1 Introduction

Thermal insulation materials are very attractive in aerospace, energy storage and other fields [1,2,3], and for people living and working in cold or high temperature environments, thermal insulation is also very important [4,5,6,7,8]. Body temperature is maintained by metabolism, and the body feels comfortable at 28–30 °C. Under extremely cold conditions, it is necessary to prevent the loss of hot air in the body. However, in the hot environment, people also hope that hot air will be emitted from the body, and excessive heat that cannot be emitted to the outside will bring serious problems to the human body [9]. In extremely cold regions, special protective clothing must be worn for activities. In case of strong wind, rain or snow, it will aggravate the low temperature and lead to human death [10]. Therefore, thermal insulation materials have attracted the attention of researchers. There are three forms of heat transfer, namely heat conduction, heat convection and heat radiation. In heat conduction, the thickness and density of fabric are the main factors affecting the heat loss because the air between fibres has low heat conductivity. In thermal convection, heat is mainly transferred by gas convection; for thermal radiation, materials with high reflectivity (such as metal fibres) can be used for heat insulation. Phase change materials are also applied in thermal protection. In a hot environment, phase change materials absorb heat, and on the contrary, they absorb cold air to maintain appropriate heat [11, 12]. At present, the most effective measure of heat insulation is to reduce heat transfer. It is understood that air, phase change materials, ice and water have been used as refrigerants for insulation [13,14,15].

Understanding the structure–function relationship is the key to developing new materials. As we can see in many available technologies, animals and plants in nature are the best source of inspiration [16,17,18,19,20]. Many organisms in nature have heat insulation functions, and polar bears are a typical example. In recent years, many heat insulation materials inspired by polar bear hairs have emerged [14, 21,22,23,24,25]. For example, Zhan et al. [22] prepared carbon nanotube aerogels with dual function as thermal insulation layer and absorption layer. Wang et al. [14] prepared multifunctional polyimide aerogel textiles with thermal adjustment in extreme environments. Cui et al. [24] prepared an insulation textile by imitating the structure of polar bear hair. There are also penguins, cocoons and other organisms with heat insulation protection in nature. They have a unique structure which determines their unique performance. As reported in the literature, the polar bear hair has membrane pore structure, the penguin feather has inverted hook structure, and the cocoon layer is tight loose [26,27,28,29,30,31,32,33]. The hierarchical structure endows them excellent thermal insulation performance. Natural hierarchies are ubiquitous, such as rough surface of lotus leaf hierarchy, honeycomb, spider web fractal structure, pore structure of wood and bone hierarchies, etc. [34,35,36,37,38,39]. In recent years, many methods have been used to mimic hierarchical structures, such as micro-emulsion electrospinning, coaxial electrospinning, multi-fluidic electrospinning, freeze-spinning, chemical deposition and template method [24, 40,41,42,43,44,45]. Hierarchical structure is not only widely applied in the field of heat insulation, but also in infrared stealth, self-cleaning, energy storage and so on [24, 44,45,46,47,48,49]. For example, Fan et al. [49] developed a coral-shaped porous hierarchical LiFePO4–graphene composite to improve the performance of LiFePO4 cathode, enabling it to provide 161 mAh g−1 and 123 mAh g−1 reversible capacities at + 60 °C and − 40 °C, respectively.

Hence, this review aims to comprehensively introduce the research progress of bionic hierarchical structure, so as to explore the potential of bionic hierarchical structure with light weight and excellent performance in the field of thermal insulation protection. After this section, Sect. 2 presents the morphological characteristics of the common hierarchical structure in nature used in thermal insulation. In Sect. 3, the heat insulation mechanism of natural hierarchical structure is discussed, and the thermal performance of hierarchical structure is analysed by fractal calculus. Section 4 provides several common preparation methods of biomimetic hierarchical structure. Thereafter, the application of bionic hierarchical structure in various fields is highlighted in Sect. 5, particularly in heat insulation, infrared thermal stealth and other fields (Fig. 1). Finally, the hierarchical structure is summarised and prospected.

Fig. 1
figure 1

Overview of hierarchical structure from morphology characterisation, thermal insulation mechanism, preparation method and application

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2 Natural Hierarchical Structure for Heat Insulation

2.1 Polar Bear Hair

The polar bear hair has a unique layered structure, which is composed by cuticle, cortex and medulla. The diameter of the medulla in the polar bear hair is about 20–30 µm, accounting for one-third to half of the fibre diameter. The cortex is composed of cortical cells and tightly packed with bundles of keratin fibres [30]. Additionally, polar bear hair is made of twisted peptide chains of alpha-keratin, which belongs to a coiled-coil α-helix protein [50]. Figure 2 shows the microstructure of polar bear hairs. We can see the scale pattern on the rough surface of polar bear hairs presented in Fig. 2a. Figure 2b, c exhibits the special core–shell structure. The porous core layer has obvious lamellar structure, and the shell layer is formed by microfibril aggregation (Fig. 2c) [30, 51].

Fig. 2
figure 2

Microstructures of polar bear hairs [30, 51]

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2.2 Silkworm Cocoon

The thin and light-weight cocoon can protect the silkworm from predator attacks and extreme weather conditions, whilst supporting its metabolic activity. This is due to the unique hierarchical structure of cocoons [32, 52,53,54]. Blossman-Myer et al. [52] explored the cocoon’ structure and its influence on the diffusion of oxygen and water vapour through the wall. The study showed that the fibre diameter of the outer layer of cocoon was 26 ± 1 μm, whilst that of the inner layer of cocoon 16 ± 1 μm (see Fig. 3a). The density of inner fibre (20.8 ± 1.2 mm−1 transect) exhibits significantly higher than that of outer fibre (8.3 ± 0.2 mm−1 transect). This hierarchical structure does not hinder the diffusion of oxygen and water vapour, providing mechanical protection for the pupa. Zhang et al. [53] studied the shapes of four kinds of cocoons, as shown in Fig. 3b–e. The inner structure of all four cocoons is compact, whilst the outer structure is relatively loose. Liu et al. [32] observed the hierarchical structure of the whole cocoon, which was divided into 15 layers from inside to outside. The combination of silk became more and more loose, and there were more and more holes. The bonding network formed amongst the innermost fibres of the cocoon is most prominent.

Fig. 3
figure 3

Morphologies of silkworm cocoons: a The cross section of the whole cocoon wall [52]. b B. mori, c S. cynthia, d A. pernyi, and e A. mylitta cocoons. The outer and inner surface morphologies of each cocoon type are shown in the third row and the fourth row, respectively [53]

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2.3 Penguin Feather

The penguin feathers have complex structures which vary by penguin species and different parts of the penguin’s body, as they serve many functions including thermal insulation and water resistance [55]. Penguin feather, similar to those of other birds, are hierarchically ordered with the branched structure built around the main shaft. All feathers consist of a shaft with calamus, which is located closer to the skin of birds. With regard to the overall structure, barbs come from rachis, and barbules from barbs. From barbules, hamuli protrudes, also known as the hooks (see Fig. 4a–c). [30, 56] The feathers are hierarchically constructed of the primary barb, which are supported by rachis, with the main cortex based on the cellular core. From the longitudinal section of penguin feathers, it can be seen that the pores inside the feather axis gradually increase from the bottom to the top of the inverted hook, which clearly shows the transition between the calamus, the axis and the two structures (see Fig. 4d). The rachis is a well-organised porous structure with an average inner diameter of 11 ± 4 μm. The bulbs were divided into large empty sections separated by a lamellar keratin membrane (see Fig. 4h), which decreased with the approach of axons [30].

Fig. 4
figure 4

Microstructures of penguin feathers. a Showing barb and barbule. b Zoom in to barb with a diameter of 12 mm and with its wrinkled surface. c Close-up of barbule with hamuli indicated with arrows. d The difference between the rachis and cortex. e Foamy structure of the rachis with pores. f zoomed in, rounded cross sections of pores made of keratin fibres, with strut formed between pores. g Histogram of pore diameters, giving the average values of 11 ± 4 μm, and h calamus with divided cortex, with the cuticula membranes [30]

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2.4 Wool Fibre

The wool fibre has a typical hierarchical structure. He et al. [57] explored the transformation mechanism of the hierarchical structure of wool fibre. As shown in Fig. 5, the main component of wool fibre is low-sulphur α-keratins. The three α-helix macromolecules are tightly twisted together to form protofibril, and multiple protofibrils are assembled into microfibrils. In the cortical cells, the microfibrils spiral into macrofibrils and eventually form wool fibres. Wool has positive cortex and sub-cortex. The positive cortex cells of wool are composed of macrofibrils with a diameter of about 200 nm. Macrofibril is also composed of microfibrils with microfibrils with a diameter of about 7–8 nm. Subcortical cells are directly composed of microfibrils, which are also composed of protofibrils with a diameter of about 2 nm [58, 59].

Fig. 5
figure 5

Hierarchical structure of wool fibres [57]

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In addition, there are many complex layered structures in natural organisms, such as natural wood with layered cellulose nanofibers [60], grapefruit peel with gradient porosity [61], bones and loofah with layered pore structures [39], beetle forewings with intercalated structures [62], leather layered fibres with multi-level porosity [63], micro/nanoscale structure with dual scale arrangement of multi-level structure on the surface of lotus leaf [64], desert silver ants with dense triangular arrays of hairs [65, 66], and stomatopod clubs with periodic spiral arranged nanofiber matrix [67]. These layered structures with special complexity have shown excellent performance in thermal insulation, energy storage, catalysis, and self-cleaning, which have attracted the interest of a wide range of researchers.

3 Fractal Model of Heat Transfer in Hierarchical Structure

3.1 Insulation Mechanism

Heat transfer is the process of heat transfer from high temperature region to low temperature region caused by temperature difference. General heat transfer can be divided into three basic modes: heat conduction, heat convection and heat radiation. Fibres and their fibre aggregates are usually mixtures of solids and gases or porous materials. Theoretically, the thermal conductivity of a porous fibre (λfiber) is determined by the sum of thermal convection (λconv), solid (λsolid) and air (λair) thermal conduction, and thermal radiation (λrad) [24, 68, 69].

$$ \lambda_{{{\text{fiber}}}} = \lambda_{{{\text{conv}}}} + \lambda_{{{\text{solid}}}} + \lambda_{{{\text{air}}}} + \lambda_{{{\text{rad}}}} . $$
(1)

Reducing heat transfer is the most effective heat insulation measure at present. The heat insulation mechanism of hierarchical structure also achieves the purpose of heat insulation by reducing heat transfer. Like the membrane pore hierarchy of polar bear hair, air cannot flow in the micropores, and the thermal convection of porous layered fibres bionic polar bear hair is greatly limited. The thermal conductivity of air is much lower than that of solid. At the same time, due to the porous layered structure, there are a large number of solid–gas interfaces, which improves the reflectivity of thermal radiation and makes fibre conducive to human heat insulation (Fig. 6a) [24]. Hierarchical structure can also slow down the solid heat transfer efficiency by designing a large number of tortuous solid conduction paths [31, 70]. Xue et al. [31] studied the heat insulation performance of domesticated silkworm cocoon and tussah cocoon by fractal calculus. The silkworm cocoon has a circular fibre cross section, and the air flow path in its hierarchical structure is indicated by the green solid line. Air is transferred through line-to-line contact between circular cross sections. The tussah cocoon presents a hierarchical structure of flat ribbon fibres, where air is transmitted through face-to-face contact between flat ribbon fibres, causing confusion in the air transfer in the hierarchical structure. The path is similar to a maze, making it difficult to transfer from the outer layer to the inner layer (green solid line in Fig. 6b). The results showed that the hierarchical structure of the cocoon made the two kinds of cocoons have good heat insulation performance. The hierarchical structure of tussah cocoon with the flat band cross-sectional fibre is different from that of domesticated silkworm cocoon with the round ones. The heat insulation performance of tussah cocoon presents better due to the complex conduction path of the flat band fibre structure. In addition, penguin feathers form a hierarchical structure through the interaction of twigs, and there are a large number of residual air and solid–gas interface. Increasing the thermal resistance of the interface can effectively shield thermal radiation and reduce heat transfer [71]. When the atmospheric environment is cold and dry, the matrix phase of wool fibre has less moisture content, more static air, the thermal conductivity of amorphous phase decreases, and most of the heat flow is maintained and uniformly dispersed in the tree-like channel network, so as to reduce heat transfer and achieve heat insulation effect [72]. In summary, the hierarchical structure can reduce the thermal conductivity by retaining a large amount of static air, slow down the heat transfer rate through a large number of tortuous conduction path, increase the solid–gas interface, improve the reflectivity of thermal radiation, and effectively shield the three forms of thermal radiation to reduce heat transfer and achieve the purpose of heat insulation.

Fig. 6
figure 6

a Heat insulation diagram of hierarchical structure [24]. b The permeability diagram of silkworm cocoon and tussah cocoon and the heat transfer in continuous medium (such as a metal) [31]. c The schematic of heat transfer in hierarchic porous media. Curves β, γ, δ and η are: continuous media, fractal media with one, two, and three iterations, respectively. On the right, squares A, B, and C correspond to curves β, γ, and δ, respectively [54]. d Hollow and membrane structure of a polar bear hair, T1 is the body temperature; and T6 is the environment temperature [74]. e Hierarchical structure of wool fibre [72]

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3.2 Fractal Model

With the extensive study of the fractal model of heat conduction by researchers, fractal order calculus has become a relatively mature theory in the field of heat conduction [73,74,75,76,77,78,79]. Fractal calculus has been widely used to reveal the thermal properties of complex porous media. For example, thermal conductivity of fibres is described by fractal derivative model. The heat transfer of hierarchical structures is also studied by fractal models, such as self-similarity of cocoons, membrane pore structure of polar bears and tree-like hierarchy of wool [31, 54, 72,73,74,75]. Fei et al. [54] studied the heat transfer performance of cocoons using fractal theory and explained the fractal heat transfer characteristics of cocoons in extreme environments. As shown in Fig. 6c, with the increase of iteration times, the slope of temperature change (ΔT) tends to be as small as possible, and the thickness of cocoons is thin, but the heat insulation performances prove good. Wang et al. [74] discussed the heat transfer fractal model of polar bear hair. The membrane pore structure of polar bear hair (Fig. 6d) plays a key role in preventing body temperature loss and has good heat insulation function. Fan et al. [72] studied the thermal properties of wool fibres based on fractal characteristics (Fig. 6e). The results show that the heat transfer along wool fibre is extremely slow, indicating that it has good thermal insulation performance. These hierarchies present organisational self-similarity, that is, obvious fractal structure. The fractal derivative models are all started from the Fourier heat conduction law, and the fractal dimension is close to the average golden value of 1.618 [54, 72,73,74]. Therefore, taking polar bear hair as an example, fractal calculus was applied to reveal the thermal insulation performance of the hierarchical structure of polar bear hair membrane pores.

Fourier's law of thermal conduction is expressed as [73]:

$$ q = \lambda \frac{\Delta T}{{\Delta x}}, $$
(2)

where q represents the heat flux, λ represents the thermal conductivity of the material, and \(\frac{\Delta T}{{\Delta x}}\) is the temperature gradient. For continuous media, it can be written as [73]:

$$ q = \lambda \frac{{{\text{d}}T}}{{{\text{d}}x}}. $$
(3)

The heat conduction of a single continuous medium can be written in the form

$$ \frac{{{\text{d}}\left( {\lambda \frac{{{\text{d}}T}}{{{\text{d}}x}}} \right)}}{{{\text{d}}x}} = Q, $$
(4)

where Q is the heat source.

Heat conduction of polar bear hair using fractal derivative [73, 80]

$$ \frac{{{\text{d}}\left( {\lambda \frac{{{\text{d}}T}}{{{\text{d}}x^{\alpha } }}} \right)}}{{{\text{d}}x^{\alpha } }} = Q, $$
(5)

where α denotes the fractal dimension of polar bear hair. The boundary condition is:

$$ T(0) = T_{0} , $$
(6)
$$ T(L) = T_{6} , $$
(7)

where T0 is the body temperature of the polar bear, T6 is the environmental temperature, L is the critical length of the hair. The fractal derivative is defined as [73, 80,81,82]:

$$ \frac{{{\text{d}}T}}{{{\text{d}}x^{\alpha } }} = \Gamma (1 + \alpha )\mathop {\lim }\limits_{{\Delta x = x_{B} - x_{A} = L_{0} }} \frac{{T(x_{B} ) - T(x_{A} )}}{{(x_{B} - x_{A} )^{\alpha } }}. $$
(8)

L0 represents the lowest level distance, beyond which there is no physical meaning.

With boundary conditions, the solution of Eq. (8) is [73]:

$$ T = \frac{Q}{2\lambda }x^{2\alpha } + \frac{{T_{6} - T_{0} - \frac{Q}{2\lambda }L^{2\alpha } }}{{L^{\alpha } }}x^{\alpha } + T_{0} . $$
(9)

The effective length of polar bear hair can be found by fractal dimension, so the temperature distribution along polar bear hair can be written as [73]:

$$ T = \frac{Q}{2\lambda }x^{2\alpha } + T_{0} . $$
(10)

It can be seen that

$$ \frac{{{\text{d}}T(0)}}{{{\text{d}}x}} = 0 $$
(11)
$$ \frac{{{\text{d}}^{2} T(0)}}{{{\text{d}}x^{2} }} = 0, $$
(12)
$$ \frac{{{\text{d}}^{3} T(0)}}{{{\text{d}}x^{3} }} = 0. $$
(13)

Formulae (11)–(13) explain that the surface temperature of polar bear hairs varies very slowly regardless of ambient temperature [73]. Thus, fractal calculus discloses the thermal insulation performance of the membrane pore hierarchy of polar bear hair.

4 Preparation of Bionic Hierarchy

Electrospinning and freeze-spinning are commonly used to prepare biomimetic complex hierarchies, such as polar bears and penguin feathers. Electrospinning is considered to be a simple and effective method for the fabrication of complex microstructures [25, 35, 41, 44, 45, 83, 84]. Process parameters, such as relative humidity and voltage polarity, have a significant impact on the formation of electrospun fibre. Humidity can affect the evaporation rate of the solvents and the solidification rate of the fibres, thus affecting the polymer fibre properties [85, 86]. Voltage polarity can enhance the mechanical properties of polymer fibres [87]. It is highly favoured by researchers to prepare biomimetic materials by high pressure. However, in large-scale production, there are challenges in the combination of excellent thermal properties and weaving. Freeze-spinning is a combination of solution spinning and directional freezing technology, which can realise continuous large-scale production [14, 24, 51]. In addition, there are other methods, such as chemical deposition, template method, etc. [40, 42, 43] (see Table 1).

Table 1 Summary of preparation methods of bionic hierarchical structure
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4.1 Electrospinning

4.1.1 Microemulsion Electrospinning

Microemulsion electrospinning (ME-ES) can fabricate superporous inorganic oxide nanofibers with hierarchical internal structures. The ME-ES solution composed of metal alkoxide and paraffin oil was fluently electrospun to nanofibers. After calcination, the hybrid nanofibers decomposed to multilevel porous inorganic nanofibers. What's more, porous nanofibers with diameters of below 100 nm are also successfully generated by this simple ME-ES approach. Chen et al. [41] prepared hierarchical porous fibres by ME-ES (see Fig. 7a). Appropriate amount of polyvinylpyrrolidone (PVP) and surfactant cetyltrimethylammonium bromide (CTAB) was dissolved in the mixture of ethanol and acetic acid, and then Ti(OBu)4 was slowly added to form a homogeneous solution. Then, paraffin oil was mixed into the solution under the agitation to obtain a transparent golden yellow microemulsion, which was electrospun into hybrid nanofibers. Hierarchical porous TiO2 nanofibers with diameters of 20–80 nm were successfully prepared after calcination. The prepared TiO2 nanofibers by Chen et al. [41] have hierarchical pore structure similar to polar bear hair. The cross section (Fig. 7b) of TiO2 nanofibers clearly displays the porous structure inside the fibre and has nanopores. And these holes are oriented along the fibre and can be hundreds of nanometers in length, as shown in the longitudinal cross-sectional scanning electron microscopy (SEM) image of the fibres (Fig. 7c). Kang et al. [25] successfully fabricated porous zirconia fibres with multi-cavity hierarchical structure of bionic polar bear hair by ME-ES. The average diameter of the bionic fibre was about 120 nm, and it had a low thermal conductivity of 0.075 W m−1 K−1.

Fig. 7
figure 7

a Schematic diagram of hierarchical porous fibres prepared by micro-emulsion electrospinning. b Cross-section SEM image of fibres showing a porous inner structure and c a broken fibre showing aligned pores along the fibre [41]

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4.1.2 Coaxial Electrospinning

Coaxial electrospinning is a technique for preparing core–shell fibres by setting two concentric jets [88]. Recently, Burgard et al. [44] combined coaxial electrospinning with self-assembly to fabricate penguin feather-like fibres. Polystyrene (PS) fibres of N,Nʹ,N″-Tris(1-(methoxymethyl)propyl)benzene-1,3,5-Tricarboxamide (BTA) seeds (about 1.6 μm in diameter) were obtained by coaxial electrospinning (seed PS fibres, Fig. 8a) and contacted with BTA solution. As a result of this process, the BTA fibres (about 200 nm in diameter) were formed on the seed PS fibres, showing an isolated fibrous branch similar to the inverted hook hierarchy of penguin feathers (Fig. 8b).

Fig. 8
figure 8

a Process diagram of preparing penguin-like fibres. b Optical microscopy images (from left to right) of non-seeded BTA fibrils grown on a glass slide, non-seeded BTA fibrils grown on a glass slide with electrospun neat PS fibres (the blue arrows indicate the locations of PS fibres) and mesostructured nonwoven [44]. c Process diagram of preparing multi-channel fibre and d SEM images of TiO2 fibres with different numbers of channel [45]

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4.1.3 Multifluidic Electrospinning

Multifluidic electrospinning is commonly used to prepare multi-channel nanofibers [89]. Zhao et al. [45] successfully spun TiO2 fibres with multi-channel hierarchical structure by multi-fluid electrospinning technology. As shown in Fig. 8c, polyethylene pyrrolidone/titanium isopropyl alcohol sol was used as shell fluid and paraffin oil as core fluid. The two fluids were insoluble with each other and formed solid multi-channel fibres under electrostatic repulsion. After calcination, the core fluid components were removed to obtain multi-channel hierarchical fibres (see Fig. 8d).

4.2 Freeze-Spinning

Freeze-spinning technology is to extrude the dispersed aqueous solution with good viscosity at a constant speed through the injector, and form a stable liquid filament controlled by a programmable pump. When the conductor slowly passes through the cold copper ring, the ice crystals are oriented and preferentially grow into layered patterns in the conductor, and the solute is discharged and assembled into form template ice, as displayed in Fig. 9a [14, 24, 51]. Cui et al. [24] successfully achieved continuous large-scale preparation of biomimetic fibres with arranged porous structures using freezing spinning technology, imitated polar bear hair, and studied the effect of freezing temperature on its morphology and the pore arrangement on its mechanical properties. Figure 9b–d exhibits clearly the layered pores arranged along the axis of biomimetic fibres. The fibres prepared at − 40, − 60, − 80 and − 100 °C had the ordered porous microstructure, which was better in strength and modulus than those at − 196 °C with random pores (see Fig. 9e–g). Afterwards, Wang et al. [14] successfully got polyimide aerogel fibres with excellent thermal insulation performance and high temperature resistance using freeze-spinning technology to mimic the porous hierarchy of polar bear hair. Shao et al. [51] fabricated biomimetic porous hierarchical fibres by freezing spinning, and knitted fabrics with excellent thermal insulation properties in air and water environments.

Fig. 9
figure 9

a Schematic diagram of freeze-spinning technology. b Radial cross-sectional SEM image showing the typical structure of a biomimetic porous fibre. c, d X-ray computed microtomography images showing the aligned lamellar pores within the biomimetic fibre along its axial direction. e Radial cross-sectional SEM images showing different porous structures of biomimetic fibres prepared at different freezing temperatures: − 40, − 60, − 80, and − 100 °C, respectively. f Radial cross-sectional SEM image and longitudinal-section SEM image showing random porous structure of fibre prepared at − 196 °C. g The average tensile strength and elongation of the fibres are correlated with their pore size [24]

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4.3 Other Methods

In addition, there are other methods to prepare similar structures like polar bear hairs. For example, inspired by the membrane pore structure of polar bear hair, Du et al. [40] deposited silicon dioxide on the carbon nanoskeleton by chemical vapour deposition, and gained multifunctional silicon dioxide nanotube aerogels by calcination (Fig. 10a–d). Zhan et al. [42] developed a template synthesis method based on two-step solution by applying tellurium nanowires as sacrificial templates (Fig. 10e). First, the hydrogel with core–shell structure of carbon-shell tellurium nanowire core was made. Second, dried. Finally, porous carbon tube aerogels with similar structure to polar bear hair were formed by calcination.

Fig. 10
figure 10

a A schematic diagram for preparation of silica carbon nanotube aerogels with membrane pore structure. b CA has super black appearance and slender skeleton. c CA/SiO2 aerogel does not show obvious surface changes, but skeletons become smooth and reinforced. d SNTA has high transparency, superhydrophobicity, and nanotube skeletons [40]. e Bioinspired manufacturing process of porous carbon aerogels [42]

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5 Application of Hierarchical Structure

5.1 Thermal Insulation and Infrared Stealth

Polar bears living in extremely cold environment show amazing thermal insulation and infrared stealth ability, which is due to the special membrane pore structure of polar bear hair. In view of low thermal conductivity, it can effectively reflect the infrared radiation from the body [26, 28, 29, 90]. Such unique porous hierarchies are commonly used in the fields of thermal insulation and thermal infrared stealth. Cui et al. [24] prepared biomimetic porous hierarchical fibres and woven them into fabrics using silk fibroin and chitosan as raw materials through biomimetic membrane pore hierarchy of polar bears, and explored the effects of pores and layers on the thermal insulation properties of the fabric. Studies have revealed that textiles woven by fibres with smaller pores have good thermal insulation properties, and the thermal insulation effect is better with the increase of layers (see Fig. 11a). Wang et al. [14] investigated the thermal insulation properties of textiles woven by polyimide fibres with porous hierarchical structure, and compared them with polyester textiles. At low temperature, the average surface temperatures of polyimide and polyester textiles are 23.4 and 23.6 °C, respectively, indicating that the insulation properties are similar. Polyester textiles have melted at 300 °C, whilst polyimide textiles still exhibit thermal insulation due to their thermal resistance (Fig. 11b). When the ambient temperature increased from 25 to 300 °C, the thermal conductivity of polyimide textiles increased from 36.4 to 160.7 mW m−1 K−1 (Fig. 11c). In addition, Shao et al. [51] studied the underwater thermal insulation performance of porous hierarchical textiles. In an underwater environment, air is trapped inside porous fibres, between fibres and rough fibre surfaces (Fig. 11d). As shown in Fig. 11e, when the water temperature was set as 5 °C, 30 °C and 50 °C, the underwater heat insulation capacities of hydrophilic porous textiles, superhydrophobic nonporous textiles and superhydrophobic porous textiles were compared. Porous superhydrophobic textiles have better thermal insulation than the other two textiles when the water temperature is higher than room temperature.

Fig. 11
figure 11

a Infrared images of textiles woven from different porous fibres [24]. b Optical and infrared images of the polyimide and polyester textiles on a hot stage. c Thermal conductivity of the polyimide textile at various environmental temperatures [14]. d Schematic illustration of water on the superhydrophobic porous textile. e Temperature statistics beneath hydrophilic porous textile, superhydrophobic nonporous textile and superhydrophobic porous textile in underwater thermal insulating test with water temperature of 5, 30 and 50 °C [51]. f Infrared emissivity and thermal conductivity of porous ZrO2 fibres. g Schematic diagram of pore formation process, thermal conductivity and infrared stealth mechanism of porous ZrO2 fibres [25]. h Optical and infrared image of a rabbit before and after wearing the commercial polyester textile and the textile woven with biomimetic porous fibres and i the rabbit wearing the biomimetic thermal stealth textile is invisible by the infrared camera, regardless of the background temperature (40, 15, − 10 °C, respectively) [24]

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Inspired by the infrared stealth of polar bears, Kang et al. [25] simulated the polar bear hair structure, prepared biomimetic porous hierarchical Zirconia (ZrO2) fibre, and studied its infrared stealth performance. The results indicate that when the test temperature increases from 25 to 150 °C, the thermal conductivity of zirconia porous fibre increases slightly in the range of 0.075–0.0806 W m−1 K−1, and the infrared emissivity in the range of 3–5 μm decreases from 0.661 to 0.598 (Fig. 11f). The schematic diagram of pore formation, thermal conductivity and infrared stealth mechanism of porous ZrO2 fibre is shown in Fig. 11g. Due to the existence of a large number of pore structures inside and on the surface of ZrO2 fibre, the solid–gas interface and phonon scattering increase, so the thermal conductivity and heat transfer coefficient decrease. In addition, Cui et al. [24] also studied the infrared stealth performance of porous fibres with bionic polar bear pore structure. Compared with polyester textiles, the rabbit wearing bionic porous textiles is almost integrated with the background under infrared thermal imager, and the thermal stealth performance of the textiles can be applied at − 10 to 40 °C, which can be used in modern military fields (Fig. 11h, i).

5.2 Other Applications

5.2.1 Self-Cleaning

Self-cleaning can be mainly divided into two categories. One is based on superhydrophilic surfaces, on which water droplets quickly spread into a thin film and wedge into the space between the substrate and any present dust. The other is based on superhydrophobic surfaces where spherical droplets easily roll to carry away contaminants [91,92,93]. Some animals and plants in nature show excellent self-cleaning function including the legs [94] or wings [95] of insects and the leaves of plants [96]. Lotus leaf is a typical example because it has a typical hierarchical micro–nano-structure, namely micro–nano-columns and nanotubes, showing superhydrophobic and self-cleaning properties. Therefore, hierarchical micro–nano-rough structures are commonly used in self-cleaning materials [97,98,99]. Chen et al. [97] successfully prepared flexible hybrid zinc oxide nanowires modified polyvinylidene fluoride microfibers by simulating the hierarchical structure of lotus self-cleaning, which has good self-cleaning performance and superhydrophobicity, and the water contact angle is greater than 150°. Chen et al. [46] fabricated a self-cleaning material with hierarchical rough structure using carnauba wax, Palygorskite (Pal) and TiOx as raw materials, as displayed in Fig. 12a–c. The sample had a swallow-like disordered multi-stage rough structure. Further amplification exhibits the formation of interlaced petals with some submicron aggregates. Studies have shown that the sample has excellent self-cleaning properties. Two different self-cleaning mechanisms for water and oil are displayed in Fig. 12d, e. Water droplets clean the contaminated surface by rolling, whilst oil droplets slide out of the surface due to its low surface tension, pushing pollutants away from the surface. The chalk powder on the cotton cloth will be completely taken away by the dripping water and oil (Fig. 12f, g), indicating a clear trajectory. After the action of continuous water and oil droplets, all chalk dust on the cotton fabric was taken away.

Fig. 12
figure 12

a Wax-Pal/PFDMS-TiOx cotton cloth. b and c Partial enlarged detail. d, e Self-cleaning of solid contaminants by water (f) and oil (g) [46]. h Heat storage capacity of PW, PMF and PMT [100]. i Catalytic effect of multi-channel TiO2 fibre (CF representative channel) [45]. j Schematic filtering principle of bionic hierarchical inverted hook fibre and k filtration effect of mesoporous nonwovens (SxGy) for the prepared fibres and nonwovens, with “x” denoting the BTA mass concentration used in the shell-solution for coaxial electrospinning and “y” the BTA mass concentration used for subsequent seeded BTA growth from the fiber's surface, respectively) [44]

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5.2.2 Energy Storage

Hierarchical structures can significantly improve some physical or chemical properties due to their interconnection and independence amongst all levels, and have broad application prospects in the field of energy storage [100,101,102,103]. Jiang et al. [101] synthesised 3D hierarchical porous NiCo2O4 by controlling the reaction rate with hydrothermal method. The synergistic effect between hierarchical structures increased the specific capacitance of supercapacitor to 584 F g−1 (40 A g−1). Zhang et al. [102] used a simple template method to make hierarchical MOS2 microbox, showing high specific capacity and excellent cycle performance. At a high current density of 1000 mA g−1, the hierarchical MoS2 microboxes can still deliver a stable discharge capacity of about 700 mA h g−1. Shi et al. [100] successfully prepared hierarchical porous Paraffin @ magnetic TiO2 (PMT) and Paraffin @ magnetic Fe3O4 (PMF) phase change materials, which were compared with the thermal energy storage of Paraffin Wax (PW). As presented in Fig. 11h, the solar-thermal storage capacity of PMF and PMT was significantly enhanced, 353.2 J g−1 and 377.6 J g−1, respectively. Compared to that of the PW (307.7 J g−1), it increased by 14.8% and 22.7%, respectively.

5.2.3 Catalysis and Filtration

Hierarchical structures are also applied in catalysis and filtration because of their porosity [44, 45]. For example, Zhao et al. [45] spun multi-channel TiO2 fibres by multi-fluid electrospinning and hierarchical porous structure, resulting in capture effect of gaseous molecules. Meanwhile, the emissivity of the incident light through multiple reflections was increased, and the photocatalytic activity of TiO2 improved. Results have shown that the more the channels, the higher the catalytic efficiency (Fig. 12i). Using PS and BTA as raw materials, Burgard et al. [44] obtained the hierarchical fibres of penguin-like villi by coaxial electrospinning combined with self-assembly, which were used in the field of filtration. Figure 12j showed a filtration schematic diagram of penguin-like fluffy multistage fibres and other common fibre structures. On the left is a filter prepared with larger fibres having large pores, which has a lower pressure drop in the filtration process but lower filtration efficiency. The middle filter is prepared with smaller fibres with small pores, which has a high filtration efficiency but high pressure drop, and the right side refers to a filter structure made of penguin-like fluffy multistage fibres, which have large pores and are grafted with smaller original fibres between the pores to intercept the particles. It has a smaller pressure drop and higher filtration efficiency. Burgard et al. showed that the density of grafted BTA fibres increased with an increase in the concentration of the crystalline species BTA on the fibre surface and more branched fibres with penguin-like villi. Therefore, the filtration effect has also been significantly improved (Fig. 12k) [44].

6 Conclusion and Perspective

In nature, the hierarchical structures are ubiquitous. For example, polar bear hair, cocoon, penguin feather and wool have typical hierarchical structures that can be used in the field of heat insulation. The hair of polar bears is composed of stratum corneum, cortex and medulla oblongata. The medulla oblongata is a porous structure with a diameter of one-third to half of the whole fibre. Each pore is separated from the membrane and has a unique hierarchical structure of membrane pores. The inner structure of silkworm cocoon is compact. From inside to outside, the pores increase, and the outer structure is relatively loose. Penguin feathers are composed of spindles and branches. The pores of the spindle increase from the top to the root, and the branches are hierarchical structure. The cortical layer of wool consists of single molecule, protofibril, microfibril and macrofibril. Because the hierarchical structure has the characteristics of multi-pores, a large number of solid–gas interfaces and complex solid conduction paths, it can greatly reduce heat transfer, making them have low thermal conductivity and excellent thermal insulation performance. Therefore, the bionics of these hierarchical structures are widely favoured by researchers, who used fractal calculus to reveal the thermal insulation performance of hierarchical structure, and prepared biomimetic hierarchical structure by electrospinning, freezing spinning, chemical deposition, sacrificial template method and so on.

At present, hierarchical structure has broad applications in many industries, such as thermal insulation and infrared stealth, self-cleaning, energy storage, catalysis and filtration, etc. Especially in the field of thermal insulation and infrared stealth, hierarchical structures can greatly reduce heat transfer and achieve the purpose of thermal insulation and infrared stealth due to their unique properties. In the future, more and more researchers will pay attention to the advantages of hierarchical structure. Exploring the fractal models of different hierarchical structures, deeply understanding the relationship between hierarchy and performance, and using simple and effective methods to bionic hierarchical structures for various fields will maybe become research hotspots. At the same time, we could also explore the performance of different hierarchical structures after combination so as to make full use of the advantages.