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Surfaces, Interfaces, and Colloids: Principles and Applications, Second Edition.
Drew Myers
Copyright
1999 John Wiley & Sons, Inc.
ISBNs: 0-471-33060-4 (Hardback); 0-471-23499-0 (Electronic)
8
Liquid–Fluid Interfaces
Liquids have several distinct characteristics that differentiate them from solid
and gas phases. One of the more important ones (from the point of view of
surface chemistry, at least) is that, unlike a gas, liquids have a relatively high
density and fixed volume, while they possess a mobility at the molecular level
that is many orders of magnitude greater than that in solids. As a result of
that mobility, interfaces involving liquids and another fluid generally (but
not always) behave as though homogeneous and therefore lack many of the
complications encountered when considering solid surfaces. The not always
qualification applies primarily in viscous liquids and those multicomponent
systems containing surface-active materials that must diffuse to the surface.
In such cases, rapid measurements of newly formed surface may produce
surprising results, as described later.
8.1. THE NATURE OF A LIQUID SURFACE: SURFACE TENSION
As pointed out in Chapter 2, it is common practice to describe a liquid surface
as having an elastic ‘‘skin’’ that causes the liquid to assume a shape of minimum
surface area, its final shape being determined by the ‘‘strength’’ of that skin
relative to other external factors such as gravity. In the absence of gravity,
or when suspended in another immiscible liquid of equal density, a liquid
spontaneously assumes the shape of a sphere. In order to distort the sphere,
work must be done on the liquid surface, increasing the total surface area
and therefore the free energy of the system. When the external force is
removed, the contractile skin then forces the drop to return to its equilib-
rium shape.
While the picture of a skin like a balloon on the surface of a liquid is easy
to visualize and serves a useful educational purpose, it can be quite misleading,
since there is no skin or tangential force as such at the surface of a pure liquid.
It is actually an imbalance of forces on surface molecules pulling into the bulk
liquid and out into the adjoining vapor phase that produces the apparent
contractile skin effect. The forces involved are, of course, the same van der
Waals interactions that account for the liquid state in general and for most
physical interactions between atoms and molecules. Because the liquid state
is of higher density than the vapor, surface molecules are pulled away from
the surface and into the bulk liquid, causing the surface to contract spontane-
140
8.1. THE NATURE OF A LIQUID SURFACE: SURFACE TENSION
141
FIGURE 8.1.
The unbalanced, inward pull of bulk liquid molecules on those at the
surface results in the phenomenon observed as surface tension. The drive to reduce
the surface area to a minimum produces the observed tendency of liquids to form
spherical drops (in the absence of gravity)—the geometry of minimum surface area
for a given volume of material.
ously (Fig. 8.1). For that reason, it is more accurate to think of surface tension
(or surface energy) in terms of the amount of work required to increase the
surface area of the liquid isothermally and reversibly by a unit amount, rather
than in terms of some tangential contractile force.
As will be seen later in the chapter, the same basic ideas that are used
to describe the liquid–vapor interface apply to the liquid–liquid interface.
However, since a second liquid phase is much more dense than a vapor phase,
the various attractive interactions among units of the two phases across the
interface, which depend on the number density of interacting units (see Chap-
ter 4), are significantly greater. For a given increase in liquid–liquid interfacial
area, the excess surface energy of each unit (and therefore the total energy)
will be lower. In other words, the net work required to increase the interfacial
area, the interfacial tension, will be reduced relative to the liquid-vapor case.
Table 8.1 lists the surface tensions of several typical liquids and their corre-
sponding interfacial tensions against water and mercury.
TABLE 8.1. Typical Liquid Surface and Interfacial Tensions at 20 C (mN m-1)
Liquid
Water
Ethanol
n-Octanol
Acetic acid
Oleic acid
Acetone
Carbon tetrachloride
Benzene
n-Hexane
n-Octane
Mercury
Surface Tension
72.8
22.3
27.5
27.6
32.5
23.7
26.8
28.9
18.4
21.8
485
Interfacial Tension versus Water
—
—
8.5
—
7.0
—
45.1
35.0 (357 vs. mercury)
51.1 (378 vs. mercury)
50.8
375
142
LIQUID–FLUID INTERFACES
There are two quick observations that one may note from the data in Table
8.1: (1) the interfacial tension between a given liquid and water is always less
than the surface tension of water; and (2) for an homologous series of materials
such as the normal alkanes, the interfacial tension between the members of
the series and water (or any other immiscible liquid) will change only slightly
as a function of the molecular weight of the material. Those characteristics
are a direct consequence of the nature of the interactions at the interface.
Where the two liquids are highly immiscible, the interfacial tension will lie
between the two surface tensions (e.g., water–alkane); if significant miscibility
exists, the interfacial tension will be lower than the lower of the two surface
tensions (e.g., water–octanol). The difference stems from the surface activity
of the molecules of the miscible liquid (in water), a topic introduced in Chapter
3 that will be addressed again in Chapter 15.
Most commonly encountered room-temperature liquids have surface ten-
sions against air or their vapors that lie in the range of 10–80 mN m
1
. Liquid
metals and other inorganic materials in the molten state exhibit significantly
higher values as a result of the much greater and more diverse interactions
occurring in such systems. Water, the most important liquid commonly encoun-
tered in both laboratory and practical situations, lies at the upper scale of
what are considered normal surface tensions, with a value in the range of
72–73 mN m
1
at room temperature, while hydrocarbons reside at the lower
end, falling in the lower to middle 20s. Materials such as fluorocarbons and
silicones may go even lower.
8.1.1. Surface Mobility
The common concept of interfacial tensions is simplistic in the sense that it
implies that the surface or interface is a static entity. There is, in reality, a
constant and for liquids and gases, rapid interchange of molecules between
the bulk and interfacial region, and between the liquid and vapor phases. If
it is assumed that molecules leave the interfacial region at the same rate that
they arrive, it is possible to estimate the exchange rate, , of an individual
molecule from the relationship
(2
mkT
)
1/2
p
0
(8.1)
where is a so-called sticking coefficient (i.e., the fraction of molecules striking
the surface that actually becomes part of it ),
p
0
is the equilibrium vapor
pressure of the liquid,
m
the mass of the molecule, and
k
Boltzmanns constant.
Assuming to lie in the range of 0.03–1.0, a water molecule at 25 C will
have an average residence time of 3 ms at the air–water interface. The
corresponding residence time for a mercury atom would be roughly 5 ms,
while that for a tungsten atom (obviously not in the liquid state) would be
10
37
s at room temperature.
8.1. THE NATURE OF A LIQUID SURFACE: SURFACE TENSION
143
With such molecular mobility, it is clear that the surface of a pure liquid
offers little resistance to forces that may act to change its shape. That is, there
will be very little viscous or elastic resistance to the deformation of the surface.
An important consequence of that fact is that a pure liquid does not support
a foam for more than a small fraction of a second (see Chapter 12). A similar
situation exists at the liquid–liquid interface. As we shall see in later chapters,
the highly mobile nature of liquid interfaces has significant implications for
many technological applications such as emulsions and foams, and forms the
basis for many of the most important applications of surface-active materials
or surfactants.
8.1.2. Temperature Effects on Surface Tension
Because of the mobility of molecules at fluid interfaces, it is not surprising to
find that temperature can have a large effect on the surface tension of a liquid
(or the interfacial tension between two liquids). An increase in surface mobility
due to an increase in temperature will clearly increase the total entropy of
the surface and thereby reduce its free energy,
G.
Since the surface tension
has been thermodynamically defined as
G
A
(8.2)
one would expect to encounter a negative temperature coefficient for s. While
that is the case for most normal liquids, including most molten metals and
their oxides, positive coefficients have been encountered. The reason for that
phenomenon is not entirely clear, although it probably results from some
change in the actual atomic composition of the surface as the temperature
is increased.
At temperatures near the critical temperature of a liquid, the cohesive
forces acting between molecules in the liquid become very small and the
surface tension approaches zero. That is, since the vapor cannot be condensed
at the critical temperature, there will be no surface tension. A number of
empirical equations that attempt to predict the temperature coefficient of
surface tension have been proposed; one of the most useful is that of Ramsey
and Shields:
Mx
r
2/3
k
s
(T
c
T
6)
(8.3)
where
M
is the molar mass of the liquid, its density,
x
the degree of associa-
tion,
T
c
the critical temperature, and
k
s
a constant.
144
LIQUID–FLUID INTERFACES
8.1.3. The Effect of Surface Curvature
Because many practical situations involve surfaces and interfaces with high
degrees of curvature, it is important to understand the effect of curvature on
interfacial properties. As pointed out in Chapters 2 and 6, there will develop
a pressure differential across any curved surface, with the pressure being
greater on the concave side of the interface. In other words, the pressure
inside a bubble will always be greater than that in the continuous phase. The
Young–Laplace equation
p
1
r
1
1
r
2
(8.4)
relates the quantities of interest in this situation, in which
p
is the drop in
pressure across a curved interface,
r
1
and
r
2
are the principal radii of curvature,
and s is the surface (or interfacial) tension. For a spherical surface where
r
1
r
2
, the equation reduces to
p
2
r
(8.5)
For a very small drop of liquid in which there is a large surface : volume
ratio, the vapor pressure is higher than that over a flat surface of equal area.
The movement of liquid from a flat interface into a volume with a curved
interface requires the input of energy into the system since the surface free
energy of the curved volume increases. If the radius of a drop is increased by
dr,
the surface area increases from 4 r
2
to 4 (r
dr)
2
, or by a factor of 8
r dr.
The free energy increase is 8
r dr.
If during the process
n
moles of liquid
are transferred from the flat phase with a vapor pressure of
p
0
to the drop
with vapor pressure
p
r
, the free energy increase also is given by
G
nRT
ln
p
r
p
0
(8.6)
Equating the two relationships leads to the expression
RT
ln
p
r
p
0
2
M
r
2
V
m
r
(8.7)
known as the Kelvin equation. In Equation (8.7), is the density,
M
the molar
mass, and
V
m
the molar volume of the liquid. It can be shown that extremely
small radii of curvature can lead to the development of significant pressure
differences in drops. For a drop of water with a radius of 1 nm, the partial
pressure ratio from (8.7) is about 3. Obviously, the condensation of liquid

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