Capillary-induced contact guidance.

Capillary-Induced Contact Guidance
Steven Lenhert,*,†,‡,¶ Ane Sesma,§ Michael Hirtz,‡ Lifeng Chi,‡ Harald Fuchs,‡
Hans Peter Wiesmann,† Anne E. Osbourn,§ and Bruno M. Moerschbacher¶
Klinik und Poliklinik fu¨r Mund- und Kiefer-Gesichtschirurgie, UniVersita¨tsklinikum Mu¨nster,
Waldeyerstrasse 30, 48149 Mu¨nster, Germany, Physikalisches Institut, Westfa¨lische Wilhelms-UniVersita¨t,
Wilhelm Klemm Strasse 10, and Center for Nanotechnology (CeNTech), 48149 Mu¨nster, Germany, Institut
fu¨r Biochemie und Biotechnologie der Pflanzen, Westfa¨lische Wilhelms-UniVersita¨t, Hindenburgplatz 55,
48143 Mu¨nster, Germany, and John Innes Centre, Colney Lane, Norwich NR4 7UH, United Kingdom
ReceiVed April 11, 2007. In Final Form: July 9, 2007
Topographical features are known to impose capillary forces on liquid droplets, and this phenomenon is exploited
in applications such as printing, coatings, textiles and microfluidics. Surface topographies also influence the behavior
of biological cells (i.e., contact guidance), with implications ranging from medicine to agriculture. An accurate physical
description of how cells detect and respond to surface topographies is necessary in order to move beyond a purely
heuristic approach to optimizing the topographies of biomaterial interfaces. Here, we have used a combination of
Langmuir-Blodgett lithography and nanoimprinting to generate a range of synthetic microstructured surfaces with
grooves of subcellular dimensions in order to investigate the influence of capillary forces on the biological process
of contact guidance. The physical-chemical properties of these surfaces were assessed by measuring the anisotropic
spreading of sessile water droplets. Having established the physical properties of each surface, we then investigated
the influence of capillary forces on the processes of cellular contact guidance in biological organisms, using mammalian
osteoblasts and germinating fungal spores as tester organisms. Our results demonstrate that capillary effects are present
in topographical contact guidance and should therefore be considered in any physical model that seeks to predict how
cells will respond to a particular surface topography.
Introduction
Cell adhesion is a fundamental biological process that provides
a challenge for physical adhesion theory because of the complex
molecular machinery that is characteristic of living systems.
Unlike the ideal wetting of a pure liquid drop on a smooth surface,
cell adhesion involves factors such as membrane elasticity,
cytoskeletal tension, and the dynamic properties of adhesive
molecules on the cell surface.1-6 These differences make it
impractical to determine an interfacial energy for a living cell
based on contact angles, as is often done in the wetting of pure
liquid droplets. However, in the context of capillary theory, it
is possible to determine certain linear relations between
topography and the shape of liquid interfaces in a way that is
independent of the specific molecular interactions involved. For
instance, in the classic experiment of a liquid filling a capillary
tube, the height of the liquid in the tube is directly proportional
to the curvature of the capillary tube, regardless of the interfacial
energies involved.1 Such capillary effects can be extended to
explain the anisotropic shape of a liquid droplet on a grooved
surface.7,8
The micro- and nanoscopic texture of a surface is known to
influence the morphology and behavior of adherent biological
cells, an effect known as contact guidance.9 Advances in
microfabrication open up promising possibilities for being
able to understand and control these biological responses by
means of precisely defined topographies with feature sizes
that are smaller than an individual cell.10-12 Well-studied
examples include wound healing and implantology,13-15 tissue
engineering,14,16-21 antifouling surfaces,22 and plant-pathogen
interactions.23-32* To whom correspondence should be addressed. E-mail: lenhert@
int.fzk.de. Present address: Forschungszentrum Karlsruhe GmbH, Institut
fu¨r NanoTechnologie, 76344 Eggenstein-Leopoldshafen, Hermann-von-
Helmholtz-Platz 1, Germany.
† Universita¨tsklinikum Mu¨nster.
‡ Physikalisches Institut, Westfa¨lische Wilhelms-Universita¨t.
¶ Institut fu¨r Biochemie and Biotechnologie der Pflanzen, Westfa¨lische
Wilhelms-Universita¨t.
§ John Innes Centre.
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10216 Langmuir 2007, 23, 10216-10223
10.1021/la701043f CCC: $37.00 © 2007 American Chemical Society
Published on Web 08/31/2007

Although topographical contact guidance has been observed
in all types of cells tested to date,33 there are still few applications
that make use of lithographically patterned surfaces. This is due
to the cost of lithographic prototyping combined with the lack
of an accurate model for contact guidance that would allow the
design of surface patterns that are optimal for specific applications.
An important first step in this direction was taken by a recent
study that demonstrated an empirical correlation between the
attachment of biological cells (zoospores and endothelial cells)
and the surface wettability of topographically microstructured
surfaces.22 While that work correlated adhesion to topography,
here we take further steps by correlating anisotropic wetting to
cell orientation and growth on nanostructured surfaces. For this
purpose, we have used state-of-the-art lithography to test the
hypothesis that capillary effects provide a physical signal that
cells can use to detect surface features, as discussed in the
pioneering contact guidance works of Weiss.34,35
The interaction of mammalian cells with surfaces is known
to be mediated by focal adhesions consisting of transmembrane
integrin proteins, which transmit information across the mem-
brane.5,36 While passive adhesion forces and membrane defor-
mations are sufficient to generate initial cell alignment to adhesive
surfaces, active processes within the cytoskeleton such as actin
polymerization quickly become involved2 and are especially
relevant to cell polarization and cell motility.6,37 In several cases,
microscopic cell protrusions known as filopodia have been
observed to interact with micro- and nanoscopic surface
topographies.19,20,38,39 Model systems such as vesicles are valuable
tools for the study of the physical forces involved in cell-surface
interactions40 and have provided experimental support for the
idea that cell adhesion can be understood from the physical point
of view of wetting transitions.4 In the tensegrity model of cellular
mechanics, molecular tension built up within the cytoskeletal
network causes the cell to respond in a way that balances external
mechanical forces acting upon the cell.41 There is evidence that
rearrangement of the cytoskeleton distorts the shape of the nucleus,
which results in changes in gene expression.33,42,43 This type of
direct mechanotransduction is one way to explain how mechanical
forces are able to switch cells between different genetic
programs.18,44,45 Indirect mechanotransduction is another mech-
anism involving molecular signal cascades, for instance, by means
of G-proteins, kinases, and ion channels.46,47
Of particular interest for biomaterial surface engineering and
host recognition of pathogens are geometry-specific contact
guidance effects, where micro- or nanostructures on a surface
induce specific cell responses. For instance, protein clustering
in focal adhesions occurs on a length scale of 5-200 nm, and
cells cultured on interfaces that have been chemically nanopat-
terned with integrin-binding RGD peptide respond preferentially
to patterns below a critical length scale of about 60-75 nm.48
The same colloidal lithography method used in that work has
also been shown to be suitable for tuning the adhesion of agarose
bead-based model systems using specific biotin-streptavidin
interactions.49 In order to better understand the molecular biology
behind contact guidance (e.g., the role of ion channels,50 annexins,
51 integrins,5,36 septins and formins,52 etc.), it is necessary to
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Capillary-Induced Contact Guidance Langmuir, Vol. 23, No. 20, 2007 10217

distinguish between purely physical contact guidance effects
and those that appear to require specific molecular machinery
in order to function.
A requirement for direct comparison between the behavior of
macroscopic liquid droplets and microscopic cells is a topo-
graphical pattern with features that are significantly smaller than
a single cell. The pattern must also be continuous over length
scales that are large enough for sessile drop measurements.
Langmuir-Blodgett (LB) lithography is particularly suitable for
both anisotropic wettability measurements53 and cell alignment
assays17 because it allows the rapid and cheap fabrication of a
range of chemically identical substrates, each having surface
areas of several square centimeters with groove dimensions that
are significantly smaller than an individual cell.54 The depth of
the grooves can be controlled between 20 and 300 nm by the etch
time, while the lateral line widths can be tuned from 100 nm to
more than 2 ím.55
Osteoblasts line the surface of bone in vivo. They are
responsible for bone formation and are therefore the focus of
many clinical treatments of bone breaks and tissue engineering.
Although little is known about the relationship between osteoblast
alignment and function in vivo, there is evidence that their
alignment on bone surfaces as well as synthetic implants is
important for the generation of bone tissue. For instance,
osteoblasts have been observed to align in vitro under strong
magnetic fields, and the same fields were found to induce directed
bone growth in vivo.13 Osteoblasts cultured on regularly spaced
grooves of subcellular dimensions show a tendency to form focal
adhesions at opposite ends of aligned cells and to migrate more
quickly in the direction of alignment.17 Although deeper grooves
have been observed to yield stronger osteoblast alignment, a
systematic study of the dependence on groove depth, width, and
pitch is necessary for a more complete understanding of the
relevant physical parameters involved in contact guidance.
Detection of the physicochemical features of surfaces is also
important for infection of plants by fungal pathogens, which
differ from animal cells in having a cell wall. A well-documented
example of topographical contact guidance of a fungal pathogen
occurs when spores of the stem rust fungus Puccinia graminis
germinate on cereal leaves. In this case, the germ tubes grow
perpendicular to the veins of the leaf in order to optimize the
chances of encountering a stoma, through which the fungus is
able to invade the plant after forming infection structures
(appressoria).26,56 This developmental process can be simulated
on artificial surfaces with microscopically grooved topographies
that mimic the geometric dimensions of guard cells on the leaf
surface.25,57 However, quantitative studies of P. graminis
alignment as a function of groove dimensions or on smooth
chemically patterned surfaces are lacking. Knowledge of the
biological mechanisms required for surface recognition and
alignment will enable us to establish which surface cues are
involved and whether germ tube alignment is a feasible target
for plant protection strategies.
The rice blast fungus Magnaporthe grisea also senses the
surface of its host in order to form penetration structures:
elaborate, heavily melanized appressoria on leaf surfaces28 and
structures resembling simple appressoria (hyphopodia) on roots.27
The amenability of M. grisea to genetic transformation has
provided some insight into the molecular mechanisms by which
this organism is able to detect surface cues.28 For example, PTH11
is a transmembrane protein identified through an insertional
mutagenesis screen for nonpathogenic mutants. PTH11 mutants
are strongly reduced in appressorium formation, and the gene
product has been suggested to be involved in host surface
recognition.31 MPG1 encodes for a hydrophobin, a small
hydrophobic cell surface protein that is highly expressed during
the first steps of host plant infection. Mutants defective in this
hydrophobin have reduced virulence and are defective in
conidiation and appressorium formation.58 M. grisea differs from
P. graminis in that it is able to penetrate directly through the
plant epidermis, apparently without a requirement for extensive
surface navigation. Although appressoria formation in M. grisea
has been studied in considerable detail,24,29 to our knowledge,
the alignment behavior of M. grisea germ tubes on surfaces has
not yet been documented.
Although the mechanisms by which cells detect and transduce
topographical information are not yet well understood,33 the effect
that surface topography will have on the shape of a pure liquid
droplet is predictable from established physical descriptions.1 In
order to distinguish cell-specific effects from behavior that may
be induced by capillary forces, we have compared the spreading
of water droplets with the alignment of three different types of
biological cells. Osteoblasts are an example of an animal cell
that has been observed to align on grooves of subcellular lateral
dimensions. P. graminis and M. grisea germ tubes are examples
of fungal hyphae, both of which are known to detect surface
cues.
Materials and Methods
Surface Fabrication. A combination of LB lithography and
nanoimprinting was used to continuously pattern polystyrene surface
areas of more than 4 cm2 with regularly spaced grooves, as described.54
In order to fabricate striped patterns with different lateral dimen-
sions,55 the transfer speed was varied between 1 and 60 mm/min,
and the surface pressure was varied between 0 and 5 mN/m. The
groove depth was controlled by the etch time. The chemically striped
(octadecyltrichlorosilane (OTS)) patterns were prepared by excluding
the etching step. The grooved silicon templates were then used for
production of the polystyrene replicas by hot embossing as
described.54 The lateral size and thickness of the sample can be
controlled by the amount of polystyrene used and the time used for
embossing. In this case, samples were approximately 4 cm2 and 1
mm thick. Polystyrene surfaces were made hydrophilic for the
anisotropic wettability studies as well as the osteoblast and M. grisea
cell culture using a 50 W O2 plasma (Templa System 100-E plasma
system) at 1 mbar for 10 s. For the osteoblast culture, the surfaces
were sterilized by immersion in 70% ethanol for 5 min.
Topographical Measurements. SFM investigations were per-
formed with a commercial instrument (Nanoscope IIIa and Dimension
3000, Digital Instruments, Santa Barbara, CA) operating in tapping
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10218 Langmuir, Vol. 23, No. 20, 2007 Lenhert et al.

mode (silicon cantilevers, Nanosensors) with resonant frequencies
of 250-350 kHz and nominal spring constants of �42 N/m. Since
the grooves have a sidewall angle of 54.7°, the groove width and
ridge width was measured at 1/2 of the groove depth. From these
dimensions, the roughness factor can be calculated with the following
formula:
Anisotropic Wetting Measurements. Water drop anisotropy was
measured by placing 13 0.5 íL drops of hemalaun dye (Sigma-
Aldrich) solution in water from an Eppendorf pipet onto each substrate
and leaving the drops to spread in ambient conditions until dry.
Photographs were then taken of the resulting drop residue, and the
aspect ratio (anisotropy) was calculated for each drop by dividing
the length of the drop in the groove direction by the width of the
drop perpendicular to the grooves. Dynamic contact angles were
measured using a commercial instrument (G2 Kontaktwinkelmess-
system, Kru¨ss). Advancing contact angles were determined by fitting
a polynomial to the shape of the drop photographed from the side
as it increased and decreased in size between volumes of 30-100
íL, at intervals of 1 íL/image. In the case of the chemical stripes,
the water drop anisotropy was calculated from the dynamic contact
angles measured as the contact line moved parallel and perpendicular
to the stripes. For this purpose, formulas 2 and 3 were derived from
geometric principles in order to relate the contact angles to the aspect
ratio of the drops. If we assume circular cross sections of the drop,
then the length (L) to width (W) ratio of the drop can be expressed
in terms of the contact angles for pairs of angles greater than 90°
by
or, in the case where the contact angles are less than 90°, by
£l and £w represent the contact angles corresponding to the long
and short axis of the drop, respectively. All wetting measurements
were repeated three to five times.
Osteoblast Culture and Analysis. Osteoblasts were cultured for
24 h in high growth enhancement medium (ICN Biomedicals GmbH,
Eschwege, Germany) supplemented with 10% fetal calf serum, 250
mg/mL amphotericin B, 10 000 IU/mL penicillin, 10 000 mg/mL
streptomycin, and 200 mM L-glutamine (Biochrom KG seromed,
Berlin, Germany) using a cell density of 2000 cells/cm2. The cultures
were incubated at 37 °C in a humidified atmosphere of 95% air and
5% CO2. The cells were fixed with glutaraldehyde and stained with
toluidine blue in order to provide contrast for optical microscopy
and analysis of cell orientation, as described.17 Micrographs were
taken from at least eight different areas per sample for image analysis.
The osteoblast anisotropy was defined as the length of the cell (in
the direction of the grooves) divided by the width (perpendicular to
the grooves). At least 100 cells were counted per measurement, and
the experiment was performed in triplicate.
Culture and Analysis of Fungi. Uredospores of P. graminis f.
sp. tritici race 32 were prepared as described,59 and the artificial
surfaces were inoculated using a settling tower. M. grisea wild type
and mutant strains Guy11, 4091.5.8, mpg1, and pth11 were cultured
and maintained as described.58 Drops of water (300-400 íL)
containing 103 conidia/mL were placed on the surfaces. The fungal
spores were incubated for 8-12 (M. grisea) or 24 (P. graminis)
hours at 23 °C and 100% relative humidity. For fluorescence
microscopy, germ tubes were stained with calcofluor and either
imaged under liquid or after drying under a stream of compressed
nitrogen gas. No observable change in the orientation of the germ
tubes could be detected in cells that were viewed under a microscope
both before and after this drying process. Micrographs for image
analysis were taken of at least 100 cells per surface in the case of
P. graminis and at least 200 cells per surface in the case of M. grisea.
The experiments were repeated three and four times.
Image Analysis. Cell orientation of the osteoblasts and P. graminis
was quantified using ImageJ (version 1.61, by Wayne Rasband;
NIH, Bethesda, MD). An ellipse was fitted to the shape of each cell,
and the orientation of the major axis of the ellipse was assumed to
be the orientation of the cells. In order to speed up the image analysis
process for the experiments with M. grisea (wild types and mutants),
customized image analysis software was developed. Briefly, this
software recognizes each cell in an optical micrograph by means of
a threshold function, and fits a straight line through it based on a
linear regression over all points that form the shape. After that, the
angle of this straight line in respect to the groove orientation is
calculated. For all cell types, only the cells that were not in direct
contact with neighboring cells were counted. We define “alignment”
as the percentage of cells that are oriented within 30° of the groove
direction. A randomly oriented distribution as is expected in the
controls (surface #1) should show 33% alignment.
Statistics. Linear regressions and ANOVA tables were calculated
using Origin 6.1. p-Values represent the probability that the correlation
coefficient (r) is zero. In the cases where data points were excluded
from the linear regression, the p-values represent conditional
probabilities, with the condition being that either the roughness factor
or individual groove volume is below a critical value. The Student’s
t test was used to test for significant alignment on the chemical
patterns. All error bars and ( values represent the standard deviation.
Results
Surface Characterization. The width, depth, and pitch of the
grooved topographies were measured by scanning force mi-
croscopy (Figure 1 and Table 1). From these measurements,
roughness factors and individual groove volumes were calculated.
These two parameters were found to be most relevant to the cell
and water-drop experiments described herein. The roughness
factor as defined by Wenzel is a unitless number that gives the
real surface area when multiplied by the apparent surface area.60
In the case of the microscopic grooves used here, this roughness
factor is determined by the groove dimensions and is therefore
anisotropic.
The anisotropic wettability of the surfaces was measured using
a classical method in which sessile drops of water are placed on
the surface and allowed to spread (Figure 2a).1 We define the
“water drop anisotropy” as the drop length in the groove direction
divided by the length perpendicular to the grooves, which can
be measured from photographs of the droplets (Figure 2a). Linear
regression analysis of the water drop anisotropy as a function
of the geometric parameters shown in Table 1 results in the
following correlation coefficients (r) and p-values: depth (r )
0.64, p ) 0.025), groove width (r ) -0.75, p ) 7.3 � 10-3),
ridge width (r ) -0.71, p ) 0.017), pitch (r ) -0.77 p ) 5.3
� 10-3), roughness factor (r ) 0.93, p < 10-4), groove volume
(r ) -0.23, p ) 0.48). The best correlation is clearly observed
with the roughness factor. Plotting water drop anisotropy against
the roughness factor (Figure 2b) for roughness factor values
below 1.2 reveals a strictly linear correlation (r ) 0.99). Beyond
this roughness value, the trend begins to deviate slightly from
linearity but still provides a reasonable means of predicting the
anisotropic wettability from the groove dimensions (with p <
(59) Moerschbacher, B. M.; Noll, U.; Gorrichon, L.; Reisener, H. J. Specific-
inhibition of lignification breaks hypersensitive resistance of wheat to stem rust.
Plant Physiol. 1990, 93 (2), 465-470.
(60) Wenzel, R. N. Resistance of solid surfaces to wetting by water. Ind. Eng.
Chem. 1936, 28, 988-994.
[2 - 2 cos(54.7°)](pitch + depth)/[pitchâsin(54.7°)] (1)
L
W )
1 + cos(180 - £w)
1 + cos(180 - £l)
[sin(180 - £l)]
sin(180 - £w)
(2)
L
W )
1 + sin(90 - £w)
1 + sin(90 - £l)
[cos(90 - £l)]
cos(90 - £w)
(3)
Capillary-Induced Contact Guidance Langmuir, Vol. 23, No. 20, 2007 10219

10-4). Both hydrophilic (Figure 2b) and hydrophobic (Supporting
Information Figure S1) surfaces show the same trends.
Mammalian Osteoblasts. Like water drops, osteoblasts align
parallel to the groove direction to different extents on different
surfaces. Figure 3a shows an extreme example of an aligned
osteoblast on surface #12. A significant correlation was observed
between the osteoblast anisotropy and the water drop anisotropy
(r ) 0.77 p ) 3.3 � 10-3; Figure 4). It can be seen that three
data points (circled in Figure 4) were slightly below the trendline.
Although a p-value of less than 0.01 is observed when all data
points are included, exclusion of surfaces with roughness factors
greater than 1.22 (#10-12) from the linear regression results in
a 5-fold increase in the significance of the correlation (r ) 0.91,
p ) 6.8 � 10-4). This p-value represents the roughness-
conditional probability of a correlation below a critical roughness
factor of 1.22, indicating that the three roughest surfaces induce
slightly less alignment than predicted by the water drop anisotropy.
P. graminis Germ Tubes. In contrast to osteoblast cells, which
align parallel to the groove direction, the overall growth direction
of germ tubes of P. graminis is perpendicular to the grooves
(Figure 3b). Although a variety of interesting germ tube
morphologies were observed, including branching, zig-zagging,
and straight growth (all observable in the same germ tube in
Figure 3b and also seen in germ tubes growing on flat control
surfaces), we focused our statistical analysis only on the
orientation of the entire germ tube as described in the methods
for the sake of automated image analysis. No significant
correlation was observed when P. graminis germ tube alignment
was compared with water drop anisotropy when considering all
data points (r ) 0.16, p ) 0.62, solid line in Figure 5a). However,
four topographies (#2, 4, 6, 7) showed a stronger alignment than
expected from the water drop anisotropy alone. These four
topographies were the ones with the largest groove volumes
(Table 1). When the data were reanalyzed for groove volumes
of less than 60 fL/ím (Figure 5; Table 1) there was a significant
correlation between germ tube alignment and water drop
anisotropy (p < 0.05).
As a complementary test of the idea that capillary effects can
affect the cell alignment of P. graminis (even in the absence of
topography), we fabricated chemically striped surfaces consisting
of parallel lines of hydrophobic OTS separated by gaps of
hydrophilic silicon oxide. Since these chemical patterns exert
anisotropic capillary forces on pure liquid droplets,53 yet have
a “groove volume” of zero, they can be used to test the hypothesis
that grooves with volumes of less than 60 fL/ím induce germ
tube alignment by capillary forces alone. In this case, the water
drop anisotropy was calculated from advancing contact angle
measurements using pure water so that the data could be shown
as the triangles in Figure 5a. Only two data points are included
here because only a slight water drop anisotropy (of �1.05) can
be measured on these surfaces. Nevertheless, we found a small
but significant difference in germ tube alignment between the
OTS-covered control and the chemically striped surfaces
(illustrated in Figure 5; “otsc” ) control; “ots” ) chemically
Figure 1. Topographical scanning force micrographs of the different grooved polystyrene topographies. The topographies are numbered
from 2 to 12, and correspond to the sample numbers in Table 1. Scale bar ) 1 ím.
Table 1. Topographical Dimensions of the Grooved Surfaces, as Determined by Scanning Force Microscopy (Representative
Measurements Are Shown in Figure 1)a
surface #
roughness
factor
groove depth
(nm)
groove width
(nm)
ridge width
(nm)
pitch
(nm)
groove volume
(fl/ím)
1 1 0 0
2 1.04 ( 0.11 105 ( 8 1200 ( 150 1650 ( 170 2850 ( 220 126.0 (18
3 1.08 ( 0.16 119 ( 15 316 ( 76 1180 ( 140 1500 ( 160 37.6 ( 10
4 1.12 ( 0.34 194 ( 13 410 ( 73 1280 ( 380 1690 ( 390 79.5 ( 15
5 1.14 ( 0.25 116 ( 27 424 ( 130 424 ( 62 848 ( 140 49.2 ( 19
6 1.18 ( 0.36 241 ( 40 289 ( 69 1140 ( 320 1420 ( 330 69.6 ( 20
7 1.20 ( 0.15 258 ( 18 235 ( 18 1080 ( 120 1310 ( 120 60.6 ( 6.3
8 1.20 ( 0.12 138 ( 12 152 ( 18 548 ( 48 700 ( 51 21.0 ( 3.1
9 1.21 ( 0.21 132 ( 16 121 ( 22 520 ( 84 641 ( 87 16.0 ( 3.5
10 1.22 ( 0.25 118 ( 17 156 ( 37 402 ( 79 558 ( 87 18.4 ( 5.1
11 1.26 ( 0.13 141 ( 7 150 ( 19 417 ( 40 567 ( 44 21.2 ( 2.9
12 1.37 ( 0.15 155 ( 23 122 ( 14 316 ( 34 438 ( 37 18.9 ( 3.6
a The values are sorted according to the roughness factor, which was calculated from the measured groove dimensions. The ( values represent
the standard deviation between measurements from eight random areas of the substrate.
10220 Langmuir, Vol. 23, No. 20, 2007 Lenhert et al.