Spinodal stratification in micellar films between oil and silica

We report on the thinning mechanisms of supported films of surfactant $\left(n\mathrm{TAB}\right)$ solutions above the critical micellar concentration. The films are formed by pressing an oil drop immersed in an aqueous surfactant solution on a silica surface. Depending on the length of the carbon chain of the surfactant and its concentration, two modes of destabilization of the stratified films are observed. The first one proceeds by heterogeneous nucleation, characterized by the lateral expansion of the domain of lower thickness as evidenced long ago in suspended micellar films. In addition, the simultaneous stepwise thinning of several domains, called spinodal stratification, is observed here in supported films. We measure the time evolution of the thickness of the films, and we discuss the selection mechanism of each destabilization mode.

Figure 1

Schematic of the experimental setup with a closeup view of the apex of the drop evidencing the dimpling of the oil and water interface. The interference image (top right) displays equal thickness interference fringes in the dimple and allows accurate thickness measurements. The barrier ring is the location of minimum thickness shown by the dotted red line. All reported thickness measurements have been made at a given point of the barrier ring.

Figure 2

Interference images of the step-by-step drainage of a water film containing five CMCs in DTAB (a) $t=197.5\mathrm{s}$, (b) $t=302\mathrm{s}$, (c) $t=308\mathrm{s}$, (d) $t=322\mathrm{s}$ after the approach, and (e) the cross indicates the location in the barrier ring at which thickness $h\left(t\right)$ was measured (bottom graph). Steps corresponding to thickness values of $h_2=38,h_1=25,\mathrm{and}{h}_0=10\mathrm{nm}$ are observed. The inset: closeup view of stepwise thinning shown by a rectangle in the main graph.

Figure 3

(Top) Interference images of the step-by-step drainage of a water film containing 2.5 CMCs in CTAB (a) $t=22\mathrm{s}$, (b) $t=24\mathrm{s}$, (c) $t=28\mathrm{s}$, (d) $t=85\mathrm{s}$ after the approach, and (e) the cross indicates the location in the barrier ring at which thickness was measured over time (bottom graph). Steps corresponding to thickness values $h_1=95$ and $h_0=70\mathrm{nm}$ are observed. The inset: closeup view of stepwise thinning shown by a rectangle in the main graph.

Figure 4

Theoretical evolution of the oscillatory disjoining pressure $\pi \left(h\right)$ with the thickness of the water film $h$ (blue/gray). The horizontal line is the imposed pressure in the drop $2\gamma /R$, and the driving force of the drainage is the difference $P-\pi \left(h\right)$. The values of $h$ at which $P-\pi \left(h\right)=0$ are denoted $h_2,h_1$, and $h_0$ and correspond to heterogeneous nucleation events.

Figure 5

Theoretical evolution of the oscillatory disjoining pressure $\pi \left(h\right)$ with the thickness of the surfactant film $h$ (blue/gray). The darker zone corresponds to a positive derivative $d\pi /dh$ leading to the development of the instability, characteristic of the spinodal thinning. The horizontal line is the imposed pressure in the drop $2\gamma /R$ and the driving force of drainage is the difference $P-\pi \left(h\right)$.

Figure 6

Black line: Intensity profile at the barrier ring for (a) OTAB five CMCs and (b) CTAB 2.5 CMCs, evidencing the characteristic wavelength $\lambda$. Red/gray line: sine curve with a spatial period $\lambda$: (a) $\lambda =51\mu \mathrm{m}$; (b) $\lambda =40\mu \mathrm{m}$.

Figure 7

(a) Thickness measured as a function of time at a point of the barrier ring for TTAB at two CMCs (blue/lighter gray), five CMCs (red/darker gray), and ten CMCs (black). The gray arrows indicate the occurrence of spinodal destabilization, and the black arrows of the nucleation event, (b) disjoining pressure isotherms for TTAB at two CMCs (blue/lighter gray), five CMCs (red/darker gray), and ten CMCs (black), according to the theoretical expression from Ref. [21] with a zoom close to the low pressures. The red dotted line corresponds to the typical experimental drop pressure $P=2\gamma /R=20\mathrm{Pa}$. Arrows indicate the events reported in (a). The whole curve is shown in the inset.