Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Holger Wack et al.
GEL BLOCKING EFFECTS DURING THE SWELLING
OF POLYMERIC HYDROGELS
Holger Wack1,*, Mathias Ulbricht2
1
Fraunhofer-Institut für Umwelt-, Sicherheits- und Energietechnik UMSICHT, Osterfelder
Straße 3, 46047 Oberhausen, Germany
2
Lehrstuhl für Technische Chemie II, Universität Duisburg-Essen, 45117 Essen, Germany
*To whom correspondence should be adressed
Tel: +49 (0) 208 8598-1121
Fax: +49 (0) 208 8598-1424
e-mail: holger.wack@umsicht.fraunhofer.de
A method to determine the swelling pressure of polymeric hydrogels which is based on the principle of
determining the swelling pressure at a given final volume of swelling is described. Data for one type of polymer
particles made from weakly crosslinked and partly neutralized poly(acrylic acid) are presented. For polymer
volume fractions between 0.05 and 0.30, swelling pressures in the range of 0.25 to 4.31 MPa were obtained after
times of up to 100 hours. Up to medium polymer volume fractions, the kinetic data is described with a combined
diffusion-relaxation model. A novel model is presented for higher polymer volume fractions. The mechanism of
the gel blocking effect which is evident in this range is explained and considered in the novel model in form of a
blocking factor. The new model is well suited for the description of the kinetics of the swelling pressure at high
and allows a quantification of the dominating mechanisms, either polymer relaxation or gel blocking. The results
obtained may be used for the design of improved self-healing sealing concepts on the basis of polymeric
hydrogels.
1
Introduction
Some high-molecular weight substances can form gels through absorption of liquids. Among
these are highly swellable polymers based on polyacrylates, that are also called “super
absorbing polymers” (SAP).
The main field of application for SAP in the form of particles is the absorption and storage of
liquids in hygienic products, such as diapers [1]. When coming in contact with aqueous
liquids the SAP swells and forms a hydrogel. SAP can take up to 1000 times of their dry
weight, while storing the absorbed liquid even under pressure. Therefore SAP are used in
several technical applications [2-4]. Recently, SAP systems were developed for self-repairing
sealings for tube connections in sewage systems and the field of civil engineering [5].
For the development of sealing products based on SAP, information about the swelling
pressure is of essential significance. Only few scientific studies have been concerned with the
application of polymer hydrogels for sealing techniques. Such materials are used mostly
empirically. Detailed analyses as well as conclusions regarding mechanisms and interrelations
between polymer structure and amount, sealing volume and sealing performance are lacking.
Several different methods can be used for the determination of the swelling pressure of
hydrogels. The analysis of the swelling pressure at a given pressure is the method that is
described in most detail [6-9].
1
© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Holger Wack et al.
Membrane osmometric determination of the swelling pressure is also suitable [10]. Other
methods are investigations via ultra centrifuge [11] or vapour pressure osmometry [12]
The analysis of the swelling pressure at a given final volume of swelling is the preferred
method for investigations related to sealing techniques, and this method is also broadly used
[13-15].
This study presents a method for determining the swelling pressure of polymeric hydrogels
relying on the analysis of the swelling pressure at a given final volume of swelling. A novel
model (gel blocking model) for the interpretation of the results obtained for SAP particles at
higher volume fraction is described.
2
Experimental
2.1
Polymer synthesis
The polymer syntheses were performed by radical polymerisation of acrylic acid (AA) and
sodium acrylate (ANa) as functional monomers and N,N´-methylene bisacrylamide (BIS) as
crosslinker monomer in solution. The redox system ammonium persulfate and sodium
bisulfite was used as initiator.
AA was first dissolved in deionised water in an ice bath. Subsequently, the required amount
of ANa for co-polymerization was obtained through partial neutralization of AA with sodium
hydroxide. Thereafter, the crosslinker BIS was dissolved in this solution, that was deaerated
by bubbling with nitrogen for 10 minutes. Next, the solution was cooled down to 5 °C and
stored for further 5 minutes. This monomer solution was then mixed with the initiator
solution; the starter concentration amounts to 0.3 %, relative to the total molar concentration
of the functional monomers. Polymerization proceeded in closed glass tubes (height 110 mm,
diameter 65 mm) for 240 min. at 60 °C. Thereafter, the polymerized hydrogels were taken
from the glass tubes and cut into small pieces. The hydrogel pieces were stored in deionised
water at 20 °C for four days for washing out of the not-reacted components, at daily exchange
of the water. Then, they were dried at 70 °C in vacuum. This drying method was chosen to
prevent the formation of porosity in the polymer particles. The dry polymer particles were
grinded in a ball mill and fractioned to different particles sizes in a sieving device.
In the present study, a polymer with AA concentration of 2.6 mol l-1 at a degree of
neutralization of 75 mol-% has been used. The BIS (crosslinker) concentration was 2.4 mol%, relative to the total functional monomer concentration. The parameters and conditions
present the composition of SAP used in technical applications.
2.2
Swelling pressure measurements
For determination of the swelling pressure the device depicted in Figure 1 was used. The
apparatus has a swelling chamber of defined volume and has been constructed for a pressure
range of 0 to 12 MPa. On a bottom plate made from stainless steel a hole plate (stainless steel)
is placed. On the hole plate a transport fabric is placed. The transport fabric is designed to
lead the solvent homogeneously towards the membrane that is placed on the transport fabric.
The membrane consists of a wire material (stainless steel) and has a pore size of 5 μm and a
thickness of 15 μm. The membrane permits a nearly resistance-free solvent penetration and a
safe encapsulation of the SAP in the swelling chamber.
2
© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Holger Wack et al.
The swelling chamber (height 10 mm, diameter 10 mm) is made of acrylic glass in order to
allow monitoring the swelling process also visually. The swelling chamber is closed by a top
cover. In the top cover a pressure sensor is built in exactly in the centre and precisely adjusted
to the level of the wall. The components of the device are sealed by gaskets to each other and
the connection is done by 8 screws that are distributed equally over the perimeter.
Figure 1: Construction of the device for determining the swelling pressure
The measurements of the swelling pressure were done with a variation of the volume fraction
of the polymer φP as defined below:
φP =
VP
1
=
VL + VP q V
(1)
with VP: polymer volume, VL: solvent volume and qV: volume-related swelling degree.
A defined mass of polymer particles mP was filled into the chamber. After closing the
chamber the swelling solvent (deionised water) was supplied. The experiments were carried
out at a temperature of 23 °C, and the swelling pressure was recorded over a period of two
weeks.
From the chamber volume VQ and the polymer mass mP, the volume fraction of the polymer
φP was calculated using the apparent density φP:
φP =
VP
mP
=
VQ ρ P VQ
3
(2)
© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Holger Wack et al.
3
Theory–kinetics of the swelling pressure development
in polymer hydrogels
3.1
The diffusion-relaxation model
The theoretical description of the kinetics of the solvent absorption of polymer hydrogels is
possible using a combined diffusion-relaxation model [16,17]. The model equations may be
adapted by including the swelling pressure p, yielding the following expression of the
combined diffusion-relaxation model:
⎡
6
p (t ) = p ∞ , D ⎢1 − 2
⎣⎢ π
∞
∑
n =1
⎤
1
2
−
exp
n
k
t
D ⎥ + p ∞ , R [1 − exp(− k R t )]
n2
⎦⎥
(
)
(3)
with p: pressure, t: time, p∞: swelling pressure in the state of equilibrium, k: rate constant, n:
control variable, the index ”D“ relates to diffusion, the index ”R“ relates to relaxation. For the
swelling pressure p∞ in the state of swelling equilibrium, the following applies:
p ∞ = p ∞,D + p ∞,R
(4)
The experimentally obtained data of the swelling pressure as function of time may be fitted
with the time constants kD und kR as parameters.
In order to improve the clarity, the two terms in square brackets in equation (2) are substituted
by ηD und ηR, and the weighting factor xD is introduced, yielding the following equation:
p(t ) = p ∞ [x Dη D (t ; k D ) + (1 − x D )η R (t ; k R )]
(5)
Consequently, the weighting factor xD obtained from the fitting provides information to what
extent the swelling pressure kinetics is dependent on diffusion or relaxation. Ultimately, the
diffusivity D may be determined from the time constant k and the particle diameter d by the
following equation:
D=
kd2
4π 2
(6)
For the calculation of the diffusivity a combined rate constant kK(DR) has been used. Therfore
the rate constants kD und kR that have been obtaind by the parameter fits are combined by
using the calculated weighting factor xD:
k K(DR) = x D k D + (1 − x D ) k R
4
(7)
© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
3.2
Holger Wack et al.
Mechanism of gel blocking
To our knowledge there are no scientific investigations about the effect of gel blocking on the
kinetics of the swelling pressure development. This may be due to the fact that for SAP used
in hygienic products a gel blocking must be strictly prevented, and therefore it has not been in
the focus of investigations. For example, for use in diapers the SAP must take up and store
liquids in the most rapid and homogeneous way.
For use in sealing techniques, however, the gel blocking is of essential importance, because a
rapid prevention of further liquid entrance may be realised using this phenomenon. In a recent
study [18], this has been described for an axial cable sealing.
A procedure for calculation of the penetration depth of water in the polymer powder that has
been filled between the separate cable wires was described. From this calculation, the period
was derived at that the swollen SAP gel stops the further penetration of water into the
polymer powder bed.
In the following, a novel model approach is presented that allows the quantification of the
impact of gel blocking on the swelling process and the swelling pressure (Figure 2).
Figure 2: Schematic depiction of the mechanism of gel blocking (for details refer to text below)
The situation at high polymer volume fractions in the swelling chamber is illustrated (1).
Upon opening the connection to the solvent reservoir, the swelling solvent penetrates into the
chamber and leads to swelling of the polymer adjacent to the membrane. The evolving
hydrogel layer blocks the further water influx into the swelling chamber (2). Therefore,
swelling of the more remote dry polymer particles must occur via transfer of the swelling
solvent from swollen to dry polymer particles. Subsequently, the relaxation process of the
polymer gel particles will occur. Now, the gel layer also blocks the transport of the swelling
solvent into the void volume of the dry polymer layer. Consequently, the solvent required for
achieving the swelling equilibrium for the entire bed of particles can reach the swelling front
only through a diffusion controlled process (3). Simultaneously, the swelling pressure
increases, that leads to a compression of the dry polymer particle bed above the swelling
front. This leads to an inhibition of the polymer chain relaxation in the polymer gel particles
because the available space decreases.
This slows down the relaxation of the swelling particles. After the solvent absorption of the
polymer particles in the entire bed is complete, there will still be a concentration gradient
between the highly swollen polymer particles above the original swelling front and the
particles in the zone where swelling has started.
5
© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Holger Wack et al.
Only after complete humidification of the chamber and complete equilibration of the swelling
degree over the entire volume of the chamber, the swelling pressure equilibrium is reached
(4).
3.3
The gel blocking model for solvent uptake and development of swelling
pressure
The solvent transport from swollen to dry polymer particles and the related relaxation of the
polymer chains may be defined as rate-determining steps for the further humidification of the
polymer particle bed and thus the swelling pressure kinetics. For the relaxation dominated
process, the following equation, with k R as rate constant, applies:
dp
= k R ( p∞ − p)
dt
(8)
For the overall description of the gel blocking including the inhibitions of solvent transport, in
particular by the grain-to-grain transport from the particles in the swelling front to the dry
particles above the swelling front, the logistic differential equation in a form suited for the
description of swelling pressure kinetics is introduced:
⎛
dp
p2 ⎞
⎟
= k B ⎜⎜ p −
dt
p ∞ ⎟⎠
⎝
(9)
The logistic differential equation has been developed for the description of growth processes
that are impeded by inhibitors. The validity of this equation has been proven to apply to, for
example, the reproduction of simply structured creatures [19]. The quadratic term in equation
(9) considers the impact of inhibition on the swelling equilibrium as described in Section 3.2.
(cf. Figure 2). The blocking factor k B is an overall rate constant of the swelling process that
will depend not only on the SAP structure and morphology as well as the respective volumes,
but also on the detailed geometry of the system studied (in particular the ratio between
chamber diameter to height; cf. Figure 2).
From the combination of equation (8) and the rearranged equation (9), the following equation
for a SAP system with relaxation and gel blocking may be derived:
⎛
dp
p ⎞
⎟
= k R ( p ∞ − p ) + k B p ⎜⎜1 −
p ∞ ⎟⎠
dt
⎝
(10)
The solution of the differential equation (10) is as follows:
p (t ) = p ∞
1 − exp(− (k R + k B ) t )
k
1 + B exp(− (k R + k B ) t )
kR
6
(11)
© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Holger Wack et al.
This equation can be fitted to the experimental data with the rate constants k R and k B as
parameters. For the further calculation of the diffusivity (cf. equation (7)) a combined rate
constant k K(RB) is used. This combined rate constant is obtained by adding together the rate
constants k R and k B :
k K(RB) = k R + k B
(12)
The derived equation is able to describe a combined relaxation-blocking mechanism. If there
is no gel blocking (kB = 0), equation (10) is transferred into the term for the description of the
pure relaxation behavior (equation (4), xD = 0). If gel blocking occurs, kB increases, and a
comparison between kR and kB can be made. Based on the comparison it is possible to
estimate that of both mechanisms is dominant for the swelling behavior of polymer hydrogels.
4
Results and discussion
The development of the measured swelling pressures for different polymer volume fractions
of particles of the crosslinked Poly(AA-ANa) in the swelling chamber is shown in Figure 3.
To enable a more precise visualization of the initial period of swelling pressure increase, the
swelling pressure data are plotted via the square root of time.
The calculated values were obtained by fitting to the diffusion-relaxation model (equation (4))
using the method of the minimum square deviation [17].
Figure 3: Swelling pressure versus the square root of time for a variation of the polymer fraction in the swelling
chamber (cf. Figure 1)
For small polymer volume fractions (φP = 0.05 and φP = 0.09), the swelling equilibrium is
reached much more rapidly (in about 11 hours) as compared to the higher polymer volume
fractions can be obtained. For a polymer volume fraction of φP = 0.17 equilibrium is observed
after about 69 hours, and for even higher volume fractions only after about 100 hours.
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© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Holger Wack et al.
The application of the diffusion-relaxation model to the measured data is also presented in
Figure 3. It is evident that the diffusion-relaxation model is well suited to describe the
swelling pressure development for low polymer fractions.
Both the curve shape and the quantitative data, reveal the transition from a diffusioncontrolled behavior at low polymer volume fractions to a relaxation-dominated behavior at
medium polymer volume fractions: The weighting factor changes from xD = 1.00 (pure
diffusion) at φP = 0.05 towards xD = 0.00 (pure relaxation) at φP = 0.17. However, for higher
polymer volume fractions φP, the diffusion-relaxation model is obviously not suited to
describe the swelling pressure time-dependence accurately because the deviations between
model and measured data are increasing with increasing φP (cf. Figure 3). In this polymer
volume fraction range, a further mechanism in addition to diffusion of the solvent and
relaxation of the polymer chains will work, and that may be described as gel blocking effect
(cf. section 3.2). Considering the application of SAP particles in the sealing technique, such
high polymer concentrations are required to achieve an optimum sealing effect. The sealing is
a construction element with a defined volume filled with SAP particles, and upon contact with
water the complete penetration of water through the particle bed must be prevented.
Figure 4 presents the application of the new gel blocking model (cf. section 3.3). Calculated
values of kR and kB were obtained by fitting to the new gel blocking model to the
experimental data (cf. equation (11)). The agreement between model and measured data is
very good. The contribution of gel blocking onto swelling pressure development increases
with increasing polymer volume fraction φP as it is evident from the increase of the respective
rate constant (blocking factor) kB.
Figure 4. Swelling pressure versus the square root of time for higher polymer fractions in the swelling chamber
(φP = 0.17 to φP = 0.30)
Furthermore, the effective diffusivity as calculated from the combined rate constant (cf.
equation (11)) is presented in Figure 5. A strong decrease of diffusivity with increasing
polymer volume fraction is observed for small values of φP until the diffusivity reaches an
almost constant value at φP ~ 0.17.
8
© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Holger Wack et al.
Figure 5: Diffusivity versus the polymer fraction (lines are to guide the eyes)
As main result of this study, the novel model allows the quantification of the significant
retardation of polymer swelling due to the gel blocking effect. When measuring the swelling
pressure as a function of time, this effect is observed only above a certain polymer volume
fraction.
Hence, one obvious precondition for gel blocking is the limitation of the available swelling
volume, i.e. that the volume of the chamber is smaller than the hydrogel volume that would be
reached in the swelling equilibrium.
5
Conclusions
This study presents a method to determine the swelling pressure of polymeric hydrogels. The
method is based on using a swelling chamber of a defined volume. Therefor the volume of the
swelling chamber is much smaller than the volume the gel can reach by free swelling to
equilibrium. Data for one type of polymer particles made from weakly crosslinked and partly
neutralized poly(acrylic acid) are presented. For polymer volume fractions φP between 0.05
and 0.30, swelling pressures in the range of 0.25 to 4.31 MPa were obtained after times of up
to 100 hours.
Up to medium polymer volume fractions, the kinetic data may be described with a combined
diffusion-relaxation model. A novel model is presented for higher polymer volume fractions.
The mechanism of the gel blocking effect that is evident in this φP range is explained and
considered in the novel model in form of a blocking factor.
The new model is well suited for the description of the kinetics of the swelling pressure at
high φP and allows a quantification of the dominating mechanisms, either polymer relaxation
or gel blocking. The results obtained may be used for the design of improved sealing concepts
on the basis of SAP.
Further studies will address the effects of polymer structure and the particle size on the
kinetics of swelling pressure development.
9
© Springer 2007
Proceedings of the First International Conference on Self Healing Materials
18-20 April 2007, Noordwijk aan Zee, The Netherlands
Holger Wack et al.
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