Determination of the Arrhenius Parameters The Arrhenius parameters (A and E) for the thermal decomposition of the sample [52-54] were determined assuming a first-order chemical reaction (n = 1). The rate constant is defined as:
where A = preexponential factor, min-1 E = activation energy, kJ/mol K R = universal gas constant, J/mol K T = temperature, K t = time, s
This equation defines the temperature dependence of the specific rate constant. A second equation that relates the reaction progress to time through the rate constant is also required:
Integrating yields the following:
where a = reaction progress
In the last equation, the right-hand side has no exact solution, and several approximate solutions to this equation have been used to determine the order of reaction, activation energy, and preexponential factor:
Taking the natural logarithm of this equation yields:
The value of E and ln(A) was evaluated from the slope and intercept of function ln[- ln(1 — a)] versus 1/T [49, 52]. The data to construct this plot are taken from the TGA curve; see Figure 15.23.
Determination of the Maximum Decomposition Temperature The value of maximum decomposition temperature was calculated from the following two equations:
Figure 15.23. 1/T vs. ln[ln(1 — a)] for determining Arrhenius parameters.
Notice that in the second of these two equations, the point of maximum decomposition can be obtained by plotting dm/m versus time or temperature, and is the minimum of this curve where mi = initial mass.
Determination of the Heat of Pyrolysis The value of the heat of pyrolysis was calculated from the following two equations:
where h = heat of pyrolysis mi = initial mass P(t) = heat flow t = time
Estimation of Required Heat of Pyrolysis for Different Compounds Polyethylene (PE) is usually referred as (C2H4)n, or h2
The total molecular weight of polyethylene is:
Mw = 200,000 - 300,000 Polypropylene (PP) is usually referred as C3H6, or
Polystyrene (PS) is CgHg
¿PE,PP,PS = Na/Mw X Mw/Mw(unit) X AHic/Na = AHic/Mw(unit)
Na/Mw X Mw/Mw(unit) X H(c-C)/Na = H(C-C)/M w(unit) Polyvinyl chloride (PVC) is C2H3CI, or h h
—^ Sc^n* + hcl rc n* h cl hPvc = [(H(c-ci) + H(c-h) + H(c-c)) — (H(h—el) + H(c=c))]/Mw(h—ci) Cellulose is C6H10O5, or ch2oh ch2oh
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