Question

Explain the main difference between the adsorption (initial) stage and ordering process (second stage) of Self=Assemble monolayer using the relevant chemical concepts, models and forces.

Answer 1

Freundlich adsorption isotherm is a purely empirical correlation for gaseous adsorbates:

where x is the mass of the adsorbate adsorbed, m is the mass of the adsorbent, P is the pressure of the adsorbate (concentration in case solute rather than gas), and k and n are empirical constants for each adsorbent–adsorbate pair at a given temperature (hence, isotherm). As the temperature goes up, the constants k and n change to reflect the empirical observation that the quantity adsorbed increases more slowly, and higher pressures are needed to saturate the surface. The function is inadequate at very high pressure because x/m has an asymptotic maximum in reality as pressure increases without limit.

Langmuir adsorption isotherm is a semi-empirical isotherm with a kinetic basis, was derived based on statistical thermodynamics, and is based on 4 assumptions:

1. All of the adsorption sites are equivalent, and each site can only accommodate one molecule.
2. The surface is homogeneous energetically, and the adsorbed molecules do not interact with each other.
3. No phase transitions
4. Only a monolayer is formed at the maximum adsorption. Adsorption only occurs on localized sites on the surface, not with other adsorbates.

However, there are always surface imperfections, adsorbed molecules are not necessarily inert, and the mechanism may not be the same for all the adsorbate molecules. The monolayer assumption issue is addressed by the BET isotherm for relatively flat (non-microporous) surfaces. The Langmuir isotherm is nevertheless the most common isotherm equation due to its simplicity and ability to fit in a variety of adsorption data, and has many applications in Langmuir–Hinshelwood surface kinetics and thermodynamics.

According to Langmuir,

where A is a gas molecule, and S is a solid adsorption site. If the surface coverage, , is the fraction of the adsorption sites occupied, at equilibrium:

(where k and k₋₁ are the direct and inverse rate constants)

or

where P is the partial pressure of the gas (or the molar concentration of the solution). For very low pressures KP, and for high pressures 1.

The adsorbate is usually a gas, and the quantity adsorbed is given in moles, grams, or gas volumes at STP (standard temperature and pressure) per gram of adsorbent. If v_mon is the STP volume of adsorbate required to form a monolayer on per gram of adsorbent, then , and an expression for a straight line is obtained as follows:

The slope and the y-intercept values help calculate v_mon and K that are constants for each adsorbent–adsorbate pair at a given temperature. v_mon is related to the number of adsorption sites via the ideal gas law. Assuming that the number of sites is just the entire area of the solid divided into the cross section of the adsorbate molecules, the surface area of the adsorbent can be calculated. The surface area of an adsorbent depends on its structure; the more pores it has, the greater the area, which has a great influence on the surface reactions.

Now, (of formation of the product; k₂ = Rate constant) when

or

At low pressure, P 0, is very small, and proportional to P; therefore, the reaction becomes first order.

Hence,

For example, decomposition of phosphine gas on Tungsten (solid heterogenous catalyst) at low pressure is a first-order reaction.