J . Phys. Chem. 1990, 94, 2128-2135
2128
I
/
0 00 10
0
2c
30
P r e s s u r e (MPa)
Figure 6. Solubility of different average molecular weight PEGS in
supercritical COz at 323 K. examined this effect by fitting our PVTdata for pure PEG(400) to the EOS. Our range for z is somewhat narrower than in the case of small molecules (6 < z < 16; 1.0 X IO-’ m3 mol-’ < uH < 1.5 X m3 mol-]). It is speculated that this might be due to the fact that polymer chains have a lower packing ratio in a lattice. Figure 6 compares the solubility of different molecular weight PEGS in C 0 2 at 323 K as a function of pressure. At a fixed temperature and pressure, the solubility drops with molecular weight. If the parent polymer has a wide molecular weight distribution, the partitioning of a narrow molecular weight fraction within the broad distribution can be controlled systematically by choice of the operating conditions. The molecular weight dependence of solubility provides a basis for supercritical fluid fractionation of polymers.
Conclusions
Phase equilibrium data of three different molecular weight PEG-C02 systems at two different temperatures are presented and correlated by using a lattice-model-based EOS. At a fixed temperature and pressure above a threshold pressure, the solubility of PEG in supercritical C 0 2 decreases with molecular weight. Along an isotherm, the enhancement of PEG solubility in C 0 2 as a function of pressure corresponds to the leveling of C 0 2 solubility in the polymer. C 0 2 solubility in the polymer drops with temperature while two competing factors, the vapor pressure of the polymer and the S C F density, govern the temperature dependence of PEG solubility in COz. The comparison of the experimental results and the model correlations indicates that the lattice model EOS provides quantitative fits to the data of PEG-C02 systems. C 0 2 is appreciably soluble in the liquid polymer. The concentrations of both components change in the coexisting phases. The unique aspect of our application is that the model must predict the composition of both phases, in contrast to previous applications where the polymer phase is pure. The modeling has been performed by using a single adjustable parameter, k,. k, is an empirical parameter that corrects for the deviation from the pairwise additivity of binary interactions and can be related to the randomness of the lattice. The results indicate that k , is apparently a weak function of temperature. Future work is needed to establish the temperature dependency of the interaction parameter. Acknowledgment. This work was supported by University Science Partners, Inc., and National Science Foundation Grant No. CBT 8419755. Registry No. PEG, 25322-68-3; COz, 124-38-9.
Nuclear Spin Relaxation Mechanisms and Mobility of Gases in Polymers’ E. J. Cain, W.-Y. Wen,* R. D. Jost, X. Liu, Z. P. Dong, A. A. Jones, and P. T. Inglefield Department of Chemistry, Clark University, Worcester, Massachusetts 01 610 (Received: March I , 1989; In Final Form: August 28, 1989)
Nuclear spin relaxation is measured for two gases sorbed in a series of glassy and rubbery polymers. The carbon-13 of labeled carbon dioxide and 129Xeof atomic xenon are the nuclei monitored in this study. Spin-lattice relaxation, spinspin relaxation, and nuclear Overhauser enhancements are reported as well as the dependence of some of these parameters on Larmor frequency. The temperature dependence of spin-lattice relaxation is also reported for some of the sorbed gases in the vicinity of the glass transition of the polymer. An abrupt change in the relaxation time is observed at temperatures 30-60 deg above the glass transition. This change is attributed to the onset of the glass transition, and the shift to high temperature reflects the high frequencies probed by spin-lattice relaxation. The field dependence of the relaxation is used to establish the mechanisms of relaxation. For CO, sorbed in silicone rubber, relaxation occurs both by the spin-rotation mechanism and by a contribution from intermolecular dipole-dipole relaxation which is indicated by an increase in spin-lattice relaxation time with field and by the presence of a nuclear Overhauser enhancement. For C 0 2 in glassy polycarbonate, these same two mechanisms are present, but relaxation through the chemical shift anisotropy mechanism becomes important at higher static field strengths. This indicates the presence of slower rotational motion in the glass relative to the rubber, and this type of change in dynamics is also likely to be the cause for the abrupt change in relaxation observed as the glass transition is approached. For Xe in glassy polycarbonate, the only mechanism clearly present is intermolecular dipole-dipole relaxation. In neither the rubber nor the glass can an interpretation involving a single correlation time for each mechanism be used to interpret field-dependent spin-lattice relaxation data plus spinspin relaxation data and nuclear Overhauser enhancement data. The failure is attributed to the presence of a distribution of correlation times present for dynamical processes in polymeric systems. A complete analysis requires a larger data base and is expected to yield detailed information on molecular level motions of gases in polymer matrices.
Introduction
The motion of small molecules sorbed in a polymer matrix can be expected to differ from small molecules in the gas phase or the liquid phase. The time scale of motion is certainly likely to ‘This work is dedicated to the memory of Robert Donald Jost.
0022-3654/90/2094-2 128$02.50/0
change, but other aspects may well be altered. Simple small molecules typically have Debye-like relaxation while polymers often exhibit complex relaxation behavior which cannot be characterized by a single-exponential correlation time.] (1) McCrum, N. G.; Read, B. E.; Williams, G. Anelastic and Dielectric Effects in Polymeric Solids; Wiley: New York, 1967.
0 1990 American Chemical Society
Mobility of Gases in Polymers The small molecules selected for this study are gases at room temperature and contain only a single spin one-half nucleus. Specifically, carbon dioxide and xenon gas were chosen and carbon- 13-enriched carbon dioxide was used to improve signal strength. Xenon was used in its natural state since the isotope of interest, Iz9Xe,has a natural abundance of 26.44%. As a pure gas, C 0 2 is expected to relax primarily by the spin-rotation (SR) mechanism*.' while mechanisms such as chemical shift anisotropy (CSA) and the dipole-dipole interaction can be present as minor contributors. Pure Xe gas has a very long relaxation time since spin-rotation is not p o s ~ i b l e ,and ~ * ~a transient spin-rotation interaction arising from the Xe-Xe collision pairs appears to be the only mechanism operative in the gas p h a ~ e . ~ , ~ After the gases are sorbed in polymers, the relative contributions of the various relaxation mechanisms are likely to change. Simple liquids like CS2 have roughly comparable relaxation contributions from CSA and SR.8 Carbon dioxide in a polymer matrix might be expected to be closer to liquid CS, than gaseous CO,. Although enriched CO, is used in the polymer experiments, homonuclear dipole-dipole relaxation is not likely since the gas is typically only 5% of the sample by weight. However, heteronuclear relaxation between protons on the polymer and the carbon-13 of the C 0 2 is likely since the protons have a significant concentration in the samples. Indeed for Xe, this heteronuclear intermolecular dipole-dipole mechanism seems most likely since there is no CSA or S R relaxation in the undistorted atom. Each relaxation mechanism provides access to a different type of motional information. Spin-rotation relaxation depends on collisional changes in the rotational angular momentum quantum number and would provide a measure of the collision frequency of the gas in the polymer matrix9 The chemical shift anisotropy mechanism depends on the rotational correlation time and thus provides information on molecular rotation.I0 The intermolecular dipole-dipole relaxation mechanism depends on the translational motion of the gas molecule through the polymer matrix and on the distance of closest approach to the polymer protons.11,'2 This mechanism provides a short-range measure of the translational diffusion coefficient of the gas molecule. The nature of the polymer matrix is also expected to influence the mobility of the gas. Diffusion of gases through rubbers is characterized by a different formalism than diffusion through glasses.13 Diffusion in rubbers is treated as though the rubber is a simple fluid and the gas is simply dissolved in the polymer. Molecular level information from spin relaxation can test this approximation. Gases sorbed in glassy polymers are described by a more complex formalism, the dual-mode model. In this model gas may be sorbed in either Langmuir type sites or dissolved sites, the latter being comparable to the mode of sorption in a rubber. Different translational diffusion times are assigned to the two types of sorbed gas in a glassy polymer. From this viewpoint one would expect changes in spin relaxation as one changes from a glassy polymer to a rubbery polymer or as one traverses the glass transition of a given polymer. Relaxation experiments are performed in glassy polycarbonate, polyisobutylene rubber, and silicone rubber. In the two rubbery polymers, T I measurements are made as a function of temperature in the vicinity of the glass (2) Jameson, C. J.; Jameson, A. K.; Smith, N. C.; Jackowski, K. J. J . Chem. Phys. 1987.86,2717. (3) Folkendt, M. M.; Weiss-Lopez, B. E.; True, N. S. J . Phys. Chem. 1988, 92,4859. (4) Hsu, J.; Wu, Z.; Happer, W. Phys. Lerr. 1985,112A,141. (5) MacKintosh, F. C.; Wu, Z . ; Happer, W. Phys. Letr. l985,112A,435. (6) Jameson, C. J.; Jameson, A. K.; Hwang, J. K. J . Chem. Phys. 1988, 89,4074. (7) Torrey, H. C. Phys. Rev. 1963,130,2306. (8) Spiess, H. W.; Schweitzer, D.; Haberlen, U.; Hausser, K.H. J . Mag. Reson. 1971,5, 101. (9) Gordon, R. G . J . Chem. Phys. 1966,44, 228; 1966,45, 1635, 1649. (10) Abragam, A. The Principles of Nuclear Magnetism; Oxford: London, 1961. (11) Hwang, L. P.; Freed, J. H. J . Chem. Phys. 1975,63,4017. (12) Freed, J. H. J . Chem. Phys. 1978,68, 4034. (13) Chern, R. T.; Koros,W. J.; Sanders, E. S.; Chen, S. H.; Hopfenberg, H.B. ACS Symp. Ser. 1983,No. 223.
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 2129 TABLE I: Relaxation Times and Nuclear Overhauser Enhancement for IVO, Dissolved in Silicone Rubber at 273 K and 11 atm frequency, M H z
TI, s T2,ms NOE
22.6
62.9
100
9.7 150 1.14
11.7
13.1
1 .o
1 .o
TABLE 11: Relaxation Times and Nuclear Overhauser Enhancement for I3CO2 Dissolved in Polycarbonate at 333 K and 5 atm frequency, MHz TI, s T2,ms NOE
22.6
62.9
126
4.6 141 1.28
3.3
2.2
1.08
16 1 .o
transition so that any change in gas mobility can be detected. In polycarbonate and silicone rubber T I ,T,, and NOE measurements are made as a function of field strength to ascertain the mechanisms contributing to relaxation. Relatively simple spin relaxation experiments are adequate to measure relaxation times since the gas resonances are fairly narrow.14 There are no strong dipolar interactions so only scalar decoupling is required to measure the nuclear Overhauser enhancement. The sample geometry is often complex with gas sorbed in a pellet of polymer or a stack of disks cut from a sheet of polymer. Because of this, line widths of the resonances are not always reliable measures of the spin-spin relaxation times and pulse experiments are sometimes required. Since several relaxation mechanisms are likely, measurements were made as a function of Larmor frequency. This experimental protocol has demonstrated merits in cases where relaxation behavior is complex and allows for a more credible interpretati~n.'~ If the general characteristics of spin relaxation of gases sorbed in polymers can be established in this report, the possibility of more complete studies and detailed analyses can be considered. The long-range goal of this work is to provide a molecular level description of rotational and translational mobility of gases in polymers. The purpose of this report is to clearly identify the appropriate mechanisms of nuclear spin relaxation for gases sorbed in polymer matrices. Experimental Section
The silicone rubber sample used in this study was provided by General Electric Co. Silicone Products Division and was designated as SE6035. The permeability to C 0 2 of this same silicone rubber was studied by Jordan, Koros, and Fleming.16 The sample density is reported as 1.10 f 0.03 g/cm3, and the cross-link density, uc/uo, as 1.24 X g mol/cm3. General Electric Co. also supplied samples of polycarbonate which were then shaped into cylindrical plugs on a lathe. Polyisobutylene (MW = 800000) was obtained from Scientific Polymer Products. Measurements were usually made on cylindrical plugs of the polymer or on rather thick films. These samples required up to several days of equilibration before equilibrium between the free gas and the sorbed gas was reached. For comparison sake, some measurements were performed on powdered samples, but those are not reported here except as specifically noted. Enriched I3CO2was supplied by Merck and had an isotopic purity of 99.8%. Natural abundance lz9Xewas also supplied by Matheson. Heavy wall N M R tubes equipped with pressure valves were obtained from Wilmad Glass and were used to contain the polymer/gas systems at pressures from 5 to 15 atm. Measurments at 2.1 T were made on a Bruker SXP, at 6 T on a Bruker WM 250, at 10 T on a Bruker W M 400, and a t 12 T (14) Stengle, T. R.; Williamson, K. L. Macromolecules 1988,20, 1428. (15) Levy, G. C.; Axelson, D. E.; Schwartz, R.; Hochmann, J. J . Am. Chem. SOC.1978,100, 410. (16) Jordan, S.M.; Koros,W. J.; Fleming, G.K. J . Membr. Sci. 1987,30, 191.
2130 The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
Cain et al. 15
10
-
5
T
130.0 128.0 126.0 124.0 122.0 120.0 118.0 116.0 114.0
PPM
0 213
233
253
273
293
313
333
353
373
393
T (K) Figure 3. Spin-lattice relaxation time vs temperature for 13C02dissolved in polyisobutylene (22.6 MHz). 10
-
h
v) Y
5
s
6
Y
I-
I
130.0 128.0 126.0 124.0 122.0 120.0 118.0 116.0 114.0
PPM Figure 1. Carbon-13 NMR spectra of 13C02dissolved in (top) powdered polycarbonate and (bottom) 5-mil polycarbonate strips. The free gas resonance is at 124.2 ppm. Both spectra recorded at 62.9 MHz. Note the relative amounts of dissolved and free carbon dioxide are not equivalent for these two samples. 15
225
250
325
350
375
400
Figure 4. Spin-lattice relaxation time vs temperature for 13C02dissolved in polycarbonate (62.9 MHz).
TABLE III: Relaxation Times and Nuclear Overhauser Enhancement for '%e Dissolved in Polycarbonate at 300 K and 12 atm frequency, MHz 24.9 69.2 126 TAexp), s 13 17.5 18 NOE(exp) 0.37
10 n v) Y
F 5
0 153
0 200
193
233
273
313
353
393
T (K) Figure 2. Spin-lattice relaxation time vs temperature for 13C02dissolved in silicone rubber (22.6 MHz).
on a Bruker WM 500. A simple 18Oo-r9O0 pulse sequence was used to measure T I while a 9Oo-~-18O0 sequence was used to measure T2. Line width was also used as a measure of T2when the observed width was much larger than the static field inhomogeneity. Gated NOE experiments were performed on the WM series instruments while continuous decoupling was employed on the SXP.
Results A typical spectrum of C 0 2gas dissolved in 5-mil strips of glassy polycarbonate is shown in Figure 1 along with a spectrum of the gas sorbed in powdered polycarbonate. Figure 2 displays T,as a function of temperature from 170 to 380 K for the 13C02/siliconerubber system taken at a carbon-13 Larmor frequency of 22.6 MHz. Figure 3 displays TI for C02 in polyisobutylene rubber at 22.6 MHz from a temperature of
213 to 373 K. For C 0 2 in glassy polycarbonate at 62.9 MHz, T I is shown as a function of temperature from 210 to 400 K in Figure 4. Table I lists TI, T2,and NOE values for the COz/ silicone rubber system at three Larmor frequencies at 273 K and 11 atm of I3CO2 Table I1 lists TI, T2,and NOE values for 13C02 in polycarbonate at 333 K and a pressure of 5 atm, while Table 111 gives comparable data for 129Xein polycarbonate at 300 K and 12 atm.
Interpretation Two resonances are Seen in Figure 1 for a sample of C02sorbed in 5-mil strips of polycarbonate. One of the resonances is for free C02gas which is present in macroscopic spaces surrounding the polymer sample while the second resonance is for gas sorbed into the polymeric glass. This spectrum is much like that reported by Stengle and Williamson14 for Xe sorbed in polyethylene except the shift between sorbed gas and free gas is smaller for C o t than for Xe. A second spectrum is shown in Figure 1 for a sample of C 0 2 sorbcd in a powdered polycarbonate. In this case, only a single resonance is observed. A possible explanation is that there is sufficiently rapid exchange between the free gas and the sorbed gas so that only a single resonance is observed. The large surface area of the powder compared to that of the film is undoubtedly significant here though a verification of this explanation would require considerable investigation. Since relaxation of gas sorbed
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 2131
Mobility of Gases in Polymers
in the polymer is of primary interest in this study, sufficiently thick samples were used so that a resolved resonance for sorbed gas could be identified. The plot of T1vs temperature for 13C02in silicone rubber, Figure 2, shows a sharp increase in T I between 190 and 210 K. This latter temperature is 40-60 deg above the glass transition temperatureI7 as measured by differential scanning calorimetry or dynamic mechanical spectroscopy. These techniques are sensitive to low-frequency response (=I Hz) while the frequencies that are characteristic of T Iare the Larmor frequencies of carbon- 13 nuclei and protons, and both of these lie in the megahertz range. The temperature associated with the glass transition depends upon the frequency of the technique used to measure it. The WLF equation can be used to correlate temperature shifts with the frequency of observation.'* For this application !5e WLF equation can be written as CAT2 - T ' ) log (W2/W') = c2 + (7-2 - TI) and the appropriate universal constants are CI = 17.44 ~2 = 51.6
(1)
Using a nominal frequency of 22.6 MHz for the I3C Ti's for the silicone rubber case, a WLF temperature shift of 42 deg is predicted which is close to the temperature of the T1change. The relaxation data for C02 in polyisobutylene (PIB) as a function of temperature, shown in Figure 3, can be used to check this interpretation. The glass transition of PIB, as determined by the standard low-frequency techniques, is 205 K, which is some 50 deg above the glass transition of silicone rubber.I7 An abrupt change for the T I of C 0 2 in PIB is observed at about 230-240 K, some 40 deg or so above the silicone rubber case. The PIB measurement was made at a carbon frequency of 22.6 MHz, and an application of the WLF equation to this case predicts a temperature shift of 38 deg to a temperature of 243 K. For the case of glassy polycarbonate, no abrupt transition in the T I of the carbon dioxide as a function of temperature was observed over the same general temperature range as was used for the two rubbers. This result is apparent in the data of Figure 4. No measurements were made in the vicinity of the glass transition since it occurs at quite a high temperature for this polymer, and the stability of the pressure sealed tube becomes a concern. If we now shift our attention to the source of relaxation above the glass transition in silicone rubber, it is necessary to consider quantitative predictions of the various possible relaxation mechanisms relative to the observed behavior summarized in Table I. The first mechanism for consideration is spin-rotation relaxation which is commonly observed for low molecular weight gases and liquids, particularly those which contain only one spin one-half nucleus. The relevant expression is9
(k)sR
=3
k 2 7 S R
In this equation, I represents the moment of inertia and ck represents the spin-rotation constant of the C02molecule. Both of these quantities are properties of the structure of C02and have known values:I9 I = 7.18 x g cm2 ck = -3.33 x io4 HZ The correlation time, TSR, is the correlation time for the rotational state of C02which fluctuates as a result of collisions. There is no frequency dependence included in the spin-rotation relaxation equation since the mechanism only makes significant contributions when 07
