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22/04/2015
1
Dynamic Light Scattering
Dr Mike Kaszuba Technical Support Manager
E-mail: michael.kaszuba@malvern.com
Agenda
› Dynamic Light Scattering Overview Brownian Motion Correlation Analysing the Correlation Function
› Data Interpretation Recommended Parameters Recommended Reports Data Interpretation Examples
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Agenda
› Dynamic Light Scattering Overview Brownian Motion Correlation Analysing the Correlation Function
› Data Interpretation Recommended Parameters Recommended Reports Data Interpretation Examples
Brownian Motion and Particle Size
Small particles diffuse rapidlyLarge particles diffuse slowly
The speed of diffusion depends upon……… Particle Size Dispersant Viscosity
Nanoparticles Emulsion Droplets
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Brownian Motion
› Velocity of the Brownian motion is defined by the translational diffusion coefficient (D)
› The translational diffusion coefficient can be converted into a particle size using the Stokes-Einstein equation
dH =3 p h D
kT
Where dH = hydrodynamic diameter, k = Boltzmann’s constant, T = absolute temperature, h = viscosity and D = diffusion coefficient
DLS Instrument Components
Laser
Cuvette containing
sample
Digital signal processor(Correlator)
Photon counting device (Avalanche photo diode)
Scattered light
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Intensity Fluctuations and Brownian Motion
SmallParticles
Time
Inte
nsity
Time
Inte
nsity
LargeParticles
Laser
Constructive and Destructive Interference
LaserDetector
LaserDetector
Constructive Interference
Destructive Interference
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Correlation in Dynamic Light Scattering
› Technique for extracting the time dependence of a signal in the presence of “noise”
› Time analysis carried out with a correlator› Constructs the time autocorrelation function G(t) of
the scattered intensity according to
where I = intensity, t is the time and t = the delay time
2
*tI
tItIG
Correlation
Time
Inte
nsity
Time
Inte
nsity
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Correlation
Time
Inte
nsity
Time
Inte
nsity
0Time
Cor
rela
tion
Coe
ffici
ent
1
0
0Time
= 0
Correlation
Time
Inte
nsity
Time
Inte
nsity
0Time
Cor
rela
tion
Coe
ffici
ent
1
0
0Time
= 1
1
1
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Correlation
Time
Inte
nsity
Time
Inte
nsity
0Time
Cor
rela
tion
Coe
ffici
ent
1
0
0Time
= 2
1
1
2
2
Correlation
Time
Inte
nsity
Time
Inte
nsity
0Time
Cor
rela
tion
Coe
ffici
ent
1
0
0Time
= 3
1
1
2
2
3
3
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Correlation
Time
Inte
nsity
Time
Inte
nsity
0Time
Cor
rela
tion
Coe
ffici
ent
1
0
0Time
=
1
1
2
2
3
3
Correlation
Time
Inte
nsity
Time
Inte
nsity
=
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Correlation Functions
Time when decay starts indicates mean size
Gradient indicates the polydispersity
of sample
Baseline
Intercept
Correlation Functions
› The correlation function can be modelled with an exponential expression such as:
Where B = baseline at infinite timeA = amplitude (or intercept)q = scattering vector = (4π n/λo) sin(θ/2)
n = dispersant refractive index o = laser wavelength θ = detection angle
D = diffusion coefficient = correlator delay time
D-2q2
e ABG
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Analysing The Correlation Function
› Correlation function contains the diffusion coefficient information required to be entered into the Stokes-Einstein equation
› The diffusion coefficients are obtained by fitting the correlation function with a suitable algorithm
Analysing The Correlation Function
Cumulants analysis› Mean size (z-average) › Polydispersity index
Distribution analysis› Distribution of sizes
Two different analyses are performed:
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Cumulants Analysis
› Defined in the International Standards ISO13321 (1996) and ISO22412 (2008)
› Only gives a mean particle size (z-average) and an estimate of the width of the distribution (polydispersity index)
› Only the dispersant refractive index and viscosity are required for this analysis
The z-Average Diameter
› Definition of the z-Average Diameter (ZD):
The intensity-weighted mean diameter derived from the cumulants analysis
› Specific to light scattering › Very sensitive to the presence of aggregates or large
contaminants due to the inherent intensity weighting
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Polydispersity Index
› Definition of the Polydispersity Index (PdI):
A dimensionless measure of the broadness of the size distribution calculated from the cumulants
analysis
› Ranges from 0 to 1 in the Zetasizer software › Values > 1 indicate that the distribution is so polydisperse, the
sample may not be suitable for measurement by DLS
Cumulants Analysis: Advantages
› ISO defined analysis› Simplest analysis of the correlation function › Ideal when only looking to determine the average
particle size of a population › As a population changes, the z-average size
obtained from cumulants will identify this very quickly Aggregation will show a rapid increase in the z-average
size, along with an increase in PdI Dissolution/deaggregation will show a slow decrease in z-
average size along with a decrease in PdI
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Cumulants Analysis: Disadvantages
› Cumulants only describes a single average size value, along with the PdI, it provides a good idea of changes in a population, and the broadness of that population
› Cumulants cannot identify individual modes in a population so it becomes less descriptive as the sample type moves further away from monomodal i.e. as the PdI increases, the usefulness of a single size value
decreases
Cumulants Analysis: Multimodal Samples › If a sample of 60nm and 220nm latex was prepared with equal
volumes of each mode present
› Cumulants cannot describe the discrete populations in a sample - it can only state that the average size is 175nm with a PdI of 0.19
› As the modality of a population increases, the ability of cumulants analysis to provide useful information about our population decreases
z-average diameter = 175nm
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Distribution Analysis
› To investigate the modality of a sample, a mathematical analysis of the correlation function is performed which can describe the distribution
› This is know as distribution analysis › The distribution analysis is more complex than cumulants› The data set is fitted to a multi-exponential model to
produce a distribution› A lot more information is required to perform this analysis:
Size range over which the distribution should be analyzed Number of size classes within this size range The expected noise level within the data set (regularizer)
Distribution Analysis
› The distribution analysis becomes useful when: The number of populations needs to be known The relative composition of these populations needs to be
known The presence/absence of a large population needs to be
determined (aggregate detection) The presence/absence of a small population needs to be
determined (fragmentation, monomer detection) The abundance of different species in a formulation needs
to be known
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Distribution Algorithms
› General Purpose (non-negative least squares (NNLS))
› Multiple Narrow Modes (non-negative least squares (NNLS))
› Protein Analysis (L-curve)
› The difference between these algorithms is the regularizer used
Regularizer
› A small amount of noise in the correlation function can generate a large number of distributions
› Regularizer can be thought of as an estimator of the noise contained in the correlogram
› It controls the acceptable degree of “spikiness” in the size distribution obtained Large regularizer values produce smooth distributions Small regularizer values produce spiky distributions
› There is no ideal regularizer value; the appropriate value depends on the sample being measured
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Available Algorithms and Associated Regularizer
Algorithm Regularizer
General Purpose 0.01
Multiple Narrow Modes 0.001
Protein Analysis Variable (appropriate value automatically determined)
Zetasizer Distribution Algorithms
› General Purpose Suitable for the majority of samples where no knowledge of
the distribution is available Will give broad, smooth distributions
› Multiple Narrow Modes Suitable for samples suspected to contain discrete
populations Will give narrow peaks
› Protein Analysis Best suited for protein samples – will give narrow peaks Automatically picks the optimal distribution
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Cumulants Versus Distribution Analysis
› It is important to note that neither analysis method makes the other invalid Cumulants analysis provides information on the average particle size
present in a population, along with a general idea of the polydispersity of that population
Distribution analysis allows us to obtain more specific information relating to the total number of modes present in a population, and how they relate to one another
› Neither analysis model provides the complete solution, but together give a greater understanding of the sample
Intensity Size Distributions
› Primary result › Based upon the intensity of
light scattered by particles› Sensitive to the presence of
large particles/aggregates /dust
› Only the dispersant viscosity and refractive index values are required
10%:90%
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Volume Size Distributions
› Derived from the intensity distribution using Mie theory
› Equivalent to the mass or weight distribution
› Particle optical properties required to make this transformation Particle refractive index Particle absorption
10%:90%
50%:50%
Number Size Distributions
› Derived from the intensity distribution using Mie theory
› Particle optical properties required to make this transformation Particle refractive index Particle absorption
10%:90%
50%:50%
98%:2%
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Size Distributions From DLS
› DLS technique tends to overestimate the width of the peaks in the distribution
› This effect is magnified in the transformations to volume and number
› The volume and number size distributions should only be used for estimating the relative amounts of material in separate peaks as the means and particularly the widths are less reliable
Volume/Number Distributions: Recommended Use
› Use the Intensity PSD for reporting the size of each peak in the distribution
› Use the Volume or Number PSD for reporting the relative amounts of each peak in the distribution
(Modal Size Report)
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Agenda
› Dynamic Light Scattering Overview Brownian Motion Correlation Analysing the Correlation Function
› Data Interpretation Recommended Parameters Recommended Reports Data Interpretation Examples
Data Interpretation Overview
› The quality of the data obtained from the measurement is essential in determining how well the distribution algorithm is going to perform
› The better the quality of the data, the more repeatable the answers obtained will be
› In order to aid the interpretation of data, a number of report pages record view parameters can be viewed
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Recommended Parameters
Parameter Name DescriptionMean Count Rate The average count rate obtained during the course of the
measurement
Attenuator The attenuator position used for the measurement
Derived Count Rate The count rate obtained taking into consideration the attenuation factor used
Cumulants Fit Error The fit error obtained from the analysis of the data with cumulants
Multimodal Fit Error The fit error obtained from the analysis of the data with either the general purpose or multiple narrow modes analysis
In Range The overall quality of the data – a value less than 90% indicates the probable presence of number fluctuations due to the presence of large particles
Measurement Position The position in the cuvette at which the measurement was taken
Recommended Reports
Report Name Description
Intensity PSD The primary result obtained from a DLS measurement
Size Quality Incorporates a number of tests on any selected record
Correlogram Shows the correlation coefficients determined at each delay time
Cumulants Fit Shows the fit of the data points by the cumulants analysis from which the z-average diameter and polydispersity index are calculated according to ISO 13321
Distribution Fit Shows the fit of the data points from the chosen distribution analysis from which the intensity size distribution is obtained
Expert System Enables a quality check to be performed on 3 or more completed measurement records
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Size Quality Report Overview
› The size quality report incorporates a number of tests on any selected record
› If any of the tests fall outside specified limits, a warning message is displayed together with advice of possible reasons for the warning
› If none of the tests fail, a “Result Meets Quality Criteria” message is displayed
Size Quality Report
Test Description Possible Reasons
Size display limits(lower and upper) used
Is z-average < lower size display limit?Is z-average > upper size display limit?
Wrong lower/upper size display limits used – need to be edited
PdI value Is PdI value ? 1? • Sample is very polydisperse and may not be suitable for DLS
• Sample contains large particles/ aggregates/dust which should be removed (filtration or centrifugation)
Intercept value Is intercept value <0.1 or > 1.0
• Sample contains large particles (number fluctuations) and should be removed
• Sample concentration too high/low and needs to be adjusted
• Sample fluorescence requires narrow band filter/different laser wavelength
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Size Quality Report
Test Description Possible Reasons
In range value Is in range value less than 90%
• Large sedimenting particles present causing number fluctuations and should be removed
• Sample fluorescence requires narrow band filter/different laser wavelength
• Sample absorbance requires different laser wavelength
Mean count rate Is mean count rate < 20kcps or > 1000kcps?
• Sample concentration too low or too high and needs to be adjusted
• Attenuator not set to automatic • Sample not stable during
measurement (aggregating/breaking up) and is not suitable for DLS
• Sample contains large particles (number fluctuations) and should be removed
Size Quality Report
Test Description Possible Reasons
Number of photons detected
Is the total number of photons detected < 10,000,000?
• Measurement duration not set to automatic
• Attenuator not set to automatic
Cumulants fit error
Is the cumulants fit error > 0.005?
• Data quality too poor for cumulants and sample may not be suitable for DLS
• Sample is too polydisperse for cumulants and therefore distribution analysis may be more appropriate
Distribution fit error
Is the distribution fit error > 0.005?
• Data quality too poor for distribution analysis and sample may not be suitable for DLS
• Sample is too polydisperse for distribution analysis and sample may not be suitable for DLS
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Count Rate Repeatability
› Perform at least 3 repeat measurements on the same sample - the count rates should be all within a few percent of one another
› Increasing count rates from successive measurements indicates: Particle aggregation
› Decreasing count rates from successive measurements indicates: Particle sedimentation (or creaming) Particle dissolution
› Random count rates from successive measurements indicates: Particle instability (aggregation, break up etc)
z-Average Diameter Repeatability
› The z-average diameters obtained from repeat measurements should be within 1 or 2 percent of one another
› Increasing z-average diameters indicates: Particle aggregation Temperature not stable (viscosity changing with time)
› Decreasing z-average diameters indicates: Particle sedimentation (or creaming) Particle dissolution Temperature not stable (viscosity changing with time)
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Results and Data Example 1
• Correlation functions do not overplot indicating sample is not stable during repeat measurements
• Sample not stable – mean count rate and z-average sizes not repeatable• Large particles present (number fluctuations) causing interference and need to be
removed• Sample polydisperse and not suitable for cumulants
Results and Data Example 2
• Correlation functions do not overplot indicating sample is not stable during repeat measurements
• Low mean count rate and intercepts – sample concentration very low• Correlation function indicates bimodal distribution and therefore cumulants not suitable• Sample polydisperse and not suitable for cumulant
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Results and Data Example 3
• Correlation functions overplot indicating sample is stable during repeat measurements• Z-average sizes, PdI and count rates are repeatable• In range values, cumulants and distribution fit errors are good• Measurement position 0.45mm and attenuator 2 indicating very high concentration,
strong scattering sample • Intercepts around 0.6 indicate presence of multiple scattering• Dilute and re-measure sample to check influence of concentration of the results
Any Questions?
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