Laser-induced structures in a polymer blend in the vicinity of the phase boundary

We have determined the diffusion, thermal diffusion, and Soret coefficients of a poly(dimethyl siloxane)/poly(ethyl-methyl siloxane) (PDMS/PEMS) polymer blend as a function of composition and temperature within the homogeneous phase. The critical slowing down of the diffusion and the corresponding critical divergence of the Soret coefficient are described within the pseudospinodal concept both for critical and off-critical compositions. These data are used to model in detail the channel-like structures that form due to the Soret effect when a focused laser beam is scanned across a polymer film of $100\mu \mathrm{m}$ thickness. A moderate vertical asymmetry is attributed to solutal convection. Although heat rapidly diffuses away from the laser focus, the composition distribution in the early stage resembles the sharp profile of the laser beam. PDMS accumulates within the center of the structures, whereas a thin PEMS-rich layer is formed that isolates the central core from the windows. Experimentally, the structures are analyzed by means of phase contrast microscopy. Possible applications as rewritable optical waveguides or tunable phase plates are briefly discussed.

Figure 1

Diffusion and Soret coefficient for critical and almost critical blends of $\mathrm{PDMS}(16.4\mathrm{kg}∕\mathrm{mol})$ with varying molar mass of PEMS. The legends give the molar masses of PDMS and PEMS, the concentrations $c$ and the critical temperature $T_c$. $T_{\mathit{sp}}$ is the temperature of the spinodal (see text). Literature data (open circles) are taken from Ref. 7. The dashed lines show the scaling behavior of $S_T\propto {ϵ}^{-\gamma }$ with $\gamma =1$ for the mean field regime and $\gamma =0.67$ for the Ising regime.

Figure 2

Diffusion coefficient $D$ and thermal diffusion coefficient $D_T$ of $\mathrm{PDMS}(16.4\mathrm{kg}∕\mathrm{mol})∕\mathrm{PEMS}(48.1\mathrm{kg}∕\mathrm{mol})$ for different mass fractions of PDMS as indicated in the legend. For concentrations close to the critical concentration diffusion slows down approaching the phase boundary. The solid lines are fits of Eq. (1) for $D_T$ and Eq. (4) for $D$. The dashed lines show an extension of the fitted function into the experimentally inaccessible range.

Figure 3

Soret coefficients for different concentrations of $\mathrm{PDMS}(16.4\mathrm{kg}∕\mathrm{mol})∕\mathrm{PEMS}(48.1\mathrm{kg}∕\mathrm{mol})$. The solid lines are plots of $S_T=D_T∕D$ with $D_T$ and $D$ according to Eqs. (1, 4), respectively. $D_T^0$ and $T_{\mathit{sp}}$ from Table .

Figure 4

(Color online) Phase diagram of polymer blend $\mathrm{PDMS}(16.4\mathrm{kg}∕\mathrm{mol})∕\mathrm{PEMS}(48.1\mathrm{kg}∕\mathrm{mol})$. The cloud points (filled squares) are obtained from turbidity measurements. The pseudospinodal points (filled circles) are only approximate and result from a fit of Eq. (4). The polynomial, describing $T_{\mathit{sp}}$, shown in the plot is used for parametrization. The color coding gives the absolute value of $S_T$ in the one-phase region.

Figure 5

Principle of experimental setup with schematic sketch of light paths of laser (solid line) and halogen lamp (dashed line).

Figure 6

(Color online) (a) Three-dimensional model of the cell. The laser beam propagates along the $z$ axis and is scanned along the $y$ axis. The two-dimensional simulation is carried out in the $\left(x\text{−}z\right)$ plane as indicated by the section plane and sketch (b). Micrographs (Fig. 7) in the experiment are taken in the $\left(x\text{−}y\right)$ plane as shown in (c). In (a) the spatial variation of the concentration in the $\left(x\text{−}z\right)$ plane is color coded [see also Fig. 9d]. The word Bayreuth and the circle have been written by repeatedly scanning the laser across the surface.

Figure 7

Spatial modulation of concentration by scanning a laser along the $y$ axis with a scanning frequency of $20\mathrm{Hz}$ and a laser power of $1\mathrm{mW}$ at two different temperatures above the critical temperature (see also Fig. 6). Pictures (A)–(C) taken at $\Delta T=1\mathrm{K}$ after $t=100\mathrm{s}$, $t=300\mathrm{s}$, and $t=2000\mathrm{s}$. Pictures (D)–(F) taken at the same time intervals but at $\Delta T=11.5\mathrm{K}$. The intensity is normalized to the one of the undisturbed sample (picture at $t=0\mathrm{s}$). To display positive and negative changes, 127 is added to the $8\text{−}\text{bit}$ gray values. Gray values greater than 127 represent an increase of intensity, values smaller than 127 represent a decrease.

Figure 8

(a) Intensity profile along the $x$ axis, averaged over the length of the written line, taken from images (Fig. 7) at $t=300\mathrm{s}$ and $t=30\mathrm{s}$ for $\Delta T=1\mathrm{K}$. The open symbols show the result from the experimental pictures. The dashed lines show the numerical simulation (for details see Sec. 4). An increase of intensity (positive values) represents accumulation of PDMS. Far away from the written line the sample remains unchanged and the measured change of intensity equals zero. (b) Maximum intensity change obtained from averaged images plotted versus time at a laser power of $1\mathrm{mW}$ (open symbols) for different temperatures $\Delta T$ above the critical temperature. The vertical solid line indicates the switch-off time of the laser. The solid lines show numerical simulations with convection; the dashed lines show numerical simulations without convection.

Figure 9

(Color online) Temperature profile (A), concentration profile at $t=100\mathrm{s}$ (B), and concentration profile at $t=2000\mathrm{s}$ for $\Delta T=1\mathrm{K}$ (D) and $\Delta T=11.5\mathrm{K}$ (C). Sample thickness ($z$ axis) $100\mu \mathrm{m}$.

Figure 10

Temperature profile (dashed line) and concentration profile (solid line) along the $z$ axis for $\Delta T=1\mathrm{K}$ and $t=2000\mathrm{s}$. The left axis shows the concentration change and the right axis belongs to the temperature profile.

Figure 11

Concentration change and temperature change plotted for each point on the $z$ axis at $t=2000\mathrm{s}$. In the center of the sample $(z=0)$ the temperature increases and the composition changes to a higher concentration of PDMS. At $z=\pm 50\mu \mathrm{m}$ the cell is held at constant temperature $\Delta T=1\mathrm{K}$ above $T_c$; only the concentration shifts. The maximum concentration change is found at the lower cell window $z=-50\mu \mathrm{m}$. The plot shows what complex area the sample occupies in the phase diagram during thermal patterning. The inset shows how the Soret coefficient varies along the $z$ axis.