Supporting Information Characterizing the Effect of Salt and Surfactant Concentration on the Counter-ion Atmosphere around Surfactant Stabilized SWCNTs using Analytical Ultracentrifugation Stephanie Lam 1, Ming Zheng 1 and Jeffrey A. Fagan 1,* 1 Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899 Disclaimers: (1) Certain equipment, instruments or materials are identified in this paper in order to adequately specify the experimental details. Such identification does not imply recommendation by the National Institute of Standards and Technology (NIST) nor does it imply the materials are necessarily the best available for the purpose. (2) Unless otherwise noted, uncertainty in this contribution is represented by error bars equal to one standard deviation of the reported value. This document contains additional analytical ultracentrifugation (AUC) data, AFM images for the (7,6) SWCNTs, buffer densities and viscosities, equation derivations, as well as calculations for quantities discussed in the main contribution. Figure S1. AUC data comparing s-distributions of SWCNT samples with sorting. As expected, the s- distribution of the nanotube sample gets narrower with more sorting. 1
Figure S2. AFM images of SG76 (top) and (7,6) SWCNTs (bottom) of various length fractions (a) before and after (b) chirality sorting. Note that not all images are measured at the same magnification. Verification of Dilute Condition for AUC Results of SV measurements as a function of nanotube concentration (OD used in the AUC experiment) indicate that the samples as measured for this contribution were in the dilute, non-interacting regime. This can be seen empirically in the results shown in Figure S3, in which the determined sedimentation coefficient distributions are invariant with SWCNT loading. All SWCNT samples used for densitometry measurements were significantly shorter (and thus more dilute from a swept volume perspective) and measured at 0.4 OD or less. The assertion of dilute regime conditions is further satisfied by calculation of the effective volume fraction occupied by the rods. A swept volume fraction << 1 implies that the systems is dilute. Knowns For a rigid rod, the spherical volume swept by the rotating rod is = 4/3 π (L/2) 3 = 1/6 π L 3 The greatest absorbance utilized across the cell was 0.4 A The approximate extinction coefficient for the (7,6) SWCNT at 376 nm is 11.5 A/(mg mm/ml) 1 The mass/nm of a (7,6) SWCNT (carbon only) is 2.11 x 10-21 g/nm The approximate rod concentration was thus (0.4 A/ 12 mm)/(11.5 A(376 nm)/(mg mm / ml)) 2.9 x 10-6 g/ml The total SWCNT length per ml in solution was thus 2
2.9 x 10-6 g/ml / 2.11 x 10-21 g/nm = 1.37 x 10 15 nm/ml And the number of rods 1.37 x 10 15 nm/ml / 456 nm/rod = 3.01 x 10 12 rods/ml = 3.01 x 10 18 rods/m 3 Spherical swept volume per rod is 4/3 * 3.14159 * (228 x 10-9 m) 3 = 4.96 x 10-20 m 3 The volume fraction (rods/m 3 * volume/rod) is thus 4.96 x 10-20 m 3 * 3.01 x 10 18 rods/m 3 0.150 As expected 0.150 << 1, supporting the assertion of a dilute system. This assertion is further supported by the results of Duggal and Pasquali, 2 who reported the number concentration of particles per unit volume of dispersion (v) for crossover from dilute to semi-dilute regime can be estimated using the equation (1/< >) for a monodisperse system of rods and (30/< >) for a polydisperse sample. The assertion of dilute regime conditions is further satisfied by calculation of the concentration of rods in the longest sample of highest concentration used in the densitometry experiments. From [2] the number concentration of particles per unit volume of dispersion (v) for crossover from dilute to semi-dilute regime can be estimated using the equation (1/< >) for a monodisperse system of rods and (30/< >) for a polydisperse sample. Using similar math as above, the most concentrated, longest nanotube case yields 2.9 x 10 12 particles/ml << 3.2 x 10 14 particles/ml prediction for the crossover limit from [2]. Lastly, the low concentration of nanotubes present in the system does not significantly affect the bulk viscosity. This is experimentally confirmed by the absence of nanotube concentration effects on the observed sedimentation coefficient in Figure S3. 3
Figure S3. s-distribution (a) and average sedimentation coefficient vs sample OD (b) of (7,6) SWCNTs dispersed in 10 g/l DOC for solutions containing varying concentrations of SWCNT. Data does not indicate the existence of any concentration dependent effects on the measured s-distribution in the concentration regime of our experiments. Note that the vertical axis is highly expanded in panel b. Fraction F3 from SEC sorting was used for these measurements. Figure S4. Tabulated values of densities and viscosities for solutions of 1% DOC (10 g/l or 24 mmol/l) in various buffers. The obtained values are averaged over 3 measurements. 4
Figure S5. Tabulated values of buffer densities and viscosities for solutions of 15 mmol/l (6.25 g/l) and 10 mmol/l (4.2 g/l) DOC in various buffers. The obtained values are averaged over 3 measurements. 5
6
Figure S6. Tabulated values of buffer densities and viscosities for solutions of 1% DOC in buffers of varying (a) H 2 O/D 2 O and (b) H 2 O/iodixanol containing NaCl. The obtained values are averaged over 3 measurements. 7
AUC Data Analysis Using UltraScan In addition to data analysis in SEDFIT, some AUC data for the (7,6) parent sample water-filled SG76 was also analyzed in UltraScan (version 3.2). Two-dimensional spectrum analysis (2DSA) was used to solve for the s and f/f 0 distributions for each sample. 3 The 2DSA method determines s and f/f 0 for the sedimenting species by numerically solving the Lamm Equation. However, unlike the c(s) model, here, one specifies both the range of s and f/f 0 values over which to solve the Equation. s values were fitted over a range from (0 to 100) Sv with 200 grid points, and f/f 0 values were fitted over a range from 1 to 15 with 70 grid points; once the range of s and f/f 0 values for the sample were determined in earlier iterations for ρ p, the s range was narrowed to (0 to 50) Sv with 200 grid points and the f/f 0 range was narrowed to 7 to 9 with 20 grid points in later iterations. Data points extracted from UltraScan were fitted using a kernel density function (KDF) as described here 4 for better visual comparison with the s- distributions extracted from SEDFIT. The bandwidth, h, in the kernel density estimation was set to 0.68. Comparison of data points obtained from analysis by UltraScan, the kernel density fit to the UltraScan data, and the s versus c(s) distribution obtained from SEDFIT are presented for water-filled SG76 SWCNTs in several different buffers below. These data were obtained during a densitometry experiment to determine the anhydrous density of a length-sorted fraction of SG76. The anhydrous density obtained for water-filled SG76 using average s values solved for with SEDFIT was (1519 ± 12) kg/m 3 with average f/f 0 (across all experiments) = 8.24 ± 0.91. The anhydrous density obtained for the same sample with s-values solved by UltraScan was (1528 ± 10) kg/m 3 with average f/f 0 (across all experiments) = 8.64 ± 0.31. It should be noted that the actual data extracted from UltraScan rather than the points from the kernel density fit were used to find ρ p for the DOC-SG76 complex. 8
Figure S7. Plots of s versus normalized concentration c(s) for DOC-coated SG76 in various buffers. The c(s) distributions obtained from SEDFIT are denoted by a solid black line. Data points obtained from UltraScan are represented by purple circles. The fit of s values obtained from UltraScan using a kernel density function with h = 0.68 to obtain a distribution, is shown for the SG76-DOC complex in 50 % D2O and 87.5 % D2O, and is plotted as a dotted purple line. 9
Figure S8. Anhydrous and buoyant densities of (7,6) F4 dispersed in 10 g/l DOC from multiple experiments. Note that the points at s η = 0 are not experimental points, but represent the extracted densities. Figure S9. Anhydrous and buoyant densities of (7,6) SWCNT of various length fractions dispersed in 10 g/l DOC. The measured densities are tabulated in the chart displayed to the right of the graph. Note that the points at s η = 0 are not experimental points, but represent the extracted densities. For better comparison to the anhydrous densities measured for the F5 and F6 fractions, the D 2 18 O point used in the extraction of (7,6) anhydrous density using the F4 fraction was removed in the fit here when extracting the anhydrous density for the (7,6) F4 sample. 10
Figure S10. Schematic of carbon nanotube annulus. Figure S11. Kratky balance for extraction of the partial specific volume (PSV) of DOC at (a) 0 mmol/l NaCl and (b) in the presence of salt. No difference between the partial specific volume of a DOC molecule and micelle were observed in our experiments. While the density of the DOC solution does change slightly with salt addition, the slope of the linear fit of 1/ρ vs DOC concentration does not, causing the PSV of DOC to remain more or less the same with increasing salt content. 11
Figure S12. Derivation of equations for anhydrous and buoyant radii for water-filled SWCNTs. The expression for closed-ended SWCNTs or SWCNTs filled with small molecules which do not readily exchange with the bulk will vary slightly. In the above equations, variables are defined as follows: m = mass, V = volume, L = length, and ρ = density. The subscript an refers to the anhydrous particle, SWCNT to the nanotube, DOC to the surfactant, core to the SWCNT core as defined in Figure S9, SWCNT-O to the outer wall of the nanotube as defined in Figure S9, and hydro to the bulk solution. Figure S13. s-distributions for (7,6) F4 SWCNTs dispersed in solutions of varying DOC concentration. 12
Figure S14. (a) Plot of solution density versus viscosity-corrected sedimentation coefficient for extraction of anhydrous and buoyant densities for the (7,6)-DOC complex dispersed in solutions of varying DOC concentrations. Filled symbols denote anhydrous density measurements and open symbols denote buoyant density measurements. All data presented here is for fraction F4 from SEC except the points used to determine the anhydrous density of (7,6) in 10 mmol/l DOC. The F5 fraction was used in this experiment. 13
Figure S15. (a) Plot showing how various properties of the SWCNT-surfactant complex change as the concentration of DOC is varied: linear packing density of DOC (black squares), the thickness of the adsorbed surfactant layer (blue circles), the percentage of the nanotube surface covered by surfactant (purple squares), and the number of water molecules associated with the SWCNT-surfactant complex (green circles). The y-axes relevant to the plotted property is the same color as the symbols representing them. Values for all plotted properties decrease with decreasing DOC concentration. (b) Plot showing how r an, r b and (r b -r an ) change with DOC concentration. As the amount of DOC in the suspending medium is decreased, r an shows only a slight decrease whereas r b and thus (r b -r an ) show a drastic decrease with decreasing DOC content. 14
Figure S16. s-distributions vs amount of added NaCl for (7,6) F5 SWCNTs dispersed in solutions containing 10 g/l DOC and (a-c) varying H 2 O/D 2 O content or (d-f) varying iodixanol concentrations. Figure S17. s-distributions for (7,6) F5 dispersed in solutions containing 10 g/l DOC with no added NaCl (filled curves) and 25 mmol/l added NaCl (empty curves). 15
Figure S18. Plot showing how various properties of the SWCNT-surfactant complex change as salt is added to the dispersion: linear packing density of DOC (black circles), the thickness of the adsorbed surfactant layer (blue squares), the percentage of the nanotube surface covered by surfactant (green triangles), and the number of water molecules associated with the SWCNT-surfactant complex (purple diamonds). The y-axes relevant to the plotted property is the same color as the symbols representing them. As seen in this plot, properties related to DOC adsorption on the SWCNT remain more or less constant until +70 mmol/l NaCl. However, the amount of water associated with the SWCNT-DOC complex steadily decreases with an increase in the quantity of added salt. Calculation of SWCNT-DOC Friction Coefficient The friction coefficient of the (7,6)-DOC complex was evaluated using the following equation 5 : 6 η 0.614 0.638 0.0135 2 0.614 0.544 0.136 where f = friction coefficient, η = the viscosity of the bulk medium, L = the length of the particle, and Y = ln(l/r b ). Using this expression and the buoyant radii determined from the densitometry results, f for the (7,6)-DOC complex was calculated for particles dispersed in aqueous solutions of 10 g/l DOC containing various quantities of NaCl. The results from this calculation are presented in the table below. The expected magnitude of increase in particle sedimentation based on a decrease in f associated with a 16
decrease in the size of the hydrated counter-ion cloud with the addition of salt is compared with the rate of increase in the experimentally measured sedimentation coefficients for (7,6) F5 SWCNTs. As seen in the table below, the expected rate of increase in sedimentation coefficient as a result of the reduction in particle hydration agrees very well with the observed increase in the experimentally measured sedimentation coefficient (with increasing NaCl content in the bulk). Sample NaCl (mmol/l) r b (nm) ±r b (nm) f (kg/s) expected "speed up" rate (7,6) F5 s in 0% D 2 O (Sv) ±s (Sv) actual "speed up" rate % diff 0 3.00 0.18 7.75E-10 1.000 9.79 0.78 1.000 0.00 10 2.76 0.12 7.59E-10 1.021 10.19 0.82 1.041 1.95 25 2.50 0.10 7.41E-10 1.045 10.26 0.71 1.048 0.26 30 2.64 0.12 7.50E-10 1.033 10.47 0.90 1.070 3.49 37.2 2.53 0.13 7.44E-10 1.042 10.50 0.86 1.073 2.93 45 2.52 0.16 7.43E-10 1.043 10.56 0.89 1.079 3.42 53.2 2.41 0.09 7.36E-10 1.053 10.54 0.79 1.076 2.23 70 2.18 0.10 7.21E-10 1.076 10.54 0.78 1.077 0.12 In the chart, r b = the buoyant radius determined from experimentally extracted buoyant densities. The expected speed up rate is the magnitude of the expected increase or decrease in sedimentation rate and is calculated by taking the ratio of the friction coefficient of the sample with respect to the friction coefficient of the (7,6)-DOC complex in 10 g/l DOC and 0 mmol/l NaCl. The actual speed up rate is the magnitude of the actual increase or decrease in sedimentation rate and is calculated by taking the ratio of the measured sedimentation coefficient of the sample with respect to the sedimentation coefficient of the (7,6)-DOC complex in 10 g/l DOC and 0 mmol/l NaCl. The % difference represents the difference in the expected and actual magnitude of increase in particle sedimentation with an increasing concentration of salt in the system. As seen in the chart, the expected and actual values are within 4 % of each other. 17
Figure S19. A filled ball and stick model of the deoxycholate molecule along with the dimensions used for calculations in this paper: a = 0.57 nm, b = 1.251 nm, and c = 0.38 nm. Dimensions were obtained using the measurement tool in Jmol, which was also used to obtain the pictures of the deoxycholate molecule shown above. Estimates for the surface area coverage of SWCNT by DOC is dependent on the projected DOC molecule size. Figure S20. (a) Plot showing how measurements of (7,6) F6 vs added NaCl compare with the same measurements made using the F5 fraction of (7,6). The observed effect of increasing buoyant density with the addition of NaCl in F6 is consistent with that observed in F5. Likewise, the exponential decay of (r b - r an ) vs solution ionic strength for F6 is the same as that observed for F5. 18
Figure S21. (a) Schematic showing buoyant radius of SWCNT-DOC complex at low ionic strength conditions (added NaCl 10 mmol/l and 10 g/l DOC). At these solution conditions, the counter-ion cloud around the SWCNT-DOC particle is very diffuse. This allows iodixanol molecules to penetrate into the cloud. Here, the buoyant radius extracted from the AUC measurements corresponds to the radius of exclusion of iodixanol from the area around the SWCNT-DOC complex, which contains water and some sodium counter-ions. (b) Schematic showing the buoyant radius of the SWCNT-DOC complex at high ionic strength conditions (i.e. conditions where (r b -r an ) κ -1 ). As NaCl is added to the SWCNT-DOC dispersion, the counter-ion cloud around the SWCNT-DOC complex collapses toward the surface of the particle. This results in a decrease in the average distance between ions in the counter-ion cloud, preventing the iodixanol molecules from penetrating into the cloud. At these conditions, the buoyant radius corresponds to the location of the outer surface of the electric double layer, and the displacement of the buoyant radius from the anhydrous surface will scale with the Debye length, κ -1. Note the number and distribution of surfactant molecules and ions is only for illustration of the phenomenological basis for the observed buoyant and anhydrous radii, and is not based on calculations. References (1) Streit, J. K.; Bachilo, S. M.; Ghosh, S.; Lin, C.; Weisman, R. B. Directly Measured Optical Absorption Cross Sections for Structure- Selected Single-Walled Carbon Nanotubes. Nano Lett 2014, 14 (3), 1530 1536. (2) Duggal, R.; Pasquali, M. Dynamics of Individual Single-Walled Carbon Nanotubes in Water by Real-Time Visualization. Phys. Rev. Lett. 2006, 96 (24), 246104. (3) Brookes, E.; Cao, W.; Demeler, B. A Two-Dimensional Spectrum Analysis for Sedimentation Velocity Experiments of Mixtures with Heterogeneity in Molecular Weight and Shape. Eur. Biophys. J. 2010, 39 (3), 405 414. (4) Thomspon, M. Representing Data Distributions with Kernel Density Estimates. AMC Tech. Br. 2006, 4 (4), 1 2. (5) Silvera Batista, C. A.; Zheng, M.; Khripin, C. Y.; Tu, X.; Fagan, J. A. Rod Hydrodynamics and Length Distributions of Single-Wall Carbon Nanotubes Using Analytical Ultracentrifugation. Langmuir 2014, 30 (17), 4895 4904. 19