As discussed in detail in Chapter II, transport of liquid mixtures through den e polymeric
membranes during pervaporation is usually described by a solution-di sion model comprising three main steps: sorption of the feed mixture into the membrane diffusion of
the sorbed fluid through the membrane, and de sorption of the on the
downstream side of the membrane.
For organophilic membranes, Spitzen et at. ( 1 987) have pointed out that w�le diffusion
is the rate-determining step, separation of the liquid mixture is usually determined by preferential sorption of the component in the polymer, i.e., the overall enric ent factor
for pervaporation follows the sorption behaviour (Mulder & Smolders, 1 986;
1 20 Ferreira, L.B., of
Zhang & Drioli, 1 995). Effectively, sorption detennines the fluid concentration inside the membrane which then establishes the driving force for transport. Diffusion of each
component of a liquid mixture through a membrane is influenced by molecular size. In the
Stokes-Einstein equation, diffusion is described as inversely proportional to the radius of the molecule - the larger the molecule the lower the diffusivity (Watson & Payne, 1 990). In the model developed for the overall pervaporation enrichment factor in the previous section, both the influence of sorption and of molecular size were adequately reflected by the activity coefficient and Van der Waals volume, respectively.
Consequently, two scenarios are possible:
+:+ in the pervaporation of components of vastly different molecular size, diffusion not
only detennines the flow rate through the membrane, but it should also strongly influence the separation ability of the membrane. In an environment where the difference in size between the penneating species is large, it would be possible that the smaller molecules, and therefore faster penneating species, could also have the higher overall enrichment factor, even if the membrane preferentially sorbed the larger molecule.
+:+ in the pervaporation of components of broadly similar molecular size, the enrichment factor should follow the trend set by sorption. For systems that have such behaviour, prediction of the sorption enrichment factor could be used to assess the appropriateness of the membrane material to separate the components, thus providing a simple tool for pre-selection of the membrane type and its applicability for a given use.
The work discussed in this chapter is based on the postulate that the second scenario is applicable to the pervaporation of aqueous mixtures of a1cohols and esters using hydrophobic membrane. Sample availability menat that the analysis was restricted to the PEBA membrane.
As discussed in Section II.3 .2.4, the FIory-Huggins equation is considered inadequate to predict sorption of polar compounds in polymers (Favre et al., 1 993), but good results were reported with the UN1QUAC equation in the presence of polar compounds (Heintz &
Stephan, 1 994a). It was therefore decided to use the UN1QUAC equation to attempt the prediction of sorption in PEBA membranes. If the molecular structure of the polymer is known, the UN1F AC equation can also be used to examine the experimental fitting of the membrane-binary interaction parameters obtained for UNIQUAC. Unfortunately, the required structural information for the PEBA membrane material was of proprietary nature
and was not available.
In order to calculate the mass fraction of the solvent inside the polymer material, it was assumed that the external solvent solution was in equilibrium with the membrane interface, therefore the component activities in both phases were the same (Equation V I ). Both for the fitting of binary interaction parameters between the membrane and solvent, and for multi component predictions, the UNIQUAC equation set (Equations V2 to V 8), as modified by Ennecking et al. ( 1 993), was used. All other parameters were extracted from the vapour-liquid equilibrium literature (Gmehling et ai, 1 977; Prausnitz et al., 1 986).
e n r M e' .,..
In
a/
= In<P . , + �q ln_i 2 ' + I - . ....!./ - + q .' _ j 'if/ J , j-Ai rj j= 1 j=1 '
L
e;'L"kj k= 1 where: [V I ] [V2] [V3 ] [V4]1 22 <I>i = E>. = I E>� = I n ) ) j= !
<P,(q/r)
nL <P/q/r)
j= !<Pi(qj'lr)
nL <P/q/lr)
j=! _ at) Ferreira, L.B., of [Y. S] [V.6] [Y. 7] ·t = e RT [V.8] ljwhere. ai thermodynamic activity of a component i in a muiticomponent solution consisting of n components;
ai thermodynamic activity of a component i inside a polymer; ay UNIQUAC iteraction parameter (J.mol-1)
ri. qi
dimensionless parameters for the relative molecular size and surface of component i related to the size and surface of a CH2 segment in polyethylene, respectively;rM. qM
dimensionless parameters for the relative molecular size and surface of the membrane material related to the size and surface of a CH2 segment in polyethylene, respectively;R
universal constant of gases in J.mol-1.K-1;T temperature in K;
.. coordination number assumed to be 1 0;
p density in kg.m-3;
The experimental work was divided into four parts:
.:. Sorption of pure components into PEBA beads at temperatures ranging from 20 to 5 5 ° C . This was done to evaluate the affinity of the membrane material for each component separately, to evaluate the time required for the beads to reach equilibrium, to assess the quantity of solvent sorbed into the membrane and use this information in planing multi component tests, and to generate interaction parameters necessary for prediction of sorption with UNlQUAC.
.:. Sorption of binary solvent solutions into PEBA beads for generation of the UNlQUAC interaction parameters .
• :. Sorption of multi component solvent solutions into PEBA beads for comparison of experimental enrichment factors with predicted values from UNlQUAC.
.:. Pervaporation of multicomponent solvent solutions through PEBA membranes for comparison of overall enrichment factors with those obtained from sorption experiments.
V. 2 SORPTIO N EXPERI M ENTS