Pomelo-inspired sandwich composites: manufacturing and cushioning property

Abstract

Inspired by pomelo peel, this study designs an effective cushioning composite with a novel sandwich structure using a columnar lattice mold and two-step foaming technique. This sandwich composite consists of a polyamide nonwoven fabric (i.e. nonwoven surface) as the surface reinforcement layer and a double-layered spacer fabric as the bottom layer for energy absorbing. The static-compression resistance and dynamic cushioning efficacy of composites are investigated, examining the influences of three parameters (i.e. the areal density of the nonwoven surface and laminating angle and the mesh size of the double-layered spacer fabric). The experimental results show that the static-compression resistance and dynamic cushioning efficacy of the composites decrease when increasing the laminating angle of the spacer fabric and the areal density of the polyamide nonwoven fabric. By contrast, with an increment in mesh size, the compression resistance and cushioning efficacy of the composites first decrease and then increase. N200PUH/L(S5) consists of a 200 g/m² nonwoven surface and a 0° laminated angle, 5 mm mesh size double-layered spacer fabric, which exhibits a higher cushioning efficacy than the pomelo peel. The acceleration of N200PUH/L (S5) was 39 g at 15 ms, and the acceleration of pomelo peel was 72 g at 7 ms, which were 60.7% and 28.5% lower than that of the blank group, respectively. The sandwich-structured composites are proven to have promising applications for low-velocity cushioning behavior, and this study combines the textile structure and foam technique, offering a perspective of designing cushioning composite sandwiches for future studies.

Keywords

Pomelo peel polyurethane foam columnar lattice spacer fabric cushioning efficacy

Polymeric foam, used to absorb impact energy, has a variety of applications, such as in the automotive industry, civil engineering, and packaging of fragile goods.^1
–3 This is mainly because foam materials can absorb the energy in the process of impact obstacles and reduce the damage of acceleration to goods or the human body. Polyurethane (PU) foam is a cushioning and energy absorbent material that has low cost and good adaptability. Via the fracture, bending, friction of the porous cell walls or the compression of interior air, PU foam absorbs the energy caused by an impact and thus protects the commodity.⁴ As PU foam has low compression resistance, some scholars have adjusted the mechanical properties of the bubble structure by doping nanoclay in PU foam,² and finally obtain sandwich composite materials with high-energy absorption ability. Saha et al.⁵ studied the effect of different kinds and shapes of inorganic nanoparticles on the mechanical properties of PU foam, but the difference of adhesion between nanoparticles and foam led to differences in the compression properties of PU foams by different kinds of nanoparticles. Most scholars have established the relationship between particle addition and foam mechanical properties. Gama et al.⁶found that the microstructure of the foam with the addition of 0.5 wt% expanded graphite is more regular and the mechanical properties are the best, mainly because the addition of particulate matter improves the mechanical properties of the microstructure.⁷ However, the addition of particulate matter will affect the viscosity of the mixed matrix, the number of nucleation centers and the nucleation rate, which will lead to the collapse and deformation of the foam cell structure. The dispersion of nanoparticles is poor, which can easily cause agglomeration, resulting in the formation of a poor cross-linking network structure between particles and foam composites. In addition, most nanoparticles have a negative impact on the foaming process, and most nanomaterials are more expensive, which limits the application of foam materials. Subsequently, the reinforcement of the PU foam surface has engaged a great number of researchers.^8,9 Islam et al.⁹ developed new sandwich composites with a composite foam core and a paper skin as the materials. The surface-reinforced structure highly influences the energy absorption and impact behaviors of the composites.^10,11 Some researchers rendered PU foam with a lattice structure, which was proven effective but also considerably increased the weight of the composites and limited the applications due to the presence of the metal lattice structure.^12,13

As cushioning materials, warp-knitted spacer fabrics have much better pressure relieving properties and higher air permeability than PU foam.¹⁴ However, the buffer capacity of high-energy and short time impact scenarios is poor, and there are some problems such as deformation offset and poor elastic recovery. Therefore, Zhi and Long¹⁵ used PU foam and spacer fabrics to make fabric-based PU foam, which remarkably strengthened the structure and energy absorption performance. Li et al.¹⁶ used low-cost spring-like sandwich flexible foam composites, which were constructed with a three-dimensional (3D) resilient concave–convex structured fabric core (RCFC) and gradient-structured maleic anhydride (MAH)-grafted styrene-ethylene/butene-styrene copolymer (SEBS-g-MAH)-filled PU foam faces, which improved the cushioning efficacy. However, few studies have examined the mechanical property of composites containing spacer fabric with different structure parameters and, therefore, this study pioneers in examining the influence of the surface structure on the mechanical and functional properties of PU foam.^17
–19 Furthermore, inspired by pomelo peel, some studies designed cushioning energy absorption materials, but the majority of them merely incorporated a gradient structure with the structure design,^20
–23 leaving few studies that comprehensively examined the mechanisms of the interior microstructure, such as PU foam filling of warp-knitted space fabric-enhanced composite materials research, the combination mode of layered spacer fabric, the volume content of fabric/foam and the mechanism of the interaction between each component of the fabric and foam. As a result, an efficient combination of a peel layer, gradient foam and periodic fiber bundles to produce composites with a bio-structure has become a popular research topic.

Therefore, this study aims at designing a novel sandwich composite for the cushioning function. Based on the features of pomelo peel, this study incorporates a two-step foaming process with a columnar lattice mold in order to provide the sandwich-structured composites with a gradient structure. A flexible polyamide nonwoven fabric serves as the reinforcing surface, PU foam at different densities serves as the porous substrate and a double-layered spacer fabric serves as a reinforcing unit that absorbs impact energy. The effects of the lamination angle/mesh size of the spacer fabric and the areal density of the nonwoven surface on the static-compression resistance and dynamic cushioning efficacy of composites are investigated, examining the mechanisms and proposing a novel design for cushioning composites.

Experimental details

Materials and preparation of sandwich composites

The composite material consists of two foam structures and the outer cortex of the fabric. Polyamide nonwoven fabrics (Far Eastern New Century Co., Taiwan) have areal densities of 200, 300 and 400 g/m², and two-liquid-type high-density flexible PU foam used as the upper foam layer is composed of polyols and isocyanate (Kuang Lung Shing Co., Taiwan). The lower foam layer is two-liquid-type low-density flexible PU foam made of polyols and isocyanate (Keshengda Trading, China). The warp-knitted spacer fabrics (YT-0638, Huayu Weaving, Jinjiang, Fujian, China) with mesh sizes of 4, 5 and 6 mm and a thickness of 5 mm are applied. The spacer fabric has a sandwich structure with the upper/lower layers being composed of 200 D polyester mono-spacer yarns, and a spacer layer being composed of 30 D polyester mono-spacer yarns. The spacer fabrics are denoted as S4, S5 and S6, where “S” represents warp-knitted spacer fabrics and the digit represents the size of the mesh. The double-layered spacer fabrics are composed of two spacer fabrics laminated at 0°, 45° and 90°, respectively. The laminate angle is the central rotation of the second spaced fabric relative to the first layer.

Composites are made using the two-step foaming process. In the first step, polyols and isocyanate with a weight ratio of 4:1 are blended at 1200 rpm for 10 s at room temperature and normal atmospheric pressure. Next, the mixture is infused quickly into a square columnar lattice mold (300 × 300 × 30 mm³), and then covered with a polyamide nonwoven fabric (hereafter referred to as the nonwoven surface) before the lid is sealed (Figure 1(a)). Composites are made by curing and demolding at room temperature. In the second step, the product with the nonwoven surface on the bottom of the first step is put in a square mold, after which the mixture of the two-liquid-type low-density flexible PU foam is infused, and then covered with a double-layered spacer fabrics before the lid is sealed, thereby forming the bionic sandwich-structured composites. Figure 1(b) shows the composite section of the bionic sandwich structure prepared by two-step foaming technology according to the teak skin structure. The upper and lower PU foam layers thus have a high and low density, respectively. In the experiment, sandwich composites have different laminating angles/mesh sizes of spacer fabrics and areal densities of the nonwoven surface. In the experiments, the sandwich composites have a different laminate angle/mesh size area density of the spaced fabric and nonwoven surfaces. The cavity diameter of high-density PU foam is concentrated at about 220 m and the number of openings is low, while low-density PU foam is about 600 m and the number is high. The ratio of the cell size cavity is about 1:2.5. Figure 1(c) shows warp-knitted spacer fabrics with different surface densities. Figure 1(d) shows the surface structure of the spaced fabric, and Figures 1(e) and (f) shows a double-layer spaced fabric with laminated angles of 0° and 90°, respectively, where the laminate angle is the angle of a spaced fabric with the y-axis after rotating along the y-axis. Specifications of the sandwich composites are listed in Table 1. The sandwich-structured composites are cuboid, the length and width are 10 cm, they are 3 cm high, the double-layered spacer fabric is 0.5 cm and the total size is 1 cm. The low-density foam of the lower cylindrical lattice structure is of 1.5 cm and the nonwoven surface is 0.5 cm with the high-density foam. We change the laminate angle and mesh size of the double-layer spacer fabric and areal densities of the nonwoven surface to test the effect of the three factors of the composite on static-compression resistance and dynamic cushioning efficacy.

Table 1.

Specifications of sandwich composite materials

Sample code	Areal density (g/m²)	Upper foam	Lower foam	Spacer fabric	Angle (°)
N400PUH/L(S4/0°)	400	High density	Low density	S4 × 2	0
N400PUH/L(S4/45°)	400	High density	Low density	S4 × 2	45
N400PUH/L(S4/90°)	400	High density	Low density	S4 × 2	90
N400PUH/L(S5)	400	High density	Low density	S5 × 2	0
N300PUH/L(S5)	300	High density	Low density	S5 × 2	0
N200PUH/L(S5)	200	High density	Low density	S5 × 2	0
N400PUH/L(S6)	400	High density	Low density	S6 × 2	0

N: polyimide nonwoven fabric, commonly known as nylon.

S4, S5 and S6: S represents warp-knitted spacer fabrics and the digit represents the size of the mesh.

As can be seen from Figure 2, pomelo peel is mainly composed of three parts: the outer cortex, gradient bubble pore structure and periodic fiber bundle interface structure.²⁴ Most of the space in the pericarp is occupied by the cell elements with the increase of bubble size gradient. In addition, the fiber bundle extends from the outer skin to the bubble structure and presents a periodic distribution.

Testing

The static-compression resistance of sandwich composites is measured at a rate of 10 mm/min using a universal testing machine (HT-2402, Hong Ta Instrument, Taiwan) as specified in ASTM D1621–1. A stereomicroscope (SMZ-10A, NIKON, Japan) is used to observe the morphology of the fractured surface of samples in order to analyze the structure. A drop-weight impact tester (Xin Zhi Electronic Automation Co., Taiwan) is used for the cushioning test (Figures 3(a) and (b)). With a load cell placed on top, the polished steel hemisphere impactor weighed 8 kg, as specified in ASTM D1596-14. The impact energy is 20 J and the drop height is 250 mm and the drop is performed along a guided column onto the specimen (100 mm ×100 mm) placed on the anvil. The contact force of the composites is measured during the impact process. Five samples for each specification are used for the tests.

Results and discussion

Effect of lamination angle of the spacer fabric on compression

Figure 4(a) shows that with a strain exceeding 15%, there is a distinctive decrease in the compression resistance of N400PUH/L(S4)/90°. At more than 15% of the strain, the spacer fabrics demonstrate compression resistance via deformation. Figures 4(b) and (c) show that when the laminating angle increases from 0° to 90° and the exerted strain is 40%, the compressive strength decreases from 150 to 125 kPa and the compressive modulus decreases from 2.15 to 1.85 kPa. Therefore, increasing the laminating angle has a negative effect on the compression resistance of sandwich composites. Previous studies commonly investigated certain parameters of spacer fabric in terms of mechanical properties. For example, the mesh shape of the surface layer and the areal density of the surface layer were pervasively discussed, instead of the laminating angle of double-layered spacer fabrics.^25
–27 Noticeably, the change of the overlapping angle of the interval fabric directly affects the distribution of the internal spacer filaments, and thus affects the flow of the PU mixed matrix fluid, and also affects the horizontal and longitudinal growth process of the foam.

Figure 4(d) shows the cross-section of sandwich composites consisting of PU foam in the vertical direction. The red dotted lines show the contact position of the double-layered spacer fabrics, and it is found that as the stacking angle increases in the composite structure, the bottom layer of the spacer fabric has a void in the internal foam. This is mainly because a high laminating angle renders the bottom double-layered spacer fabric with a greater level of vacancy. The PU mixtures then acquire more diffusion resistance but lower Gibbs free energy over the interface between the spacer yarns and mixtures.^28
–30 As a result, the nucleation efficiency expedites and the radius of cells diminishes, leaving some space in the spacer fabrics unfilled with PU foam.

Effect of the mesh size of spacer fabric on compression

Figure 5 indicates that when the mesh size increases from 4 to 6 mm, the compression resistance of sandwich composites first descends and then ascends. With the strain being 20%, the stress–strain curves of both N400PUH/L(S4) and N400PUH/L(S5) have a distinct inflection point, indicated by the arrow in Figure 5(a). This is mainly because when the strain is close to 20%, the spacer fabric layer starts deform against compression. In light of Figure 5(b), S6 has a higher crook degree of spacer yarns than S5, but it demonstrates greater resistance against deformation. Namely, the compression resistance of the sandwich composites is dependent on the crook degree of spacer yarns.³¹ Specifically, with the mesh size being 6 mm and the strain being 40%, the composites have the maximum compression resistance, which is 175 kPa (Figure 5(c)), contrary to the finding of previous studies that spacer fabrics made of a small mesh size possessed higher compression strength.^27,32 However, the bending degree of the spacer wire in the process of compression determines the compression resistance of the spacer fabric with the same surface layer structure.³³ This study finds that the spacer yarns of S6 possess the highest crook degree, which provides S6 with lower compression resistance. However, N400PUH/L(S6) has the highest compression strength, which is ascribed to the interface structure and variations of the spacer fabric–foam layer inside the composites under compression deformation. Figure 6 shows the compression process.

Figure 6 shows that the low-density foam near the high–low-density PU foam interface is more prone to deformation at the beginning of the compression process. When the strain reaches 20%, one of the double-layered spacer fabrics indicated by the red arrows commences to significantly exhibit compression deformation. The N400PUH/L (S6) deformation degree of composites containing spacer fabric S6 is the most obvious. In our recent report, the gradient foam structure is proposed when using the double-layered spacer fabric in the free foaming process.³⁴ Therefore, the foam inside the spacer fabrics obtains lower cell diameters, resulting in higher compression resistance. In particular, N400PUH/L(S6), which is composed of a 6-mm mesh size, appears to have tabular deformation. It is easier for the spacer yarns of S6 to contact the nonwoven surface easily and then reach the densification stage.³¹ When the strain is 30%, the upper high-density PU foam layer of N400PUH/L(S4) and N400PUH/L(S5) starts deformation. In particular, N400PUH/L(S4) demonstrates the densification in the most partial areas. By contrast, S6 is composed of a large mesh size and deformation is absent in the upper layer of high-density PU foam. The results suggest that the spacer fabric and high-density PU foam layer are jointly responsible for the compression deformation based on their stress tolerance. S4 spacer fabrics have a small mesh size and the constituent spacer yarns are highly resistant against deformation. With the stress waves being propagated to the spacer fabrics of S4, the constituent spacer monofilaments with high modulus first facilitate the stress waves to propagate.³⁵ However, the partial areas of S4 reach densification earlier and subsequently the stress wave is dissipated via the local composites. When the monofilaments begin to buckle, the foam inevitably limits the mobility of spacer monofilaments so that the stress waves are mainly propagated via the foam. The compression resistance of S5 is lower than that of S4, which is ascribed to the fact that the spacer yarns of S4 are more resistant against deformation. During the compression process, the spacer fabric–foam layer of N400PUH/L(S6) reaches densification, which builds a plate-like structure that retards the efficient propagation of local stress and thus improves the compression resistance via the entire composites.

Effect of areal density of the nonwoven surface on compression

Figure 7(a) shows that the compressive deformation process of sandwich composites is not positively correlated with the areal density of the nonwoven surface. However, the increase of surface density of nonwovens leads to the increase of volume content of nonwovens and the decrease of compression resistance of composites. Figure 7(b) shows that with an increase in the areal density from 200 to 400 g/m², the compression strength decreases from 138 to 117 kPa at the strain of 40%. When the areal density of the nonwoven surface increases, there are more nucleation sites of foaming in the fiber–foam the interface. Subsequently, the Gibbs free energy required by nucleation decreases,^29,30 which accelerates foam growth and decreased nucleation radius eventually and eventually causes an irregular cell morphology. In addition, the thickness of the nonwoven surface takes up more space, which results in a decrease in the thickness of the upper PU foam layer (Figure 7(c)). During the compression process, the load-bearing foam unit weakens the compressive resistance because of the decrease of thickness.

Effect of laminating angle of spacer fabrics on the cushioning property

Figure 8(a) shows the effect of the laminating angle on the temporal variations of the contact force. Firstly, the impactor strikes the sandwich composites, causing compressive deformation so as to dissipate and absorb the impact energy. The contact force steadily increases, and when the samples reach the densification stage, the contact force upsurges accordingly until the impactor is stopped by the steel platform, which then triggers the reduction of the contact force.³⁶ During this process, the kinetic energy of the impactor is transformed into the deformation energy that is dissipated through the sandwich composites.³⁷ The impactor produces deceleration behavior through the deformation of the buffer material, the buffer material absorbs and stores the impact kinetic energy, the impact acceleration of the impactor is reduced and the impact contact force between the impactor and the buffer material is reduced.

Figure 8(b) shows that increasing the laminating angle from 0° to 90° increases the peak contact force from 3200 to 3400 N. The increase in peak contact force meant equivalently an increase in acceleration, which was detrimental to the cushioning efficacy.³⁸ N400PUH/L(S4)/0° demonstrates a comparatively higher energy absorption with a specified contact force, and it can complete the whole energy transformation when the contact force is lower (Figure 8(c)). This finding is consistent with the results of compression resistance (Figure 4). When an impact force is exerted, the incomplete structure between the PU foam and the spacer yarns eventually decreases the cushioning efficacy.¹⁵ In addition, the composite structure can avoid the failure of spacer fabric to a great extent.

Effect of mesh size of spacer fabric on the cushioning property

Based on Figures 9(a) and (b), N400PUH/L(S6), which is composed of large mesh size spacer fabrics, receives the lowest contact force. The contact force–energy curves in Figure 9(c) also indicate that with a specified contact force, N400PUH/L(S6) can absorb the maximum amount of energy, which is in agreement with the findings in Figure 5. The variation in the mesh size affects the deformation of the spacer fabric–foam layer because the energy absorption process depends on the difference in the deformation level. During the foaming process, spacer fabrics of a large mesh size provide the composites with a homogeneous plate-like composite layer, which bears the propagation of stress via the whole structure. Conversely, the composites composed of small mesh size spacer fabrics can only absorb energy via local densified areas separately. The phenomenon of stress concentration is not conducive to the absorption and dissipation of stress wave energy.

Effect of areal density of the surface layer on the cushioning performance

Figures 10(a)–(c) show that regardless of whether it is the nonwoven surface layer or the double-layered spacer fabric being impacted, N200PUH/L(S5) yields the lowest peak contact force among all samples. The peak contact force is proportional to the areal density of the nonwoven surface. Figure 7 shows that a high areal density reduces the thickness of the upper PU foam layer, and the presence of irregular cell morphology between the upper PU foam and the nonwoven surface undermines the deformation resistance of the composite. This result can be proven by Figure 10(d). When a contact force exceeding 2.2 kN is exerted, N200PUH/L(S5) demonstrates a greater level of energy absorption. Comparing the front and back sides, N200PUH/L(S5) also has better energy absorption when the contact force exceeds 1.5 kN.

The different cushioning efficacies on the front and back side are due to two decisive factors. One factor is that the upper PU foam layer next to the nonwoven surface has a small cell size and high foam density. By contrast, the lower PU foam layer next to the spacer fabrics has a low density. The gradient difference in the density of PU foam from a high density to a low density is helpful for energy absorption, which is consistent with the findings in previous studies.^21,39 The other factor is that when the impactor hits the nonwoven surface, the impactor densifies the high-density and small-cell-size PU foam. Afterward, following an increasing force, the nonwoven surface exhibits inferior fovea, which improves the cushioning property of the sandwich composites.⁴⁰ Nonetheless, the nonwoven surface layer remains intact when the side of the spacer fabric is impacted. These findings conform with those in a previous study that concluded that without the peel, pomelos demonstrated considerably lower energy absorption.⁴¹

Cushioning performance of sandwich composites and pomelo peel

According to the theorem of momentum, a longer duration of impact leads to a lower acceleration and a lower dynamic force.⁴² As Figure 11(a) shows the blank group, which refers to composite material prepared by the high-density polyether polyol and isocyanate primary foaming process, and no array interface structure exists within the structure; pomelo peel or sandwich composites are used as cushioning materials, and they have a smaller contact force and longer impact duration compared with the blank group. The peak contact force is 3170 N for the sandwich composite, 4410 N for pomelo peel and 8134 N for the blank group. The corresponding impact times for the three groups are 14.78, 9.96 and 3.82 ms, respectively. The results show that the sandwich composite has a prolonged impact duration and a lower contact force compared to the pomelo peel.

Transient acceleration G(t) is proportional to the impact contact force and can be calculated by Newton’s second law

G (t) = \frac{F (t)}{m}

(1)

The weight of the hammer head (m) is 8 kg, F represents the impact contact force and G(t) represents the acceleration during the hammer head reduction shock, in 9.8 m/s².

The initial velocity (v₀) at which the hammer head reaches the sample surface is

v_{0} = \sqrt{2 g h}

(2)

In the formula, g represents the gravity acceleration and h represents the falling height of the hammer head.

The instantaneous speed (v(t)) of the impact process of the hammer head and buffer material is

v (t) = \sqrt{2 g h} - \int_{0}^{t} G d t

(3)

Then, the depth S(t) of the sample in the impact process can be calculated

S (t) = \int_{0}^{t} v (t) d t

(4)

S (t) = \sqrt{2 g h t} - \int_{0}^{t} \int_{0}^{t} G d t d t

(5)

The energy absorption E of the buffer material after elastoplastic deformation is the integral of F(t) – S(t).

The differences in acceleration is computed for comparisons, and the maximal acceleration is 39 g at 15 ms for the sandwich composite and 72 g at 7 ms for the pomelo peel, which are 60.7% and 28.5% lower than that of the blank group (Figure 11(b)). Similarly, Figure 11(c) also confirms that the sandwich composite can complete the absorption of impact energy when a low contact force is applied. It is worth mentioning that pomelo peel shows apparent plastic failure, while the sandwich composite almost does not exhibit any failure after repetitive impact testing cycles.

Conclusions

Pomelo peel is mainly composed of three parts: the outer cortex, gradient bubble pore structure and periodic fiber bundle interface structure. Inspired by the feature of pomelo peel, this study employs a two-step foaming process, columnar lattice mold and PU foam with a gradient structure as a porous substrate to produce sandwich composites. Polyamide nonwoven flexible fabric serves as the reinforcing surface, the upper layer is a high-density PU foam and the lower layer composite low-density PU foam serves as the porous substrate; the bottom layer is a double spacer fabric as a reinforcing unit that absorbs impact energy. The effects of the laminating angle/mesh size of the spacer fabric and areal density of the polyamide nonwoven surface on the static-compression resistance and dynamic cushioning efficacy of sandwich composites are investigated. Increasing the laminating angle generates vacancy inside the spacer fabrics, and with the specified strain being 40%, the compressive strength of the sandwich composites decreases from 150 to 125 kPa, and the peak contact force increases from 3200 to 3400 N. In addition, when the mesh size increases from 4 to 6 mm, the compressive resistance and cushioning efficacy of the composites first descend and then ascend. In particular, the spacer fabric–foam layer of N400PUH/L(S6) is transformed into a plate-like structure, which retards the rapid propagation of stress through partial areas and provides the composites with higher compressive resistance and energy absorption. Moreover, when the areal density of the nonwoven surface increases from 200 to 400 g/m² and the strain is specified as 40%, the compressive strength of the sandwich composites decrease from 138 to 117 kPa. Regardless of whether being impacted from the front or back side, N200PUH/L(S5) yields the lowest contact force and optimal cushioning efficacy. Finally, N200PUH/L(S5) shows an acceleration of 39 g at 15 ms and pomelo peel shows an acceleration of 72 g at 7 ms, which are lower than those of the blank group by 60.7% and 28.5%, respectively.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This research is funded by National Natural Science Foundation of China, Natural Science Foundation of Fujian Province and Natural Science Foundation of Tianjin City.

ORCID iD

Jia-Horng Lin

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