Water and Solute Permeability of Plant Cuticles: Measurement and ...

8.5 Water Permeability of Synthetic Polymers as Affected by Temperatures 255
log P wv or D
60
-9.5
-10.0
-10.5
-11.0
-11.5
-12.0
-12.5
-13.0
Temperature (°C )
50 40 30 21 13 5
log P wv = -537 x - 8.15 (r 2 =0.94)
3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7
1/T x 1000 (Kelvin -1 )
log K wv = 1607 x -3.54 (r 2 = 0.98)
log D = -1918 x -5.49 (r 2 = 0.99)
-3
2.6
Fig. 8.9 Temperature dependence of Pwv, D, und Kwv for polyvinyl chloride. Data taken from
Doty et al. (1946)
For polyvinyl chloride, D was also determined by Doty et al. (1946) using the
hold-up time method (2.5). With increasing temperature (1 to 55 ◦ C), D increased
slightly (7.8 × 10 −11 –17 × 10 −11 m 2 s −1 ), while Pw increased from 2.2 × 10 −13 to
54 × 10 −13 m 2 s −1 (Fig. 8.9). The partition coefficient Kwv can be calculated from
these data using (3.17). Kwv decreased with increasing temperature from 246 to
31cm 3 vapour per cm 3 polymer.
From the slopes given in Fig. 8.9, the energies of activation can be calculated.
For EP and ED 10.3 and 36.7kJ mol −1 are obtained, and by difference (8.18) the
enthalpy of sorption or the heat of solution ∆HS of −26.4kJ mol −1 is obtained. The
enthalpy change for transfer of water into PVC is negative, indicating it to be a
spontaneous process, but with increasing temperature decreasing amounts of water
are sorbed (c.f. Sect. 8.1). For the other polymers in Fig. 8.8, D was not measured
and ED remains unknown. With polystyrene EP is zero, and this implies that ED and
∆HS are numerically equal but have opposite sign.
In Table 8.2, some additional data including rather polar polymers (EC, CA,
PEMA) have been collected. At 25 ◦ C, some of the polymers are in the glassy state
(PET, Nylon, PVA, EC and PEMA). In this collection, Pwv was highest with cellulose
acetate (which is used for desalination membranes) and lowest with polyvinyl
acetate. They differ by a factor of 251. PVA has the lowest diffusion coefficient
of 5.1 × 10 −15 m 2 s −1 . For the other polymers, D varies from 1.1 × 10 −11 (EC) to
1.2 × 10 −12 m 2 s −1 (nylon, rubber HCl) by a factor of 9. Partition coefficients (Kwv)
in the range of partial pressures where sorption isotherms are linear (3rd column)
ranged from 7,255 (PVA) to about 8 for PE.
2.4
2.2
2.0
1.8
1.6
1.4
log K wv