December 15, 2011 Synthesis and Rapid Characterization of Amine-Functionalized Silica SUPPORTING INFORMATION Erick Soto-Cantu, Rafael Cueto, Jerome Koch and Paul S. Russo* Department of Chemistry and Macromolecular Studies Group Louisiana State University, Baton Rouge, LA 70803, USA *To whom correspondence should be addressed: chruss@lsu.edu Control of Particle Size by Shrinkage
It is common to find reports about increasing the diameter of the resulting colloidal silica after the hydrolysis is completed. The subsequent addition of TEOS can increase the particle size of colloidal silica in a predicted manner. For some applications, it may be necessary to decrease the particle size instead of increasing it. Hydrogen fluoride (HF) has been used to completely etch silica out of other components in particles. The reaction is favored by the formation of stable and volatile silicon fluoride. It is possible to use this reaction in order to decrease the particle size of colloidal silica (procedure in next paragraph). The volume of the spheres, and hence their mass, is proportional to the third power of the radius. A radius of ½ of the original was planned. Therefore, the mass of the particles would be reduced to (½)3 = ⅛ of its original value. A mass of HF equal to ⅞ of the chemical equivalent of the original mass of silica was added. As can be seen in Figure SI-1, the diameter of the silica particles was reduced. The a b Figure SI-1. TEM images of silica particles. a): Before and b): After HF etching. average diameter before etching was 269 nm ± 20 nm and after etching is 160 nm ± 32 nm (both measured from the TEM images in Figure 2). The size reduction represents 40% of the original size as opposed to the 50% predicted. The polydispersity increased from ± 7.4% to ± 20.0%. The increase in polydispersity is accentuated because smaller particles have larger specific surface area hence can react at a faster rate than larger ones. This size reduction method might be
adequate for particles of very low polydispersity values and for small differential reduction values. Procedure to Etch Colloidal Silica with Hydrofluoric Acid Caution: HF is highly and painfully toxic. Work should not begin without appropriate training, a trained laboratory partner, and an adequate supply of calcium gluconate. Colloidal silica (10 ml) obtained by the modified method described in the previous section (conc. 8.6 mg/ml) was placed in a 50 ml polypropylene tube. Then 10 ml of a 1% HF solution was added to the silica dispersion. The mixture was magnetically stirred and allowed to react at room temperature for 9 hours. After that, the resulting colloidal silica was centrifuged at 5900 g for 30 minutes. The silica pellet was subsequently re-dispersed in absolute ethanol. This washing procedure was repeated at least 5 times. Core-Shell Form Factor for Fitting Scattering Envelopes The experimental observation (Figure 4 of main text) that the scattering level is higher than expected for a uniform particle suggests the existence of structural features smaller than the particles themselves. One possibility would be gradients or inhomogeneities in the interior of the particles for example, variations in density and corresponding variations in refractive index. A simple way to assess this is with a core-shell model. The appropriate form factor for core-shell particles given by Aden and Kerker 1 simplifies in the Rayleigh-Gans-Debye limit 2 to: 3;4 I 2 6 ( m1 1) 3 j1( x) 3 ( m2 m1 ) 3 j1( fx) ( ) qr R 2π x + f ( m 1 1) fx (SI-1)
In Eq. SI-1, R is the outer radius of the core-shell particle (see Figure 6) and x = qr. t n 2 n 1 n 0 2R Figure SI-2. Parameters of the core-shell model; see text. The term j 1 (x) represents the first-order spherical Bessel function i.e., j sin( x) x) = x 1( 2 cos( x) x (SI-2) Eq. SI-1 contains two relative indices of refractive index: m 1 = n 1 /n 0 and m 2 = n 2 /n 0, where 0, 1 and 2 stand for solvent, shell and core, respectively. The term f stands for the fraction of the linear particle dimension within the core: f = R t R (SI-3) The equations above were cast into an Excel workbook. Figure SI-3 shows data from a particular time slice from the data set measured for the silica standard particles (see Figure 3C and 4 of the main text). For a particular set of parameters, the core-shell model does a much better job of fitting the high-angle data; however, some data at intermediate angles are not fit as closely as they are by the uniform sphere model. Excel s Solver nonlinear least squares fit routine offers quite a few operational options. Several of these were tried, and several initial guesses were attempted, with the result that the fit tends to one that looks as shown in Figure SI-3; however, the parameter space must be fairly flat because parameters could be varied over a fairly wide
range without gravely altering the fit. For example, the diameter of the putative core ranged over at least 10% and its shell refractive could be varied over at least 50%. In such a case, a full grid search over the parameters would be appropriate. This was not attempted because there is no reason to think a sharply defined core-shell structure exists in the first place. It does seem, though, that internal inhomogeneities of some kind can account for the excess scattering at high angles. Figure SI-3. Core-shell (red curve) and uniform sphere (blue curve) calculations overlaid onto data for commercial silica sphere standard (67 minutes elution time from Figure 3C of the main text).
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