026 Van der Meeren

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					    026 Accurate particle size distribution determination by
Nanoparticle Tracking Analysis based on 2-D Brownian dynamics
                                       Hans Saveyn1, Bernard De Baets2, Patrick Hole3, Jonathan Smith3 and Paul Van der Meeren1

                                   Particle and Interfacial Technology Group, Ghent University, Coupure Links 653, B-9000 Gent (Belgium)

                  Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure Links 653, B-9000 Gent

                             NanoSight Ltd., 2 Centre One, Lysander Way, Old Sarum Park, Salisbury, Wiltshire SP4 6BU (United Kingdom)



During the last years, nanoparticles are becoming increasingly important in various applications, e.g. ranging from chemical
mechanical polishing over sunscreens to pharmaceutical nanosuspensions. In all of these applications, the particle size
distribution is of utmost importance since it determines not only the efficacy of these products, but may also affect adverse (e.g.
ecotoxicological) effects.

For several decades, dynamic light scattering (DLS) has been the method of choice for the rapid characterisation of the size
distribution of submicron suspended particles. Recently, Nanoparticle Tracking Analysis (NTA) has been introduced as an
alternative technique for dispersed submicron particles (Malloy & Car, 2006). Hereby, the particle size is derived from the average
displacement between successive photos due to Brownian motion (Fig.1). As compared to DLS, NTA has the advantage that it
has a higher resolution for multimodal samples. In addition, it provides direct visual information from which aggregation
                                                                                phenomena are visually observable. On the other
                                                                                hand, measurements on monomodal latex
                                                                                dispersions revealed that the particle size
                                                                                distribution width is largely overestimated. It is
                                                                                the purpose of this paper to overcome this
     70                                                                         limitation based on a thorough analysis and

                                                                                simulation of the 2-D Brownian motion of
                                                                                dispersed particles.

              60                                                                                               Figure 1. Experimentally determined track,
                                                                                                               consisting of 37 subsequent steps (of each 33
                                                                                                               ms), of a 100 nm latex particle in Brownian
                                                                                                               motion in water of 20.5 °C as determined by the
                                                                                                               LM10 (Nanosight) system. The track length is the
                250                     260            270                280           290           300
                                                                                                               summation of all 37 individual step lengths,
                                                                                                               whereas the average step length corresponds to
                                                                                                               the track length divided by the number of steps.

First of all, the 2-D displacement of monomodal particles in Brownian motion was simulated. Hereby, the track length, i.e. the
cumulative distance moved in subsequent intervals of 33 ms was determined. Dividing the track length by the number of steps in
the track, a step length distribution is obtained. Figure 2 reveals that the average value of the step length distribution is not
affected by the number of steps, whereas its distribution width is gradually reduced. However, even considering tracks of 20
steps, a significant broadening around the average value is predicted, even though all particles were assumed to be perfectly
identical spheres. As a further consequence of the width of the step length distribution, a particle size distribution of overestimated
width is obtained. The simulated results were confirmed by experimental data, whereby the apparent particle size distribution was
obtained as a function of the track length.

                                                                                                                    Figure 2. Simulated average step length
                   0.3                                                                                              distribution (within a period of 33 ms) of
                                                                                                                    125 nm particles in water of 25 °C as a
                                                                                               1 step               function of the number of steps within the
                  0.25                                                                         5 steps              track.
                                                                                               10 steps
                   0.2                                                                         15 steps             In a second part, the average step length

                                                                                               20 steps             distribution was simulated for a specified
                                                                                                                    particle size distribution on the one hand,
                  0.15                                                                                              as well as for a given distribution of the
                                                                                                                    number of steps within the tracks on the
                                                                                                                    other hand. Optimisation of the fit of this
                                                                                                                    simulated average step length distribution
                                                                                                                    to the experimentally determined step
                  0.05                                                                                              length distribution yields a reliable estimate
                                                                                                                    of the average as well as (true) width of the
                                                                                                                    particle size distribution. This curve fitting
                    0                                                                                               approach, based on a physical model, not
                         0                    500                  1000                 1500                2000
                                                    AVERAGE STEP LENGTH (nm)
only enables an accurate determination of the particle size distribution width. In addition, it also enables to obtain more reliable
results since all tracks (rather than a limited sub-set of sufficiently long tracks) may be used during data-analysis.

In conclusion, a physical model is presented to simulate the average step length distribution during Nanoparticle Tracking
Analysis experiments as a function of the particle size distribution and the distribution that describes the number of steps within
the tracks. Based on this model, inversion of the experimentally determined step length distribution allows one to obtain a much
more reliable estimation of both the average size and the distribution width, thereby avoiding the artificial broadening of
experimentally determined particle size distributions, as was observed up to now.

MALLOY,A. AND CARR,B. (2006). Nanoparticle tracking analysis – The Halo ™ system. Particle & Particle Systems
Characterization, 23, pp. 197

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