89213317 dynamic light scattering

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Dynamic light scattering

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Hypothetical dynamic light scattering of two samples: Larger particles on the top and

smaller particle on the bottom

Dynamic light scattering (also known as photon correlation spectroscopy orquasi-

elastic light scattering) is a technique inphysics that can be used to determine the sizedistribution profile of smallparticles insuspension orpolymers in solution.[1] It can also be

used to probe the behavior of complex fluids such as concentrated polymer solutions.

Contents

[hide]

1 Description

2 Multiple scattering

3 Data analysis

o 3.1 Introduction

o 3.2 Cumulant method

o 3.3 CONTIN algorithmo 3.4 Maximum entropy method

o 3.5 Applications

4 See also

5 References

6 External links
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[edit] 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 250nm). If the lightsource is alaser, and thus is monochromatic andcoherent, then one observes a time-

dependent fluctuation in the scattering intensity. These fluctuations are due to the fact thatthe small molecules in solutions are undergoing Brownian motionand so the distancebetween 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 iscritical to remove dust and artifacts from the solution.

The dynamic information of the particles is derived from an autocorrelation of the intensity

trace recorded during the experiment. The second order autocorrelation curve is generatedfrom the intensity trace as follows:

where is the autocorrelation function at a particular wave vector, , and delaytime, , and is the intensity. 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 time period has elapsed, there is no correlation between the

scattered intensity of the initial and final states. This exponential decay is related to themotion of the particles, specifically to the diffusion coefficient. To fit the decay (i.e., theautocorrelation function), numerical methods are used, based on calculations of assumed

distributions. If the sample is monodisperse then the decay is simply a single exponential.

The Siegert equation relates the second-order autocorrelation function with the first-order

autocorrelation function as follows:

where the parameter 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. The most important use ofthe autocorrelation function is its use for size determination.

[edit] Multiple scattering
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Dynamic light scattering provides insight into the dynamic properties of soft materials by

measuring single scattering events, meaning that each detected photon has been scattered

by the sample exactly once. However, the application to many systems of scientific andindustrial relevance has been limited due to often-encountered multiple scattering, wherein

photons are scattered multiple times by the sample before being detected. Accurate

interpretation becomes exceedingly difficult for systems with nonnegligible contributionsfrom multiple scattering. In particular for larger particles and those with high refractive

index contrast, this limits the technique to very low particle concentrations, and a large

variety of systems are, therefore, excluded from investigations with dynamic lightscattering. However, as shown by Schaetzel,[2] it is possible to suppress multiple scattering

in dynamic light scattering experiments via a cross-correlation approach. The general idea

is to isolate singly scattered light and suppress undesired contributions from multiple

scattering in a dynamic light scattering experiment. Different implementations of cross-correlation light scattering have been developed and applied. Currently, the most widely

used scheme is the so called 3D-dynamic light scattering method.[3][4]The same method can

also be used to correct static light scattering data for multiple scattering contributions.[5]

Alternatively, in the limit of strong multiple scattering, a variant of dynamic light scatteringcalled diffusing-wave spectroscopy can be applied.

[edit] Data analysis

[edit] Introduction

Once the autocorrelation data have been generated, different mathematical approaches canbe employed to determine from it. Analysis of the scattering is facilitated when particles do

not interact through collisions or electrostatic forces between ions. Particle-particle

collisions can be suppressed by dilution, and charge effects are reduced by the use of salts

to collapse the electrical double layer.

The simplest approach is to treat the first order autocorrelation function as a single

exponential decay. This is appropriate for a monodisperse population.

where is the decay rate. The translational diffusion coefficient Dt may be derived at a

single angle or at a range of angles depending on the wave vectorq.

with
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where is the incident laser wavelength, n0 is the refractive indexof the sample and is

angle at which the detector is located with respect to the sample cell.

Depending on theanisotropyandpolydispersity of the system, a resulting plot of /q2 vs. q2

may or may not show an angular dependence. Small spherical particles will show no

angular dependence, hence no anisotropy. A plot of /q2

vs. q2

will result in a horizontalline. Particles with a shape other than a sphere will show anisotropy and thus an angular

dependence when plotting of /q2 vs. q2.[6] The intercept will be in any case the Dt.

Dt is often used to calculate the hydrodynamic radius of a sphere through the Stokes

Einstein equation. It is important to note that the size determined by dynamic light

scattering is the size of a sphere that moves in the same manner as the scatterer. So, for

example, if the scatterer is a random coil polymer, the determined size is not the same asthe radius of gyration determined bystatic light scattering. It is also useful to point out that

the obtained size will include any other molecules or solvent molecules that move with the

particle. So, for example, colloidal gold with a layer of surfactant will appear larger by

dynamic light scattering (which includes the surfactant layer) than by transmission electronmicroscopy (which does not "see" the layer due to poor contrast).

In most cases, samples are polydisperse. Thus, the autocorrelation function is a sum of the

exponential decays corresponding to each of the species in the population.

It is tempting to obtain data for and attempt to invert the above to extract G().

Since G() is proportional to the relative scattering from each species, it containsinformation on the distribution of sizes. However, this is known as an ill-posed problem.

The methods described below (and others) have been developed to extract as much useful

information as possible from an autocorrelation function.

[edit] Cumulant method

One of the most common methods is thecumulant method,[7][8]from which in addition tothe sum of the exponentials above, more information can be derived about the variance of

the system as follows:

where is the average decay rate and is the second order polydispersity index (or an

indication of the variance). A third-orderpolydispersity index may also be derived but this

is necessary only if the particles of the system are highly polydisperse. The z-averagedtranslational diffusion coefficientDz may be derived at a single angle or at a range of

angles depending on the wave vectorq.
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One must note that the cumulant method is valid for small and sufficiently narrow G().[9]

One should seldom use parameters beyond 3, because overfitting data with many

parameters in a power-series expansion will render all the parameters including and 2,

less precise.[10]

The cumulant method is far less affected by experimental noise than the methods below.

[edit] CONTIN algorithm

An alternative method for analyzing the autocorrelation function can be achieved through

an inverse Laplace transform known as CONTIN developed by Steven Provencher.[11][12]

The CONTIN analysis is ideal forheterodisperse,polydisperse, and multimodal systemsthat cannot be resolved with the cumulant method. The resolution for separating two

different particle populations is approximately a factor of five or higher and the difference

in relative intensities between two different populations should be less than 1:105.

[edit] Maximum entropy method

The Maximum entropy method is an analysis method that has great developmental

potential. The method is also used for the quantification ofsedimentation velocity datafrom analytical ultracentrifugation. The maximum entropy method involves a number of

iterative steps to minimize the deviation of the fitted data from the experimental data and

subsequently reduce the 2 of the fitted data.

[edit] Applications

DLS is used to characterize size of various particles including proteins, polymers, micelles,carbohydrates, and nanoparticles. If the system is monodisperse, the mean effective

diameter of the particles can be determined. This measurement depends on the size of the

particle core, the size of surface structures, particle concentration, and type of ions in the

medium.[13]

Since DLS essentially measures fluctuations in scattered light intensity due to diffusing

particles, the diffusion coefficient of the particles can be determined. If there are particles

of varying sizes, an array of diffusion coefficients are found. Based on Einstein'stheoretical relationships between diffusion and particle size, the diffusion coefficient is

then used to calculate the 'hydrodynamic diameter' of the spherical particle. The larger theparticle size, the slower it will diffuse.[14] The DLS software displays the particle population

at different diameters. If the system is monodisperse, there should only be one population,whereas a polydisperse system would show multiple particle populations.[15]

Stability studies can be done conveniently using DLS. Periodical DLS measurements of a

sample can show whether the particles aggregate over time by seeing whether the

hydrodynamic radius of the particle increases. If particles aggregate, there will be a larger
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population of particles with a larger radius. Additionally, in certain DLS machines, stability

depending on temperature can be analyzed by controlling the temperature in situ .[14]

[edit] See also
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89213317 dynamic light scattering

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