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Understanding the Formation of Surface Relief Gratings in Azopolymers:
A Combined Molecular Dynamics and Experimental Study
Milena Merkel, 1 Amala Elizabeth, 2, 3 Marcus Böckmann, 4 Harry Mönig, 2, 3 Cornelia Denz, 1 and Nikos L.
Doltsinis 4
1) Institut für Angewandte Physik, Westfälische Wilhelms-Universität Münster, Corrensstr. 2/4, 48149 Münster,
Germany.
2) Physikalisches Institut, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 10, 48149 Münster,
Germany.
3) Center for Nanotechnology, Heisenbergstr. 11, Münster 48149, Germany
4) Institut für Festkörpertheorie, Westfälische Wilhelms-Universität Münster and Center for Multiscale Theory & Computation,
Wilhelm-Klemm-Str. 10, 48149 Münster, Germany.
(Dated: 30 September 2022)
The formation of surface relief gratings (SRGs) in thin films of poly-disperse-orange3-methyl-methacrylate is investigated
using atomistic molecular dynamics simulations and compared to experimental results. For this purpose, the film
is illuminated with a light pattern of alternating bright and dark stripes in both cases. The simulations use a molecular
mechanics switching potential to explicitly describe the photoisomerization dynamics between the E and Z isomers of
the azo-units and take into account the orientation of the transition dipole moment with respect to the light polarisation.
Local heating and elevation of the illuminated regions with subsequent movement of molecules into the neighboring
dark regions is observed. This leads to the formation of valleys in the bright areas after re-cooling and is independent of
the polarization direction. To verify these observations experimentally, the azopolymer film is illuminated with bright
stripes of varying distance using a spatial light modulator. Atomic force microscopy images confirm that the elevated
areas correspond to the previously dark areas. In the experiment, the polarization of the incident light makes only a
small difference, since tiny bead-like structures form in the valley only when the polarization is parallel to the stripes.
I. INTRODUCTION
The light-induced modification of azo-containing polymer
films has been a vivid research field since the first reports
describing the phenomenon in the late 1990’s 1–7 . As a consequence
of the E/Z photo-isomerisation of the azobenzene
(AB) photochromic unit, a large variety of macroscopic structural
changes in azopolymer materials, such as bending of
free-standing films, genuine solid-to-liquid transformations
(’liquefication’) or the formation of surface relief gratings
(SRGs) can occur 4,8–11 .
In the latter phenomenon, trenches and hills form on the
surface of a polymer film due to effective mass transport induced
by inhomogeneous irradiation 7,12 . For this purpose,
mostly periodic interference patterns are used, but also more
sophisticated patterns, such as optical vortices or differently
polarized Bessel beams 4,12–15 . Interestingly, the resulting
SRGs are extremely diverse in terms of shape, depth or stability.
Even the position of the peaks, whether in the low or
high intensity regions of the illumination pattern, varies 7,16 .
While in most applications mass transport is seen to be directed
away from the illuminated (bright) regions, and in the
direction of the incident light polarisation, several exceptions
can be found in literature. For example, Holme et al. 17 observed
the formation of hills in the bright regions for a liquid
crystalline polyester in contrast to an amorphous peptide
oligomer showing trenches. Furthermore, a more rigid backbone
of the polyester leads to the formation of trenches instead
of hills. Yadavalli et al. 18 in turn observed a formation of
hills in either the bright or the dark regions, depending on the
strength of the interaction between the azobenzene-containing
side chains and the backbone.
Also the dependence of the direction of material movement
on polarization is controversial. For example, Karageorgiev
et al. 19 prepared two orthogonal trenches on a thin film surface
prior to illumination and found that only the one parallel
to the polarisation vector was erased. Meanwhile, previous
publications have suggested that SRG formation is independent
of polarization under high-intensity cw and pulsed
irradiation 7,20,21 .
Furthermore, while the majority of applications have the
azo-chromophore either covalently linked (with spacer units
of variant length) to the polymer backbone or incorporated
into it, the azo-unit may also be present only as an additive
to the polymer composition, with surprisingly low concentrations
down to 1% 22 . In some cases, pulsed laser experiments
have produced SRGs even in samples with absorbing, but nonisomerizing
chromophores, suggesting a thermal origin of the
structures 7,20,21,23–26 .
All things considered, these varying and partially contradicting
results may be due to the wide range of different
experimental conditions in terms of material, illumination
intensity, exposure time, wavelength, light polarization or
pattern 10,11,16 . Accordingly, a large number of different theories
about the physical mechanism of SRG formation exist,
such as the isomerization pressure model, the asymmetric diffusion
model or the fluid dynamics model 13,27–30 . However,
none of the models can explain all of the observed features.
In this contribution, we investigate the response of a
thin film of the azo-polymer poly-disperse-orange3-methylmethacrylate
(PDO3M) to photo-stimulus both experimentally
and computationally. In the experiment, the polymer film
was illuminated with a pattern of dark and bright stripes of
varying distance generated by a spatial light modulator and

Sample title 2
the surface profile was read out using atom force microscopy.
The computational treatment comprised atomistic molecular
dynamics simulations explicitly taking into account the photoisomerization
dynamics and the light polarization 31 . This
combined approach allows for new insight into the mechanistic
aspects of the surface relief forming process. A particular
focus lies on the role of the light polarization direction relative
to the stripe pattern.
II.
COMPUTATIONAL DETAILS
Our atomistic computational model consists of a 20 nm
thick quasi-infinite periodic slab with a unit cell of size
19.3×32.1×50 nm 3 (z being the plane normal direction) containing
1944 16-meric PDO3M molecules (i.e., a total of
995 328 atoms and 31 104 AB chromophore units) that can
be partitioned into a bright (irradiated) half and a dark (not
irradiated) half, as shown in Fig.1. To maintain the shape of
the slab, the polymer backbone atoms at the bottom (i.e., with
z ≤0.9 nm) were fixed by constraints.
Laser-induced E ↔ Z photoswitching was then simulated
by repeatedly applying our molecular mechanics switch 31–33
(that we extended to include the Z → E direction (cf. SI)) every
50 ps to all chromophore units in the active region whose
transition dipole moment, D, was sufficiently aligned with
the polarisation vector, P, of the incident light. We chose
the two polarisation directions P = (1, 0, 0) (x-direction) and
P = (0, 1, 0) (y-direction).
The overall heating of the slab due to the energy uptake
of ≈ 2.8 eV per photoactivated chromophore was controlled
by a moderate heat bath of Nosé-Hoover type (τ = 80 ps,
T = 300 K) applied separately to the bright and dark regions,
respectively, in order to prevent the extreme temperatures observed
in our previous studies 31 .
In order to further probe orientation and finite size effects,
we carried out simulations with two different partitionings of
dark and bright regions as shown in Fig. 1. In the first partitioning,
the slab was divided into two halves along the y-
direction. With the two polarisations considered, this resulted
in the setups ’yy’ and ’yx’ (Fig. 1). The second partitioning
consisted in dividing the system in two halves in x-direction,
resulting in the ’xy’ and ’xx’ setups.
The molecular dynamics simulations were performed using
an in-house modified version Gromacs ?
III.
RESULTS AND DISCUSSION
In this section we describe the observed surface modifactions.
We first present the results from theory and experiment
in two separate sections and then discuss the implications on
the mechanistic aspects.
FIG. 1. Schematic representation of the different simulation setups.
A. Molecular dynamics simulations
The computer simulations mimick, due to the periodic
boundary conditions, alternating bright and dark stripes on
the thin film surface with the stripes oriented either parallel
to the x (’vertical’) or the y axis (’horizontal’), respectively
(cf. Fig. 1).
This general setup of the periodic MD box is visualised in
Fig. 2 together with the resulting surface profile.
FIG. 2. View of the periodic simulation box. Top row: complete box
with periodic continuation displayed for the first top layers (highlighted
via colour scheme) and ’bright’ area indicated by a yellow
rectangle. Bottom row: resulting final surface profile obtained after
photostimulation and re-cooling (see text).
The time evolution of the emerging height profiles for the
four different setups is shown in Fig. 3, where we have plotted
the maximum z-value of the molecules with a given position
along the axis perpendicular to the bright- dark separation,
or in other words, the profile seen when viewing the sample
parallel to the stripes.
Focussing first on Fig. 3a), it is seen that the photoirradiation
within the first 1 ns leads to a significant increase in height

Sample title 3
especially in the centre of the bright region (blue curve) due
to the energy input by repeated photoexcitation (note that the
centre of the dark region around y = 8 nm is nearly unaffected
throughout). In the time window 1–2 ns, the increase in the
centre comes to a halt and the elevation begins to shift to the
bright/dark boundary (red curve). This latter effect is dominant
in the remaining illumination time window (2–5 ns) and
is accompanied by a drop in height in the central bright region
(orange, black, yellow). After re-cooling to 300 K, a trench of
≈ 1 nm depth is clearly visible in the centre of the bright region
together with two hills (≈1 nm) formed at the bright/dark
boundary (green curve). The effect is similar when changing
the direction of polarisation as seen from Fig.3c), but is
significantly less pronounced upon changing the bright/dark
separation to ’horizontal’ (cf. Fig.3b), d)).
T / K
T / K
900
800
700
600
500
400
300
0 1 2 3 4 5 6
900
800
700
600
500
400
300
0 1 2 3 4 5 6
0 1 2 3 4 5 6 7 8 9 10 11
0 1 2 3 4 5 6 7 8 9 10 11
all
bright
dark
t / ps
t / ns
z / nm
20
18
FIG. 4. Time evoultion of global (bulk, bright and dark region) temperature
for the four different MD setups.
16
14
20
-15 -10 -5 0 5 10 15
-10 -5 0 5 10
0 ns
0.5 ns
1.0 ns
2.0 ns
3.0 ns
4.0 ns
5.0 ns
re-cooled
ter 1 ns. While the temperature bath manages to maintain a
bulk average temperature of about 600 K (see above), a hot
’bubble’ appearing in the bright region is clearly visible, with
peak temperatures of about 1400 K in the ’vertical’ setup and
roughly 200 K lower for the ’horizontal’ setup.
z / nm
18
16
14
-15 -10 -5 0 5 10 15
y / nm
-10 -5 0 5 10
x / nm
FIG. 3. Time evolution of the slab height profiles observed for the
four different MD setups.
The characteristics of the thermal energy uptake due to photoexcitation
is shown in Fig. 4, which presents the time evolution
of the overall bulk system temperature together with the
average values for the bright and dark regions, respectively.
In the first 1 ns, the system is seen to heat up from the initial
value of 300 K to a global average of roughyl 600 K in all
cases. Afterwards, the temperature remains stable for the remaining
duration. The pronounced fluctuations are due to the
photoexcitation cycles every 50 ps. A closer look at this analysis
reveals some subtle differences between the global average
temperatures of the ’vertical’ and ’horizontal’ setups. While
the overall system temperature of the ’vertical’ setups plateaus
at about 630 K, it converges to about 580 K for the ’horizontal’
setup. Furthermore, it is seen that the average temperature in
the bright region is ca. 100 K higher in the ’vertical’ setup as
compared to the ’horizontal’ partitioning (800 K vs. 700 K).
At the same time, the average temperature of the dark region is
lower for the ’vertical’ than for the ’horizontal’ setup. This is
attributed to the different widths of the bright and dark stripes
in the two setups, the narrower horizontal stripes allowing for
a more rapid exchange of heat between the two regions.
Going beyond temperature averages, Fig. 5 presents the
temperature distributions across the slab profile as reached af-
z / nm z / nm
FIG. 5. Temperature distribution of slab profile observed for the four
different MD setups after 1 ns.
The lower overall temperature reached in the two ’horizontal’
setups corresponds to a slightly lower (≈ 10 %) number of
activated chromophore units as can be seen from Fig. 6, where
the number of photoactivated E → Z and Z → E azo chromophore
units is shown, respectively, as a function of time
together with their sum (blue line). Here, it is seen that –
starting from an all-E situation – in each of the four setups a
kind of ’steady state’ is reached with about 58 % E → Z and
42 % Z → E excitation.
Next, we turn to the drift motion and the associated mass
transport (cf. Fig. ??), which is ultimately responsible for the
formation of a surface pattern. We begin our detailed analysis
of the molecular motion involved with Fig. 7, which presents
the average root mean square displacements (total rmsd and
cartesian components x, y and z) of the molecules represented

Sample title 4
no. of active NN units
no. of active NN units
4000
3000
2000
1000
4000
3000
2000
1000
0
0 1 2 3 4 5
0 1 2 3 4 5 6 7 8 9 10
E2Z
Z2E
total
rmsd / nm
rmsd / nm
1.6
1.2
0.8
0.4
0.0
-0.4
-0.8
0 1 2 3 4 5 6
1.6
1.2
0.8
0.4
0.0
-0.4
0 1 2 3 4 5 6 7 8 9 10 11
x
y
z
tot
x
y
z
tot
0
0 1 2 3 4 5
t / ns
0 1 2 3 4 5 6 7 8 9 10
t / ns
-0.8
0 1 2 3 4 5 6
t / ns
0 1 2 3 4 5 6 7 8 9 10 11
t / ns
FIG. 6. Time evoultion of photoexcitation of azo chromophore units
for the four different MD setups.
by their center of mass (COM) in the ’bright’ and ’dark’ region
for the four different setups. Generally, it is seen that
initially the rmsd in the bright region is dominated by the z-
component (blue line) for all four setups, implying an initial
height increase. Later on, the growth in z slows down, while
x and y-components rise more rapidly. the In the case of the
’yx’ and ’yy’ setups, movement starts to be dominated by the
y-component from about 1 ns onwards.
For the horizontal setups ’xx’ and ’xy’ (Fig. 7b,d), the
molecules are seen to travel much more slowly, which is in
line with their reduced temperature (Fig. 4). The general behaviour
of the x, y, and z components is similar to the vertical
setups, except for the fact that the x and y components never
diverge meaning that there is no preferred direction of mass
transport.
All four setups have in common that mass transport occurs
from the bright to the dark region. However, in contrast to
our expectation and seemingly at odds with many previous
works, molecular displacement is practically independent of
the polarisation direction. As it is known that the influence of
polarisation depends on many factors including the chemical
nature of the material and the light intensity, we aimed to verify
our computational observations by performing matching
experiments using the same material (see below).
B. Experimental
In order to experimentally verify the computational results,
we illuminated a PDO3MA azopolymer film with different
intensity patterns. These consisted of bright stripes of varying
distance, while their width remained the same. This way, the
position of the peaks of the SRG, whether in the illuminated
or dark regions, can be determined. Moreover, we varied the
polarization of the light to investigate its impact on the SRG
formation.
For fabrication of the azopolymer samples, 3 wt% of
FIG. 7. Time evolution of average COM root mean square displacement
(RMSD) split into individual cartesian components and
dark/bright regions for the four different MD setups. The curves for
the dark region are plotted with negative RMSD for better distinction.
poly-disperse-orange3-methyl-methacrylate (PDO3M)
(Sigma-Aldrich) were added to tetrahydrofuran (THF) and
stirred for 2 hours. In the meantime, glass substrates were
cleaned via ultrasonication in acetone and isopropyl alcohol
for 10 min each and subsequently treated in UV/ozone to
improve wettability. The azopolymer solution was spincoated
at 1000 rpm for 10 s on the glass substrates and finally
annealed on a hotplate at 110 ◦ C for 1 h.
To generate stripe patterns with different distances of the
bright stripes we utilized the setup shown in Fig. 8. Light
from a laser diode with a wavelength of 405 nm is modified by
a half-wave plate to ensure a polarization parallel to the long
side of the employed LETO phase-only spatial light modulator
(SLM) (HOLOEYE). The SLM is based on a reflective
LCOS microdisplay with a full high definition (1920 × 1080
pixel) resolution and a pixel pitch of 6.4 µm. It is used to tailor
the transverse intensity distribution of the reflected wave.
Therefore a blazed grating consisting of a linear phase ramp
between 0 and 2π with a grating period of ten pixels and a tilt
angle of 51 ◦ is addressed to the SLM 34 . The reflected beam is
focused with a lens on a pinhole to separate the first diffraction
order containing the desired pattern from residual light and
imaged with a second lens on the sample, resulting in a 10×
demagnification of the pattern. Using an infinity-corrected objective
and a lens, the generated light pattern can be observed
with a CMOS camera. After illumination, the azopolymer
sample surfaces were examined with the atomic force microscope
(AFM) NaioAFM from Nanosurf with the Naio Control
Software (version 3.6), operated at ambient conditions. Using
the sharp tip in the AFM, high resolution topography maps
can be obtained, see Fig. 9. On the left, the different illumination
patterns used to inscribe the SRGs in the films. Next to
them, images of the respective AFM measurements of the topographies
and the corresponding line profiles are shown. In
each case, the bright stripes have a width of 12.8 µm. The dis-

Sample title 5
FIG. 8. Scheme of the experimental setup. λ/2: half-wave plate,
SLM: phase-only spatial light modulator, M: mirror, L: lens, P: pinhole,
S: sample, MO: infinity-corrected microscope objective and
Cam: camera.
tance between the stripes varies between 25.6 µm (Fig. 9a),
31.4 µm (Fig. 9b) and 37.2 µm (Fig. 9c). For all of them,
the polarization of the light is perpendicular to the stripes and
the illumination time is 20 h. The intensity varies slightly between
158 mWcm −2 (Fig. 9a), 164 mWcm −2 (Fig. 9b) and
151 mWcm −2 (Fig. 9c).
The line profiles extracted from the topography images can
provide insight into the roughness of the surface, which can be
directly correlated to the polymer motion. Line profiles for the
sample in Fig. 9a show a valley of approximately 12 µm wide
and a plateau which is 26 µm wide. The average depth/height
of these features is between 60 nm and 100 nm. The line profiles
of the other two samples show valleys of the same width,
while the width of the plateaus varies. Thus, comparing the
dimensions of the topographical features in these images to
the respective illumination patterns, we can conclude that the
azopolymer has the tendency to move away from the bright
regions in the illumination pattern and accumulate in the dark
regions.
Moreover, the influence of the polarization on the SRG formation
is investigated. While in Fig. 9 the polarization is perpendicular
to the stripes, in Fig. 10 it is parallel. Otherwise
the illumination parameters are the same as in Fig. 9a with an
illumination time of 20 h and an intensity of 158 mWcm −2 .
Again the width of the valleys correspond to the width of the
bright stripes and the plateaus to the dark regions in between.
Also the depth of the structures is again in the range of 60 nm
to 100 nm as for the illumination with perpendicular polarization.
The only difference is the appearance of small bead-like
structures of 10 nm to 20 nm height in the valleys.
FIG. 9. Illumination patterns with different distances between the
bright stripes and the respective AFM topography images and line
profiles: (a) 25.6 µm, (b) 31.4 µm and (c) 37.2 µm. The line profiles
are extracted across the whole width of the respective scan image at
points indicated by the colored arrows. Laser light polarized perpendicular
to the striped pattern is used.
C. Merging theory and experiment
The simulation predicts that during illumination maxima
form in the exposed regions and then migrate from the sides
into the dark regions, as has been observed similarly earlier
by Yadavalli et al. 35 . Double-peak substructures similar to
those formed in our simulation after cooling have also been
FIG. 10. Illumination pattern with 12.8 µm wide bright stripes with
25.6 µm in between and respective AFM topography images and corresponding
line profiles of the illuminated azopolymer sample. The
line profiles are extracted across the whole width of the scan image at
points indicated by the colored arrows. The polarization of the laser
beam is parallel to the illumination pattern.

Sample title 6
observed in other publications under pulsed illumination or
depending on the material 23,36,37 . In the experiment, the dark
regions are identical with the elevated areas, which, when
compared with the simulation, equates to a full movement of
the material out of the illuminated regions. This is consistent
with the significantly longer illumination times of 20 h in the
experiment, compared to only a few picoseconds in the simulation.
We conclude that very short cw or pulsed illumination
can induce a double peak with maxima at the interfaces of illuminated
and dark regions, while a longer illumination leads
to a maximum in the dark region.
In both the simulation and in the experiment, the polarization
of the incident light has no or only a minor impact on
the surface modulation. In the experiment, small bead-like
structures of 10 nm to 20 nm height emerge in the valleys.
These are not predicted in the simulation. This difference
could again be due to the different time and length scales of
simulation and experiment. The illumination times of only picoseconds
and stripe sizes of a few nanometres investigated
in the simulation cannot be realized in these experiments and
vice versa.
The reason for this rare (virtual) independence of SRG
formation on polarization could be the high fluence used in
these experiments. While in most SRG experiments, the
azopolymer films are illuminated for a few seconds to several
minutes with intensities in the range of tens to hundreds
of mWcm −2 , here the films are illuminated for 20 hour
with over 150 mWcm −2 and thus with a significantly higher
fluence 4,7,16 . Also in our simulations, the fluence is very
high with ... photons per .. Our experiment and simulation
are thus consistent with publications claiming polarizationindependent
SRG formation under high-intensity cw and
pulsed irradiation 7,20,21,23–26 .
With regard to the cause of photomigration, the simulations
clearly show that the conversion of light-energy into local heat
is a prerequisite for this phenomenon to occur. In the fluence
regime studied here, mass transport appears to take place in
the direction of the negative temperature gradient and can thus
be described my the theory of thermal diffusion 38 .
IV.
CONCLUSIONS
We have carried out a combined experimental and theoretical
study of the surface relief grating formation in the azopolymer
poly-disperse-orange3-methyl-methacrylate. On the experimental
side, azopolymer polymer films were illuminated
with light patterns of bright and dark stripes created by a spatial
light modulator. The surface profile was subsequently
characterized using atom force microscopy. Thus is could be
established that mass transport occurred away from the bright
stripes into the dark stripes. Furthermore, the polarisation direction
was seen to have a minor effect. These experimental
findings were corroborated by atomistic molecular dynamics
simulations that explicitly modelled the photoisomerisation
dynamics and light polarisation. The simulations further
showed that local heating due to light-absorption is necessary
for mass transport to occur. In the high-fluence regime investigated
in this work, mass transport appears to be dominated by
the temperature gradient rather than any more subtle effects
related to the photoisomerisation dynamics.
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ACKNOWLEDGMENTS
We wish to acknowledge the support of the author community
in using REVTEX, offering suggestions and encouragement,
testing new versions, . . . .
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
Appendix A: A little more on appendixes
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