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The effects of microwave heating on the kinetics of isothermal dehydration of equilibrium swollen poly(acrylic-co-methacrylic acid) hydrogel.


Hydrogels are three-dimensional cross-linked polymeric structures that have the capability to swell in aqueous environments [1], Hydrogels are considered of great significance in various fields like medicine, pharmacy, hygienic devices, agrochemistry, and ecology. The widest practical application of hydrogels, particularly in agrochemistry and ecology, is based on their ability to reversibly absorb (swelling) and release (dehydrate) water [2, 3], In order to optimize their applications, it is very important to know the mechanism and kinetics of both hydrogel swelling and hydrogel dehydration. The swelling behaviour and swelling kinetics of various types of hydrogels have been extensively studied [4, 5], However, the mechanism and kinetics of the dehydration of hydrogels has not been sufficiently studied.

Hawlader et al. used a one-dimensional diffusion model to describe the heat and the mass transfer, from the wet to the dry region of the hydrogel, during its drying process [6]. The kinetics of water diffusion, during the drying of polyacrylamide hydrogel, was investigated by Roquez with associates [7]. Kemp et al. has examined the applicability of a variety of kinetic models to fit the kinetics of hydrogels in the process of drying [8]. The mechanism of drying polyacrylamide hydrogel, based on the changes in fluorescent spectra during drying, was presented in the research of Evinger et al. [9].

The normalized Weibull function of probability distribution of the dehydration time was used for modelling the kinetics of both the isothermal and the nonisothermal dehydration of equilibrium swollen poly(acrylic acid) hydrogel in the work of Adnadjevic et al. [10]. The kinetics of isothermal dehydration of the equilibrium swollen poly (acrylic-co-methacrylic acid) hydrogel (PAM) was explained by the existence of energetic distribution of the dehydration centres [11], In the work of Adnadjevic et al. it is shown that the kinetics of the isothermal dehydration of PAM hydrogel is kinetically limited by the rate of the changes in the fluctuation structure of the hydrogel caused by dehydration. The dominant effect on the kinetics of dehydration of PAM hydrogel, in the range of 0.1 [less than or equal to] [alpha] [less than or equal to] 0.8, is referred to as the so-called "[lambda]-relaxation process," whereas in the range of [alpha] [greater than or equal to]0.8, it is referred to as the "[alpha]-relaxation process" in hydrogels [12].

Siorousazar et al. investigated the kinetics of isothermal dehydration of the polyvinyl alcohol nanocomposite hydrogels containing Na-montmorillonite nanoclay and found that the kinetics can be best described with the power-law equation and that the dehydration mechanism changes with temperature. At the temperature of 293 K, the dehydration kinetic can be described as a non-Fickian diffusion, whereas at temperatures higher than 310 K, it proceeded as Fickian diffusion [13].

Microwave heating (MWH) significantly accelerates the rate of chemical reactions, gives higher yields of the products and improves the properties of the products, which is the reason why the use of microwaves has started attracting more and more attention [14], Microwave heating is a widely accepted, nonconventional energy source for organic synthesis [15], polymer synthesis [16], material science [17], and different physicochemical processes, such as sintering [18], nucleation and crystallization [19], adsorption [20], and so forth. The effect of microwave irradiation on the kinetics of chemical reactions is explained by thermal effects, such as overheating, hot-spots, selective heating or as the consequence of specific microwave effects [14, 21].

Based on detailed literature survey, to the best of our knowledge, there is no existing data on the kinetic of isothermal dehydration of the PAM hydrogel or other hydrogels under the isothermal microwave heating. Jaya and Durance [22] investigated the effects of microwave power on vacuum drying kinetics of alginate-starch gel. In spite of that, there has been extensive research on microwave drying of biomaterials examining a broad spectrum of fruits and vegetables and their kinetics [23-25].

Keeping in mind that the introduction of a hydrophobic methacrylic acid as a copolymer unit of polymer chain of poly(acrylic acid) could lead to the changes in the physical state of the water absorbed and the kinetics of dehydration in comparison to poly(acrylic acid) hydrogel, the major objectives of this work are as follows: (1) to study comprehensively the kinetics of isothermal dehydration of synthesized PAM hydrogel in the conditions of microwave heating, (2) to compare the kinetics data of isothermal dehydration in the conditions of conventional heating to those in microwave heating, and (3) to postulate the novel mechanism of the effects of microwave heating on the kinetics of hydrogel dehydration.



Acrylic acid (99 wt%) and methacrylic acid (99 wt%) were supplied by Merck KGaA, Daramsathd, Germany, stored in a refrigerator and melted at room temperature before use. AVV-methylene bisacrylamide (p.a) (MBA) was purchased from Aldrich Chemical, Milwaukee. The initiator, 2,2-azobis-[2-(2-imidazolin-2-il)-propane] dihydrochloride (VA-044) was supplied by Wako Pure Chemical Industries, Osaka, Japan. Sodium carbonate ([Na.sub.2]C[O.sub.3]) (p.a) and toluene (p.a) were obtained from Merck KGaA, Daramsathd, Germany. Buffer solutions and the O.IN HC1 standardized solution were supplied by Zorka-Pharma, Sabac, Serbia. Distilled water was used in all experiments. The buffers of pH = 4 and pH = 7 were potassium dihydrogenphosphate-disodium hydrogen phosphate and the buffers of pH = 9 was borax-hydrochloric acid solution.

Hydrogel Synthesis

The poly(acrylic acid-co-methacrylic acid) hydrogel (PAM) was synthesized in a procedure based on free-radical crosslinking copolymerization of acrylic acid and methacrylic acid (1:1 mol ratio) 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 the 0.1 wt% solution of MBA. After being stirred well and nitrogen bubbled 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 another 20 min. Immediately, the prepared reaction mixture was poured into glass molds and placed in an oven at 353 K for 5 h. Afterwards, the obtained gel-type product was transformed into the [Na.sup.+] form (60%) by neutralization with 3% solution of [Na.sub.2]C[O.sub.3]. The resulting hydrogel was stamped into approximately equally sized discs and immersed into excess distilled water. The water was changed every 5 h, except during night time, for 7 days, in order to remove the sol fraction. Subsequently, the washed-out hydrogel was dried in an air oven in the temperature regime 353 K for 2 h, 363 K for 3 h and 378 K to constant mass. The obtained product (xerogel) was stored in a desiccator until further use.

Determination of the Swelling Degree and Equilibrium Swelling Degree

The swelling degree (SD) and equilibrium swelling degree ([SD.sub.eq]) was determined in distilled water at different temperatures: 298, 303, and 313 K and for buffer solutions at 298 K, by ordinary gravimetric procedure [5]. For every pH value and temperature, swelling measurements from at least three samples were taken and the mean values were used.

Determination of the Xerogel Density

The xerogel density ([[rho].sub.xg]) of the synthesized sample was determined by the method of pycnometer [5].

Xerogel Structural Properties

The following structural properties of the synthesized poly (acrylic-co-methacrylic acid) xerogel: average molar mass, between the network crosslinks ([M.sub.c]), crosslinking degree ([[rho].sub.c]), the number of elastically effective chains totally induced in a perfect network per unit volume ([V.sub.e]) and the distance between the macromolecular chains (d), have been determined by the method of Gudeman and Peppas [26].

ATR-FTIR Spectroscopy

ATR-Fourier transform infrared spectra of synthesized PAM xerogel was recorded by Thermo Scientific Nicolet 67000 FT-IR, with a Smart Orbit adapter. The diamond background sample spectra was obtained during 16 scans and the sample spectra was obtained during 32 scans.

Dehydration under Microwave Heating

The isothermal dehydration of the PAM hydrogel under microwave heating (MWH) was investigated by using a new, own-constructed device. The samples of the equilibrium swollen hydrogel with average weight of 500 [+ or -] 10 mg were placed into a pan made out of teflon. The pan with the sample was attached for teflon's filament and connected with the analytical balance to measure the changes in the sample weight with [+ or -]0.1 mg accuracy. The analytical balance was connected through an interface to the PC processor in order to perform continuous measurements of the sample weight during the dehydration at defined temperature. The Balint software was used for this purpose. The teflon's filament, along with the pan, was placed in the central part of a commercially available monomode microwave unit (Discover, CEM Corporation, Matthews, NC). The machine consists of a continuously focused microwave power delivery system with an operator selectable power output from 0 W to 300 W. All the dehydration processes were done in a microwave field of 2.45 GHz. The microwave unit was modified with a device to keep the temperature under isothermal MW measurements. The used microwave unit automatically maintains the required temperature in the reaction system by rapid variation (every few seconds) in input power and/or in [N.sub.2] flow change. When the sensor of the instrument detects a decrease in the temperature of the reacting system in comparison to the required temperature, the input power of the microwave field automatically increases and [N.sub.2] flow decreases, and opposite, when an increase in temperature in the reacting system is detected the input power of the microwave field is automatically decreased and [N.sub.2] flow is increased in order to achieve the desired temperature.

The isothermal dehydration of the PAM hydrogel was performed at the temperatures of 293, 303, 313, 323, and 333 K. The temperature of the hydrogel was monitored by using a calibrated fiber-optic probe inserted into the device. The temperature was measured with the accuracy of [+ or -] 1 K. The temperature, pressure, and profiles were monitored using commercially available software provided by the manufacturer of the microwave reactor.

The degree of the dehydration was calculated as:

[alpha] = [m.sub.0] - m/[m.sub.0] - [m.sub.f] (1)

where [m.sub.0], m, [m.sub.f] refer to the initial, actual and final mass of the sample respectively. The isothermal conversion curve represents the dependence of the degree of conversion ([alpha]) on the reaction time (t) at constant experimental temperature (T).


The kinetic model of dehydration and the values of the kinetic parameters were evaluated with the application of the following methods.

Model-Fitting Method

According to the model-fitting method, kinetic reaction models of solid state are classified in five groups, depending on the reaction mechanism: (1) power law reaction, (2) phase-boundary controlled reaction, (3) reaction order, (4) reaction explained with the Avrami equation, and (5) diffusion controlled reactions. The model-fitting method is based on the following. The experimentally determined conversion curve [[alpha].sub.exp] = f[(t).sub.T] must be transformed into the experimentally normalized conversion curve [[alpha].sub.exp] = f[([t.sub.N]).sub.T], where [t.sub.N] is the normalized time [t.sub.N], which was defined with the equation:

[t.sub.N] = t/[t.sub.0.9] (2)

where [t.sub.0.9] is the moment in time in which [alpha] = 0.9 [27]. The kinetic model of the investigated process was determined by analytically comparing the normalized experimental conversion curves with the normalized model's conversion curves. The kinetics model of the researched process corresponds to the one for which the sum of squares of the deviation of its normalized conversional curve gives minimal values from the experimental normalized conversional curve.

A set of the reaction kinetic models used to determine the model which best describe the kinetics of the process of PAM isothermal dehydration, is shown in Table 1.

Differential Isoconversion Method

The activation energy of the investigated dehydration process for various dehydration degrees was established using the Friedman method [41] which is based on the following. The rate of the process in condensed state is generally a function of temperature and conversion:

d[alpha]/dt = [PHI](T, [alpha]) (3)

that is,

d[alpha]/dt = k(T) x f([alpha]) (4)

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

k(T) = A x exp (-[E.sub.a]/RT) (5)

where [E.sub.a] is the activation energy, A--the pre-exponential factor and R--the gas constant. We then get the following equation:

(d[alpha])/dt) = Aexp (-[E.sub.a]/RT) x f([alpha]) (6)

Considering that the reaction rate constant is only a function of the temperature, which is known as the isoconversional principle of Friedman, Eq. 6 is easily transformed into:

ln [(d[alpha]/dt).sub.[alpha]] = ln[A x f([alpha])] - [E.sub.a,[alpha]]/RT] (7)

That allows the evaluation of the activation energy for the particular degree of dehydration.


Characterisation of the PAM Xerogel/Hydrogel

The ATR-FTIR spectra of the PAM xerogel is presented in Fig. 1.

The absorption peak at 3431 [cm.sup.-1] corresponds to the O--H stretching vibration in carboxylic groups. The peaks at 3063 and 2938 [cm.sup.-1] are attributed to the C--H stretching in the C[H.sub.2] and C[H.sub.3] groups, respectively. The peak at 1548 [cm.sup.-1] belongs to the asymmetric stretching C=O vibration in -COONa and the 1689 [cm.sup.-1] is related to the stretching C=O vibration for the carboxylic acid group. The peak at 1448 [cm.sup.-1] corresponds to the asymmetric deformation band from the absorption peak at 2938 [cm.sup.-1]. The peak at 1403 [cm.sup.-1] corresponds to the symmetric stretching of the C=O vibration in -COONa, the 1260[cm.sup.-1] is a C--O stretching vibration coupled with OH in plane bending of COOH groups, The peak at 1180 [cm.sup.-1] is C-O stretching vibration coupled with OH in plane bending of -COONa groups. The band at 1041 [cm.sup.-1] is attributed to C--H in the plane bending vibration in C[H.sub.3] and at 834 [cm.sup.-1] belongs to the out of plane bending vibration [42, 43]. The presence of characteristic bands in the ATR-FTIR spectra of the PAM, with wave numbers at 1689, 3063, 2938, 1260, 1050 [cm.sup.-1], which are typical for the acrylic and methacrylic acid, as well as the absence of bands at 1640 for --C=C--, confirm the structure of synthesized PAM xerogel.

The basic structural properties of the PAM xerogel are shown in Table 2. Based on the results presented in Table 2, it can be concluded that the PAM xerogel used in this experiment was a slightly crosslinked network, mesoporous, with a high equilibrium swelling degree.

Figure 2 presents the isothermal kinetics swelling curve of the PAM hydrogel in distilled water at different temperatures. With the increase in temperature, the equilibrium swelling degree increases which implies on the positive temperature sensitivity. Figure 3 shows the effect of pH values on the equilibrium swelling degree of the PAM hydrogel measured at different buffer media at 298 K. Based on the presented results it may be concluded that the synthesized PAM hydrogel exhibited pH sensitivity. The most significant increase in [SD.sub.eq] happened at pH range from pH 6 to pH = 9.

Dehydration Kinetics of the PAM Hydrogel Dehydration under MWH

The experimentally obtained isothermal conversion curves at various operating temperatures for the PAM hydrogel dehydration, under microwave heating, are shown in Fig. 4.

The conversion curves of PAM dehydration, under the microwave heating, are complex and the three specific shapes of the change of the increase in the dehydration degree on time: a linear, nonlinear and a saturation stage (plateau), for all of the dehydration temperatures can be clearly seen. The increase in dehydration temperature leads to the decrease in the duration of both linear and nonlinear changes in the degree of dehydration with time, as well as in the value of time required to attain the saturation stage. The shape of these conversion curves are similar to the comparable curves obtained from conventional heating [11]. However, the duration of the PAM dehydration under the microwave heating is significantly shorter. In fact, the dehydration is accomplished in only 5 min at 333 K whereas for conventional heating it needs 50 min at same temperature, which clearly indicates that the rate of dehydration under MWH is significantly higher than that under the conventional conditions.

With the aim to preliminary determine the kinetic model for the dehydration under microwave heating, the shape of the dependence of the isothermal dehydration rate (d[alpha]/dt) on the degree of dehydration was evaluated. Figure 5 presents the dependences of (d[alpha]/dt) on the degree of dehydration.

The rate of dehydration convexly decreases with the increase in the degree of dehydration at all of the dehydration temperatures. The maximal dehydration rate is achieved in the very beginning of the process, that is, when [alpha] [right arrow] 0. The established change in the rate of dehydration with the degree of dehydration leads to the assumption that the dehydration rate was not controlled by the rate of the diffusion process, but with the rate of decrease in the interface of the surface [29].

With the aim to evaluate the kinetic complexity of the researched process, the dependence of the apparent activation energy on the degree of the dehydration was determined by applying the differential isoconversional method. Therefore, the dependences of ln[(d[alpha]/dt).sub.[alpha]] on 1/T were examined and given in Fig. 6 for various degrees of dehydration. Because the dependences of ln[(d[alpha]/dt).sub.[alpha]] on 1/T for all dehydration degrees give straight lines, based on their slopes and intercepts, the kinetic parameters of PAM hydrogel dehydration ([E.sub.a,[alpha]] and ln[A.sub.[alpha]]) were calculated. Figure 7 presents the dependence of the [E.sub.a,[alpha]] on the degree of dehydration for the MWH process of PAM hydrogel dehydration.

The activation energy is independent on the degree of dehydration for dehydration under the microwave heating. Since the independence of [E.sub.a,[alpha]] from the degree of dehydration is typical for the kinetically elementary (single-stage) processes, it can be concluded that the investigated dehydration is an elementary kinetics process and that the MWH does not lead to changes in the mechanism of the dehydration process in comparison to the conventional one.

The model-fitting method was used to determine the kinetic model of isothermal dehydration under microwave heating. For that reason, the isothermal normalized experimental conversion curves of the PAM hydrogel dehydration under MWH were determined for the examined temperatures and presented in Fig. 8.

The normalized experimental conversion curves of the PAM hydrogel dehydration obtained under microwave heating were the same for all of the examined temperatures. By analytically comparing the [[alpha].sub.exp]=f([t.sub.N]) with the normalized models conversion curves [alpha]=f([t.sub.N]) for different solid state reaction models, it was established that the kinetics of isothermal dehydration of the PAM hydrogel under microwave heating, can be mathematically described by the phase-boundary controlled reaction (contracting surface), which is given by the following expression:

[1 - [(1 - [alpha]).sup.0.5]] = [k.sub.M] x t (8)

where [k.sub.M] is the model rate constant for the dehydration of the PAM hydrogel under MWH.

When the dehydration can be described by the Eq. 8, the dependence [1 - [(1 - [alpha]).sup.0.5]] on time should give straight lines whose slopes give the [k.sub.M] values. The dependence of [1 - [(1 - [alpha]).sup.0.5]] on time for the PAM dehydration under MW heating at different temperatures is presented in Fig. 9.

The dependence of [1 - [(1 - [alpha]).sup.0.5]] on time for the dehydration of PAM under MWH over the entire range of degrees of dehydration, at all of the examined temperatures give straight lines which confirms the validity of the selected kinetics model and enables us to calculate the values of the [k.sub.M]. The effects of dehydration temperature on the [k.sub.M] values are given in Table 3.

The [k.sub.M] values increase with the increase in dehydration temperature in accordance with the Arrhenius equation. Therefore, the kinetic parameters of the PAM hydrogel dehydration ([E.sub.a] = 52.2 kJ[mol.sup.-1]; ln (A/[min.sup.-1]) = 17.8) were calculated using the Arrhenius equation. The values of the models rate constant for PAM hydrogel dehydration are approximately 4.6-5.9 times higher for the microwave heating than for the conventional heating [12]. The activation energy for PAM hydrogel dehydration, under microwave conditions, is ~8% lower than the value of [E.sub.a] for the conventional heating, whereas the value of the pre-exponential factor is as far as 2.2 times lower than that for the conventional heating.

If we compare the results of the performed kinetics analyses of isothermal dehydration under MWH with the ones obtained using the conventional method we can conclude that microwave heating does not lead to the change in the mechanism of the kinetic model of the dehydration, but provokes a decrease, both in the value of [E.sub.a] and the pre-exponential factor. Unfortunately, the obtained results cannot be compared to the literature data, since there is no presented data on the kinetics of isothermal dehydration under microwave heating conditions for identical or comparable hydrogels. Jaya and Durance found that microwave vacuum drying kinetics of alginate-starch gel could be described with exponential functions [22] which is significantly different from the kinetics model established in this investigation and it is not applicable for the PAM hydrogel dehydration under MWH.

However, in the already existing literature, there has been extensive research on microwave drying, a broad spectrum of fruits and vegetables have been examined. A number of successful drying models have been developed to explain the convective drying kinetics of various agricultural products for use in design, construction, and control of drying systems. However, less effort has been devoted to the modelling of the microwave drying process including the process parameters embedded into the drying model to explain the influence of processing variables on microwave drying kinetics. The Newton and the Page equations were mainly used to describe the microwave drying kinetics of several materials including: banana, pear, carrot, kiwi, garlic, parsley model fruit gel and olive pomace [23-25], However, they were not adequate to describe dehydration of the PAM hydrogel under MWH.

The established kinetics elementarily of the isothermal dehydration of the PAM hydrogel under the MWH, the kinetic model of dehydration and calculated values of the constant rates and kinetic parameters enable us to impartially conclude whether the increase of the dehydration rate under the MWH is a consequence of overheating or specific microwave effects. Keeping in mind that the Arrhenius equation is still valid for microwave heated dehydration, based on known values of the constant rate under MWH ([k.sub.M]) and the constant rate for conventional heating (Ten) [11], we can calculate the degree of increasing the isothermal constant rate of dehydration for MWH (K) [14].

K = [k.sub.M]/[k.sub.CH] = Aexp(-[E.sub.a]/[RT.sub.MW])/[A.sub.CH]exp(-[E.sub.a,CH]/RT) (9)

where [E.sub.a,CH] is activation energy and [A.sub.CH] is the pre-exponential factor under the conditions of conventional heating.

In the case when the increase in the rate of dehydration under the MWH would occur due to the overheating, it would be: [E.sub.a,CH] = [E.sub.a] and [A.sub.CH] = A. Based on Eq. (9) it is possible to find the temperature at which the process would occur under MWH ([T.sub.MW]) [14]:

[T.sub.MW] = [E.sub.a,CH] X T/[E.sub.a,CH] - RTlnK (10)

Table 4 shows the values for the isothermal degree of the dehydration rate increase and calculated values for the [T.sub.MW].

Since the calculated values of [T.sub.MW], are on average higher for 25 K than the actually measured values of the average temperature, we can conclude that the dehydration rate increase under MWH is not a consequence of overheating, but a result of specific microwave effects which leads to the change in the values of kinetic parameters, [E.sub.a] and lnA in the case of MWH.

The established decrease in the values of [E.sub.a] and lnA under microwave heating compared to the conventional heating permits the possibility of new explanation of the influence of microwave heating on the kinetics of isothermal dehydration based on integration of Larsson model of activating the molecule via selective energy transfer (SET model) [44] and Linert concept of isokinetic temperature [45]. The basic assumptions of the SET model are: (a) there is the possibility of coupling between vibration modes of absorbed water (v) and vibration modes of reaction environment ([omega]), (b) the activated complex for the dehydration is formed via the resonant (selective) transfer of required energy from the reaction environment to resonant vibration mode of absorbed water, (c) the value of transferred energy is quantized and it is determined by the number of resonant vibration quanta (n) which are exchanged between the reaction environment and the resonant vibration mode of absorbed water, (d) resonant transfer of energy causes the change in the value of anharmonicity factor of the resonant vibration mode.

Based on the assumptions above, in accordance with the SET model, considering this resonance system as a classical forced damped harmonic oscillator, it is possible to get the expression for reaction rate constant and isokinetic temperature ([T.sub.ic]):


where [DELTA][E.sub.i] = [hcv.sub.i] is the energy increment between the two levers [n.sub.i] and [n.sub.i+1], h is the Planck constant and c is the velocity of light.

As n [summation over (i)] [DELTA][E.sub.i]=[E.sub.a], Eq. (11) can be rewritten in the following form:

ln k=ln A + [E.sub.a]/R (1/[T.sub.ic] - 1/T) (12)

where the [T.sub.ic] is the isokinetic temperature:


For resonance conditions, Eq. (13) can be transformed to:

[T.sub.ic] = Nhcv/2R = 0.175v (14)

where v is given in [cm.sup.-1] and [T.sub.ic] is in K degrees.

In accordance with Linert concept, isokinetic temperature is in a relationship with the equation of compensation effect by the expression:

[T.sub.ic] = 1/R x b (15)

where b is the slope of compensation Eq. (16):

lnA = a + b x [E.sub.a] (16)

where a is the parameter of compensation equation

In the case of the existence of compensation equation which connects the values of the kinetic parameters ([E.sub.a] and lnA) calculated under different experimental conditions (CH and MWH) it is possible to calculate the values for the [T.sub.ic] and the v, based on the known value of the b. There is a functional relationship between the calculated values of the kinetic parameters of dehydration under the conventional and microwave heating which is expressed as:

ln[A.sub.F]=7.36 + 0.20 x [E.sub.a,F] (17)

where [E.sub.a,F] and In[A.sub.F] are the activation energy and preexponential factor in a defined experimental conditions (CH and MWH). The calculated values for the [T.sub.ic] and the v are presented in Table 5.

In accordance with Larson's model the value of activation energy is given by the expression:

[E.sub.a] - RT = nv(1 + nx) (18)

where x is anharmonicity factor and n is the integer vibration quantum number. Based on the known values of the [E.sub.a] and v, the values of n and x are calculated as follows:

n = [E.sub.a] - [sup.a]R/v (19)


The values of v, n, and x for dehydration under MWH and CH are given in Table 5.

From the results given in Table 5, it could be concluded that MWH does not lead to the changes in the mechanism of activation of absorbed water molecules for dehydration. Both in the case of MWH and CH the mechanism of activation is identical and goes via resonant transfer of required energy ([E.sub.a]) from the reaction environment to the resonant vibration mode of absorbed water which have the value of wave number v = 837 [cm.sup.-1] which is in relationship with intermolecular vibration of absorbed water molecules [46].

Due to that, both the vibration energy of absorbed water and the amplitude of the resonant mode are increased which enables the release of water from hydrogel, that is, dehydration. The number of resonant vibration quanta required for the activation of water molecules under MWH is lower than the number of quanta under CH. The decreased value of number of quanta necessary for the activation of water molecules under microwave conditions are most likely caused by the increased energy of the ground vibration level of resonant oscillator due to the absorption of microwave energy. Therefore, the increase in the dehydration rate and decrease in the [E.sub.a] and lnA for MWH is a consequence of the increase in the energy of the ground vibration level of resonant oscillator in absorbed water molecules which is caused by absorption of microwave energy.


A novel device for the evaluation of the kinetics of isothermal dehydration under the microwave heating is constructed. The rate of isothermal dehydration of the PAM hydrogel under MWH is ~5 times higher than that for conventional heating. The microwave heating does not lead to a change in the kinetic complexity of the kinetic model of isothermal dehydration of the PAM hydrogel. The values of Arrhenius kinetic parameters under the MWH are lower than the comparative values under conventional heating. The values of Arrhenius kinetics parameters obtained from dehydration under the MWH and CH are in mutual relationship with the compensation equation. The activation of the absorbed water molecules for dehydration is achieved by a resonant selective transfer of energy from the reaction environment to the absorbed molecule of water, both for CH and MWH. The selective transfer of energy occurs at resonant frequency with the wave number, v = 837 [cm.sup.-1], which corresponds to the intermolecular vibration of the absorbed water. The activation energy of the dehydration process is a quantized value and it is predetermined by a number of the resonant quanta which are selectively transferred from the reaction environment to the resonant oscillator. The increase in the isothermal rate of dehydration under the MWH in comparison to the CH is a consequence of the increased value of energy of the ground state of the resonant oscillator, under the conditions of MWH, when compared to CH. The suggested mechanism of microwave action is possible to be applied to wider range of chemical reaction and physicochemical process.


The authors acknowledged Ms Mirjana Cvetkovic for kindly recording ATR-FTIR spectra at Institute for chemistry, technology and metallurgy, Department for chemical and instrumental analyses, Belgrade.


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Jelena Jovanovic, (1) Biljana Potkonjak, (2) Tanja Adnadjevic, (3) Borivoj Adnadjevic (1)

(1) Faculty of Physical Chemistry, Belgrade University, Belgrade, 11050, Serbia

(2) ACT Cosmetics Canada Inc. Unit # 1, Toronto, Ontario, Canada

(3) Department of Genetic Research, Institute for Biological Research Sinisa Stankovic, Belgrade, 11060, Serbia

Correspondence lo: J. Jovanovic; e-mail:

Contract grant sponsor: Ministry of Science and Technical Development of the Republic of Serbia (Project No. 172015-01).

DOI 10.1002/pen,24195

Published online in Wiley Online Library (

TABLE 1. The set of kinetics models used to
determine the kinetics model of dehydration.

                                               General expression of
                                                the kinetics model,
Model   Reaction mechanism                           f([alpha])

P1      Power law                                4[[alpha].sup.3/4]
P2      Power law                                3[[alpha].sup.2/3]
P3      Power law                                2[[alpha].sup.1/2]
P4      Power law                              2/3[[alpha].sup.-1/2]
R1      Zero-order (Polany-Winger equation)              1
R2      Phase-boundary controlled reaction    2[(1 - [alpha]).sup.1/2]
          (contracting area, i.e.,
          bidimensional shape)
R3      Phase-boundary controlled reaction       3[(1 - a).sup.2/3]
          (contracting volume, i.e.,
          tridimensional shape)
F1      First-order (Mampel)                       (1 - [alpha])
F2      Second-order                           [(1 - [alpha]).sup.2]

F3      Third-order                            [(1 - [alpha]).sup.3]

A2      Avrami-Erofe'ev                       2(1 - [alpha])[[-ln(1 -
A3      Avrami-Erofe'ev                       3(1 - [alpha])[[-ln(l -
A4      Avrami-Erofe'ev                       4(1 - [alpah])[[-ln(1 -
D1      One-dimensional diffusion                    l/2[alpha]
D2      Two-dimensional diffusion              1/[1 - ln(1 - [alpha])]
          (bidimensional particle shape)
D3      Three-dimensional diffusion             3[(1 - [alpha]).sup.
          (tridimensional particle shape)         2/3]/2[1 - [(1 -
          Jander equation                        [alpha]).sup.1/3]]
D4      Three-dimensional diffusion              3/2[(1 - [alpha])
          (tridimensional particle shape)         .sup.-1/3] - 1)

           Integral form of
         the kinetics model,
Model         g([alpha])         Refs. No

P1        [[alpha].sup.1/4]      [28]
P2        [[alpha].sup.1/3]      [28]
P3        [[alpha].sup.1/2]      [29]
P4        [[alpha].sup.3/2]      [29]
R1             [alpha]           [30]
R2       [1 - [(1 - [alpha])     [31]
R3       [1 - [(1 - [alpha])     [31]
F1         -ln(1 - [alpha])      [32]
F2          [(1 - [alpha])       [33]
             .sup.-1] - 1
F3        0.5[[(1 - [alpha])     [33]
            .sup.-2] - 1]
A2       [[-ln(l - [alpha])]     [34-36]
A3       [[-ln(l - [alpha])]     [34-36]
A4       [[-ln(l - [alpha])]     [34-36]
D1         [[alpha].sup.2]       [37]
D2       (1 - [alpha])ln(1 -     [38]
          [alpha]) + [alpha]
D3       [[1 - [(1 - [alpha])    [39]
D4      (1 - 2[alpha]/3) - [(1   [40]
         - [alpha]).sup.2/3]

TABLE 2. The basic physicochemical properties of the PAM xerogel.

           [SD.sub.eq],   [[rho].sub.x],    [10.sup.-5]
Property   g [g.sup.-1]   g [cm.sup.-3]    g [mol.sup.-1]

Value          180            1.317             2.14

Property   mol [m.sup.-3]   d, nm

Value           6.15         123

TABLE 3. The effect of temperature on the [k.sub.M] values.

T, K   [k.sub.M], [min.sup.-1]

293             0.029
303             0.059
313             0.120
323             0.207
333             0.393

TABLE 4. The effect of temperature at the K and the [T.sub.MW].

T, K    K     [T.sub.MW], K

293    5.58        317
303    5.41        328
313    5.08        339

TABLE 5. The values of v, n, and x under conventional and microwave

Variable           CH        MWH

v, [cm.sup.-1]   837       837
n                  6         5
x                 -0.022    -0.001
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Author:Jovanovic, Jelena; Potkonjak, Biljana; Adnadjevic, Tanja; Adnadjevic, Borivoj
Publication:Polymer Engineering and Science
Geographic Code:1USA
Date:Jan 1, 2016
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