*2.4. Contaminants Emission Model*

For the VOCs emission of building materials, the quasi-steady-state ER can be described by the following equation [46]:

$$E(t) = 2.1 \frac{D\_m C\_0}{\delta} \exp\left(-2.36 \frac{D\_m t}{\delta^2}\right) \tag{6}$$

where *E* is the emission rate factor, *t* is the emission time, δ is the material thickness, *C*<sup>0</sup> is the initial emittable concentration inside the material, *Dm* is the diffusion coefficient. The correlation between *C*<sup>0</sup> and *T* can be described by the following equation [47]. The correlation between *Dm* and *T* can be described by the following equation [48]. Equation (9) is obtained by substituting Equations (7) and (8) into Equation (6) and then taking the logarithm on both sides.

$$C\_0 = \frac{C\_1}{T^{0.5}} \exp\left(-\frac{C\_2}{T}\right) \tag{7}$$

$$D\_m = D\_1 T^{1.25} \exp\left(-\frac{D\_2}{T}\right) \tag{8}$$

$$\ln \frac{E(t)}{T^{0.75}} = A - \frac{B}{T} - 2.36F0\_{\text{m}} \tag{9}$$

where *T* is the temperature in *K*. *C*1, *C*2, *D*<sup>1</sup> and *D*<sup>2</sup> are all constants determined only by the physical and chemical properties of pollutants

$$A = \ln \frac{2.1C\_1D\_1}{\delta}, \; B = C\_2 + D\_2, \; F0\_m = \frac{D\_mt}{\delta^2}.$$

To quantify the pollutants released by materials in a certain period of time, Equation (10) is included.

$$M = \int\_{t\_s}^{t\_\varepsilon} AE(t)dt\tag{10}$$

where *M* is the total quality of the released contaminants, *ts* is the start time, *te* is the end time, *E*(*t*) is the emission rate, *A* is the surface area.
