Static Light Scattering (SLS) is a technique used to determine the size and shape of particles in a sample based on how they scatter light at various angles. Unlike Dynamic Light Scattering (DLS), SLS measures the intensity of scattered light at different angles but does not focus on time-dependent fluctuations, making it more suitable for analyzing larger or non-Brownian particles.

The intensity of scattered light in SLS can be related to the size of the particles through the Rayleigh-Debye scattering equation for spherical particles, or more generally, through models like Mie Theory.

🗯️MATLAB snippet

Here’s a basic guide to simulating static light scattering in MATLAB, focusing on spherical particles using a simplified Rayleigh or Mie scattering approximation.

Key Concepts of Static Light Scattering:

1. Scattering Intensity: The scattering intensity depends on the particle size, the wavelength of light, and the scattering angle.
2. Rayleigh Scattering: For particles much smaller than the wavelength of light, the scattering intensity is inversely proportional to the fourth power of the wavelength.
3. Mie Theory: For particles comparable in size to the wavelength of light, Mie theory is used to compute the scattering cross-section and scattering angle dependence.

Example MATLAB Code for Mie Scattering:

The following MATLAB code demonstrates static light scattering for spherical particles using Mie theory. We'll use the MieScattering function from the MiePlot MATLAB package, or an approximation for small particles (Rayleigh scattering).

Step 1: Install the Mie Theory Function

You can use a Mie scattering function available in the MATLAB File Exchange (e.g., mie.m), or you can implement a basic scattering model.

Step 2: MATLAB Code Example for Static Light Scattering:

 % Static Light Scattering Simulation in MATLAB
 ​
 % Constants
 wavelength = 650e-9;  % Wavelength of light (650 nm)
 radius = 100e-9;     % Particle radius (100 nm)
 angle_range = linspace(0, pi, 180);  % Scattering angle range from 0 to 180 degrees
 ​
 % Refractive index of the particle (e.g., silica)
 n_particle = 1.45;
 ​
 % Refractive index of the medium (e.g., water)
 n_medium = 1.33;
 ​
 % Size parameter (dimensionless)
 size_parameter = (2 * pi * radius) / wavelength;
 ​
 % Calculate the scattering intensity (simplified model for Rayleigh scattering)
 % The Rayleigh scattering intensity is proportional to (sin(θ))^2 / λ^4 for small particles
 intensity_rayleigh = (sin(angle_range).^2) / wavelength^4;
 ​
 % Plot the scattering intensity as a function of angle
 figure;
 polarplot(angle_range, intensity_rayleigh, 'LineWidth', 2);
 title('Rayleigh Scattering Pattern');
 ax = gca;
 ax.ThetaTickLabel = {'0', '30', '60', '90', '120', '150', '180'};
 ax.ThetaTick = 0:30:180;
 ax.RLim = [0, max(intensity_rayleigh)*1.2];
 ​
 % If using Mie scattering, you can implement Mie theory functions or
 % use the MiePlot package to calculate the intensity for a more complex
 % particle size and refractive index dependency.

Explanation:

• Wavelength and Radius: We define the wavelength of the light and the particle size. The wavelength is typically in the visible spectrum, while the radius is set for a nanoparticle.
• Size Parameter: The size parameter ( $x = \frac{2\pi r}{\lambda}$ ) is used to calculate the scattering behavior.
• Rayleigh Approximation: The formula used here for Rayleigh scattering is simplified for small particles. The scattering intensity depends on the angle ( $\theta$ ) and wavelength ( $\lambda$ ).
• Polar Plot: The polarplot function in MATLAB is used to plot the scattering intensity as a function of angle.

Step 3: Running the Code