## Thursday, 7 June 2018

### Enhanced Reactivity of Powders, Number of Surface Atoms; Inter-Atomic and -Molecular Forces.

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'Materials in powdered form are much more reactive'.
'Inter-atomic forces are attractive and short ranged'

Powdered materials are highly reactive because more of their atoms lie on the surface making them available to react with the atoms of the medium.
Put it another way:

1.  The percentage of atoms on the surface increases as the particle size in the powder decreases.  And,

2.  Forces between atoms in the material and in the surrounding medium are effective over such short distances that only the number of surface atoms determine the reactivity of the powdered material.

I shall examine these statements in detail here.
Catalysts, nano-particles, the digestive system, design of fireworks etc. are some examples that demonstrate how large surface area of small particles plays a crucial role in determining the enhanced reactivity.

Note:  We talk about atoms of a material for convenience.  Our discussion is equally valid for molecules.

Let us look at the first point: The percentage of atoms on the surface increases as the particle size in the powder decreases.

Consider a cube weighing 1 gram of a material
of gram atomic weight M grams (1 mole of material)
(We consider a cube as the algebra is easier to follow - the discussion is valid for other shapes too.  Also, effects due to crystal structures etc are ignored in our discussion).

Number of atoms in 1 mole of material is given by Avogadro constant NA  where
N = 6.023 x  1023                                                                     eq. 1
Hence, Number of atoms in 1 gram of material     N = NA /M         eq. 2
Since M is a small number (M = 27 for aluminium), number of atoms in a gram of material is very large  -----   2.23 x 1022  for aluminium.
If the density of the material is d g/cm3,
then the volume of the cube of mass 1 gram is 1/d cm3

Notice that we can use eq.4 to calculate the average spacing between two atoms in a material.
For aluminium, M= 27 g and density d = 2.7 g/cm3

Eq. 4 gives, for Al, the inter-atomic spacing = 2.55 x 10-8 cm or 0.255 nm
{1 nano-meter = 10-9 meter = 10-7 cm}

We now use eq. 12 to calculate percentage of surface atoms for a material.
The left hand figure shows the situation for a 1 gram cube of Al (M = 27 g, d = 2.7 g/cm3

The straight line log-log graph shows how the percentage of surface atoms increases rapidly with the number of small cubes.  The number of surface atoms for a single cube is only 0.000021% but increase to almost 100% for 1020 cubes when a mono-layer of atoms is formed.

The combined surface area of small cubes may also be calculated from eq.6  and is
S = 6 s2 P   = 6 (P/d2)1/3                      eq. 13

For Al, density = 2.7 g/cmand  S = 3.094 P1/3 cm2                      eq. 14

For  P = 1018,     S = 3.094 10cm2   or 309 m2

This means that the 1 gm Al cube has now
a surface area equal to  a 17.6 m x 17.6 m field!

The case of other materials is similar as shown in the following slide:

The important conclusion from this analysis is that materials in finely powdered form have very large surface area and a large fraction of atoms reside on the surface.  These atoms can participate in reactions with atoms of surrounding medium with a corresponding enhanced reactivity.

A second interesting observation is, that atoms are very closely spaced  - approximately 0.25 nm apart.  The last line of the slide also shows that the inter-atomic separation in all materials is very similar - particularly for Al, Ag and Pt even though they have very different atomic masses. This spacing is comparable to the size of atoms and also to the typical distance over which interatomic forces operate.  We shall now look at these observations in more detail.

Force Between Two Atoms:

The force depends on the separation distance between the two atoms.  The discussion is general and the atoms do not have to be of the same type - they may come from different elements.

An atom of atomic number Z consists of a central nucleus of positive charge equal to Ze, with negatively charged Z electrons, each of charge -e, surrounding the nucleus.  The atom is overall electrically neutral with most of its mass concentrated in the nucleus. The electrons are attracted to the protons inside the nucleus to provide stability.

It will be useful to have a plot of  sizes of various atoms.  The size of an atom is determined by the extent of its electron cloud and the slide is a plot of atomic radii.

Forces between atoms are Coulomb forces -- forces between charged particles.  Like charges repel and opposite charges attract each other.  Being overall neutral, at large separation distances, say greater than a few nano-meters (nm), atoms do not interact with each other.

In the following, I shall describe the origin and nature of inter-atomic forces in a simplified fashion.  The scope of this blog does not allow a more in-depth discussion which may be found in 1, 2, 3

As the two atoms get closer, their electron clouds  start to overlap.  Electrons are also in motion and their distribution changes with time.  Electrons feel attractive force due to the positively charge nuclei of the two atoms, and electron density in the overlap space increases.  This results in weak attractive forces (negative potential energy) to come in play at modest separations.
If the atoms get very close - separation less than 0.2 nm - then the positively charged nuclei are no longer effectively shielded by negative electrons and the nuclei repel each other with sharply rising potential energy V(r). (See slide).
The minimum of the potential energy is where the two atoms feel no force F(r) and the separation there is the equilibrium separation R.

We can make an interesting observation from the potential energy curve in the slide above.  As the atoms are not strictly stationary (atoms are not at absolute zero temperature), they are confined at the bottom of the approximately parabolic potential well and execute vibrations with the energy determined by the temperature of the material.  At higher temperatures, the amplitude of vibration is greater and the atoms do come closer to each other with increased probability of a chemical reaction happening.  This situation is explained in the next slide:

Inter-molecular Forces:  In a molecule, two or more atoms are held together by chemical bonds.  These bonds form as a result of the sharing (co-valent or molecular bond) or exchange of electrons among atoms (ionic bond).
Just like inter-atomic  forces, two molecules also experience attractive and repulsive forces between them. Such inter-molecular forces are much weaker than the forces (bonds) that hold the atoms of a molecule together, but have a profound affect on the way a molecule's chemical and physics properties are determined.
Density:  Atoms and molecules feel a strong repulsive force if their separation is reduced beyond a certain value. This means that the number of molecules that may be packed in a given volume has an upper limit - saturation density.  This is true for solids and liquids (also for nuclei which experience a short range repulsive force although on a much smaller length scale of femto-meters
or 10-15m).  For solids, atoms or molecules are fixed in space and may prefer an ordered crystalline structure which may affect their density (liquid water and ice is a case where water is more dense than ice).
In liquids, thermal motion causes molecules to overcome the attractive inter-molecular forces and molecules can wander randomly in the body of the liquid.  The liquid will have higher volume - reduced density - as temperature is increased.

If the temperature is increased more than a certain level (boiling point), then the molecules of the liquid can break completely free of the attractive forces and we have a gaseous state. In gases, the density depends on the temperature and pressure.

Macroscopic Properties of liquids and gases:   Inter-molecular forces manifest themselves as bulk properties of liquids and gases (fluids) in the form of viscosity, surface tension, capillary action etc.  Low-temperature response of gases is greatly affected by the inter-molecular forces.

In this blog, I have discussed two main topics - increase in surface area as the size of a particle is reduced and the role of inter-atomic (and molecular) forces in determining the physical and chemical properties of substances.
By decreasing the particle size, one is providing a greater number of surface atoms/molecules that are within the range of attractive forces of the molecules of the surrounding medium and available for chemical reactions.  The result in reactivity may be and is indeed exploited in a very large number of situations in nature and design of industrial processes.  I hope to discuss some of the applications in a future publication.

I wish to reemphasize that it is the surface area of powdered materials that is important as a large surface area allows the possibility of surface atoms (or molecules) to react with reactants in the surrounding medium. A good example is of a pile of dried milk powder that will not ignite even if a roaring Bunsen flame is played on it.  However, if the powder is sprinkled onto a flame, a spectacular fireball is produced which demonstrates the increased reaction rate by increasing surface area.
Powdered materials are one way to increase surface area.  In liquids and gases, molecules are free to move about and already available for reaction with other molecules.  Liquids are on average 1000 times more dense than gases with a much larger number density of reactants available.