Phase separation of thin-film polymer mixtures under in-plane electric fields

Phase-separation dynamics of polymer thin-film mixtures of polystyrene (PS) and poly(methyl methacrylate) (PMMA) are observed while an in-plane electric field is applied, instead of the out-of-plane fields usually employed previously. The phase separation is accompanied by the formation of PS dewetting holes at zero or weak fields. The dewetting velocity at $0.25\mu \text{m}/\text{min}$ is a few times slower than that seen in regular bilayer dewetting. With the increasing of the field strength, we observe the formation of PS droplets in PMMA matrix, a reversal from zero- or low-field conditions. The PS dewetting holes are also suppressed. At further increased fields, PS droplets quickly penetrate up to the top of the PMMA matrix, leading to smaller and more irregular final PS droplets. This is manifested in the dramatic decrease in the growth exponent of the droplet size $\mathcal{L}$ from $\mathcal{L}\sim t^{1.5}$ to $\mathcal{L}\sim t^{0.1}$. These morphology changes are explained by the electrostatic energy resulted from the PS and PMMA dielectric contrast.

Figure 1

(Color online) The sketch of the setup. (a) The side view of the setup (not in scale). The polymer thin film is placed in the middle of two metal electrodes and two slides are used as windows covering on the top and bottom of the electrodes. Beside the outer temperature control cell (only portions are shown), there is another set of (tune) thermal couple and heater nearby the electrodes to maintain the temperature fluctuation within $\pm 0.1°\text{C}$. The outer cell and object are all cover by Kapton tape and grounded with a high-voltage transformer which provides the electric field. (b) The detail geometry of the electrodes and the thin film. The film with slide substrate is held by slides at the center of the electrodes. The distance between electrodes is 2 mm.

Figure 2

A typical evolution of a $1.6\text{−}\mu \text{m}$-thick film undergoing phase separation at $E=0$. The times are (a) 10 min, (b) 31 h, (c) 63 h, and (d) 131 h. (e) is a typical morphology near dewetting holes at 500 min in another sample, and (f) is an illustration of the side view of (e). The small inset of (a) and the inset of (d) with widths $50\mu \text{m}$ are enlargements of area A and the center of the puddle D, respectively. The larger inset in (a) is the initial spinodal pattern and the width of the inset is $60\mu \text{m}$. The inset in (b) with a whole width of $60\mu \text{m}$ and time intervals of 30 min is the time series of larger trapped PMMA droplets breaking the PS film. (a)–(d) are in the same scale and the scalar bar is $150\mu \text{m}$. The scale bar in (e) is $60\mu \text{m}$.

Figure 3

Illustration of pathways to final morphologies at different electric fields.

Figure 4

(Color online) The effective radius $R$ increases linearly with time for holes at $E=0\text{V}/\mu \text{m}$ (hollow) and $0.2\text{V}/\mu \text{m}$ (solid). Times for different data sets are shifted to overlap. The solid line is the fitting of data between 0 and 150 min. The average dewetting velocity is $0.25\mu \text{m}/\text{min}$. The two insets with the same scale are the corresponding images of the holes.

Figure 5

Phase-separation evolution of a $1.6\text{−}\mu \text{m}$-thick sample with an applied electric field at $E=0.62\text{V}/\mu \text{m}$. The field is in the left-right direction, and parallel to the paper. The times are (a) 5, (b) 100, (c) 300, (d) 430, (e) 630, and (f) 1000 min. (a)–(d) are in the same scale with the scalar bar in (a) being $20\mu \text{m}$. Similarly for (e) and (f) with the $50\mu \text{m}$ scale bar.

Figure 6

Detail sequences of (PS) droplets marked by J in Fig. 5a being absorbed into the bicontinuous network. Droplets such as ${\text{D}}_1$ and ${\text{D}}_2$ become smaller and smaller and finally merge into the network as indicated at the last image. The width of each image is $20\mu \text{m}$ and the time intervals between successive images are 10 min.

Figure 7

PS droplets can coarsen through the collision-induced-collision (CIC) mechanism: the flow generated by the collision of droplets A and B induces the secondary collision of the nearby droplet C. The elapsed times between successive images are 30, 80, and 40 min. The width of each image is $10\mu \text{m}$ and $E$ is $0.62\text{V}/\mu \text{m}$.

Figure 8

These images demonstrate the initial penetration of a PS droplet in (b) and (c), and how another embedded droplet is subsequently absorbed by the first droplet in (d). The elapsed times between successive images are 80, 60, and 70 min. The width of each image is $10\mu \text{m}$ and the field strength is $E=0.62\text{V}/\mu \text{m}$.

Figure 9

Simple calculations of electric energy with dielectric contrast. The electric field $E_0=0.6\text{V}/\mu \text{m}$ is applied in $x$ direction with potential $\varphi \equiv E_{0}x+{\varphi }^{\ast }$, where ${\varphi }^{\ast }$ is periodic in $x$ and $y$ directions. (a) The droplets (light gray) with a diameter of $5\mu \text{m}$ and matrix (dark gray) configuration with equal area fraction and sharp interfaces. The dielectric constants are ${ϵ}_1$ for droplets and ${ϵ}_2$ for matrix (see text). (b) The contour lines of equal potential $\varphi$ with ${ϵ}_1=5$ $\left({ϵ}_{\text{PMMA}}\right)$ and ${ϵ}_2=3$ $\left({ϵ}_{\text{PS}}\right)$. (c) The same as (b) but with ${ϵ}_1$ and ${ϵ}_2$ switched.

Figure 10

Phase-separation evolution of a $1.6\text{−}\mu \text{m}$-thick sample with an applied electric field at $E=0.9\text{V}/\mu \text{m}$. The field is in the left-right direction and parallel to the paper. The times are (a) 20, (b) 51, (c) 300, (d) 550, and (e) 1000 min. (f) shows the large-scale crack of the film. The black rectangle on the left side of (f) is the electrode. The insets in (f) are the enlargement and the sketch of one subcrack of the area marked by Z in (f). (a)–(d) are in the same scale with the scalar bar at $50\mu \text{m}$ in (a). The scale bar in (e) is $50\mu \text{m}$. The width of (f) is about 1 mm.

Figure 11

The temporal changes of domain sizes $\mathcal{L}$ under different field strengths. The slopes of solid guide lines (growth rate exponents) decrease significantly from $E=0.7$ to $0.8\text{V}/\mu \text{m}$. The marker ${\tau }^{\ast }$ demonstrates the definition of the time that domains start coarsening and ${\mathcal{L}}^{\ast }$ is the final domain size.

Figure 12

The time ${\tau }^{\ast }$ at different electric fields $E$.

Figure 13

The final domain sizes ${\mathcal{L}}^{\ast }$ at different electric fields $E$.