Page 118 - Separation process principles 2

3.2 Diffusion Coefficients 83

Table 3.12 Diffusivities of Solutes in Rubbery Polymers
Diffusivity,
Polymer Solute Temperature, K cm2/s
Polyisobutylene n-Butane
i-Butane
n-Pentane
n-Hexadecane
Hevea rubber n-Butane
i-Butane
n-Pentane
n-Hexadecane
Polymethylacrylate Ethyl alcohol
Polyvinylacetate n-Propyl alcohol
n-Propyl chloride
Ethyl chloride
Ethyl bromide
Polydimethylsiloxane n-Hexadecane
1,4-Polybutadiene n-Hexadecane
Styrene-butadiene rubber n-Hexadecane

smaller molecules have higher diffusivities. A more detailed From (3-50),
study of the diffusivity of n-hexadecane in random styrene1
butadiene copolymers at 25°C by Rhee and Ferry [21] shows
a large effect on diffusivity of fractional free volume in the
polymer.
Diffusion and permeability in crystalline polymers de- Membrane thickness = 22 - zl = Az = P~(pi - p2)IN
pend on the degree of crystallinity. Polymers that are 100%
crystalline permit little or no diffusion of gases and liquids.
For example, the diffusivity of methane at 25OC in poly-
oxyethylene oxyisophthaloyl decreases from 0.30 x low9 to
0.13 x lop9 cm2/s when the degree of crystallinity in- As discussed in Chapter 14, polymer membranes must be very
creases from 0 (totally amorphous) to 40% [22]. A measure thin to achieve reasonable gas permeation rates.
of crystallinity is the polymer density. The diffusivity of
methane at 25°C in polyethylene decreases from
0.193 x to 0.057 x cm2/s when the specific grav-
Cellular Solids and Wood
ity increases from 0.914 (low density) to 0.964 (high den-
sity) [22]. A plasticizer can cause the diffusivity to increase. As discussed by Gibson and Ashby [23], cellular solids
For example, when polyvinylchloride is plasticized with consist of solid struts or plates that form edges and faces of
40% tricresyl triphosphate, the diffusivity of CO at 27°C in- cells, which are compartments or enclosed spaces. Cellular
creases from 0.23 x to 2.9 x lop8 cm2/s [22]. solids such as wood, cork, sponge, and coral exist in nature.
Synthetic cellular structures include honeycombs, and
foams (some with open cells) made from polymers, metals,
EXAMPLE 3.10
ceramics, and glass. The word cellulose means "full of little
Hydrogen diffuses through a nonporous polyvinyltrimethylsilane cells."
membrane at 25OC. The pressures on the sides of the membrane are A widely used cellular solid is wood, whose annual world
3.5 MPa and 200 kPa. Diffusivity and solubility data are given in production of the order of 1012 kg is comparable to the pro-
Table 14.9. If the hydrogen flux is to be 0.64 kmol/m2-h, how thick duction of iron and steel. Chemically, wood consists of
in micrometers should the membrane be? lignin, cellulose, hemicellulose, and minor amounts of or-
ganic chemicals and elements. The latter are extractable, and
SOLUTION the former three, which are all polymers, give wood its struc-
ture. Green wood also contains up to 25 wt% moisture in the
Equation (3-52) applies. From Table 14.9,
cell walls and cell cavities. Adsorption or desorption of
D=160~10-~~m~/s H=S=0.54~10-~mol/m~-~a moisture in wood causes anisotropic swelling and shrinkage.