Abstract
Controlling the thermal expansion of materials is of great technological importance. Uncontrolled thermal expansion can lead to failure or irreversible destruction of structures and devices. In ordinary crystals, thermal expansion is governed by the asymmetry of the microscopic binding potential, which cannot be adjusted easily. In artificial crystals called metamaterials, thermal expansion can be controlled by structure. Here, following previous theoretical work, we fabricate three-dimensional (3D) two-component polymer micro-lattices by using gray-tone laser lithography. We perform cross-correlation analysis of optical microscopy images taken at different sample temperatures. The derived displacement-vector field reveals that the thermal expansion and resulting bending of the bi-material beams leads to a rotation of the 3D chiral crosses arranged onto a 3D checkerboard pattern within one metamaterial unit cell. These rotations can compensate the expansion of the all positive constituents, leading to an effectively near-zero thermal length-expansion coefficient, or over-compensate the expansion, leading to an effectively negative thermal length-expansion coefficient. This evidences a striking level of thermal-expansion control.
Highlights
Within the range of validity of the continuum approximation, any connected structure composed of one constituent material A and voids within will show exactly the same thermal length-expansion coefficient as the bulk constituent material A
Discussed theoretically a related two-dimensional structure composed of bimetallic strips showing a negative effective compressibility
The amplitude of the rotations can be adjusted by the ratio of the thermal length-expansion coefficients of the constituent materials A and B
Summary
By using 3D gray-tone two-photon laser lithography, we fabricate micro-structured two-component metamaterials using a single photoresist, leading to an effectively negative thermal length-expansion coefficient from all-positive constituents. Upon reducing the temperature difference to ΔT = 10 K, we find essentially the same behavior as for ΔT = 20 K, albeit with worse signal-to-noise ratio (not depicted) From these data at ΔT = 20 K, we extract an average effective metamaterial thermal length-expansion coefficient of αL =(−5 ± 0.5) × 10−5 K−1. We have fabricated and characterized micrometer-scale two-component polymer-based metamaterials exhibiting an effectively negative thermal length-expansion coefficient from positive constituents. The necessary two components plus voids have been realized by 3D gray-tone laser lithography using only a single photoresist
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