Gas Transport in Glassy Polymers: Prediction of Diffusional Time Lag
Abstract
:1. Introduction
2. Theoretical Background
2.1. NELF Model
2.2. Transport Model
- (i)
- the thermodynamic factor α1;
- (ii)
- the mobility coefficient L1, which is a purely kinetic quantity.
2.3. Diffusional Time Lag
- (i)
- the problem of transient one-dimensional penetrant diffusion in a glassy polymeric membrane is solved numerically (finite elements method), considering the appropriate boundary conditions (for each upstream penetrant pressure) given by the solubility values provided by the NELF model, and using the local mobility values calculated from Equation (6);
- (ii)
- from the results obtained at each upstream pressure, the penetrant mass permeated per unit area Q(t) is calculated at any time according to Equation (9);
- (iii)
- the time lag is determined from the intercept on the time axis of the steady state line asymptotically reached by the quantity Q(t).
- (a)
- the solubility curve (penetrant concentration vs. pressure) is first inspected and described by the NELF model, which makes use of polymer density, as well as values of swelling (ksw) and binary interaction (k12) coefficients; when not available, the last two parameters are retrieved from the analysis of the experimental data;
- (b)
- steady state transport data (penetrant permeability vs. upstream pressure) is analyzed and modeled, using the solubility coefficient dependence of penetrant pressure provided by the NELF model, thus retrieving the parameters L10 and β;
- (c)
- transient transport properties (diffusional time lag vs. upstream pressure) are finally calculated in a predictive fashion, making use of the description of penetrant solubility and mobility obtained, with no additional parameters.
3. Results
3.1. Gas Transport in Glassy Bisphenol a Polycarbonate (PC)
3.2. Gas Transport in Glassy PVC
3.3. Gas Transport in Glassy Poly(Ethylmethacrylate) (PEMA)
4. Conclusions
Author Contributions
Conflicts of Interest
References
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Species | T* (K) | p* (MPa) | ρ* (g/cm3) | Ref. |
---|---|---|---|---|
CO2 | 300 | 630 | 1.515 | [24] |
N2 | 145 | 160 | 0.943 | [44] |
Ar | 190 | 180 | 1.400 | [45] |
CH4 | 215 | 250 | 0.500 | [44] |
He | 9.3 | 4 | 0.148 | [45] |
PC | 755 | 534 | 1.275 | [24] |
PVC | 680 | 620 | 1.487 | [30] |
PEMA | 602 | 568 | 1.221 | [46] |
Polymer | Gas | k12 | ksw (bar−1) |
---|---|---|---|
PC | CO2 | 0.022 | 0.00120 |
N2 | −0.018 | 0.00004 | |
Ar | 0.030 | 0.00009 | |
CH4 | 0.035 | 0.00014 | |
He | −1.090 | ≈0 | |
PVC | CO2 | 0.080 | 0.00070 |
N2 | 0.210 | ≈0 | |
Ar | 0.206 | ≈0 | |
CH4 | 0.142 | 0.00003 | |
PEMA | CO2 | 0.025 | 0.00210 |
N2 | 0.032 | 0.00003 | |
Ar | 0.061 | 0.00009 | |
CH4 | 0.017 | 0.00024 |
Polymer | Gas | L10 (cm2/s) | β | Ref. |
---|---|---|---|---|
PC | CO2 | 1.3 × 10−8 | 16.2 | [23] |
N2 | 1.2 × 10−8 | 0 | [30] | |
Ar | 2.0 × 10−8 | 0 | [30] | |
CH4 | 3.9 × 10−9 | 9 | [30] | |
He | 5.2 × 10−6 | 0 | [30] | |
PVC | CO2 | 1.5 × 10−9 | 22 | [30] |
N2 | 1.8 × 10−9 | 0 | [30] | |
Ar | 3.1 × 10−9 | 0 | [30] | |
CH4 | 4.7 × 10−10 | 0 | [30] | |
PEMA | CO2 | 2.5 × 10−8 | 39.5 | [23] |
N2 | 4.2 × 10−8 | 0 | [30] | |
Ar | 6.0 × 10−8 | 5 | [30] | |
CH4 | 1.1 × 10−8 | 10 | [30] |
Polymer | Gas | Relative Average Deviation εave | |||
---|---|---|---|---|---|
DMS-TI | DMS-PI | DDM | STM-GP | ||
PC | CO2 | 45.2 | 13.5 | 11.4 | 11.0 |
Ar | 40.4 | 18.3 | 11.8 | 9.3 | |
CH4 | 92.6 | 30.0 | 21.6 | 12.2 | |
N2 | 48.6 | 13.9 | 10.1 | 10.8 | |
He | 47.6 | 9.4 | 9.6 | 21.5 | |
PVC | CO2 | 8.2 | 4.6 | 17.2 | 4.3 |
Ar | 26.9 | 24.4 | 18.4 | 7.4 | |
CH4 | 39.2 | 18.6 | 7.9 | 5.7 | |
N2 | 28.3 | 24.1 | 16.4 | 4.8 | |
PEMA | CO2 | not applicable | 17.4 | ||
Ar | 5.8 | 3.7 | 1.7 | 6.8 | |
CH4 | 11.6 | 6.5 | 4.7 | 5.6 | |
N2 | 10.3 | 10.3 | 10.3 | 4.6 |
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Minelli, M.; Sarti, G.C. Gas Transport in Glassy Polymers: Prediction of Diffusional Time Lag. Membranes 2018, 8, 8. https://doi.org/10.3390/membranes8010008
Minelli M, Sarti GC. Gas Transport in Glassy Polymers: Prediction of Diffusional Time Lag. Membranes. 2018; 8(1):8. https://doi.org/10.3390/membranes8010008
Chicago/Turabian StyleMinelli, Matteo, and Giulio C. Sarti. 2018. "Gas Transport in Glassy Polymers: Prediction of Diffusional Time Lag" Membranes 8, no. 1: 8. https://doi.org/10.3390/membranes8010008