The bonded energy terms of the polymer chain consist of (a) the ...... volume distribution of a polymer with intrinsic microporosity (PIM-1), Journal of Membrane ...
Supporting Information
Structural Characteristics and Transport Behavior of Triptycene-based PIMs Membranes: A Combination Study Using ab initio Calculation and Molecular Simulations Yi-Rui Chena, Liang-Hsun Chena, Kai-Shiun Changa, Tzu-Hao Chena, Yi-Feng Linb and Kuo-Lun Tunga * a b
Department of Chemical Engineering, National Taiwan University, Taipei 106, Taiwan
R&D Center for Membrane Tech./ Dep of Chem. Eng., Chung Yuan University, Chungli, Taiwan
Contents: Supporting Information 1:
Model construction using 21-step method………........................…...S2
Supporting Information 2:
COMPASS forcefield, charge parameter, partial charge distribution, and ab initio calculation…..……………….….....…………..…….....S4
Supporting Information 3:
Details of the theoretical calculation and the properties ………...... S11
Supporting Information 4:
Slices of simulation models across x, y, z axes for the four membranes.…................................................................................…S21
Supporting Information 5:
Simulated and experimental solubility, diffusivity, and gas permeability data of the five gases in the four membranes …………........ S23
Supporting Information 6:
MSD diagrams of the H2, O2, N2, CO2, and CH4 for the four membranes during a 3,000-ps MD simulation.………………….......…...S25
Supporting Information 7
The van der Waals volume, FFV, and FAV codes…….……….........S26
Supporting Information 8:
Cavity size analyses using the MATLAB software ….……….…...S28
References
….………..……………………………............................................S33
S1
Supporting Information 1: Model construction using 21-step method Table S1. A similar 21-step MD compression and relaxation scheme [1, 2] Step
Slow Decompression Conditions
Duration (ps)
Cycle
1
NVT, Tmax
100
1
2
NVT, Tfinal
100
1
3
NPT, 0.002×Pmax (0.01 GPa ), Tfinal
500
3
4, 5
NVT, Tmax, Tfinal
100, 100
1
6
NPT, 0.02×Pmax (0.1 GPa ) , Tfinal
300
2
7, 8
NVT, Tmax, Tfinal
100, 100
1
9
NPT, 0.2×Pmax (1 GPa ) , Tfinal
100
2
10,11
NVT, Tmax, Tfinal
100, 100
1
12
NPT, 0.6×Pmax (3 GPa ) , Tfinal
100
1
13, 14
NVT, Tmax, Tfinal
100, 100
1
15
NPT, 1×Pmax (5 GPa ) , Tfinal
100
1
16, 17
NVT, Tmax, Tfinal
100, 100
1
18
NPT, 0.6×Pmax (3 GPa ) , Tfinal
100
1
19, 20
NVT, Tmax, Tfinal
100, 100
1
21
NPT, 0.2×Pmax (1 GPa ) , Tfinal
100
1
22, 23
NVT, Tmax, Tfinal
100, 100
1
24
NPT, 0.1×Pmax (0.5 GPa ) , Tfinal
100
2
25, 26
NVT, Tmax, Tfinal
100, 100
1
27
NPT, 0.01×Pmax (0.05 GPa ) , Tfinal
100
2
28, 29
NVT, Tmax, Tfinal
100, 100
1
30
NPT, Pfinal (0.0001 GPa ) , Tfinal
100
1
31
NPT, Pfinal (0.0001 GPa ) , Tfinal
1,000
1
* Tmax= 800K (beyond the glass temperatures of the four polymer membranes); Tfinal = 298K; Pmax= 5 GPa; Pfinal =1 bar
S2
Table S2. The experimental properties of the four membranes: surface area, pore volume, diffusivity, density. Experimental properties
Order of materials
Surface area (m2/g)
PTMSP (949)[3] > PIM-Trip-TB (899)[4] > KAUST-PI-1 (752)[3] > PIM-PI-1 (600)[5]
Pore volume (cm3/g)
PTMSP (0.96)[3] > PIM-Trip-TB (0.55)[4] > KAUST-PI-1 (0.53)[3] > PIM-PI-1 (-)
Diffusivity (10-8 cm2/s)
N2 : PTMSP (4400)[6] > PIM-Trip-TB (135)[4] >KAUST-PI-1 (53)[3] > PIM-PI-1 (20)[5]
Density
PTMSP (0.75)[3] < KAUST-PI-1 (1.09)[4] < PIM-Trip-TB (1.10)[3] < PIM-PI-1 (1.15)[5]
O2 : PTMSP (5200)[6] > PIM-Trip-TB (462)[4] >KAUST-PI-1 (226)[3] > PIM-PI-1 (56)[5]
(g/cm3) In experimental analyses, the surface areas, the pore volumes, and the diffusivities all follow the order of: PTMSP > PIM-Trip-TB > KAUST-PI-1 > PIM-PI-1. The microstructures and transport properties are closely related to the material densities. However, the densities increase in the order of: PTMSP < KAUST-PI-1 < PIM-Trip-TB < PIM-PI-1. We inferred that there may be minor deviation in the experimental measurement of the PIM-Trip-TB density and the density may range between 1.04 and 1.08 g/cm3. Therefore, the deviation between the simulated and the experimental densities of PIM-Trip-TB membrane should be lower.
S3
Supporting Information 2: COMPASS forcefield, charge parameter, partial charge distribution, and ab initio calculation. 2-1 The COMPASS force field is as follows [7]: 4 3 2 E K 2 b b0 K 3 b b0 K 4 b b0 b
(a) 4 3 2 H 2 0 H 3 0 H 4 0
(b)
V1 1 cos 10 V2 1 cos 2 20 V3 1 cos 3 30 (c) K x x Fbb ' b b0 b ' b '0 F ' 0 ' '0 2
b
x
b'
'
(f)
(e)
(d)
Fb b b0 0 b b0 V1 cos V2 cos 2 V3 cos3 b
b
(h)
(g) b ' b '0 V1 cos V2 cos 2 V3 cos3 b'
(i) Aij K ' cos 0 ' '0 2 9 i j rij ' (j)
Bij 3 6 rij (k)
qi q j i j rij (l)
(1)
The energy terms are divided into three categories: bonded energy terms, cross-terms, and non-bonded energy terms. The bonded energy terms of the polymer chain consist of (a) the covalent bond stretching energy terms, (b) the bond angle bending energy terms, and (c) the torsion angle rotation energy terms. The energy of the torsion angle was fitted using a Fourier series function. The out-of-plane energy, or improper term (d), is described as a harmonic function. The cross-interaction terms include the dynamic variation for bond stretching, bending, and torsion angle rotation (e–j). The last two terms, (k) and (l), represent the van der Waals 9-6 Lennard-Jones potential and the Coulombic electrostatic interaction, respectively.
S4
2-2 Non-bonded charge interaction parameters for the simulation of the PTMSP, PIMPI-1, PIM-Trip-TB, and KAUST-PI-1 membranes.
(a) PTMSP
(b) PIM-PI-1
(c) PIM-Trip-TB
(d) KAUST-PI-1
Figure S1 Chemical structure of (a) PTMSP, (b) PIM-PI-1, (c) PIM-Trip-TB, (d) KAUST-PI-1. Numbers correspond to atoms for simulation parameters list in Table S3
S5
Table S3. Non-bonded charge interaction parameters for the simulation of the PTMSP, PIM-PI-1, PIM-TripTB, and KAUST-PI-1 membranes. PTMSP
PIM-PI-1 QEq
Number
Charge (eV)
PIM-Trip-TB QEq
Number
KAUST-PI-1 QEq
Number
Charge (eV)
Charge (eV)
QEq Number
Charge (eV)
1
-0.406
1, 2, 20, 21, 24, 25, 54, 55,
0.259
1, 19
0.199
1, 2, 25, 26, 29, 30, 59, 60
0.250
2
-0.032
3, 4, 18, 19,
-0.130
2, 20
0.039
3, 4, 23, 24,
-0.130
3
-0.024
5, 6, 9, 12, 13
0.000
3, 17
-0.135
5, 6, 21, 22
-0.013
4
0.483
7, 11
0.010
4, 18
-0.155
7, 8
0.040
5,6,7
-0.432
8, 10
-0.195
5, 16
0.030
9, 10,
0.045
11, 12, 13, 14, 15, 16, 17, 18, 19
0.104
14, 15, 16, 17,
-0.380
6, 15
0.017
11, 12, 13, 14,
-0.100
8,9,10
0.110
22, 23, 56, 57
-0.545
7, 8
-0.122
15, 18
-0.146
28, 29, 50, 51
-0.034
9, 10,
0.045
16, 17, 19, 20,
-0.390
26, 27, 52, 53
-0.110
11, 14
-0.111
27, 28, 61, 62
-0.545
30, 31, 46, 47
0.378
12, 13
-0.106
31, 32, 57, 58
-0.110
32, 33, 48, 49
-0.510
21, 24
-0.349
33, 34, 55, 56
-0.034
34, 45
-0.395
22, 23
-0.125
35, 36, 51, 52
0.378
35, 40
0.186
25
0.012
37, 38, 53, 54
-0.510
36, 37, 38, 39
0.009
26, 27, 28, 29, 30, 31, 32, 33, 34, 35
0.090
39, 50
-0.395
41, 42, 43, 44
-0.326
36, 37, 38, 39, 40, 41
0.110
40, 45
0.186
58, 59, 76, 77
0.130
41, 42, 43, 44
0.009
66, 67, 68, 69
0.113
46, 47, 48, 49
-0.326
60, 61, 62, 63, 64, 65,70, 71, 72, 73, 74, 75,
0.130
63, 64, 83, 84
0.120
80, 81, 82, 83, 84, 85,86, 87, 88, 89, 90, 91
0.167
65, 72
0.150
78, 79, 92, 93
0.163
66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78,
0.147
79, 80, 81, 81
0.100
87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98
0.167
85, 86, 99, 100
0.163
* It is noted that the QEq charges are slightly affected by the surrounding atoms.
S6
Table S4. Atomic charges and bond lengths of the CO2, CH4, N2, O2 and H2. Molecule
Atom
Atom Charge (e)
Bond length (Å)
CO2
C O
0.75 -0.375
1.180
CH4
C H
-0.668 0.167
1.099
N2
N
0
1.102
O2
O
0
1.208
H2
H
0
0.740
S7
2-3 The partial charge distributions of the four membranes and the five gases. PTMSP
PIM-PI-1
PIM-Trip-TB
KAUST-PI-1
Figure S2 The partial charge distributions of the PTMSP, PIM-PI-1, PIM-Trip-TB, and KAUST-PI-1 membranes. S8
CO2
CH4
O2
N2
H2
Figure S3 The partial charge distributions of the CO2, CH4, O2, N2, and H2.
S9
2-4 The partial charge distributions calculation In order to explain the five gas molecules in the four membranes of sorption and diffusion behavior. We use ab initio calculation to obtain the partial charge distribution and explain the interaction between the polymer membranes. The parameters for the ab initio calculation are listed as follows: Ab initio calculations on CASTEP [8, 9] that uses Kohn-sham density functional theory [10-12] and plane-wave pseudopotential method [13, 14]. Ultrasoft pseudopotentials, which give lower cut-off energies than norm-conserving pseudopotentials, are used with the generalized gradient approximation (GGA) [15] based on the Perdew–Burke–Ernzerhof exchange–correlation functional.(PBE) [16, 17]. Due to four monomer is molecule not crystal, use a Gamma k-point sampling grid are chosen after convergence testing A cutoff energy is set to be 500 eV and the standard quasi-Newtonian BFGS optimization method is employed to relax the structure to its minimum energy configuration. The convergence criteria for total energy, maximum ionic force, maximum ionic displacement, maximum stress and self-consistent field (SCF) tolerance are 1 105 eV/atom, 3 10-2 eV/Å , 1 10-3 Å, 5 102 GPa and
210 -7 eV/atom
respectively. 2-5 Charge equilibration (QEq) charges To establish the polymer models closer to the experimental densities, and to describe the dynamic interaction between the polymer membranes and the gases, we used the ab initio calculation to obtain the QEq charge [18] on each atom. The COMPASS forcefield charges cannot readjust to match the electrostatic environment.
2-6 Energy minimization The standard quasi-Newtonian BFGS optimization method is employed to optimization the structure to its minimum energy configuration. The convergence criteria for total energy, force, stress, and displacement are 0.0001 kcal/mol, 0.005 kcal/mol/Å, 0.005 GPa, and 5×10-5 Å, respectively.
S10
Supporting Information 3: Details of the theoretical calculation and the physical properties 3-1 Dihedral Angle Profiles Dihedral angle profiles are used to examine the stiffness of polymer chains. Four consecutive atoms in the backbone are used to calculate the dihedral angle θ. The dihedral angle is defined as the angle between the two planes formed by the first three and last three atoms. For the most extended planar conformation, the dihedral angle θ is ±180°. Figure S4 illustrates the schematic diagrams of the analyzed atomic segments for the dihedral angle analysis.
Figure S4 Schematic diagrams of the analyzed atomic segments for the dihedral angle analysis.
S11
3-2 Fractional Free Volume (FFV) and Fractional Accessible Volume (FAV) The Fractional Free Volume (FFV) value of a membrane can be estimated using the following equations [19, 20]: FFVSim. =
V-V0
(2)
V
V0 = 1.3Vw
(3)
where V is the cell volume at T = 298 K and Vw is the van der Waals volume obtained from the van der Waals surface without using the contribution method from Bondi's group [19]. The FFV is obtained when the probe size is equal to zero. For the Fractional Accessible Volume (FAV) analysis, the accessible volume was probed using a hard, spherical particle with a specific radius; a factor of 1.3 was not adopted. The van der Waals volume, FFV, and FAV of the membrane model can be obtained from the codes in Supporting Information7.
S12
Figure S5 Free volume morphologies of the (a) PTMSP, (b) PIM-PI-1, (c) PIM-Trip-TB, and (d) KAUSTPI-1 membranes. The blue and gray regions indicate the pathways and polymers in the membrane, respectively.
S13
3-3 Cavity Size Distribution (CSD) To characterize the cavity size distribution, Hofmann et al. proposed the V_connect and R_max approaches to calculate the free volume distribution of membranes [21]. Heuchel et al. then applied these two approaches to the PIM-1 polymer. The simulation results obtained from the R_max method agreed well with the experimental results from the PALS (Positron Annihilation Lifetime Spectra) [22] than those from the V_connect method. To calculate the cavity size, we developed an image analysis algorithm in MATLAB. We was found that calculated cavity size distribution is closer to the experimental result when the simulation model was set with a slice thickness of 2.5Å. The details of the MATLAB program and calculations are given as Supporting Information8. The algorithm is based on the Euclidean distance transform (EDT) and can be found in our previous study [23, 24]. The cross-sectional images of the six membrane models in the x, y, and z directions were used for further analyses. In each direction, we selected nine images of a membrane model at various positions. Then, the cross-sectional images of the membrane models were treated as a MATLAB photograph, as illustrated in Figure S6. For each cross-sectional image, the area occupied by the cavity size elements was calculated. The pore size distribution can be obtained from the values of the effective pore diameter.
Figure S6 Picture of the model cross-sections of the membrane models constructed in this work. The white and black areas represent the cavity size element and polymer element, respectively.
S14
3-4 Sorption analysis A dual-mode sorption model is used to describe the sorption of gas molecules in glassy polymers. This model is based on Henry’s law and the Langmuir-type sorption. The dual-mode sorption model is expressed by [25, 26]: C = CD + CH = kD p + S≡
C p
c'H b p
(4)
1+b p
= SD + SH = kD +
c'H b
(5)
1+b p
where C is the total gas concentration in a glassy polymer; CD is the gas concentration based on Henry's law sorption; CH is the gas concentration based on the Langmuir sorption; p is the operating pressure; kD is the Henry's law coefficient; b and cH' are the Langmuir hole affinity parameter and the capacity parameter, respectively; S is the solubility of the penetrant; and SD and SH are solubility values based on Henry's law and the Langmuir-type sorption, respectively. Gas permeation through a polymer membrane is an indicator of the membrane performance and is governed by the sorption and diffusion behavior of the gas. To describe the gas permeation through a polymer membrane, the “solution-diffusion” mechanism is generally used, in which molecular sorption in a membrane can be divided into three steps: (1) the molecule is absorbed in the membrane matrix, (2) the absorbate reacts or exchanges sorption sites in the membrane matrix, and (3) the absorbate desorbs from the membrane matrix. In this study, the sorption behavior of five gases (CO2, CH4, N2, O2, and H2) in the four membranes was examined at 298 K. To study the sorption behavior, the relative probabilities (ratios) of the different Monte Carlo step types were simulated by the Metropolis Monte Carlo method [27]. There are five types of step: exchange, conformer, rotation, translation, and regrowth. The sorption calculation in this work was carried out 5,000,000 times. Because of the oscillation of the sorption loading in the system at the beginning of the simulation, the data were collected after 500,000 calculations. The molecular sorption between a membrane and the gases was described by the COMPASS force field, which is the same as the force field used for the model construction. In the force field, the non-bonded van der Waals interactions were estimated by a 9-6 Lennard-Jones potential, and the Coulombic interactions were calculated by Ewald sums. The number of S15
the gas molecules adsorbed on the membrane per unit cell can be calculated using the Metropolis Monte Carlo method. Then, the solubility can be obtained from the following equation:
SCO2 =
g amount Avg. CO2 Loading [ MwCO2 [ per cell] gmol] cm3 ( )×( )×(1000 [ g amount L ]) ρCO [ ] 6×1023 [ ] 2 L gmol 3
Å cm3 Cell Volume [ ] × 10-24 [ 3 ] ×P [bar] per cell Å
Solubility Unit1 =
Gas Volume cm3 [ 3 ] Polymer Volume × Pressure cm ×bar
SCO2 = Solubility Unit2 =
amount Avg. CO2 Loading [ g mg per cell] ( )×(MwCO2 [ ] )×(1000 [ g ]) amount gmol 6×1023 [ ] gmol 3
g Å cm3 Cell Volume [ ] ×10-24 [ 3 ] ×ρ [ 3 ]×P [bar] per cell cm Å Cell
SCO2 =
=
(7)
Gas Weight mg [ ] Polymer Weight ×Pressure g×bar
(
Solubility Unit3
(6)
amount ] mgmol per cell )×(1000 [ ]) gmol 23 amount 6×10 [ ] gmol
Avg. CO2 Loading [
3
g Å cm3 Cell Volume [ ] ×10-24 [ 3 ] ×ρCell [ 3 ]×P [bar] per cell cm Å Gas Mole mgmol [ ] Polymer Mole ×Pressure gmol×bar
S16
(8)
3-5 Surface Area In a polymer membrane, the geometric surface area and pore volume can influence gas sorption and diffusion. Previous paper, the surface areas were calculated from the solvent accessible surface, and the pore volumes and pore size distributions were obtained with the Connolly surface [28]. The BET (Brunauer–Emmett–Teller) surface areas were calculated from the simulated isotherms with the same method that is commonly used for experimental isotherms by using the BET equation [29]: n=
P nm × C × ( P ) 0
(9)
P P [1 + (C-1) × ( P )] × [1 - ( P )] 0 0
which may be rearranged to P (P )
C-1 P 1 ×( )+ P nm × C n× [1 - ( P )] nm × C P0 0 0
=
(10)
where P=P0 is the relative pressure, n is the quantity of nitrogen adsorbed at 77K (gmol/g) and nm is the BET monolayer capacity. Therefore, the BET plot of ((P/P0 ) ) / [n× [1 -(P/P0 )]] versus P=P0 will have the slope = (C - 1)/(nm × C ) and the intercept 1/(nm × C). The equations may be solved to obtain the relevant BET parameters, usually C >>1 and slope ≈1/nm. [30]. The specific BET surface area (SABET) is obtained from the relationship: SABET = nm Na
(11)
where Na is Avogadro’s number and is the average area occupied by each molecule in the complete monolayer. In a close-packed liquid monolayer of nitrogen, cross sectional areas of adsorbed N2 (N2; 77K) = 0.162 nm2 [31]. The results of the BET model transformed from the nitrogen adsorption isotherm at 77K of the four membranes in Figure S7 and Table S5.
S17
Figure S7 The results of the BET model transformed from the nitrogen adsorption isotherm at 77K of the four membranes
Table S5 Comparison of the simulated and experimental surface areas for the PTMSP, PIM-PI-1, PIMTrip-TB, and KAUST-PI-1 membranes. P ) C-1 P 1 P0 = ×( )+ P nm × C n× [1 - ( )] nm × C P0 P0 (
Membrane
(y=
PTMSP PIM-PI-1 PIM-Trip-TB KAUST-PI-1
m×x
+
y = 98.9 × x +0.09 y = 200.9 × x +0.01 y = 134.8 × x +0.03 y = 165.0 × x +0.02
nm ≈ 1/slope (gmol / g)
Simulated Surface Area (m2 / g)
Experimental Surface Area (m2 / g)
0.01011 0.00497 0.00741 0.00606
972 465 727 583
949 [3] 600 [5] 899 [4] 752 [3]
b)
The BET surface areas were calculated using the sample average adsorption isotherms of N2 at 77 K. Pressure range of 0.0001 < P=P0 < 0.02 for four membranes.
S18
3-6 Mean-squared Displacement (MSD) and Self-diffusivity During the MD simulations, one hundred gas molecules were randomly inserted into the simulation box to calculate their MSD diagrams and self-diffusivities. The diffusion behavior of five gases (CO2, CH4, N2, O2, and H2) in the four membranes was studied at 298 K. Each MSD analysis was carried out for 3,000 ps in the NVT ensemble. Because of the non-linear oscillations at the beginning of the simulation, the data were collected after 1,000 ps. The MSD of gas molecules can be calculated with Einstein’s relationship: 1
MSD (t) = N ∑Ni=1〈[ri (t0 +t)-ri (t0 )]2 〉= B + 6D∙t,
(12)
where N is the total number of atoms, ri (t0+t) and ri (t0) are the positions at time t0+t and time t0, respectively, B is a constant, and D is the self-diffusion coefficient. Figure S8 shows the schematic diagrams of the model for the gas diffusion in the polymer membranes
S19
NPT, 1atm, 298K, 1000ps, Final State (↓)
Polymer
Gas
NVT, 298K, 3,000 ps → Obtain MSD diagram
Figure S8 Schematic diagram of the model for the gas diffusion in the polymer membranes. (Hydrogen atoms are omitted from all models for clarity.)
S20
Supporting Information 4: Slices of simulation models across x, y, z axes for the four membranes x-direction
y-direction
S21
z-direction
Figure S9 Slices of simulation models across x, y, z axes for the PIM-PI-1, PIM-Trip-TB, KAUST-PI-1, and PTMSP membranes (slice thickness: 2.5 Å).
S22
Supporting Information 5: Simulated and experimental solubility, diffusivity, and gas permeability data of the five gases in the four membranes. Table S6 Simulated and experimental solubility data of the five gases in the four membranes. Experimental data are listed without parentheses for methanol treated but not age, in parentheses for PIM-TripTB and KAUST-PI-1 aged for 100 day and 15 day, respectively. Solubility (10-2 cm3(S.T.P)/ (cm3.cmHg)) H2
CO2
O2
N2
CH4
PTMSP
Sim. Exp. [6]
0.4 -
9.9 8.2
3.6 1.7
2.9 1.5
7.1 4.2
PIM-PI-1
Sim. Exp. [5]
0.2 0.4
38.7 62.0
4.6 2.8
3.6 2.4
12.4 11.0
PIM-Trip-TB
Sim. Exp. [4]
0.3 -
57.7 87.4
8.5 5.9
6.3 4.7
20.1 18.5
(114.0)
(7.3)
(6.6)
(29.1)
56.0 -
6.7 3.6
5.2 3.2
17.6 -
(53.0)
(4.0)
(3.4)
(11.2)
KAUST-PI-1
Sim. Exp. [3]
0.2 -
Table S7 Simulated and experimental diffusivity data of the five gases in the four membranes. Experimental data are listed without parentheses for methanol treated but not age, in parentheses for PIM-Trip-TB and KAUST-PI-1 aged for 100 day and 15 day, respectively. Diffusivity (10-8 cm2/s) H2
CO2
O2
N2
CH4
PTMSP
Sim. Exp. [6]
89800 -
5040 3300
7740 5200
7120 4400
4430 3600
PIM-PI-1
Sim. Exp. [5]
21700 1200
45 17
148 56
75 20
29 7
PIM-Trip-TB
Sim. Exp. [4]
41700 >7800
218 111 (35)
777 462 (148)
254 135 (29)
111 49 (8)
KAUST-PI-1
Sim. Exp. [3]
34600 -
127 -
389 226
123 53
52 -
(46)
(158)
(31)
(10)
S23
Table S8 Simulated and experimental permeability data of the five gases in the four membranes. Experimental data are listed without parentheses for methanol treated but not age, in parentheses for PIM-Trip-TB and KAUST-PI-1 aged for 100 day and 15 day, respectively. Permeability (Barrer) H2
CO2
O2
N2
CH4
PTMSP
Sim. Exp. [6]
34737 -
50103 27000
27984 9000
20820 6600
31441 15000
PIM-PI-1
Sim. Exp. [5]
3569 530
1743 1100
679 150
270 47
360 77
PIM-Trip-TB
Sim. Exp. [4]
10507 8039 (4740)
12571 9709 (3951)
6583 2718 (1073)
1602 629 (189)
2231 905 (218)
KAUST-PI-1
Sim.
7490
7112
2626
642
918
4183 (3983)
(2389)
827 (627)
169 (107)
(105)
Exp. [3]
S24
Supporting Information 6: MSD diagrams of the H2, O2, N2, CO2, and CH4 for the four membranes during a 3,000-ps MD simulation
Figure S10 MSD diagrams of the H2, O2, N2, CO2, and CH4 for the (a) PTMSP, (b) PIM-PI-1, (c) PIM-Trip-TB, and (d) KAUST-PI-1 membranes during a 3,000-ps MD simulation.
S25
Supporting Information 7: The van der Waals volume, FFV, and FAV codes (i) The van der Waals volume, FFV code #!perl use strict; use MaterialsScript qw(:all);
my $newStudyTable = Documents->New("KAUST-PI-1-M01_FFV.std"); my $calcSheet = $newStudyTable->ActiveSheet; $calcSheet->ColumnHeading(0) = "Occupied Volume"; $calcSheet->ColumnHeading(1) = "Free Space"; $calcSheet->ColumnHeading(2) = "vdw Volume"; $calcSheet->ColumnHeading(3) = "Total Cell Volume"; $calcSheet->ColumnHeading(4) = "FFV"; $calcSheet->ColumnHeading(5) = "Density";
my $Doc = $Documents{"KAUST1-PI-1-M01_0000ps.xsd"} ; my $avField = $Doc->CalculateSolventField (Settings(GridInterval => 0.15)); $avField->VDWScaling = 1; $avField->IsVisible = "YES"; my $ISO = $avField->CreateIsosurface([IsoValue => 0, HasFlippedNormals => "NO"]); my $OccV = $ISO->EnclosedVolume ; $calcSheet->Cell(0, 0) = $OccV ; $calcSheet->Cell(0, 1) = $Doc->Lattice3D->CellVolume - $OccV ; $calcSheet->Cell(0, 2) = 1.3 * $OccV ; $calcSheet->Cell(0, 3) = $Doc->Lattice3D->CellVolume ; $calcSheet->Cell(0, 4) = (($Doc->Lattice3D->CellVolume)-(1.3 * $OccV))/($Doc->Lattice3D->CellVolume) ; $calcSheet->Cell(0, 5) = $Doc->SymmetrySystem->Density ; $avField->Delete;
###……100 ps frame , 200 ps frame……etc
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(ii) The FAV code #!perl use strict; use MaterialsScript qw(:all);
my $Doc = $Documents{"KAUST-PI-1-M01_1000ps.xsd"} ; my $newStudyTable = Documents->New("KAUST-PI-1-M01_FAV_1000ps.std"); my $calcSheet = $newStudyTable->ActiveSheet; $calcSheet->ColumnHeading(0) = "Probe Radius"; $calcSheet->ColumnHeading(1) = "Accessible Volume"; $calcSheet->ColumnHeading(2) = "Total Cell Volume"; $calcSheet->ColumnHeading(3) = "Fractional Accessible Volume"; #$calcSheet->ColumnHeading(3) = "3D Model";
my $SolR = -0.05 ;
#solvent radius
for (my $i=0; $iCalculateSolventField (Settings(MaxSolventRadius => 3, GridInterval => 0.4)); $avField->VDWScaling = 1; $avField->IsVisible = "YES"; my $ISO = $avField->CreateIsosurface([IsoValue => $SolR, HasFlippedNormals => "NO", IsoSurfaceKind => "accessible"]); #accessible volume my $OccV = $ISO->EnclosedVolume ;
$calcSheet->Cell($i, 0) = $SolR ; $calcSheet->Cell($i, 1) = $Doc->Lattice3D->CellVolume - $OccV ; $calcSheet->Cell($i, 2) = $Doc->Lattice3D->CellVolume ; $calcSheet->Cell($i, 3) = (($Doc->Lattice3D->CellVolume) - $OccV)/($Doc->Lattice3D->CellVolume) ; #$calcSheet->Cell($i, 3) = $Doc ;
#Clean up last solvent information $avField->Delete; }
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Supporting Information 8: Cavity size analyses using the MATLAB software To calculate the cavity size, we developed an image analysis algorithm in MATLAB. The algorithm is based on Euclidean distance transform (EDT), and can be referred to our previous study. [23]
MATLAB M-file Script clc; clear all; close all;
tic disp('Create a new folder named "Fig", and place all the images which you want to analyze into the folder .') cell_length=input(' Input the cell length of the image (Angstrom)=') pixel=input(' Input the pixel of the image=') saveFig = 1; % 1 to save the figure. savexls = 1; % 1 to save into Excel.
%%% Part1-Set the parameter C = 15;
% The number of cavity
th = 100;
% Light intensity range 0~255
Tolc = 0.1;
% Toleration area of convergence
Tol_Area = 0.02; % Toleration area of convergence Scale = cell_length / pixel; % Cell length of image / pixel of image list = dir(['Fig/*.jpg']); F = length(list); Filename = extractfield(list, 'name'); colname_xls2 = cell(1,2*F); phi=0.8; %Because the pore shape is not fully circular, the correction in sphericity is required.
%%% Part2-Analyze the cavities for f = 1 : F
X0 = imread(['Fig/' Filename{f}]); fprintf(['%g:' Filename{f} '\n'],f) colname_xls {1,f} = Filename{f}(1:end-4); colname_xls2{1,2*f-1} = colname_xls{1,f}; colname_xls2{2,2*f-1} = 'BinCenters'; colname_xls2{2,2*f} = 'counts';
if length(X0(1,1,:)) == 3
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X0 = rgb2gray(X0); end
[M0 N0] = size(X0); X01 = double(X0); X = round(((X01 - min(min(X01))) / (max(max(X01)) - min(min(X01))) * 255)); XA = X;
X1 = zeros(size(XA)); X1(find(XA > th)) = 1;
[D,IDX] = bwdist(X1,'euclidean'); X2 = abs(X1 - 1);
Ds=D; for i = 1 : C maxD = max(max(Ds)); [raw,col] = find(Ds == maxD,1); tol = 1; a = 1; Area = 0; % calculation of area while tol > Tol_Area range = [raw-a raw+a col-a col+a]; if range(1) < 1 range(1) = 1; end if range(2) > M0 range(2) = M0; end if range(3) < 1 range(3) = 1; end if range(4) > N0 range(4) = N0; end
D_area = Ds(range(1):range(2),range(3):range(4)); Area(a) = bwarea(D_area);
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if a > 1 Tol(a) = abs(diff(Area(a-1:a)) / Area(a)); tol = Tol(a); end a = a + 1; end range0=range; % The sphericity is considered to obtain a more accurate cavity size distribution. b = a * phi; range = round([raw-b raw+b col-b col+b]); if range(1) < 1 range(1) = 1; end if range(2) > M0 range(2) = M0; end if range(3) < 1 range(3) = 1; end if range(4) > N0 range(4) = N0; end D_area = Ds(range(1):range(2),range(3):range(4)); Area0 = bwarea(D_area); % Saving Data radius(i) = sqrt(Area0 / pi); center(i,:) = [raw,col]; X_mean(i) = mean(mean(Ds));
%%% Part3-Delete the cavities that have been analyzed Ds(range0(1):range0(2),range0(3):range0(4)) = zeros(size(Ds(range0(1):range0(2),range0(3):range0(4)))); end
radius=radius*phi; hist_p = 0:0.5:10; [counts,BinCenters]
= hist(radius*Scale,hist_p);
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Data_MeanTol(:,f) = X_mean; Data_Center(:,:,f) = center; Data_Diameter(:,f) = radius*Scale*2; Data_HistData(:,(2*f-1):2*f) = [BinCenters' counts'];
%%% Part4-Save the images that have been analyzed if saveFig == 1 figure(1) imshow(uint8(X)) hold on; plot(center(:,2),center(:,1),'r.') viscircles([center(:,2) center(:,1)],radius); hold off; saveas(gcf,[Filename{f}(1:end-4) '.png']); close(1) end
end
toc
%%% Part5-Save the data automatically if savexls == 1 % Writing Data into Excel warning('off','all') fprintf('\nWriting data into Excel.....\n')
% fprintf('%g\n',f) filename_xls = 'DataFile.xlsx';
[a1 a2] = size(Data_Diameter); A = round(Data_Diameter*100) / 100; A = mat2cell(A,ones(1,a1),ones(1,a2));
[status,message] = xlswrite(filename_xls,colname_xls,'Radius','A1'); [status,message] = xlswrite(filename_xls,A,'Radius','A2'); [status,message] = xlswrite(filename_xls,colname_xls2,'HistData','A1'); [status,message] = xlswrite(filename_xls,Data_HistData,'HistData','A3');
Data_Diameter_All = Data_Diameter (Data_MeanTol>Tolc);
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hist_all = 0:0.5:20; [counts_all,BinCenters_all]
= hist(Data_Diameter_All,hist_all);
hist(Data_Diameter_All,hist_all); saveas(gcf,['Hist_figure' '.png']); colname_xls3 = {'Diameter-BinCenters', 'counts'}; [status,message] = xlswrite(filename_xls,colname_xls3,'HistData_All','A1'); [status,message]=xlswrite(filename_xls,[BinCenters_all' counts_all'],'HistData_All', 'A2'); close end
fprintf('Finished. \n')
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References [1] G.S. Larsen, P. Lin, K.E. Hart, C.M. Colina, Molecular Simulations of PIM-1-like Polymers of Intrinsic Microporosity, Macromolecules, 44 (2011) 6944-6951. [2] L.J. Abbott, K.E. Hart, C.M. Colina, Polymatic: a generalized simulated polymerization algorithm for amorphous polymers, Theoretical Chemistry Accounts, 132 (2013) 1-19. [3] B.S. Ghanem, R. Swaidan, E. Litwiller, I. Pinnau, Ultra‐Microporous Triptycene‐based Polyimide Membranes for High‐Performance Gas Separation, Advanced materials, 26 (2014) 3688-3692. [4] M. Carta, M. Croad, R. Malpass-Evans, J.C. Jansen, P. Bernardo, G. Clarizia, K. Friess, M. Lanc, N.B. McKeown, Triptycene induced enhancement of membrane gas selectivity for microporous Troger's base polymers, Advanced materials, 26 (2014) 3526-3531. [5] B.S. Ghanem, N.B. McKeown, P.M. Budd, J.D. Selbie, D. Fritsch, High-performance membranes from polyimides with intrinsic microporosity, Advanced materials, 20 (2008) 2766-2771. [6] T. Merkel, V. Bondar, K. Nagai, B. Freeman, Sorption and transport of hydrocarbon and perfluorocarbon gases in poly (1‐trimethylsilyl‐1‐propyne), Journal of Polymer Science Part B: Polymer Physics, 38 (2000) 273-296. [7] H. Sun, COMPASS: an ab initio force-field optimized for condensed-phase applications overview with details on alkane and benzene compounds, The Journal of Physical Chemistry B, 102 (1998) 73387364. [8] M. Segall, P.J. Lindan, M.a. Probert, C. Pickard, P. Hasnip, S. Clark, M. Payne, First-principles simulation: ideas, illustrations and the CASTEP code, Journal of Physics: Condensed Matter, 14 (2002) 2717. [9] S.J. Clark, M.D. Segall, C.J. Pickard, P.J. Hasnip, M.I. Probert, K. Refson, M.C. Payne, First principles methods using CASTEP, Zeitschrift für Kristallographie, 220 (2005) 567-570. [10] W. Kohn, L.J. Sham, Self-consistent equations including exchange and correlation effects, Physical Review, 140 (1965) A1133. [11] L. Sham, W. Kohn, One-particle properties of an inhomogeneous interacting electron gas, Physical Review, 145 (1966) 561. [12] W. Kohn, L. Sham, Quantum density oscillations in an inhomogeneous electron gas, Physical Review, 137 (1965) A1697. [13] M. Segall, C. Pickard, R. Shah, M. Payne, Population analysis in plane wave electronic structure calculations, Molecular Physics, 89 (1996) 571-577. [14] M. Segall, R. Shah, C. Pickard, M. Payne, Population analysis of plane-wave electronic structure calculations of bulk materials, Physical Review B, 54 (1996) 16317. [15] J.P. Perdew, W. Yue, Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation, Physical review B, 33 (1986) 8800. [16] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Physical review letters, 77 (1996) 3865.
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[17] J.P. Perdew, K. Burke, Y. Wang, Generalized gradient approximation for the exchange-correlation hole of a many-electron system, Physical Review B, 54 (1996) 16533. [18] A.K. Rappe, W.A. Goddard III, Charge equilibration for molecular dynamics simulations, The Journal of Physical Chemistry, 95 (1991) 3358-3363. [19] A. Bondi, van der Waals volumes and radii, The Journal of physical chemistry, 68 (1964) 441-451. [20] W. Lee, Selection of barrier materials from molecular structure, Polymer Engineering & Science, 20 (1980) 65-69. [21] D. Hofmann, M. Heuchel, Y. Yampolskii, V. Khotimskii, V. Shantarovich, Free volume distributions in ultrahigh and lower free volume polymers: comparison between molecular modeling and positron lifetime studies, Macromolecules, 35 (2002) 2129-2140. [22] M. Heuchel, D. Fritsch, P.M. Budd, N.B. McKeown, D. Hofmann, Atomistic packing model and free volume distribution of a polymer with intrinsic microporosity (PIM-1), Journal of Membrane Science, 318 (2008) 84-99. [23] F.H. She, K. Tung, L.X. Kong, Calculation of effective pore diameters in porous filtration membranes with image analysis, Robotics and computer-integrated manufacturing, 24 (2008) 427-434. [24] K.-L. Tung, K.-S. Chang, T.-T. Wu, N.-J. Lin, K.-R. Lee, J.-Y. Lai, Recent advances in the characterization of membrane morphology, Current Opinion in Chemical Engineering, 4 (2014) 121127. [25] S. Kanehashi, K. Nagai, Analysis of dual-mode model parameters for gas sorption in glassy polymers, Journal of Membrane Science, 253 (2005) 117-138. [26] W.R. Vieth, P.M. Tam, A.S. Michaels, Dual sorption mechanisms in glassy polystyrene, Journal of Colloid and Interface Science, 22 (1966) 360-370. [27] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, 21 (1953) 1087. [28] L.D. Gelb, K. Gubbins, Characterization of porous glasses: Simulation models, adsorption isotherms, and the Brunauer-Emmett-Teller analysis method, Langmuir, 14 (1998) 2097-2111. [29] S. Brunauer, P.H. Emmett, E. Teller, Adsorption of gases in multimolecular layers, Journal of the American chemical society, 60 (1938) 309-319. [30] J. Rouquerol, P. Llewellyn, F. Rouquerol, Is the BET equation applicable to microporous adsorbents?, Studies in surface science and catalysis, (2007) 49-56. [31] I.M. Ismail, Cross-sectional areas of adsorbed nitrogen, argon, krypton, and oxygen on carbons and fumed silicas at liquid nitrogen temperature, Langmuir, 8 (1992) 360-365.
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List of Figures Figure S1. Chemical structure of (a) PTMSP, (b) PIM-PI-1, (c) PIM-Trip-TB, (d) KAUST-PI-1. Numbers correspond to atoms for simulation parameters list in Table S3 Figure S2: The partial charge distributions of the PTMSP, PIM-PI-1, PIM-Trip-TB, and KAUST-PI-1 membranes. Figure S3: The partial charge distributions of the CO2, CH4, O2, N2, and H2. Figure S4 Schematic diagrams of the analyzed atomic segments for the dihedral angle analysis. Figure S5 Free volume morphologies of the (a) PTMSP, (b) PIM-PI-1, (c) PIM-Trip-TB, and (d) KAUSTPI-1 membranes. The blue and gray regions indicate the pathways and polymers in the membrane, respectively. Figure S6 Picture of the model cross-sections of the membrane models constructed in this work. The white and black areas represent the cavity size element and polymer element, respectively. Figure S7 The results of the BET model transformed from the nitrogen adsorption isotherm at 77K of the four membranes Figure S8 Schematic diagram of the model for the gas diffusion in the polymer membranes. (Hydrogen atoms are omitted from all models for clarity.) Figure S9 Slices of simulation models across x, y, z axes for the PIM-PI-1, PIM-Trip-TB, KAUST-PI-1, and PTMSP membranes (slice thickness: 2.5 Å). Figure S10 MSD diagrams of the H2, O2, N2, CO2, and CH4 for the (a) PTMSP, (b) PIM-PI-1, (c) PIMTrip-TB, and (d) KAUST-PI-1 membranes during a 3,000-ps MD simulation.
List of Table Table S1. A similar 21-step MD compression and relaxation scheme. Table S2. The experimental properties of the four membranes: surface area, pore volume, diffusivity, density. Table S3. Non-bonded charge interaction parameters for the simulation of the PTMSP, PIM-PI-1, PIMTrip-TB, and KAUST-PI-1 membranes. Table S4. Atomic charges (from QEq calculate) and bond lengths of the CO2, CH4, N2, O2 and H2. Table S5 Comparison of the simulated and experimental surface areas for the PTMSP, PIM-PI-1, PIMTrip-TB, and KAUST-PI-1 membranes. Table S6 Simulated and experimental solubility data of the five gases in the four membranes. Table S7 Simulated and experimental diffusivity data of the five gases in the four membranes. Table S8 Simulated and experimental permeability data of the five gases in the four membranes.
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