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ISSN 0023-1584, Kinetics and Catalysis, 2018, Vol. 59, No. 6, pp. 820–827. © Pleiades Publishing, Ltd., 2018.
Original Russian Text © A.K. Gatin, M.V. Grishin, N.V. Dokhlikova, N.N. Kolchenko, S.Yu. Sarvadii, B.R. Shub, 2018, published in Kinetika i Kataliz, 2018, Vol. 59, No. 6,
pp. 787–794.
Initial Stages of Deuterium Adsorption on Gold Nanoparticles
A. K. Gatina, M. V. Grishina, *, N. V. Dokhlikovaa, N. N. Kolchenkoa, †, S. Yu. Sarvadiia, and B. R. Shuba
aSemenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, 117977 Russia
* e-mail: mvgrishin68@yandex.ru
Received January 24, 2018
Abstract—The parameters of deuterium adsorption on the surface of gold nanoparticles supported onto highly
oriented pyrolytic graphite were determined. It was established that surface coverage with the adsorbate at a
level of single nanoparticles began at a graphite–gold interface; thereafter, the entire surface was filled.
Keywords: gold nanoparticles, deuterium, adsorption, interface
DOI: 10.1134/S0023158418060034
INTRODUCTION
Many of the currently used catalysts include
nanoparticles. In particular, gold nanoparticles are
contained in catalysts for low-temperature CO oxida-
tion [1], aerobic oxidation of methanol to methyl for-
mate [2], production of vinyl acetate and vinyl chlo-
ride [3], isomerization of epoxides into unsaturated
alcohols [4], benzylation of aromatic substances [5],
and many others processes. They are also used in the
catalytic reactions of the hydrogenation of unsaturated
organic compounds [6], carbonyl compounds [7], and
nitro-containing [8] compounds, the heterogeneous
hydroformylation of olefins [9], etc. In addition, cata-
lysts with supported gold nanoparticles are used in
hydrogenation reactions with hydrogen transfer (the
reduction of carbonyl compounds [10] and amines
[11], the hydrochlorination of alkynes [12], etc.). In
these processes, the dissociative adsorption of molec-
ular hydrogen and the interaction of the resulting
atomic hydrogen with the surface of nanoparticles play
an important role. In particular, with the use of calo-
rimetry, transmission electron microscopy (TEM),
and X-ray diffraction (XRD) analysis, Barton and
Podkolzin [13] found that the formation of water from
hydrogen and oxygen molecules could occur on gold
nanoparticles supported on silica at temperatures of
383–433 K and a pressure of several kilopascals. They
also reported the results of the corresponding quan-
tum-chemical calculations.
The results obtained in the studies of gold nanopar-
ticles supported on alumina [14, 15] confirm the con-
clusions of Barton and Podkolzin [13] concerning the
interaction between gold and hydrogen. It is believed
that low-coordinated gold atoms and/or surface
defects, such as vacancies and impurity atoms, can be
the centers of hydrogen adsorption and dissociation.
However, Fujitani et al. [16] used X-ray photoelectron
spectroscopy (XPS) and mass spectrometry to
demonstrate that the most probable adsorption center
is the site of contact between the gold nanoparticle and
the rutile TiO2 carrier. However, the results of calcula-
tions performed by Boronat et al. [17] are inconsistent
with this assumption. It was emphasized that the sites
of hydrogen adsorption are low-coordinated gold
atoms that are not directly bound to the carrier; in this
case, stoichiometric and “reduced” TiO2 was consid-
ered as the carrier. Panayotov et al. [18] hypothesized
that hydrogen dissociation occurs at the low-coordi-
nated gold atoms; then, the H atoms migrate to the
carrier. Earlier, we used scanning tunneling micros-
copy and spectroscopy to study the dissociative
adsorption of hydrogen on gold nanoparticles sup-
ported onto graphite [19, 20]. Although nanocatalytic
systems, including those containing gold nanoparti-
cles, have been studied for many years, the micro-
scopic mechanisms of elementary events in model
reactions remain unclear.
In the majority of methods used for studying the
physicochemical and catalytic properties of nanopar-
ticles (TEM, photoelectron microscopy, mass spec-
trometry, calorimetry, etc.), averaged information is
obtained, and it refers to a large ensemble of nanopar-
ticles that occur in different states. This fact does not
make it possible to relate the individual structure
peculiarities of nanoparticles with their chemical
properties. The problem can be solved with the use of
probe methods (in particular, scanning tunneling
microscopy and spectroscopy) whose spatial resolu-
tion allows one to study chemical interactions between
gaseous reactants and solid surfaces at the level of sin-
gle molecules and single defects. Thus, Grishin et al.
[20] found that the adsorption of hydrogen causes a
†Deceased.
KINETICS AND CATALYSIS Vol. 59 No. 6 2018
INITIAL STAGES OF DEUTERIUM ADSORPTION 821
change in the local electronic structure of gold
nanoparticles. This effect allowed us (as will be
shown below) to observe the evolution of a distribu-
tion of adsorbed deuterium atoms on the surface of
gold clusters.
The aim of this work was to determine the adsorp-
tion sites of deuterium (as a hydrogen isotope) on the
surface of gold nanoparticles at various sample expo-
sures in a gas atmosphere containing D2 and to analyze
the dynamics of surface coverage of the nanoparticles
with the adsorbate with increasing exposure. The
results of an experimental and numerical study of the ini-
tial stages of deuterium adsorption on gold nanoparticles
supported onto the surface of highly oriented pyrolytic
graphite (HOPG) will be presented below.
EXPERIMENTAL
The experiments were carried out using a setup
consisting of a scanning tunneling microscope (STM),
an Auger spectrometer, a quadrupole mass spectrometer,
and auxiliary equipment at a temperature of 300 K and a
residual gas pressure of 2 × 10–10 Torr. The setup had
two chambers; one of them contained the STM, and
the other contained equipment required for sample
preparation, the Auger and mass spectrometers, and
an oil-free ion pump, which provided a necessary vac-
uum. Tips prepared from platinum–iridium and tung-
sten wires by standard procedures were used as STM
probes.
The nanoparticles were applied to the surface of
HOPG by impregnation. For this purpose, the carrier
was immersed in an aqueous solution of HAuCl4 with
a metal concentration of 5 × 10–6 mg/L. Then, the sam-
ple was dried, placed in a vacuum chamber, and calcined
under ultrahigh-vacuum conditions at 500–750 K for
several hours. The duration of calcination was deter-
mined based on the results of studying the morphol-
ogy of the sample surface in STM. The degree of sur-
face coverage of the carrier with nanoparticles did not
exceed 5%.
The morphology and electronic structure of the
sample surfaces at the level of single nanoparticles and
the results of their modification due to interaction
with an adsorbate, which was molecular deuterium
(D2), were determined by topographic and spectro-
scopic measurements performed on the STM. It is well
known [21] that, on a nanocontact between a metallic
sample and a conducting needle, an S-shaped curve of
the STM tunneling current as a function of voltage
(current-voltage characteristic (CVC)) is observed. A
consequence of changes in the elemental composition
of the sample (for example, as a result of chemical pro-
cesses) can be the transformation of its electronic
structure from metallic to semiconductor (or a sub-
stantial decrease in the density of states in the vicinity
of the Fermi level), which leads to the appearance a
section with zero current (a band gap) in the S-shaped
curve [22–26]. Thus, the shape of the CVCs can serve
as an indicator of changes in the chemical composition
of the surface of nanoparticles. Henceforth, the term
CVC of nanoparticles will refer to the CVC of a tunnel-
ing contact that includes a nanoparticle, and the CVC
of graphite will mean the CVC of a tunneling contact
without a nanoparticle.
The elemental composition of the sample surfaces
was analyzed by Auger spectroscopy, and the data
obtained were compared with the results of spectro-
scopic measurements on the STM.
The composition of the gas atmosphere in the
setup at all stages of the experiment was controlled
using the results of mass-spectrometric measurements.
In the experiments described below, the pressure of
molecular deuterium did not exceed 1 × 10–6 Torr, the
residence time of the sample in an atmosphere of gas-
eous reactants was chosen in accordance with a speci-
fied exposure, which was measured in Langmuir units
(1 L = 1 × 10–6 Torr s).
The quantum-chemical simulation of the interac-
tion of atomic deuterium with an interface between
gold and carbon (carrier) clusters was carried out
within the DFT framework. The atomic and elec-
tronic structures of the test systems were calculated
using the OpenMX-3.7 and Quantum Espresso-5.1.1
quantum-chemical software packages. In the first
package, the basic set was given by numerical atomic-
centered functions; in the second package, the expan-
sion in plane waves was used. The calculation was carried
out in the generalized gradient approximation with the
use of the PBE functional, without taking into account
the spin polarization.
RESULTS AND DISCUSSION
Our study included experiments performed with
the use of a scanning tunneling microscope and a
quantum-chemical simulation of the adsorption of
deuterium atoms on a gold cluster in contact with two
graphene nanoflakes, which imitated the edge of an
HOPG terrace.
Experimental Studies
Figure 1a shows the image of a section of the sur-
face of HOPG with supported gold nanoparticles as an
example. Figures 1b and 1c show the averaged CVCs
of the nanoparticles and graphite and the Auger spec-
trum of the sample, respectively. According to the
results of an analysis of topographic images and spec-
troscopic data, the gold nanoparticles were distributed
on the surface of HOPG in such a way that most of
them were included in clusters grouped at graphite
surface defects (terrace edges), but isolated nanoparti-
cles were also found. The nanoparticles had a rounded
shape. A lateral size distribution maximum corre-
sponded to a range of 4–8 nm at a height of 1.5–2.0 nm.
822
KINETICS AND CATALYSIS Vol. 59 No. 6 2018
GATIN et al.
Fig. 1. Gold nanoparticles on HOPG: (a) topographic
image, (b) CVC of nanoparticles and graphite before expo-
sure in an atmosphere with deuterium, (c) Auger electron
spectrum of sample. Au and C refer to gold and graphite,
respectively.
32 000
32 500
33 000
33 500
34 000
34 500
100 200
Intensity, arb. units
(c)
300 400 500
Auger electron energy, eV
–4
–3
–2
–1
0
1
2
3
4
–1
Tunneling current, nA
(b)
(а)
40 × 40 nm
Au
Au
C
C
0 1
Voltage, V
The spectroscopic measurements showed that the
CVCs of the nanoparticles and graphite were close to
each other and had an S-shape. Note that the tunnel-
ing current measured on a nanoparticle over the entire
range of voltages was somewhat higher in absolute
value than the tunneling current on graphite; that is,
the local conductivity of the nanoparticles was some-
what higher than the conductivity of graphite. The
increase in the tunneling current of the nanoparticles
was related to the fact that the density of states near the
Fermi level of metal nanoparticles is greater than that
of HOPG (a semimetal). The absence of residual
impurities from gold was conf irmed by the results of
the elemental analysis of sample surfaces: the Auger
electron spectra exhibited maximums at 272 eV and
69, 141, and 160 eV, which correspond to the presence
of carbon and gold, respectively, while signals from
other elements were not detected.
An exposure of the sample in an atmosphere con-
taining deuterium caused significant perturbation of
the local electron density of nanoparticles. This is evi-
denced by a change in the electronic structure of
nanoparticles as the exposure in the presence of D2 was
increased. The left-hand parts of Fig. 2 show the topo-
graphic images of HOPG surface sections with the sup-
ported nanoparticles and the points at which CVCs were
measured on the nanoparticles, and the right-hand
parts represent the averaged CVCs at these points.
As can be seen in Fig. 2, after an exposure of 200 L,
a region in which the measured current was lower than
the current in graphite (hereinafter, a region of
reduced conductivity) appeared at the outer edge of
the nanoparticles. In this case, the current at center of
the nanoparticle was still greater than the current in
graphite (Fig. 2a). Furthermore, the CVC curves cor-
responding to individual points at the edge of the
nanoparticle had zero-current sections. Such curves
were not observed before the exposure of the sample in
the presence of deuterium. As the exposure in an
atmosphere with deuterium was increased to 800 L,
the width of the low-conductivity region at the periph-
ery of the particle increased; the number of points cor-
responding to CVCs with a zero-current region also
increased. In this case, the central part of the nanopar-
ticles retained its properties (Fig. 2b). After an increase
in the exposure to 1400 L, points at which the CVC
curve contained a zero-current section appeared in
this region; however, the averaged conductivity of the
central part still slightly exceeded the conductivity of
graphite (Fig. 2c). Finally, at an exposure of about
2000 L, the number of points on the nanoparticle sur-
face at which the CVC curves had a zero-current sec-
tion was approximately one third of the total number
of points at which the measurements were performed.
Large areas (comparable in size to regions observed at
the center and at the periphery of nanoparticles upon
small exposures) with increased and decreased con-
ductivity disappeared form the nanoparticle surface.
In this case, the CVC curves with a zero-current sec-
KINETICS AND CATALYSIS Vol. 59 No. 6 2018
INITIAL STAGES OF DEUTERIUM ADSORPTION 823
tion and without such a section were randomly distrib-
uted over the entire surface of the nanoparticle. In a
sense, the surface became homogeneous. The results
of the formal averaging of CVCs at the center of the
particle and at its periphery showed that the conduc-
tivity in these regions was lower than the conductivity
of graphite (Fig. 2d). This conclusion is true of both
the nanoparticles that form clusters and the isolated
nanoparticles. Note that the dissociative adsorption of
deuterium (or hydrogen) occurs only at gold nanopar-
ticles supported on graphite. In cases where gold
nanoparticles were arranged on a gold substrate, simi-
lar effects were not observed [29]. Furthermore, the
adsorption of atomic deuterium, which was formed
from D2 due to various processes occurring in the
setup, on the nanoparticles can also be excluded
because the STM chamber was constructively sepa-
rated from the sample preparation chamber, where the
continuously operating ion pump, which can also
serve as a source of D atoms, was arranged.
An increase in the exposure to 3000 L did not cause
noticeable changes in the shape of CVCs measured on
the surface of the nanoparticles. It was found earlier
[27] that the adsorption of atomic hydrogen on the
surface of free gold nanoclusters led to a decrease in
the density of states in the vicinity of the Fermi level,
and this caused a decrease in the conductivity of the
nanoclusters. Taking into account the results of theo-
retical studies and the experimental data described
above, we can conclude that, in our case, the dissocia-
tive adsorption of deuterium occurred on the surface
of gold nanoparticles, and the stationary surface cov-
erage with the adsorbate came into play predomi-
nantly at the gold–graphite interface and then propa-
gated to the entire surface of the nanoparticle. It
should be noted that the time taken for establishing the
final (stationary) state of the system was very long (up
to a day). This fact is indicative of the existence of sig-
nificant activation barriers for both the surface migra-
tion of deuterium adatoms and a structural rearrange-
ment of the nanoparticle.
Quantum-Chemical Simulation
We simulated the adsorption of atomic deuterium
in the system of a gold nanoparticle applied to the edge
of an HOPG terrace. The purpose of the calculations
was to compare the binding energies of the adatom in
various positions with respect to the surface and to
establish corresponding changes in the local density of
states of the system, which affect the topographic and
spectroscopic features of STM–STS measurements.
The quantum-chemical simulation of the interaction
of atomic deuterium with an interface formed by gold
clusters and carbon was carried out within the frame-
work DFT. The atomic and electronic structure of the
test systems was calculated using the Open MX 3.7 and
Quantum Espresso-5.1.1 quantum-chemical software
packages. In the former package, 17 valence electrons
Fig. 2. Density of electronic states in different active sites
in the gold nanoparticle–HOPG system. Topographic
images and CVCs of gold nanoparticles and graphite at
various stages of the experiment: (a) exposure, 200 L;
image size, 22 × 22 nm; (b) exposure, 800 L; image size,
18 × 18 nm; (c) exposure, 1400 L; image size, 7 × 7 nm;
and (d) exposure, 2000 L; image size, 12 × 12 nm. Curves
A, B, and D correspond to points A (in the nanoparticle-
free region of graphite), B (the peripheral region of
nanoparticles), and D (the central region of nanoparticles)
in the topographic images.
–4
–3
–2
–1
0
1
2
3
4
Tunneling current, nA
(а)
(b)
(c)
(d)
B
A
D
–4
–3
–2
–1
0
1
2
3
4
B
A
D
–4
–3
–2
–1
0
1
2
3
4
B
A
D
–4
–3
–2
–1
0
1
2
3
4
–2 –1 0 1 2
Voltage, V
B
A
D
824
KINETICS AND CATALYSIS Vol. 59 No. 6 2018
GATIN et al.
of gold and 4 valence electrons of carbon were taken
into account. The basis set was a set of numerical
atom-centered primitive functions, which roughly
corresponded to a double set of Slater orbitals. A plane
wave basis set was used in the latter package. The gen-
eralized gradient approximation and the PBE func-
tional were used in both of the packages. The model of
a broken border of graphene was a carbon cluster con-
taining 138 atoms; 90 and 48 C atoms were contained
in the bottom and top layers of this cluster, respec-
tively. The distances and the entire atomic structure
corresponded to the parameters taken for bulk graph-
ite. In the course of the calculations, the positions of
carbon atoms were fixed. An icosahedral isomer of a
13-atom gold cluster, whose atomic structure signifi-
cantly changed upon the interaction with the carbon
cluster, was the model of a gold nanoparticle. Unlike
the original 13-atom icosahedron, the cluster surface
acquired an inhomogeneity. Two tentative regions can
be recognized in this cluster: an interface, namely, the
boundary with a broken edge of the carbon cluster,
which imitated the carrier, and a vertex, that is, an area
that did not border the carrier. It is most likely that this
atomic structure of a gold cluster in the system that
simulated the nanoparticle at the edge of the graphite
terrace does not correspond to the global minimum of
the potential energy surface of the system, but the task
of global optimization was beyond the scope of this
work. In the subsequent calculation of the interaction
of the cluster with deuterium atoms, the atomic struc-
ture of the resulting gold–carbon system was fixed,
except for a few cases marked with asterisks in Table 1.
In our case, this simplification was justified by the fact
that the relaxation of the atomic structure of a
graphene flake (the deformation of edges) does not
substantially change the local density of states in the
vicinity of the gold cluster [28].
Table 1 (entry 1) summarizes three arbitrary cases
of the adsorption of a deuterium atom on a gold clus-
ter. It is impossible to unambiguously characterize the
optimized position of the deuterium atom on the clus-
ter surface as bridge or hollow; it is likely that a combi-
nation of these positions should be considered. The
bond lengths correspond to the distance of the D atom
to the nearest gold atom. Entry 2 characterizes the
adsorption of a deuterium atom on a gold–carbon
interface. Figures 3a and 3b illustrate the adsorption
on the outer surface of graphene (hereinafter, over
graphene) and on its inner layers (hereinafter, under
graphene), respectively. In the latter case, three vari-
ants of modeling the dynamics of the behavior of
neighboring gold atoms at the adsorption site are pos-
sible; correspondingly, there are three degrees of their
influence on the steady-state binding energy, that is,
the estimation of the contribution of the atomic
mobility of the nanoparticle. In the first variant, all of
the gold atoms are fixed (E1); in the second variant,
the two nearest gold atoms are not fixed (E2); and in
the third variant, none of the 13 gold atoms is fixed
(E3). As follows from a comparison between the cal-
culated bond energies, the nearest gold atoms are most
important because the difference between the Au–D
bond energies in the cluster with mobile gold atoms
nearest to the adatom of deuterium and in the cluster
with frozen gold atoms (E2 – E1 = 0.43 eV) is greater
than the difference between the above bond energies
in the cluster with the mobile gold atoms nearest to
deuterium and in the cluster in which all of the gold
atoms are defrosted (E3 – E2 = 0.06 eV). Thus, the
interaction of deuterium with a gold cluster can be
Table 1. The energies and bond lengths of the deuterium atom with the surface in the Au13C138 cluster
* The atomic structure of the resulting gold–carbon system was not determined.
Entry D atom adsorption
site D atom position Bond energy, eV Bond length, Å Bond angle, deg
1 Gold cluster − −3.09 1.57 −
−2.90 1.58 −
−3.19 1.74 −
2 Gold–carbon
interface
Over graphene −2.59 1.16 90
Under graphene −3.33 1.12 101
−3.76* 1.11 108
−3.82* 1.10 109
3 Two deuterium atoms
at the gold–carbon
interface
Over graphene −3.56 1.16
1.12
90
133
Under graphene −3.93 1.12
1.12
90
133
4 Graph ene b ounda r y – −4.54 1.12 133
5 Graphene plane – −1.49 1.20 90
KINETICS AND CATALYSIS Vol. 59 No. 6 2018
INITIAL STAGES OF DEUTERIUM ADSORPTION 825
considered local because the perturbation of the
atomic and electronic structures occurs at the atoms
closest to deuterium. Entry 3 in Table 1 characterizes
two cases of the adsorption of two deuterium atoms at
the gold–carbon interface on neighboring atoms over
graphene and under graphene; it allows one to evalu-
ate the mutual influence of chemisorbed deuterium
atoms on each other and the binding energy of D
atoms with the Au13C138 cluster. The bond lengths and
bond angles are indicated for each of the two deute-
rium atoms. The fourth row represents the case of the
interaction of a deuterium atom with a graphene
boundary without a gold cluster. Entry 4 shows a vari-
ant of the interaction of a deuterium atom with a
graphene boundary that does not contain a gold clus-
ter. Finally, entry 5 refers to the interaction of the D
atom with a graphene plane, which also did not con-
tain a gold cluster. It is obvious that strong differences
in the bond energies in the last two cases are due to the
Fig. 3. Projected density of electronic states for different active centers in the gold nanoparticle–HOPG system: (a) the energy
spectrum of the cluster and the carrier (adsorption on the outer surface of graphene), (b) the energy spectrum of the cluster and
the carrier (adsorption on the inner layers of graphene), and (c) the energy spectrum of the cluster vertex (1) in the absence of
hydrogen and (2) in the presence of hydrogen.
0
1
2
3
4
5
–5 –4
Density of states, eV–1
(а)
(b)
–3 –2 –1 0 1
1
2
2
0
1
2
3
4
5
–5 –4 –3 –2 –1 0 1
1
2
2
(c)
0
2
4
6
8
10
–5 –4 –3 –2 –1 0 1
1
2
2
Energy, eV
826
KINETICS AND CATALYSIS Vol. 59 No. 6 2018
GATIN et al.
electronic and atomic structure peculiarities of the
graphene flake.
As follows from Table 1, the largest bond energy
between a deuterium atom and a gold cluster was
observed at the gold–HOPG interface. Although the
calculated absolute values of the bond energies of deu-
terium noticeably exceeded the real ones (possibly,
because we did not use the basis set superposition error
(BSSE) correction), the difference between the ener-
gies of adsorption on the interface and on the cluster
was small. The migration of deuterium adatoms
requires the overcoming of a significant activation bar-
rier. This was confirmed previously by Gatin et al.
[19], who experimentally established the high strength
of a bond between atomic deuterium and gold
nanoparticles on graphite, and a longer time (about a
day) taken to establish a stable state of the system
required for performing STM–STS measurements.
Figure 3 indicates a characteristic change (in this
case, a decrease) in the local density of states near the
Fermi level near the adatom due to deuterium adsorp-
tion. Figure 3 shows the sums of the densities of states
projected onto the circled atoms in the Au13 C138 sys-
tems, which (dotted curve) contained and (solid
curve) did not contain the adsorbed atoms of deute-
rium at different adsorbate positions. Summation over
a set of projectors simulated a situation typical of the
STM studies of metal clusters (the curvature of a probe
is much smaller than the curvature of the test sample),
when the tunneling current was formed by several
cluster atoms. In this case, the matrix elements of the
wave functions of the probe and cluster atoms were
assumed the same for simplicity. Figure 3 shows the
following arrangements of the D atom: (a) above the
gold–graphite interface, (b) under the gold–graphite
interface, and (c) on the gold cluster. It can be seen
that the largest changes in the density of electronic
states near the Fermi level were observed in the first
two cases, which correspond to the maximum energies
of adsorption of the deuterium atom.
Thus, the results of the quantum-chemical calcula-
tions qualitatively correspond to our experimental
results, which indicate the preferential adsorption of
deuterium at the periphery of gold nanoparticles at
small sample exposures in an atmosphere with deute-
rium, and conclusions drawn in previous publications
[19, 20], where it was demonstrated that the adsorp-
tion of hydrogen on gold nanoparticles decreased local
conductivity.
CONCLUSIONS
Thus, in this work, we experimentally and theoret-
ically studied the adsorption of deuterium on gold
nanoparticles supported onto the surface of HOPG.
We found that, at small exposures, the interface
between the gold nanoparticle and HOPG (carrier)
was a preferred site for the adsorption of deuterium.
The deuterium atoms can propagate to the entire sur-
face of the nanoparticles as the exposure is increased
and the adsorption sites on the interface are filled.
ACKNOWLEDGMENTS
This study is supported by the State assignment
0082-2014-0011 (registration number АААА-А17-
117111600093-8) and RFBR (grants 15-03-02523, 16-
03-00046, 18-03-00060).
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Translated by V. Makhlyarchuk
