Supplementary information:
1. Calculation of PDI and SD from TEM data
Our TEM calculation of PDI is based on analogy to organic polymer chemistry (see Methods section), in which average molecular weights can be measured based on either weight averages or number averages, and the breadth of the statistical distribution is defined as:
PDI=weight average molecular weight/number average molecular weight = MW/MN.
For references see the classical textbook by Hiemenz (1984).
The PDI is normally stated when nanoparticle sizes are under discussion, but the CV provides the major direct parameter for comparison with data obtained by other methods, and is easily converted to Standard Deviation σ by use of the formulae:
CV = and CV = σ / n.
In this notation, the Standard Deviation σ is defined as:
σ=MN.[]=MN.[]
In our adapted version, σ=MN.[]=MN.[].
It follows that the Coefficient of Variation CV = σ / n can be stated as a formula containing the PDI: CV== in polymer chemistry. In our adapted version this becomes: CV==.
2. Accuracy of PCS measurements
PCS digitally measures the intensity fluctuations of light scattered by particles moving erratically in the suspension; these fluctuations are shorter for smaller particles because these diffuse more quickly. During a single sampling period, multiple measurements are taken of the intensity of the scattered light, and for each sampling period the intensity-intensity autocorrelation function is calculated. This function determines the correlations between the measurements of the fluctuating signal. Since the particle positions and velocities change erratically with time as the sample period proceeds, they bear decreasing resemblance to the initial values of the sample period, so the correlations fade away exponentially with a characteristic decay time . The parameter , representing half the characteristic decay time of the autocorrelation, =/2, combines the particle movements with their light-scattering properties: =DK2. It can be calculated by several methods (Chu, 1974; Chu et al., 1979; Goll & Stock, 1977; Ostrowsky et al., 1981; Provencher, 1979), but commonly a cumulative Gaussian analysis (Frisken, 2001; Koppel, 1972) is used. In the equation, D represents the diffusivity (or Z-average diffusion coefficient) of the particles, as given by the Stokes-Einstein equation: D=, where k is the Boltzmann constant, T is the temperature in degrees Kelvin, is the viscosity and r is the particles' (mean) radius. The light-scattering properties of the particles are denoted in the equation by K, which represents the light scattering vector: K=4..(n/).sin(/2), where n is the refractive index of the medium, the wavelength of the (laser) light employed, and the scattering angle. The radius of the light-scattering particles is therefore defined by the equation . It is evident from this equation that the accuracy of the results obtained for nanoparticle size depends critically on including in the calculations the correct values for several physical parameters, including the temperature, the viscosity and refractive index of the medium in which the particles are suspended, the wavelength and scattering angle of the laser light and its measurement; the laser source employed must remain stable, and the temperature constant, throughout the measurement. Although the results depend critically on these parameters, their precise values are generally not available (e.g., viscosity and refractive index of the medium) and approximate values are entered into the calculation. As a result, higher accuracy is most easily obtained by measuring calibration particles (see for example Chang et al., 1982). In practice however, calibration measurements are generally omitted and the results are accepted as generated from the approximate parameters. In addition to these sources of error, PCS is extremely sensitive to small changes in the proportion of large (non-Rayleigh-scattering) particles in the preparation (Chang et al., 1982; Goll et al., 1982), for example aggregates of nanoparticles.