Introduction

Sound pollution has been perceived as an important issue in recent centuries. Various motions produce sounds that propagate as an acoustic wave through a gas, liquid, or solid medium [1]. Human beings can distinguish acoustic waves only in the frequency range of 20 Hz–20 kHz (the audio frequency range). However, Kumar claimed that an unpleasant sound corresponds to spectral frequencies between 2500 and 5500 Hz [2]. The ear is more sensitive to sounds between 3000 and 4000 Hz. An unpleasant noise is primarily associated with noise intensity at frequencies between 2000 and 5000 Hz [3]. Various sets of sounds, such as transportation, road traffic, construction, industrial plants, public work, home appliances, and buildings, have several disadvantages: sleep disturbance, fatigue, hypertension, hearing impairment, and decreased school performance [4, 5]. Due to fast urbanization, industrial development, transportation, and the drastic increase in vehicles, sound pollution has become a critical issue globally [6, 7]. Therefore, it is of utmost importance to develop sound absorption materials to counteract the adverse effect of these unpleasant sounds and reduce the reverberant noise levels. Sound absorption materials are usually used as: (1) interior lining for apartments, automotive, aircraft, and ducts; (2) enclosures for noise equipment; and (3) insulations for appliances [8, 9]. They are very beneficial in controlling sound transmission due to their ability to absorb most of the sound energy striking the material, with very little reflection. They can be located near the source of noise or close to the receiver, or in various paths (above barriers). There is a wide range of sound-absorbing materials, but porous materials have the highest range of sound absorption coefficient. A porous absorbing material is a solid that contains cavities and channels so that sound waves can enter and pass through them. These porous materials can be divided into two main groups: closed-cell and open-cell materials. In closed-cell materials, pores are entirely isolated from their neighbors, while in open-cell materials, pores have continuous connections with each other. The openness or closeness of pores affects the macroscopic properties such as bulk density, mechanical strength, and thermal conductivity. In sound absorption, open-cell materials are more efficient than closed-cell ones [10, 11]. Polymeric foams are extensively used in various applications, including sound-absorbing materials, due to their favorable properties compared to counterpart materials. However, their foam applications are limited owing to poor mechanical strength and low thermal and dimensional stability. The addition of various types of nanoparticles and fibers to foams can lead to a new class of materials (composite) that are lightweight, high in strength, and multifunctional [12, 13]. Among different polymer foams, polyurethane (PU) foams have become the most important class of polymeric foams for sound absorption applications, mainly due to their low density, lightweight, good mechanical properties and ease of manufacturing [14, 15].

In this article, sound absorption mechanism is briefly explained, and then various types of sound-absorbing materials are reviewed. Next, recent works on sound absorption properties of various polymer foams are summarized, which is followed by an introduction on foam formation processing methods. Then the acoustic properties of polyurethane (PU) foams are extensively investigated. In the subsequent section, the effect of various types of nanoparticles and fibers on sound absorption properties of PU foams is listed, and their most effective parameters are specified. Finally, porosity is defined, and the results of recent works on the correlation between porosity and sound absorption behavior are examined.

Sound absorption

Sound absorption coefficient

When sound waves strike a surface, the total sound energy may be expressed as below:

$${E}_{i} = {E}_{r} + {E}_{a} + {E}_{t},$$

where Ei is the total incident sound energy, Er is the reflected sound energy, Ea is the absorbed sound energy, and Et is the transmitted sound energy (Fig. 1) [16].

Fig. 1
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Schematic of the sound absorption process. Reprinted with permission from Ref. [17]

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The sound absorption coefficient (α) is defined as the ratio of absorbed energy to incident energy quantifying the amount of sound absorbed by a material.

$$\alpha =\frac{{E}_{a}}{{E}_{i}}.$$

The absorption coefficient depends on the frequency [17]. The impedance tube method is extensively used to measure sound absorption coefficients of acoustic materials as a function of frequency [18, 19].

The measurement method is based on the relationship between the incident and reflected sound from the sample surface. The sound pressure is measured by two microphones at two different locations near the sample. Then, the calculation of α is performed by invoking a transfer function based on the pressure differences between the two microphone positions. These pressure differences depend on the degree of reflection and absorption of the standing waves that are influenced by the sample under test. Figure 2 illustrates a schematic of the impedance tube system. The impedance tube is equipped with two microphones (Mic.1 and Mic.2), a loudspeaker (located at one end of the tube), a sample holder, and frequency analysis. A loudspeaker propagates broadband random sound waves at one end of the tube, which are transmitted to the surface of a sample at the other end. The reflected waves are recorded by the microphones on the tube wall before the calculation of normal incidence absorption coefficient by the analyzer. The specimen is positioned on the rigid plate, and no air gap at the backside of the sample is allowed to exist. The distance between the loudspeaker and the specimen should be long enough (900 mm) due to the propagation of the plane wave in the tube. The impedance tube system used in the experiment includes a large tube with a diameter of 100 mm and a small tube with a diameter of 30 mm to measure the absorption coefficients at low frequencies (63–1600 Hz) and high frequencies (1600–6300 Hz) limits, respectively. The full frequency range for the sound absorption coefficients presented in this report is a combination of the values measured in the large tube (63–1600 Hz) and the small tube (1600–6300 Hz) which gives the measured frequency range of 63–6300 Hz. The measurement of the sound absorption coefficient was repeated four times. All the tests were accomplished at formulated temperature conditions of 22 °C, relative humidity of (45 ± 10)% and pressure of 101.7 kPa [20]. Samples of 30 mm (low) and 100 mm diameter (high), and 20 mm thickness have been prepared for carrying out this test (Fig. 2) [21].

Fig. 2
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Schematic diagram of sound absorption measurement system. Reprinted with permission from Ref. [155]

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Sound absorption mechanism

Active or passive noise control is a means of sound emission reduction. A power source is used in active sound control, while a noise-reducing material (such as sound absorbers or sound insulators) is applied in passive noise control. Their mechanism and their frequency region are shown in Fig. 3. Passive noise control is more cost- and energy-efficient as it does not need any power source. However, it does not perform well at low frequencies. This is the main weak point of passive sound absorbers that has been investigated in many studies to improve their sound absorption behavior at low frequencies [22].

Fig. 3
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a Active and passive noise control mechanisms, and b frequency response region of the active and passive noise control methods. Reprinted with permission from Ref. [22]

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When sound waves penetrate the surface of a passive sound absorber, sound energy is converted into heat energy through frictional and viscous resistance in the fibrous or cellular structure of porous materials [18]. Although there are differences in the configuration of porous materials, the sound absorption mechanisms are similar. Sound energy is reduced due to (1) air movement in the pores that creates friction with the walls of pores, and as a result, the sound energy is converted into heat and then dissipated; (2) air in the pores which are intermittently compressed and released, leading to energy reduction through the process of energy conversion; (3) the resonance of pore walls that the sound energy would be converted into mechanical and heat energy [18, 23, 24].

Sound absorption materials

Sound absorption materials absorb most of the sound energy hit on them and some are slightly reflected. Therefore, sound-absorbing materials can be considered as valuable materials for noise control [25]. There are two main types of sound absorbers: resonant sound absorption materials and porous sound absorption materials [18, 26, 27].

Resonant sound absorption materials can be classified as Helmholtz resonators (HR), membrane absorbers, and perforated panels. These materials usually exhibit good sound absorption properties at low frequencies, but the main disadvantage is their sound absorption ability only in a narrow frequency range [18]. The Helmholtz resonator is made up of a cavity connecting with an external duct through an orifice. It is an efficient device for noise reduction in a narrow band at its resonance frequency [28]. Due to the durable, tunable, and simple HR features, it has been used in various duct structure systems, such as ventilation and air conditioning systems in buildings, automotive duct systems, and aero-engines [28, 29].

Moreover, their applications extend to other fields such as notch filters and ultrasonic metamaterials [30, 31]. Membranes can be used in various applications, including sound absorbers in a lightweight, durable, translucent, flexible, and designable form [32]. A conventional membrane absorber comprises a single leaf impervious membrane placed in front of a rigid wall, with an air cavity between them [32, 33]. Their sound absorption characteristics depend on the surface density, membrane tension, and back-cavity depth [33]. Membrane absorbers are effective sound absorbers only at one or two octaves of their resonance frequency. Therefore, they are usually combined with microperforated panels (MPPs) to increase their sound absorption bandwidths [33]. Panel sound absorbers are typically used to absorb low-frequency noise in architectural applications such as concert halls, theaters, recording studios, and so on. In these systems, flexible panels are usually made of metal, wood, gypsum, or plastic board overlaid on an air space that can be partially or completely filled with porous materials [34, 35].

Porous sound absorption materials are made up of channels, cracks, or cavities. They can be divided into three main categories based on their microscopic configurations: cellular, fibrous, and granular. Open-celled foams are examples of cellular materials, while fibrous materials include those made from natural or synthetic fibers. Asphalt, porous concrete, granular clays, sands, gravel, and soils are examples of granular materials [25, 36].

The ability of a material for sound absorption is affected by various factors such as thickness, density, porosity, tortuosity, compression, airflow resistance, fiber size, surface impedance, and position of sound absorption material [8, 37].

Acoustic foams

Noise reduction materials are often made of porous foams because of their low density and high specific surface area [38]. Metallic and polymeric foams are the two main types of acoustic foams.

Metallic foams

Metal foam is one kind of porous material, which acts as an effective sound absorber because it has both metallic and porous structured properties [39]. Metallic foams have gained significant attention because of their multifunctional abilities, such as ability to absorb while being lightweight and having high stiffness, mechanical isolation, fire protection, and chemical stability, and so forth [40, 41]. Among all different kinds of metals, aluminum (Al) foams have been investigated extensively [42, 43]. Open-cell Al foams have relatively good sound absorption ability because sound energy is consumed by viscous friction between air molecules and pore walls and thermal heat [44]. Closed-cell Al foams cannot be as good as open-cell sound absorbers because air permeability is a fundamental requirement in sound absorption materials. Sound absorption properties of closed-cell Al foams can be significantly enhanced by modifying their surface and structure [45]. Unlike Al foams, titanium foams [46] and nickel foams [38] have been quite rarely investigated in their standpoints of acoustic properties. The vast majority of studies on porous metal materials generally focus on acoustic properties under normal conditions. Wang experimentally investigated the sound absorption features of metal foams at high sound pressure levels, which is faced in aircraft engine liners and combustion chambers for rocket engines [47].

Polymeric foams

Polymer foams are polymer matrices containing many holes inside and are known as porous materials. They have some advantages such as low density, good heat insulation, good sound absorption, high specific strength, and resistance to corrosion [48]. Polymer foams can be characterized by their density, cell size, and wall thickness. They can be divided into two main groups depending on the processing method: open-cell foam (cells are connected) and closed-cell foam (cells are isolated) (Fig. 4). In the closed-cell foams, the sections are isolated, making them more rigid than open-cell foams.

Fig. 4
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Images of open-cell and closed-cell foams. Reprinted with permission from Ref. [50]

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In contrast, interconnected cells in open-cell foams make them more flexible with better absorbent properties [49]. However, closed-cell foams possess higher strength and more excellent resistance to air or water vapor leakage. The choice of foam depends on the application performance and specific characteristics.

Low mechanical strength, poor surface quality, and low thermal and dimensional stability are weak points of polymer foams that can be improved by adding various types of fibers and nano-size particles [51, 52]. Polymer foams with nanoparticles (polymer nanocomposite foams) have unique structures and properties due to the tailorable characteristics of nanoparticles. Shape, size, and surface chemistry can easily be customized to control foam structure and properties [49]. The strength, surface area, and damping properties of polymer nanocomposite foams have increased compared to those of conventional polymer foams [53, 54].

Polymeric foams as sound absorbers

Polymeric foams have been extensively used as efficient sound absorbers in buildings and various types of vehicles. They are particularly suitable for weight-sensitive applications, such as sound absorption in aircraft cabins, due to their low-density, resulting from the cellular structure of the foams [55]. Polyimide (PI) foams can be used as an effective sound absorption material in aircraft and rockets in particular, as they have outstanding acoustic properties reported in Table 1 [56, 57]. The acoustic performance of PI foam was optimized through chemical and physical reticulation [58]. Moreover, the sound acoustic behavior of PI, especially at low-frequency regions, was improved through structural design such as cellular structure precision controlling and sharp holes introducing [59]. The effect of 4,4-diamino diphenyl ether (ODA) on the sound absorption properties of polyimide (PI) foam was investigated. By adding ODA, PI foam showed a high acoustic absorption coefficient, while PI foam without ODA has a vast acoustic broadband [60].

Table 1 Sound absorption behavior of various polymeric foams
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The effects of manufacturing parameters such as foaming temperature, particle size, and percentage of foaming agent on the sound absorption properties of PMMA foams were investigated. The sound absorption behavior of various PMMA foams produced at different foaming temperatures with different NaCl particle sizes and different NaCl contents has been studied. The results show that the PMMA sample B, which has been foamed at a temperature of 80 °C, and the PMMA sample E, foamed using higher NaCl particle sizes (˃500 µm), and the PMMA sample F, containing 70% NaCl, have the best sound absorption performance [61].

The acoustic performance of polyether urethane (PEU) foam was examined by adding a low amount of carbon nanotubes (CNT) and discovered a limitation on the addition of CNTs to improve the sound absorption properties of PEU foam. PEU foam, containing 0.05% CNT, showed the best sound absorption behavior [62].

The sound absorption properties of open-cell polyolefin (PO) foams are investigated. The results reveal that the open-cell PO foams show better acoustic absorption performance than the closed-cell ones. They can be considered as an excellent alternative to PU foams for acoustic absorption due to their superb acoustic behavior [63, 64]. Another study on the hybrid polyethylene (PE)/polypropylene (PP) showed that closed-cell hybrid PE/PP foams have good sound absorption behavior over a broad frequency range and are especially effective at low frequencies. With the increase of perforation density, the absorption peak increases, and the sound curve moves to higher frequencies because of the higher surface area for air frictional losses [65]. In another investigation on the sound absorption properties of polypropylene (PP) foam, a novel strategy was developed to produce cavity-integrated acoustic foams. The cavity-integrated acoustic foams exhibit significantly better sound absorption behavior in comparison with acoustic foams without a cavity. The cavity-integrated foams presented a peak absorption coefficient of 0.65–0.95 in a frequency range of 950–1200 Hz [66].

The sound absorption performance of polylactic acid (PLA) was studied in different studies, and the data are gathered in Table 1 [67, 68]. The effect of thermal annealing on the sound absorption coefficient of polyvinylidene fluoride (PVDF) foam was studied. A significant increase in the sound absorption was demonstrated after the thermal annealing of the PVDF foams at 140 °C [69]. Polyvinyl formal foam is another polymeric foam whose acoustic behavior was studied, and the results are summarized in Table 1 [70].

A mixture of 70% meta-kaolin and 30% blast furnace slag powders is employed as a raw material in the production of inorganic polymeric foams (IPF). The effect of density on sound absorption behavior of IPF was investigated. Sound absorption coefficients increase with decreasing density. Thus a sample with a density of 400 kg/m3 shows the best acoustic performance [71]. The sound absorption performance of rigid and flexible green biopolymer foam was studied. A flexible foam offers better acoustic properties compared to a rigid foam mainly due to its morphology structure. Flexible foams give an open-cell structure, while rigid foams have a closed-cell structure [72].

Polymeric foam formation methods

There are three main foaming methods: (1) mechanical foaming: air is added to the polymer by mechanical stirring. Figure 5 shows a schematic diagram of mechanical foaming. There is no additional foaming agent, and the process is simple. This method is safe, cost-effective with high efficiency. However, this method needs more equipment [48]. (2) Physical foaming: in this method, a low-boiling-point (BP) liquid and a polymer are mixed to form a homogeneous mixture. This is usually done through heating and pressurization, as shown in Fig. 6. Consequent pressure reduction or temperature increase results in a supersaturation state and gas-forming nuclei and expanding. Physical foaming agents such as carbon dioxide and nitrogen are low in cost, so they are economical. This method does not release any pollutants. It has little effect on the characteristics of produced foam. But, this method needs high technical equipment and special injection molding machine [12, 48]. (3) Chemical foaming: this method can be carried out in two different ways. As shown in Fig. 7a, a blowing agent is added to a molten polymer, and mixed, which is followed by a gas release. After this, foam is produced by heating and pressurizing. In a second way (Fig. 7b), two different polymers are mixed, and the chemical reaction between them produces inert gases, and then foam is produced. Unlike physical foaming, chemical foaming can be performed with an ordinary injection molding machine. However, the cost of the mold is high. It requires a second clamping pressure device during the high-pressure foaming process [48].

Fig. 5
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Schematic diagram of mechanical foaming. Reprinted with permission from Ref. [48]

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Fig. 6
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Schematic diagram of physical foaming. Reprinted with permission from Ref. [48]

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Fig. 7
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Schematic diagram of chemical foaming. Reprinted with permission from Ref. [48]

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The physical foaming method is a preferred technique for polymeric foam production due to the lack of hazardous chemical components [49]. Supercritical fluids, especially CO2, have gained attention for polymer foaming processes as physical blowing agents. CO2 is stable, non-toxic, non-flammable, low cost, easily accessible, and recyclable. It has a relatively high solubility in polymers, diffuses into polymer melt, and reduces the viscosity. CO2 can be used in both the continuous (extrusion) and non-continuous (injection molding) foaming processes [73, 74].

Foams can be produced by both continuous processes such as extrusion foaming and non-continuous processes such as batch foaming and injection molding foaming [12]. Foam extrusion molding and foam injection molding are two main processing techniques [48]. Continuous extrusion foaming (both single- and twin-screw extruders) is the most commonly used method in the plastic foam industry. A blowing agent such as carbon dioxide (CO2) or nitrogen (N2) is usually used in extrusion molding. Extruder consists of several heating zones and is heated to a specified temperature according to process conditions. Then, a polymer is added to the hopper of the extruder. A syringe pump is used to introduce a blowing agent (supercritical fluid) in the barrel zone. The supercritical fluid is dissolved in the polymer melt and produces a homogenous mixture. When this mixture passes through a die, a rapid pressure drop induces phase separation and cell nucleation. Pressure drop, especially its rate, is the main driving force for cell nucleation. Finally, microcellular foams were obtained [48, 75, 76]. Foam injection molding is more suitable for the production of complex components than extrusion foaming [77]. This method is extensively used in civil and mechanical construction, automotive and aerospace industries, packaging, transportation, and household products [78]. In the injection foaming method, a polymer is molten, and a supercritical fluid is injected into the barrel. They mix and form a homogeneous solution. This solution is injected into the cavity and undergoes a rapid decrease in pressure, which is the driving force for cell nucleation and growth [79, 80].

Polyurethane foams

Polyurethanes (PU) are synthesized by the reaction between diisocyanate/polyisocyanate and polyols in the presence of catalysts [81, 82]. Isocyanate is responsible for PU reactivity and curing properties [83], while polyols lead to long flexible segments, which produce soft elastic polymers [84]. The role of catalysts is to accelerate the reaction between the isocyanate and polyols and allow the reaction at lower reaction temperature [85, 86].

Polyurethanes (PU) are the most versatile kind of polymers. They have a wide range of materials with various properties mainly due to their structural diversity, resulting from the type of polyols or polyisocyanates from which PUs are made [86,87,88]. PUs have the durability and toughness of metals and the elasticity of rubbers simultaneously, which made them appropriate alternatives to metals, plastics, and rubbers in various applications [85, 89].

PUs can be used as foams, coatings, elastomers, sealants, and adhesive-based products [54]. The most important PU application is in its foam, which is the primary market of PU [90]. PU foams can be categorized into flexible and rigid foams based on open or closed cells [91]. There are some differences between these two types. Rigid PU foams (RPUFs) are a kind of highly cross-linked polymer with a fundamentally close cell structure. They have numerous desirable properties such as low density, low thermal conductivity, good mechanical properties, high strength-to-weight ratio, superb damping abilities, low moisture permeability, low water absorption, excellent weather ability, and excellent dimensional stability [92, 93]. Flexible PU foams (FPUFs) are highly cellular polymers. They exhibit excellent viscoelasticity, making them suitable for packaging applications, comfortable cushions in furniture and automotive, bed mattresses, carpet underlays, and tough floor covers [54, 94, 95]. Additionally, they can be considered as good sound absorbers, mainly in transportation, due to their low density, flexibility, and ease of manufacturing [91, 96]. However, FPUFs are easily ignitable and highly explosive, limiting their more significant usage [94].

PU foams account for the largest market among polymeric foams. A wide range of PU foam applications are briefly listed here. (1) Automotive industry: flexible polyurethane foams are extensively used for automotive seat construction because they can make seats more comfortable [97]. Also, due to a high sound absorption efficiency of PU foams, they are used as sound absorption materials to control and decrease noise and vibration levels in vehicles. Apart from these, they can also be used in car bodies, doors, windows, ceilings, and bumpers because PU foams can increase the performance/weight ratio [98]. (2) Aerospace industry: shape memory PU (SMPU) foam has been applied in hinges, foldable truss booms, coilable truss booms, STEM booms, solar arrays, deployable panels, reflector antenna, and morphing wings in aerospace applications [99]. (3) Building and construction applications: owing to excellent heat insulation capacity, highly desirable strength-to-weight ratio, low cost, easy installation, versatility, and durability, PU foams are extensively used in different parts of buildings. This could be considered as a positive trend because PU foams reduce energy consumption and conserve natural resources and the environment [100,101,102]. (4) Radar absorption applications: PU foams can be used as the core materials in the sandwich structures, which are appropriate structures for this purpose due to their high strength-to-weight ratio [103, 104]. (5) EMI (electromagnetic interference) shielding applications: PU foams have gained attention in this regard owing to their flexibility, lightweight, corrosion resistance, and ease of processability compared with metals, which are made of traditional shields. The main disadvantage of PU foams for this purpose is their low electrical conductivity, which can be improved by adding various kinds of carbon fillers such as carbon black, carbon fibers, carbon nanotubes, and graphene [105, 106]. (6) Biomedical applications: PU foams have been used as central venous catheters, vascular grafts, cardiac valves, mammary prostheses, ocular implants, and drug delivery systems [14]. Improvements in biostability of PU foams through using more stable polysiloxanes and polyolefins and surface modification by the addition of nanoparticles such as graphene, graphene oxide, and CNTs, made them desirable materials for drug release systems, scaffolds, or stents in soft tissue engineering, the absorption of biological fluids or as biocatalytic air filters, with high pH resistance, resistance to solvents, or high temperatures [14, 107,108,109]. (7) Oil absorbents: PU foams can be considered as a good absorbent because of some features such as oleophilicity, hydrophobicity, high uptake capacity, high uptake rate, oil recovery from absorbents, retention over time, reusability, and biodegradability of absorbents [92].

PU foaming methodologies

Foams are a type of materials containing gaseous cavities surrounded by a liquid or solid. Once cured, they consist of cells, which can be opened with interconnected cells or closed with separate cells, which are often non-permeable [110]. Various methods can be used to produce PU foams with various properties suitable for different applications. Molding, slabstock, and spraying are standard techniques used at large scales. In the molding procedure, the reactants are injected into a mold. After curing, the molded foam is detached. This method is extensively used to produce seat cushions for furniture and vehicles. In the slabstock process, the reactants are continuously poured into a moving conveyor. Cushioning and comfort materials are usually produced by this method. In the spraying technique, PU is projected on a surface or cavity. This is typically used to make insulation layers on flat surfaces such as roofs [14]. Polyurethane spray foams may either be open cells or closed cells. Open-cell polyurethane spray foam has a high-density range of 6.4–19 kg/m3 [92]. A new technology named three-dimensional (3D) printing has been recently used to produce PU foams [111, 112]. This technology provides an opportunity for engineers to design products in tailored sizes and shapes for packaging applications.

PU foams as sound absorbers

As mentioned earlier, PU foams are extensively used as construction materials not only as thermal insulators but also as sound absorbers, especially for industrial applications, theaters, offices, and sound studios [14]. Additionally, PU foams are frequently used in the automobile industry to provide comfortable driving conditions for passengers and drivers. In vehicles, undesirable noise is generated from two different sources: airborne noise (500–8000 Hz) due to collisions of air molecules with the car and structure-borne noise (30–500 Hz) due to mechanical vibrations [14, 113, 114]. A significant number of research works have been done to investigate the effect of various types of nanoparticles and fibers on the sound absorption of PU foams and try to enhance the sound absorption coefficient of PU foams.

The effect of various nanoparticles with different dimensions on the sound absorption properties of PU foam is listed in Table 2.

Table 2 Effect of nanoparticles on sound absorption behavior of PU foam
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Figure 8 indicates the sound absorption coefficient (α) of PU foam with additive species (MWCNT/PFA). As seen in this figure, the maximum sound absorption coefficient is shifted to lower frequencies range with increasing MWCNT in the range of up to 1% by weight [116].

Fig. 8
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Sound absorption coefficient of PU foam with additive species (MWCNT/PFA) and frequency. Reprinted with permission from Ref. [116]

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Figure 9 shows the sound absorption coefficient (α) of polyurethane composite foams (a) including talc filler for 0–1% by weight contents and (b) three types of fillers (talc, zinc borate, aluminum hydroxide) at 1% by weight [120]. As seen in Fig. 9a, the increase in talc fillers changes the maximum sound absorption coefficient (α) of composites to lower frequencies. However, as seen in Fig. 9b, the maximum sound absorption also depends on the hydrophobicity of nanoparticles. The pore size of composite foams with hydrophobic fillers is smaller than that of foams with hydrophilic fillers due to differences in cell decay phenomena. This difference in the surface properties of fillers, including the pore size and pores of the composite foams, significantly affects the sound absorption properties of the composite material and the sound absorption efficiency of the foams, causing the sound absorption coefficient to follow a similar trend with its drop modulus. This shows that the measurement reflects the energy lost between the polymer chains and the filler material through microstructural deformation [120].

Fig. 9
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Sound absorption coefficient of polyurethane composite foams a including talc filler at various contents, and b three types of fillers (talc, zinc borate, aluminum hydroxide) at 1% by weight. Reprinted with permission from Ref. [120]

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Table 3 represents the effect of various synthetic and natural fibers on the sound absorption behavior of PU foam. As seen in this table, the best sound absorption behavior of PU foam with synthetic fiber belongs to PU with 0.07% polyethylene fiber with sound absorption of 82–85% in the frequency range of 1600–6300 Hz and with a frequency peak at 5000 Hz [130]. Table 3 also indicates the sound absorption behavior of PU-5% natural fiber rice hull (RH) foam that has a sound absorption of about 98% in the frequency range of 50–1000 Hz and a frequency peak at about 850 Hz [131].

Table 3 Effect of fibers on sound absorption behavior of PU foam
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The effect of the formation of interpenetrated polymer networks (IPN) on the acoustic behavior of PU foam was investigated with different ratios of PU/PMMA. PU/PMMA IPN foams have better sound absorption properties compared to PU and PMMA homopolymers. The 75:25 IPN sample showed the highest sound absorption coefficient compared to other ratios, especially in the frequency range of 1500–4000 Hz. The acoustic performance of the foams improved at a particular frequency because of the formation of IPN foams [140]. Table 4 and Fig. 10 represent the effect of interpenetrating polymer networks (IPN) on the sound absorption behavior of PU foams.

Table 4 Effect of interpenetrating polymer networks (IPN) on sound absorption behavior of PU foams
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Fig. 10
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Sound absorption coefficients of PU and IPN foams with different PU/PMMA mass ratios. Reprinted with permission from Ref. [140]

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Porosity and sound absorption

One of the most important factors that should be considered in the acoustic behavior of porous materials is the number, size, and type of pores. There should be sufficient pores on the surface of materials to allow the sound waves to enter the porous materials, pass through the pores, being dissipated by air friction, and consequently to be absorbed [8, 141]. Porosity is defined as the ratio of the air volume contained within a porous material to the total volume of the material [142]. The porosity value for porous materials is between 0 and 1, while for polymer foams and fibrous materials is in the range of 0.95–0.99 [27]. Porous materials are categorized into three main types of foams depending on the degree of cell opening: open-cell foams, closed-cell foams, and semi-open foams [143]. Generally, materials with open pores have superior sound-absorbing properties than materials with closed pores [144]. Semi-open foams with adequate cell openness can be appropriate sound absorbers [145]. The relationship between the cell openness of PU foam and acoustic behaviors was studied. The PU foam with the greatest cell openness demonstrated better sound absorption performance than others [143, 146]. The effect of pore size on the sound absorption properties of PMMA was investigated. The results revealed that nanoporous PMMA shows a different acoustic behavior compared to microporous PMMA. Microporous PMMAs show one wide peak, while nanoporous PMMAs exhibit two narrower peaks at different frequencies. Besides, nanoporous PMMAs do not absorb sound at high frequencies (6000 Hz), unlike microporous PMMAs [147]. In a study on phenolic foam, it is evident in SEM images that by adding epoxy resin to such foam it has reduced its pore size. With the increase in the amount of epoxy, the pore size becomes smaller, and the distribution of pores becomes more concentrated and homogeneous. The sound absorption performance of phenolic foam was considerably improved by adding epoxy resin from 35% for the pure phenolic foam to 70% for foam with 5% epoxy resin. With the increase in epoxy resin (from 5 to 10% and 15%), the sound absorption coefficient increased significantly. It can be concluded that the higher open-cell porosity and more homogeneous cell distribution result in a higher sound absorption coefficient. Besides, the sound absorption coefficient of phenolic foam increases by reducing pore size [148]. In polyurethane foams, the results revealed that with the reduction of mean cell diameter, the acoustic damping efficiency in low-frequency ranges enhances [149]. For fully reticulated PU foam, reducing pore size increases airflow resistivity and improves sound absorption behavior [150]. The relationship between sound absorption properties of flexible polyurethane (FPU) foam and cell structure was investigated by controlling the cavities and pores in the foam by applying two different kinds of gelling catalyst DBTDL (dibutyltin dilaurate 95%) and DABCO (33% triethylenediamine and 67% dipropylene glycol). DBTDL catalyst is more active in gelling than DABCO, which results in a higher number of small pores and cavities in the FPU foam. Thus, DBTDL-catalyzed foams have lower density values than DABCO-catalyzed foams. Density reduction results in a decrease in sound absorption. However, many small cells compensate for the negative effect of low density on sound absorption by providing irregular transmission routes for the sound waves [114]. In polyurethane composite foam, the effect of magnesium hydroxide (MH) on pore size, porosity, and sound absorption coefficient was investigated. Significant differences were not shown in the pore size by the addition of MH. Therefore, it cannot be a crucial point to comprehend the sound absorption behavior of PU composite foam. In this case, the porosity is the only influencing factor on sound absorption behavior. An increase in open porosity improves the sound absorption properties until an optimum amount, where after that, an increase in porosity has a negative impact on the sound absorption coefficient. The optimum porosity of PU composite foam is 63% with 1% MH, which has reached the highest noise reduction coefficient of 0.53 [113]. Additionally, the effects of multiwall carbon nanotube (MWCNT) and perfluoroalkane (PFA) additives on the sound absorption properties of flexible polyurethane foams were studied. With increasing PFA content up to 1.25 phr, the cell size of the PU foam reduced. Further increase of PFA to 1.75 and 2.50 phr leads to increase in cell size. Therefore, the minimum cell size of 431 µm is achieved by 1.25 phr of PFA. Similar trends were shown by adding hexamethyldisiloxane (HMDS) and MWCNT and the optimum amount was reported to be 1.25 phr and 0.5 phr. The results suggest that a reduction of the cell size within the PU foam by the addition of additives improves the sound absorption behavior [116]. Similar trends in the relationship of cell size and sound absorption coefficient of PU foam were observed by the addition of talc, zinc borate (ZB), and aluminum hydroxide (AH) [120]. Moreover, in another research, the impacts of pore size on the acoustic absorption properties of the closed-cell PU foams were studied. Over the frequency range of 125–2000 Hz, the sound absorption coefficient of closed-cell PU foam increased by pore size increment. Foams with larger pores contained more air and could produce more frictional heat and thus reduce sound energy and improve acoustic properties. Besides, the investigation on the influence of open porosity on the sound absorption coefficient of open-cell PU foam showed that acoustic absorption behavior improved with an increase in open porosity over the frequency range of 125–4000 Hz [146]. Furthermore, in another study, the results revealed that PU foams with uniform cell structure and small cell size have better sound absorption properties than samples with non-uniformed cell structure and large cell size. With decreasing pore size, the number of pores increases. Therefore, the high number of pores results in a high number of cavities which can produce irregular transmission routes of sound waves [151] (Fig. 11).

Fig. 11
figure 11

Acoustic analysis of the75PU-25PMMA IPN nanocomposite foams with different nanoclay contents in the frequency range of 50–6300 Hz. Reprinted with permission from Ref. [36]

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The effect of the number of pores on the sound absorption performance of PU foam was studied. The experimental results showed that the sound absorption coefficient of the PU foam is affected by pore numbers. The more pores exist in a foam, the better would be the sound absorption performance [152]. Moreover, in studying the effect of the porosity on sound absorption coefficients, it was demonstrated that sound absorption at low frequency increases with the increase of the porosity of the kapok-based fiber nonwoven fabrics. The easy movement of the fibers is due to more porosity, which leads to a further reduction of sound waves and, as a result, better sound absorption behavior [153]. Another research proved this direct correlation between porosity and sound absorption coefficient for silica-fume-based foams [154]. In other words, samples with higher values of total porosity exhibit superior sound absorption properties. Table 1 indicates the effect of different components in polymeric foams on pore size, open porosity, and the sound absorption coefficient. As seen in this table, the epoxy component in phenolic foam (PF) has an essential effect on increasing the sound absorption coefficient up to 99%. Besides, polyurethane (PU) foam with pore sizes of about 70 µm and fully reticulated PU foam with DABCO catalysts show promising results in the sound absorption coefficient up to 99% (Tables 5, 6).

Table 5 Effect of pore size and open porosity on sound absorption coefficient
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Table 6 Abbreviation list
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Conclusion

Porous materials, particularly polymeric foams, are the most effective sound absorbers among a wide range of existing sound-absorbing materials. Polyurethane (PU) foams have become the most important class of polymeric foams for sound absorption applications because of their low density, lightweight, good mechanical properties, and ease of manufacturing.

Mechanical foaming, physical foaming, and chemical foaming are the three main foaming methods. The physical foaming method is a preferred technique for polymeric foam production owing to the lack of hazardous chemical components. Foam extrusion molding as a continuous process and foam injection molding as a non-continuous process are the most commonly used techniques for the plastic foam industry.

Various types of nanoparticles and fibers are used to improve the acoustic performance of PU foam. Generally, the effect of nanoparticles on the enhancement of sound absorption is more than the effect of fibers. The addition of CNT, nanoclay, nano-silica, PE fiber, and rice hull significantly increases the sound absorption properties of PU foam. The formation of interpenetrating polymer networks (IPNs) can substantially increase the sound absorption coefficient of PU foams. However, the effect of the IPNs is rarely investigated and can be an area for future investigations.

Pore size and open porosity are the most critical factors influencing the acoustic behavior of foams. Commonly, materials with open pores have superior sound-absorbing properties than materials with closed pores. The higher open-cell porosity and more homogeneous cell distribution result in better sound absorption performance. The addition of nanoparticles and fibers affects the cell size and open porosity of the foams and consequently improves the sound absorption behavior of PU foams.