**Aurelia Blazejczyk 1,\*, Cezariusz Jastrzebski <sup>2</sup> and Michał Wierzbicki <sup>2</sup>**


Received: 23 April 2020; Accepted: 19 May 2020; Published: 9 June 2020

**Abstract:** This article introduces an innovative approach to the investigation of the conductive– radiative heat transfer mechanism in expanded polystyrene (EPS) thermal insulation at negligible convection. Closed-cell EPS foam (bulk density 14–17 kg·m−<sup>3</sup> ) in the form of panels (of thickness 0.02–0.18 m) was tested with 1–15 µm graphite microparticles (GMP) at two different industrial concentrations (up to 4.3% of the EPS mass). A heat flow meter (HFM) was found to be precise enough to observe all thermal effects under study: the dependence of the total thermal conductivity on thickness, density, and GMP content, as well as the thermal resistance relative gain. An alternative explanation of the total thermal conductivity "thickness effect" is proposed. The conductive–radiative components of the total thermal conductivity were separated, by comparing measured (with and without Al-foil) and simulated (i.e., calculated based on data reported in the literature) results. This helps to elucidate why a small addition of GMP (below 4.3%) forces such an evident drop in total thermal conductivity, down to 0.03 W·m−<sup>1</sup> ·K −1 . As proposed, a physical cause is related to the change in mechanism of the heat transfer by conduction and radiation. The main accomplishment is discovering that the change forced by GMP in the polymer matrix thermal conduction may dominate the radiation change. Hence, the matrix conduction component change is considered to be the major cause of the observed drop in total thermal conductivity of EPS insulation. At the microscopic level of the molecules or chains (e.g., in polymers), significant differences observed in the intensity of Raman spectra and in the glass transition temperature increase on differential scanning calorimetry(DSC) thermograms, when comparing EPS foam with and without GMP, complementarily support the above statement. An additional practical achievement is finding the maximum thickness at which one may reduce the "grey" EPS insulating layer, with respect to "dotted" EPS at a required level of thermal resistance. In the case of the thickest (0.30 m) panels for a passive building, above 18% of thickness reduction is found to be possible.

**Keywords:** expanded polystyrene; graphite particles; thermal conductivity; thermal resistance; thickness effect; phonon-photon transport; Raman spectroscopy; thermal analysis

#### **1. Introduction**

Large-scale application of EPS foams with closed cells as thermal insulation in construction engineering requires the sustainable improvement of the thermophysical features of traditional building materials [1–5]. When introducing various technological changes in chemical composition, besides improving measurement and simulation techniques, it is important to understand the physical consequences caused by such changes. A better understanding may allow for the generation of knowledge, as well as let scientists improve the modelling of thermal processes. Moreover, it may allow engineers to develop novel materials and encourage industry stakeholders by more effectively optimizing the production costs of these materials, along with better thermal insulation performance.

A traditional solution for high quality thermal protection in buildings is by using high-thickness insulating layers made of conventional thermal insulation that, together with other more advanced options, comprises "the best building practice". Advanced thermal insulation materials, such as super insulating materials (SIMs) (e.g., vacuum insulation materials (VIMs) and aerogels), phase change materials (PCMs), gas-filled materials (GFMs), and nanoinsulation materials (NIMs), promise to be the most beneficial for applications in the building sector [6–8]. In addition, modern systems, such as adaptive facades, dynamic facades, and active envelopes, provide architectural alternatives, which are a novel platform for energy efficiency, visual comfort, and daylight distribution, as well as branding and image. However, installing conventional thermal insulation of high thickness in external walls remains an attractive option, especially in harsh climate countries, due to the low market prices of materials and the costs of their installation [9–12]. When designing a building, one of the first steps to consider is reaching the required level of thermal protection, in terms of thermal transmittance *U*-value, which ranges from ca. 0.1 W·m−<sup>2</sup> ·K−<sup>1</sup> for high-energy standards up to 3 W·m−<sup>2</sup> ·K−<sup>1</sup> or more for low-energy standard [13]. The challenge is to obtain such values by selecting the most appropriate and cost-effective materials, which provides the thinnest possible insulation with the highest thermal effectiveness.

Conventional polymeric foams applicable in the building sector include both products of very low bulk density (below 20 kg·m−<sup>3</sup> ), such as extruded polystyrene (XPS) or EPS (herein under study), and products of low bulk density (up to 45 kg·m−<sup>3</sup> ), such as phenolic foam (PhF), polyurethane (PUR), and polyisocyanurate (PIR) foams, as well as XPS and EPS foams. A popular option is the industrial production of polymer composite, such as EPS foams that include graphite fillers [14–16], due to low cost, lightweight, and moderate dispersibility in polymer matrix [17,18], in particular, graphite microparticles (GMP) [19–25]. These are typically applied in the form of panels for the thermal insulation of buildings. Despite the problem of possible overheating due to solar radiation causing panel deformation [26,27], this choice offers designers relevant insulation thickness reduction. The thickness of "pure" EPS panels in the external walls of passive buildings (*U*-value = 0.1 W·m−<sup>2</sup> ·K−<sup>1</sup> for Central European climates) can reach up to *d* = 0.30 m. As it is of interest to reduce the thickness (at a given *U*-value), one may study the material's thermal insulation performance [28–30]. Some optimization is possible by observing heat transfer via the apparent thermal conductivity λ ′ and resistance *R* ′ as a function of the EPS sample thickness *d*, with relation to the variable bulk density ρ and concentration of fillers, such as GMP.

Following measurements in accredited laboratories, EPS manufacturers have declared its thermal conductivity coefficient λ<sup>D</sup> and thermal resistance *R*<sup>D</sup> values [31,32]. However, the literature has barely discussed the so-called thickness effect, which has the apparent impact of the sample thickness (in its lower range) on the material's thermophysical parameters [33,34]. On the other hand, the thickest samples have rarely been measured and reported [35]. The latter may be due to common technical difficulties when measuring insulation panels above 0.1 m in thickness, which is not suitable for most of the (too narrow) plate instruments (GHP and HFM). Besides the main purpose of thermal transport analysis, this work also tries to fill this gap, explaining these technical issues (i.e., experimental knowledge regarding thin and thick case measurements). Therefore, the extra purpose is demonstrating a methodical approach that may answer the following two questions:


In each polymeric insulating material, one must initially assess the thickness effect relevance by testing thin slices of the foam panel. Herein, it is done, concerning EPS of very low bulk density, by using an experimental method in accordance with the recommendations of the European Committee for Standardization CEN, as described in Standards [30,32,35,36].

Besides considering technical issues and providing correct data for engineers, this paper aims to contribute to the general discussion about the thermal transport mechanisms in polymeric insulating materials and better understanding them. Example of such discussions describing mainly EPS insulation can be found in the recognized literature [37–49]. In particular, it has been reported that, when incorporating industrially higher concentrations of GMP into an EPS polymer matrix, the total thermal conductivity can be reduced by opacifying the insulation product for thermal radiation, which is absorbed by the carbon atoms in graphite or scattered by the larger graphite microparticles. Unfortunately, the quantitative analysis of the three major thermal components—radiation, air conduction, and polymer matrix conduction—over a wide thickness range of the insulating EPS layers with different GMP industrial concentrations is missing, in general.

Therefore, the main scientific purpose is analysing heat transfer through EPS foam of very low bulk density and separating it into its radiative and conductive thermal components. To the authors' knowledge, this is the first successful approach of separating thermal components to examine EPS in relation to the identified spectral features of the Raman spectrum. As for convection of insulating gas, it is proved to be negligible in EPS, as well as also other polymeric foams with a closed or open-cell structure of diameter up to 0.004 m (4 mm) [1,27,50–52]. The closed cells in the expanded beads of "pure" EPS at various densities are of size ranging from 0.05 to 0.40 mm [27,38,53]. The scientific aim of the present paper was achieved by comparing experimental and literature data [42]. As a result, we observe the effect of change in conductive–radiative heat transfer mechanism triggered by the GMP at two different industrial concentrations. Its apparent impact on each particular thermal component is then analysed and discussed.
