- Email: [email protected]
Correlations between gas permeation and free-volume hole properties of polyurethane membranes
European Polymer Journal 39 (2003) 2345–2349 www.elsevier.com/locate/europolj
Correlations between gas permeation and free-volume hole properties of polyurethane membranes Zhi Fen Wang a, Bo Wang
a,*
, Yu Run Yang b, Chun Pu Hu
b
a
b
Department of Physics, Wuhan University, Wuhan 430072, China Institute of Material Science and Engineering, East China University of Science and Technology, Shanghai 200237, China Received 28 January 2003; received in revised form 16 June 2003; accepted 14 July 2003
Abstract A series of polyurethane films based on hard segments consisting of toluene diisocyanate and 1,4-butanediol and different soft segments consisting of hydroxyl terminated polybutadiene, hydroxyl terminated polybutadiene/styrene and hydroxyl terminated polybutadiene/acrylonitrile were synthesized by solution polymerization separately. Positron annihilation lifetimes were measured at room temperature for all samples studied. We found that both the free volume size and fractional free-volume decreased with the increase of hard segment content. On the other hand, direct relationship between the gas permeability and the free-volume has been established based on the free-volume parameters and gas diffusivity measured. Experimental results revealed that the free-volume plays an important role in determining the gas permeability. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Positron annihilation; Free-volume; Gas permeability
1. Introduction Gas permeation in non-porous materials, such as polymers, has been extensively studied because of their technological importance in industrial applications, such as coating and gas separation. The permeability, P , can be written as a simple product of an average diffusivity, D, and an effective solubility, S (P ¼ D S) [1,2]. The average diffusivity or the diffusion coefficient, D, provides a measure of the effective mobility of the penetrant in the polymer matrix. The size and shape of holes available in a polymer control the rate of gas diffusion and its permeation properties. The free-volume theories based on Cohen and Turnbull [3] are applied to investigate gas permeation [4–12]. Gas diffusion coefficients in
*
Corresponding author. Tel.: +86-27-87682379; fax: +86-2787654569. E-mail address: [email protected] (B. Wang).
a series of polymers can successfully follow the equation predicted by the free-volume theory [12]: ln D ¼ A
B fV
ð1Þ
where A is related to the size and shape of the diffusion molecule, B is related to the minimal hole size of polymer matrix required for a diffusional jump or hopping to occur and fV is the fractional free-volume. Due to the superior hydrolytic stabilities and high mechanical performances, hydroxyl terminated polybutadiene based PU (HTPB-PU) is used in many fields, e.g. as binders in rocket propellants, sealants and coating materials. HTPB-PU is used for gas separation because of the low temperature flexibility and high segregation between hard and soft segments [13–15]. In this regard, it is very important to study gas permeation of HTPBPU. Hydroxyl terminated polybutadiene/styrene and hydroxyl terminated polybutadiene/acrylonitrile based PUs (HTBS-PU and HTBN-PU) have been applied for many years as modified materials of HTPB-PU.
0014-3057/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0014-3057(03)00181-2
2346
Z.F. Wang et al. / European Polymer Journal 39 (2003) 2345–2349
In this work, we applied positron annihilation lifetime (PAL) method to study free-volume hole properties of HTPB-PU, HTBS-PU and HTBN-PU. Correlation between the free-volume hole properties and gas permeation was discussed.
2. Experimental 2.1. Sample preparation Polyurethane membranes with hard segments of toluene diisocyanate (TDI), 1,4-butanediol (BDO) and different soft segments of HTBS, HTBN and HTPB were synthesized by solution polymerization separately. We changed in the ratio of the hard segment content to the soft segment content in order to investigate the effect of hard segment content on free-volume in PU membranes studied. Glass transition temperature (Tg ) was measured by differential scanning calorimetry (DSC). The physical and gas permeation properties of these PU membranes have been listed in Table 1.
get the best v2 (<1.2) and most reasonable standard deviations. The shortest lifetime (s1 200 ps) attributes to para-positronium annihilation and the free positron annihilation. The intermediate lifetime (s2 400 ps) is the lifetime of the positron annihilating in the defect of crystalline region. The longest lifetime (s3 1–3 ns) is due to o-Ps pick-off annihilation in free-volume holes of amorphous region [16]. Using the following semiempirical equation and o-Ps lifetime, we obtained the average free-volume hole radius [17–19]:
s3 ¼
All PAL spectra were recorded at room temperature with an Ortec ‘‘fast–fast’’ lifetime spectrometer. The time resolution was 250 ps (fwhm). We used a 22 Na with 20 l Ci as radioactive positron source and put the source between two pieces of same samples like sandwich. A million counts were collected for each spectrum. All of the PAL spectra were analyzed by finite-term lifetime analysis method using PATFIT program. In these PU membranes, the finite-term lifetime decompose a PAL spectrum into three terms of negative exponentials. We
ð2Þ
where s3 (o-Ps lifetime) and R (hole radius) are expressed , respectively. R0 equals to R þ DR where DR in ns and A ). is the fitted empirical electron layer thickness ( ¼ 1.66 A 3 ), for The volume of free-volume holes, Vf (in A spherical cavities can be calculated: Vf ¼
2.2. Positron annihilation lifetime spectroscopy
1 1 1 R 1 2pR sin ¼ 1 þ k3 2 R0 2p R0
4pR3 3
ð3Þ
where R can be calculated from Eq. (2). Furthermore, the relative fractional free-volume (%) is expressed as an empirically fitted equation as: fV ¼ CVf I3
ð4Þ
where Vf can be calculated from Eq. (3), I3 (in %) is the o-Ps intensity and C is an arbitrarily chosen scaling factor for a spherical cavity.
Table 1 Physical and gas permeation properties in HTPB-PU, HTBS-PU and HTBN-PU Sample
Hard segment content (wt%)
Type of soft segment
Tgs0 a (°C)
Tgs b (°C)
Wss (%)
D c (CO2 )
P d (CO2 )
B1 B2 B3 B4 BS1 BS2 BS3 BS4 BN1 BN2 BN3 BN4
24.8 37.2 51.1 62.1 24.8 36.9 51.1 62.0 24.9 36.7 51.9 62.9
HTPB2270 HTPB2270 HTPB2270 HTPB2270 HTBS2412 HTBS2412 HTBS2412 HTBS2412 HTBN2362 HTBN2362 HTBN2362 HTBN2362
)77.9 )77.9 )77.9 )77.9 )68.3 )68.3 )68.3 )68.3 )44.4 )44.4 )44.4 )44.4
)74.3 )72.8 )74.9 )74.4 )62.4 )62.7 )63.2 )63.3 )29.5 )32.7 )33.4 )31.5
95.8 94.1 96.5 95.6 93.1 93.5 94.0 94.1 81.9 85.6 86.4 84.2
141 110 81 43.6 99 74 43 22 28 23 11 6
147 112 89 55.1 104 73 54 26 29 23 13 8
a
Tgs0 represent the glass transition temperature for pure soft segment. Tgs represent the glass transition temperature for soft matrix. c D in 108 cm2 /s. d P in barrers, where 1 barrer ¼ 1010 cm3 (STP) cm/(cm2 s cmHg). b
Z.F. Wang et al. / European Polymer Journal 39 (2003) 2345–2349
3. Results and discussion
3.4
2600 HTPB-PU HTBS-PU HTBN-PU
o - P s life t ime τ3 (ps )
2500 2400 2300 2200 2100 2000 1900 1800 25
30
35
40
45
50
55
60
Hard Segment Content (wt%) Fig. 1. o-Ps lifetime vs. hard segment content.
65
R(A)
3.2 3.1 3.0 2.9 2.8 2.7 20
25
30
35
40
45
50
55
60
65
Hard Segment Content (wt%)
Fig. 2. Mean free-volume hole radius vs. hard segment content.
3.5
Fractional Free Volume
Table 1 shows that the higher the hard segment content was, the lower the gas permeability was in HTPB-PU, HTBS-PU and HTBN-PU, respectively. These results of PU membranes are in agreement with the previous reports by Huang et al. [14,15]. The effects of chemical compositions on gas permeability are due to the free-volume and the nature of chain packing. Fig. 1 shows that variations of o-Ps lifetimes with different hard segment content. From Fig. 1, we can see that the o-Ps lifetimes decrease as the hard segment content increases. There is a direct correlation between the o-Ps lifetime and the free-volume hole size. As shown in Figs. 2 and 3, the free-volume hole size (R) and fractional free-volume (fV ) decrease with the increase of hard segment content. This can be explained in terms of molecular structure and the packing of polymer chains. In HTPB-PU, HTBS-PU and HTBN-PU, the flexibility and the loose packing of soft segment result in increase of the concentration of free-volume holes capable of supporting gas diffusion in soft segment region. The hard segments tend to form cluster aggregates because of the effect of hydrogen bond resulting in enhanced physical cross-linking, and some shorter ones of ‘‘free state’’ disperse into soft segment region. There are two effects introduced by the increase of hard segment content. One is the enlargement of hard segment of cluster aggregate and the other is the restriction of the movement of soft segment. This may be the suitable explanation for the trend of the gas permeability and the fractional free-volume with the increase of hard segment content.
HTPB-PU HTBS-PU HTBN-PU
3.3
3.1. Effect of hard segment content on the free-volume and gas permeability
20
2347
HTPB-PU HTBS-PU HTBN-PU
3.0
2.5
2.0
1.5 20
25
30
35
40
45
50
55
60
65
Hard Segment Content (wt%) Fig. 3. Fractional free-volume vs. hard segment content.
3.2. Effect of different soft segment on the free-volume and gas permeability From Table 1, we have the following observations: the average diffusion coefficient, D, has a decreasing order of HTPB-PU > HTBS-PU > HTBN-PU under the same amount of hard segment content. As shown in Figs. 2 and 3, the hole size and fractional free-volume have an increasing order of HTBN-PU < HTBSPU < HTPB-PU under the same amount of hard segment content. The effect of different soft segment on gas permeability is mainly attributed to the free-volume. The degree of phase segregation also influences the freevolume in PU membranes. The gas permeability and fractional free-volume are smaller for HTBS-PU than for HTPB-PU. In HTPB based PU, hydrogen bond can’t be formed between soft segments and hard segments, because the soft segments can’t offer the strong electronegativity element which is needed by formation of hydrogen bond. Compared to HTPB-PU, although in HTBS-PU, hydrogen bond can’t be formed between the soft segments and the hard segments, rigid benzene rings increase the stiffness of the polymer chains and restrict chain mobility. Therefore
Z.F. Wang et al. / European Polymer Journal 39 (2003) 2345–2349
1 Wss ð1 Wss Þ ¼ þ Tgs Tgs0 Tgh0
160
DCO2 (10-8cm2/s)
such groups decrease the sizes of free-volume hole and reduce the gas permeability. In HTBN-PU, –CN of acrylonitrile in HTBN can form hydrogen bond with –NH of the hard segments, resulting in enhanced physical cross-linking between soft segments and hard segments. Compared to HTPB-PU and HTBS-PU, the fractional free-volume and gas permeability of HTBN-PU decreased distinctly. These observations are in good agreement with the results measured by DSC. In Table 1, Wss representing the content of pure soft segment in the soft matrix can be calculated from FOX equation [20]:
3.3. Correlations between the gas permeability and the free-volume Fig. 4 shows the diffusion coefficient for CO2 molecule, changing with the average free-volume, Vf . The diffusion coefficient increased as the average free-volume increased in HTPB-PU, HTBS-PU and HTBN-PU, re3 ) [1] is spectively. The molecular volume of CO2 (70.9 A smaller than the mean free-volume of PU membranes as shown in Fig. 4. It is known that a larger diffusion coefficient needs a larger free-volume. The average diffusivity, D, provides a measure of the effective mobility of the penetrant in the polymer matrix. When a gas molecule is comparable in size with the available hole size in a material, its diffusion is restricted. On the other hands, if the gas molecule size is smaller than the statistical average free-volume, it will diffuse through a material with a large diffusion constant. This could provide an explanation of why the gas permeation increase as a function of free-volume hole size. The fractional free-volume, fV , can reflect any change in amorphous regions where gas molecules can permeate
80
40
80
90
100
110
120
130
140
150
Vf (A3)
ð5Þ
where Tgs0 and Tgs represent the glass transition temperature for pure soft segment and soft matrix, respectively. Tgh0 representing the glass transition temperature of the pure hard segment (TDI/BDO) is 72 °C [21]. Wss can denote the degree of phase separation in polyurethane. From Table 1, we can obtain that Wss for HTPB-PU, HTBS-PU and HTBN-PU are approximate 95.5%, 94% and 84%, respectively. The degree of phase separation of HTPB-PU is the highest which denotes that there are less hard segments dispersing into the soft segment region. Wss for HTBS-PU is quite close to the one for HTPB-PU. Compared to HTPB-PU and HTBS-PU, the degree of phase separation of HTBN-PU decreases clearly and more hard segments disperse into soft segment region. The difference of phase separation degree between HTPB-PU, HTBS-PU and HTBN-PU influences the fractional free-volume and the gas permeability.
HTPB-PU HTBS-PU HTBN-PU
120
0
Fig. 4. Diffusion coefficient of CO2 vs. hole volume.
resulting from the increase of hard segment content and different soft segment. From Table 1 and Fig. 3, we have the following observations: HTBN-PU with highest hard segment content has the lowest fractional freevolume and the lowest gas permeability. According to the Eq. (1), correlation between the diffusion coefficient, D, and fractional free-volume, fV , is identified in Fig. 5. A plot of measured values of ln D vs. 1=fV yields a fair good straight line, in agreement with prediction of the Fujita theory [12] (straight line obtained by linear regression is ln D ¼ 9:51–13:36 (fV1 )). The result is in agreement with the previous reports about the Fujita theory [1,22]. It can be concluded, therefore, that the free-volume plays an important role in determining the gas permeability. These results establish general correlations between the structural features of PU membranes, their gas permeability and, the free-volume hole properties.
HTPB-PU HTBS-PU HTBN-PU
5
4
ln D
2348
3
2
1 0.30
0.35
0.40
0.45 (fV)
0.50
0.55
0.60
-1
Fig. 5. Logarithm of diffusion coefficient of CO2 vs. the inverse of fractional free-volume. Straight line is linear regression based on Eq. (1).
Z.F. Wang et al. / European Polymer Journal 39 (2003) 2345–2349
4. Conclusion The results of the free-volume properties obtained by PAS and gas permeability in PU membranes reveal that the effect of free-volume on the gas permeability is very large. The diffusion coefficient, D, and the fractional free-volume, fV , in HTPB-PU, HTBS-PU and HTBNPU, respectively, decrease with the increase of hard segment content. D and fV have a decreasing order of HTPB-PU > HTBS-PU > HTBN-PU under the same amount of hard segment content. Direct correlation is observed between gas diffusion properties and free-volume hole properties. The gas diffusivity increases as the fractional free-volume increases.
Acknowledgements This work was supported by the National Natural Science Foundation and Key Technologies R&D Foundation of Hubei Province. References [1] Jean YC, Yuan JP, Liu J, Deng Q, Yang HJ. J Polym Sci, Part B: Polym Phys 1995;33:2365. [2] Koros WJ, Fleming GK, Jordon SM, Kim TH, Hoehn HH. Prog Polym Sci 1988;13:339. [3] Cohen MH, Turnbull D. J Chem Phys 1959;31:1164.
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[4] Haraya K, Hwang ST. J Membr Sci 1992;71:13. [5] Park JK, Paul DR. J Membr Sci 1997;125:23. [6] Kobayashi Y, Haraya K, Hattori S, Sasuga T. Polymer 1994;35:925. [7] Hill AJ, Weinhold S, Stack GM, Tant MR. Eur Polym J 1996;32:843. [8] Eastmond GC, Daly JH, McKinnon AS, Pethrick RA. Polymer 1999;40:3605. [9] Nagel C, Gunther-Schade K, Fristch D, Strunskus T, Faupel F. Macromolecules 2002;35:2071. [10] McGonigle EA, Liggat JJ, Pethrick RA, Jenkins SD, Daly JH, Hayward D. Polymer 2001;42:2413. [11] Yampolskii YP, Korikov AP, Shantarovich VP, Nagai K, Freeman BD, Masuda T, et al. Macromolecules 2001;34: 1788. [12] Fujita H. Polym J 1991;23:1499. [13] Chen SH, Yu KC, Houng SL, Lai JY. J Membr Sci 2000;173:99. [14] Huang SL, Ruaan RC, Lai JY. J Membr Sci 1997;123: 71. [15] Huang SL, Lai JY. J Membr Sci 1995;105:137. [16] Jean YC. Microchem J 1990;42:72. [17] Tao SJ. J Chem Phys 1972;56:5499. [18] Eldrup M, Lightbody D, Sherwood JN. Chem Phys 1981. [19] Nakanishi H, Wang SJ, Jean YC. In: Sharma SC, editor. Positron Annihilation Studies of Fluids. Singapore: World Science; 1988. [20] Fox TG. Bull Am Phys Soc 1956;1:123. [21] Cuve L, Pascault JP, Boiteux G, Seytre G. Polymer 1991;32(2):343. [22] Sha HJ, Harrison IR. J Polym Sci, Part B: Polym Phys 1992;30:915.
Correlations between gas permeation and free-volume hole properties of polyurethane membranes Zhi Fen Wang a, Bo Wang
a,*
, Yu Run Yang b, Chun Pu Hu
b
a
b
Department of Physics, Wuhan University, Wuhan 430072, China Institute of Material Science and Engineering, East China University of Science and Technology, Shanghai 200237, China Received 28 January 2003; received in revised form 16 June 2003; accepted 14 July 2003
Abstract A series of polyurethane films based on hard segments consisting of toluene diisocyanate and 1,4-butanediol and different soft segments consisting of hydroxyl terminated polybutadiene, hydroxyl terminated polybutadiene/styrene and hydroxyl terminated polybutadiene/acrylonitrile were synthesized by solution polymerization separately. Positron annihilation lifetimes were measured at room temperature for all samples studied. We found that both the free volume size and fractional free-volume decreased with the increase of hard segment content. On the other hand, direct relationship between the gas permeability and the free-volume has been established based on the free-volume parameters and gas diffusivity measured. Experimental results revealed that the free-volume plays an important role in determining the gas permeability. Ó 2003 Elsevier Ltd. All rights reserved. Keywords: Positron annihilation; Free-volume; Gas permeability
1. Introduction Gas permeation in non-porous materials, such as polymers, has been extensively studied because of their technological importance in industrial applications, such as coating and gas separation. The permeability, P , can be written as a simple product of an average diffusivity, D, and an effective solubility, S (P ¼ D S) [1,2]. The average diffusivity or the diffusion coefficient, D, provides a measure of the effective mobility of the penetrant in the polymer matrix. The size and shape of holes available in a polymer control the rate of gas diffusion and its permeation properties. The free-volume theories based on Cohen and Turnbull [3] are applied to investigate gas permeation [4–12]. Gas diffusion coefficients in
*
Corresponding author. Tel.: +86-27-87682379; fax: +86-2787654569. E-mail address: [email protected] (B. Wang).
a series of polymers can successfully follow the equation predicted by the free-volume theory [12]: ln D ¼ A
B fV
ð1Þ
where A is related to the size and shape of the diffusion molecule, B is related to the minimal hole size of polymer matrix required for a diffusional jump or hopping to occur and fV is the fractional free-volume. Due to the superior hydrolytic stabilities and high mechanical performances, hydroxyl terminated polybutadiene based PU (HTPB-PU) is used in many fields, e.g. as binders in rocket propellants, sealants and coating materials. HTPB-PU is used for gas separation because of the low temperature flexibility and high segregation between hard and soft segments [13–15]. In this regard, it is very important to study gas permeation of HTPBPU. Hydroxyl terminated polybutadiene/styrene and hydroxyl terminated polybutadiene/acrylonitrile based PUs (HTBS-PU and HTBN-PU) have been applied for many years as modified materials of HTPB-PU.
0014-3057/$ - see front matter Ó 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0014-3057(03)00181-2
2346
Z.F. Wang et al. / European Polymer Journal 39 (2003) 2345–2349
In this work, we applied positron annihilation lifetime (PAL) method to study free-volume hole properties of HTPB-PU, HTBS-PU and HTBN-PU. Correlation between the free-volume hole properties and gas permeation was discussed.
2. Experimental 2.1. Sample preparation Polyurethane membranes with hard segments of toluene diisocyanate (TDI), 1,4-butanediol (BDO) and different soft segments of HTBS, HTBN and HTPB were synthesized by solution polymerization separately. We changed in the ratio of the hard segment content to the soft segment content in order to investigate the effect of hard segment content on free-volume in PU membranes studied. Glass transition temperature (Tg ) was measured by differential scanning calorimetry (DSC). The physical and gas permeation properties of these PU membranes have been listed in Table 1.
get the best v2 (<1.2) and most reasonable standard deviations. The shortest lifetime (s1 200 ps) attributes to para-positronium annihilation and the free positron annihilation. The intermediate lifetime (s2 400 ps) is the lifetime of the positron annihilating in the defect of crystalline region. The longest lifetime (s3 1–3 ns) is due to o-Ps pick-off annihilation in free-volume holes of amorphous region [16]. Using the following semiempirical equation and o-Ps lifetime, we obtained the average free-volume hole radius [17–19]:
s3 ¼
All PAL spectra were recorded at room temperature with an Ortec ‘‘fast–fast’’ lifetime spectrometer. The time resolution was 250 ps (fwhm). We used a 22 Na with 20 l Ci as radioactive positron source and put the source between two pieces of same samples like sandwich. A million counts were collected for each spectrum. All of the PAL spectra were analyzed by finite-term lifetime analysis method using PATFIT program. In these PU membranes, the finite-term lifetime decompose a PAL spectrum into three terms of negative exponentials. We
ð2Þ
where s3 (o-Ps lifetime) and R (hole radius) are expressed , respectively. R0 equals to R þ DR where DR in ns and A ). is the fitted empirical electron layer thickness ( ¼ 1.66 A 3 ), for The volume of free-volume holes, Vf (in A spherical cavities can be calculated: Vf ¼
2.2. Positron annihilation lifetime spectroscopy
1 1 1 R 1 2pR sin ¼ 1 þ k3 2 R0 2p R0
4pR3 3
ð3Þ
where R can be calculated from Eq. (2). Furthermore, the relative fractional free-volume (%) is expressed as an empirically fitted equation as: fV ¼ CVf I3
ð4Þ
where Vf can be calculated from Eq. (3), I3 (in %) is the o-Ps intensity and C is an arbitrarily chosen scaling factor for a spherical cavity.
Table 1 Physical and gas permeation properties in HTPB-PU, HTBS-PU and HTBN-PU Sample
Hard segment content (wt%)
Type of soft segment
Tgs0 a (°C)
Tgs b (°C)
Wss (%)
D c (CO2 )
P d (CO2 )
B1 B2 B3 B4 BS1 BS2 BS3 BS4 BN1 BN2 BN3 BN4
24.8 37.2 51.1 62.1 24.8 36.9 51.1 62.0 24.9 36.7 51.9 62.9
HTPB2270 HTPB2270 HTPB2270 HTPB2270 HTBS2412 HTBS2412 HTBS2412 HTBS2412 HTBN2362 HTBN2362 HTBN2362 HTBN2362
)77.9 )77.9 )77.9 )77.9 )68.3 )68.3 )68.3 )68.3 )44.4 )44.4 )44.4 )44.4
)74.3 )72.8 )74.9 )74.4 )62.4 )62.7 )63.2 )63.3 )29.5 )32.7 )33.4 )31.5
95.8 94.1 96.5 95.6 93.1 93.5 94.0 94.1 81.9 85.6 86.4 84.2
141 110 81 43.6 99 74 43 22 28 23 11 6
147 112 89 55.1 104 73 54 26 29 23 13 8
a
Tgs0 represent the glass transition temperature for pure soft segment. Tgs represent the glass transition temperature for soft matrix. c D in 108 cm2 /s. d P in barrers, where 1 barrer ¼ 1010 cm3 (STP) cm/(cm2 s cmHg). b
Z.F. Wang et al. / European Polymer Journal 39 (2003) 2345–2349
3. Results and discussion
3.4
2600 HTPB-PU HTBS-PU HTBN-PU
o - P s life t ime τ3 (ps )
2500 2400 2300 2200 2100 2000 1900 1800 25
30
35
40
45
50
55
60
Hard Segment Content (wt%) Fig. 1. o-Ps lifetime vs. hard segment content.
65
R(A)
3.2 3.1 3.0 2.9 2.8 2.7 20
25
30
35
40
45
50
55
60
65
Hard Segment Content (wt%)
Fig. 2. Mean free-volume hole radius vs. hard segment content.
3.5
Fractional Free Volume
Table 1 shows that the higher the hard segment content was, the lower the gas permeability was in HTPB-PU, HTBS-PU and HTBN-PU, respectively. These results of PU membranes are in agreement with the previous reports by Huang et al. [14,15]. The effects of chemical compositions on gas permeability are due to the free-volume and the nature of chain packing. Fig. 1 shows that variations of o-Ps lifetimes with different hard segment content. From Fig. 1, we can see that the o-Ps lifetimes decrease as the hard segment content increases. There is a direct correlation between the o-Ps lifetime and the free-volume hole size. As shown in Figs. 2 and 3, the free-volume hole size (R) and fractional free-volume (fV ) decrease with the increase of hard segment content. This can be explained in terms of molecular structure and the packing of polymer chains. In HTPB-PU, HTBS-PU and HTBN-PU, the flexibility and the loose packing of soft segment result in increase of the concentration of free-volume holes capable of supporting gas diffusion in soft segment region. The hard segments tend to form cluster aggregates because of the effect of hydrogen bond resulting in enhanced physical cross-linking, and some shorter ones of ‘‘free state’’ disperse into soft segment region. There are two effects introduced by the increase of hard segment content. One is the enlargement of hard segment of cluster aggregate and the other is the restriction of the movement of soft segment. This may be the suitable explanation for the trend of the gas permeability and the fractional free-volume with the increase of hard segment content.
HTPB-PU HTBS-PU HTBN-PU
3.3
3.1. Effect of hard segment content on the free-volume and gas permeability
20
2347
HTPB-PU HTBS-PU HTBN-PU
3.0
2.5
2.0
1.5 20
25
30
35
40
45
50
55
60
65
Hard Segment Content (wt%) Fig. 3. Fractional free-volume vs. hard segment content.
3.2. Effect of different soft segment on the free-volume and gas permeability From Table 1, we have the following observations: the average diffusion coefficient, D, has a decreasing order of HTPB-PU > HTBS-PU > HTBN-PU under the same amount of hard segment content. As shown in Figs. 2 and 3, the hole size and fractional free-volume have an increasing order of HTBN-PU < HTBSPU < HTPB-PU under the same amount of hard segment content. The effect of different soft segment on gas permeability is mainly attributed to the free-volume. The degree of phase segregation also influences the freevolume in PU membranes. The gas permeability and fractional free-volume are smaller for HTBS-PU than for HTPB-PU. In HTPB based PU, hydrogen bond can’t be formed between soft segments and hard segments, because the soft segments can’t offer the strong electronegativity element which is needed by formation of hydrogen bond. Compared to HTPB-PU, although in HTBS-PU, hydrogen bond can’t be formed between the soft segments and the hard segments, rigid benzene rings increase the stiffness of the polymer chains and restrict chain mobility. Therefore
Z.F. Wang et al. / European Polymer Journal 39 (2003) 2345–2349
1 Wss ð1 Wss Þ ¼ þ Tgs Tgs0 Tgh0
160
DCO2 (10-8cm2/s)
such groups decrease the sizes of free-volume hole and reduce the gas permeability. In HTBN-PU, –CN of acrylonitrile in HTBN can form hydrogen bond with –NH of the hard segments, resulting in enhanced physical cross-linking between soft segments and hard segments. Compared to HTPB-PU and HTBS-PU, the fractional free-volume and gas permeability of HTBN-PU decreased distinctly. These observations are in good agreement with the results measured by DSC. In Table 1, Wss representing the content of pure soft segment in the soft matrix can be calculated from FOX equation [20]:
3.3. Correlations between the gas permeability and the free-volume Fig. 4 shows the diffusion coefficient for CO2 molecule, changing with the average free-volume, Vf . The diffusion coefficient increased as the average free-volume increased in HTPB-PU, HTBS-PU and HTBN-PU, re3 ) [1] is spectively. The molecular volume of CO2 (70.9 A smaller than the mean free-volume of PU membranes as shown in Fig. 4. It is known that a larger diffusion coefficient needs a larger free-volume. The average diffusivity, D, provides a measure of the effective mobility of the penetrant in the polymer matrix. When a gas molecule is comparable in size with the available hole size in a material, its diffusion is restricted. On the other hands, if the gas molecule size is smaller than the statistical average free-volume, it will diffuse through a material with a large diffusion constant. This could provide an explanation of why the gas permeation increase as a function of free-volume hole size. The fractional free-volume, fV , can reflect any change in amorphous regions where gas molecules can permeate
80
40
80
90
100
110
120
130
140
150
Vf (A3)
ð5Þ
where Tgs0 and Tgs represent the glass transition temperature for pure soft segment and soft matrix, respectively. Tgh0 representing the glass transition temperature of the pure hard segment (TDI/BDO) is 72 °C [21]. Wss can denote the degree of phase separation in polyurethane. From Table 1, we can obtain that Wss for HTPB-PU, HTBS-PU and HTBN-PU are approximate 95.5%, 94% and 84%, respectively. The degree of phase separation of HTPB-PU is the highest which denotes that there are less hard segments dispersing into the soft segment region. Wss for HTBS-PU is quite close to the one for HTPB-PU. Compared to HTPB-PU and HTBS-PU, the degree of phase separation of HTBN-PU decreases clearly and more hard segments disperse into soft segment region. The difference of phase separation degree between HTPB-PU, HTBS-PU and HTBN-PU influences the fractional free-volume and the gas permeability.
HTPB-PU HTBS-PU HTBN-PU
120
0
Fig. 4. Diffusion coefficient of CO2 vs. hole volume.
resulting from the increase of hard segment content and different soft segment. From Table 1 and Fig. 3, we have the following observations: HTBN-PU with highest hard segment content has the lowest fractional freevolume and the lowest gas permeability. According to the Eq. (1), correlation between the diffusion coefficient, D, and fractional free-volume, fV , is identified in Fig. 5. A plot of measured values of ln D vs. 1=fV yields a fair good straight line, in agreement with prediction of the Fujita theory [12] (straight line obtained by linear regression is ln D ¼ 9:51–13:36 (fV1 )). The result is in agreement with the previous reports about the Fujita theory [1,22]. It can be concluded, therefore, that the free-volume plays an important role in determining the gas permeability. These results establish general correlations between the structural features of PU membranes, their gas permeability and, the free-volume hole properties.
HTPB-PU HTBS-PU HTBN-PU
5
4
ln D
2348
3
2
1 0.30
0.35
0.40
0.45 (fV)
0.50
0.55
0.60
-1
Fig. 5. Logarithm of diffusion coefficient of CO2 vs. the inverse of fractional free-volume. Straight line is linear regression based on Eq. (1).
Z.F. Wang et al. / European Polymer Journal 39 (2003) 2345–2349
4. Conclusion The results of the free-volume properties obtained by PAS and gas permeability in PU membranes reveal that the effect of free-volume on the gas permeability is very large. The diffusion coefficient, D, and the fractional free-volume, fV , in HTPB-PU, HTBS-PU and HTBNPU, respectively, decrease with the increase of hard segment content. D and fV have a decreasing order of HTPB-PU > HTBS-PU > HTBN-PU under the same amount of hard segment content. Direct correlation is observed between gas diffusion properties and free-volume hole properties. The gas diffusivity increases as the fractional free-volume increases.
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