**Nov 8, 2019**

Instruments:

Dynamic Light Scattering (DLS) is a measurement technique that provides a fast and simple method for submicron and nanoparticle sizing.

### Theoretical Basis for Light Scattering

Light scattering is a phenomenon that is observed when light, usually monochromatic laser light, is scattered by randomly oriented objects in solution. Inhomogeneities result in scattered light; in a perfectly uniform continuum, there would be no deflection of the path of laser light as it passes through a medium. The intensity of light scattered is proportional to size, molecular weight, and to the difference in refractive index (Δn) between the scattering center (n^{sample}) and solvent (n^{solvent}). As long as Δn is nonzero, light scattering should occur.

### Dynamic vs. Static Light Scattering

Commercial light scattering instruments tend to exploit one of two basic principles in order to extract information from this scattered light. Static Light Scattering (SLS) requires extremely accurate photon counting, meaning the magnitude of the scattered light is often the most important parameter. This method is used to obtain parameters such as M_{w}, R_{g}, and A_{2}. In contrast, Dynamic Light Scattering (DLS) exploits the collective motion of a large ensemble of randomly oriented particles dispersed in some medium.

DLS relies on the fact that freely diffusing particles, moving randomly due to Brownian motion, will produce rapid fluctuations in scattered laser light. These fluctuations are rapid, on the order of tens of nanoseconds to hundreds of milliseconds, and are directly related to the motion of particles. Temporal autocorrelation is used to quantify the speed at which these photo pulses become decorrelated from some initial state, which is then related directly to the motion of particles.

### Making a Dynamic Light Scattering Measurement

In order to be able to measure a real sample using DLS, the sample needs to be dispersible in a solvent. A considerable amount of attention needs to be paid to preparing dust-free solutions, as well as to avoiding overly concentrated samples (e.g., high volume fraction). DLS is intended to be used in dilute solution conditions, so it is worth noting that not all samples that are measurable, will necessarily be suitable for analysis.

**More information**: Guide for DLS sample preparation

### Turning Scattered Light into Particle Size Information

The signal that arises from the scattered intensity from the laser light is collected and transformed into an autocorrelation function which is the basis for measuring a particle size distribution. In this technique, rapid fluctuations in the intensity of scattered light arise from the random motion of dispersed particles. This random, or Brownian, motion of particles and proteins is analyzed by autocorrelation to give either a simple mean size and polydispersity, or more complete distribution data even for multimodal distributions. The diameter obtained from Dynamic Light Scattering is often referred to as the hydrodynamic diameter and is inversely proportional to the diffusion coefficient. Large particles scatter more light and diffuse more slowly than small particles. The hydrodynamic diameter is related to the diffusion coefficient via the Stokes-Einstein equation, where size is inverse with the rate of diffusion.

When a distribution of sizes is present, the effective diameter measured is an average diameter which is weighted by the intensity of light scattered by each particle. This intensity weighting is not the same as the population or number weighting used in a single particle counter such as in electron microscopy. However, even for narrowly dispersed samples, the average diameters obtained are usually in good agreement with those obtained by single particle techniques.

### The Stokes-Einstein Equation and Dynamic Light Scattering

The relationship between the translational diffusion coefficient **D _{t}**, the primary quantity measured in DLS, and hydrodynamic particle size,

**d**, is inverse, and is given by the Stokes-Einstein Equation:

_{h}**D _{t} = K_{b} T / 3πηd_{h}**

Where the Boltzmann constant (**K _{b}**), Temperature (

**T**), and bulk viscosity (

**η**) are all known values, and only the particle size,

**d**, is a property of the particle.

_{h}For a known scattering angle, **θ**, and refractive index, **n**, the scattering vector **q** is calculated from the following expression where **λ _{o}** is wavelength of the laser:

**q** = 4πn/λ_{o} sin(**θ**/2)

A given autocorrelation function (**ACF**), typically represented as a function of delay time, **C(τ)** is deconvoluted into either a single-exponential, stretched-exponential, or sum of exponentials. Where **B**, is a constant background term, and **A**, an optical constant determined by instrument design:

**C(τ)=B⋅[1+A⋅exp(-2Γτ)]**

The result of this deconvolution is a characteristic linewidth or decay rate, **Г**, and typically also a polydispersity index (**PDI**). Polydispersity refers to the broadness of a given distribution, which can result from either a single broad population or the coexistence of multiple discrete populations.

This linewidth,** Г**, is related to the translational diffusion coefficient (**D _{t}**) as follows:

**Г = D _{t}⋅q^{2}**

Dynamic Light Scattering is sometimes referred to as Quasi-Elastic Light Scattering (QELS) or Photo-Correlation Spectroscopy (PCS).

### Applications of Dynamic Light Scattering

The most common industrial applications of DLS are formulations development and quality control (QC). Most industrial formulations are used to stabilize an active component so that it can be stored or delivered; this frequently requires surfactants, buffers, viscosity modifiers, and polymeric additives. The objective is to keep materials stable and soluble. The function of QC is to look for consistency and, in some specific cases, to detect aggregation or fouling. This process is very similar across a wide variety of industries including biopharma, oil recovery, personal care, food formulations, cosmetics, and many more.

DLS is also used in a number of common R&D activities including the design of novel materials, development or screening of new biomolecules, aggregation studies, preparing new self-assembled structures, drug delivery and release, nanogels, and in studying various exotic surfactant systems.

**More information**: Find more examples of DLS applications in our Application Library

### Dynamic Light Scattering Instruments

There are two common approaches to producing a commercial light scattering instrument. The vast majority will use either fixed detection angles (cuvettes or flow cells), or will allow for continuous rotation of the detector on a rotation stage (goniometer). The NanoBrook series uses fiber optics to provide up to three fixed scattering angles and can accommodate a cuvette-based sample holder. It is designed for ease of use and employs two of Brookhaven’s core technologies: DLS and Zeta Potential. In contrast, the BI-200SM Research Goniometer is a continuous multi-angle instrument and is flexible enough to solve a wide array of research problems. The Research Goniometer is exclusively a DLS and SLS instrument.

Read more about the NanoBrook series of instruments here.

Learn more about the BI-200SM Research Goniometer here.