Slow dynamics in an azopolymer molecular layer studied by x-ray photon correlation spectroscopy

We report the results of x-ray photon correlation spectroscopy (XPCS) experiments on multilayers of a photosensitive azo-polymer which can be softened by photoisomerization. Time correlation functions have been measured at different temperatures and momentum transfers $\left(q\right)$ and under different illumination conditions (dark, UV or visible). The correlation functions are well described by the Kohlrausch-Williams-Watts (KWW) form with relaxation times that are proportional to $q^{-1}$. The characteristic relaxation times follow the same Vogel-Fulcher-Tammann law describing the bulk viscosity of this polymer. The out-of-equilibrium relaxation dynamics following a UV photoperturbation are accelerated, which is in agreement with a fluidification effect previously measured by rheology. The transient dynamics are characterized by two times correlation function, and dynamical heterogeneity is evidenced by calculating the variance $\chi$ of the degree of correlation as a function of ageing time. A clear peak in $\chi$ appears at a well defined time ${\tau }_{\text{C}}$ which scales with $q^{-1}$ and with the ageing time, in a similar fashion as previously reported in colloidal suspensions [O. Dauchot et al., Phys. Rev. Lett. 95, 265701 (2005)]. From an accurate analysis of the correlation functions we could demonstrate a temperature and light dependent cross-over from compressed KWW to simple exponential behavior.

Figure 1

(Color online) Experimental setup. The incoming and reflected x-ray beams are indicated by continuous (red online) lines. The sample is aligned at an angle of $\alpha =0.15°$ with respect to the incident beam. UV/blue light sources provide photoperturbation as needed. The beam stop blocks the specular reflected x-ray beam before the Maxipix detector, which collects the diffuse scattering.

Figure 2

Normalized correlation functions for PA4 at $72°\text{C}$ under UV illumination, together with the best KWW fits (solid lines). Data are offset in steps of 0.3 for clarity. Inset: best fitting values for the compression exponent $\gamma$.

Figure 3

Relaxation times $\left(\tau \right)$ in the equilibrium state as a function of $q$ at the different temperatures and illumination conditions indicated in the caption.

Figure 4

Top left: temperature evolution of the exponent $n$ at different illumination conditions; top right same for $\gamma$ averaged over the investigated $q$ range; the dashed lines are guides to the eyes. bottom left: XPCS measurement of the photoinduced acceleration of dynamics, quantified by the ratio of relaxation times $\left({\tau }_{\text{UV}}/{\tau }_{\text{DK}},{\tau }_{\text{vis}}/{\tau }_{\text{DK}}\right)$ bottom right: interfacial shear rheometry measurement of photoinduced fluidification: evolution of the shear modulus $\left|G^{\ast }\right|$ in a Langmuir molecular layer of PA4 in dark and under UV light.

Figure 5

Arrhenius plot of relaxation time $\left(\tau \right)$ in dark and under UV illumination, at $q=0.09{\text{nm}}^{-1}$. Lines are the VFT laws discussed in the text.

Figure 6

Two-times correlation function during the cis-to-trans transformation at $72°\text{C}$. UV light was switched off at the initial time $t_0=0$. The arrow indicates the diagonal along which ageing time increases.

Figure 7

Top: Variance of the two times correlation function for PA4 at $72°\text{C}$ under UV illumination and in dark. Note the presence of a peak only for the UV data. Bottom left: $q$ dependence of the peak time ${\tau }_c$ for the UV data compared to that of the relaxation time $\tilde{\tau }$ Dashed lines indicate the $\tau \propto q^{-1}$ power laws discussed in the text bottom right: $q$ dependence of the amplitude of the peak ${\chi }^{\ast }$.

Figure 8

Top: off equilibrium evolution of the variance $\chi$ for PA4 at $72°\text{C}$. UV photoperturbation was switched on at $t_{\text{age}}=0$. Note the shift of the peak as a function of the ageing time. Bottom left: ageing dependence of the peak time ${\tau }_c$ compared to that of the relaxation time $\tau$. Dashed lines indicate their corresponding equilibrium values. Bottom right: amplitude of the peak ${\chi }^{\ast }$ at different ageing times.