Raman Research Institute, C. V. Raman Avenue, Sadashivanagar, Bangalore , India

Transcription

1 Use of ultrasound attenuation spectroscopy to determine the size distribution of clay tactoids in aqueous suspensions Samim Ali *, Ranjini Bandyopadhyay Raman Research Institute, C. V. Raman Avenue, Sadashivanagar, Bangalore , India * samim@rri.res.in ranjini@rri.res.in

2 Figure S1: Representative AFM images of Laponite tactoids scanned in contact mode with different size windows. (a) and (b) correspond to the friction flattened images used for lateral size measurement. (c) is a representative topographical image which is used to measure platelet thickness as shown in (d). Sample preparation: 10 microlitres of sample (0.1% w/v) was deposited on a freshly cleaved mica surface and dried quickly at T = 120 o C.

3 Figure S2: (a) Diameter distribution estimated from 150 Laponite platelets selected in AFM micrographs is shown in figure S1. (b) The thickness distribution estimated for 30 isolated Laponite platelets selected carefully from AFM micrographs.

4 Figure S3: Loss of acoustic energy in a 3 % w/v Laponite suspension, plotted versus length of gap between transducers, at frequencies 19.2 MHz (squares), 43.7 MHz (circles), 66.9 MHz (up triangles), 81.0 MHz (down triangles) and 99.5 MHz (diamonds). The solid straight lines are linear fits that show the validity of Beer-Lambert law (Equation 7 of the main paper). The gap between the two transducers is varied using a micrometer-precision step motor. Supplied values: The following values are used in Equation 3 to estimate PSDs. Density of water at 25 o C, ρ m = g/cc Viscosity of water at 25 o C, η m = 0.89 mpas Density of Laponite particle, ρ p = 2.53 g/cc Density of Na-Montmorillonite, ρ p = 2.6 g/cc Sound speed in solid media,c p = 6000 m/s

5 Method of Graphical Solutions: The Jennings-Parslow 1 relation for ESD of anisotropic particle under Stokes drag, ( ) [ ( ) ] can be written as ( ) ( ) or,.eqn. 1 When and are plotted against d (as shown in Figures 2 and S2),the solution for the thickness t and disc diameter d corresponds to the intersection of the functions and for the supplied values of d s. For Laponite platelets, d varies between 25 nm and 30 nm. The value of thickness t is adjusted to find an average value of d = 27.5 nm in the graphical solutions in Figure 2 (main article). Reference:1. Jennings, B. R.; Parslow, K. Particle size measurement: The equivalent spherical diameter.proc. R. Soc. Lond. A 1988, 419,

6 Figure S4: The graphical solution of Equation 8 for the median size d 1 = 30.1 nm obtained when the attenuation spectrum of a 1% w/v Na-Montmorillonite suspension is fitted to the bimodal distribution. The solution corresponds to a disc of thickness t = 1.5 nm and diameter d = 254 nm.

7 Figure S5:(a) A representative AFM image of Na-Montmorillonite sheets scanned with window size 5 µm X 5µm in tapping mode. (b) Thickness profile analysis of two typical particles using the PicoScan software (Molecular Imaging Company). Figure S6: (a) Thickness distribution and (b) diameter distribution of six particles shown in the AFM micrograph in Figure S5 (a). The thickness distribution indicates the presence of tactoids composed of one to two platelets. The average tactoid thickness t = 1.5±0.1 nm and average diameter d = 282±30 nm.

8 Figure S7: Bimodal size distributions of aggregates of 3% w/v Na-Montmorillonite suspension at t w = 5hrs (squares), 47 hrs (circles) and 93hrs (triangles).