Extended Discussion on Thermal Metamaterials with Terrace-Shaped Temperature Distribution for Efficient Adaptive Multi-Temperature Control

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Temperature plays an essential role in myriad daily life scenarios and industrial applications. With the varied temperature requirements for diverse objects, the advent of adaptive multi-temperature control (AMTC) has become imperative. In our manuscript, we probed the complexities introduced by inescapable heat transfer and intrinsic material properties in state-of-the-art technologies, using goods transportation as our focal case study. A promising avenue we explored is the application of thermal metamaterials, celebrated for their ability to modulate temperature distribution, as a means to achieve efficient AMTC. While our article gave a nod to the influence of terrace structures on our thought process, this is but a snapshot of the underlying design rationale for metamaterials in AMTC. We elaborate on this for the benefit of our readers.

Drawing from the structure of a mountain, as illustrated in Fig. 1, everyday experiences tell us that smooth-surfaced mountains can pose significant challenges for climbers (Fig. 1a). However, when the mountain is interspersed with multiple platforms, it naturally offers a more navigable terrain (Fig. 1b). Two elemental observations can be gleaned from this analogy. Firstly, the principle of height monotonic continuity, implies that optimizing elevation from one step can minimize the energy required for subsequent steps. This principle is easily visualized: when ascending, each step leverages the elevation achieved by the previous step, allowing climbers to either maintain or elevate their height. Conversely, in descent, height monotonic continuity is emblematic of energy conservation, as portrayed in Fig. 2a. Imagine placing a ball at the peak with a certain initial velocity and assuming no surface friction. The ball would effortlessly roll to the base without any added energy input. The second observation pertains to the platforms, which serve as intermediary respites that reduce the gradient of the climb, thus easing the ascent. With these insights as our backdrop, how might we draw parallels in the realm of temperature control?

Fig. 1 | A terrace-shaped structure on the mountain facilitates easier ascent and descent. In a, the climb is more challenging for the person in red, compared to the easier route for the person in blue in b.
Fig. 2 | An analogy between height (a) and temperature (b) distribution. Note: b is adapted from a figure in our manuscript. AMTC stands for adaptive multi-temperature control. For general reference, height, temperature, and position are expressed in arbitrary (arb.) units. The square, circle, and triangle symbols represent objects with different temperature requirements.

Let us simplify our analogy by relating height development directly to temperature control, as depicted in Fig. 2b. Continuing with the two elements from height development, for the principle of height monotonic continuity, Fig. 2b leverages the monotonic continuity in temperature distribution. Since any medium between a pair of heat and cold sources naturally exhibits a temperature gradient from high to low, it is straightforward to replicate this phenomenon in practical applications. For instance, in a heat conduction system, by tuning the thermal and structural parameters, one can achieve a terrace-shaped temperature distribution. The platforms in our analogy correspond to designated controls for objects with distinct temperature needs. As per the aforementioned principle, by designing specific thermal and structural parameters, we can cater to these varying temperature requirements.

We further discuss two critical aspects of implementing and testing AMTC in real-world scenarios.

Firstly, it is imperative to establish a pair of heat and cold sources. These sources are essential in providing the high- and low-temperature boundaries for the system. Using goods transportation as a reference, it is crucial to develop mobile sources that can provide consistent temperatures, ensuring a steady-state terrace-shaped temperature distribution. The use of phase change materials (PCMs) in contemporary cold chain logistics offers a solution. A familiar case can be drawn from transporting ice cream in a warm environment. Using a thermally insulated container can limit the heat exchange between the ice cream and the external environment. Pairing this with a PCM, whose phase change temperature aligns closely with that of the ice cream, can further enhance the duration of temperature maintenance. By using two PCMs with differing phase change temperatures (Tp), we fabricate the mobile heat and cold sources. As numerous studies have already formulated PCMs with optimal Tp and favorable properties, selecting appropriate PCMs for AMTC in our research is a straightforward task.

Secondly, testing the AMTC's efficiency in our fabricated multi-temperature maintenance container demands a careful selection of test objects. In cold chain logistics research, conventional temperature maintenance tests often involve placing a real object inside the container. In our study, however, there are nine distinct zones designed for goods with varying temperature requirements. While we could test with nine real goods of different initial temperatures, for broader applicability, it is beneficial to use simulacra with consistent thermal properties. The ideal simulacra should:

  • Mimic the thermal properties of actual goods;
  • Allow easy preparation at different initial temperatures;
  • Maintain stability across several tests.

Given these requirements, the water emerges as the ideal simulacra. By preparing water with varied initial temperatures and positioning them in their respective zones, we can gauge the container’s multi-temperature maintenance efficacy by monitoring the real-time temperature variation rates of the simulacra. For more specialized applications, this water-based simulacrum can be substituted with actual goods as needed.

In summary, the efficacy of the thermal metamaterial we employed to achieve high-efficiency AMTC is attributed to: (1) their capacity to harness heat transfer between objects at diverse temperatures, resulting in a terrace-shaped temperature distribution in steady-state scenarios; (2) their seamless integration with phase change technology; and (3) the versatility of our testing approach for real-world multi-temperature maintenance containers. Additional developmental strategies discussed in our manuscript may further enhance its applicability.

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