journal article in attachment
1-Briefly introduce the topic of the paper. What is it, and why is it important?
2) Thermodynamic background / theory. explain the equations that are applied
3) What is measured. Describe the actual measurement, or what should be measured (if you are describing a method).
4) Comparison to data. Either show how the thermodynamic principles introduced above have been compared to data, or discuss how they could be. Make sure it is clear what thermodynamic information is determined.
5) Reflection. Discuss the limitations in the cases the model can capture, the reasons for any deviations or limitations. Are there ways that the model could be improved?
6) References. Provide references cited. The primary source should be peer‐reviewed, and other journal articles or books can be used for support. Provide the authors, article title, journal, volume, pages (or article number), and year, in a consistent citation format. Non‐peer reviewed sources that have no author attribution (such as Wikipedia) are much less valuable sources of information.
Enthalpy of Swelling of Potassium Polyacrylate
and Polymethacrylate Hydrogels. Evaluation
of Excluded-Volume Interaction
Alexander P. Safronov,* 1 Yelena A. Smirnova,
1 Gerald H. Pollack,
3 Felix A. Blyakhman
1 Chemistry Department, Urals State University, 620083, Lenin St. 51, Yekaterinburg, Russia Fax: 007-343 2615 978; E-mail: firstname.lastname@example.org
2 Physics Department, Urals State University, 620083, Lenin St. 51, Yekaterinburg, Russia
3 Department of Bioengineering, Box 357962, University of Washington, Seattle WA 98195, USA
Received: February 16, 2004; Revised: May 17, 2004; Accepted: May 18, 2004; DOI: 10.1002/macp.200400067
Keywords: calorimetry; enthalpy of swelling; hydrogels; polyelectrolytes
The basic features of the phase behavior of polyelectro-
lyte gels are relatively well described in the literature.
Essentially, they deal with the swelling/collapse phase
transition under the influence of various kinds of triggering
agents. While being first predicted in theory by Dusek and
the abrupt transition from the highly swollen
to the compact contracted state of the gel was experimen-
tally observed in the basic study of Tanaka. 
numerous works devoted to phenomenological observa-
tion of the transition in different gels as well as to structural
and dynamic study of the phenomenon have appeared.
Details can be found in several reviews [3,4]
and books. [5,6]
The theory for the swelling/collapse phase transition in
polyelectrolyte gels [7,8]
is basically the development of the
theory for the coil/globule phase transition in the single
polymer chain [9,10]
and considers the competition between
several types of interaction inside the gel. The counterparts
are: repulsive and attractive Coulomb forces between
charges present, osmotic pressure of counter-ions, entropic
elasticity of the network, and non-valent interactions
between the network and the solvent. While the first three
are universal, the latter is the specific indication of the
Summary: The enthalpy of swelling over the entire con- centration range in potassium polyacrylate and polymetha- crylate hydrogels with varying charge density was measured by means of isothermal Calvet microcalorimetry at 298 K. Concentration plots of the enthalpy of swelling at polymer volume fractions up to 50% were used for evaluation of Flory-Huggins binary parameter of interaction. Apparent values of w determined directly from experimental plots revealed extremely strong concentration dependence at high degrees of swelling. This was taken as evidence for the overlap of electrostatic and excluded-volume interactions. The separate evaluation of these contributions to the enthalpy of swelling was performed using the recent theory developed for the enthalpy of dilution in semi-dilute polyelectrolyte solutions. The mean value of the parameter w over a wide range of swelling for the uncharged poly(acrylic acid) and poly(methacrylic acid) gel was found equal to 0.21and �0.50 respectively. The ionization of the gel network due to the introduction of potassium salt residues resulted in the pro- gressive decrease in the quality of the solvent. At 40–50% of
ionization, the binary interaction parameter was about 2.8 both for potassium polyacrylate and polymethacrylate hydrogels. That value is much more than the critical value for liquid-liquid phase separation in non-electrolyte polymer solutions.
Macromol. Chem. Phys. 2004, 205, 1431–1438 DOI: 10.1002/macp.200400067 � 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Full Paper 1431
chemical nature of the components. Usually it is defined as
excluded-volume interaction and is expressed either by
Flory-Huggins binary parameter of interaction w or in terms of virial coefficients of the system.
Although there is no doubt in the general validity of
the theory for polyelectrolyte gels, its practical appli-
cation often meets difficulties: one can readily explain
the observed effects a posteriori, rather than make any
numerical predictions a priori. The reason is quite simple:
the values of the parameters of excluded-volume inter-
action are usually not known for the given polyelectrolyte
This indicates that an important piece of a puzzle is
missing: namely, thermodynamic data on polyelectrolyte
gels. Such data could provide appropriate information on
basic aspects of gel physicochemistry. Indeed, one can find
no thermodynamic data in the aforementioned reviews.
Experimental determination of the excluded-volume in-
teraction parameter w in non-electrolyte polymer solutions is described elsewhere.
 Basically, direct thermodynamic
methods include: (i) using Flory-Huggins expression for the
chemical potential of the solvent to fit experimental data
measured by means of osmotic pressure, vapor sorption,
light scattering, etc.; (ii) calculation of w from the position of the binodal on the phase diagram of polymer solution if
there is a liquid-liquid phase separation; and (iii) analysis
of the enthalpy of mixing or the enthalpy of dilution of
polymer solution. In principle any of these approaches
can be used with minor modifications for non-electrolyte
However, the methods cannot be easily extended to
polyelectrolyte solutions and gels. In this case, (i) the
chemical potential of the solvent depends rather on the
presence of counter-ions than on w; (ii) usually there is no liquid-liquid phase separation in the solution; (iii) the
enthalpy of the system depends not only on w (excluded volume interactions) but on electrostatics as well.
Recently, one of us addressed a similar problem in the
solution of the natural polysaccharide chitosan and a
hydrophobically modified derivative. 
the enthalpy of infinite dilution was measured for chitosan
solutions of different concentration. Special theoretical
consideration had been made that separately evaluated
the contributions from electrostatic and excluded-volume
interactions. As a result, binary parameter of interaction in
chitosan acetate solution was evaluated close to zero
(�0.01), while for hydrophobically modified chitosan it was more negative (�0.21), indicating the importance of hydrophobic interactions in chitosan solutions.
In the present study we extend the proposed approach
to polyelectrolyte gels. We measure the enthalpy of swel-
ling of polyelectrolyte gels of potassium polyacrylate and
polymethacrylate with different charge density and evalu-
ate the excluded-volume parameter of interaction w. This gives us the quality of solvent as dependent on the nature of
gel, which is highly relevant in theoretical consideration of
swelling/collapse phase transition.
Gels of poly(acrylic acid) (PAAc) and poly(methacrylic acid) (PMAc) were made by free-radical polymerization of partially neutralized acrylic and methacrylic acids, respectively with N,N0-methylenediacrylamide as a cross-linker in aqueous solu- tion. All reagents were purchased from Merck (Schuchardt, Hohenbrunn). In order to provide a series of gels with varying electric charge density, 0, 25, 50, or 75% of methacrylic acid monomers were neutralized by the required amounts of potassium hydroxide before polymerization. In each case the overall monomer (acid and its potassium salt) concentration was 2.7 M, while the cross-linker to monomer concentrations were set at 1:100. Potassium persulfate (0.5 g � l�1) was used as initiator. Polymerization was carried out in PE probe tubes 10 mm in diameter for 1 h at 80 8C and then 3 h at 50 8C. After polymerization, gel samples were washed in distilled water to remove the sol fraction and free salts. Water was renewed every day for 3 weeks. The degree of swelling of gel samples was determined by measuring the net weight of the residue after drying.
Since acids and their potassium salts have different activity in free radical polymerization, the actual molar fraction of potassium acrylate and methacrylate monomer units in final extracted gels is different from that in monomer mixture. The former was determined by element analysis. It gave 0, 11, 25, 39% of potassium acrylate and 0, 13, 30, 47% of potassium methacrylate monomer units in equilibrium gels relative to 0, 25, 50, and 75% of potassium salt in the monomer mixture.
All calorimetric measurements were carried out using commercial isothermal Calvet microcalorimeter DAK-1-1 (Chernogolovka, Russia) with 10 ml cells and sensitivity 10
�6 J � s�1. The values of heat effects from 0.05 to 1 J were
measured with ca. �5% accuracy, the values of heat effects 0.005–0.05 J with ca. �10%. All calorimetric measurements were made at 298 K.
Experimentally, we measured the heat effects of the equi- librium swelling of gel samples containing different amounts of water. First, gel samples were dried to constant weight and small portions (ca. 20 mg) were placed in thin glass microbulbs ca. 0.3 ml involume. Required amounts of water were added to create gels with different degrees of swelling. While high degrees of swelling were obtained by direct pouring of water into the microbulb, low degrees of swelling were achieved by the sorption of water vapor onto the dry gel in a vacuum. Thus, gels were obtained with water content ranging from the highest possible value (equilibrium degree of swelling), down to the completely dry gel. Typically, the set of the samples covering the entire concentration range included three to five gels with water content above 90%, and the rest with 10% steps in water content diminution. The bulbs with gels of varying polymer/ water ratio were sealed and stored until equilibrium uniformity of composition was achieved. The experimental procedure included breaking the bulb in the calorimetric cell in excess water and measuring the enthalpy of swelling to equilibrium. Thus, the concentration dependence of the enthalpy ofswelling
1432 A. P. Safronov, Y. A. Smirnova, G. H. Pollack, F. A. Blyakhman
Macromol. Chem. Phys. 2004, 205, 1431–1438 www.mcp-journal.de � 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
was obtained. All enthalpy data were obtained at pH ¼ 7 of water/gel system provided by the large excess of water. No pH-control agents were added in order to avoid unexpected influence on ionic and molecular interactions.
Results and Discussion
The values of the enthalpy of swelling of potassium poly-
acrylate gel are plotted in Figure 1 against the weight
fraction o2 of polymer in the binary water/gel system. The abscissa of each point corresponds to the initial polymer
content in the given gel with certain initial degree of
swelling. The ordinate indicates the enthalpy change per 1 g
of dry polymer during the swelling of the given gel from the
initial degree of swelling up to equilibrium. The enthalpy of
swelling of the gel is the analogue of the enthalpy of infinite
dilution of linear polymer solution of certain concentration
o2. However, in the case of gel the final polymer con- centration corresponds not to the infinite dilution but to the
weight fraction o2 1 of polymer in the equilibrium gel. The
values of the equilibrium degrees of swelling a1 as well as o2 1
at 298 K for all studied gels are listed in Table 1. One
can see that o2 1
corresponds to the semi-dilute regime of
polyelectrolyte, which is quite important for further anal-
ysis. The equilibrium degree of swelling increases and
the polymer concentration o2 1 decreases with the increase
in the fraction g of potassium acrylate monomer units in the gel.
The curves presented in Figure 1 are rather complicated
in their shape. Typically, the enthalpy of swelling for dry gel
is large and negative (except PAAc gel with g ¼ 11%). When the water content in gel is about 5–80%, the enthalpy
of swelling has rather large positive values. However, at
higher water content close to equilibrium degree of swelling
the enthalpy becomes negative again (except for the gel
with g ¼ 0), albeit with relatively low values. The negative sign in this concentration range is in accordance with the
behavior of the enthalpy of dilution for linear PAAc salts
reported in ref. 
With the fraction of salt residues increasing from 0 to
11%, the enthalpy of swelling first shifts up to more positive
values, but with further increase of g shifts down. Without doubt, such complicated character of enthalpy of swelling
plots stems from the superposition of different contribu-
tions to its value. At least three can be readily mentioned
DHsw ¼ DHV þ DHe þ DHg ð1Þ
DHV is the enthalpy difference between non-valent excluded-volume interactions in the gel with certain con-
centration of water and the gel swollen to equilibrium
degree. This contribution reflects the difference in hydra-
tion for the different degrees of swelling. DHe is the electrostatic term. At a given degree of swelling there is
certain balance between electrostatic attraction and repul-
sion in the system of charged monomer units and counter-
ions. As the gel swells, this balance is changing as well that
affect the enthalpy of the gel. The third term, DHg is restricted to very low water content; the gel is almost dry.
Such gels exist in the glassy state with a non-equilibrium
elevated level of enthalpy. During swelling water acts as
plasticizer for the glassy structure, and thereby provides a
relaxation of enthalpy down to its equilibrium value. As a
result, much heat is evolved during the swelling of dry
polymer gels. This contribution governs the enthalpy of
swelling plot at high polymer content.
The influence of the glassy state of the polymer on the
thermodynamic functions of mixing was systematically
considered in ref. 
and the following semi-empirical ex-
pression for the enthalpy of infinite dilution was obtained.
DHg ¼ e22j0vj 1=j0v�2 2 ð2Þ
Here j2 is the volume fraction of polymer in the initial solution, jv
0 is thevolume fraction of metastablevoidsin the
polymer glassy structure, e22 is the cohesion energy of polymer matrix. The two latter are the fitting parameters of
the theory. Since jv 0 is far less than unity, the exponent in
Equation (2) is very large. Consequently, at low j2 in wide
Figure 1. Enthalpy of swelling of potassium polyacrylate hydrogels in water at 298 K. Fraction of potassium acrylate monomer units: 0% (1), 11% (2), 25% (3), 39% (4).
Table 1. Equilibrium composition of hydrogels.
Gel g a1 o2 1
PAAc 0 13 7.7 11 120 0.83 25 140 0.70 39 180 0.54
PMAc 0 11 9.2 13 37 2.7 30 50 2.0 47 76 1.3
Enthalpy of Swelling of Potassium Polyacrylate and Polymethacrylate Hydrogels . . . 1433
Macromol. Chem. Phys. 2004, 205, 1431–1438 www.mcp-journal.de � 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
concentration range DHg is close to zero and sharply increases at high j2 values.
Analysis of the glassy structure of the gels with low water
content is beyond the scope of the present study. Therefore,
we will restrict further consideration of the enthalpy of
swelling to the concentration range of highly and moder-
ately swollen gels and will not take into account the
character of the curves at high polymer content.
In highly and moderately swollen gels only two first
terms are present in Equation (1).
According to Flory-Huggins theory for polymer solu-
tions, the enthalpy of dilution from the initial concentration
(j2,i) down to the final concentration (j2,f) related to 1 basemol of polymer is given by the following equation:
DHdil ¼ wRTðj2;i � j2;f Þ ð3Þ
In the case of the gel, the final concentration of swelling is
always the same and refers to the equilibrium degree of
swelling. Thus, the enthalpy of swelling becomes a linear
function of polymer concentration in the gel, whose slope
corresponds to wRT value. Since plots for all gels are not linear we may calculate only apparent values wapp using Equation (3) from experimental plots of DHsw at low and intermediate polymer content. Therefore the experimental
values of the enthalpy of swelling per g of polymer were
converted to J per basemol and the weight fraction of
polymer to its volume fraction using the increments of Van
der Waals volume of groups taken from ref. 
. The plots
were interpolated and the first derivative was taken analy-
tically. It gave the RTwapp value at a certain volume fraction of polymer in the gel.
Figure 2 presents the concentration dependence of wapp for PAAc gels with different g. The distinct difference between PAAc and its salts can be noticed. In the former,
wapp values are positive, not large, and almost independent of concentration. In the case of PAAc salts, a strong
concentration dependence is apparent: wapp is negative at
low polymer content, very steeply increases towards large
positive values in a rather narrow concentration range,
passes through maximum, and then gradually decreases. It
seems unrealistic to assign non-valent interactions as the
only source of the shape of such complex curves. We
suppose that such character of wapp plots for PAAc salts stems from a superposition of electrostatic and excluded-
volume interactions as indicated in Equation (1).
In order to evaluate excluded-volume interactions in
polyelectrolyte gels one should subtract the electrostatic
term DHe from the experimental data of the enthalpy of swelling DHsw. Classic theoretical consideration of electro- static contributionto the enthalpy of dilution was performed
in early works of Scerjanc 
and Manning. 
was limited only to dilute polyelectrolyte solutions and can
not be applied to gels where efficient polymer coils may be
overlapping. This makes gels akin to semi-dilute polyelec-
trolyte solutions. Theoretical consideration of the enthalpy
of dilution in such solutions was made in ref. 
have used this approach for the enthalpy of swelling of
Following ref. 
we consider a system of strongly
charged cross-linked polyelectrolyte chains with counter-
ions in a salt-free solution. The average distance between
chains is much less than their contour length between cross-
links. The total electrostatic energy of the gel may be
separated into the following parts:
Etot ¼ Ea þ ED þ Eel ð4Þ
Ea is the energy of the counter-ions adsorbed on the charged
ED is the Debye electrostatic energy of the ionic system;
Eel is the elastic energy of the stretched charged chains.
The expressions for these terms were taken from ref. 
Ea ¼ e2Na
2bD ð1 � b2Þlnj2 ð5Þ
ED ¼ � e2Na
� �3=2 ffiffiffiffiffiffiffiffiffiffiffi 8puj
Eel ¼ e2Na
� �5=7 u�2=7
� �10=7 ð7Þ
e is the elementary charge, a the monomer length, b the
distance between charges in the polyelectrolyte chain, D the
dielectric constant, and u is the charge density parameter
u ¼ e2
It was shown in ref. 
that parameter u � 1 for strong polyelectrolytes, and this value was used in further analysis. Parameter b is the fraction of ‘‘free’’ counter-ions in the gel network; (1 � b) being the fraction of counter-ions
Figure 2. Apparent binary interaction parameter in potassium polyacrylate hydrogels at 298 K. Fraction of potassium acrylate monomer units: 0% (1), 11% (2), 25% (3), 39% (4).
1434 A. P. Safronov, Y. A. Smirnova, G. H. Pollack, F. A. Blyakhman
Macromol. Chem. Phys. 2004, 205, 1431–1438 www.mcp-journal.de � 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
‘‘condensed’’ at charged macromolecular chains. b is eval- uated implicitly from the following equation:
ln 1 � b b
¼ ln j1�ub2 1 � j2
Taking into account that the swelling results in negligible changes of the total volume of the liquid system, we may calcu- late the electrostatic contribution to the enthalpy of swelling directly from the values of the gel’s total electrostatic energy corresponding to a given and equilibrium degree of swelling:
DHeðj2Þ ¼ Etotðj 1 2 Þ � Etotðj2Þ ð8Þ
Since the total electrostatic energy according to Equation
(4)–(7) depends on the distance between charged monomer
units in the polymer chain, DHe will also depend on the degree of ionization of the gel.
The potassium polyacrylate gel contains both acid and
salt monomer units which tend to dissociate in water.
However,the former is averyweakelectrolyte: lessthan 1%
of such monomer units dissociate. Meanwhile, all potas-
sium acrylate monomer units dissociate, providing negative
electric charge on the polymer network arising from the
carboxylate groups and positively charged potassium
counter-ions in the surrounding solution. Therefore, gels
of poly(acrylic acid) were assumed essentially uncharged,
whilegels with the increasing fraction of potassium acrylate
monomer units had increasing degrees of ionization. To be
definite, in the present study we considered the fraction of
potassium acrylate monomer units as the degree of ioniza-
tion of the gel network.
Figure 3 presentsa plot of the electrostatic contributionto
the enthalpy of swelling against the polymer volume
fraction, calculated for PAAc gels with increasing degrees
of ionization. The length of acrylic acid monomer unit was
taken a ¼ 2.6 A, the mean distance between charges in
the chain was calculated as b ¼ a/g. The values of DHe are negative over the entire concentration range. The plots are
concave at high water content (high degree of swelling) and
then almost linear with its decreasing. It is reasonable to
suppose that negative concave part of DHsw plots at low polymer content in Figure 1 stems mainly from electrostatic
Negative values of DHe mean that swelling of polyelec- trolyte gel is favorable as far as electrostatics is involved.
Mathematically, the negative sign of DHe originates from Ea, the energy of the adsorbed counter-ions defined ac-
cording to Equation (5). Physically, swelling decreases the
enthalpy of gel because it changes the fraction of condens-
ed and free counter-ions. At low degree of swelling (high
volume fraction of polymer) counter-ions are mostly
absorbed on the chains. The value of Ea contributes both
from the energy of attraction between counter-ions and
the chain and the energy of repulsion between condensed
counter-ions. The distance between neighboring condens-
ed counter-ions is small and the repulsion between them is
strong. With polymer volume fraction decreasing, some
counter-ions tend to desorb. Each of desorbing counter-ions
‘‘takes away’’ a portion both of repulsion and attrac-
tion. Besides, desorption also increases the mean distance
between counter-ions remaining absorbed and thereby
decreases the repulsion between them, which is a pure gain
Taking into account negative values of DHe we may suppose that the negative sign of DHsw as well as wapp at high water content (Figure 1, 2) stems mostly from electrostatic
interactions in the gel.
The estimation of DHe provided an opportunity to calcu- late excluded-volume contribution to the enthalpy of swel-
ling according Equation (1). Values of DHV are presented in Figure 4. They are large and positive which means poor
Figure 3. Model concentration dependence of electrostatic contribution to the enthalpy of swelling of PAAc gels with 11% (1a), 25% (2a), 39% (3a) of ionized units, and PMAc gels with 13% (1b), 30% (2b), 47% (3b) of ionized units.
Figure 4. Contribution of excluded-volume interactions to the enthalpy of swelling of potassium polyacrylate hydrogels. Frac- tion of potassium acrylate monomer units: 0% (1), 11% (2), 25% (3), 39% (4).
Enthalpy of Swelling of Potassium Polyacrylate and Polymethacrylate Hydrogels . . . 1435
interaction between solvent and polymer. Positive DHV values fit fairly well linear regressions for each degree of
ionization. The slope of linear regression increases with the
degree of ionization.
Data presented in Figure 4 show that once electrostatic
contribution to the enthalpy of swelling is eliminated, the
enthalpy of swelling fairly well obeys the predictions of the
Flory-Huggins theory over a wide range of gel swelling
[Equation (3)]. In terms of solution concentration, this
range corresponds to semi-dilute and moderately concen-
trated regimes. Table 2 presents the values of w and wRT calculated from the slope of the regressions in Figure 4
using Equation (3). Note that w is positive for the uncharged PAAc gel. Ionization leads to further substantial increase in
w values that become well above the critical w ¼ 0.5 for liquid-liquid phase separation in non-electrolyte polymer
solutions. This means that interior gel water is a very poor
solvent for polymer chains. Provided the gel was uncharg-
ed, such solvent quality would inevitably result in gel col-
lapse. However, in polyelectrolyte gels, osmotic pressure of
counter-ions and electrostatic interactions prevent this.
The source of such poor solvent quality cannot be ascer-
tained without any doubt. In fact, any polymer or other
organic substance dissolved in water participates both in
hydrophilic and hydrophobic interactions. For some reason
in charged polyelectrolyte gels, the balance of force is
shifted towards segregation. We may suppose that this is
due to the general disturbance of water solution in the
charged network. Actually, the solvent in this case is not
water anymore, but a water solution of free counter-ions.
Possibly the counter-ions compete with polar groups of the
polymer for hydration shells and thereby make the medium
unfriendly to macromolecules. If so, one would predict the
influence of the nature of counter-ions on the w value in polyelectrolyte gels, which is to be checked in future
Within the scope of the present work we have compared
PAAc gels with its homologue, gels of poly(methacrylic
acid). Figure 5 presents plots of the enthalpy of swelling for
hydrogels of PMAc and its potassium salts with increasing
degree of ionization. Generally they have the same main
features as shown in Figure 1.
However, DHsw is negative for the PMAc gel over the entire concentration range. Plots of DHsw for ionized gels reveal positive values of enthalpy in the intermediate con-
centration range, but less positive than for PAAc gels. On
the contrary, the enthalpy of swelling for dry gels is more
negative. Since this concentration range is under the domi-
nance of polymer glassy structure, this looks quite reason-
able while bearing in mind general difference between
acrylates and methacrylates from the viewpoint of glassy
structure. However, this will not be discussed in the present
work, since we restrict our consideration to the concentra-
tion range of highly and moderately swollen gels.
The experimental plots of DHsw for PMAc gels were treated in the same manner as described above for PAAc
gels. Figure 6 presents plots of wapp calculated directly from DHsw at low and moderate polymer volume fraction by using Equation (3). Qualitatively the plots are the same as
Table 2. Flory-Huggins binary interaction parameter for the hydrogels.
Gel g wRT w
% K � J � mol�1
PAAc 0 0.53 0.21 11 5.07 2.05 25 5.64 2.28 39 6.82 2.76
PMAc 0 �1.25 �0.50 13 2.48 1.00 30 4.93 1.99 47 6.77 2.74
Figure 5. Enthalpy of swelling of potassium polymethacrylate hydrogels in water at 298 K. Fraction of potassium methacrylate monomer units: 0% (1), 13% (2), 30% (3), 47% (4).
Figure 6. Apparent binary interaction parameter in potassium polymethacrylate hydrogels at 298 K. Fraction of potassium methacrylate monomer units: 0% (1), 13% (2), 30% (3), 47% (4).
1436 A. P. Safronov, Y. A. Smirnova, G. H. Pollack, F. A. Blyakhman
for PAAc (Figure 2) except negative values of wapp for the uncharged PMAc gel.
The electrostatic contribution to the enthalpy of swelling
of PMAc gels was calculated according Equation (4)–(8)
using the values of the degree of ionization for these gels
mentioned above. Then, the excluded volume contribution
was determined by subtracting DHe from experimental DHsw values for gels with up to 50% polymer content. The concentration dependence of DHV for PMAc gels is pres- ented in Figure 7. The values fit satisfactorily well linear
regressions that allow calculating Flory-Huggins binary
interaction parameter according to Equation (3). Its values
are presented in Table 2.
Generally, the same dependence is revealed for w as that for PAAc gels: the higher the ionization degree of the gel,
the higher are the positive values of w and the poorer is the quality of the solvent. The possible reason is mentioned
The binary interaction parameter for PMAc gels basic-
ally is lower than that for PAAc. The difference is substan-
tial for uncharged gels: in the case of PMAc w is negative, while PAAc reveals positive values. At first glance this
looks unexpected since monomer units in PMAc contain a
hydrophobic methyl residue and one may a priori suppose
weaker interaction with water in this case. However, one
should take into account that water solutions provide an
opportunity for hydrophobic hydration of non-polar groups.
Although details of this process are still under discussion,
and there is no adequate theory for it, it was shown for
many aqueous solutions [12,19,20]
that hydrophobic hydra-
tion provides exothermic heat effects. Probably, this is due
to the extra structuring of water around hydrophobic
moieties. Hence, we suppose that this might be the reason
why PMAc gels improve the interaction with aqueous
media. A more certain conclusion at this point might be
made by involving temperature studies of the degree of
swelling and phase separation in gels upon heating. It was
shown that hydrophobic hydration leads to LCST (lower
critical solution temperature) in aqueous solution of some
linear polymers. 
However, such studies are beyond the
scope of the present work.
However, as the degree of ionization increases, the
difference between PAAc and PMAc vanishes. This seems
reasonable from the expected influence of charged groups
and ions on water structure. Since original water structure is
disturbed by ions, hydrophobic hydration is suppressed,
details of molecular interactions become obscure, and gels
of different origin reveal rather similar poor interaction with
Enthalpy of swelling of polyelectrolyte poly(acrylic acid)
and poly(methacrylic acid) hydrogels is sensitive to the
water content and to the degree of ionization. At least
three separate contributions to the enthalpy of swelling may
be specified. At low water content the influence of the
tive values of the enthalpy of swelling of dry gels. At high
water content corresponding to almost an equilibrium
degree of swelling the main contribution is from long-range
electrostatic forces between charges located on the gel’s
network and counter-ions. This concentration region is
characterized by negative values of the enthalpy of swel-
ling, which increase with the degree of ionization of the gel.
At intermediate water content the electrostatic contribution
becomes comparable with excluded-volume interactions in
the gel. Non-valent excluded-volume interactions in PAAc
and PMAc charged gels provide positive values of enthalpy
of swelling that tend to grow with the increase in network
charge density. The Flory-Huggins binary parameter of
interaction for these gels is very large and positive both in
the case of apparent value estimated directly from experi-
mental DHsw plots, or the corrected value obtained using theoretical consideration for the electrostatic contribution
to the enthalpy of swelling.
The difference in the enthalpy of swelling between PAAc
and PMAc gels is distinct at zero degree of ionization.
Although the former is usually considered as more hydro-
philic, its interaction with water is weaker. PMAc gels
interact with water exothermically, which may be con-
sidered as manifestation of hydrophobic hydration. While
being ionized, PAAc and PMAc gels become much more
similar. Water becomes a very poor solvent for both. Pos-
sibly this is due to the influence of counter-ions on the
structure of gel’s internal water. In general, the poor quality
of the gel’s internal solvent should definitely be taken into
account when considering phase transitions in charged
PAAc and PMAc hydrogels.
Figure 7. Contribution of excluded-volume interactions to the enthalpy of swelling of potassium polymethacrylate hydrogels. Fraction of potassium methacrylate monomer units: 0% (1), 13% (2), 30% (3), 47% (4).
Enthalpy of Swelling of Potassium Polyacrylate and Polymethacrylate Hydrogels . . . 1437
 K. Dusek, D. Patterson, J. Polym. Sci. A-2 1968, 6, 1209.  T. Tanaka, Phys. Rev. Lett. 1978, 40, 820.  M. Shibayama, T. Tanaka, Adv. Polym. Sci. 1993, 109, 1.  O. Ye. Philippova, Polym. Sci. C 2000, 42, 208.  ‘‘Physical Networks – Polymers and Gels’’, W. Burchard,
S. B. Ross-Murphy, Eds., Elsevier, Amsterdam 1993, p. 231.  ‘‘Polymer Gels and Networks’’, Y. Osada, A. R. Khokhlov,
Eds., Marcel Dekker, New York 2002, p. 381.  A. R. Khokhlov, Polymer 1980, 21, 376.  A. Yu. Grosberg, A. R. Khokhlov, ‘‘Statistical Physics of
Macromolecules’’, AIP, New York 1994.  P. G. De Gennes, Phys. Lett. A 1972, 38, 339.
 I. M. Lifshitz, A. Yu. Grosberg, A. R. Khokhlov, Rev. Mod. Phys. 1978, 50, 683.
 K. Kamide, S. Matsuda,M. Saito, Polym. J. (Tokyo) 1988,20, 31.
 A. P. Safronov, A. Yu. Zubarev, Polymer 2002, 43, 743.  H. Daoust, M.-A. Chabot, Macromolecules 1980, 13, 616.  A. P. Safronov, L. V. Adamova, Polymer 2002, 43, 2653.  M. A. Kabayama, H. Daoust, J. Phys. Chem. 1958, 62,
1127.  M. S. Walas, ‘‘Phase equilibria in chemical engineering’’,
Butterworths, London 1985.  J. Scerjanc, D. Dolar, D. Leskovsek, Z. Phys. Chem.
(Leipzig) 1967, 56, 207.  G. Manning, J. Chem. Phys. 1969, 51, 924.  G. Nemethy, H. A. Sheraga, J. Chem. Phys. 1962, 36,
3401.  [20a] A. A. Tager, A. P.Safronov,S. V. Sharina, I. Yu. Galaev,
Colloid Polym. Sci. 1993, 271, 868; [20b] A. A. Tager, A. P. Safronov, S. V. Sharina, I. Yu. Galaev, Colloid Polym. Sci. 1994, 272, 1234.
1438 A. P. Safronov, Y. A. Smirnova, G. H. Pollack, F. A. Blyakhman