Dynamic Light Scattering - sysmex.nl · 22/04/2015 2 Agenda › Dynamic Light Scattering Overview Brownian Motion Correlation Analysing the Correlation Function › Data Interpretation

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Dynamic Light Scattering

Dr Mike Kaszuba Technical Support Manager

E-mail: [email protected]

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



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



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


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


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


• 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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• 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?

Documents

Dynamic Light Scattering - sysmex.nl · 22/04/2015 2 Agenda › Dynamic Light Scattering Overview Brownian Motion Correlation Analysing the Correlation Function › Data Interpretation