Isokinetic Parameters of Thermal Degradation of Powder of [ Cd ( N-Boc-gly ) 2 ( H 2 O ) 2 ]

The coordination polymer [Cd(N-Boc-gly)2(H2O)2]n undergoes thermally induced degradation in temperature region between 60 and 900C. Kinetic parameters were determined for dehydration (63-123C) and further degradation processes (123-461C) using different isoconversional and non-isoconversional methods. Due to appearance of kinetic “compensation effect”, isokinetic temperatures were determined for individual degradation processes and correlated with resonant vibrational frequencies ascribed to Cd-OH2 coordination bond, Cd-O (O from N-Boc-glyH ligand) coordination bond and C-O covalent bond.


Introduction
Organometallic coordination polymers have, due to their favorable physical and chemical properties enabling them variety of potential applications, recently been attracting considerable scientific interest [1][2][3][4][5][6].Key point in manipulating network structures of the coordination polymers is the selection of appropriate ligands as building blocks [7], and metal ions with suitable coordination geometries [8].Water molecules are usually present in inner or outer sphere of complex, beside organic ligands.Coordination polymers containing Cd(II) have been considered to be particularly significant because of their ability to form bonds with different donors simultaneously, large bond radius, various coordination modes and special physical properties of Cd(II) ion [9][10][11].N-substituted amino acids stand out as ligands with especially interesting biological properties [12][13][14].Multidisciplinary study concerning Co(II), Cd(II) and Zn(II) complexes containing N-Boc-gly ligand have shown antimicrobial and antifungal activity of these complexes [15].
One of the characteristics of organometallic coordination polymers is thermal instability, which leads to stepwise structural transformations at elevated temperatures, including dehydration and degradation resulting in deterioration of favorable properties.Therefore, detailed understanding of structural transformation kinetics is of a huge importance.In this study, kinetics of thermally induced degradation of Cd(II) coordination polymer with N-benzyloxycarbonylglycinato ligand ([Cd(N-Boc-gly) 2 (H 2 O) 2 ] n ) was analyzed, with special emphasis on isokinetic parameters.

Experimental procedure
The coordination polymer [Cd(N-Boc-gly) 2 (H 2 O) 2 ] n was synthesized in powder form according to procedure published in ref [16], in a simple reaction between CdCl 2 •2.5H 2 0 and N-Boc-glyH (molar ratio 1:2, ethanol-water mixture, pH [5][6]. Thermal stability of the prepared Cd(II) coordination polymer and thermally induced degradation were examined by thermogravimetry and differential scanning calorimetry, using TA Instrument SDT Q600.Measurements were carried out under non-isothermal conditions from room temperature to 900 o C, with Al 2 O 3 as a reference, at constant heating rates of 5, 10, 15, 20 o C/min, on samples weighing around 6 mg, in nitrogen, with flow rate of 100 cm 3 min -1 .

Solid-state kinetic analysis
The rate of thermally activated single-step transformation in solid-state can be represented using equation [17,18]: where t is the time, T is the temperature, k(T) is the rate constant, α is the conversion degree and f(α) is the conversion function concerning the kinetic model.For non-isothermal measurements, the value of conversion degree at temperature T is equal to the ratio of the area between the initial peak temperature and temperature T, to the total peak area.Replacing rate constant k(T) with Arrhenius equation yields the expression for the rate of conversion: (2) where R is the gas constant, while A (pre-exponential factor) and E (activation energy) are Arrhenius parameters.Constant values of activation energy with regard to temperature and conversion degree can only be expected for a single-step reaction, and, based on a quasisingle-step reaction, activation energy in Equation 2 becomes an apparent quantity (E a ).For non-isothermal experiment at constant heating rate, Equation 2 can be transformed into: (3) where β is heating rate (β = dT/dt and dα/dt β(dα/dT)).Rearranging and integrating this equation, integral form of the conversion function (g(α)) can be derived: (4) where p(x) is the temperature integral for x = E a /RT which does not have analytical solution.

Results and discussion
Study of thermal stability of [Cd(N-Boc-gly) 2 (H 2 O) 2 ] n coordination polymer showed that it was thermally stable up to around 60 o C, when multi-step degradation occurred (Fig. 1).Shift of DSC and DTG peaks to higher temperatures with increase in heating rate was observed, indicating that individual degradation processes are thermally activated.
The individual degradation processes were identified according to mass loss in order to establish the reaction mechanism (Scheme 1).The first process, which occurred in the temperature range 63-123 o C, was identified as dehydration, in which two coordinated water molecules were released from each monomer unit.Dehydration was followed by further degradation, which involved loss of one N-Boc-gly fragment in the temperature range 123-269 o C and one C 6 H 5 CH 2 O-fragment in the temperature range 269-461 o C. Degradation process continued at higher temperatures, but the effect was not well defined in the obtained thermograms and therefore it was not further discussed.
In order to investigate thermally induced degradation of [Cd(N-Boc-gly) 2 (H 2 O) 2 ] n in more detail, kinetic parameters of individual processes were determined from DTG curves applying different isoconversional and non-isoconversional methods.
First, overall values of Arrhenius parameters were determined using Kissinger's and Ozawa's methods [19,20], which are based on dependence of peak temperature on heating rate.Obtained results (Table I) exhibited good accordance with kinetic parameters describing organic polymer degradation, which have been published in the literature [21][22][23].Further examination was conducted by applying Vyazovkin's and Ortega's isoconversional methods [24][25][26], which yield the effective values of E a at various α.According to Vyazovkin's method [25,26], E α is determined from the minimum of function Ф(E α ), for a series of measurements at different heating rates: ) ) where i and j refer to individual heating rates.Ortega's method [24,26] takes into account the two first terms of Taylor's series expansion of Δp(x α ) = p(x α ) -p(x α-Δα ) leading to expression: , , ln ) where ΔT α,i = T α,i -T α-Δα,i .Constant values of E a with respect to conversion degree were obtained in the case of dehydration (Fig. 2. a), showing that it is a single-step process.On the other hand, processes corresponding to further degradation exhibited change in E a higher than 10% of E a value (Fig. 2. b and c), suggesting that these processes are complex, consisting of several overlapping steps.The values of E a determined using Vyazovkin's and Ortega's isoconversional methods as well as Kissinger's and Ozawa's methods are in excellent agreement.

Tab. I Overall values of kinetic parameters determined using Kissinger's and Ozawa's methods
Kissinger's method Ozawa's method E a (kJmol -1 ) A (min -1 ) E a (kJmol -1 ) A (min -  Utilization of model-fitting approach, according to which different forms of the conversion function are introduced into certain model-fitting equation and fitted, enables determination of invariant kinetic parameters (IKP) without knowing the true model, if isokinetic relationship applies.Using Coats-Redfern equation [27], values of Ea and A were determined for various kinetic models, for all degradation processes (Table II).Obtained kinetic parameters differed in a wide range of values depending on applied model, but they were linearly correlated by "compensation effect" exhibiting the existence of artificial isokinetic relationship (Fig. 3), which can be represented by: lnA j = a + bE j (7) where a and b are intercept and slope of the straight line, while index j refers to reaction model [28].Repeating this procedure on data sets obtained at different heating rates, pairs of parameters a and b were obtained for each heating rate.Linear relation between parameters corresponding to different heating rates was established:   It was suggested that the occurrence of a real isokinetic relationship is connected with a resonant vibrational energy exchange [29], with frequency: where k B is Boltzmann constant and h is Planck constant.It usually corresponds to mid-or far-infrared region of the spectrum.Using the values of kinetic parameters obtained for different kinetic models (Table II), isokinetic temperature was determined as the intersection point of the straight lines corresponding to individual models (Fig. 4

Conclusion
The coordination polymer [Cd(N-Boc-gly) 2 (H 2 O) 2 ] n exhibited multi-step degradation after heating at temperatures higher than 60 o C, which included clearly defined processes of dehydration and release of N-Boc-gly and C 6 H 5 CH 2 O-fragments.Application of isoconversional methods revealed that dehydration (process 1) was a single-step process, while the release of fragments (process 2 and 3) were complex processes, involving several overlapping steps.The obtained values of apparent activation energy for second and third step of 120 and 260 kJ/mol, respectively, additionally support conclusion that the second step correspond to breaking coordination bond while the third step is breaking of covalent bond.The existence of isokinetic relationship was observed for all degradation processes, allowing determination of invariant kinetic parameters.Using the obtained values of isokinetic temperatures, resonant vibrational frequencies were found: 7.83•10 12 s -1 (261 cm -1 ) for process 1; 9.64•10 12 s -1 (321 cm -1 ) for process 2 and 1.35•10 13 (449 cm -1 ) s -1 for process 3, which can be assigned to Cd-OH 2 coordination bond, Cd-O (O from N-Boc-glyH ligand) coordination bond and C-O covalent bond, respectively.
), and it was equal to 103, 190 and 374 C for individual processes, respectively.The values of resonant vibrational frequency were then calculated: 7.83•10 s (261 cm ) for process 1; 9.64•10 s (321 cm ) for process 2 and 1.35•10 (449 cm ) s for process 3. The values of obtained vibrational frequency can be assigned to Cd-OH for process 1, Cd-O (O from N-Boc-glyH ligand) coordination bond for process 2, and C-O covalent bond for process 3 [30].

Fig. 4 .
Fig. 4. Arrhenius lines plotted by data given in Table II, for individual processes of degradation, at heating rate β = 15 o Cmin −1 .
Tab. II Kinetic parameters obtained by applying Coats-Redfern equation on different conversion functions, at heating rate β = 15 o Cmin −1 .