Sculpting the OilWater Interface to Probe Ion ... - ACS Publications

J. Phys. Chem. B 2001, 105, 2483-2498

2483

FEATURE ARTICLE Sculpting the Oil-Water Interface to Probe Ion Solvation Kai Wu, Martin J. Iedema, Gregory K. Schenter, and James P. Cowin* Pacific Northwest National Laboratory, Box 999, M/S K8-88, Richland, Washington 99352 ReceiVed: August 24, 2000; In Final Form: January 9, 2001

Solvation of ions at oil-water interfaces is so important in cell wall and enzyme function, colloidal chemistry, fuel cells, and other areas that substantial effort has been made to understand the process via molecular-scale simulations of well-specified model systems. Here we report a series of experiments probing ion transport and solvation in composite films that have a geometrical specificity that rivals what theory is routinely able to employ. Proton/hydronium transport across the water-organic interface has been studied using a novel “soft-landed” ion technique that allows precision tailoring of the interfaces (including initial ion position) and sensitive monitoring of the ion motion via the electric potential generated by the ions. There are two main findings. First, the ion solvation by water at the organic-aqueous interface is probed continuously for various monolayers of water present in simple and complex sandwiched structures. The potential trap created by the solvation can be systematically overwhelmed by the collective electric field of the ions, giving us some unique information about both the trap depth and shape. A simple Born model for the trap reproduces some, but not all, of the details experimentally observed. Second, ion transport in several organic glasses is well-predictable by continuum viscosity models at electric fields up to approximately 108 V/m.

1. Introduction Transport across water-organic interfaces is a fundamental phenomenon in biology: cells of all organisms live or die by their ability to control the movement of molecules and ions across cell walls/membranes and from outside a protein to deep within it to an active site. For example, proton transport is one of the dozen “major players” in cellular transport.1 Ion transfer involves abandoning the aqueous region with its high solvation power to enter a lipid or protein (or RNA/DNA) environment. This easily could involve a potential barrier of about 1 eV (96 kJ/mol), a severe kinetic and thermodynamic impediment for which nature has devised many schemes to surmount.1 This subject has been studied for many years (see, for example, ref 2) and recently has received renewed interest. In biology, new methods have allowed a much more detailed study of the means of cellular transport.1 Industrial chemical processes often require transport across, or reaction at, the interface of emulsions of organics and aqueous solutions.3 Widely applicable fuel cells await resolving better transport of ions through membrane partitions.4 Developing environmentally safer chemical processes has pushed supercritical CO2 chemistry, including surfactants and transport agents, for two-phase applications5-7. Although the basic issues of ion transport in bulk media are fairly well understood, this is not the case near interfaces. Recent work has made it clear that water and organics in nanometer spaces8 or at interfaces between bulk media9 have transport properties that are substantially different from those of the bulk. Even such a standard notion as the efficiency of tunneling for long-range proton transport along proton acceptor chains is being reassessed.10,11 * To whom correspondence should be addressed.

Ion transport across the interface between two media was treated in 1920 by Born,12 who derived a continuum fluid equation describing the energy of an ion in a medium, and numerous improvements to continuum theories have been introduced.13,14 Molecular dynamics approaches have been developed to study liquid-liquid systems.15 We refer the readers to reviews by Benjamin16,17 and papers by Dang and coworkers.18-20 Theoretical calculations have generated many interesting predictions that in many cases await adequate experimental verification. One of our research goals is to provide such experimental evidence. To test conceptual ideas or theoretical modeling of ions interacting with the oil-water interfaces, it is essential that experiments be able to control the geometry of the interface and the initial ion location and observe sensitively the effects of this on the ion motion through the films. Our original experiments were influenced by various other groups’ innovative efforts to study liquidlike phenomena in an ultrahigh vacuum. Recreating electrochemical interfaces has long been a pursued goal.21-23 Although they are valuable, previous experiments had an obvious limitation that 3-dimensional liquid-solid interfaces were not really constructed, largely because the ions were created by reactions at surfaces or from prior contact with electrolytes. This left the ions nearly at equilibrium at the metal interface, and the ion transport processes and electrochemical potentials were not adequately explored. Borrowing somewhat from the use of spacer layers to probe energy transfer near surfaces,24 one of our current team (Cowin) was involved in an initial effort to recreate aqueous interfaces.25 To probe the distance through water films that photoelectrons could travel, at cryogenic temperatures, zero to tens of mono-

10.1021/jp003053b CCC: $20.00 © 2001 American Chemical Society Published on Web 02/24/2001

2484 J. Phys. Chem. B, Vol. 105, No. 13, 2001 layers (MLs) of water were deposited by a molecular beam on a single-crystal metal surface. An electron-sensitive molecule, CH3Cl, was then placed on top of water. Methyl fragments produced via dissociative electron attachment of the CH3Cl by laser-induced photoemitted electrons from the substrate were finally monitored. By changing the water thickness, the mean free path of the electron was determined to be about 2 MLs, in good agreement with subsequent theory.26 This result motivated us to start a program that uses molecular beams to recreate liquid-solid and liquid-liquid interfaces. Three main technological issues need be addressed: (1) making true liquid films at the molecular level, (2) devising a “chemist’s ion beam” that gently places ions into/on these films, and (3) observing the behavior of the ions. Observation of the ion behavior is the simplest task. We simply use no counterions, abandoning charge neutrality. Charge neutrality in bulk systems is required, a coulomb of charge creates 1010 V at a meter distance. In our nanometer liquid films, nonneutrality creates only tenths to tens of volts across the films. This film voltage also provides the driving force to test the ions’ mobility and the means to monitor their progress. This will be discussed in detail later. Also, we do not have to sort out the motion of the counterion from that of the primary ion of interest. The chemist’s ion beam is one among the several recently developed soft-landed ion beams, all of which attempt to minimize damage because of the kinetic energy of the ions. Some methods use cushioning layers to suppress damage. For example, Kern’s group27 employed an argon buffer layer to dissipate the kinetic energy of incoming silver cluster ions. Cooks’ group28 used low-energy (∼ 10 eV) ion beams as projectiles to deposit polyatomic ions on a relatively soft fluorinated self-assembled monolayer (F-SAM) film surface and studied the depth profile of the ion in the target film and the ion lifetimes. They also used reactive soft-landed ions to modify organic surfaces.29 Some other soft-landed ion experiments are reviewed by Kleyn30 and Cowin and co-workers.31 Our soft-landing source, developed in collaboration with Ellison’s group at the University of Colorado, Boulder, differs from others mainly in that it is unusually gentle, with an ion kinetic energy of less than or around 1 eV. Our ion source also produces many important aqueous ions31 (including polyatomic ones) such as Cs+, NH4+, and D3O+. Another difference is the research mission: Ours is the only soft-landed ion experiment we are aware of that is dedicated to the study of liquid interfaces and solvation phenomena. Vapor-deposited solvent films on cryogenic surfaces have long been used for matrix isolation spectroscopy and are typically amorphous with a liquidlike structure so long as the deposition temperature is low enough.32 We adopt this technique and use solvents that become true liquids upon warming. A solvent that readily forms a glass has a glass temperature, Tg, below which it is liquid in structure but translationally motionless on a molecular scale. Above Tg, the glass turns into a true liquid whose viscosity and kinetics can be controlled at will via temperature. 3-methylpentane (3MP) is an excellent glassformer (never crystallizing upon warming) with a Tg of 77 K.33 Methylcyclohexane (MCH) and Decalin (a bicyclic hydrocarbon) have glass transition temperatures of 85 and 134 K.34,35 Even vapor-deposited water is widely believed to form a true glass with a Tg of 135 K (this is, however, still open for debate36). Vapor deposition of films with a molecular beam well below the glass temperatures also permits sculpting of interfaces, as Figure 1 suggests. The left diagram depicts a composite film

Wu et al.

Figure 1. “Sculpted” composite film for the study of ion solvation effect. In left panel, a layer of water is put between two 5 layers of 3MP. Three hydronium ions (H3O+) initially sit on top of the film at low temperature. As the assembly warms (right panel), the ions drift down toward the grounded metal substrate (black block) driven by the collective electric field that the ions generate. Two ions already pass through the water layer, picking up a shell of water molecules (hydration). One ion still lingers in the water layer because of the solvation energy trap established at the 3MP-water interfaces.

grown on a metal substrate consisting of about 5 molecular layers of 3MP at the bottom, 1 layer of water in the middle, and another 5 layers of 3MP on the top. This “parfait-like” structure is capped by a sparse layer of hydronium ions (H3O+). As the temperature is later raised above the Tg of 3MP, the evolution of the system is monitored. One might suppose that the initially fine molecular structure on the left of Figure 1 would hopelessly interdiffuse before being sampled by the ions. However, as discussed later, an ion being pushed by the collective electric field on the order of 0.01 V/Å (108 V/m) typically moves much faster than a neutral. So even if we replace the water layer in Figure 1 with a completely miscible solvent like toluene, the ions would pass through it before the toluene layer could spread by a single molecular diameter. Strongly associated immiscible layers like water should resist diffusing away from each other until much higher temperatures. Shown in Figure 1, on the right, is the lingering of the ions in the water layer caused by attractive solvation forces in the aqueous phase, a major subject of this study. Also shown is the expected pick-up of a hydration sphere by an ion passing through the water layer. The above three strategies form our new soft-landed ion approach to attack ion transport and solvation issues. As will be shown, this approach could be limited by evaporation and crystallization of the film. It is, however, adequate for many unique studies. In this paper, we focus on the transport processes of ions (mainly hydronium ions) in liquids and across sculpted liquid interfaces. We’ll start by introducing how the soft-landed ion approach experimentally works. Then we will study ion transport processes in various pure organic films and theoretically simulate them with simple ion mobility models. Afterward we will move to ion transport in sculpted films: across water-oil interfaces and through micelle-like organic-water-organic films. Furthermore, we will discuss various aspects of the ion solvation energy trap developed at the water-oil interfaces and try to

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Figure 2. Schematic drawing of the ion source used to prepare hydronium ions (D3O+). At right is the ion beam image on a phosphor screen in the UHV chamber after deceleration. The dark cross is the shadow of an alignment cross in front of the phosphor screen. It is absent during actual ion deposition onto the sample.

quantitatively evaluate the depth and shape of the trap based on our experimental data and theoretical calculations. Finally, we will present our perspectives for future research directions in this and related areas. All of the studies presented here are looking at ion solvation between 90 and 150 K, quite a bit lower in temperature than many of the systems that help motivate our studies. Because solvation barriers are on the order of 0.5 to 1 eV, it is preferable to probe these kinetically from 90 to 150 K, to drop the rates down to on the order of 1 s-1, consistent with our current Kelvin probe measurement speed. We hope just the same that a determination of the solvation, barriers, and kinetics for these cryogenic systems can provide insight into room-temperature solvation. 2. General Experimental Methods Details of the experimental technique can be found elsewhere.31,37,38 The experimental setup consists of three main components: a main ultrahigh vacuum (UHV) chamber (base pressure e 2 × 10-10 Torr), an ion source, and a three-stage differentially pumped molecular beam. The substrate is an atomically clean Pt(111) single crystal (10 mm in diameter). It can be heated from 30 to 1400 K at ramping rates from 0.01 to 10 K/s. The molecular beam is utilized to deposit films on the substrate. Water and most organic solvents like 3MP and MCH have sticking probabilities near unity around 30 K.39,40 Their coverages are expressed in MLs, with one ML defined as the amount of the solvent molecules required to just saturate the first layer that binds more strongly than subsequent layers. This can be judged by the saturation of the highest temperature desorption peak in a temperature-programmed desorption (TPD) profile. The film thickness of a θ-ML film is estimated to be θ × 3.45 Å for water, θ × 3.55 Å for 3MP, and θ × 3.41 Å for MCH, according to their bulk densities at 90-140 K and the surface densities of their first ML on Pt(111).41-43 The TPD measurements are carried out with a quadrupole mass spectrometer that monitors the desorbing molecules as the sample is warmed at a linear rate. 2.1. Ion Source. Figure 2 shows the schematic drawing of the ion source. The ion source can produce pure ions (cations or anions). The drawing shows the source for the preparation of pure hydronium ions (D3O+). An electron beam is used to bombard D2O vapor in the nozzle to form hydronium ions (e + D2O f 2e + D2O+; D2O+ + D2O f D3O+ + OD).37 The ions are first extracted and then accelerated to 300 eV for transport. The ion beam then passes through a Wien filter (perpendicular electric and magnetic velocity filter) to single out D3O+. The D3O+ ions are finally decelerated from 300 to e1.2 eV over the last centimeter of travel to the sample. The sample can be replaced with a shielded phosphor screen to check

J. Phys. Chem. B, Vol. 105, No. 13, 2001 2485

Figure 3. Typical experimental procedure, see the text for details.

the ion beam profile under deceleration conditions. A typical image of the ion beam is shown in Figure 2. The D3O+ ion beam is 1-4 nA in its current intensity and 9 mm in diameter. Because water has a strong effect on the ions (as shown later), it is crucial to keep contamination by background water (H2O and D2O) particularly low. The ion beam is differentially pumped with five pumps, plus two liquid nitrogen cryopumps, and has two 5° bends to reject neutrals. TPD measurements verify that the unintended water contamination is less than 0.01 ML. 2.2. Experimental Procedure. A typical experimental procedure shown in Figure 3 consists of three steps: (1) vapordeposit structured films at low temperatures with the molecular beam that strikes the substrate surface perpendicularly; (2) a certain amount of ions are dosed onto the structured films; (3) the assembly is finally temperature-ramped, during which the film voltage change and film desorption are monitored by a Kelvin probe and a quadrupole mass spectrometer, respectively. In some cases, the solvent is also deposited on top of the ions. 2.3. Measuring Ion Position. The ions produce a net voltage across the film that depends on the ions’ position. This voltage is continuously measured to monitor the ion motion. The film acts as a planar capacitor. Ion deposition is essentially a charging process of the capacitor, generating a “film voltage”

Vf )

QL A0

(1)

where L is the film thickness, 0 the vacuum permittivity, the dielectric constant of the film, and A the area. We can conveniently measure this voltage to better than 10 mV using a McAllister Kelvin probe.44 A 6 mm gold-coated disk of the Kelvin probe vibrates about 0.1-1 mm away from the sample as driven by a computer. The probe senses the surface potential of the sample (including the film voltage generated by the ions) through the probe’s weak capacitive coupling to the sample. The work function is measured every 2-3 s. That the ions are initially at the top of the film upon deposition can be confirmed via eq 1. For example, a 3MP film of 83 ML (∼ 29.4 nm) in thickness after depositing a total ion charge Q of 0.30 µC (determined through integration of the measured ion current against ion dosing time) was found to have a Vf of 8.5 V as measured by the Kelvin probe. Equation 1 predicts 8.4 V for ions on top of the 3MP film with a dielectric constant of 1.9 at 30 K.45,46 This and similar successful comparisons indicate that the initial geometry consists of ions at the top of the film, indicative of a successful deposition process. During their motion in the film, the ions produce a charge distribution F(z) (z is the distance from the metal surface). This distribution will broaden as the ions move a cross the film,46 pulled by their self-generated electric field. The ions closest to the substrate experience the highest field, move the fastest, and hence stay in front. For a pure and uniform film, if we denote

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Figure 5. Temperature evolution of the film voltage (solid) and TPD profile (dashed) for D3O+ on 83 ML 3MP. The 0.2 K/s temperature ramp is interrupted twice, allowing the sample to cool. The film voltage stays constant during the cooling as the ions are now frozen in place, only to resume their journey upon rewarming.

Figure 4. (A) Simultaneous film voltage and TPD measurements for D3O+ on 166 ML 3MP. Both film and ion depositions are carried out at about 33 K. The “split” feature of the TPD profile (the shaded area) is due to the Kelvin probe. About half of the surface area is blocked by the Kelvin probe so that the desorbing molecules behind the probe are forced to bounce between the substrate surface and the Kelvin probe many times before they completely escape. Refer to ref 46 for more details. (B) A close-up comparison of the experimental and theoretically calculated film voltage curves.

the average height of the ions above the substrate surface (the bottom of the film) as h (at a particular moment in time), then the film voltage Vf can be shown to be46

Vf )

∫0Ldz F(z)z ) Q0hA

1 0

(2)

Q, 0, and A are constant and is nearly so for hydrocarbons.45 According to eq 2, any change in Vf directly monitors the ion motion in the bulk film through h. Here is assumed to be independent of z. Composite films with thin layers of water (or alcohol) will be a more complicated capacitor. The ith layer below a charge element F(z) dz contributes to the film voltage by (Li/i)F(z) dz. This means the dielectric contribution to Vf by the water layer is fairly negligible, because L is small and large, and is essentially ignored in the analyses in this paper. The water layer still has a profound influence on Vf(t) by altering the F(z,t) term. 3. Ion Transport in Pure Organic Films 3.1. Prototypical Case Study: D3O+ Motion in 3MP. Before discussing the ion motion in sculpted composite liquid interfaces, we first examine ion transport in pure organic glasses. Figure 4A shows data for hydronium ions placed on top of an amorphous film of 3MP.41 The film is 59 nm (166 ML) thick, and the ions are placed on it at 33 K, well below the glass temperature of 3MP, 77 K.33 No ion motion is observed at 33 K, and the developed film voltage is consistent with eq 2, with

all ions located on top of the film. In Figure 4A, as the sample is ramped at 0.2 K/s, the film voltage initially stays nearly constant until 75 K and then decreases slowly up to 85 K and sharply between 85 and 95 K. It remains fairly constant to 120 K and finally decreases by about 0.3 V as the temperature approaches 250 K. The desorption of 3MP (TPD spectrum), also shown in Figure 4A, occurs above 120 K. The TPD peaks at 133 K.41 The constant film voltage below 75 K indicates no ion motion. As the temperature increases above the glass temperature (77 K33), the 3MP film begins to turn into a liquid in which the ions become mobile. By 95 K, the ions have completed their motion across the whole film. The multilayer of 3MP now sitting on top of the ions desorbs near 133 K, showing negligible effect on the film voltage. There is a small voltage change just below 250 K due to the change of work function caused by the loss of the tightly bound first ML of 3MP. Rather than using a simple linear ramp, we can raise and then hold the sample at constant temperature or reverse the temperature ramp. An example of the latter is shown in Figure 5. When the temperature ramp is interrupted during the ion motion and the sample is allowed to cool, the ion motion essentially stops. When the ramp restarts, the ion motion resumes close to the temperature where its previous motion is interrupted. 3.2. Theoretical Calculation of the Film Voltage. The temperature evolution of the film voltage shown in Figure 4A can be calculated by estimating the drift velocity of the ions in the electric field within the film, using the known viscosity of 3MP.33 The electric field is the gradient of the electrostatic potential. This has contributions both from a collective potential that scales as the charge per unit area (eq 1) and a chemical potential independent of Q/A. The chemical potential is due to each individual ion interacting with the ith interface at zi, including the “image attraction” of an individual ion to the metal substrate. These are short-range interactions, decaying as 1/(z - zi) or faster. The collective effect arises as each ion interacts not only with its own image in the interfaces but also with the images of all of the other ions as well. At ion coverages on the order of 1/1000 of a ML, the ions are spaced about 32 molecules apart, whereas the images are a minimum of 2 L away (2 L typically being 166 or 332 ML in this study). This creates a nearly planar potential. Calculations for a biological membrane/ aqueous interface with imbedded ions have shown in detail how planar a similar collective potential is.47 The chemical potential is calculated with the Born model.12 A hollow sphere of radius r0 immersed in the film with the ion

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D)

µkT nqe

(4)

The time evolution of the ion distribution F(z) of positive ions of charge nqe is

d(F(z)E Bz(z)) dF(z) d2F(z) )D -µ 2 dt dz dz

Figure 6. Born potential curve for an ion (3 Å in radius) moving from free space (vacuum) into a 166 ML 3MP film on Pt(111). The zero ion position is at the 3MP-Pt interface.

charge at the center of the sphere is used. To bring the ion from the vacuum into an infinite bulk dielectric with a dielectric constant of , the energy released is (1 - 1/)qe2/(8π0r0), where r0 is the Born radius of the ion. Near a single planar interface between two semiinfinite dielectric media with dielectric constants of 1 (z < 0) and 2 (z > 0), an accurate analytical expression exists for this energy17,48-50 (in eV):

a ≡ z/r0

U)

[( )

f ≡ (2 - 1)/(1 + 2)

-qe 1 18π0r0 2

(

(

)))]

1 f 1 2 2a + 1 f2 + ln + 2 2a 4 1 - 4a2 2a 2a - 1 U)

(

[

(

-qe 1 1(1 + a + f(2 - a) + 8π0r0 22

)

if a > 1

]

1 1 f (1 + a)(1 - 2a) + ln(2a + 1) (1 - f)2(1 - a) 2 1 + 2a 2a 21 2

if 0 e a e 1 (3) The above expression is valid for z > 0. For z < 0, replace 1 with 2, and z with -z.17 Compared against a direct numerical solution of the Poisson’s equation, it is found to be accurate. It is also found that we can superimpose two of these equations to accurately (1% or so) give the potential with two interfaces present (the metal-organic and organic-vacuum), when the film is as thick as the 83 or 166 ML films here. This produces a short-range (≈5 nm) repulsion from the vacuum interface ( ) 1) and similar attraction to the metal interface ( approaches infinity). Both are about 0.85 eV for r0 of 3 Å, as shown by the curve in Figure 6. This potential is added to the collective electrostatic potential to give the total potential. The gradient of this potential gives the force on the ions. 3.3. Theoretical Simulation of the Ion Motion. Ions within an organic film may move in two ways: a thermal randomwalk motion and a systematic drift motion driven by an external electric field. These two motions can be separately described by two coefficients, the temperature-dependent diffusion coefficient D and the ion mobility µ, which are bridged by the Einstein relation51

(5)

It can be shown46 that when the film voltage is much larger than kT/qe, the first term at the right side of eq 5 is small compared to the second and, hence, can be ignored in many circumstances. However, we will later use the same simulation program to calculate the ion escape from potential minimums. In that case, the first term is essential, the random thermal walk determines how an ion climbs over a barrier. So, we keep the first term throughout our calculations. For computational purposes, the film is divided into 4000-10 000 slabs, and eq 5 is numerically propagated in time by the implicit matrix approach.52 Time steps used are on the order of 0.05 s. We use the Stokes-Einstein equation and Stokes equation to estimate the ion mobility and the diffusion coefficient, respectively, using the published viscosity of 3MP33 via eq 6:

µ(t) ) µ(T(t)) ≈

nqe 6πη(T(t))r1

; D(t) ≈

kT (6) 6πη(T(t))r1

where t is the time, µ(t) is the ion mobility, η(T) is the temperature-dependent viscosity of the organic film, nqe is the ion charge, and r1 is the ion hydrodynamic radius. T(t) ) βt, where β is the linear temperature-ramping rate, typically 0.2 K/s in this study. The radii r0 from eq 3 and r1 from eq 6 need not be the same, but for simplicity, here we assume they are. The Stokes-Einstein relation need not be highly accurate, and deviations from it for either materials near the glass temperature,53 or in ultrathin or confined liquids,8,9 are active areas of research. It remains, however, a good point of reference and often works surprisingly well. Equations 5 and 6 also apply to neutral molecules for which the second term on the right of eq 5 is zero. If one follows the motion of an ion and a neutral of similar hydrodynamic size, the ion will traverse the film in a time of t ) L/(µVf/L) during which the neutral will explore (Dt)1/2. After a little algebra, one gets that the neutral will explore L(kT/(nqeVf))1/2 of the film, whereas the ion traverses the whole film. For a 5 V film voltage at 120 K, (kT/(nqeVf)1/2 ≈ (0.01 eV/5 eV)1/2 ≈ 0.045. So in the time period that an ion traverses an 83 ML film at a 5 V film voltage, a neutral (in the absence of other forces) will only explore about 3.4 MLs. The simulation result is shown in Figure 7A for an 83 ML 3MP film for the same conditions as the experiment shown in Figure 4B. The temperature is ramped at 0.2 K/s, so the temperature axis is also proportional to time. At any moment in time, the ion density is represented with a color table (white to black, representing highest to lowest ion density, respectively) versus average ion height above the Pt substrate. To show the wide range of magnitudes, each adjacent color change represents an ion density change by a factor of 10. The simulation shows that the ions at the upper left move into the film as soon as the film becomes reasonably fluidic. Note as expected that the ion distribution quickly becomes spatially broad. Also shown is the mean ion height h calculated at each temperature. This temperature-dependent height h(T) is then compared with experimental data in Figure 4B. For an assumed ion size of 3 Å, the


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Figure 8. High electric field effect on D3O+ motion in 30 ML MCH. The electric field strengths are 4.4 × 108 V/m (solid curve) and 1.2 × 109 V/m (dashed curve). The film and ion depositions were carried out at 34 K, and the temperature ramping rate was 0.2 K/s.

Figure 7. Theoretical simulations for ion motions in 166 ML 3MP/Pt (A) and 83 ML 3MP/4 ML H2O/83 ML 3MP/Pt (B) on Pt(111) at a ramping rate of 0.2 K/s. The curves indicate the temperature evolutions of the film voltages, also showing the average ion height above the substrate surface. The voltage curves in panels A and B are exactly the dashed curve in Figure 4B and the dashed curve c in Figure 20A, respectively. The colors represent the ion density as functions of the ion height and film temperature. Each adjacent color change (from bright to dark) means the ion density decreases by a factor of 10. A simple comparison of the ion density in the two films permits one to immediately identify that in the sandwich film most of the ions are trapped in the aqueous phase until above 103 K, while in the pure 3MP film most of the ions have already drifted across the whole film up to 92 K.

theory fairly well predicts the falloff temperature of the film voltage. However, the falloff width of the theoretical curve is narrower than the experimental one by a factor of 2, as discussed in ref 41. 3.4. Electric Field Effect. The validity of eq 6 can be in question for electric fields as high as we have here. This is illustrated with data on MCH films. MCH has a slightly higher glass temperature than 3MP, 8534 versus 77 K. We have explored ion motion across these films over a field range from 107 to above 109 V/m. The latter may seem too high to be relevant to common physical phenomena, but it is only 0.1 V/Å,

a full order of magnitude below a typical electrochemical double-layer potential. Two singly charged ions in a nonpolar organic solvent will mutually attract/repel at a higher field strength than this when closer than 9 Å. The ion motion in MCH (see the solid voltage curve in Figure 8 with an electric field of 4.4 × 108 V/m) is similar to that in 3MP. Using θ × 3.41 Å for the thickness of θ ML MCH and 3 Å for the hydrodynamic radius of D3O+, the theoretical prediction (not shown here) is in fair agreement with the experiment, deviating similarly as does 3MP. At an electric field of 1.2 × 109 V/m (the dashed curve in Figure 8), the film voltage decreases well below the glass transition temperature of MCH, deviating from eq 6. Ion motion below the glass temperature is also observed (data not shown here) for 3MP and Decalin at similar fields. Severe deviations from the Stokes-Einstein law for organics are routinely seen for fields on the order of 108 V/m in pulsed ion mobility studies.54 The mechanisms for this deviation are not well understood, though our results are in qualitative accord with the notion that the force on the ion exceeds the local yield stress of the material. The local yield stress should decrease with temperature, disappearing somewhat above the glass temperature. At fields near 107 V/m, the leading edge of the voltage drop more closely resembles the theoretical predictions, but the slope discrepancy at the half-height still persists. A very recent paper55 showed that glassy organic films could spontaneously distort (“dimple”) under high field conditions (107-108 V/m, comparable to ours). This could play some role in our experiments, though large-scale motions of the film should be in general accordance with eq 5. Therefore, although a 3 Å ion moves 59 nm, a viscous region of radius 30 nm could move around 6 Å. It is not clear how this would lead to either the low- or high-temperature tail or a factor of 2 in the falloff width of the experimental film voltage. 3.5. Ion Motion Modes in Different Films. Figure 9 summarizes ion motion in various nonpolar or slightly polar films.56 It can be categorized into four groups: (1) Typical ion motion in a good glass-former, 3MP (Figure 9a). The ion motion is mainly controlled by the viscous drag of the medium and can be fairly well described by the Stokes-Einstein law57 for films thicker than 10 ML and fields at or below several times 108 V/m. (2) No ion motion in a crystalline film, i.e., solid CO2 (Figure 9b). (3) Ion motion interrupted by homogeneous crystallization in highly unstable glasses. Examples are shown for D3O+ and Cs+ motion in vapor-deposited hexane (Figure 9c) and CCl4 (Figure 9d). The ions can initially move in the amorphous glassy films above their glass temperatures but stop

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Figure 10. Film voltage versus temperature curves as a function of the added water coverage on top of 83 ML 3MP on Pt(111). The filmgrowth temperature is 30 K and temperature-ramping rate is 0.2 K/s. The water coverage is from left to right: 0, 1.5, 2.0, 6.0, and 35 bilayers. The dashed curves are the theoretical simulations with an energy trap at the top of the 3MP film. For the 35 ML water case, the simulation is unstable at or above 135 K because of the technical problem of the calculation (double precision no longer precise enough), so only the stable part of the calculated curve is shown.

Figure 9. Ion motion in various materials. Temperature evolutions of the film voltages (thin solid curves) and TPD profiles (dashed peaks) for D3O+ in (a) 166 ML 3MP, (b) about 200 ML CO2, (c) 67 ML hexane (solid curve), (d) 80 ML CCl4, and (e) 30 ML MCH. In panel c, the dotted curve is the temperature evolution of the film voltage for Cs+ in a 67 ML hexane film, very similar to that for D3O+. In panel e, the film voltage curves have been normalized in order to compare the curve shapes. Their initial voltages are 4.4 V (thin solid curve) and 13.3 V (thick solid curve). The thin solid curve in e is for the MCH film prepared at 34 K, and the thick curve is for the same thick MCH film that is preannealed to 110 K before the ion deposition.

moving when the films crystallize. The amount of solvent motion required for crystallization can be estimated from the ion motion (using the Einstein relation, eq 4) as approximately one molecular diameter.46 (4) Ion motion perturbed by substrateinduced crystallization. When the MCH film is prepared at 30 K, D3O+ ion motion in it is very similar to that in 3MP, as shown in Figure 9e. However, if the film is preannealed to 110 K or above before the ion dosing, there appears a distinct tail in the film voltage curve (thick solid curve in Figure 9e). The tail progressively increases in height with the preannealing temperature. If the film is preannealed to 139 K, then the film voltage hardly changes until the film starts to evaporate.42 This shows that the substrate surface induces film crystallization. 4. Ion Motion in Sculpted Films Here we show how we can fabricate model interfaces to answer various qualitative questions concerning ion motions in the vicinity of the oil-water interface. In section 5, we shall answer more quantitative questions. 4.1. The Water-Oil Interface. 4.1.1 Experimental ObserVation of the Ion Motion Delay at the Water-Oil Interface. The first question is how much water is required to fully solvate an ion at the oil-water interface. This question is the subject of

our recent publication.58 Some representative plots of Vf versus T from this experiment are shown as the solid curves in Figure 10. The initial film structure is H2O/D3O+/3MP/Pt, as depicted by the inset in Figure 10. The most profound feature is that the ion motion occurs at much higher temperatures as the H2O coverage increases. It is very sensitive to the H2O coverage, even in the submonolayer region. Obviously, the D3O+ motion in the 3MP film is delayed by the addition of H2O on top of the ions, because of solvation of the ion. The plot of the falloff temperature of the film voltage versus the top water layer thickness58 shows that by 12 ML water the shifting of the curves reaches its asymptotic limit. Hence, we can conclude that about 12 ML water is required to reach the limit of full solvation for an ion at that oil-water interface. In data not shown here, we have examined whether there is a kinetic barrier for the ions to traverse a thin film of water. For 5 ML or less water, it makes no difference whether the water is placed on top of or underneath the ions. 4.1.2. Spatial Extent of the SolVation Effect. A simple question arises: How far from the oil-water interface does the solvation potential reach? To answer this question, more complex composite films were used, a water/3MP(shield)/D3O+/3MP/ Pt. A 3MP layer is added between the water layer and ions in the structure used in Figure 10. One can change the thickness of this shield 3MP layer to determine how thick the shield 3MP layer should be in order to shield the hydration effect completely. As shown in Figure 11, with a thickness of 4 ML (about 14 Å) for the shield 3MP layer (solid curve), the ions do not feel any solvation effect at all. They move into 3MP as if the top water layer were nonexistent, in sharp contrast with the ion motion in water/D3O+/3MP (dashed curve). This demonstrates that the water solvation effect is localized near the water-oil interface. Similar experiments with shield layers of 1, 2, and 3 ML will help explore this potential reach in more detail. 4.2. Ion Motion Delayed by Added Water in a Reverse Micelle. A reverse micelle analogue can be fabricated by placing


Figure 11. Shielding the solvation potential. Normalized film voltage curves for D3O+/83 ML 3MP/Pt (solid curve), 4 ML H2O/D3O+/83 ML 3MP/Pt (dashed curve), and 4 ML H2O/4 ML 3MP D3O+/83 ML 3MP/Pt (dotted curve). The initial voltages are 6.6 (solid), 4.2 (dashed), and 4.7 V (dotted), respectively. All films and ions are deposited at 34 K, and the ramping rate is 0.2 K/s.

Figure 12. Trapping ions in a water layer. Temperature evolution of the film voltage for D3O+ migration through (a) 166 ML 3MP/Pt, (b) 83 ML 3MP/2 ML H2O/83 ML 3MP/Pt, and (c) 2 ML H2O/166 ML 3MP/Pt. All films are grown at 30 K, and the temperature is ramped at 0.2 K/s. The inset shows the initial film structure for curve b, not in proportion. Adapted from ref 43 with permission.

thin water layers in the middle of an organic film, as illustrated in Figure 1. This was reported in part in our paper in Langmuir.43 Various structures are used to answer different questions. Figure 12 shows the temperature evolution of the film voltage (trace b) for D3O+ motion across a micelle-like film: 83 ML 3MP/2 ML H2O/83 ML 3MP/Pt (about 60 nm in total thickness), all deposited at 30 K. Ions deposited on the top of the film initially create a film voltage of 9.6 V that does not change below 80 K. When the assembly is further warmed, the film voltage rapidly decreases between 84 and 92 K, then hesitates near 95 K, and finally rapidly drops between 98 and 100 K. The most interesting point in this experiment is that the film voltage pauses near 95 K at about half of the initial voltage, as one would expect from eq 2, if the ions migrate down and become temporarily trapped in the thin aqueous layer. Because an ion moves much faster than a neutral,46 the water layer is not expected to be able to diffuse before being sampled by the ions.

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Figure 13. Trapping ions in a water layer. of variable thickness. Normalized temperature evolution of the film voltage as a function of the thickness of the added water layer in the 83 ML 3MP/H2O/83 ML 3MP/Pt sandwich film. The water coverage is (a) 0.0, (b) 1.0, (c) 2.0, (d) 4.0, and (e) 10 ML (the unscaled starting voltages are 7.6, 8.5, 9.7, 9.6, and 8.9 V, respectively). Also shown are the corresponding TPD profiles of 3MP. The sharp peak at about 150 K of the TPD profile e is due to the volcanic desorption of 3MP. Adapted from ref 43 with permission.

Also shown in Figure 12 is the temperature evolution of the film voltage for D3O+ in pure 166 ML 3MP (trace a), i.e., the water layer in the above-described sandwich film being left out. Without the water layer in the middle of the film, the voltage just drops in a single step between 84 and 94 K with no pause. This clearly indicates that the pause in voltage for the micellelike film is due to the water layer. We also studied the D3O+ motion in 2 ML H2O/166 3MP/Pt films, at similar fields as in the original sandwich film, as displayed by trace c in Figure 12. It is very similar to the second drop of the Vf versus T curve (trace b) for the micelle-like film. Trace c does not show the first voltage drop as for the micelle-like film because the water layer of the 2 ML H2O/166 3MP/Pt film immediately traps the ions before they can migrate. 4.2.1. Effect of the Thickness of the Added Water Layer. Figure 13 shows the thickness effect of the added water layer on the ion transport in the reverse micelle films. To compare the Vf vs T curve shapes, all initial voltages (≈8-10 V) have been normalized to 1.0. It is clear that with the increase of the water layer thickness the voltage pause becomes more and more pronounced and the second voltage drop shifts to higher temperatures. For the 10 ML H2O case, the film voltage stays at half the initial value over a very broad temperature range (95-120 K) until 3MP desorption starts. The 10 ML water layer forms a nearly impermeable barrier to ion motion. This film also partially blocks the evaporation of the underlying 3MP molecules. This creates the so-called “molecular volcano” eruption59 when cracks are abruptly formed during water ice crystallization, as shown in Figure 13 by the very narrow TPD peak of 3MP around 150 K, much higher than the normal 3MP desorption temperature, 134 K. In all curves for water coverage higher than 1 ML in Figure 13, the film voltage clearly lingers at half of the initial voltage, unambiguously showing that the ions are trapped by the aqueous phase. 4.2.2. Sensing the Water Layer Position. As stated above, the motion of neutral molecules (either 3MP or water) is expected to be much slower than that of the ions. Therefore,

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Figure 15. Ion hydration by various solvents. Temperature evolution of the normalized film voltage for 83 ML 3MP/4 ML H2O/83 ML 3MP/ Pt (solid curve), 83 ML 3MP/6 ML PrOH/83 ML 3MP/Pt (dotted curve), and 83 ML 3MP/8 ML MeOH/83 ML 3MP/Pt (dashed curve). All films are fabricated at 34 K. The initial voltages are 7.7 (solid), 8.6 (dotted), and 9.0 V (dashed), respectively.

Figure 14. Detecting where the water is. (A) Temperature evolution of the film voltage for 41 ML 3MP/ 4ML H2O/125 ML 3MP/Pt (dotted curve), 83 ML 3MP/ 4ML H2O/83 ML 3MP/Pt (solid curve), and 125 ML 3MP/ 4ML H2O/41 ML 3MP/Pt (dashed curve). Also shown are the TPD profiles for 3MP (× 1) and H2O (× 200). Again the shaded area in TPD is due to the blocking effect of the Kelvin probe. (B) Corresponding normalized film voltage curves from A to compare the shapes. The cartoon at the right side shows the initial sandwich film structure with the middle water layer at different positions. Adapted from ref 43 with permission.

the probing ions should be able to sense the aqueous phase before the water molecules significantly diffuse into the 3MP films or vice versa. If the water layer is buried in different positions of the 3MP film, the ions should pause at different positions and the film voltage profile should reflect the difference. Figure 14 displays the results. When the water layer is buried at 3/4, 1/2, and 1/4 of the 3MP film height (166 ML), the voltage pause occurs expectedly at about 1/4, 1/2, and 3/4 of the initial film voltage, respectively, which can be clearly seen by the normalized film voltage curves in Figure 14B. This further demonstrates that the voltage pause at half of the initial voltage in Figures 10 and 11 is due to the trapping of the ions by the aqueous phase. 4.2.3. SolVation by SolVents Other Than Water. We can explore the relative solvation abilities of various solvents in our synthetic reverse micelles. Water’s strong solvation stems from its high dielectric constant. If we try other solvents of less dielectric strength, the trapping strength is expected to decrease. Water, methanol, and n-propanol near room temperature have dielectric constants of 72, 36, and 20, respectively.45 Figure 15 shows the experimental observation of the ion motion delay for sandwich films with middle layers of water, methanol (MeOH), and n-propanol (PrOH). The trapping in the solvating layer is clearly a function of its composition. It is shown that the temperature where the film voltage has fallen to 10% the initial value is nearly linear with the water layer thickness for

Figure 16. Motion of the water layer. Temperature evolution of the film voltage for D3O+ motion in 83 ML MCH/8 ML H2O/83 ML MCH prepared at 34 K and preannealed to 120 K for about 1 min before cooling down to 34 K for ion deposition.

less than 10 ML.58 Assuming that this linear relationship also holds for methanol and propanol, then we can extract some numerical measure of the solvation power of the middle solvent (water or alcohols) as ∆T1/4/θs, where θs is the thickness of the middle solvent. ∆T1/4 ) T1/4 - T1/4(3MP), where T1/4 is the temperature at which half the ions have escaped the trap (thus the voltage drops to 1/4 the initial value) in Figure 15 and T1/4(3MP) is the T1/4 value for the 3MP film without any solvating layer (Figure 12). The solvation powers are water (3.75 K/ML) . methanol (0.81 K/ML) > propanol (0.75 K/ML), in coincidence with the order of their dielectric constants at roomtemperature mentioned above. Admittedly, these results are very preliminary, but in general, these studies show that the relative solvation properties of a wide range of solvents in nanometerscale controlled geometries can be explored.

2492 J. Phys. Chem. B, Vol. 105, No. 13, 2001 4.2.4. Neutral SolVent Diffusion. Diffusion of water in the sandwich structures shown above could lead to changes in the film morphology, particularly as the thicker water layers delay the ion penetration to higher temperatures. For thin water layers where the ions move through the film only a few degrees higher than they would without the water, the much more rapid motion of ions under these fields compared to neutral diffusion likely prevents significant structural changes during the ion motion. This should be further slowed, as each water molecule strongly binds to the rest of the water layer, and has a potential barrier unfavorable for its leaving. However, at 130 K, the 3MP and MCH solvents are orders of magnitude less viscous than near 90 K, so neutral diffusion will be inhibited only by the unknown barrier to water molecules diffusing laterally along the waterorganic film or “evaporating” into the organic film. Such diffusion at higher temperatures would have some interesting driving forces. An ion in the water film ought to attract mobile water molecules, making the film locally thicker and the trap deeper. The electric field at the water-organic interface directly under the ion is locally higher than anywhere nearby. If a water molecule migrates to this location to lower its energy, this locally decreases the distance between the water layer and the Pt substrate, which in turn increases the field even more locally and attracts more water molecules. This could lead to growth of a water whisker or an icicle. If the supply of water is enough and the organic layer thin enough, the whisker or icicle could reach the Pt surface. The complications are more likely important for thicker water films, where the temperature of ion passage is highest. They provide some interesting opportunities to test these notions. Two examples are given in the following. One simple experiment is that we can warm the micelle-like film to higher temperatures before ions are deposited on top. If the water layer drastically diffuses, then we would expect either that the voltage curve shows no pause or that the film voltage is diffuse at the half film voltage (or half-height). Figure 16 gives the result. Interestingly, the film voltage is similar to that for the film prepared at 34 K without preannealing (see Figure 13), implying that the water does not seriously diffuse up to 120 K. However, the shape of the voltage curve does change, i.e., the plateau around half of the initial film voltage is rather more diffuse than flat, suggesting that the water film may be still intact, but its vertical position in the film may be varying with lateral position. Moreover, the second voltage drop is not so steep, implying that there may be a broadening of the water layer. Another simple experiment is to make a double sandwich. By putting one water trap, say, at the 2/3 point in an organic film and the other at the 1/3 point, the ions could be delayed in the upper trap, permitting the water at the lower trap to undergo structural rearrangements. Results of such an experiment with two equally thick water layers is shown in Figure 17, for 83 ML 3MP/4 ML H2O/83 ML 3MP/4 ML H2O/83 ML 3MP/Pt. The voltage shows two pauses, one sharply at 2/3 of the initial voltage and a second more broad near 1/3 of the initial film voltage. The presence of the second layer is clear when compared against the film without the second layer (dotted curve in Figure 17). Because the trap depth of the second trap is expected to be the same as that of the first one, it is expected that the second trap should only cause a shoulder, as observed. Simulation results of the ion escape across a double well show that detailed interpretations of this must include field effects (discussed in the next section) and will be subject of future studies.

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Figure 17. Temperature evolution of the film voltage for D3O+ motion in a “double-sandwich” film: 83 ML 3MP/4 ML H2O/83 ML 3MP/4 ML H2O/83 ML 3MP/Pt. The arrows indicate the voltage pauses. The dotted curve is the experimental curve for the film without the lower water layer, namely, 83 ML 3MP/4 ML H2O/166 ML 3MP/Pt. The drawing at the right side of the figure shows the initial film structure of the “double-sandwich” film. Adapted from ref 43 with permission.

Figure 18. Calculated shift of the temperature (at the half initial voltage T1/2) with the thermodynamic radius of the ion for its motion in a 83 ML 3MP film at a ramping rate of 0.2 K/s. The inset shows the simulated temperature evolution of the film voltage (the initial voltage is 4.0 V) as a function of the ion radius (increased by 1 order of magnitude between two adjacent curves from left to right, as the arrow indicates).

5. Determining the Solvation Trap Potential Depth and Shape 5.1. General Goals. Many physical phenomena have been illustrated above, using the ability to sculpt the oil-water interfaces. We now seek to extract quantitative information about the solvation potential an ion feels near the oil-water interface, using these and similar experiments. The tens of degrees delay of the ion motion caused by layers of water or alcohols cannot be solely explained by an increase of the hydrodynamic radius of the hydrated ion. Figure 18 shows, versus the ion hydrodynamic radii, the temperature predicted by our ion mobility models for the ions to move

Feature Article halfway through an 83 ML film of 3MP, with an initial film voltage of 4 V and a ramping rate of 0.2 K/s. A shift of 10 K in temperature requires around 5 orders of increase in ion radius. This large radius is simply not possible because there are not enough water molecules in either the water/3MP/Pt or the 3MP/ water/3MP/Pt composite films to create such huge ion balls nor is the organic layer thick enough for such a ball to move within it! Instead, the dominating factor must be an energy change preventing the ions from entering the organic phase in the form of a trap or barrier. Using the sculpted films, we can determine the depth of the trap (or height of the barrier), the main slope of the trap, and the fringing potential. The data shown above can be quantitatively compared against various theoretical models to further our understanding of the potentials and kinetics that control the ion transport across the organic-water interface. Ideally one would do this by a direct molecular dynamics simulation, following the motion of thousands of water and solvent molecules individually interacting with each other and the ions via parametrized potentials. Our ion motion occurs over periods of seconds. Molecular dynamics cannot readily be followed for seconds: Nanoseconds are more likely the practical limit. However, potentials and kinetics derived from molecular dynamics over nanoseconds can be a reasonable starting point for extrapolating kinetics to seconds. In this paper, we forego such a detailed analysis. Instead we look for a parametrized potential trap out of which a kinetic escape resembles our data. Such a potential will be compared against a reasonable model, the Born potential. We shall find that not only the trap depth but also its slope can be deduced. Either a potential maximum (barrier) or minimum (trap) can keep the ion from traversing the water layer. Which one exists can be inferred by comparing Figures 10 and 12. In Figure 12, the ion has to traverse the water layer. In Figure 10, the ions are placed just below the water layer. If the water layer acts as a barrier, then the ions placed on the Pt side of the barrier should not be affected by it, because the collective electric field will pull the ions directly to the Pt substrate. However, that is clearly not the case. The effect of 0-5 ML of water is the same whether the ion is placed on top or under the water film. This is consistent with an attractive trap that pulls the ion back into it, even when the ion starts under the water layer. A 15 ML or thicker water film shows true kinetic barriers to ion motion through the water phase. For simplicity, we will focus on the water layer thinner than 5 ML for the remainder of this paper when ions must traverse the film. 5.2. Kinetic Model and Assumptions. The equation of motion for an ion given in eq 5 does not explicitly contain a trap potential, but it can be easily added by either of two ways. The first way was previously used to analyze data for the “oil”water interface shown in Figure 10, as a function of water film thickness.58 In that work, a kinetic trap was placed at the top of the 3MP film. The ions escaped by an assumed Arrhenius rate with an activation energy presumed to be equal to the trap depth, with an assumed preexponential of 1013 s-1. Once an ion escaped the trap, it migrated via eq 5 away from the trap. Randomwalk returns to the trap were ignored (not so severe an error under intense field conditions). We had concluded that 15 ML or thicker water layers made a solvation trap that was 0.4 eV deep and that the dependence of the trap depth on water thickness was very well fit by a Born model, with a Born radius of the ion of 4.6 Å and a water dielectric constant on the order of 100. The Born model had been calculated using an analytical approximation used by Conway.13 We have since compared his

J. Phys. Chem. B, Vol. 105, No. 13, 2001 2493 analytical equation against numerical and other analytical calculations and found that the Conway approximation is only accurate for small differences in the dielectric constant at the interface, not the case here. We also did not permit the ions to fall backward into the trap. Also, since then, we more fully appreciate the effect of the electric field on the trap, which we hereafter use to our advantage. As discussed below, the electric field that the ions collectively generate can greatly alter the trap depth. To see this and make use of it, a physical rather than just a phenomenological trap is needed. The trap can be added to eq 5, if we add to the nqe*E term a new one equal to the spatial gradient of the trap potential. The ions will experience a drift velocity generated by the force coming from the gradient in the collective electric potential (largely because of the other ions) or from the gradient in the chemical potential (trap) of an individual ion interacting with solvents at the interface. This is immediately appealing, because we no longer have to assume an Arrhenius preexponential factor for the ion to escape the trap: The particles simply randomwalk out of the potential trap. However we need the diffusivity and mobility of the ion in the thin water film and in the adjacent 3MP films. Glasses near interfaces can have different flow properties from those of the bulk.9 However, for simplicity, we will assume bulk 3MP’s viscosity throughout the material, including the water layer. This added term determines the ion escape from the potential minimum provided that the ion motion in the crucial region of the trap can be well described by diffusion in pure 3MP. This is not unreasonable, and we have evidence to this effect, as will be shown later. We also need a hydrodynamic radius for the ion, which probably changes after the ions encounter the water layer. And we need a Born radius to calculate the potential very near the vacuum or metal interface. For simplicity, an unchanging (Born and hydrodynamic) ion radius of 5 Å is used throughout. 5.3. Expected Electric Field Effect. As soon as we started the process of fitting trap potentials, we were surprised to find that the collective electric field of the ions was often strong enough to grossly perturb the effect of the solvation trap. Figure 19 shows the potential trap for an ion under a collective electric field up to 6 × 108 V/m that is easily accessible to our experiments. The trap depth, 0.26 eV shown here, is reasonable (and, as shown later, not arbitrary). A Lorentzian form (∝ 1/(1 + 4*(z - z0)2/(∆z)2)) is used for the trap shape, where ∆z is the Lorentzian fwhm (full width at half-maximum) set at 6 Å. A flat bottom has been grafted into the minimum of the trap to permit them to better resemble Born-potential traps to be discussed later. The charge that creates the field is placed at the left edge of the trap bottom. What is remarkable is that the field strengths we can easily access are high enough to progressively lower and eventually eliminate any barrier delaying the ion motion. At 6 × 108 V/m, the applied potential slope is greater than the maximum slope of the original trap potential, completely eliminating the maximum to the left of the trap center. This makes it very clear that, to characterize the unperturbed trap, fairly low fields must be used. However, much more than that, this gives us an exciting new possibility: by looking at the field dependence of the escape of the ions from the trap, we should be able to measure not only the depth of the trap but its shape as well! In addition, the potential diagram also explains why the shielding experiment shown in Figure 11 worked so well. Let’s look at the dashed potential curve in Figure 19. It shows the expected potential for ions placed 3.4 ML 3MP away from the


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Figure 19. Calculated dependence of the ion-trapping barrier on the collective electric field generated by the ions for the 83 ML 3MP/ 4 ML H2O/83 ML 3MP/Pt film. The zero ion position refers to the metal substrate surface (the 3MP-Pt interface). A distance of 5 Å is used as the hydrated ion radius. The numbers in the panel indicate the electric field strength for each potential curve. The energy well adopts the Lorentzian form (fwhm ) 6 Å) with a flat bottom (8 Å wide). At zero electric field, the well depth is 0.26 eV. The dashed curve diverging from the zero electric field curve is for the ions initially sitting at z ) 28.3 nm (the white ion position), 3.4 ML 3MP below the water layer.

water layer. The collective ion field in Figure 19, dashed curve (2.3 × 108 V/m), is similar to that in Figure 11 (1.5 × 108 V/m). At the initial position of the ions, the potential is actually at a local maximum, with the left-hand slope much steeper than the right-hand slope. The result is that most of the ions will move to the left and not be trapped. Experiments to measure the fraction of ions that do trap would be a sensitive measurement of the local slope of the potential, and are planned. 5.4. Experimental Field Effect on Trapping. To test the effects of field on trapping, a series of experiments have been carried out with a constant physical trap and various electric fields. The trap is made by placing 4 ML of water between two 83 ML thick films of 3MP (a sandwich composite film). Ions are then added to the top of the assembly in varying amounts near 30 K, to reach various starting voltages. The temperature is finally ramped at 0.2 K/s. The resulting Vf vs T curves are shown in Figure 20A. What is observed is a dramatic change as the field progresses from low to high field. The effect is more clearly seen in Figure 20B, where all initial voltages have been normalized to unit height. This makes the curves in Figure 20B proportional to the average ion height in the film. All curves show a drop to about 1/2 the initial voltage around 90 K. This is because the ions migrate down through the top layer of 3MP. The ion motion within the top layer does show the expected increase in drift velocity with field. Then the ions sit in the trap until they can escape. The important observation is how profoundly the ion escape from the trap is altered by the electric field: At 3.9 × 108 V/m, the trap has nearly ceased to even delay the ions. 5.5. Fitting a Potential. To find a trap potential that reproduces the results in Figure 20, we can simulate the ion motion by using eq 5 with the gradient of the trap potential added to the collective E-field term. An example of such a calculation is shown in Figure 7B. In this calculation, a Lorentzian trap (0.26 eV in depth and 6 Å in fwhm) is placed in the middle of a 166 ML 3MP film with enough ions put on top of the film to match one of the starting voltages of Figure 20A. The starting voltage is only 20% different from that for the calculation in Figure 7A where no trap is present. For the

Figure 20. Electric field effect on the D3O+ trapping/escape from the 83 ML 3MP/ 4 ML H2O/83 ML 3MP/Pt at a ramping rate of 0.2 K/s. In A, the solid and dotted curves are from the experiment and theory, respectively. See text for the details about the theoretical calculations. The electric field strength is (a) 0.21, (b) 0.55, (c) 1.1, (d) 3.2, and (e) 3.9 × 108 V/m. B shows the corresponding normalized film voltage curves to compare the curve shapes. The arrow indicates the increase of the electric field E.

case with the trap, the ion motion is followed over a wider temperature range. As the temperature is ramped, the ion density in Figure 7B moves initially just as it does with no trap present. But then the ions fall into the trap. By 96 K, in either Figure 7A or Figure 7B, the ion density in the upper part of the film drops below 10-10 of its initial value. The ions begin to escape the trap as the temperature is raised. Because the color shading is based on the log scale of the ion density (1 decade per color), it does not easily show the details for the ion escape from the trap. One can instead use the curve that gives the average ion height (left axis) and the predicted film voltage (right axis). By 110 K, half of the ions have escaped the trap and the film voltage is now 1/4 its initial value. Delayed by the trap, the ions escaping the trap at a higher temperature will find that ion motion in the lower organic film will be very fast. The net effect is that the density of ions below the trap will be at a steady-state value determined by the rate of release of ions from the trap. This density is seen in Figure 7B from 92 to 113 K (and extends higher in temperature at yet

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Figure 21. T1/4 vs electric field as a function of the input trap. T1/4 is the temperature where the film voltage falls to a quarter of its initial value. The shape of the input trap is determined by the trap depth and width (fwhm). The dots are the experimental data obtained from Figure 20. The solid curve is for the best fit from theory. The trap index in the panel, for example, (0.26 eV - 6 Å), means the trap depth and width (fwhm) are 0.26 eV and 6 Å, respectively.

lower density). Note that this density has a maximum around 100 K at a temperature well below the maximum rate of ion escape from the trap (near 105 K). This is because the rate of escape Re from the trap is equal to the ion flux in the lower region, which is nearly equal to FµE (the product of the ion density, ion mobility, and electric field). This means that F is approximately equal to Re/(µE). So, the temperature at which the ion density peaks below the trap is shifted from that of the peak escape rate because of the rapid temperature dependence of µ. Similar calculations were done for many different parameter sets. To compare with the experiment, we plotted, against the electric field, the predicted temperature T1/4 where a half of the ions have escaped from the trap and, hence, the film voltage is then equal to 1/4 the original film voltage. Figure 21 shows the theoretical and experimental results for T1/4 vs E. There is a unique set of parameters that fit the data, a fwhm of 6 Å and a well depth of 0.26 eV. If we alter the well depth, we raise or lower the curve. If we change the fwhm, we change the slope of the curve. Only a fwhm of 6 Å and a well depth of 0.26 eV fit the T1/4 data well. We next look at how well the best fit potential reproduces the detailed Vf versus T curves. The predicted temperature evolutions of the film voltages in Figure 20 parts A and B resemble the experimental curves, with some deviations. Some of the more noticeable differences occur before the ions get trapped. The deviations at the highest electric field, where the ions move earlier than the theory predicts, is due to the highfield-dependent ion mobility in the 3MP (similar to the case for MCH in Figure 8). At low electric field the ions move in the top part of the film a little more slowly than theory. We have seen clear indications that 3MP’s viscosity is shifted somewhat by proximity to interfaces. This is being explored carefully in separate experiments and is ignored in the present analysis. The theory also predicts a long tail of the Vf curves as the ions escape the trap. The trapping potential, when most of the ions are still in the trap, shows strong reduction in the barrier for the ion escape because of the electric field, as shown in Figure 19. As ions begin to leave the trap, the field decreases, making the trap deeper for the remaining ions. This makes for


Figure 22. Energy barrier (trap) vs water layer thickness. The solid points are inferred from the experimental data. Dotted and dashed curves are calculated using the Born model with a dielectric constant w of the water layer of 5 and 100, respectively. The solid curve is a simple fit of the solid points. The ion Born radius is assumed to be 5 Å.

a long tail in the theoretical escape and a common high temperature edge for all theoretical curves in Figure 20A. This is not experimentally observed. Despite these differences in detail that are the subject of ongoing studies, we are able to find a potential that clearly reproduces the overall effect of the electric field on the trapping of the ions. This gives us some confidence that some knowledge about the solvation potential depth and shape can be gained. In simulations not shown here, we have looked at curves related to our best fitted curve to see what part of the potential was in fact well determined. In reference to Figure 19, the field effect on the ion trap is entirely on its left side (toward the substrate). The ion trapping is nearly insensitive to the change of the righthand side of the potential. Thus, it is not experimentally determined. The potential is assumed to be symmetric in Figure 19, a plausible though not necessarily a true quality. Furthermore, flat bottoms are also inserted into the potential, as shown in Figure 19. This also does not alter the predicted escape from the trap very much. The true well fwhm is not determined. What the ion motion is sensitive to is the typical slope of the left side of the curve that depends on the Lorentzian width. We get similar trapping in a 0.26 eV deep triangular well if we make the slope of the left side about 0.26 eV/(6 Å). 5.6. Well Depth Versus Water Thickness. The analysis above looked at a single physical system, 4 ML of water between two 83 ML 3MP films. The well depth and shape should vary with water layer thickness, as seen in Figures 10 and 13. According to the above discussions, we should be able to much better determine the potential now than in our previous work.58 To definitively obtain the well depth, field-dependent data would be needed for each water film thickness. At the present time, this is only available for the 4 ML water case. However, if we assume in the interim that the left-hand side of the trap is always a Lorentzian with a 6 Å fwhm, we can determine for each water coverage what well depth would give the observed temperature for ions leaving the trap. The result of this simulation is shown as the dotted curves in Figure 10. A fairly good fit is obtained for all water coverages, except for the highest one, 35 ML. The well depth inferred from the experiment is shown as a function of water coverage in Figure 22 (solid points). Notice that though we tried to minimize field


Wu et al.

TABLE 1: Energy Changes for Ions Transferring from Bulk Water into a Second Phase Energy Change eV kJ/mol 0.51a 0.82 0.75 0.65 0.61 0.031 0.39 0.47 a

49a 79 71 63 59 3.0 38 45

ion

second phase

[at 298 K]

D3O+ ClCs+ ClClN(CH3)4+ Na+ Cl-

3MP CCl4 CCl4 ClCH2CH2Cl CH2Cl2 C6H5NO2 H2O-vapor interface H2O-vapor interface

1.9 2.2 2.2 10 8.9 35

H2O’s in solvation shell unknown 7f3 8f4 7f3

T (K)

ref

Sculpting the OilWater Interface to Probe Ion ... - ACS Publications

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