Synthesis, Characterization, and Gas Permeation Properties

90
Dendronization of Ethyl Cellulose
volume/cm 3 of polymer) is commonly used to estimate the efficiency of chain packing
and thus the amount of space (free volume) available for gas permeation in the
polymer matrix. FFV is calculated by the following equation: 16
FFV = (υsp – υ0)/ υsp ≈ (υsp – 1.3 υw)/ υsp
where υsp and υ0 are the specific volume and occupied volume (or zero-point volume at
0 K) of the polymer, respectively. Typically, occupied volume (υ0) is estimated as 1.3
times the van der Waals volume (υw), which is calculated by the group contribution
method. 17
Measurement of Gas Permeation Parameters. The P values were
calculated from the slopes of the time-pressure curves in the steady state where Fick’s
law holds. 18 The gas diffusion coefficients (D) were determined by the time lag
method using the following equation:
D = l 2 /6θ
here, l is the membrane thickness and θ is the time lag, which is given by the intercept
of the asymptotic line of the time-pressure curve to the time axis. The membrane
thickness was controlled so that the time lag would be in the range of 10–300 s,
preferably 30–150 s. When the time lag was < 10 s, the error of measurement
became relatively large. If the time lag was, on the contrary, > 300 s, the error arising
from the baseline drift became serious. The gas solubility coefficients (S) were
calculated by using the equation, S = P/D.
Results and Discussion
Dendron Synthesis. A series of G1 and G2 amide-containing dendrons with
branched alkyl periphery and focal carboxyl moiety (Chart 1) were prepared via a
convergent pathway 19 as shown in Scheme 1. The first generation amide-containing