Mechanistic Modelling for Optimising LTES-Enhanced Composites for Construction Applications

Abstract

This study addresses the optimisation of latent heat thermal energy storage (LTES) composites for construction applications by utilising mechanistic modelling. The work focuses on enhancing the performance of phase change materials (PCMs) incorporated into expanded perlite (EP) for building energy efficiency by delivering sorption capacity models analysing factors such as particle size, surface area, and pore volume, particularly highlighting the performance of EP as a PCM carrier due to its high porosity (around 90%) and large surface area (up to 20 m²/g), which allowed for improved energy storage density and heat transfer. Key challenges in the integration of PCMs into construction materials, such as limited thermal conductivity and leakage during phase transitions, are explored. The model evaluates key parameters affecting sorption, such as temperature, pressure, and surface characteristics of the materials. The results indicate that while higher temperatures enhance sorption in larger pores, they reduce efficiency in smaller ones, leading to a slight overall decrease in total sorption capacity at elevated temperatures. The sorption capacity of water is a value slightly above 2 kg/kg EP, while the PCM RT27 exhibits a sorption capacity of 0.59 kg/kg EP. These results represent the optimised sorption performance in terms of temperature between 40 °C and 50 °C. Furthermore, applying vacuum impregnation is investigated in relation to the pore radii of the EP particles. Larger pore radii show a noticeable improvement in overall sorption capacity from 0.59 kg/kg EP to 0.68 kg/kg EP as pressure increases, especially beyond 4 × 10⁵ Pa. The contribution of inter-particle sorption remains stable, while the intra-particle sorption in large pores drives the overall capacity upward. The findings convey significant findings in optimising the design of LTES-enhanced composites for improved energy storage, thermal regulation, and structural integrity in building applications.

1. Introduction

The European Commission has set climate neutral targets to reduce carbon emissions by 40% by 2030. The penetration of Renewable Energy Sources (RES) will be increased by up to 32% and energy performance will be enhanced by 32.5%. This is attributed to the European climate law that expects the EU countries to overall minimise their carbon-related emissions by 55% by 2030. Buildings have a significant environmental impact accounting for a staggering 37% of global emissions, originating from the consumption of natural resources, extensive energy usage, and the generation of pollutants during both construction and operation [1]. Investigating the benefits deriving from shifting electricity demand in buildings highlights the potential for exploiting the available thermal energy storage capacity resulting from the envelope mass of a building for applying pre-heating or pre-cooling strategies. This concept introduces a passive energy storage system named ‘structural thermal energy storage’ which employs the mass of the structural elements—i.e., walls, slabs and ceilings—to store thermal energy and retrieve it at a later time. The efficiency of this strategy has been proven for ages, with a typical case being the passive night cooling of heavyweight buildings as a traditional way to treat the heated thermal mass of stone or concrete in hot climates.

Several studies have investigated the opportunity to increase building envelope thermal mass by utilising composite materials, through incorporating low-cost carriers, like industrial minerals, for absorbing phase change materials (PCMs). PCMs provide a way for exploiting the latent heat when storing thermal energy. In principle, any material that undergoes a phase change process when absorbing or releasing thermal energy can be used as Latent Thermal Energy Storage (LTES). A fundamental characteristic of LTES materials is that there is a phase change temperature at which the material changes from one state (solid or liquid or gas) to another without a change in chemical composition. However, the integration of such composites in building envelopes like cement-based mortars or loose fill applications should maintain desired properties like workability, durability, and hydration reaction time, also ensuring competitiveness in relation to environmental footprint and cost.

For the sorption of the organic PCM into the porous media, inorganic minerals are considered a main form of liquid sorbents. They have been widely used for absorption and adsorption of several liquid types at diverse levels [2]. The ability of a sorbent to evenly distribute and capture a liquid within its pores is the main parameter in determining its effectiveness. This is affected by the sorbent’s unique internal structure and geometry; however, internal structure is more complex to demonstrate due to complicated liquid flow behaviour. The pores of sorbents usually dictate the efficiency of the resultant sorption capacity. Liquid properties such as viscosity and density also affect the overall sorption capacity. Nevertheless, because of the complexity of liquid sorption mechanisms and the difficulty in identifying the liquid flow behaviour, theoretical approaches have been assumed by different authors to simulate and assess the melted PCM sorption phenomenon within expanded perlite (EP) sorbent.

The porous PCM composite can be fabricated by impregnating PCM into porous supporting materials through either direct (natural) immersion or vacuum impregnation [3,4,5]. The direct (natural) immersion method (DIM) is performed by soaking the porous supporting material directly with the melted PCM at atmospheric pressure conditions to for the PCM to be absorbed naturally. DIM is characterised as a simpler technique and easier operation; however, the operation time is longer and the adsorption rate of porous matrix is also lower [5]. The vacuum impregnation method (VIM) is performed by impregnating the liquid PCM into the porous supporting material under very low-pressure conditions in order to evacuate the air and moisture and enable a larger absorption the PCM [5]. VIM often results in porous composite PCMs with extremely excellent performance as it greatly improves the adsorption rate of porous matrix and reduces the leakage rate of PCM even after many thermal cycles. Nevertheless, this method is only performed in a laboratory environment due to the high production costs and the lack of technical support.

Despite the potential benefits of LTES-enhanced composites, several obstacles prevent their widespread adoption in building materials. First, low thermal conductivity limits their ability to transfer heat quickly, which reduces the speed and efficiency of energy storage and release. Second, leakage during phase transitions, particularly from solid to liquid, presents a significant challenge, as it can compromise the integrity of building materials and reduce the longevity of the system. Another underexplored challenge is the optimisation of LTES composites’ behaviour when integrated into composite materials.

To tackle these challenges, the balances between thermal conductivity and leakage prevention must be carefully managed to maximise the overall efficiency of LTES-enhanced building materials. For this purpose, the concept of mechanistic modelling is introduced in Figure 1, which is based on a combination of mathematical modelling (knowledge-driven) and machine/deep learning (data-driven) [2]. Mechanistic models provide a detailed and accurate representation of the processes, allowing for a deeper understanding of the underlying phenomena. Both data-driven and knowledge models generate novel results and insights. Data-driven models, such as those utilising machine learning and deep learning, are highly flexible and capable of handling complex, high-dimensional data with numerous parameters. They excel in identifying patterns and relationships within data but often require large, high-quality datasets to train effectively and are prone to overfitting. In contrast, knowledge-driven models rely on an established theoretical understanding of thermophysical processes, using mathematical equations to simulate system behaviour. While they offer clearer, more interpretable results, they may struggle with scenarios involving unknown or highly complex interactions.

Mechanistic modelling has found diverse applications across multiple scientific fields, by integrating both theoretical understanding and empirical data [6,7,8,9,10]. N.J. Barrow [11] developed a mechanistic model for phosphate sorption and desorption in soils, addressing the adsorption of phosphate on variable-charge surfaces, electrostatic potential distribution, and solid-state diffusion. This model provided a deeper understanding of phosphate behaviour in soils and its broader implications for nutrient cycling and environmental management. Pierre Schaetzel et al. [12] proposed a mechanistic theory for monolayer adsorption and sorption, focusing on a simplified process of colonising free sites within a polymer matrix or on adsorbent surfaces. Their model offered a unified approach to understanding sorption and adsorption, emphasising the need for future research to address more complex phenomena. Finally, Jinhao Sun et al. [13] investigated dynamic moisture sorption in dual-porous insulation materials, using NMR experiments to differentiate the roles of micro- and nano-scale pores in moisture adsorption. Their model highlighted the importance of understanding moisture transport mechanisms in multi-scale porous materials. The common thread among these diverse applications is the ability of mechanistic models to reveal the underlying processes governing system behaviour, from species adaptation and disease progression to drug interactions and material properties.

Mechanistic models can offer a thorough analysis by simulating the phase behaviour, transport properties, and interactions between the PCM and the porous matrix. These models incorporate microscale and nanoscale pore structures, predicting how PCMs will distribute within the material and how variables like pore size distribution, surface area, and material composition affect the sorption process. Additionally, mechanistic models simulate heat transfer dynamics during the phase transition, with focus on the efficiency with which the PCM stores and releases thermal energy. Mechanistic models enable the prediction of their thermal behaviour and the optimisation of their design by using computational analysis and mathematical formulations, which describe the phenomena modelled. However, the establishment of an accurate model for describing the heat transfer and fluid flow processes of an LTES-enhanced composite is considered quite complex. Therefore, the necessity for developing models able to simulate the thermal properties of the PCMs and predict the thermophysical performance of the LTES-enhanced composites is highlighted.

This study seeks to address these gaps by correlating the microscopic material scale (sorbent ability to sorb LTES materials) and the macroscopic process scale (sorbent loading with LTES material) in relation to operation parameters. Predictive algorithms, including machine learning models, are developed in MATLAB R2024a software and applied to evaluate the performance of LTES materials, tailoring their properties for specific applications and improving the overall efficiency of passive energy storage systems. Model development was inspired by the need for increasing the thermal mass of buildings by developing optimised LTES-enhanced composite materials tailored to each use case [14]. The work also highlights the potential for exploring additional LTES materials by employing basic characterisations or leveraging existing data from the literature. Using simplified material characterisation methods, the mechanistic models could efficiently screen several promising LTES materials for their suitability in building applications.

In this frame, the model predicts the effectiveness of synthesised composite materials in relation to the sorbent physical properties and the LTES materials’ thermophysical behaviour. At higher level, the model provides the vision for developing new generation composites by identifying the optimum thermophysical properties required for both carrier and LTES material functionalities. This approach holds the potential to revolutionise the creation of novel materials, transcending the limitations of traditional discovery pathways, and granting precise control over material behaviours.

2. Materials and Methods

2.1. Identification of Materials and Main Properties

EP is characterised by a unique cellular structure comprising numerous closed air cells encased within a glassy and porous outer surface. This structure results in a low bulk density of about 32–400 kg/m³. The chemical inertness of EP, having an approximate pH of 7, is a critical attribute, rendering it stable and non-reactive in various pH environments. Furthermore, the non-combustible nature aligns with its fire-resistant capabilities, enhancing its suitability in fire-sensitive applications. Lastly, EP has especially good sorption properties and is reported to significantly improve the absorption capacity of various kinds of sorbents used for the removal of pollutions [15]. The combination of these properties renders EP as a versatile material in sectors ranging from industrial insulation and construction to environmental engineering [16,17,18,19]. The selection of EP among diverse mineral porous materials originates from the documented availability of methods to tailor its structural properties. Controlled expansion processes enabling the development of EP with desired parameters for sorption capacity, such as particle size distribution and bulk density, particle size distribution [20] or a bulk density [21], are essential for optimising ratio of sorption. By controlling its EP surface and pore structure, EP can effectively encapsulate and retain PCMs, enhancing their thermal efficiency and mitigating leakage issues. The typical physical properties of EP are given in

Table 1. Typical physical properties of expanded perlite [22,23,24,25,26,27].

Property	Value
Free moisture, maximum (%)	0.5
Specific gravity	2.2–2.4
Specific heat (J/kg K)	837
Thermal conductivity at 24 °C (W/m·K)	0.04–0.06
Oil absorption [%wt.]	50–225
Water absorption [%wt.]	200–600

.

Organic PCMs, such paraffins, are proven to be the most advanced materials to store energy in a form of latent heat and release the energy depending on the temperature differences [28]. Both organic PCMs and oils are derived from similar raw materials, including petroleum and natural plant sources, which results in analogous molecular structures and, consequently, comparable physicochemical properties. These properties not only determine the materials’ performance in their respective applications but also influence how effectively they can be incorporated into systems designed for thermal energy storage, thermal management, and sorption processes. The physical phenomenon of mass transfer in the EP open pores is analysed for water and oils. At the beginning, the high sorption rate is a combined result of oil concentration gradient and the capillary pressure existing within the sorbent pores. The following properties in

Table 2. Measures of water and oil sorbates.

Oil	Contact Angle [°]	Surface Tension [N/m]	Density [kg/m3]	Dynamic Viscosity [kg/(m·s)]	Melting Point [°C]	Melting Enthalpy [kJ/kg]	Freezing Enthalpy [kJ/kg]	Refs.
Water	31	0.0728 (20 °C)	998.2 (20 °C)	0.00100 (20 °C)	0.0	333.5	333.5	[29]
Linseed Oil	33	0.025 (20 °C)	932 (20 °C)	0.02800 (40 °C)	−24.0	-	-	[30]
n-Dodecane	13.79	0.0254 (20 °C)	749.5 (20 °C)	0.00150 (20 °C)	−10.0	-	-	[31]
n-Octane	20	0.0217 (20 °C)	702.3 (20 °C)	0.00054 (20 °C)	−57.1	-	-	[32]
n-Octadecane	140	-	850 (10 °C) 774 (35 °C)	-	28.0	256.5	-	[33]
RT27	35◦	0.0038 (30 °C)	782 (10 °C) 766 (35 °C)	0.02000 (20 °C)	27.3	201.5	199.7	[34,35]

provide a comprehensive framework for assessing and leveraging the performance of oil sorption applications, guiding the development of materials optimised for specific types of sorption conditions.

2.2. Inter-Particle Capacity Model Development

This section is focused on the inter-particle sorption of melted PCM onto the open cavities of the surface of the EP, with an emphasis on determining inter-sorption capacity geometrically and the specific aspects of this interaction.

2.2.1. Definition and Assumptions of Inter-Particle Capacity Model

The analysis is focused on the determination of capacity that the carrier (e.g., EP) provides based on physicochemical properties of the sorbent and the sorbate and the environmental conditions during the process. The optimisation of the sorption is investigated by manipulating different physical and operational parameters to achieve the maximum oil sorption capacity.

The interaction between a liquid sorbate and a porous sorbent is very complex and difficult to be expressed numerically [36]. From this perspective, the inter-particle capacity model relies on the following assumptions, which are crucial for simplifying the modelling process and making it feasible to predict the behaviour of these materials in various conditions:

• In the context of modelling the sorption of melted PCMs, their behaviour is assumed to be like that of oil. This is possible, given that the viscosity and fluidity of melted organic PCMs are similar and comparable to oil within specific temperature ranges [37]. In addition, the melted PCM has a surface tension similar to oil which enables the use of existing models and data related to oil’s wetting behaviour on various surfaces.
• The active (available) space area for capturing PCM is determined geometrically. The key parameters dominating the model are the particle size and the liquid/solid interfacial properties.
• Empirical parameters are introduced to ensure realistic boundaries of the system and sorption rates [36].
• The surface cells in the inter-particle area with noncircular cross-sectional shapes are addressed as sequent, parallel, cylindrical capillary tubes with equivalent diameters equal to the hydraulic diameter [38].

2.2.2. Inter-Sorption Kinetics

The Washburn equation is a fundamental principle in analysing sorption, capillarity, and wicking in porous materials. The Washburn method is particularly relevant in the context of understanding how liquids move through porous structures and has been utilised for the estimation of the liquid penetration depth with loose powders [39]. In this method, a porous media is placed into an open-ended glass capillary column. The column is immersed into a liquid (e.g., water). In this course, the liquid is sorbed into the column, until reaching the maximum penetration depth h(t) [39], depending on the infiltration time t, the surface cells radius R, the surface tension γ, the dynamic viscosity η of the fluid, and the contact angle θ between the fluid and the solid [40].

This model reflects the process of inter-particle and intra-particle sorption of PCM into EP particles. The sorbent consists of EP particles of random radii packed in a cubic control unit, which serves as the boundaries of the system. Within the boundaries, the particles of EP (referred to as ‘i’) contain solid material (referred to as ‘s’) and open pores (referred to as ‘p’), while the active (available) space area for capturing PCM is considered as surface cells (referred to as ‘c’).

The level of packing efficiency determines the number of particles, i, included in the control unit and the available surface cells. As the packing efficiency is increased, the contact regions of particles within the boundaries are intensified. This observation can affect the maximum penetration depth h(t) causing fluid to be wicked to the surface cells and thus fail to migrate to the deeper contact regions. Therefore, a more compact and compressed control unit is expected to present a lower penetration depth because it is homogeneously filled with fluid [39].

The inter-particle sorption capacity refers to the ability of a material to adsorb or absorb liquid substances in the spaces between its particles. For the present system, the total mass of the liquid PCM sorbed to the surface cells of EP by definition can be expressed as

M_inter = ρ_inter · V_inter

(1)

where ρ_inter is the density of the melted PCM, [kg/m³]; and the V_inter is the volume that is occupied by the melted PCM, [m³]. The density of the PCM is dependent on the temperature of the liquid and the operational conditions and it is determined experimentally.

The total volume of the liquid PCM can be expressed as:

V_inter = SA_c · h(t)

(2)

where SA_c refers to the surface area of the open surface cells (c) on EP particles, [m²]; and the h(t) is the capillary rise of a fluid into a capillary (equivalent to the penetration depth).

The SA_c of the surface cells on EP particles is analysed to parameters characterising the material as

SA_c = SSA_c · ρ_i · V_i

(3)

where SSA_c refers to the specific surface area of surface cells on the EP surface, [m²/kg]; ρ_i is the particle envelope density of EP, [kg/m³]; and V_i is the volume of a particle. The SSA_c is acquired by deep learning SEM image processing and the V_i of a particle is calculated for a spherical particle with diameter D_i determined through the PSD analysis.

Next, the capillary rise of a fluid in relation to time is determined with reference to a modified Washburn method [39,40], as follows:

h(t)² = (R_eq · γ_PCM · cosθ)/2μ · t

(4)

where t refers to the infiltration time, [sec]; γ_PCM is the surface tension of the liquid PCM, [N/m]; μ refers to the dynamic viscosity of the fluid, [kg/m/s], θ is the contact angle between the fluid and the solid, which is characterised hydrophilic for values <90°, [deg] [40]; and R_eq refers to the equivalent radius of the inter-particle surface cells on EP surface, [m]. In order to maintain hydrostatic equilibrium, the Young–Laplace equation is utilised to express the maximum capillary rise of a fluid [36,38]:

h = (2 · γ_PCM · cosθ)/(ρ_inter · g · R_eq)

(5)

where g is the acceleration due to gravity, [m/s²].

To calculate the equivalent radius R_eq of the inter-particle surface cells on the EP surface, the inter-solid porosity is employed. The value is acquired by the SEM image characterisation. The equivalent radius is then calculated in relation to the inter-solid porosity and the diameter of the particle D_i determined through the PSD analysis [38,39,40,41]:

R_eq = (φ_c/1 − φ_c) · (D_i/2)

(6)

where φ_c is the surface porosity or volume fraction, [-].

Lastly, the term cosθ is related to the contact angle between the fluid and the solid. This term is modified in the case of particulate surfaces in accordance with the Wenzel model which presents a correlation between contact angle and surface roughness. The modified roughness factor is defined as the ratio of specific surface actual area to the specific geometric surface area. In case the surface is smooth, R_o is equal to one, and it is increased for rougher surfaces [40,42]. It is assumed that the geometric shape of the particles is spherical, and the modified roughness factor is extended to the following:

R_o = SSA_c · ρ_i · D_i/6

(7)

Subsequently, the contact angle term is modified as follows:

cosθ = R_o · cosθ_ο

(8)

where θ is the contact angle of a rough surface, θ_ο is the contact angle of a flat surface, and R_o is surface roughness factor.

Once these parameters are determined, the total mass of the liquid PCM sorbed to the open surface cell of each EP particle within the system boundaries can be calculated. Given the previous statements and the integration of the circularity factor CF, the inter-particle sorption capacity can then be expressed as follows [36]:

Γ_inter = 2/3 · (γ_PCM·cosθ/g) · (1 − φ_c/φ_c) · (1/ρ_i) · (SSA_{c_per_volume} · CF)²

(9)

The specific surface area (SSA_c) of the open cavities (surface cells) on the particle’s surface is important, as a higher SSA_c offers more area for PCM sorption, directly enhancing the sorption capacity. The role of the particle’s density (ρ_i) as well as the surface porosity or volume fraction (φ_c) is inversely proportional to the sorption capacity. A higher particle density is correlated to lower surface cavities and open pore channels to sorb and retain the sorbates. Higher surface porosity, implying shallower surface cell spaces within the thinner and weaker particle matrix, allows for lower PCM infiltration, thus counteracting sorption capacity.

2.3. Intra-Particle Capacity Model

This section is focused on the intra-particle sorption of melted PCM onto the open pores of the EP, with an emphasis on determining intra-sorption capacity geometrically as well as defining the specific aspects of this interaction.

2.3.1. Definition and Assumptions of Intra-Particle Capacity Model

The absorbency phenomena is characterised by the transport of liquid into a porous material by the immiscible displacement of air from pores, due to the capillary action. For this purpose, a data-driven model is developed, opting to simulate the intra-particle sorption capacity into the EP pores. The analysis is focused on the determination of capacity that the carrier provides based on physicochemical properties of the sorbent and the sorbate and the environmental conditions during the process. The optimisation of the sorption is investigated by manipulating different physical and operational parameters to achieve the maximum oil sorption capacity. Capillary suction appears in all directions; however, emphasis is given to the vertical ascent providing precise mathematical formulations [43]. For this purpose, the absorption mechanism is considered as a flow through capillary tubes using standard capillary flow equations [44].

Several theoretical models are discussed and incorporated into determining the intra-particle sorption capacity. The results will facilitate the determination of the optimal parameters to increase the efficiency of TES materials for building construction. To facilitate the mathematical formulation of the sorption into a porous medium, the following assumptions are considered:

• Incompressible Newtonian liquid quasi-steady state and fully developed laminar flow with no-slip boundary conditions and without any flow acceleration inside the pores [45].
• Similarly to the inter-particle sorption model, the melted PCM is assumed to act as an oil.
• Empirical factors are introduced to account for realistic limits and sorption rates. The interconnectivity of pores within the porous medium is not considered [46].
• The capillary sorption model considers one-dimensional (1D) flow in straight tubes.
• The through open pores in the intra-particle area with noncircular cross-sectional shapes are addressed as sequent, parallel, cylindrical capillary tubes with equivalent diameter equal to the average BET diameter.

2.3.2. Intra-Sorption Kinetics

Several fundamental concepts and models can be found in the literature describing fluid flow through porous media, capillary action, and the dynamics of liquid sorption. Darcy’s Law focuses on bulk flow through a medium, the Young–Laplace equation describes the capillary pressures at fluid interfaces, the Hagen–Poiseuille Law focuses on flow through capillaries, and the Lucas–Washburn model focuses on the dynamics of capillary absorption.

The Lucas–Washburn model is a standard approach used to describe the capillary-driven flow of a liquid into a porous medium or through narrow channels, such as those found in capillary tubes. In the general form of Lucas–Washburn, it can be observed and has been validated experimentally that the wetted length L of the tube is directly proportional to the square root of saturation time. At low values of t, where L can be expressed, the following equation, also known as the Washburn equation [36,43,44,47], can be used:

L = sqrt (r_c² · ΔP/4μ) · sqrt (t)

(10)

Despite the benefits and the wide use of this model, the Lucas–Washburn equation has limitations. It may not accurately describe fluid flow in highly heterogeneous or anisotropic porous media, where the structure and connectivity of the pores vary significantly. Additionally, for very early or late times during the absorption process, deviations from the model’s predictions can occur due to dynamic contact angle effects or when gravitational forces become non-negligible. A modification and extension of the Lucas–Washburn model has been developed to address these and other complexities, allowing for more accurate predictions under a broader range of conditions.

2.3.3. Intra-Particle Capacity Model Development

This model is designed to demonstrate the process of the intra-particle sorption of PCM into EP pores. The system consists of open ‘through’ pores of cylindrical shape with a radius equal to the average pore radius obtained from BET. Within these boundaries, the particles of EP (referred to as ‘i’) contain solid material (referred to as ‘s’) and open pores (referred to as ‘p’), while the active (available) space area for capturing PCM is considered as surface cells (referred to as ‘c’).

The intra-particle sorption capacity refers to the ability of a material to adsorb or absorb liquid substances in the open pores. For the present system, the total mass of the liquid PCM sorbed to the surface cells of EP by definition can be expressed as

M_intra = ρ_intra · V_intra

(11)

where ρ_intra is the density of the melted PCM, [kg/m³]; and the V_intra is the volume that is occupied by the melted PCM, [m³]. The density of the PCM is dependent on the temperature of the liquid and the operational conditions and it is determined experimentally.

The total volume of the liquid PCM can be expressed as

V_intra = n_p · V_p

(12)

where n_p refers to the number of pores (p) on the EP particle, and the V_p is the volume of an ideal average cylindrical pore [m³]. The number of pores n_p can be obtained if assumed that all pores have equal diameter (acquired from BET experimentally). The volume of the pore V_p is calculated geometrically as a correlation of the L_p which represents the length of the average pore and the wetted length of the capillary.

V_p = A_p · L_p

(13)

where A_p is the surface area of a pore [m²].

Next, the wetted length of the capillary can be obtained from the Lucas–Washburn model considering the capillary radius as the pore radius—refer to Equation (10). The parameter ΔP stands for the pressure difference applied to a drop of liquid across a sorbent’s particle [Pa]. This is in fact the factor causing the movement of the liquid substance through the open pores. The pressures originate from the aggregate of the gravitational force, the external pressure, and the capillary action (surface tension) [36,44]. The total pressure acting downward is given by

ΔP = P_b + P_w + P_c

(14)

where P_b is the external pressure, [Pa]; P_w is the pressure derived from the weight of liquid drop, [Pa]; and P_c stands for the capillary pressure provided by the Young–Laplace equation [43,44,48,49]. These are given by

P_w = ρ_PCM·g · V_w/π/r_c²

(15)

P_c = 2 · γ_PCM · cosθ/r_c

(16)

where r_c is the capillary radius, γ_PCM is the surface tension of the liquid against the gas (or another immiscible liquid), and θ is the contact angle at the liquid–solid–air interface.

Once these parameters are determined, the total mass of the liquid PCM sorbed to the open pores for each EP particle within the system boundaries can be calculated. It is also noted that the SSA_i is acquired by the BET measurements and the mass of the particle M_i is obtained from the inter-particle sorption model [kg]. The intra-particle sorption capacity can be then expressed, given the previous statements as

Γ_intra = ρ_PCM · φ · SSA_i · ∑L_{eq_i}/N_particles

(17)

where L_eq is the equilibrium capillary rise that is reached when the pressure drop is reduced to zero [m]; determined by the Lucas–Washburn model.

The porosity (φ) and specific surface area (SSA) of the EP are essential; higher porosity and larger surface area increase the available space for PCM sorption, enhancing the sorption capacity. The sum of equilibrium capillary rises, and ∑L_eq represents the cumulative effect of capillary action across all pores, which is a function of the physical and chemical interactions between the PCM and the pore walls. The Lucas–Washburn model’s consideration of pressure differences and capillary forces further details how these forces drive the PCM into the pores.

3. Results

The data obtained the physical and thermodynamic parameters of a a commercial EP of LBD 90 kg/m³ (EPConv90) acquired by technical sheets from the Estroperl^® and the Perlindustria V5 products. The module is able to regenerate the observed particle of EPConv90, as shown in Figure 2. The real EP particle exhibits a rough and irregular texture with a porous structure. Its surface is uneven, showing multiple cavities and indentations. In contrast, the simulated EP particle, while attempting to replicate the porous structure, displays a more uniform texture. The pores and cavities are more regular in shape and distribution, and the overall shape is more spherical compared to the real particle.

The level of accuracy in the numerical simulations of PCMs can be significantly influenced by whether constant properties or temperature-dependent properties are used. For this reason, the model utilises temperature-dependent properties, which are captured from the literature studies [50]. The thermophysical properties of the sorbate scenarios investigated in this work are shown in Figure 3.

Figure 3a depicts the density of the tested substances as a function of temperature from 0 °C to 100 °C providing a clear and thorough understanding of their thermal expansion behaviours. RT27 starts with a density of around 850 kg/m³ at 0 °C but shows a notable discontinuity around 28 °C, dropping suddenly to about 810 kg/m³. Beyond this discontinuity, the density continues to decrease with temperature, reaching around 760 kg/m³ at 100 °C. This indicates that RT27 undergoes a significant phase change around 28 °C, drastically reducing its density. The RT27 is the only substance exhibiting a phase transition around 28 °C, significantly impacting its density. Even though these oils do not exhibit phase change, they are tested in this work because they can be found extensively in the research studies for sorption in EP, and they are expected to demonstrate similar behaviour to RT27 due to their properties.

Figure 3b presents the contact angle (CA) of water, linseed oil, n-Dodecane, n-Octane, and RT27. Water has a CA of approximately 31 degrees. Linseed oil shows a CA of around 33 degrees, slightly higher than water. RT27 exhibits a CA of around 35 degrees, similar to linseed oil. This high CA suggests that RT27, like linseed oil, forms droplets and has high surface tension, making it less likely to spread on the surface. In essence, higher contact angles indicate high surface tension and droplet formation. Despite not undergoing phase changes, linseed oil, n-Dodecane, and n-Octane are tested due to their validated performance in sorption in EP and are expected to exhibit similar wetting behaviour to RT27.

Figure 3c depicts the surface tension of water, linseed oil, n-Dodecane, n-Octane, and RT27 as a function of temperature from 0 °C to 100 °C. Water starts with a surface tension of approximately 0.075 N/m at 0 °C, and this value decreases almost linearly as the temperature increases, reaching about 0.06 N/m at 100 °C. RT27 exhibits a surface tension of around 0.020 N/m at 0 °C, which is also considered constant due to a lack of surface tension curves. This suggests that RT27, like the oils, has a relatively low surface tension that decreases slightly with temperature. Overall, the surface tension of all substances decreases as temperature increases, consistent with the principle that higher temperatures reduce intermolecular forces.

Figure 3d demonstrates the dynamic viscosity of water, linseed oil, n-Dodecane, n-Octane, and RT27 as a function of temperature from 0 °C to 100 °C. RT27 exhibits a dynamic viscosity of around 0.004 kg/m·s at 28 °C, which decreases slightly to about 0.0008 kg/m·s at 100 °C. It is noted that for this case the dynamic viscosity is measured only when the PCM is in a liquid state. The dynamic viscosity of all substances decreases as temperature increases, with water and the oils showing this behaviour to varying degrees. Water and the oils (linseed oil, n-Dodecane, and n-Octane) display significant reductions in viscosity with increasing temperature, which is common as higher temperatures reduce intermolecular interactions.

3.1. Sorption Capacity Analysis

The sorption model is designed to quantify, predict, and optimise the sorption capacity of EP particles for the different sorbate scenarios investigated in this work including the water, the linseed oil, the n-Dodecane, the n-Octane, and the RT27. The total sorption capacity of the EPCONV90 is illustrated below in Figure 4. The process is performed under atmospheric pressure (101,325 Pa) at 50 °C temperature. As it is observed, water exhibits the highest total sorption capacity, with a value slightly above 2 kg/kg EP. The high sorption of water is likely due to its polar nature and the potential presence of hydrophilic sites in the composite that attract water molecules. Linseed oil shows a moderate sorption capacity, around 0.75 kg/kg EP. This lower sorption compared to water suggests that the oil’s viscosity and molecular size might also affect its absorption, leading to moderate uptake. In this regard, the behaviour of the rest of the oils is consistent with n-Dodecane to demonstrate a sorption capacity close to 0.79 kg/kg EP. RT27 exhibits a sorption capacity similar to linseed oil, around 0.6 kg/kg EP. This indicates that the EP has a specific sorption characteristic for PCM materials. The similar sorption capacities of linseed oil and RT27 might suggest that the composite’s structure supports the encapsulation and retention of both types of fluids efficiently.

According to the experimental studies in the literature, the predicted values are aligned with the expected sorption capacity of EP water and oils. As shown in Table 1, the typical oil absorption is 50–225 %wt. and water absorption is 200–600 %wt. The predicted values are not optimised as they are close to the lower acceptable values. This observation may be derived from the operational conditions of the sorption process which coincide with the DIM method. DIM is associated with longer operation time as well as lower sorption rates in comparison to the VIM. Sorption under very low pressure (VIM) is not technologically as mature as DIM and the cost of the process is significantly higher; therefore, for this case, the DIM was modelled. To ensure that the PCM-enhanced composite is optimum, an optimisation investigation is performed on all the operational parameters.

The validation and re-calibration of the sorption capacity model is performed by utilising laboratory data by measuring the EP oil absorption according to the ASTM D1438-95 standard (linseed oil sorption) [30]. Respectively, the use of linseed oil is required for model validation as the sorbates to be tested have a higher viscosity than water and are expected to perform differently [50]. The studies used as reference for the validation of the sorption capacity model comprise experimental works that performed direct impregnation of oils (e.g., linseed oil, organic paraffins, light cycle oils) into expanded mineral carriers (e.g., EP, expanded vermiculite, diatomite) for a period of 2001 until 2024 [51,52,53,54,55,56]. From the results shown in Figure 5, it is observed that for reference studies, the median max ratio of oils sorbed into porous media is about 50%, while the sorption capacity per mass % median value reaches 80%. This result corresponds to mixing ratios of 0.8:1 for 50% of the reviewed studies. The sorption capacity wt.% varies from 50 to up to 200 %, which is also expected and validated from previous works [22,23,24,25,26,27]. This study reflects the same median values for both parameters and demonstrates a range of observations relevant to the reference studies. The minimum and maximum values of both max ratio and sorption capacity are consistent with the experimental variations.

3.2. Inter-Particle Sorption Analysis

Figure 6 presents the inter-particle sorption capacity of EPCONV90 for the different sorbates. As it is observed, inter-particle sorption dominates the process as it is around 98% of the total sorption for all cases. This observation is consistent with the DIM method applied and depicts that a major quantity of sorbate is captured to the open cavities of the EP surface instead of the open pore channels.

By solving the equation of inter-particle sorption, it is proven that there five variables that drive the phenomenon, including the surface tension (γ_PCM) and the contact angle (θ_ο) of the PCM, as well as the particle density (ρ_i) of the sorbent, the specific surface area (SSA_c) of the open cavities (surface cells) on the particle’s surface and the porosity or volume fraction (φ). To provide in depth insights on the impact of these parameters on the sorption capacity, an investigation is performed for the RT27, by applying realistic ranges to each parameter. Through this process, their effect is proven separately.

The sorbent’s particle density (kg/m³) exhibits a behaviour that aligns with the influence of the sorbate’s contact angle on inter-sorption capacity. Figure 7 depicts a substantial drop of the inter-sorption capacity as the particle density is increased. This trend can be attributed to the fact that denser particles typically offer fewer available pores or reduced surface area, both of which are critical factors in capturing and retaining sorbates. In essence, denser materials, characterised by compact structures, tend to be less porous, which inherently limits their ability to accommodate sorbates effectively. The findings underscore the necessity of designing and selecting highly porous structures when developing PCM-enhanced composites. By maximising the surface area and creating more available pores, these materials can significantly improve sorption capacity, leading to better performance in energy storage, thermal regulation, and related applications.

The available surface area influences the performance of the sorption. In particular, the specific surface area (SSA_c) of the open cavities on the EP surface indicates a positive correlation on the capacity of sorption as shown in Figure 8. For this purpose, the SSA_c ranges from 400 m²/g to 1000 m²/g, while the inter-sorption capacity grows from approximately 0.1 kg/kg at the lower end to almost 1 kg/kg at the upper end of the SSA_c spectrum. The results suggest that SSA_c is a critical factor in enhancing the sorption ability of a material. Materials with higher SSA_c provide more active sites for sorption, resulting in a greater capacity for retaining or absorbing the sorbate.

The last crucial parameter to be analysed is the surface porosity or volume fraction φ_c(-), which is determined by SEM imaging analysis. Figure 9 displays a negative correlation between surface porosity and inter-sorption capacity. As surface porosity increases, the inter-sorption capacity decreases sharply at first and then gradually levels off at higher porosity values. At low surface porosity (around 0.3), the inter-sorption capacity is at its highest, reaching around 1.4 kg/kg. This suggests that the material’s surface structure is denser, with deeper cell cavities and stronger matrix integrity, allowing for higher PCM infiltration and retention. As surface porosity increases from 0.3 to 0.9, the inter-sorption capacity gradually decreases. This decline can be explained by the fact that higher porosity leads to a thinner, weaker matrix with shallower cell spaces. These shallower cavities provide less volume for PCM infiltration and retention. The structural integrity of the material is compromised with increased porosity, resulting in less capacity to sorb the PCM. This figure effectively introduces the negative effect of a fragile and weak media surface on the inter-sorption capacity due to the compromised structure of the sorbent material. This concept highlights the trade-off between porosity and structural integrity in PCM-enhanced composites, emphasising the need for careful design when selecting materials to optimise sorption capacity.

3.3. Intra-Particle Sorption Analysis

Intra-particle sorption capacity enables the quantification of a sorbate infiltrating into the open pores and pore channels of an EP particle. Figure 10 presents the intra-particle sorption capacity of EPCONV90 for the different sorbates. The first observation derives from the previous figures, indicating that by employing the DIM, the quantity that can be impregnated into the porous material is significantly limited compared to the surface open cavities. The main contributor is the lack of pressure difference that would remove the captured air from the pores and allow the sorbate to be sorbed. Additionally, water has the highest intra-sorption capacity, outperforming the other tested sorbates, followed by linseed oil, with the hydrocarbons and RT27 having lower but comparable capacities. This outcome is foreseen, considering that water molecules are relatively small compared to many other liquids, particularly the hydrocarbons like n-Dodecane and n-Octane. Smaller molecules can more easily penetrate the porous structures of the sorbent material, allowing for greater infiltration and sorption.

A similar parameter-based analysis is performed for the intra-particle sorption capacity. Four thermophysical properties are identified with high impact on the intra-particle sorption, including the porosity [-] and SSA [m²/g] of the sorbent. The results in Figure 11 illustrate a positive linear relationship between the intra-particle sorption capacity and the SSA of the sorbent, as measured using the BET method. As the SSA increases, the intra-particle sorption capacity correspondingly increases, following a nearly perfect linear trend. The SSA is a critical parameter in determining how much sorbate the carrier can accommodate, as it directly correlates with the available contact area for sorbate molecules to adhere to and infiltrate the sorbent. Higher SSA values suggest that the material provides more internal surfaces and pore space for the PCM to interact with, resulting in greater intra-particle sorption capacity. The observed linearity of the relationship suggests that the surface area is uniformly distributed throughout the sorbent, allowing for consistent and predictable increases in sorption capacity with rising SSA. In practice, this finding emphasises the importance of designing sorbent materials with high specific surface areas to optimise their performance in terms of PCM retention.

3.4. Analytical Investigation of Sorption Operational Parameters

The model structure and simulation setup designed to optimise the sorption process of PCM into EP particles is outlined in this section. The primary objective is to evaluate how different operational parameters—temperature and pressure—affect the sorption rate and capacity, with the goal of determining the optimal conditions to maximise performance. The model framework consists of a multi-scale approach, capturing both inter-particle sorption (macroscopic) and intra-particle sorption (microscopic) behaviours of the PCM-EP system. Accordingly, the sorption capacity model is utilised to quantify, predict, and optimise the sorption capacity of the EP—EPCONV90 particles for the RT27. It is noted that the operational conditions selected for the estimation of EPCONV90 capacity consist of atmospheric pressure (101,325 Pa) at a 50 °C temperature.

For the investigation of the temperature influence on the sorption performance, a temperature range from 28 °C to 60 °C is demonstrated. This range is chosen because the melting temperature of RT27 is 27.3 °C, and heating beyond 60 °C can lead to degradation and loss of functionality in the organic PCM. The model framework remains unchanged with respect to the inter-particle and intra-particle models, as temperature is already incorporated as a variable in the system. By optimising within this range, the aim is to enhance sorption efficiency while maintaining the thermal stability of the PCM.

The next parameter is the applied pressure during the sorption process. As described previously, there are two main LTES-enhanced composite preparation methods including DIM performed at atmospheric pressure conditions and the VIM performed into a vacuum/pressure chamber and applying vacuum. The inter-particle and intra-particle models demonstrate a DIM sorption and therefore, for the purpose of this analysis, a modification is applied to the total pressure term in the Darcy’s law, expressed as [57,58,59]

ΔP = P_v · P_m · P_w · P_c

(18)

where the external pressure is divided into P_v, the vacuum pressure [Pa]; P_m is the applied mechanical pressure [Pa]; P_w is the pressure derived from the weight of the liquid drop, [Pa]; and P_c stands for the capillary pressure provided by the Young–Laplace equation. For small-scale impregnation systems, the applied mechanical pressures produced by impregnation rollers can range from 0 to 10⁶ Pa (=15 psi) [59]. The VIM method can apply a vacuum pressure of up to 6.55 × 10⁶ Pa (=95 psi) to the vacuum chamber for removing any air bubbles from the carrier’s porous materials and facilitate the sorption of the PCM. In case vacuum-assisted impregnation is not being used, P_v is equal to zero.

Sorption Operational Parameters Analysis

The results are divided into two subsections: the effect of temperature on sorption behaviour and the influence of pressure on the sorption process. The simulations, as depicted in Figure 12, Figure 13 and Figure 14, demonstrate how temperature affects both inter-particle and intra-particle sorption of PCM into EP across a range from 28 °C to 60 °C.

For inter-particle sorption, Figure 12 shows that this process remains relatively stable throughout the temperature range. The sorption capacity stays within a narrow band, with only a slight decrease as temperature increases. This stability suggests that inter-particle sorption is less affected by temperature changes, likely due to the larger pore sizes in the EP matrix, which provide easier access for PCM infiltration. Since the larger pores are not highly sensitive to changes in PCM viscosity or diffusivity, the overall inter-particle sorption capacity remains mostly unaffected by the increase in temperature.

In contrast, Figure 13 depicts that intra-particle sorption, which involves the absorption of PCM into the smaller pores of the EP particles, is more sensitive to temperature variations. As temperature rises, the intra-particle sorption capacity decreases more noticeably. While higher temperatures increase the diffusivity of PCM molecules, the reduction in viscosity seems to favour infiltration into larger pores, reducing PCM uptake in the finer, more restrictive pores. This behaviour supports the idea that although higher temperatures enable faster sorption in larger pores, they reduce the efficiency of sorption in smaller pores, where PCM molecules face greater resistance.

Figure 14, which combines the effects of both inter-particle and intra-particle sorption, shows a slight overall decline in total sorption capacity as temperature increases. The marginal decrease in total sorption is mainly due to the reduction in intra-particle sorption at higher temperatures, even though inter-particle sorption remains stable. This suggests that the reduced capacity in smaller pores slightly outweighs the increased uptake in larger pores, leading to a net decline in overall sorption.

These results demonstrate that while increasing temperature accelerates sorption in larger pores, it has a limiting effect on the absorption of PCM into smaller pores, ultimately lowering overall sorption capacity at higher temperatures. As the temperature increases from 28 °C to 60 °C, a noticeable improvement is expected in the sorption rate. At 28 °C, the PCM is near its melting point, which leads to a slower sorption process due to its higher viscosity. An optimal temperature of between 40 °C and 50 °C strikes a balance between sorption rate and capacity, particularly in applications where maximising intra-particle sorption is important. This temperature allows for efficient infiltration without compromising the overall capacity by excessively favouring larger pores at the expense of smaller ones.

Figure 15 illustrates the effect of varying pressure on the inter-particle and intra-particle sorption of PCM into EP, with pressures tested up to 6.55 × 10⁵ Pa, simulating conditions with and without vacuum application. Inter-particle sorption remains almost constant across the range of applied pressures, stabilising at approximately 0.59 kg of PCM per kg of EP. This indicates that pressure has little to no influence on the inter-particle sorption process, which is primarily governed by larger pores and cavities. Since these pores are easier for PCM to access, pressure does not significantly impact the penetration of PCM into the larger spaces between particles.

In particular, the intra-particle sorption demonstrates a linear increase in intra-particle sorption as pressure rises. This suggests that higher pressure facilitates PCM’s penetration into the smaller pores within the EP particles, gradually increasing the intra-particle sorption capacity. The linear trend indicates that pressure enhances the accessibility of finer pores to PCM, thus improving the efficiency of the sorption process at the microscopic level. While the overall increase is minimal, it is primarily driven by the enhanced intra-particle sorption at higher pressures. The total sorption capacity remains close to 0.59 kg PCM per kg of EP, suggesting that the contribution of intra-particle sorption becomes more pronounced at elevated pressures, though it does not result in a substantial overall gain.

The results highlight that pressure has a differential impact on the two types of sorption. For applications requiring enhanced PCM absorption into the finer pores of EP, applying vacuum or higher pressure would be advantageous. However, for applications where inter-particle sorption is the primary concern, atmospheric pressure is sufficient, as it does not limit the process. It is worth noting that the EPCONV90 sample is characterised by a pore radius of 0.53 nm. For intra-particle sorption, larger pores (53 nm) exhibit a significant increase in sorption capacity as pressure rises, after approximately 4 × 10⁵ Pa. This suggests that larger pores allow PCM to infiltrate more easily, and the effect of pressure is especially pronounced in driving PCM deeper into these larger pores. The sharp increase in sorption capacity at higher pressures indicates that pressure helps overcome flow resistance within these large pores, leading to a near-complete saturation of the EP’s available volume. The enhanced sorption capacity in large pores under high pressure makes this approach particularly suitable for large-scale thermal energy systems.

In contrast, smaller pores (0.53 nm and 5.3 nm) show minimal changes in intra-particle sorption across the same pressure range. The limited effect of pressure on smaller pores can be attributed to the inherent difficulty of penetrating fine structures, even under high pressure. For small pores, factors such as surface tension and capillary forces create significant resistance to PCM flow, preventing substantial increases in sorption. This suggests that pressure is not an effective mechanism for improving sorption in systems dominated by small pores. Instead, other strategies, such as modifying PCM properties (e.g., reducing viscosity) or increasing temperature, may be necessary to enhance sorption performance in these fine pore structures.

The overall sorption results, in Figure 15, which combine both inter-particle and intra-particle sorption, follow a similar pattern. Larger pore radii (53 nm) show a noticeable improvement in overall sorption capacity as pressure increases, especially beyond 4 × 10⁵ Pa. The contribution of inter-particle sorption remains stable, while the intra-particle sorption in large pores drives the overall capacity upward. In contrast, smaller pores remain largely unaffected by pressure changes, with only a slight increase in total sorption observed. This indicates that while pressure can enhance overall sorption in systems with larger pores, its effect is limited for systems with predominantly small pores.

The pore-size-dependent behaviour observed in the simulations reveals key insights into how pressure and pore structure interact in PCM-EP systems. Larger pores allow for easier penetration of PCM, making them highly responsive to pressure increases, while smaller pores are more resistant to pressure-driven sorption. For systems with larger pores, applying vacuum or high pressure significantly boosts sorption capacity, making it an effective method for maximising PCM uptake. On the contrary, for systems with smaller pores, where the pressure effect is minimal, alternative approaches such as optimising temperature or modifying PCM properties may be more effective. The extended analysis also emphasises the importance of tailoring pore size distribution in EP to optimise sorption performance. A multi-scale pore structure, comprising both large and small pores, could provide the best of both scales, allowing for pressure enhanced sorption in larger pores while leveraging temperature or other modifications to improve sorption in smaller pores. To summarise, increasing pressure significantly enhances sorption in systems with larger pores, while its effect on smaller pores remains limited.

4. Discussion

The mechanistic models play a primary role in integrating theoretical analysis with experimental validation, particularly in the development and optimisation of LTES-enhanced composites. The sorption capacity model, with its ability to simulate complex material behaviours and predict performance, serves as an essential bridge between theoretical assumptions and practical, real-world outcomes. This integration enables a more profound understanding of material performance under varying environmental conditions, which is crucial for enhancing energy efficiency in buildings.

The work also highlighted the potential for exploring additional LTES materials by employing basic characterisations or leveraging existing data from the literature. By using simplified material characterisation methods, the mechanistic models could efficiently screen several promising LTES materials for their suitability in building applications. Basic material characterisations allow to focus on new, innovative materials without extensive experimental trials. Additionally, existing data on organic and inorganic LTES materials reveal their desirable properties, such as minimal subcooling, stable cycling behaviour, and low toxicity, making them excellent candidates for energy-efficient building materials. In this frame, the effectiveness of designing and analysing new materials from both theoretical and experimental perspectives, leading to optimised composites, is demonstrated. By combining theoretical models with experimental data, the team validated the predictions made by mechanistic models and fine-tuned material compositions to meet specific application needs. For instance, a composite made of expanded perlite and paraffin-based PCMs, initially optimised through modelling, showed improved thermal conductivity and latent heat storage compared to other formulations. Subsequent experimental validation confirmed the superior performance of this composite in reducing indoor temperature fluctuations and improving thermal comfort. This iterative process, integrating model-based design and experimental testing, proved highly efficient for rapid innovation and material optimisation.

Among the different scientific areas addressed in this work, there are topics that can be further explored. The mechanistic models delivered are tailored to specific building applications including the loose fill as a layer of the building envelope and the LTES-enhanced mortar as an interior layer directly interacting with the space heating systems. The selection of these cases is derived from the literature trends, the technoeconomic feasibility considerations, and the availability of experimental data. However, it is addressed that the selection of the most appropriate positioning of LTES composites in the building needs to be expanded. There are plenty of alternatives including roofs, floors, and furniture as well as applying LTES-enhanced composite to the exterior layers of the building blocks. For this reason, the placement of such TES systems can affect the performance of the system as well as the overall energy performance of the building. This investigation could benefit from this mechanistic work by being incorporated into the BIM models to facilitate the analysis of the thermodynamic behaviour and the optimisation. The vision for the mechanistic model developed is to be provided with open-source access rights serving as a tool for directly evaluating the thermophysical behaviour of construction materials and alternative building envelope scenarios.

In this framework, the role of LTES-enhanced composite layers within a building block is primarily harnessed as an additional passive thermal mass. However, their role can be broadened to serve as heat flow buffers and actively interact with the space heating systems and the meteorological conditions. By positioning thin layers to the exterior of the building envelope, the LTES-enhanced composite would block thermal energy flow from external global irradiance gains into the building and therefore reinforce the insulation systems in place. The benefits of this approach are believed to be multiple, thus inspiration for future investigation. The mechanistic model enables the investigation of multiple materials, considering that specific thermophysical properties are determined. In this regard, the exploration of commercial and new LTES materials is promoted in order to select the most suitable sorbate tailored to each case. In conclusion, this research has addressed critical technological and industrial challenges related to the integration of LTES composites in building applications, demonstrating significant advancements in both material performance and mechanistic modelling.

5. Conclusions

The study introduces a mechanistic model for LTES composite design to be applied for construction applications focusing on the integration of PCM in EP. This is accomplished through developing sorption capacity modelling of critical influencing parameters, which mainly consists of factors concerning size of the particle, area of surface, and pore volume. This study identified EP as a highly performing sorbent for PCMs, wherein energy storage density was enhanced due to the improvement of the sorption operating conditions. With an attempt to solve the integration challenges of LTES materials, the study connected the microscopic scale to the macroscopic scale under different operational conditions. Predictive algorithms, such as machine learning models implemented in MATLAB, were applied to test the performance of LTES materials and, hence, their properties could be oriented for mortars and loose-fill applications.

This study presented the key findings related to the optimisation of LTES-enhanced composites. The optimised LTES-enhanced composite reached a total sorption capacity of 0.68 kg of PCM per kg of EP through VIM at 4 × 10⁵ Pa, which was 15% higher than that obtained from DIM. The relative contribution of inter-particle sorption to the total thus reached 98%, underlining the vital role played by the open surface cavities in the EP for retaining the PCM. Amongst the analysed sorbates, water showed by far the largest sorption capacity above 2 kg of water per kg of EP, while RT27 exhibits at atmospheric conditions only a capacity of 0.59 kg PCM per kg of EP. The provided optimisation of operation parameters of the RT27 case revealed highest sorption capabilities for temperatures ranging between 40° and 50 °C. Pressure also played an important part-for large pores, at least 53 nm in radius, VIM enhances sorption capacity by up to 10% for pressures greater than 4 × 10⁵ Pa. The mechanistic model also proves that the basic characterisation techniques of the materials efficiently screened the LTES materials, and the composite performance was well predicted based on the physical properties and thermophysical behaviour of sorbents. The models developed in this research identified the optimal thermophysical properties of sorbents and LTES sorbates for the design of next-generation composites. In conclusion, this research work sets up a reliable framework for the evaluation and design of LTES-enhanced composites.