Nanodielectric mapping of a model polystyrene-poly(vinyl acetate) blend by electrostatic force microscopy

We present a simple method to quantitatively image the dielectric permittivity of soft materials at nanoscale using electrostatic force microscopy (EFM) by means of the double pass method. The EFM experiments are based on the measurement of the frequency shifts of the oscillating tip biased at two different voltages. A numerical treatment based on the equivalent charge method allows extracting the values of the dielectric permittivity at each image point. This method can be applied with no restrictions of film thickness and tip radius. This method has been applied to image the morphology and the nanodielectric properties of a model polymer blend of polystyrene and poly(vinyl acetate).

Figure 1

(Color online) Numerical simulations based on ECM of the curves $a_{\Delta f_0}\left(t,{\epsilon }_r\right)$, where $t$ is the sample thickness and ${\epsilon }_r$ is the relative dielectric permittivity, for a tip radius $R=19\text{nm}$ and a tip-sample distance $z_0=18\text{nm}$. $M\left(t,a_{\Delta f_0}\right)$ and $N\left(t,a_{\Delta f_0}\right)$ are typical points obtained from AFM topography and EFM images (Fig. 3), respectively, on the PS matrix and the PVAc nodules of the studied polymer blend thin film. ${\epsilon }_r$ can be deduced by interpolating these points with simulated curves.

Figure 2

(Color online) (a) Typical topographic profile of PVAc islands in a PS matrix. Both tip and polymer film are represented at the same scale. The dash line represents the tip motion during the second scan. (b) Topography and frequency shift measured by the double pass method at $+5$ and $-5\text{V}$ on the PVAc/PS films. The black line corresponds to the profile appearing in (a).

Figure 3

(Color online) (a) Topography of the PVAc/PS film. (b) Corresponding map of the coefficient $a_{\Delta f_0}$. Values of $t$ and $a_{\Delta f_0}$ at points M (PS matrix) and N (PVAc nodule) have been reported in Fig. 1 where they have been interpolated with ECM simulated curves in order to extract the corresponding value of ${\epsilon }_r$.

Figure 4

(Color online) (a) Map of the dielectric constant of the PVAc/PS film obtained by processing images shown in Fig. 3. (b) Typical profile of the dielectric permittivity across the PVAc/PS interface.