K.J. KOKESAND F. A. LONG
VOl. 75
[CONTRIBUTION FROM DEPARTMENT OF CHEMISTRY, CORNELL UNIVERSITY ]
Diffusion of Organic Vapors into Polyvinyl Acetate] BY K.J. KOKESAND F. A,LONG RECEIVED SEPTEMBER 8, 1953 The diffusion at 40 of vapors of propyl chloride, allyl chloride, propylamine, isopropylamine and carbon tetrachloride into films of polyvinyl acetate has been studied as a function of concentration. Two other vapors, 1-propanol and benzene, have been sfudied a t three temperatures, 30, 40 and 50". The diffusion is Fickian and for low concentrations of penetrant the data all follow the equation D = DOexp(av1) where UI is volume fraction of penetrant in the polymer. The values the diffusion coefficient for the pure polymer, vary with size and shape of the diffusing molecule but do not appear of DO, to depend strongly on the chemical nature of the penetrant. However, the slope, a,of In vs. V I increases with the value of the Flory-Huggins interaction parameter, XI,for the penetrant-polymer mixture. For the penetrants acetone, propanol and benzene the energies of activation forDo are all 40 kcal. per mole withi,nexperimental error. The temperature coefficient of the melt viscosity of polyvinyl acetate has been measured and a t a temperature of 45' the energy of activation for viscous flow is about 45 kcal., which suggests that the activation processes for viscous flow and for diffusion of the larger organic vapors are similar.
Introduction Data on the rate of diffusion of organic vapors into polymers are now available for several systems. When the polymer-penetrant mixtures are above their second-order transition, Fick's law applies with, however, a diffusion coefficient which increases with concentration.'-4 For other systems Fick's law is not obeyed and the diffusion is termed non-Fickian or anomalous.-'--' The influence of size and shape of the penetrant molecule has been studied in some detail for two polymers, polyisobutylene2 and poly~tyrene.~Both of these are non-polar polymers and with polystyrene the interpretation is complicated by the fact that the diffusion is anomalous, a t least for low concentrations of ~ e n e t r a n t . ~ In this paper we report studies on the influence of penetrant molecule on the rate of diffusion into the polar polymer, polyvinyl acetate This polymer is non-crystalline and can be conveniently studied a t temperatures above that for the second-order transition of the pure polymer, 30". Previous studies with acetone and polyvinyl acetate have shown that a t temperatures of 30' or higher the diffusion obeys Fick's law.4 Most of the studies reported here are a t 40°,but for two of the systems temperature coefficient studies have been made. Finally we have made studies of the temperature coef3icient of the melt viscosity of polyvinyl acetate to see how the energy of activation for viscous flow compares to that for small molecule diffusion. Experimental Diffusion coefficients were determined from rates of sorption and desorption of vapors in polymer films, using the apparatus described earlier. * Carefully dried films of known area were suspended from a quartz spiral balance in :til evacuated chamber. A t zero time the organic vapor was admitted and thc rate of sorption \vas determined by following the weight increase of the film as a function of time. After sorption equilibrium was reached, the chamber was rapidly evacuated and the rate of desorption \vas measured. Measureinents \iere in;irlc for wveral vapor pressures of each diffu>ing s p e c i e (1) W o r k supported b y d g r a n t f r ~ i n utiict: uf Ordnance Kestarcti, U. S. Army. (2) S. Prager and F. A. Long, THISJ O U R N A L , 73, 4072 (1961). (3) G. S. P a r k , Trans. F a v n d o y S a c , 46, 684 ( 1 9 5 0 ) ; 48, 11 (1R5Z). ( 4 ) R. J. Rokes, F. 4. Lotii: and J. I,. Hoard, J . Chem. P h y s . , 20, 1711 (19.52) J . Pol>,irie? .Yci ( A ) Leu hlunrielkarn ani1 i,', h I-,>c~g, !e) I. Cr,iuk and G. 6 ]':irk, T~'ii?ir.F o r a d a y .xoi , 17; 1:. .I,J , o n ~alii1 R J Iicikes, 7'111sJor
,
6 , -13i (1Hdl) -72) I.
Descriptions of the polyvinyl acetate used and of the method of film preparation are given in a previous publication.4 All of the organic liquids were redistilled and dried prior to use. The melt viscosity of polyvinyl acetate was measured with capillary viscometers similar to those described by Fox and Flory.8 Bubble-free samples of the polymer were prepared by heating to 217" in a nitrogen atmosphere. During sample preparation a slight discoloration occurred; however, since different samples gave similar results, this slight reaction apparently has little or no effect on the viscosity. The experimental conditions were always such that the viscosity, 7, was independent of the rate of shear; hence the flow w a s Seirtonian. Values of 7 were calculated from the dimensions of the viscometer and the pressure using Poiseuilk's equation. Except for the highest values, 7 was precise to 10% and in no case was the error greater than 20%. Calculations Diffusion coeflicients were calculated from the measureiuents of sorption and desorption using essentially the method described p r e ~ i o u s l p . ~ ~ The * relevant form of Fick'.; law is
where t is time, D is the diffusion coefficient, and c is concentration, in grams solvent per gram polymer, a t a distance x from the film surface. The usual boundary condition of instantaneous equilibration a t the surface of the film i? assumed. From the Boltzmann solution of Fick's law for the case of an "infinite solid" it follows that during the initial stages of sorption and desorption, i.e., before the coiicentration a t the film center changes appreciably
where Q is weight of vapor sorbed or desorbed a t time t , Qe is the equilibrium weight sorbed or desorbed, 1 is film thickness and K(c,, cf) is a function only of the initial and final equilibrium concentrations. When both sorption and desorption data are available for a concentration interval 0 -+ cy, then a good approximation for the integral diffusion coefficient a t the concentration cy is given by*J
where KB(O,(.I) and &(Cy, 0) are the initial slopes (froin eq. 2) for sorption and desorption, respectively. From rneasurernents a t varying values of ci and cf, D can be obtained its a function of concentration. Values of D ,the ordinary diffusion coeflicient, can if desired be calculated from the relation
D
= d(cl))/dc
(4)
For a more precise evaluation of D, account should be taken of the change in film thickness with diffusion into the fil1n.Q This correction is small for low concentrations of ( 8 ) 7'. C. Fox and P.J. Flory, i b i d , , 20, 2384 (1948). ( ! I ) C,. S. I l n r t l e y and J. Crank. T r a n s FaI'a.lay S o r . , 45, 801 ( 1!I -14, I j
Dec. 20, 1953
DIFFUSION OF ORGANIC VAPORSINTO POLYVINYL ACETATE
penetrant and hence has not been made for the data reported here. All values of diffusion coefficients are reported for the units cm.2 per sec.
Results and Discussion Sorption-desorption experiments a t 40' have been carried out with polyvinyl acetate and the following organic vapors : 1-propanol, propyl chloride, propylamine, isopropylamine, allyl chloride, benzene and carbon tetrachloride. Figure 1 shows typical plots of Q/Qe vs. dt/l for sorption and desorption experiments, in this case for the system benzene-polyvinyl acetate. All plots are initially linear indicating that the diffusion is Fickian in the sense that eq. 2 is obeyed. The fact that for both concentration intervals the slope for sorption is greater than for desorption and also the fact that the slopes of both sorption and desorption are larger for the higher concentration show that the diffusion coefficient increases with Concentration. Except in the case of allyl chloride, all the sorptiondesorption plots are similar in form to those in Fig. 1. With allyl chloride the sorption plots show a slight curvature a t the very start although the corresponding desorption plots are initially linear. The reason for Ahis behavior is not known. In the calculation of D for this system this initial lack of linearity was ignored and the slope of the linear portion of the sorption curve was employed.
the data for the lower concentrations of Figs. 2 and ?can be summarized ig terms of the two parameters Do and p. Values of Doand /3 are shown in columns 3 and 4 of Table I for the sorption-desorption data on polyvinyl acetate. For diffusion of carbon tetrachloride only the one point of Fig. 3 is available; the listed DOvalue of Table I was obtained by assuming a value of 70 for the parameter 0. For completeness, data are also given for diffusion of acetone3 and methanollO into polyvinyl acetate. Acetone
3
2
+ I4 2
2 1
0
0 I
. 0.6 L
0.04
Fig. Z.-Concentration
d
\
W
Methanol
4
/.
1.0 t
6143
0.08 6 , g./g. dependence of acetate, 40'.
0.12
5
for polyvinyl
0.4
0.2
u 2 4 6 z/i/lo x 103, niin.l/Z ern.-'. Fig. 1.-Sorption (S) and desorption ( D ) of benzene by 0
polyvinyl acetate a t 40'. Along with each curve are the initial and final concentrations of benzene in grams per gram polymer.
For all of_the penetrants the integral diffusion coefficient, D, was evaluated as a function of concentration from the' slopes of sorption-desorption plots using eq. 3. The results of these calculations for experiments-at 40' are shown in Figs. 2 gnd 3 as plots of log D vs. c. It may be seen that D is a strong function of concentration varying as much as a thousand-fold in the concentration rangcstudied. Furthermore, each of the plots of log D vs. c is linear a t low solvent con_centrations. This logarithmic relation between D and c appears to be quite general and has been found to hold for most polymersmall molecule systems for which diffusion is F i ~ k i a n . " ~ If this relationship is expressed as D
= &¶c
(5)
2
+
lQ
3
3
/ chloride ::;:-"
R. J. KOKESAND F. A. LONG
6144
VOl. 75
There is a definite effect of molecular shape of the penetrant on the rate of diffusion. Diffusion of isopropylamine is slower than that of the normal propylamine and diffusion of carbon tetrachloride D = DOeuci (6) is much slower than would be expected from its Park3 has pointed out that this formulation may molar volume. The influences of size and molar have more physical significance than eq. 5 . For volume are shoqin more completely in Fig. 4 which the narrow concentration ranges studied here there is a plot of log D Ovs. molar volume. The straight is little choice between the two equations. Equa- line in this plot is drawn in primarily for convenition 5 is perhaps slightly preferable simply because ence in discussion. It is evident, a t least for the it utilizes directly determined experimental quan- straight chain compounds, that there is an aptities, i.e., for the calculation of v1 of eq. 6 it is usu- proximately linear relation between log DO and ally necessary to assume additivity of volumes of molar volume. Propyl alcohol falls somewhat off penetrant and polymer. However, for convenience the curve as do allyl chloride and benzene. Howin later discussion we have included in Table I ever, the striking departure-is for carbon tetracalculated values of the parameter a for all pene- chloride. Even though the Do value for this comtrants except methyl alcohol, where the assumption pound is only crudely estimated i t is evident from of volume additivity seenis particularly dubious, Fig. 3 also that this spherical molecule diffuses and carbon tetrachloride, where too few data are much more slowly compared to the straight chain available. compounds than would be expected from its molar volume alone. This result is consistent with preTABLE I vious studies. Prager and Long2 noted that for DIFFUSIONCOEFFICIENTS INTO POLYVINYL ACETATE,40' diffusion of hydrocarbons into polyisobutylene 10I 2 W , cc 1 branching was a more important variable than Penetrant mole cm 2/sec P XI molar volume; Park,3 in his extensive study with .. .. Carbon tetrachloride 9 8 . 6 ( 3 x 10-4) (70) polystyrene, noted this same effect The results 0.48 53 46 0.36 from all these studies lead to the same conclusion: 91 Benzene 13 64.5 63 .75 that both the size and shape of the penetrant mole90 Propyl chloride 1 7 78 55 88.4 .67 cules markedly influence the magnitude of the Isopropylamine 5 1 80 49 .58 rate of diffusion into polymers. 84 6 Propylamine 48 13 44 .28 83 5 Allyl chloride The physical significance of the parameters- P 1 1 96 7 8 1 10 and LY of eq. 5 and 6 is less clear than that of Do. 76 Propyl alcohol 13 61 in 5 45 0 35 Prager and Long? suggested that the generally obAcetone 41 3 1 . 4 x 108 24 Methyl alcohol served increase of D with concentration may be Table I also gives values of Vn, the molar volume due to the fact that polymer-penetrant "bonds" for the liquid penetrant a t 40' and of XI, the inter- are weaker than those between polymer segments. action parameter for equilibrium between the pene- This implies a relation between the extent of polytrant and polyvinyl acetate. Values of x1 were mer-penetrant interaction and the value of the calculated from equilibrium sorption data," under slope a(or p). A useful measure of solvent-polythe assumption that the volumes of penetrant and mer interaction is the Flory-Huggins parameter polymer were additive, using the well-known equa- x1 of eq. 7 which has large values for poor solvents and small or negative values for good solvents. tion 1 2 . 1 3 Table I gives values of x1 a t 40' for several of the 111 ( p / p ~ = ) In v1 zly X ~ W ~ (7) penetrants studied. Figure 5 gives a plot of x1 vs. where v- and v2 are volume fractions of diluent and the parame$er a, which is simply the slope of a polymer, respectively, and X~ is the interaction plot of In D vs. volume fraction of penetrant. Tt parameter. is apparent from Fig 5 that there is a good correAll of the organic penetrants of Table I are sol- lation between x1 and a in the sense that for large vents for polyvinyl acetate except for propanol values of x1 the slope of the In D us V I curve is which is only a limited swelling agent. It is note- large. In other words diffusion increases more rapworthy that propanol gives by far the largest value idly with concentration for a poor solvent than for a of XI, 1.10. For the solvents, the x1 values range good solvent. from 0.28 to 0.75. The question of correlation between solvent type The penetrants of Table I involve still other vari- and rate of diffusion was discussed recently by ations beyond this difference in solvent power. BoyerI4 for the case of plasticizer molecules. AlThere are variations in size, in shape and in func- though pointing to some data in which high x1values tional group. This last seems to have little if any are associated with large diffusion rates of plaseffect on the diffusion coefficient For -the sev- ticizer, Boyer also pointed to cases of the opposite eral propyl compounds of Table I the DO values sort, ie., where plasticizers with very low x1 values vary only about 10-fold and most of the variations diffused more rapidly. According t o the results of can be more easily explained in terms of changes in the present study, to predict diffusion rates one either molar volume or shape, than by changes in must actually consider not only the solvent ability functional group. of a penetrant-molecule but also its size and shape. (11) R. J. Kokes, 4 . I
