NTA is an open source Nanoparticle Tracking Analysis package for R.
A laser beam is passed through a prism and into the particle suspension. The particles scatter the laser beam, which allows for detection via a CCD, EMCCD or CMOS camera sensor. The camera captures a video of the particles moving in Brownian motion.
Image analysis on a frame by frame basis allows for tracking of particles. The average distance travelled by each particle is calculated on the x and y axis. These values allow the particle diffusion coefficient (Dt) to be determined. If the sample temperature (T) and solvent viscosity (η) are known, then the sphere-equivalent diameter (d) of the particles can be identified using the Stokes-Einstein equation:
Dt = (T * Kb) / (3 * π * η * d)
Where Kb is Boltzmann's constant.
The amount of light scattered by a particle in any given direction is a function of many variables, including incident illumination power, wavelength, angle and polarization, particle size, refractive index (real and imaginary) and shape, as well as solvent refractive index.
The theory of light scattering is well established (Bohren and Huffman, 1983; Kerker, 1969) and the formula for Rayleigh scattering of small particles of radius a, refractive index n1 in a liquid of refractive index n2 is given by:
I/Iin = ( (16 * π^4 * a^6) / (r^2 * λ^4) ) * ( (n^2 - 1) / (n^2 + 2) ) * sin(ψ)
Where λ is the wavelength of the incident light beam, n the relative refractive index (n2/n1), Iin is the incident power per unit area, I the scattered power per unit area a distance r from the scattering region and ψ is the angle between the input polarization and the scattering direction.
The total scattering (Iscat) into an aperture of collection angle θ (numerical aperture NA = sin θ) is then:
Iscat = ( (64 * π^4 * a^6) / (λ^4) ) * ( (n^2 - 1) / (n^2 + 2) ) * ηo * Iin
Where:
ηo = ( (1 - cos θ) / 4 ) + ( (1 - cos^3 θ) / 12 )
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