**1. Introduction**

Noise pollution belongs to one kind of environmental pollution, which is regarded as one of four major environmental problems in the world together with water pollution, air pollution, and light pollution. Noise pollution causes people's mood level and sleep quality to decline, and continues to slowly affect the human body system and increase the incidence of various diseases, even to a life-threatening level [1]. Secondly, noise will also accelerate the aging rate of conveyor belts, gears, bolts, and other mechanical structures, thus affecting the accuracy and service life of instruments and equipment, seriously affecting the safety of a building [2]. More and more scholars focus on developing environmentally friendly sound-absorbing materials and striving to improve their sound-absorption performance in recent years.

Lignocellulose insulation materials, natural materials, and recycled materials have been widely used in the field of sound-absorption in recent years. Tudor et al. [3] studied the sound-absorption coefficient of bark insulation board made of cork bark spruce and larch. The results showed that cork bark was an underrated material, and that compared with wood-based composites, engineered spruce bark was even better at absorbing sound than MDF, particleboard, or oriented particleboard. Tudor et al. [4] also analysed the acoustic performance of bark boards and found that the optimal density of bark boards

**Citation:** Lyu, L.; Zhang, D.; Tian, Y.; Zhou, X. Sound-Absorption Performance and Fractal Dimension Feature of Kapok Fibre/ Polycaprolactone Composites. *Coatings* **2021**, *11*, 1000. https:// doi.org/10.3390/coatings11081000

Academic Editor: Philippe Evon

Received: 30 July 2021 Accepted: 19 August 2021 Published: 22 August 2021

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to obtain the best sound-absorption coefficient was about 350 kg/m3, and that these lightweight panels achieved better sound-absorption performance at a higher thickness (especially at lower frequencies). Smardzewski et al. [5] determined the normal surface impedance and sound-absorption coefficient of several woods from Europe and tropical regions, and the results showed that oak, ash, sapele, and pine had the highest soundabsorption coefficient at the frequency of 2 kHz. Asdrubali et al. [6] studied the acoustic properties of sustainable materials and found that sustainable products made from natural and recycled materials are effective substitutes for traditional synthetic materials. Fouladi et al. [7] used fresh coconut shell fibres and industrially prepared coconut shell fibres with an added binder as raw materials to study the sound-absorption coefficients of the two fibres as porous materials. The results showed that the industrially prepared fibres had poorer sound-absorption performance at low frequencies than fresh coconut shell fibres due to the addition of the binder. For commercial use, however, fibres must be mixed with additives to enhance properties such as hardness, antifungal, and flammability. Therefore, methods such as increasing air gaps or perforating plates should be used to improve the acoustic properties of industrially treated coconut shell fibres.

According to its formation mechanism and structure, porous sound-absorption materials can be divided into fibrous sound-absorption materials, granular sound-absorption materials, and foam plastic plates. When sound waves penetrate the surface of porous materials, the sound waves cause the vibration of the object, and then cause the vibration of the pores and gases inside the material. A large part of the sound energy can be consumed by the motion between the sound waves and the pore walls, and the transmission of sound waves is reduced due to the friction effect and viscous effect. The transmitting sound wave is weakened, thus achieving the purpose of sound insulation and absorption. At the same time, due to the different temperature of the pore wall and the small hole of the material, the gas will flow to realise heat exchange, and then lead to the loss of heat, resulting in the reduction in sound energy, to achieve the purpose of sound absorption. In addition, because of the influence of the frequency and friction of high frequency sound waves, the vibration speed of air particles will become faster, and then improve the speed of heat exchange; therefore, porous materials can achieve good sound-absorption effect in the range of high frequency sound waves.

Sound-absorbing materials have a wide range of application prospects, but the traditional sound-absorbing materials have many shortcomings, such as short service life, secondary pollution, performance instability, and so on. The emergence of new soundabsorbing materials makes up for the deficiency of traditional sound-absorbing materials to some extent [8]. Compared with traditional fibre sound-absorption materials, the soundabsorption coefficient of fibre sound-absorption composite materials is greatly improved, and many of them can reach more than 0.8, which makes up for the limitation of traditional fibre sound-absorption materials in the application range, to a large extent. Moreover, fibrous composites have less impact on the environment than conventional materials, generally have lower overall energy requirements for manufacturing and installing these materials, and are less harmful to human health. Replacing traditional sound-absorption materials with fibre composites has a significant impact on all phases of the building life cycle (construction, operation, end of life) [9].

Kapok fibre is a single cell fibre with a smooth surface, cylindrical shape, and no torsion. As a natural cellulose fibre, it is biodegradable and recyclable [10]. Due to its advantages such as softness, high hollow rate, anti-bacterial, and anti-mite, it has attracted extensive attention and has a good development prospect in the textile field [11]. Kapok is a kind of natural fibre, which has excellent sound-absorption performance due to its high degree of emptiness and small fibre diameter [12]. Because kapok fibre belongs to the short fibre category and is affected by its hollow structure, fibre strength is low, and has weak adhesion and poor elasticity; therefore, the technical difficulty of single spinning kapok yarn is high, and the application of economic benefits in textile and clothing is poor [13]. The large hollow structure of kapok fibre can be well utilised by making it into soundabsorbing composite material, which has low technical requirements and high economic benefits. The research and development of kapok fibre products can not only reduce the over-dependence on oil and other non-renewable resources, but also respond to the national strategic goal of ecological environment protection and sustainable development [14].

Dresden Technical University in Germany [15] focused on the study of kapok fibre and wool fibre. By comparing their differences in heat insulation and sound insulation, it was finally concluded that kapok fibre material had better heat insulation and sound insulation performance than wool fibre material. Liu et al. [16] developed a sound-absorbing nonwoven composite material based on kapok fibre and hollow polyester fibre, and used the impedance tube method to study the sound-absorbing performance of kapok fibre nonwoven composite material in the low-frequency region of 100–500 Hz. Makki et al. [17] studied the sound-absorption properties of nonwoven, layered warp knitting, and layered double-layer fabric made of kapok fibre at frequencies from 100 to 5000 Hz. The results showed that the best sound-absorption effect was obtained by combining kapok nonwovens with double-layer fabric with a thickness of 11.25 mm. Azieyanti et al. [18] prepared reinforced polypropylene composites using jute and kapok fibres as raw materials and compared jute and kapok fibre-reinforced polypropylene sound insulation effect composites; the results showed that the performance of the composite material, along with the increase in the quality percentage of jute and kapok fibre, increased the filling amount to 30% when the performance of the composite material was best. Liu [19] used polyethene film to fabricate the kapok fibre nonwoven fabric. The research on the sound-absorption coefficient and specific surface impedance of composite materials in the frequency range of 100–2500 Hz was carried out using the impedance tube method. The results showed that the multilayer composite had better sound-absorption performance than the single-layer non-woven fabric at low frequency.

A fractal is defined as a mathematical object with a fraction (not an integer) dimension. In the 1990s, Yu proposed a method to determine the effective thermal conductivity of reinforced fibre materials and irregular porous materials, that is, the fractal theory method, but in the research process, the calculation method and process were too complex to be applied in practice. In 2001, Yu conducted another study on fractal calculation methods and published a paper [20] in which it was pointed out that the fractal characteristics of porous media could be described by a general model. Chen's [21] use of fluid science, fractal theory, the study of space structure of the fibre porous metal processing, the fractal model of flow resistance rate, and the effectiveness of the proposed model was verified by experiment, which showed that the fractal model could intuitively reflect the relationship between the geometric parameters and flow resistance rate of material. In order to design fibre-porous metal, sound-absorbing material provides a theoretical support. According to the heat conduction model of down fibre aggregate, Fu [22] calculated the fractal dimension of hollow polyester fibre under different volume fractions by the box-counting method and calculated the heat transfer coefficient of the aggregate. The predicted value calculated by the model was in good agreemen<sup>t</sup> with the measured value, which proved that the heat conduction model was effective. According to the box-counting method fractal theory, Lyu [23] calculated the fractal dimension of discarded feather/EVA sound-absorption composite material. By Matlab programming, the fractal dimension between the mass and density of discarded feathers was calculated, and then the relationship between the fractal dimension and the maximum sound-absorption coefficient was derived quantitatively.

Fractal geometric properties mainly included self-similarity, wholeness, fractal dimension, organisational depth, and recursion, which interweaved, reinforced, and supported each other [24]. Kapok fibre is the most hollow fibre, and its hollow structure is self-similar to the porous structure of the whole nonwoven fibres. In kapok fibre, the intercross and stacking of macromolecular chains are similar to the whole, and most macromolecular chains are six membered rings, benzene rings, and other molecular chains. The gap between macromolecular chains is similar to that of the whole porous. Kapok fibre sound absorption of the pore size and distribution of composite materials has obvious fractal characters;

according to the fractal theory and image processing technology, intuitive characterisation of fibre morphology parameters can be directly extracted: one is the characterisation of porosity, a single pore area, fractal dimension, and pore number, pore structure parameters, such as the size and distribution of these parameters can reflect the pore; the second is the parameters that characterise the state of the fibre. These parameters can reflect the orientation distribution of the fibre. The relationship between structure and sound-absorption property, structure, and fractal dimension of kapok fibre sound-absorption composite was established. Finally, the fractal method is used to solve the sound-absorption performance of kapok fibre.

This article introduces a kind of composite material made of kapok fibre and polycaprolactone by the hot-pressing method. The effects of volume density, mass fraction of kapok fibre, and thickness on the sound-absorption performance of composites were researched using a single-factor experiment. The sound-absorption performance of the composites was investigated by the transfer function method. This research used the box dimension method to calculate composites' fractal dimension by using the Matlab program based on the fractal theory. It analysed the relationships between fractal dimension and volume density, fractal dimension and mass fraction of kapok fibre, and fractal dimension and thickness. The quantitative relations between fractal dimension and maximum soundabsorption coefficient, fractal dimension, and resonant sound-absorption frequency were derived, which provided a theoretical basis for studying sound-absorption performance.

#### **2. Materials and Methods**
