ISO 13319-2:2023

INTERNATIONAL ISO
STANDARD 13319-2
First edition
2023-09
Determination of particle size
distribution — Electrical sensing zone
method —
Part 2:
Tunable resistive pulse sensing
method
Détermination de la distribution granulométrique — Méthode de
détection de zones électrosensibles —
Partie 2: Méthode par détection d'impulsions résistives accordable
(TRPS)
Reference number
© ISO 2023
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ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 2
5 Principles . 3
6 General operation . 5
6.1 Determination of particle size . 5
6.2 Determination of particle concentration . 6
6.3 Calibration . 6
6.4 Dynamic range . 7
6.5 Coincidence events . 7
6.6 Off-axis particle transport . 8
6.7 Polarization . 8
6.8 Dielectrophoresis . 10
6.9 Drag . 11
7 Operational procedure .11
7.1 General . 11
7.2 Instrumental components . 11
7.3 System set-up and optimization . 11
7.3.1 General . 11
7.3.2 Preparing fluid cell and stretching the TPU aperture .12
7.3.3 Wetting the TPU aperture .12
7.3.4 Establishing stable baseline current .12
7.3.5 Coating the TPU aperture .12
7.3.6 Optimising measurement parameters and running calibration .12
7.3.7 Adjusting conditions for the sample and recording data .13
7.3.8 Re-calibrating to ensure system stability . 14
7.4 Sample preparation . 14
7.4.1 General . 14
7.4.2 TRPS suspension requirements . 15
7.4.3 Preventing contamination . 15
7.4.4 Removing proteins and solutes . 16
7.4.5 Maintaining sample integrity . 16
7.4.6 Enhancing suspension stability . 16
Annex A (informative) TRPS best practice .17
Annex B (informative) Troubleshooting factors that affect TRPS measurements .18
Annex C (informative) Size distribution and concentration measurements of phospholipid
nano- and micro-bubbles .19
Annex D (informative) Method development for TRPS particles measurements .20
Bibliography .21
iii
Foreword
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sieving, Subcommittee SC 4, Particle characterization.
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iv
Introduction
Monitoring particle size distributions and particle concentrations are required in various fields, where
particle dispersions in liquid play a role. The electrical sensing zone technique has, since its discovery
by W. H. Coulter around 1950, been widely employed for size and count analysis of (blood) cells, bacteria
and other fine particles. Over the last decades, the application range has expanded to nanoparticles,
such as liposomes, exosomes, and nano- and micro-bubbles, as a result of improved electronics and
aperture fabrication. The tunable electrical sensing zone technique is useful for the determination of
the size distribution, concentration and zeta potential of micro- and nanoparticles suspended in a liquid.
The purpose of this document is to provide the background and procedures for application of tunable
electrical sensing zone equipment for particle size distribution and concentration measurements, so as
to improve the reproducibility and the accuracy of the acquired results.

v
INTERNATIONAL STANDARD ISO 13319-2:2023(E)
Determination of particle size distribution — Electrical
sensing zone method —
Part 2:
Tunable resistive pulse sensing method
1 Scope
This document specifies the measurements of particle size distribution and concentration of suspended
particles, ranging from 40 nm to 100 µm, using tunable resistive pulse sensing (TRPS). This document
provides a comprehensive overview of the methodologies that are applied to achieve reproducible and
accurate TRPS measurement results. This document also includes best practice considerations, possible
pitfalls and information on how to alleviate or avoid these pitfalls.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
aperture
small diameter hole through with suspension is drawn
[SOURCE: ISO 13319-1:2021, 3.2]
3.2
sensing zone
volume of electrolyte within and around the aperture in which a particle is detected
[SOURCE: ISO 13319-1:2021, 3.3]
3.3
pulse frequency
number of pulses per duration
3.4
detection range
size range between the smallest and largest detectable particle diameter
3.5
dynamic range
ratio between the largest and smallest detectable particle diameter
3.6
electrokinetics
phenomena that are associated with the tangential liquid motion in respect to a charged surface
[SOURCE: ISO 26824:2022, 3.17.16]
3.7
electrophoresis
movement of charged colloidal particles or polyelectrolytes, immersed in a liquid, under the influence
of an external electric field
[SOURCE: ISO 13099-1:2012, 2.2.4]
3.8
electroosmosis
motion of liquid through or past a charged surface, e.g. an immobilized set of particles, a porous plug, a
capillary or a membrane, in response to an applied electric field, which is the result of the force exerted
by the applied field on the countercharge ions in the liquid
[SOURCE: ISO 13099-1:2012, 2.2.1]
3.9
electrophoretic mobility
electrophoretic velocity per unit electric field strength
Note 1 to entry: Electrophoretic mobility is expressed in metres squared per volt second.
[SOURCE: ISO 13099-3:2014, 3.2.5, modified — the symbol “μ” and the former Note 1 to entry have been
deleted.]
3.10
zeta potential
difference in electric potential between that at the slipping plane and that of the bulk liquid
Note 1 to entry: Slipping plane is the abstract plane in the vicinity of the liquid/solid interface where liquid starts
to slide relative to the surface under influence of a shear stress.
Note 2 to entry: The zeta potential is expressed in volts.
[SOURCE: ISO 13099-1:2012, 2.1.8]
4 Symbols
For the purpose of this document the following symbols apply.
A pulse height of particle i
i
C particle number concentration
C particle concentration at which coincidence probability is 5 %
D aperture diameter
d particle diameter
E electric field
f Clausius-Mossotti factor
CM
F dielectrophoretic force
dep
f pulse frequency
p
K calibration constant of concentration
C
K calibration constant of diameter
d
L aperture length
N true count of particles
n observed count of particles
P pressure
S applied stretch
U voltage
V analysis volume
m
V sensing volume
sens
є є absolute permittivity of the fluid
0 fl
5 Principles
TRPS is an electrical sensing zone technique that can be used for characterization of the particle size
distribution, concentration and zeta potential of synthetic (e.g. metallic, polymeric or ceramic particles),
biological particles [e.g. nano-pharmaceuticals or extracellular vesicles (EVs)] and naturally occurring
organic and inorganic nano- and microparticles suspended in liquids. A dilute suspension of particles in
an electrolyte passes through an aperture in a membrane. There is an Ag/AgCl electrode on both sides
of the membrane, between which an electric potential is applied, which causes a stable ionic current
passing through the aperture. When a particle translocates the aperture, it causes a resistive pulse due
[1]
to the replacement of conductive electrolyte solution by a non-conductive solid particle . The height,
width and frequency of these pulses provide all the information required to determine particle size,
[2]
concentration and zeta potential . Particle passage through the aperture is caused by:
— a pressure difference across the aperture for particle size determination and concentration;
— a voltage difference between the two electrodes across the aperture for zeta potential measurement;
— both a voltage and a small pressure difference between the two electrodes across the aperture for
simultaneous measurement of particle size and zeta potential.
More background and a schematic of the instrumentation is given in ISO 13319-1 and Figure 1. Pressure
can be monitored directly via a pressure sensor as shown in Figure 1 or indirectly via a flow rate meter.
Key
1 pressure module
2 pressure sensor
3 nanoparticle/microparticle suspension
4 aperture
5 voltage source
6 amplifier
7 analogue to digital converter
8 computer
9 output device
Figure 1 — Schematic representation of TRPS instrument
There are three main differences between conventional electrical sensing zone and TRPS equipment.
Firstly, calibration standards are typically used to calibrate the aperture and provide traceable and
accurate TRPS measurements. However, measurements can also be done without the use of calibration
standards, in particular when fixed aperture geometries are applied.
The second difference is that pressure (pressure module) and voltage (voltage source) are tunable
to allow for full control of convective and electrokinetic velocity contributions of single particles
translocating the aperture, a prerequisite for measuring particle size, concentration and zeta potential.
The third difference is the use of both fixed and tunable apertures for TRPS application. While
there are several chip and aperture providers using 3D printed microfluidic and glass-based fixed
geometry apertures that can be used, there are also tunable apertures, for example, made in an elastic
thermoplastic polyurethane (TPU) membrane. Despite having several aperture options, the focus is on
tunable TPU aperture based TRPS operation.
TPU apertures are formed by generating a micron-sized hole into an elastic TPU membrane, which
can be stretched mechanically to the desired size for measurement. Thus, the aperture can be tuned
to the optimum size for the particles at hand. A schematic of the setup is given in Figure 2. For very
polydisperse samples, a range of apertures can be required for the full measurement of the sample size
distribution and concentration (see example in Figure C.1).
NOTE In Figure 2, jaws are used for clamping and stretching/relaxing the membrane.
a) TRPS with a tunable TPU aperture b) Detail of a TPU aperture
Key
1 stretching device
2 top fluid cell
3 ground electrode
4 tunable aperture
5 signal electrode
6 bottom fluid cell
7 current
Figure 2 — Schematic representation of TRPS with a tunable TPU aperture
6 General operation
6.1 Determination of particle size
As in the conventional electrical sensing zone technique, a pressure drop over the aperture causes
the suspension to flow through it and the pulse height resulting from particle passage is regarded
directly proportional to particle volume (see ISO 13319-1). TRPS is a particle by particle, as opposed
to an averaging ensemble measurement technique, with each pulse corresponding to a single particle.
Calibration, if required, is executed through the application of certified reference materials with
[3]
traceable certified values . The calibration factor relates the height of the measured pulses to volume-
equivalent diameters, as shown in Formula (1).
dA=K (1)
id i
where
d is the size of particle i (volume-equivalent diameter);
i
K is the calibration constant;
d
A is the pulse height of particle i.
i
6.2 Determination of particle concentration
At sufficient pressure drop over the aperture, convection is the dominant transport mechanism. Then,
the stochastic pulse frequency ( f ), which is equal to the particle count rate at 0 coincidence probability,
p
[4]
is proportional to the product of the particle concentration (C) and the fluid flow rate (Q) . Since the
fluid flow rate is proportional to the applied pressure drop (P), the particle concentration can be
calculated as the slope of the linear relationship of pulse frequency versus applied pressure, with K
C
being a calibration constant [see Formula (2)]. Formula (2) also applies to scenarios where convection
Δf
p
is not the dominant transport mechanism, with the slope (equal to ) of the linear f versus P
p
ΔP
relationship determining the particle concentration.
Δf
 
p
C = K (2)
 
C
ΔP
 
The use of a calibration standard of known concentration allows the determination of the concentration
of a sample at a single pressure, if convection is the dominant transport mechanism. This is typically
the case for larger particles and larger apertures. Particle concentration and size can be determined
simultaneously.
However, concentration measurements over a defined particle size range are typically obtained with a
multi-pressure calibration procedure, where particle rates for sample and calibration are analysed at
[5],[6]
two or more pressures . Particle concentrations are calculated from the slope of the linear particle
rate versus pressure dependence, while particle sizes are determined individually from the respective
resistive pulse heights, which are linearly related to particle volumes [see Formula (1)]. This includes
information about the size distribution, i.e. the number concentration of each size population within
a sample, given by the number of particles per ml and per nm (bin-size). An example of a typical TRPS
concentration measurement is shown in Figure C.1.
A summary of recommended setting for TRPS size distribution and concentration measurements using
TRPS instrumentation with a tunable TPU aperture is shown in Table 1, and reference guidance to
aperture selection can be found in Table 2.
Table 1 — Typical settings for various TRPS measurements using TRPS instrumentation and
TPU apertures
Parameter
Applied voltage Applied pressure Sample size range Sample concentration Reference
≤5 V ≤2,5 kPa 40 nm to 100 μm Size dependent [3] and [7]
6.3 Calibration
TRPS instruments are preferably calibrated with monodisperse polystyrene particles, whose certified
mean diameter is traceable to the International System of Units (SI), however that does not exclude
the use of quality control materials such as silica particles or liposomes, depending on the application
at hand. For particle TRPS concentration measurements, using elastic TPU apertures, the knowledge
of the aperture characteristics is generally unavailable. It is therefore required to use a calibration
standard with known particle size and number concentration to obtain the concentration information
of the analytes. However, it is possible to calculate particle concentration by predicting the size and
geometry of the aperture through the measured background current at a given voltage. Nevertheless,
calibration increases measurement reproducibility and traceability and hence it is predominantly
[6]
used . For TRPS concentration measurements, calibration and sample are typically measured in
alternation in order to virtually eliminate the impact of any change in aperture geometry occurring
during the measurement process.
The concentration of the standards is determined gravimetrically (mass fraction of solids) with the
knowledge of the mean particle diameter and particle density. Concentration standards are typically
bare polystyrene particles, whose certified mean diameter is traceable to the international system
of units (SI) or alternatively carboxylated polystyrene standards. Ideally, the standards should have
concentration values that are traceable to SI, but unfortunately such standards are not available yet.
The linearity of the counting system can be tested by obtaining three repeat measurements of the total
counts (across all channels) at an arbitrary concentration. The concentration is then reduced and three
further repeat total counts obtained (see ISO 13319-1).
Table 2 gives reference guidance to TPU aperture selection, target calibrant and sample particle
concentrations. The size range shown can be detected across the standard stretch of 3 mm to
7 mm under optimal setting conditions. Note that target concentrations lie well below the particle
concentration C , at which the coincidence probability is 5 % (see Table 3) for respective apertures.
Table 2 — Guidance on TPU aperture size selection, calibrant and particle concentration
Average tunable TPU Range of measured Range of possible polystyrene Target particle
aperture diameter particle diameters standard particle diameters concentration
−1
nm nm nm ml
300 40 to 225 70 to 100 1 × 10
400 50 to 330 100 to 200 1 × 10
800 85 to 500 200 to 400 2 × 10
1 500 185 to 1 100 400 to 800 5 × 10
4 000 490 to 2 900 1 000 to 2 000 5 × 10
15 000 2 000 to 11 300 4 000 5 × 10
6.4 Dynamic range
The dynamic range is the ratio between the largest and smallest diameter of spherical particles that
can be detected. The detection range at its lower end is determined by the electrical noise of the system,
that originates from thermal motion of charge carriers, dielectric noise due to the energy dissipated by
[8]
the dielectric aperture substrate, amplifier noise and flicker noise . Hence, it depends on many factors,
including the aperture material, aperture thickness, the choice of electronic components, temperature,
etc. In practice, the lower limit of the detection range is defined as the diameter of a spherical particle
that causes a relative current change of 0,05 %.
The upper limit of the detection range has been defined as half of the smallest constriction of an
aperture, which has been experimentally proven to be an appropriate value, with an aperture blocking
kept at a low level. The dynamic range for a typical conical TPU aperture is ranging from 4 (for a fixed
stretch) to 15, with the upper limit achievable over the full aperture stretch range.
6.5 Coincidence events
Coincidence events occur, when two or more particles translocate the sensing zone at the same or
slightly different time. Consequences and calculation of coincidence events have been dealt with in
ISO 13319-1. In order to keep such events at a minimum, particle concentration needs to be kept under
a certain level. Table 3 shows estimated particles per ml for the coincidence probability to be 5 %. The
probabilities that a given number of particles are found within sensing zone of the aperture follows the
[9]
Poisson distribution. Formula (3) is derived from the Poisson distribution :
V
sens
− N
V
m V
m
n=−(1 e) (3)
V
sens
where
n is the observed count of particles;
N is the true count of particles;
V is the analysis volume;
m
V is the sensing volume.
sen
Table 3 — Particle number concentrations with 5 % coincidence probability and analysis
volumes for typical TPU aperture diameters — Small aperture opening of conical apertures
a b
Aperture diameter Particle concentration with 5 % coincidence Analysis volume
D C V
5 m
−1
nm ml ml
8 −4
4 000 3,7 × 10 1 × 10
9 −5
1 500 6 × 10 1 × 10
11 −7
400 4 × 10 5 × 10
a
Calculated from 90 % (of total aperture resistance) sensing zone of a conical aperture with a cone angle of 10°.
b
Analysis volume equivalent to 5 000 counts.
6.6 Off-axis particle transport
As detailed earlier, the sizing method can be summarized, using the simple relation that the pulse
height is proportional to particle volume, while applying calibration particles of known diameter. Size
histograms are constructed under the assumption that each pulse height accurately reflects the size
of a single particle according to this relationship. However, the size distribution width is not solely
determined by particle size dispersity. It also depends on different trajectories particles can take
through the aperture, with resistive pulses increasing in size with the distance of the particle from the
[10]-[13]
central axis of cylindrical apertures . Distribution broadening and associated size shifts can be
reduced significantly by working with relatively (compared to the particle sizes) small apertures and
using a calibration-based methodology.
6.7 Polarization
In TRPS, a transient pulse in ionic current is observed, when an individual colloid particle passes
through an aperture which separates two fluid reservoirs. The pulse is typically resistive, but under
certain experimental conditions conductive pulses as well as biphasic pulses, with both resistive and
[14]
conductive components are observed . Factors, that impact on the type and height of the pulse are
the ionic strength and type of the electrolyte, aperture size and shape asymmetry, aperture surface
charge, applied voltage and particle surface charge.
The ionic distribution in a conical TPU aperture is affected by concentration polarization, that also
[15]
causes ion current rectification of asymmetric nanopores . When a positive voltage is applied across
a negatively charged aperture, positive ions move freely from one fluid cell to the other, while negative
ions are electrostatically repelled by the membrane. This results in a net increase in ion concentration
near the cathode and a net decrease in ion concentration near the anode. Figure 3 shows the schematic
cross-section through a membrane, showing a conical aperture with a pressure gradient (P − P )
2 1
applied across and one particle translocating it. Both the particle and the aperture are negatively
charged. Ionic concentration polarization is qualitatively indicated by the distribution of “+” and “−”
signs. The polarization leads to a zone that is enriched with ions and another one that is depleted of ions
on opposite sides of the conical aperture.
Key
1 pressure at small pore entrance 4 ion enrichment
2 pressure at large pore entrance 5 ion deficiency
3 aperture
Figure 3 — Concentration polarization
Concentration polarization as shown in Figure 3 can lead to underestimation of measured particle size,
with the size shift increasing with increasing particle surface charge, increasing particle size for a given
aperture size, decreasing applied pressure, increasing voltage, and decreasing aperture stretch and
aperture size. The increase of pressure will disrupt the polarization profile of the ions and hence reduce
the size shift effect, while increased voltage will increase the electric field, increase the polarization and
hence increase the size shift effect. Through the application of pressure and using a calibration-based
methodology, this polarization dependent size shift effect can be minimised and rendered negligible.
In TRPS, using conical TPU apertures, biphasic pulses are not observed at electrolyte concentration
[14]
of phosphate buffered saline above approximately 50 mM . Biphasic pulses are co
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