Nanoparticle Trajectory Analysis

Nanoparticle trajectory analysis is a method for visualizing and studying nanoparticles in solutions developed by Nanosight (UK) ^[1] . It is based on the observation of the Brownian motion of individual nanoparticles, the speed of which depends on the viscosity and temperature of the liquid, as well as on the size and shape of the nanoparticle. This allows you to use this principle to measure the size of nanoparticles in colloidal solutions ^[2] ^[3] ^[4] ^[5] . In addition to size, it is simultaneously possible to measure the intensity of light scattering by an individual nanoparticle, which allows discriminating nanoparticles by their material. The third parameter measured is the concentration of each of the fractions of the nanoparticles.

The method is actively gaining popularity in the scientific community. Thus, at the beginning of autumn 2012, the number of scientific publications using the Nanoparticle Trajectory Analysis method reached 400 ^[6] , of which more than 100 - in 2012 alone.

Content

Physical basis of the method

Measurement scheme in the method of analyzing nanoparticle trajectories

A typical picture of radiation scattering on individual nanoparticles obtained in the method of analyzing the trajectories of nanoparticles (one frame of video)

A typical 2D trajectory of the Brownian motion of a single nanoparticle (screenshot of NTA Software 2.2 ^[7] ).

To visualize nanoparticles, their solution is illuminated with a focused laser beam. Separate nanoparticles with a size of less than a wavelength behave like spot diffusers. When observing the illuminated volume of the solution through an ultramicroscope from above, at right angles to the laser beam, individual nanoparticles look like bright dots against a dark background. A highly sensitive scientific camera records video of Brownian motion of such points. This video is transmitted in real time to a personal computer for processing: the selection of individual nanoparticles at each frame and the tracking of particle movements between frames.

The speed of Brownian motion, expressed as the rms displacement of a particle over a certain time, is related to the size of a particle by the Stokes-Einstein equation . Strictly speaking, two-dimensional (2D) particle diffusion is recorded in the Nanoparticle Trajectory Analysis method, but the independence of all three of its orthogonal components allows the equation to be rewritten in the following form, changing only the numerical coefficient:

{<(x,y)^{2}> \over 4}=D_{t}t={\frac {k_{B}Tt}{3\pi \eta d}},

{\ displaystyle {<(x, y) ^ {2}> \ over 4} = D_ {t} t = {\ frac {k_ {B} Tt} {3 \ pi \ eta d}},}

Where $<(x,y)^{2}>$ ${\ displaystyle <(x, y) ^ {2}>}$ - the average square of the displacement of the particle over time intervals $t$ ${\ displaystyle t}$ (duration of one video frame),

D_{t}

{\ displaystyle D_ {t}}

- the coefficient of translational (translational) diffusion,

k_{B}

{\ displaystyle k_ {B}}

- Boltzmann constant ,

T

{\ displaystyle T}

- absolute temperature

\eta

{\ displaystyle \ eta}

- fluid viscosity

d

{\ displaystyle d}

- hydrodynamic particle diameter.

With the accumulation of statistics on individual particles, it is summed up in the form of a histogram of a particle size distribution. The number of steps on the trajectories of nanoparticles can be different. At the same time, for too short paths (2-5 steps), the error in measuring the size is high due to low statistical confidence. Therefore, only particles with the number of steps that satisfy the requirements of the required accuracy of analysis are included in the histogram of the distribution of particle sizes.

In addition to the particle diameter calculated in this way, the scattering intensity of the same particle, averaged over all frames, is measured. These data can potentially be used to discriminate nanoparticles in a sample by their material, as well as to detect the presence of highly anisotropic nanoparticles (rods, tubes, plates).

Based on the known volume of the observation region and the number of particles counted in it, the absolute concentration of each fraction in pcs / ml is calculated.

Particle Size Range

The Nanoparticle Trajectory Analysis method can be used for colloidal solutions of particles ranging in size from 10 ^[8] to 1000 ^[2] nm . The range strongly depends on the nature of the particular sample. The lower limit is determined by the optical properties of the nanoparticle material ^[9] . Nanoparticles must diffuse enough light in order to be visible against the background noise. So, for gold and silver nanoparticles the lower limit is 10 nm, for oxide materials - 15-20 nm, for proteins and polymers - about 20-25 nm. The upper limit of the measurement range can be specified by a number of limiting factors:

Sedimentation stability of the colloidal system. With a high difference in the density of the material of the particles and the solution, particles with a size of less than 1000 nm will already quickly precipitate, preventing measurements.
The manifestation of significant anisotropy in the shape of the spot of scattered radiation due to the appearance of preferential directions of scattering.
In the absence of the mentioned restrictions, the upper limit of the range is set by the accuracy of measuring the position of the particle in individual frames in comparison with its displacement between frames. For a typical case of aqueous solutions, this limit is approximately 1000 nm, however, it can vary both upwards and downwards depending on the viscosity of the solvent used.

Discrimination of particles by their material

The dependence of the measured scattering intensity on the size for individual nanoparticles in the NTA method. The sample is a sol of MnO ₂ nanoparticles.

Picture of the dependence of the scattering intensity on the size in the presence of two types of particles in the solution.

The averaged scattering intensity measured for each particle can be used to discriminate nanoparticle fractions by material. For particles with a size much shorter than the wavelength, Rayleigh scattering law is valid. Intensity $I$ ${\ displaystyle I}$ radiation scattered by a particle with a diameter $d$ ${\ displaystyle d}$ depends on the following factors:

I=I_{0}{\frac {1+\cos ^{2}\theta }{2R^{2}}}\left({\frac {2\pi }{\lambda }}\right)^{4}\left({\frac {\left|m_{r}\right|^{2}-1}{\left|m_{r}\right|^{2}+2}}\right)^{2}\left({\frac {d}{2}}\right)^{6}

{\ displaystyle I = I_ {0} {\ frac {1+ \ cos ^ {2} \ theta} {2R ^ {2}}} \ left ({\ frac {2 \ pi} {\ lambda}} \ right ) ^ {4} \ left ({\ frac {\ left | m_ {r} \ right | ^ {2} -1} {\ left | m_ {r} \ right | ^ {2} +2}} \ right ) ^ {2} \ left ({\ frac {d} {2}} \ right) ^ {6}}

Where $I_{0}$ ${\ displaystyle I_ {0}}$ - intensity of incident unpolarized beam with wavelength $\lambda$ ${\ displaystyle \ lambda}$ ,

R

{\ displaystyle R}

- distance to particle,

\theta

{\ displaystyle \ theta}

- scattering angle

m_{r}

{\ displaystyle m_ {r}}

- the complex refractive index of the material particles relative to the solvent,

m_{r}=n_{r}-ik_{r}

{\ displaystyle m_ {r} = n_ {r} -ik_ {r}}

where

n_{r}

{\ displaystyle n_ {r}}

- the refractive index of the material particles relative to the solvent,

k_{r}

{\ displaystyle k_ {r}}

- relative absorption coefficient,

i

{\ displaystyle i}

- imaginary unit

$I_{0}$ ${\ displaystyle I_ {0}}$ , $R$ ${\ displaystyle R}$ , $\theta$ ${\ displaystyle \ theta}$ and $\lambda$ ${\ displaystyle \ lambda}$ are constant during the experiment for all particles, so the expression is simplified to

I\sim {d}^{6}R_{i}

{\ displaystyle I \ sim {d} ^ {6} R_ {i}}

Where $R_{i}$ ${\ displaystyle R_ {i}}$ - the scattering ability of the material particles, $R_{i}=\left({\frac {\left|m_{r}\right|^{2}-1}{\left|m_{r}\right|^{2}+2}}\right)^{2}$ ${\ displaystyle R_ {i} = \ left ({\ frac {\ left | m_ {r} \ right | ^ {2} -1} {\ left | m_ {r} \ right | ^ {2} +2} } \ right) ^ {2}}$

So on the chart $I(d)$ ${\ displaystyle I (d)}$ Particles consisting of the same material, with some experimental error, should fall on the curve $d^{6}$ ${\ displaystyle d ^ {6}}$ . In the presence of particles consisting of different materials, several groupings of points belonging to different curves will be observed on this graph ^[10] .

It should be noted that in practice the strict separation of the two branches related to different materials of particles is observed for several reasons quite rarely:

Significant variations in the measured intensity of particles due to the different location relative to the focal plane of the lens and the axis of the laser beam. This effect is the main source of experimental errors (spread of points) on the graphs $I(d)$ ${\ displaystyle I (d)}$ .
Camera pixel saturation (overexposure) for the central spot area of the brightest particles. This leads to the appearance of a plateau on a power dependence.
A continuous rather than a discrete change in the effective optical properties of the material of the particles or significant variations in their shape. In this case, there is not a power dependence, but a sector continuously filled with dots between two power functions.

Fluorescent particle analysis

Measurement scheme of fluorescent particles in the method of analysis of nanoparticle trajectories

When studying solutions of fluorescent nanoparticles, for example, quantum dots , latex nanoparticles with a fluorescent dye incorporated into the polymer or specifically fluorescently labeled biological nanoparticles ( exosomes , liposomes , virus particles , etc.), a special equipment configuration is used ^[11] ^[12] . A long-wavelength light filter is added between the sample and the video camera, cutting off the radiation elastically scattered by particles (with a laser wavelength). Thus, only fluorescent particles are recorded on video. This makes it possible to selectively study only the fraction of nanoparticles of interest to the researcher against the background of a significantly superior number of ordinary ones.

In the fluorescent mode, similarly to the basic configuration, the particle size distribution ^{[12] is} measured and their concentration is measured. Two consecutive measurements - one without, the other with a light filter - allow us to estimate the proportion of fluorescent particles in their total number.

Separately, it is worth noting that the method does not allow for the investigation of individual molecules of organic fluorescent dyes. For this purpose, fluorescence correlation spectroscopy is used .

Measurement $\zeta$ ${\ displaystyle \ zeta}$ $\ zeta$ -potential particles

Measurement Scheme

\zeta

{\ displaystyle \ zeta}

-potential in the method of analyzing nanoparticle trajectories.

The trajectory of the nanoparticle in the electric field

A modification of the nanoparticle trajectory analysis method, called Z-NTA, allows measurement $\zeta$ ${\ displaystyle \ zeta}$ -potential ^[approx. ^1] individual particles ^[13] . When a constant potential difference is applied to a solution, the nanoparticles in it begin to move from one electrode to another at a speed depending on their $\zeta$ ${\ displaystyle \ zeta}$ -potential. Average speed $<u>$ ${\ displaystyle <u>}$ in this direction is used to calculate $\zeta$ ${\ displaystyle \ zeta}$ -potential of each particle according to the Helmholtz-Smoluchowski equation:

\zeta \ ={\frac {4\pi \eta <u>}{\epsilon _{0}\epsilon E}},

{\ displaystyle \ zeta \ = {\ frac {4 \ pi \ eta <u>} {\ epsilon _ {0} \ epsilon E}},}

Where $\eta$ ${\ displaystyle \ eta}$ - fluid viscosity

\epsilon _{0}

{\ displaystyle \ epsilon _ {0}}

- electric constant ,

\epsilon

{\ displaystyle \ epsilon}

- the relative dielectric constant of the fluid,

E

{\ displaystyle E}

- electric field strength .

As already mentioned, the orthogonal components of the Brownian motion of particles are independent. Therefore, the random motion of a particle in the direction perpendicular to the directional electrophoretic one can be used to simultaneously measure its size.

This allows not only to obtain a histogram of the distribution of nanoparticles by $\zeta$ ${\ displaystyle \ zeta}$ -potentials, but also to study how it depends on the particle size ^[13] .

Notes

↑ The term electrokinetic potential is also used in the Russian literature.

Links

↑ Nanosight Ltd official website
↑ ¹ ² V. Filipe, A. Hawe, W. Jiskoot, "Critical evaluation of Nanoparticle Tracking Analysis (NTA) by NanoSight for the measurement of nanoparticles and protein aggregates" [1]
↑ Considerations in Particle Sizing. Part 2: Specifying a Particle Size Analyzer [2]
↑ I. V. Fedosov, I. S. Nefedov, B. N. Khlebtsov, V. V. Tuchin, “Measurement of the diffusion coefficient of nanoparticles by microscopy of selective planar illumination” [3] (not available link) DOI: 10.1134 / S0030400X09120030
ST ASTM E2834-12 Standard Guide for Nanoparticle Tracking Analysis (NTA) [4]
↑ List of publications in refereed journals and papers at conferences using the Nanoparticle Trajectory Analysis method Archived copy (Unsolved) (not available link) . Circulation date October 18, 2011. Archived October 17, 2011.
Nan Nanoparticle Tracking Analysis (NTA) software (Unreferenced) (not available link) . The appeal date was August 23, 2011. Archived July 14, 2011.
↑ 10 nm Silver Nanoparticles Imaged Moving under Brownian Motion
↑ Fundamental questions about NTA Archived July 14, 2011.
↑ D.Griffiths, P.Hole, J.Smith, A.Malloy, B.Carr "Size and Count of Nanoparticles by Scattering and Fluorescence Nanoparticle Tracking Analysis (NTA)" [5] (not available link)
↑ Visualization, Fluorescent and Fluorescently-Labelled Nanoparticles [6] Archive dated July 14, 2011 on Wayback Machine
² ¹ ² V.Filipe, R.Poole, M.Kutscher, K.Forier, K.Braeckmans, and W.Jiskoot "Fluorescence Single Particle Tracking" for Biological Fluids and Complex Formulations [7]
↑ ¹ ² Zeta Potential Analysis using Z-NTA (Unrefered) (inaccessible link) . The appeal date is September 7, 2011. Archived August 22, 2011.

Nanoparticle Trajectory Analysis

Content

Physical basis of the method

Particle Size Range

Discrimination of particles by their material

Fluorescent particle analysis

Measurement $\zeta$ ${\ displaystyle \ zeta}$ $\ zeta$ -potential particles

Notes

Links

See also

More articles:

Nanoparticle Trajectory Analysis

Content

Physical basis of the method

Particle Size Range

Discrimination of particles by their material

Fluorescent particle analysis

Measurementζ {\ displaystyle \ zeta} -potential particles

Notes

Links

See also

More articles:

Measurement $\zeta$ ${\ displaystyle \ zeta}$ $\ zeta$ -potential particles