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Surface Energetic Principles for Moisture Storage in Porous Materials

1.1 Introduction

Most natural mineral materials, with the exception of crystals, have a pore system whose pores can range from very fine nanometer (nm)‐sized pores to the millimeter (mm) range. A recognized classification of pore sizes has been made by International Union of Pure and Applied Chemistry (IUPAC). In the 2015 update of the 1985 report [1]. In this paper, the pores are classified into macropores, mesopores, and micropores.

Building materials such as natural stone, brick and especially concrete cover the full pore size range mentioned. Concrete materials usually contain a substantial concentration of particularly fine pores, which are classified in the group of nanopores.

These porous materials can therefore store liquids in the pore system, especially water, which can be carried in vapor form or in liquid form via surface forces.

The capillary absorbed liquid content is measured in [kg/ or in [, the velocity usually with good approximation as in [kg/ with the material coefficient in [kg/( when constant fluid supply is ensured.

To describe the storage of liquid from vapor uptake, the resulting water content is presented in the form of sorption isotherms as a function of the external relative humidity or after converting the relative humidity to the corresponding capillary pressure in the material.

In a number of (building) materials, such as brick products, a portion of the pores is so large that it is no longer filled by vapor adsorption, even at about 100% relative humidity. These pores can then only be filled capillary by external liquid‐water supply. This water fraction is called the superhygroscopic range of total water uptake. In such cases, the total moisture storage is described by the so‐called moisture storage function.

As indicated in the schematic moisture storage function in Figure 1.1a, many authors allow the hygroscopic range of the moisture storage function to extend only to about relative humidity, when in fact it must be defined to about 100% RH. The reason for this is the difficulty of precisely setting the moisture and measuring it accurately in this ‐near range. If the material also contains large pores that cannot be filled by capillary action – for example, air pores – the associated pore volume, which can usually only be filled under pressure, is assigned to the overhygroscopic range.

Figure 1.1 (a) Model of the water‐storage function for cement‐bound material.

Source: Adapted from Fagerlund [2] and Eriksson et al. [3].

(b) Sample moisture adsorption and desorption storage functions for building materials as a function of capillary pressure .

Source: Carmeliet and Roels [4]/Sage Publications.

The curve region above RH can be determined using the pressure plate experiment [5, 6], and Espinosa–Franke [7] as a so‐called suction stress curve depending on the applied capillary pressure. The mutual conversion of is done with Eq. (1.1). In this way, moisture‐storage functions can also be represented completely as a function of instead as, for example, by Carmeliet in Figure 1.1. At relative humidity, the associated capillary pressure is [Pa].

This means that in Figure 1.1a,b only the lower section of the curves (in the hygroscopic region) was determined by sorption measurements. The overhygroscopic ranges thus concern additional capillary water absorption as well as further water absorption under pressure also with (partial) filling of the processing‐related or artificially inserted air pores.

Using the Eq. (1.39) explained in more detail in Section 1.3.2, the vapor pressure dependence of the adsorption and desorption curves can be converted to the corresponding dependence on the associated capillary pressure in [Pa] as follows:

Sorption tests on building materials, in particular cement‐bound materials, yield desorption curves that deviate significantly from the adsorption curves or moisture storage functions during water absorption. The reason for this behavior will be discussed in more detail in Section 4.6. Measurements by, for example, Feldman and Serada [8] or Ahlgren [9] have already made this clear in 1968 and 1972, see Figure 1.2a,b. The measurements also show that a transition between an absorption and desorption curve, or vice versa, occurs on a “short path,” referred to as scanning loops or scanning isotherms. The main focus of Chapters 2, 3, and 4 will be to show the effects of this behavior on the moisture transport and the moisture household of corresponding material bodies.

Figure 1.2 (a) Adsorption and desorption isotherms and scanning loops measured on HCP of Portland cement .

Source: Feldman and Sereda [8]/Springer Nature.

(b) Principle course of moisture storage functions including scanning isotherms of building materials.

Source: Ahlgren [9]/Lund Institute of Technology/CC BY 4.0.

It will be shown that the individual moisture storage functions may have a fundamental importance for the moisture balance of porous materials and the modeling of moisture transport.

1.2 Surface Energy and Spreading of Liquids on Solid Surfaces

Since pore water within moist porous bodies is transported by capillary pressure (and vapor pressure) in the presence of sufficiently fine pores, and therefore capillary pressure is a crucial quantity with respect to moisture transport, the origin of capillary pressure within the pore system is first addressed. This first requires explanations of the role of the surface energy of the substances involved.

1.2.1 Explanations on Surface Energy and Surface Tension

The  molecular arrangement on a water surface surrounded by air is shown schematically in Figure 1.3. In contrast to the interior of water, where the molecules are surrounded by similar molecules in all spatial directions and therefore force effects between the molecules cancel each other out in the summation, the surface lacks balancing molecular partners on the air side.

Therefore, a molecular arrangement is formed at the surface, which leads to inwardly directed cohesive forces (hydrogen bonds) and force effects in the surface  plane.

Figure 1.3 Orientation of water molecules and schematic representation of the attractive forces at the liquid surface, by D. Drummer, Erlangen‐Nürnberg, Germany.

To increase the liquid surface area, work must be done to overcome the cohesive forces of a considered amount of water while the volume remains unchanged. The work to be done per unit area to increase this surface area A is called the surface energy  [LV means liquid versus air], here abbreviated as , corresponding to Eq. (1.2) in differential formulation:

Using Figure 1.4, it can be shown how surface energy can be determined by surface enlargement in a model experiment:

• A water membrane (producible by addition of surfactant) of dimension  is stretched by  with force F. The surface (front and back) increases by . The work done to increase the surface  is given in Figure 1.4 using Eq. (1.2).
• The displacement work is  ( and F measured).

Figure 1.4 Testing Model : Measuring the surface energy and surface tension by the work of displacement and the boundary force on a (soap)–watermembrane.

Figure 1.5 Measuring of the surface tension by the bracket‐method

The formulations of the work  describe the same change in the sample and therefore must be equal in magnitude. Thus,  Eq. (1.3) yields the magnitude of the (specific) surface energy of the surfactant‐added water. It can be seen that the special molecular orientation or the resulting surface cohesion in surface plane of the water membrane can introduce an edge force leading to an increase of the surface area, which is called the surface stress. From Eq. (1.3), it can be derived at the same time that the boundary force F related to the unit of the boundary length in [m] corresponds to the surface energy  of the liquid.

The true value  for non‐surfactant water can be determined fairly accurately with the experiment shown in Figure 1.5, in which a wire stretched in a stirrup structure is lifted out of a water surface via a precision balance. The water surface around the wire is lifted until it breaks off when the maximum force F is reached. The surface energy of water is 0.07275 [Nm/ = N/m] at 20 C, correspondingly 72.75 [mN/m].

Figure 1.6 Measuring surface tension and corresponding liquid surface shapes by two different methods [10]....