Dynamic Light Scattering: An Introduction in 30 Minutes Introduction coefficient by using the Stokes- reducing the diffusion speed and Einstein equation; resulting in a larger, apparent Dynamic Light Scattering (sometimes hydrodynamic diameter. Conversely, referred to as Photon Correlation kT higher conductivity media will Spectroscopy or Quasi-Elastic Light dH()= suppress the electrical double layer Scattering) is a technique for 3πηD and the measured hydrodynamic measuring the size of particles diameter. typically in the sub micron region. where:- The performance of a DLS instrument Brownian Motion d(H) = hydrodynamic diameter is normally verified by measurement of a suitable polystyrene latex DLS measures Brownian motion and D = translational diffusion coefficient standard. If the standard needs to be relates this to the size of the particles. diluted prior to measurement, then k Brownian motion is the random = Boltzmann’s constant dilution in an appropriate medium is movement of particles due to the T = absolute temperature important. The International Standard bombardment by the solvent on DLS (ISO13321 Part 8 1996) says molecules that surround them. η = viscosity that dilution of any polystyrene Normally DLS is concerned with standard should be made in 10mM measurement of particles suspended NaCl. This concentration of salt will within a liquid. Note that the diameter that is suppress the electrical double layer The larger the particle, the slower the measured in DLS is a value that and ensure that the hydrodynamic Brownian motion will be. Smaller refers to how a particle diffuses within diameter reported will be the same as particles are “kicked” further by the a fluid so it is referred to as a the hydrodynamic diameter on the solvent molecules and move more hydrodynamic diameter. The certificate or the expected diameter. rapidly. An accurately known diameter that is obtained by this temperature is necessary for DLS technique is the diameter of a sphere Surface Structure that has the same translational because knowledge of the viscosity is Any change to the surface of a diffusion coefficient as the particle. required (because the viscosity of a particle that affects the diffusion liquid is related to its temperature). The translational diffusion coefficient speed will correspondingly change the The temperature also needs to be will depend not only on the size of the apparent size of the particle. An stable, otherwise convection currents particle “core”, but also on any adsorbed polymer layer projecting out in the sample will cause non-random surface structure, as well as the into the medium will reduce the movements that will ruin the correct concentration and type of ions in the diffusion speed more than if the interpretation of size. medium. Factors that affect the polymer is lying flat on the surface. The velocity of the Brownian motion is diffusion speed of particles are The nature of the surface and the defined by a property known as the discussed in the following sections. polymer, as well as the ionic translational diffusion coefficient concentration of the medium can (usually given the symbol, D). Ionic Strength of Medium affect the polymer conformation, which in turn can change the apparent The ions in the medium and the total size by several nanometres. The Hydrodynamic ionic concentration can affect the Diameter particle diffusion speed by changing the thickness of the electric double Non-Spherical Particles The size of a particle is calculated layer called the Debye length (K-1). All particle-sizing techniques have an from the translational diffusion Thus a low conductivity medium will inherent problem in describing the size of non-spherical particles. The produce an extended double layer of ions around the particle, sphere is the only object whose size 1 DLS technical note MRK656-01 can be unambiguously described by a wavelength. The d6 term tells us that a observed. single figure. 50nm particle will scatter 106 or one million times as much light as a 5nm Figure 1 shows the theoretical plot of Different techniques are sensitive to particle. Hence there is a danger that the log of the relative scattering different properties of the particle, e.g. intensity versus particle size at angles the light from the larger particles will o projected area, density, scattering swamp the scattered light from the of 173 (the detection angle of the intensity, and in general will produce 6 Zetasizer Nano S and Nano ZS in smaller ones. This d factor also o different mean sizes and size means it is difficult with DLS to aqueous media) and 90 (the distributions for any given sample. measure, say, a mixture of 1000nm detection angle of the Nano S90 and Even the size in a microscope image and 10nm particles because the Nano ZS90) assuming a laser will depend on parameters set such contribution to the total light scattered wavelength of 633nm, real refractive as edge contrast etc. It is important to by the small particles will be index of 1.59 and an imaginary understand that none of these results extremely small. The inverse refractive index of 0.001.Mie theory is are inherently “correct”. 4 the only theory that explains correctly relationship to λ means that a higher the maxima and minima in the plot of scattering intensity is obtained as the The hydrodynamic diameter of a non- intensity with angle and will give the wavelength of the laser used spherical particle is the diameter of a correct answer over all wavelengths, decreases. sphere that has the same translational sizes and angles. Mie theory is used diffusion speed as the particle. in the Nano software for conversion of If the shape of a particle changes in a Mie Theory the intensity distribution into volume. When the size of the particles way that affects the diffusion speed, then the hydrodynamic size will becomes roughly equivalent to the change. For example, small changes wavelength of the illuminating light, in the length of a rod-shaped particle then a complex function of maxima will directly affect the size, whereas and minima with respect to angle is changes in the rod’s diameter, which will hardly affect the diffusion speed, will be difficult to detect. The conformation of proteins and macromolecules are usually dependent on the exact nature of the dispersing medium. As conformational changes will usually affect the diffusion speed, DLS is a very sensitive technique for detecting these changes. Light Scattering Theories Rayleigh Scattering If the particles are small compared to the wavelength of the laser used (typically less than d =λ/10 or around 60nm for a He-Ne laser), then the scattering from a particle illuminated by a vertically polarised laser will be essentially isotropic, i.e. equal in all directions. Figure 1: Theoretical plot of the log of the relative intensity of scattering versus particle size at angles of 173o (the detection angle of the Nano S, and Nano ZS in The Rayleigh approximation tells us aqueous media) and 90o (the detection angle of the Nano S90 and Nano ZS90) 6 4 that Ι α d and also that Ι α 1/λ , assuming a laser beam at a wavelength of 633nm, real refractive index of 1.59 where Ι = intensity of light scattered, and an imaginary refractive index of 0.001 d = particle diameter and λ = laser 2 DLS technical note MRK656-01 How DLS Works In dynamic light scattering, the speed at which the particles are diffusing due to Brownian motion is measured. This is done by measuring the rate at which the intensity of the scattered light fluctuates when detected using a suitable optical arrangement. How do these fluctuations in the intensity of scattered light arise? Imagine if a cuvette, containing particles which are stationary, is illuminated by a laser and a frosted glass screen is used to view the sample cell. A classical speckle pattern would be seen (figure 2). The speckle pattern will be stationary both in speckle size and position because the whole system is stationary. The dark spaces are where the phase additions of the scattered light are Figure 2: Schematic representation of a speckle pattern mutually destructive and cancel each other out (figure 3A). The bright blobs of light in the speckle pattern are where the light scattered from the particles arrives with the same phase and interfere constructively to form a bright patch (figure 3B). For a system of particles undergoing Brownian motion, a speckle pattern is observed where the position of each speckle is seen to be in constant motion. This is because the phase addition from the moving particles is constantly evolving and forming new patterns. The rate at which these intensity fluctuations occur will depend on the size of the particles. Figure 4 schematically illustrates typical intensity fluctuations arising from a dispersion of large particles and a dispersion of small particles. The small particles cause the intensity to fluctuate more rapidly than the large ones. Figure 3: The observed signal depends on the phase addition of the scattered light falling on the detector. In example A, two beams interfere and ‘cancel each other out’ resulting in a decreased intensity detected. In example B, two beams interfere and ‘enhance each other’ resulting in an increased intensity detected. 3 DLS technical note MRK656-01 between the intensities of two signals. If the signals at t+2δt, t+3δt, t+4δt etc. The two signals are strongly or well are compared with the signal at t, the correlated. correlation of a signal arriving from a random source will decrease with time If the signal, derived from a random until at some time, effectively t = ∞, process such as Brownian motion, at t there will be no correlation. is compared to the signal at t+2δt, there will still be a reasonable If the particles are large the signal will comparison or correlation between be changing slowly and the the two signals, but it will not be as correlation will persist for a long time good as the comparison at t and t+δt.