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Lecture notes for Lecture #6, October28th, 2010
Definitions
Pairwise potential:
The potential energy between two atomic sized, neutral, non
interacting, symmetric particles is very well described by the pairwise potential.
The
parameters listed below are important features of the pairwise potential
r
0
:
This defines the equilibrium distance between the two atomic sized, neutral,
symmetric particles.
r
min
: this is the minimum separation that will ever occur between the two
particles
r
max
: this is the maximum separation that will occur between the two particles
σ
:
This defines the distance between the centers of the two particles. When the
two particles are just touching, the distance between their centers is
σ
.
ε
:
Often, 1
ε
used to define the depth of the well.
Nearest Neighbors:
When investigating the structure of molecules, we can identify those
atoms that are equidistant to one reference atom. These are called nearest neighbors.
Next
–
Nearest neighbors:
As above, when investigating molecular structure, we can
identify those atoms that are equidistant to one reference atom, further away than the
nearest neighbor atoms, yet closer than the Nextnext Nearest neighbor atoms. Atoms that
satisfy this requirement area called NextNearest Neighbors.
Modes
–
This is new terminology for specifying the
“
way a substance has energy
”
The Pairwise Potential Curve as a Tool
The pair wise potential curve, shown below, graphically specifies the potential energy
between two particles as a function of the changing separation between those two
particles. An application of the information in the pair wise potential curve provides us a
way to 1) determine if a particle is bound, and 2) surmise the energy required to
completely disassociate that molecule. Let us see how this works.
First, let us more clearly label and discuss all the parameters above.
r
0
When these two particles are separated by a distance
r
0
the force of attraction equals
the force of repulsion, giving a net force of zero. The point or location where the net
force is zero is, by definition, the location of the equilibrium position. On the graph
below, r
0
corresponds to the rcoordinate of the location where the potential energy is a
minimum. The energy coordinate (in units of
ε
) is just the corresponding depth of the
well
ε
.
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:
We have seen that the equilibrium position, the distance at which the net force
between the particles is zero, occurs not when they are touching, but a little bit apart from
that, where the net force is zero. Remember that the force always points in the direction
that will minimize the potential energy. If the potential energy is already a minimum, no
additional force is required, as the natural state of affairs, the state of lowest potential
energy or equilibrium, is already achieved.
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 Fall '08
 PARDINI
 Physics, Energy, Potential Energy

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