ISO 22412:2017

INTERNATIONAL ISO
STANDARD 22412
Second edition
2017-02
Particle size analysis — Dynamic light
scattering (DLS)
Analyse granulométrique — Dispersion lumineuse dynamique (DLD)
Reference number
©
ISO 2017
© ISO 2017, Published in Switzerland
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ii © ISO 2017 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and units . 3
5 Principle . 4
6 Apparatus . 5
7 Test sample preparation . 7
7.1 General . 7
7.2 Concentration limits . 7
7.3 Checks for concentration suitability. 7
8 Measurement procedure . 8
9 Evaluation of results .10
9.1 General .10
9.2 Correlation analysis .11
9.2.1 Cumulants method .11
9.2.2 Distribution calculation algorithms .11
9.3 Frequency analysis .12
10 System qualification and quality control .13
10.1 System qualification .13
10.2 Quality control of measurement results .13
10.3 Method precision and measurement uncertainty .14
11 Test report .14
Annex A (informative) Theoretical background .16
Annex B (informative) Guidance on potential measurement artefacts and on ways to
minimize their influence .25
Annex C (informative) Online measurements .28
Annex D (informative) Recommendations for sample preparation .29
Bibliography .33
Foreword
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The procedures used to develop this document and those intended for its further maintenance are
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different types of ISO documents should be noted. This document was drafted in accordance with the
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This document was prepared by Technical Committee ISO/TC 24, Particle characterization including
sieving, Subcommittee SC 4, Particle characterization.
This second edition of ISO 22412 cancels and replaces ISO 22412:2008 and ISO 13321:1996.
iv © ISO 2017 – All rights reserved

Introduction
Particle size analysis in the submicrometre size range is performed on a routine basis using the dynamic
light scattering (DLS) method, which probes the hydrodynamic mobility of the particles. The success of
the technique is mainly based on the fact that it provides estimates of the average particle size and
size distribution within a few minutes, and that user-friendly commercial instruments are available.
Nevertheless, proper use of the instrument and interpretation of the result require certain precautions.
Several methods have been developed for DLS. These methods can be classified in several ways:
a) by the difference in raw data acquisition (autocorrelation, cross-correlation and frequency
analysis);
b) by the difference in optical setup (homodyne versus heterodyne mode);
c) by the angle of observation.
In addition, instruments show differences with respect to the type of laser source and often allow
application of different data analysis algorithms (e.g. cumulants, NNLS, CONTIN, etc.).
INTERNATIONAL STANDARD ISO 22412:2017(E)
Particle size analysis — Dynamic light scattering (DLS)
1 Scope
This document specifies the application of dynamic light scattering (DLS) to the measurement of average
hydrodynamic particle size and the measurement of the size distribution of mainly submicrometre-
sized particles, emulsions or fine bubbles dispersed in liquids. DLS is also referred to as “quasi-elastic
light scattering (QELS)” and “photon correlation spectroscopy (PCS),” although PCS actually is one of
the measurement techniques.
This document is applicable to the measurement of a broad range of dilute and concentrated
suspensions. The principle of dynamic light scattering for a concentrated suspension is the same as
for a dilute suspension. However, specific requirements for the instrument setup and specification of
test sample preparation are required for concentrated suspensions. At high concentrations, particle-
particle interactions and multiple light scattering can become dominant and can result in apparent
particle sizes that differ between concentrated and dilute suspensions.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 9276-1, Representation of results of particle size analysis — Part 1: Graphical representation
ISO 9276-2, Representation of results of particle size analysis — Part 2: Calculation of average particle
sizes/diameters and moments from particle size distributions
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— IEC Electropedia: available at http:// www .electropedia .org/
— ISO Online browsing platform: available at http:// www .iso .org/ obp
3.1
particle
minute piece of matter with defined physical boundaries
Note 1 to entry: A physical boundary can also be described as an interface.
Note 2 to entry: A particle can move as a unit.
[SOURCE: ISO 26824:2013, 1.1, modified]
3.2
average hydrodynamic diameter
x
DLS
hydrodynamic diameter that reflects the central value of the underlying particle size distribution
Note 1 to entry: The average particle diameter is either directly determined without calculation of the particle
size distribution, or calculated from the computed intensity-, volume- or number-weighted particle size
distribution or from its fitted (transformed) density function. The exact nature of the average particle diameter
depends on the evaluation algorithm.
Note 2 to entry: The cumulants method yields a scattered light intensity-weighted harmonic mean particle
diameter, which is sometimes also referred to as the “z-average diameter.”
Note 3 to entry: Arithmetic, geometric and harmonic mean values can be calculated from the particle size
distribution according to ISO 9276-2.
Note 4 to entry: Mean values calculated from density functions (linear abscissa) and transformed density
functions (logarithmic abscissa) may significantly differ (ISO 9276-1).
Note 5 to entry: x also depends on the particle shape and the scattering vector (and thus on the angle of
DLS
observation, laser wavelength and refractive index of the suspension medium).
3.3
polydispersity index
PI
dimensionless measure of the broadness of the size distribution
Note 1 to entry: The PI typically has values less than 0,07 for a monodisperse test sample of spherical particles.
3.4
scattering volume
volume defined by the intersection of the incident laser beam and the scattered light intercepted by the
detector
3.5
scattered intensity
intensity of the light scattered by the particles in the scattering volume
3.6
count rate
photocurrent
I
s
number of photon pulses per unit time
Note 1 to entry: It is also a photodetector current which is proportional to the scattered intensity as measured
by a detector.
3.7
validation
proof with reference material that a measurement procedure is acceptable for all elements of its scope
Note 1 to entry: Evaluation of trueness requires a certified reference material.
3.8
reference material
RM
material, sufficiently homogeneous and stable with respect to one or more specified properties, which
has been established to be fit for its intended use in a measurement process
[SOURCE: ISO Guide 30:2015, 2.1.1, modified]
2 © ISO 2017 – All rights reserved

3.9
certified reference material
CRM
reference material characterized by a metrologically valid procedure for one or more specified
properties, accompanied by a certificate that provides the value of the specified property, its associated
uncertainty, and a statement of metrological traceability
[SOURCE: ISO Guide 30:2015, 2.1.2, modified]
3.10
qualification
proof with reference material that an instrument is operating in agreement with its specifications
4 Symbols and units
C(Γ) normalized distribution function of decay rates or dimensionless
characteristic frequencies
D translational diffusion coefficient metres squared per m /s
T
second
D collective diffusion coefficient metres squared per m /s
c
second
D self-diffusion coefficient metres squared per m /s
s
second
f frequency, f = ω/(2 π) hertz Hz
(1)
g (τ) normalized electric field correlation function dimensionless
(2)
G (τ) scattered intensity correlation function arbitrary units
G(Γ ) normalized distribution function of the individual arbitrary units
j
decay rate Γ
j
I scattered intensity, count rate, photocurrent arbitrary units
s
I intensity of the incident light arbitrary units
M number of steps in the histogram dimensionless
n refractive index of the suspension medium dimensionless
P(ω) power spectrum arbitrary units
PI polydispersity index dimensionless
ΔQ scattered light intensity-weighted amount of particles in dimensionless
int,i
size fraction i,
i.e. x < x < = x
i−1 i
x within this document: hydrodynamic diameter of a nanometres nm
particle
average hydrodynamic diameter nanometres nm
x
DLS
−1
scattered light intensity-weighted average value of the reciprocal seconds s
Γ
distribution function of the decay rate or characteristic
frequency
−1
Γ maximum decay rate (histogram method) reciprocal seconds s
max
−1
Γ minimum decay rate (histogram method) reciprocal seconds s
min
η viscosity of the suspension medium millipascal seconds mPa·s
θ scattering angle degrees °
λ wavelength of the laser light in vacuum nanometres nm
−2
μ second cumulant of the distribution function of decay reciprocal square s
rates or characteristic frequencies seconds
ρ particle density grams per cubic g/cm
centimetre
τ correlation time seconds s
−1
q modulus of the scattering vector reciprocal nm
nanometres
φ particle volume fraction dimensionless
ω angular frequency radian per seconds rad/s
5 Principle
Particles suspended in a fluid are in constant Brownian motion as the result of the interaction with
[1]
the molecules of the suspending fluid. In the Stokes-Einstein theory of Brownian motion , particle
motion of smooth spheres at very low concentration is determined by the suspending fluid viscosity
and temperature, as well as the size of the particles. Thus, from a measurement of the particle motion in
a fluid of known temperature and viscosity, the particle size can be determined.
[2][3][4][5][6]
The DLS technique probes the particle motion optically. The suspended particles are
illuminated with a coherent monochromatic light source. The light scattered from the moving
suspended particles has a time-dependent phase imparted to it from the time-dependent position. The
time-dependent phase of the scattered light can be considered as either a time-dependent phase shift
or as a spectral frequency shift from the central frequency of the light source. Measured over time,
random particle motion forms a distribution of optical phase shifts or spectral frequency shifts. These
shifts are determined by comparison either with all scattered light (homodyne or self-beating mode)
or by using a portion of the incident light as reference (heterodyne mode). Regardless of the setup, the
optical signals received from the particles are related to the scattering efficiency of the particles and
are thus scattered intensity-weighted.
Sedimentation of particles, dependent on their density, sets an upper limit to the particle size that can
be assessed by the technique; typically, the upper limit is much less than 10 μm.
DLS was developed for static suspensions. Provided that orthogonal flow and observation axes are
adopted, flowing samples may, under some circumstances, be measured if the procedure is properly
validated (see Annex C).
Different modes of diffusion, particle-particle interaction, multiple scattering and fluorescence can
significantly influence the apparent particle diameter calculated from a DLS experiment. Annex B
should be consulted.
4 © ISO 2017 – All rights reserved

6 Apparatus
A typical apparatus consists of the following components:
6.1 Laser, emitting coherent monochromatic light, polarized with its electric field component
perpendicular to the plane formed by the incident and detected rays (vertical polarization). Any kind of
lasers may be used, e.g. gas lasers (He-Ne laser, Ar-ion laser), solid-state lasers, diode-pumped solid-state
lasers and laser diodes.
6.2 Optics, lenses and equipment used to focus the incident laser light into a scattering volume and
to detect scattered light. Optical fibres are often used as a part of the detection system and for light-
delivering optics.
The use of a coherent optical reference allows using interference between the scattered light and
the reference to measure the frequency shift of the scattered light. Two methods of referencing are
commonly used and are illustrated in Figures 1 a) and b).
a) Homodyne b) Heterodyne c) Cross-correlation
(= two simultaneous homodyne
experiments)
Key
1 laser
2 sample
3 detector
4 correlator or spectrum analyser
5 beam splitter
6 lens
Figure 1 — Typical optical arrangement for DLS
— In homodyne detection (also referred to as “self-beating detection”) [Figure 1 a)], the mixing at the
optical detector of all of the collected scattered light provides the reference for frequency- or phase-
difference measurement.
— In heterodyne detection [Figure 1 b)], the scattered light is mixed with a portion of the incident
light. The unshifted incident light provides the reference for the frequency- or phase-difference
measurement.
NOTE In DLS, “heterodyne” is understood as mixing of scattered light with unscattered light from the
same source. This convention differs from, for example, the use in optical interferometry.
— In a cross-correlation setup [Figure 1 c)], two homodyne scattering measurements are performed
simultaneously in such a way that the two scattering vectors and scattering volumes are the same, but
the corresponding wave vectors are not coincident. These two laser beams produce two correlated
fluctuation patterns. The correlation is not perfect, since on the one hand, both detectors collect
light from the other scattering experiment, and on the other hand, multiply scattered light of the
incoming laser beams is totally uncorrelated. The two contributions of the multiply scattered light
to the detector signal, however, do not contribute to the time-dependent signal but to an enhanced
background.
6.3 Test sample holder, allowing fluctuations of the sample temperature to be controlled to
within ±0,3 °C. While precise knowledge of the sample temperature is required for evaluation, it is not
necessary to regulate the temperature to any defined value.
6.4 Photodetector, with an output that is proportionally related to the intensity of the collected
scattered light. A photomultiplier tube or an (avalanche) photodiode is typically used. Detectors can be
placed at any angle. Data collection can be performed in a linear or logarithmic manner.
6.5 Signal processing unit, capable of taking the time-dependent scattered light intensity signal
and outputting the autocorrelation function, cross-correlation function or power spectrum of the input
signal. This correlation can be performed by hardware and/or software correlators, operating linearly,
logarithmically or in a mixed mode.
The resulting output from either mode contains a distribution of characteristic frequencies or time-
dependent phases representative of the particle size of the suspended particles. Photon detection has a
probability distribution of photon arrival times, which means that a fluctuating signal is obtained even
if the intensity of the incident light is constant. The intensity of the photons arriving at varying time
intervals is superimposed on this already fluctuating signal. In correlation analysis, the uncorrelated
signal is constant, whereas the signal associated with the diffusing particles decays exponentially.
In spectrum analysis, the uncorrelated signal is akin to a DC or zero frequency term which is not
recorded. The time-dependent component is analysed to determine the particle-size distribution using
the theory of DLS.
6.6 Computation unit, capable of signal processing to obtain the particle size and/or particle size
distribution. Some computation units also function as the signal processing unit.
— Evaluation via the autocorrelation function allows determination of a mean diameter without
determination of the particle size distribution, but determination of the distribution is also possible.
— Evaluation via the frequency distribution determines the particle size distribution using the power
spectrum of the signal.
— Evaluation via photon cross-correlation allows quantification/minimization of the effects of
multiple scattering, thus extending the useful concentration range towards higher concentrations
(however, the effect of particle-particle interaction cannot be eliminated). The disadvantage of this
method is that it requires a more complex optical setup.
6.7 Instrument location, placed in a clean environment, free from excessive electrical noise and
mechanical vibration and out of direct sunlight. If organic liquids are used as the suspension medium,
there shall be due regard to local health and safety requirements, and the area shall be well ventilated.
The instrument shall be placed on a rigid table or bench to avoid the necessity for frequent realignment
of the optical system.
WARNING — DLS instruments are equipped with a low- or medium-power laser whose radiation
can cause permanent eye damage. Never look into the direct path of the laser beam or its
reflections. Ensure highly reflecting surfaces are not in the path of the laser beam when the
laser is on. Observe local regulations for laser radiation safety.
6 © ISO 2017 – All rights reserved

7 Test sample preparation
7.1 General
Test samples should consist of well-dispersed particles in a liquid medium. Dispersion procedures like
sonication, filtration, etc. may influence the result and therefore have to be reported. The suspension
liquid shall
a) be sufficiently transparent (non-absorbing) and non-fluorescent at the laser wavelength,
b) be free of particulate contamination,
c) not dissolve, swell or coagulate the particulate material,
d) have a known refractive index that is sufficiently different from that of the particulate materials,
e) have a known value of viscosity within ±2 % over the operational range of temperature to be
used, and
NOTE As x is directly proportional to η, the uncertainty of x will always be larger than the
DLS DLS
uncertainty of η.
f) meet the guidelines of the instrument for low background scattering.
(This can be checked by measuring the count rate for the suspending medium alone and the dark
count with no sample or solvent present. The former should be at least one order of magnitude
lower than the sample, and the latter should be within the recommended range for the instrument.)
Inadequate suppression of the double layer can have a significant influence on the hydrodynamic
diameter. A medium with ionic strength high enough to suppress the electric or diffuse double layer
can improve agreement between results obtained by DLS and electron microscopy. A conductivity of
1 mS/cm is usually sufficient to achieve this between the hydrodynamic diameter and that obtained by
microscopy techniques, especially for small particles.
Water is often used as a suspension medium. The use of freshly deionised and filtered (pore size 0,2 µm)
water is recommended. A trace of ionic additive (e.g. NaCl at a concentration of 10 mmol/l = 0,6 g/l) may
be added to such samples to reduce the double-layer thickness. However, precaution has to be made
that such ionic strength adjustment will not make sample unstable or that the additive does not react
with the sample (e.g. Cl with Ag ions).
7.2 Concentration limits
The lower concentration limit of the working range of DLS is determined, amongst other factors like
particle size, detector sensitivity, etc., by the number of particles that are present in the scattering volume.
The scattered light intensity (e.g. expressed as count rate or I ) of the sample containing the dispersed
s
particles should ideally be ≥10 times the signal obtained by the suspension medium alone. Scattered
intensity ratios below 10, either caused by low particle mass fractions or by very broad particle size
distributions, will result in higher variation of results and poorer precision.
The maximum concentration of dispersed particles that can be measured without the concentration
influencing the particle size reported is determined by particle-particle interaction and multiple
scattering. This concentration limit should be determined empirically by dilution (see Annex B).
7.3 Checks for concentration suitability
Different instruments adopt differing optical observation angles and optical arrangements. The
observations and checks given are for the general case, but the specific instrument operational advice
should also be considered.
The following observations and checks are recommended.
a) Visually inspect the dispersed sample prior to placing it into the instrument. At low concentrations,
the sample will look almost transparent. At higher concentrations, a milky or opaque appearance
is seen.
b) Ensure that the sample is placed in the instrument prior to performing the measurement, allowing
the sample to equalize its temperature. Check the count rate or signal level. The count rate or signal
level (I ) can be adjusted by changing an aperture in the receiver (which also changes the degree
s
of coherence of the detector), by adjusting the gain of the receiver or by adjusting the laser power
itself, either by adjusting the power applied to the light source (limited adjustment) or by employing
a neutral density filter in front of the light source or in front of the detector.
c) For instruments using correlation analysis in autocorrelation mode, conduct a measurement using
appropriate correlator settings and examine the intercept value which should be above the value
specified by the vendor of the instrument. A low value of intercept may result from either a poorly
aligned optical system, multiple scattering or from very weakly scattering samples requiring
the detector aperture be increased, resulting in a multiple coherence area detection. For larger
particles, the measurement volume may need to be increased to accommodate an adequate number
of particles. This can also reduce the intercept value. A lower-than-expected intercept value may
also be caused by sample absorbance or fluorescence. All of these factors may reduce the intercept
value requiring further tests to establish the reason.
d) Measurements performed at different concentrations should give the same results within their
measurement uncertainties. A decreasing particle size with increasing concentration indicates a
significant amount of multiple scattering, a change of viscosity of the suspension caused by different
viscosities of diluent and original suspension and/or collective motion of particles. Measurement at
different concentrations is also used to extrapolate the particle size to infinite dilution [see Clause
8, list item k)].
−5 −4
In many applications, a volume fraction (ϕ) of dispersed particulate material in the range 10 to 10
fulfils the requirements for particle sizes below about 500 nm. For cross-correlation or backscatter
techniques, higher concentrations can be achieved dependent on the sample. For polydisperse and/or
larger particles, it may not be possible to find a concentration that satisfies all requirements without
either increasing the coherence aperture of the receiver or increasing the diameter of the incident
laser beam in order to increase the measurement volume. If this is the case, then the intercept values
obtained may not meet the criterion set out in c). For particle sizes above 1 µm, the requirements c) and
d) can only be fulfilled in exceptional cases.
All sample preparation steps (suspension medium, particulate concentration, dispersion procedure)
should be recorded. (Recommendations for sample preparation are given in Annex D.)
8 Measurement procedure
a) Switch the instrument on and allow it to warm up. Typically about 15 min to 30 min is required
to stabilize the laser intensity and to bring the sample holder to an equilibrium at the desired
temperature.
NOTE 1 Monitoring the temperature rather than controlling it is sufficient for many applications provided
a known value of viscosity is available for the reported monitored temperature.
b) A measurement cell filled only with suspension medium should be checked to ensure a low count
rate or signal level, without radical fluctuations, which could indicate particle contamination. A
high count rate or signal level might indicate cell flare or dirty cell walls. For instruments that
provide background subtraction, measure and store the background signal for the dispersion
medium being used.
c) Visually inspect the sample for the presence of optically visible particles, flocs, fibres and other
possible contaminants. If these are present, repeat the sample preparation.
8 © ISO 2017 – All rights reserved

d) Transfer a required amount of sample to a suitable and clean measurement cell. The measurement
cell may be disposable (e.g. plastic) or re-usable (e.g. optical-quality glass or quartz). Compared
to disposable plastic cells, glass cells have as main advantage that there can be less refraction
when light scatters across the cell and thus the actual observation angle will be the same as
the geometrical angle between the detector and the incident light beam. The material of the
measurement cell must be chemically compatible with the dispersion medium and the particles.
Prior to sample loading, clean the cuvettes with filtered de-ionised water or solvent if non-aqueous
dispersions are measured. In case of residual impurities, a mild surfactant or soap solution,
specifically for optical cells, may be used. Rinse the cuvettes several times with filtered de-ionised
water in order to remove residual surfactant. Let the water drain away by inverting the cuvette.
Keep cleaned cuvettes capped until needed.
The pore size of the filter used for filtering the water or solvent should be appropriate to the
application. Ideally, a membrane with a pore size smaller than the smallest particle to be measured
should be used.
Alternatively, disposable plastic cuvettes (e.g. PMMA, polystyrene) may be used. The walls of plastic
cuvettes are easily scratched and do not provide the optical quality of glass or quartz. Therefore,
disposable cuvettes should not be used with weak scattering samples, and should be cleaned only
by rinsing with suspending medium and/or use of a particle-free air stream to remove loose dust
on the cell walls. Take care not to touch the cuvette windows with bare hands or to wipe cuvette
surface with any potentially abrasive material (including optical paper or tissue).
Place the test sample in the instrument or place the measurement probe into the sample. Allow
temperature equilibrium to be established. The temperature value should be known to better
than ±0,5 °C with minimal fluctuation of the value during the measurement.
An alternative method for instruments without a temperature sensor in the cell is to measure
the room temperature and then set the instrument to control the sample holder temperature to
within ±0,3 °C of the room temperature. Samples can then equilibrate at room temperature and
be measured immediately after insertion in the sample holder. Alternatively, samples can be
equilibrated in a temperature-controlled bath whose temperature is controlled to ±0,3 °C of that
of the instrument sample holder. In this case, dry the outside of the cell before inserting it into the
DLS instrument.
Uncertainties in particle size determined in aqueous suspensions will be approximately 2 % per
degree Celsius at ambient temperature if the test sample has not reached thermal equilibrium.
NOTE 2 For a temperature change of 3 °C, it can take about 10 min for the liquid in the measurement
volume of a measuring cell holding a 1 ml of sample to thermally equilibrate.
e) Ensure that no air bubbles are entrapped in the test sample for non-air bubble samples. Ensure that
no bubbles are attached to the walls of the cell.
f) Record test sample identification, date and time of the measurement and measurement
duration, number of individual measurements, measurement temperature, temperature
fluctuations during measurement, refractive index and viscosity of the suspension medium,
particle concentration/dilution, wavelength of laser and scattering angle, as well as the particle
concentration, if known.
g) Check the average scattered intensity of the sample.
For homodyne optical arrangements, it is preferred that the average scattering intensity be
controlled by adjusting the light output power, using neutral density filters, or by minimizing
the detector aperture, to maintain detection coherence, while adjusting the receiver sensitivity
within the limits specified by the manufacturer. The scattering signal from the test sample should
be ≥10 times the signal from the dispersing medium alone.
For heterodyne optical arrangements, the reference signal should be substantially greater than the
test sample scattering signal (a ratio reference signal: scattering signal of 10:1 should be aimed for).
It is preferred that the reference signal can be blocked so that the scattering signal can be assessed
as being greater than the suspension signal alone.
h) Measurements should not be continued if the light signal intensity contains isolated bursts of high
count rates which may indicate contamination of the test sample.
i) Measurements should not be continued if the correlation function does not decline monotonically
or if the power spectrum is not of Lorentz type.
j) Record the average particle diameter, x , and polydispersity index, PI, for each of the
DLS
measurements performed using the cumulants method.
k) If a systematic concentration dependence of the average particle size is observed, the results of an
extrapolation to infinite dilution (or the results obtained at the lowest acceptable concentration)
shall be reported. The dilution shall be performed with particle-free suspension medium,
containing the same concentration of salts, surfactants, pH, etc., in order to not alter the particle-
solution interactions.
Although the checks described here will minimize biasing effects due to multiple scattering,
particle interactions may, in particular for particles below 100 nm (diameter) at volume fractions
above 0,01, bias the estimation of the average diameter. Therefore, for unknown dispersed systems,
it is recommended that measurements are performed on at least two concentrations varying by a
factor of at least two.
l) Check at the end of the measurement that no significant sedimentation has occurred in the test
sample, either by visually checking for sediment or by inspecting the results of multiple, sequential
measurements for trends. If sedimentation is found, then it should be decided whether it is small
enough so that its effects on the precision of the measurement are acceptable or whether the
sample is unsuitable for DLS measurements.
9 Evaluation of results
9.1 General
DLS is a low resolution method that is not capable of resolving narrowly spaced peaks in the particle
size distribution. The low resolution also means that values away from mass-median-diameter, D ,
will have increasingly large uncertainties.
The original signal obtained by DLS is scattered intensity weighted. Many instruments allow calculation
of volume or number-weighted results from the scattered intensity-weighted signal. For most methods,
this involves smoothing of the scattered intensity-weighted particle size distribution, Q , which
int
introduces uncertainties. A second issue affecting all methods is the highly nonlinear dependence of
the scattering intensity on the particle size. Therefore, transformation of scattered intensity-weighted
distributions to volume number distributions is not recommended and number distributions from DLS
are specifically deprecated, especially for methods involving the smoothing of Q .
int
A particle size distribution determined by DLS is based on different physical properties than one
determined by, for example, laser diffraction (diffraction of light) or microscopy (transmission of
electrons), and therefore they can be different.
Note that, for a given size distribution, the distribution C(Γ) of decay rates or characteristic frequencies
is dependent on laser wavelength and state of polarization and on the scattering angle θ. Hence, x
DLS
and PI are of a given sample depending on those quantities.
Different algorithms exist for the evaluation of results. These algorithms will, for the same sample,
often give different results. Reporting of the algorithm and any internal settings or choices, together
with the results, is therefore crucial. This clause summarizes those algorithms that are sufficiently
standardized today. More information on the theoretical background is given in Annex A and a very
brief overview is found in Reference [7].
10 © ISO 2017 – All rights reserved

9.2 Correlation analysis
9.2.1 Cumulants method
The cumulants analysis compresses the entire multi-exponential decay distribution into the exponent
and then expands the exponent into a polynomial expression. Two parameters describing particle size
distributions, i.e. the average particle diameter x and the polydispersity index PI, are determined
DLS
[4]
by a variant of the so-called “cumulants method” .
Obtaining x and PI from the correlation function using the cumulants method can be accomplished
DLS
by a nonlinear least-squares fitting of the correlation function by using the gradient method, the Gauss-
Newton method or the Levenberg-Marquadt method. x and PI can also be obtained by a linear least
DLS
squares fit to the logarithm of the correlation function with proper statistical weighting for each data
point, since the operation of taking the logarithm of the data affects the weighting of the data points.
The data points now are not equally significant, although the error associated with counting statistics
may not be significantly different between correlator channels. The average value and polydispersity
obtained from the cumulants method are scattering intensity weighted.
9.2.2 Distribution calculation algorithms
In these algorithms, the distribution of diffusion coefficients for a particle suspension or molecular
solution is calculated by applying a multi-exponential fitting algorithm to the correlation function. The
output of these algorithms is a particle size distribution from which, if needed, an average particle size
can be determined.
9.2.2.1 Regularized non-negative least squares (NNLS)
The non-negative least squares (NNLS) algorithm fits the exponential decay of the correlation function
algebraically. There are a variety of parameters that can be altered in an NNLS algorithm, but the two
principal ones are the “weighting scheme” and the “alpha parameter” or “regularizer.” Data weighting
is used in DLS algorithms to amplify subtle changes in the larger and more significant correlation
coefficients over noise in the baseline. In the absence of data weighting, noise in the baseline can lead to
the appearance of artefact peaks and erroneous data interpretation.
The regularizer or alpha parameter in NNLS-based dynamic light scattering algorithms controls the
acceptable degree of “spikiness” in the resultant distribution. Deconvolution of the DLS-measured
correlation function is accomplished using an inverse Laplace transform that is ultimately reduced
to a linear combination of eigenfunctions. The caveat to this approach is that when the eigenvalues
are small, a very small amount of noise can make the number of possible solutions extremely large,
hence the labelling of the DLS method as an ill-posed problem. In order to overcome the problem, a
stabilizing term, in the form of the “first derivative” of the d
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