ISO/TS 22295:2021

TECHNICAL ISO/TS
SPECIFICATION 22295
First edition
2021-05
Space environment (natural
and artificial) — Modelling of
space environment impact on
nanostructured materials — General
principles
Environnement spatial (naturel et artificiel) — Modélisation de
l'impact de l'environnement spatial sur les matériaux nanostructurés
— Principes généraux
Reference number
©
ISO 2021
© ISO 2021
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
below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved

Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions and abbreviated terms . 1
3.1 Terms and definitions . 1
3.2 Abbreviated terms . 2
4 Nanostructured materials . 2
5 Main space environment components and processes . 3
5.1 General . 3
5.2 Space radiation . 3
5.2.1 General. 3
5.2.2 Special features of nanostructured materials response . 3
5.3 Atomic oxygen of the Earth’s upper atmosphere . 4
5.3.1 General. 4
5.3.2 Special features of nanostructured materials . 5
5.4 Hot magnetosphere plasma . 5
5.4.1 General. 5
5.4.2 Special features of nanostructured materials response . 5
5.5 Heating, cooling and thermal cycling . 6
5.5.1 General. 6
5.5.2 Special features of nanostructured materials . 6
5.6 Meteoroids and space debris . 6
5.6.1 General. 6
5.6.2 Special features of nanostructured materials . 6
5.7 Solar UV and VUV radiation . 6
5.7.1 General. 6
5.7.2 Special features of nanostructured materials . 7
6 Multiscale approach to simulation of space components impact on nanostructured
materials . 7
6.1 Multiscale simulation methods . 7
6.1.1 General. 7
6.1.2 Quantum (electronic) scale . 8
6.1.3 Atomistic scale (molecular dynamics and Monte Carlo) .12
6.1.4 Mesoscale .13
6.1.5 Macroscale (continuum methods) .14
6.2 Radiation damage modelling .15
6.2.1 General.15
6.2.2 Quantum scale . .15
6.2.3 Atomistic scale .16
6.2.4 Mesoscale .16
6.2.5 Macroscale .17
6.3 Modelling of atomic oxygen impact .17
6.3.1 General.17
6.3.2 Quantum scale . .18
6.3.3 Atomistic scale .19
6.3.4 Mesoscale .19
6.3.5 Macroscale .19
6.4 Modelling of charging effects .20
6.4.1 General.20
6.4.2 Quantum scale . .20
6.4.3 Atomistic scale .20
6.4.4 Mesoscale .21
6.4.5 Macroscale .21
6.5 Modelling of heating/cooling and thermal cycling effects .21
6.5.1 General.21
6.5.2 Atomistic scale .21
6.5.3 Mesoscale .22
6.5.4 Macroscale .22
6.6 Modelling of meteoroids and space debris impact .22
6.6.1 General.22
6.6.2 Atomistic scale .22
6.6.3 Mesoscale .23
6.6.4 Macroscale .23
6.7 Modelling of solar UV and VUV radiation effects.23
6.7.1 General.23
6.7.2 Quantum scale . .23
7 Outlook .23
Annex A (informative) Multiscale simulation methods: software for simulation in different
space and time scales .24
Bibliography .27
iv © ISO 2021 – All rights reserved

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 20, Aircraft and space vehicles,
Subcommittee SC 14, Space systems and operations.
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.
Introduction
In the near future nanomaterials and nanoelements will be widely applied in spacecraft and space
engineering. Nanomaterials superiority in mechanical, thermal, electrical and optical properties
over conventional materials will evidently inspire a wide range of applications in the next generation
spacecraft intended for the long-term (~15 to 20 years) operation in near-Earth orbits and the automatic
and manned interplanetary missions as well as in the construction of inhabited bases on the Moon.
The near-Earth’s space is described as an extreme environment for materials due to high vacuum,
space radiation, hot and cold plasma, micrometeoroids and space debris, temperature differences, etc.
Existing experimental and theoretical data demonstrate that nanomaterials response to various space
environment effects can differ substantially from the one of conventional bulk spacecraft materials.
Therefore, it is necessary to determine the space environment components, critical for nanomaterials,
and to develop novel methods of the mathematical and experimental simulation of the space
environment impact on nanomaterials.
Modelling is a very important scientific tool for explaining various phenomena and predicting the
behaviour of existing and designing materials under different conditions. In the case of nanotechnologies,
modelling and simulations become even a more significant method of studying nanomaterials and
processes in the nanoscale due to difficulties of observing and measuring many nanoscale phenomena
experimentally. In computational nanotechnology, it is necessary to develop new integrated approaches
for different length and time scales that enable explaining mechanisms of mesoscale phenomena and
predicting emerging material macro-properties.
The changes in the materials properties, caused by the space environment impact, are determined with
structural parameters and processes that are related to different spatial scales: from the size of atoms
and molecules to the size of macroobjects. There are a variety of simulation methods but most of them
can be applied only for a special space and time range/scale because of underlying approximations. To
estimate the durability of nanostructured materials to the space environment impact it is necessary to
investigate both fundamental effects of incident atom/particle interaction with nanosized structures
within very short time intervals and resulting effects of material damage and changes in their
properties, that can be observed at micro- and macroscale within much longer periods. Thus, in general
case to study the whole set of elementary processes and resulting effects it is necessary to apply the
multiscale simulation approach.
The main concept of this document is:
— for main space environment components to choose the most important space and time scales;
— for every scale to choose the most important physical and chemical processes that occur in
nanostructured materials under the influence of the given space environment component and can
be considered as elementary for the chosen scale;
— for every process to determine a method (or a group of methods) that can be used for their simulations
under space environment conditions;
— for every chosen method to describe necessary and possible approximations as well as its limitation
when used for simulation of the given process.
vi © ISO 2021 – All rights reserved

TECHNICAL SPECIFICATION ISO/TS 22295:2021(E)
Space environment (natural and artificial) — Modelling of
space environment impact on nanostructured materials —
General principles
1 Scope
The document considers peculiarities of the space environment impact on a special kind of materials:
nanostructured materials (i.e. materials with structured objects which size in at least one dimension
lies within 1 nm to 100 nm) and specifies the methods of mathematical simulation of such processes. It
emphasizes the necessity of applying multiscale simulation approach and does not include any special
details concerning concrete materials, elements of spacecraft construction and equipment, etc.
This document provides the general description of the methodology of applying computer simulation
methods which relate to different space and time scales to modelling processes occurring in
nanostructured materials under the space environment impact.
The document can be applied as a reference document in spacecraft designing, forecasting the
spacecraft lifetime, conducting ground-based tests, and analysing changes of material properties
during operation.
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 10795, Space systems — Programme management and quality — Vocabulary
ISO 17851, Space systems — Space environment simulation for material tests — General principles and
criteria
ISO/TS 18110, Nanotechnologies — Vocabularies for science, technology and innovation indicators
ISO/TS 80004-1, Nanotechnologies — Vocabulary — Part 1: Core terms
ISO/TS 80004-2, Nanotechnologies — Vocabulary — Part 2: Nano-objects
ISO/TS 80004-6, Nanotechnologies — Vocabulary — Part 6: Nano-object characterization
3 Terms and definitions and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 10795, ISO/TS 18110,
ISO/TS 80004-1, ISO/TS 80004-2, ISO/TS 80004-6 and ISO 17851 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/
3.2 Abbreviated terms
AMD accelerated molecular dynamics
CC coupled cluster
CI configuration interaction
DFT density functional theory
DFTB density functional based tight-binding
ESD electrostatic discharge
HF Hartree–Fock method
kMC kinetic Monte Carlo
MC Monte Carlo
MD molecular dynamics
MP Møller-Plesset perturbation theory
QM/MM quantum mechanics – molecular mechanics
UV ultraviolet radiation
VUV vacuum ultraviolet radiation
4 Nanostructured materials
The peculiar properties of nanomaterials are determined by the presence in their structure of
nanoobjects – particles or grains, fibres, platelets, etc. with at least one linear dimension in nanoscale
[1]–[5]
(size range from approximately 1 nm to 100 nm) . The lower boundary of this range approaches the
size of atoms and molecules; and its upper one separates nanoobjects from microobjects.
The strong influence of the material nanostructure on its properties is caused by the so-called
nanometre length scale effects which can be of classical and quantum nature. The nanoscale effects
appear when the size of structural objects becomes comparable with a certain parameter of material
which has a considerable influence on some physical-chemical processes in the matter and consequently
[1],[2]
on the material properties . A mean free path of charged particles, a diffusion length, etc. may be
regarded as such a parameter in the case of classical length scale effects; and for quantum ones its role
is usually played by the de Broglie wavelength.
Another parameter of nanostructures is called dimensionality; it corresponds to the number of
dimensions that lie within the nanometre range, and is used for analysing the quantum confinement
[1],[2]
effects . According to this parameter, all objects may be divided into four groups:
— 3D-objects – bulk materials;
— 2D-objects – nanofilms, nanoplatlets;
— 1D-objects – nanofibres, nanotubes, nanorods, etc.;
— 0D-objects – nanoparticles, nanopores, nanocrystals, quantum dots, etc.
In a 3D-object, electrons can move freely in all three dimensions. In a film whose width is comparable
with the de Broglie wavelength (2D-object), electrons move without restrictions only in the film plane,
but in the perpendicular direction they are in a deep potential well; that’s why 2D-objects are usually
called quantum well. In 1D-objects, or quantum wires, two dimensions are comparable with the de
2 © ISO 2021 – All rights reserved

Broglie wavelength. If the electron movement is limited in three directions, a nanostructure becomes a
0D-object, or a quantum dot with discrete electronic states.
Due to nanosized scale effects, nanostructured materials acquire novel mechanical, thermal,
electrical, magnetic and optic properties, which can surpass the properties of conventional bulk
[1],[2],[6],[7]
materials . Nanocomposites with nanoclays, nanotubes and various nanoparticles as fillers
are one of the most promising materials for space applications. They may be used as light-weighted
and strong structural materials as well as multi-functional and smart materials of general and specific
applications, e.g. thermal stabilization, radiation shielding, electrostatic charge mitigation, protection
[8]
of atomic oxygen influence and space debris impact .
Therefore, the creation of polymer nanocomposites with fillers of various shape and composition may
play the pivotal role in spacecraft development and implementation of challenging space projects.
Among possible fillers, the main attention is paid to carbon nanostructures: fullerenes, carbon
[6],[7]
nanotubes (CNT), graphene that represent particular allotropic forms of carbon . Due to superior
mechanical properties, high electric and thermal conductivity of these nanostructures, one may
develop various light-weighted and strong multifunctional nanocomposites. Of special interest are CNT
structural analogues, boron nitride nanotubes (BNNTs), that are electrical insulators and in addition to
[9],[10]
excellent mechanical properties and high thermal stability possess high resistivity to oxidation .
5 Main space environment components and processes
5.1 General
The space environment has a significant damaging effect on many materials, including nanostructured
materials. During the flight, the spacecraft is influenced by a set of space environment components:
electrons and high-energy ions, cold and hot space plasma, solar electromagnetic radiation, meteoroids
[11]–[18]
and space debris, vacuum and other factors . As a result of this impact, various physical and
chemical processes take place in the materials and elements of the spacecraft equipment, leading to
deterioration of their operational parameters. Depending on the nature of the processes triggered by
the impact of the space environment, the changes in the properties of materials and equipment elements
can have different time scales, be reversible or irreversible, and present a different degree of danger for
on-board systems. To evaluate the potential effects of the space environment on material properties
and the characteristics of spacecraft equipment, it is important to determine the combinations of the
most significant factors in various areas of outer space. In this case it should be regarded as effects
[12]
caused by the impact of individual components of the space environment, and their combined effect .
5.2 Space radiation
5.2.1 General
Ionizing radiations of the Earth's radiation belts are electron and proton flows with energies from
[11]–[15]
several hundred eV to several hundred MeV . As a result of different penetrability and energy,
ionizing particles exert influence on all materials independent of their location, both on the exterior of
spacecraft (coatings, blankets) and inside it. The dominant degradation mechanism depends on type
of material, LET, type of ray, etc. Ionizing radiation breaks chemical bonds but in other cases may lead
to cross-linking in polymers. These processes cause decomposition, embrittlement, colour change
and darkening, change in electrical resistivity, mechanical strength degradation, etc. Wire insulator
indicates decrease in breakdown voltage or cracks.
5.2.2 Special features of nanostructured materials response
Existing experimental and theoretical data demonstrate that nanostructured materials response to
[19]–[24]
space radiation can differ substantially from that of conventional bulk spacecraft materials .
When an electron or ion with high energy interacts with a nanostructure, only a small amount of
energy of the incident particle is imparted to it. Therefore, a nanostructured object is characterized by
a small number of additional charge carriers or structural defects that appear due to the irradiation;
and their number is reduced with increasing incident particle energy, which is opposite to the situation
in conventional materials.
The migration of structural defects and charges in nanostructures and conventional materials also
differ: already at the stage of the ballistic cascade, the displaced atoms have more opportunities to leave
a nanoobject due to its higher surface area to volume ratio as compared to the bulk material, which leads
[21],[24]
to a cascade slowdown within the nanostructure . In the conventional bulk materials, displaced
atoms can freely reach the surface, causing the material to swell while leaving the vacancies behind.
These point defects can aggregate, forming larger obstacles to dislocation motion and causing hardening
[7]
and embrittlement . In nanostructured materials which contain a large number of nanoscale grains,
the grain boundaries can capture interstitials and then fire them back into the lattice to destroy any
[20]
vacancy that comes within a few nanometres of the grain boundary . Therefore, in nanostructured
materials, which are characterized by the presence of large number of grain boundaries, there exists an
efficient mechanism which implies that boundaries act as sinks for defects and prevents accumulation
of radiation-induced defects within the grain. Controlling radiation-induced-defects via interfaces is
considered to be the key factor in reducing the damage and imparting stability in certain nanomaterials
[22],[23]
under conditions where bulk materials exhibit void swelling and/or embrittlement .
Thus, processes of formation of structural defects and charge carriers due to the ionizing radiation, as
well as subsequent processes of carriers and defects migration and recombination, differ substantially
in conventional bulk materials and nanostructured materials. The influence of these processes on the
[19]–[22]
radiation damage of nanomaterials is ambiguous . In addition, it is necessary to take into account
that the relationship between the stability of nanostructures to the formation and accumulation
of radiation defects and the radiation resistance of nanomaterials, determined by a change in their
[20],[21]
performance characteristics, can be very complicated . By now, there is no sufficiently complete
and generally accepted description of the specific radiation effects in nanostructures and their effect
on the properties of nanomaterials and spacecraft elements built on them.
Special features of nanostructured materials response to the space radiation:
— presence of grain boundaries or interfaces (nanocrystalline materials, nanocomposites) acting as
sinks for defects;
— possibility to use structures and substances possessing enhanced radiation tolerance as fillers in
nanocomposites;
— ability of defect healing and enhanced sputtering due to high aspect ratio (nanostructures).
5.3 Atomic oxygen of the Earth’s upper atmosphere
5.3.1 General
Atomic oxygen (AO) space environment in low Earth orbits is very dangerous for polymeric materials.
High translational energy of O atoms due to the spacecraft orbital velocity enhances their reactivity, so
atomic oxygen is capable to break bonds in polymeric materials and create a thin oxidized layer on the
surface of some metallic materials, resulting in polymer erosion and severe structural and/or optical
properties deterioration.
In general, AO affects near-surface layers of materials, and the ram facing surface of the spacecraft
suffers the highest AO fluence. However, oxygen atoms can be reflected and penetrate into covered area
via multiple reflections.
Some metals like silver and osmium are rapidly oxidized when exposed to AO. In the case of polymers,
the hyperthermal oxygen flux causes fragmentation of the polymer chains and formation of volatile
species. As a result, a typical carpet-like relief is grown on the surface (buried regions and profile
peaks). Its topology is specific to polymer type.
There are two main approaches to improve the durability of conventional polymeric materials to AO:
— thin surface coatings or ion implantation;
4 © ISO 2021 – All rights reserved

— embedding AO resistant fillers into polymeric matrices.
5.3.2 Special features of nanostructured materials
Nanostructured materials (nanocomposites) can possess a higher durability to AO if they consist of AO
resistant nanosized fillers (e.g. Si-containing and metal oxide nanoparticles). Under AO exposure, on
the nanocomposite surface forms a layer consisting of nanofillers and protecting underlying polymer
layers against AO attack.
5.4 Hot magnetosphere plasma
5.4.1 General
Hot magnetosphere plasma consists of particles with an average kinetic energy of 10 eV to 10 eV and
[11]–[14],[16]
is located mainly at heights measured by tens of thousands of kilometres . Main processes
induced by hot magnetosphere plasma are as follows:
— surface and internal charging;
— surface defect formation and sputtering (see 5.2).
Charging of spacecraft materials in hot magnetosphere plasma is the accumulation of electric charge
on the external spacecraft surface. This accumulated charge can be distributed unevenly on the surface
due to its low conductivity (so-called differential charging of the spacecraft surface).
The main consequence of spacecraft charging is electrostatic discharges (ESD), which create
electromagnetic interference to the performance of on-board devices, and in some cases damage and
destroy construction and equipment elements.
The phenomenon of charging is related to three groups of processes:
— leakage of electron and ion plasma currents to the spacecraft surface;
— exchange of charged particles between the spacecraft surface and the environment;
— redistribution of electric charges on the spacecraft surface.
The processes of the first group do not depend on properties of spacecraft materials.
The processes of the second groups imply the consideration of all types of secondary emission due to
impacts of plasma electrons and ions incident to the surface as well as photoelectron emission induced
by solar radiation. However, charging can lead to the appearance of high negative potential (up to
several tens of kilovolts) of a certain construction element on the spacecraft and thereby initiate field
emission from its surface. The intensity of this emission is closely related to the form and size of edges.
The redistribution of electric charges on the spacecraft surface (the third group) is the most important
factor which reduces gradients of electric potential: tangential ones between different elements on the
surface and normal ones between the charged surface of dielectric materials and the metallic frame. So
to describe the charging effects in spacecraft materials, it is necessary to take into account the electric
conductivity of different objects which is related closely to their electronic structure.
5.4.2 Special features of nanostructured materials response
Nanostructured materials consisting of non-conductive polymeric or ceramic matrices with conductive
nanofillers (nanotubes, nanoparticles, nanosheets, etc.) possess high surface and volume electric
conductivity under certain conditions, namely, high enough concentration of fillers and their good
[1],[2],[6],[7]
dispersion . Due to this important feature, their usage on the spacecraft surface can minimize
negative ESD effects. However, it should be taken into account that embedding nanosized fillers into the
polymer and ceramic matrices can lead to the deterioration of other properties that can be important
[8]
for spacecraft operation (e.g. optic transparency ). Additionally, some nanostructures (e.g. CNT) are
considered as very efficient field emitters that can be used for reducing the negative potential of the
spacecraft due to the charging effects.
5.5 Heating, cooling and thermal cycling
5.5.1 General
The materials on the outer spacecraft surface are subjected to periodic heating and cooling by solar
radiation in the temperature range of 180 K to 390 K, depending on the orientation of the spacecraft
surface with respect to the Sun. Such a periodic change in the temperature of materials (thermal
cycling) requires considering two distinct physical phenomena:
— heat transfer;
— repeated thermal expansion and compression.
The first phenomenon is closely related to thermal conductivity and ensures the efficiency of the
performance of spacecraft thermal control systems. The second one causes mechanical stress within
the materials and at their contacts, which can lead to material destruction.
5.5.2 Special features of nanostructured materials
Embedding nanofillers with a high thermal conductivity (e.g. CNTs) can lead to substantial improvement
[1],[2],[6]–[8]
of thermal properties of materials owing to:
— increasing thermal conductivity;
— reducing thermal expansion coefficient.
5.6 Meteoroids and space debris
5.6.1 General
Impacts of hypervelocity hard particles (micrometeoroids and space debris) cause erosion on the
[11]–[13]
material surface due to the formation of craters and cracks . The most serious changes happen in
the uppermost layers of materials, but underlying layers can be damaged by heat.
5.6.2 Special features of nanostructured materials
Nanostructured materials can possess higher tolerance to hypervelocity particle impacts owing to the
presence of hard nanofillers that are able to reduce the damage:
— reinforcement by incorporation hard nanosized fillers;
— enhanced fracture strength (or crack resistivity) by embedding flexible nanofillers.
5.7 Solar UV and VUV radiation
5.7.1 General
Short-wave solar UV and VUV electromagnetic radiation is one of the most important factors causing the
degradation of materials on the outer spacecraft surface. Under its influence, the optical, mechanical,
electrical, and thermal properties of materials can be altered substantially.
UV and VUV radiation can break chemical bonds, so this space component influences strongly polymeric
materials located on the external spacecraft surface. UV and VUV can cause bond scissor (if the bond
energy corresponds to the light wavelength) or induce cross-linking depending on polymer composition
and structure. As a result of structural changes, UV and VUV can induce changes of polymer mechanical
(brittleness) and optical (colour darkening) properties.
6 © ISO 2021 – All rights reserved

5.7.2 Special features of nanostructured materials
In general cases, UV and VUV radiation interacts with materials at atomic level and influence mainly
chemical bonding, so important changes in mechanisms of its influence on nanostructured materials
are not expected. However, solar radiation can cause changes in the interface between main matrices
and nanofillers as well as in properties of nanofillers themselves. These processes can alter the
interaction between the matrices and fillers, thereby leading to changes of macroscopic properties of
nanocomposites.
In addition, UV and VUV solar radiation influences the secondary emission properties of materials,
including photoelectron emission (see 5.3).
6 Multiscale approach to simulation of space components impact on
nanostructured materials
6.1 Multiscale simulation methods
6.1.1 General
To estimate the durability of nanostructured materials to the space environment impact it is necessary
to investigate both fundamental effects of incident particle interaction with nanosized structures
within very short time intervals and resulting effects of material damage and changes in their
properties, that can be observed at micro- and macroscale within much longer periods. Thus, in general
case to study the whole set of elementary processes and resulting effects, it is necessary to apply the
[25]–[27]
multiscale simulation approach .
Four most significant and fundamentally different groups of methods are usually considered:
— quantum mechanics (ab initio) and semi-empirical methods;
— molecular dynamics;
— mesoscale methods;
— continuum methods.
Quantum mechanical, or quantum chemistry methods are based on numerical solving of the
Schrödinger’s formula and do not require any empirical assumptions, so they are usually called ab
initio methods (“ab initio” comes from the Latin phrase “from first principles”). These methods can be
–10 –9
effective only for small size systems no more than 100 atoms and in the region of 10 m to 10 m.
Semi-empirical methods are a combination of ab initio methods coupled with data from empirical
studies. Such methods are computationally much more efficient than the ab initio method and can be
3 4
applied for systems consisting of 10 to 10 atoms, but they are limited to systems for which parameters
exist. Methods of this group are particularly useful in the study of organic chemistry and the structure
and reactions of organic molecules.
The molecular dynamics (MD) method enables enlarging the size of modelling objects to the upper
6 7
border of the nanoscale range and increasing the number of particles up to 10 to 10 . Within this
approach, atoms are considered to be hard spheres that are connected to other atoms by a spring.
An important feature of the method is the use of empirical potentials, or force fields that determine
the forces acting between particles and can affect significantly results of calculations. This method
enables predicting the time evolution of a system of interacting particles and determining the system
parameters, from which the macroscopic properties can be derived. Sometimes for reducing calculation
volume the various types of Monte Carlo technique are applied in this space and time range.
In the case of large systems, the accumulation of detailed information on the movement of each atom
limits the capabilities of the MD method. Therefore, for time intervals of the order of microseconds and
above, one should apply the methods that are developed for the mesoscale. However, before doing so, a
special coarse-graining procedure which enables transferring from molecular objects to mesosystems
should be carried out. An important shortcoming of mesoscale approach is the absence of universal
principles for this procedure which leads to an ambiguous interpretation of the results obtained.
The continuum methods are used to model processes and objects at the macro level: for objects and
phenomena with characteristic dimensions of more than a few tens of micrometres at typical times of
the processes from fractions of a second to hours and years. These methods are based on statistical
regularities and suggest the possibility of averaging calculation parameters within the specified cell
...