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Article

Acoustic Applications of a Foamed Geopolymeric-Architected Metamaterial

by
Giuseppe Ciaburro
1,*,
Gino Iannace
1,
Laura Ricciotti
1,2,*,
Antonio Apicella
1,2,
Valeria Perrotta
1,2 and
Raffaella Aversa
1,2,*
1
Department of Architecture and Industrial Design, University of Campania, Luigi Vanvitelli, 81031 Aversa, Italy
2
Advanced Material Lab, Department of Architecture and Industrial Design, University of Campania, Luigi Vanvitelli, 81031 Aversa, Italy
*
Authors to whom correspondence should be addressed.
Appl. Sci. 2024, 14(3), 1207; https://doi.org/10.3390/app14031207
Submission received: 29 December 2023 / Revised: 30 January 2024 / Accepted: 30 January 2024 / Published: 31 January 2024
(This article belongs to the Section Acoustics and Vibrations)
Browse Figures
Versions Notes

Abstract

:

Featured Application

In this paper, a metamaterial design based on lightweight geopolymeric elements was reported for applications in acoustic insulation.

Abstract

The paper compares and evaluates the influence of the presence of perforations on the sound absorption coefficient (SAC) of a negative stiffness metamaterial based on a foamed ceramic geopolymer. Chemical–physical, microstructural, dynamic–mechanical, and sound characterisations are presented. A rigid, lightweight geopolymeric porous material has been prepared using an inorganic/organic monomeric mixture containing oligomeric sialates and siloxanes foamed with aluminium powder. This process results in an amorphous rigid light foam with an apparent 180 Kg/m3 density and a 78% open-pore. The viscoelastic characterisation by dynamic mechanical analysis (DMA) carried out from 10−3 to 103 Hz indicates the behaviour of a mechanical metamaterial with negative stiffness enabling ultrahigh energy absorption at straining frequencies from 300 to 1000 Hz. The material loss factor (the ratio of dissipative/elastic shear moduli) is about 0.03 (essentially elastic behaviour) for frequencies up to 200 Hz to suddenly increase up to a value of six at 1000 Hz (highly dissipative behaviour). The corresponding storage and loss moduli were 8.2 MPa and 20 MPa, respectively. Impedance tube acoustic absorption measurements on perforated and unperforated specimens highlighted the role of perforation-resonant cavities in enhancing sound absorption efficiency, particularly within the specified frequency band where the mass of the negative stiffness foamed geopolymer matrix magnifies the dissipation effect. In the limits of a still exploratory and comparative study, we aimed to verify the technological transfer potentiality of using architected metamaterials in sustainable building practices.

1. Introduction

Several researchers have recently worked to create sustainable building materials. One of the fundamental prerequisites for sustainable construction methods and environmental impact assessments is using green building materials and their manufacturing process [1]. There is a direct correlation between the energy used to produce different building materials and the carbon dioxide emitted while producing the same materials. Both energy consumption and gas emissions, primarily carbon dioxide and monoxide, are rising [2,3]. The European Commission recently adopted several significant measures to achieve (Directive 2002/49/EC as updated in recently amended by the delegated directive (EU) 2021/1226 of 21 December 2020) climate neutrality in the EU by 2050, including an intermediate target of a 55% net reduction in greenhouse gas emissions by 2030 [4,5].
As a result, researching sustainable alternatives to ordinary cementitious materials is a rapidly evolving field focused on the potential use of alkali-activated geopolymers (GPs) as sustainable binders in the building and construction industries.
An average reduction in greenhouse gas emissions during the life cycle of geopolymer concrete was estimated to be 62–66%, with a range of up to 80% compared to an equivalent amount of ordinary Portland cementitious binder used in reference concrete of similar strength [6,7,8].
Geopolymers are a type of aluminosilicate material synthesised by an inorganic polycondensation reaction (also known as “geopolymerisation”) between solid aluminosilicate precursors, and alkaline solutions such as sodium hydroxide (NaOH), potassium hydroxide (KOH), sodium silicate (Na2SiO3), potassium silicate (K2SiO3), or highly concentrated aqueous alkali hydroxide.
From the process perspective [9], alkaline metal salts and hydroxides [8] (i.e., sodium silicate and NaOH) are needed to dissolve the metastable aluminosilicate [8,10] and catalyse the complex polycondensation reaction [11,12] involving linear and cyclic sialate oligomers to form an amorphous structural glass [9] to be used as new, durable [13,14], and more environmentally friendly construction materials [15]. During the alkaline-activated dissolution, the chemical bonds of the kaolin metastable aluminosilicate are fragmented down into hydrated silicate [OSi(OH)3]− and aluminate [Al(OH)4]− ionic precursors [9,16,17,18] involved in the creation of cyclic and linear sialates [9].
Geopolymers are inorganic materials utilised in various fields, including building, repairing and restoring concrete structures, 3D printing, fire-resistant materials, biomaterials, and others [16,17,18]. In addition, they have very interesting properties like low shrinkage [19] and bond strength [20] for cement structure repairs, thermal stability [21], chemical and freeze–thaw resistance [21,22], long-term durability [22,23], and potentially reliable use in greener technologies [24] and recyclability [25]. Advanced applications like catalysts, moisture sensors, heat storage, pH regulators, immobilisation of heavy metal, and new ceramic biomaterial are also under study [25,26,27,28,29,30,31,32,33,34]. The polycondensation process flexibility allows the specialisation of ceramic–organic hybrids [32,33] and composite materials [34,35,36,37,38] with specific rheological and viscoelastic and chemo-physical properties [10] such as slurry thixotropy or final glassy geopolymer mechanical properties and biocompatibility for their applications as speciality materials.
Geopolymers, depending on the Si/Al and activating solution vs. metastable aluminosilicate solid/liquid ratios or the addition of fillers, can be tailored to have a variety of densities, ranging from high-density systems such as mortars and concretes to porous low-weight materials [39,40,41,42,43]. In particular, porous materials can be prepared by incorporating foaming agents into the geopolymer paste during consolidation. Blowing agents, including hydrogen peroxide, metallic Al, and Si powders, can be used [44,45,46]. Using this synthesis approach [47,48], porous materials with pore sizes ranging from nanometres to a few millimetres and total porosity up to 90% can be obtained without the use of high-temperature treatments such as burnout of organics and sintering required for the production of traditional porous ceramics [49].
Processing of geopolymer-based materials enables the development of porous materials with targeted thermal and acoustic conductivity properties. Still, the presence of pores and the highly heterogeneous structure unavoidably affect their mechanical properties, resulting in low compressive strengths (around 1 MPa or less, depending on the corresponding apparent density) [46]. Sodium or potassium silicate alkali-activated kaolin geopolymers [49,50] foaming with fumed silica or silicon powder [47] resulted in consolidated foams with thermal conductivity values of 0.15 Wm−1K−1 or less. The ability of such systems to generate porosity by releasing molecular hydrogen and achieve significant percentages of pore volume (>60%) has already been demonstrated [51]. Porous geopolymer from fly ash precursors with hydrogen peroxide [52] or sodium perborate [53] as foaming agents resulted in consolidated foams with an 80% porosity, a thermal conductivity of 0.08 Wm−1K−1, and compressive strengths ranging from 0.80 to 0.40 MPa. Nevertheless, fly ash-based geopolymer foams with similar bulk densities varying from 400 to 800 kg/m3 obtained higher compressive strengths using aluminium powders as a blowing agent [53].
Adding aluminium powder to the alkaline-activated metakaolin mixture improved the geopolymer’s mechanical properties [54,55].
Due to these improved connectivity and microstructural properties, we aim to develop aluminium-foamed geopolymers with still lower apparent densities of 180–200 Kg/m3, which could further strengthen their applications as thermal and acoustic insulating materials [56,57,58,59,60,61]. Noise impacts the psychology and physiology of animals and humans, leading to accidents and health problems [58,59,60,61]. When sound strikes a material with visible porosity (exposed pores), the acoustic waves are absorbed, their energy is converted to heat, and the sound is dispersed (acoustic absorption) [61]. Several modern acoustic materials need to be more sustainable regarding energy consumption and greenhouse gas emissions; others may be hazardous to human health. Mineral wools are commonly used for thermal and sound insulation due to their high performance and low cost, but their fibres can settle in the lung alveoli when breathed, causing skin discomfort. As a result, they may be unsuitable for interior noise reduction applications [59].

2. Materials and Methods

2.1. Materials

A high-purity metakaolin (BASF MetaMax®) that meets ASTM C-618 Class N pozzolans specifications [62], sodium silicate solution (Prochin Italia S.r.l., Caserta, Italy), and reagent grade sodium hydroxide (Sigma Aldrich, Burlington, MA, USA) were used to prepare the alkaline activating solution and the reacting geopolymer slurry. Oligomeric dimethylsiloxane (Globasil AL20, Globalchimica S.r.l., Turin, Italy) and 60 μm mean size aluminium powder (Sigma Aldrich, USA) were used as slurry viscosity stabiliser and foaming additives, respectively. The house chemical specifications of the metakaolin and sodium silicate, as received, are reported in Table 1.

2.2. Reactive Slurry Preparation, Foaming, and Curing Procedures

Figure 1 describes the mixing, foaming, and hard-setting procedures and the formation of monomeric chemical precursors while preparing the foamed samples. These phases start with the alkaline-activated metakaolin reacting slurry preparation (“0” and “1” in the upper part and right part of the Figure), continue with the addition of the viscosity stabiliser and foaming additives (“2” and “3” in the Figure), and finally, to the end with the mould casting and hard setting in controlled temperature and humidity conditions (“4” in the Figure).
Sodium hydroxide pellets were first dissolved in the silicate aqueous solution in a ratio of 0.13/1, sealed, left to cool down and equilibrated at room temperature for 24 h before use. Next, the manually mixed metakaolin powder and activating solution slurry (mixed in a solid-to-liquid ratio of 1.4/1.0) was sonicated for three minutes using a vertical mechanical ultrasound sonicator (UP100H, Hielsher, Germany). After sonication, the freshly prepared geopolymeric suspension was promptly added with 10% by weight of the oligomeric dimethyl-siloxane mixture and stirred for 10 min in a mixer (AM40-D ARGO LAB, Carpi, Italy) operating at 800 rpm. Foaming was obtained by adding 1% by weight of aluminium powder in the activated slurry and further stirring it for 5 min at 1000 rpm.
The reactive and additivated geopolymeric slurry composition is reported in Table 2.
The sialates polycondensation process, occurring in the reactive foamed slurry and transforming it from a liquid of increasing viscosity and elasticity into a solid glass, consists of three main steps [9,10,11]:
1. Free tetrahedra of hydrated silicate [OSi(OH)3]− and aluminate [Al(OH)4]− ionic precursors are formed [8,9] when metakaolin dissolves in the concentrated alkali solution (Equation (1) and upper part of Figure 1).
(Metakaolin) Al2Si2O7 (s) + 4OH− (l) + 5H2O → 2Al(OH)4− (l) + 2[OSi(OH)4]−.
2. Inorganic linear and cyclic sialate oligomers are formed by polycondensation of the hydrated silicate and aluminate hydroxyl groups [63,64]. Namely, the principal oligomers initially formed in the alkaline reacting liquid determined by NMR [64] are sialates with a ratio Si/Al = 1/1, silate–siloxo with a ratio Si/Al = 2/1, and sialate–disiloxo with a ratio Si/Al = 3/1, and are reported in Figure 1 as phase “0”.
3. The sialates’ oligomer poly-condensation reaction continues increasing macro-molecular weight and complexity by branching and crosslinking, reaching a gelled rubbery state before hardening into an amorphous glass (phases from 1 to 4 in Figure 1).
The addition of the aluminium powder has been described as influencing the evolution of the forming geopolymer [55]. Its reaction in the aqueous alkaline medium [55] results in the formation of gaseous molecular hydrogen and aluminium hydroxide (Equation (2)) that promptly dissolves in the alkaline solution, forming additional hydrated aluminate (Equation (3) equilibrium reaction from left to right):
2Al (s) + 6H2O (l) → 2Al(OH)3 (s) + 3H2 (g),
Al(OH)3 (s) + Na+ (l) + OH− (l) ↔ Na+ (l) + Al(OH)4− (l).
As indicated before, in the initial polymerisation stages, metakaolin (Al2Si2O7) particles start to dissolve in the alkaline activating solution (Equation (1)), forming hydrated silicate and aluminate ionic precursors. When the metallic aluminium powder is added, sodium hydroxide is consumed to form molecular gaseous hydrogen (Equations (2) and (3)), further increasing the hydrated aluminate concentration in the reacting solution (direct reaction Equation (3)), but when exceeding saturation, the hydrated aluminate undergoes a reverse reaction (Equation (3) from right to left) regenerating the hydroxyl ions’ OH− concentration, while precipitating aluminium hydroxide gels on the metakaolin reactive surfaces. This event hinders metakaolin reactivity. Nevertheless, the neo-formed aluminium hydroxide gel dissolves again (direct Equation (2)) as the concentration of hydrated aluminate [Al(OH)4]− is reduced by its reaction with hydrated silica precursor [OSi(OH)3]− to form the sialates’ oligomers (reported on the right part of Figure 1). This aluminium hydroxide precipitation/dissolution mechanism reduces the actual metakaolin dissolution rate and reactivity, slowing the kinetics of the geopolymerisation process [55]. However, this phenomenon has been described to lead to a better connectivity of the polysialate gelled particles and a better microstructural geopolymer development [54,55].
After the stirring procedures following the dimethylsiloxane and aluminium powder addition, the still liquid foamed slurry was poured into cylindrical moulds (100 mm diameter and 300 mm length) and cured at >95% relative humidity and 60 °C for 24 h (phase “4” in Figure 1). The hard stetted specimens were then kept at room temperature for six days at a relative humidity higher than 95% and matured in the air for 21 days.

2.3. Methods

2.3.1. Architected Mechanical Metamaterials: New Design Approaches and Perspectives

An innovative approach to developing new sound absorption materials comes from the challenge of developing architected metamaterials whose properties and behavioural responses depend on mating material properties and spatial morphologies. Such metamaterials are a class of artificial materials whose geometry and composition are engineered to show peculiar properties or programmed responses not found in conventional materials. However, there are further opportunities to develop new metamaterials derived from observing naturally evolved biosystems where structure randomness is part of their functional efficiency. The increasingly prominent role that disorder plays in novel design strategies for such architected mechanical metamaterials has been recently highlighted [65,66]. These papers propose a new scientific approach within and beyond the mechanical domain, categorising mechanical metamaterials concerning multifunctionality and autonomy [65] for developing new classes not anchored to purely rational and mechanistic approaches. Incorporating disorder into a mechanical metamaterial’s design, typically periodic in repeating a structural unit, can improve functionalities over ordered structures [66], such as negative stiffness structures that absorb energy via buckling, enabling ultrahigh energy absorption efficiencies [67].
In this perspective, we start from examples of biological materials with disordered structures that suggest new bioinspired and biomimetic approaches to explore the potentiality of architected metamaterials by emulating these evolutionary natural-born materials [65,66,67,68,69,70,71]. Cellular materials of the animal and vegetal reigns exploit anisotropy and morphology to increase their mechanical efficiency, placing structured material where most is needed to resist the applied loads while presenting unusual properties [67,68].
Until now, research on these metamaterials has been focused on passive periodic “mechanical-metamaterials” with tunability of their mechanical properties. Nevertheless, according to this “disorder” bioinspired criterium [66,69], such 3D-architected metamaterials could enable the creation of mechanobiological active pore structure interconnectivity, leading to unexpected physical properties [68,69,70,71].
Examples of biological materials with disordered structures that elucidate how disorder can enhance functional efficiency are given in Figure 2.
Evolution-engineered natural metamaterials resemble these non-regular and orthotropic trabecular micro-structures reported in the figure. Porous materials are present as evolution-adapted complex architected morphologies in the natural reigns, i.e., as cellulosic-based woods or leaves (Figure 2a,b), in hard tissues containing nanoparticles, spines, and spicules structures such as the trabecular silica and hydroxyapatite skeletons in sponges or animal bones (Figure 2c,d), or as lignin and cellulose lightweight suber cortex and iris leaves (Figure 2d,e). In these evolutionary examples, functional holes or pores supply nutrients, maintain a sustainable lightweight structure, and allow fluid permeability, thermo-insulation, bouncing, and other evolutionary requirements.
Gains and drawbacks posed by casualty [65,66] disclose the opportunities deriving from disorder-driven new design strategies to optimise architected metamaterials and propose new characterisation methods to highlight experimental data-driven approaches for the design [65] and bioinspired systemic vs. systematic new materials design approach [71].
New 3D-architected acoustic metamaterials can be advanced systems able to handle complex acoustic waves and vibrations. The design of metamaterials based on lightweight geopolymeric porous elements could be driven by the knowledge of their chemical-physical, microstructural, dynamic-mechanical, and acoustic properties. Our paper intends to pair and integrate viscoelasticity dynamic mechanical and acoustic characterisation methods to create experimental findings for enhanced data-driven designs. This challenge could lead to newly architected metamaterials with improved acoustic performances.
We can identify a “metamaterial” when a particular combination of system morphology and physical properties shows unusual and unexpected properties. In our case study, we intend to investigate the morphology and the viscoelastic properties observed in a porous geopolymer-based 3D-architected “metamaterial” exposed to high deformation frequencies and correlate them with the level of sound energy absorption and structure resonance characteristics. The amorphous and porous potential metamaterial will be obtained by foaming a geopolymeric slurry containing silicon rubber and aluminium powder additives and further modifying it by differently perforating the ceramic foams. The system will be described for its morphological, macro-structural, and dynamic mechanical properties and ability to promote resonance and sound absorption. The acoustic absorbing efficiency of the developed geopolymer metamaterials will be estimated by applying semiempirical formulas and numerical models.

2.3.2. Morphological Characterisation

Scan electron microscopy at magnifications from 10× to 1100× of the foamed geopolymeric material was performed using a Neoscope JCM-6000 operating in low vacuum and at high voltage (15 kV) on samples without metallisation.

2.3.3. Dynamic Mechanical Analysis Test Procedures and Theoretical Bases

The dynamic mechanical analyses have been run on a Mettler Toledo Dynamic Mechanical Analyzer (DMA-SDTA 1+) operating in shear force (max 0.5 N) and displacement (max 10 μm) control modes.
The oscillatory shearing viscoelastic properties of the geopolymer were monitored in a frequency sweep from 10−3 to 103 Hz. The dynamic mechanical characterisation discerns and isolates the viscous and elastic components of the system’s mechanical response to an external oscillatory solicitation (Figure 3a).
Two identical size specimens, 10 × 10 × 5 mm, as reported in Figure 4, have been symmetrically sandwiched in the sample assembly reported in Figure 3b (with a 5 mm thickness gap) between three circular steel plates of 20 mm diameter.
The two stationary outer parts of the sample assembly are connected with a force sensor (the white part of the sample holder in Figure 3b) while the central disk moves at a controlled sinusoidal strain of steady amplitude (maximum displacement Δx = 10 μm) and oscillation frequency f (or expressed as the angular frequency of ϖ = f 6.28 rad/s):
γ(t) = γ0 sin ϖ t.
Due to the intrinsic characteristics of this test, we may be able to exploit the results in terms of viscous and elastic components derived from the experimentally measured complex shear moduli (enclosing both energy dissipative and storage contributions) according to the mechanical response time delay (δ) of the material to an imposed oscillatory deformation. The force sensor detects the counter forces to keep the side plates in position:
F/A = τ(t) = τ0 sin (ϖ t + δ).
The recorded shear stress τ(t), once correlated with the applied sinusoidal shear rate dγ(t)/dt of (Equation (1)), measures the apparent shear modulus G* containing both the elastic and viscous responses of the sample:
G* = τ(t)/dγ(t)/dt.
The vectorial representation of the apparent modulus with a real and an imaginary part is used to account for the two components and separate them using the delay time δ:
G* = G′ + iG″,
the delay time δ, defined in Figure 3b, is the phase angle shift indicating the direction of the complex modulus (previously named apparent modulus) G* (blue vector in Figure 3c). At the same time, the two components are the vectors G′ and G″ (green and red, respectively) with magnitude:
G′ = G* sin(δ)         Storage modulus,
G″ = G* cos(δ)               Loss modulus.
The direction of the elastic vector (storage modulus), which belongs to the purely elastic behaviour of the tested medium, is parallel to the direction of the applied deformation (the horizontal axis in Figure 3c). Conversely, the direction of the viscous vector (loss modulus) is orthogonal to that of the applied deformation (vertical axis in Figure 3c). Phase shift angles ranging from 0° (for purely elastic behaviour) to 90° (for purely viscous behaviour) indicate the relative predominance of the material elastic-storage (G′) and viscous-dissipative (G″) varying responses of the material under mechanical deformation. The ratio between the loss and storage mechanical response components is a loss factor and, according to Equation (10), is the tangent of the shift angle (tanδ). This parameter provides a measure of the relative predominance of the dissipative (tanδ > 1) and elastic (0 < tan δ < 1) character of the material:
Loss factor = tan δ = G″/G′.

2.3.4. Acoustic Characterization

This study investigated the material’s static airflow resistivity (SAR) under ISO 9053:1991 [72]. Airflow resistivity measures how easily air can pass through a material, which is a critical parameter in determining the sound absorption properties of a porous material. An alternating air flow method was adopted [73]. This method is recognised for its simplicity, accuracy, and ability to measure resistivity over various airflow velocities [73,74]. The setup employed a specially designed device comprising a cylindrical tube, a piston system with a rotating cam for generating alternating airflow, and a pressure microphone for measuring the pressure fluctuations within the tube (Figure 5a). The measurements were repeated with different cams to assess their impact on the airflow resistivity of the tested material [73].
The alternating air flow method has several advantages over other methods, including:
  • It requires a smaller sample size than the impedance tube method. This is because the sound field is more uniform around the sample, reducing the edge effects.
  • It can measure airflow resistivity over a broader range of airflow velocities than other methods. This is because the geometry of the impedance tube does not restrict the airflow.
  • It is faster than other methods. This is because the measurement does not require a frequency sweep.
The alternating air flow method is a powerful tool for measuring airflow resistivity. It is particularly well-suited for measuring SAR of materials with high airflow resistivity or for measuring SAR over a wide range of airflow velocities.
The sound absorption coefficient (SAC) measurements were carried out under ISO-10534-2:1998 [75].
Sound absorption coefficient measurements play a crucial role in understanding the acoustic properties of materials [76]. Accurate and reliable measurements are essential for designing spaces with optimal acoustic conditions. One widely accepted method for determining sound absorption coefficients is the impedance tube, which has proven effective in various applications using perforated panels [77,78]. This is the case of our samples consisting of perforated geopolymeric ceramic foams.
Sound absorption refers to the process by which sound energy is absorbed by a material rather than being reflected. The sound absorption coefficient quantifies this behaviour and is defined as the ratio of absorbed sound to incident sound energy.
The impedance tube (or Kundt tube) is the classic apparatus used for measuring the speed of sound in gases and determining the acoustic properties of materials, including sound absorption coefficients. The device consists of a long, narrow tube filled with the material under investigation (Figure 5b). A sound source generates standing soundwave at one side while a movable piston at the opposite side of the tube varies its length until resonance occurs. The impedance tube used in our tests is the Model SCS type 9020B/K operating on the principle of tested material natural resonance frequency. Namely, the standing wave within the tube sets up high- and low-pressure areas, causing the material to vibrate at the same frequency as the sound wave. By adjusting the tube’s length until resonance is achieved, we can determine the wavelength of the sound wave. This information, along with the frequency of the sound source, allows for calculating the speed of sound in the material. The sound absorption coefficient (SAC) can be deduced from the sound speed and the material’s density [75].
This study used an impedance tube with the following dimensions: an internal diameter of 10 cm (corresponding to an upper-frequency limit of 2000 Hz), a length of 56 cm, and two ¼″ microphones placed at 5 cm for measurements above 200 Hz. These dimensions were selected to ensure accurate and reliable measurements across various frequencies.
Ensuring repeatability of measurements in an impedance tube is critical to obtaining reliable and consistent results. In our study, we developed and strictly used this standardized procedure for all samples for sample preparation, placement in the impedance tube, and measurement acquisition. We ensured that the samples used in the measurements were homogeneous. Preliminary multiple replicate measurements for each sample confirmed repeatability.
As indicated in our previous work [79], starting from the sample thickness, the sound absorption test needs to establish the wave number. Subsequently, surface impedance (zs) and sound absorption coefficient (α) were computed based on this information, employing the following equations:
z s = − j z c c o t ⁡ ( k c d )
where zc (Pa·s/m) is the characteristic impedance and d (m) is the sample thickness.
Sound pressure reflection coefficient R was evaluated using the surface impedance (zs) and the air density ρ 0 (kg/m3):
R = z s − ρ 0 c z s + ρ 0 c
The sound absorption coefficient (α) is calculated from the sound pressure reflection coefficient R:
α = 1 − | R | 2

3. Results and Discussion

3.1. Morphological Characterisation

Figure 6 shows the geometry, size, and morphology of the samples used in the acoustic tests. A homogeneous foamed structure is produced when aluminium micro-powder and dimethylsiloxane are added to the geopolymeric reactive slurry as foaming agents and viscosity stabilisers.
Examining Figure 6 and the electron scanning microscopies shown in Figure 4 and Figure 7, it is possible to recognise macropores relatively uniformly distributed in the specimen, resulting in a good homogeneity in dimension and shape. Moreover, the sample has a geometrically calculated apparent density of 0.180 Kg/m3 and an open porosity of 78% [40].
The foamed geopolymer’s internal morphology and fine structure have been investigated by electron scanning microscopy and are shown in Figure 7.
The foam morphology is characterised by a multi-walled, partially open cell regular structure. The size of the foam pores ranges from 1.5 to 2.0 mm (Figure 7a). The cell’s walls are characterised by irregular thicknesses (Figure 7b) that, in the case of Figure 7c, range from 35 to 8 μm.
The fine structure of the dense part of the foamed geopolymer is characterised by spherical inclusions, such as that indicated by arrows in Figure 7d. A circle highlights their corresponding negative footprints. Spheroid sizes ranges from about 1 to 3 μm, which can be attributed to the silicon rubber phase separated during geopolymerisation (indicated as blue areas in phase 2 of Figure 2). The reaction of polymethylsiloxane oligomers typically occurs through a radical mechanism catalysed by metal complexes (e.g., Sn(IV)) [80]. The addition of the catalyst into the reaction medium would favour the 4-polymerisation reaction of the polydimethylsiloxane oligomers, causing the polymer separation and segregation from the forming polymeric matrix, leading to the formation of the polysiloxane aggregates shown in Figure 7d.

3.2. Dynamic Mechanical Analysis

Figure 8 shows the viscoelastic response at 25 °C of the foamed geopolymeric hybrid material undergoing a mechanical six-decade frequency sweep from 1 × 10−3 Hz to 103 Hz in a logarithmic scale relationship between frequency and shear modulus. The storage (G′ blue dots) and loss (G″ green dots) shear moduli and the loss factor (red dots) are reported on the left axis (in MPa) and the right axis, respectively.
According to the Loss factor rheogram of Figure 8 (red curve), the system behaves at very low frequencies, 1 × 10−3 Hz, as highly dissipative, as could be expected from an amorphous polymeric viscoelastic medium, with a loss factor of about six, signifying that the loss modulus G″ is six times higher than the elastic storage modulus G′. Therefore, most of the imposed deformation energy is dissipated in viscous processes at this low frequency of cycling loading. As frequency increases, however, the loss factor (tan δ) progressively decreases, stabilising itself from above 4 × 10−3 to 0.1 Hz to values oscillating around 0.07 and from 0.1 to about 100 Hz to still lower values of 0.03. In this wide frequency range, the material behaves as an almost entirely elastic medium where the storage modulus is up to 150 times higher than the loss modulus, signifying that the applied deformation energy is not lost in dissipative viscous processes. For frequencies from 100 Hz to 1000 Hz, the dissipative character of the material progressively increases, becoming predominant from above 400 Hz.
The tested structure then shows a distinctive characteristic that collocates it among the negative stiffness metamaterial, where properties depend on their architecture other than chemical composition [81,82]. However, although these structures have been described to have limitations in reusability after energy absorption [82], in the present and previous studies [83], the fabricated geopolymeric foams preserve the performances of negative stiffness structures in terms of energy absorption and keep their original configuration even after severe cyclic loading at 1000 Hz as depicted in Figure 7a for a sample that underwent the high-frequencies shear DMA test.

3.3. Sound Absorption Coefficient Results

In this study, different samples of the foamed geopolymer were used, and to increase the sound absorption properties, these samples were assembled to simulate a Helmholtz resonator [84]. Helmholtz resonators consist of a cavity connected to the environment by a small opening called the resonator neck, which is typically much smaller than the cavity. When a sound wave strikes the inlet of the resonator, the air in the neck oscillates, much like an oscillating piston [85]. At the same time, the air inside the cavity is alternately compressed and expanded, acting like a spring.
Resonators exhibit heightened absorption at their resonant frequency but minimal absorption at other frequencies. Consequently, it becomes feasible to construct precisely calibrated devices for absorbing specific frequencies. To simulate the behaviour of the Helmholtz resonator, two samples of different thicknesses (40 mm and 60 mm) were used with perforations of various thicknesses and lengths. Eight different combinations of samples were assembled to measure performance as a sound-absorbing material (Table 3 and Figure 9).
Initially, our investigation involved the measurement of static flow resistance, a parameter assessed under the guidelines stipulated in ISO 9053:1991 [72]. Multiple measurements were conducted on various samples, each constructed by positioning the bulk material within a 20 mm thick support. The acquired measurements were subsequently averaged to derive representative values for analysis. We measured a static flow resistance of 27.000 Rayl/m.
Figure 10 illustrates the sound absorption coefficient values measured at normal incidence, plotted against frequency. The data represents each of the eight sample types listed in Table 3.
Upon conducting an initial analysis of the sound absorption coefficient trends, a notable observation emerges, indicating that the configuration involving double specimens featuring perforations to simulate the characteristics of a resonator yields the most favourable outcomes [86]. Specifically, the curves associated with the doubled specimens exhibit elevated sound absorption coefficient (SAC) values, particularly within 250 Hz to 1250 Hz. This suggests that including double specimens with perforations significantly enhances the absorption capabilities in the specified frequency spectrum. The distinct advantage becomes evident as these configurations outperform others in effectively attenuating sound across the analysed frequencies.
In Table 4 we compared the measured values of the sound absorption coefficient of the metamaterials under investigation in this study with those already available in the literature of two of the most common synthetic materials (fiberglass and sprayed cellulose fibre).
From the comparison, we can verify that the SAC of the materials studied are comparable with those of the materials already available in the literature [87], or even better as is the case at 125 Hz.
To better understand the behaviour of the different types of combinations, we compare them by groups.
Figure 11 compares the solid and perforated length of a single-layer sample with a thickness of 20 mm. We can see that the solid sample returns slightly higher values in the frequency range from 160 Hz to 800 Hz. For higher frequencies, the perforated sample returns higher values than the SAC. The observed variations between the solid and perforated single-layer samples, both having a thickness of 20 mm along the entire length, can be justified by the distinct acoustic characteristics of the materials at different frequency ranges. The solid sample exhibits slightly higher values from 160 Hz to 800 Hz in the frequency range. A possible explanation for this behaviour could be related to the negative stiffness and highly dissipative characteristics of the foamed geopolymeric samples occurring at frequencies above 100 Hz (see DMA tests of Figure 8) that are magnified by the additional resonance effects introduced by perforations. At higher frequencies, the perforated sample surpasses the solid sample, reaching higher sound absorption coefficient values (SAC) values.
This trend can be elucidated by the perforations’ capacity [77,78] to introduce acoustic impedance mismatches, leading to increased sound absorption efficiency at higher frequencies. The perforations likely contribute to dissipating sound energy effectively in this frequency range, demonstrating their advantage over the solid counterpart [85,86]. Therefore, the observed variations in sound absorption performance between the solid and perforated samples can be rationalised by considering the specific frequency-dependent characteristics of the foamed material (behaving as a negative stiffness metamaterial) and the unique acoustic mechanisms associated with each perforation configuration of the samples [77,78].
Figure 11a compares the single-layer sample with a thickness of 40 mm, solid and perforated for the entire length. We can see that the solid sample returns higher values in the frequency range from 160 Hz to 500 Hz. As described before, the perforated sample returns higher SAC values at higher frequencies, even in this case. Compared with Figure 11, we can see that the sample with greater mass slightly increases the acoustic absorption coefficient at low frequencies. While the sample with greater thickness at higher frequencies presents lower values. It is also noted that the change in performance occurs at lower frequencies for the sample with greater thickness. The differences observed in Figure 11b between the solid and perforated single-layer samples, with a thickness of 40 mm along the entire length, can be explained by considering the impact of the higher mass of the negative stiffness high dissipative foamed geopolymer on acoustic absorption across the specific frequency range highlighted by the dynamic mechanical analysis (Figure 8).
Conversely, at higher frequencies, the perforated sample exhibits higher SAC values. The perforations in the material introduce mechanisms such as Helmholtz resonance and greater surface area, enhancing its ability to absorb sound energy at higher frequencies. This phenomenon aligns with the perforated sample’s advantage in dissipating sound energy efficiently in the higher frequency range. When comparing Figure 11b with Figure 11a, the influence of thickness becomes apparent. The sample with a greater thickness (40 mm) exhibits a slight increase in acoustic absorption coefficient at low frequencies compared to the 20 mm thick sample. However, at higher frequencies, the thicker sample presents lower SAC values. This shift in performance at lower frequencies for the thicker sample suggests that the acoustic behaviour is more sensitive to thickness variations in this frequency range. The observed trends in Figure 11b can be justified by considering the interplay between mass, thickness, and perforations, which collectively influence the acoustic absorption characteristics of the material across different frequency ranges.
Figure 11c compares the single-layer sample with a thickness of 20 mm and a full 40 mm and the double sample with a full thickness of 60 mm. We can see that the solid double sample at 60 mm thickness returns higher values in the frequency range from 250 Hz to 2000 Hz. For the single-layer samples, we see that at frequencies from 160 to 500, the 40 mm thickness sample returns values higher than the sac, while at higher frequencies, it is the one at 20 mm, which returns higher values. The observed trends are in Figure 11c, comparing the single-layer samples with thicknesses of 20 mm and 40 mm, along with the double sample with a total thickness of 60 mm, which can be justified by considering the interplay of thickness and configuration on acoustic absorption characteristics. For the solid double sample with a thickness of 60 mm, higher values in the frequency range from 250 Hz to 2000 Hz are likely attributed to the combined effect of increased mass of negative stiffness metamaterial and its thickness. The additional thickness contributes to enhanced low- and mid-frequency absorption capabilities, while the increased mass further aids in the dissipation of sound energy across the specified frequency range. The synergy of these factors results in the solid double sample exhibiting higher sound absorption coefficient (SAC) values within this frequency band. When comparing the single-layer samples, the 40 mm thick sample returns higher values than the SAC in the frequency range from 160 Hz to 500 Hz. This can be attributed to the increased mass and thickness, which contribute to improved low-frequency absorption. In contrast, the 20 mm thick sample returns higher values at higher frequencies. This shift in performance is likely due to the thinner sample being more responsive to higher frequencies, where the mass and thickness are not as critical, and other acoustic mechanisms, such as perforations or resonance, might play a more significant role. The observed trends in Figure 11c emphasise the importance of considering both thickness and configuration in the context of acoustic absorption. The thickness of the material influences its performance across different frequency ranges, with the combination of increased negative stiffness metamaterial mass and thickness generally contributing to improved absorption capabilities, especially in the low- to mid-frequency range. The specific configuration, such as the presence of perforations or the arrangement of layers, further modulates the acoustic behaviour, leading to the observed variations in SAC values across the frequency spectrum.
Figure 11d compares the solid and perforated double-layer samples with a thickness of 60 mm for a length of 20 mm. We can see that the drilled samples have a higher SAC in the frequency range from 400 Hz to 1600 Hz compared to the double solid one at 60 mm. The trends observed in Figure 11d, where the solid and perforated double-layer samples with a thickness of 60 mm and a length of 20 mm are compared, can be explained by the impact of perforations on the acoustic absorption characteristics within specific frequency ranges. The frequency ranges from 400 Hz to 1600 Hz, and the perforated double-layer samples exhibit higher sound absorption coefficient (SAC) values than the double solid sample at 60 mm thickness. This phenomenon is likely attributed to drilled perforations, which introduce additional mechanisms for sound absorption. Perforations can lead to Helmholtz resonance and increased surface area, which enhance sound absorption efficiency, particularly within the specified frequency band where the mass of the negative stiffness behaviour of the foamed geopolymer matrix could magnify the dissipation effect. The perforated double-layer configuration is better suited to capitalise on these additional acoustic absorption mechanisms, resulting in higher SAC values in the mid-frequency range.
In contrast, the solid double-layer sample may rely more on mass and thickness for absorption, and in this specific frequency range, the perforated configuration proves more effective. The observed trends in Figure 11d highlight the significance of perforations in influencing the acoustic absorption characteristics of double-layer samples, particularly in the mid-high frequency range where the mass of the negative stiffness metamaterial becomes relevant. Perforations enhance resonance, magnifying sound energy dissipation and leading to higher observed SAC values than the solid counterpart at 60 mm thick.

4. Conclusions

The paper compares and evaluates the influence of the presence of perforations on the sound absorption ability of the foamed ceramic polymer that, according to dynamic mechanical characterization, behaves as a metamaterial with negative stiffness. In this perspective, the presented data have a simple comparative sense to elucidate the ongoing phenomena leading to SAC improvements, and the test repetitions were carried out in the same experimental condition on differently configurated samples. This preliminary investigation underscores the pivotal role of sustainable building materials in green design and construction, particularly architected metamaterials. Focused on integrating environmentally friendly building materials with exceptional acoustic insulation properties, this research unveils a novel approach through designing and characterising lightweight geo-polymer-based metamaterials. The essence of sustainability is embedded in the selection of materials that not only fulfil structural requirements but also contribute to the overall well-being of the environment. Adopting architected metamaterials represents a promising avenue in this endeavour, as it offers a unique synergy between structural integrity and eco-friendliness. In this context, the foamed geopolymer structure emerges as a noteworthy innovation, embodying an organic-inorganic system augmented by incorporating an oligomeric polysiloxane and aluminium powder as a foaming agent. A standout feature of the developed metamaterial is its remarkably low apparent density of 180 Kg/m3, coupled with a substantial 78% open-pore foam structure. This achievement contributes to the material’s lightweight nature and positions it as an ideal candidate for applications demanding efficient sound insulation. Creating such a structure symbolises a meticulous process combining various elements to yield a “metamaterial” with multifaceted benefits.
One of the significant contributions of this research lies in its comprehensive characterisation of the metamaterial. The chemical-physical, microstructural, dynamic-mechanical, and sound properties were systematically examined, providing a holistic understanding of its capabilities. We pair acoustic and dynamic mechanical tests with a critical interpretation of the chemical and morphological aspects related to the processing of aluminium powder foamed geopolymers. The lightweight ceramic geopolymeric foams showed unusual viscoelastic properties, such as being highly dissipative at high deformation rates (which is just the opposite of what you can expect from viscoelastic materials) that allowed us to further investigate this foamed system as a potential base for the preparation of acoustic architected metamaterials. The foamed geopolymer’s success as an acoustic wave absorption metamaterial is particularly noteworthy, presenting promising prospects for its utilisation in sound insulation applications.
The dynamic mechanical viscoelasticity analysis adds another layer of insight, revealing the negative stiffness metamaterial’s exceptional energy dissipation characteristics across a spectrum of frequencies. Notably, the material exhibits high energy dissipation at very low frequencies and frequencies exceeding 300 Hz. The shear modulus values of approximately 8.2 MPa in its elastic component and around 20 MPa as its dissipative component. Beyond the laboratory findings, the practical applications of this metamaterial are significant. Its attributes position it as a game-changer in sound absorption, with potential applications ranging from residential buildings to industrial settings where noise control is paramount. The lightweight nature of the material further facilitates ease of handling and installation, making it an attractive option for various construction scenarios. In the broader context of sustainable architecture, integrating architected metamaterials such as the lightweight geo-polymer-based foam presented in this study aligns with the principles of environmental responsibility. These metamaterials reduce the ecological footprints associated with construction activities by offering a viable alternative to traditional building materials. The emphasis on acoustic insulation adds a layer of human-centric design, recognising the importance of creating spaces prioritising comfort and well-being.
In the limits of a still exploratory study, we aimed to verify the technological transfer potentiality of using architected metamaterials in sustainable building practices. The lightweight geopolymer-based foams could be considered a compelling model example, showcasing a harmonious blend of eco-friendliness, structural efficiency, and acoustic performance. As the architectural landscape continues to evolve, innovations in materials science, exemplified by this research, play a pivotal role in shaping a future where construction is synonymous with durability and environmental stewardship.

Author Contributions

Conceptualization, G.I. and R.A.; methodology, G.C. and L.R.; software, G.C. and V.P.; validation, G.I., R.A. and A.A.; formal analysis, R.A. and G.I.; investigation, G.C., L.R. and V.P; data curation, V.P. and G.C.; writing—original draft preparation, R.A. and G.C.; writing—review and editing, A.A. and G.I.; visualisation, V.P.; supervision, R.A. and G.I. All authors have read and agreed to the published version of the manuscript.

Funding

Prin 2022. Geopolymers for Advanced Eco-Architecture: A Chemorheology and Thermo-kinetic investigation for developing 3D Printable formulations—GEA.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Acknowledgments

The authors deeply acknowledge Giuseppina Roviello and Claudio Ferone of the Department of Engineering of the University Parthenope for their technical and scientific support in preparing the foamed geopolymeric samples.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Scheme of the foamed sample preparation by geopolymerisation.
Figure 1. Scheme of the foamed sample preparation by geopolymerisation.
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Figure 2. Examples of evolutionary adapted porous structures in living organisms [65,66,67,68,69,70,71].
Figure 2. Examples of evolutionary adapted porous structures in living organisms [65,66,67,68,69,70,71].
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Figure 3. Viscoelasticity principles and analysis tools: (a) Shear behaviours in purely viscous liquid and purely elastic solid; (b) DMA shear test tool and viscoelastic behaviour measurements; (c) Vector representation of complex shear modulus and storage and loss components relationships.
Figure 3. Viscoelasticity principles and analysis tools: (a) Shear behaviours in purely viscous liquid and purely elastic solid; (b) DMA shear test tool and viscoelastic behaviour measurements; (c) Vector representation of complex shear modulus and storage and loss components relationships.
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Figure 4. Morphology of the foamed geopolymers specimens 10 × 10 × 5 mm used in the DMA tests (Magnification × 10).
Figure 4. Morphology of the foamed geopolymers specimens 10 × 10 × 5 mm used in the DMA tests (Magnification × 10).
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Figure 5. (a) Airflow resistance measurements instrument. (b) Impedance tube for measuring the absorption coefficient at normal incidence (Model SCS type 9020B/K).
Figure 5. (a) Airflow resistance measurements instrument. (b) Impedance tube for measuring the absorption coefficient at normal incidence (Model SCS type 9020B/K).
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Figure 6. Geometry, size, and morphology of the samples used in the acoustic tests.
Figure 6. Geometry, size, and morphology of the samples used in the acoustic tests.
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Figure 7. Scanning electron microscopy of the morphology and fine structure of the foamed hybrid geopolymer after use in the acoustic tests and DMA viscoelastic characterisation: (a) 30×, (b) 70×, (c) 240×, and (d) 1100×.
Figure 7. Scanning electron microscopy of the morphology and fine structure of the foamed hybrid geopolymer after use in the acoustic tests and DMA viscoelastic characterisation: (a) 30×, (b) 70×, (c) 240×, and (d) 1100×.
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Figure 8. Frequency sweep viscoelastic response of the foamed hybrid geopolymer in the dynamic mechanical tester operating at 25 °C and in the range of frequencies from 10−3 to 103 Hz.
Figure 8. Frequency sweep viscoelastic response of the foamed hybrid geopolymer in the dynamic mechanical tester operating at 25 °C and in the range of frequencies from 10−3 to 103 Hz.
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Figure 9. Samples of different thicknesses and perforation design.
Figure 9. Samples of different thicknesses and perforation design.
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Figure 10. Sound absorption coefficients for perforated and not perforated (see legend) geopolymeric foamed samples.
Figure 10. Sound absorption coefficients for perforated and not perforated (see legend) geopolymeric foamed samples.
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Figure 11. Sound absorption coefficient for foamed geopolymer samples: (a) Single-layer samples full and drilled (thickness: 20 mm); (b) Single-layer samples full and drilled (thickness: 40 mm); (c) Single- and double-layer samples full (thickness: 20 mm, 40 mm, 60 mm); (d) Double-layer samples full and drilled with different configurations.
Figure 11. Sound absorption coefficient for foamed geopolymer samples: (a) Single-layer samples full and drilled (thickness: 20 mm); (b) Single-layer samples full and drilled (thickness: 40 mm); (c) Single- and double-layer samples full (thickness: 20 mm, 40 mm, 60 mm); (d) Double-layer samples full and drilled with different configurations.
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Table 1. Chemical composition (by weight %) of the metakaolin and sodium silicate solution used to prepare the foamed geopolymer.
Table 1. Chemical composition (by weight %) of the metakaolin and sodium silicate solution used to prepare the foamed geopolymer.
CompoundMetakaolinSodium Silicate
SiO252.227.40
Al2O345.1-
Na2O0.228.15
K2O0.15-
TiO21.75-
Fe2O30.42-
CaO0.04-
MgO0.04-
P2O50.08-
H2O-64.45
Table 2. Geopolymer slurry composition that was used to prepare the foamed samples.
Table 2. Geopolymer slurry composition that was used to prepare the foamed samples.
Raw Materials (wt%)Foamed Geopolymer
Metakaolin33.7
NaOH6.5
Sodium silicate49.8
Polysiloxane10.0
Al 11.0
1 aluminium powder.
Table 3. Properties of different combinations of samples.
Table 3. Properties of different combinations of samples.
Sample LayoutThickness (mm)Sample TypeHole Thickness (mm)Hole Diameter (mm)
Single20full--
Single20drilled207
Single40full--
Single40drilled207
Double20,40full--
Double20,40drilled20,207
Double20,40drilled20,209
Double20,40drilled20,2011
Table 4. One band octave sound absorption coefficient for samples under study and most commonly used commercial materials.
Table 4. One band octave sound absorption coefficient for samples under study and most commonly used commercial materials.
Frequency (Hz)Single, 20 FullSingle, 20, Drilled, 20,7Single, 40 FullSingle, 40, Drilled, 20,7Double, 20, 40 FullDouble, 20,40 Drilled, 20,20,7Double, 20,40 Drilled, 20,20,9Double, 20,40 Drilled, 20,20,11Fiberglass 25 mmSprayed Cellulose Fiber 25 mm
1250.220.140.140.180.130.130.190.210.060.08
2500.220.100.300.210.410.320.280.280.20.29
5000.170.150.380.350.500.810.740.640.650.75
10000.310.390.220.390.400.780.850.790.90.98
20000.370.940.490.570.550.630.510.660.950.93
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MDPI and ACS Style

Ciaburro, G.; Iannace, G.; Ricciotti, L.; Apicella, A.; Perrotta, V.; Aversa, R. Acoustic Applications of a Foamed Geopolymeric-Architected Metamaterial. Appl. Sci. 2024, 14, 1207. https://doi.org/10.3390/app14031207

AMA Style

Ciaburro G, Iannace G, Ricciotti L, Apicella A, Perrotta V, Aversa R. Acoustic Applications of a Foamed Geopolymeric-Architected Metamaterial. Applied Sciences. 2024; 14(3):1207. https://doi.org/10.3390/app14031207

Chicago/Turabian Style

Ciaburro, Giuseppe, Gino Iannace, Laura Ricciotti, Antonio Apicella, Valeria Perrotta, and Raffaella Aversa. 2024. "Acoustic Applications of a Foamed Geopolymeric-Architected Metamaterial" Applied Sciences 14, no. 3: 1207. https://doi.org/10.3390/app14031207

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