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Thermodynamic Parameters Evaluation of - and -cages in Na+, Ba2+, Fe3+, Co2+, Ni2+ and Cu2+ Exchanged Zeolite a Using Quantum Mechanical Theory and Fermi Dirac Statistics.

Byline: Hamida Panezai, Abdul Nabi, Mohammad Yaqoob, Nusrat Munawar, Syed Haider Shah and Syed Mohsin Raza

Summary

The aim of present paper is to investigate the effects of non-framework cations, their hydration capacity and the role of phonons (acoustical and optical) on the thermodynamic characteristics of Type-A zeolite using Quantum mechanical theory and Fermi Dirac Statistics. This study is motivated by the lack of an accurate measurement capability of thermodynamic properties of zeolites by the existing methods reported in literature, that is why we have suggested the quantum mechanical and Fermi Dirac statistical approaches. Thermal analysis data for zeolite samples were obtained by thermogravimetric and differential thermal analysis (TG-DTG) technique at a heating rate of 10 K min1 in order to evaluate the desorption behavior of water. The results showed that the thermal stability of these samples was found to be dependent mainly on the electropositive non- framework cations.

Meanwhile, on the basis of thermodynamic parameters, the sizes of a- and AY- cages in Na-A and its derivative zeolite were calculated using Fermi Dirac Statistics. Thereafter, semi-quantum effects (logarithmic behavior) of specific heat, entropy and enthalpy were observed in all samples as manifestations of the production of phonons due to gaining of thermal energy. As a result, Debye temperature would increase due to localization of heat energy in the Brillouin zone, and the calculated specific heat capacities showed almost no changes after cation exchange. However entropy and enthalpy first exceeds NaA in Ba2+, Ni2+ and Cu2+ and then decrease in Fe3+ and Co2+.

These demonstrations indicated that Ba2+, Ni2+, Cu2+ Fe3+ and Co2+ cations influenced both the entropy and enthalpy as a result of the interaction of cations with the zeolite framework, which confirmed that the changes in the lattice mode were dependent on the increase or decrease in the electrostatic interactions between the cations and the framework zeolite.

Keywords: Zeolite A; TG-DTA technique; Thermodynamic parameters; Quantum mechanical theory; Fermi Dirac statistics; - and - cages.

Introduction

Zeolites are crystalline, hydrated aluminosilicates showing an open three dimensional structure consisting of cations needed to balance the electrostatic charge in the framework of silica and alumina tetrahedra. The open structure has made the use of zeolites in several industrial processes such as catalysis, ion exchange and adsorption that are well explained in the literature [15].

Sodium A-zeolite is of the cubic symmetry [6]. Rigidly anionic crystalline aluminosilicate framework of synthetic sodium A-zeolite containing a- and AY-cavities / cages which have direct access through 8 and 6 oxygen rings, respectively and the 12 Na+ ions per unit cell (pseudo) are located at three non-equivalent sites in dehydrated zeolites. The intra- crystalline surface area of the dehydrated Type-A zeolite depends on the aspects such as the chemical nature of the cation, location and the thermal stability of the lattice structure [7, 8].

The capacity of changing the composition of a given zeolite e.g. by lattice atom substitution or by introducing metal cations and organic molecules into the pores while maintaining the same crystal structure or contrarily the ability to prepare different crystal structures with the same composition, make them extraordinarily versatile materials with interesting structure-function relationships, which finds many important applications in the energy and chemical processing sectors [9].

The inorganic ion exchangers are superior than organic due to their thermal stability, resistance to radiation and having high selectivity for certain elements [10, 11]. Their selectivity not only depends on the exchanging cations and sorption media but also on the thermal treatment. Therefore, the equilibrium state for both physical and chemical systems can be treated quantitatively using thermodynamics. Temperature is a key factor in determining the importance of enthalpy and entropy of a system [10, 11].

According to Hemingway and Robie [1] the best estimation of thermodynamic properties would be achieved from the simultaneous analysis of synthesis and stability data, calorimetric data and different metastable equilibrium measurements. Each of them would place limits upon one or more of the thermodynamic characteristics of a given zeolite phase. Their calculated results of natural phillipsite and clinoptilolite provided valuable information; however, they did not estimate the configuration entropies because of lack of information regarding the degree of order of zeolitic water.

In this case, Tarasevich et al. [12] used the direct calorimetric measurements and sorption- analytical method to determine the heats of exchange of the Mn2+, Co2+, Cu2+, and Ni2+ cations on the Na+ form of clinoptilolite over the entire range of solid phase fillings with sorbed cations.

After that, Greenstein et al. [9] investigated the effects of non-framework cations and the role of phonon scattering mechanisms on the thermal transport properties of zeolite LTA using the three- omega method over a wide range of temperature (150450 K). Overall, previously developed modeling approach derived from semi empirical relaxation time scattering rates along with full anisotropic dispersion, has been further modified and used to calculate the thermal properties of LTA and to analyze its phonon dynamics. This approach provided insight into heat transport in nanoporous materials and has been shown to be transferable to multiple materials. However, accurate predictions of the influences of each type of metal cation on the thermal conductivity of zeolite LTA following mentioned-above methods are rare.

The standard enthalpies (H) and entropies (S) of ion exchange were calculated from isotherms at only two or three temperatures and according to their data analysis the accuracy of the determination of H and S was within measurement errors. For more accurate calculations of the thermodynamic parameters of transition metal exchange using exchange isotherms were made possible by the sorptionanalytic method and direct calorimetric measurements of the heats of ion exchange [12]. The accuracy of calculations of thermodynamic characteristics of ion exchanged samples in relation with water content can also be improved by the application of quantum theory and Fermi Dirac Statistics.

The interest in the calculation of the Debye temperature has been increasing in both semi- empirical and theoretical phase diagram calculations since the Debye model offers a simple but very effectual method to explain the phonon contribution to the Gibbs energy of crystalline phases. The energy calculations are often used together with the Debye and Gruneisen model to derive thermo physical properties and phase stabilities at finite temperatures [13]. The quantum mechanical calculations of transition metals exchanged synthetic zeolite-A widely used in investigations has also been studied scantily.

With the aim to further contribute to the knowledge of location and thermal behavior of cations inside zeolites particularly if the zeolitic water content is under consideration with the temperature, this paper provides a deeper investigation of the thermal and structural analysis of the parent Na-A and cation exchanged derivatives: Ba2+, Fe3+, Co2+, Ni2+ and Cu2+ and a newly developed quantum theory of dielectricity was put forward. The selection of cations has been made to study the implications of size and charge density on ion exchange (their access to the a- and AY-cages) and cation-framework interaction.

Experimental

Reagents and Solutions

All plastic ware was cleaned in nutrient free detergent (2%, v/v) (Neutracon, Decon Laboratories, UK), rinsed with ultra-high purity (UHP) water (0.067 S cm1, Elga, Purlab Option, UK), soaked overnight in hydrochloric acid (10% v/v), thoroughly rinsed with UHP water and stored in zip-lock plastic bags to avoid contamination. All of the reagents were of analytical grade, supplied by BDH, Fisher Scientific, UK, unless stated otherwise, and all solutions were prepared in UHP water.

Na-A zeolite (70 g, obtained from UOP, USA) was stored over saturated calcium nitrate solution in a desiccator for complete hydration for several days at room temperature. An hydrated fraction (2.5 g) of hydrated NaA zeolite for each sample was taken in 75 mL UHP water and reduced its pH from 1112 to 7.0 by addition of HCl solution (1x103 mol L1). Then 200 mL FeCl3.6H2O solution (5x103 mol L1) was added at intervals and stirred for 4 h at 333 K. The slurry was cooled, and then filtered with a fine filter paper. The exchanged sample was rinsed several times with hot UHP water. The wet samples were dried over night at 353 K in the oven. Partially dehydrated sample was stored again in a desiccator over saturated calcium nitrate to rehydrate for several days. On complete rehydration sample was characterized by thermogravimetric analysis (TGA) and differential thermal analysis (DTA) techniques.

The concentration of the Fe3+ ion before and after exchange was analyzed by titration against EDTA solution (0.01 mol L1) using variamine blue as an indicator till the color changes from blue to yellow. The exchanged concentration of the Fe3+ ion in the NaA zeolite was determined by subtracting the concentration of Fe3+ ions in the filtrate from the concentration in the original solution.

Out of total 19 samples, 4 samples of Fe3+ and Ba2+, 3 samples of Ni2+ and Cu2+ and 5 samples of Co2+ exchanged A-zeolite were prepared by the above procedure. Murexide was used as an indicator for CuCl2.2H2O, CoCl2.6H2O and NiCl2.2H2O solutions (1.7x102 mol L1 each). The color change was observed from greenish yellow to violet in the case of CuCl2.2H2O and from yellow to violet in the case of CoCl2.6H2O and NiCl2.6H2O.

During the titration, murexide indicator was used for CoA, NiA, and CuA and Methyl thymol blue for BaA samples [14]. The exact molecular formula for each cation exchanged Na-A zeolite samples are given in Table-1.

Table-1: Summary of cation exchanged Type-A zeolite and percentage of zeolitic water.

###Molecular###Percent of zeolitic

S. No. Sample

###Formula###Water, (%)

###01###NaA

###Na12 [(SiO2)12(AlO2)12]12###30.0

###02###1FeA###Fe 0.95 Na 9.2 A###27.8

###03###2FeA###Fe 1.85 Na 6.5 A###33.1

###04###3FeA###Fe 2.5 Na 4.5 A###34.9

###05###4FeA###Fe 3 Na 3 A###38.6

###06###1CoA###Co 0.99 Na 10 A###39.2

###07###2CoA###Co 1.965 Na 8.1 A###30.7

###08###3CoA###Co 2.621 Na 6.8 A###32.6

###09###4CoA###Co 3 Na 6 A###32.1

###10###5CoA###Co 3.22 Na 5.6 A###33.6

###11###1NiA###Ni 0.98 Na 10.04 A###31.25

###12###2NiA###Ni 1.9 Na 8.2 A###32.56

###13###3NiA###Ni 3.7 Na 4.6 A###35.36

###14###1CuA###Cu 0.99 Na 10.02 A###30.95

###15###2CuA###Cu 1.96 Na 8.08 A###29.45

###16###3CuA###Cu 2.90 Na 6.2 A###31.67

###17###1BaA###Ba 1 Na 10 A###25.9

###18###2BaA###Ba 1.99 Na 8.0 A###26.8

###19###3BaA###Ba 2.9Na 6.2A###23.9

###20###4BaA###Ba 3.8 Na 4.4 A###22.3

Thermal analysis (TGA, DTA) measurements were carried out for the determination of zeolitic water and thermal characteristics of all zeolite samples using a simultaneous thermal analyzer (STA-40 NETZSCH, Germany). Different weights about 6.50 10 mg, for each hydrated samples was taken using high purity nitrogen as purge gas at heating rate of 10oC min1 was employed. The content of zeolitic water was calculated by the percent weight loss of samples. The thermal stabilities of the crystal lattices of framework were investigated from exothermic curves of DTA, heated in the temperature range from 30 up to 1000oC.

Results and Discussion

The percentage of zeolitic water content of hydrated zeolite and its cation exchanged forms were measured by the TGA curves and their summaries are given in Table-1. It shows the zeolitic water content lost per unit cell of hydrated Na-A zeolite is around 30%, comparably, 39% water content per unit cell of hydrated Na-A zeolite was reported by Barrer and Meier [15] and 41% was calculated by Akbar [8]. The standard value of water content is considered to be 37% [16]. The less zeolitic water content in our samples might be due to partial dehydration during the transportation of samples for TGA and DTA analysis. The results (Table-1) showed that the water content per unit cell of the hydrated Fe3+, Ni2+, Co2+, Cu2+ and Ba2+ exchanged Type A zeolites increased with the increasing number of cations per unit cell of the zeolite. The main reasons might be related to the influence of different cations in cation exchangeable zeolite-A on their pore volume.

In general, a small divalent cation increases the void volu me by reducing the total number of cations and increasing the space unoccupied [8, 17]. As reported previously [1820], that exchangeable ions with low charge densities were present in a less hydrated environment and also interacted more strongly with the zeolite framework. Hence, small ions possess a faster access to the internal channels of the zeolite and could easily replace the larger ones. Contrary to this larger, less strongly hydrated cations tended to concentrate in zeolite in contrast to smaller, more hydrated ions, which tended to remain in solution, depending on the type of zeolite. Therefore, the nature of non- framework cations play a key role in water-cation, water-oxygen and water-water interactions [21] and their contribution to the thermodynamic characteristics is significant [22].

The Pauling ionic radii for Co2+ and Na+ ions are 0.74 and 0.95 [23], respectively, therefore, the empty space in the cavities increases by exchanging 2Na+ ions by one Co2+ ion. In addition, Co2+ ions have the capability of performing complexes with water molecules, in which the water molecules are strongly coordinated to Co2+ ions and they are, therefore tightly packed. The zeolitic water content of hydrated Co-A zeolites listed in Table-1 is in good agreement with those obtained by Akbar [8]. Table-1 shows that the water content per unit cell of Ni-A zeolite (Ni2+ radius 0.69 ) is higher than Co2+A-zeolites (Co2+ radius 0.74 ), resulting in a greater hydration ability of Ni2+ than that of Co2+ in hydrated A zeolite [8, 23], implying a high degree of ordering of water molecules around Ni2+ ions.

Furthermore, it has been shown (Table-1) that the increase in the percentage of zeolitic water content per unit cell of Cu2+A zeolite samples is less than Co-A and Ni-A zeolite samples. This might be due to greater ordering of water molecules around Co2+ and Ni2+ ions as compared to Cu2+ ions. John- Teller effect is responsible for the formation of the elongated octahedral (tetragonal) complex of Cu2+ in hydrated Cu2+A-zeolites [7]. The percentage water content of Ba2+ exchanged Type-A is less as compared to unexchanged NaA and transition metal exchanged samples. It is due to the larger size of Ba2+ (1.35 ) ion and also its inability to form any water complex. These observations on the cation- framework interaction suggested that larger the electropositivity of the non-framework cation lower are the binding energies of the framework element (Si 2p, Al 2p and O 1s) [24], which is in confirmation of our results.

Zeolites skeleton are metastable and are formed by irreversible reactions; consequently, their structures do not exhibit thermodynamic equilibrium with experimental equilibrium and traditional calorimetric procedures. Therefore, their thermodynamic properties cannot be explained properly [2528]. For the solution of this problem, the newly developed quantum theory of dielectricity [26, 27, 29] was applied. Based on such an idea quantum mechanical and Fermi-Dirac statistical calculations were performed. From the exothermic peaks of DTA curves (Fig. 1af) of the NaA zeolite and its cation exchanged samples, the thermodynamic parameters (enthalpy, entropy and specific heat), peak temperature, peak width, transition temperature, Debye velocity, Debye temperature, Debye wave vector, Fermi wave vector were calculated first and corresponding the most important the sizes of a- and AY-cages were calculated as listed in Table-2 and -3. The exothermic peaks are in the temperature range from 373K to 1287K.

Table-2: Results of specific heat, transition temperature, entropy and enthalpy obtained from the exothermic peaks of DTA of both unexchanged and cation exchanged Type-A zeolite.

###Peak###Transition

S.###Peak###Peak###Mass of###Specific Heat C###Peak Width###Entropy S Enthalpy

###Sample###Temp.###Temp

No.###No###Nature###Sample ( Kg)###(J/KgK)###T (K)###(J/K) H (J)

###Tp (K)###Tt(K)

###Exother-

01###NaA###01###7.0###1.13###485###369###T1=450###6.5###2917

###mic

###T2=558###5.22

###02###2.89###1185###279###12.5###5619

###10.1

###03###2.68###1287###282###12.0###5273

###9.5

02###1NiA###01###7.5###1.13###496###354###T1=458###7.0###3047

###T2=565###5.4

###02###3.00###1220###281###14.0###6319

###11.0

03###2NiA###01###10###1.20###511###368###T1=396###11.0###4324

###T2=654###7.0

###02###2.05###900###289###15.0###5879

###9.0

###03###3.10###1253###285###22.0###8834

###13.5

04###3NiA###01###7.580###1.20###517.4###354###T1=454###7.0###3185

###T2=691###5.0

###02###2.60###1084###280###12.0###5437

###8.0

05###1CuA###01###8.0###1.13###484###354###T1=447###7.15###3196

###T2=721###4.43

###02###2.72###1135.2###280###14.0###6078

###8.4

06###2CuA###01###8.0###1.13###493###371###T1=444###7.65###3396

###T2=654###5.0

###02###2.34###1010###287###12.0###5370

###8.20

###03###3.10###1253###285###16.0###7073

###11.0

07###3CuA###01###7.505###1.20###500###380.7###T1=450###7.33###3300

###T2=638###5.2

###02###2.30###991###282.24###11.0###4841

###7.6

08###1BaA###01###8.186###1.13###491.5###351###T1=462###7.1###3275

###T2=647###5.1

09###2BaA###01###7.353###1.13###488.4###369###T1=462###6.67###3080

###T2=650###5.0

###02###2.80###1146###285###12.5###5760

10###3BaA###01###7.0###1.13###480.4###332###T1=447###6.0###2601

###T2=821###3.2

###02###3.14###1265###284###14.0###6259

###7.62

11###4BaA###01###7.0###1.21###523###354###T1=496###6.0###2963

###T2=792###4.0

12###1FeA###01###7.667###1.20###505###352###T1=455###7.0###3136

###T2=698###4.5

13###2FeA###01###8.0###1.20###502###362###T1=448###7.5###3355

###T2=673###5.0

14###3FeA###01###7.691###1.13###484###373###T1=444###7.3###3231

###T2=710###4.55

15###4FeA###01###7.0###1.10###473###366###T1=419.4###7.0###2839

###T2=687###4.0

###Exother-

16###1CoA###01###7.762###1.00###373###292###T1=436###5.0###2149

###mic

###T2=629###3.41

###02###1.13###484###380###7.63###3328

###5.3

###03###2.64###1115###284###13.42###5853

###9.30

17###2CoA###01###6.534###1.00###373###291###T1=437.3###4.13###1805

###T2=655###3.0

###02###1.10###462###355###6.0###2529

###4.0

###03###2.60###1098###284###11.02###4821

###7.36

18###3CoA###01###7.167###1.00###384###298###T1=427###5.0###2062

###T2=591###3.5

###02###1.13###490###384###7.35###3134

###5.30

###03###2.64###1104###285###12.55###5355

###9.0

19###4CoA###01###7.399###1.00###390###300###T1=446###5.0###2165

###T2=583###4.0

###02###1.10###463###393###7.0###3173

###5.44

###03###1.21###530###308###6.2###2757

###5.0

###04###2.70###1130###281###12.6###5612

###9.62

20###5CoA###01###7.751###1.00###393###288###T1=436###5.0###2186

###T2=573###4.0

###02###1.10###459###298###6.0###2504

###4.4

###03###1.21###533###314###6.8###2955

###5.0

###04###2.72###1133###284###14###5965

###10.41

Table-3: Results of Debye wave vector, Debye velocity, Debye temperature, sizes of a- and AY-cages and Fermi wave vector of unexchanged and cation exchanged Type-A zeolite.

###Debye Velocity D###Debye Temp D###Size of###Size of###Fermi Wave Vector kF

S. No.###Sample###Debye Wave Vector

###(x104 m sec1)###(K)###cage 2D (nm)###-cage 2F (nm)###(x109 m1)

###kD (x109 m1)

###1###Na A###14.0###2.25###2401###0.89796###1.1326###11.10

###2###1FeA###13###2.40###2401###0.9670###1.2193###10.31

###3###2FeA###13.4###2.35###2401###0.9382###1.1849###10.61

###4###3FeA###13.7###2.29###2401###0.9176###1.1606###10.83

###5###4FeA###13.9###2.26###2401###0.9044###1.1418###11.01

###6###1CuA###12.9###2.44###2401###0.9746###1.2325###10.2

###7###2CuA###13.11###2.40###2401###0.9589###1.2088###10.4

###8###3CuA###13.3###2.40###2401###0.9452###1.1933###10.53

###9###1NiA###12.9###2.44###2401###0.975###1.2325###10.2

10###2NiA###13.1###2.40###2401###0.9597###1.2088###10.4

11###3NiA###13.5###2.33###2401###0.9312###1.1749###10.7

12###1CoA###12.85###2.45###2401###0.9783###1.2308###10.21

13###2CoA###13.11###2.40###2401###0.9589###1.2088###10.4

14###3CoA###13.23###2.38###2401###0.9502###1.1973###10.5

15###4CoA###13.33###2.36###2401###0.9431###1.1860###10.6

16###5CoA###13.4###2.35###2401###0.9382###1.1860###10.6

17###1BaA###12.8###2.50###2401###0.9821###1.2447###10.1

18###2BaA###12.8###2.50###2401###0.9821###1.2325###10.2

19###3BaA###12.9###2.44###2401###0.9746###1.2205###10.3

20###4BaA###13.0###2.42###2401###0.9670###1.2205###10.3

The heat capacity, enthalpy and entropy of Na-A sample are plotted in Fig. 2, and it can be seen that the specific heat was apparently changing linearly with temperature, following the T3/2 variation, which could be attributed nearly to Debye specific heat of solids (T3-variation). This behavior was observed at relatively low temperatures. However, at relatively high temperatures, semi quantum effect (logarithmic behavior) of the specific heat of solids, especially in the proposed case of zeolite, was observed. At 1220K, a peak in NaA was observed, which was due to acoustic phonons only.

The semi-quantum effect (logarithmic behavior) was observed in enthalpy (Fig. 2) and entropy (Fig. 2). The acoustic phonons were produced due to disorder (entropy) in the crystalline phase. This shows that peaks in specific heat or in enthalpy or in entropy were the manifestations of the disorder phenomenon and that these phonons have become free. Phonons were actually quanta of vibrations in the lattices. Vibrations of lattices become pronounced due to gaining thermal energy. The TG curve also illustrates a sharp desorption of water after gaining thermal energy. This confirms the dependence of specific heat capacity, enthalpy and entropy on water content.

However Na+ associated with the framework oxygen proved to be the governing parameter and it can be attributed to the increase in the thermodynamic characteristics of hydrated Na-A sample at transition temperatures to the movement of Na+ ions provoked by water leaving behind adsorption sites in the framework structure of zeolite, which is f ound in agreement with the literature [30]. It has also found that there are two types of water present in Na-A zeolite. At low temperatures the weakly attached water (physisorbed) were removed first and at high temperatures as shown in Fig. 1a, the strongly bonded water (chemisorbed) are removed.

Four samples with different concentrations of Fe-exchanged A-zeolite were prepared. It was observed that the relationship of temperature with specific heat was directly and with concentration was inversely proportional. In Fe3+ exchanged Type-A zeolites a logarithmic profile (T3/2-variation) in the specific heat with curvature at relatively low temperatures, i.e., below about 485 K was observed. The Fe3+ ion was ferromagnetic (whether ferrous or ferric). Below 485 K, the optical phonons and at 540K, the acoustical phonons were produced and both were quantized in Brillouin zones. These observations were apparent both in enthalpy and entropy profiles. The shape of such profiles was like Grunession function. However, Fe3+ ion shows very different behavior than the other cations (Na+, Ba2+, Co2+, Cu2+ etc). The high polarity of Fe3+ ions in zeolites inhibits disorder and maintains crystallinity.

Both the optical and the acoustical phonons due to this profile were quantized in Brillouin zones. The temperatures used in our experimental study for iron- exchanged samples of zeolite remain below 510K where the iron ions remain itinerant (Ising model is applicable). The same trends are observed in all its other samples.

Fig. 1e shows TG and DTA profiles of Cu2+ exchanged Na-A zeolite. In Cu2+ exchanged samples of Na-A, a logarithmic profile (T3/2-variation) is observed however, in some cases, a linear trend, for specific heat, enthalpy and entropy (Fig. 4), is also observed with curvatures at relatively high temperatures. The acoustical phonons were produced at above 1000K and were quantized in Brillouin zones. A broad phase transition exothermic curve at maximum temperature of around 505K, showed the heat capacity value in the range 1.13-1.20 J Kg1 K1. This result is ascertained with the zeolitic water content (3031%) lost. All the three thermodynamic characteristics were increased and water content was decreased with the increasing temperature.

The profiles of specific heat, entropy and enthalpy (Fig. 5) with logarithmic behavior (T3/2 effect) were observed in case of NiA zeolites. The curvatures at relatively high temperatures indicated that acoustical phonons are produced but quantized in Brillouin zones. Ni2+ ions in zeolites were ferromagnetic but not polar and itinerant as in the case of Fe3+ ions. The specific heat, entropy and enthalpy (thermodynamic characteristics) showed the same increasing trend as seen in Na-A. However, the calculated zeolitic water content (3135%) was higher than Na-A zeolite, which is attributed to the small ionic radius of Ni2+ (0.69 A ) [23].

In the case of cobalt exchanged zeolite samples a crystal clear logarithmic profile (T3/2- variation) for specific heat, enthalpy and entropy (Fig. 6) with curvatures at relatively low temperatures is seen. The thermal recovery processes in ion exchanged cobalt samples of zeolites were occurred at about 550K to adjust Brillouin zones, with the exception of Co4A sample in which optical phonons were generated and became free, whereas in the remaining samples, the acoustical phonons were quantized in Brillouin zones.

In Ba-exchanged Type-A zeolite samples, the specific heat was changing linearly with temperature, following approximately the (T3/2- variation), which could be attributed nearly to Debye specific heat of solids (T3-variation). The shape of the profile associated with specific heat, enthalpy and entropy (Fig. 7) was logarithmic. With increasing concentration of barium, the acoustical phonons were produced with relatively higher energies but were quantized in Brillouin zones. Optical phonons were produced at very high energies or frequencies of lattice vibrations (elastic or super-elastic behavior of lattices). Optical phonons were produced at relatively low temperatures. For Ba2+ exchanged samples a less water content as listed in Table-1, in total is observed and this water content showed a decreasing trend with the increasing ion exchange degree, which confirms the weak interaction of Ba2+ with water molecules due to its larger size (1.35 A ) [23].

Debye wave vector values decreased from original sample (NaA) towards the cation exchanged samples whereas in ion exchanged samples of same category Debye wave vector values was increased with increasing concentration. It ranges from 14.0x109 m1 to 12.8x109 m1 but the overall Debye wave vector was almost constant for all samples. In contrary, Debye velocity on ion exchange increases and decreased when concentration was increased, because we know that the sound velocity decreases in cage like solid structures. The same behavior was observed in case of all cation exchanged zeolites. Results of Debye wave vector, Debye velocity, Debye temperature, sizes of a- and AY-cages and Fermi wave vector of unexchanged and cation exchanged Type-A zeolite samples are given in Table-3. In the case of Cu2+ the Debye velocity remains constant in higher concentrations while for Ba2+ it remains constant only in the first and second sample.

Debye temperature was almost constant in all the samples and its high values (2401K) were because of two reasons, first the structure of zeolite was crystalline and it has already been reported that hard materials exhibit an elevated Debye temperatures and second it behaves as an insulator [31, 32] therefore, the heat energy will be localized in the Brillouin zones, with different modes and in the form high energies. The Brillouin zones could be envisaged like deep quantum wells, the brims of which open up in a- and AY-cages. In other words, the channels or pores in zeolites were acting like deep quantum wells.

The total melting point temperature of the three metals Na, Si and Al was almost 2900K that was higher than the 2401K. This justifies the accuracy of the proposed work. The atomic concentration as well as electron concentrations were calculated by employing the formula (N/V) [33], and using well established formulas given in Table-4, Debye wave vector (k D ) and Fermi wave vector (k F ) values were determined and it was found that k F less than k D ; as required for a semi disordered system such as amorphous/crystalline or metallic ion exchanged zeolites [34].

Table-4: Formulas of Fermi Dirac Statistics for calculations of Debye wave vector, Debye wave length, Debye velocity, size of AY-cage, Debye temperature, Fermi wave vector, Fermi wave length, and size of a-cage.

S. No.###Formula###Unit

1###Debye wave vector###m1

2###Debye wave length###nm

3###Debye velocity###m sec1

4###Size of AY-cage###nm

5###Debye temperature###K

6###Fermi wave vector###m1

7###Fermi wavelength###nm

8###Size of a-cage###nm

We accomplished new findings on the experimental results of Type-A zeolite and its different cations (Fe3+, Cu2+, Ni2+, Co2+ and Ba2+) exchanged samples on the basis of quantum mechanical calculations and well established formulas of Fermi Dirac statistics. Particularly, sizes of the cages present in NaA and its ion exchanged forms were calculated using Debye and Fermi wavelengths, respectively.

The results showed that the size of AY-cage increases on cation exchange in Type-A zeolite but when the concentration of the cations was increased, making cation exchanged samples of different concentrations; however, the increasing behavior of AY-cage is altered. For example in Fe1A the cage size 0.97 nm was decreased to 0.90 nm in Fe4A.

The sizes of a-cages show the same increasing trend that of AY-cages from NaA zeolite to cation exchanged samples (NaA less than FeA less than CoA less than CuAless than NiA less than BaA). As the concentration of the cation increased in the NaA-zeolite, the size of the a- cage decreased. It might be due to partial collapse of the crystalline structure of zeolite at high temperature [8]. After 625K (350C), complete dehydration takes place, due to which the Co2+, Ni2+, Cu2+, Fe3+ and Ba2+ ions located in the 6-rings made trigonal planar structures with the oxygen. It has already been experimentally proved that the internal surface area of highly exchanged (more than 80%) zeolite Type-A decreased [8] possibly due to partial structure collapse and contraction of the ring size and ultimately the cage size due to energetic vibrations of phonons in the aluminosilicate framework.

Our results for the sizes of both the cages; a- cage is in the range (1.13 1.24 nm) and AY-cage (0.90 0.98 nm) were almost in conformity with those reported in the literature [16]. Debye velocity increases on cation exchange in NaA zeolite depending on the cation nature. Its increasing order is as; NaA less than FeA greater than CuA = NiA less than CoA less than BaA. But with the increasing cation concentration Debye velocity decreases, because the quantum wells (Brillouin zones) spit cations in the cages, thus becoming shallower. These cations become free ionic bonds (dangling bonds) and were responsible for reducing the sound velocity. To our knowledge it has been the first time that the sizes of cages and channels of zeolite-A have been reported by using Fermi Dirac statistics.

Conclusions

Depending on the size of cation, the zeolitic water content is in the increasing order as Ba less than Fe less than Na less than Cu less than Ni less than Co. Percentage of zeolitic water loss progressively increased on increasing the cation concentration in FeA, CoA, NiA and CuA zeolite samples, but decreased in BaA zeolite samples depending on the size, nature as well as complex formation ability. The vibrations of lattices become pronounced due to gaining of thermal energy and a logarithmic profile (T3/2-variation) for thermodynamic parameters (specific heat, enthalpy and entropy) was observed in all the ion exchanged samples of Type-A zeolite. The heat energy will be localized in the Brilluoin zones, with different modes and high energies, the brims (channels or pores) of which open up in a- and AY-cages of zeolites.

The calculated wavelengths correlates well to the unit cell parameters and found in agreement with the theoretical prediction for a- and AY-cages in Type A zeolites, which further confirm the fact that the development of a cage was the result of the excitation of ions by phonon [26]. Iron is ferromagnetic, polar and remain itinerant, while nickel being ferromagnetic is not polar and itinerant. The sizes of a- and AY-cages increase when a small radius cation replaces a large radius cation; contrarily these are decreasing with the increasing concentration of the cation due to two reasons. First it might be due to energetic phonons vibrations in the framework or due to the decreasing Debye velocity. The thermodynamic parameters; specific heat capacity, enthalpy and entropy depend greatly on the temperature as well as on the water content.

Acknowledgments

One of the authors (HP) acknowledges financial support from the higher education Commission, Pakistan (No. 20-1204/RandD/08 2149), and the Department of Education, Provincial Government of Balochistan, for grant of study leave for her PhD degree program and the Department of Chemistry, University of Balochistan for providing research facilities. HP is also thankful to the University of Peshawar for recording thermal analysis curves of the zeolite samples. HP is grateful to Prof. Sher Akber (late) for his intensive co- operation and valuable guidance.

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