Znd. Eng. Chem. Res. 1992,31, 2140-2146
2140
Greek, B. F.; Layman, P. L. Higher Costa Spur New Detergent Formulations. Chem. Eng. News 1989,Jan 23,29-49. Greaser, R. Fr. Pate-nt APPL 82/10.368,1982. Gutierrez, M. L. Sintesis de zeolita A de sodio. Ph.D. Thesis, Universidad Complutense de Madrid, Spain, 1977. Hermans, P. H.; Weidinger, A. X-Ray Diffraction Determination of Crystallinity of Polycarbonate from Bisphenol A. Makromol. Chem. 1963,64,137-9. KurzendBfer, C. P.; Liphard, M.; Von Rybinski, W.;Schwuger, M. J. Sodium-Aluminum-Silicates in the washing process. Part IX: Mode of action of zeolite A additive systems. Colloid Polym. Sci. 1987,265,542-7.
Ruiz, J. C. Sintesie de zeolita 4A de sodio a partir de caolines. Ph.D. Thesis, Universidad Complutense de Madrid, Spain, 1986. Schwuger, M. J.; Liphard, M. Sodium-Aluminum-Silicates in the washing process. Part X Cobuilders and optical brighteners. Colloid Polym2 Sci. 1989,267, 336-44. Uguina, M. A. Sintesis de zeolitaa X e Y de sodio. PbD. Thesis, Universidad Complutense de Madrid, Spain, 1979. Wolf, F. DDR Pat. 43221;Br. Pat. 1051621;Fr. Pat. 1387644,1985. Received for review February 14,1992 Reoised manuscript received May 11, 1992 Accepted June 1, 1992
Migration Studies of Acrylonitrile from Commercial Copolymers Michael Markelov BP America, 4440 Warrensville Center Road, Cleveland, Ohio 44128 Montgomery M. Alger General Electric Company, P.O. Box 8, Schenectady, New York 12301
Tim
D.Lickly
Dow Chemical, 1701 Building, Midland, Michigan 48674
Edward M, Rosen* Monsanto Company, 800 N. Lindbergh Blvd., St. Louis, Missouri 63167
Migration experiments were designed and conducted to estimate the diffusivity of acrylonitrile (AN) in four commercial copolymers in contact with water: ABS-248, ABS-LGA, SAN, and CYCOLAC. A new analytical result was used that accounts for the nonuniform concentration profile of the AN due to desorption before the start of the controlled experiment. Introduction The migration of trace amounts of solvents, reaction by-products, additives, and monomers from polymers has received considerable study. In particular, the migration of vinyl chloride monomer (VCM) in poly(viny1chloride) has received active attention (Koros and Hopfenberg, 1979a,b; Berens and Hopfenberg, 1977). The migration of acrylonitrile (AN) from commercial copolymers is similar in that the migrant is of low concentration and the diffusivity in a given polymer would be expected to be a function of temperature alone. The models which describe the migration (Gandek,1986; Schwope et al., 1990)may require a number of parameters such as the partition coefficient as well as a mass-transfer coefficient between the polymer and the external phase. These parameters have been studied by Gandek and Hatton (1986) and Gandek et al. (1989a,b). The design of a migration experiment to evaluate the diffusivity must account for the possible effects of a nonuniform concentration profile, temperature changes, partitioning effects, and possible boundary layer resistance. With these issues in mind this study describes the experiments and analysis carried out to determine the diffusivity of the AN in the copolymers. Theory Boundary Conditions. The general model for mass transfer assumes a semi-infinite flat sheet of polymer, of half-thickness1, in which the solute migrates to the surface and then into the external phase. One of the most popular analytical models is a solution to Fick’s second law due to Boltzmann (Crank, 1975):
* Author to whom correspondence should be addressed.
Mt is the amount of solute diffusing from time 0 to t , Co is the initial concentration of AN, t is the time measured from the time the concentration is uniformly distributed, D is the diffusivity of the solute in the polymer, and r = Dt/12. Gandek (1986) calls this domain infinite-infinite since it assumes that the AN migrates from an infinite polymer into an infinite external phase or “sink”. The following boundary conditions are assumed 1. The initial concentration of AN is uniformly distributed throughout the polymer at time zero. 2. The AN concentration at the surface and in the “sink” is zero. This assumes there is no boundary layer resistance in the fluid. When more than approximately50% of the migrant has diffused, eq 1breaks down and an infinite series solution is needed (Crank, 1975): c
Since the polymer is finite the value of 1 must be known. (In eq 1 , l cancels out as the polymer is infinite.) If Mt vs time data and Coare known, the value of D can be determined by regression ( h e n and Silverman, 1990). Gandek (1986) characterized this as the finite-infinite domain since it assumes a finite polymer and an infinite external phase of zero AN concentration. When the external phase is a fluid, is of finite volume, and is perfectly mixed but the polymer is infinite, then the “infiitefmite” model should be used: M I = Cola[l - erluaerfc ( ~ ‘ / ‘ / a ) ] (3)
0888-5885/92/2631-2140$03.00/00 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 9, 1992 2141 where CY = KV/Al and T = Dt/12. Since the polymer is infinite, the value of 1 cancels out. This equation has an additional parameter, K, the partition coefficient between the polymer and the fluid. This accounts for the fact that the sink is not of zero concentration but depends on the parameter a (and hence K ) . As 7 goes to infinity, the concentration of the AN in the polymer and the fluid is determined by the value of ff.
Change in Diffusivity. Once migration starts in any of the above models, the concentration profile goes from flat to very curved at the surface. If the diffusivity changes at time t l , say due to a temperature change, then the model, developed for constant temperature, is no longer valid. Recently, a modification to the Dt (actually T ) term in the models has been developed (McDonald, 1991) to account for the change in D at time tl. The (Dt)1/2term in eq 1 must be replaced with the following: n
n-1
j=1
1-1
(Dt)1/2* [ E(DjAtj)]1/2- ['c(DjAtj)]1/2
(4)
If there are two temperature changes from the time the initial concentration profile is flat, and the changes take place at times tl and t2,then the amount of migration for each time period (until the final time t3) are amount of migration over time tl at temperature T1
MI = (2CO/~'/~)[Dl(tl - 0)]1/2
(5)
amount of migration over time (t2 - t l ) at temperature T2
M2 = (2Co/~'/~)[[Ditl + D2(t2 -
- (DltJ1/2] (6)
amount of migration over time (t3- t 2 ) at temperature T3 M3
= (2Co/~'/~)[[D1t1 + Dz(t2 - ti) + D3(t3 - t2)11/2- P i t i + D202 - ti)11/21 (7)
Then the total migration is Mt = Mi + M2
+ M3
(8)
If all the temperatures are equal (Dl = D2 = D3), then Mt = (2Co/~1/2)(Dt)1/2
(9)
which is nothing more than eq 1 which applies at constant temperature with t3 = t. In many applications more than 50% of the migrant diffuses and eq 2 must be used instead of eq 1. For the nth step between time tj and tj-l the amount diffused (when the temperatures are all the same) is
- n- M Col
5
8 e-(2m+l)z&?(Dtfi1/4P) m=0(2m+ 1 ) 2 ~ 2 m 8 e-(2m+l)'&?(Dt,/4D (10) m=0(2m+ 1 ) 2 ~ 2
c
When temperature changes have taken place, McDonald (1991) has shown that eq 10 must be modified to be
-n M -Col
5
8 e-[(2m+1)2*1/41r. m=o(2m + 1)W 8 2 m=0(2m+ 1 ) 2 ~ 2
,-[(2m+l)2*2/4](r.+r)
where
(11)
7,
= n-1 j=l
Tj,
T
=
5
Tj,
j=n-1
Tj
=
DjAtj
12
(12)
When T, = 0 (uniform concentration profile), eq 11 reduces to eq 2 since the first term in eq 11 becomes equal to 1and T = Dt/12 where t is the total time. The total amount of migration is the sum of each increment: Mt = M I + M2 ... M, (13)
+
Experiments Equipment. A cell was designed to allow both static and dynamic experimenta to be performed on the same sample of polymer. A polymer plaque separates the cell in two 80-mL chambers. Both chambers were filled simultaneously with water preheated to the temperature of the experiment. Both chambers were equipped with valva on the top and on the bottom of the cells. The valves on one chamber stayed closed for the duration of the experiment (static migration), and the water sample from this chamber was analyzed only at the end of the test. The other chamber was periodically emptied, analyzed, and refilled with fresh preheated water in equal time incrementa (dynamic migration). The cell, valves, and refill water were placed into a thermostated chamber for the duration of the experiment. At low temperatures (
