Chapter 19: Processes at Solid Surfaces

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If you look around, I mean nearly every major industrial process, things like making microchips or cleaning up car exhaust, it all happens right there at the boundary between two things.

Welcome to the deep dive.

Today we're going for a really rapid but hopefully comprehensive shortcut through the well the pretty dense physical chemistry of solid surfaces.

We're relying on a core textbook chapter to give you that atomic level view looking at how molecules actually stick, how they react, and how they transfer charge.

Yeah surfaces really are the engines of modern chemistry and they're deceptively complex when you first look at them.

So our mission today is to kind of structure this material for you.

We'll move logically from you know the basic physical structure of a solid surface right through to the complex map that governs how those surfaces drive chemical reactions and electrical currents.

We're really trying to make this technical stuff feel immediately applicable, maybe even memorable.

Okay let's dive in then.

Starting right at the beginning.

Defining what this active interface actually is.

Right.

So when we talk about surfaces, the first thing is distinguishing between adsorption, that's a particle attaching to the surface, and absorption.

Absorption being where it goes inside into the bulk material.

Exactly.

Absorption is surface only.

Absorption is penetration.

And we have names for the players, the particle sticking, that's the adsorbent.

And the solid it sticks to?

That's the adsorbent, or sometimes you'll hear it called the substrate.

Same thing.

Okay and what's really interesting I think is that the most active places on this surface, they aren't usually the nice smooth flat parts, are they?

If you could zoom right in on a real solid, what would we actually see?

Yeah you'd see atomic ruggedness.

It's not perfectly flat, we actually categorize these imperfections.

You have these flat atomic layers we call terraces.

Like steps on a patio.

Kind of, yeah.

And the edges between those layers, those are literally called steps.

And then if you have a defect or a corner along one of those steps, that's a kink.

Kinks.

And these kinks and steps, they are incredibly important because those are the spots where an incoming molecule can interact with maybe two or three surface atoms all at once.

Ah, so it's trapped more effectively?

Much more effectively.

It creates a much stronger binding site.

Think about it like a billiard ball rolling on a flat table versus falling neatly into a corner pocket.

The pocket holds it better.

So the defects are actually the chemical hot spots.

Yeah.

Makes sense.

But okay, even if we manage to make a perfectly flat, ideal surface, the sources immediately point out this massive problem.

Just keeping it clean.

Oh, it's a kinetic nightmare.

Seriously.

Yeah.

If you use the kinetic theory of gases, let's say you have a perfectly clean surface and you expose it to just ordinary nitrogen gas, room temperature, one bar pressure.

Standard conditions.

Standard conditions.

The collision flux, the rate at which molecules hit the surface is enormous.

A single atom on that surface gets struck something like a hundred million times every single second.

Wow.

A hundred million times a second.

Yeah.

So your pristine surface is gone instantly.

Instantly.

It would be completely covered in whatever random contaminant molecules are floating around before you could blink.

Okay.

That sounds, yeah, completely impossible to study.

So the fix for this kinetic chaos has to be just getting rid of most of the gas, right?

Drastically lowering the pressure.

Exactly.

That's why serious surface science requires what we call ultra high vacuum or UHV.

These UHV systems pump things down to incredibly low pressures.

How low are we talking?

So low that the collision flux just plummets.

Instead of a hundred million hits per second, maybe a single surface atom only gets hit once every say a hundred thousand seconds or even a million seconds.

Which translates to?

Roughly once a day.

So UHV gives you maybe a full working day to do your experiment on a clean surface before it gets significantly contaminated.

Okay.

That gives us the necessary window.

So once a molecule does arrive at this clean surface and sticks, we need to classify how it's sticking.

There are two main ways, right?

Physisorption and chemisorption.

That's right.

Physisorption or physical adsorption, that's the weaker interaction.

It's driven by those long range kind of general sticky forces between molecules called van der Waals forces.

Like the forces that gases condense into liquids.

Precisely.

And the energy released, the enthalpy change is pretty small.

Similar magnitude to condensation may be around say minus 20 kilojoules per mole.

The key thing is the molecule itself stays intact.

It doesn't chemically change.

And the energy dissipation process is called accommodation.

Yes.

That's the term for how the incoming molecule sheds its excess kinetic energy as it settles onto the surface.

Okay.

So if physisorption is weak clang, then chemisorption must be the serious commitment.

It really is.

Chemisorption involves forming a genuine chemical bond, usually a covalent bond, between the molecule and the surface.

It's short range and much stronger.

How much stronger?

Typically maybe 10 times stronger enthalpy wise.

Think energies around minus 200 kilojoules per mole.

It's a strong bond.

And that much energy often means the molecule itself changes.

Very often.

The strong interaction can easily break bonds within the absorbed molecule.

For example, a hydrogen molecule, H2, might hit the surface and chemisorb as two separate hydrogen atoms, each bonded individually to the surface.

Okay.

Let's think thermodynamics for a second.

If absorption happens spontaneously, the Gibbs energy change, delta Gd has to be negative.

Right.

But when a gas molecule sticks to a surface, it loses a lot of freedom to move around.

Its entropy goes way down.

So delta T is always negative for adsorption.

Yes.

So looking at delta G, delta HTD, it's a negative.

That delta T delta T term is positive.

For delta G to be negative overall, what does that force delta H2 to be?

That's a crucial point.

It forces delta Hg, or the enthalpy change, to be negative and usually significantly negative to overcome the entropy loss.

So adsorption basically has to be exothermic.

It must release heat to happen spontaneously.

Makes sense.

Okay.

Now how do we actually see all this happening?

We need tools, atomic level magnifying glasses.

What's in the surface scientist toolkit?

Well, the star player for actually seeing individual atoms is the scanning tunneling microscope, the STM.

How does that work?

Is it like a tiny finger feeling the surface?

Sort of, but using quantum mechanics, it relies on electron tunneling.

You bring an incredibly sharp metal tip, like atomically sharp, extremely close to a conducting surface, just hovering above it.

Okay.

And electrons can actually tunnel across that tiny vacuum gap.

The amount of current that tunnels is exponentially sensitive to the distance between the tip and the surface atom right below it.

So tiny changes in height cause big changes in current.

Exactly.

So you scan the tip across the surface, keeping the current constant by moving the tip up and down, and you basically map out the atomic bumps.

You get an image of the atoms.

And STM isn't just for static pictures, right?

The source has mentioned using it to watch things move.

Yeah, that's really powerful.

You can actually track a single adsorbed atom as it randomly hops around on the surface.

That's surface diffusion.

And by watching how fast it hops at different temperatures, you can figure out the energy barrier it needs to overcome to move from one site to the next.

That's the activation energy for diffusion, EAAF value.

Cool.

Okay.

What about figuring out the overall arrangement of surface atoms, not just seeing individuals?

For that, a key technique is low energy electron diffraction, or AAA.

You gently bounce low energy electrons off the surface and they diffract, creating a pattern on a screen.

Like x -ray diffraction for bulk crystals.

Very similar principle, yes.

But LAY is surface sensitive.

It tells you about the arrangement of atoms just in the top few layers.

And AAA is often how we discover surface reconstruction.

Reconstruction, what's that?

That's where the atoms in the very layer of the solid decide to arrange themselves differently than the atoms deeper inside the bulk crystal.

They reconstruct into a new pattern.

And that different pattern would affect how things stick to it.

Absolutely.

A reconstructed surface can have very different chemical properties than the unreconstructed bulk material would suggest.

Okay.

And lastly, how do we know what elements are actually on that surface, if we suspect contamination, for instance?

For chemical identification, we have spectroscopic techniques.

X -ray photoelectron spectroscopy, XPS, uses x -rays to knock out core electrons, and their energy tells you what element they came from.

Auger electron spectroscopy, AES, is another one involving electron cascades that also gives you elemental fingerprints.

Both tell you what's there.

Right.

Okay.

So we can see the surface, identify what's on it, and even watch atoms move.

Let's switch gears now from seeing to quantifying.

How much stuff is actually sticking?

This brings us to the idea of adsorption isotherms.

Exactly.

The adsorption isotherm is basically the key plot here.

It shows you how much of the surface is covered.

We call that the fractional coverage, the defurge as you change the pressure of the gas above it to L dollars while keeping the temperature constant.

Hence isotherm.

And the simplest model, the one everyone learns first, is the Langmuir isotherm.

Now, this one comes with some pretty strict assumptions, doesn't it, to make the math work out nicely?

It does.

It paints a very simple picture.

You have to assume.

One, only a single layer of molecules can stick a monolayer.

No stacking allowed.

Okay.

One layer only.

Two, all the adsorption sites on the surface are identical.

Every spot is equally sticky.

Makes sense for a simple model.

Three, a molecule can only stick to an empty site.

And four, maybe the most important simplification,

the adsorbed molecules don't interact with each other.

They don't attract or repel their neighbors.

So like isolated molecules just sitting on identical spots in a single layer.

Pretty much.

And if you make those assumptions, you can derive the isotherm by thinking about dynamic equilibrium.

The rate at which molecules stick, the adsorption rate, must equal the rate at which they leave, the adsorption rate.

And the adsorption rate depends on the pressure of the gas and the number of empty sites available.

Right.

Proportional to phi and a dollar theta, the fraction of empty sites.

Well, the adsorption rate just depends on how many sites are already filled.

Exactly.

Proportional to theta, the fraction of covered sites.

You set those rates equal, do a little algebra.

And you get the Langmuir equation.

Theta frac alpha one plus alpha phi, where alpha is related to the sticking probability and adsorption rate.

That's the one.

And the beauty of it is that it predicts a specific shape for the coverage versus pressure curve.

And you can test it experimentally.

If you plot your data in a specific linearized way, usually pd dollar versus pvi, where alvi is the volume adsorbed, you should get a straight line if the Langmuir model holds.

And from the slope and intercept of that line, you can figure out the constant alpha dollar and also the volume of gas needed to make a perfect monolayer.

Exactly.

It gives you a way to measure that monolayer capacity, which is often very useful.

Now, what happens if the molecule isn't simple, if it breaks apart when it sticks?

Like your H2 example turning into two H atoms, does Langmuir handle that?

It can be adapted.

If a molecule A2 dissociates into two A fragments upon adsorption, the math changes slightly because now for one A2 molecule to stick, it needs to find two adjacent empty sites on the surface simultaneously.

Ah, that's a tougher requirement.

It is.

And that extra constraint makes the adsorption less sensitive to pressure.

The resulting isotherm for dissociative adsorption shows that the coverage now scales with the square root of the pressure, roughly alpha 12, especially at low pressures, a much weaker dependence.

Okay, so Langmuir is strictly for monolayers.

But we know, especially with physisorption, molecules can stack up.

What model handles multilayers?

That's where the BEAT isotherm comes in, named after Brunauer, Emmett, and Teller.

It was specifically developed to model multilayer adsorption.

How does it work conceptually?

It basically treats the first adsorbed layer using Langmuir -like ideas, but then it assumes that subsequent layers absorb on top of the first layer, almost like the gas is condensing into a liquid.

The first layer acts as the substrate for the second, the second for the third, and so on.

And what's the main use case for the BEAT model?

Its biggest application, by far, is in industry for determining the specific surface areas of porous solids.

Things like catalysts, activated carbon, materials for filters.

The BET analysis lets you figure out the volume of gas needed just for that first crucial monolayer.

And from that, you can calculate the total surface area.

It's a standard characterization method.

Got it.

Now, staying with isotherms but changing focus slightly, what about temperature?

How does adsorption change with temperature?

Temperature has a huge effect, as you'd expect, since adsorption is exothermic.

If you want to measure the strength of the adsorption, specifically the enthalpy change at a fixed amount of surface coverage, you measure the isosteric enthalpy of adsorption, delta.

Isosteric, meaning constant coverage.

Exactly.

You basically see how much you need to increase the pressure as you increase the temperature, just to keep the surface coverage constant.

Because higher T makes things dissolve more easily, so you need higher P to push them back on.

Precisely.

And if you plot the natural log of the pressure needed versus one over the temperature, you get a straight line whose slope is directly related to that isosteric enthalpy of adsorption.

It's like a van't Hoff plot, but for adsorption.

Okay.

Let's think about the kinetics again, the actual sticking process.

The sources mention this idea of a precursor state.

What's that?

Right.

This is important for understanding sticking probabilities.

The idea is that an incoming molecule doesn't necessarily go straight from the gas phase into the strongly bound chemisorb state.

Often, it first lands gently in a shallow, weakly bound state,

essentially a physisorb state.

That's the precursor state.

Like a temporary landing zone.

Exactly.

From that precursor state, the molecule might then find a proper chemisorption site and transition into the deeper potential well, overcoming a small activation barrier to do so.

Or if it doesn't find a good spot quickly, it might just gain enough energy to hop back off the surface entirely, desorbing from the precursor state.

So it's like an intermediate step.

And desorption getting off the surface, that's always an activated process, right?

You have to put energy in to break the bond.

Always.

Desorption requires overcoming the activation energy for desorption.

EEAA say, the deeper the well, stronger the adsorption, the bigger that barrier is.

And the time a molecule spends stuck on the surface depends exponentially on that barrier.

Yes.

The average time a molecule stays adsorbed, or the residence half -life, is very sensitive to EA and temperature.

Higher temperature or lower barrier means shorter residence time.

How do we measure that desorption energy barrier experimentally?

The main technique is temperature programmed desorption, or TPD, sometimes called thermal desorption spectroscopy, TDS.

Okay, TPD, how does it work?

You adsorb your molecules onto the cold surface, then you heat the surface up gradually, usually at a linear rate, while monitoring the pressure of the gas desorbing from it with a mass spectrometer.

So you watch for molecules popping off as it gets hotter.

Exactly.

As the temperature rises,

molecules gain enough thermal energy to overcome the desorption barrier, and you see a surge in the desorption rate, which shows up as a peak in your signal.

And the temperature at which that peak occurs tells you something.

It tells you a lot.

The peak temperature is directly related to the activation energy for desorption.

A peak at low temperature means weak binding.

A peak at high temperature means strong binding.

Can it distinguish different binding sites, like terraces versus kinks?

Oh yes.

TPD is often sensitive enough that if you have molecules absorbed on different types of sites with different binding energies, like terraces, steps, kinks, you'll actually see multiple desorption peaks appear at different temperatures.

It's a very powerful way to characterize the energetics of the surface.

Okay, fantastic.

Now we get to the real payoff, right?

Using all this knowledge about sticking in surface sites to actually make chemical reactions happen, or to drive electrical currents.

This takes us into catalysis and electrodes.

Absolutely.

This is where surface science really impacts technology.

Let's start with heterogeneous catalysis.

Heterogeneous,

meaning the catalyst is in a different phase from the reactants, usually a solid catalyst with gas or liquid reactants.

Correct.

The whole point of the catalyst is to provide a surface that lowers the overall activation energy for a reaction.

It does this typically by chemisorbing the reactants, weakening their internal bonds, and bringing them together in the right orientation to react.

And there are two main mechanisms proposed for how reactions happen on the surface.

The first is the Langmuir -Hinshelwood mechanism, or LH.

Right.

The LH mechanism is probably the most common model.

It assumes that the reaction happens between two molecules, say A and B, that are both already adsorbed onto the surface.

So it's an encounter between A adsorbed and B adsorbed, leading to products.

A add plus B add goes to products.

Exactly.

And the rate laws that come out of this can get quite complicated, depending on how strongly A and B adsorb relative to each other.

The source has mentioned something interesting about reaction orders changing.

Yes, that's a key consequence.

For example, if one reactant, say A, adsorbs very strongly and the pressure is high, the surface can become saturated with A.

The coverage gets close to one.

So pretty much all the sites are full of A.

Right.

In that case, the rate of the reaction might become independent of the pressure of A in the gas phase.

Adding more A doesn't help, because there are no empty sites left for it.

The reaction becomes zeroth order with respect to A.

That's counterintuitive.

More reactant doesn't mean faster reaction.

Not if the surface is already full.

Conversely, if adsorption is weak and coverage is low, the rate will typically be first order, directly proportional to the pressure.

So the observed reaction order can change depending on the conditions.

OK, what's the alternative mechanism?

The alternative is the Eley -Radeal mechanism, or ER.

In this case, the reaction happens when a molecule from the gas phase directly strikes a molecule that is already adsorbed on the surface.

So B from the gas hits A adsorbed to make products.

Exactly.

B gas plus A goes to products.

This mechanism is thought to be less common than LH, but it definitely occurs in some systems, particularly some involving hydrogen atoms.

Now, putting all this together, the sticking strength, the reaction leads to this concept of the volcano curve for catalyst activity.

Ah, yes, the volcano plot.

It's a really useful conceptual tool.

You plot the rate of the catalytic reaction, the activity on the y -axis, against some measure of the adsorption strength of a reactant or intermediate on the x -axis, often the enthalpy of adsorption.

And it looks like a volcano in the middle.

It typically does.

If the adsorption is too weak, left side of the volcano, the reactants don't stick long enough or strongly enough to react effectively.

They just bounce off.

Activity is low.

Right.

If the adsorption is too strong, right side of the volcano, the reactants or, more often, the products stick too well.

They bind so tightly they can't get off the surface easily.

So they poison the active site.

Exactly.

They block the site, preventing further reaction cycles.

The surface gets immobilized.

Activity is low again.

So the best catalysts are right at the peak of the volcano.

Precisely.

They strike that perfect balance.

Strong enough adsorption to facilitate the reaction, but weak enough binding that the products can desorb quickly and free up the site for the next cycle.

It turns out that metals near the middle of the transition series often hit this sweet spot for many important reactions.

Fascinating.

Okay.

Let's pivot from gasoline catalysis to the interface between a solid electrode and a liquid electrolyte solution.

Electro processes.

This is battery chemistry, fuel cells, electroplating.

All crucially dependent on this interface.

When you put a charged electrode into an ionic solution, the ions in the solution rearrange themselves near the surface.

Positive ions cluster near negative electrode, negative ions near a positive one.

This forms what we call the electrical double layer.

Like two layers of charge facing each other across the interface.

Kind of.

Our models have evolved.

The early Helmholtz model pictured it simply as two rigid sheets of charge, like a parallel plate capacitor.

Too simple.

A bit too simple.

The Stern model is more realistic.

It includes a compact rigid layer of ions right next to the electrode, the Stern layer, but also acknowledges a more spread out diffuse layer further out, where ions are jostling around due to thermal energy but still feel the electrode's influence.

And the potential difference across this whole double layer region is the key driving force.

Yes.

That potential difference, called the Galvani potential difference, is what drives the electron transfer reaction's oxidation or reduction at the electrode surface.

Now, when we actually make current flow, say by applying an external voltage to drive a reaction, the potential changes.

We talk about over potential.

Right.

The over potential, Ada, is simply the extra potential you have to apply beyond the equilibrium potential to get a certain amount of current to flow.

So AeA, where Eti is the actual working potential.

Why is extra potential needed?

Because electron transfer isn't infinitely fast.

There are activation energy barriers for both the oxidation anodic process and the reduction cathodic process.

Applying an over potential effectively lowers the barrier for one direction and raises it for the other, creating a net flow of current.

And the relationship between how much current flows,

the current density, and how much over potential you apply is described by the famous Butler -Vulmer equation.

Indeed.

The Butler -Vulmer equation is central to electrode kinetics.

It mathematically connects the net current density to the over potential, taking into account the activation barriers for both the forward and reverse reactions.

What happens when the over potential is zero at equilibrium?

At $ $ $,

the Butler -Vulmer equation tells you the net current is zero.

But crucially, the forward cathodic and reverse anodic reactions are still happening, just at equal and opposite rates.

The magnitude of that rate, expressed as a current density, is called the exchange current density, $ $ $.

So $ $ $ is like the intrinsic speed limit of the electrode reaction at equilibrium.

That's a great way to put it.

A high $ $ $ means the electrode is very reversible, electrons can swap back and forth easily.

A low $ $ $ means it's sluggish.

And if we go to high over potentials, either very positive or very negative.

Then the Butler -Vulmer equation simplifies.

One direction of current, either anodic or cathodic, starts to dominate completely.

In this high over potential regime, the equation predicts an exponential relationship between current density and over potential.

Which leads to the practical Tafel plot.

Exactly.

If you plot the natural logarithm of the current density, Ln end -daters, versus the over potential at high values of Edalo, you should get a straight line.

That's a Tafel plot.

And what can we learn from that straight line?

Two very important kinetic parameters.

The slope of the Tafel line gives you the transfer coefficient alpha, which essentially tells you how symmetrical the activation energy barrier is, how much the applied potential affects the forward versus the reverse reaction barrier.

And the intercept?

The intercept, when extrapolated back to zero over potential, gives you the exchange current density, $J.

So Tafel plots are a standard way to measure $J and alpha.

Finally, how do we watch these electrode processes happen dynamically?

We use voltammetry.

This involves applying a controlled potential to the electrode and measuring the resulting current.

The most common type is probably cyclic voltammetry, or CV.

Cyclic, meaning the potential goes back and forth.

Yes.

In CV, you sweep the applied potential linearly up to a certain value, and then immediately sweep it linearly back down to the starting point, often forming a triangular waveform.

You plot the measured current versus the applied potential.

And you get a characteristic shape, a voltammogram.

You get a voltammogram, which typically shows peaks in the current corresponding to oxidation or reduction events happening as the potential sweeps past their equilibrium values.

What can the shape of those peaks tell us?

A lot about the reaction mechanism and kinetics.

For a simple, fast, reversible electron transfer, the forward and reverse peaks will be roughly symmetrical in height and separated by a specific potential difference.

And if it's not reversible?

If the electron transfer step itself is slow, irreversible, or if the product of the electron transfer quickly undergoes a subsequent chemical reaction, the voltammogram becomes very asymmetrical.

The reverse peak might be much smaller, shifted, or even completely absent.

So CV is a powerful diagnostic tool.

It's really quite amazing, is that we started this deep dive thinking about single nitrogen molecules hitting one surface atom 100 million times a second.

Yeah.

And we've ended up using basically the same core physical chemistry ideas, adsorption, activation barriers, rates, to understand and quantify how a car battery actually delivers power.

It really does all connect back.

So to quickly recap the essential framework for you.

One, the physical structure of the surface, especially those defects like steps and kinks, governs how strongly things stick.

That was 19a territory.

Two, we quantify that sticking using adsorption isotherms.

Langmuir gave us the simple monolayer picture.

Bead extends it to multilayers and measuring surface area.

The topic 19b.

Got it.

Three, surface reactions, like in catalysis, often proceed via mechanisms like Langmuir -Hinshelwood, and their efficiency is beautifully captured by that volcano curve idea.

Not too strong, not too weak binding.

That's 19c.

Makes sense.

And four, electrode processes are all about that charged interface, the double layer.

The Butler -Vulmer equation relates current to overpotential, driven by the exchange current density J $10, and we probe it with techniques like voltammetry, especially CV, topic 19d.

That really ties it all together.

Okay, so here's a thought to leave you with.

We heard that the exchange current density J $1, which is critical for battery power, can be really sensitive to the specific crystal face of the electrode material that's exposed to the electrolyte.

Like, G $ for depositing copper is apparently quite different on a copper and 100 phase versus a copper and 11 phase.

That's absolutely true.

The atomic arrangement matters.

So the question is, thinking ahead, could future battery designers actually use nanostructuring techniques, building electrodes almost atom by atom, to deliberately expose only the crystal faces that have the highest intrinsic J $11?

Could we engineer the interface at the nanoscale to maximize power density and charging speed?

That's precisely where a lot of cutting edge research is heading.

Controlling that atomic architecture at the interface is likely key to the next generation of energy storage.

Well, thank you for joining us for this deep dive into processes at solid surfaces.

We really hope this served as an effective and maybe even memorable shortcut to understanding these crucial concepts.

We certainly hope you feel well informed.

And with that, thank you from the last minute lecture team.