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/c - fp &- Non-Migration Level of Vinyl Chloride Monomer in PVC A. J. HAEFNER and G. A. HUGHMARK Ethyl Corporation Baton Rouge, Louieiana Recent evidence confirms previous findings that VCM in levels of 1 ppb in PVC bottle resins are nonmigratory and that such resins can be produced in commercial quantities. This is an update on the paper presented at the SPE Meeting in April, 1968. At that time we reported experimental data that indicated a nonmigration level of about one ppb VCM in PVC. Our recent work confirms this non-migration -level. EXPERIMENTAL PROGRAM A three part program was conducted following discussion and review by FDA scientists. All low level VCM analyses in PVC were determined with the FDA analytical method using flame ionization detection. 1. PVC liottle resin was batch steam stripped as a dilute slurry in water at 100C. Heat up with steam plus strip time at temperature was lVi h. In termediate and final samples were filtered and dried at mild conditions prior to duplicate anal ysis. The experimental data are as follows. Time (min) initial IS m (SI fm.il (90) VCM (ppm) 0.0031.0.0025 0.(XX)5,0.0006 O.fXXIG,0.fXXIS 0,0007,0.(XX)4 0.0007.0.0006 2. PVC bottle resin with an initial VCM concen tration of 0.7 ppin was steam stripped as an aqueous slurry at 50, 70, and 100C to develop diffusion coefficient and activation energy data as a function of temperature and concentration at low VCM levels. Sequential strips for 6 min at 100"C, 45 min at 70C, and 3.5 h at 50"C were used. Samples were filtered and dried after each strip prior to analysis. Unfortunately, we encountered a problem in the drying procedure with the material from the third strip so that these data are not valid. Similarly, feed analysis for the fourth strip at 50 and 70C are not available. Experimental data are as follows: Stripping After After After After temp, *C first strip second strip fourth strip fifth strip 50 0.025 ppm 0.0074 ppm 0.0001 ppm 0.0012 ppm 0.0113 0.0004 0.0009 70 0.030 0.0040 0.0000 0.0021, 0.0030 0.0006 0.0010 100 0.012 0.0030 0.0010 0.0019 0.0010 Composite 0.023 0.0120 0,0091 Feed for the fourth strip at 100C analyzed 0.0010 and 0.0004 ppm VCM, so a fifth strip was not re quired at this temperature. 3. Sixteen-ounce PVC bottles with an initial concentration of about 0.0014 ppm VCM were filled with 50 percent aqueous ethanol and stored at 120F for six weeks and 21.5 weeks prior to analysis of the bottle walls. Bottles from the same batch were filled with vegetable oil and stored at 120F for six weeks. Analysis of six bottles from the same batch as w'as used for storage showed 0.0011, 0.0013, 0.0012, 0.0019, 0.0014, and 0.0013 ppm VCM at the time of filling. Analysis of bottles from this batch six weeks later showed 0.0014 ppm VCM and 0.0018 ppm about twelve weeks later. Also, samples of the ethanol and water for the aqueous ethanol were analyzed to assure that there were no interferences in these on the FID chromatograms. Analysis of six bottles after each of the storage tests showed the following results; 50 Percent aqueous ethanol \cgctahle oil 6 Weeks 21.5Weeks tl.OtKM ppin 0.0009 ppm 0.WXI7 0 0012 tl.0<X)7 0.0005 0.0007 o.otxu 0.0013 Average 0 OOOfi.y 0.U0087 6 Weeks 0.0030ppm 0.0016 0.0040 0.0060 0.0032 0.0009 0.0031 " ^vvfrfU* 0,00076 tl tin* O.lMHH ppm imhvtv pvliininttlt'd hvuin*ttl a^urvnt \CM Iff** during aiwil* **. IOURNALOF VINYL TECHNOLOGY MARCH 1979, VOL 1 NO 1 UCC 029029 A. I, Hacfner and C, A. Hughmarit DATA INTERPRETATION Results from the first part of the experimental program demonstrate that VCM is reduced to a concentration of about 0.0006 ppm in PVC resin at 100C and that no further reduction in VCM occurs with continued steam stripping at this tempera ture. Results from the second part of the program indicate that the non-migration VCM concentra tion is about 0.001 ppm and is independent of temperature between 50 and 100C. The results from the third part of the program show that the VCM in the PVC bottles filled with 50 percent aqueous ethanol decreased to slightly less than one ppb after six weeks storage at 120"F and then apparently remained constant for the next 15 weexs. This also indicates a non-migration level at about one ppb VCM in PVC. The VCM level in the PVC bottles filled with vegetable oil show a statistically significant increase in apparent VCM in the bottles after six weeks storage at 120'F. We suspect that non-VCM components were absorbed by the bottles from the oil and that these represent interference with the FID anal ysis. Interpretation of the data from the second part of the program is complicated by lack of complete data resulting from the problem in the drying pro cedure. Diffusion coefficients and activation ener- ies can be estimated from the data. The stripping ata are analyzed bv assuming that the VCM re moval is controlled by diffusion from uniform spheres to a boundary with zero VCM. The rela tionship between the concentration after a period of stripping and the initial concentration is given by: C_ 6 v e C. ir* n1 where C. * initial concentration, C = concentra tion at time /, D - diffusivitv, and ti particle radius. Generally one or two terms of this equation are adequate for these experiments. The term D/a1 is useful in calculating the diffusivitv from PVC resin data because the particle radius is unknown. This equation is applicable because one week was allowed for equilibration of VCM in the PVC be tween strips. D/a* u ') Stripping temp, *C First strip Second strip Third strip SO 2.25x10" 3.74x10" No vulid data 70 9.96x10* 5.21x10'" No valid data 100 1.01 x 10 ' 4.91 x 10 1 No valid data Prior data obtained with high VCM levels in this PVC resin show correlated Dla1 values of 8 x 10'* and 6.5 x 10''s"1 at 70 and 100C, respectively. The values obtained in this work are in good agreement with the prior correlated values. The VCM contents measured after the fourth strip include the effects of both the third strip and die fourth strip for the 50 and 70*C runs. For the 100eC run the VCM content was not changed by the fourth strip. Likewise, no significant change in VCM content was noted from the fourth to the fifth strip for the 50 and 70C runs. The results of the fourth and fifth strips at 50 and 70C and the re sults of the third and fourth strips at 100aC are taken as measures of the same residual VCM con centration. A major uncertainty exists in any attempt to es timate diffusion coefficients and the activation energy for diffusion for 50 and 70C for the lowest levels of VCM. For the 100C strips it is clear that the minimum residual level is reached at the end of the third strip but this residual level may have been reached after the third strip or required some or all of the fourth strip to reach this residual level. Values of the diffusion coefficient estimated from the average of all VCM determinations and the as sumption of 1 or 2 strips are as follows: Value of D/s*,**1 One strip Two strips Stripping temp, AC required required 50 1.56 x 10 7.55 x 10-* 70 6.79 x 10 * 2.64 x U) 100 5.76 x 10 1 Not required The values of Dla1 are shown in Fig. 1. The val ues for the first strip fall very nearly on a straight line and yield a value for the activation energy of 18.2 Kcal. The values for the second strip show a break and yield 19,0 Kcal for the activation energy between 100 and 70C and 29.0 Kcal for the activa tion energy between 70 and 50C. Treatment of the data from the third and fourth strips can yield a range for the activation energy between 70 and 50*C. If it is assumed that one strip is required for both 50 and 70C then the activation energy be tween 70 and 50C is 14.3 Kcal while if it is as sumed that one strip is required at 70C and two are required at 50"C the activation energy is 24.2 Kcal. In both cases the activation energy for the 100-70C temperature segment is 18.1 Kcal. These values are as lot lows.- Activation energy, Kcal/g mole Strip Initial VCM, ppm 100-70C 70.WC 1 2 3 and 4 0.7 0.023 0.0105 15.2 15.2 19.0 29.0 15.1 14.3-24.2 CONCLUSIONS FROM EXPERIMENTAL PROCRAM A non-migration level of 0.0006 to 0.001 ppm has been demonstrated Ibr PVC resin that is used in bottle compound. This non-migration level ap pears to be independent of temperature in the range of 50 to 100C. s iOtJRNAI. OF VINYl. TFCIIXOI, <TCY, MAHDt l,l> VO! 1 IJCC 029030 Non-Migrotim Level ofVinyl Chloride Monomer in PVC FUTURE WORK We plan to repeat the second and third parts of the experimental program including CCMS anal ysis of the bottles after vegetable oil storage to separate VCM from inteferring components. This is expected to explain the apparent increase in VCM that was shown with vegetable oil. Repeti tion of the experiments to obtain data for better definition of diffusion coefficients and activation ' energies can be accomplished by elimination of the drying problem that occurred with the work reported in this paper. An experimental program shall also be carried out to determine the replicability of the analytical method for PVC bottles. The entire bottle wall from a bottle is required for a single analysis so replication data are not available for what is known to be a large, constant VCM composition sample. Similarly, variability in VCM concentration is not known for bottles in the same batch. This shall also be determined. This work is required because of tire small differences in VCM concentration that are required with these experimental programs. PVC bottles stored at 120F with 50 percent aqueous ethanol.as contents show a non-migration level of about O.OOOtS ppm. SUMMARY Experimental data continue to show that there is a non-migration level of about one ppb for VCM in PVC bottle resin and in PVC bottles with food simulating solvents. With the possible require ment for a PVC compound at tne non-migration level, we have produced a commercial quantity of compound in the one to two ppb VCM range to demonstrate capability of manufacture of this compound. JOURNAL OF VINYL TECHNOLOGY, MARCH 1979, VOL. 1. NO 1 7 ucc 029031 The Diffusion of Gases and Vapors in Rigid PVC A. R. BERENS The BFGnodrich Company Research it Development Center Brecktville, Ohio 44141 Gravimetric sorption rate measurements have been carried out for COt, HiO, and ten Ci-C* organic vapor* at low concentrations (< 0.2%) in PVC films and uniform-particle powders at 30*C. The domi nant transport process in all cases appears to be Fickian diffusion. A distinguishable contribution of relaxation-controlled swelling was observed for the more soluble vapors, such as acetone and benzene. A significant contribution of surface adsorption to the total sorption pro cess was detected only for the n-alkanes, among the penetrants studied. Diffusion coefficients, determined from half-sorption times and polymer dimensions, range from 4 * 10'* ein*/sec for HsO to 1.5 x 10'" cni'/sec for n-hcxane. Dilfusivities determined in this study, in combination with those for gases reported by Tikhomorov, et al. (Makromol. Client. 118 177 (1968)), define a continuous curve, cover ing more than nine orders of magnitude, when plotted as a function of the molar volume constant, b, of the van der Waals equation of state for gases and vapors. INTRODUCTION Current concern about possible environmental and physiological effects of minor, low-molecular-weight constituents of plastic materials has accentuated the importance of diffusion studies involving small molecules in glassy polymers. Knowledge of the diffusivitv of small organic molecules in polymers is essential both for the de sign of processes for removing residual monomers or solvents and for the prediction of migration rates for remaining trace ingredients. Until quite recently, studies of diffusion in glassy polymers have been largely limited to gaseous penetrants or to organic solvents at rather high concentrations. The diffusivities of a number of gases in unplasticized poly(vinvl chloride) (PVC), for example, were reported by Tikhomorov, cl til. (1). hor organic liquids or vapors at high relative pressures, sorption be havior in glassy polymers is quite complex; due to the superposition of diffusion and relaxation controlled swelling (2), the transport process cannot be described by simple Fickian diffusion equations. Hopfenberg and Frisch (3) suggested that simple Fickian diffusion is to be expected at very low penetrant activities or concentrations in glassy polymers; experimental studies under these conditions, however, have l>een hampered by the prohibitively long soqition times encoun tered with organic vapors in conventional polymer film specimens. Thus there has been a notable lack of experimental data in the area of current concern, i.e., the diffusion of small or ganic molecules at low concentrations in rigid polymers. In a recent study of the diffusion of vinyl chloride monomer (VCM) in PVC (4-6), gravimetric sorption measurements were per formed with polymer powder samples of welldefined geometry. In powder samples, diffusion path lengths can be reduced by orders of mag nitude below the practical limit of film thick ness, and it is thus feasible to investigate diffu sion processes which require inconveniently long times in films. At very low relative VCM pressure (Prel < --0,01, where P,,, = P/Pn, with P, the saturated vapor pressure), the sorption of VCM by PVC was found to follow simple Fic kian kinetics; the diffusivitv, >. was readily de termined from the half-soqstion time, f0.i. and the powder particle diameter, d, as D - 7.66 x 10-3 f #.s (l) At somewhat higher VCM pressure, the sorption process involved both Fickian diffusion and a slower, relaxation-controlled swelling; because of the rapid diffusion time in fine powders, it was still possible to estimate D from the early part of the soqition vs time curves (5). The present study was undertaken in order to determine whether simple Fickian diffusion might generally be observed for low concentrations of s lOURNAI.OF VINY1 TFCHNPI OCY. MARCH !-. VO! 1 NO 1 ucc 029032 Tht Diffusion of Casts and Uipors in Rigid PVC small organic molecules in unplasticized PVC. Gravimetric sorption experiments were performed using PVC powder samples with a range of vapors in an effort to relate dilTusivity to the molecular size of the penetrant and thus to provide a basis for predicting migration rates of residuals from PVC and, perhaps, other rigid polymers. EXPERIMENTAL Materials PVC homopolymer samples were prepared by emulsion and suspension polymerization tech' niques and were used in the powder form ob tained directly from the polymerization by normal recovery and drying procedures. Particle structure was characterized bv optical and electron micro scopy and by nitrogen-adsorption surface area measurements. Samples of uniform particle diameter ranging from 0.11 to 0.44 /*m were ob tained by emulsion polymerization. The two suspension-type PVC samples consisted of --100 /am agglomerates of 1.4 anil 3.3 fim primary parti cles, respectively; in VCM sorption experiments, these samples followed uniform-sphere.Fickian kinetics governed by the primary particle diameter (4). Some sorption-rate measurements were also made on a sample of rigid PVC film 50 /am in thickness. Research grade organic penetrants were employed throughout. Equipment and Procedures The time dependent weight changes of PVC samples upon exposure to penetrant vapors at pre determined pressures were determined using the Cahn electrobalance and vacuum system de scribed previously (4). Most of the data reported here were obtained at 30C in sorption experi ments covering the vapor pressure interval from vacuum to Prrt * -0.1. The amount of vapor sorbed in each experiment was < 4 mg per g PVC; the average penetrant concentration in the PVC during the experiment was thus * 0.2 per cent. For each sapor, sorption experiments were performed with PVC samples of several different particle sizes; experiments yielding half-sorption times from 10 to 3600 s were included for cal culations of diffusivities from Eq 1. With HiO and COa, t,_, for the lurgest-purticle powder was too short to measure; diffusivities for these penetrants were obtained from sorption measurements on the 50 ixm film sample, using the expression corre sponding to Eq 1 for planar geometry, >-0.049 f* *0.5 where f is the film thickness (7). (2) RESULTS AND DISCUSSION Sorption-Time Curves For Fickian diffusion in a powder consisting of uniform spherical particles of diameter d, gravimetric sorption data obey the relation (4,7) 1- * 6" VVt ._11 exp(-4)/*irW) (3) w .Ti n1 where Af, is the weight of penetrant sorbed at time t after an instantaneous change in pressure and M m is the total sorlied at equilibrium. This expression firedicts that a plot of M, vs t '" will be essentially inear until M, * 0.6 Af. and then will curve to approach Mm asymptotically. A curve of similar form is also predicted for Fickian sorption in a plane film ofthickness ((7): __ 1____ Mi - M,, 1 - 8 I 17* a.l (2a + 1) exp(-0(2/t + If-tPtlf*) (4) For all of the sorption experiments reported here, plots of M, vs t'" are linear over a substantial portion of the total course of the experiment. This finding clearly indicates that the dominant trans port process for all of the penetrants studied, at low concentrations in PVC, is simple Fickian dif fusion. For many of the experiments, the uniform- sphere Fickian diffusion model, Eq 2, accurately describes the gravimetric data throughout the sorption process. Examples of M, vs r ` plots obey ing this relation are shown in Fig. J, for the sorp tion of ethanol in the 0.44 /im PVC powder, and Fig. 2, for n-propanol in the 0.22 ixm sample. Equation 4 similarly descrilies the sorption results on the film sample, as illustrated by the CO. sorp tion data plotted in Fig. 3 In a number of cases, sorption experiments yielded Mt vs C* plots which are initially linear but do not approach equilibrium as promptly as predicted by Eq 2. This behavior is illustrated by die data for the sorption of acetone and b nzene plotted in Figs. 4 and 5, respectively. The curs es obtained by fitting Eq 3 to the initial portions of the experimental data are also shown in these fig ures. Sorption in excess of the Fickian curve may reasonably be attributed to relaxation-controlled swelling (5). The contribution of relaxation to the total sorption, in experiments covering a similar Prr, interval, seems greater for those penetrants having the higher solubility in PVC. For a given penetrant, the contribution of relaxation, relative to Fickian soqition, increases as the P,,t increment of the experiment is increased. In the experiments considered here, the combination of small P,,, intervals with small particle size (hence rapid dif- JOL'RN'AL OF VINYL TECHNOLOGY, MARCH 1979, VOL. 1. NO. 1 ucc 029033 A. R. BrrotS Fig. 1. M, vt t ' fur sorption of ethanol in 0.44 pm P\'C pow der at 30*C, Pj-i -- 0 -- 0.046. Pointi, experimental; curve, Eq 3 with M. - 1.41 mglg, D -4.8 x JO" cmVr. Fig. 2. M, is l'`> for sorption of n-propanol in 0.22 pm rYC powder at 30*C, P,,, 0 -- 0.108. Points, rz/icrinicntdl; curve. Eq3with .U. -1.13 mglg, D - 6.7 x 10'"cm1* Table 1. Summary of DifFusivity' Measurements at 30*C Penetrant PVC sample H,0 H.O 50/ini film 50 pm film CO.(ZS'C) 50 rsm film P,,! interval 0-.19 .19-.41 0.-.008 Fickian sorption mg/* D.cm'/s 0.15 27 4.5 a 100.60 36 3.4 a 10 ` 1.35 1470 8.4 a 10-' van der Waal* b. liter/mol 191 0.0305 0.0427 Methanol 3.3 sun powder 3.3 pm |Xiwder 3.3 M<n |>owdcr 1.4 pm powder O-.Olh .018-.035 .035-064 0-.100 0.45 0.17 o. m 1.3 12 20 30 12 6.9 a 10" 4 .2 x 10 " 2.8 a 10 " 1.3 a 10 " 0.0670 \ CM (ref. 4) 2.0 a 10 ' 0.080 test) Ethanol 0.44 Mm powder 0-.39 0.44 pm powder Q-.046 Aietone 0.44 nm powder 0-.010 n-Propanol 0.44 pm powder 0-.108 0.22 pm powder 0-.108 0.11 Mm powder 0-.104 Benzene 0.22 am powder 0-.059 n-Butaiie 0.44 mm powder (4.037 0.44 Mm powder 0-.101 0.22 Mm powder 0-.011 7.3 1.41 3.2 1.34 1.13 2.0 10.4 0.88 2.0 0.77 45 3.3 a 10" 31 4.8 a 10-11 106 1.4 a 10 15 132 1.1 a 10-'* 55 6.7 a 10 " 40 2.3 a 10" 210 1.8 a 10-" 780 1.9 a 10 '* 560 2.6 a 10 " 156 2.4 a 10 " 0.0841 0.0994 0.1019 0.1154 0.1226 n-Butanol n-Pentane n-llexune 0.44 Mm powder 0-.125 0.22 Mm powder 0-.125 0.11 am powder 0-.120 0.22 pm powder 0-.028 0.22 M>n powder 0-.102 0.11 Mm jiowder 0-.102 0.22 juit powder 0-.103 0.11 Mm powder 0-.05S 0.11 M'n powder 0-109 0.45 1.63 2.54 900 1.6 a 10 '* 272 1.4 a 10 * 90 1.0 a 10-" 1.3 4S0 7.7 x 10" 3.0 200 1.8 a 10" 2.7 53 1.8 a 10" > 4.0 -3600 1.0 a 10 2.6 700 1.3 a 10" 3.0 400 2.3 a 10-11 0.138<est> 0.1460 0.1735 IOURNALOFVINYI TFCHNOIOO \.H ' V UCC 029034 The Diffusion of Gat* and \tpors in Rigid PVC IS - illustrate this behavior. The rapid initial weight gain increased with increasing molecular weight of the n-alkane, for a given Prtl interval and PVC particle size or surface area, and increased in ap proximate proportion to the specific surface area of the PVC powder sample, for a given penetrant and Pret interval. This rapid weight gain, therefore, may reasonably be attributed to surface adsorption of the n-alkanes. Conversely, the absence of a de Fig. 3. A/, is t'; for sorption of CO, in 50 PVC film at 2VC, Pr,, - 0-> 0.008. Points, experimental; curve. <f 4 with A/ i .35 rng/j>. D 8 < x i0_1* cnilis. tectable, nearly instantaneous weight gain for the other penetrants studied here indicates that sur face adsorption was negligible in all other cases. The separate contributions of adsorption, diffu sion, and relaxation processes to the total sorption may be estimated from the M, vs t `` curves as indi cated in Figs. 6 and 7. Fig. 4 SI, i j r ` * /<ir sorption of acetone in 0.44 pm P\'C powtier at JO'C, 0 -- 0.0/03. Points, i ipi riiiwnlul, curve, Ft/ J ii itli A/ 3.3 iii^k, D " / < x ia-'*cmt/,, fusion equilibration) produces sorption curves which seem dourly separable into diffusion and relaxation contributions. For n-butane, n-pentane, and n-hexane, the gravimetric sorption data show a nearly instan taneous initial weight gain, followed by sortition of the ditfnsion-plns-relaxation torn) observed with other penetrants. The M, vs t-' plots in Figs. 6 and 7 Diffusion Coefficients For each of the penetrants studied, D has been calculated, through Eqs 1 or 2, from the halfsorption times, /M, for the Fickian portion of the experimental sorption-time curves. The experi ments and results are listed in Table 1. Where usa ble data were obtained on more than one PVC sample with a given penetrant, the agreement seems satisfactory. The diiTusivities of 11,0 and CO* agree quite well with those reported by Tikhomorov, et al. (1). For the organic vapors, D ranges from --4 x 10'" em'/s for methanql to -- 10",4cm5/s for n-hexane. Correlation of D with Penetrant Size The strong trend of decreasing dilfusivity with increasing penetrant molecular weight suggests a correlation of P with the size of the penetrant lUUKNAl.UI- VINAI. IU IINOI Ut.Y. MAKl II 1070. VOl,. I. Ml I I! ucc 029035 A. R. Bnni molecules. One measure of molecular size, avail able for most of the penetrants studied, is the con stant b ofthe van der Waals equation ofstate (8) |p+J^_j(V-#ifc)-ni?r (5) Here, b is the effective volume of the molecules in one mol of gas, in liters/mol. Published values of b (9) for the penetrants studied-are listed in Table 1; interpolated estimates are given for vinyl chloride and n-butanol. In Fig. 8, dilfusivities determined in this study are plotted against b\ a smooth corre lation is seen to exist. Also plotted in Fig, 8 are the difTusivities of gases in PVC at 25* determined by Tikhomorov, et al. (I). Together, the two sets of data define a single smooth curve; only the points for the noble gases, neon, argon, and krypton, appear to lie sig nificantly away from the curve. The combined data for gases and organic vapors thus show a con tinuous correlation with molecular volume extend ing over more than nine orders of magnitude of D, from 2.8 x 10"* to -10"'* em'/s, This strong dependence of D upon penetrant size, for PVC lielow its T,, contrasts markedly with the effect of penetrant size in rubbery polymers (10). For the same range of penetrant size, values of D in natural rubber at 40C fall in the much nar rower range of 10"* to 10"" em'/s; D for C to C, n-alkanes in polyisohutylene at 35* is essentially constant at ~3 x 10"* em'/s. Diffusion of small Fig. 7. Af, u t^ for .toqition of n-hcranc in 0.11 (un PVC ponder al 30V, Pm 0 -- 0.100. Points, experimental, curve, Eq3 uiithM. 3.0mg/g,D 2.3 x i0_lrm'/j(adsorption,2 0 mglg). molecules in rubbery polymers presumably in volves cooperative motion of the penetrant and polymer chain segments ofsimilar size; the narrow range of the observed dilfusivities suggests that segmental motions involving from four to nine chain atoms occur at similar frequencies. In the glassy state, such segmental motion is effectively quenched, and diffusion probably occurs by jumps of penetrant molecules between sites or boles fro zen into the polymer matrix. Diffusivity, then, may be a measure of the probability of finding holes large enough to hold a penetrant molecule. The very wide range of dilfusivities found in this study seems to suggest that the probability of finding such holes is a continuous and sharply decreasing function of increasing hole size. The very limited oata available on diffusivity of organic vapors in other glassy polymers suggests that very low magnitudes of > are not unique to PVC. Enscore, et al. (11) have reported D of the order of 10"** em'/s for n-hexane in polystyrene at 30*C. Preliminary experiments in tnis laboratory on the sorption of acrylonitrile in stvrene/ acrylonitrile copolymer powders at 50C indicate a D of approximately 4 x 10"11 em'/s. Further appli cation of the polymer powder/vapor sorption method may Ire expected to provide important in formation on the rate and median isms of stnal 1molecular transport in a variety of glassy polymers. Practical Implications The results of this study seem to provide some useful generalizations in regard to tire practical problems of removal and migration of lowmolecular weight residuals from rigid plastic ma terials. The dominance of Fickian diffusion in governing the transport process at low penetrant concentrations, and the consequent dependence of diffusion time upon the square of particle diameter, suggest that polymers should Ire pro- 12 ini lRNAl OF V1NV1 TrrUNOLOCY. MARCH 1"" VOI 1 NO 1 ucc 029036 The Diffusion of Casts and topers m Rigid PVC duced in the smallest feasible particle size, and that "stripping" should be performed while the polymer is in this form, in order to achieve most rapid and effective removal of residual monomers or solvents. On the other hand, the very low diffusivities of small organic molecules in glassy rolvmers indicates that migration of residuals from abricated rigid plastic products will lie extremely slow. Berens and Daniels (12) have applied Fiekian diffusion equations to predict the rate of mi gration of residual monomer from PVC pipe, for example, and have shown that a pipe containing < 1 ppm residual VCM will yield <<1 ppb VCM strate that the transport of small molecules at low concentrations in rigid PVC is predominantly a Fickian diffusion process. The technique of gravimetric sorption using fine polymer powders is capable of determining diffusivities at least as low as 10'" cm*/s. These experiments also can dis tinguish and quantify the individual contributions of surface adsorption, Fickian diffusion, and relaxation-controlled swelling to the total sorption process. Diffusivity values now available, deter mined at 25-30*C, span the range from 2.8 x 10'* (helium) to 1.5 x lO'^cmVs (n-hexane). Over this entire range, diffusivity appears to be a smooth, continuous function of the molecular size of the penetrant, as measured by the molar volume term, b, of the van der Waals equation of state. This cor relation seems quite relevant both to the basic understanding of transport processes in the glassy state and to the practical problems of removal and migration of residual monomers and solvents from rigid plastic materials. ACKNOWLEDGMENTS The author is grateful to Miss Ronna Gander for assistance with experiments and calculations, to Dr. K. Given for suggesting the van der Waals molar volume as a useful measure of penetrant size, to Prof, H. B, Hopfenlverg for continued help ful discussions, and to the BFGoodrich Company for permission to publish this work. in water contained in the pipe under any expected service conditions. The diffusivity data presented here may prov ide a reasonable basis for similar es timation of migration rates of other low molecular weight, minor constituents of rigid plastic prod ucts. CONCLUSIONS The results of this study, in conjunction with previous data for gaseous penetrants (1), demon REFERENCES 1. H. P. Tikhomnrox, II. B. Iluplenlx-ri;, V. Stunnett, .iml ]. L. WiU iuno., Mukromol, Cliem., 118.177 (1968). 2. II. B. Hiiplcnlieri> .iml V. St.uim.-tt, in "The Plnslc. of Glassy Polymen." Cli 9, R. N. Haward, ed,, Wiley. New York (1973). 3. H. B. Hoplenlrent .uul ILL. Friseh,J. Puhjm. Sci. (B), 7, 405 (1969). 4. A. B. Hcrcns, Puhjnicr, 18,697 (1977). 5. A. H. Hcrcns ami II- B. Hopleiiherjr, Polymer, 19, 489 (197S). 6. A. R. Berens,) Membrane Sci.. 3 247 (1978). 7. J. Crank, "Tin- Mathematics of Diflnsion." Clarendon Press. Oxford (19.56). 8. C. F. Pnittonaml S. II. Maron, "Fundamental Principles of Physical Chemistry," Macmillan, New York (1947). 9. "Ilundhook of Clicuiistry & Physics," 47th ed., p. D-104, Chemical Rubber Cm, Clex eland (1966). 10. C.J. van Aiuernngfn, Rubber C/ient. 0 Tech., 37, 1065 (1964). 11. D. J. Enscorc, II. B. liopfenher|(, and V, T, Stunnett, Polymer, 18.79311977), 12. A. H. Berens and C. A. Daniels, Polym. Eng. Sci., 16, 552 (1976). JOL'RNAL OF VINYL TECHNOLOGY, MARCH 1979, VOL. 1, NO. 1 ucc 029037