Thermodynamics of Surfaces and


Feb 22, 2014 (7 years and 5 months ago)


Thermodynamics of Surfaces and

What is thermodynamics dealing with?

Thermodynamics is the branch of science that id
concerned with the principles of energy
transformation in macroscopic system.

Macroscopic properties of matter arise from the
behavior of a very large number of molecules.

Thermodynamics is based upon experiments and
observation , summarized and generalized in the
laws of thermodynamics.

These laws are not derivable from any other
principles: they are in fact improvable and
therefore can be regarded as assumptions only.

Some Definitions

Intensive variables

Extensive variables

System, isolated, open, closed





Thermodynamic state

Equilibrium between phases in
heterogeneous closed system

What does equilibrium mean?

A system is in

if no further spontaneous changes
takes place and if the same state can be reached by
other directions.

A phase?

A phase equilibrium is defined when the same
species are present in different phases.

A heterogeneous closed systems is composed of
two or more phases, with each phase is
considered as an open system within an overall
closed system.

Equilibrium between phases in
heterogeneous closed system

If the system initially, is not in an internal
then any process should occur in irreversible

So, according to first law:

And, combining with

both reversible and irreversible processes)

Equilibrium between phases in
heterogeneous closed system

Or finally:

Equilibrium between phases in
heterogeneous closed system

Equilibrium between phases in
heterogeneous closed system

Equilibrium between phases in
heterogeneous closed system

Equilibrium between phases in
heterogeneous closed system

Equilibrium between phases in
heterogeneous closed system

Equilibrium between phases in
heterogeneous closed system


and Contact Angle



and contact angle

In the case of a liquid that forms a uniform
film (i.e., where

0), the solid is said to be
completely wetted by the liquid, or that the
liquid wets the solid.

Where a nonzero angle is formed, there exists
some controversy as to how to describe the
system. If a finite contact angle is formed (

0), some investigators describe the system as
being partially wetted.

Others prefer to make a distinction based on the
size of the contact angle. For example, a given
worker may define as ‘‘wetting’’ any liquid that
produces a contact angle of 30 or less on a solid.
Between 30 and 89 the system would be
‘‘partially wetting,’’ and 90 and above

Alternatively, any system with 0<

180 would
be partially wetting, and only for 180 would the

term be applied.

While the contact angle of a liquid on a solid may be
considered a characteristic of the system, that will be
true only if the angle is measured under specified
conditions of equilibrium, time, temperature,
component purity, and other parameters.

The great utility of contact angle measurements stems
from their interpretation based on equilibrium
thermodynamic considerations. As a result, most
studies are conducted on essentially static systems in
which the liquid drop has (presumably) been allowed
to come to its final equilibrium value under controlled

As an application, contact angles, for example, can be
extremely useful as

test of the cleanliness of
sensitive surfaces such as glass or silicon wafers for
microelectronics fabrications.



are ‘‘high energy’’ and are completely
wetted by pure water.

If the surface is contaminated by something such as an
oil that interferes with the processing of the material
(e.g., the coating of a

polymer), a drop of
water will have a nonzero contact angle, and the
contamination will be immediately apparent.

Contact angle hysteresis

For systems that have ‘‘true’’ nonzero contact
angles, the situation may be further complicated
by the existence of contact angle hysteresis.

Thus, the contact angle one observes may vary
depending on whether the liquid is advancing
across fresh surface (the advancing contact angle,
A) or receding from an already wetted surface
(the receding contact angle, R) (Fig. 17.3).

As an operational convenience, many, if not most,
static contact angles measured and reported are
in fact advancing angles. For a given system, it
will be found that


In practice, very few systems exhibit a complete
lack of hysteresis, so that the problem can be
operational as well as philosophical.

One should keep in mind that when discussing
contact angle data, one must always be aware of
how the angle has been measured in order to
interpret its significance properly.

Why hysteresis

In dynamic contact angle studies, additional
complications arise because the movement of the
wetting line is not always a steady, continuous process.

It is often observed that the movement is ‘‘jerky,’’ with
the drop or liquid front holding a position for a time
and then jumping to a new configuration.

This phenomenon is often referred to as a ‘‘stick

process’’ and is not fully understood as yet. It has also
been observed that in dynamic systems, the values of


will vary as a function of the velocity of
wetting line movement, with

increasing with
velocity and


Why hysteresis

When used with Young’s equation and other such
relationships, the contact angle provides a relatively
simple yet sensitive insight into the general chemical
nature of a surface through such thermodynamic
quantities as the work of adhesion. Unfortunately, as
already mentioned, contact angles often exhibit
hysteresis and cannot be defined unambiguously by

It is always important to know as much as possible
about the cleanliness, topography, homogeneity, and
other characteristics of a solid surface, as well as the
purity and composition of the liquid employed, when
attempting to interpret contact angle data.

Why hysteresis

Although the existence of contact angle
hysteresis has been recognized for at least 100
years, the root of the ‘‘evil’’ has not always
been understood. In addition to the
physicochemical adsorption process already
mentioned, which leads to differences in
advancing and receding contact angles, it is
recognized that several physical and kinetic
factors also contribute to the overall problem.

Contact Angle Measurement

There are a variety of simple and inexpensive

The most common direct methods (Fig. 17.4) include
the sessile drop (
a), the captive bubble (b), the sessile

bubble (
c), and the tilting plate (d). Indirect methods

and geometric analysis of the
shape of a meniscus.

For solids for which the above methods are not
applicable, such as powders and porous materials,
methods based on capillary pressures, sedimentation
rates, wetting times,

rates, and other
properties, have been developed.

The Effects of Surface Roughness on
Contact Angles and Wetting

FIGURE 17.5. The apparent contact angle of a liquid on a surface may differ from

that expected, the ‘‘true’’ contact angle (
a), due to irregularities

either physical or


including surface roughness (
b) or chemical heterogeneity (c).

The Effects of Surface Roughness on
Contact Angles and Wetting

The theoretical discussion of contact angle and wetting to this point
has assumed implicitly that the solid surface in question is a
smooth, ideal plane.

In fact, of course, very few solid surfaces even begin to approach
such a state.

The finest polished glass surface, for example, will usually have
asperities of 5 nm or more.

Commonly encountered polished surfaces, will be much rougher

by factors of 10


The earliest, and still most useful, quantitative attempt to correlate
the observed contact angle of a liquid on a solid with the surface
roughness is the Wenzel relationship which proposes a
thermodynamic relationship such that

Wenzel relationship:


is defined as the surface roughness
factor, the ratio of the true and
surface areas of the solid (Fig. 17.5
b). Defining
the apparent contact
angle as


Recall Young equation

(with new notations)

FIGURE 17.7.
Young’s equation
for determining the
contact angle was

based on an
analysis of the force
balance among the
three surface
tensions involved.

The last equation may be taken as a fundamental definition of the effect of

surface roughness on wetting and spreading phenomena.

As a final note on the effects of surface roughness,
examination of the Equation, leads to a useful rule of
thumb for some important applications of wetting and
spreading phenomena; that is:

If the ‘‘true’’ contact angle of a liquid (an adhesive, say)
is less than 90 on the smooth surface, the angle will be
even smaller on a rough surface.

For a true contact angle 90, roughness will increase
the apparent angle. Mathematically the situation can
be described as:

Heterogeneous Surfaces

Roughness represents just one aspect of the effects of the
nature of the solid surface on contact angles and wetting

A second potentially important factor is that of the chemical
heterogeneity of the surface (Fig.


It is possible to

the following relationship relating
apparent contact angle to the chemical composition of a

Heterogeneous Surfaces

f1 and f2 are the fractions of the surface
having inherent contact angles
1 and 2.

f2= 1
f1, the equation can be written in
terms of one

Theoretically, if the inherent contact angles of a
test liquid on the homogeneous surfaces are
known, then the composition of a composite
surface can be determined from a simple contact
angle measurement.

Heterogeneous Surfaces

Experiments employing specially prepared
composite surfaces have shown that contact
angle data can give results that agree
reasonably well ( 15%) with more
sophisticated surface composition data
obtained using, for example, X
photoelectron spectroscopy (XPS).