Transition Met. Chem., 12, 289-291 (1987) Thermal decomposition of Mo Iv complexes 289 Thermal decomposition of molybdenum(IV)dialkyldithiocarb- amates: application of a new method to kinetic studies Rafaei Lozano*, Jesfis Romfin, Juan C. Avil6s and Amparo Moragues Departamento de Quimica Inorgdnica y Analltica, Facultad de Farmacia, Universidad Complutense, 28040 Madrid, Spain Antonio Jerez and Enrique Ramos Departamento de Quimica Inorgdnica, Facultad de Qulmicas, Universidad Complutense, 28040 Madrid, Spain Smnmary We describe the application of a new method (differential scanning calorimetry, d.s.c.) to the kinetic analysis of the thermal decomposition under dinitrogen of several ad- ducts with pyridine of Mo w dialkyldithiocarbamates. The adducts are of the form [Mo/(dtc)a(pyh] (dtc=Et/, n-Pr2, i-Pr 2, t-Bu2, or N-methyl-cyclo-hexyl- dithiocarbamate and py). From d.s.c, curves, the activation energies for the loss of two pyridine molecules were calculated, and the mechanism was deter- mined. A relationship between activation energies and the steric requirements of the ligands was also determined. Introduction The determination of kinetic parameters by non- isothermal methods offers advantages over conventional isothermal studies (~). However, the methods usually em- ployed for kinetic analysis (2-9) lead to ambiguous results, specially if the reaction studied is diffusion-controlled. In other papers, we have reported the synthesis, thermal behaviour, and kinetic studies by the procedure of Thomas and Clarke (~~ of several [Mo2(dtc)4(py)/] (dtc = Et2, n-Pr2, i-Pr2, t-Bu2, or N-methyl-cyclohexyl- dithiocarbamate and py). Most recent/y, we reported a new method to study the kinetics of nonisothermal decomposition reactions of solids by d.s.c.~sk This paper reports a study by differential scanning calorimetry of the thermal loss of two pyridine molecules from adducts of dialkyldithiocarbamatomolybdenum(IV) complexes (Equation 1), EMo2(dtc)4(py)2] (solid) [Mo2(dtc)4 ] (solid)+ 2py (gas) (1) we have determined the mechanism by the method described by us (~5), and we have calculated the activation energy for this process. Results and discussion The d.s.c, curves of all the compounds show an endo- D1 thermic peak between 101.5 and 209 ~ C, the mass loss D2 accompanying this endothermic transition corresponding D3 on the TG curves to the loss of two molecules of pyridine. The residue is [Mo/(dtc)4] in all cases (13). D4 The rate of a thermal decomposition reaction of a solid can be expressed by the Arrhenius Equation (2). F1 d:~ R2 ~ f = Ae- E~/RTf(c~) (2) * Author to whom all correspondenceshould be directed. In Equation (2), c~is the fraction of material which has reacted at time t, Ea is the activation energy, f(a) is a function which depends on the actual reaction mechanism and A is the pre-exponential Arrhenius factor. We have collected in Table 1 the mathematical expressions of the functions f(c0 corresponding to some of the mechanisms of thermal decomposition found in the literature (1). For the case where the temperature of the sample is increased at a constant rate, we can write Equation (3), where fl is heating rate, tiT~dr. d~ _ c( = fie - E~/R rf(c~) (3) dT Upon integration, this gives Equation (4). f( d~ -A fr'e-r"/Rrf(cOdT (4) f(~ fl o By differentiating the logarithmic form of Equation (2) with respect to dln(1 - a), we obtain Equation (5). dln(dcqdT) dlna' E a d(1/T) dlnf(~) dln(1 - cr - dln(1 - cz) - R dln(1 - ~) ~-dln(1 - cr or Alnc( E, A(1/T) Alnf(c~) (5) Aln(1 -- a) R Atn(1 - cr Aln(1 - c~) Thus the plots of (Aln~'-Alnf(~))/Aln(1 -a) versus A(1/T)/Aln(1 -:~) should be a straight line with a slope -Ea/R, irrespective of thef(~) employed. However, we can select the f(e) that best fits the actual mechanism of the reaction studied by means of the intercept value, which, in ideal agreement with Equation (5), should be zero. From the d.s.c, curve ofadduct [Mo2(Et2NCS/)4(py)a ] we constructed the Table 2. Table 1. Kinetic equations Mechanism f(~) Rate-controlling process R3 1/2e [--ln(1--~)] -1 3/2(1--a) 2/3 1 --(1 _~)1/3 [3/2(1--e)-1/3] -1 (!-~) 2(l-e) 1/2 3(1-~) 1" One-dimensional diffusion. Two-dimensional diffusion. Three-dimensi0nal diffusion; Jander equation. Three-dimensional diffusion; Ginstling-Brounshtein equation. Random nucleation. Phase-boundary reaction (cylindrical symmetry). Phase-boundary reaction (spherical symmetry). 0340-4285/87 $03.00+ .I2 9 I987 Chapman and Hall Ltd