2124
J. Phys. Chem. 1990, 94, 2124-2128
High-pressure Phase Equilibria of Poly(ethylene glycol)-Carbon Dioxide Systems Manouchehr Daneshvar, Seecheol Kim, and Esin Culari* Department of Chemical and Metallurgical Engineering, Wayne State University, Detroit, Michigan 48202 (Received: June 5, 1989)
Phase equilibrium data of different molecular weight poly(ethy1eneglycol)-C02 mixtures are presented and correlated by using a lattice-model-based equation of state. The data were obtained at 313 and 323 K over a pressure range up to 29 MPa. Typical temperature, pressure, and molecular weight dependences of the solubility data are discussed. The model correlates the data quantitatively by using a single adjustable parameter, k,, in a modified mixing rule for the interaction energy of the mixtures. A finite lattice coordination number, z = 10, and a constant lattice site volume, uH = 9.75 X 10” m3/mol, are used, and the sensitivity of the model to the assumed values of z and uH are discussed. Although other investigators have previously applied lattice models to supercritical systems, in this study the lattice model has been applied to a more challenging case where the solvent dissolves appreciably in the polymer and hence the supercritical phase is no longer in equilibrium with a pure solute. This is accomplished with a single adjustable parameter.
Introduction Supercritical fluid (SCF) fractionation of polymers has received widespread attention in the past few Polymers are inherently polydisperse materials, and their separation into narrow molecular weight fractions is normally a difficult task. Supercritical fluid solvents offer a potential advantage for such a separation. The solubility of different homologous series members of a polymeric material in a supercritical fluid can be systematically varied by changing operating conditions. Qualitatively, the solubility of a polymer in supercritical fluids decreases with the degree of polymerization. A knowledge of the phase equilibrium data is needed to design and develop supercritical separation processes. The correlation and extension of existing equilibrium data is an important step in the application and development of such processes. For supercritical fluid systems, the data are limited because the highpressure phase equilibria experiments are difficult to perform. Despite the growing interest in supercritical fluid technology, there has been a limited amount of information in predicting or correlating phase behavior quantitatively. The higher density and compressibility of a supercritical fluid on one hand and the size, structure, and polarity differences between the molecules of the solvent and the solute on the other hand make the development of mathematical models a nontrivial task. Gubbins et aL3 have reviewed different techniques of studying fluid-phase behavior of the mixtures. In general, the modeling of the phase behavior can be performed either by a Monte Carlo technique or an equation of state approach. So far, Monte Carlo simulation methods have been successfully applied to mixtures of small molecules of similar sizes. Their applications to systems comprising a large solute and a small solvent are limited. The equations of state have been extensively used in phase equilibria modeling. This is primarily due to the fact that the fundamental thermodynamic functions can easily be obtained from an equation of state (EOS). Either the EOS may be applied to the gas phase only, while one of the standard activity coefficient methods is used for the solute phase, or it may be applied to both phases4 An appropriate EOS that can be applied to polymeric materials, supercritical solvents, and their mixtures over a wide range of density is needed to describe the phase behavior of supercritical fluid-polymer systems. Such an EOS is based either on the perturbed hard chain theory or on the lattice model. In this study, the equilibrium phase compositions of different average molecular weight poly(ethy1ene glycol)-C02 systems were modeled by using ( I ) Krukonis, V. f o l y m . News 1985, 1 1 , 7. (2) Kumar, S. K.; Suter, U. W.; Reid, R. C. Fluid Phase Equilib. 1986, 29, 373. (3) Gubbins, K. E.; Shing, K. S.; Streett, W. B. J . f h y s . Chem. 1983.87, 4573. (4) King, M . B.; Bott, T. R. Sep. Sci. Techno!. 1982, 17(1), 119.
0022-3654/90/2094-2 124$02.50/0
an EOS based on a lattice model. The experimental data covers a range of pressures up to 29 MPa at 313 and 323 K. The pure component parameters are needed in order to use the EOS. The parameters for carbon dioxide are available in the literature, while the parameters for poly(ethy1ene glycol) (PEG) were obtained from PVT measurements of the pure polymer. A new mixing rule for the interaction energy of the mixtures was used. Experimental Section The experimental apparatus used to obtain the vapor-liquid composition data is a countercurrent circulation system. It is designed to operate at temperatures up to 373 K and pressures up to 35 MPa. Equilibrium is achieved by circulating both the liquid and vapor phases. The S C F phase is drawn from the top and driven to the bottom of the equilibrium vessel while the polymer phase is drawn from the bottom and driven to the top. The temperature is measured with a thermocouple installed inside the vessel to within f 0 . 3 K. The circulation lines are maintained at the vessel temperature with heating tapes and controllers that are run off the thermocouples attached to different locations on the lines. The pressure is measured with a pressure transducer installed on the vessel to within f0.003 MPa. Two high-pressure, six-port switching valves with sample loop volumes of 0.5350 (the upper phase) and 0.1086 mL (the lower phase) are installed on the circulation lines. These valves are used to take the samples from both phases at equilibrium. A typical equilibration time is approximately 30 min, and the sampling is performed after allowing at least an hour. The CO, content and the polymer amount of each phase are then determined, and the coexisting compositions are calculated. A detailed description of the experimental setup and procedure has been presented e l ~ e w h e r e . ~Three polymer samples with nominal molecular weights of 400, 600, and 1000 (Aldrich Chemical Co., Inc.) were used. A colorimetric technique was applied to measure the polymer amounts in the sample^.^ Modeling Background The vapor-liquid equilibrium data of PEG-C02 systems were modeled by using a lattice-model-based equation of state. Several investigators have used this approach for different By fixing the lattice cell size and the coordination number, Panayiotou and Vera* were successful in calculating the thermodynamic properties of pure polymers and polymers in common solvents. The real advantage of this approach emerges in treating mixtures where the mixing of lattices of unequal cell size or coordination (5) Daneshvar, M.; Gulari, E. Supercritical Fluid Science and Technology; ACS Symposium Series 406; American Chemical Society: Washington, DC,
1989; p 72. ( 6 ) Sanchez, I . C.; Lacombe, R. H. J . f h y s . Chem. 1976, 80(21), 2352. (7) Sanchez, I. C.; Lacombe, R. H. J . folym. Sri. folym. Lett. Ed. 1977, 15, 71.
( 8 ) Panayiotou, C.; Vera, J. H. folym. J . 1982, 1 4 ( 9 ) , 681.
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 2125
Phase Equilibria of PEG-CO, Systems number is eliminated. Kumar et aL9 used a similar approach to model the phase behavior of different solutes with supercritical fluids. Our approach in many aspects is similar to those in ref 8 and 9. However, we used a different combining rule for the interaction energy of mixtures to model the equilibrium phase behavior of PEG-C02 mixtures. In this study, PEG samples are liquids and supercritical C 0 2 is appreciably soluble in the polymer phase. The data comprise measurements of concentrations of both components in coexisting phases. Therefore, the model is applied to correlate phase equilibria where the concentrations of both components are changing, in contrast to applications of similar models to solid polymers with supercritical fluid systems where the polymer phase is pure. In a lattice model approach the molecules are assumed to occupy a three-dimensional lattice. In our calculations, the coordination number, z, and the cell size, uH,of the lattice are fixed to 10 and 9.75 X IO" m3/mol, respectively. Our results indicate that the model is not sensitive to the specific values of these parameters. For the pure component case, the lattice is occupied by NI molecules of rl-mer (rl can be fractional) and NH number of holes. The interior mers of the chain are bonded to two other mers and therefore are surrounded by z - 2 nonbonded neighbors, while the mers at the end of the chain have one bonded mer and z 1 nonbonded neighbors. The effective chain length q1 is related to z and r l according to the following relationship: zql = (rl - 2)(z
- 2)
+ 2(z - 1 ) = r l ( z - 2) + 2
(1)
The total number of sites and the total volume of the lattice are given by N = NH Nlrl V = (NH + Nlrl)vH (2)
+
where NlrIvHrepresents the hard core volume or occupied volume and N H u H the free volume. Following this notation and the approach of Panayiotou and Vera,* one obtains the pure component EOS as follows:
where P, T, and D are the reduced quantities and 0 is the effective surface area fraction of the molecules in the lattice. The reducing are defined by the following pressure, P*, and temperature, P, expression: ( ~ / 2 ) t I l = P*vH = R P (4)
0 represents the fraction of sites in the lattice that are occupied by the molecules. M
O= NH
I
+ qINl
--
a
ql/rl + (ql/rl) -
rM =
q M = CXjqj
CXjrj
U*M
=
CXjU*j
(6)
where xi is the mole fraction of species i in the relevant phase. Considering the pairwise additivity of the interaction energies, the following expression for the characteristic energy of the system is obtained: =
C.xoiojrijcij i j
(7)
Here, rijis the nonrandom factor that can be obtained from the quasi-chemical approach.I0 2
r.. JJ = 1 + [ 1 - 40&( 1 - g)]'/2
i # j
(8)
where g = exp(Oh/kT) A6
=
€11
(9)
+ €22 - 2tl2
(10)
The nonrandom factor, rii,corrects for the nonrandom distribution of the molecules, and it should satisfy the symmetry and mass balance conditions. Nii + XNij = Nizqi for all i, and
rij= rji
j
for i # j (11)
0 is the total surface area fraction and Oi is the surface area fraction of the ith component. The following combining rule for the interaction energy of the unlike molecules is introduced: e.. 'J = ( € .1'. €JJ. . ) ' / 2 ( 1 -
kij)
i #j
(12)
Similarly to the pure component case, the expressions for the EOS and the chemical potentials of each component can then be derived, as shown in ij
--Pi = X ( T ) kT
+ (q/r)
- 1
+ In qi - In BiO +
ri(0.5z - 1 ) In *(20itiirii
T€*M
(
D
+ (q/r)- 1 D
qio2
+
)-i
+ 2ojCijrij + o l e l l +
(5)
Each fluid is characterized by two pure component parameters, and e l l . The specific hard core volume, u * , is used to reduce the volume in the EOS. The pure component EOS assumes a random distribution of molecules and holes. In the case of pure components, the nonrandom approximation does not provide any advantage over random approximation.8 For mixtures, it was assumed that the molecules are nonrandomly distributed while the holes are evenly distributed in the system. The nonrandomization of the holes is an approximation that introduces a very small deviation while it makes the solution of the quasi-chemical equations analytical. The EOS for the pure components is extended to the mixture of N , molecules of rl-mer, N2 molecules of +mer, and NH number of holes. This requires the formulation of the mixing rules. The coordination number z and the lattice site volume uH are assumed to have the same values as pure components and are independent of composition. The mixing rules for q M , rM, and v * are ~ formulated as V*
0,(1 -
0lrll rli)In + 0*(1 f32r12
where i = 1 or 2, j = 3 - i, and 6..is the Kronecker delta. The reducing parameters are obtainel from ( Z / ~ ) € * M= R P = P*VH (15) The nonrandom distribution of molecules introduces an extra term
_____
(9) Kumar, S. K.; Suter, U. W.; Reid, R. C. Ind. Eng. Chem. Res. 1987, 26, 2532.
(10) Guggenheim, E. A. Mixtures; Clarendon Press: Oxford, England, 1954.
2126
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
Daneshvar et al.
TABLE I: Pure Component Parameters for Some Common Polymers and C02
component poly(ethy1ene glycol) poly(propy1ene oxide) poly(viny1 acetate) poly(n-butyl methacrylate) poly(dimethy1siloxane) carbon dioxide
c,,lR, K
VI.
102.950 104.169 119.184 115.856 89.841 82.026
cm3 g-'
0.7213 0.9162 0.7850 0.8810 0.891 1 0.8798
ref a
8 8 8 8 9
i
-0.03
0" 0
0
a
C
0 .-1
" F
0.10:
-0.02
0
2
1
5 -O.O'
TABLE 11: Experimental Data for PEC-CO2 Systems
Xa
P
P, MPa PEG(400) + CO, at 313 K
P
42.45 43.17 43.38 46.06 53.06
0.421 0.524 0.8 14 1.246 1.328
54.37 55.59 55.70 57.20 62.43 62.42 61.40 61.39
0.149 0.202 0.254 0.393 0.440 0.555 0.848 0.882
35.06 36.49 36.58 37.04 39.75
0.868 0.886 1.617 1.713 2.125
48.40 51.10 53.65 53.60 58.28 58.63
0.04 1 0.079 0.127 0.175 0.183 0.243
50.20 49.73 53.88 52.85 55.30 57.79
0.020 0.025 0.044 0.066 0.072 0.075
~I
1.41 3.00 6.49 7.94 9.90 12.48
2.59 5.78 14.02 28.60 32.25 40.23
1.13 2.37 3.61 5.84 7.13 8.02 10.49 13.68 14.86
1.83 4.69 7.1 1 12.5 1 13.85 24.38 41.47 46.25 50.76
1.92 4.06 7.15 8.31 12.00 15.33
1.64 3.48 7.07 10.8 1 25.01 27.81
1.99 3.95 7.21 9.25 11.80 13.88 16.79
2.85 6.86 13.56 19.02 21.56 44.13 45.98
1.75 3.59 5.15 8.47 10.20 I I .90 15.07
3.86 7.06 12.05 17.52 18.52 24.24 45.83
0.237 0.297
13.92 17.10 18.39 20.41 22.07
0
10
20
s
0 00
1
X"
,b
i
1
"This study.
P, MPa
a,
E x -
30
Pressure (MPa)
Figure 1. Plot of phase equilibrium data of PEG(400)-C02 system at 323 K. The upper and lower curves correspond to the left and right
vertical axes, respectively. Symbols are the experimental data, and the solid lines are the lattice model correlations with k , = 0.095 f 0.002. 1 .oo
0.04
PEG(600) + C 0 2 at 313 K 15.86 18.80 20.40 21.44 22.75 25.16 26.92 28.42 0.108
PEG(400) + C02 at 323 K
0.241 0.515
18.35 20.38 22.17 23.27 26.43
0 01
PEG(600) + C02 at 323 K
0.010 0.020
18.03 20.36 22.71 24.33 27.45 29.00
0
10
20
30
Pressure (MPa)
Figure 2. Phase equilibrium behavior of PEG(600)-C02 system at 323 K. The upper and lower curves correspond to the left and right vertical
axes, respectively. Symbols are the experimental data, and the solid lines are the lattice model correlations with k,, = 0.122 f 0.002. l 0
°
1
0 Oo5
PEG(1000) + C 0 2 at 323 K 18.01 19.32 21.65 23.01 24.51 26.31 0.016
" X = weight percent of C 0 2 in polymer phase. Y = weight percent of polymer in SCF phase. in the mixture EOS compared to the pure component EOS. This additional term is usually very small and can be neglected. However, it is included in our numerical program for the sake of generality. Determination of Pure Component Parameters In order to use the lattice-model-based equation of state to correlate the vapor-liquid equilibrium data of PEG-C02 systems, the pure component parameters, tii and u*, are needed. The parameters for supercritical C 0 2 are available in the literature and are listed in Table I. These parameters are obtained by fitting experimental P-Vdata to the equation of state along an isotherm. Generally, the parameters for the components below their critical points are obtained from vapor pressure data. For polymers, vapor pressure data are not available; therefore, the liquid compressibility data are normally used. For some common
Pressure (MPa)
Figure 3. Phase equilibrium behavior of PEG( 1000)-C02 system at 323 K. The upper and lower curves correspond to the left and right vertical
axes, respectively. Symbols are the experimental data, and the solid lines are the lattice model correlations with k, = 0.098 f 0.002. polymers, Panayiotou and Veras have calculated the pure component parameters. In fact, in the absence of data, Kumar et al. have used these values above the glass transition temperature, Tg, for polystyrene from ref 8 at a temperature far below T . For PEG, tii and v* are not available in the literature. By mJifying the polymer phase sampling section of our apparatus, we measured liquid compressibility data of PEG(400) at 313 K. We then calculated the parameters by fitting the data to the pure component EOS. The values of bii/Rand u* used in this study along with those for a few other polymers are listed in Table I. Results and Discussion The five sets of phase equilibrium data of PEG-CO, systems are listed in Table 11, and three sets for different molecular weight PEGS at 323 K are plotted in Figures 1-3. The data comprise
The Journal of Physical Chemistry, Vol. 94, No. 5, I990 2127
Phase Equilibria of PEG-CO, Systems TABLE 111: Calculated Binary Interaction Parameters for Different Nominal Molecular Weight Samples
temperature polymers PEG(400)
PEG(600) PEG( 1000)
313 K 0.084 0.002 0.091 0.002
* *
323 K 0.095 f 0.002 0.122 f 0.002 0.098 f 0.002
measurements of compositions of coexisting phases at various pressures along an isotherm. It was observed that the solubility of PEG in supercritical CO, is a strong function of molecular weight. The threshold pressure above which the solubility is detected increases with molecular weight; the threshold pressures corresponding to the solubility limits are about 10 MPa for PEG(400) and 15 MPa for PEG(600). At pressures below P, or CO,, the solubility of C 0 2 in PEG varies linearly with pressure, while at pressures above the threshold pressure, it remains relatively constant. The leveling of CO, solubility with pressure is due to the fact that its activity does not change with pressure at higher pressures. For all data, there appears to be a correspondence between the leveling of C 0 2 solubility in the polymer phase and the enhancement of PEG solubility in the S C F phase. A possible explanation for this correspondence is that a preferential partitioning of CO, into the S C F phase drives a certain amount of polymer from the polymer phase into the SCF phase on the basis of the criterion of phase equilibria. This effect, together with the solvent density increase due to pressure, causes the enhancement of the solubility of polymer in the S C F phase. The data were correlated by using the EOS and the chemical potential expressions derived in the previous section as follows: The general equilibrium criteria require the equality of the chemical potential of each component in both phases. The mixture EOS must be applied to each phase. Thus, a set of four equations are generated and must be satisfied. The fitting procedure starts by providing the experimental data and the pure component parameters. Then, the set of equations is solved simultaneously by using the modified Levenberg Marquardt numerical method to determine the binary interaction parameter, k,. The k , values determined by this procedure are listed in Table 111. k , is the only adjustable parameter in this model. Essentially, kij is an empirical parameter that corrects for the deviation from the pairwise additivity of binary interactions. It is introduced in the specific mixing rule (eq 12). k , affects the nonrandom correction factor, ripthrough A€ and g (eq 9, 10). Therefore, the relative changes in k , can be related to the randomness of the lattice. Our results indicate that k , is apparently a weak function of temperature. More extensive study is needed to establish the temperature dependency of the interaction parameter. The knowledge of this parameter makes the model predictive of other operating conditions. In Figures 1-3, the model correlations (solid lines) are compared to the experimental data. The PEG-C02 systems are treated as pseudobinary mixtures by assuming each PEG sample to be monodisperse with its molecular weight equal to its nominal molecular weight. This assumption is based on the relatively narrow molecular weight distribution of commercially available PEGS (for example, M,/M, = 1.05 for PEG(600) is measured in this study by using fast atom bombardment mass spectrometry). The lattice model provides quantitative fits to the experimental data of PEG-C02 systems. We also attempted to estimate the uncertainties on k , based on the deviations of the model correlations from the experimental data beyond the experimental uncertainties. The value of f0.002 is found to be a realistic uncertainty (Table 111). In Figures 4 and 5, the model correlations are compared to the experimental data at two different temperatures of 313 and 323 K. The solubility of CO, in the liquid polymer phase drops with temperature for both PEG(400) and PEG(600) because C 0 2 , which is a volatile component, evaporates out of the liquid phase very effectively with an increase in temperature. In the SCF phase, the solubility of PEG in C 0 2 highlights the effect of two competing factors: polymer vapor pressure and S C F density. In Figure 4,
0.03
0" 0 C
.-+-0 F 5 0
0.10
0.02
L i L
0.01
0.01
5
0.00
b
1'0
30
Pressure (MPa)
Figure 4. Comparison of the phase equilibrium data of PEG(400)-C02 mixture at 313 and 323 K. The upper and lower curves correspond to the left and right vertical axes, respectively. Open and closed symbols denote experimental data at 313 and 323 K, respectively. The solid and dashed lines are lattice model fits. 1. o o j
10.04
0
10
20
, 005
30
Pressure (MPa)
Figure 5. Comparison of the phase equilibrium data of PEG(600)-CO, mixture at 313 and 323 K. The upper and lower curves correspond to the left and right vertical axes, respectively. Open and closed symbols denote experimental data at 313 and 323 K, respectively. The solid and dashed lines are lattice model fits.
the temperature increase from 313 and 323 K does not affect the solubility of PEG(400) in CO,, which indicates that the increase of the vapor pressure of the solute and the decrease of the CO, density are compensating each other. On the other hand, in Figure 5, the solubility of PEG(600) in C 0 2 drops with temperature. PEG(600), the higher molecular weight sample, has a lower vapor pressure. Therefore, the decrease in its solubility upon heating is governed by the decrease in the CO, density or its solvation power. In the vicinity of the critical point of CO,, the model shows a sudden change in the slope of the composition vs pressure curve for the S C F phase. The model is expected to perform poorly in the critical region because its derivation is based on the mean field approximation, which is valid in the fluid regions not affected by high fluctuations, Le., away from the critical point. This was not a concern in this study because the solubility of PEG in C 0 2 starts at conditions far away from the critical point of CO,. The composition dependence of the interaction energy was investigated by introducing a modified mixing rule. In the case of k i . = k.j,the original mixing rule is recovered. If the assumption = kjj is relaxed, a second interaction parameter is introduced. The fits of data with two parameters yielded kjj equal to kji for all the cases studied. Therefore, the interaction energy of the mixture was described with a single interaction parameter independent of composition. Kumar et aL9 have examined the sensitivity of the pure component lattice EOS to the value of z and vH for small molecules. Their results indicate that over a range of z and uH (6 < z < 26; 1.0 X lod7 m3 mol-' < vH < 1.5 X m3 mol-'), the EOS is capable of fitting the pure component data. In this study, we
iij
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
