Swelling behavior of thin, surface-attached polymer networks

Article abstract of DOI:10.1021/ma034737v

The swelling behavior of thin, surface-attached cross-linked dimethylacrylamide (DMAAm) films in contact with water has been characterized with multiple-angle nulling ellipsometry and compared to the swelling of nonattached, bulk DMAAm networks. The polymer networks are fabricated by cross-linking thin films of statistical copolymers composed of DMAAm and a photoreactive benzophenone derivative monomer. Covalent attachment of the film to the surface is achieved by means of a benzophenone-based silane monolayer. UV illumination simultaneously cross-links and chemically links the layer and chemically links the layer to the surface, forming stable networks that do not delaminate upon swelling. It is observed that the surface-attached networks swell less than the nonattached, bulk networks at the same cross-link density; however, the swelling of surface-attached networks is larger than that suggested by simple geometric considerations for swelling in one dimension. The results are in qualitative agreement with Flory-Rehner theory extended to one-dimensional swelling.

Full text of DOI:10.1021/ma034737v

882
Macromolecules 2004, 37, 882-887
Swelling Behavior of Thin, Surface-Attached Polymer Networks
Rya n Toom ey, Da n iel F r eid a n k , a n d J u1 r gen Ru1 h e*
Institute for Microsystem Technology, University of Freiburg, Georges-Ko¨hler-Allee 103,
D-79110 Freiburg, Germany
Received J une 2, 2003; Revised Manuscript Received October 3, 2003
ABSTRACT: The swelling behavior of thin, surface-attached cross-linked dimethylacrylamide (DMAAm)
films in contact with water has been characterized with multiple-angle nulling ellipsometry and compared
to the swelling of nonattached, bulk DMAAm networks. The polymer networks are fabricated by cross-
linking thin films of statistical copolymers composed of DMAAm and a photoreactive benzophenone
derivative monomer. Covalent attachment of the film to the surface is achieved by means of a
benzophenone-based silane monolayer. UV illumination simultaneously cross-links and chemically links
the layer and chemically links the layer to the surface, forming stable networks that do not delaminate
upon swelling. It is observed that the surface-attached networks swell less than the nonattached, bulk
networks at the same cross-link density; however, the swelling of surface-attached networks is larger
than that suggested by simple geometric considerations for swelling in one dimension. The results are in
qualitative agreement with Flory-Rehner theory extended to one-dimensional swelling.
In tr od u ction
-3/5 power. However, as surface-attachment restricts
the swelling to one dimension, a smaller dependence is
expected on the cross-link density.
Thin layers of surface-attached polymer networks
offer a powerful route toward soft surfaces with well-
defined mechanical, physical and biochemical proper-
ties.1-4 First, polymer networks provide a soft 3-dimen-
sional scaffold capable of hosting a wide-array of func-
tionalities, ranging from proteins to inorganic nanopar-
ticles. Second, polymer networks can undergo substantial
swelling and contraction in response to specific stimuli,5-8
making them excellent candidates for “smart” surfaces
with sensing and actuating characteristics. While mac-
roscopic gels have been hindered by slow response times,
the collective diffusion of the network is the rate-
limiting step; therefore, reducing their dimensions to
the microscale should significantly enhance perfor-
mance, making them especially attractive in microsys-
tems technology.9,10
In this paper, we use a simple photochemical tech-
nique for producing surface-attached polymer networks.
The fabrication approach is based on the photocross-
linking of films of statistical copolymers comprising
methacryloyloxybenzophenone (MaBP) and dimethyl-
acrylamide (DMAAm). Irradiation of the DMAAm-
MABP films with UV light (λ ) 350 nm) triggers the
n,π* transition in the MaBP segments, leading to a
biradical triplet state that is capable of abstracting a
hydrogen from almost any kind of neighboring aliphatic
C-H group, forming a stable C-C bond.17 The approach
can be used with essentially any technique of film
formation which yields thin coatings of controllable
thickness (e.g., spin or dip casting).
The swelling behavior of the surface-attached
DMAAm-MaBP layers was characterized with multiple-
angle null ellipsometry in an ATR configuration, an
analytical technique that yields information about the
thickness and refractive index profile of the swollen
layer.18 Ellipsometric measurements reveal that the
swelling degree of the surface-attached networks is
related to the MaBP content in the layer, which can be
varied by one of two methods. In the first, the MaBP
fraction in the copolymer can be controlled during the
synthesis, i.e., by adjusting the ratio of the two monomer
concentrations in the monomer feed during the polym-
erization process. In the second method, the cross-link
density can be controlled by blending DMAAm-MaBP
copolymer with DMAAm homopolymer.
A critical issue for understanding and predicting the
properties of surface-attached polymer networks is the
impact of confinement on their swelling behavior.11
Chemical linkage of the network to a surface prevents
swelling parallel to the substrate, effectively confining
the volume change to one dimension, or normal to the
surface. Such an effect will impact important properties
such as the structure, mechanical properties, dynamics,
and permeability of the network. It has already been
observed that confinement of N-isopropylacrylamide
(NIPAM) networks raises the volume phase transition
temperature in comparison to that with unconfined
networks.7,12 Furthermore, it was recently reported that
surface-attached NIPAM gels have a total volume
change around 15-fold while the corresponding bulk gels
have experienced a volume change as large as 100-
fold.13,14 For isotropic, neutral networks, the widely
applied Flory-Rehner theory has met with some success
in describing the relationship between the cross-link
density and the equilibrium swelling in a good sol-
vent.15,16 For sufficiently low cross-link densities, the
Flory-Rehner theory predicts that the equilibrium
swelling of a gel scales as the cross-link density to the
In addition to the generation of the surface-attached
gels, the corresponding nonattached bulk gels were
prepared under identical conditions and compared to the
swelling of the surface-attached gels to understand the
effect of confinement on their swelling behavior.
Exp er im en ta l Section
DMAAm )Ma BP Syn th esis. A series of DMAAm-MaBP
copolymers was synthesized by statistical free-radical copo-
lymerization of N,N-dimethylacrylamide monomer (Aldrich)
and 4-methacryloyloxybenzophenone (MaBP) monomer. The
* Corresponding author. E-mail: ruehe@imtek.uni-freiburg.de.
10.1021/ma034737v CCC: $27.50 © 2004 American Chemical Society
Published on Web 01/13/2004

Macromolecules, Vol. 37, No. 3, 2004
Thin, Surface-Attached Polymer Networks 883
Ch a r t 1. Ch em ica l Str u ctu r e of th e DMAAm -Ma BP
P olym er s
Ta ble 1. Ch em ica l Com p osition s of th e DMMAm -Ma BP
P olym er s
content of MaBP (mol %)
feed
polymer
mol wt Mw polydispersity Mw/Mn
0.0
0.5
1.0
3.0
10.0
0.0
1056 000
155 000
113 000
92 800
2.4
2.5
3.3
3.0
5.4
not detectable
1.0
3.6
14.3
134 000
structure of the polymers are shown in Chart 1. The polym-
erization was initiated using 0.1% R,R′-azoisobutyronitrile
(AIBN), and the reactions were carried out at 60 °C for 15 h
in DMF under nitrogen after degassing the reaction mixtures
by three freeze and thaw cycles. The polymer was purified by
double precipitation in diethyl ether, typically yielding ap-
proximately 65% of a white powder. The MaBP monomer was
synthesized from 4-hydroxybenzophenone and methacroyl
chloride via a typical esterification reaction in dichloromethane
solvent and triethylamine as the acid scavenger. The proper-
ties of the polymers are listed in Table 1. For characterization,
the 1H NMR spectra were recorded on a Bruker MSL 300
spectrometer (300 MHz). The molecular weight Mw and the
molecular weight distribution (polydispersity Mw/Mn) of the
copolymers were determined by gel-permeation chromatogra-
phy with an Agilent instrument equipped with an RI detector
and software from PSS.
Su r face-Attach ed Networ k P r epar ation . Thin DMAAm-
MaBP copolymer films were prepared by dip-coating LaSFN9
prisms (Hellma, Germany) in DMAAm-MaBP/2-propanol
solutions. The 2-propanol content was adjusted to yield films
of approximately 100 nm in thickness. Before dip-coating, the
prisms were activated in 1 M sulfuric acid for 1 min and rinsed
thoroughly in Millipore water and ethanol. To aid in the
attachment of the polymer network to the prism surface, a
benzophenone-based silane (4-(3′-chlorodimethylsilyl)propyl-
oxybenzophenone) was immobilized at the surface.19 The
samples were dried under nitrogen and irradiated under a high
pressure mercury lamp for 30 min. Immediately after UV
illumination, the samples were characterized with ellipsom-
etry.
Ch a r a cter iza tion of th e Su r fa ce-Atta ch ed Netw or k s.
The dry and swollen profiles of the surface-attached films were
measured with a home-built variable-angle nulling ellipsom-
eter in an ATR configuration. The light-source was a He-Ne
laser with a wavelength of λ ) 633 nm. The experimental setup
has been described in detail elsewehere.18 The refractive index
of the LaSFN9 prism is n ) 1.845, and in contact with water
the critical angle of total reflection is 46.3°. The main features
used for analysis of the ellipsometry data occur close to the
critical edge, and so angular scans of the samples were taken
between 40 and 55° with 0.1° increments. The thickness of all
films were in the optical range, giving rise to sufficient features
in the recorded spectra to infer the refractive index profile.
To analyze the data, model refractive index profiles were
generated, and the ellipsometric parameters were numerically
calculated using the matrix optical formulation.20 The param-
eters of the model were adjusted to minimize the differences
between the simulation and experimental data. The polymer
F igu r e 1. Representative ellipsometry delta and psi scans
against the angle of incidence for a series of DMAAm surface-
attached networks. The percentage of MaBP corresponds to
the average molar concentration of the cross-linkable monomer
in the network. All dry thicknesses were approximately 100
nm. The continuous lines represent the best fits with the
structural profiles shown in Figure 3.
volume fraction φ(z) was determined from the refractive index
profile n(z) with the Lorentz-Lorenz equation using an
effective medium approximation:21
2
2
2
nsolvent - n0
n(z)2 - n0
φ(z) )
/
(1)
2
2
2
2
(
) (n(z) + 2n
)
nsolvent + 2n0
0
where n0 is the refractive index of the polymer and nsolvent is
the refractive index of the solvent.
Resu lts a n d Discu ssion
The equilibrium swelling of the surface-attached
DMAAm networks was measured for a series of MaBP
concentrations, where the average molar MaBP fraction
was varied over 2 orders of magnitude, from 0.05% to
10%. The MaBP content was controlled by one of two
methods. In the first method, the MaBP molar fraction
was varied in the synthesis of the DMAAm-MaBP
copolymer. In the second method, DMAAm-MaBP(1%)
copolymer with 1% MaBP molar content was blended
with DMAAm homopolymer, where the molecular weight
of the DMAAm homopolymer is approximately an order
of magnitude larger than the DMAAm-MaBP copoly-
mer. The latter method also leads to stable networks
provided that the molecular weights and blending ratio
between the two polymers are chosen appropriately.
Blending offers a simple route to adjust the cross-link
density without the need to synthesize a new polymer
each time to tune the equilibrium swelling of the
network.
Figure 1 shows the measured ellipsometry Ψ and ∆
pairs for a series of the surface-attached DMAAm
networks as a function of MaBP content in contact with
aqueous solution. The MaBP content in each of the
samples was controlled by blending DMAAm homopoly-
mer and DMAAm-MaBP(1%). The data are reported

884 Toomey et al.
Macromolecules, Vol. 37, No. 3, 2004
F igu r e 2. Ellipsometry delta scan for the 0.05 mol %
DMAAm-MaBP sample with the best fit for a two-parameter
box-model (dashed line) and a three-parameter error-function
model (solid line).
F igu r e 3. Polymer fraction profiles that represent the fits in
Figure 1 for the 1%, 0.2%, and 0.05 mol % DMAAm-MaBP
samples.
in terms of the average MaBP molar ratio in the layer.
The dry layer thickness of each sample was approxi-
mately 100 ( 10 nm with a refractive index of 1.51 (
0.02, as measured by ellipsometry. Immediately after
the dry layer measurement, water was added to the cell
and the transition to the final swollen state was
monitored. In all cases, the swelling kinetics was
relatively fast, occurring in less than 30 s, which is the
time needed for a single measurement. All measure-
ments produced constant readings in Ψ and ∆ im-
mediately following exposure to water.
Inspection of the ellipsometric spectra in Figure 1
shows significant changes in both the ellipsometric ∆
and Ψ scans as the average MaBP content is decreased,
corresponding to an expansion of the profile with
decreasing cross-link density. To model the swollen
films, initially a simple box-model with a uniform
polymer volume fraction was used; however, reasonable
fits were found only at sufficiently high MaBP content.
As the MaBP content was decreased, the uniform layer
model no longer adequately described the swollen
profile. For instance, Figure 2 shows the ∆ scan for the
0.05% MaBP sample modeled with the uniform box
profile, denoted by the dashed line. While the simulation
captures most of the features of the experimental data,
the simulation shows a more pronounced oscillation in
∆ at low incidence angles than the experimental data.
The fit at low angles could be consequently improved
by permitting roughness at the outer edge of the profile,
which dampens the low angle oscillation in the simula-
tion while preserving the remaining features of the
curve. It was assumed the roughness is described by
an error function, thus the profile was modeled as
F igu r e 4. Cartoon depicting the swollen structure of the
surface-attached polymer network at high (a) and low cross-
link densities (b). At sufficiently low cross-link density,
peripheral chains are more likely to penetrate into the solvent
giving rise to a more diffuse interface.
interfacial width took on values of σ ) 100 nm and σ )
200 nm, respectively. While a finite interface width is
expected under all conditions, features much less than
the wavelength of light cannot be resolved with ellip-
sometry. The estimated precision in the interface width
is (50 nm. The physical explanation for the interface
stems from a small number of chains that extend beyond
the network. The outer edge of the layer becomes
rougher at lower cross-link densities since the polymer
chains are not as tightly confined to the interface and
can more easily penetrate into the solvent, as shown in
Figure 4. It is suspected that the interface width is a
strong function of the molecular weight of the individual
polymer chains; however, this effect was not studied in
the present experiments.
From the model fits, both the average thickness Le
and the average polymer volume fraction φe in the
swollen layers were independently determined. There-
fore, two quantities can be calculated that characterize
the swelling of the layer:
φe
z - Le
φ(z) )
1 - {erf}
[
(2)
( )
(
)
]
2
σ
Le
R )
(3)
L0
where φe is the average polymer volume fraction in the
layer, Le is the central position of the interface, and σ
is the width of the interface. The solid line in Figure 2
corresponds to the improved fit using the box model with
an error-type interface, involving three adjustable pa-
rameters altogether. More sophisticated models were
not considered as the data do not have sufficient
structural sensitivity to justify their use.
where R measures the linear swelling in the direction
perpendicular to the surface. The thickness L0 repre-
sents thickness of the dry film. Furthermore,
φ0
S )
(4)
φe
Figure 3 shows the volume fraction profiles which best
describe the 1% MaBP, 0.2% MaBP, and the 0.05%
MaBP swollen layers using the aforementioned three-
parameter model. For the 1% MaBP case, the data could
be fit with the absence of an interface (σ ≈ 0 nm). For
the 0.2% MaBP and the 0.05% MaBP samples, the
where S is the volumetric swelling degree in the gel,
and φ0 represents the volume fraction occupied in the
prepared state. If the attached networks swell only
perpendicularly to the surface with no swelling parallel
to the surface, then the linear degree of swelling R and

Macromolecules, Vol. 37, No. 3, 2004
Thin, Surface-Attached Polymer Networks 885
F igu r e 7. Comparison of the overall degree of swelling
between the surface-attached (b) and unconstrained bulk
DMAAm networks (9).
F igu r e 5. The linear degree of swelling R versus the volu-
metric degree of swelling S for a series of surface-attached
DMAAm-MaBP networks. The solid lines represents the
relationship between the two quantities if the surface-attached
networks undergo pure uniaxial swelling (S ) R) and swelling
in three dimensions (S ) R3).
cross-links. Since blending would be expected to alter
the cross-link distribution, it is reasonable to expect a
difference in the behavior of both systems; however, this
effect may be small, and in order to confirm the effect,
a much more exhaustive study would have to be
conducted. For the blended samples, when the average
MaBP content was reduced below 0.05%, the networks
were no longer stable and delaminated from the surface
upon exposure to water, effectively limiting the range
of MaBP contents that could be measured. The trend
line corresponds to a best fit slope of -1/3, suggesting
that the swell ratio of the surface-attached network
scales as approximately the cube root of the number of
segments between cross-links.
To explore the significance of this scaling dependence
of the surface-attached DMAAm networks, the equiva-
lent bulk networks were prepared using the same
preparation conditions. In each case, approximately 0.05
g of the polymer was deposited to a glass substrate from
chloroform forming a layer approximately 500 µm thick.
The layers were thoroughly dried under vacuum and
then UV irradiated for 30 min, the same irradiation
time as for the surface-attached gels. The layers were
then exposed to water. As they swelled, they eventually
delaminated from the glass surface and were allowed
to reach equilibrium (approximately 1 week). The swol-
len gels were then weighed and their degree of swelling
was defined as S ) me/mo where me,o is the mass of the
polymer gel in the equilibrium swollen state and dry
state, respectively. Assuming the density of the dry
DMAAm network is close to 1, the degree of swelling
as determined by weighing the wet and dry gels corre-
sponds to the definition of eq 4.
Figure 7 shows a comparison of the volumetric degree
of swelling S as a function of MaBP content for both
the surface-attached and the nonattached gels. It is
readily seen that the nonattached networks swell to a
much higher degree than the surface-attached networks
at all cross-link densities. As the nonattached networks
can swell isotropically, this observation is consistent
with the idea that higher degrees of freedom permit the
network to swell to a greater extent than a gel that is
mechanically or physically constrained. For the nonat-
tached gel, the degree of swelling in all three dimensions
is presumed to be equal, Rx ) Ry ) Rz, where Ri is the
linear deformation Le/Lo in the i direction. Therefore,
by constraining the network to the surface, from simple
geometric considerations, it may be expected that the
degree of swelling of the surface-attached network will
F igu r e 6. Average degree of swelling S vs the MaBP content
for a series of DMAAm surface-attached networks. As denoted
by the symbol, the MaBP content was varied either through
the synthesis conditions of the DMAAm-MaBP copolymer (2)
or by blending DMAAm homopolymer with DMAAm-MaBP-
(1%) (b). The solid line corresponds to a best fit power-law S
[MaBP content]-1/3
.
the volumetric degree swelling S must be necessarily
equal, in other words
Le φ0
)
(5)
L0 φe
Figure 5 shows a logarithmic plot of S vs R for a series
of DMAAm-MaBP surface-attached networks with
swell ratios S between approximately 2 and 12. Also
shown are two trendlines corresponding to S ) R and S
) R3, which represent swelling in one dimension and
three dimensions, respectively. Since the uncertainty in
the measurement and model fits leads to approximately
a 10% precision in the degree of swelling calculated with
either method, it therefore it can be concluded that
within the experimental error of the experiment, S )
R, and the layers are undergoing pure uniaxial exten-
sion normal to the surface.
Figure 6 shows the relationship between the volu-
metric swelling degree S of the surface-attached layers
and the average MaBP content in the layer. The
samples were produced by either blending DMAAm
homopolymer/DMAAm-MaBP(1%) copolymer or by di-
rectly altering the MaBP content in the copolymer, as
denoted by the symbol in the figure. It is remarkable to
note that all the samples follow a general trend with
respect to the average MaBP content. To a first ap-
proximation, it is expected that the degree of swelling
S should not only depend on the average cross-link
density, but also on the topological distribution of those
be the cube root of the unconstrained network, or Ssa
)
Suc1/3. For example, at 0.1 mol % MaBP, the uncon-
strained network swells approximately 64 times. It then

886 Toomey et al.
Macromolecules, Vol. 37, No. 3, 2004
F igu r e 8. Comparison of the linear degree of swelling R
between the surface-attached (b) and nonattached (9) DMAAm
networks. The value R for the nonattached networks is
approximated as the cube root of their average degree of
F igu r e 9. Log-log plot showing the relationship between the
volumetric swelling degree S for surface-attached and nonat-
tached DMAAm networks prepared under identical conditions.
The degree of swelling in the surface-attached networks scales
as the 5/9 power of the degree of swelling in the nonattached
networks, in qualitative agreement with the extension of
Flory-Rehner theory to one-dimension. A 1/3 power-law rela-
tionship from simple geometric arguments is also plotted for
comparison.
swelling, R ) S1/3
.
may be expected that the surface-attached network
should only swell by a factor of (64)1/3 ) 4. However,
the surface-attached gel swells to approximately 8 times
its dry thickness, much larger than expected by this
simple relationship.
freedom in which the network can swell:
Figure 8 compares the linear swelling degree of the
unconstrained networks Ruc ) Suc with the linear
-1/(d + 2)
1/3
1
R ≈
(10)
1
swelling degree Rsa for the surface-attached networks.
It is consistently observed that the linear swelling
degree of the surface-attached networks exceeds the
linear swelling degree of the nonattached networks,
becoming more pronounced at the lowest cross-link
densities. This observation can be understood by a
simple phenomenonological model based on a Flory-type
expression for the free energy.22 Upon immersion in a
good solvent, the equilibrium structure of a polymer
network is subject only to two opposing forces: the
thermodynamic force of mixing, which favors swelling,
and the elastic retractile force of the network, which
opposes swelling. The free energy of the system can be
written as
[
]
( /2 - ø)φ0Nc
As swelling is confined to fewer dimensions, R shows a
stronger dependence on the cross-link density 1/ Nc,
where Nc is the number of segments between cross-
links. Since the volumetric swelling degree S ) Rd, the
dependencies of both S and R can be determined for
three-dimensional and one-dimensional swelling in a
good solvent:
-1/5
-3/5
1
1
Ruc
≈
Suc
≈
[unconstrained]
(11)
(
φ Nc
)
(
φ Nc
)
0
0
and
∆G ) ∆Gmix + ∆Gelastic
The mixing free energy is
(6)
-1/3
-1/3
1
1
Rsa
≈
Ssa
≈
[surface-attached]
(12)
(
φ Nc
)
(
φ Nc
)
0
0
∆Gmix
) n1ln(1 - φ) + øn1φ
(7)
kT
The experimental observations presented in Figure 8,
wherein the surface-attached networks show greater
linear deformation than the equivalent unconstrained
networks, can be qualitatively understood within the
context of the presented model. As surface attachment
limits swelling to one dimension, the polymer concen-
tration in a surface-attached network is still a factor R2
greater than in the equivalent unconstrained network
at the same linear extension R. Consequently, the
surface-attached network experiences a higher mixing
osmotic pressure, which is partially relieved by further
extension in its swelling direction, thus leading to a
higher linear swelling ratio than possible in the uncon-
strained network. Equations 11 and 12 predict that the
volumetric degree of swelling in the surface-attached
network should be approximately the square root of the
degree of swelling in the unconstrained network:
where k is the Boltzmann constant, T is the absolute
temperature, n1 is the number of solvent molecules, φ
is the polymer fraction in the swollen gel, and ø is the
Flory polymer-solvent interaction parameter. The ex-
pression for the elastic free energy is
∆G
d
2
elastic ) ν [R2 - 1 - ln R]
(8)
( )
kT
where ν is the number of cross-links in the network and
d is the number of dimensions in which the network
can swell. Noting that the polymer volume fraction φ
in the swollen network is related to its linear deforma-
tion R through
φ0
φ )
(9)
Rd
5/9
Ssa ) Suc
(13)
Minimization of the free energy ∆G of the swollen
network yields the following relationship between the
equilibrium linear deformation R and the degrees of
Figure 9 shows this dependency superimposed on a plot
of Ssa vs Suc for the series of the DMAAm-MaBP

Macromolecules, Vol. 37, No. 3, 2004
Thin, Surface-Attached Polymer Networks 887
polymers shown in Figure 7, along with a simple cube
root relationship. As already discussed, the cube root
relationship stemming from simple geometric consid-
erations does not adequately describe the experimental
data, which are better described by the dependence
given in eq 13. It should be noted that the model predicts
a numerical prefactor of unity in eq 13, which overpre-
dicts the observed experimental results by about 25%.
This small discrepancy may have a number of causes.
First, it was assumed that the specific density of the
dry network was the same as water, which would lead
to an overestimate of the volumetric degree of swelling
Suc for the nonattached networks from its mass if the
specific density is less than water. Second, while it has
been found that the volumetric swelling degree of
isotropic networks in a good solvent is well described
by S ) pNc3/ 5, the slope p cannot be correctly predicted
with the Flory-Rehner model.23 It has been argued that
the free energy expression for network swelling must
be connected to the physical structure of the gel, which
may lead to different expressions of the prefactor p in
the unconstrained and constrained swelling cases.
Ack n ow led gm en t. This work has been supported
by the DFG in the framework of the SFB428 (“Struk-
turierte Makromolekulare Netzwerksysteme”).
Su p p or tin g In for m a tion Ava ila ble: Text giving a de-
tailed mathematical derivation of eq 10. This material is
available free of charge via the Internet at http://pubs.acs.org.
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Con clu sion s
Chemically attaching a polymer network to a surface
reduces the degrees of freedom in which the network
can swell, affecting its swollen internal structure. This
work establishes a first step to understanding the effect
of surface-attachment on the equilibrium structure of
neutral polymer networks, providing a basis to interpret
and predict the properties of hydrogels in confined
environments. For instance, the mobility and diffusion
of a guest species or a target signal within a polymer
network and the dynamic response of that network is
intimately tied to the internal structure of the network.
Surface-attached polymer networks are expected to find
considerable use in microfluidic devices, a rapidily
expanding field, due to the tremendous design flexibility
unique to polymers. Cross-linked polymer structures
should permit a broad range of autonomous chemical
sensing, fluid regulating, and mechanical actuating
components in microfluidic systems.
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