## 2 Model for Pressure and Strain Induced by Photoisomerization  
### Dynamics of Volume Change and Pressure Build-up  
Several theoretical models were developed and theoretical studies carried out to describe the role played by photoisomerization in the control of the optical response of LC and amorphous photomechanical materials (see, for example, [30; 31; 32; 33]). Molecular mobility in glass-forming materials, depends, in any temperature and pressure conditions, primarily on the polymer's free volume \(V_{f}\) with \(V_{f}=V-V_{\infty}\), and \(V\) is the specific volume, and \(V_{\infty}\) an occupied volume. \(V_{\infty}\) includes the volume of the molecules and the volumes corresponding to their rotational and vibrational motions. Next, we discuss an original model, albeit an extreme case model, of the photomechanical response of azo-polymers where the occupied volume of the molecules is nearly equal to the specific volume, i.e., negligible free volume, and no extra free volume is created by photoisomerization, i.e., negligible photoexpansion. In other words, the model assumes that the chromophores are interacting, i.e., not isolated, like in LC materials [34; 35], and the space, i.e., volume, occupied by nonphotoisomerizable matter remains unchanged and follows the motion of the light-activated chromophores. The total concentration \(N\) of the chromophores is equal to the initial concentration of the trans molecules, and light is assumed to be absorbed throughout the thickness of the sample, i.e., an optically thin sample, irradiated perpendicular to its plane and with an average absorbed intensity \(I_{A}\). Assuming that each isomer has an occupied volume which includes the volume needed for isomerization, i.e., \(v_{c}\) for the cis isomer and \(v_{t}\) for the trans isomer, the volume fractions of the azo-polymer film, occupied by the trans and cis populations, are given by \((1-\alpha)Nv_{t}\) and \(\alpha Nv_{c}\), respectively (vide infra). \(N\) is the total density of the chromophores, and it is equal to the reciprocal of the specific volume \((N=1/V)\), and \(\alpha\) is the extent of the cis isomers. The total volume occupied by the isomers is \(V=V_{c}+V_{t}\) where \(V_{c}\) (\(V_{t}\)) is the volume occupied by the total cis (trans) population \(n_{c}\) (\(n_{t}\)). Noting that, \(n_{c}=VN_{c}\) and \(n_{t}=VN_{t}\) with \(N_{c}\) and \(N_{t}\) as the respective concentrations of the cis and trans populations, and using \(V=n_{c}v_{c}+n_{t}v_{t}\), we obtain \(1=\alpha Nv_{c}+(1-\alpha)Nv_{t}\); therefore \(V=\alpha v_{c}+(1-\alpha)v_{t}\). The volumes \(V\), and \(v_{t}\) and \(v_{c}\) are expressed in \(cm^{3}/molecule\). It is useful to express \(V\) as \(V=\alpha(v_{c}-v_{t})+v_{t}\) and to introduce a reduced volume \(v_{R}=(V-v_{t})/(v_{c}-v_{t})=\alpha\). An all-cis sample may be achieved for photoreactions where only the trans isomer absorbs actinic light, such as ultra-violet (UV) light excitation of trans-azobenzene [36]; for light excitations absorbed by both isomers, the photostationary state (pss) is a balance between the cis and trans isomers [37]. For one-way trans\(\rightarrow\)cis photoisomerization, \(\alpha\) varies between zero at time t and one for t going to infinity. In other words, the volumes occupied by the azo-polymer at the initial time and infinity are given by the volumes occupied by the trans and cis isomers, respectively. In all cases, for a given absorbed irradiation intensity, \(I_{A}\), at a given wavelength, \(\lambda\), the time evolution of the irradiated volume of the azo-polymer is identically given by the evolution of the extent of the cis isomer, which in turn is defined by the absorption cross section of the isomers \(\sigma\) and the isomerization quantum yields \(\phi\) (vide infra) [36, 37].