Introduction

Abstract

The mere facts that some 25% of social housing (i.e. more than 14 million units) in the 27 member states of the European Union is suffering from dampness and molds (Bonnefoy et al. 2003) and that approximately 4.6 million of current US asthma cases are estimated to be attributable to dampness and molds exposure (Mudarri and Fisk 2007) underline that indoor molds should be considered as a widespread and profound societal problem.

Appendix 1. Thermodynamic definition of water activity and relative humidity

The water activity

From the Gibbs-Duhem equation

$$\mathop \Sigma \nolimits_i n_i \cdot {\text{d}}\mu _i = - S \cdot {\text{d}}T + {\text{V}} \cdot {\text{d}}P$$

(1)

where n _i is the number of moles of i in the system, and V, T and S the volume, the temperature and the entropy of the system, respectively, it follows that the variation of the chemical potential μ _i of substance i with pressure P is given by

$$\upsilon _i = \left( {\frac{{\partial V}}{{\partial n_i }}} \right)_{P,T\left\{ {n/ni} \right\}} = \left( {\frac{{\partial \mu _i }}{{\partial P}}} \right)_{T,\left\{ n \right\}}$$

(2)

If substance i is an ideal gas then

$$\upsilon _i = \left( {\frac{{\partial \mu _i }} {{\partial P}}} \right)_{T\left\{ n \right\}} = \frac{{R \cdot T}} {P}$$

(3)

and hence

$$\mu _i = \mu _{i,0} + R \cdot T \cdot \ln \left( P \right)$$

(4)

If i is a component of a mixture of gases, P is replaced by p _{i, v} , the partial pressure of i. The reference state μ _i,0 is the chemical potential of the gas under a partial pressure of 10⁵ Pa, and is a function of the temperature T only

The concept of an ideal gas is useful in discussions of thermodynamics of gases and vapors. Many cases of practical interest are treated adequately by ideal gas approximations. Description of the properties of solutions, however, is much more complicated. Since the vapor pressure of a component above the solution is a good measure of the tendency to escape from the solution, and therefore reflects the physical state of affairs within the solution, the activity a _i of a component i in the solution was introduced. When equilibrium between the component i and its vapor exists, the chemical potential μ _i,1 of i in the solution equals the chemical potential μ _i,v of i in the vapor phase.

$$\mu _{i,l} = \mu _{i,v} = \mu _{i,0} + R \cdot T \cdot \ln \left( {P_{i,v} } \right)$$

(5)

Comparison to the chemical potential of pure solvent $\mu _i^*$ in a reference state introduces the activity a _i of i in the solution. It is emphasized that the activity depends strongly on the reference state chosen.

In case of pure solvent i

$$\mu ^\diamondsuit _{i,l} = \mu _{i,0} + R \cdot T \cdot \ln \left( {p^\diamondsuit _{i,v} } \right)$$

(6)

From Equation 5 and 6 follows

$$\mu _{i,l} - \mu ^\diamondsuit _{i,l} = R \cdot T \cdot \ln \left( {a_i } \right)$$

(7)

Two definitions of the activity a _i can be found in the literature (Thain 1967, Moore 1978, Hoppe et al. 1983)

$$a_i = \frac{{p_{i,v} \left( {P_H,T} \right)}} {{p^\diamondsuit _{i,v} \left( {P_H,T} \right)}}$$

(8)

and

$$a_i = \frac{{p_{i,v} \left( {P_H,T} \right)}} {{p^\diamondsuit _{i,v} \left( {P_{H,fixed},T} \right)}}$$

(9)

with

$$P_{H,fixed} = 10^5 {\text{Pa}}$$

(10)

As long as the vapor behaves as an ideal gas, the activity a _i of a component i in the solution equals the ratio of the partial pressure of i above the solution to the vapor pressure of pure i in the reference state. Again, it is emphasized that equilibrium between the liquid and vapor phase is required. The first definition (Equation 8) of the activity implies that the activity of the pure solvent always is 1 (Thain 1967). The consequence of the second definition (Equation 9 with Equation 10) is that the activity slightly depends on the total hydrostatic pressure P _h (Moore 1978, Hoppe et al. 1983).

For non-ideality, a new function called fugacity ƒ was introduced (Moore 1978). In that case, the activity a _i is calculated from the ratio of ƒ _i of i in the solution and $f_i^*$ of pure i in a reference state. However, since the vapor pressure in the indoor environment is sufciently low (<2.3×10³ Pa), non-ideality may be neglected.

The relative humidity

$$RH = \frac{{p_{w,w} \left( {P_B,T} \right)}}{{p_{w,v}^\diamondsuit \left( {P_B,T} \right)}}.100\% = \frac{{p_v \left( {P_B,T} \right)}}{{p_{vs} \left( {P_B,T} \right)}}.100\%$$

(11)

Although Equation 11 resembles the definition of the activity in Equation 8, consideration of the assumptions underlying Equation 8 shows marked differences. The RH concerns water in the vapor phase, whereas a _w refers to water in another state, either liquid or bound to the substrate. Furthermore, the RH is a measurable quantity, and a _w can only be deduced from other quantities such as the RH under equilibrium conditions and the osmotic pressure (see Chapters 1 and 2).