Relationship between the Local Dynamics and Gas Permeability of

Jul 24, 2012 - Broadening of the dynamic scattering law (S(Q,ω)) was clearly observed for para-substituted PCPA ... This implies that the local mobil...
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Relationship between the Local Dynamics and Gas Permeability of Para-Substituted Poly(1-chloro-2-phenylacetylenes) Rintaro Inoue,*,† Toshiji Kanaya,*,† Toshio Masuda,*,‡ Koji Nishida,† and Osamu Yamamuro§ †

Institute for Chemical Research, Kyoto University, Uji, Kyoto-fu 611-0011, Japan Department of Environmental and Biological Chemistry, Faculty of Engineering, Fukui University of Technology, 3-6-1 Gakuen, Fukui 910-8505, Japan § Neutron Scattering Laboratory, Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan ‡

ABSTRACT: Local dynamics of para-substituted poly(1chloro-2-phenylacetylene) (PCPA) derivatives was studied using quasielastic neutron scattering. Broadening of the dynamic scattering law (S(Q,ω)) was clearly observed for parasubstituted PCPA derivatives even in the glassy state, and the observed S(Q,ω) was well fitted to a sum of narrow and broad Lorentzians, which represent the slow and fast motions, respectively. The half-width at half-maximum (Γ) of the narrow Lorentzian exhibited a positive correlation with the CO2 and CH4 permeability coefficients (P), while the Γ from the broad Lorentzian hardly changed despite of the variation of permeability coefficient, indicating that only the narrow component (i.e., the slow motion) contributes to the gas permeability. The Γ from the narrow component was approximately proportional to the diffusion coefficient (D) of the CO2 and CH4 gases, whereas it did not correlate with solubility coefficient (S). This implies that the local mobility affects the gas permeability through the diffusion term. The slow motion with a time scale of several tens of picoseconds seems to play an essential role for the gas permeability in glassy polymers.

1. INTRODUCTION

of highly gas-permeable substituted polyacetylenes is poly[1phenyl-2-(p-trimethylsilyl)phenylactetylene] (PTMSDPA) (Chart 1b) whose PO2 is about 1500 barrers.3 More recently, it has been found that the PO2 values of polymers having 1,1,3,3-tetramethylindan and either phenyl (Chart 1c) or pfluorophenyl (Chart 1d) reach 14 400 and 17 900 barrers, which are even larger than that of PTMSP.4 These highly gas-permeable substituted polyacetylenes have several common features including stiff main chain based on carbon−carbon alternating double bonds, spherical substituents of suitable sizes, high glass transition temperatures usually above 200 °C, and membrane-forming ability by solution casting.1b,f The gas permeability of rubbery polymers is discussed in terms of the product of solubility coefficient and diffusion coefficient, whereas that of glassy polymers is explained by so-called dual-mode mechanism which includes both the Henry-type solution and the Langmuir-type adsorption.1a,c Highly gas-permeable substituted polyacetylenes have low apparent density due to molecular-scale voids, which is more quantitatively discussed on the basis of excess free volume. Thus, the high gas permeability of these polymers is attributed to the presence of molecular-scale voids. Approximately, the gas permeability of substituted polyacetylenes is

It is well-known that some polyacetylenes with bulky substituents exhibit very high gas permeability among the synthetic polymers.1 For example, poly[1-(trimethylsilyl)-1propyne] [poly(TMSP)] (Chart 1a) has proved to show higher gas permeability, e.g., oxygen permeability coefficient (PO2 5000−10 000 barrers), than does poly(dimethylsiloxane) (PO2 ca. 600 barrers), which was known to be the most gaspermeable among all the existing polymers.2 Another example Chart 1. Chemical Structure of (a) Poly(TMSP), (b) PTMSDPA, (c) Polyacetylenes Having 1,1,3,3Tetramethylindan and Phenyl, and (d) Polyacetylenes Having 1,1,3,3-Tetramethylindan and p-Fluorophenyl

Received: June 15, 2012 Revised: July 17, 2012 Published: July 24, 2012 © 2012 American Chemical Society

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was impossible to determine the values due to chemical decomposition. FFV of Polymer Membranes. Fractional free volume (FFV) was calculated by using the equation

discussed in terms of solubility and diffusion of gases. It is expected that the diffusion of gases is affected by the mobility of the dynamics of polymer matrix in addition to the presence of the molecular-scale voids. Therefore, we have investigated the effects of local mobility of the substituted polyacetylene matrix on the gas permeability in previous papers5,6 using quasielastic neutron scattering (QENS), which is one of the powerful tools to investigate local molecular motions in a time range of picoto nanoseconds.7,9 It was found that the local mobility of substituted polyacetylenes showed a clear correlation between the gas permeability coefficient for oxygen PO2 and the local flux F, which is defined as the product of the relaxation rate (Γ) and the mobile fraction (f m) in substituted polyacetylene matrix, and local flux F was proportional to the diffusion coefficient of O2 gas (DO2). The results clearly suggested that the local mobility of substituted polyacetylene matrix is one of the important factors controlling the gas permeability. We also synthesized poly(1-chloro-2-phenylacetylene) (PCPA) (see Chart 2). It is noted that the gas permeability

FFV =

vsp − v0 vsp

≈

vsp − 1.3vw vsp

(1)

where vsp, v0, and vw are the specific volume, occupied volume, and van der Waals volume of polymer, respectively. Gas Permeability and Diffusion Coefficients of Polymer Membranes. Gas permeability coefficients were calculated from the slopes of time−pressure curves in the steady state under the condition where the Fick’s law holds. The diffusion constants (D) were measured by the time-lag method using the equation

D=

d2 6θ

(2)

where d is the thickness of membrane and θ is the time lag given by the intercept of asymptotic line of the time−pressure curve to the time axis. QENS Measurement. QENS measurements were performed with a time-of-flight (TOF) spectrometer AGNES6,13,14 installed at the C31-1 cold neutron guide in JRR-3 reactor, Tokai. The wavelength of incident neutron was 4.22 Å, and the energy resolution, which was evaluated from the full width at half-maximum (fwhm) at elastic position, was 0.12 meV. All the measurements were performed at room temperature. Because of large incoherent atomic scattering from hydrogen atoms, the observed differential cross section was dominated by incoherent scattering. QENS measurements were performed after 3 months after sample preparation due to the schedule of beam time. In order to avoid thermal aging15 and related deterioration, all the samples were stored in desiccators at room temperature, which is far below Tg under the vacuum state.

Chart 2. Chemical Structure of Para-Substituted Poly-(1chloro-2-phenylacetylene) (PCPA) Derivatives in the Present Study

3. RESULTS AND DISCUSSION The observed dynamic scattering laws [S(Q,ω)] from five parasubstituted PCPA derivatives are shown in Figure 1. The spectra were obtained by summing up nine spectra from different values of length of scattering vector (Q) to get high counting statistics, and the scattering intensities were normalized to the elastic peak for the convenience of

of PCPA is relatively low among substituted polyacetylenes (e.g., PO2 5.1 barrers).10,11 However, a salient feature of this polymer is excellent solubility;12 hence, various ring substituents can be introduced to study the effect of substituents on gas permeability. In contrast, poly(diphenylacetylenes) are soluble and membrane-forming only in the case where they have bulky substituents such as a trimethylsilyl group. Thus, the relationship between the gas permeability and substituents of PCPA was studied, taking the advantage of good solubility of PCPA and its derivatives in organic solvents.10 It was eventually found that all the para-substituted PCPA derivatives exhibited higher gas permeability than that of PCPA, while both the fractional free volume (FFV) and gas permeability increased and then decreased with increasing size of para-substituents. Especially, the PCPA derivatives having Si(n-Pr)3 or SiEt3 at the para position exhibited about 1 order of magnitude higher gas permeability coefficient than that of PCPA despite quite low FFV values. This result suggests that the gas permeability is governed not only by FFV but also by other factors like the local mobility of para-substituents. Hence, we decided to study the relationship between the local mobility and the gas permeability of para-substituted PCPA derivatives using QENS.

2. EXPERIMENTAL SECTION Materials. Chemical structures of five para-substituted PCPA derivatives used in the present study are shown in Chart 2. The details of monomer synthesis and polymerization conditions have already been reported elsewhere.10 Membranes whose thicknesses were less than 100 μm were prepared by casting toluene solutions of the polymers onto a Petri dish. All the para-substituted PCPA derivatives are in the glassy state at room temperature, and their glass transition temperatures (Tg) are much higher than room temperature though it

Figure 1. Dynamic scattering laws S(Q,ω) of para-substituted poly(1chloro-2-phenylacetylene) (PCPA) derivatives whose elastic peaks were normalized to 1. The solid curves have been drawn by fitting eq 3, and the dashed curve describes the resolution function. 6009

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comparison. Though all the measurements were performed at room temperature (298 K), which is far below Tg, the observed spectra showed quasielastic broadening compared to the resolution function determined by a vanadium measurement, implying that some parts of para-substituted PCPA derivatives were moving stochastically even in the glassy state. In order to evaluate the dynamic properties of parasubstituted PCPA derivatives, we focused on the Q dependence of elastic scattering intensity [Iel(Q)], where Iel(Q) was obtained by integrating the observed S(Q,ω) within the energy resolution on Q. The plots of Iel(Q) against Q2 for these polymers are shown in Figure 2. Under the Gaussian

Figure 3. (a) Relationship between fractional free volume (FFV) and values of PCO2 and PCH4. (b) Relationship between FFV and ⟨u2⟩.

Figure 2. Q2 dependence of elastic scattering intensity, Iel(Q), of PCPA derivatives. The solid lines have been drawn by fitting Iel(Q) = exp[−⟨u2⟩Q2].

approximation we evaluated mean-square displacement ⟨u2⟩ through equation Iel(Q) = exp[−⟨u2⟩Q2]. The ⟨u2⟩ values were as follows: 0.158 Å2 (R = H), 0.158 Å2 (R = Br), 0.196 Å2 (R = Me), 0.220 Å2 (R = SiEt3), and 0.235 Å2 (R = Si(n-Pr)3). It seems that the ⟨u2⟩ values of the polymers having bulky groups are larger than those of the polymers with small groups, meaning that the local dynamics of para-substituted PCPA derivatives is strongly affected by the para-substituents. We plotted the CO2 and CH4 permeability coefficients (PCO2 and PCH4) against FFV to find that the gas permeability coefficients were not correlated to FFV clearly, as shown in Figure 3a. Then, we plotted the ⟨u2⟩ values against FFV in Figure 3b. Again, we could not observe an obvious correlation between FFV and ⟨u2⟩ but rather observed a negative correlation between them, suggesting that FFV is not related to local dynamics of PCPA derivatives at all. Focusing on the FFV dependences of gas permeability and the mean-square dependence ⟨u2⟩, there seems to be a similar tendency between the gas permeability and the mean-square dependence ⟨u2⟩. Hence we plotted the relationship between PCO2 and PCH4 and ⟨u2⟩ in Figure 4. It appears that a positive correlation exists between gas permeability and ⟨u2⟩ for both CO2 and CH4, although the data points are somewhat scattered. This loose but positive correlation indicates that the local dynamics probed by QENS affects the gas permeability of para-substituted PCPA derivatives. A similar tendency was observed for other previously reported systems of substituted polyacetylenes.5,6

Figure 4. (a) Relationship between ⟨u2⟩ and PCO2. (b) Relationship between ⟨u2⟩ and PCH4.

In order to understand the correlation between local dynamics and gas permeability in more detail, we performed curve fitting to the observed S(Q,ω). Kanaya et al. reported that the S(Q,ω) of substituted polyacetylenes could not be described by single Lorentzian but double Lorentzians,6 indicating the existence of two dynamic processes with different relaxation times in the time range examined. In the present data 6010

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permeability. The correlations of PCO2 and PCH4 with Γ from the broad and narrow components (Γb and Γn) are shown in Figures 6a and 6b, respectively.

analysis we also used the following model function to describe the observed S(Q,ω) S(Q , ω) = [1 − A n (Q ) − Ab(Q )]δ(ω) + A n (Q )L(Γn, Q , ω) + Ab(Q )L(Γb, Q , ω) + Bin (Q )

L(Γi, Q , ω) =

Γi 1 2 π Γi + ω 2

(3)

(i = n and b) (4)

where δ(ω) represents a δ-function describing immobile parts of molecule within the energy resolution, and Li and Ai (i = n and b; n and b denote narrow and broad, respectively) are Lorentz functions and their fractions in S(Q,ω), respectively. The half-widths at half-maximum Γn and Γb of the narrow and broad Lorentzians are the relaxation rates or inverse of the relaxation times of the slow and fast components, respectively, and Bin(Q) represents an inelastic background. The results of curve fitting are shown by solid lines in Figure 5a,b for the derivatives having R = Si(n-Pr)3 and SiEt3 groups,

Figure 6. (a) Correlations between PCO2 and relaxation rates Γ for the narrow and broad components. (b) Correlations between PCH4 and relaxation rates Γ for the narrow and broad components.

Both PCO2 and PCH4 values are independent of the Γb from the broad component, whereas they correlated with the Γn from the narrow component, indicating that only the narrow component has influence on the gas permeability. Figure 7 shows the correlations of PCO2 and PCH4 to fractions An and Ab. We could not observe a clear correlation between Ab and both PCO2 and PCH4, which indicates that the broad component is not responsible for the gas permeabilities. Contrary to our expectation, we could observe no evident relationship between An and gas permeability, either. Kanaya et al. introduced the local flux (F), which was defined as a product of An and Γn, to understand the correlation between local mobility and gas permeability under the assumption that both the fraction and the relaxation time contribute to gas permeability.5 We delineated the plot of F against P in Figure 8. When the correlation between P and Γ for the narrow component was compared with the correlation between P and F, almost the same tendency was observed, indicating that Γ for the narrow component is the leading term for the change of P, while A has little effect on P or irresponsible for P for the PCPA derivatives. We will discuss below the correlation between Γn and P values. Some data points in Figure 6 appreciably deviated from the linear relationship, suggesting that the gas permeability coefficient is controlled not only by local mobility but also by other factors such as chemical affinity, molecular structure, and free volume. Hence we tried to divide the gas permeability coefficient into dynamic and other contributions. In the case where only the solution−diffusion mechanism governs, the gas permeability coefficient is expressed by the product of the solubility coefficient (S) and the diffusion coefficient (D); i.e.,

Figure 5. Curve fitting to model function (eq 3) for (a) the PCPA derivatives having p-Si(n-Pr)3 and (b) the one having p-SiEt3.

respectively. We could observe no systematic deviations from the observed S(Q,ω) for all the derivatives, indicating that the model function we adopted is appropriate to describe the observed S(Q,ω). By using the evaluated Γ and A values, we examined the relationship between the local dynamics and the gas 6011

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Figure 7. (a) Correlations between PCO2 and fractions An and Ab of the narrow and broad components. (b) Correlations between PCH4 and fractions An and Ab of the narrow and broad components.

Figure 9. (a) Correlation between SCH4 and Γ for component. (b) Correlation between SCO2 and Γ for component. (c) Correlation between DCH4 and Γ for component. (d) Correlation between DCO2 and Γ for component.

the the the the

narrow narrow narrow narrow

mobility is directly related to the diffusion coefficient. The slopes of solid lines in Figure 9 are around unity for both CO2 and CH4. The present analysis has thus revealed that the local mobility has influence on the gas permeability through the diffusion coefficient. To interpret the close correlation between the diffusion coefficient and the local flux of substituted polyacetylenes, the random gate model6 was postulated by Kanaya et al. before, and we examine whether this model is applicable to the parasubstituted PCPA derivatives or not briefly. The detailed explanation of this model has been given in a previous paper,6 and its outline is described here. The macroscopic diffusion coefficient16 based on the random gate model is given by D=

1 (⟨l 2⟩ 6

+ 6⟨r 2⟩)

τ0 + τ1

(5)

where ⟨r ⟩, ⟨l ⟩, τ0, and τ1 are mean-square displacement (MSD) for the random motion in a cavity, MSD for the escape motion from a cavity, the resident time in the cavity, and the traveling time from a cavity to another, respectively. If we assume that a gas molecule can escape from a cavity with a frequency comparable to the time scale of slow dynamic component by QENS, resident time τ0 in the cavity is at least 0.1 meV, which roughly corresponds to 40 ps. The traveling time is roughly evaluated through the relation τ1 = ⟨l2⟩0.5/v, where v is the mean velocity of gas molecule. We assumed 10 Å for ⟨l2⟩0.5 as an example to calculate τ1 as ca. 2.5 ps. On the basis of this estimation, we found that τ0 is much larger than τ1, indicating that most of gas molecules stay in the cavity. Then eq 5 can be reduced to the following simple equation: 2

Figure 8. (a) Correlations between PCO2 and local fluxes (F) for the narrow and broad components. (b) Correlations between PCH4 and local fluxes (F) for the narrow and broad components.

P = S × D. Although, in a strict sense, this relationship with concentration and pressure independent values of S and D holds only with rubbery polymers at low sorbent concentration, we tentatively adopted it for the present polymers. We plotted the correlations between either S or D and Γn in Figure 9. While no obvious correlation is observed between S and Γn, D shows a linear relationship for Γn, which suggests that the local 6012

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D=

⟨l 2⟩ 6τ0

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4. CONCLUSION In this paper, we have studied the local dynamics of parasubstituted PCPA derivatives using quasielastic neutron scattering. We observed an obvious correlation between the gas permeability coefficients and the mean-square displacement evaluated from the Q2 dependence of elastic scattering intensity, suggesting the contribution of local mobility to the gas permeability. In order to understand the dynamic properties of para-substituted PCPA derivatives in more detail, we fitted the double Lorentzians to the observed S(Q,ω) to find it successful, indicating the existence of two stochastic processes within the time range. It was found that the Γn from the narrow Lorentzian component exhibited clear correlations with the CO2 and CH4 permeability coefficients, whereas the Γb from the broad component was almost independent of the CO2 and CH4 permeability coefficients. This finding suggests that only the narrow component with a time scale of several tens of picoseconds is responsible for the gas permeability of parasubstituted PCPA derivatives. Γn was approximately proportional to D, while it was not correlated to S. This implies that the local mobility is related to the gas permeability through diffusion coefficient. The random gate model, which was postulated to explain the gas permeability of substituted polyacetylenes, was also applicable to interpret the mechanism of gas permeability of the present polymers. It is concluded that the slow motion with a time scale of several tens of picoseconds is indispensable for the gas permeability of glassy polymers.

(6)

If we assume that resident time τ0 is related to τn through τ0 ∼ τn/α, we finally obtain eq 7: D=α

⟨l 2⟩ ⟨l 2⟩ =α Γn 6τn 6

(7)

where α is a numerical constant of ∼1. Equation 7 represents the linear relationship between Γn and D, which actually holds as seen in Figures 9c,d. Thus, the random gate model provides a plausible explanation for the role of local mobility in the gas permeability of para-substituted PCPA derivatives. Finally, the physical meaning of the observed dynamics of para-substituted PCPA derivatives is discussed. For this purpose, the following results previously reported should be noted regarding the dynamics of amorphous polymers investigated by inelastic neutron scattering. It is known that the low-energy excitation or the so-called boson peak is universally observed for glass-forming materials including polymers at temperatures far below Tg. In principle, the intensity of the boson peak increases with temperature according to the Bose−Einstein population factor, indicating that the motion is harmonic. With further increasing temperature, an anharmonic motion or the so-called fast process starts at temperatures below Tg. The onset temperature of the fast process is about 20−50 K below bulk Tg for the polymers without side groups like polybutadiene (PB)17 and the polymers with small side groups like polychloroprene (PCP).18 On the other hand, the onset temperature of the fast process is far below bulk Tg for the polymers having large side groups.8,19,20 For example, the onset temperature of the fast process of polystyrene (PS) is around 200 K, which is about 170 K below bulk Tg due to the internal degrees of freedom of the side chain. We just observed QENS for the para-substituted PCPA derivatives and did not observe the boson peak at 298 K even for PCPA, which indicates that the side groups in these polymers have high degrees of freedom of motions even at temperatures below Tg. Furthermore, the Γb value from the broad component is approximately the same as the Γ of the fast process observed for PS, suggesting that the origin of the broad component of para-substituted PCPA derivatives is also the fast process. Concerning the narrow component, such slow motion with a time scale of several tens of picoseconds has only been observed at temperatures above Tg for simple polymers like PB21 and PS,20 while the slow motion has been seen at temperatures above bulk Tg and not below bulk Tg. At present, it is considered that the origin of slow motion is the conformational transition of main chain in PB and PS. In the case of para-substituted PCPA derivatives, the main chain is too stiff to move at temperatures below bulk Tg due to the presence of double bonds in the main chain. However, a large degree of freedom of substituents in PCPA derivatives enables the motion which is related to gas permeability even at temperatures even far below bulk Tg, resulting in the assistance of diffusion of gas molecules in glassy polymers. It implies that the slow motion with a time scale of several tens of picoseconds is essential for the gas permeability in glassy polymers.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (R.I.), [email protected]. jp (T.K.), [email protected] (T.M.); Tel +81-774-383143; Fax +81-774-38-3146. Notes

The authors declare no competing financial interest.

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REFERENCES

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