Structure and rheology of organoclay suspensions

We have characterized a montmorillonite-based organoclay dispersed in three different nonaqueous solvents using a combination of x-ray scattering, small-angle neutron scattering (SANS), and ultrasmall angle neutron scattering (USANS), together with rheological measurements. Consistent with these measurements, we present a structural model for the incompletely dispersed clay as consisting of randomly oriented tactoids made of partially overlapping clay sheets, with transverse dimensions of several microns. Intersheet correlation peaks are visible in x-ray scattering, and quantitatively fit by our model structure factor. SANS and USANS together show a power law of about $-3$ over a wide range of wave numbers below the intersheet correlation peak. Our model relates this power law to a power law distribution of the number of locally overlapping layers in a tactoid. The rheology data show that both storage and loss moduli, as well as yield stress, scale with a power law in volume fraction of about three. Equating the gel onset composition with the overlap of randomly oriented tactoids and taking into account the large transverse dimensions of the tactoids, we predict the gel point to be at or below 0.006 volume fraction organoclay. This is consistent with the rheology data.

Figure 1

Two methods to extract the scattering length density for Cloisite 6A. For the power law fits, the intensity was estimated by taking parameters, $A$, from an equation of the form $A{q}^{-2.709}$ fit to each data set. For the second estimate, the intensity at $q=0.000134{\mathrm{\AA }}^{-1}$ was used for each data set. By averaging these two results we obtain the final $\mathrm{SLD}:1.13\pm 0.18\times {10}^{10}{\mathrm{cm}}^{-2}$.

Figure 2

The relationship between scattering length density (SLD) of the Cloisite-type organoclays and their composition. The as-received organic contents are indicated on the left vertical axis. The experimentally-determined SLD’s for Cloisite 15A and 6A [this study] are indicated by the arrows. The wt. percent and mole fraction DTDM corresponding to these SLD’s are indicated by, respectively, the solid and open symbols. SLD’s for both organoclays are consistent with the expulsion of excess surfactant into the solvent down to that required for charge neutrality, 0.7 mole fraction DTDM.

Figure 3

The SANS data for 0.008 volume fraction Cloisite 6A in $p$-xylene-$d$10, circles, are compared with the calculated scattering intensity for powder-averaged, single-plate organoclay sheets. Each sheet consists of a $9.2\mathrm{\AA }$ metal oxide core covered on both faces by a DTDM $+$ solvent layer, $19.4\mathrm{\AA }$ thick. The solid, dotted, and dashed lines demonstrate the effects of decreasing lateral dimension of this disk-shaped object (diameter=$2R$). Clearly additional structure is present.

Figure 4

X-ray scattering data (squares) compared with model (line). Initially these SAXS data are used to fix values of the interlamellar spacing ($p$-xylene, $\Delta =48\mathrm{\AA }$, and THF, $\Delta =46\mathrm{\AA }$) and the Gaussian deviation about this mean value $(\xi =3)$. Subsequently the $k$ parameter of the distribution for the number of layers per stack is optimized using the SANS and USANS data. The models plotted here were calculated from the SANS optimized parameters in Table , appropriately broadened through use of a finite slit broadening function (see text).

Figure 5

The scaled experiment data for $S\left(q\right)$, circles, are obtained by taking the ratio of the experimental intensity to that of the calculated single-plate scattering for 0.008 volume fraction Cloisite 6A in $p$-xylene-$d10$. The amplitude and background corrections from Table were applied to the calculated values. We compare this with $S\left(q\right)$ calculated from the model distribution with $y=1$. Here, $k$ parameters corresponding to three different average numbers of layers per stack $(⟨N⟩)$ are displayed. The best-fit value from Table provides an excellent description of the low-q dependence. At higher $q$, our data exhibit an elevated background due to incoherent scattering and the form factor for neutron scattering is small hence we do not observe the peaks in $S\left(q\right)$. However, these are observed in SAXS, as detailed in Fig. 4.

Figure 6

The scattering data from Cloisite 6A in $p$-xylene-$d10$ are compared with lines calculated from the model parameters in Table . Individual organoclay sheets assemble into structures that are laterally extended and vertically stacked. The distribution of stack heights are described by a probability distribution described in the text. To attain these fits we require amplitude factors, which are linear in clay volume fraction up to $5\mathrm{wt}.\%$ clay, and incoherent backgrounds, which are linear in clay volume fraction throughout (see Table ).

Figure 7

The average tactoid sizes, as calculated from fitted parameters for distributions of the number of layers per stack, are essentially invariant across a very broad concentration range for $p$-xylene. The slightly lower values for TDF and ${\mathrm{CDCl}}_3$ are only marginally outside the estimated error range. The highest concentration $p$-xylene samples exhibit significantly lower average stack heights, which may result from inter-tactoid correlations.

Figure 8

Cumulative distributions for the number of sheets per tactoid calculated from data in Table for four representative examples. Note that in each case the most probable number of sheets per tactoid is one. Also indicated is the average number of sheets for each example.

Figure 9

Tactoid structure suggested by scattering parameters. Overall dimension set by extended power law to lowest q values from USANS. Our distribution for the number of layers per stack suggests the average number of sheets per stack is about 2, but the frequency of single sheets is nearly 80%.

Figure 10

Storage $\left(G^{\prime }\right)$ and Loss $\left(G^{″}\right)$ moduli exhibit power law scaling versus volume fraction organoclay. The expected scaling of $(\varphi -{\varphi }^{*})$ where ${\varphi }^{*}$ is the overlap concentration is not observed because ${\varphi }^{*}$ is small.

Figure 11

Steady shear viscosity for indicated volume fractions of Cloisite 6A in $p$-xylene. Shear thinning is evident across the entire composition range. We vary the shear rate from low to high in order to avoid hysteresis in the rheology.

Figure 12

Yield stress ${\tau }_y$, defined as ${\tau }_y=\eta \left(\dot{\gamma }\right)\dot{\gamma }$ for $\dot{\gamma }\to 0$, shows a power law scaling with volume fraction clay equal, to within error, to that for the storage modulus, $G^{\prime }\sim {\varphi }^{3.2}$. A similar scaling of yield stress has been observed for Laponite gels (see text).