Proceedings e report - Firenze University Press

L*
80
60
40
10 -2
WOOD SCIENCE FOR CONSERVATION OF CULTURAL HERITAGE
120hour 960hour
10 3
Aging time [h]
12288hour
untreated
1619year
7680hour
10 8
59
ΔE
40
20
0
10 -2
120hour
10 3
960hour
Aging time [h]
7680hour
12288hour
1619year
Fig. 2: The relationship between aging time and the lightness (L*) or the color difference (ΔE)
( :90 o C, :120 o C, :150 o C, :180 o C, :naturally aging).
3.2. Kinetic Analysis
The concepts of kinetics are often applied to accelerated aged phenomena of materials to predict the
lifetime in natural ageing conditions. It is empirically known that the chemical reaction can be
described by Arrhenius equation:
Ea
k = Aexp(
- )
(3)
RT
where k is the rate constant of the chemical reactions, A the frequency factor, Ea the apparent
activation energy, R the gas constant and T the absolute temperature. It represents the dependence of
the reaction rate on the temperature and the apparent activation energy. By determining the time which
the chemical reaction achieves the arbitrary criterion of properties at different aging temperatures, the
reciprocal of treatment temperatures can be plotted versus the logarithm of the determined time. This
plot is called the Arrhenius plot. The apparent activation energy is then calculated from the slope of
the Arrhenius plot. This allows determining the degradation rate at any temperature by extrapolating
the Arrhenius plot.
As mentioned above, the extrapolation procedure generally uses only one processed data point from
each accelerated aging temperature curve, eliminating most of the experimental points from analysis.
This elimination sometimes makes it difficult to accurately predict the change during natural aging. To
determine the activation energy using all of the data, we used the time-temperature superposition
(TTSP) method [5]. TTSP is a well-known methodology that is frequently used to describe the
mechanical and electrical relaxation behavior of polymers. The Arrhenius approach applying the
TTSP method has been successfully used for years in polymers to make predictions of thermal aging
at ambient conditions. According to the principle of the TTSP method, both time and temperature are
equivalent, i.e. the material parameter values obtained for short times at a given temperature is
identical with that measured for longer times at a lower temperature when the curves are shifted on a
logarithmic time axis. The curves of the measured material parameter vs. logarithmic loading time at
different temperatures can be superimposed by proper scale changes on the time axis. The shift
distance along the logarithmic time axis is called the time-temperature shift factor aT given by
a = t / t
(4)
T
where tref is the test time at a reference temperature Tref, and tT is the time required to give the same
response at the test temperature T. Combining Eqs. (3) and (4) gives
⎡ E ⎛ ⎞⎤
a
⎢ ⎜
1 1
a
⎟
T = exp − ⎥
(5)
⎢
⎜ ⎟
⎣
R ⎝ Tref
T ⎠⎥⎦
ref
T
10 8