Isothermal Dehydration of the Poly (acrylic-co-methacrylic acid

Oct 6, 2010 - To whom correspondence should be addressed. Tel.: +38111-3336871. Fax: +38111-2187133. E-mail: [email protected]...
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Ind. Eng. Chem. Res. 2010, 49, 11708–11713

Isothermal Dehydration of the Poly(acrylic -co-methacrylic acid) Hydrogel Borivoj Adnadjevic´* and Jelena Jovanovic´ Faculty of Physical Chemistry, Studentski trg 12-16, 11001 Belgrade, Republic of Serbia

The isothermal thermogravimetric dehydration curves of an equilibrium swollen hydrogel of a poly(acrylicco-methacrylic acid) (PAM) hydrogel at temperatures in the range of 293-313 K were determined. By applying a model-fitting method, it was established that the isothermal dehydration of equilibrium swollen PAM hydrogel was a phase-boundary-controlled process with kinetics limited with the rate of the decrease of the area of hydrogel pores. Based on the results of a differential isoconversional method, it was concluded that, in the degree of dehydration range of 0.1 e R e 0.8, the activation energy is independent of the degree of dehydration, whereas, for R > 0.8, it decreases with increasing degree of dehydration. It is assumed that the kinetics of the isothermal dehydration of hydrogel is determined with the changes in the fluctuation structure, because of dehydration. It is established that the dominant effect on the kinetics of dehydration of PAM hydrogel in the range of 0.1 e R e 0.8 is referred to as a so-called “λ-relaxation process”, whereas in the range of R g 0.8, it is the so-called “R-relaxation process” in hydrogels. 1. Introduction Hydrogels represent an important class of smart materials, which have important application in various fields such as medicine, pharmacy, hygienic devices, agrochemistry, and ecology. Hydrogels can be applied as carriers for controlled and target drug release, artificial muscles, regenerative tissues, as well as being used as a replacement for soft tissues, coating for burns, artificial cartilage, artificial glottis, contact lenses, biosensors, textile materials for special applications, superabsorbents for hygienic devices, in agriculture and horticulture either as carriers for agrochemicals or reservoirs for water.1,2 The synthesis of hydrogels based on acrylic acid, as well as methacrylic acid and their copolymers, and the influence of the temperature and pH of the surrounding medium on the equilibrium degree of swelling and the swelling kinetics, have been described in the literature.3-8 The kinetics of the isothermal dehydration of equilibrium swollen poly(acrylic acid) (PAA) hydrogels has been investigated.9,10 Applying the model-fitting method, Jankovic et al.9 established that a change in dehydration temperature caused a change in the dehydration kinetics model. Adnadjevic et al.10 established that the isothermal dehydration of the PAA hydrogel can be mathematically described by a Weibull distribution function (WDF) of the reaction times. The objective of this paper was to determine the kinetics model and the kinetic parameters (activation energy (Ea) and preexponential factor (ln A)) of the isothermal dehydration of the PAM hydrogel and to establish the effect of methacrylic acid as a comonomer unit in the hydrogel polymer network on the kinetic parameters as well as on the model of the kinetics of dehydration. 2. Materials and Methods 2.1. Materials. Materials for hydrogel synthesis: acrylic acid (99.5%) (AA) and methacrylic acid (MA) were supplied by Merck KGaA (Daramsatdt, Germany). N,N-methylene bisacrylamide (p.a.) (MBA) was purchased from Aldrich Chemical Co. (Milwaukee, WI, USA). The initiator, 2,2-azobis-[2-(2-imidazolin-2-yl)-propane] dihydrochloride (VA044), (99.8%) was supplied from Wako Pure Chemicals Industries, Ltd. (Osaka, Japan). Sodium carbonate (Na2CO3) (p.a.) was obtained from Merck KGaA (Darmstadt, Germany). * To whom correspondence should be addressed. Tel.: +381113336871. Fax: +38111-2187133. E-mail: [email protected].

2.2. Hydrogel Synthesis. The poly(acrylic acid-co-methacrylic acid) hydrogel (PAM) was synthesized using a procedure based on radical polymerization of acrylic acid and methacrylic acid (1:1 mol ratio), and cross-linking of the polymers formed, using the previously described procedure,11 which consists of the following. A 20 wt % solution of acrylic acid and methacrylic acid (1/1 (mol/mol)) was prepared and mixed with 0.1 wt % solution of MBA. After stirring well to ensure homogeneity of the reaction mixture and nitrogen bubbling through the mixture for half an hour, the initiator solution (0.06 mol % of the monomer) was added and the reaction mixture was once again rapidly stirred and bubbled with nitrogen for an additional 20 min. Immediately, the prepared reaction mixture was poured into glass molds and placed in an oven at 80 °C for 5 h. Then, the obtained gel-type product was transformed to the Na+ form (60%) by neutralization with a 3% solution of Na2CO3. The resulting hydrogel was stamped into approximately equally sized discs and immersed in excess distilled water. The water was changed every 5 h, except overnight for seven days to remove the sol fraction of polymer and unreacted monomer. Subsequently, the washed-out hydrogel was dried in an air oven in the temperature regime of 80 °C for 2 h, 90 °C for 3 h, and 105 °C to constant mass. The obtained product (xerogel) was stored in a vacuum exicator until use. 2.3. Equilibrium Swelling Degree and Xerogel Structural Properties. The equilibrium swelling degree (SDeq) for distilled water at 298 K was determined via ordinary gravimetric procedures.11 The following structural properties of the synthesized poly(acrylic-co-methacrylic acid) xerogel were calculated: xerogel density (Fxg), average molar mass between the network cross-links (Mc), degree of cross-linking (Fc), the number of elastically effective chains totally induced in a perfect network per unit volume (Ve), and the distance between the macromolecular chains (d). Xerogel densities of the synthesized samples were determined by measurements with the pycnometer method, using the equation Fxg )

mxgFT m1 + mxg - m2

(1)

where mxg is the weight of the xerogel sample; m1 the weight of pycnometer filled with toluene, used as the nonsolvent; m2 the weight of pycnometer filled with toluene and with xerogel sample in it; and FT the density of the toluene (FT ) 0.864 g/cm3).

10.1021/ie9016896  2010 American Chemical Society Published on Web 10/06/2010

Ind. Eng. Chem. Res., Vol. 49, No. 22, 2010 Table 1. Equilibrium Degree of Swelling and Basic Structural Properties of the PAM Xerogel structural property

value

SDeq Fx Mc Fc d

197 g/g 1200 kg/m3 227 000 g/mol 6.1 × 10-6 mol dm-3 240 nm

R)

Mc )

ln(1 - υ2,s) + υ2,s + χυ2,s2

(2)

where VH2O is the molar volume of H2O, υ2,s the polymer volume fraction in the equilibrium swollen state, and χ the FloryHuggins interaction parameter between the solvent (H2O) and the polymer. The values of υ2,s and χ were calculated by the following expressions: υ2,s ) χ)

1 1 + FxgSDeq

(3)

ln(1 - υ2,s) + υ2,s υ2,s

The cross-linking degree was calculated as Fc )

13

M0 Mc

(5)

where M0 is the molar mass of the repeating unit. The linear distance between two adjacent crosslinks was calculated as

[ ( )]

d ) lυ2,s-1/3 2Cn

Mc M0

(7)

3. Methods Used To Evaluate the Kinetics Model and Kinetic Parameters The kinetics model and kinetic parameters were evaluated by applying the following methods. 3.1. Model-Fitting Method. According to the model-fitting method, the kinetics reaction models are classified into five groups, depending on the reaction mechanism: (1) power law reaction, (2) phase-boundary controlled reaction, (3) reaction order, (4) reaction described by the Avrami equation, and (5) diffusion-controlled reactions. The model-fitting method is based on the following. The experimentally determined conversion curve Rexp ) f(t)T must be transformed to the normalized conversion curve Rexp)f(tN)T, where tN is the so-called normalized time. The normalized time (tN) was defined by the equation tN )

(4)

2

m0 - m m0 - mf

where m0, m, and mf refer to the initial, actual, and final mass of the sample. The isothermal conversion curve represents the dependence of the degree of conversion (R) on the reaction time (t) at a constant experimental temperature (T).

The value of Mc was determined using eq 2, as proposed by Flory and Rehner:12 -FxgVH2Oυ2,s1/3

11709

1/2

(6)

Here, Cn is the Flory’s characteristic ratio and l is the carbon-carbon bond length.14 The equilibrium swelling degree and basic structural properties of the PAM xerogel that was used in this investigation are presented in Table 1. The PAM xerogel used in this investigation has slightly crosslinked network, with chains between crosslinks with an average molar mass of Mc ) 2.27 × 105 g/mol. The polymer network is porous, with mean pore diameters of 240 nm. Because of the lower density of crosslinking (Fc ) 5.6 × 10-6 mol/cm3) of the polymer network, the PAM has a higher equilibrium degree of swelling of 197 g/g and differs from the PAA xerogel in all other structural properties of the previously investigated PAA hydrogel. 2.4. Thermogravimetric Measurements. The isothermal thermogravimetric curves were recorded by a simultaneous differential scanning calorimetry-thermogravimetric analysis (DSC-TGA) thermal analyzer (Model 2960, TA Instruments, New Castle, DE, USA). The analyses were performed with 20 ( 2 mg samples of equilibrium swollen hydrogel in platinum pans under a nitrogen atmosphere at a gas flow rate of 10 mL min-1. Isothermal runs were performed at nominal temperatures of 293, 298, 303, 308, and 313 K. The samples were heated from the start to the selected dehydration temperature at the heating rate of 300 K/min and then held at that temperature for a given reaction time. The degree of dehydration (R) is expressed as

t t0.9

(8)

where t0.9 is the moment in time at which R ) 0.9.15 The kinetics model of the investigated process was determined by analytically comparing the normalized conversion curves with the normalized model’s conversion curves. The chosen kinetics model is the one for which the sum of squares of the residual of the models normalized curve is minimal. A set of the reaction kinetics models used to determine the model that best describes the kinetics of the process of PAM isothermal dehydration is shown in Table 2.15,16 3.2. Determination the Dependence of Activation Energy on the Degree of Dehydration. The activation energy of investigated dehydration for various dehydration degrees was established by the Friedman method,17 which is based on the following. The rate of the process in the condensed state is generally a function of temperature and conversion: dR ) Φ(T, R) dt

(9)

dR ) k(T)f(R) dt

(10)

i.e.,

where dR/dt is the reaction rate, Φ(T,R) is function of R and T, R the degree of conversion, k(T) the rate constant, t the time, T the temperature, and f(R) the reaction model associated with a certain reaction mechanism. The dependence of the rate constant on temperature is ordinarily described by the Arrhenius law:

( )

k(T) ) A exp -

Ea RT

(11)

where Ea is the activation energy, A the pre-exponential factor, and R the gas constant. We then get the following equation:

( dRdt ) ) A exp(- RT )f(R) Ea

(12)

Accepting the fact that the reaction rate constant is an extent of conversion and is only a function of temperature, which is

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Table 2. Set of Kinetics Models Used To Determine the Kinetics Model of the Dehydration of the PAM Hydrogel model P1 P2 P3 P4 R1 R2 R3 F1 F2 F3 A2 A3 A4 D1 D2 D3 D4

general expression of the kinetics model

reaction mechanism power law power law power law power law zero-order (Polany-Winger equation) phase-boundary controlled reaction (contracting area, i.e., bidimensional shape) phase-boundary controlled reaction (contracting volume, i.e., tridimensional shape) first-order (Mampel) second-order third-order Avrami-Erofe’ev Avrami-Erofe’ev Avrami-Erofe’ev one-dimensional diffusion two-dimensional diffusion (bidimensional particle shape) three-dimensional diffusion (tridimensional particle shape), Jander equation three-dimensional diffusion (tridimensional particle shape), Ginstling-Brounshtein

known as the isoconversional principle of Friedman, eq 12 can be easily transformed to

integral form of the kinetics model

f(R) 4R3/4 3R2/3 2R1/2 (2/3)R-1/2 1 2(1 - R)1/2

g(R) R1/4 R1/3 R1/2 R3/2 R [1 - (1 - R)1/2]

3(1 - R)2/3

[1 - (1 - R)1/3]

1-R (1 - R)2 (1 - R)3 2(1 - R)[-ln(1 - R)]1/2 3(1 - R)[-ln(1 - R)]2/3 4(1 - R)[-ln(1 - R)]3/4 (1/2)R 1/[-ln(1 - R)]

-ln(1 - R) (1 - R)-1-1 0.5[(1 - R)-2 - 1] [-ln(1 - R)]1/2 [-ln(1 - R)]1/3 [-ln(1 - R)]1/4 R2 (1 - R) ln(1 - R) + R

3(1 - R)2/3/2[1 - (1 - R)1/3]

[1 - (1 - vR)1/3]2

(3/2)[(1 - R)-1/3 - 1]

[1 - (2R/3)] - (1 - R)2/3

The experimentally obtained isothermal conversion curves (the dependence of R versus time) at different operating temperatures for the PAM hydrogel dehydration are given in Figure 1. The conversion curves of PAM dehydration are of characteristic shape and exhibit three specific shapes of changes in the degree of dehydration (conversion) relative to dehydration time. Actually, these shapes are a linear stage, a nonlinear stage, and a saturation stage (plateau). With increasing dehydration temperature, the slope of the linear change in the degree of dehydration of PAM hydrogel versus time decreases while the

duration of both linear and nonlinear changes decreases, for all dehydration temperatures. Figure 2 presents the isothermal changes in dehydration rate, relative to the degree of dehydration. At all of the investigated temperatures, the rate of dehydration linearly decreases with increasing degree of dehydration. The maximal dehydration rate is achieved at a small degree of dehydration, i.e., when R f 0. Based on the established shape of changes in the rate of dehydration with the degree of dehydration, it may be assumed that the dehydration rate was not controlled by the rate of the diffusion process but by the rate of the decrease in interface of surface.18 With the intention of proving this hypothesis, the kinetics model of the PAM hydrogel dehydration was determined by applying a model-fitting method. The normalized conversion curves of the PAM dehydration were determined (Re vs tN) and are presented in Figure 3. The normalized conversion curves of the PAM hydrogel dehydration at all of the investigated temperatures are identical, which indicate the same kinetics model of dehydration, independent of temperature within the investigated temperatures. By analytically comparing the expression Re ) f(tN) with the

Figure 1. Isothermal conversion curves of the PAM hydrogel dehydration at 293, 298, 303, 308, and 313 K.

Figure 2. Changes of dehydration rate of the PAM hydrogel with dehydration degree at 293, 298, 303, 308, and 313 K.

( dRdt )

ln

R

) ln(A + f(R)) -

Ea,R RT

(13)

This allows evaluation of the activation energy for a particular degree of conversion. 4. Results and Discussion

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Table 3. Effect of Isothermal Dehydration Temperature on the kM Values and Kinetic Parameters of the PAM Hydrogel Dehydration Isothermal Process temperature, T (K)

km (min-1)

range of applicability, R (%)

293 298 303 308 313

0.0052 0.0077 0.0109 0.0159 0.0236

95 99 95 99 99

Ea ) 54.5 ( 0.5 kJ/mol ln A ) 18.26 ( 0.1 (A expressed in units of min-1)

The change of dehydration rate, relative to the degree of dehydration, is dR ) 2kM(1 - R)1/2 dt Figure 3. Normalized conversion curves of the PAM dehydration at 293, 298, 303, 308, and 313 K.

Figure 4. Plot of [1 - (1 - R)1/2] versus time for the PAM dehydration at 293, 298, 303, 308, and 313 K.

normalized models conversion curves R ) f(tN) for different solid-state reaction models, it was found that the PAM hydrogel dehydration can be described by the phase-boundary-controlled reaction model (contracting area), for which the following expression is valid: [1 - (1 - R)1/2] ) kMt

(14)

where kM is the model rate constant. When the PAM hydrogel dehydration can be described by eq 14, the dependence of [1 - (1 - R)1/2] on time should give straight lines, whose slopes give the kM values. The dependence of [1 - (1 - R)1/2] on time for the PAM dehydration at different temperatures is presented in Figure 4. Since the plot of [1 - (1 - R)1/2] versus time for the PAM dehydration gives a straight line at all of the investigated temperatures, in the range of R ) 0-0.95, it can be stated, with great certainty, that the kinetics of the PAM hydrogel dehydration is determined by eq 14. The established kinetic model of isothermal dehydration of hydrogel enables one to derive an analytical expression for the conversional dehydration curve: R ) kM t - 2kMt 2

(15)

(16)

The obtained analytical expressions for R ) f(t) and dR/dt ) f(R) completely describe the established experimental conversion curves and calculated changes of dR/dt ) f(R). The effects of temperature of isothermal dehydration on the kM values and kinetic parameters of the PAM hydrogel dehydration isothermal process are given in Table 3. Because the kM values exponentially increase with temperature, it was possible to determine the model’s kinetic parameters, the activation energy (Ea,M), and the pre-exponential factor (ln AM), using the Arrhenius equation, which are also presented in Table 3. Based on the previously presented results, it may be concluded that the introduction of methacrylic acid as a copolymer unit of polymer chains of poly(acrylic acid) leads to the considerable changes in the mechanism and kinetics of dehydration of absorbed water (change in the kinetics models and a significant increase in the values of the kinetic parameters (Ea, ln A)). Keeping in mind that the kinetics of dehydration is determined with the rate of decreasing interface of surface and that the activation energy of dehydration is higher than the enthalpy of water evaporation, it may be concluded that the established changes are consequence of the differences in the structure of the absorbed water in PAM and PAA hydrogel. This assumption is consistent with the theoretical calculation of Tamai et al.,19 by which the introduction of methacrylic acid in a polymer chain of poly(acrylic acid) leads to the increase in the so-called hydrophobic interaction between the polymer network and absorbed water molecules. This causes the formation of specific structures of clusters and leads to changes in the structure of the absorbed water in the PAM hydrogel. The calculated kinetic parameters and the established kinetics model of the PAM hydrogel dehydration isothermal process enable us to propose a possible mechanism for that process. In agreement with the definition by Peppas,20 free space between macromolecular chains of hydrogel exists. This space is often regarded as a “pore”. A structural parameter that is often used in describing the size of the pores is the correlation length, mesh size (d), which is defined as the linear distance between two adjacent crosslinks. If we suppose that, during the dehydration, d linearly decreases with time, then we can write the following equation: d ) d 0 - kdt

(17)

where d is the mesh size at time t, d0 the mesh size at time t0, and kd the rate constant of the decrease in d. Assuming that the pore has a cylindrical shape for that type of pore, the volume

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of the absorbed water in the pore is Vp ) 0.785d2H, where H is the cylinder height. For n number of pores, the volume of the adsorbed water in the equilibrium swollen hydrogel would be the V0 ) 0.785 nd2H. Because weight is defined as weight ) volume × density (F) the weight of n cylindrical pores is m0 ) 0.785nFHd2. By definition, R)

m0 - m m0

(18)

Therefore, for n pores, R)

0.785nFHd02 - 0.785nFHd2 0.785nFHd02 R)1-

(19) Figure 5. Dependence of ln(dR/dt) on 1/T for different degrees of dehydration.

2

d d02

(20)

Substituting the value of d from eq 17 gives R)1-

(

d0 - kdt d0

)

(21)

)

(22)

2

which can be rearranged to give 1-R)

(

d0 - kdt d0

2

If km )

kd d0

(23)

we get 1 - (1 - R)1/2 ) kMt

(24)

The obtained form of eq 24 is equal to the previously determined kinetics model of the isothermal dehydration of the PAM hydrogel, which confirms the previously assumed kinetics model of dehydration of the PAM hydrogel. To investigate the possible effects of the degree of dehydration of the investigated dehydration process, the kinetic parameters of PAM hydrogel dehydration were determined by applying the iso-conversional method. Using that method, the kinetic parameters were determined for different degrees of dehydration. The dependence of ln(dR/dt) on inverse temperature (1/T) are given in Figure 5 for different degrees of dehydration. Because the dependence of ln(dR/dt) on 1/T for all degrees of dehydration gives a straight line, based on their slopes and intercepts, the kinetic parameters of PAM hydrogel dehydration (Ea and ln A) were determined. Figure 6 presents the dependence of Ea on the degree of dehydration. The activation energy of the isothermal dehydration process of PAM hydrogel in the degree of dehydration range of 0.1 e R e 0.8 is practically independent of the degree of dehydration. In contrast to that, for R > 0.8, the activation energy decreases with increasing degree of dehydration. The independence of activation energy on the degree of dehydration and its very good consistency with the value of the model’s activation energy implies an elementary kinetics character (overall single-stage) of the investigated dehydration process in that range of the dehydration degree and confirms the validity of the suggested kinetics model of dehydration.

Figure 6. Dependence of the Ea on the degree of dehydration.

Bearing in mind that the activation energy values for the entire range of degrees of dehydration are higher than the enthalpy of water evaporation, it can be assumed that the physical state of water in the absorbed hydrogel is different than the physical state of ordinary water. The high value of activation energy for the investigated dehydration process and its characteristic dependence on the dehydration degree can be explained in the following manner. Swollen hydrogel is a viscoelastic system,21 and dehydration leads to the decreasing mass and volume, which means that one can assume that, in the dehydration process, hydrogel presents a fluctuation structure. In that case, the kinetics of dehydration is determined with the kinetics of the structural changes in the fluctuation structure (i.e., submolecular structure of hydrogel as a whole). Because the Ea value is ∼57 kJ/mol in the conversion range of 0.1 e R e 0.8, we can claim, with great certainty, that the basic structural change in the hydrogel caused by the dehydration is destroying ordered microblocks that are interconnected in a unique network. Therefore, the dominant effect on the kinetics of dehydration has the so-called “λ-relaxation process” connected with the rearrangement of submolecular structure (i.e., with the destroying and re-establishing the microblocks of fluctuating structure). For that process, an activation energy of Ea) 50-60 kJ/mol is characteristic, as well as a relaxation time of τ ) 6.0 × 10-2-1.3 × 10-2 s, and a linear dimension of the kinetics unit that is defined as l ) 25-50 nm.22 The calculated values of mesh size for t ) 0 correspond well with the linear dimension of the kinetics unit. In contrast, decreasing values of the activation energy of the dehydration process for degrees

Ind. Eng. Chem. Res., Vol. 49, No. 22, 2010

of dehydration of R g 0.9 are related to a loss of elasticity of free segments of the hydrogel network (i.e., with the hydrogel transition from the viscoelastic state to the glassy state). Dominant effects on the kinetics of dehydration then have the so-called “R-relaxation process”, for which the following values are characteristic: Ea ) 45-50 kJ/mol; τ ) 1.3-0.1 × 10-3 s, and l ) 2-3 nm. 4. Concluding Remarks The introduction of a methacrylic acid group into a polymer chain of poly(acrylic acid) leads to changes in the kinetics model and increases in the kinetic parameters of dehydration. The isothermal dehydration of the equilibrium swollen PAM hydrogel is a phase-boundary-controlled process with kinetics that are limited by the rate of the decrease of surface of hydrogel pores. The isothermal dehydration conversion curves were defined by the expression R ) km2t2 - 2kmt and the change in the rate of dehydration with the degree of dehydration is defined by the equation dR ) 2km(1 - R)1/2 dt The dehydration kinetics of the PAM hydrogel is predetermined with the kinetics of structural changes in fluctuation in the hydrogel structure caused by the dehydration. In the range of 0.1 e R e 0.8, dominant effect is the so-called “λ-relaxation process”, whereas in the range of R g 0.8, it is the so-called “R-relaxation process” (i.e., processes of transition to a glassy state). Acknowledgment This investigation was supported by the Ministry of Science and Technical Development of the Republic of Serbia (through Project No. 142025G).

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ReceiVed for reView October 28, 2009 ReVised manuscript receiVed August 26, 2010 Accepted September 1, 2010 IE9016896