# The Ability to Control VOC Emissions from Multilayer Building Materials
## 2 Materials and Methods  
### Emission Modelling Proposal  
In order to determine the VOC emission profiles from heated floors in time based on the experimental results, the authors propose the following approach and model. The emission factor may be calculated as follows:  
\[EF=C\cdot\frac{n}{L} \tag{11}\]  
where \(EF\) is the emission factor (\(\mu\)g/m\({}^{2}\)/h), \(C\) is the chamber's air concentration (\(\mu\)g/m\({}^{3}\)), \(n\) is the ventilation air change (h\({}^{\prime 1}\)) and \(L\) is the loading factor (m\({}^{2}\)/m\({}^{3}\)).Based on studies, the following emission model is proposed:  
\[EF=R_{1}+R_{2}=R_{01}\cdot e^{-k_{1}t}+R_{02}\cdot e^{-k_{2}t} \tag{12}\]  
where \(R_{1}\) is the component of the emission factor connected to the desorption process and \(R_{2}\) is the component connected with diffusion. \(R_{01}\) and \(R_{02}\) are the initial emission factors, and \(k_{1}\) and \(k_{2}\) are the specific coefficients that account for the decrease in emission concentrations during the time of the test, respectively. \(R_{1}\) is considered to reflect a desorption process from a floor system's surface, whereas \(R_{2}\) is considered to reflect a diffusion process in a multilayer floor system. Factors \(k_{1}\) and \(k_{2}\) are the coefficients in h\({}^{-1}\) that account for the decrease in emission rate during the test. The coefficients \(k_{1}\) and \(k_{2}\) are also used for each system, and numerical methods determine each experiment's boundary conditions. \(k_{1}\) and \(k_{2}\) were assumed to have values that were independent of any particular VOC. When adsorption onto chamber walls and inflow impact from outdoors is negligible, the mass balance of a test chamber according to composed of components is also presented in the literature (ASTM D 5116-06) and can be described as follows:  
\[\frac{dC(t)}{dt}=L\cdot EF(t)-n\cdot C(t) \tag{13}\]where \(C(t)\) is the concentration of VOC (in \(\text{$\upmu$g}/\text{m}^{3}\)) at time \(t\) (h). Substituting Equation (12) for Equation (13), assuming an initial VOC concentration of zero, provides the following test chamber concentration decaying model:  
\[C(t)=\frac{L\cdot R_{01}\left(e^{-k_{1}t}-e^{-nt}\right)}{(n-k_{1})}+\frac{L \cdot R_{02}\left(e^{-k_{2}t}-e^{-nt}\right)}{(n-k_{2})} \tag{14}\]  
The authors investigated this model by comparing simulation results with actual indoor air concentration-by-time sequences in a test chamber. The \(R_{01}\) and \(R_{02}\) coefficients are calculated on the basis of the results of laboratory tests of VOC in the chamber in practice, using the formulas:  
\[R_{01}=\frac{\left(\frac{\Delta C_{1}}{\Delta T_{1}}+n\cdot C_{1}\right)}{L} \tag{15}\]  
and  
\[R_{02}=\frac{\left(\frac{\Delta C_{2}}{\Delta T_{2}}+n\cdot C_{2}\right)}{L} \tag{16}\]  
where \(\Delta C_{1}\) (\(\text{$\upmu$g}/\text{m}^{3}\)) is the difference between the maximum concentration of VOC (in \(\text{$\upmu$g}/\text{m}^{3}\))assessed in the chamber and the initial concentration in the chamber at time 0, \(\Delta t_{1}\) is the time to reach the maximum VOC concentration in the chamber from time 0, \(\Delta C_{2}\) is the difference between the second curve breakpoint concentration of a VOC (\(\text{$\upmu$g}/\text{m}^{3}\)) assessed in the chamber and the final concentration in the chamber at time 480 h and \(\Delta t_{2}\) is the time to reach the final VOC concentration in the chamber from the time of the second curve breakpoint. As the authors found out on the basis of preliminary analyses, model (14), composed of elements presented in the literature (ASTM standard, also see Section 1.2), better reflects the nature of emissions from single-layer products. In our case, due to several layers of multilayer floor products and the upper layer (ceramic tiles, wooden \"parquet\" panel), the standardised approach gives only sufficient traceability with the obtained results--the potential trend lines coincide very moderately with the model for one layer (without the use of the emission delay factor).