Supporting Information for. Concentration dependent effects of bovine serum albumin on graphene

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1 Supporting Information for Concentration dependent effects of bovine serum albumin on graphene oxide colloidal stability in aquatic environment Binbin Sun, Yinqing Zhang, Wei Chen, Kunkun Wang, Lingyan Zhu Key Laboratory of Pollution Processes and Environmental Criteria (Ministry of Education), Tianjin Key Laboratory of Environmental Remediation and Pollution Control, College of Environmental Science and Engineering, Nankai University, Tianjin , P. R. China Summary Number of Pages: 18 Page S2-S5: Calculation of (X)DLVO interaction energy Page S6-S16: Figure S1 Figure S11 Page S17-S18: References To whom correspondence should be addressed. Phone: Fax: S1

2 Calculation of (X)DLVO interaction energy According to the DLVO theory, the total interaction energy between GO nanoparticles, VTOT (KBT), can be modeled as the integration of the attractive van der Waals attraction, V VDW (K B T), and electrostatic double-layer repulsion forces, V EDL (K B T). 1 It should be mentioned that all the above interaction energies are normalized by K B T. V TOT = V VDW + V EDL (S1) The attractive van der Waals attraction is calculated using Hamaker approach and Gregory s formulation: 2 V VDW = Ar NP 6h(1+ 14h λ ) (S2) Where A is the Hamaker constant for GO nanoparticles ( J was used in this study); r NP is the radius of nanoparticles (m), h is the separation distance between nanoparticles (m); λis the characteristic wavelength 100 nm. The electrostatic double-layer repulsion could be calculated as follows: 3 V EDL = πr NP ε 0 ε r 2ϕ 1 ϕ 2 ln 1+exp(-κh) +(ϕ 2 +ϕ 2 1-exp(-κh 1 2 ) ln 1-exp(-2κh) (S3) Where ε 0 is the vacuum permittivity ( C 2 /Jm), ε r is the relative dielectric permittivity of water (78.4), ϕ 1 and ϕ 2 are the surface potentials of GO nanoparticles. κ (cm -1 ) is the Debye reciprocal length and can be calculated by using the equation: 4 κ= 2N A Ie 2 Tε r ε 0 K B (S4) Where N A is the Avogadro number ( mol -1 ), e is the electron charge ( C), I is the ionic strength of the background electrolyte (mol/m 3 ), K B is Boltzmann constant ( J/K), and T is Kelvin temperature (298 K). If the particles were stabilized by BSA molecules, two traditional repulsive potentials should be S2

3 considered: a repulsive osmotic energy term, V osm and elastic steric repulsion, V elas. 5 V osm is due to the exclusion of water molecules surrounding the polymers on the close particle-surface approach. V osm 0 kbt = 2d h V 4r π 1 h φ χ k T 2 2 osm NP 2 = p d B υ1 Vosm 4rNPπ 2 1 h 1 h = φ p χ ln kbt υ1 2 2d 4 d 2 d h< 2d h> d Where υ 1 is the volume of a solvent molecule (0.03 nm 3 ); χ is the Flory-Huggins solvency parameter. BSA is relatively hydrophilic polymers, and have the similar globular structure and molecular weight to virus, so 0.49 chosen here. 6-8 d was the thickness of adsorption layer (4.9 nm), calculated by the Ohshima s soft theory. φ p is the calculated volume fraction of polymer within the brush layer. φ Γ r 2 max NP p = ρp ( d+ rnp) rnp Γ max is the maximum surface concentration (Kg/m 2 ). Based on the unique two-dimensional structure of GO and the BET surface area of GO powder was not accurate for the surface area of GO. The theoretical specific surface area of graphene 2630 m 2 /g was used here. 9 The sorption experiments indicated that the saturation adsorption amount of BSA on GO was 2000 mg/g. After calculation, the Γ max is 0.76E-06 Kg/m 2. The compression of the adsorbed BSA layer below the thickness of the unperturbed layer (d) leads to a loss of entropy and gives rise to the elastic repulsion (V elas ): Velas 0 k T = d h B S3

4 2 h h Velas 2π r NP 2 2 h h h pd p ln d φ ρ 6ln d = kbt MW d d 2 2 d d > h Where M W is the molecular weight of the BSA: 67 Kg/mol. ρ p was the density of BSA, 1.41 g/cm 3. Previous research indicated that for proteins with high molecular weight, a value ρ p =1.41 g/cm The total extended DLVO (XDLVO) interaction energy is: VTOT = VVDW + VEDL + Vosm + Velas Ohshima s Soft Particle Theory: In this study, the characteristics of adsorbed organic matter layers (layer thickness, d, soft parameter, λ f and charged density, ZN) was obtained by fitting EPM data (µ e ) of GO NPs in the presence of BSA with Ohshima s soft theory. 5, 11 Specially, the detailed calculation formula was as follows: κ ε ε ϕ / κ + ϕ d ezn 8 ε ε k T zeζ e / λ e / κ µ e = + + λd md r 0 0 m DON r 0 B m f tanh η 1/ κ m+ 1/ λ a ηλ ηλze 4kBT 1/ λ 1/ κm Where µ e is the electrophoretic mobility (EPM). η is the water viscosity, λ is the softness parameter. κ m is the Debye-Hückel parameter of the surface layer. ψ 0 is the surface potential at the boundary of the adsorbed layer and the bulk solution. ψ DON is the Donnan potential within the adsorbed layer. Z is the valance of the charged functional groups in the adsorbed layer, N is the number density of the charged groups. Z is the valence of bulk ions, and ζ is the ζ-potential of the bare particles. The equations for ψ DON, ψ 0, f (d/a), and κ m are given below. ψ DON 2 kbt ZN ZN = ln ze 2zn 2zn 1/2 S4

5 ψ 2 1/2 2 1/2 kbt ZN ZN 2zn ZN 4kBT κmd zeζ 0 = ln e tanh ze 2zn 2zn ZN 2zn ze 4kBT d 2 1 f = 1 + a d / a 2 1/4 ZN κm κ = 1+ 2zn ( ) 3 Where n is the concentration of bulk ions. The three parameters (d, λf, and ZN) were unknown. The MATLAB (the Mathworks, Novi, MI) code employing iterative least squares minimization was used for this fitting the EPM data. The fitted results indicated that the parameters obtained by the theory were good. After calculation, the fitting results were as follows: S5

6 Figure S1. (A) The representative atomic force microscopy (AFM) image of GO. (B) Distribution of lateral size of GO, which was obtained by at least 150 GO nanosheets from five different AFM images. S6

7 Figure S2. The adsorption isotherms of BSA on GO (200 mg/l) at ph 5.5 and 25 C. S7

8 Figure S3. Representative aggregation profiles of GO (10 mg/l) as a function of electrolyte concentration and type: (A) NaCl, (B) MgCl 2, (C) CaCl 2 at ph 5.5 ± 0.2 and 25 C. S8

9 Figure S4. Zeta potentials of GO changed as functions of electrolyte concentrations : (A) NaCl, (B) MgCl 2 and CaCl 2 at ph 5.5 ± 0.2 and 25 C. S9

10 Figure S5. The D h of BSA changed as a function of time in the presence of high electrolyte concentration and types at ph 5.5 ± 0.2 and 25 o C. S10

11 Figure S6. The effect of BSA concentration on the aggregation kinetics of GO (10 mg/l) at the fixed salt concentration : (A) 120 mm NaCl, (B) 3.33 mm MgCl 2 and (C) 0.83 mm CaCl 2 at ph 5.5 ± 0.2 and 25. S11

12 mm Na + 50 mm Na + 60 mm Na + 75 mm Na + 90 mm Na mm Na + A mm Mg mm Mg mm Mg mm Mg mM Mg mm Mg 2+ B D h (nm) D h (nm) Time (s) 0.25 mm Ca mm Ca mm Ca mm Ca mm Ca mm Ca 2+ C Time (s) D h (nm) Time (s) Figure S7. Representative aggregation profiles of GO (10 mg/l) in the presence of 2 mg C/L BSA as a function of electrolyte type and concentration: (A) NaCl, (B) MgCl 2, and (C) CaCl 2 at ph 5.5 ± 0.2 and 25 C. S12

13 Figure S8. TEM pictures of GO (10 mg/l) in different solutions after incubation for 5 minutes. (A) GO only, (B) GO + 2 mg C/L BSA, (C) GO + 60 mm NaCl, (D) GO + 60 mm NaCl + 2 mg C/L BSA, (E) GO + 60 mm NaCl + 30 mg C/L BSA. S13

14 Figure S9. The effect of BSA concentration on the initial aggregation kinetics of GO in the absence of electrolyte at ph 5.5 ± 0.2 and 25 C. The BSA concentration was chosen as 0.13, 0.4, 2, 5, 7.5, 10, 15, 20 and 30 mg C/L. S14

15 Figure S10. The effect of adding order on the GO initial aggregation. The GO concentration was kept at 10 mg/l, while the BSA was chosen as 2, 5 and 30 mg C/L in the presence of 60 mm NaCl. S15

16 Figure S11. (X)DLVO particle-particle interaction energy profiles at different solution chemistry conditions. The insets show the close-up of the respective secondary energy minimum region. S16

17 Reference 1. Hogg, R.; Healy, T. W.; Fuerstenau, D. W. Mutual coagulation of colloidal dispersions. Trans. Faraday. Soc. 1966, 62, Gregory, J. Approximate expressions for retarded van der waals interaction. J. Colloid. Interface. Sci. 1981, 83, (1), Elimelech, M.; O'Melia, C. R. Effect of particle size on collision efficiency in the deposition of Brownian particles with electrostatic energy barriers. Langmuir 1990, 6, (6), Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, Phenrat, T.; Saleh, N.; Sirk, K.; Kim, H.-J.; Tilton, R. D.; Lowry, G. V., Stabilization of aqueous nanoscale zerovalent iron dispersions by anionic polyelectrolytes: adsorbed anionic polyelectrolyte layer properties and their effect on aggregation and sedimentation. Journal of Nanoparticle Research 2008, 10, (5), Vincent, B.; Luckham, P. F.; Waite, F. A., The effect of free polymer on the stability of sterically stabilized dispersions. Journal of Colloid and Interface Science 1980, 73, (2), Einarson, M. B.; Berg, J. C., Electrosteric Stabilization of Colloidal Latex Dispersions. Journal of Colloid and Interface Science 1993, 155, (1), Wong, K.; Mukherjee, B.; Kahler, A. M.; Zepp, R.; Molina, M., Influence of Inorganic Ions on Aggregation and Adsorption Behaviors of Human Adenovirus. S17

18 Environmental Science & Technology 2012, 46, (20), Zhu, Y.; Murali, S.; Cai, W.; Li, X.; Suk, J. W.; Potts, J. R.; Ruoff, R. S., Graphene and Graphene Oxide: Synthesis, Properties, and Applications. Advanced Materials 2010, 22, (35), Fischer, H.; Polikarpov, I.; Craievich, A. F., Average protein density is a molecular-weight-dependent function. Protein Science 2004, 13, (10), Nakamura, M.; Ohshima, H.; Kondo, T., Electrophoretic behavior of antigenand antibody-carrying latex particles. Journal of Colloid and Interface Science 1992, 149, (1), S18