Combined Thermogravimetric Determination of Activity Coefficients and Binary Diffusion Coefficients—A New Approach Applied to Ferrocene/n-Tetracosane Mixtures

Abstract

The use of isothermal thermogravimetry is investigated for combined measurements of activity coefficients and diffusion coefficients in binary mixtures, where the vapor pressure is dominated by one compound. The coupling of evaporation with gas phase and condensed phase diffusion leads to an unsteady mass loss, which depends on the activity coefficient and both, gas phase and condensed phase, diffusion coefficients, as is explained. This can be used to measure two of these properties, if the remaining parameters are known. This concept is evaluated for the ferrocene/n-tetracosane system. The former is a flame-retardant, and the latter was regarded as a substitute for a polymer, with simpler behavior. Between 341 and 399 K, the activity coefficient for ferrocene is measured to drop from above 3 to values near 1, while the diffusion coefficients are weakly temperature dependent, with values around 2 × 10–9/m2·s–1. In addition, the vapor pressures of the two pure substances were re-evaluated for this temperature range. This relatively simple method seems to be useful for the determination of such properties of other flame-retardant-related systems.

Mechanism and Kinetics of the Thermal Decomposition of Fe(C5H5)2 in Inert and Reductive Atmosphere: A Synchrotron‐Assisted Investigation in A Microreactor

“…x T = 7.4 × 10 −5 to 8.2 × 10 −4 from previously measured vapor pressure data by the group. [5] Given this, reasonable Arrhenius plots were derived using the integral method for the unimolecular dissociation reaction of ferrocene (see Section 2.6). Since unimolecular gas-phase dissociation reactions of metal-organic precursors often follow firstorder kinetics, which was also determined here experimentally, the rate constant was approximated using the Arrhenius law shown in Equation ( 6):…”

“…Three separate experiments operating at an evaporator pressure of 1500 mbar and sublimation temperatures of 323/333/353 K were conducted. Assuming thermal equilibrium, the precursor mole fractions at the reactor inlet are calculated from the vapor pressure data [ 5 ] to be between x Fe(C5H5)2 = 7.4 × 10 −5 – 8.2 × 10 −4 . After sublimation, the mixture is expanded through a 100 µm pinhole into a resistively heated silicon‐carbide (SiC) [ 102 ] flow reactor with an inner diameter of 1.0 mm and a heated length of 10 mm.…”

“…This results in $${x_{{\rm{Fe}}{{({{\rm{C}}_5}{{\rm{H}}_5})}_2}}}({T_0})$$ = 7.4 × 10 −5 to 8.2 × 10 −4 from previously measured vapor pressure data by the group. [ 5 ] Given this, reasonable Arrhenius plots were derived using the integral method for the unimolecular dissociation reaction of ferrocene (see Section 2.6). Since unimolecular gas‐phase dissociation reactions of metal‐organic precursors often follow first‐order kinetics, which was also determined here experimentally, the rate constant was approximated using the Arrhenius law shown in Equation (): $$\[ \begin{array}{*{20}{c}}{{k_{{\rm{uni}}}}\left( T \right) = {A_0}\,\cdot\,\exp \left( {\frac{{{E_a}}}{{RT}}} \right)}\end{array} \]$$where A 0 represents the collision frequency and E a is the molar activation energy in kJ mol −1 .…”

“…Ferrocene is characterized by a relatively high vapor pressure at moderate temperatures, it is nontoxic and stable in air and therefore an easy to handle precursor for the synthesis of functional materials. [5] In particular, the use of ferrocene has been successfully established in the preparation of iron-containing thin films for optoelectronic devices [6,7] or iron thin films in an oxidative atmosphere in metallurgical applications. [8] Upon thermal decomposition of Fe(Cp) 2 , iron nanoparticles (Fe-NP) can be formed which may subsequently act as functional nanomaterials for energy conversion and storage systems.…”