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Journal Article And Discuss How Thermodynamics Is Applied By The Authors

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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:

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

Patterson, [1]

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. [2]

Since then

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.

[11] 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

polymer gels.

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. [12]


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.

Experimental Part

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 � 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. [13]

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

so far.

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. [14]

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 � 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. [16]

. 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 [17]

and Manning. [18]

However, it

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. [12]


have used this approach for the enthalpy of swelling of

polyelectrolyte gels.

Following ref. [12]

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. [12]

Ea ¼ e2Na

2bD ð1 � b2Þlnj2 ð5Þ

ED ¼ � e2Na


b D

� �3=2 ffiffiffiffiffiffiffiffiffiffiffi 8puj

p ð6Þ

Eel ¼ e2Na




� �5=7 u�2=7

b D

� �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

defined by:

u ¼ e2


It was shown in ref. [8]

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 � 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

in enthalpy.

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

Macromol. Chem. Phys. 2004, 205, 1431–1438 � 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim



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

Macromol. Chem. Phys. 2004, 205, 1431–1438 � 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim



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. [20]

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

polymer’sglassy structuredominates,providinglargenega-

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

Macromol. Chem. Phys. 2004, 205, 1431–1438 � 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim



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