I'm going to give a brief introduction to the idea of adsorption in this screen-cast
and then derive the Langmuir isotherm which is perhaps the simplest model of adsorption.
So what we mean by adsorption is the preferential concentration of a species on the surface
of a solid or a liquid where a surface is defined as any interface between two phases.
We will concentrate on a solid here.
And this can be adsorption for a gas phase or from the liquid phase.
Adsorption depends on a molecule being adsorbed so is used often for separations.
The most common way to carry out adsorption is on a high surface area material because
the larger the surface are the more locations for adsorption to take place and therefor
the more effective the adsorption would be.
We obtain high surface areas by having pores.
So what I've drawn is a very schematic representation of a cross section of a solid sphere.
Now this is not to scale but the idea is that there are small pores running through this
solid so that we can have a lot of surface area per volume and if we were to look at
a blow- up of one of these is we would have a pore where we could have molecules adsorbing
on the surface of these pores and what we are interested in then is this reduction.
So the terms that we are going to use, the concentration of B in the liquid phase and
we will look at the absorption for the liquid but the exact same idea is going to apply
to absorption from the gas phase.
And we will look at the amount absorbed.
So this is moles per kg of solid.
So we concentrate the molecules from the liquid phase preferentially on the surface where
we have B dissolved in some solvent and the solvent in very weak layer does not adsorb
at all.
The terminology that is often used in adsorption is what fraction of this surface is covered
with component B. So we are just going to look at one species in this introduction but
the same ideas apply when we have multiple species all which adsorb.
So the fraction of the surface that is covered with B would be the amount of B adsorbed at
some concentration of the liquid phase over the maximum amount we could adsorb or what
is called the saturation amount that we could adsorb on the surface.
And then what we are interested in is equilibrium adsorption.
The Langmiur isotherm that we are measuring this at constant temperature and at equilibrium
we can potentially adsorb and desorb molecules.
So the rate of adsorption onto the surface is the same as the rate of desorption so we
have a constant amount adsorbed.
The rate of adsorption is equal to a rate constant for adsorption.
The concentration of B in the liquid phase and then the fraction of sites that are vacant
and available for adsorption.
So this assuming molecules only adsorb where there is not already a B molecule adsorbed.
There is a finite number of these sites.
And this adsorption rate is equal to a rate constant for desorption and the fraction of
the sites that are equal to molecule B. if there is more B on the surface then the rate
the B is desorbing would also be higher.
And then we would use the fact that the fraction of vacant sites plus the fraction of sites
occupied by B must add to 1 since there are no other molecules adsorbing for this simple
example.
So we could made this simple substitution for theta B. So I have made this substitution
and then I have simplified a bit and this rate constant for adsorption and this rate
constant for desorption we are going to define as our rate equilibrium constant.
So if we now solve for the fraction of surface occupied by B it is the absorption equilibrium
constant, the concentration in the liquid phase, over 1+ the adsoprtion equilibrium
constant, concentration at the liquid phase.
And this is the Langmuir isotherm.
This is commonly used to create simple models of adsorption on solids from both the liquid
phase and the gas phase.
And if we were to plot what this looks like.
So here is how the fractional coverage varies as a function of concentration.
Somewhere up here the coverage is 1.
At low concentrations of B in the liquid phase this is going to be linear.
Just the adsoprtion equilibrium constant times the concentration of B in the liquid phase.
At high enough concentrations, this is where the concentration becomes saturated and theta
B approaches 1.
So we could measure absorption just by taking advantage of our ability to measure concentrations
and doing a mass balance.
So we could imagine we have a container with a solvent that is not going to adsorb and
the concentration of B then in the solvent, for simplicity just call this this initial
concentration of B in the liquid phase.
We then add the solid, stir this well, let it get to equilibrium but now measure a final
concentration of B.
This final concentration of course is what we use in the Langmuir Isotherm, and the final
concentration is less than the initial concentration because of adsorption on the solid surface.
We know the volume of the starting liquid.
We measure the difference in these concentrations.
We can calculate how much has adsorbed.
We can calculate qB and we can make measurements up to saturation to determine the saturation
coverage.
The amount adsorbed is a function of temperature so as we raise temperature the adsorption
equilibrium constant decreases and this is because the activation energy for adsorption
is less than the activation energy for desorption so the desorption rate constant increases
faster with temperature.
This is very similar to chemical reactions because adsorption is exothermic.
And so raising T we decrease that equilibrium constant.
So I am showing here a better plot of the Langmuir Isotherms at three temperatures,
T1, T2, T3, where T3 is higher than T2 which is higher than T1.
And so as the temperature goes up we have to go to much higher concentrations to get
close to saturation.
Now that Langmuir isotherm is only an approximation.
And it has a number of assumptions, many of which are not going to apply in many situations.
So here are the assumptions, one that the surface is uniform and this is certainly not
the case.
2 that we have monolayer adsorption which is often a very good approximation.
Then we have one molecule per site, this may or may not be good.
It also assumes the molecules don't interact as the molecules get close together, for example
when a catalyst surface adsorbing from the gas phase, get much higher concentrations
so molecules that are close together, repulsive interactions can be important.
If affects then how much adsorbs.
And then adsorption only happens with collision with a vacant site because we assume the adsorption
is proportional to the fraction of vacant sites available.
But of course this is certainly not always the case, molecules can collide with a site
already occupied and move along the surface to a vacant site.
But the Langmuir isotherm is a good approximation to understand this idea of adsorption.