Dynamic Light Scattering

Mark Jarchow & Marty Reichert

Spring 2015

Abstract

The method of dynamic light scattering was used to examine the light scattered from 45° , 90° , and 135° angles with the aid of a mirror placed inside of a cuvette. By using a laser to illuminate a solution of polystyrene spheres suspended in water and analyzing the fluctuations in the intensity of the scattered light, the time constant could be measured and compared to a theoretical value. the experiment validtated the use of the mirror for a 45° degree angle, but more work is needed to definitively confirm the use of the mirror when examining an angle of 135°.

Introduction

When examining a system of particles suspended within a medium, dynamic light scattering is used to determine properties of the system such as the size of the particles, or the viscosity of the medium. In order to determine these properties, a laser is focused into the middle of a cuvette containing a medium, such as water, and the particles. The light scattered off of the particles is examined with the use of a photodetector, and then the method of autocorrelation is used to determine similarities in the fluctuations of the scattered light.

The cuvette was rectangular in shape which presented a problem when viewing angles other than 90° difficult to measure because the refraction of the light through both the glass and the medium had to be accounted for. The experiment examined a work around to this problem by using a mirror angled at 22.5° so that when measuring the 45° and 135° degree angles, the incoming light as well as the scattered light would pass through the cuvette normal to the plane of the glass.

Theory

Light incident upon a single particle, light will be scattered in all directions. When light is incident upon many particles in the same solution, light will be scattered off in all directions, each with the same intensity. However, because particles are distributed randomly throughout the medium, the light will hit each particle at a different phase, emitting scattered light that has the same magnitude, but a different phase from each particle. The light scattered off one particle will interfere constructively or destructively with the light scattered off of another particle close by. The overall scattered light from the system will fluctuate due to the constructive and destructive interference between all the particles within the system.

As the particles move throughout the medium, they undergo brownian motion. The diffusion of the particles is given by the Stokes-Einstein equation:

where k_B; is Boltzmann's constant, T is the temperature in kelvin, η is the viscosity of the medium, and r is the radius of the particle.

The scattering vector is defined as

The autocorrelation function was defined as

In short, the autocorrelation function measured the similarity between two points. The autocorrelation function could be approximated by

where

Methods and Apparatus

The Apparatus setup used in the lab consisted of a laser, which was collimated using an aperture and then passed through a 75mm converging lens to focus the light beam. The lens was placed on a translational table so that the focal of the lens could be adjusted depending on the angle which we were measuring. The focused light was sent through the center of a square cuvette which contained a mixture of 0.304 micron spheres suspended in water. A piece of tape which had a 0.5mm hole was placed on the side of the cuvette which faced the photodiode. The photodiode was placed 31 cm from the cuvette.

To examine scattering angles other than 90° with the square cuvette, a mirror was placed inside at a 22.5°, as shown below [original figure]. When measuring at a 45° and 135° angles, the scattered light would reflect off the mirror and exit the cuvette at 90°.

The incoming signal from the photodiode was passed through a current amplifier which was set to amplify the incoming signal by 1 micro A/V. The voltage amplifier then amplified the signal by a factor of 10^4 . Both the voltage amplifier and the current amplifier were set to pass only the frequencies between 3Hz and 3kHz.

A Labview program was used to collect the incoming data. The program was set to collect data at a sampling frequency of 100kHz for 2^16 samples, giving a data collection time of roughly 1.5 seconds. Labview was also used to perform the autocorrelation of the incoming signal. 200 data sets were taken by labview then lumped into 10 groups, each consisting of 20 data sets each. The 20 data sets within each group were averaged to give 10 averaged autocorrelations for each angle.

Picture showing the setup for the lab.

Picture showing the beam of light as it passes through the cuvette filled with the spheres.

Picture of the pattern made on the wall from the laser light passing through the cuvette.

Results and Conclusion

Results and Conclusion

An example of an average signal is shown below.

To analyze any background noise, two background tests were run. One test with the lights off in the room and the laser off to get the shot noise of the photodiode, and another with the laser on, with nothing but water in the cuvette. The unnormalized correlation plot of the background runs is shown along side with the unnormalized correlation plots of the 135°, and 90° scattering angles. The unnormalized correlation plot for the 45° scattering angle was too large to fit on the graph without dwarfing the other angles.

The results of the averaged, normalized correlation functions from the all three angles along with the predicted curves is shown below. Each line on the plot represents 20 averaged correlations for each angle.

Each of the averaged correlations were fitted to an exponential equation, y = A + Be^(C*x), where C was equal to τ_c. The results of the values determined in the fits, along with the accepted values are shown below.

The final results were obtained by taking the average of all the fit values for each angle, and the standard deviation gave the uncertainty. The results are shown in the table below.

The 45° scattering angle gave a result that was 2.1 standard deviations from the accepted value. The 90° scattering angle gave a result that was 2.6 standard deviations from the accepted value. The 135° scattering angle gave a result that was 0.75 standard deviations from the accepted value.

Although the results for the 135° scattering angle gave the closest results, after the average was taken, the plot of the values showed a very wide spread in the data which was concerning. Therefore, with the use of a mirror in the cuvette, we were able to study the 90°, and the 45° scattering angles but not the 135° angles.

We would like to thank our advisers William Zimmermann and Clement Pryke for their help throughout the semester.