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Conformation and structural changes of diblock
copolymers with octopus-like micelle formation in
the presence of external stimuli
K Dammertz, A M Saier, O Marti and M Amirkhani
Institute for Experimental Physics, Ulm University, Albert-Einstein-Allee 11, 89081
Ulm, Germany
E-mail: [email protected]
Abstract. External stimuli like vapors or electric fields can be used to manipulate
the formation of AB-diblock-copolymers on surfaces. We study the conformational
variation of PS-b-PMMA, PS and PMMA adsorbed on mica and their response to
saturated water or chloroform atmosphere. Using specimen with only partial polymer
coverage, new unanticipated effects were observed. Water vapor, a non-solvent for
all three polymers, was found to cause high surface mobility. In contrast, chloroform
vapor (a solvent for all three polymers) proved to be less efficient. Furthermore, the
influence of an additionally applied electric field was investigated. A DC field oriented
parallel to the sample surface induces the formation of polymer islands which assemble
into wormlike chains. Moreover, PS-b-PMMA forms octopus-like micelles (OLMs) on
mica. Under the external stimuli mentioned above, the wormlike formations of OLMs
are able to align in the direction of the external electric field. In absence of an electric
field, the OLMs disaggregate and exhibit phase separated structures under chloroform
vapor.
PACS numbers: 82.35.Jk, 82.35.Gh, 83.80.Uv, 68.47.Pe, 68.08.-p, 68.08.Bc, 68.35.bm
Submitted to: J. Phys. D: Appl. Phys.
Diblock copolymers with octopus-like micelle formation under external stimuli 2
1. Introduction
Block copolymers (BCPs) consist of two or more covalently bonded incompatible
blocks [1]. Due to the different chemical nature and conformational flexibility of
each block, BCPs can undergo distinct phase transitions and therefore spontaneously
form nanostructures via the molecular self-assembly process [2]. The morphology
of bulk BCPs is determined by the Flory Huggins segmental interaction parameter,
the total degree of polymerization, the volume fraction of the blocks and boundary
conditions [3, 4, 5]. Additionally, when a thin BCP film is confined to the surface of a
solid substrate and is exposed to gas environment, its nanoscale morphology strongly
depends on interfacial interactions (polymer-substrate and polymer-atmosphere) as well
as commensurability effects between the film thickness and the natural spacial period
of BCPs [5, 6, 7].
Studying ultra thin polymer films is of great interest, both for applications and for the
gain of scientific knowledge. When the characteristic length scales of a film approach
molecular dimensions, the long-range interactions are cut off at a finite thickness [8]. If
enough mobility can be provided to the molecules, lowering the thickness of a polymer
film destabilizes its surface, which in turn greatly affects the film stability.
To provide mobility or alter the conformation and morphology of BCPs, external stimuli
like thermal annealing [9], solvent vapor annealing (SVA) [10, 11], chemically patterned
substrates [12], electric fields (EFs) [13, 14, 15] or solvent evaporation [16] can be used.
Solvent annealing is one of the most widely applied technique. During SVA, polymeric
systems take up solvent molecules and thus affect the film morphology by changing the
polymer-polymer and polymer-surface interactions. In general, small solvent molecules
increase the mobility of polymers due to plasticizing effects and may also function
as a lubricant between the molecules and the substrate [17, 18]. Additionally, the
final structure of BCPs can be varied by choosing different solvents, dependent on
their particular selectivity [19, 20, 21]. Therefore, SVA can also be used to cause
destabilization and dewetting of polymeric systems [22]. In this case, dewetting occurs
due to short-range polar interaction forces between the polymer, the surface and the
solvent.
Furthermore, for BCPs, the interaction of each block with solvent molecules offers
the possibility to manipulate the dewetting process by using different solvents. In
addition to the dewetting process of polymers, which may occur for any type of
polymer with sufficient mobility, the morphology of thin film BCPs can be affected
by commensurability effects. Typically, a thin film with a thickness below 10 nm is
incommensurate with the natural period of the polymer film [23].
Applying an external electric field is another common method to influence the
conformation and dynamics of a polymer chain. The distinctive dielectric properties
of the two BCP blocks cause different torques for each component in the presence of
EFs, competing with interfacial energies due to BCP-substrate and BCP-atmosphere
interactions [24]. Furthermore, fluctuations at the interface of microdomains will be
Diblock copolymers with octopus-like micelle formation under external stimuli 3
amplified [25]. Hence, EFs, as well as SVA, can destabilize and dewet a polymeric
system [26, 27].
In recent years, the effect of external stimuli on thin diblock copolymer (DBCP) films
has been extensively investigated. However, the behavior of single chains or isolated
islands of DBCPs exposed to electric fields and/or long term solvent annealing was
not studied so far. SVA was applied to several different types of single polymer chains
[28, 29, 30, 31, 17], where it was found that a repetitive exposure of P2VP to water and
ethanol could cause a change in conformation from an elongated to a collapsed polymer
form [31]. Kumaki et al. transfered single polymer chains of PS-b-PMMA from a water
surface onto mica substrates and analyzed their response in humid atmosphere [32].
In our work, we study the conformation and configuration of DBCPs with micelle-
like structure under the influence of SVA and EFs. When a substrate is coated by a
DBCP solution of appropriate low concentration, an octopus-like micelle (OLM) may
form instead of an uniform thin polymer film. For this structure, each polymer chain
is in contact with a few other chains and can be distinguished from other molecules
by imaging techniques. Hence, the effect of external stimuli on DBCPs can be studied
on a microscopic level. The structure has two major differences compared to ultra-
thin films; first, islands are clearly separated from each other, cutting of the long-range
forces parallel to the substrate. Second, both DBCP blocks are in direct contact with
the substrate and upper surface.
2. Experimental Methods
2.1. Sample Preparation
Polystyrene (PS, Mw=101.000), Poly(methyl methacrylate) (PMMA, Mw=120.000) and
Polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA, Mn=104.000, block ratio
1:1) were purchased from Sigma-Aldrich. We diluted the polymer samples in chloro-
form (SupraSolv grade, Merck), purchased from VWR international. Solutions with
concentrations from 0.002 to 2 g/l were spin-cast (Laurell Technologies Corporation,
WS-400B-6TFM/Lite) on freshly cleaved muscovite mica (Plano GmbH) with 3000 rpm
for 80 seconds.
Right after the preparation, we placed the samples either in a custom build high voltage
vapor chamber (Figure 1) or put them directly into a desiccator to dry them in vacuum
for at least 1 day. The samples prepared for the chamber were not dried in the beginning
to allow a higher surface mobility during the experiment.
The solvent and/or a horizontal electrical DC field (30 kV/cm) oriented parallel to the
surface was applied at room temperature. The exposure times which lead to a specific
conformation of PS, PMMA or PS-b-PMMA strongly depend on the quality of the used
mica sheet itself. Since muscovite-mica is a natural product, we left our samples for a
’sufficient time’ in the vapor chamber (in this work always for one week) to be sure that
no further changes are expected from longer times. However, if the surface quality is
Diblock copolymers with octopus-like micelle formation under external stimuli 4
poor (for instance mica sheets with higher roughness), all movements are suppressed,
resulting in a weak reaction.
2.2. Setup
Our high voltage chamber (Figure 1), completely built from PTFE, consists of carefully
isolated electrodes with a removable sample holder in the middle and teflon tubes to
apply vapors to the system. Different vapor molecules can pass into the chamber by
slowly purging nitrogen gas (N5, IndustrieGase AG, Germany) through a gas washing
bottle filled with the desired solvent.
Figure 1. Schematic top view of the high voltage chamber. Setup to apply
vapors and/or a parallel electric DC field.
2.3. AFM
We performed our measurements with a MultiMode SPM (Bruker MMAFM-2, 1997) in
tapping mode, using standard silicon cantilevers (Olympus OMCL-AC240TS, resonance
frequency 70 kHz, spring constant 2 N/m, tip radius 6-9 nm). Pictures were taken with
512 x 512 pixel at 1 Hz scanning frequency. Image analysis and editing was done with
NanoScope(TM) and Gwyddion [33].
3. Results and Discussion
3.1. Conformational behavior of PS-b-PMMA on mica
The AB-diblock-copolymer PS-b-PMMA contains one polar (PMMA) and one non-polar
(PS) block and is therefore able to form OLMs on mica (Figure 2). While depositing
Diblock copolymers with octopus-like micelle formation under external stimuli 5
a PS-b-PMMA solution on surface, the PMMA blocks will be randomly trapped and
adsorbed in a predominant elongated conformation due to their strong affinity to mica.
On the contrary, the PS chains remain in the solvent till all chloroform is evaporated.
Therefore, the PS chains are forced to collapse into flat globular islands at the end of
the evaporation process. At a polymer concentration high enough that the distance be-
tween two BCP chains is comparable to one polymer length, the PS blocks of different
polymer chains assemble into bigger globules. The size of resulting OLMs is concen-
tration dependent and reaches from single polymers (Figure 2a) up to big agglomerates
covering large areas (Figure 2c-d). The height of single PS cores ranges from 1-3 nm,
the strongly adsorbed star-like PMMA shell around is between 0.3 nm and 0.8 nm thick.
Hence, single PMMA blocks can be easily identified.
As long as the polymer concentration is low (0.02-0.2 mg/ml), islands with a diameter
between 0.5 nm and 2 nm are well distributed and cover approximately 2-25 % of the
sample surface (Figure 2a,b). For higher concentrations, the diameter of the PS cores
increases up to 30 nm (Figure 2b) until they loose their round appearance (Figure 2c)
and start to accumulate into a dense film (Figure 2d).
For this work, a polymer concentration that provides well separated, not too small
OLMs is most suited to analyze the molecular response to external stimuli. Hence,
we used polymer concentrations of approximately 0.02-0.2 mg/ml for all measurements
presented here. Due to strong interactions of PS-b-PMMA with preparation tools like
vessels or pipes, the concentration is slightly changing for different samples.
The formation of OLMs was also theoretically studied a few years ago [34]. Williams
describes the influence of good and bad solvent conditions to irreversibly grafted poly-
mer chains. A collapse of these chains and the formation of OLMs can be observed by
varying the grafting density under bad solvent conditions, which resembles our evapo-
ration process.
To confirm that the surface pattern formation of PS-b-PMMA depends only on the in-
teraction energy between all molecular components of the system and not on the surface
structure of mica, the experiment was repeated on silicon. We found that the overall
structural formation of PS-b-PMMA is the same. Furthermore, dip-coated samples are
indistinguishable from spin-coated samples (see Supporting Information). Hence, the
conformation and position of the micelles is just driven by the competing interaction
energies of the present materials. Using dynamic light scattering (DLS), we could also
show that the micelles are not present in solution. Accordingly, the patterns are formed
during the coating process. In addition to our experimental work, we performed sim-
ulations which likewise support our hypothesis on the origin of OLMs (manuscript in
preparation). Our results agree therefore quite well with existing studies about the for-
mation of OLMs as a random adsorption process of free PMMA blocks from solution and
a subsequent collapse of the PS chains as a result of the evaporating solvent [34, 35, 36].
Diblock copolymers with octopus-like micelle formation under external stimuli 6
Figure 2. PS-b-PMMA spin-cast on mica. Polymer concentration 0.002 (a), 0.02
(b), 0.2 (c) and 2 (d) mg/ml. OLMs with appropriate density are formed between 0.02
and 0.2 mg/ml.
3.2. Influence of water, ethanol and chloroform vapor
A very useful and common way to move polymers on surfaces is to apply a suitable vapor
to the system. In our study, we tested the response of PS, PMMA and PS-b-PMMA to
water vapor, a non-solvent, and chloroform vapor, a solvent for all three polymers. The
experiments were also done in combination with an applied electric field, described in
section 3.3.
Figure 3. PS 0.02 mg/ml on mica. Initial conformation (a), under water (b) and
under chloroform atmosphere (c).
Figure 4. PMMA 0.02 mg/ml on mica. Initial conformation (a), under water (b)
and under chloroform atmosphere (c).
Diblock copolymers with octopus-like micelle formation under external stimuli 7
Considering the two blocks of PS-b-PMMA separately, one can observe that PS ho-
mopolymers form homogeneously distributed globules with a concentration dependent
size on mica (Figure 3a). The height of spin-cast PS globules for a polymer concentration
of 0.02 mg/ml varies between 6-8 nm. Contrary to the formation process of an OLM, no
strongly adsorbing PMMA block is present. Therefore, the PS chains are slightly more
mobile during the evaporation process and form bigger and rounder globular islands.
The development of the molecular configuration resembles a dewetting process, driven
by the repulsive interaction between PS and the polar surface of mica.
In the presence of water vapor, we observed a slight movement and deformation of the
PS globules (Figure 3b). This reaction is a consequence of the strong attractive interfa-
cial energies between water and mica. For this reason, water tends to interact strongly
with the surface and is therefore applying pressure to the PS islands. As PS is a non-
polar polymer, the separated globular islands can not be moved over long distances. The
minimum and maximum height of the globules, ranging from 5-8 nm, is not significantly
changing compared to the initial state (Figure 3a).
As chloroform is a good solvent for PS, it likewise elongates on the surface when exposed
to chloroform vapor. The sample areas are mainly covered with extended chains, but
agglomerates with peak heights up to 100 nm can also be found (Figure 3c). However,
most of the structures are between 2 nm and 8 nm in height. Since applying chloroform
vapor to our system results in a very thin solvent film parallel to the mica surface, the
PS chains favor a flat, elongated conformation. Due to the very short timescale of the
subsequent evaporation process and the molecular configuration parallel to the surface,
the PS chains are not able to recollapse into a globular conformation after drying the
sample. Compared to water vapor, the conformational change and movement of PS is
much stronger under chloroform vapor.
Spin-cast PMMA homopolymers show an adsorbed extended conformation on mica,
covering as much surface area as possible (Figure 4a).
Contrary to the case of PS, we observed a quite strong movement of PMMA chains un-
der the influence of water vapor. For long exposure times (7 days), a distinct translation
of the chains accumulating into big, flat polymer domains (height less than 1 nm) or
globular structures (height 2-3 nm) could be found (Figure 4b). By carefully scanning
many areas on the samples, we observed elongated as well as collapsed conformations,
mainly concentrated in one region. Additionally, wide fields of the samples are clean.
Since PMMA contains hydrophilic ester groups, it can weakly interact with water, al-
though PMMA is indissoluble in water. Furthermore, PMMA chains are able to ’swim’
on water surfaces [32, 37]. As already stated above, water has a very strong affinity to
mica and is therefore able to displace molecules with lower interaction energies from the
surface. PMMA can therefore be desorbed and moved by water molecules ’crawling’
below the chains. The added mobility of such a system is very high, which explains
the observed strong horizontal translation of the polymers. As PMMA still has the
tendency to interact with mica, the polymer chains are more or less dragged into wide,
flat areas and do not accumulate so frequently into higher structures.
Diblock copolymers with octopus-like micelle formation under external stimuli 8
Under chloroform atmosphere, we observed an agglomeration process of PMMA chains
with a subsequent formation of partitioned areas on the surface (Figure 4c). The height
of these pancake-like PMMA structures is mostly below 1 nm, as expected for single
chains deposited side by side. However, at the center of these pancake-like structures, we
often found big PMMA agglomerates up to 60 nm in height. In contrast to the results
under water vapor, many parts of the sample are still covered with elongated PMMA
chains. We could not find any totally polymer free area which means that the overall
translation distance is smaller under the influence of chloroform vapor. Additionally,
many regions with weak or no reaction to the solvent stimulus could be observed. The
main reason for this differing behavior is the low attractive interaction of chloroform
with mica. Hence, PMMA is able to interact freely with the surface as well as with
the solvent molecules. Because PMMA does not really favor any of them (chloroform is
not a good solvent for PMMA), the resulting mobility is smaller compared to a system
exposed to water vapor. However, because the self-interaction of PMMA chains sur-
rounded by chloroform molecules may dominate, thicker structures can also be formed.
The same behavior was found for all concentrations tested (0.001-2.5 mg/ml), ranging
from single, well separated molecules up to thin continuous films.
The reaction of PS-b-PMMA to water vapor is shown in Figure 5. After long expo-
sure times (7 days), we found a collapse of PMMA strands forming a corona around PS
islands. In addition, the OLMs start to displace slowly and agglomerate into long worm-
like chains. The mean height of the OLMs is the same as for the initial state, 1-3 nm.
Compared to free PMMA chains under water vapor, we did not observe an extended
state for the PMMA block when bound to PS. As described above, water molecules try
to squeeze in between the PMMA chains and the substrate. Since one OLM can not
be displaced so easily due to its relatively inert PS core, the PMMA chains are forced
to collapse. Nevertheless, the presence of the polar polymer seems to provide enough
mobility to enable larger displacements of OLMs compared to pure PS which lead to
partial aggregation. Another interesting effect can be seen in Figure 5b. The formation
of a hole in a dense layer of OLMs shows that the accumulation process needs some kind
of nucleation core which results from local density fluctuations or contamination. Hence,
the development of the found structures starts at one specific point and proceeds from
the inner area to the outer side. Therefore, starting from a nucleus, small aggregations
can move as well as single OLMs and build up bigger clusters.
Under chloroform atmosphere, the initially formed surface micelles disaggregate due to
the elongation of the PS part (Figure 6). As already observed for PMMA, the poly-
mers agglomerate into large non-continuous pancake-like islands. For PS-b-PMMA, the
height of the accumulated polymers mostly ranges from 2-4 nm, but also structures up
to 140 nm high can be found. The main hypothesis is the same as already described for
the single components of PS-b-PMMA. The additional mobility of the block polymer is
high compared to PMMA homopolymers, but lower as for free PS. Additionally, due to
the repulsive interaction between the two components of the block-polymer and their
different affinity to the solvent as well as to the surface, phase separation (spinodal
Diblock copolymers with octopus-like micelle formation under external stimuli 9
decomposition) occurs. Therefore, structures with PMMA chains in the inner region of
one polymer domain surrounded by dense elongated PS chains are formed. Furthermore,
some single chains are not yet incorporated and driven towards an already agglomerated
area.
Figure 5. PS-b-PMMA in water vapor. Polymer concentration 0.02 mg/ml,
exposure to water vapor for 7 days. (a)-(c) show different sample regions.
Figure 6. PS-b-PMMA in chloroform vapor. Polymer concentration 0.02 mg/ml,
exposure to chloroform vapor for 7 days. (a)-(c) show different sample regions.
3.3. Influence of an external electric field
To effectively displace polar polymer chains by DC fields oriented parallel to the sample
surface, one has to provide mobility to the polymer chains. If an external EF is applied
to a dry sample, the adsorption force dominates and therefore no effect can be observed.
As described above, single PMMA chains react under saturated water atmosphere with
strong translation and agglomeration into flat polymer areas (height below 1 nm). In
combination with EFs, PMMA chains form ’droplets’ of approximately 2-6 nm height,
which attach to each other and produce randomly oriented wormlike structures (Figure
7a,b). Due to the polar nature of the PMMA side chains, such polymer droplets with
well defined, circular boundaries can be created. The resulting structures act more as
particles than single chains. After one polymer droplet is formed, it exhibits a macro-
scopic dipole which leads to the observed development of wormlike chains in the same
Diblock copolymers with octopus-like micelle formation under external stimuli 10
way as it is well known for the behavior of polar particles.
Figure 7. PMMA and PS in 30 kV with water. PMMA (a,b) and PS (c,d)
concentration 0.02 mg/ml, exposure to water vapor and a parallel DC field of 30kV
for 7 days.
Compared to the initial state, PS globules show an increased undulation of the
boundary and a strong tendency to fuse into bigger globules (height between 5-25 nm,
Figure 7c,d). Additionally, we observed a development of short wormlike chains due to
small induced dipoles. Similar to the behavior of PMMA, the described structures do
not orient in the direction of the external EF.
PS-b-PMMA OLMs also produce wormlike chains in EFs under water vapor (Figure
8). As described above, the PMMA corona collapses in humid atmosphere, and the
height of OLMs does not change compared to the initial state. Since the parallel DC
field affects the polar parts in the collapsed PMMA corona and induces a small dipole
in PS cores, the anticipated mobility of OLMs is much stronger under EFs due to
interfacial fluctuations, resulting in a translation of all OLMs attaching to wormlike
structures (Figure 8a and b, 9a and b). Although they contain a relatively weak mobile
PS core, the OLMs can move over very long distances. Furthermore, we could observe
a clear alignment in the direction of the EF (Figure 8c, 9c) for some samples. The
final structure attained after one week strongly depends on the quality of the surface
(e.g. surface roughness or contamination). If the exposure time to external stimuli is
longer than 7 days or the surface has a lower roughness, the OLMS can also fuse at
the contact points (Figure 9). In contrast, if a sufficient polymer density fluctuation or
surface contamination is missing, the essential nucleation centers may be more difficult
to form. The adjacent formation of wormlike structures can therefore be appreciable
slowed down (even after 5 days, no significant reaction can be observed).
Diblock copolymers with octopus-like micelle formation under external stimuli 11
Figure 8. PS-b-PMMA in 30 kV with water. Polymer concentration 0.02 mg/ml,
exposure to water vapor and a parallel DC field for 7 days. The inner image in (c)
shows the PSD of (c).
Figure 9. PS-b-PMMA under 30 kV in water vapor. Polymer concentration
0.02 mg/ml, exposure to water vapor and a parallel DC field for 8 days.
The power spectral density of Figure 8c (shown in the upper right corner of the
picture) indicates the observed directionality due to the influence of EFs. Based on the
average radial distribution of the autocorrelation function, we determined a character-
istic length scale d of 75 nm (see red line in Figure 8c). This length scale corresponds
to the average size of the polymer free areas between each aligned region, formed by
the attached chains shown in Figure 8c. Although we found numerous places where an
alignment can be clearly observed, many scan areas (maximum 12 µm2) show just a
wormlike formation.
Diblock copolymers with octopus-like micelle formation under external stimuli 12
Figure 10. PS-b-PMMA under 30 kV in chloroform vapor. Polymer
concentration 0.02 mg/ml, exposure to chloroform vapor and a parallel DC field for 7
days.
Under chloroform vapor in combination with an external EF, PS-b-PMMA form
pancake-like structures with a mean height between 2 nm and 6 nm (Figure 10). In
contrast to the effects found in chloroform atmosphere without EFs, no phase separa-
tion could be observed. A possible explanation for this characteristic response is the
dipolar nature of the used polymers, which enables high conformational fluctuations
under the influence of EFs. Hence, no equilibrium state can be achieved, essential to
initiate spinodal decomposition. Alignment of the pancake-like polymer structures has
not been observed in this experiment due to the lower mobility provided by chloroform
compared to water vapor, but is most likely after longer exposure times or under higher
field strength.
4. Conclusion
In this work, we presented the response of PS-b-PMMA OLMs as well as their single
components on mica to external stimuli (water vapor, chloroform vapor and parallel
DC field). In humid atmosphere, PMMA and PS-b-PMMA gain high mobility due to
the energetic competition between water molecules and PMMA chains regarding their
surface occupancy. Since PS is a non-polar polymer and the initially formed globules are
relatively big, the observed effects are smaller for this polymer. Subjected to an external
electric DC field of 30 kV/cm, all three polymers can form (partially aligned) wormlike
chains in their respective molecular conformation (see above). Under chloroform vapor,
the mobility of PS-b-PMMA and PMMA is lower compared to water vapor. The
resulting pancake-like polymer structures exhibit phase separated domains if no electric
field is applied. PS on the other hand clearly favors an interaction with solvent molecules
over one with the surface and therefore undergoes quite strong changes in conformation
and position. The predominant globules elongate completely in chloroform atmosphere
and are trapped in this conformation after drying the sample.
The methods presented to stimulate polymeric systems and the observed effects are
promising tools to manipulate polymeric materials in ultra thin films, applicable to
Diblock copolymers with octopus-like micelle formation under external stimuli 13
nanotechnology, condensed matter and life-science. With the proper choice of polymers,
vapors and surface characteristics, the desired systems can be altered on single molecule
level.
Acknowledgments
The authors thank Martin Muller (Institute of Experimental Physics, Ulm Univeristy)
for technical support, Jens-Uwe Sommer (Leibniz-Institute of Polymer Research Dresden
and Institute of Theoretical Physics, TU-Dresden) and Christoph Jentzsch (Leibniz-
Institute of Polymer Research Dresden) for helpful discussions.
Diblock copolymers with octopus-like micelle formation under external stimuli 14
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Supplementary data for
Conformation and structural changes of diblock
copolymers with octopus-like micelle formation in
the presence of external stimuli
K Dammertz, A M Saier, M Amirkhani and O Marti
Institute for Experimental Physics, Ulm University, Albert-Einstein-Allee 11, 89081
Ulm, Germany
E-mail: [email protected]
PACS numbers: 82.35.Jk, 82.35.Gh, 83.80.Uv, 68.47.Pe, 68.08.-p, 68.08.Bc, 68.35.bm
Submitted to: J. Phys. D: Appl. Phys.