Anisotropy of Sheared Carbon-Nanotube Suspensions

We measure the anisotropy of sheared carbon-nanotube suspensions for a broad range of concentration, aspect ratio, and strain rate using a variety of methods. Our measurements highlight the importance of excluded-volume interactions in the semidilute regime, with scaling in terms of a dimensionless shear rate. Our results also suggest that such interactions might be exploited to fractionate carbon nanotubes by length in simple shear flow.

Figure 1

(a) Scaled $\Delta n^{\prime }$ vs Pe, where the left inset is an electron micrograph of the MWNTs and the right inset is an AFM image of the SWNTs ($\mathrm{\text{scale bar}}=150\mathrm{nm}$). The measured $S$ has been scaled onto the data and the line is a power-law fit. (b) Analogous plot of $\Delta n^{\prime \prime }$, where the left inset is a SVM of a MWNT ($\mathrm{\text{scale bar}}=5\mu \mathrm{m}$) and the right inset is a SANS pattern for S1 ($\mathrm{\text{scale bar}}=0.06{\mathrm{nm}}^{-1}$).

Figure 2

Scaled $x$ and $z$ projections of the diagonal elements of $S_{\mu \nu }(\mathbf{q})$, where (a) and (b) are the measured $hh$ and $vv$ patterns for 0.2% M1 at $\dot{\gamma }=36{\mathrm{s}}^{-1}$. Data for each $\varphi$ correspond to the same Pe, with $S\approx 0.45$. The 0.1% and 0.4% M1 data are at $\dot{\gamma }=153{\mathrm{s}}^{-1}$ and $9{\mathrm{s}}^{-1}$, respectively. The curves are computed profiles and the line is $q^{-1}$.

Figure 3

Scaled polar projections of the off-diagonal element of $S_{\mu \nu }(\mathbf{q})$, where (a) and (b) are the measured $hv$ patterns for 0.2% M1 at $\dot{\gamma }=36{\mathrm{s}}^{-1}$ and 0.4% M1 at $9{\mathrm{s}}^{-1}$, respectively. The black curve is the computed profile. The histogram is the ODF measured with SVM and the dashed curve is a Gaussian fit.

Figure 4

The (a) $vv$ and (b) $hh$ patterns for 0.2% M1 at $\dot{\gamma }=14{\mathrm{s}}^{-1}$, $t=1\min$, where (c) and (d) show the same at $t=19\min$. The inset (e) shows a micrograph in the bulk for 0.1% M1 at $\dot{\gamma }=14{\mathrm{s}}^{-1}$, $t=19\min$, while (f) shows the same near a wall. As in Figs. 1, 2, 3 the gap in (a)–(f) is $200\mu \mathrm{m}$. Lowering the gap to $20\mu \mathrm{m}$ leads to irreversible fibrillation, as shown in (g) for 0.2% M1 at $\dot{\gamma }=100{\mathrm{s}}^{-1}$. The scale bar in (e)–(g) is $25\mu \mathrm{m}$. The lower panel shows projected length and orientation histograms for (e) and (f).