Butterfly Wing Microstructure Inspired Solid/Porous Alternating Layered Structures: In Situ Visualization of Confined Foaming

Abstract

This study explores confined foaming in micro‐/nano‐layered (MNL) solid/porous alternating structures inspired by the hierarchical architecture of Ulysses butterfly wings. Biomimetic MNL films composed of alternating polycarbonate (PC) and polymethyl methacrylate (PMMA) layers (17–513 layers) are fabricated via advanced coextrusion and foaming techniques. In situ visualization reveals confinement effects dependent on layer thickness; while nucleation primarily occurrs at PC/PMMA interfaces due to reduced energy barriers, a strong confinement zone within 10 µm of the interfaces significantly restricts cell growth, most notably in the 129‐layer and 513‐layer samples, where single‐cell rows are observed. Thermal regulation tests show that the 513‐layer bio‐mimic structure reduces temperature rise by 80%, 65%, and 50% compared to polyethylene (PE) film, a three‐layer sandwich structure, and butterfly wings, respectively. It also exhibits exceptional delay in heat accumulation under radiative conditions, with a time to reach half of the maximum temperature rise of 165 s, compared to 20 s (PE) and 40 s (both three‐layer and butterfly wing). The bio‐mimic architecture also exhibits strong anisotropic thermal conductivity, effectively suppressing through‐thickness heat transfer while enhancing lateral dissipation. These results connect nature‐inspired design and practical implementation, highlighting the potential of bio‐mimic MNL structures for advanced thermal management applications.

Inspired by butterfly wings, multilayered solid/porous films with micro/nano‐layered architecture are fabricated via confined foaming. In situ visualization reveals confinement‐driven nucleation behavior. The resulting structures exhibit enhanced solar reflectivity, anisotropic thermal conductivity, and superior thermal regulation, delaying heat accumulation beyond conventional designs.

1. Introduction

As global temperatures soar to unprecedented levels, with 2023 marking record warmth for both land and ocean areas,^{[ 1 ]} effectively managing heat has become a critical challenge across diverse sectors, from electronics to construction.^{[ 2 ]} Escalating heat waves underscore the need for materials capable of both withstanding thermal stress and efficiently dissipating heat, spurring intense research into innovative solutions.^{[ 3 ]} Increasingly, scientists are drawing on nature's unparalleled engineering, using biomimicry to develop multifunctional materials that integrate thermal management with other essential physical and functional properties. Natural systems exhibit sophisticated architectures that provide synergy induced mechanical, hydrodynamic, optical, and conductive properties, among others.^{[ 4} , ⁵ , ⁶ , ^{7 ]} By emulating these complex structures, researchers are pioneering bio‐inspired materials that echo remarkable designs found in nacre,^{[ 8} , ⁹ , ¹⁰ , ^{11 ]} botanical systems,^{[ 12} , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ , ^{20 ]} human biology,^{[ 21} , ²² , ²³ , ²⁴ , ²⁵ , ²⁶ , ²⁷ , ^{28 ]} and animal/insect adaptations.^{[ 29} , ³⁰ , ³¹ , ³² , ³³ , ^{34 ]}

For instance, over millions of years, the wings of lepidopterans have evolved to adapt to global environmental changes, resulting in some of nature's most intricate and sophisticated architectures that ensure species survival. Specifically, butterfly wing architecture spans multiple length scales. At the macro‐scale, lightweight, porous layers feature micro‐pores, while robust, rigid layers overlay these porous regions. Together, these layers are reinforced by complex, interconnected support structures, including ridges, cross ribs, and struts at the nano‐scale.^{[ 35} , ³⁶ , ^{37 ]} This multi‐layered hierarchical structure provides exceptional optical, thermal management, and mechanical performance, enabling butterflies to withstand a range of environmental challenges.^{[ 38 ]}

Specifically, the porous scales, detailed by periodic chitin microstructures, referred to as photonic crystals, scatter and refract light at specific wavelengths (visible to near‐IR), tailoring the optical properties and inducing structural coloration in the wings.^{[ 39} , ⁴⁰ , ^{41 ]} Additionally, the interaction of these structures with light across the UV to near‐IR spectrum plays an important role in heating butterfly wings and bodies by absorbing solar heat. This absorbed heat is used to actively regulate the butterflies' body temperature, maintaining it within an optimal range (20–50 °C, regardless of habitat) to support peak aerodynamic performance.^{[ 42} , ^{43 ]} This intrinsic thermal management is crucial for flight, as butterflies, being cold‐blooded, depend on external heat for muscle function. By achieving optimal body temperature, these scales enable efficient wing movements, enhancing aerodynamic performance and allowing for longer, more agile, and sustained flight. In contrast, the rigid scales provide durability and protection from environmental stresses, further enhancing the wings' resilience and longevity.^{[ 39 ]} Together, this multi‐layered assembly architecture not only optimizes aerodynamic efficiency but also exemplifies nature's ingenious approach to achieving synergy‐induced multifunctionality.^{[ 44 ]}

Currently, micro‐/nano‐layered (MNL) coextrusion technology, coupled with advanced cellular foaming, has the potential of applications ranging from protective packaging^{[ 45 ]} and lightweight insulation^{[ 46 ]} to soundproofing,^{[ 47} , ^{48 ]} and flame retardants.^{[ 49 ]} MNL coextrusion is an advanced polymer processing method that creates hundreds to thousands of alternating layers using 2–5 polymers, with individual layer thicknesses as small as 10 nm.^{[ 50} , ⁵¹ , ^{52 ]} Meanwhile, polymer cellular foaming introduces porous structures into the polymer matrix through phase separation. The integration of these two manufacturing technologies results in the creation of multi‐layered composite materials that combine the precise control of layered architecture with the lightweight, insulating properties of foamed structures, offering enhanced cell morphology control, improved thermal management, mechanical strength, and broader functional performance.

However, a significant challenge in this process lies in systematically controlling the individual layer thickness while selectively foaming the alternating layers, ensuring precise control over cell size (pore size) to achieve the desired solid/porous alternating structure.^{[ 53} , ^{54 ]} To address this, it is essential to gain a deeper understanding of the underlying mechanisms that govern the foaming process, in order to enhance both manufacturing precision and the theoretical framework of process–structure–property relationships. In this work, we employ a state‐of‐the‐art in situ foaming visualization system to validate the proposed nucleation and growth mechanisms. Specifically, we investigate how varying confinement conditions, modulated by individual layer thickness, affect foaming dynamics. Special attention is given to capturing transient behaviors that can only be observed through real‐time visualization. By capturing the temporal evolution of cell nucleation and growth, this approach provides quantitative insight into how adjacent solid layers regulate bubble formation and expansion, offering a more comprehensive understanding of confined foaming phenomena than was previously possible through static, post‐foaming analysis alone.

Thus, for the first time, this work introduces systematically crafted butterfly‐inspired multi‐layered structures, fabricated using MNL coextrusion with subsequent physical cellular foaming, offering tunability and customization for a variety of advanced applications. These synthetic structures, illustrated in Figure  1 , incorporate alternating solid and porous polymer layers, specifically designed to reflect and scatter sunlight, mimicking the natural hierarchical architecture and intrinsic performance of butterfly wings. Additional structural comparisons are provided in Figure S1 (Supporting Information)^{[ 55 ]} to highlight the bio‐inspired correlation. Specifically, the similar cell size distribution within these samples function similarly to the butterfly's porous scales, efficiently scattering light and reducing heat transmission.^{[ 56} , ⁵⁷ , ^{58 ]} Hence, our bio‐mimic multi‐layered composites leverage nature's engineering to achieve superior optical and thermal management performance, showcasing the potential of bio‐inspired design to enhance sustainability, energy efficiency, and material performance.

Figure 1.

Microstructure of Ulysses butterfly wings alongside bio‐mimetic MNL porous/solid alternating structures inspired by butterfly wing morphology.

As a result, this comprehensive analysis highlights the significance of the butterfly‐inspired design in achieving exceptional optical and thermal management performance in multi‐layered composites. In fact, our novel materials can be tailored to surpass the performance of nature's Ulysses butterfly, under artificial sunlight, showing up to 50% and 400% improvements in maximum temperature reduction and increase in the time required to reach 1/2 peak temperature, respectively, demonstrating the bio‐mimic structure's exceptional ability to delay heat accumulation under radiative conditions. Ultimately, these butterfly‐inspired multi‐layered composites are cost‐effective and industry‐ready, offering lightweight, multifunctional components with enhanced performance and the potential to revolutionize industries from the thermal management of electronics^{[ 59 ]} to aerospace engineering,^{[ 60 ]} and beyond.

2. Experimental Section

2.1. Materials

Two pairs of different grades of Polycarbonate (PC) and Polymethyl Methacrylate (PMMA) were used to meet the specific requirements for in situ visualization experiments and thermal management experiments. For visualization experiments, PC was LEXANTM 105 and PMMA was ARKEMA V045‐100. For thermal management experiments, PMMA films were OPTIX Acrylic with a thickness of 0.254 mm and a glass transition temperature of 115 °C, and PC was RowTec PC1 Graphic Arts Polycarbonate film with a thickness of 0.508 mm and a glass transition temperature of 150 °C. Bone‐dry carbon dioxide (CO₂) from Air Liquide was used as the foaming agent for both experiments.

2.2. Experiments

First, MNL sheets are prepared with a coextrusion system equipped with different numbers of layer multipliers, as illustrated in Figure  2A. PC and PMMA are first dried in a vacuum oven at 90 °C for 4 hours, then melted and extruded with two extruders, respectively, at 230 °C and pumped out at a 1:1 volume ratio, then combined in the feedblock into a three‐layer structure, with PC as the skin and PMMA in the middle. The feedstream then enters the layer multipliers, where it is first divided horizontally and then stacked back together vertically, causing the layer number to double after each layer multiplier. Due to the initial three‐layer structure, after the first layer multiplier, the layer number becomes 5 instead of 6 because the PC layers of the two separated feed streams are combined together during the stacking. Therefore, by applying 3–6 layer multipliers, MNL sheets were obtained with 17–129 layers, with a sheet thickness of ≈2.5 mm.

Figure 2.

A) The coextrusion system used to produce the MNL structures, B) the high‐pressure in situ visualization system capturing the foaming process in real‐time, and C) the MNL solid/porous alternating structure, illustrating the layered configuration before and after the foaming process.

After obtaining the MNL sheets, a Leica 2125RT microtome was used to obtain thin slices of the cross‐section of the MNL sheets with a thickness of 60 ± 7 µm. The thin samples are then placed in a custom‐made in situ visualization batch foaming system for foaming and observation. The system is illustrated in Figure 2B. The key component of the system is a visualization chamber made from optically transparent sapphire. With the addition of a lens and a high‐speed camera magnification and recording system, the foaming process was recorded in real time.

During the foaming process, the samples were placed between the bottom sapphire and a glass cover to mimic the bulk condition where the lateral directions were all confined by film layers and would not expand freely.^{[ 54 ]} The sample was then saturated at 10 MPa with CO₂ for 10 minutes at 90 °C, conditions selected to optimize cell visibility under optical visualization system. After that, the pressure was quickly released, and the foaming process was recorded by a high‐speed camera. The temperature and pressure profiles are shown in Figure S2 (Supporting Information).

To produce samples sufficiently large for thermal management property tests, MNL samples with initial dimensions of approximately 1.5 × 20 × 25 mm were foamed under confined conditions at 90 °C and 20 MPa. This process resulted in solid/porous alternating samples with final dimensions of approximately 3.5 × 20 × 25 mm.

2.3. Characterizations

As shown in Figure 2C, after the foaming process, only the PMMA layers are foamed, while the PC layers remain solid under the applied foaming conditions. To characterize the cell nucleation and growth process in real time, the video captured by the high‐speed camera was converted into individual image frames. Using image processing tools such as ImageJ, the study overlaid and compared sequential frames to determine whether new bubbles had nucleated. The number of cells was then counted over time and categorized into interface‐nucleated and bulk‐nucleated cells, as shown in Figure S3 (Supporting Information).

Furthermore, for each video, six representative cells were selected, and their growth was tracked over time by measuring their size in successive frames, as also demonstrated in Figure S3 (Supporting Information). For the 17 to 65‐layer samples, three of the selected cells were nucleated at the interfaces, while the other three were nucleated in the bulk. In the 129‐layer sample, all cells were nucleated at the interfaces.

The cell density N_A was calculated using Equation (1), where A is the cross‐sectional area of the selected PMMA layer before foaming, and n is the number of nucleated cells within the selected area. The cell size was represented as the equivalent cell diameter D, determined by Equation (2), where a is the area of the selected cell. These calculations allowed to quantitatively analyze the temporal evolution of cell density and size across different samples and nucleation conditions.

$$N_A=\frac{n}{A}$$ (1)

$$D=2\sqrt{\frac{a}{\pi }}$$ (2)

To address the limitations of the optical microscope, samples and foaming conditions were selected that ensured most cell sizes exceeded 10 µm for in situ visualization system experiments, warranting the accuracy of observations.

However, for consistency and superior thermal and optical properties, 513‐layer samples were used and prepared following the same method as in the previous study to demonstrate the similarity between the samples and butterfly wings.^{[ 54 ]}

A scanning electron microscope (SEM, FEI Quanta FEG 250) was used to observe both a Ulysses butterfly wing specimen and the 513‐layer bio‐mimic samples, as shown in Figure 1. To further highlight the thermal regulation properties of the bio‐mimic samples, two sets of experiments were conducted.

First, the ability of the samples to provide protection against strong sunlight were tested by using an artificial light source (Dolan‐Jenner Fiber‐Lite Model 180 Fiber Optic Illuminator), which ensured controlled and consistent irradiation conditions across all samples and provided a reasonable approximation of the solar spectrum.^{[ 61 ]} The light source was positioned 3 cm from the sample to minimize heat conduction and isolate the effect of radiation. The sample temperature was monitored in real time using a thermal camera (Topdon TC001 Plus).

To obtain more accurate measurements of temperature response under well‐controlled conditions, the temperature inside an enclosed space (shielded by the sample) was recorded using thermocouples, as shown in Figure S4 (Supporting Information). To quantify and compare the thermal regulation performance of different samples, the study defines a characteristic parameter, t_1/2, representing the time required to reach half of the maximum temperature rise. This metric offers a consistent and intuitive means to assess thermal response, particularly during the early stage where heat transfer dominates. Additionally, the cooling behavior of the samples was also investigated using this setup.

Next, the anisotropic thermal conductivity of the bio‐mimic samples was investigated by placing different surfaces of the sample in contact with a metal plate maintained at a constant temperature of 90 °C. The temperature profiles of the samples were recorded over time to assess directional heat conduction, as illustrated in Figure S5 (Supporting Information).

3. Results and Discussion

3.1. MNL Coextrusion of PC/PMMA Films

In this study, PC and PMMA were selected as the constituent materials for the multilayer structure based on their complementary physical and processing properties. Both polymers are widely adopted in industrial‐scale coextrusion owing to their excellent melt processability, thermal stability, and mechanical robustness. Although immiscible, PC and PMMA exhibit partial interfacial compatibility under coextrusion, ensuring stable layered interfaces.^{[ 62 ]} A key rationale for this material pairing lies in their markedly different responses to supercritical CO₂ foaming: PMMA is highly foamable under the selected conditions, while PC remains stable and resists foaming.^{[ 53} , ^{54 ]} This contrast allows the formation of alternating solid (PC) and porous (PMMA) layers with well‐defined interfaces, essential for achieving the desired anisotropic thermal and optical performance.

In coextrusion systems, particularly in MNL coextrusion, where the contact time between PC and PMMA layers is extended due to the layer multipliers, it is essential to ensure that the two materials have well‐matched viscosities and elasticities to minimize flow instability.^{[ 63 ]} For this reason, the PC and PMMA grades used in this experiment were carefully selected based on their viscosities at the extrusion temperature, especially within the shear rate range relevant to the layer multipliers,^{[ 53 ]} as shown in Figure S6 (Supporting Information). The coextrusion temperature was set to 230 °C to ensure complete polymer melting while preventing PMMA degradation, which tends to occur at temperatures above 270 °C.^{[ 64 ]}

Using this selected PC/PMMA pair, MNL sheets with 17 to 129 layers were successfully produced, each with individual layer thicknesses ranging from 13 to 300 µm, as shown in Figure S7 and Table S1 (Supporting Information). The observed variation in individual layer thicknesses is attributed to minor inconsistencies in flow rates and shear stress differences across the layers, particularly within the layer multipliers.^{[ 65} , ^{66 ]} These factors impact the uniformity of the polymer streams, resulting in variations in layer thickness.

In the subsequent in situ visualization experiments, layers with thicknesses of approximately 20, 50, 100, and 200 µm were selected to represent the 17‐layer, 33‐layer, 65‐layer, and 129‐layer samples, respectively. This selection was made to ensure consistent results and minimize the influence of layer thickness variation on the in situ visualization study.

3.2. Confined Foaming in MNL Solid/Porous Alternating Structures

MNL solid/porous structures exhibit unique characteristics distinct from conventional isotropic foams, primarily due to the confining effects imposed by the solid film layers.^{[ 53} , ^{54 ]} In isotropic foam samples, cells tend to expand uniformly in all directions, forming spherical or equilateral polygonal shapes depending on wall thickness.^{[ 67 ]} In contrast, MNL foam samples exhibit a distinct alternating structure of solid and porous layers, enabled through carefully selected materials and foaming conditions. Under our employed batch foaming conditions, the PMMA foam layers become softened due to the plasticization effect induced by CO₂ ^{[ 68 ]} and undergo significant expansion during the foaming process. Meanwhile, the solid PC layers remain rigid due to their higher glass transition temperature (T_g) (Figure S8, Supporting Information), preventing any substantial deformation or cell nucleation within the PC layers throughout the process.^{[ 69 ]} The rigid PC layers constrain the lateral expansion of the PMMA foam layers due to the strong adhesion between the PC and PMMA layers,^{[ 70 ]} as a result, the foam layers are restricted from expanding laterally and can only grow vertically within the MNL structure.

In this study, our theories were validated through real‐time observations obtained from our in situ visualization system. As shown in Figure  3 , the cell nucleation and growth dynamics over time exhibit distinct patterns across different samples, consistent with the predicted behavior.

Figure 3.

Images from video frames showing cell nucleation and growth over the first 1.2 seconds after depressurization for 17 to 129‐layer samples, with individual layer thicknesses ranging from 200 to 20 µm. All images share the scale bar shown in the upper left corner.

From the images taken at zero seconds, it was observed that under the optical microscope, the PMMA layers appear brighter than the PC layers. This contrast arises because the visible light transparency of the PC layers (88%) is lower than that of PMMA layers (92%), according to the resin manufacturer's data. The interface areas between the PC and PMMA layers appear even darker, which can be attributed to the difference in refractive indices between the two materials and the fact that the interfaces are not perfectly perpendicular to the cross‐section surfaces.^{[ 71 ]}

In the images taken at 0.4 seconds, the appearance of bubbles was observed, which are darker than both the PC and PMMA matrices, across all samples.^{[ 72 ]} Notably, the majority of these bubbles form near the PC/PMMA interfaces. This provides a clear illustration of the early stage of the foaming process in our MNL foaming system. To further explain this phenomenon, it is best to refer to classical nucleation theory, where a parameter known as the critical radius (R_cr) governs the fate of nucleated bubbles.^{[ 73 ]} Bubbles larger than R_cr grow spontaneously, while those smaller than Rcr collapse. Theoretically, Rcr is a function of the thermodynamic state, which is determined by the local pressure (P_local), the system temperature (T_sys), and the dissolved gas concentration (C). This can be estimated using the following equation:^{[ 74 ]}

$$R_{\mathrm{c}r}=\frac{2{\gamma }_{lg}}{P_{bub,cr}-\left(P_{sys}+\mathrm{\Delta }{P}_{local}\right)}=\frac{2{\gamma }_{lg}}{P_{bub,cr}-P_{local}}$$ (3)

P_bub,cr is the pressure inside the critical bubble and is related to the C, γ_lg represents the surface tension at the polymer/gas interface, P_sys is the system pressure, and ΔPlocal refers to the local pressure variation. The term (P_sys+ΔP_local) represents the local pressure, P_local. In this equation, the difference between P_bub,cr and P_local indicates the degree of supersaturation, which serves as the driving force for the foaming process. The greater the degree of supersaturation, the smaller R_cr, making bubble nucleation more likely.

Before the pressure drop, P_bub,cr is equal to P_local, due to the equilibrium state of CO₂ dissolved in the PMMA matrix. Under this condition, R_cr is theoretically infinite, meaning that no bubbles would grow. However, after depressurization, P_sys drops rapidly, significantly reducing R_cr, thereby enabling the foaming process to begin.

Furthermore, in our foaming system, only the PMMA layers undergo foaming and exhibit a tendency to expand in volume, while the PC layers remain solid. This induces tensile forces near the PMMA/PC interface, as the PC layers constrain the expansion of the PMMA layers. This translates into a negative ΔP_local, which further reduces R_cr, thereby facilitating the foaming process. This partially explains why most bubbles nucleated at the interfaces, as seen in the 0.4‐second images.

Another major factor contributing to this phenomenon is heterogeneous nucleation. The free energy required to form a critical bubble, homogeneously (W_hom) and heterogeneously (W_het), can be expressed as:^{[ 75 ]}

$$W_{hom}=\frac{16{\gamma }_{lg}^3}{3{\left(P_{bub,cr}-P_{local}\right)}^2}$$ (4)

$$W_{het}=\frac{16{\gamma }_{lg}^{3}F\left({\theta }_c,\beta \right)}{3{\left(P_{bub,cr}-P_{local}\right)}^2}=W_{hom}F\left({\theta }_c,\beta \right)$$ (5)

where F(θ_c,β) is an energy reduction factor that physically represents the ratio of the volume of a heterogeneously nucleated bubble at the nucleating site to the volume of a spherical bubble with the same radius of curvature. The value of F(θ_c,β) depends on the surface geometry of the heterogeneous nucleation site, which determines β, and the contact angle θ_c between the bubble surface and the nucleating agent surface, measured in the polymer phase, as illustrated in Figure S9 (Supporting Information). By definition, F(θ_c,β) is always less than 1, indicating that nucleation on heterogeneous sites, such as the PMMA/PC interfaces in our system, requires less energy than nucleation in the bulk.

Taking this one step further, if the cell nucleation rate is considered to be equivalent to the rate at which a critical‐size bubble gains molecules and grows, the homogeneous nucleation rate (J_hom) and heterogeneous nucleation rate (J_het) can be derived by combining classical nucleation theory with molecular kinetics:^{[ 74 ]}

$$J_{hom}=N\sqrt{\frac{2{\gamma }_{lg}}{\pi m}}\exp \left(-\frac{16\pi {{\gamma }^3}_{lg}}{3k_b{T}_{sys}{\left(P_{bub,cr}-P_{local}\right)}^2}\right)$$ (6)

$$J_{het}=N^{\frac{3}{2}}Q\left({\theta }_c,\beta \right)\sqrt{\frac{2{\gamma }_{lg}}{\pi mF}}\exp \left(-\frac{16\pi {{\gamma }^3}_{lg}F\left({\theta }_c,\beta \right)}{3k_b{T}_{sys}{\left(P_{bub,cr}-P_{local}\right)}^2}\right)$$ (7)

where N is the number of gas molecules per unit volume, m is the molecular mass of the dissolved gas molecules, and k_b is Boltzmann's constant. Q(θ_c,β) is the ratio of the liquid‐gas surface area of the heterogeneously nucleated bubble to that of a spherical bubble with the same radius of curvature, also determined by θ_c and β. Comparing Equations (6) and (7), it can be concluded that, under the same conditions, J_het will almost always be higher than J_hom. This means that at the beginning of the foaming process, when conditions such as dissolved gas concentration (C), system temperature (T_sys), and local pressure (P_local) are nearly identical, J_het would be higher, leading to the observations seen in our 0.4‐second images.

However, when comparing the 0.8‐second images with the 0.4‐second images, it is discernible that most of the new bubbles in the 17 to 65‐layer samples nucleated during this period are in bulk. This phenomenon is primarily caused by the depletion of gas near the interface region due to bubble nucleation and growth at the interface during the first 0.4 seconds. To understand this, we refer back to Equation (3). The critical radius (R_cr) is a value that continuously changes during the foaming process as the dissolved gas concentration (C) decreases, with gas being consumed by nucleating and growing cells. The decrease in C results in a lower P_bub,cr, which in turn increases R_cr, making it more difficult for bubbles to nucleate. Similarly, the decrease in P_bub,cr increases the nucleation energy barrier (W) and decreases the nucleation rate (J), as shown in Equations ((4), (5), (6), (7)). This effect prevents further nucleation at the interfaces.

In contrast, the 129‐layer sample behaves differently from the others. No bulk nucleation is observed in the 129‐layer sample during the 0.4 to 0.8‐second period, nor throughout the entire foaming process. This is because the thickness of the PMMA layers, ≈20 µm, is similar to the expected cell size under these conditions, leading to a strong confinement effect that significantly hinders cell nucleation and growth in the bulk. This observation will be further elaborated in the following discussion section.

During the 0.8 to 1.2‐second period, almost no new cells are nucleated, and cell growth becomes the dominant process. This is primarily due to the presence of numerous nucleated cells, which significantly reduce the local CO₂ concentration around them. The decrease in C, in turn, increases R_cr (as described by Equation (3)), making further cell nucleation less favorable. As the foaming process continues, R_cr continues to increase because the available gas is consumed for cell growth and simultaneously diffuses out of the system. Eventually, this leads to cell collapse. To preserve the cell structure before collapse occurs, it is necessary to freeze the sample, which is achieved by rapidly lowering the sample's temperature in this experiment.

Although the essential mechanisms behind cell nucleation and growth in our MNL confined foaming system have been covered in this section, further discussion is needed to explain the differences in cell density and cell size between MNL samples foamed under the same conditions. From Figure  4(A3), it can be concluded that higher cell densities are generally observed in samples with a greater number of layers. To better understand this, cell nucleation is categorized into two types: interface nucleation, where the nucleated cells are in contact with the interfaces during their nucleation and growth, and bulk nucleation, where the cells have no contact with the interfaces, as illustrated in the dotted frames in Figure 4(A1) and Figure S3 (Supporting Information).

Figure 4.

Cell density and equivalent cell diameter over time for 17 to 129‐layer samples: A1) bulk cell density, A2) interfacial cell density, A3) overall cell density including all cells across PMMA foam layers, B1) bulk equivalent cell diameter, B2) interfacial equivalent cell diameter, and B3) average equivalent cell diameter across all cells. The shaded schematic in (A1) illustrates the distinction between interface cells and bulk cells.

By comparing Figure 4 (A1) with (A2), it is observed that for samples with 17 to 65 layers, the bulk cell densities remain almost the same; however, interface cell densities increase as the number of layers increases. The similarity in bulk nucleation densities can be attributed to the identical foaming conditions applied to all samples, resulting in nearly identical values for C, P_sys, and T_sys, especially at the beginning of the foaming process. This leads to similar cell nucleation rates according to Equation (6). In contrast, the interface cell densities increase with the number of layers because the presence of more interfaces naturally results in more sites for heterogeneous nucleation, as expected. Therefore, with higher layer numbers, more cells are nucleated at the interfaces, leading to an overall increase in cell density.

Furthermore, from Figure 4(A1–A3), several key factors distinguish the 129‐layer sample from the others. First, all cells in the 129‐layer sample nucleated at the interfaces, with no bulk nucleation observed. Second, the cell nucleation period is extended, as evidenced by the presence of new cells nucleating during the 0.8–1.2 second period in the 129‐layer sample, a phenomenon not observed in the other samples. Third, the 129‐layer sample exhibits significantly higher cell nucleation compared to the other samples. These notable differences in the 129‐layer sample can be attributed to the strong confinement effect that emerges when the layer thickness approaches the interfaces’ “strong confinement range”, which will be explained further together with cell growth behavior in the following paragraphs.

In Figure 4(B1–B3), it is observed that cell size decreases consistently as the number of layers increases, with the average cell size in the 129‐layer sample being ≈34% smaller than that in the 17‐layer sample. This reduction in cell size is attributed to the confinement effect imposed by the adjacent PC/PMMA interfaces, which influences cell growth both near the interfaces and within the bulk.

To clarify how this confinement effect functions, we refer back to Equation (3), which establishes that the pressure difference between P_bub and P_local drives cell growth. An increase in P_local, indicative of local compressive stress, inhibits cell expansion. For cells growing near the PC/PMMA interfaces, where the PC layers restrict the movement of the PMMA matrix, greater force is required for the bubbles to displace the PMMA and expand. This restriction leads to a higher P_local and, consequently, decreased cell growth near the interfaces. As shown in Figure 4(B2), cell growth near interfaces is generally slower than bulk cell growth, particularly in the early stages. Interestingly, for samples with 17 to 65 layers, when the equivalent cell size reaches ≈10 µm, the growth rate of interface cells increases slightly. Since P_bub tends to decrease as cells enlarge over time, this suggests that P_local decreases when cells are ≈10 µm from the interfaces, thereby enabling more rapid growth at this stage.

Based on the above observations, it is hypothesized that, under our experimental conditions, the PC/PMMA interfaces exert a strong confinement effect within a thickness range of ≈10 µm, with the confinement becoming increasingly pronounced as the layer thickness decreases below this range. To test this hypothesis, the behavior in 129‐layer samples was examined. If our assumption holds, a layer thickness smaller than 20 µm would experience a persistent confinement effect throughout the PMMA layers, leading to two anticipated outcomes. (1) The cell growth rate would continue to decrease over time, resulting in a generally lower growth rate compared to samples with thicker layers. (2) Due to inhibited cell growth, additional gas would be available for cell nucleation, leading to a higher nucleation density.

These phenomena were clearly observed in the 129‐layer samples, which have an approximate individual layer thickness of 20 µm, thereby supporting our hypothesis regarding the confinement effect. It is important to note that the specific confinement range of ≈10 µm may be specific to the experimental conditions used in this study—namely, the foaming temperature and pressure. The viscoelastic behavior of PMMA is expected to influence this confinement range; for example, higher temperatures or increased CO₂ content could enhance chain mobility, potentially reducing the extent of the confined region. Additionally, while polymer interdiffusion at the PC/PMMA interface may contribute to this effect, prior studies have shown that the interdiffusion thickness of PC/PMMA in such multilayer systems typically remains within tens of nanometers,^{[ 76 ]} orders of magnitude smaller than the thinnest layers used in this study. Therefore, its influence is considered negligible in our context.

A clear understanding of this critical confinement thickness, governed by interfacial interactions and material properties, is essential for guiding the design and optimization of MNL solid/porous bio‐mimic structures for advanced functional applications.

3.3. Thermal Management Properties

As tiny creatures with large surface areas, butterflies must regulate heat from sunlight to avoid overheating.^{[ 77} , ^{78 ]} They achieve this by engineering the scales on their wings to selectively reflect sunlight, with both the photonic crystal and pores structures.^{[ 79 ]} Inspired by these natural adaptations, we tested our bio‐mimic structures to replicate this thermal management function and to investigate the fundamental mechanisms underlying their performance. In this section, we aim to demonstrate the thermal regulation capabilities of our solid/porous bio‐mimic samples and provide a comparison with real butterfly wing specimens.

In our previous study,^{[ 54 ]} we demonstrated both through simulation and experimental validation that a 513‐layer MNL porous/solid alternating structure can achieve a high solar reflectance of 93.5%, infrared emissivity of 91.2%, and low thermal conductivity of 29.7 mW m⁻¹·K⁻¹, owing to its tailored cell morphology, layered architecture, and optimized void ratio. Building on these findings and incorporating a deeper understanding of confined foaming mechanisms, we designed our current bio‐mimic structure that can closely match the pore size distribution of Ulysses butterfly wings, as illustrated in Figure S1 (Supporting Information). To assess how the engineered structure interacts with solar irradiation, we conducted direct observations using controlled artificial sunlight to ensure repeatability. For consistency with our prior methodology, similar fabrication techniques were employed to prepare the 129‐layer and 513‐layer bio‐mimic samples used in the thermal management experiments. These samples measured approximately 3.5 × 20 × 25 mm, with an average void fraction of ≈57% and sufficient mechanical integrity (tensile strength ≈30 MPa). The 129‐layer samples exhibited average pore sizes of ≈4 µm and a cell nucleation density of ≈10¹⁰ cells/cm³, while the 513‐layer samples maintained similar nucleation density but featured finer pore sizes ranging from 0.4 to 2 µm.

To begin, the artificial sunlight was positioned at full power (having an intensity close to 1 sun) behind the samples and used a thermal camera to directly observe the temperature profile on the front surface, as shown in Figure  5(A1–A3). In the initial images, taken 3 seconds after the light source was activated, it is observed that light penetrated both the butterfly wing specimen (A1) and the 513‐layer MNL sample (A2), causing the thermal camera to register infrared irradiance equivalent to temperature increases (ΔT) of over 70 and 50 °C, respectively. In contrast, the 513‐layer solid/porous bio‐mimic sample (A3) exhibited no noticeable change in infrared emission, indicating effective blockage of light penetration and superior thermal protection.

Figure 5.

A1) Infrared image of a dried Ulysses butterfly wing specimen under full‐power illumination over time. A2) Infrared image of the 513‐layer MNL structure under full‐power illumination over time. A3) Infrared image of the 513‐layer bio‐mimetic structure under the same conditions. White dashed lines in (A1)–(A3) outline the sample areas. A4) Maximum temperature change (ΔT) on the back surface (unilluminated side) of different samples over time. B1) Schematic of the environment box for testing temperature regulation with/without direct irradiation. B2) Temperature change (ΔT) inside the box under different covers and irradiance levels over time.

Over the subsequent 120 seconds, both the butterfly wing and the 513‐layer MNL sample continued to heat up, with the hottest region centered around the illuminated area. Conversely, the 513‐layer bio‐mimic sample displayed only a slight, uniform temperature increase across the surface, without any distinct hot spot.

In Figure 5(A4), the highest infrared signal from the back surface of all samples was recorded, including the 129‐layer MNL, 513‐layer MNL, butterfly wing specimens, the 129‐layer and 513‐layer bio‐mimic structures, and a reference three‐layer sandwich structure composed of solid PC/foamed PMMA/solid PC, representing a conventional multilayered configuration. These signals were translated into temperature variations for a comprehensive comparison. The results show that once the light source was activated, the maximum ΔT jumped to 83 °C for the 129‐layer MNL sample, 54 °C for the 513‐layer MNL sample, and 73 °C for the butterfly wing specimen. These temperatures remained nearly constant throughout the experiment. This behavior is attributed to the semi‐transparent nature of these samples, which allowed both visible light and infrared radiation from the light source to pass through, causing the thermal camera to instantly register the thermal signal.

Interestingly, based on ΔT, the 513‐layer MNL sample was 26% more effective at blocking artificial sunlight than the butterfly wing, while the 129‐layer MNL sample was 14% less effective. The enhanced protection provided by the MNL samples is due to the multiple reflections at the PC/PMMA interfaces caused by the refractive index difference, with a greater number of interfaces facilitating increased reflection.^{[ 80 ]}

As for the three‐layer sandwich reference sample, the maximum ΔT rose rapidly to 15 °C within the first second, followed by a gradual increase to 32 °C over the duration of the experiment. This delayed thermal response is attributed to the scattering effect of the foamed PMMA layer, which enhances solar reflection, and the improved through‐thickness thermal insulation provided by the porous foam structure.

In contrast, both the 129‐layer and 513‐layer bio‐mimic samples exhibited a gradual increasing temperature, with maxim ΔT of approximately 20 and 8 °C, respectively. This behavior is attributed to the porous structures in the bio‐mimic samples, which effectively scattered and reflected most of the incident energy. Despite lacking the complex photonic crystal structures found on butterfly wing scale surfaces, the 513‐layer sample demonstrated up to 9 times greater effectiveness in blocking artificial sunlight compared to natural butterfly wings. The energy that was not reflected was absorbed within the bio‐mimic structure through multiple reflections between the layers, preventing direct light penetration and significantly enhancing thermal protection. As expected, the 513‐layer bio‐mimic sample demonstrated a temperature rise ≈75% lower than that of the three‐layer sandwich reference and 60% lower than the 129‐layer bio‐mimic sample. These findings highlight the critical roles of both the high number of interfaces and smaller cell sizes (as shown in Figure S10, Supporting Information) in maximizing solar reflectivity, consistent with our previous observations that cell sizes ≈2 µm offer superior light‐scattering properties.^{[ 54 ]}

To further investigate how these properties translate into practical temperature regulation, we devised an environmental test box designed to minimize heat exchange, except through a single, well‐defined opening. This opening was completely covered by either the test sample, a conventional three‐layer sandwich structure (solid PC/foamed PMMA/solid PC), or a polyethylene (PE) film used as a worst‐case reference scenario. The schematic of this setup is shown in Figure 5(B1) (with a photo of the experimental setup provided in Figure S11, Supporting Information). The results are presented in Figure 5(B2).

The PE film, which offers minimal protection against sunlight, allowed the temperature inside the environmental box to rise rapidly. It exhibited a t_1/2 (the time required to reach 50% of the final temperature rise) of ≈20 seconds. After 10 minutes of irradiation, ΔT reached 10, 20, and 43 °C as the artificial sunlight power increased from 50% to 75% and 100% intensity, respectively. Notably, under the artificial sunlight power range chosen, the temperature increase is closely matched with that observed under real sunlight conditions during a sunny day (Figure S12, Supporting Information).

In comparison, the conventional three‐layer sandwich structure provided moderate solar protection, with final ΔT values of 6.3, 13, and 28.8 °C under the same illumination levels, and a t_1/2 of ≈40 seconds (i.e., twice as long as that of the PE film), indicating a significant improvement in thermal buffering.

Surprisingly, the thin butterfly wing specimen demonstrated slightly better performance than the much thicker three‐layer sandwich structure. It also exhibited a t_1/2 of also ≈40 seconds, with final ΔT values of 4.9, 9.7, and 19.6 °C at increasing light intensities. These results represent roughly a 25% reduction in temperature rise compared to the conventional three‐layer sandwich structure, highlighting the natural effectiveness of butterfly wing microarchitecture in managing solar heat gain. It is important to note, however, that the butterfly sample used was a static, dried specimen with substantially lower thickness than our fabricated MNL samples and lacked any biological activity (e.g., fluid transport, scale mobility). These constraints may underestimate the full thermal buffering capacity of butterfly wings in living organisms.

In contrast, the 513‐layer bio‐mimic samples exhibited superior thermal regulation, achieving a t_1/2 of ≈165 seconds (i.e., eight times longer than the PE film). The final amount of temperature increases were 2.2, 4.2, and 10 °C under varying irradiation powers, indicating an approximate 80% reduction compared to the PE film, a 65% reduction compared to the sandwich structure, and a 50% reduction relative to the butterfly wing specimen. These results are consistent with the infrared imaging data, confirming that the 513‐layer bio‐mimic structure provides significantly enhanced protection and temperature regulation against intense sunlight, outperforming even natural butterfly wings.

Furthermore, when the artificial sun is turned off, the temperature beneath the bio‐mimic samples decreases much more slowly compared to the other samples, owing to the superior thermal insulation properties of the bio‐mimic structure. This delayed temperature drop is also essential for thermal regulation, helping to maintain a more stable internal temperature over time.

To further investigate the thermal insulation properties of our bio‐mimic samples, particularly the anisotropic thermal conductivity introduced by the layered structure, thermal conductivity experiments were conducted using a 90 °C hot plate as the heat source. These experiments aimed to examine heat conduction through the thickness direction and the in‐plane directions, as shown in Figure  6 .

Figure 6.

A1) Infrared images showing heat conduction through the thickness direction of a 513‐layer MNL structure after contact with a 90 °C hot surface. A2) Infrared images of a 513‐layer bio‐mimetic structure under the same conditions. A3) Temperature change (ΔT) measurements at the center of both samples and additional 129‐layer samples over time. B1) Infrared images showing in‐plane heat conduction through a 513‐layer MNL structure over time after contact with a 90 °C hot surface. B2) Infrared images of a 513‐layer bio‐mimetic structure under the same conditions. B3) Temperature change (ΔT) measurements at ≈10 mm from the hot surface over time for both samples.

Comparing Figure 6 (A1) and (A2), it is observed that the 513‐layer bio‐mimic sample exhibits significantly lower thermal conductivity compared to the 513‐layer solid MNL sample. This reduction is attributed to the foamed PMMA layers, which effectively hinder heat conduction through the thickness direction.

In Figure 6(A3), the surface temperature over time for the 129‐layer and 513‐layer samples was compared. The results indicate that thermal conductivity through the thickness direction is similar for both the 129‐layer and 513‐layer MNL samples, as anticipated, since the additional interfaces at these layer thicknesses have a limited impact on thermal conductivity.^{[ 81} , ^{82 ]} In contrast, the 129‐layer bio‐mimic sample exhibited a 28% lower ΔT compared to the MNL samples, while the 513‐layer bio‐mimic sample showed a 44% lower ΔT than the MNL samples. Additionally, when comparing the two bio‐mimic samples, the 129‐layer bio‐mimic sample demonstrated a 25% higher ΔT than the 513‐layer bio‐mimic sample. This suggests that the smaller cell size (0.4–2 µm) in the 513‐layer bio‐mimic structure is more effective at reducing heat conductivity than the larger cell size (≈4 µm) in the 129‐layer bio‐mimic sample.

In contrast, for the lateral direction, as shown in Figure 6(B1–B3), there is no significant difference in thermal conductivity between the MNL samples and the bio‐mimic samples. This is because heat can travel laterally through the continuous PC solid layers, bypassing the porous PMMA layers.

The observed anisotropic thermal conductivity arises from the unique architecture of the bio‐mimic structure. In the through‐thickness direction, heat must traverse alternating porous PMMA layers and solid PC layers. The PMMA layers, featuring well‐defined closed‐cell morphologies, serve as effective thermal insulators,^{[ 83} , ^{84 ]} while the solid PC layers provide relatively higher thermal conductivity.^{[ 54 ]} This alternating low–high conductivity pathway disrupts uniform heat flow through the thickness, significantly reducing the effective thermal conductivity in that direction. In contrast, continuous PC layers enable more efficient heat conduction in the in‐plane direction. Such anisotropic behavior aligns with prior findings in multilayered systems where contrasting thermal properties between layers result in direction‐dependent heat transfer performance.^{[ 85} , ⁸⁶ , ⁸⁷ , ^{88 ]}

Such anisotropic thermal conductivity, inspired by the bio‐mimic structure of butterfly wings, is highly desirable in various applications, such as the thermal management of electronics^{[ 59 ]} and aerospace engineering.^{[ 60 ]}

4. Conclusion

Inspired by the sophisticated architecture of Ulysses butterfly wing scales, this study developed bio‐mimic structures with alternating layers of PC and PMMA by combining MNL coextrusion with controlled polymer foaming. A comprehensive investigation of the confined foaming process was conducted, revealing the ability to finely tune cell size to match the pore size distribution found in natural butterfly wings. This bio‐inspired configuration offers unique advantages in thermal regulation, highlighting the versatility and potential of MNL structures for advanced material applications.

In situ visualization experiments were conducted on this structure for the first time to investigate the confinement effect of adjacent PC layers on the foaming behavior of PMMA layers by varying the individual layer thickness from 20 to 200 µm under controlled foaming conditions (90 °C, 10 MPa). The results reveal that the rigid PC layers function as both heterogeneous nucleation sites and confinement barriers, particularly restricting cell growth within ≈10 µm from the PC/PMMA interfaces. This restriction becomes increasingly pronounced closer to the interface, significantly suppressing cell expansion and leading to the formation of distinctive morphologies, such as single rows of cells observed in the 129‐layer sample. This confinement‐driven control of nucleation and growth enables the creation of bio‐mimic structures with cell size distributions closely resembling those found in butterfly wings.

The thermal regulation experiments underscore the exceptional performance of the bio‐mimic design, particularly in comparison to conventional polyethylene (PE) film, a three‐layer sandwich structure, and natural butterfly wing specimens. When subjected to artificial sunlight, the 513‐layer bio‐mimic sample exhibited temperature rise reductions of approximately 80%, 65%, and 50% relative to the PE film, sandwich structure, and butterfly wing, respectively. Additionally, the time required to reach half of the maximum temperature rise (t_1/2) was extended to ≈165 seconds, significantly longer than the 20 seconds for the PE film and 40 seconds for both the sandwich structure and butterfly wing. This substantial delay in heat accumulation underscores the effectiveness of the alternating solid/porous architecture in reflecting and scattering solar radiation, providing superior thermal protection beyond naturally evolved structures.

In addition, anisotropic thermal conductivity experiments in the through‐thickness direction revealed that the 513‐layer bio‐mimic sample exhibited a 44% lower ΔT (temperature change) than the solid MNL samples and a 25% lower ΔT compared to the 129‐layer bio‐mimic sample, indicating that smaller pore sizes more effectively reduce thermal conductivity through the thickness direction. In contrast, no significant difference was observed in lateral thermal conductivity between the MNL and bio‐mimic samples, owing to the continuous PC layers that facilitate lateral heat transfer.

The findings from this study not only offer a pathway to replicating the intricate microstructure of Ulysses butterfly wings—by advancing the understanding of confined foaming mechanisms—but also successfully emulate their adaptive functions, including efficient light scattering, enhanced thermal insulation, and anisotropic heat conduction. This bio‐inspired strategy highlights the advantages of achieving complex functionalities through micro‐ and nano‐scale structural design and opens promising new directions for the development of high‐performance materials.

Conflict of Interest

The authors declare no conflict of interest.

Author Contributions

J.Z. conceptualized the idea for the study, designed the methodology, performed the investigation, and wrote the original draft. L.Z. designed the methodology and performed the investigation. J.L., J.K., and A.F. performed the investigation. N.D.S. wrote the original draft. L.B. performed the investigation and visualization. P.C.L. conceptualized the idea for the study; wrote, reviewed, and edited the manuscript; performed the supervision, acquired the resources, and performed the funding acquisition.

Supporting information

Supporting Information

Zhao J., Zhang L., Lee J. U., et al. “Butterfly Wing Microstructure Inspired Solid/Porous Alternating Layered Structures: In Situ Visualization of Confined Foaming.” Small 21, no. 40 (2025): e08472. 10.1002/smll.202508472

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.