Dynamic Light Scattering (DLS), Photon Correlation Spectroscopy (PCS), or Quasi-Elastic Light Scattering (QELS) – this technique goes by many names, but what does it measure, how is it measured, and what do the results mean? From John Tyndall’s early attempts in 1869 at explaining our world’s signature blue hue to Lord Rayleigh’s prompt answer two years later, the light scattering technique, specifically elastic light scattering, has ventured quite a long way with practical DLS applications in a variety of industries. This blog post serves to assess and assuage questions and concerns about this technique that truly puts an emphasis on dynamic.
Q: What is DLS?
A: Dynamic Light Scattering is a non-invasive technique that measures the size distribution of particles in a dispersion through passing a monochromatic light through a sample.
Q: What is a dispersion, and is it the same as a solution?
A: A solution is a “homogenous mixture of two or more substances in relative amounts that can be varied continuously up to what is called the limit of solubility.”[1] A dispersion is a heterogenous mixture, but due to the nature of materials in the nanometer range, often get mislabeled as solutions. Per NIH “Basically, dispersion and solubilization are different phenomena. Dispersion and solubilization can be defined as a system, in which particles of any nature (e.g., solid, liquid, or gas) are dispersed in a continuous phase of a different composition (or state) and a process, by which an agent increases the solubility or the rate of dissolution of a solid or liquid solute, respectively. Hence, in general, the dispersion of solute particles in solvents leads to the formation of colloids or dispersion, and solutions may be obtained as a result of solubilization of solute molecules or ions in the specified solvent. Furthermore, dispersion is mostly related to solute particles, whereas solubility or solubilization is generally connected with solute molecules or ions.”[2]
Q: What if I don’t have particles?
A: “Particle” as a term is loosely used in the field of particle size analysis. Any dispersed material; i.e. particle, emulsion droplet, globules, micelle, liposome, etc., will all be referred to as particles for the sake of simplicity in all further descriptions.
Q: How is it measured?
A: When a light source is passed through a sample, the dispersed particles interact with photons to create scattered light; this interaction is the basis of the signal DLS uses for analysis. If no signal is observed, then the sample might be a solution or the concentration may be too low. Dispersed particles will be moving in Brownian motion, which is, random movement of particles in a dispersion medium that is a result of the collision between carrier molecules with particles. As particles diffuse across a solution through Brownian motion, the assumed spherical particles cause a Doppler shift as photons interact with a sample’s electric field, changing the wavelength of the incoming light; this change is relative to the size of the particle.[3] In simple terms, fluctuations in scattered light can be used to generate a particle size distribution as the fluctuations are relative to the rate of motion which can be used to calculate the particles size; for example, smaller particles move faster than larger particles.
Using the Stokes-Einstein equation listed below, several factors are controlled in order to calculate the hydrodynamic diameter of a population of particles.
D_t=(TK_b)/3πɳd
Where: T= Temperature, Kb= Boltzmann constant, ɳ= viscosity, Dt= Translational diffusion coefficient, and d= hydrodynamic diameter
Based on this equation, there are two factors that are important to ensure that an accurate size result is obtained: temperature and viscosity. When analyzing samples by DLS, it is imperative that an accurate analysis temperature and sample viscosity, are utilized in the calculation.
Q: What does the instrument actually measure to get my particle size?
A: Because the theory behind DLS focuses on a particle’s interaction with photons (light), what is being measured is actually fluctuations of scattered light, which are used to calculate the hydrodynamic diameter. Each suspended particle has an ionic shell that surrounds it based on its net charge, which was previously described in our blog on zeta potential. This figure illustrates the ionic shell, double layer, which is highly exaggerated. This shell typically only constitutes a few nanometers of the overall hydrodynamic diameter.
Q: How does the ionic shell affect my particle size results?
A: To summarize the theory behind the electrical field of a particle using an excerpt from Jong Kim’s Electrical double layer: revisit based on boundary conditions, “When solid surface contacts an aqueous solution including the electrolyte, the solid surface becomes charged due to the difference of electron (or ion) affinities between the solid surface and the solution or the ionization of surface groups. In addition, the surface charges cause a special structure at the interface, so called the electrical double layer”[4] Put simply, as a particle migrates through a dispersion, there will be a double layer of ions, mostly opposite in charge, that surround the particle. This double layer of ions are relative to the surface charge of the particle. To clarify, an emulsion is not solid but continuous, and, yet, ionic layers still form around them based on their charge. The charge is typically imparted based on the stabilization materials such as micelles.
Knowing that the electrical double layer of the particle is of great importance when analyzing via DLS, it is thus imperative that the pH and conductivity of the sample dispersion medium be maintained lest the ionic shell or surface charge of the particle be changed, which would affect size results.
Q: What would impact the double layer?
A: Increasing or reducing the free ions in the dispersion medium. With the introduction of more free ions, for example, diluting with Phosphate Buffered Saline (PBS) when the sample is dispersed in water, a particle’s hydrodynamic diameter may increase due to the increased availability of free ions added to the electric double layer. Conversely, in the event that the free ion concentration is reduced, for example, if water is used to dilute a sample suspended in PBS, the double layer may be stripped. Thus, the double layer’s contribution to the hydrodynamic diameter would be reduced. Best practices are maintaining the ionic concentration of a sample while diluting when possible.
Q: How does the instrument take the fluctuations of light scatter and get translational diffusion coefficient or particle size?
A: Fluctuations in scattered light will produce an increased frequency with faster moving particles (smaller). An example below illustrates theoretical intensity fluctuations. The higher frequency on the right would indicate a faster particle.
Conversion of these intensity fluctuations to the translational diffusion coefficient needed to get an average hydrodynamic particle size requires an auto-correlation function. An auto-correlation function is simply copying the raw intensity fluctuations, shifting the copy over time, and comparing it to the original at each time increment.
From the auto-correlation function, a correlation curve can be generated by plotting the correlation of the base signal to the copy of the signal shifted at each time increment. In a correlation curve the length of correlation will be representative of the rate of diffusion or average hydrodynamic size. The rate of decay of the curve will relate to the broadness of the distribution.
The graphic here displays two correlation curves of two different sample sizes, the left being a sample with a smaller particle size, as evidenced by the top of the curve (correlation time) being shorter in length, and the right containing larger particulate, as evidenced by the longer correlation time. The diffusion information from these curves is what is directly used to generate an average hydrodynamic size.
Q: I have had DLS run on my sample before, and the results were on an intensity-weighted basis, what does that mean?
A: DLS analysis signal is largely affected by the size and concentration of particulate. Specifically, the size of an individual particle directly affects the amount of light scattered (signal) the particle contributes. Larger particulate will scatter more light, American Society for Testing and Materials (ASTM) dictates per ASTM E2490-09 (2021) 8.9.1, “as the intensity is proportional to d6 (or V2 or MW2). In simple terms if we have one 100 nm particle it is equivalent in intensity weighting terms to 1012 (1000 billion) 1 nm particles”. This means DLS will always be skewed by larger particles within the sample’s population.
The intensity weighting of DLS makes it highly sensitive to small populations of agglomerates, which can be used for screening of samples.
Q: I have done some work with Laser Diffraction in the past, and I always get my data with volume-weighting. Can DLS also produce volume-weighted data?
A: When it comes to particle size, there are typically three manners in which that data is presented: volume-weighed, intensity-weighted, or number-weighted. When looking at population statistics it is common to see data on a number weighted basis, each individual count has the same weighting. For example, if we count 100 particles and 10 of them are 100 nm, then 10% of the population would be attributed to 100 nm on a number weighted basis.
Volume-weighted results are not weighted by the individual counts of the particles, but instead by their spherical equivalent volume. Figure 1 is an illustration of the differences between number and volume-weighted results. Volume-weighted results are often desired in specific industries such as pharmaceuticals, as they reflect where most of the sample mass is within the population.
DLS can convert intensity results to volume results; however, per ASTM E2490-09 (2021), section 8.10.1 Conversion of the Intensity Distribution to Other Particle Size Distributions:
“In mathematical terms, this deconvolution is termed ill-posed or ill-conditioned that means, in practical terms that it is ill advised. Small changes in collected data can give rise to enormous changes in derived result and as such treat any derived result with caution and skepticism. To convert intensity to volume distribution would involve the manipulation of perfect noise-free data with accurately measured refractive indices using Mie Theory. A further conversion to number should never be attempted. If number distribution is desired then an instrument that collects such information should be used in the first place.”
Q: What information can DLS provide?
A: Based on the description of how DLS operates, it should be self-evident that DLS is most ideal for a monomodal population of particles. DLS is designed to give an average size and width, but has some ability to deconvolve the data into three populations for broader distributions. Per ASTM E2490-09 (2021) section 8.3.5:
“The deconvolution of a single (measured) exponential decay curve to a set of exponential curves, each corresponding to a single particle size, that sum to give the measured exponential is clearly an ill-conditioned problem and taking further terms beyond the fifth power (which would exactly fit six points or histogram bins if these were assumed) is usually meaningless as this degree of information is not inherent in the raw plot. Normally we do not go beyond the third term.”
This means DLS can provide an average and a width (polydispersity index) to a single population of particles or using alternative algorithms, averages and widths of up to three populations in a sample.
Q: What makes a sample not suitable for DLS?
A: The four main factors that may cause issues with DLS are the size of the particulate of interest, the broadness of the distributions, the signal a sample produces, and the viscosity of the carrier. Other factors can influence the results, but these are the main four that would determine suitability for the technique.
Q: What is an appropriate size range for DLS?
A: DLS is advertised by instrument manufactures to cover 1 nm to 10 µm. This range can be analyzed on DLS, but some of this range listed is better suited for other techniques. Since DLS evaluates particles freely moving in Brownian motion, larger particles may settle, which would be movement not dictated by Brownian motion. As a general rule, particles larger than 1 µm would be better suited to instruments that can maintain particle suspension. Techniques such as Image Analysis, Laser Diffraction, or Single Particle Optical Sensing, would be better suited to particles above 1 µm in size.
Q: How do I know if my sample is too broad for DLS?
A: One of the foremost factors is the Polydispersity Index, often referred to as PDI. PDI is a representation of the overall width of the analyzed distribution. It is what is used to determine if a single mean result should be used (PDI <0.2) or if alternative algorithms should be used to break down multiple populations (PDI ≥0.2). Per ASTM recommendation samples with PDI > 0.7 are not likely suitable for DLS. If your sample is approaching a PDI of 0.5 it might be worth considering a higher resolution technique like a particle counter.
Q: What concentration is appropriate for DLS?
A: The appropriate concentration will be relative to the size of the suspended particles. If you do not already know your particle size here are some techniques you can use to see if your sample might be suitable. First if the sample has some turbidity to it, then it might have sufficient concentration. Second if you pass a laser through your sample, as is shown here (left vial), and see a high amount of scatter, then the sample might be viable for DLS.
Due to the intensity skew of DLS, larger populations of particles will need lower concentrations to be viable. Below are examples of Thermo Fisher NIST traceable polystyrene reference size materials. All three vials are approximately 1% concentration. The 20 nm reference material is almost clear and would be able to be run neat on DLS. The turbidity increases in the 100 nm reference material meaning, depending on the instrument setup, it can be run neat or diluted further and be analyzed. The 500 nm reference material is almost opaque due to the high amount of light scattered per particle and would likely require dilution to be analyzed. Due to the relation of size and concentration to accurate results, it is recommended a concentration linearity study be conducted in any method development work on DLS.
Q: How viscous is too viscous?
A: The limits on viscosity are sample dependent, but as a general rule staying below 10 cPs is usually appropriate. To know the effects of changes in viscosity on your sample, a study to evaluate appropriate ranges would be recommended.
When settling is a concern, increasing viscosity is often considered to prevent the settling affect. Unfortunately, Brownian motion is also impacted when changing viscosity. Even though the Stokes-Einstein equation accounts for viscosity in the calculation of particle size, there is usually a point at which increasing viscosity will not be proportional to the decrease in Brownian motion observed by the instrument.
By Cesar Estrada, Particle Characterization Chemist II.
References
[1] Britannica, The Editors of Encyclopaedia. “solution”. Encyclopedia Britannica, 1 Nov. 2022, https://www.britannica.com/science/solution-chemistry. Accessed 5 December 2022.
[2] Geckeler KE, Premkumar T. Carbon nanotubes: are they dispersed or dissolved in liquids? Nanoscale Res Lett. 2011 Feb 11;6(1):136. doi: 10.1186/1556-276X-6-136. PMID: 21711654; PMCID: PMC3211183.
[3] Sartor, Marta. “Dynamic Light Scattering to determine the radius of small beads in Brownian motion in a solution”. University of California San Diego, https://neurophysics.ucsd.edu/courses/physics_173_273/dynamic_light_scattering_03.pdf
[4] Sartor, Marta. “Dynamic Light Scattering to determine the radius of small beads in Brownian motion in a solution”. University of California San Diego, https://neurophysics.ucsd.edu/courses/physics_173_273/dynamic_light_scattering_03.pdf
