J . Phys. Chem. 1990, 94, 5917-5921
.
. .. . PH
Figure 15. Comparison between the theoretical and experimental be-
5917
As a consequence, the free-energy minization has been performed with respect to the all independent variables which can be, in principle, measured, such as the sizes of the filled and unfilled reverse micelles, the occupation ratio, and the water amount of the oil phase. Practically, the most relevant constraints that have been maintained are those relative to the spherical shape of the reverse micelle and that of the constancy of the total interfacial area. The model represents an improvement also with respect to the version previously proposed by us19 in which some other constraints were maintained. Some relevant aspects of the related experimental results are well reproduced by the model; in particular: (i) the steep rise of the protein uptake curves as a function of the salt bulk concentration; (ii) the effect of pH; (iii) the variation of the filled and unfilled micelles radii following the protein uptake.
havior of the extraction vs the pH of the bulk water. Continuous line: theoretical results; points are taken from ref 7. for other proteins, e.g., lysozyme.
Acknowledgment. We thank Dr.M. Leser (ETH Zurich) for useful discussions and for having made available the data of w o reported in Figure 9. This work was supported by M.P.I. (40%).
Concluding Remarks The peculiarity of the present model is the maximum reduction of the arbitrary constraints in describing the protein uptake process.
Registry No. AOT, 577-1 1-7; NaCI, 7647-14-5; KCI, 7447-40-7; LiCI, 7447-41-8; cytochrome c, 9007-43-6.
Theory of Gas-Solid Adsorption Chromatography on Heterogeneous Adsorbents M. Jaroniec: X. Lu, and R. Madey* Department of Physics, Kent State University, Kent, Ohio 44242 (Received: May 19, 1989; In Final Form: March 5. 1990)
Presented here is a general integral equation for describing the total net retention volume in gassolid adsorption chromatography (GSC). This integral equation contains a distribution function that characterizesthe energetic heterogeneityof a solid adsorbent. For the gamma-type distribution function, this integral generates a simple analytical equation for the total net retention volume. Application of this analytical equation for describing the retention of n-hexane and 1-hexeneon controlled porosity glass demonstrated its utility for evaluating the physicochemical quantities that characterize gas-solid interactions and the energetic heterogeneity of the adsorbent.
Introduction Gas chromatography (GC) is one of the most attractive methods used in the physicochemical studies.I4 One of its variants, gassolid adsorption chromatography (GSC), is utilized often for studying adsorption and There is an extensive literature dealing with the use of GSC for evaluating the adsorption isotherms, the specific surface area of adsorbents and catalysts, the fundamental thermodynamic functions, and even the adsorbent heterogeneity. These problems are discussed in the recent monograph by P a r y j ~ z a k . ~ Although significant developments in the theory of gas adsorption on heterogeneous solids occurred during the past two decades,g17there is no comparable development in the GSC theory of retention on heterogeneous adsorbents. In the 1970s, some dealing with the use of GSC for evaluating adsorbent heterogeneity were published and described in recent monographs.’.* Experimental and theoretical ~ t u d i e s ~ Jrevealed & ~ ~ the great utility of GSC measurements for characterization of adsorbents and catalysts and for evaluation of the energetic heterogeneity of these solids. In this article, a theory of retention in GSC is formulated on the basis of a general integral equation, which represents the total ‘Permanent address: Institute of Chemistry, M. Curie-Sklodowska University, 20031 Lublin, Poland. 0022-3654/90/2094-59 17$02.50/0
net specific retention volume for energetically heterogeneous solids. A simple analytical equation for the total net specific retention (1) Conder, J. R.; Young, C. L. Physicochemical Measuremeni by Gas Chromatography; Wiley: Chichester, U.K., 1979. (2) Laub, R. S.; Pecsok, R. L. Physicochemical Applications of Gas Chromatography; Wiley: New York, 1979, ( 3 ) Locke, D. C. Ado. Chromatogr. 1976, 14, 87. (4) Katsanos, N. A.; Karaiskakis, G. Adu. Chromatogr. 1984, 24, 125. ( 5 ) Vidal-Madjar, C.; Gonnord, M. F.; Guiochon, G. Ado. Chromatogr. 1975, 13, 177. (6) Kiselev A. V.; Jashin, I. Gas Chromatography; Nauka: Moscow, 1967 (in Russian). (7) Paryjczak, T. Gas Chromatography in Adsorpiion and Catalysis; Wiley: Chichester, U.K., 1986. ( 8 ) Jaroniec, M.; Madey, R. Physical Adsorption on Heierogeneous Solids; Elsevier: Amsterdam, 1988. (9) Jaroniec, M. Ado. Colloid Interface Sci. 1983, 18, 149. (10) Jaroniec, M.; Patrykiejew, A.; Borowko, M. Prog. Surf. Membr. Sci. 1981, 14, I . (11) Jaroniec, M.; Brauer, P. Surf. Sci. Rep. 1986, 6, 65. (12) Jaroniec, M.; Choma, J. Chem. Phys. Carbon 1989, 22, 197. (13) Cerfolini, G. F. Spec. Period Rep.: Colloid Sci. 1982, 4, 53. (14) Cerfolini, G. F . Thin Solid Films 1974, 23, 129. (1 5 ) House, W. A. Spec. Period Rep: Colloid Sci. 1982, 4, 1. (16) Ostrovsky, V. E. Usp. Khim. 1976, 45, 850. (17) Sircar, S.; Myers, A. L. Surf. Sci. 1988, 205, 353. ( I 8 ) Waksmundzki, A.; Rudzinski, W.; Suprynowice, Z.; Leboda, R.; Lason. M. J. Chromatogr. 1974, 92, 9.
0 1990 American Chemical Society
5918
Jaroniec et al.
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990
volume VN,l is generated by this integral equation for heterogeneous solids with the gamma-type distribution function of the Henry’s constant K. Prior to this work, no analytical equation existed for VNdthat satisfies Henry’s law and gives a satisfactory description of gas retention by a heterogeneous solid. Experimental verification of this analytical equation demonstrated its utility for describing retention in GSC and for characterizing the adsorbent heterogeneity.
Theory Thermodynamic quantities are usually evaluated from the net specific retention volume VN, which is defined as follows:1 VN = (VR- V d / m
(1)
Here VR is the corrected retention volume, V, is the void retention volume, and m is the adsorbent mass. The net specific retention volume VN is associated with the specific adsorbed amount n through the following relationship:22 VN
= j(an/ap)T
where L
no =
VN = j R T ( d n / d p ) T
(3)
Here p is the adsorbate pressure and R is the universal gas constant. Equation 3 was utilized also in previous works dealing with GSC.’s-21 For heterogeneous solid surfaces, the total specific adsorbed amount n, is a simple sum of the amounts nl adsorbed on the I-th type of adsorption site for I = 1, 2, ..., L; i.e., L
En/ I= 1
(4)
Here L is the total number of different types of adsorption sites. According to eqs 2 and 4,we have
En?
I= I
Here no denotes the total number of adsorption sites andfi is the fraction of adsorption sites of the I-th type. If the total number of types of adsorption sites is large (i.e., L a),then the summation in eq I O may be replaced by integration
-
where
(2)
Here p is the adsorbate density in the free gas phase, T is the absolute temperature, and j is the compressibility correction factor.22 For typical GSC systems, the adsorbate in the bulk (mobile) phase may be considered as ideal over a large region of adsorbate pressures. With this assumption, eq 2 gives
nt =
presentation of eq 6 in the following form
Fo(c) = n°F(c)
(14)
Here e is the adsorption energy, e, is the minimum adsorption energy, and F(c) is the distribution function o f t normalized to unity:
An analogous integral equation to eq 13 was considered elsewhere.Ig Adsorption on the I-th type of adsorption site may be represented by an isotherm equation that describes gas adsorption on an energetically homogeneous solid. It was shown elsewhereI9 that the Jovanovic-type isotherm equation leads to a simple equation for the retention volume PN.The Jovanovic adsorption isotherm is given by23 8 = 1 - exp(-Kp) (16) where
For low adsorbate pressures, eq 16 reduces to the Henry’s law 8 = Kp
or L vN,t
=
xVNJ I= I
Here denotes the total specific net retention volume and VN,/ denotes the net specific retention volume referring to the I-th type of adsorption site. Let us denote the relative coverage of adsorption sites of the I-th type by 81; then
(18)
where K is the Henry constant for an energetically homogeneous solid and KOis the temperature-dependent preexponential factor of this constant.s It was shown elsewheres that at moderate pressures eq 16 produces an adsorption isotherm analogous to the Langmuir isotherm. The specific retention volume PNassociated with eq 16 is given by P N = jRTK exp(-Kp) (19) Substitution of eq 19 to the integral eq 13 gives
where
VN,t(p)
= jRTno
jm K exp(-Kp)
F(c) de
(20)
tm
81 = nl/np
(8)
Here np is the total number of adsorption sites of the I-th type. Let us define a specific retention volume PN,/ associated with the relative coverage 8,: PNJ
= jRT(a81/ap)T =
(9)
vN.l/n?
The specific retention volume PN,/ defined by eq 9 permits ~~~
~~~
(1 9) Suprynowicz, Z., Jaroniec, M.; Gawdzik, J. Chromatographia 1976, 9, 161 (20) Gawdzik, J.; Suprynowicz, 2.;Jaroniec, M. J . Chromatogr. 1977, 131, 7. (21) Leboda, R.; Sokolowski, S. J . Colloid Interface Scr. 1977, 61. 365 (22) Conder, J. R , Prunell, J. H . Truns. Faraday Soc. 1968, 64, 3100
where K is a function of the adsorption energy c (cf. eq 17). Equation 20 may be transformed to the following form
VN,,= jRTno
K exp(-Kp) G(K) dK
Jm
K,
(21)
where G(K) = (RT/K)F(e(K))
(22)
Km = KOexP(em/RT) (23) Here K, is the constant K associated with the minimum adsorption energy em. (23) Jovanovic, D. S . Kolloid 2.Polym. 1969, 235, 1203
Gas-Solid Adsorption Chromatography
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 5919
Because the distribution function G(K) is associated with the normalized energy distribution function F(t)(cf. eq 15), it satisfies the following normalization condition:
Ll
G ( K ) dK = 1
p+I
G(K) = r ( m + l ) (K - K,)"' exp[-q(K - K,)]
for K L K, (25)
Here q and m are parameters of the gamma distribution. Substitution of eq 25 to the integral eq 21 gives
sm
K(K - K,,Jm exp[-Kp -
K,
d K - Km)1 dK (26) To solve the integral eq 26, let us introduce the new variable k=K-Km
(27)
Equation 26 rewritten in terms of the new variable k assumes the following form: VN,~= bRTnoqm+l/I'(m+l)]
1-(k + K,)km exp[-qk 0
(k
= URTnoqm+l/I'(m+l)](K, exp(-K,,,p) exp[-k(p+q)] dk
+ exp(-K,,,p)
xm
sm 0
+ Km)pl dk
km x
km+I exp[-k(p+q)] dk) (28)
The integrals appearing in eq 28 may be solved analytically;26the final equation for the total net specific retention volume is VN,~= jRTno exp(-K,,,p)
(
p)m+l[ Km +
-
1
(29)
Equation 29 may be expressed in terms of the average value
K and the dispersion uK;these quantities characterize the gamma
distribution function given by eq 25. The average value K associated with the gamma distribution function (viz., eq 25) is given by K=Km+Kf
uK is
(24)
From the several analytical functions that satisfy physical requirements, the gamma-type distribution function is the best one because it is capable of representing simple distributions with almost symmetrical, asymmetrical, or even exponential shapes. The gamma distribution function satisfies all physical requirement$ and leads to the relatively simple eq 29 for the net specific retention volume. Experimental studies of gas adsorption on heterogeneous solids24-25showed that this distribution is useful for representing heterogeneities of many solid adsorbents. SircarZ4 derived an isotherm equation for gas adsorption on heterogeneous solids by solving the adsorption integral equation for the gamma-type distribution function and the Jovanovic-type local isotherm equation. In this derivation, he neglected the minimum adsorption energy, which provides a significant contribution to the overall Henry constant on a heterogeneous solid. The derivation here is based on the integral equation for the total net specific retention volume and takes into account the abovementioned minimum adsorption energy. The above arguments led us to represent the distribution G(K) by the following gamma-type function:
VN,~= URTnoqm+I/r(m+1)]
The dispersion
(30)
expressed as follows: (TK
=
(m
+ I)Il2 4
(32)
and q = R f / u K 2
(33)
Thus m
+ 1 = (K'/uK)~
It is easy to show that the extrapolated retention volume VN,O = I i m W O ) VN,l associated with eq 29 is given by (34) The retention volume VN,Odefines the second gas-solid virial ~cefficient.~~2' The first derivative of the specific retention volume VN,t with respect to the adsorbate pressure p is associated with the third gassolid virial coefficient; calculation of this derivative for eq 29 gives
Equation 29 expressed in terms of K,, K', and uK assumes the following form vN,t
=
(vN,o/R)
(1
exp(-Kd)
+ puK2/K?-cR'/uK)'[K, + E'( 1 + paK2/X?-']
(36)
where K,K', and uK are defined by eqs 30,3 1, and 32, respectively.
Experimental Section Experimental verification of eq 36 was made by using the retention measurements reported el~ewhere.'~The gas-solid chromatographic (GC) measurements were carried out for nhexane and I-hexene on a controlled porosity of glass. The adsorbate 1-hexene from Poly Science Corp. (USA) had G C purity, whereas n-hexane from Reachim (USSR) was chemically pure. The controlled porosity glass was prepared in the Department of Physical Chemistry, M. Curie-Sklodowska University, Lublin, Poland:' from sodium borosilicate glass, which had the following composition: 7% Na20, 23% B2O3, and 70% S O 2 . The preparation method was analogous to that used by Haller.2s The BET specific surface area of this porous glass was equal to 50.5 m2/g. The G C measurements were carried out on a (GDR) Chromatron (GCHF 18.3) gas chromatograph with a thermal conductivity detector. Hydrogen purified by filtration through 5A molecular sieve pellets was used as a carrier gas with a flow rate of 50 cm3/min. The chromatographic column (3 m X 4 mm id.) was filled with 13.39 g of porous glass with a particle size between 0.2 and 0.3 mm. Before measurements, this column was conditioned overnight by flowing carrier gas at 473 K. All measurements were carried out at 374.2 f 0.1 K. The thermal conductivity detector was calibrated by injecting different amounts of the adsorbate with 1, 10, and 50 mm3 Hamilton microsyringes into a GLC column with 15% squalane on 0.2-0.3 mm Polsorb C.29 The experimental dependences of the specific retention volume VN,ton the adsorbate pressure p for n-hexane and 1-hexene were measured by the peak maximum elution method.30 These measurement conditions were chosen in order to minimize dynamic effects. Results and Discussion In order to illustrate the properties of the retention eq 36 associated with the gamma distribution function G(K), we cal-
where (27) Waksmundzki, A.; Suprynowicz, Z.; Gawdzik, J.; Dawidowicz, A.
(24) Sircar, S. J . Colloid Interface Sei. 1984, 101, 452. (25) Sircar, S. J . Chem. Soc., Faraday Trans. I 1984, 80, 1101. (26) Gradshteyn, 1. S.;Ryzhik, 1. M. Tables of Integrals, Series, and Products; Academic Press: New York, 1980.
Chem. Anal. (Wursaw) 1974, 19, 1033.
(28) Haller, W. J. Chem. Phys. 1965, 42, 686. (29) Dollimore, D.; Heal, G . R.; Martin, D. R. J . Chromatogr. 1970, 50, 209. (30) Huber, J . F. K.; Gerritse, R. G . J . Chromatogr. 1971, 58, 137
Jaroniec et al.
5920 The Journal of Physical Chemistry, Vol. 94, No. 15, 1990
TABLE I: Retention Parameters for a-Hexane and 1-Hexene on Controlled Porositv Class at 374.2 KE VN,O* Km, R’, OK, mL/g atm-l atm-l atm-’ 7.2 2.38 f 0.02 2.84 k 0.02 21.0 f 0.2 24.0 5.20 f 0.02 13.13 f 0.02 91.4 f 0.2
h
Y
adsorbate
Y
n-hexane I-hexene
103~0,
atm-I 1.60 1.23
a VN,O from eq 34, K, from eq 23, R’from eq 31, uK from eq 32, and KO from eq 17.
2 h
Y
Henry Constant, K (l/atm)
3
Figure 1. Distribution function G ( K ) calculated according to eq 25 for K, = 5 atm-I, K‘ = IO atm-I, and uK = 7, 15, and 30 at&.
E
v
0.5-
-. 0.3-_ 0.2-.
0.4
-O K = --- U K =
I;
‘I
7
“
2
15
2
5
“1 0
1
I
n-hexane * 1-hexene
o-bo
........ 0 ~ = 3 0
,it
5
I
0 10
0.05
0.15
Adsorbate Pressure, p ( a t m ) Figure 4. Specific retention volume VN,i for n-hexane (open circles) and 1-hexene (closed circles) on controlled porosity glass at 374.2 K in comparison to the theoretical lines predicted by eq 36.
0.1-h
F
2 w
0.0i 20
25
30
35
4.0
Adsorption Energy, a (kJ/mole)
Figure 2. Energy distribution function F(c) calculated according to eqs 37 and 25 for KO = 1.6 X IO-’ atm-’ and other parameters as in Figure
I. 3
2.+ B
I
-.
0.00 0
1:O
20
30
40
Henry Constsmt, K ( l / a t m )
Figure 5. Distribution function G ( K j for n-hexane and 1-hexene on controlled porosity glass at 374.2 K.
2
0.04 0.00
0.10
0.05
0.15
020
Adsorbate Pressure, p (atm) Figure 3. Retention volume v N , i / V,,: calculated according to eq 36 for the parameters as in Figure 1.
culated theoretical curves G(K),F(c), and VN,t. Figure 1 shows the gamma distribution function G ( K ) calculated for K , = 5 atm-I, E ’ = IO atm-I, and three different values of uK = 7, 15, and 30 atm-I. Because the maximum of the gamma distribution G ( K ) (viz., eq 25) occurs at K* = K, m/q, a peak-shaped distribution is observed for m > 0, which is equivalent to uK < K’. For uK = 7 atm-’ and R’= IO a t d , it is shown in Figure 1 that the G ( K ) curve is a peak-shaped distribution; however, for uK > R’the G(K) curves decrease exponentially. Figure 2 shows the curves of the energy distribution function F(c) associated with those shown in Figure 1. These curves were calculated according to the following equation:
+
F(c) = (RT)-’K(e) G ( K ( c ) )
(37)
where K is defined by eq 17. In these calculations, KOwas assumed to be equal to 1.6 X atm-I. It follows from Figure 2 that the F(c) curves have shapes analogous to the G ( K ) curves. Figure 3 presents the retention curves VN,i/VN,: associated with the distribution curves shown in Figures 1 and 2. These curves decrease monotonically and intersect in the region of moderate pressures. At a low pressure, the fact that the value of VN,,/VN,o
decreases when g K increases means that the ratio VN,t/V~,: is relatively small for strongly heterogeneous surfaces. To verify eq 36 experimentally, we used the retention volumes at 374.2 K for n-hexane and 1-hexene on controlled porosity glass.19 The specific retention volumes for n-hexane on controlled porosity glass were measured over a wider region of the equilibrium pressures than that for 1-hexene. The last retention point for n-hexane was measured at p = 0.21 atm, whereas the last retention point for 1-hexene was measured at p = 0.13 atm. In order to compare the chromatographic parameters for both n-hexane and 1-hexene on controlled porosity glass, the numerical analysis of the retention measurements was performed for the same pressure region; to satisfy this condition, we rejected the last eight experimental points for n-hexane, which were measured between p = 0.14 atm and p = 0.21 atm. In this region, the specific retention volume depends slightly on the equilibrium pressure; therefore, these points do not provide useful information about the adsorbent heterogeneity of the controlled porosity glass studied. Table I presents the best-fit parameters K,, K’,and uK for the systems studied. These parameters were calculated by using a nonlinear least-squares optimization procedure, which permits estimation of the errors for all best-fit parameters. Figure 4 shows the experimental specific retention volume VN,t for n-hexane and I-hexene plotted (as circles) against the adsorbate pressure p in comparison to the theoretical lines predicted by eq 36. It follows from this figure that eq 36 gives an excellent representation of these retention measurements. The distribution functions G ( K ) calculated for these systems according to eq 25 are shown in Figure 5 , whereas the energy distribution functions F(e) are plotted in Figure 6. These functions show an exponential behavior. The
J. Phys. Chem. 1990, 94, 5921-5930 h
2
>
0.08
-
0.08
E v ~
I(
I!
Lr
3 a
0.04
2
s a
0.02
t=l
2
0.00,
:
'
W
-n-hexane --- 1-hexene
I'
v
I\, ,
(25
30
35
Adsorption Energy,
E
--40
(kJ/mole)
Figure 6. Energy distribution function F(c) for n-hexane and I-hexene on controlled porosity glass at 374.2 K.
values of KOfor n-hexane and 1-hexene required to calculate F(t) were reported elsewhereI9 and are given in Table I. The parameters K,, E', and uK given in Table I characterize the adsorbent heterogeneity of the controlled porosity glass with respect to n-hexane and I-hexene. The parameter K , is defined by eq 23; it follows from this equation that K,,, is associated with the minimum adsorption energy for an adsorbate-adsorbent system. The sum of the parameters K , and K'gives the average value of the Henry constant K for a heterogeneous solid. The constant K = KO exp(c/RT) is associated with the exponentially averaged adsorption energy, which characterizes a heterogeneous adsorbent. The dispersion uK is associated with the width of the distribution function and characterizes the degree of the adsorbent heterogeneity in the sense that a small value of uK indicates a small
5921
energetic heterogeneity with respect to a given adsorbate, whereas a high value of uK is associated with strong energetic heterogeneity in the adsorbent-adsorbate system. Comparison of the parameters K and uK obtained for n-hexane and 1-hexene shows that K for I-hexene is higher than that for n-hexane because 1-hexene interacts strongly with the surface of the controlled porosity glass. Because of this strong interaction of I-hexene with the glass surface, this adsorbate is a better detector of the surface heterogeneity of the porous glass than n-hexane, which shows a weaker interaction with the glass surface. This observation is confirmed by the uKvalues; the dispersion uK for n-hexane is smaller than that for 1-hexene. The fact that both values of the dispersion uK are relatively high means that the energetic heterogeneity of the porous glass studied is significant. Because this porous glass contains boron and sodium atoms in addition to silanol groups, which appear in silica, the boron and sodium atoms represent the source of this significant increase in the energetic heterogeneity of the sodium borosilicate glass.jl Conclusion It is shown that eq 36 associated with the gamma distribution function G ( K ) gives a good representation of the total net specific retention volume measured as a function of the adsorbate pressure. The parameters of this equation are useful for calculating physicochemical quantities that characterize the adsorbate-adsorbent interactions and the adsorbent heterogeneity.
Acknowledgment. This work was supported in part by the National Science Foundation under Grant No. CBT-8721495. (3 1) Gawdzik, J.; Suprynowicz, Z.; Jaroniec, M. Chromarographia 1977,
IO, 191.
Fluorescence Quenching In Double-Chained Surfactants. 2. Experimental Results D. D. Miller: L. J. Magid,$and D. F. Evans**$ Eastman KodaklResearch, 66 Eastman Avenue, Rochester, New York 14650; Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996-2200; and Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 (Received: July 5, 1989; In Final Form: January 30, 1990)
The aggregation behavior of single- and double-chained ionic surfactants ( C I ~ N ~ C CI6N3ClOAc, IB~, C14N3ClBr,2CloN2ClBr, 2CI2N2CIOAc,2C12N2ClBr,2C14N2ClBr,2Cl4N2C10Ac,and ~ C ~ ~ N ~ C I Oand AC zwitterionic ) phospholipids (dicaproyland dipalmitoylphosphatidylcholine(2c6Pc and 2c,6Pc, respectively)) is investigated by time-resolved fluorescence quenching and small-angle neutron scattering measurements as a function of surfactant concentration, salt, and temperature. The double-chain surfactants with acetate as counterions form micelles whose aggregation number increases with surfactant concentration but is relatively independent of temperature. The transformation of the corresponding bromide surfactant from liposomes to micelles with increasing temperature is delineated; at intermediate temperatures, the solution contains mixtures of micelles and vesicles. Mixtures of zwitterionic surfactants transform from liposomes to micelles as the mole fraction of 2C6PC increases, with a vesicle-micelle equilibrium at intermediate values. The aggregation numbers for the single-chain acetate and bromide surfactants, which at low temperatures differ by a factor of 2, appear to approach one another at higher temperatures. These observations are analyzed in terms of specific counterion headgroup interactions and their variation with the field variables.
Introduction A major challenge in colloid science is to relate amphiphilic microstructure to molecular and field variables such as temperature, pressure, surfactant concentration, and added salt. With double-chain amphiphiles this problem is particularly acute because such compounds can assemble to form small spherical
'Eastman Kodak/Research. *Universityof Tennessee. @Universityof Minnesota.
0022-3654/90/2094-5921$02.50/0
micelles, vesicles, microtubules, or bilayers that constantly transform from one structure to another as temperature, counterions, and concentrations are varied.' The apparent simultaneous coexistence of several structures constitutes an added complexity.* ( I ) Miller, D. D.; Bellare, J. R.; Evans, D. F.; Talmon, Y.;Ninham, B. W. J . Phys. Chem. 1987, 91, 674. (2) Miller, D. D.; Evans, D. F. Fluorescence Quenching in Double-Chained Surfactants. 1. Theory of Quenching in Micelles and Vesicles. J . Phys. Chem. 1989, 93, 323.
0 1990 American Chemical Society
