Phase-transition oscillations induced by a strongly focused laser beam

We report the observation of a surprising phenomenon consisting in a oscillating phase transition which appears in a binary mixture when this is enlightened by a strongly focused infrared laser beam. The mixture is poly-methyl-meth-acrylate (PMMA)–3-octanone, which has an upper critical solution temperature at $T_c=306.6\text{K}$ and volume fraction ${\varphi }_c=12.8\%$ [Crauste et al., arXiv:1310.6720, 2013]. We describe the dynamical properties of the oscillations, which are produced by a competition between various effects: the local accumulation of PMMA produced by the laser beam, thermophoresis, and nonlinear diffusion. We show that the main properties of this kind of oscillations can be reproduced in the Landau theory for a binary mixture in which a local driving mechanism, simulating the laser beam, is introduced.

Figure 1

PMMA-octanone coexistence diagram obtained from cloud point measurements [13] performed at different fixed concentration ${\varphi }_o$ by decreasing the temperature at various rates. The parabolic fit $T_{eq}\left({\varphi }_o\right)$ is done using the data obtained at the two slowest ramp rates.

Figure 2

Droplet oscillation. Images of the octanone-PMMA sample at a volume fraction 12.8% in PMMA at room temperature $298\text{K}$. The six images have been taken at 10 s time intervals using a microscope objective $\times 63$; the image size is $15\mu \text{m}$. A droplet, rich in PMMA, growts for the first 30 s and then it decreases. This oscillatory phenomenon is produced by an infrared laser beam of intensity 130 mW, which is focused inside the sample by the objective. At the top left of each image, we can see an interface of another PMMA-rich phase which is at equilibrium because at this temperature, the medium is in the heterogeneous phase. The bright point is the reflection of the laser beam.

Figure 3

Growth velocity of the droplet in the first instants of their formation as a function of the laser power. It is measured from the time which is needed by a growing drop to reach the diameter $d$. The measurement is repeated on various droplets in different positions of the sample. The dispersion of the points in the plot could be due to the heterogeneities of polymer concentration in the cell.

Figure 4

(a) Radius of PMMA-rich droplets as a function of time for different detection thresholds (red: 155, green: 160, blue: 168 in gray scale over 255) of the droplet edge in the image analysis normalized to the maximum measured radius. The collapse of all the curves ensures that the time evolution of the radius measured by this method correctly describes the droplet dynamics. The plotted data have been recorded in a sample with a PMMA volume fraction ${\varphi }_c=12.8\%$ (laser beam of intensity 134 mW). (b) Droplet radius as a function of time at two different powers (130 and 170 mW) of the focused laser beam. The oscillation frequency is a function of the laser power.

Figure 5

Numerical solution of Eq. (1). Mass fraction $\phi$ as a function of time, measured at the forcing point (a) and at $x_o+0.05$ at two different values of $\xi$ (b). Regular oscillations appear for $\xi$ larger than a threshold value ${\xi }_o\simeq 1.5/S_{\xi }$. The bigger $\xi$, the faster the oscillations are. (c) Size of the PMMA-rich phase calculated numerically from Eq. (1). The size is estimated as the radius of the domain in which $\phi$ is larger than a defined threshold value, which is $-0.9$ here. The radius oscillations are smaller and faster when the source term is bigger.