## 2 Materials and Methods
### Analytical Model  
The analytical model describing the performed experiments was based on the analytical model for determining the static quantities in an IGU, as described in [8; 9], hereinafter referred to as the base model. This model assumes that the gas in the gap satisfies the ideal gas law:  
\[\frac{p_{0}\cdot v_{0}}{T_{0}}=\frac{p_{\text{op}}\cdot v_{\text{op}}}{T_{ \text{op}}}=n\cdot\text{R}=\text{const} \tag{1}\]  
where:  
\(p_{0}\), \(T_{0}\), \(v_{0}\)--initial parameters of the gas in the gap: pressure [kPa], temperature [K], volume [m\({}^{3}\)]; it is assumed that, under these conditions, the component panes are not deformed,  
\(p_{\text{op}}\), \(T_{\text{op}}\), \(v_{\text{op}}\)--operating parameters of gas in the gap--analogously; they change to the rhythm of the temporary weather conditions,  
\(n\)--number of moles of gas confined in the gap [-],  
R--universal gas constant, i.e., 0.00831446 kJ-m/(mol\(\cdot\)K). In the case of the test, as shown in Figure 3, the initial pressure is equal to the atmospheric pressure during the test \(p_{\text{a}}\) [kPa] and the temperature during the test \(T_{\text{a}}\) [K] is assumed to be constant; therefore:  
\[p_{\text{a}}\cdot v_{\text{st}}=p_{\text{fin}}\cdot v_{\text{fin}} \tag{2}\]  
where:  
\(p_{\text{fin}}\)--final pressure in the gap [kPa],  
\(v_{\text{st}}\), \(v_{\text{fin}}\)--initial and final volumes of the gap-conduits-syringe system [m\({}^{3}\)]. Figure 2: Scheme of the test set-up: (**a**) side view; (**b**) cross-section. As the base model assumes a linear dependence of the deflection \(w\) [m] of a component glass pane under the resultant load \(q\) [kN/m\({}^{2}\)], the change in the gap volume \(\Delta v\) [m\({}^{3}\)] (resulting from the deflection of one of the panes limiting it) can be determined from the formula:  
\[\Delta v=\alpha_{\rm v}\cdot q=\alpha_{\rm v}\cdot(p_{\rm fin}-p_{\rm a}) \tag{3}\]  
where \(\alpha_{\rm v}\)--proportionality factor calculated from the base model [m\({}^{5}\)/kN]. For the injection test, the equation of state (2) can be written as:  
\[p_{\rm a}\cdot\left(v_{\rm st}^{*}+v_{\rm sy}\right)=p_{\rm fin}\cdot\left[v_{ \rm st}^{*}+\left(v_{\rm sy}-v_{\rm in}\right)+\left(\alpha_{\rm v1}+\alpha_{ \rm v2}\right)\cdot(p_{\rm fin}-p_{\rm a})\right] \tag{4}\]  
where:  
\(v_{\rm st}^{*}\)--the sum of the initial volume of the gap \(v_{0}\) and volume of the connecting conduits \(v_{\rm co}\) [m\({}^{3}\)],  
\(v_{\rm sy}\)--volume of syringe [m\({}^{3}\)],  
\(v_{\rm in}\)--volume of air injected into the gap [m\({}^{3}\)]; if \(v_{\rm sy}=v_{\rm in}\), Equations (4) and (5) can be simplified, \(\alpha_{\rm v1}\), \(\alpha_{\rm v2}\)--proportionality factors of component panes [m\({}^{5}\)/kN]; furthermore, the symbol \(\Sigma\alpha_{\rm v}=\alpha_{\rm v1}+\alpha_{\rm v2}\) is used. The final pressure can be determined from Equation (4):  
\[p_{\rm fin}=\frac{p_{\rm a}\cdot\Sigma\alpha_{\rm v}-v_{\rm st}^{*}-v_{\rm sy }+v_{\rm in}}{2\cdot\Sigma\alpha_{\rm v}}+\sqrt{\left(\frac{p_{\rm a}\cdot \Sigma\alpha_{\rm v}-v_{\rm st}^{*}-v_{\rm sy}+v_{\rm in}}{2\cdot\Sigma\alpha _{\rm v}}\right)^{2}+\frac{p_{\rm a}\cdot(v_{\rm st}^{*}+v_{\rm sy})}{\Sigma \alpha_{\rm v}}} \tag{5}\]  
For the suction test, Equations (4) and (5) take the form:  
\[p_{\rm a}\cdot v_{\rm st}^{*}=p_{\rm fin}\cdot\left[v_{\rm st}^{*}+v_{\rm out }+\Sigma\alpha_{\rm v}\cdot(p_{\rm fin}-p_{\rm a})\right] \tag{6}\]  
\[p_{\rm fin}=\frac{p_{\rm a}\cdot\Sigma\alpha_{\rm v}-v_{\rm st}^{*}-v_{\rm out }}{2\cdot\Sigma\alpha_{\rm v}}+\sqrt{\left(\frac{p_{\rm a}\cdot\Sigma\alpha_{ \rm v}-v_{\rm st}^{*}-v_{\rm out}}{2\cdot\Sigma\alpha_{\rm v}}\right)^{2}+ \frac{p_{\rm a}\cdot v_{\rm st}^{*}}{\Sigma\alpha_{\rm v}}} \tag{7}\]  
where \(v_{\rm out}\)--volume of air sucked out of the gap [m\({}^{3}\)]. From the resulting \(p_{\rm fin}\) values, the resultant load \(q\) can be calculated, and subsequently the deflection and stress of the component panes can be derived using the base model.