2560
J . Phys. Chem. 1990, 94, 2560-2566
Alkali Metal Ion Transport through Thin Bilayers Robert T. Hamiltont and Eric W. Kaler*%t Department of Chemical Engineering, BF- 10, University of Washington, Seattle, Washington 981 95 (Received: April 13, 1989; In Final Form: October 10, 1989)
The mechanism of alkali-metal transport across the bilayer wall of vesicles made from double-tailed synthetic surfactants has been determined. In aqueous solution, the alkali-metal cations sodium, potassium, and cesium pass through the bilayer of sodium 4 4 1-heptylnonyl)benzenesulfonateand sodium 4-( 1-nonylundecyl)benzenesulfonate as unhydrated, unassociated cations. Transport occurs through transient holes in the vesicle bilayer; surfactant monomers rearrange such that only head groups are exposed to the aqueous medium in the pore (so-called "inverted pores"). Other mechanisms such as passage of hydrated ions or solvation of ions or ion pairs in the membrane are not active. Measured activation energies for cation transport through pure bilayers are consistent with the proposed mechanism.
1. Introduction Observations of dispersions of unilamellar surfactant vesicles offer potential for insight into the fundamental mechanisms of ion transport across pure membrane bilayers, and in a more practical vein such dispersions may be useful as a microscale separations medium. While vesicle solutions typically encapsulate less than 1% of the aqueous solution in which they are formed, the high vesicle surface area (- IO4 cm2/mL of solution at 1% surfactant) means that high transport rates can be achieved. For systems with a low concentration of the desired component, concentration via encapsulation into the vesicle interior would be a desirable first step in recovery. If the ability of natural membranes to allow selective transport between interior and exterior phases can be mimicked by the addition of dopants to the vesicle bilayer, then vesicular solutions will offer real promise for use in separation schemes. The objective of this work is the elucidation of the mechanism of ion transport in vesicles made from surfactant only, an important first step in the understanding of transport in more complex systems containing both surfactant and dopants such as ionophores. Phospholipids are commonly used for biological ~tudies,l-~ since phospholipids are a major component of animal cells, but are not suited for industrial use as they are subject to chemical and biological degradation. The cation permeability of pure phospholipid vesicles is also difficult to measure because the rates of transport are so small that other effects, such as vesicle fusion followed by dumping of contents, may obscure the signal of interest. The difficulty of measurement is well shown by the differing cation selectivity sequences reported, namely, equal permeation of all cations,] impermeability with respect to sodium and potassium: potassium and sodium permeability equal for phosphatidylcholine (PC) vesicles but potassium permeability greater than sodium for phosphatidylserine vesicles,2 and sodium permeability greater than rubidium permeability for multilamellar PC vesicles but the reverse for unilamellar PC vesicle^.^ We have thus turned to shorter tailed synthetic surfactants in an effort to understand transport without the detractions inherent in natural systems.* The double-tailed anionic surfactant sodium 4-( I-heptylnonyl)benzenesulfonate(SHBS) (Figure la) is commercially available and is chemically and biologically stable. SHBS is known to form small unilamellar vesicles upon prolonged s o n i ~ a t i o n a, ~feature essential to the measurement of intrinsic permeabilities. We have also synthesized sodium 4 4 1-nonylundecy1)benzenesulfonate (SNUBS) (Figure lb) in order to study the effect of hydrocarbon tail length on cation permeability. Anionic surfactants such as SHBS and SNUBS are good choices for vesicle formation. The measured surface potential of these vesicles is large (--60 mV), inhibiting degradation via floccu-
'
Weyerhaeuser Paper Co.. Weyerhaeuser Technology Center 2B42, Tacoma, WA 98477. Department of Chemical Engineering, University of Delaware, Newark, DE 19716.
0022-3654/90/2094-2560$02.50/0
lation,1° and the relatively thin bilayer allows permeation at conveniently measurable rates. We report here the permeability of SHBS and SNUBS bilayers to sodium, potassium, and cesium salts in aqueous solution. These cations are ideal for basic transport studies as they are simple univalent spheres, eliminating complex steric effects and allowing us to probe only the effect of increasing permeant size. By also varying temperature, the anion species, and the thickness of the vesicle bilayer, a picture is constructed of the mechanism of permeation for these simple species. In contrast to membranes made of thicker bilayers (or macroscopic oil phases), transport occurs through transient holes in the vesicle bilayer. There is little interaction between the cation and the hydrocarbon portion of the bilayer. 2. Materials and Methods SHBS was obtained from the IRCHA Co. (Vert-le-Petit, France) and purified by one recrystallization from acetone at 50 "C. Purity by HPLC (gradient elution from 50% 0.005 M tetrabutylammonium phosphate/50% acetonitrile to 100% acetonitrile in 20 min) was found to be >98%. SNUBS was synthesized via the method of Doe and Wade" and recrystallized from diethyl ether. In a typical permeability experiment, 6 mL of the appropriate radiolabeled solution (42K, 24Na, or 134Cssalts) was added to a vial containing 0.06 g of either SHBS or SNUBS. The surfactant solution was then sonicated at 30% power in a Heat Systems Ultrasonics Model W-225R (20 kHz, 200 W). The sample was sealed during sonication and immersed in a propylene glycol bath which was cooled by circulation through a constant-temperature bath held at 10 "C. The sample temperature was thus held between 25 and 30 "C. Samples were sonicated for 12 h to convert all liquid crystals to unilamellar vesicles. If some liquid crystal phase remained, sonication was continued until no liquid crystal phase was visible to the naked eye. For experiments conducted above room temperature, the sample was equilibrated at the ( 1 ) Bangham, A . D.; Standish, M. M.; Watkins, J. C. J . Mol. Biol. 1965, 13, 2 3 8 .
( 2 ) Papahadjopoulos, D. Biochim. Biophys. Acta 1971, 241. 254. ( 3 ) Hauser, H.; Oldani, D.; Phillips, M. C . Biochemistry 1973,12,4507. ( 4 ) Eisenberg, M.; Gresalfi, T.; Riccio, T.; McLaughlin, S. Biochemistry 1979, 18, 5213. ( 5 ) Mimms, L, T.;Zampighi, G.; Nozaki, Y.; Tanford, C.; Reynolds, J . A. Biochemistry 1981, 20, 8 3 3 . (6) Louni, L.; Rigaud, J. L.; Gary-Bob, C. M. Stud. Phys. Theor. Chem. 1983, 24, 319. ( 7 ) El-Mashak, E. M.; Tsong, T. Y . Biochemisrry 1985, 24, 2884. ( 8 ) Hamilton, R. T.; Kaler, E. W. J . Colloid InterfaceSci. 1987,116, 248. ( 9 ) Franses, E. I.; Talmon, Y.; Scriven, L. E.; Davis, H. T.; Miller, W. G. J . Colloid Interface Sei. 1982, 86, 449. ( IO) Johnson, N. W.; Kaler, E. W. J . Colloid Interface Sci. 1987, 116,444. ( I I ) Doe, P. H.; El-Emary, M.; Wade, W. H. J . Am. Oil Chem. SOC.1977, 54, 570.
0 1990 American Chemical Society
Alkali Metal Ion Transport through Thin Bilayers
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2561 VRCM,RL=O =7
(b)
Figure 1. Vesicle-forming synthetic surfactants: (a) sodium 441heptylnony1)benzenesulfonate (SHBS), (b) sodium 4 4 1-nonylundecy1)benzenesulfonate (SNUBS).
temperature of interest for 2 h immediately after sonication. Samples were then centrifuged 30-45 min at 41 200g, and the supernatant was removed for use. All steps after sonication were conducted at the temperature at which the permeability was to be measured. Production of a monodisperse vesicle solution, and accurate measurement of the vesicle radius, is essential to determination of the intrinsic bilayer permeability. Quasielastic light scattering (QLS) was used as described earlier9 to measure vesicle radii in the supernatant. The method of cumulantsi2was used to find the z-average radius, while the exponential sampling methodi3 was used to test for pol dispersity in the sample. The vesicle radius obtained was 105 , with a standard deviation/mean of -0.15. Both SHBS and SNUBS vesicles were found to be of the same size. Some samples used were bimodal with the small peak at 105 A and the large peak at -320 A, with the peaks being of about equal light scattering intensity. At the scattering angle of 90°, large vesicles scatter much more light than small vesicles; hence, the presence of approximately equal intensity peaks in a bimodal distribution indicates that the small vesicle population predominates, and in these samples the vesicle radius was also taken as 105 A. Permeabilities were measured by the method of Johnson and Bangham.14 After QLS measurement 1 mL of the supernatant was eluted through an isotonic 1.5 X 4 cm bed of Bio-Rad Bio-Gel P6DG desalting gel. This step removes radioactivity exterior to the vesicles without imposing an osmotic gradient on the vesicle wall. Passage through the column did not change the average size of the vesicles although, for a unimodal sample, the polydispersity was increased. One milliliter of the eluent (of which 0.5-0.7% was encapsulated) was collected and pipetted into a dialysis bag ( 2 5 ” Spectrapore 12000 to 14000 M W cutoff tubing), and the bag was immersed in a larger vial containing 15 mL of nonradioactive isotonic solution. The large vial was rotated at about 100 rpm to ensure good mixing. Samples of the exterior phase were taken at measured intervals. The total radioactivity of the sample was found by cutting the dialysis bag at the end of the experiment, mixing, and then sampling the solution. Radioactivity levels were measured on a Packard Tri-Carb 300 liquid scintillation counter using Ecolite (WestChem). The permeation process from vesicle interior to the receiving phase outside the dialysis bag is described by the differential equations
K
Here CM,is the permeant concentration inside the vesicles, CM,o is the permeant concentration outside the vesicles but inside the dialysis bag, and CM,R is the permeant concentration outside the dialysis bag in the receiving phase. vi, V,, and VR are the volumes respectively in the vesicles, outside the vesicles but inside the dialysis bag, and outside the dialysis bag. A,, and Abagare the area of the vesicle membrane and dialysis bag, and p1 and p 2 are the volume permeabilities of the vesicle and the dialysis bag (cm3/s). p 2 (measured independently) was found to be 4.4 X cm3/s, as compared to a typical value for p , of -lo-’ cm3/s. Vesicle membrane and dialysis tubing areas were 3 X lo4 and 28 cm2 per sample. Equation 3 recognizes that the first tracer atoms leaving the bag are coming from the saturated dialysis bag, a fact that the governing equations (1) and (2) do not model. The parameter 7 is thus the fraction of tracer in the receiving phase at the start of the experiment. Equation 4 defines the initial slope in terms of a,the fraction of tracer in the dialysis bag but not in the vesicles. 0.995. If the gel column is not used, then a = Vo/(V, + VJ If the gel column is completely effective, then a = 0. vCi and VRCR are simply q and nR,the number of tracer ions in the vesicle interior and receiving phase, respectively. Equations 1-4 are thus formally identical with those solved p r e v i o ~ s l y . ~ The J ~ exact solution for the fraction of tracer outside the dialysis bag is
-
-
with the initial conditions (12) Koppel, D.E.J . Chem. Phys. 1972, 57, 4814. ( 1 3 ) Ostrowsky, N.; Sornette, D.; Parker, P.; Pike, E. R. O p f .Acfa 1981, 28, 1059. (14) Johnson, S. M.; Bangham, A. D. Biochim. Biophys. Acfa 1969,193, 82.
(3)
(5)
m+,-= Y2[-B f (B2 - 4C)i/2] Ai = v - A , - D / C
where NT is the total number of counts in the system. The measured signal nR/NT was fit to eq 5 by using a nonlinear least-squares program with a, 7, and pi as parameters. The value of 7 was always less than 5% of NT, and a was between 0.005 and 0.3 for all experiments. The intrinsic vesicle permeability Pi (cm/s) was on the order cm/s and was found from the volume permeability p1 and the membrane area Amemvia
PI = PI/Amem
(6)
3. Theory Transport mechanisms for ionic permeation fall into two broad classes: those in which the ion samples the interior hydrocarbon phase of the bilayer (partitioning models) and those in which the ion sees only water and surfactant head groups (pore models). While partition models have traditionally been invoked for the passage of ions through hydrophobic media such as bulk hydrocarbon membraned5 and liposomes,l&’*there is evidence that the (15) Lamb, J . D.; Christensen, J. J.; Izatt, S. R.; Bedke, K.;Astin, M. S.; Izatt, R. M. J . A m . Chem. SOC.1980, 102, 3399. (16) Walter, A.; Gutknecht, J. J . Membr. B i d . 1986, 90, 207.
2562
Hamilton and Kaler
The Journal of Physical Chemistry, Vol. 94, NO. 6, 1990
mechanism of ion transport in pure bilayers is transport through transient pores.'+21 We first derive expressions for ion transport based on both the partitioning and the pore model theories and then compare the predictions to experiment. In all cases the flux is found25to be of the form jM = Pl(CM,i - CMJ; thus, the permeabilities derived from the application of eq 5 to the experimental data are the correct intrinsic permeabilities for each model examined. Partitioning Models. If the ion of interest partitions into the vesicle bilayer, the flux across the bilayer is assumed to be proportional to the concentration gradient in the bilayer (Fick's law). The ion may cross the bilayer as a single ion or as a neutral ion pair. The resulting expressions for P , in an isotonic system where the permeating species is a tracer atom areZ2 PI = D M H / L
single ion
PI = DMxKH,,,HxCx/L
ion pair
(7)
BAz) = B,r exp(-W(z) / R n
(1 1)
Here B , , is the arrival rate of cations at the bilayer surface, from either the vesicle interior (r = i) or the vesicle exterior (r = o), and is proportional to the ion concentration at the bilayer surface. W(z) is the work required to penetrate the bilayer to depth z. The arrival rate of cations at the vesicle surfaces can be calculated from the Smoluchowski equation26and is given by
(8)
Here HM and Hx are the cation and anion partition coefficients, DM and D M xare the cation and ion pair diffusion coefficients, K is the equilibrium constant for the ion pairing reaction, Cx is the anion concentration, and L is the membrane thickness. The chemical potentials of the cations in each phase (membrane and aqueous) are necessarily equal, as are the chemical potentials of the anions in each phase. This yields22 H = (HMHx)ll2
barrier that the permeating cations must overcome. Cations arrive at the bilayer surface at a rate proportional to the solution concentration at the bilayer surface (which for charged vesicles can be found from DLVO theoryz5),and the depth of permeation is related to the internal energy of the colliding cation. Since the energy distribution of ions in solution is given by a Boltzmann distribution, the arrival rate at depth z in the bilayer B,(z) is
(9)
where
Here R is the gas constant and T the absolute temperature. The chemical potential difference between an ion in an aqueous phase and an ion in a membrane phase is roughly the difference in the Born energy of the ion in each phase,23 so
Here y is the surface concentration enhancement found from DLVO theory25and DM is the diffusion coefficient of the permeating cation.22 The cation flux out of the vesicle is then j~ = tB,i - Bs,J exp(-W(z)/RT)
(14)
In order to express eq 14 in the desired form of jM = P l ( C M ,-i CM,J,an average vesicle radius Ravg= R, - L / 2 is used in both eqs 12 and 13. The penetration work W ( z )can be written as the sum of three terms. The first contribution is the work required to move from the bilayer surface to the plane of the head groups ( WG). The second and third terms are the work to move from the plane of the head groups to the bilayer center. This consists of electrostatic work (WE) and the work required to penetrate from the head group plane to the bilayer center through the hydrocarbon tail groups (WT).
The work required to move from solution to the plane of the head groups can be written as where
with r i the ion radius, z the ion valence, e the electron charge, t the dielectric constant of the medium (either membrane or aqueous phase), and co the dielectric constant of vacuum. Accounting for the finite thickness of the 30-A membrane24 changes the Born energy by only 4%; hence this correction was not used. The preceding model assumes that the membrane behaves like a continuous hydrocarbon phase, that the barrier to entrance into the membrane is adequately described by a simple partition expression, and that resistance to transport in the membrane is like that in a continuous phase. We suggest that a more realistic model of ion partitioning accounts for both the noncontinuous nature of the bilayer and the amphiphilic nature of the bilayer molecules. In this case the membrane is modeled not as a separate phase but as an energy (17) Trauble, H. J . Mol. Biol. 1971, 4 , 193. (18) Laprade, R.; Ciani, S.;Eisenman, G.; Szabo, G. Membranes 1975, Y $97 J , 1 L I .
(19) Abidor, I. G.; Arakelyan, V. B.; Chernomordik, L. V.; Chizmadzhev, Yu. A,; Pastushenko, V . F.: Tarasevich, M. R. Bioelecfrochem. Bioenerg.
1979, 6, 37. (20) Weaver, J . C.; Powell, K. T.; Mintzer, R. A. Bioelecfrochem.Bioenerg. 1984, 12, 405. (21) Exerowa, D.; Kashchiev, D. Confemp. Phys. 1986, 27, 429.
(22) Cussler, E. L. Dif/usion: Mass Transfer in Fluid Systems; Cambridge University Press: Cambridge, MA, 1984. (23) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1985. (24) Parsegian. V. A. Nature 1969, 221. 844.
wG
= All
+XMhyd
Here Ak is the change in chemical potential given by the Born equation, AHhydis the dehydration energy of the cation, and x is the fractional dehydration energy required to enter the bilayer. The electrostatic work is that to move the cation from the plane rHG,to the middle of the of the head groups, at separation r,,, bilayer, at separation L / 2
+
Here Q Mis the charge of the cation. QHG, the charge per head group, can be found from the surface charge density us of the vesicles. rHGt the head group radius, was estimated from CPK models to be 3 A. The radius of the cation in the membrane phase is rmem.The majority of experiments were conducted in 0.1 M salt where the Debye length is 10 A, much less than the vesicle radius of 105 A, so the flat plate results for us for intermediate surface potentials may be used.23 Accurate calculation of the energy required to penetrate the bilayer tail groups is difficult. As an estimate, the molar cohesive energy of a CH2 group may be combined with the average displacement upon insertion of a cation into a medium of CH2 groups to obtain wT.27 Combining the above results in eq 14 yields
-
PI = ( D M Y / R ~exp[-(WG ~~) + WE+ W T ) / R T ~ (16) (25) Shaw, D.J. Introduction to Colloid and Surface Chemistry; Butterworth and Co.: London, 1983. (26) Fuchs, N. A. The Mechanics of Aerosols; Pergamon Press: Oxford. 1964.
Alkali Metal Ion Transport through Thin Bilayers
The Journal of Physical Chemistry, Vol. 94, No. 6,I990 2563
F-
00 0 00
01
O
02
Solution Molority Figure 2. Effect of molarity on the cation permeability of SHBS vesicles
at 296 K. Horizontal lines are a guide to the eye. The Pore Model. An accepted mechanism of conduction and permeation in pure bilayers is the formation of transient pores in the bilayer."21 Thermal fluctuations produce a temporary hole in the bilayer, and the surfactant head groups rearrange so that the walls of the pore are lined with head groups, thereby forming a so-called "inverted pore".lg The hydrocarbon portion of the surfactant is not exposed to the aqueous medium, and permeating ions see only surfactant head groups. To calculate the ion flux, we write the collision rate per membrane area times the fraction of membrane area available for transport: jout
= (Bs,i - 4JVp/Amem)
(17)
Here B , , is the collision frequency with the membrane surface as in eq 12,f is the total area of pores per milliliter of solution larger than t i e permeating ion (of cross-sectional area ai), and A,, is the membrane area per milliliter of solution. If n(a) da is the number of pores per membrane area between pore area a and a da, then
+
As a first-order approximation, we assume that the pore area distribution can be written n(a) = no exp(-kla/RT) exp(-k21/RT) (19) Here no is the pore formation frequency factor (A-2 mL-'), exp(-kla/RT) is the probability of forming a pore of area a, and exp(-k,l/RT) is the probability of forming a pore of depth 1. Since a pore must completely traverse the membrane for transport to occur, 1 is set to L, the bilayer thickness. With this definition of n(a) the integral of eq 18 is easily done, and the resulting expression for PI is P, =
-DMYno RT[ ai + RavgAmcm k~
y]
exp[-k,ai/RT] exp[-k,L/RT] (20)
Here ai is the cross-sectional area of the smallest pore that can accommodate the ion. The maximum number of discrete pores that can occupy the bilayer (no) is the number of sites of the area of the surfactant head groups and is thus simply one-half of the number of molecules of surfactant in the bilayer. 4. Results
The results for cation transport in SHBS and SNUBS vesicles are given in Figures 2-4. Each data point and error bar represent the results of at least three separate replicate experiments. The error bars represent the 90% confidence interval. Figures 2 and 3 show that, with the exception of sodium fluoride, there is no effect of either molarity or anion type on cation permeability. Cation permeability decreases with increasing atomic number (Figure 4a). Figure 4a includes data for all of the anions plotted in Figure 3 except NaF. The cause of the anomalously high permeability of N a F is not known.
O
' 14
Cl-
~ 16
.
~ 18
Br
I -
. 20
~ 2 2
. 24
~
.
l
Anion R a d i u s i i Figure 3. Effect of anion type on the cation permeability of SHBS vesicles at 296 K in 0.1 M alkali-metal halide solution. Horizontal lines are a guide to the eye.
The cesium (as CsC1) permeability of SHBS vesicles increases with temperature, more than doubling in value from 295 to 310 K, giving an activation energy of 70 kJ/mol of cation. Increasing the bilayer thickness by four CHI groups (SNUBS vesicles) results in a 30-fold decrease in the cesium permeability (Figure 4c). The cesium permeability of SNUBS vesicles also increases with temperature, with an activation energy of 79 kJ/mol (Figure 4d). Finally, the effect of cation type on the permeability of SNUBS vesicles (Figure 4e) is similar to that seen in SHBS vesicles (Figure 4a). The permeability of glucose was found to be -1/5 that of cesium, showing that vesicles remain intact over the course of the experiment (-20 min for SHBS). 5. Discussion Partitioning Models. The simple partitioning mechanism described by eq 7 and 8 is an inadequate description of the experimental results. The effects of anion type, cation type, and solution molarity should be pronounced. The constancy of bilayer permeability with solution molarity (Figure 2), as opposed to the linear relation predicted by eq 8, shows that ion pairing is not occurring, and the absence of any effect of anion type shows that ion partitioning is not taking place (Figure 3). Further, the decrease in cation permeability with increasing naked cation radius reinforces the conclusion that partitioning is not happening. For comparison, eq 7 predicts that, for a membrane of dielectric constant 2 , PcsI 104Pcscland Pcscl 1026PNacl.These large effects would easily be apparent if either ion was partitioning. Consider the second partitioning model (eq 13). Since the hydrated radii of ions are all very similar (except for sodium and fluorine), a strong anion or cation effect would not be observed. A nonlinear least-squares fit of eq 13 (with five parameters; ionic radii for sodium, potassium, and cesium, the dielectric constant of the membrane, and the energy for insertion into the hydrocarbon tails) finds that the data cannot be represented with a partition model even if an unrealistically high value (78.0) of the membrane dielectric constant is used.,' This points to the fact that a pore model is more appropriate for describing the data, since the energy penalty for partitioning into the bilayer is prohibitively high. The Pore Model. Application of eq 20 with two fitted parameters ( k l , k 2 )results in excellent agreement with the data (Figure 4a-e; all are fit with the same value of k l and k 2 ) . Permeabilities for three alkali-metal cations in SHBS vesicles are matched at all temperatures studied. The effect of increasing the bilayer thickness by four CH2 groups, resulting in a 30-fold decrease in permeability, is described, as are the permeabilities for two alkali-metal cations in SNUBS vesicles and cesium in SNUBS vesicles at three temperatures. Since the measured activation energies are too low for dehydration of the cation to be occurring (-40 kJ/mol compared to the necessary2* -300 kJ/mol), either the hydrated cation is
-
-
(27) Hamilton, R. T. Ph.D. Dissertation, University of Washington, 1989. (28) Jain, M. K. The Biomolecular Lipid Membrane: a System; Van Nostrand Reinhold Co.: New York, 1972.
.
Hamilton and Kaler 15-
/: u
.o
E
0
e
05
'
CS'
K'
NZ.
00
l
'
l
j
l
!
290
310
300
330
320
T/ K
C
0 06
" $
6
q
004
Q a
P9C
300
00 2
0 oc
310
190
120
'4C
160
180
TiK
Cation R a d i u s i i
28
29
3C
31
32
33
34
35
36
37
Bilayer Thicknessii
Figure 4. (a) Effect of cation type on the permeability of SHBS vesicles at 296 K in 0.1 M alkali-metal halide solution. D , = 2 X cm2/s, y = 10, no = 1.04 X IO1', Rsvg= 105 A, A,, = 2.6 X lo4 cm2/mL, L = 30 A. Line is fit to eq 20. (b) Effect of temperature on the cesium permeability of SHBS vesicles in 0.1 M CsCI. Line is fit to eq 20 with the same parameters as in (a). (c) Effect of bilayer thickness on the cesium permeability of SHBS and SNUBS vesicles in 0.1 M CsCl at 296 K. Here the biIayer thickness is taken as the saturated portion of the hydrocarbon chains on the surfactant. Line is fit to eq 20 with the same parameters as in (a). (d) Effect of temperature on the cesium permeability of SNUBS vesicles in 0.1 M CsCI. Line is fit to eq 20 with the same parameters as in (a). (e) Effect of cation type on the permeability of SNUBS vesicles at 296 K in 0.1 M alkali-metal halide solution. Line is fit to eq 20 with the same parameters as in (a).
passing through the pore or the hydration shell is being replaced by the surfactant head groups, which may or may not be hydrated. The high permeability of sodium argues that the hydration shell is not retained since hydrated sodium has a cross-sectional area 16 times that of naked sodium. More significantly, when the hydrated ion radius is used in eq 20, the observed selectivity sequence is not reproduced. The surfactant head groups may themselves be hydrated so that the cation hydration shell is replaced, not by the anionic head groups, but by water molecules already present as the head group hydration shell. Unfortunately, there are no direct measurements of the degree of hydration of surfactant head groups. If the head groups are assumed to be unhydrated, then the area of the pore is equal to the area of the cation and the values of k , and kz are 0.71 and 1.7 kJ/(mol.A). On the other hand, hydration of the head groups reduces the effective pore size. An estimate of the effect is made by assuming the presence of a 2.8-A hydration layer" on the surfactant head groups. In that case the values for the parameters k , and k , are 0.22 and 1.9 kJ/(mol-A). As a rough check on the validity of these results, note that the surface pressure
of phospholipid bilayersz8 is on the order of 0.3 kJ/(mol.AZ), in reasonable agreement with the value of k , when the surfactant head groups are hydrated. The molar cohesive energy implied by k2 is -2 kJ/mol of CH2, of the same order as, but less than, the molar cohesive energy of a CH2gfoupz3(6.9 kJ/mol of CHI). The cesium activation energies predicted by the pore model are 70 kJ/mol (SHBS) and 79 kJ/mol (SNUBS). A value of 60 f 12 kJ/mol has been measured for cesium permeation in SHBS vesicles.29 An extrapolation to lecithin vesicles, for which L 60 A, yields an activation energy of 126 kJ/mol, a result in qualitative agreement with the diverse literature valuesiAMof 62.8, 117.2, and 125.6 kJ/mol. The energy of pore formation can also be determined from the classical expression for the free energy of a curved surface per area of
-
(29) Kilpatrick, P. Private communication, 1989. (30) Hunt, G . R. A.; Tipping, L. R. H.; Belmont, M. R. Biophys. Chem. 1978, 8, 341. (31) Frank, F. C . Discuss. Faraday SOC.1958, 25, 19.
Alkali Metal Ion Transport through Thin Bilayers
Here K , is the splay and K, the saddle splay bending constants of the bilayer. c1 is the curvature of the pore wall normal to the bilayer (1 /rbilaycr), cz is the curvature of the pore wall parallel to the bilayer (-1 /rple),and co is the natural curvature of the bilayer (1 /RvaicIc).To this energy must be added the resistance to pore formation imparted by the surface pressure ro of the bilayer. The energy for the formation of a single pore is then
where Awallis the area of the pore wall (a half-torus) and APre is the area of the pore. Values for Kc and K, are not known for SHBS or SNUBS, but K, has been estimated32and K , m e a s ~ r e d ~for " ~phospholipids. ~ A reasonable value for each is erg. With r0 set to 36 dyn/cm (the fitted value of k l in eq 20), the free energy of formation of erg. The measured value for cesium a pore is gprc= 1 X erg. is 70 kJ/mol = 1.2 X From eq 17, the flux of ions against the bilayer is 11 ions/(Az.s). ions/(A2.s). This The flux of ions through the bilayer is 2 X low efficiency indicates that cations are not greatly inducing the formation of pores, a mechanism postulated for phospholipid bilayers;39 rather, cations take advantage of a small population of existing pores to cross the bilayer. Bilayer Permeability and the Eisenman Selectivity Theory. E i ~ e n m a nhas ~ ~proposed a model that explains the equilibrium ion specificity of many substrates such as clays and glass electrodes. In this theory the cation selected from solution is a function of the anionic site field strength, and in fact the selectivity of bilayers is viewed as governed by equilibrium ion adsorption to the monomer head groups.41 Eisenman suggests that a chain of phosphate or carboxyl groups "would provide the most obvious pathway (or formal "pore") for the passage of ions"40 across a biological membrane. The equivalent pore radii measured in biological membranes is 4-6 A, larger than the ionic radii of any of the alkali metals. Hence, alkali-metal specificity in these biological systems is probably due to equilibrium binding effects. For SHBS and SNUBS bilayers this analysis must be applied with caution. Regardless of how the cation gets to the surface, passage through the bilayer will be a function of the bilayer pore properties. Unlike pure phospholipid bilayers, SHBS and SNUBS bilayers are able to sustain an equilibrium population of pores. The pore radius in SHBS and SNUBS bilayers thus has no lower limit, and pores will exist that are too small for cesium or potassium but large enough for sodium. If the Eisenman mechanism is relevant to SHBS and SNUBS bilayers, it must then affect the preexponential factor in eq 20, which may itself be a function of temperature. The flux of sodium in the presence of specific surface interactions would then be a function of both the bilayer pore properties and the cation/anionic site interactions. If sodium binds more strongly than cesium to the bilayer surface, the equivalent surface concentration of sodium will be larger than that used in the pore model, and the sodium permeability will be higher than the predicted value. As Figure 4a shows, eq 20 describes the observed cation behavior without (32) Szleifer, 1.; Kramer, D.; Ben-Shaul, A,; Roux, D.; Gelbart, W. M. Phys. Rev. Lett. 1988, 60, 1966. (33) Helfrich, W. 2.Naturforsch. 1973, 28C. 693. (34) Harbich, W.; Servuss, R. M.; Helfrich, W. Z . Naturforsch. 1978, 33A, 1013. (35) Harbich, W.; Helfrich, W. 2.Naturforsch. 1979, 34A, 1063. (36) Beblik, G.; Servuss, R.-M.;Helfrich, W. J . Phys. (Les Ulis, Fr.) 1985, 46, 1773. (37) Schneider, M. B.; Jenkins, J. T.; Webb, W. W. J . Phys. (Les Ulis, Fr.) 1984, 45, 1457. (38) Engelhardt, H.; Duwe, H. P.; Sackmann, E. J. Phys., Lett. 1985, 46, L-395. (39) Parsegian, V. A. Ann. N . Y . Acad. Sci. 1975, 264, 161. (40) Eisenman, G.In Membrane Transport and Metabolism; Kleinzellar, A., Kotyk, A., Eds.; Academic Press: New York, 1961. (41) Diamond, J. M.: Wright, E. M . Annu. Reu. Physiol. 1969, 31, 581.
The Journal of Physical Chemistry, Vol. 94, No. 6,1990 2565 including specific surface interactions. We conclude that if specific adsorption to the anionic head groups is occurring, it is a small effect in comparison to the steric interaction between cations and pores. The permeabilities measured here are assumed to be intrinsic properties of the SHBS and SNUBS vesicle bilayers. This is only true if the vesicles are truly unilamellar and if the vesicle population size distribution is known. Obviously, if multilamellar structures are present, then the measured permeability will reflect the added hindrance caused by several bilayers in series. Similarly, from eq 4 it can be seen that the number flux out of a vesicle is dependent on Vi, the encapsulated volume, which is dependent on the cube of the vesicle radius. While knowledge of the size distribution is theoretically sufficient to calculate the total membrane area, in practical terms, due to the limitations of existing polydispersity determination methods, a unimodal distribution (and preferably a narrow unimodal distribution) is necessary to allow accurate calculation of the vesicle volume and membrane area. It is for this reason that surfactant solutions were sonicated for 12-18 h, since prolonged sonication of SHBS solutions has been shown to produce unilamellar vesicle^.^ It is worthwhile to reiterate that the extremely low permeabilities of phospholipid vesicles (due to the relative thickness of the bilayer) are difficult to measure because the leakage of ion can easily be dominated by other mechanisms such as vesicle breakage, reversion to liquid crystals, or dumping on aggregation and fusion. Thus, the pore model predicts a lecithin permeability of approximately cm/s, while measured values14 are on the order of cm/s. With SHBS vesicles, one-tenth of the interior cesium is leaked in about 4 min; with lecithin vesicles, the same leakage (at cm/s) would take more than 5 days. At cm/s lecithin vesicles are effectively impermeable. For this reason studies that attempt to measure lecithin vesicle permeabilities over short time periods are likely to produce results that are subject to large uncertainties. Bilayer lipid membrane studiesz8are even more difficult because the low total area of the system (typically 0.01 vs lo4 cmz in vesicle systems) limits the rate of transport even further. Thus, the reported selectivity sequences for pure bilayers are at and in fact, pure phospholipid bilayers have been reported to be impermeable to cations,6 a most reasonable conclusion. The dominant mechanism of ion transport in unilamellar vesicles with thin bilayers is transport through pores; the fact has implications for both the study of facilitated transport and the study of the physical properties of bilayers. That ionophores may form pores or channels in vesicle bilayers is seen to be more likely when the bilayer itself already contains a pore population. An ionophore that would be unlikely to span the unperturbed bilayer may find a role in stabilizing an already existing pore. This stabilization would have a strong effect on the ion transport rates, since the population of pores in the pure bilayer is As a result of this, the bilayer transports less than 1 part in 10I2of the ions impacting on the vesicle surface. 6. Conclusions The mechanism of cation transport through thin unilamellar vesicle bilayers is by passage of the naked ion through transient pores in the bilayer. The independence of transport on solution molarity or anion type rules out ion pair formation and any partitioning mechanisms. Surfactant monomers rearrange to line the pore wall such that only head groups contact the aqueous phase, and these pore wall head groups likely retain at least one layer of water hydration. The intrinsic permeability of the bilayer is decreased by a factor of 30 when the 30-8, bilayer is thickened by 5.6 8, (two CH2 groups per surfactant tail). This strong dependence on bilayer thickness helps explain the diverse selectivity (42) Not all ionophores are active in forming pores, however. For example, simple ionophores such as the crown ethers are considered to facilitate transport across phospholipid bilayers via a diffusion mechanism. See for example: Eisenman, G.; Szabo, G.; Ciani, S. M.; McLaughlin, S.;Krasne, S. In Progress in Surface and Membrane Science; Danielli, J. F., Rosenberg, M. D., Cadenhead, D. A,, Eds.; Academic Press: New York, 1973; Vol. 6.
2566
J . Phys. Chem. 1990, 94, 2566-2572
sequences reported for phospholipid vesicles: with a thickness of 60 A the lecithin bilayer is effectively impermeable to ions, and measured ion fluxes will be dominated by nonpermeation effects unique to the particular experimental system. The activation energies for cesium transport are 70 and 79 kJ/mol for SHBS and SNUBS, respectively. The energy required to form a pore of a given area is comparable to the measured surface pressures of lecithin bilayersz8(36 dyn/cm), and the energy to form a pore of a given depth is of the same order, but less than,
the molar cohesive energy of a CH, groupz3 (2 vs 6.9 kJ/mol of CH,). Acknowledgment. This work was supported by the National Science Foundation (Grant PYIA-8351179) and by the Standard Oil Company (Ohio) with matching funds under the National Science Foundation's Presidential Young Investigator Program. For part of his tenure R.T.H. was supported by Link Foundation and National Science Foundation Fellowships.
Electron Paramagnetic Resonance Studies of Doped TiO, Colloids Michael Gratzel and Russell F. Howe* Institute de chimie physique, Ecole Polytechnique Federale, CHlOl5 Lausanne, Switzerland (Received: May 12, 1989; In Final Form: October 2, 1989)
An EPR study is reported of TiOz colloids doped with transition metals Fe, V, and Mo. Irradiation of aqueous Fe-doped colloids causes the growth of Ti3+signals, including a signal due to aqueous Ti3+resulting from dissolution of the colloid; these changes are attributed to inhibition of hole-electron recombination by Fe3+dopants. Electron and hole trapping by charge-uncompensated and charge-compensated Fe3+sites, respectively, is observed on irradiation of Fe-doped Ti02 powders at 77 K. Vanadium doping of aqueous colloids causes a similar inhibition of hole-electron recombination, producing initially aqueous V 0 2 + and ultimately Ti3+on irradiation. The fading of V4+ signals on irradiation of V-doped powders at 77 K may be due to either hole or electron trapping; this is inhibited in the presence of hydrogen and oxygen. Interstitial Mo6+ in Mo-doped powders behaves as an irreversible electron trap on irradiation at 77 K or room temperature; substitutional Mo5+on the other hand is a reversible hole trap.
Introduction Recent measurements in this laboratory have shown that doping colloidal Ti02particles with Fe3+or V4+drastically augments the lifetime of the hole-electron pairs created by band gap irradiation.1,2 The importance of the hole-electron recombination kinetics in determining the photocatalytic activity of colloidal semiconductors has been discussed by numerous authors.) EPR measurements' showed that irradiation of the Fe3+-doped TiO, colloids caused fading of the EPR signals of Fe3+ and the growth of an intense signal previously identified4 as Ti3+cations located at the surface of the colloids. This signal is produced from undoped Ti02colloids only when irradiation is carried out in the presence of hole scavengers such as poly(viny1 a l ~ o h o l ) . ~ There have been several previous EPR studies of the effects of irradiation on transition metal doped TiOz In particular, Mizushima et a1.6 used measurements of changes in EPR signal intensities when doped single crystals of rutile were irradiated with monochromatic light to deduce energy levels of the impurity cations within the band gap. The present study examines in more detail the Fe3+-doped colloids described previously' and extends the investigation to colloids doped with vanadium and molybdenum. Our objectives were to compare the photoresponse of aqueous colloidal dispersions with dry powders and with previous data for single-crystal and polycrystalline TiO,, in order to understand how and why transition-metal doping alters the hole-electron recombination rates and hence the photocatatytic performance. Experimental Section Fe3+-dopedcolloidal TiO, samples were prepared as previously described,l by hydrolysis of TiCI, in the presence of aqueous FeCI,. V4+ doping was achieved in a similar manner by using aqueous VOS04. Aqueous ammonium molybdate was used as a source of Mo6+ dopant. Dry powders were prepared by evaporating the water from colloidal dispersions in a rotavap at 40 "C. The *Address correspondence to this author at Department of Chemistry, Auckland University, Private Bag, Auckland, New Zealand.
0022-3654/90/2094-2566$02.50/0
V4+-doped powder was subsequently heated in air to 800 OC, converting anatase to rutile. Aqueous colloidal dispersions were examined in sealed quartz tubes after degassing by bubbling argon. Dry powders were Torr) in a high-vacuum cell outgassed at room temperature ( fitted with a quartz side arm. Irradiation was carried out with a 200-W xenon lamp fitted with a high-efficiency parabolic reflector; the radiation was passed through Pyrex and water filters to remove ultraviolet and infrared components. For in-situ irradiation experiments, radiation was focused onto the front face of the EPR sample cavity, from which the cover plate had been removed. A Varian E l 15 spectrometer operated at 9 GHz was equipped with a Hewlett Packard frequency counter and Bruker N M R probe. Spin concentrations were estimated by comparison of integrated signal intensities with an aqueous CuS04 standard. Computer-simulated powder spectra were obtained with the program pow9 on an IBM 4341 computer at Auckland University. UV-visible absorbtion spectra were measured on a Hewlett Packard diode array spectrophotometer. Results Iron-Doped Colloids. The EPR spectra of frozen aqueous dispersions of iron-doped colloids showed two features similar to those described previously,' at g = 4.27 and g = 1.99 (Figure la). On irradiation at room temperature, the g = 4.27 feature was immediately removed, a new signal appeared at g = 1.92 (Figure 1b), and a dark gray-green color developed. The g = 1.99 feature, ( 1 ) Moser, J.; Gratzel, M.; Gallay, R. Helu. Chim. Acfa 1987, 70, 1596.
(2) Moser, J. These No. 616, Ecole Polytechnique Federale de Lausanne, 1986. (3) Kalyanasundaram, K.; Gratzel, M.; Pellizzetti, E. Coord. Chem. Reu. 1985, 69, 57 and references therein. (4) Howe, R. F.; Gratzel, M. J . Phys. Chem. 1985, 89, 4495. (5) Faughan, B. W.; Kiss, Z . J. Phys. Reu. Left. 1968, 21, 1331. (6) Mizushima, K.; Tanaka, M.; Asai, A.; lida, S., Goodenough, J. B. J . Phys. Chem. Solids 1979, 40, 1129. (7) Thorp, J. S.; Eggleston, H. S. J . Mater. Sci. 1985, 20, 2369. (8) Amorelli, A,; Evans, J. C.; Rowland, C. C.; Egerton, T. A. J . Chem. Soc., Faraday Trans. I 1987, 83, 3541. (9) Nilges, M. Ph.D. Thesis, University of Illinois-Urbana Champaign, 1979.
0 1990 American Chemical Society
