Brownian Motion

What is Brownian Motion and Why Is It Important?

In 1827, Scottish botanist Robert Brown looked through a microscope at pollen grains suspended in water, and discovered the pollen was moving in a random fashion – tiny particles did not slow or stop, but were in constant motion. This phenomenon, we now call Brownian Motion, is not unique to pollen but is commonly observable in daily life. It is not specific to biology either but instead has been proven mathematically and is due to physics. Most people might have noticed dust particles dancing in a ray of light in a dark room or the diffusion of pollutants/smoke in the air or diffusion of calcium in bones – these are all examples of Brownian motion. 

Brownian motion is the random movement of particles due to the bombardment by the molecules that surround them. Understanding Brownian motion is important because it provides us with the evidence that atoms exist. Einstein’s mathematical model of Brownian motion from 1905 is one of his least well known but very important contributions to physics. It described how tiny visible particles suspended in a liquid are bombarded or moved by invisible water molecules around them causing them to jiggle. The model explained this motion in detail and was able to accurately predict the irregular random motions of the particles which could be directly observed under a microscope. Einstein’s theory of Brownian motion offered a way to prove that molecules exist despite the fact that molecules are too small to be seen directly. Soon after a French physicist J.B. Perrin conducted a series of experiments that confirmed Einstein’s predictions. The theory also helped to understand how particle size is related to their speed of movement. 

What causes Brownian motion?

While Brownian motion of small particles has been observed quite easily using a light microscope and studied for the past 200 years, the mechanism that drives Brownian motion is not well understood. What we do know is that Brownian motion is caused both by the structure and physics of fluids, i.e., liquids and gases. According to kinetic theory as proposed by J.C. Maxwell, L. Boltzmann and R.J.E. Clausius, all matter is in motion; atoms and molecules especially within liquids and gases are in constant vibrating motion. These particles will travel in straight lines until redirected by a collision. Particles within gases and liquids are constantly moving, colliding, and moving toward equilibrium.  

There are mainly 4 factors that affect Brownian motion: temperature, particle number, particle size, and viscosity. The larger the particle or molecule and the more viscous the dispersion medium, the slower the Brownian motion will be. Smaller particles are “kicked” further by the solvent molecules and move more rapidly. In addition, a high temperature and a high number of particles, all increase the rate of motion.

How do you measure Brownian motion?

Given particle speed of movement or Brownian motion can be correlated to particle size, various analytical measurement techniques have been developed that exploit this relationship. 

Dynamic Light Scattering (DLS) – Malvern Zetasizer

Dynamic light scattering measures Brownian motion and relates this to the size of the particles. DLS, sometimes referred to as Photon Correlation Spectroscopy or Quasi Elastic Light Scattering (QELS), is a non-invasive, well-established technique for measuring the size and size distribution of molecules and particles dispersed in a liquid typically in the submicron region and extending to lower than 1nm using the latest technology pioneered by the manufacturer MalvernPanalytical. Typical applications of dynamic light scattering are the characterisation of particles, emulsions or molecules which have been dispersed or dissolved in a liquid. Common samples analysed by DLS include colloidal silica, titanium dioxide, ceramics, carbon dots, lipid nanoparticles, proteins and adeno-associated virus (AAV). The sensitivity of modern systems is such that it can also be used to measure the size and concentration of macromolecules in solution with little dilution using small sample volumes (3µL). 

The Malvern Zetasizer which utilises sophisticated DLS technology works by determining the rate at which the intensity of the scattered light fluctuates when detected using an optical arrangement. Briefly, a cuvette containing particles in suspension (moving under Brownian motion) is illuminated by a laser causing the light to be scattered at different intensities. The small particles cause the intensity to fluctuate more rapidly than the large ones. Analysis of the intensity fluctuations yields the velocity of the Brownian motion and hence the particle size which is measured as the hydrodynamic diameter. 

The speed of movement of particles or velocity of the Brownian motion is defined by a property known as the translational diffusion coefficient. The size of the particle or the diameter that is obtained by DLS indicates how a particle diffuses within a fluid and is essentially related to the diameter of a sphere that has the same translational diffusion coefficient as the particle.

The size of a particle is calculated from the translational diffusion coefficient by using the Stokes-Einstein equation;

d(H)= kT/3πηD

where:-

d(H) = hydrodynamic diameter

D = translational diffusion coefficient

k = Boltzmann’s constant

T = absolute temperature

η = viscosity

Factors that can affect the velocity of Brownian motion

A number of factors can affect the accuracy and precision of DLS measurements, including temperature stability and accuracy. An accurately known temperature is necessary for DLS because knowledge of the viscosity is required (because the viscosity of a liquid is related to its temperature). The temperature also needs to be stable, otherwise convection currents in the sample will cause non-random movements that will impact the correct interpretation of size.

The measurement of the particle translational diffusion coefficient will depend not only on the size of the particle “core”, but also on any surface structure that will affect the diffusion speed, as well as the concentration and type of ions in the medium. The ions in the medium and the total ionic concentration can affect the particle diffusion speed by changing the thickness of the electric double layer which is called the Debye length. A low conductivity medium will produce an extended double layer of ions around the particle, reducing the diffusion speed and resulting in a larger, apparent hydrodynamic diameter. Conversely, higher conductivity media will suppress the electrical double layer reducing the measured hydrodynamic diameter. Any change to the surface of a particle that affects the diffusion speed will correspondingly change the apparent size of the particle. Similarly, an adsorbed polymer layer projecting out into the medium will reduce the diffusion speed more than if the polymer is lying flat on the surface. The nature of the surface and the polymer, as well as the ionic concentration of the medium can affect the polymer conformation, which in turn can change the apparent size by several nanometers.

DLS will not be applicable when the particle motion is not random. Therefore the maximum particle size that can be measured reliably by DLS is sample dependent and is normally defined by the onset of particle sedimentation. All particles will sediment and the rate will depend upon the particle size and relative densities of the particles and suspending medium. For successful DLS measurements, the rate of sedimentation should be much slower than the rate of diffusion since a consequence of slow diffusion is long measurement times. The presence of sedimentation can be determined using the Malvern Zetasizer by checking the stability of the count rate from repeat measurements of the same sample. Count rates which are decreasing with successive measurements indicates that sedimentation is present and the Expert Advice system will highlight this to the user.

Nanoparticle Tracking Analysis (NTA) – New Malvern NanoSight Pro

The advent of advanced computer technology with video analysis has allowed scientists to make automated measurements with visual validation to understand the dynamics of the motion and more accurately quantify the particles in a suspension. 

Nanoparticle tracking analysis (NTA) utilises the properties of both light scattering and Brownian motion to obtain the particle size distribution of samples in liquid suspension.  Simply, a laser beam is passed through the sample chamber, and the particles in suspension in the path of this beam scatter light in such a manner that they can easily be visualised via a microscope onto which is mounted a camera. The camera captures video files of the particles moving under Brownian motion within the field of view. Intuitive software simultaneously identifies and tracks the center of each of the observed particles, and determines the average speed moved by each particle. This value allows the particle diffusion coefficient to be determined from which, if the sample temperature and solvent viscosity are known, the sphere-equivalent hydrodynamic diameter of the particles can be identified using the Stokes-Einstein equation. 

Both NanoSight NTA and Zetasizer DLS measure the diffusion coefficient and derive the size from that diffusion coefficient. DLS provides excellent population statistics for an average size (by intensity) and average size distribution or polydispersity index. NTA on the other hand provides single particle tracking for a highly peak-resolved distribution by number combined with concentration determination and a fluorescence mode allows differentiation of suitably labelled particles. For biomedical research, using a fluorescently tagged drug molecule makes it possible to determine how many drug delivery nanoparticles had successfully been loaded with drug molecules. Integrating a combination of both DLS and NTA systems can help take advantage of the complementary information the two techniques can provide.

The new NanoSight Pro nanoparticle tracking analysis (NTA) system from Malvern Panalytical integrates advanced engineering with machine learning to provide the most detailed NTA solution for the characterization of bio- and nanomaterials.  Smart tools built into the software automate workflows and help remove subjectivity to generate extremely accurate and reproducible size and concentration data. An upgraded temperature controller allows stress and aggregation studies to be performed at up to 70°C. Advances in fluorescence measurement provide powerful insights into sample specificity while opening new possibilities in diagnostic, biomarker analysis and therapy applications. Previous limitations linked to small biological particles and other low scatterers are overcome by NanoSight Pro, which is optimised for use with samples including exosomes, viruses, vaccines, and drug delivery systems.

Ensure High Quality in Analytical Characterisation with ATA Scientific

NanoSight is already trusted by scientists around the world for its superior data quality and ease of use, with thousands of publications referring to NanoSight NTA data. As the world continues on it’s journey into developing better products to improve our daily lives especially related to research focused on drug delivery, viruses and vaccines, high-quality analytical characterisation is now even more important. Contact us for a free demonstration to discover how we can help you achieve more.