
dimensional antichiral models with different node radii are shown in the Supporting Information (Figure S2). Preparation of the Three-Dimensional Anti-tetrachiral Samples. The three-dimensional anti-tetrachiral model cannot be fabricated by a traditional manufacturing process since it has a very complex bimaterial internal structure. Therefore, we fabricated the three-dimensional tetrachiral samples with l = 15 mm and t = 1.5 mm by a multi-3D printing process (Objet350
aluminum and copper as the raw materials. Aluminum has a relatively high thermal expansion coefficient of 2.3 × 10−5 1/K, whereas copper has a lower coefficient of 1.85 × 10−5 1/K. A cutting machine was used to cut the bimetal plates into strips with a thickness of 1 mm. The circular node was designed as a ring with grooved ears, and both the grooved ears and bimetal strips were drilled so that they could be firmly tightened with a screw, as shown in Figure 4. The fabricated samples of the twoD
DOI: 10.1021/acsami.6b05717 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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Figure 6. (A, D) Experimentally measured results of an anti-tetrachiral sample with r = 40 mm, t = 1 mm, and l = 100 mm at 303.15 and 773.15 K, respectively. (C) Comparison of the simulated and experimentally measured relationship between the node radius (r) and the effective CTEs along two orthogonal directions for the two-dimensional anti-tetrachiral samples. (B, E) Experimentally measured results of an anti-trichiral sample with r = 40 mm, t = 1 mm, and l = 100 mm at 303.15 and 773.15 K, respectively. (F) Comparison of simulated and experimentally measured relationship between the node radius (r) and the effective CTE for the two-dimensional anti-trichiral samples. For both the simulation and experiments, α1 = 1.85 × 10−5 1/K and α2 = 2.3 × 10−5 1/K. The measurement unit in (A, B) and (D, E) is millimeters. U.S.) was used to determine the temperature on the surface of the sample in real time for all the samples. Since the thermal deformation temperature for the component materials of the three-dimensional samples is lower than 373.15 K, we carried out the three-dimensional experiment in a vacuum drying oven (DZF-6050, Shanghai Jinghong technology Corp., China.). The temperature in the oven was uniformly increased from 293.15 to 343.15 K (the CTE of the rubber-like material is higher than the rigid opaque material in this temperature range, as shown in Figure 5A) with a heating rate of 4.5 K/min. The computer-controlled CCD camera was fixed on the viewing window of the oven to take digital photographs from the same height and angle for all measurements. To accurately measure the deformation of the samples in the pictures recorded by the CCD camera, we used commercial software (Photoshop) to determine the length of the samples at different temperatures. Rulers placed in the three- and two-dimensional measurement setup were used as a reference for measurement. It must be mentioned that, to avoid the measurement error produced by the expansion of the ruler, all of the measurement for each sample in Photoshop was carried out by referring to the ruler in the picture recorded at room temperature (293.15 K). To improve the measurement accuracy, we made two measurements along each orthogonal direction for the two-dimensional anti-tetrachiral samples and calculated the average values, as shown in Figure 6A,D. The same process was used for the two-dimensional anti-trichiral samples, except that we measured three lengths along three directions with equal included angles because the anti-trichiral model exhibits 3-fold rotational symmetry, as shown in Figure 6B,E. The complete measurement photograph for the two-dimensional anti-tetrachiral and anti-trichiral samples are shown in Figures S4 and S5 of the
connex2, Stratasys Ltd.). The node radius r is varied from 15 to 25 mm with an increment of 2.5 mm. Two materials with different CTEs were chosen as lower-CTE (rigid opaque material: VeroWhitePlus RGD835) and higher-CTE (rubberlike material: TangoPlus FLX930) materials to fabricate the three-dimensional models. The fabricated model with a node radius of 20 mm is shown in Figure 5. The complete photograph of the three-dimensional samples with different node radii is shown in the Supporting Information (Figure S3). The relationship between the CTE of the selected materials and the temperature was measured by a dilatometer (Netzsch Dilatometer DIL402PC), and the results are plotted in Figure 5A. From the figure, we can see that the rubber-like material (TangoPlus FLX930) has a higher CTE than the rigid opaque material (VeroWhitePlus RGD835) in the testing temperature range.
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EXPERIMENTAL SECTION
A measurement setup was constructed to verify the thermal expansion properties of the proposed two-dimensional antichiral models, as shown in Figure 4A. The experimental setup was composed of three parts: the heating platform and its controller, the CCD camera, and a computer. The sample was placed on the heating platform and covered with a quartz jar to prevent air convection. The computer-controlled CCD camera was positioned above the heating platform to observe the deformation of the sample in real time. To ensure soft lighting during the experiment, two light-compensating lamps were placed above the measurement equipment. An infrared camera (TiS65, Fluke Corp. E
DOI: 10.1021/acsami.6b05717 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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Supporting Information, respectively. For the three-dimensional tetrachiral sample, we made four measurements in each photograph recorded from the front view of the sample, as shown in Figure 5C, and then calculated the average values.
Research Article
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.6b05717. Figure S1 shows the complete simulation results of the two- and three-dimensional antichiral structures. Figure S2 represents the photographs of the fabricated twodimensional antichiral samples with different node radii. Figure S3 presents the photograph of the fabricated three-dimensional anti-tetrachiral samples with different node radii. Figures S4 and S5 present the complete measured results of the two-dimensional anti-tetrachiral model and anti-trichiral model with different node radii, respectively (PDF)
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RESULTS AND DISCUSSION The experimentally measured relationship between the effective CTE and the node radius (r) for the two-dimensional antitetrachiral and anti-trichiral samples is plotted in Figure 6C,F to provide a better comparison with the simulation results. As evident in these figures, both the simulation and experimental results show that the structures exhibit isotropic negative thermal expansion and the values of effective CTEs are proportional to the node radius (r). Reasonable agreement was achieved between the simulation and experimental results, with the experimental data generally showing lower values of the thermal expansion coefficient compared to the simulation results. This discrepancy mainly resulted from the friction between the heating platform and the sample. In Figure 6C, the measured value of the effective CTE for the anti-tetrachiral system reaches −68.1 × 10−6 1/K over a large operating temperature range from 303.15 to 773.15 K. The measurement result for the three-dimensional antitetrachiral sample is shown in Figure 5B, which indicates the relationship between the node radius (r) and the effective CTE of the sample. From the figure, we can see that the samples present a negative thermal expansion property from 293.15 to 343.15 K, and the magnitude of the effective CTE shows a proportional trend with the increase of the node radius of the sample. The discrepancies of the experiment were mainly caused by the gravity of the nodes. The three-dimensional experiment was not carried out as accurately as the twodimensional experiment due to the limitation of the measurement instrument and the precision of the multimaterial 3D printing fabrication process. However, it should be noted that, although the experiment result is imperfect, it provides a new way to realize the artificial three-dimensional NTE material and experimentally demonstrates its feasibility. We believe that, in the short future, more 3D bimaterial anti-tetrachiral models with a finer internal structure could be constructed with the development of precision manufacturing. This method proved to be a cheap and feasible way to promote the practical applications of the artificial negative thermal expansion materials. Efforts will be made on further improving the performance of the three-dimensional NTE material.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
J.Z. conceived the idea. L.W. designed experiments and carried out numerical calculations. B.L. revised the full paper. All authors contributed to scientific discussion and critical revision of the article. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China under Grant Nos.11274198 and 51532004 and the Science and Technology Plan of Shenzhen City under grant JCYJ 20150827165038323.
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REFERENCES
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CONCLUSIONS In conclusion, we proposed two- and three-dimensional artificial materials with substantial negative thermal expansion property and demonstrated their fabrication by bimaterial strips and a multimaterial 3D printing process. For both the twodimensional and three-dimensional samples, the relationship between the negative thermal expansion of the metamaterials and the node radius of the models was investigated. Large and tailorable negative CTEs were obtained with this approach. The mechanism proposed here is theoretically scale independent, meaning that the concept of manipulation of thermal expansion could be extended to the micro- or nanoscale if appropriate component materials and fabrication processes are available. These models have extensive potential applications in areas such as aerospace engineering, architectural engineering, and other domains which involve great temperature ranges that might cause thermal fatigue and cracking. F
DOI: 10.1021/acsami.6b05717 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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