Ph.D. thesis (pdf) - dirac

A.4. DBP 199
peak differently at different temperatures and it consequently has an effect on the
determined temperature dependence of the peak position.
A.4 DBP
O
O
O
O
Dibutyl-phthalate (DBP) is a benzene ring with two identical side groups. The sum
formula is C 16 H 22 O 4 and the density at ambient conditions is ρ = 1.0459 g/mL.
The sample used for the experiments is from Sigma-Aldrich and it has been used as
acquired.
The dynamical quantities are determined in this work and we also discuss the
agreement with literature data. We find m P = 67, m ρ = 56 and T g = 176 and
dT g /dP = 0.1 K.MPa −1 in the low pressure limit. We moreover find that the exponent,
x = d log e(ρ)/d log ρ is dependent on density (see section 5.2.1).
The determination of m ρ and x requires knowledge of the density dependence of the
relaxation times. To do this, we need the pressure and temperature dependence of
the density. However, this data is only available at high temperatures [Bridgman,
1932]. In the following we give a detailed description of how we have extrapolated
these data to lower temperatures and higher pressures and we carefully verify that
the extrapolations do not lead large errors on the results reported in section 5.2.1.
The expansion coefficient, α P , is calculated at two temperatures from the data of
Bridgman [1932], this gives a weakly decreasing α P with decreasing temperature.
We assume that the temperature dependence of α P is linear in the whole temperature
range and integrate α P ρ dT to obtain ρ on the atmospheric pressure isobar. The
pressure dependence of the densities reported by Bridgman [1932] are well described
by the Tait equation fits given by Cook et al. [1993], these fits give temperature dependent
Tait parameters c and b (which are directly related to the compressibility
and its first order pressure derivative). We have linearly extrapolated the temperature
dependence of these parameters and used the corresponding temperature
dependent Tait equation to calculate the pressure dependence along each isotherm.
The extrapolation of the derivatives rather than direct extrapolation of the densities
gives is expected to give a smaller error on the obtained density. We have moreover
checked that this procedure gives physically reasonable pressure and temperature
dependencies of the expansivity and the compressibility [Minassian et al., 1988].