2486
J. Phys. Chem. 1991, 95, 2486-2492
or (hT - h0) = KShO[Ml (6b) where (hT - ho) and ho represent membrane-bound and free TB, respectively. Thus, eq 5 can also be written In ( h T - h,) = -kW + In hoKs[M] (5')
Figure 3 shows the plots of l / k 9 vs [MI (Table 11) according to eq 4. Straight lines are obtained, indicating that the reaction occurs primarily in the aqueous phase. The values of k, obtained from these plots (by least-square fits) are in excellent agreement with those obtained by direct determination (Table 11). Values of Ks obtained from the kinetic measurements (eq 4) are given in Table I, as well as those of AG, AH, and AS. In the concentration region under study, Ks and P, calculated on a molar basis, can be interconverted by a factor that is the phospholipid partial molar volume, V,calculated assuming the lipid density given in ref 8 and an average molecular weight for EPC of 770. Taking P = 0.77 L mol-', Table I evinces very good agreement between Ks values calculated from direct paitition measurements and from the kinetic data. The kinetic and thermodynamic data are also in very good agreement with those found for another family of benzoates, analogues of the local anesthetic tetracaine (Bianconi and Schreier, submitted). The binding of TB to EPC bilayers is a spontaneous, endothermic process, driven by an increase in entropy. This result can be rationalized by envisioning the partition process as consisting
of two steps: loss of hydration water and incorporation into the bilayer. The former implies an increase in entropy, whereas the latter imposes an increased ordering of the solute, and reduction in entropy. AS > 0 (Table I) indicates that the first step predominates. Similar results were found for other solutes by Katz and Diamond.19 In conclusion, this work shows that EPR spectra of TB can be used (1) to investigate the polarity of its location in the bilayer (similar to that of decanol), (2) to determine its orientation (the x axis and the long molecular axis preferentially oriented parallel to the bilayer normal, Figure l), (3) to estimate its partitioning into the membrane and the thermodynamics of partitioning (Table I), and (4) to measure the kinetics of its alkaline hydrolysis in the presence of bilayer membranes (Table 11). The decrease in k\k with increasing EPC concentration shows that zwitterionic membranes protect the solute from hydrolysis, the protection increasing with increasing ionic strength. This may explain, at least in part, the higher therapeutic effect and the higher toxicity of the more lipophilic local anesthetics.I0 _ _
Acknowledgment. We thank FAPESP for a Ph.D fellowship to M.L.B. and CNPq for a research fellowship to S.S.This work was supported by FAPESP and FINEP. We are grateful to Mr. W. R. Toselli for preparing EPC and to Miss C. F. Rodrigues for W i n g the manuscript. (19) Katz, Y . ; Diamond, J. M. J . Membr. Biol. 1974, 17, 101.
Kinetic Detalls of a Gas/Porous Adsorbent System by the Frequency Response Method Yusuke Yasuda,* Yoji Suzuki, and Hirofumi Fukada Faculty of Science, Toyama University, Toyama 930, Japan (Received: July 30, 1990;
In Final Form: October 8, 1990)
On the basis of actual data on the frequency response (FR) of CH,, CzH6,and C3Ha/5A zeolite systems it is shown that various transport processes of diffusion and also adsorption-desorption occurring simultaneously can be separately investigated by the present method. The FR data of the light hydrocarbons reveal that (i) in the higher equilibrium temperature (T,) range the overall sorption kinetics is partially blocked by the surface resistance, (ii) in the lower T, range the overall kinetics is explained well by the dual-mode sorption model involving mobile and immobile adspecies, and (iii) only in the intermediate narrow T, range is the transport controlled by a single intracrystalline diffusion process. The Fickian diffusivities deduced from the FR data of the complex system involving a number of the additional phenomena were 1 order of magnitude higher than the values obtained from classical sorption-rate measurements and 4 orders of magnitude lower than those by the NMR method. The advantages of the present new method are discussed.
1. Introduction
In many important uses of porous adsorbent such as selective sorption, molecular sieving, and catalysis, one stage involves migration of sorbate within the crystals. It must be one of the most fundamental problems to determine the diffusivity in order to characterize the porous media. However, determining reliable intracrystalline diffusivity has not been easier than expected, because for steady flow the overall process may be limited by a number of additional phenomena, such as intercrystalline transport or finite rates of adsorbate supply, surface barrier, and adsorption heat dissipation. Intracrystalline diffusion of CH4, C2H6,or C3Hs in SA zeolites has been widely studied by both sorption and NMR methods.I-l0 (1) Karger, J. AIChE J . 1982, 28, 417. (2) Ruthven, D. M.; Loughlin. K. F. Trans. Faraday Soc. 1971.67, 1661. (3) Ruthven, D. M.; Derrah, R. I.; Loughlin. K. F. Can. J . Chem. 1973, 51, 3514.
The most striking features of the early results are that the diffusivities determined by the NMR method are several orders of magnitude higher than the values obtained from classical sorption rate measurements under apparently similar conditions.' This paradox is still unresolved satisfactorily." Recently, a frequency response (FR) method has been proposed.I2 The advantages of the new method are as follows: (i) (4) Caro, J.; Karger, J.; Pfeifer, H.; Schdlner, R. 2. Phys. Chem. 1975,
256, 698.
(5) Caro, J.; KHrger, J.; Finger, G.; Pfeifer, H.; SchMner, R. 2. Phys. Chem. 1976, 257,903. (6) Klrger, J.; Caro, J. J . Chem. Soc., Faraday Trans. 1 1977, 73, 1363. (7) Klrger, J.; Ruthven, D. M. J. Chem. Soc.,Faraday Trans, I 1981, 77, 1485. (8) Kirger, J. AIChE J . 1982, 28, 417. (9) Karger, J.; Pfeifer. H.; Richter, R.; FILrtig, H.; Roscher, W.; Seidel, R. AIChE J. 1988, 34, 1185. (10) Kirger, J.; Pfeifer, H.; Rosemann, M.; Feokistova, N. N.; Zdanov, S. P. Zeolites 1989, 9, 247. (11) Karger, J.; Ruthven, D. M. Zeolites 1989, 9, 267.
0022-365419 112095-2486%02.50/0 0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 9.5, No. 6, 1991 2487
Gas/Porous Adsorbent System
Figure 1. Three-stage, I, 11, and 111, model for the transport processes in a gas/porous adsorbent system. X denotes the molecule in the gas space; A, adspecies on the external surface; C, adspecies within the micropore; B, adspecies on the internal surface. Stage I is characterized by K+; stage 11, by b; stage 111, by K-B.
Case-1: X [ Z A l y ( C 1 W
Case-2: X Z A x ( C 1 SA
a,
10
1
P,/torr
Figure 3. Adsorption isotherms of the light hydrocarbons over 5A zeolites (19.6 g). The numbers beside the lines indicate Tis in centigrade units: (A) the results of C,H,; (0) the results of C2H6;(0)the results of CH+
Figure 2. Five different cases derived from the three-stage model in Figure 1 valid to explain the FR data in this work.
because the method is a resonance method, it would be profitable to investigate a complex system;I3-l5(ii) because the method may be carried out under various conditions of T,and P,, dependence of the mobility on T, and P, would easily be observed,(iii) because the perturbation due to the volume change is small enough, adsorption heat dissipation may be neglected,16*"(iv) even a coupled rate equation for a binary gas mixture may be linearized and then decoupled.18 Consequently, it seems of interest to apply the FR method to the light hydrocarbon/5A zeolite systems involving the paradoxical results. 2. Theoretical Section A three-stage model illustrated in Figure 1 is introduced, where X denotes a molecule in the gas phase; A the adspecies on the external surface; C, that within the micropores; B, that on the internal surface. It is assumed that the migration of C species obey Fick's law and the boundary condition at the mouth of the micropore is determined by A ( t ) . The adsorption-desorption rate process at stages 1 and 111 may be characterized by K-A and K-B, respecti~e1y.l~It should be emphasized that all FR data obtained in this work may be explained by the present model, though a more detailed microdynamic model has been p r o p o ~ e d . ' ~ * ~ ~ If the migration of B species is considerable and may be described by Fick's law, B is replaced by C2as illustrated in Figure 2; although various cases are possible, only five are considered valid to explain the FR data observed in this work. The FR data of a system may be expressed, respectively, by the in-phase and out-of-phase components of
b / P ) cos cp - 1 = Kf,(w) (U/P)
sin
cp
= Kf,(w)
(1) (2)
(12) Yasuda, Y. J . Phys. Chem. 1982.86, 1913. (1 3) Yasuda, Y. J. Phys. Chem. 1976.80, 1867. (14) Yasuda, Y. J . Phys. Chem. 1976,80, 1870. (15) Yasuda, Y.; Saeki, M. J. Phys. Chem. 1978,82, 74. (16) Yasuda, Y.; Sugasawa, G. J . Card 1984,88, 530. (17) Yasuda, Y.; Yamamoto, A. J. Coral. 1985, 93, 176. (18) Yasuda, Y.; Matsumoto. K. J. Phys. Chem. 1989, 93, 3195. (19) Kocirik. M.; Struve, P.; Fiedler, K.; BLllow, M. J. Chem. Soc., Faradoy Trow. I 1988,84, 3001. (20) Barter, R. M. J . Chem. Soe.. Farodoy Truns. 1990.86, 1123.
where u denotes the relative amplitude of the volume variation; p is that of the pressure variation induced by the volume change; cp is the phase-lage between the volume and pressure variations; w is the angular frequency of the sinusoidal variation. The value of K is given by the asymptote of the in-phase component as w 0 and is expected to agree with K, defined by
-
-(
RTo d(A ve
+ C + E) dP,
).
(3)
+
where {d(A C + B)/dP), is the gradient of the adsorption isotherm given in Figure 3 and (RTo/Ve)is the conversion factor." The FR data obtained from the systems illustrated in Figure 2 may be distinguished from each other as follows: Case 1 : The adsorption and desorption rates are very fast and the overall transport is controlled by the intracrystalline diffusion. The two components of the FR may be described by1z*'6 f , ( w ) = 83,(b;w)
(4)
f , ( w ) = S,,(b;w)
(5)
where 83c and 83s denote the-characteristic functions that are explicitly given in eq A l l ; D is the Fickian diffusional time constant. Case 2: The overall rate of sorption is partially blocked by the finite rate of adsorbate supply. The two components may be described byz' f i ( w ) = ~ ~ 8 ~ ~ ( { , b ; wj) = c or s
where the parameter { is given by { = aK-,/b
(6) (7)
These characteristic functions, L Y ~ ~and , asL, are explicitly given in eqs A16 and A17. It is worth noting that each eq 6 approaches eq 4 or 5 in the extreme case: lim ~yB~~({,b;w) = B,(b;w)
f--
(9)
Case 3: The molecules migrating within the micropores are trapped also at definite sites on the internal surface. The two components would be given by f i ( W ) = k183j(bi&O +) k2(r,(K-&O) = C O r S (10)
(21) Yasuda, Y.; Nakamura, K.; Maruyama, K.; Morishita, S.In Zeolites for rhe nineties; Recent Research Reports at 8th International Zeolite Conference; Jansen, J. C., Moswu, L., Post, M. F. M., Eds.; Akzo Chemicals: Amsterdam, 1989; p 297.
Yasuda et al.
2488 The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 TABLE I: ExpcrlmcaW Conditions and Panmeters Determined by Curve F i t t i g
exp. n 0 . O P- 1 P-2 P-3 P-4 P-5 P-5' P-6
T,/K
473 423 393 363 333 333 273
P,b/Torr 6.4 7.2 5.7 5.6 4.8 10.8 8.9
P-6' E- 1 E-I' E-2 E-3 E-3' E-3'' E-4 E-4' E-4" E-5 A- 1
273 393 393 363 333 333 333 303 303 303 273 273 273 252 223 195
10.7 5.3 7.6 5.7 3.2 5.5 8.5 3.3 4.6 11.9 7.5 4.3 9.0 5.4 5.4 5.1
A-I'
A-2 A-3 A-4
K,
KI 0.70 1.95 3.05 4.0 3.0 2.2 3.6 [4.7 0.8 0.44 0.44 0.88 2.5 2.2 2.1 5.0 4.6 3.8 6.6 0.67 0.96 1.9 4.4 7.O [9.5
1 .o
2.6 4.7 8.8 19.4 12.7 8.8 5.2 0.44 0.44 1.9 1.9 1.9 4.4 4.3 3.9 13.6
1.8 5.3 15.6
j35 60 100
100 m
100 m m
20 20 100 m m
m m m
m m
30 60 200 200 m m
b,/min-l 2.84 1.18
0.60 0.54 1.60 2.8 1.8 0.90 0.80 9.9 9.9 3.8 1.60 1.55 1.38 0.44 0.5 1 0.62 0.82 9.5 9.5 3.5 1.20 0.54 0.30
b,/min-' (Icglm1n-l)
K2 0 0 0 4.8 17.0 10.2 5.5 4.2 4.3 0 0 0 0 0 0 0 0 0 8.4 0 0 0 0 9.3 6.2
1.7 x 1.3 x 5.4 x 5.4 x (0.10) 5.4 x
10-3 10-3 10-4
10-3 10-4
Kl/K, 0.7 0.75 0.65 0.45 0.15 0.17 0.41 0.53 0.15
( K I + KZ)/K,
1.o
1.3 1.2 1.1
0.7 0.8 0.7 1.o 1.o
1.o 1.o 1 .O] 1.o 1.o 1 .o
1 .o 1 .o
1.o 1 .o 1.1
1.27 X IO-*
3.5 x 10-3 (6.5 X
1.1 1.o
1.1 1.1 1.o
0.49
1.1
1.1 0.8 0.45 0.61
1.1 0.8 1.o 1 .O]
OP, E, or A denotes the run with propane, ethane, or methane, respectively. b l Torr = 133.3 Pa. TABLE 11: Transition Temperatures (re), Heats of Adsorption (AH,,), rod Activation Energ&s of Intracrystalliw Diffusion (FD) adsorbate T,"/K AH.db/kJ mol-! E d k J mol-l AHSd/RT, 28.9 1.* x IO 33.9 (29.5)c C3H8 3.5 X IO2 28.9 x IO 27.6 (25.2) C2H6 3.2 X 10, x 10 26.2 CHI 2.4 X IO* 21.7 (18.0)
"Corresponds to the dotted line in Table I. from the adsorption isotherms in Figure 3.
ref 29. 'Calculated
where a, and a, denote the characteristic functions for the adsorption-desorption rate process13 and are given in eqs A3 and A4; ki ( i = 1 or 2) is defined as
ki K,/(KI K1 K2
E
+ K*)
(11)
(RTo/ Ve)(dCl/dP)e
(12)
(RTo/ K)(dB/dP)e
(13)
Case 4: The molecules migrating within the micropores, C, are divided into the mobile and immobile ads cies, CI and C2, respectively. If the diffusional time constants and 4 are very different, the FR may be described by the sum of the individual functions, and we have
log IW r a d min-'1
E
fl(w) =
kI83,(8l;~) + k283,(b,;~)
i = c or s
I
I
I
1
(14)
where ki is defined as in eq 11 and K,is given by
4
W o / Ve)(dC,/dP)e
(15)
Case 5: When the surface resistance is considerable in case 4, eq 14 is modified as f l ( w ) = kI(r83j(t$b,;w) + k283,(b2;w)
i = c or s
(16)
3. Experimental Section The FR apparatus and the procedure have been described el~ewhere.~~.*~ Commercial synthetic SA zeolites, Linde SA (binder free), were used. The powders were formed into pellets under pressures of (22) Yasuda, Y.; Yamada, Y.; Matsuura, 1. In Proceedings of the 7th International Zeolite Conference Tokyo,Japan, 1986; Murakami, Y..Iijima, A., Ward, J. W., Eds.; Kodansha-Elsevier: Tokyo, 1986; p 587.
I
----
_-
1 2 log ( d r a d min-'1 Figure 4. FR data of the C3H8/5Asystem: (a) at T, = 200 OC (exp no. P-I); (b) at T, = 120 OC (exp no. P-3); (c) at T,= 90 OC (exp no P-4). (0) the in-phase components; (a) the out-of-phase components. The solid curves are theoretical (see text).
ca. 1 X lo3 kg/cm2, cut into small pieces, and dehydrated at 383 K for 24 h. The temperature was then raised to 623 K, and the system was evacuated at that level for at least 48 h up to
