Research ArticleCONDENSED MATTER PHYSICS

Impact of surface roughness on liquid-liquid transition

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Science Advances  17 Feb 2017:
Vol. 3, no. 2, e1602209
DOI: 10.1126/sciadv.1602209
  • Fig. 1 Comparison of pattern evolution between LLT on smooth unrubbed and rubbed surfaces.

    Pattern evolution observed at Ta = 218 K in an unrubbed smooth (A) and a rubbed (B) cell with phase-contrast microscopy. The pattern formation process can also be seen in movies S1 and S2 for (A) and (B), respectively. The cell thickness is 10 μm for both cases. Scale bars, 20 μm. Schematics illustrate cross-sectional views of the ordering processes.

  • Fig. 2 Dynamic acceleration of LLT on rubbed surfaces relative to that on unrubbed ones.

    Temporal change of P(I) during LLT at Ta = 218 K for a smooth (A) and a rubbed (B) cell. a.u., arbitrary units. (C) Time evolution of the normalized dielectric relaxation strength of liquid II, ΔεII(t)/ΔεII, at Ta = 219 K (squares) and 220 K (circles) for rubbed (blue) and unrubbed (red) cells. It is found that, for both temperatures, the evolution of ΔεII becomes two or three times faster in rubbed cells than in usual cells.

  • Fig. 3 Anisotropic wetting morphologies induced by rubbing.

    (A) A confocal micrograph of the 10× rubbed substrate. The color in the image corresponds to the height level: The planar area appears yellow. Black indicates height lower than the planar surface, corresponding to scratches (grooves) formed by rubbing, whereas blue indicates height higher than the planar surface, corresponding to ridges or impurities on the substrate. Note that the depth of the microgrooves is less than the resolution of optical and phase-contrast microscopy. Because of the random nature of grooves, their precise characterization by AFM was difficult. (B) A transient pattern observed with phase-contrast microscopy during LLT on the 10× rubbed substrate at Ta = 220 K. The white arrow indicates the rubbing direction (that is, the x direction). The complete filling of a wedge by liquid II appears as a filament-like shape (regions enclosed by the blue rectangles), whose situation is depicted in the upper right schematic. In addition, the partial filling by liquid II, whose situation is depicted in the lower right schematic, is also observed. Such coexistence of various wetting patterns may be a consequence of distributions of the wedge angle, depth, and length of grooves formed by rubbing. (C) A 2D power spectrum pattern of the image in (B) [see Tanaka et al. (45) for the calculation method]. Scale bars, 50 μm (A and B).

  • Fig. 4 Relationship between the wedge-filling transition, wetting transition, and spinodal point of LLT.

    In the top row, we show schematics of the free energy F for two situations, where liquid I is unstable (left) and metastable (right) against liquid II. In our system, the contact angle of liquid II decreases toward zero when approaching TSD because the interfacial tension vanishes toward TSD = 215.5 K (21). Thus, a transition from partial to complete wetting (wetting transition) takes place at the wetting temperature TW above TSD. For a wedge whose angle is α, the decrease of θ near TSD and TW also induces a transition from partial to complete filling (wedge-filling transition) at the filling temperature TF, where the condition θ(TF) = 90° − α is satisfied. The two phase-contrast microscopy images indicate the formation of the liquid II phase on a well-developed wedge at 218 and 220 K, respectively. Scale bars, 10 μm. Partially filled liquid II begins to appear in the form of droplets above 220 K. The filling temperature TF of our system is thus considered to be located around 220 K. Note that, in the rubbed cell we used, the surface of the substrate was coated by polyimide, whose contact angle was estimated as 81° at 220 K from our previous study (21). The wedge angle of the microgrooves is thus estimated as 9°. Because of the high contact angle, TW is expected to be located near the spinodal temperature TSD, that is, TWTSD, which makes it very difficult to experimentally determine the wetting transition TW on a planar polyimide surface.

  • Fig. 5 Pattern evolution during SD-type LLT on a rubbed substrate.

    (A) Pattern evolution observed with phase-contrast microscopy at Ta = 214 K. We observed the initial growth of the amplitude of the order-parameter (S) fluctuations through its coupling to the density (at 200 min) and its coarsening in the later stage (at 300 and 400 min) during LLT. This pattern evolution is identical to that of typical SD-type LLT in triphenyl phosphite (15, 44). The white arrow indicates the rubbing direction. Scale bar, 50 μm. Insets (at 200 and 300 min) are 2D power spectrum images obtained by digital image analysis (40), which is isotropic, unlike in the case of NG-type LLT (see Fig. 3C). (B) A direct comparison of ΔεII(t)/ΔεII at Ta = 214 K between the rubbed and smooth unrubbed surface case. (C) Temperature dependence of the ratio of the incubation time of LLT between the rubbed surface case (τR) and the smooth unrubbed surface case (τ0). We define τR and τ0 as the time when an SD-like pattern appears on the surface and when the area fraction of droplets of liquid II in liquid I matrix reaches 0.02, respectively. LLT on the rubbed surface proceeds spontaneously without an activation energy below TF, whereas LLT in bulk does so only below TSD. Above TSD, LLT in the unrubbed surface case (or in bulk) proceeds by overcoming an activation barrier required for nucleation of liquid I droplets.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/2/e1602209/DC1

    section S1. The shape of the intensity distribution function P(I)

    section S2. The AFM observation of the rubbed substrate

    fig. S1. Relation between a phase-contrast image and the intensity distribution function.

    fig. S2. AFM image of the rubbed surface.

    movie S1. LLT in the smooth unrubbed cell observed at 218 K (the same process as Fig. 1A).

    movie S2. LLT in the rubbed cell observed at 218 K (the same process as Fig. 1B).

    movie S3. LLT in the rubbed cell at four different temperatures.

  • Supplementary Materials

    This PDF file includes:

    • section S1. The shape of the intensity distribution function P(I)
    • section S2. The AFM observation of the rubbed substrate
    • fig. S1. Relation between a phase-contrast image and the intensity distribution function.
    • fig. S2. AFM image of the rubbed surface.

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.mp4 format). LLT in the smooth unrubbed cell observed at 218 K (the same process as Fig. 1A).
    • movie S2 (.mp4 format). LLT in the rubbed cell observed at 218 K (the same process as Fig. 1B).
    • movie S3 (.mp4 format). LLT in the rubbed cell at four different temperatures.

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