1478
J. Phys. Chem. 1992,96, 1478-1482
is practically the same as the radius r for the phenol molecule in solution (2.77 A). This value can be obtained using the virial coefficient data given by Matteoll and LeporlI6 for the virial expansion of the osmotic pressure in this system. When the mole fraction of phenol is ca 0.008,[ starts to increase rapidly, until it has been doubled at a phenol concentration of ca. 0.016. The magnitude of this correlation length when compared to the molecular radius indicates a slight association between phenol and water molecules. This agrees with the aggregate formation assumption at those concentrations. (16) Matteoll, E.; Leporl, L. J. Phys. Chem. 1982, 86, 2994.
In conclusion, the whole picture of the aggregate formation as it is invoked in the interpretation of bulk and surface properties in phenol W agrees with the information extracted from the MDC's presented in this paper. In addition, it is important to note that MDC measurements are sensible enough to give part of the picture of the organization in the bulk of the solution in this kind of borderline systems.
+
Acknowledgment. We acknowledge the partial support of the DGAPA Grants IN 104189 and 102689. We thank J. Abarca for help in running the samples, and J.O.achowledges the support of CONACYT. Registry No. Phenol, 108-95-2.
Extension of Kohler-Strnad Viscoslty Model for Ionic Rod-Shaped Micelles of Low Axial Ratlo. Application to Sodium Deoxycholate Micelles A. Coello, F. Meijide, E.Roddguez N&z, and J. Wzquez Tato* Departamentos de Quimica Ffsica e Ffsica Aplicada, Universidade de Santiago, Campus de Lugo, 27002 Lugo, Spain (Received: June 18, 1991)
An extension of Kohler-Stmad model (J. Phys. Chem. 1990,94,7628) for the evaluation of viscosity measurements of ionic surfactants forming rod-shaped micelles of low axial ratio is proposed. The method is applied to sodium deoxycholatemicelles in aqueous solution of sodium chloride, chlorate, and salicylate at different electrolyte and surfactant concentrations. It has been observed that the difference between the fractional counterion association at the two terminal hemispherical caps and at the cylindrical part of the rod micelles, and the standard work for the reversible transfer of a surfactant ion between both parts, depend on the anion of the electrolyte used.
Introduction Viscosity measurements of bile salts solutions have been published in a number of unrelated papers by several authors.'-ll In general, all authors have found that viscosity depends on pH, electrolyte concentration (normally NaCl), temperature, buffer used to keep the pH constant, and bile salt concentration. At pH values close to neutrality several authors have found that the viscosity depends on the elapsed time from the preparation of solution,136but it becomes constant after a time (typically 1 hour). This behavior was attributed to a thixotropic effect (due to the mechanical influence of the viscometer)' and was interpreted in terms of a polymer-like aggregation and degradation of the aggregates as a consequence of the shearing stresse6 Also common is the observation of different regions for the dependence of viscosity with bile salt concentration. For NaDC, NaC and NaDHC (see Glossary for abbreviations) at the lowest bile salt concentrations, Fontell' observes a behavior of the viscosity typical for electrolyte solutions; since at intermediate concen( I ) Blow, D. M.; Rich, A. J. Am. Chem. Soc. 1960,82, 3566. (2) Vochtcn, R.; Joos, P. J . Chim. Phys., Chim. Biol. 1970, 67, 1372. (3) Fontell, K. Kolloid-2. 2. Polym. 1971, 246, 614. (4) Kratohvil. J. P. Colloid Polym. Sci. 1975, 253, 251. (5) Barry, B. W.; Gray, G. M. T. J. Colloid Interface Sci. 1975, 52, 314, 327. (6) Sugihara, G.; Tanaka, M.; Matuura, R. Bull. Chem. SOC.Jpn. 1977, 50, 2542. (7) DArrigo, G.; Sesta, B.; La Mesa, C. J. Chem. Phys. 1980, 73, 4562. (8) Sesta, B.; La M m , C.; Bonincontro, A.; Cametti, C.; Di Biasio, A. Ber. Bunsen-Ges. Phys. Chem. 1981,85,798. (9) Giiveli, D. E. Colloid. Polym. Sci. 1986, 264, 707. (IO) Gtiveli, D. E. J . Chem. SOC.,Faraday Trans. 1 1985, 81, 2103. (1 1) Zakrzewska, J.; Markovic, V.; Vucelic, D.; Feigin, L.; Dembo, A,; Mogilevsky, L. J . Phys. Chem. 1990, 94, 5078.
trations the viscosity obeys Vand'sI2 equation, he accepts that the micelles are spherical in shape and highly hydrated. Finally, this author deduces that micelles are anisometric at the highest concentrations of bile salts. Similarly, Vochten and Jm2observed the existence of a second cmc (which is dependent on NaCl concentration) and Sesta et ala8observed a break point in the expected straight line according to Vand's12 equation which was interpreted in terms of a primary superaggregation. Giiveli9 has evaluated the viscosity for NaDC from the apparent specific volume suggesting the existence of secondary aggregates. A similar conclusion was obtained by the same authorlo for NaTDC from his evaluation of Schurtenbergeret al.I3results of light scattering. He also concluded that the secondary micelles (formed at [NaTDC] > 40 g/dm3 and [NaCl] = 0.8 M) are rodlike in shape and flexible. Other viscosity measurements imply the study of mixed micelles of bile salts and tetralkylammonium bromides carried out by Barry and Gray,Swho found a minimum in the viscosity for an equimolecular mixture of both surfactants, or the studies by Sesta et al.'I in water solutions of urea. It is clear from this short review on viscosity for bile salts solutions that although important conclusions have been obtained, most of the information is essentially qualitative or semiquantitative in nature. This in fact reflects the state of art in the theoretical background necessary for interpretation of viscosity data. Recently, Kohler and StrnadI4 have published a new evaluation of viscosity measurements of dilute solutions of ionic surfactants (for references of previous models see the literature (12) Vand, V. J . Phys. Colloid Chem. 1948, 52, 277. (13) Schurtenberger, P.; Mazer, N.; KBnzig, K. J. Phys. Chem. 1983,87, 308. (14) Kohler, H. H.; Strnad, J. J . Phys. Chem. 1990, 94, 7628.
0022-3654/92/2096-1478$03.00/00 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1479
Kohler-Strnad Viscosity Model cited by these authors). This theory allows the determination of the energy transfer of a monomer from the bulk solution to the cylindrical or hemispherical parts of a rod-shaped micelle. They have applied the theory to a typical long alkyl chain surfactant as hexadecylpyridiniumnitrate or bromide. The mathematic approximations introduced by Kohler and Stmad in their model (see eq 6 of their paper) originate that the final resulting equations are only valid for rod-shaped micelles of axial ratio (expressed as (f)v0.5) higher than 6. Therefore, we first present an extension of such model for lower axial ratios. Second, since the rigid steroid nucleus of bile acids and salts determines a quite different structure of bile salts micelles (for which different models have been p u b l i ~ h e d ' ~and J ~ criticized elsewhere") compared with linear alkyl chain micelles, it should be interesting to determine the corresponding transfer energies for NaDC micelles in different electrolyte solutions and compare them with the values for the micelles of linear alkyl chain surfactants. Kolder-Stnud Association Model for Rod-ShapedMicella For the interpretation of viscosity data Kohler and Strnad (KS model) use two types of models: one to describe viscosity as a function of the size distribution of the rods, and one to describe the actual size distribution of the micelles as a function of the composition of the solution. According to their association model for the formation of rod-shaped micelles (eq l), the corresponding nA [ysns yc(n - n,)]B M (1)
+
K(n)
+
exPk[PoM(n) - nPoA - (y$
+ (ys - rc)ns)P"B]/kBn
(2) equilibrium constant is given by eq 2, where n is the total aggregation number, n, the aggregation number in the two hemispherical caps, y, and ycare the fractional counterion association coefficients of the hemispherical and cylindrical parts of the micelle, A is the surfactant ion, B is the counterion, and PO'S are the chemical potentials for the micelle, monomer, and counterion. poM(n)is supposed to be a linear function of n, i.e. PoM(n)= woS + (n - n s ) ~ O c (3) where N O , and PO, are independent of n. The standard works, wo, and woc,for the reversible transfer of a free surfactant ion from the bulk solution to the hemispherical and cylindrical parts of the micelle are Wos = P0s - P o A - ?&OB (4) Woc = P0c - P o A - Y&OB (5) Therefore, the standard work, Awo, for the reversible transfer of a surfactant ion from the hemispherical to the cylindrical part of the micelle will be AwO woC- wO, (6) and if the effect of a variable counterion concentration cB is included, then the standard work becomes AW* AWo - kBTAy In (CB/C,) (7) where Ay = yc- 7,. Other definitions given by Kohler and Strnad are the characteristic concentrations c*, and c*, given by
exp(wO,/kBT) = (c*,/c,)~+~. exp(wO,/k&I = (c*c/c,)l+~c and a further critical micelle concentration, cmc, by
(8) (9)
cmc c * ~ ( c * ~ / c B ) ~ c (10) They also define the reduced concentration f Agiven by (15) (a) Small, D.M. Adv. Chem. Ser. 1968,8431. (b) Carey, M. C.; Small, D.M. Arch. Int. Med. 1972, 130, 506. (16) Esposito, G.; Giglio, E.; Pavel, N. V.; Zanobi, A. J. Phys. Chem. 1987, 91, 356. (17) Campanelli, A. R.; de Sanctis, S. C.; Giglio, E.; Pavel, N. V.; Quagliata, C. J . Inclusion Phenom. Mol. Recog. Chem. 1989, 7 , 391.
= ZA/Co8 (1 1) where EA is the concentration of surfactant ions incorporated into micelles, c, is the surfactant concentrationin the condensed state (c, = (NAt9)-'; NA is the Avogadro constant, t9 is the volume of a surfactant molecule), and 6 is given by 6 = eXp(n,AW*/kBT) (12) From eqs 7 and 12 is deduced f A
6j/Si
= (cB,/cB,)-~'".
(13)
From eqs 8-10, 6 may be rewritten as
6
(~~)-Ayq(~*~)(l+~rA~)q(C*,)-(l+r3s
(14)
Kohler-Stmad Viscosity Model Extended to Micelles of Low Axial Ratio For the viscosity model Kohler and Stmad start with a limiting expression of the theoretical "intrinsic viscosity" or "shape factor" (defined by eq 15; see the appendix of their paper) which is valid Aqre1/4
Aqlre~= (7
with
b
2n
-to)/~c
(15)
1
only for axial ratios, f (defined by eq 16) higher than 3, although in later approximations this limiting value is increased till approximately twice the original one ( q is viscosity of the solution, qo viscosity of the solvent (pure or not), a micelle diameter, and b micelle length). It is not possible to apply directly the KS model to viscosity measurements for NaDC micelles in electrolyte solutions, since Esposito et a1.16 have found axial ratios ranging from 2.8 (at 0 ionic strength) to 6.6 (at 0.75 ionic strength) in NaCl water solutions. A quite simple extension of KS model for micelles of axial ratios lower than 12, is to approximate the exact s ~ l u t i o n ' ~ Jfor * - the ~~ dependence of s on f to the second-order polynomial defined by eq 17: s = p + qf+ r p (17) With values o f p = (2.5 - q - r), q = 0.1859, and r = 0.09742, the average relative error between the calculated and exact equation is 1.6%. Since micelles are polydisperse particles, the intrinsic viscosity, s (given by eq 15), equals the volume average of the right-hand side of eq 17, Le. = (p + 4 f + r f ) , = p + q ( n , + Taking into account eq 16, it follows that
rV),
3
s = (p
(18)
+ 4q/9 + r/9) + (2q/3 + 4r/9)- (n), + (4r/9)- (n2) n,
ns2
(19) where (n),/n, and (n2),/h2 are calculated by using the previous association model. Accepting the asymptotic relations (eqs 23 of KS paper)
(ny),/n;
eq 19 is reduced to s = (p 4q/9 r/9)
+
+
= (v
+ i)!(fA)0,5v
(20)
+ (4q/3 + 8r/9)(fA)0.S+ (8r/3)fA (21)
When f A2 6 (which is the case of the values shown in Table I), the error introduced by this simplification is lowfr than 10%.14 Starting from s experimental values, we obtain r A from eq 21, which following eq 1 1 should be a straight line with slope l/(ca6). Knowing the rest of parameters (see Results and Discussion) we can calculate the standard works wo, and wo,. (18) Simha, R. J . Phys. Chem. 1940,44, 25. (19) Kuhn, W.; Kuhn, H. Helu. Chim. Acta 1945, 28, 97.
Coello et al.
1480 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
50]
A
TABLE I: Experimental Values of the IaMnsic Vkasity for NaDC in Different Electrolyte Solutio" INa+l/M [NaDCI/M s = Aw,J& f, slow C1- Anion
CNs:j=6;4 M [Ns,]=0.3 M [No 3=0.2 M
0.25
0.30
SA
concentrations.
0 0
A
30
*
1
0.5 0.5 0.5 0.5 0.3 0.3 0.3 0.3
0.250 0.200 0.150 0.100 0.250
289 f 2 229 f 12 209 f 5 188 f 8
11.80 10.81 8.99 8.82 7.46 7.25 6.73 5.33
30.0 26.5 20.0 19.5 14.5 14.0 13.5 7.5
161 f 6
14.59 11.40 9.70 7.98 16.53 12.72 9.87 7.69
0.200 0.150 0.100
39.5 28.5 22.5 16.5 46.5 33.0 23.0
153 f 4
172 f 7
15.5
a For the calculation of f, see eq 21 in the text. The slopes correspond to plots of Figures 1-3.
10-
n
0.00
0.176 0.143 0.141 0.114 0.106 0.0857 0.0706 0.057 1
35.3 23.0 46.0 40.5 22.5 33.0 26.5 15.5 37.5 20.0 17.5 6.0
Sal- Anion
[Na']=0.5 M [Na']=0.4 M CNa'l=0.3 M [No']=0.2 M
i
20
0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2
13.31 9.85 16.34 14.76 10.25 12.65 10.91 7.72 13.90 9.03 8.28 4.72
Chlorate Anion
Figure 1. Reduced concentration f, vs FA at different sodium chloride
rA
0.4 0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.2
0.122 0.0800 0.218 0.160 0.0972 0.164 0.120 0.0729 0.2 0.109 0.0800 0.0486
0.5
0.05
0.10
0.15
0.20
concentrations.
Results and Discussion Table I shows the experimental results of the intrinsic viscosity at different NaDC and electrolce concentrations. vs EA at different Na+ conFigures 1-3 show the plot of centrations for the three electrolytes used. The corresponding slopes are also shown in Table I. To calculate 6 from such s l o p is necessary to know c,. From the X-ray study by Campanelli and co-workersZ0on NaDC
404
301
SA
Figure 2. Reduced concentration f, vs F A at different sodium chlorate
Experimental Section The NaDC was from Sigma and was used without further purification. Other inorganic and organic chemicals were Merck. The solutions were tested by conductimetrictitration against HC1. Densities were measured in an Anton Paar Model DMA-45. Viscosities were measured in a simple falling ball viscometer. Its reproducibility is better than 0.5%. The pH of all solutions was in the range 7.8-8.1, high enough to ensure that the concentration of deoxycholic acid is negligible. All measurements were camed out at 25.0 f 0.1 OC. Volume fractions, 4, were obtained from the measurement of density of solutions. Once s was obtained from experimental measurements, eq 21 was used to calculate FA. Since the NaDC concentrations are relatively high, the experiments were designed to obtain the viscosity at constant [Na+] concentrations by adding the necessary amount of NaX (X = chloride, chlorate, salicylate).
501 20
I I I I , I I I , I I I , I Y r m , , , , , , ' ' ' ' ' ~ , , I , , , , l , , , , , n m
0.00
0.05
0.10
0.15
0.20
0.25
0.30
SA
Figure 3. Reduced concentration f, vs EA at different sodium salicylate concentrations.
crystals, a volume of 12.15 nm3 is deduced for the volume of a cell. This cell contains 72 molecules of water and 18 molecules of NaDC. Accepting that each water molecule has a volume of 0.03 nm3 (deduced from its molar volume at 25 OC), the volume occupied by all water molecules is 2.16 nm3. Therefore, the volume of NaDC can be estimated as 10/18 nm3. This implies that c, = 2.99 M. From the slopes in Table I we calculate the corresponding 6 values. Figures 1-3 and Table I show that the anion of the electrolyteused influences the values of 6: it decreases with increasing [Na+] in the presence of chloride anion, and it is ~~
~~~
(20) Campanelli, A.; Ferro, D.; Giglio, E.; Impexatori. P. Thermochim. Acta 1983, 67,223.
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1481
Kohler-Strnad Viscosity Model
TABLE Ik Values of the Fractional Counterion Asmciation Coefficients, Standard Works for the Reversible Transfer of a Surfactant Ion from the Bulk Solution to the Micelle, and Characteristic Concentrations for NaDC in Different Electrolyte Concentrations electrolyte anion
c1c10; SalN03OROWS
Y C
0.21 0.21 0.21 0.76
c*,/mM 2.37 2.37 2.37 0.60
wo,/kBT -8.64 -8.64 -8.64 -15.17
6)
Ys
0.174 0.21 0.23 0.735
0
-0.019 0.025
c*$/mM 4.69 4.18 3.23 0.61
was/ kBT
Awe/ keT
-7.58 -7.95 -8.40 -14.91
-1.06' -0.69' -0.24' -0.26b
correspond to NaDC. *The nitrate row corresponds to the values obtained by Kohler and StrnadI4 for hexadecylpyridinium nitrate.
-6.30; In(
AY
0.036
1
3
-6.40;
-6.50;
-6.60;
-6.701 0 I I , / / / ~ I I I I , 1 I I I , I I I I I I I / II I I / I I I I I I I I L I , I I I I
I , , ,
-1.60 -1.40 -1120 -1.00 -01801'lE;160 In
(cg)
reversible work for the transfer of a single surfactant ion from the hemispherical caps to the cylindrical part of the micelle, Awo, is almost 5 times more favorable for the bile anion in the presence of chloride anions, twice in the presence of chlorate, and equal in the presence of salicylate. The big difference when NaCl is used as the electrolyte (the only one which can directly be compared with the Kohler and Strnad result) may be interpreted as an indication of a different internal structure of the micelle formed by long-chain surfactants and bile salts. This is consistent with the model proposed by Giglio et al." in which there are hydrogen bonds and ion-dipole and ion-ion interactions in the center of the helical micelle and hydrophobic interactions through methyl groups at the surface of the micelle. This situation is just the opposite of normal micelles where the hydrophobic groups are inside of the micelle and the hydrophilic groups (normally, ionic groups) are on the surface. It is easy to show that the thermodynamical model proposed by Kohler and Strnad for a rod-shaped micelle with terminal hemispherical caps is equivalent to a system formed by spherical (eq 24) and cylindrical micelles (without terminal caps, eq 25).
Figure 4. Plot of In S vs In (cB/M) according to eq 23 (see text) for
n,A
NaDC in sodium chloride solutions.
constant when the anion is chlorate and increases in the presence of salicylate. The value of yccan be estimated as the slope of log (cmc/M) vs log ([Na+]/M) and ZA is calculated as cA(total) - cmc. We have used the experimental results from Carey and Small" and Vochten and Joos2 obtaining the equation log (cmc/M) = -3.176 - 0.21 log ([Na+]/M) (22) Le., yc = 0.21. By measuring the freezing point depression, we have observed that the intercept and the slope in eq 22 are not influenced by the electrolyte anion. Therefore, we have used the same values for all three sets of experiments. According to eq 14 (or eq 13) the plot of In 6 vs In (cB/M) should be a straight line. The fit of experimental results gives In 6 = -(7.00 f 0.13) - (0.44 f 0.11) In (cB/M) (23) for the chloride set of experiments (Figure 4). In the case of chlorate there is not a clear tendency, and consequently we have accepted that Ay = 0. Finally, in the presence of salicylate, we have only two experimental points but the slope of that plot should be positive. To obtain Ay from eq 23, it is necessary to know 4.Esposito et a1.I6 have found that the structure for NaDC micelles is a left-handed helix with a pseudo-six-fold screw axis. We will accept here that n, is 12, i.e., six NaDC molecules for each terminal of the helix. Following Small15this number is close to the maximum number of molecules which can be packed in a back-to-back configuration in a primary micelle. Taking into account eqs 10 and 22, a value of 2.37 mM is obtained for c*, and from eq 9, wO, can be estimated. From these calculations and eqs 14 and 23, values of c*, are obtained, and using eq 8, wo, is calculated. Finally, Awo is also deduced. Table I1 resumeS all the obtained values, and we have also written the values obtained by Kohler and StmadI4for hexadecylpyridinium nitrate. For this surfactant wo, and wocare approximately double the values we have obtained here. This means that the standard work for the reversible transfer of a surfactant ion from the bulk solution to the micelle is 2 tima more favorable for the long-chain surfactant than that for rigid deoxycholate ion. However, the
n& with
+ TsnsB * M, + ycn,B M, n, = n - n,
In fact, this is a direct consequence of the linear function for the calculation of poM(n)expressed by eq 3. The corresponding equilibrium constants will be K S ( ~ S=) exP(-nswos/ kB T )
(26)
Kc(nc) = exp(-ncwOc/kBT) Therefore, K(n) (eq 2) is
(27)
K(n) = K,(ns) Kc(n,) (28) Using previous values and considering n, = 84 (which corresponds to a total aggregation number of 96 determined by Esposito et at [NaCl] = 0.60 M), values of log K, = 38, log K, = 307, and log K = 345 are deduced. The value of log K, is much lower than the one reported by MoroiZ1for sodium dodecyl sulfate (log K, = 240, n, = 68) or that deduced from Kohler and StrnadI4 results for hexadecylpyridinium nitrate (log K, = 518; n, = 80). We can also estimate a value of wo, = -8.13kBT for sodium dodecyl sulfate from the log K, and n, values given above. A comparison of all wo, values indicates that equilibrium constants depend more strongly on the aggregation number than on the standard works for the reversible transfer of a surfactant ion from the free solution to the spherical micelle. On the other hand, Mazer et a1.22have carried out a QLS study on sodium salts of TC, TDC, TCDC, and TUDC bile acids solutions. They analyze their experimental results according to a stepwise thermodynamical model following the primarysecondary association model of Small.I5 The polymerization constant K for the aggregation of a primary micelle to a secondary micelle is supposed to be the same for each aggregation step. In eq 29 we write the simplest polymerization reaction, i.e., the formation of (21) Moroi, Y . J . Colloid Interface Sci. 1988, 122, 308. (22) Mazer, N. A.; Carey, M. C.; Kwasnick, R.F.;Benedek, G.B. Biochemistry 1979, 18, 3064.
J. Phys. Chem. 1992, 96, 1482-1490
1482
a secondary micelle from two primary micelles: M,+ M,* M, K
(29)
Accepting that yc = ya i.e., Ay = 0 and n, = ns, we deduce that
K = ~(n)/[Ks(ns)l*
(30)
or
K = exp(-n8Awo/kBn
(31)
Mazer et report an aggregation number of 10 for the formation of a primary micelle, Le., n, = 10. Accepting our Awo values and AGO = -RT In K,it is deduced that AGO varies in the range -1.3 to -6.7 kcal/mol. Although several simplifications are involved, such values are very close to those obtained by Mazer et al. (from -3.8 to -6.7 depending on experimental conditions) for the above-mentioned bile salts. Giglio et al.” have demonstrated the advantages of the helical model compared with the Small model for deoxycholate derivatives. The previous aggreement could mean that such a model is also valid for other bile salts.
The effect of the electrolyte anion on the value of Ay found in this paper has not been considered in KS model and further developments are required. Acknowledgment. We thank the Xunta de Galicia for financial support (project XUGA29906A90). Glossary cmc critical micelle concentration QLS quasi-elastic light scattering NaDC sodium deoxycholate NaC sodium cholate NaDHC sodium dehydrocholate NaTDC sodium taurodeoxycholate TC taurocholic acid TDC taurodeoxycholic acid TCDC taurochenodeoxycholic acid TUDC tauroursodeoxycholic acid Salsalicylate anion M mol d n i 3 mM mol m-’ Registry No. NaDC, 302-95-4; NaCI, 7647-14-5;NaClO,, 7647-14-5; Nasal, 54-21-7.
Molecular Dynamics Studies on Zeolites. 6. Temperature Dependence of Diffusion of Methane In Siiicaiite P. Demontis, G.B. Suffritti,* Dipartimento Chimica, Universith di Sassari, Via Vienna 2, I-071 00 Sassari, Italy
E.S . Fois, Dipartimento di Chimica Fisica ed Elettrochimica, Uniuersith di Milano, Via Golgi 19, I-20133 Milano, Italy
and S. Quartieri Istituto di Mineralogia e Petrografa, Universitd di Modena, Via S. Eufemia 19, I-41 100 Modena, Italy (Received: June 20, 1991)
The effect of the temperature on the diffusion of methane in silicalite was studied by molecular dynamics both using a model where the vibrations of the zeolite framework are taken into account and keeping the framework Fled. Methane molecules were represented by Lennard-Jones particles. The diffusion coefficients were evaluated at four different temperatures in the range 150450 K and resulted in good agreement with experiment. The effect of the vibrating framework on the diffusive process is discussed and a detailed analysis of the behavior of methane molecules in silicalite is reported.
Introduction The elucidation of the behavior of fluids within narrow pores and cavities has received much recent attention.I-l0 Among the (1) Rowlinson, J. S.;Widom, B. Molecular theory of capillarity: Clarendon Press: Oxford, 1982. (2) Henderson, J. R. Mol. Phys. 1983, 50, 741. (3) Walton, J. P. R. B.; Quirke, N. Chem. Phys. Lett. 1986, 129, 382. (4) Davis, H. T. Chem. Phys. 1987.86, 1474. Vanderlick, T. K.; Davis, H.T.J. Chem. Phys. 1987,87.1791. Vanderlick, T. K.; Scriven,L. E.;Davis, H. T. J. Chem. Phys. 1989,90, 2422. ( 5 ) Snook, I. K.; van Megen, W. J. Chem. Phys. 1980, 72,2907. (6) Magda, J. J.; Tirrell, M.; Davis, H. T. J. Chem. Phys. 1985,83, 1888. ( 7 ) Heffelfinger, G. S.;van Swol, F.;Gubbins, K. E. Mol. Phys. 1987,61, 1381. (8) Panagiotopoulos, A. 2.Mol. Phys. 1987, 62, 701. (9) Woods, G. B.;Panagiotopoulos, A. Z.; Rowlinson, J. S . Mol. Phys. 1988, 63, 49. (10) Heffelfinger,G. S.; van Swol, F.; Gubbins, K. E. J. Chem. Phys. 1988, 89, 5202.
different methods employed to study this topic, computer simulation experiments are playing an increasingly important role, because many properties of fluids in porous media become inaccessible to experimental measurements when the characteristic dimensions of the confining medium approaches molecular scale. These techniques have been mostly employed within idealized representations of pores, generally a slit, a cylinder, or a sphere, in order to confirm the results of some theoretical approaches. In this paper we attempt to model a real microporous material, namely a molecular sieve (zeolite), in order to compare an atomic description with the available experimental results. The importance of zeolites, a variety of porous aluminosilicates which are well-known for their industrial applications as adsorbants, molecular sieves, and catalysts, has stimulated conspicuoustheoretical work*I-l3 in order to elucidate their interesting properties. (11) Sauer, J.; Zahradnik, R. Inr. J. Quantum. Chem. 1984, 26, 793. (12) Suffritti, G. B.; Gamba, A. Int. Reu. Phys. Chem. 1987, 6, 299.
0022-365419212096-1482$03.00/00 1992 American Chemical Society
