Solution
One-half of a monolayer requires an exposure of approximately 0.5 L. Using
equation 22.22 and the definition from equation 22.23:0.5 L (2.0 10 ^11 torr) (time)
1 101
L
(^6) torrs
The last term is a conversion factor between the units involved and comes
straight from equation 22.23. We solve this equation algebraically for time:
time
The langmuir and torr units cancel; the only remaining unit, seconds, is in
the denominator of the denominator, which makes it in the numerator.
Solving numerically:
time 2.5 104 s
It will take almost 7 hours for one-half of a monolayer to form. This exam-
ple shows that at such low pressures, surfaces can be kept relatively clean for
quite a while if an ultrahigh vacuum is maintained.
These calculations are approximate because they assume that any gas atom
or molecule that hits a surface will stick there. In reality, this depends on the
identity of the gas species, the identity of the surface, and the temperature of
the gas and/or the surface.
The student should be aware that it takes special vacuum equipment to
maintain an ultrahigh vacuum. First, a clean surface must be inside a special
vacuum chamber that has no leaks—which is easier said than done. In addi-
tion, special vacuum pumps must be used to get to such high vacuums and
stay there. The normal oil-filled rotary vacuum pump can only maintain a vac-
uum of about 10^4 torr or so, a full four orders of magnitude higher than what
is necessary for ultrahigh vacuum. Special vacuum pumps (like turbomolecu-
lar pumps, titanium sublimation pumps, or liquid-helium-based cryopumps)
are needed and can be extremely expensive.
Assume that we do, in fact, have a clean surface. What makes the surface so
special that it has properties different from the bulk? The answer lies in un-
derstanding the chemical nature of a bulk solid. Figure 22.18a shows a two-
dimensional solid in which the atoms are all connected to each other in all di-
rections. That is, they are all bonding to their neighboring atoms. Figure 22.18b
shows what happens when this two-dimensional solid is cracked so that a new
surface is exposed to the environment. The atoms at the surface make bonds
to the atoms in the bulk, but there are no atoms to bond with on the other side
of the surface. The atoms at the surface have atomic orbitals that are not (as
yet) interacting with—bonding to—any other atomic or molecular species.
These empty orbitals, sometimes referred to as “dangling bonds,” are very re-
active and will interact extremely easily with other chemical species. This
model accounts for several properties of surfaces, not just their ability to eas-
ily adsorb molecular species from the surrounding environment. Empty or-
bitals of adjacent atoms sometimes interact with each other, causing a slight
rearrangement of the surface layer(s) so that the surface structure is somewhat
different from the bulk. (This was alluded to earlier in the chapter.) Figure
22.19 shows an example of the structural rearrangement of a surface.
0.5 L
(2.0 10 ^11 torr)
1 101
L
(^6) torrs
782 CHAPTER 22 Surfaces
Bonds to
neighboring
atoms
(a)
Dangling
bonds at
surface
(b)
Figure 22.18 (a) In the bulk of a solid, atoms
interact with other atoms all around them. The
arrows imply that bonding continues in that di-
rection to other atoms. (b) At the surface, atoms
interact with other atoms in all directions except
one. In that direction, there is an “unsatisfied”
bond called a dangling bond that can easily in-
teract with other chemical species. Compare this
diagram with Figure 22.1, which shows the im-
balance of forces that ultimately cause surface
tension.
Figure 22.19 Sometimes the dangling surface
bonds interact with each other. When they do, the
exact structure of the surface can differ substan-
tially from the bulk structure, as shown. This fig-
ure is merely illustrative; what happens in real
surfaces depends on the material.