Surface chemical analysis — Scanning probe microscopy — Procedure for the determination of elastic moduli for compliant materials using atomic force microscope and the two-point JKR method

This document describes a procedure for the determination of elastic modulus for compliant materials using atomic force microscope (AFM). Force-distance curves on the surface of compliant materials are measured and the analysis uses a two-point method based on Johnson-Kendall-Roberts (JKR) theory. This document is applicable to compliant materials with elastic moduli ranging from 100 kPa to 1 GPa. The spatial resolution is dependent on the contact radius between the AFM probe and the surface and is typically approximately10-20 nm.

Analyse chimique des surfaces — Microscopie à sonde locale — Lignes directrices pour la détermination des modules d’élasticité des matériaux souples en utilisant un microscope à force atomique

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Status
Published
Publication Date
28-Jan-2020
Current Stage
6060 - International Standard published
Start Date
29-Jan-2020
Due Date
15-Oct-2019
Completion Date
29-Jan-2020
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ISO 21222:2020 - Surface chemical analysis -- Scanning probe microscopy -- Procedure for the determination of elastic moduli for compliant materials using atomic force microscope and the two-point JKR method
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INTERNATIONAL ISO
STANDARD 21222
First edition
2020-01
Surface chemical analysis — Scanning
probe microscopy — Procedure for
the determination of elastic moduli
for compliant materials using atomic
force microscope and the two-point
JKR method
Analyse chimique des surfaces — Microscopie à sonde locale —
Lignes directrices pour la détermination des modules d’élasticité des
matériaux souples en utilisant un microscope à force atomique
Reference number
ISO 21222:2020(E)
©
ISO 2020

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ISO 21222:2020(E)

COPYRIGHT PROTECTED DOCUMENT
© ISO 2020
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address
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Email: copyright@iso.org
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Published in Switzerland
ii © ISO 2020 – All rights reserved

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ISO 21222:2020(E)

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols (and abbreviated terms) . 4
5 Review of contact mechanics . 4
5.1 Introduction . 4
5.2 Hertzian model . 5
5.3 Derjaguin-Muller-Toporov (DMT) Model . 5
5.4 Johnson-Kendall-Roberts (JKR) model . 6
5.5 JKR–DMT transition . 6
6 Procedure of determination of elastic modulus . 6
6.1 Introduction and limitations . 6
6.2 Measurement of deflection sensitivity and spring constant . 7
6.3 Measurement of tip radius . 7
6.4 Measurement of force-distance curve . 7
6.5 Force-distance curve conversion . 8
6.6 JKR two-point method . 9
6.7 Uncertainties . 9
6.8 Reporting results . 9
Annex A (informative) Example measurements .11
Annex B (informative) Result of Inter-laboratory Comparison .15
Bibliography .17
© ISO 2020 – All rights reserved iii

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ISO 21222:2020(E)

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 201, Surface chemical analysis,
Subcommittee SC 9, Scanning probe microscopy.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
iv © ISO 2020 – All rights reserved

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ISO 21222:2020(E)

Introduction
Atomic force microscope (AFM) is a member of the scanning probe microscope (SPM) family and is
used to image surfaces by mechanically scanning a probe over the surface. In AFM, a surface force is
monitored as the deflection of a compliant cantilever, which has a probe tip at its free end in order to
interact with surfaces. AFM can provide amongst other data: topographic, mechanical and chemical
information about a surface depending on the mode of operation and the property of the probe tip.
Accurate force measurements and sample deformation measurements are needed for a wide variety
of applications, especially to determine the elastic moduli of compliant materials such as organics
and polymers at surfaces. For quantitative force measurements, it is necessary to select an adequate
contact mechanic model used to calculate the elastic modulus, and also use the appropriate calculation
procedure.
This document describes a procedure for the determination of the elastic moduli for compliant materials
using AFM. Force-distance curves are obtained on the surfaces of compliant materials and are used for
the calculation of elastic modulus based on Johnson-Kendall-Roberts (JKR) two-point method.
© ISO 2020 – All rights reserved v

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INTERNATIONAL STANDARD ISO 21222:2020(E)
Surface chemical analysis — Scanning probe microscopy
— Procedure for the determination of elastic moduli for
compliant materials using atomic force microscope and the
two-point JKR method
1 Scope
This document describes a procedure for the determination of elastic modulus for compliant materials
using atomic force microscope (AFM). Force-distance curves on the surface of compliant materials are
measured and the analysis uses a two-point method based on Johnson-Kendall-Roberts (JKR) theory.
This document is applicable to compliant materials with elastic moduli ranging from 100 kPa to 1 GPa.
The spatial resolution is dependent on the contact radius between the AFM probe and the surface and is
typically approximately10-20 nm.
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 18115-2, Surface chemical analysis — Vocabulary — Part 2: Terms used in scanning-probe microscopy
ISO 11775, Surface chemical analysis — Scanning-probe microscopy — Determination of cantilever normal
spring constants
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 18115-2 apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
force-distance curve
force-displacement curve
pairs of force and distance values resulting from a mode of operation in which the probe is set
at a fixed (x, y) position and the probe tip is moved towards or away from the surface as the force is
measured
Note 1 to entry: The force is usually monitored using the cantilever deflection.
[SOURCE: ISO 18115-2:2013, 5.56]
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ISO 21222:2020(E)

3.2
normal spring constant
spring constant
force constant
k
z
quotient of the applied normal force at the probe tip by the deflection of the cantilever in that
direction at the probe tip position
Note 1 to entry: The normal spring constant is usually referred to as the spring constant. The full term is used
when it is necessary to distinguish it from the lateral spring constant.
Note 2 to entry: The force is applied normal to the plane of the cantilever to compute or measure the normal force
constant, k . In application, the cantilever in AFM can be tilted at an angle, θ, to the plane of the sample surface
z
and the plane normal to the direction of approach of the tip to the sample. This angle is important in applying the
normal spring constant in AFM studies.
[SOURCE: ISO 18115-2:2013, 5.92, modified — Note 1 to entry has been deleted and the following notes
renumbered.]
3.3
pull-in force
pull-on force
force exerted by the surface on the probe tip at snap-in
[SOURCE: ISO 18115-2:2013, 5.123]
3.4
pull-off force
force required to pull the probe free from the surface
Note 1 to entry: This force is generally measured from the force-distance curve as the value between the force
minimum and the zero of force as the probe moves away from the surface.
[SOURCE: ISO 18115-2:2013, 5.124]
3.5
tip radius
radius describing the surface curvature in a region at the apex of
a stylus or probe tip
Note 1 to entry: It might be necessary to describe the tip by radii in different azimuths.
Note 2 to entry: In practice, tips can only approximate a sphere for a very small region at the tip.
[SOURCE: ISO 18115-2:2013, 5.161]
3.6
tip-sample contact radius
maximum radius of the contact area between the tip and the sample at the maximum indentation depth
[SOURCE: ISO 18115-2:2013, 5.163]
3.7
work of adhesion
energy required when two condensed phases, forming an interface of unit area, are separated reversibly
to form unit areas of the free surfaces of those two phases
Note 1 to entry: This term is sometimes also known as the work of separation or the Dupré work of adhesion.
[SOURCE: ISO 18115-2:2013, 5.175]
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ISO 21222:2020(E)

3.8
Hertzian model
model of tip and surface contact between elastic solids that ignores any surface forces and adhesion
hysteresis
Note 1 to entry: This approach, derived by Hertz and described in Reference [1] describes the contact between
elastic solids. It ignores any surface forces and adhesion hysteresis and applies at high loads where there are no
surface forces present.
[SOURCE: ISO 18115-2:2013, 4.4]
3.9
DMT model
Derjaguin-Müller-Toporov model
model of tip and surface contact in which adhesion forces are taken into account but the tip-sample
[2]
geometry is constrained to be Hertzian
Note 1 to entry: This approach applies to rigid systems with low adhesion and small radii of curvature. The
adhesion forces are taken into account but the tip-sample geometry is constrained to be Hertzian, i.e. Hertzian
mechanics with an offset to account for surface forces.
[SOURCE: ISO 18115-2:2013, 4.3]
3.10
JKR(S) model
Johnson-Kendall-Roberts (-Sperling) model
model of tip and surface contact in which adhesion forces outside the contact area are ignored and
[3]
elastic stresses at the edge of the contact area are infinite
Note 1 to entry: In this work, adhesion forces outside the contact area are ignored and elastic stresses at the edge
of the contact area are infinite. At contact, short-range attractive forces suddenly operate, and the tip-sample
geometry is not constrained to remain Hertzian. Adhesion hysteresis is described and loading and unloading
are abrupt processes. This approach applies to highly adhesive systems with low stiffness and high radii of
curvature.
[SOURCE: ISO 18115-2:2013, 4.5]
3.11
Maugis model
Maugis-Dugdale model
model of tip and surface contact between a sphere and a flat surface incorporating the elastic modulus
[4]
and work of adhesion
Note 1 to entry: This analysis is a complex mathematical description of the contact mechanics between a sphere
and a flat surface which applies in all material possibilities through a parameter that is a function of reduced
elastic modulus, reduced curvature radius, work of adhesion and the tip-sample interatomic equilibrium
distance. At the limits, when this parameter tends to infinity or zero, the Maugis mechanics tend to the JKR(S) or
DMT mechanics, respectively.
[SOURCE: ISO 18115-2:2013, 4.6]
3.12
COS model
Carpick-Ogletree-Salmeron model
model of tip and surface contact between a sphere and a flat surface giving a simple general equation
[5]
that approximates Maugis' solution to within 1 % accuracy
Note 1 to entry: The general equation is amenable to conventional curve-fitting routines and provides a rapid
method of determining the approximate value of the parameter described by Maugis.
[SOURCE: ISO 18115-2:2013, 4.2]
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ISO 21222:2020(E)

4 Symbols (and abbreviated terms)
The abbreviated terms are:
AFM Atomic force microscopy
a Tip-sample contact radius
D Cantilever deflection
E Elastic modulus of sample
k Normal spring constant
z
K Elastic coefficient of sample
F Normal load
F Normal load of Hertzian model
1
F Molecular attraction
a
F Pull-off force
pull-off
R Tip radius
u Standard uncertainty in the cantilever deflection
D
u Standard uncertainty in the elastic modulus
E
u Standard uncertainty in the normal spring constant
kz
u Standard uncertainty in the tip radius
R
u Standard uncertainty in the indentation depth of sample
δ
w Work of adhesion
Z vertical scanner displacement
z Atomic equilibrium separation
0
δ Indentation depth of sample
μ Tabor parameter
ν Poisson’s ratio of sample
5 Review of contact mechanics
5.1 Introduction
Contact mechanics plays a key role in understanding the phenomena occurring around the contact
between a probe tip and a surface. It can give answers about, for example, how much contact radius
and indentation depth are induced by a given load and how much stress is applied around a probe
apex. In particular, contact mechanics is necessary to calculate the mechanical properties from the
experimental force–distance curves.
This clause introduces several contact mechanics theories with the aim of applying them to force
spectroscopy AFM measurements. The following discussion assumes the contact between a spherical
4 © ISO 2020 – All rights reserved

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ISO 21222:2020(E)

probe tip with radius of curvature (tip radius), R and a flat surface with elastic modulus, E and Poisson’s
ratio, ν. The so-called elastic coefficient, K is defined in Formula (1):
4 E
K= (1)
2
3
1−v
5.2 Hertzian model
The Hertzian theory about the contact between two elastic bodies relates the contact radius a to the
normal load F by Formula (2):
1
3
Ka
F = (2)
1
R
It also relates the indentation depth, δ to the contact radius a by Formula (3):
13/
2
2
 
F
a
1
δ == (3)
 
 2 
R
RK
 
This Formula is used for a spherical probe with a tip radius of R.
[6]
NOTE This theory was developed by Hertz in 1882 .
5.3 Derjaguin-Muller-Toporov (DMT) Model
The DMT model assumed, in addition to Hertzian repulsion, the existence of molecular attraction
forces, which would not be able to change the contact profile appreciably. The net normal load F is given
by F = F + F , where F is Hertzian repulsion given by Formula (2) and F is the molecular attraction
1 a 1 a
(<0). Thus the profile predicted by the DMT model is the same as Hertzian profile, but smaller net
normal load is required. Owing to the assumption that the indentation depth has the identical form
with Formula (3), F and δ can be directly related by Formula 4:
12//32
FK=+RFδ (4)
a
The attractive interaction F depends on the profile near the contact perimeter and is typically
a
represented as a function of the contact radius a. At the point contact (a → 0), elastic displacement on
the surface profile vanishes in the case of DMT model, hence F can be approximated to Bradley’s value
a
for the pull-off force, F , as shown in Formula 5:
pull-off
FF≈=−2πwR (5)
a pull−off
where w is the work of adhesion.
[2]
NOTE This adhesive contact theory was developed by Derjaguin et al. in 1975 . By 1960s, several
experimental results had been reported that are contradictory to the Hertz theory, especially at low loads. These
observations strongly sugges
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