SUPPORTING INFORMATION FOR “COLLOIDAL STABILITY OF SILVER NANOPARTICLES IN BIOLOGICALLY RELEVANT CONDITIONS”, by Robert I. MacCuspie.
Definitions of Aggregate and Agglomerate
ISO Definitions of Aggregate and Agglomerate
Aggregate
Descriptor – strongly bonded or fused particles where specific surface area may be significantly smaller than the sum of calculated specific surface areas of individual components; the physical dimensions of a particle determined by specified measurement conditions. A sample of particles of differing sizes is described by a size distribution.
Agglomerate
Descriptor – collection of loosely bound particles or aggregates or mixtures of the two – resulting external specific surface area is similar to the sum of the specific surface areas of the individual components.
ASTM Definitions of Aggregate and Agglomerate (from ASTM Standard E2456)
Agglomerate, n—in nanotechnology, a group of particles held together by relatively weak forces (for example, Van der Waals or capillary), that may break apart into smaller particles upon processing, for example.
Aggregate, n—in nanotechnology, a discrete group of particles in which the various individual components are not easily broken apart, such as in the case of primary particles that are strongly bonded together (for example, fused, sintered, or metallically bonded particles).
OECD Definitions Clarification
( , page 53)
Aggregate - Particle comprising strongly bonded or fused particles where the resulting external surface area may be significantly smaller than the sum of calculated surface areas of the individual components. The forces holding an aggregate together are strong forces, for example covalent bonds, or those resulting from sintering or complex physical entanglement. Aggregates are also termed secondary particles and the original source particles are termed primary particles. (30 ISO/TC229, Nanotechnologies – Terminology and Definitions for Nano-objects – nanoparticle, nanofibre and nanoplate, ISO/TS 27687 ISO Copyright Office, Geneva, 2007, p. 8.)
Agglomerate - Collection of loosely bound particles or aggregates or mixtures of the two where the resulting external surface area is similar to the sum of the surface areas of the individual components(31 ISO/TC229, Nanotechnologies – Terminology and Definitions for Nano-objects – nanoparticle, nanofibre and nanoplate, ISO/TS 27687 ISO Copyright Office, Geneva, 2007, p. 7.). For this to be the case all primary particles would need to be at the surface of the agglomerate, which is impossible. …a more accurate statement would be “where the surface area measured by gas absorption – BET – is similar to the sum of the surface areas of the individual components”
Surface Plasmon Resonance of AgNPs in complex media
The wavelength of the characteristic surface plasmon resonance (SPR) absorbance peak, referred to as max, typically falls near 380 nm to 400 nm for AgNPs, but can be red-shifted either when AgNPs change surface coatings or come into close proximity to one another,[7] and can be either red- or blue-shifted based on changes in the surrounding media.[8] When electrolyte solutions are added to a solution of metal nanoparticles, the local increase in the concentration of ions near the surface of the nanoparticle will cause rearrangement of the electrical double layer, which changes the dielectric function of the environment surrounding the nanoparticle and thus shifts the maximum wavelength of the surface plasmon resonance.[9] These shifts were reported to be observed to occur on the timescale of less than two min, therefore the change in absorbance when measured in one hour intervals allows these SPR-shift reactions to go to completion immediately compared to the aggregation reactions. Additionally, the UV-Vis waterfall plots of the full spectra at each time prove there was no shift in the max over the course of the time studies, indicating that double layer rearrangement from local changes in ion concentrations did not interfere with the quantification of single AgNPs remaining in solution. Therefore, as the decrease in UV-Vis absorbance provides a rate of disappearance of single AgNPs, it necessitates the hypothesis that the single AgNPs that disappeared were entering into aggregates upon disappearance.
DLS Theory
A bit of background on DLS is necessary to interpret the results in Figure 1. DLS measures the diffusion coefficient based on correlating the fluctuations in scattered light intensity, and then calculates the hydrodynamic particle size, dp,h, using the Stokes-Einstein relationship,
(1)
where Dz is the measured diffusion coefficient, k is the Boltzman’s constant, T is the thermodynamic temperature, and µ is viscosity of the solution. In the Rayleigh limit, the intensity of light scattered by a single particle is proportional to its volume squared. Thus, any average property of a mixture of single AgNPs and aggregates determined by light scattering will also be weighted by the volume squared called the ‘Z-average’ particle size.
Initial characterization of AgNP stock solutions
Dynamic Light Scattering (DLS)
DLS of unpurified citrate-capped AgNP product.
Mean Z-average diameter: 20.7 nm ± 0.2 nm. Mean of 5 measurements with uncertainty of one standard deviation.
DLS of citrate-capped AgNP after purification by stirred cell ultrafiltration.
Mean Z-average diameter: 19.9 nm ± 0.8 nm.
DLS of BSA-capped AgNPs
Mean Z-average diameter 35.7 nm ± 0.6 nm
UV-Vis spectra of AgNPs
Atomic Force Microscopy (AFM)
Edge is 6.00 µm, Z color scale is 50 nm.
The morphology of the citrate stabilized 20 nm diameter AgNPs is spherical. No significant aggregation or agglomeration is observed.
Aggregation/Agglomeration Models
Using the Smoluchowski model, the average diameter of the aggregates (Daggr) is given by
(2)
where DNP is the diameter of the primary nanoparticles, tp is the aggregation time constant, and df is the fractal dimension of the aggregates.[1]
The aggregation time constant is
(3)
Where µ is the viscosity, rp is the radius of the particle, W is the stability ratio (derived from Ua and Ur, the attractive and repulsive forces, respectively, from Deryaguin-Landau-Verwey-Overbeek (DVLO) theory discussed shortly) kB is the Boltzman constanst, T is the temperature, and p is the volume fraction of the particles. It is generally reported that df 1.8 for diffusion limited colloidal aggregation (DLCA) and df 2.1 to 2.5 for reaction limited colloidal aggregation (RLCA), corresponding to a weak and strong repulsive barrier, respectively.[1,2] Based on recent work with gold nanoparticles, at salt concentrations of less than 500 mmol·L-1 a crossover from RLCA at early times to DLCA at later times is expected.[3]
Experimentally, Daggr was found to follow power-law kinetics where the diameter of the aggregates is proportional to time (t) raised to an exponent (),
(4)
where was fitted to be 0.49 for the data in Figure 1(a) with an R2 value of 0.975 using a least squares fit. Since = 1/df this fit provides a fractal dimension of 2.0, which is closer to RLCA aggregation kinetics.[2] It is appeared that the reaction had begun to turnover from RLCA to DLCA between 30 min and 75 min into the reaction, thereby lowering the fractal dimension below predicted RLCA values, since fitting only the first 30 min of data in Figure 1(a) using equation (4) led to an of 0.56 with an R2 value of 0.977, corresponding to a fractal dimension of 1.8 and therefore DLCA kinetics at the earliest stages.
Classical DLVO theory[4] shows that colloidal stability is derived from the sum of the van der Waals attractive forces (Ua) and the electrostatic repulsive forces(Uer),
(5)
The electrostatic repulsive forces are dependent upon the Debye length, -1. The Debye length was the charge screening length, or the distance at which charge screening or shielding became significant. In other words, if a particle is a distance less than -1 away from a second particle, then the second particle “feels” the repulsive force from the charge of the first. If the composition of a solution is known, -1 can be calculated analytically using the Debye-Hückel equation,[5]
(6)
for N charges, with each i charged species of number concentration ni and charge zi, at thermodynamic temperature T, where e, rs, and 0are the elementary charge, relative permittivity of the medium, and electric constant or vacuum permittivity, respectively. Therefore, the composition and concentration of the electrolytes in the colloidal solution will feed into the rate of aggregation, as equations (6), (5), and (3) all feed into equation (2). For the case of Figure 3, the colloidal stability of AgNPs in various concentrations of NaCl, the -1 at each of the NaCl concentrations are summarized in Table 1. As would be expected, when -1 is close to or less than twice the diameter of the AgNP, aggregation is very rapid for citrate AgNPs which follow DLCA kinetics, suggesting that there is negligible repulsive force between AgNPs. When -1 is greater than twice the diameter of the citrate AgNP or when there is some steric repulsive force provided by a bulky biocompatible coating such as BSA protein, the AgNPs are more stable and follow RLCA kinetics, which is in agreement with having a repulsive energy barrier between AgNPs that is large enough to provide colloidal stabilization against most inter-particle collisions but that is possible to overcome in some cases.
Similar concentration-dependent results were found for monobasic sodium phosphate in that above a critical concentration, which was less than the concentration for NaCl due to phosphate having a greater ionic charge, citrate AgNPs were unstable in less than one hour. Based on this data it appears that the phosphate concentration played a bigger role than the phosphate counter-ion effects, which will be discussed later.
From Figure 3(b), the BSA coating significantly reduced rates of aggregation compared to citrate AgNPs. The effects of charge screening were reduced significantly by the BSA coating. BSA AgNPs had a half-life of about 15 h even in 154 mmol·L-1 NaCl solutions, compared to about 15 min for citrate AgNPs. In the case of the BSA AgNPs, equation (5) should be modified to include an additional term to account for the contribution of steric repulsion, Usr, towards the colloidal stabilization of AgNPs.
U = Ua + Uer + Usr(7)
Thus, the BSA provided an increased stabilization against aggregation compared to citrate, due to the added steric stabilization provided by the high molecular weight (approximately 66 kDa[6]) of the BSA coating on the AgNPs.
Table SI-1. Debye Length for NaCl concentrations used.
NaCl concentration (mmol·L-1) / Debye Length (nm)1 / 305
5 / 136
10 / 96.3
50 / 43.1
100 / 30.5
154 / 24.5
Formulations of pH buffers
Fisher Stock # / Buf-fer pHSB96 / 2 / Water / 99.43% / KCl / 0.40% / HCl / 0.10% / MeOH / 0.02% / HCOH / 0.05%
SB97 / 3 / Water / 98.86% / HCl / 0.07% / KHP / 1.00% / MeOH / 0.02% / HCOH / 0.05%
SB98 / 4 / Water / 98.93% / KHP / 1.00% / MeOH / 0.02% / HCOH / 0.05%
SB108 / 7 / Water / 99% / KH2PO4 / <1% / NaOH / <1%
SB114 / 9 / Water / 99.17% / Na4 EDTA / 0.03% / NaOH / 0.10% / KCl / 0.40% / Boric Acid / 0.30%
SB116 / 10 / Water / 97.80% / Potassium Carbonate / 0.60% / KOH / 0.20% / Na2 EDTA *2H2O / 1.00% / Potassium Borate / 0.40%
KHP = Potassium Hydrogen Phthalate; MeOH = methyl alcohol; HCOH=formaldehyde; EDTA = ethylenediamenetetraacetic acid;
Imagine for a moment a hypothetical scenario wherein oral ingestion was a route of exposure to NPs, a range of pH conditions could possibly be encountered. Gastric juices in the stomach can be as acidic as pH 2, and food that travels through to the intestines experiences increasing alkalinity to pH 8 or 9. If NPs were then adsorbed into the bloodstream, a pH of 7.4, and managed to enter a cell, perhaps by endocytosis and ultimately a lysosome, a mildly acidic environment of pH 4.5 would be encountered also.
Composition of buffers
The composition of 1X PBS used in this study was 154 mmol·L-1 NaCl, 1.058 mmol·L-1 K2HPO4, 5.600 mmol·L-1 Na2HPO4, dissolved in distilled water.
Note, 1X PBS compositions commercially available were found to range from 137 mmol·L-1 to 154 mmol·L-1 sodium chloride (NaCl) concentration, 0 mmol·L-1 to 2.7 mmol·L-1 potassium chloride, and either 5.6002 mmol·L-1 monobasic sodium phosphate (Na2HPO4) with 1.058 mmol·L-1 monobasic potassium phosphate (K2HPO4) or an unspecified total of 11.9 mmol·L-1 of monobasic and dibasic sodium or potassium phosphates.
The concentration dependence of colloidal stability of citrate AgNPs, nominally 20 nm, in NaH2PO4. There were transient increases in the observed absorbance values at later times in many of the samples studied that manifested via increased uncertainty at later times in many experiments. These increased uncertainties were likely due to the evolution of bubbles in the cuvettes, visually observed after removal of the cuvettes from the spectrometer at the experiments’ completion, that likely formed as a consequence of not degassing the solvents. However, by averaging the data from no less than three trials of the experiment the noise from these stochastic interferences was significantly reduced.
Figure SI-1.
Figure SI-1. Black = 5.600 mmol·L-1 NaH2PO4 + 1.6mM KH2PO4 (1X PBS phosphate mix without NaCl), red = 5.600 mmol·L-1 NaH2PO4, green = 0.0100 mmol·L-1 NaH2PO4, yellow = 0.100 mmol·L-1 NaH2PO4, blue = 0.500 mmol·L-1 NaH2PO4, pink = 1.00 mmol·L-1 NaH2PO4, teal = 5.00 mmol·L-1 NaH2PO4, gray = 10.0 mmol·L-1 NaH2PO4. Data points in this plot were from one representative UV-Vis experiment.
Formulations of Cell Culture Media used
*Note, the number of decimal places reported here are the same used by the vendor. No effort was made to confirm that the correct number of significant figures were reported.
Cat# / 12-169F / 30585 / 30607Vendor / Lonza / Hyclone / Hyclone
Paper Abbv: / AMEM / DHM / DHG
Constituent: / mgL-1 / mg L-1 / mgL-1
CaCl2•2H2O / 265.00
CaCl2 (anhydrous) / 200.0000 / 200.0000
Fe(NO3) •9H2O / 0.1000 / 0.1000
KCl / 400.00 / 400.0000 / 400.0000
MgSO4•7H2O / 200.00
MgSO4 (anhydrous) / 97.6700 / 97.6700
NaCl / 6800.00 / 6400.0000 / 6400.0000
NaHCO3 / 2200.00 / 3700.0000 / 3700.0000
NaH2PO4•7H2O / 140.00
NaH2PO4•H2O / 125.0000
Glucose / 1000.00
D-Glucose / 4500.0000 / 4500.0000
Lipoic Acid / 0.20
Phenol Red•Na / 10.00 / 15.9000
Sodium Pyruvate / 110.00 / 110.0000
L-arginine / 25.00
L-arginine•HCl / 126.40 / 84.0000 / 84.0000
L-asparagine•H2O / 50.00
L-aspartic Acid / 30.00
cysteine•HCl•H2O / 100.00
L-cysteine / 24.00
L-cysteine•2HCl / 62.5700 / 62.5700
L-glutamic Acid / 75.00
glycine / 50.00 / 30.0000 / 30.0000
L-histidine•HCl•H2O / 42.00 / 42.0000 / 42.0000
L-isoleucine / 52.40 / 104.8000 / 104.8000
L-leucine / 52.40 / 104.8000 / 104.8000
L-lysine•HCl / 73.00 / 146.2000 / 146.2000
L-methionine / 15.00 / 30.0000 / 30.0000
L-phenylalanine / 33.00 / 66.0000 / 66.0000
L-proline / 40.00
L-serine / 25.00 / 42.0000 / 42.0000
L-threonine / 47.60 / 95.2000 / 95.2000
L-tryptophan / 10.20 / 16.0000 / 16.0000
L-tyrosine / 36.20
L-tyrosine•2Na•2H2O / 103.7900 / 103.7900
L-valine / 46.80 / 93.6000 / 93.6000
ascorbic acid / 50.00
D-biotin / 0.10
D-Ca panthothenate / 1.00 / 4.0000 / 4.0000
choline chloride / 1.00 / 4.0000 / 4.0000
folic acid / 1.00 / 4.0000 / 4.0000
i-Inositol / 2.00
myo-inositol / 7.0000 / 7.0000
niacinamide / 4.0000 / 4.0000
nicotinamide / 1.00
pyridoxal•HCl / 1.00
pyridoxine•HCl / 4.0000 / 4.0000
riboflavin / 0.10 / 0.4000 / 0.4000
thiamine•HCl / 1.00 / 4.0000 / 4.0000
vitamin B12 / 1.33
Constituent / mg/L / mg/L / mg/L
Paper Abbv / AMEM / DHM / DHG
Reference List
[1]R.Prasher, P.E.Phelan and P.Bhattacharya, Nano Letters 6 (2006) 1529-1534.
[2]M.Y.Lin, H.M.Lindsay, D.A.Weitz, R.C.Ball, R.Klein and P.Meakin, Nature 339 (1989) 360-362.
[3]F.Zhang, D.Dressen, M.Skoda, R.Jacobs, S.Zorn, R.Martin, C.Martin, G.Clark and F.Schreiber, European Biophysics Journal 37 (2008) 551-561.
[4]E.J.W.Verwey and J.Th.G.Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1948).
[5]D.Y.C.Chan, P.Linse and S.N.Petris, Langmuir 17 (2001) 4202-4210.
[6] in: Standard Reference Material 927d, Bovine Serum Albumin (7 % Solution), 2006) pp. 1-5.
[7]M.D.Malinsky, K.L.Kelly, G.C.Schatz and R.P.Van Duyne, Journal of the American Chemical Society 123 (2001) 1471-1482.
[8]J.Duan, K.Park, R.I.MacCuspie, R.A.Vaia and R.Pachter, The Journal of Physical Chemistry C 113 (2009) 15524-15532.
[9]J.K.Daniels and G.Chumanov, Journal of Electroanalytical Chemistry 575 (2005) 203-209.