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Oscillatory instabilities in phase separation of binary mixtures: Fixing the thermodynamic driving
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View: Figures


Image of FIG. 1.
FIG. 1.

The experimental setup: (a) The sample is placed in a water bath with an automated temperature control. It is illuminated by two independent light sources which allow a separate detection of the scattered light intensity and shadow-graph imaging of the sample. (b) Rectangular fluorescence cuvette loaded with a homogenous solution. The solution-air meniscus is visible.

Image of FIG. 2.
FIG. 2.

Dependence of the apparent specific heat on temperature for mixtures of (a) methanol and hexane and (b) polystyrene in cyclohexane. The compositions and ramp rates are as follows: (a) and from top to bottom , , and , respectively; (b) and (top), (bottom). In the insets the relevant parts of the respective phase diagrams are given. The solid lines are guides to the eye. Note the logarithmic scale of the composition axis in the phase diagram of (b).

Image of FIG. 3.
FIG. 3.

In order to construct space-time plots from the videos taken during the experiments the average gray scale in horizontal direction is determined for each single picture of the video. The space-time plot is then obtained by assembling these vertical lines of pixels to one new picture. The frames numbered 1, 2, and 3 are used to show schematically the construction of the space-time plot. Note that, for the sake of clearity, the width of these stripes is highly exaggerated in the plot. The upper right image depicts the space-time plot of an experiment with M/H which was cooled with a constant cooling rate of throughout the experimental run. The dark part in the beginning of the experiment represents the cooling of the homogeneous sample until separation sets in.

Image of FIG. 4.
FIG. 4.

Model free energy: as a function of external parameters (like temperature or pressure) the system may be either homogeneous (only one minimum in the free energy) or biphasic (two minima in the free energy).

Image of FIG. 5.
FIG. 5.

Part of the phase diagram for mixtures of methanol and hexane. The points depict the phase-transition temperature, as determined from turbidity measurements. The solid line consists of two parabolic fits to the data points which are connected by a horizontal line. denotes the width of the biphasic region.

Image of FIG. 6.
FIG. 6.

Sketch of the temperature (left axis, solid line) and the actual cooling rate (right axis, dotted line) as function of time. The evolution of temperature and cooling rate, respectively, consists of three major parts. A: linear cooling until the temperature is about below the binodal. B: The coexisting phases build up during a relaxation period at constant temperature. C: The system is continuously driven deeper into the biphasic region during the cooling ramp. The form of this ramp is chosen such that is kept constant. Specifically, the data refer to M/H at a reduced cooling rate .

Image of FIG. 7.
FIG. 7.

Images visualizing the changes of the turbidity in a mixture of methanol and hexane, , which is cooled linearly until below the binodal, kept at this temperature for 20 min, and thereafter cooled with a reduced rate of . The images (a)–(h) are taken by video microscopy, and (i)–(k) by the shadow-graph technique.

Image of FIG. 8.
FIG. 8.

Accelerated cooling ramps lead to oscillations over a wide range of temperatures and to a large number of oscillations during one run of the experiment. (a) The space-time plot for M/H cooled at a rate . The letters A, B, and C are defined in Fig. 6. The numbering of the oscillations corresponds to the numbering in Fig. 9. (b) The space-time plot for PS/cH cooled at a rate . Note the difference in time scales: (a) covers about 90 min, whereas (b) covers approx. 10 h.

Image of FIG. 9.
FIG. 9.

(a) The methanol-poor branch of the phase diagram for the experiments leading to Fig. 8(a), where the staircaselike line indicates the evolution of the composition. The inset shows the decrease of the methanol concentration between successive oscillations as function of the number of oscillation . (b) The evolution of of the composition for both experiments shown in Fig. 8. In contrast to the M/H case the steps in the composition are not equidistant in the PS/cH system.

Image of FIG. 10.
FIG. 10.

The time difference between two successive oscillations does not depend on the concentration of the sample, but it is strongly affected by variation of the reduced cooling rate . (a) The period for different compositions (▵), (∎), (☉), and (⊡) for a reduced cooling rate of . (b) for the PS/cH systems with at .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Oscillatory instabilities in phase separation of binary mixtures: Fixing the thermodynamic driving