DIFFUSION OF O2 IN POLYMERS BY PHOSPHORESCENT QUENCHING
3677
Measurement of the Diffusion of Oxygen in Polymers by
Phosphorescent Quenching’
by Ellis I. Hormats and Fred C. Unterleitner Quantum Physics Laboratmy, General Dynamics, Electronics Division, Rochester, New York (Received December 28, 1964)
14601
The rate of diffusion of oxygen into bulk polymers may be measured through use of the quenching of phosphorescence of aromatic organic compounds dissolved in the polymer. The diffusivity of oxygen from the pure gas into polymetbyl methacrylate was found to be cm.2/sec. a t 22’ while from air it was found to be 2.3 X cm.2/sec. The 3.3 X measured diff usivity is independent of the phosphor concentration used for the memurements.
Introduction The usual method for measuring the diffusion of gases through plastic materials is based on the technique of measuring the quantity of gas that permeates a thin film of the materialJ2thus limiting measurements to those plastics that may be obtained as thin films. Other methods based on measurements of the rate of gas sorptions&and the oxygen bleaching of radiation-induced color centersabhave been developed. Comprehensive reviews have been recently published.* This paper presents a method of measuring the rate of diffusion of oxygen in transparent bulk polymers based on the quenching by oxygen of phosphoresence of organic materials dissolved in the polymer. It has been observed in this laboratory and independently by others5 that plastic rods in which certain organic phosphors have been dissolved to show, over a period of time, a phosphorescent core surrounded by a dark region when illuminated by ultraviolet light. With time this core becomes smaller until it eventually disappears. This effect depends on the concentration of oxygen in the plastic and so may be used to measure the rate of diffusion of oxygen into the polymer. The line of demarcation, the terminator, is assumed to occur at the minimum concentration of oxygen required to quench the phosphorescence of the activator. The quenching is due to a nonradiative energy-transfer process and is completely reversible. This has been demonstrated by restoration of the phosphorescence
when oxygen is removed by diffusion outward into a vacuum. Polymethyl methacrylate was chosen as the polymer for study as it is being used extensively as a glassy matrix for triplet state studies. The organic phosphor should be one that shows oxygen quenching, that phosphoresces in the blue or green region so it may be easily photographed, that has well-separated phosphorescent and fluorescent bands so fluorescent light may be easily removed by an optical filter, and that has a high quantum efficiency at room temperature so the phosphorescent emission will be much brighter than the background. Triphenylene meets these requirements so it was used as the phosphor.
Experimental Section Materials. Monomeric methyl methacrylate (Rohm ~
(1) Presented at the 147th National Meeting of the American Chemical Society, Philadelphia, Pa., April 1964, before the Division of Polymer Chemistry. (2) (a) ASTM Procedure D1434; ASTM Std., 9, 460 (1958); (b) P. Meares, J . Am. C h a . SOC.,76, 3415 (1954); ( c ) V. Stannett, M. Srwarc, R. Bhargava, J. Meyer, A. Myers, and C. Rogers, “Permeability of Plastic Films and Coated Papers t o Gases and Vapors,” TAPPI Monograph Series No. 23, TAPPI, New York, N. Y. (3) (a) A. S. Michaela, W. R. Veith, and H. J. Bixler, J. Polyner Sci., B 1 , 1 9 (1963); (b) R. E. Barker, ibid., 58,533 (1962). (4) (a) N. N. Li, R. B. Long, and E. J. Henley, I d . Eng. Chem., 57, 19 (1965); (b) C. E. Rogers, “Physics and Chemistry of the Organic Solid State,” Vol. 11, Interscience Publishers, Inc., 1965, Chapter 6. (5) (a) M. A. El-Sayed, J . Opt. Soc. Am., 5 3 , 797 (1963); (b) M. Windsor, Chem. Eng. News, 41, 53 (1963); (c) G. Oster, N. Geacintov, and A. U. Khan, Nature, 196, 1089 (1962).
Volume 69,Number 11 November 1966
3678
& Haas) inhibited with 25 p.p.m. of hydroquinone was thoroughly purified.6 Triphenylene (Rutgerswerke-Aktiengesellschaft) was recrystallized once from alcohol. a,a-Azodiisobutyronitrile (Borden Chemical Co.), the polymerization catalyst, was used as received. The polymerized samples were prepared by dissolving the requisite amount of triphenylene and catalyst in the monomer. The catalyst concentration in all cases was 0.033% by weight; the phosphor concentration is presented later. The solution was then transferred to Pyrex polymerization tubes, 1.0-cm. i.d. and 30 cm. long, with a bulb of 2.5-cm 0.d. and 6 cm. long a t one end and an 18/9 ball joint at the other, for connecting to a vacuum system. Set A was sealed off with no further treatment. Sets B and C were thoroughly degassed by repeated freezing and evacuation and then filled to 1 atm. with dry nitrogen, before being sealed, except as indicated. The polymerization was carried out with the monomer in the 1.0-cm. diameter section a t 42' for 5 days, at 65 and 75' each for 1 day in a water bath, and a t 115' for 1 day in an oven, followed by slow cooling t o room temperature. Samples were removed, cut to length, and their ends squared and polished using a series of five grades of emery paper and a buffing wheel. Care was taken to prevent contamination of the cylindrical surface during these operations. The rods for sets A and C were placed into 25-mm. 0.d. X 20-cm. Pyrex tubes with a flat Pyrex window a t one end cemented in place by epoxy cement. The rods were supported a t each end by a copper wire ring. These tubes were then sealed to the vacuum system, evacuated, filled with the requisite atmosphere, and sealed off. Not more than 2 hr. elapsed between opening the polymerization tube and the final seal-off. The rods for set B were kept in 50ml. beakers in an aluminum desiccator over silica gel. The elevated temperature tubes for set A were placed in a water bath at the requisite temperature; the tubes at room temperature were stored in a cupboard. The diameters and lengths of all rods were measured with a micrometer before sealing. The extensive purification of the monomeric methyl methacrylate was necessary to minimize phosphorescence of the polymer. Material, cleaned with sodium hydroxide only, had a strong, slowly decaying, yellow phosphorescence after polymerization. On the other hand, the extensively purified material had a barely detectable phosphorescence even a t 77'K. The yellow phosphorescence is due to small traces of residual hydroquinone as indicated by the phosphorescent spectra. Also, some blue-green phosphorescence possibly due to peroxides was noted. This was particularly strong when benzoyl peroxide was used as the The Journal of Physical Chemiatry
ELLISI. HORMATS AND FREDC. UNTERLEITNER
polymerization catalyst. When t-butyl hydroperoxide was used as the polymerization catalyst, it quenched the phosphorescence of triphenylene. Thus a,aazodiisobutyronitrile, which had no deleterious effect, is the polymerization catalyst most suited for this application. Measurements. A photographic method was used for the measurement of the ratio of the diameter of the phosphorescent core to the sample diameter. This was necessary to minimize exposure of the sample to ultraviolet light as would be experienced if direct measurements were made with a filar eyepiece since it was observed that exposures to ultraviolet light caused the phosphorescent core to grow back into the quenched region a t an initial rate of about 0.7yo/min. The rod or the Pyrex tube, with the sample against the flat window, was supported horizontally in a frame about 5 cm. below and parallel to a Long Wave Mineralight (Ultraviolet Products, Inc.). The sample was photographed through a Wild 145 stereomicroscope a t 3 X on Polaroid 3000 film using a Corning sharp cutoff CS3-70 filter (15Y0 a t 500 mp, 7501, a t 520 mp) to filter out scattered ultraviolet light and fluorescence of both phosphor and polymer. With proper exposure, about 30 sec., both the core and the outer edge were clearly visible and separated by a dark area (Figure 1). The illumination of the edge is a light pipe effect from the central core. The measurements of the diameters were carried out using the Wild microscope at 3X with a mechanical stage equipped with a micrometer reading to 0.001 in., the next place being estimated. Since the limit of the micrometer was 1.0 in., a 0.5000in. gauge block was used to extent the range to cover the photograph. Restoration by Vacuum. A partially quenched sample (Al) was placed in a 50-mm. diameter Pyrex tube, on one end of which was sealed a flat Pyrex
Figure 1. Coordinate system of partly quenched plrtstic rod. ( 6 ) A. R. Schultz, J . Phys. Chem., 65, 967 (1961).
DIFFUSION OF Oz IN POLYMERS BY PHOSPHORESCENT QUENCHING
window. I n a 15-mm. diameter side arm, a few grams of Wood’s metal was placed to act as an oxygen getter. The assembly was evacuated on a high vacuum system to 5 X 10-5 torr and sealed off. The Wood’s metal was melted by immersing the side arm in boiling water, to getter any oxygen present. The sample was observed at regular intervals as described above. After each observation the Wood’s metal was again melted to getter released oxygen. After the sample had been kept under vacuum for about 2 weeks it was observed when the sample was viewed endwise under ultraviolet illumination that there was a glowing ring enclosing a dark ring and a glowing core. Within a few days more the glowing ring moved inward to merge with the glowing core. This indicates that the quenching oxygen in the outer layer diffuses outward dropping below the level for quenching near the outer surface, thus restoring the glow. The hump in oxygen concentration between these two regions drops as oxygen diffuses outward until its inhibiting effect on the triphenylene phosphorescence is removed and the two glowing regions coalesce. The spectrum of restored phosphorescence and the unquenched phosphorescence are identical, thus showing the complete reversibility of the process.
3679
T the terms of eq. 2 with m 2 2 may be neglected to a first approximation. For example, at a T of 0.083, the term with m = 2 is about 4.6%, and m = 3, about 0.05% of the first term. Thus eq. 2 may be put into the form In Jo(PIR) = In Q
+ P12Dt/a2
(3)
where
Q
= ‘/z[PiJi(Pi)l(l
- v/V)= 0.624(1 - v/V)
(4)
Since the terminator corresponds to a certain concentration of oxygen, required to quench the phosphorescence in a given sample, it thus corresponds to a certain v/V. Thus Q is fixed for a given sample, and a semilog plot of Jo(PmR)us. t will give a straight line for large t, the slope, S, being related to the diffusion coefficient by
D
(5)
= Sa2/Pi2
and the intercept a t t = 0 giving v/V through eq. 4. This is a consequence of the one-term approximation since the boundary condition that v = 0 at t = 0 for all r except r = a was used in solving the differential equation.
Diffusion Equation
Results and Discussion
The reversible diffusion and solution of low molecular weight gases in polymers obey Henry’s and Fick’s laws with the diffusion coefficient independent of concentration. 2b,c Expressed in cylindrical coordinates
The determinations of the diffusion coefficients and quenching concentrations were carried out using semilog plots. The resultant graphs for the different conditions are given in Figures 2 to 4 and summarized in Tables I to 111. These semilog plots of Jo(PIR) us. time were fitted to the experimental data by leastsquare calculations; the diffusion coefficient was obtained from the slope, and the quenching coefficient from the intercept. It was noted that the points representing long times (over 40 days) generally fell onto a straight line with the earlier points below. The earlier points deviate owing to contributions from the m = 2 and greater terms. Calculation of these terms to m = 6 for run B-1 a t t = 10, using the D obtained from the least-square fit and applying this as a correction, lifted the value of Jo to the indicated point on Figure 3. The results obtained from the one-term solution as presented in Tables I to I11 form the basis for the following conclusions. Diflusion Coeficienl. The small concentrations of activating molecules that must be dissolved in the polymer in this procedure did not affect the diffusivity, as shown by the constancy of D for a 100-fold change in triphenylene concentration (e.g., B-1, B-2, B-3).
where T , 0, and 2 are the radial, angular, and axial coordinates, respectively, v is the concentration of the diffusing substance, t is the time, and D is the diffusion coefficient. Since the cylinder is completely surrounded by gas, diffusion is independent of 8. Since the sample is long compared to its diameter and it is viewed from the end so the maximum diameter of the core is seen, diffusion may be considered to be independent of 2. At the start (t = 0) the concentration of oxygen in the polymer is 0 (v = 0). The conaentration of oxygen in the surface of the polymer (r = a ) is constant (v = V). This concentration V is proportional to the concentration of oxygen in the surrounding gas by Henry’s law. Solving the equation by standard methods’ under these restrictions gives
where T = Dt/a2, R = r/a, and the @, terms are the roots of the equation Jo(Pm) = 0. For large values of
__ (7) J. Crank, “Mathematics of Diffusion,” Oxford University Press, London, 1956, p. 66, eq. 5.22, 5.24. ~
Volume 69,Number 11 November 1966
ELLISI. HORMATS AND FREDC . UNTERLEITNER
3680
1.0
Table I: Diffusion Coefficients and Quenching Ratio for Oxygen in Polymethyl Methacrylate 106 X moles of
triphenylene/ g. of Temp., Run polymer OC. Gas
A-1 A-2 A-3 A-4
43.9 43.9 43.9 43.9
22 22 22 72
Air Nz 0% Air
Diffusivity, cm.2 aec.-l x 109
O.d.,
cm.
Quenching ratio
0.970 2 . 3 f 0.7" 0.51 f 0.05" 0.970 0.0 ... 0.970 3 . 3 f 0 . 5 0.48 f 0 . 0 4 0.970 2 . 8 f O . 1 0.43 f 0.04
Precision based on least-square-curve-fitting statistics.
~
Table 11: Effect of Concentration of Triphenylene on Diffusion Coefficient and Quenching Ratio"
60
40
20
~
80
120
100
B1 B-2 B-3 B-4 B-5 B-6' B-7"
Time (Da)s)
Figure 2. Time dependence of diffusion a t various temperatures: 0, -----, air, 22', A-1; a, - - - -, 02, 22', A-3; A, -, air, 72", A-4.
0.9
-
0.8
-
0.7
-
106 X moles of phosphor/g. of Run polymer
437.0 44.0 4.26 0,426 0,0426 437.0 4.26
Diff uaivity, cm.2 sec. -1
O.d.,
x
cm.
0.993 0.980 0.985 0.983 1.003 1.062 1.054
Quenching ratio
109
2.31 f O.OZb 0.149 f 0.004* 2.2 f0.1 0.26 f 0 . 0 2 2.3 f0.2 0.29 i0.03 Too faint for photography Too faint for photography 2.4 f0.3 0.32 f0.03 1.7 f 1.0 0.3 f0.1
Precision based on leastAll samples stored in air a t 22'. square-curve-fitting statistics. ' Monomer saturated with oxygen before cure.
Table 111: Effect of Gas Composition on Diffusion Coefficient and Quenching Ratio"
t I
I
I
0
20
40
I
I
60 80 Time (Days)
Run
Gas
02 01-Nz 01-Nz
I
I
c-1
100
120
C-2 C-3 c-4
Figure 3. Time dependence of diffusion of oxygen from air at various triphenylene concentrations a t 22': e, ,437 x 10-8 mole/g. of polymer, degassed monomer; 0 , - -, 43.7 x 10-6 mole/g. of polymer, degassed monomer; 8 , -__-_-_ , 4.37 X 10-8 mole/g. of polymer; degassed - -,437 X 10-6 mole/g. of monomer; 69, polymer, Orsaturated monomer; e, - - - -, 4.37 x 10-1 mole/g. of polymer, 02-saturated monomer.
-
01
Compn., mole fraction of Press., OZ torr 1.0 0.5 0.2 1.0
190 750 750 750
O.d.,
om. 0,9553 0,9377 0,9338 0,9453
Diffusivity, cm.: sec.-l
x
3.6 2.31 2.2 3.34
109 & 0.cb
f 0.06 f0.1 f 0.01
Quenching ratio
*
0.53 0.04b 0.24 0.01 0 . 1 3 f 0.01 0.463 0.001
* *
a Temperature 22'; 4.30 X mole of triphenylene/g. of Precision based on least-square-curvefitting statispolymer. tics.
-
That the quenching is due to oxygen diffusion into the sample is clearly established since in the sample sealed in dry nitrogen (A-2) a nonphosphorescent layer did not appear, whereas those sealed in pure oxygen or air did show quenching. The Journal of Physical Chemistry
The activation energy for diffusion is quite small, +740 cal./mole. This low activation energy is probably due to diffusion freely occurring through tunnels slightly larger than the diameter of the oxygen molecule rather than by a site-to-site movement. MearesZb postulates that in the glass region the polymer consists of densely packed chains with no freedom of rotation separated by regions where the chains are disordered
3681
DIFFUSION OF O2IN POLYMERS BY PHOSPHORESCENT QUENCHING
1'
"
---
I
/
I
I
20
I
40
I 60
I 80
I
100
I
Time (Days)
Figure 4. Time dependence of diffusion at various gas concentrations: 0, 100% 02,1 atm.; 0, 100% 02, 0.25 atm.; El, 50% 02-50% Nz,1 atm.; A, 20% 0280% Nz,1 atm.
in which are the "holes" through which the molecules move. Diffusing molecules must pass through the densely packed regions to go from disordered region to disordered region. It may well be that in polymethyl methacrylate the disordered regions actually are interconnected, forming continuous "tunnels." Thus, little energy is expended in pushing through ordered regions, resulting in a low activation energy. An interesting and unexpected effect is the change in diffusivity in the presence of another gas, namely, nitrogen. The diffusivity at 22' in an atmosphere of pure oxygen was found to be 3.3 X sec.-l, while with 0.2 inole fraction oxygen in nitrogen the rate was found to be 2.3 X loV9cm.2 set.-' as measured by triphenylene quenching. Stannett, et a1.,2cfound no interaction between the components in a mixture in their permeation studies on polymers above the glass transition. In our experiments below the glass transition, it was observed that the diffusivity of oxygen from a mixture is about 67% of the dzusivity from pure oxygen. Diffusivity of gases through polymethyl methacrylate seems to involve movement through cracks and holes of molecular size; thus, there would be competition between nitrogen and oxygen molecules for these holes, and so the presence of nitrogen molecules could interfere with the diffusion of oxygen molecules. Quenching Ratio. The quenching ratio, the ratio of oxygen concentration a t the terminator ( v ) to the con-
centration of oxygen in the surface layers, ie., solubility ( V ) ,is obtained through eq. 4 from the intercept at t = 0. This is equivalent to the value of v/V obtained using the first terms of eq. 2 only. The relationships between runs are rather erratic. Comparing run B-3 with C-3 and A-1 with B-2, which are identical in conditions but from different batches of polymer, it is noted that the quenching coefficients differ by approximately a factor of 2 in each case. On the other hand, the diffusion coefficient is quite consistent for these four runs. Since it is apparent that the quenching coefficient depends partly on polymer properties, no attempt will be made to draw conclusions from this data. Comparison with Other Data. Diffusion of oxygen in polymethyl methacrylate has been measured by bleaching of color centers produced by high energy irradiation.8b The diffusion coefficient at 22' was found to be about 6.2 X 10-lo cm.2 set.-' which is about 0.185 of the value of 3.3 X cm.2 set.-' of this paper. Considering the simplifications in the mathematics in both cases the agreement is quite reasonable. Barker's activation energy includes the activation energy of trapping as well as the activation energy of diffusion, hence the wide discrepancy between these figures.
Conclusions The measurement of oxygen diffusion through phosphorescent quenching provides methods for study of gas diffusion in bulk polymers. Other transparent polymers may be investigated by this same technique. Opaque materials may be studied by removing slices from the end of the sample and immediately photographing the phosphorescent ring while illuminating the end. The primary requirement on the material to be studied is that a quenchable phosphor be soluble in it. If a rectangular rather than a circular cross section is used, a cosine function or error function of the distance replaces the Bessel function with a resultant simplification in calculation. Since the terminator will be a straight line in this case, measurements of its location should also be easier. The major limitation on this method is that the diffusing gas or vapor must quench phosphorescence. This limits the gas to oxygen and possibly to nitric oxide. It may be possible to study diffusion of other gases by measuring their interference with oxygen diffusion as was noted for the slower diffusion rate of oxygen from air compared to that from pure oxygen. Acknowledgments. The authors wish to acknowledge the many helpful discussions with Dr. Ernest Brock and Dr. Jack Taylor and the valuable assistance of Mr. Kermit Mercer with the experimental work. Volume 6 9 , Number 11
November 1966
