Chapter 9: Modern Theory: Principles

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Welcome back to The Deep Dive.

Today we are absolutely not talking about boring rust.

If you are picturing a rusty bumper on an old pickup truck or a squeaky gate hinge, I want you to wipe that image from your mind right now.

Today we are talking about a war.

It really is a war.

It's a microscopic, relentless, billion -year -old battle of energy versus speed.

It is the story of why the universe is constantly trying to destroy the metals we use to build our civilization and how engineers use a very specific combination of math and chemistry to fight back.

We are digging into what is arguably the holy grail of this field, chapter 9 of Mars G.

Fontana's Corrosion Engineering titled Modern Theory Principles.

And that title, Modern Theory, is doing a lot of heavy lifting.

It sounds a bit academic, but it's actually the, you know, the turning point where corrosion science really grew up.

Right.

I think we need to set the stage here.

When Fontana says modern, he is not talking about something invented last Tuesday.

This text is a classic.

So what's the shift he is describing?

What was the old theory that we moved away from?

Well, before this modern approach took over, people looked at corrosion as these tiny, isolated, almost random events.

Imagine looking at a piece of steel under a microscope.

You would see a speck of BERT and say, aha, that's a local anode.

And then a clean spot next to it and say, that's a cathode.

They treated them as like little local cells.

Which is technically true, right?

Corrosion is electrochemical.

There are anodes and cathodes.

It is true, but it's terrible for engineering.

It is just too chaotic.

You can't model a billion tiny specks of dirt mathematically.

You can't predict the lifespan of a pipeline based on specs.

The modern theory, which is really an electro kinetic approach, it zooms out.

It treats the entire metal surface as one generalized electrode.

So it simplifies the geometry so we can actually use calculus on it.

Exactly.

It stops guessing about where the dirt is and starts calculating rates based on energy and potential.

It turns corrosion from a descriptive art into a, well, a predictive science.

It lets us derive equations that describe the rate of the reaction per unit area, regardless of the microscopic details.

Okay.

So our mission today is to decode this modern electrochemical theory.

And looking at the roadmap in chapter nine, it seems like Zontana breaks this down into four distinct pillars.

He does.

It's a perfect logical progression.

First, we have thermodynamics that tells us if the metal wants to corrode.

Okay.

Second, kinetics, which tells us how fast it will corrode.

The speed.

Third, mixed potential theory, where we smash those two together to get the real answer.

And finally, passivity, the weird magic trick where reactive metals just stop reacting.

I like that structure.

Let's start with the energy, thermodynamics, section one, the potential for destruction.

I love the analogy the book uses right off the bat in figure nine to one, the mechanical analogy.

The ball on a hill is just the best way to understand the driving force of nature.

Listeners, I want you to visualize this.

Imagine a heavy ball sitting at the very top of a steep hill.

That ball represents your metal.

Let's say a block of pure magnesium or a steel beam.

And it's sitting there with a lot of potential energy, a huge amount of chemical energy.

Think about it.

We spent a massive amount of energy refining that metal.

We dug up iron ore, which is basically rust.

We blasted it in a furnace, stripped away the oxygen and forced it into a metallic state.

We push the ball up the hill.

It's unstable.

It does not want to be there.

And at the bottom of the hill?

That's the valley.

That represents the corrosion product, the rust, the oxide, the ore.

That is a state of low energy.

Nature loves low energy.

Nature wants to sleep.

So if you give that ball even the slightest nudge, it naturally rolls down the hill to get back to the bottom.

We call that a spontaneous reaction.

Okay.

So this height of the hill, this difference in energy between the refined metal and the pile of rust, this is what we measure mathematically.

Right.

This is the change in free energy or delta G.

And here's the first equation you have to burn into your brain.

Delta G equals minus NFE.

Let's unpack that because usually when people see variables, they tune out.

But this defines the universe of corrosion.

Delta G is the energy change.

Correct.

If delta G is negative, the reaction is spontaneous.

Negative means the ball is rolling down.

It means energy is being released.

And on the other side of the equal sign, we have specific variables.

Right.

N is the number of electrons.

Right.

F is the Faraday constant, which is just a massive number representing the electrical charge of a mole of electrons, roughly 96 ,500 Coulombs per equivalent.

And EE is star of the show.

E is the cell potential, the voltage.

And there's a negative sign in front of them.

That negative sign is critical.

Since N and F are always positive numbers, for delta G to be negative, which means corrosion happens, E, the voltage, has to be positive.

So broadly speaking, this equation answers the question, is it possible?

Exactly.

It tells you if the universe permits this metal to corrode.

It tells you if the transition from metal to rust releases energy.

But, and this is a huge but, there is a catch.

The text calls it the fatal flaw of relying only on thermodynamics.

I think I know where you are going.

It's the difference between can and will.

It's the classic engineering trap.

Thermodynamics predicts direction, not velocity.

Just because the ball can roll down the hill doesn't mean it is rolling down the hill right now.

It might be stuck behind a rock.

Or the slope might be so gentle that it takes a million years to reach the bottom.

So you could calculate a massive negative delta G for a metal, thinking it's going to vanish in seconds.

But in reality, it sits there for a hundred years.

Exactly.

Aluminum is the poster child for this.

I mean, if you look at the thermodynamics of it sits way up high on that hill.

If you believe the thermodynamics alone, an aluminum airclane should explode into white dust the moment it touches humid air.

It really, really wants to be an oxide.

But we build airplanes out of it.

We wrap our leftovers in it.

Because of the speed bump.

Because of kinetics, it creates a barrier that stops the ball from rolling.

But before we get to kinetics, we have to finish with the energy.

We have to measure this potential somehow.

We need to know where different metals sit on that hill.

And this leads us to the EMF series.

But the book makes a really interesting philosophical point here about the standard half cell.

It says you cannot measure the potential of just one electrode.

It's like trying to hear the sound of one hand clapping.

It's impossible.

Voltage is a difference between two points.

Think about a multimeter.

It has two probes, red and black.

You can't stick the red probe on a piece of zinc and hold the black probe in thin air and expect a reading.

You need a reference point to complete the circuit.

And the reference the scientific community agreed on is hydrogen.

Hydrogen electrode.

Two H plus plus two electrons equal H2.

We arbitrarily decided, okay, this reaction has a potential of .0000 volts.

It's our sea level.

Everything else is measured relative to that.

If a metal gives up electrons easier than hydrogen, it's negative.

If it holds them tighter, it's positive.

So when we look at table nine to one in the text, the standard EMF series, we see gold is way up at plus one point five volts.

Positive means noble.

It's inert.

It creates a potential higher than hydrogen.

It holds onto its electrons tightly.

It's, you know, comfortable at the top of the hill.

It doesn't want to react.

And zinc is down at minus point seven six three volts.

Negative means active.

Zinc is practically begging to give away its electrons and corrode.

This gives us the standard prediction rule.

If you connect two metals electrically, the one with the more negative potential will be the anode and corrode.

The more positive one acts as the cathode and survives.

So in a zinc copper cell, which is figure nine to three in the text, zinc is negative minus point seven six is most V and copper is positive plus point three four V.

Zinc gets eaten.

Copper is safe.

Right.

That's the battery principle.

That's how a Duracell works.

But again, with the butts, those tables assume standard conditions.

That means pure metals, 25 degrees Celsius.

And most importantly, unit activity.

Unit activity implies a concentration of one mole per liter of the metal ions in the water, right?

Roughly, yes.

And let's be honest.

How often is a sewage pipe, a chemical reactor or the ocean perfectly calibrated to one mole per liter of dissolved metal at exactly 25 degrees?

Never.

It's a messy soup out there.

Exactly.

So to find the real potential in the real world, we need to adjust that standard number.

We need to correct for the environment.

We need the Nernst equation.

Equation 9 .9.

E equals E naught plus 2 .3 times RT over NF log of the activity of the oxidized species over the reduced species.

It looks scary.

It looks like a nightmare, but conceptually, it is just a correction factor.

E naught is the value from the book, the standard potential.

The rest of that junk just adjusts that value based on how much stuff is dissolved in the water.

Specifically, look at the log term.

It's the log of the oxidized species divided by the reduced species.

There's a rule of thumb here that I found really helpful to visualize this, the 59 millivolt rule.

Yes.

This simplifies everything and is great for mental math.

For a reaction with one electron, every time you increase the concentration of the oxidized stuff, the corrosion product in the water by a factor of 10, the potential raises by 59 millivolts.

Let's say you have copper dissolving in acid.

As the copper dissolves, the water gets full of copper ions.

The concentration goes up.

And as that concentration goes up, the copper potential becomes more positive.

It becomes more noble.

It essentially becomes harder and harder to corrode the copper, the more copper gunk you have piling up in the solution.

The Nernst equation tells us that the environment changes the energy landscape.

If the solution is saturated with metal ions, the metal might stop corroding simply because the potential has shifted.

Okay.

So thermodynamics gives us the potential.

It tells us zinc wants to corrode and gold does not.

It tells us the direction.

But as we said with the Illumina airplane, we don't care about wants.

We care about how fast.

We need to talk about speed.

We need to talk about kinetics.

This is the crucial transition to section two.

If thermodynamics is the map telling you where the destination is, kinetics is the speedometer.

And in the world of corrosion, speed is not measured in miles per hour.

It's measured in amperes.

Current.

Specifically, current density amperes per square centimeter.

You have to remember, corrosion is literally the flow of electrons.

When iron turns into rust, it releases electrons.

One ampere of current flowing out of a piece of iron corresponds to a very specific calculable amount of metal dissolving every hour.

Faraday's law again.

So if we can measure the current, we know exactly how fast the pipe is falling apart.

Precisely.

If you tell me this pipe is generating one milliamp per square centimeter, I can tell you exactly how many millimeters of wall thickness you are losing per year.

There's a direct conversion factor.

But where does this current start?

The text introduces a concept that I think trips a lot of people up.

Exchange current density or I naught.

It is a brain twister.

We have to go back to our metal sitting in acid.

Let's say it's at equilibrium.

The net voltage is zero.

To the naked eye, nothing is happening.

But at the atomic level, it is a mosh pit.

Complete chaos.

Metal atoms are jumping into the solution and becoming ions.

At the exact same time, ions from the solution are crashing onto the metal and becoming atoms again.

The forward rate equals the backward rate.

I like the analogy of the airport for this.

Right.

Imagine an airport terminal.

If 100 people walk in the front door and 100 people walk out the back door every minute, the number of people inside the building stays the same.

The net change is zero.

But the traffic, the 100 people, is the exchange current density.

Exactly.

It's a measure of how busy the surface is.

And this number, I naught, varies wildly between different metals.

Figure 912 is the key here.

It compares hydrogen evolution on platinum versus mercury.

And the difference is massive, right?

It's logarithmic.

We're talking factors of millions.

On platinum, the exchange current density for hydrogen is huge.

It is incredibly easy for hydrogen to swap electrons on a platinum surface.

The airport doors are spinning at light speed.

Platinum is a busy surface.

It's a great catalyst.

In mercury.

On mercury, I naught is tiny.

The doors are rusted shut.

Maybe one person gets through every hour.

It is very, very hard to perform the hydrogen reaction on a mercury surface.

Why does this matter?

We are not building bridges out of mercury.

Because this intrinsic busyness or laziness of the surface determines how easy it is to start corrosion.

Platinum is a catalyst.

Mercury is an inhibitor.

But to actually move the reaction, to get a net current, to get the metal to dissolve, we have to push it away from this equilibrium.

We have to polarize it.

Polarization.

This is a word engineers throw around a lot.

In simple terms, this is friction.

That is the best way to think of it.

Electrochemical friction.

Polarization, denoted by the Greek letter eta, is the extra energy, the extra voltage you have to pay to force the reaction to go at a certain speed.

It's the deviation from equilibrium potential.

The text breaks this down into two types of friction.

Activation and concentration.

Let's start with activation polarization.

Activation polarization is when the bottleneck is the chemistry itself.

It's the energy barrier to transfer an electron from the metal to the molecule.

It's like trying to push a heavy rock.

To move it faster, you have to push harder.

This gives us the Tafel equation.

Right.

Eta equals beta log i over i -naught.

If you plot potential versus the log of the current, that's figure 913, you get a straight line.

The slope of that line is beta, the Tafel constant.

A steep slope means you have to apply a ton of extra voltage just to get a little bit more current.

It's a chemically sluggish reaction.

So that's the chemical speed limit.

Yeah.

But what happens when the reaction gets so fast that the chemicals physically cannot get to the surface in time?

That is the second type.

Concentration polarization.

Imagine a hungry monster eating apples.

Okay, I'm with you.

At first, the bottleneck is how fast the monster can chew.

That's activation polarization.

But let's say the monster is a super eater.

He eats instantly.

Now, the bottleneck isn't chewing.

It is how fast you can throw apples at him.

The delivery system.

The diffusion of ions.

Exactly.

The ions have to swim through the water to hit the electrode.

If the reaction is too fast, the surface gets starved.

The concentration of ions right at the metal surface drops to zero because they're being consumed instantly.

And that creates a hard speed limit.

The text calls this the limiting diffusion current, or IL.

Right.

No matter how much harder you push, no matter how much potential you apply, you cannot go faster than IL because the ions literally cannot swim any faster through the solution.

The curve goes vertical.

But we can change that limit, can't we?

Yeah.

Figure 916 implies we can.

Yes.

How do you get apples to the monster faster?

You throw them harder.

You stir the bucket.

Velocity.

Agitation.

If you look at the graph, increasing the velocity of the fluid pushes the vertical cliff of the limiting current to the right.

Which explains why pipes corrode faster at bends or where the water is turbulent.

The flow brings fresh fuel to the fire.

Exactly.

It removes the diffusion limit.

So total polarization is just the sum of the two.

The chemical friction plus the diffusion friction.

That tells us the total resistance of the system.

Okay.

We have the friction curves, kinetics.

We have the starting points, thermodynamics.

Now we have to put them together.

This is the heart of Chapter 9, mixed potential theory.

This is where it all clicks.

Section 3, where the lines cross.

The Evans diagram.

This diagram is the tool every corrosion engineer uses.

So I want to paint a picture for the listener.

Visualize a graph.

Y axis is potential volts.

X axis is current density.

But it's logarithmic.

We are going to draw two lines.

Line number one represents the metal dissolving.

The anodic reaction M goes to M plus plus an electron.

This line starts low and slopes UP.

As potential gets higher, the metal wants to dissolve more.

Got it.

Sloping up.

Line number two is the cathodic reaction.

Let's assume it's hydrogen evolution.

Two H plus plus two electrons gives you H2 gas.

This line starts high and slips down in.

So we have an X.

And where X marks the spot.

That intersection is everything.

That point tells you the corrosion potential, E core, and much more importantly, the corrosion current, I core.

That value on the X axis is the actual rate the metal will rot.

The text calls this the second hypothesis of mixed potential theory.

Contribution of charge.

It's simple physics.

You can't build up a pile of electrons on the metal.

Every electron released by a dissolving metal atom must be consumed immediately by a hydrogen ion or some other electron grabber.

So total oxidation rate equals total reduction rate.

The intersection point is the only place in the universe where that equation balances.

This leads to one of my favorite examples in the book because it totally flips expectations.

The case of zinc versus iron in acid.

It is a classic puzzle.

Look at the thermodynamics.

Zinc is at minus 0 .76 volts.

Iron is at minus 0 .44 volts.

Zinc is much more negative.

It has a huge driving force.

It should corrode much faster.

But if you put pure zinc in hydrochloric acid, it fizzes slowly.

You put iron in, it boils.

Why?

Look at the diagram.

It's not about the metal line.

It is about the hydrogen line.

Right.

We talked about exchange current density I naught.

Exactly.

Zinc is a terrible surface for hydrogen evolution.

Its I naught for hydrogen is tiny.

So the hydrogen line on the zinc diagram starts way, way back on the left side of the graph.

So even though the zinc line, the metal, is high energy, the hydrogen line, the partner, is weak.

Exactly.

When you draw the slope down from that tiny starting point, it intersects the zinc line at a relatively low current.

Zinc is ready to party, but hydrogen didn't show up.

And iron.

Iron is a great catalyst for hydrogen.

Its I naught is high.

So the hydrogen line starts further to the right.

So when it slopes down, it intersects the iron line at a much higher current.

So iron corrodes faster, not because it wants to dissolve more, but because it is better at helping the acid do its job.

Precisely.

Thermodynamics says zinc is worse.

Kinetics explains why iron is worse.

This is why you can't trust standard potentials alone.

You have to look at the intersection point.

That is a massive aha moment.

It's a partnership.

The metal needs a partner to take the electrons.

If the partner is slow, the corrosion is slow.

Which brings us perfectly to section four.

What happens if we swap the partner?

What if we add an oxidizer?

The text mentions adding ferric salts or just blowing oxygen into the acid.

Right.

Before, we just had hydrogen taking electrons.

Now imagine we add ferric ions, phi three plus.

They are hungry for electrons too.

They want to become F2 plus.

So now the metal has two customers buying its electrons.

Exactly.

In the diagram, figure 920, we now have two reduction lines sloping down.

We have to sum them up.

This pushes the total reduction line way to the right.

And if the downward line moves right, the intersection moves right.

And moving right on the x -axis means higher current, higher corrosion rate.

This is why oxygen is so dangerous to active metals like copper or iron and acid.

It acts as a depolarizer.

It basically opens a second checkout lane at the supermarket, allowing the metal atoms to leave the store twice as fast.

It's pouring gas on the fire.

Usually, yes.

But, and here's the plot twist of the century.

Sometimes adding a strong oxidizer doesn't make it faster.

Sometimes it stops the corrosion dead.

This is the weird phenomena I mentioned.

Faraday noticed this in the 1840s.

If you throw iron into dilute nitric acid, it dissolves violently.

Bubbles, heat, chaos.

But if you throw it into concentrated nitric acid, which should be stronger, it does nothing.

Nothing.

It looks like platinum.

It's completely inert.

It's passive.

And the scratch test is the kicker.

Oh, I love the scratch test.

You have this passive iron sitting quietly in the acid.

You take a glass rod and scratch the surface.

Suddenly, boom!

It explodes into activity at the scratch, bubbling away until the film heals itself.

Because you broke the shield.

You broke the film.

Passivity is caused by a super thin, invisible film, usually an oxide that forms on the surface.

We're talking 30 angstroms thick.

That is barely a whisper of atoms.

But it acts as a barrier.

The diagram for this, figure 925, is probably the most complex but important shape in the book.

It's not just a straight line up anymore.

No.

It's the active -passive curve.

Listeners, try to visualize this.

The anodic line, the metal dissolving, starts sloping up like normal.

Current increases as voltage increases.

This is the active region.

It behaves like normal metal.

Then it hits a peak.

The nose.

The nose.

The critical anodic current density.

I see.

This is the danger zone.

The corrosion is at its maximum here.

The metal is dissolving as fast as it possibly can.

But if you push the potential just a little bit higher, past the nose.

Current crashes.

It falls off a cliff.

It drops by orders of magnitude from amps down to microamps.

And then it stays low and flat.

That flat valley is the passive region.

The metal is protected.

It's coated in that film.

So the goal of an engineer is to get the metal over the nose.

Exactly.

Figure 927 illustrates the three scenarios of how the reduction line interacts with this weird nose shape.

It is all about where the lines cross.

Case 1.

Your oxidizer is weak, like dilute acid.

The reduction line crosses the metal line below the nose.

You're in the active zone.

High corrosion.

Your pipe dissolves.

Skip into case 3, which is the best one.

Case 3 is stable passivity.

Your oxidizer is strong, like concentrated acid or oxygen interacting with stainless steel.

The reduction line is effectively floating high up.

It misses the nose entirely and only intersects the curve in the passive valley.

That is stainless steel.

Right.

Stainless steel creates such a stable chromium oxide film that the nose is very small and easy to jump over.

The intersection happens in the safe zone.

But what about case 2, the unstable one?

That is the nightmare scenario.

Imagine the reduction line cuts right through the nose.

It intersects the curve in three places.

It touches the active zone, the negative slope of the nose, and the passive zone.

This thing gets confused.

It goes haywire.

It oscillates.

It cycles between active corrosion and passivity.

The metal literally pulses as it eats itself.

It can't decide if it wants to be active or passive.

You want to avoid case 2 at all costs.

So to passivate a metal, you need a strong enough oxidizer to push the system past the critical current.

It is ironic.

To stop corrosion, you have to initially threaten the metal with a very strong oxidant to force it to build a shield.

The best defense is a strong offense.

It applies perfectly here.

You force the metal into shock, and it puts up its shield.

Now, we have talked about the film forms.

But section 6 dives into how it grows.

It's not like peening a wall, is it?

No.

It creates a dynamic structure.

The book discusses the point defect model, or PDM, popularized by McDonald.

It simplifies a very complex quantum mechanical process.

The film is growing, but it's solid.

How do atoms move through a solid?

Vacancies.

Missing pieces in the lattice.

Imagine a checkers board that's full of checkers.

You can't move any pieces.

But if you remove one checker of vacancy, now the neighbor can move into that spot, and the hole moves the other way.

So oxygen vacancies move one way,

and metalcations vacancies move the other.

Right.

And this leads to the growth of the film, but it also explains the death of the film pitting.

This is the breakdown mechanism.

The PDM suggests that if the metalcations moving through the film pile up at the interface faster than they can dissolve into the water, you get a traffic jam.

And a traffic jam of vacancies creates a void.

Yes.

The vacancies condense into a void, or a gap between the metal and the oxide film.

Imagine a blister forming under paint.

The film separates from the metal.

Once that happens, the film collapses, because it has no support.

And that collapses a pit.

A concentrated point of attack.

This is why chloride is so bad.

It accelerates this vacancy movement.

It makes the traffic jam happen faster.

But the text mentions a hero.

Molybdenum.

Type 316 stainless steel.

It has 2 % molybdenum.

The PDM explains why it works.

The molybdenum effectively complexes with those vacancies.

It grabs them and stops them from moving so fast it prevents the traffic jam.

It's the traffic cop.

Exactly.

He keeps the vacancies flowing smoothly so they don't pile up and create a void.

It stabilizes the passivity and prevents pitting.

It is incredible that we have a mathematical model for something as chaotic as a rough spot.

It is.

And that's the power of Chapter 9.

It gives us the tools to diagnose failures that look random to the untrained eye.

So let's wrap this up.

We have covered a lot of ground.

We did.

We started with thermodynamics.

The ball on the hill.

Negative delta G means it can happen.

Then we went to kinetics.

The airport.

Exchange current density and polarization tell us the speed limit.

We combine them in mixed potential theory.

The Evans diagram.

The intersection point determines the reality.

Finally, passivity the shield.

The active passive nose and the delicate oxide film that saves our infrastructure.

It really changes how you look at a piece of metal in water.

It's not just sitting there.

It's a buzzing circuit.

It is.

And here's my final thought for the listeners to chew on.

We talked about natural corrosion.

But realize this.

If corrosion is just a circuit defined by an intersection on a graph,

that means we can hack the graph.

We don't just have to pick better metals.

We can apply an external current to the metal to manually force the voltage down.

That's cathodic protection.

Or force the voltage up into the passive region, which is anodic protection.

We are not just observers of this battle.

Because we understand the diagram, we can actively interfere with the electronics of nature.

We can rig the game.

Exactly.

We can rig the game.

I love that.

Chapter 10 is going to get into the nitty gritty of measuring this stuff in the lab.

But this theoretical bedrock in Chapter 9 is absolutely essential.

You can't fix it if you don't understand the circuit.

Well said.

Thanks for breaking it down with us.

And to our listeners, stay curious and keep those electrons flowing exactly where you want them to.

See you next time.