ASTM E2865-12(2018)

Standard Guide for Measurement of Electrophoretic Mobility and Zeta Potential of Nanosized Biological Materials

SCOPE
1.1 This guide deals with the measurement of mobility and zeta potential in systems containing biological material such as proteins, DNA, liposomes and other similar organic materials that possess particle sizes in the nanometer scale (  
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Historical
• Publication Date: 31-Dec-2017
• ICS: 07.120 - Nanotechnologies
• Technical Committee: E56 - Nanotechnology
• Drafting Committee: E56.02 - Physical and Chemical Characterization

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E2865 − 12 (Reapproved 2018)
Standard Guide for
Measurement of Electrophoretic Mobility and Zeta Potential
of Nanosized Biological Materials
This standard is issued under the fixed designation E2865; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope ISO 13099-2 Colloidal Systems — Methods for Zeta-
Potential Determination — Part 2: Optical Methods
1.1 This guide deals with the measurement of mobility and
ISO 13321Particle Size Analysis — Photon Correlation
zetapotentialinsystemscontainingbiologicalmaterialsuchas
Spectroscopy
proteins, DNA, liposomes and other similar organic materials
that possess particle sizes in the nanometer scale (<100 nm).
3. Terminology
1.2 The values stated in SI units are to be regarded as
3.1 Definitions—Definitions of nanotechnology terms can
standard. No other units of measurement are included in this
be found in Terminology E2456.
standard.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 Brownian motion—is the random movement of par-
1.3 This standard does not purport to address all of the
ticles suspended in a fluid caused by external bombardment by
safety concerns, if any, associated with its use. It is the
dispersant atoms or molecules.
responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter-
3.2.2 dielectric constant—the relative permittivity of a ma-
mine the applicability of regulatory limitations prior to use.
terialforafrequencyofzeroisknownasitsdielectricconstant
1.4 This international standard was developed in accor-
(or static relative permittivity).
dance with internationally recognized principles on standard-
3.2.2.1 Discussion—Technically,itistheratiooftheamount
ization established in the Decision on Principles for the
of electrical energy stored in a material by an applied voltage,
Development of International Standards, Guides and Recom-
relative to that stored in a vacuum.
mendations issued by the World Trade Organization Technical
3.2.3 electrophoretic mobility—the motion of dispersed par-
Barriers to Trade (TBT) Committee.
ticlesrelativetoafluidundertheinfluenceofanelectricalfield
(usually considered to be uniform).
2. Referenced Documents
3.2.4 isoelectric point—point of zero electrophoretic mobil-
2.1 ASTM Standards:
ity.
E1470Test Method for Characterization of Proteins by
3.2.5 mobility—see electrophoretic mobility.
Electrophoretic Mobility (Withdrawn 2014)
E2456Terminology Relating to Nanotechnology
3.2.6 redox reaction—a chemical reaction in which atoms
2.2 ISO Standards: have their oxidation number (oxidation state) changed.
ISO 13099-1 Colloidal Systems — Methods for Zeta-
3.2.7 stability—the tendency for a dispersion to remain in
Potential Determination — Part 1: Electroacoustic and
the same form for an appropriate timescale (for example, the
Electrokinetic Phenomena
experiment duration; on storage at 358K).
3.2.7.1 Discussion—In certain circumstances (for example
water colloid flocculation) instability may be the desired
This guide is under the jurisdiction of ASTM Committee E56 on Nanotech-
property.
nology and is the direct responsibility of Subcommittee E56.02 on Physical and
Chemical Characterization.
3.2.8 van der Waals forces—in broad terms the forces
Current edition approved Jan. 1, 2018. Published January 2018. Originally
between particles or molecules.
approved in 2012. Last previous edition approved in 2012 as E2865 – 12. DOI:
10.1520/E2865-12R18.
3.2.8.1 Discussion—These forces tend to be attractive in
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
nature (because such attractions lead to reduced energy in the
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
system) unless specific steps are undertaken to prevent this
Standards volume information, refer to the standard’s Document Summary page on
attraction.
the ASTM website.
The last approved version of this historical standard is referenced on
3.2.9 zeta potential—the potential difference between the
www.astm.org.
dispersion medium and the stationary layer of fluid attached to
Available from International Organization for Standardization (ISO), 1, ch. de
la Voie-Creuse, CP 56, CH-1211 Geneva 20, Switzerland, http://www.iso.org. the dispersed particle.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2865 − 12 (2018)
3.2.10 zwitterionic—a molecule with a positive and a nega- movement may be hindered. In this circumstance, although a
tive electrical charge. movement can be detected and measured, it may provide
3.2.10.1 Discussion—Amino acids are the best known ex-
interpretation issues when a conversion to zeta potential is
amples of zwitterions.
attempted.
4.3.3 Zeta potential tends only to be important in the sub-5
4. Summary of Practice
µm (and thus relevant to the sub-100 nm region considered in
4.1 Introduction—It is not the intention of this guide to
this text) region where van der Waals attractive forces are of a
spend any significant time on the theory of zeta potential and
similar order of magnitude as inertial forces. Thus if sedimen-
the routes by which a particle acquires charge within a system.
tation (function of size and density of the particle with respect
Indeed it may be more appropriate to deal only with the
to the medium it resides) is occurring or has occurred, the
movement or mobility of particles under an electrical field
system is clearly not ideal for a zeta potential or mobility
where conversion to zeta potential is not even attempted. The
measurement. With significant settling the measurement of
relevant text books (for example, see Hunter (1) ) should be
mobility is obviously compromised. The lower limit for
consulted along with the more academic ISO references (ISO
measurement of electrophoretic mobility is in effect deter-
13099-1 and ISO 13099-2). The IUAPC report (2) is also very
mined by the signal to noise which is a complex function of
useful, albeit fairly theoretical, but it does contain a section
size, concentration and relative refractive index of the particu-
(4.1.2) entitled ‘How and under which conditions the electro-
late system. An unambiguous statement of the lower size is
phoretic mobility can be converted into ζ-potential’. The
therefore not possible.
Corbett and Jack paper (3) contains excellent practical advice
4.3.4 Zeta potential and its (assumed) relation to system
for measurement of protein mobility and is recommended.
stability are reasonably well understood in aqueous systems.
4.2 Test Method E1470 is based around a sole vendor’s
The classic examples are indicated in Thomas Riddick’s text
equipment, but this does not deal with the basis of the
(4). The obvious or stated link with formulation or product
measurement or provide guidance in the practice of the
stability is not obvious for organic media where the counter-
measurement. It is one intention of this guide to address those
ions will be strongly bound to the particle surface and the
deficits.
position of the diffuse layer will be difficult to identify in an
4.3 The following aspects need emphasis:
(effectively) insulating external medium. Again, what is often
4.3.1 Zetapotentialisafunctionoftheparticulatesystemas
forgotten, is that conductivity is required in the ‘background’
-1
a whole – so the environment that the particle resides in (pH,
solution (typically 0.001 molL sodium chloride (NaCl) is
concentration, ionic strength, polyvalent ions) will directly
utilized) so that an electrical field can be correctly applied
influence the magnitude and, in certain circumstances, the sign
without effects such as electrode polarization (causing voltage
of the acquired charge. In particular, small quantities (parts per
irregularities) occurring. Mobility or zeta potential measure-
2+
million) of polyvalent ions (for example calcium ions (Ca ),
ments should not be made in de-ionized water. In non-polar
3+
iron(III)ions(Fe ))orotherimpuritiescansignificantlyaffect
dispersant liquids, conversion of observed mobility to zeta
the magnitude of the zeta potential. It is obvious, but often
potential may need some understanding of the position and
ignored, that there is no such concept of the zeta potential of a
thickness (single atom or molecule?) of the double layer, but
powder.
this is not relevant to measurements in (aqueous) biological
4.3.2 The calculation of zeta potential from mobility mea-
media.
surement typically refers to the unrestricted mobility of a
4.3.5 Itismobility(movement)thatisusuallymeasuredand
particle in suspension. In crowded environments (that is high
the conversion to zeta potential relies on application of the
concentration) particle-particle interactions occur and the
Henry equation. (See also Fig. 1).
5 εζ f~κα!
The boldface numbers in parentheses refer to a list of references at the end of
U 5 (1)
E
6πη
this standard.
FIG. 1 Equation (1)
E2865 − 12 (2018)
where: et al. (6)). 1/κ can be envisioned as the "thickness" of the
electrical double layer (the Debye length) and thus the units of
U = the electrophoretic mobility (measured by
E
κarereciprocallength.Thusf(κα)isdimensionlessandusually
instrument),
assignedthevalue1.00or1.50.Forparticlesinpolarmediathe
ε = the dielectric constant of the dispersion medium,
maximum value of f(κα) is taken to be 1.5 (Smoluchowski
ζ = the (calculated) zeta potential,
f(κα) = Henry’s function (see below), and
approximation) and for particles in non-polar media the mini-
η = theviscosityofthemedium(measuredorassumed).
mum value of f(κα) is 1 (Hückel approximation). It is the
former that we are considering in this text. The literature does
4.3.5.1 Itisimportanttospecifytheunitsofmeasurementas
indicate intermediate values for f(κα) but in most biologically
failure to get these correct will lead incompatibility of units on
relevant media the value of 1.5 is the most appropriate.
the right and left hand side of the above equation. The normal
4.3.5.4 In terms of viscosity, η, the SI physical unit of
SI units (metre, kilogram, second) are not often utilized in this
dynamic viscosity is the pascal-second (Pa·s), (equivalent to
area as they are too large for practical purposes (diffusion
N·s/m , or kg/(m·s)). Water at 293K has a viscosity of
distances of one metre are not routinely encountered!) — see
0.001002 Pa·s. The cgs physical unit for dynamic viscosity is
additional unit information in Ref. (5). We need to remember
the poise (P). It is more commonly expressed, particularly in
that the mobility and diffusion coefficient are a flux (and thus
ASTM standards, as centipoise (cP). Water at 293K has a
area) per unit time. The mobility will be scaled by the field
viscosity of 1.0020 cP.
(volts/distance). Ref. (5) recommended units for electropho-
2 -1 -1 -1
retic mobility are m s V . This can be expressed as (ms )/
NOTE 1—At room temperature (assumed 298K) in water, all of the
-1
(Vm ) or a velocity per unit field. In practice, the electropho- expressions are constants except for the (measured) mobility and the
equation defers to:
retic mobility, U , has more convenient units of µm /Vs Often
E
mobilities are expressed in confused units (for example, the
Zetapotential 5 K*electrophoreticmobility, U ; 12.85*U (2)
E E
-1
oft-utilized µmcm /Vs because this gives rise to mobility
where the value of K (collective proportionality constant) is ~12.85 if
thezetapotentialistobestatedinmVandthisfallsoutnaturallyfromthe
values in the convenient 610 region). Mobilities expressed
-1
Henry equation if the deprecated µmcm /Vs unit is used for electropho-
with a negative sign imply a negative zeta potential.
retic mobility.
4.3.5.2 ε is the dielectric constant of the dispersion medium
dimensionless/nounitsasitisaratiooftherelativepermittivity 4.3.5.5 As well as movement under the constraint of an
ofthematerialtovacuumwhoserelativepermittivityisdefined electric field, some degree of Brownian motion will also occur
as 1. and may need to be considered. In biological media of
4.3.5.3 f(κα) is usually referred to as “Henry’s function” relatively high ionic strength the Hückel model (f(κα)=1)for
where α is the radius of the particle. κ is referred to as the zetapotentialcalculationisinappropriateandthevalueoff(κα)
Debye parameter and can be calculated from the electronic should be calculated from the measured size and the known
charge, Boltzmann’s and Avogadro’s constants, the absolute ionic strength (or measured conductivity) (see Fig. 2).
temperature and the ionic strength. The charged region around 4.3.6 Systems of positive charge tend to provide more
a particle falls to about 2% of the surface charge at a distance measurement difficulties from a practical perspective than
approximately 3/κ from the particle. For ionic strength around thoseofinherentnegativecharge.Thisisbecausemostorganic
-1
0.01 molL then 3/κ is around 10nm and for ionic strength media including plastic sample cells are inherently negatively
-5 -1
around10 molL then3/κisaround280nm(seeKoutsoukos charged at neutral pH and may attract particles of opposite
FIG. 2 Graphical Representation of the Henry Function and the κa Values for Four Example Particle Size and Ionic Strength Combina-
tions
E2865 − 12 (2018)
charge removing them from suspension and altering the wall measure a few µLof sample with specific experimental set-ups
potential. It is useful to have some form of automation for pH as the electrodes need to be of a finite size and distance apart.
adjustment – for example a titrator. This eases the adjustment In many instances a few millilitres of solution or suspension
of pH and additive concentration. will make life easy, especially if flushing of a cell is needed,
but this is not always available. If the material can be held as
4.3.7 It is of no value to state a zeta potential value without
a ‘plug’ it may be possible to work with considerably less
description of the manner in which it was measured together
quantity.
with vital measurement parameters. Zeta potential without a
4.4.4 Biological material is often contained in buffered
stated pH, ionic compostion, and electrolyte concentration
solutions of relatively high ionic concentration. For example,
value is close to meaningless.
phosphate buffered saline (PBS) is constituted of 0.0032
4.4 Biological Molecules and Entities—Again, a few obvi-
-1
molL di
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E2865 − 12 E2865 − 12 (Reapproved 2018)
Standard Guide for
Measurement of Electrophoretic Mobility and Zeta Potential
of Nanosized Biological Materials
This standard is issued under the fixed designation E2865; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This guide deals with the measurement of mobility and zeta potential in systems containing biological material such as
proteins, DNA, liposomes and other similar organic materials that possess particle sizes in the nanometer scale (<100 nm).
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
E1470 Test Method for Characterization of Proteins by Electrophoretic Mobility (Withdrawn 2014)
E2456 Terminology Relating to Nanotechnology
2.2 ISO Standards:
ISO 13099-1 Colloidal systemsSystems — Methods for zeta-potential determinationZeta-Potential Determination — Part 1:
Electroacoustic and electrokinetic phenomenaElectrokinetic Phenomena
ISO 13099-2 Colloidal systemsSystems — Methods for zeta-potential determinationZeta-Potential Determination — Part 2:
Optical methodsMethods
ISO 13321 Particle Size Analysis — Photon Correlation Spectroscopy
3. Terminology
3.1 Definitions—Definitions of nanotechnology terms can be found in Terminology E2456.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 Brownian motion—is the random movement of particles suspended in a fluid caused by external bombardment by
dispersant atoms or molecules.
3.2.2 dielectric constant—the relative permittivity of a material for a frequency of zero is known as its dielectric constant (or
static relative permittivity).
3.2.2.1 Discussion—
Technically, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in
a vacuum.
This guide is under the jurisdiction of ASTM Committee E56 on Nanotechnology and is the direct responsibility of Subcommittee E56.02 on Physical and Chemical
Characterization.
Current edition approved Jan. 1, 2012Jan. 1, 2018. Published June 2012January 2018. Originally approved in 2012. Last previous edition approved in 2012 as E2865 –
12. DOI: 10.1520/E2865-12.10.1520/E2865-12R18.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
The last approved version of this historical standard is referenced on www.astm.org.
Available from International Organization for Standardization (ISO), 1, ch. de la Voie-Creuse, CP 56, CH-1211 Geneva 20, Switzerland, http://www.iso.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2865 − 12 (2018)
3.2.3 electrophoretic mobility—the motion of dispersed particles relative to a fluid under the influence of an electrical field
(usually considered to be uniform).
3.2.4 isoelectric point—point of zero electrophoretic mobility.
3.2.5 mobility—see electrophoretic mobility.
3.2.6 redox reaction—a chemical reaction in which atoms have their oxidation number (oxidation state) changed.
3.2.7 stability—the tendency for a dispersion to remain in the same form for an appropriate timescale (for example, the
experiment duration; on storage at 358K).
3.2.7.1 Discussion—
In certain circumstances (for example water colloid flocculation) instability may be the desired property.
3.2.8 van der Waals forces—in broad terms the forces between particles or molecules.
3.2.8.1 Discussion—
These forces tend to be attractive in nature (because such attractions lead to reduced energy in the system) unless specific steps
are undertaken to prevent this attraction.
3.2.9 zeta potential—the potential difference between the dispersion medium and the stationary layer of fluid attached to the
dispersed particle.
3.2.10 zwitterionic—a molecule with a positive and a negative electrical charge.
3.2.10.1 Discussion—
Amino acids are the best known examples of zwitterions.
4. Summary of Practice
4.1 Introduction—It is not the intention of this guide to spend any significant time on the theory of zeta potential and the routes
by which a particle acquires charge within a system. Indeed it may be more appropriate to deal only with the movement or mobility
of particles under an electrical field where conversion to zeta potential is not even attempted. The relevant text books (for example,
see Hunter (1) ) should be consulted along with the more academic ISO references (ISO 13099-1 and ISO 13099-2). The IUAPC
report (2) is also very useful, albeit fairly theoretical, but it does contain a section (4.1.2) entitled ‘How and under which conditions
the electrophoretic mobility can be converted into ζ-potential’. The Corbett and Jack paper (3) contains excellent practical advice
for measurement of protein mobility and is recommended.
4.2 Test Method E1470 is based around a sole vendor’s equipment, but this does not deal with the basis of the measurement
or provide guidance in the practice of the measurement. It is one intention of this guide to address those deficits.
4.3 The following aspects need emphasis:
4.3.1 Zeta potential is a function of the particulate system as a whole – so the environment that the particle resides in (pH,
concentration, ionic strength, polyvalent ions) will directly influence the magnitude and, in certain circumstances, the sign of the
2+
acquired charge. In particular, small quantities (parts per million) of polyvalent ions (for example calcium ions (Ca ), iron (III)
3+
ions (Fe )) or other impurities can significantly affect the magnitude of the zeta potential. It is obvious, but often ignored, that
there is no such concept of the zeta potential of a powder.
4.3.2 The calculation of zeta potential from mobility measurement typically refers to the unrestricted mobility of a particle in
suspension. In crowded environments (that is high concentration) particle-particle interactions occur and the movement may be
hindered. In this circumstance, although a movement can be detected and measured, it may provide interpretation issues when a
conversion to zeta potential is attempted.
4.3.3 Zeta potential tends only to be important in the sub-5 μm (and thus relevant to the sub-100 nm region considered in this
text) region where van der Waals attractive forces are of a similar order of magnitude as inertial forces. Thus if sedimentation
(function of size and density of the particle with respect to the medium it resides) is occurring or has occurred, the system is clearly
not ideal for a zeta potential or mobility measurement. With significant settling the measurement of mobility is obviously
compromised. The lower limit for measurement of electrophoretic mobility is in effect determined by the signal to noise which
is a complex function of size, concentration and relative refractive index of the particulate system. An unambiguous statement of
the lower size is therefore not possible.
The boldface numbers in parentheses refer to a list of references at the end of this standard.
E2865 − 12 (2018)
4.3.4 Zeta potential and its (assumed) relation to system stability are reasonably well understood in aqueous systems. The classic
examples are indicated in Thomas Riddick’s text (4). The obvious or stated link with formulation or product stability is not obvious
for organic media where the counter-ions will be strongly bound to the particle surface and the position of the diffuse layer will
be difficult to identify in an (effectively) insulating external medium. Again, what is often forgotten, is that conductivity is required
-1
in the ‘background’ solution (typically 0.001 molL sodium chloride (NaCl) is utilized) so that an electrical field can be correctly
applied without effects such as electrode polarization (causing voltage irregularities) occurring. Mobility or zeta potential
measurements should not be made in de-ionized water. In non-polar dispersant liquids, conversion of observed mobility to zeta
potential may need some understanding of the position and thickness (single atom or molecule?) of the double layer, but this is
not relevant to measurements in (aqueous) biological media.
4.3.5 It is mobility (movement) that is usually measured and the conversion to zeta potential relies on application of the Henry
equation. (See also Fig. 1).
εζ f κα
~ !
U 5 (1)
E
6πη
where:
U = the electrophoretic mobility (measured by instrument),
E
ε = the dielectric constant of the dispersion medium,
ζ = the (calculated) zeta potential,
f(κα) = Henry’s function (see below), and
η = the viscosity of the medium (measured or assumed).
4.3.5.1 It is important to specify the units of measurement as failure to get these correct will lead incompatibility of units on
the right and left hand side of the above equation. The normal SI units (metre, kilogram, second) are not often utilized in this area
as they are too large for practical purposes (diffusion distances of one metre are not routinely encountered!) — see additional unit
information in Ref. (5). We need to remember that the mobility and diffusion coefficient are a flux (and thus area) per unit time.
2 -1 -1
The mobility will be scaled by the field (volts/distance). Ref. (5) recommended units for electrophoretic mobility are m s V .
-1 -1
This can be expressed as (ms )/(Vm ) or a velocity per unit field. In practice, the electrophoretic mobility, U , has more
E
2 -1
convenient units of μm /Vs Often mobilities are expressed in confused units (for example, the oft-utilized μmcm /Vs because this
gives rise to mobility values in the convenient 610 region). Mobilities expressed with a negative sign imply a negative zeta
potential.
4.3.5.2 ε is the dielectric constant of the dispersion medium dimensionless/no units as it is a ratio of the relative permittivity
of the material to vacuum whose relative permittivity is defined as 1.
4.3.5.3 f(κα) is usually referred to as “Henry’s function” where α is the radius of the particle. κ is referred to as the Debye
parameter and can be calculated from the electronic charge, Boltzmann’s and Avogadro’s constants, the absolute temperature and
the ionic strength. The charged region around a particle falls to about 2 % of the surface charge at a distance approximately 3/κ
-1 -5 -1
from the particle. For ionic strength around 0.01 molL then 3/κ is around 10 nm and for ionic strength around 10 molL then
3/κ is around 280 nm (see Koutsoukos et al. (6)). 1/κ can be envisioned as the "thickness" of the electrical double layer (the Debye
length) and thus the units of κ are reciprocal length. Thus f(κα) is dimensionless and usually assigned the value 1.00 or 1.50. For
particles in polar media the maximum value of f(κα) is taken to be 1.5 (Smoluchowski approximation) and for particles in
non-polar media the minimum value of f(κα) is 1 (Hückel approximation). It is the former that we are considering in this text. The
literature does indicate intermediate values for f(κα) but in most biologically relevant media the value of 1.5 is the most
appropriate.
4.3.5.4 In terms of viscosity, η, the SI physical unit of dynamic viscosity is the pascal-second (Pa·s), (equivalent to N·s/m , or
kg/(m·s)). Water at 293 K has a viscosity of 0.001002 Pa·s. The cgs physical unit for dynamic viscosity is the poise (P). It is more
commonly expressed, particularly in ASTM standards, as centipoise (cP). Water at 293 K has a viscosity of 1.0020 cP.
NOTE 1—At room temperature (assumed 298 K) in water, all of the expressions are constants except for the (measured) mobility and the equation defers
to:
FIG. 1 Equation (1)
E2865 − 12 (2018)
Zeta potential 5 K*electrophoretic mobility, U ; 12.85*U (2)
E E
where the value of K (collective proportionality constant) is ~12.85 if the zeta potential is to be stated in mV and this falls out naturally from the Henry
-1
equation if the deprecated μmcm /Vs unit is used for electrophoretic mobility.
4.3.5.5 As well as movement under the constraint of an electric field, some degree of Brownian motion will also occur and may
need to be considered. In biological media of relatively high ionic strength the Hückel model (f(κα) = 1) for zeta potential
calculation is inappropriate and the value of f(κα) should be calculated from the measured size and the known ionic strength (or
measured conductivity) (see Fig. 2).
4.3.6 Systems of positive charge tend to provide more measurement difficulties from a practical perspective than those of
inherent negative charge. This is because most organic media including plastic sample cells are inherently negatively charged at
neutral pH and may attract particles of opposite charge removing them from suspension and altering the wall potential. It is useful
to have some form of automation for pH adjustment – for example a titrator. This eases the adjustment of pH and additive
concentration.
4.3.7 It is of no value to state a zeta potential value without description of the manner in which it was measured together with
vital measurement parameters. Zeta potential without a stated pH, ionic compostion, and electrolyte concentration value is close
to meaningless.
4.4 Biological Molecules and Entities—Again, a few obvious points will need mentioning:
4.4.1 Many materials such as proteins contain charges and may be zwitterionic (contain both positive a
...