6.3 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Dynamic light scattering | 1/4 | https://en.wikipedia.org/wiki/Dynamic_light_scattering | reference | science, encyclopedia | 2026-05-05T10:04:18.544311+00:00 | kb-cron |
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using the intensity or photon autocorrelation function (also known as photon correlation spectroscopy – PCS or quasi-elastic light scattering – QELS). In the time domain analysis, the autocorrelation function (ACF) usually decays starting from zero delay time, and faster dynamics due to smaller particles lead to faster decorrelation of scattered intensity trace. It has been shown that the intensity ACF is the Fourier transform of the power spectrum, and therefore the DLS measurements can be equally well performed in the spectral domain. DLS can also be used to probe the behavior of complex fluids such as concentrated polymer solutions.
== Setup == A monochromatic light source, usually a laser, is shot through a polarizer and into a sample. The scattered light then goes through a second polarizer where it is collected by a photomultiplier and the resulting image is projected onto a screen. This is known as a speckle pattern (Figure 1).
All of the molecules in the solution are being hit with the light and all of the molecules diffract the light in all directions. The diffracted light from all of the molecules can either interfere constructively (light regions) or destructively (dark regions). This process is repeated at short time intervals and the resulting set of speckle patterns is analyzed by an autocorrelator that compares the intensity of light at each spot over time. The polarizers can be set up in two geometrical configurations. One is a vertical/vertical (VV) geometry, where the second polarizer allows light through that is in the same direction as the primary polarizer. In vertical/horizontal (VH) geometry the second polarizer allows light that is not in the same direction as the incident light.
== Description == When light hits small particles, the light scatters in all directions (Rayleigh scattering) as long as the particles are small compared to the wavelength (below 250 nm). Even if the light source is a laser, and thus is monochromatic and coherent, the scattering intensity fluctuates over time. This fluctuation is due to small particles in suspension undergoing Brownian motion, and so the distance between the scatterers in the solution is constantly changing with time. This scattered light then undergoes either constructive or destructive interference by the surrounding particles, and within this intensity fluctuation, information is contained about the time scale of movement of the scatterers. Sample preparation either by filtration or centrifugation is critical to remove dust and artifacts from the solution. The dynamic information of the particles is derived from the autocorrelation of the intensity trace recorded during the experiment. The second order autocorrelation curve is generated from the intensity trace as follows:
g
2
(
q
;
τ
)
=
⟨
I
(
t
)
I
(
t
+
τ
)
⟩
⟨
I
(
t
)
⟩
2
{\displaystyle g^{2}(q;\tau )={\frac {\langle I(t)I(t+\tau )\rangle }{\langle I(t)\rangle ^{2}}}}
where g2(q;τ) is the autocorrelation function at a particular wave vector, q, and delay time, τ, and I is the intensity. The angular brackets
⟨
⋅
⟩
{\displaystyle \langle \cdot \rangle }
denote the expected value operator, which in some texts is denoted by a capital E. At short time delays, the correlation is high because the particles do not have a chance to move to a great extent from the initial state that they were in. The two signals are thus essentially unchanged when compared after only a very short time interval. As the time delays become longer, the correlation decays exponentially, meaning that, after a long period has elapsed, there is no correlation between the scattered intensity of the initial and final states. This exponential decay is related to the motion of the particles, specifically to the diffusion coefficient. To fit the decay (i.e., the autocorrelation function), numerical methods are used, based on calculations of assumed distributions. If the sample is monodisperse (uniform) then the decay is simply a single exponential. The Siegert equation relates the second-order autocorrelation function with the first-order autocorrelation function g1(q;τ) as follows:
g
2
(
q
;
τ
)
=
1
+
β
[
g
1
(
q
;
τ
)
]
2
{\displaystyle g^{2}(q;\tau )=1+\beta \left[g^{1}(q;\tau )\right]^{2}}
where the first term of the sum is related to the baseline value (≈1) and the parameter β is a correction factor that depends on the geometry and alignment of the laser beam in the light scattering setup. It is roughly equal to the inverse of the number of speckle (see Speckle pattern) from which light is collected. A smaller focus of the laser beam yields a coarser speckle pattern, a lower number of speckle on the detector, and thus a larger second-order autocorrelation. The most important use of the autocorrelation function is its use for size determination.