shows typical experimental curves corresponding to the voltage oscillations of the used piezoelectric transducer (PA signal) recorded on the nanocomposite structure porous silicon-liquid for two different thicknesses of the porous layer. Liquids with different viscosity values (alcohol and acetone) were used to fill the nanopores of the porous matrix. The experimental PA signals obtained for the mesoporous silicon layer with empty pores (‘porous silicon-air’ structure) are shown for comparison. Simulated PA signals for the nanocomposite structure porous silicon-liquid are presented in Figure
for different values of thermal conductivity and fluid permeability of the porous matrix and compared with the corresponding experimental curves.
Time-dependent PZT voltage measured for composite porous silicon-liquid structure for liquids with different viscosities. Porosity of the used porous Si layer is 65% and its thicknesses are (a) 50 and (b) 30 μm
Theoretical time-resolved photoacoustic signal. (a) Influence of liquid viscosity and (b) influence of porous matrix permeability to liquids
As one can see from Figures
, the PA signal obtained for the porous Si-liquid structure is significantly different from the PA signal obtained on the similar structure without liquid (see reference
], for example). In particular, at least two main characteristic features of the transient PA signals recorded from the nanocomposite structure porous Si-liquid can be noted: (1) a sharp initial rise is followed by (2) a more or less pronounced bend. These features become to be well resolved especially for relatively high porosity and larger thickness values, and the following characteristic sequence can be observed: sharp rise -maximum -bend -minimum -additional slight signal growth. These features are ensured by the TIP appearance (first feature) and relaxation (second feature) of the liquid inside the pores. The TIP arises due to significant differences between the parameters of the liquid and solid matrices (in particular, thermal expansion coefficients and compressibility). The time positions of these features depend on the thermophysical properties of liquid and solid matrix composites, fluid viscosity, the permeability K
, and the thickness of the porous layer.
As we can see in Figure
a, the first feature shifts toward the lower time range when thermal conductivity increases. It can be explained by the fact that thermal energy achieves more rapidly in Si wafer. Consequently, it leads to (a) the decrease of the liquid heating and (b) the general changes of relation between thermoelastic stresses and TIP contributions in the resulting structural deformations. Figure
b illustrates influence of porous matrix permeability on the temporal shape of the PA signal. The first feature is shifted to the lower time edge with increasing permeability. The similar qualitative result is observed if the liquid viscosity decreases. This is due to the fact that the TIP relaxation time increases as a result of decreasing dissipative forces. Taking into account all these effects, the experimental PA signals can be perfectly fitted by the mathematical model described previously and by considering general thermophysical properties of the porous matrix-liquid composite, viscosity, permeability K, and thickness of the porous layer (for example, see comparison between experimental and simulated signals shown in Figure
Several fitting results of the time-resolved PA signals are shown in Figure
. The order of magnitude of the porous Si permeability for well wetting liquids is found to be about 10−18
which is in good agreement with the value determined previously from gas permeability measurements
]. Thermal conductivity values of our nanocomposite structure (approximately 1 to 3 W/(m K) for different samples) correspond quite well to the experimental values of thermal conductivity of porous silicon reported earlier