Introduction

The use of foam concrete (basically made up of cement, sand, foaming agent and water) is a good alternative to ordinary concrete in terms of reducing excessive weight on structures and offering low thermal and sound conductivities. Foam concrete is lightweight and has a higher strength-to-weight ratio. The presence of multiple pores in foam concrete provides good thermal and air-borne sound isolation, enabling its use in various environmental conditions. The usage of foam concrete can be classified according to density ranges. 300–600 kg/m3 foam concrete is generally used as insulating and filling material. 600–1200 kg/m3 foam concrete is used in non-load bearing structures, while that of 1200–1600 kg/m3 is commonly used in load-bearing structures [1]. Aerated concrete is classified into two groups according to the pore formation method: air-entrained concrete and foam concrete [2]. Gas-forming chemicals such as Al powder, CaH2, TiH2, MgH2 and H2O2 are mixed into the mortar in the air-entraining method [3, 4]. The resulting gaseous products lead to the porous structure. Pre-foaming process and mixed foaming process are the two mechanical ways used in the foaming method. The foaming agent is mixed with the mixing water and then added to the mortar in the pre-foaming process whereas it is directly mixed with the mortar in mixed foaming process. Protein and synthetic-based foaming agents can be used in order to produce foam. Protein-based foaming agents produce smaller air bubbles than synthetic-based foaming agents which give higher compressive strength to foam concrete [5, 6].

As a general trend, the higher the porosity in foam concrete the lower the thermal conductivity [1]. It was reported in the study of Weigler and Karl that 20% entrained air in the concrete increased the thermal resistance by 25%, reduced the thermal conductivity coefficient by 0.04 W/m K and concrete dry density by 100 kg/m3 [7]. Additionally, the size distribution of air voids is also important to determine the conductivity. Relatedly, Batool and Bindiganavile investigated air-void size distribution in a cement-based foam. They observed that the mixtures with a narrower range of air-void size distribution exhibited greater conductivity, while a wider range of larger void size distribution resulted in reduced conductivity [8]. Another important parameter affecting the thermal conductivity of the foam concrete is its density. Mydin [9] stated that lower-density foamcrete had greater porosity and therefore exhibited lower thermal conductivity. Ganesan et al. [10] worked with foam concrete samples of 700, 1000 and 1400 kg/m3 density and measured thermal conductivity coefficients of 0.24, 0.49 and 0.74 W/m K, respectively. The reason for this was that the porosity %s in the samples were detected as 68, 57 and 35%, respectively. Similarly, it was stated that the compressive strength and thermal conductivity of foam concrete increased with increasing density [1].

It was reported that the sound absorption rate of foam concrete was 10 times that of normal concrete [11]. In the investigation of Zhang et al. 20–25 mm thick geopolymer foam concrete samples exhibited remarkably high absorption coefficients ranging from 0.7 to 1.0 in the low-frequency region of 40–150 Hz [12]. Satisfying acoustic absorption coefficients between 0.8 and 1.0 in the medium frequency region of 1600–2500 Hz were measured for alkali-active slag foam concretes which were produced using 35% foam content [13]. It was reported in the same study that there was a linear correlation between the density and acoustic properties of the foam concretes. Consequently, the acoustic properties were improved by decreasing the density.

In the literature, scanning electron microscopy (SEM) has been used to examine the structural differences in the foam concretes [14]. SEM is designed to directly examine the surfaces of solid objects and it is among the most flexible tools for elemental analysis as well as for examining and analyzing microstructure topography. Therefore, SEM analysis has become a fundamental technique used in the concrete industry. The integration of the SEM technique with a widely used energy dispersive X-ray spectroscopy (EDS) can be particularly useful in identifying concrete issues such as the alkali-aggregate effect in concrete. SEM is also an instrumental analysis technique for the study of microstructural behavior and performance for sustainable concrete. In addition, it can be used in conjunction with particle size distribution (PSD) and X-ray fluorescence (XRF) for material characterizations in sustainable concrete containing recycled glass.

SEM is essential in all industries that require the characterization of bulk objects. Additionally, existing SEMs produce electronic files making data transfer easy. However, despite these advantages, there are some limitations regarding the use of SEM. The materials examined with the help of SEM must be stable and fit inside the optical frame. Also, most equipment requires samples to remain stable in vacuum. In addition, EDS sensors in SEMs cannot detect extremely light atoms (H, He, Li). Due to these disadvantages of SEM, optical microscopy was used in some studies of the literature to determine original concrete mix ratios, general properties, the type of cement used in hardened concrete, and to examine the microstructure quality of concrete [15,16,17]. Another reason for preferring optical (holographic) microscopy is its low cost. An optical microscope system suitable for routine research can be 25–30 times cheaper than an electron microscope system when costs are compared [18].

Significant magnification in light microscopy is limited to the visible wavelengths of the electromagnetic spectrum (approximately 400–800 nm). Additionally, the highest resolution that can be achieved in advanced imaging is on the order of 170 nm. However, in practice, the resolution achieved is often much higher than this value due to the optical factors such as numerical aperture value of the objective, sample examination medium (air, oil) and image depth of field [19].

The digital holographic microscopy (DHM) method is a widely used high-resolution, non-destructive, and full-field imaging technique [20]. Using the DHM technique, it is possible to create a hologram of the object wave with a reference wave and then digitally reproduce the original object wave from this hologram plane. Additionally, stability can be increased and the system cost can be further reduced by using the lateral shearing digital holographic microscopy (LSDHM) method. On the other hand, the microscopic fringe projection profilometry (MFPP) technique has been frequently used in recent years to obtain surface profilometry of microstructured 3D surfaces [21]. In this technique, a projector and a camera are used to display surface information. A new surface is created by projecting modulated sinusoidal fringe patterns onto the object with the help of a projector. 3D information containing the depth information of the target image is encoded on the created surface. The encoded information is recorded with a camera. Then, the shape geometry is reconstructed by estimating the phase values from the obtained image. These phase values provide information about the height of target surface. However, in the MFPP method, micro-scale surfaces with a very short height range are measured. Additionally, this method requires complex configurations such as Ronchi gratings, liquid crystal on silicon (LCoS) and additional optical components. To address the deficiencies in the MFPP system and provide highly stable microstructured 3D surface imaging, a hybrid optical sensor (HOS) formed by the combination of MFPP and LSDHM was proposed by Ustabas Kaya [22].

In this study, the use of this HOS, called combined digital holographic microscopy (CDHM), was proposed for the first time to examine the pore radii of produced foam concretes. Thus, unlike existing studies in the literature, the pore radii of foam concretes were calculated by eliminating the limitations of the most commonly used optical and electron microscopy techniques. The hologram recording required for the visualization of the produced foam concretes was made with the CDHM system and the image could be reconstructed in 3D using the Fourier transform method. Thus, amplitude, phase and frequency information could be obtained for the foam concrete samples and their pore radii were determined.

The contributions of this paper can be listed as follows:

  • The CDHM to measure the pore radii of the produced foam concretes was proposed for the first time. Since it is a cost-effective, cleaner, and faster method, it provides very high accuracy in pore radii measurement compared to SEM. Also, unlike in SEM, it allows examining the entire surface at once without scanning the surfaces from different angles. In this way, less time is spent on analysis.

  • Using the CDHM system for hologram recording and reconstruction allows 3D visualization of foam concrete samples.

  • It is worth noting that there are many studies in the literature emphasizing the importance of the type and amount of pore-forming material used in adjusting the pore size [23,24,25,26,27,28]. Accordingly, the relationship between the measured CDHM pore radii of foam concretes and the % of foaming agent used during sample preparation was determined.

  • Then, it was observed how the foam concrete density and thermal conductivity coefficient would change with the change in radius.

  • It was also a matter of curiosity how the thermodynamic stability of foam concrete might change depending on the % of foaming agent.

Materials and methods

Materials

CEM I 42,5 R Portland cement and silica sand with a grain size of 1–3 mm supplied from Bartın cement factory of Sanko [29] were used as concrete components. GENFIL brand protein-based organic liquid was used as the foaming agent. This agent is a highly efficient, organic resin-based foaming agent developed for the production of cellular lightweight and lightweight building elements in the construction industry. The foaming agent, with a density of 1.05 kg/l, consists of anti-bacterial, enzyme-based, active proteins and is organic [30]. To prepare foam concrete containing 0.75% (w/w) foaming agent (total weight:weight of Portland cement and silica sand), the following procedure was followed: 600 g of Portland cement, 200 g of silica sand and 270 ml of distilled water were mixed in a container with a mixer. In a separate container, a mixture of 6 g of foaming agent and 55 ml of water was whipped with a mixer and foamed. The two mixtures were then combined and mixed for another 5 min. The resulting mud mixture was poured into a 10 × 10 cm mold and left to dry at room temperature for 28 days. This mixture was referred to as Sample 1 throughout the manuscript. Similarly, samples containing 1%, 2.5%, 5% and 7.5% (w/w) foaming agent were named Samples 2–5, respectively. The experimental procedure was the same for all samples except that 8, 20, 40 and 60 g of foaming agent were used for Samples 2–5, respectively. Thermal conductivity coefficients of foam concretes were measured with KD2 Pro, Decagon Devices [31].

Experimental imaging system of combined digital holographic microscopy

The combined system presented in Fig. 1 was used to visualize the foam concrete structures produced in this study. This system was created by combining the LSDHM system with the MFPP system.

Figure 1
figure 1

The combined digital holographic microscopy (CDHM) system.

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LSDHM was the part that illuminated the object to be imaged. It was also the part that created the holographic recording medium which recorded the information in this object. A He–Cd laser light source with a wavelength of 425 nm was used to illuminate the system with LSDHM. The light coming out of the source was first reflected on a mirror (M) after being collimated with a convex lens (L1) with a distance of 100 mm. Then this beam was reflected on the shearing glass plate (SGP). The reason for using SGP was to create the interference pattern (IP) that formed the holographic image recording medium. The IP was also named a hologram.

Thanks to the front and back surfaces in the structure of the SGP, an interference pattern is formed after the beam coming from the laser source is divided into two branches and combined. In addition, the hologram created with SGP has an inner and an outer part that contains object information and does not contain any object information. The schematic representation of the created IP using SGP, which was presented in Fig. 2a, was first proposed by Seo et al. [32, 33]. Figure 2b showed the effective interference area (EIA) created by our proposed system. It was also called a reference (raw) hologram.

Figure 2
figure 2

a The created interference pattern (IP) using shearing glass plate (SGP), b the effective interference area (EIA) created by the proposed system.

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The mathematical expression of this IP (hologram) is presented in Eq. 1.

$$I_{0} \left( {x,y} \right) = \left| {\left\{ {O_{1} \left( {x,y} \right) + R_{1} \left( {x,y} \right)} \right\} + \left\{ {O_{2} \left( {x,y} \right) + R_{2} \left( {x,y} \right)} \right\}} \right|^{2}$$
(1)

In this equation, the area where the information about the object is recorded in the beam reflected from the front surface of the SGP is called \(O_{1}\). The part of the beam reflected from this surface where there is no information about the object is expressed as \(R_{1}\). On the other hand, the parts that contain object information and those that do not contain object information in the beam reflected from the back surface of the SGP are defined as \(O_{2}\) and \(R_{2}\). A hologram is formed at the point where \(O_{1}\) and \(R_{2}\) overlap. However, the problems of DC bias and virtual image, which are undesirable in this region and inevitably arise as a result of the self-referencing configuration in LSDHM, are eliminated by the second mirror (L2). Hence, the EIA is comprised in this area. The region marked (3) in Fig. 2a shows the part where EIA occurs. The object to be displayed is placed in the EIA area, where the hologram is created using LSDHM. The objects intended to be imaged in this study were foam concrete structures.

In this study, holograms of foam concrete structures were recorded with the MFPP arm of the proposed system. Recording was performed with a complementary metal oxide semiconductor camera (CMOS). The CMOS camera had a maximum pixel resolution of 1024 × 1024 and a pixel pitch of 14 μm. It also had the feature of recording holograms at a frame rate of 60 Hz (60 frames per second-fps). A zooming lens (ZL) and microscopic objective (MO) were used to obtain high-resolution images before recording with the camera. While the surface to be viewed was enlarged with the MO with a 6X magnification ratio, the focus was adjusted with the ZL. To make the most accurate focus setting, the distance of the camera lens to the object was calculated according to the magnification ratio of the MO, the focal length of the CMOS, the size of the area to be imaged, and the appropriate camera pixel size determined [34].

Holograms recorded with a CMOS camera are transferred to the computer via an interface. In projection systems such as MFPP, it is necessary to calculate the change in phase values of fixed points in the displayed holographic medium. In this context, phase deviations should be converted into height values by mathematical modeling. The phase deviation is called fringe deformation [35, 36]. MFPP parameters should be used to express this deformation mathematically. Using these parameters, Eq. 2 can be rewritten as follows:

$$I\left( {x,y} \right) = 2I_{0} \left( {x,y} \right)\left. {\left\{ {1 + \cos 2\pi \left. {\left[ {\frac{xcos\left( \alpha \right)}{{f_{p} }} + \varphi \left( {x,y} \right)} \right.} \right]} \right.} \right\}$$
(2)

Here, the angle between the MFPP arm and the holographic recording medium created by LSDHM is defined as \(\alpha\). The fringe pitch of holograms is expressed as \(f_{p}\).

To extract the information about the object recorded in the holograms, the Hilbert Transform (HT) is used [37]. In other words, the reconstruction process is performed using HT. The surface profiles of the materials on which holographic recording is made differ from each other. Therefore, it is necessary to calculate the height information on these surfaces as it changes.  Equation 3 is used to relate the phase information obtained from holograms with height information.

$$h = f_{p} \frac{{\varphi \left( {x,y} \right)}}{2\pi } \frac{sin\beta }{{sin\alpha }}_{ }$$
(3)

Here the height information is expressed as \(h\). The angle between the MFPP arm and the displayed holographic area is given by \(\beta\). Phase images containing height information are obtained in 2D. These 2D images are defined as wrapped phase images. However, the values are discontinuous in 2D-wrapped phase images. Phase unwrapping is performed to obtain continuous values using Goldstein’s branch-cutting method. As a result, 3D-unwrapped phase images are obtained [38].

Computational chemistry methods

Quantum chemical calculations were carried out as complementary studies to observe the effect of the protein-based foaming agent on the stability of the considered foam concretes. The protein-based foaming agent used in the experiments was commercially available and frequently used in the construction industry, but the chemical formula of the protein mixture in the agent was not clearly stated. This was why a simple protein model of the Glycine–Alanine dipeptide anion (Gly–Ala)− was designed to mimic the foaming agent used and minimize processing time on a theoretical level. Due to the abundance and alkaline nature of Portland cement in foam concrete, the anionic (basic) form of the dipeptide molecule was taken into account in the calculations. The molecular interactions between SiO2, (Gly–Ala)− foaming agent, and the air-abundant N2 molecule were modeled in three different ways. Note that one of the interacting molecules is SiO2; because it was abundantly present in Portland cement and was initially added as a silica sand additive to the foam concrete slurry mixture. To observe the effect of the amount of foaming agent used on the stability of the air bubble formed, three different [SiO2…(Gly–Ala)]nn−…N2 interactions were modeled and optimized (n = 1–3). More specifically, n = 1 represented 0.75%, n = 2 represented 2.5% and n = 3 represented 7.5% (w/w) foaming agent used in the synthetic route. Molecular models were named with their original names as Sample 1 (n = 1), Sample 3 (n = 2) and Sample 5 (n = 3), respectively (Fig. 3). The suggestion in the molecular modeling was that the (Gly–Ala)− dipeptide foaming agent first interacted with SiO2 in certain proportions. Then, the newly formed complex came into contact with air and captured the N2 molecule.

Figure 3
figure 3

[SiO2…(Gly–Ala)]nn−…N2 interactions optimized using ONIOM two-layer model (M06-2X/6-31+G(d,p):UFF) (n = 1–3). Molecular models were named with their original names as Sample 1 (n = 1), Sample 3 (n = 2), and Sample 5 (n = 3), respectively. High layer atoms were shown as ball and bond type representation while low layer atoms were shown as tube. Hydrogen bonds were presented in Å.

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All calculations were performed in the gas phase at 298.15 K and 1 atm using Gaussian 09 program software [39]. The structure optimizations were performed using ONIOM two-layer model (M06-2X/6-31+G(d,p):UFF) [40]. Due to the presence of hydrogen bonds between peptide bonds (–CO–NH–) and N2 molecules in the complexes, high-level calculations were performed on these two parts, while low-level calculations were performed on the less effective remaining part (Fig. 3). The interaction energies of the optimized complexes were calculated at the DFT M06-2X/6-31+G(d,p) level of theory and corrected by basis set superposition error (BSSE) contributions [41, 42]. BSSE corrections use the Boys and Bernardi counterpoise technique [41, 43] due to the overlapping of the wave functions of the moieties [44]. Calculations for all molecules considered included zero-point energy corrections and had no imaginary frequencies, indicating that they represented no transition states or saddle points on their potential energy surfaces.

Results and discussion

Results of SEM and CDHM

The original images, 3D-reconstructed phase images obtained from CDHM, and SEM images of Samples 1–5 were presented in Figs. 4, 5, 6, 7 and 8. Note that the entire original image was converted into a 3D-reconstructed phase image, however, four different sections of the original sample were examined in SEM imaging. Pore radii measured by SEM and proposed CDHM methods were shown in Table 1. SEM radii were taken as actual values in % relative error (RE%) calculations. The striking point was that as the % of foaming agent used in the samples from Sample 1 to Sample 5 increased, the pore radius of the resulting foam concrete also increased (Table 1). The measured CDHM radii gave results very close to that of the SEM and the relative errors were found to be between (− 5.6) and (+ 5.8)%. The lowest relative error with a value of − 4.2% belonged to Sample 5, which had the highest pore radius.

Figure 4
figure 4

a Original image, b 3D-reconstructed phase image, c–f SEM images of Sample 1. The colored lines demonstrate diameters.

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Figure 5
figure 5

a Original image, b 3D-reconstructed phase image, c–f SEM images of Sample 2. The colored lines demonstrate diameters.

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Figure 6
figure 6

a Original image, b 3D-reconstructed phase image, c–f SEM images of Sample 3. The colored lines demonstrate diameters.

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Figure 7
figure 7

a Original image, b 3D-reconstructed phase image, c–f SEM images of Sample 4. The colored lines demonstrate diameters.

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Figure 8
figure 8

a Original image, b 3D-reconstructed phase image, c–f SEM images of Sample 5. The colored lines demonstrate diameters.

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Table 1 The average radius determined by the SEM and CDHM methods for each sample
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Densities and thermal conductivity coefficients

Densities and thermal conductivity coefficients of Samples 1–5 were presented in Table 2. As expected, as the density of foam concrete decreased, thermal conductivity coefficient decreased and thermal insulation increased. Another important point was that the sample with the highest thermal insulation was Sample 5, which had the highest pore radius. In general, as the number of pores increases, thermal insulation is expected to increase. However, it was observed that thermal insulation in the samples was independent of the number of pores and depended only on the pore radius. For example, the number of pores per unit area in Sample 4 was clearly higher, but the thermal insulation was lower than that in Sample 5, which contained fewer pores (Figs. 7, 8; Table 2). As a result, it was concluded that thermal insulation depended only on the density and pore radius of the samples.

Table 2 Densities and thermal conductivity coefficients of  Samples 1–5
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Molecular modeling results

In the molecular models in Fig. 3 representing Samples 1, 3 and 5, hydrogen bonds were detected between the peptide bonds (–CO–NH–) and the air molecule N2, with bond lengths varying between 2.47 and 2.52 Å. The number of moles of the complexed foaming agent ([SiO2…(Gly–Ala)]−) interacting with the air molecule N2 increased from 1 to 3 sequentially in the samples (Fig. 3). The interaction Gibbs free energy was calculated to be positive (endothermic) in Sample 1, while it was calculated to be increasingly negative (exothermic) in Samples 3 and 5 (Table 3). Therefore, the thermodynamic stability order of the samples was found to be Sample 5 > Sample 3 > Sample 1. Combining the previous sections and this section, the following results were obtained: increasing the % of foaming agent, or more precisely the pore radius, in the examined samples allowed to produce thermodynamically more stable and thermally more insulating foam concretes.

Table 3 BSSE corrected interaction Gibbs free energies of Samples 1, 3 and 5 modeled in Fig. 3
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Conclusions

Since the proposed hybrid imaging method CDHM gave results very close to SEM, it was concluded that it could be used reliably in determining the foam radii of foam concretes with similar material content as in the study. In the samples examined, it was observed that as the % of foaming agent increased, the pore radii in foam concretes increased and, accordingly, the densities decreased. As a result, the thermal insulation properties increased. Additionally, ONIOM quantum chemical calculations showed that as the % of the foaming agent increased, it provided a more stable interaction with air, creating more stable foams.

In conclusion, this study contributes to the growing body of knowledge about foam concrete materials and their engineering applications, providing valuable information on factors affecting foam stability, thermal insulation and material density. The findings pave the way for further advances in foam concrete technology, with potential applications ranging from sustainable construction to energy-efficient building materials.