5.1.5 Dielectric screening
The interactions that we have discussed thus far are electrostatic in origin,
involving charged species (ions) and either permanent or induced
dipoles. We have discussed these interactions in terms of pair potentials,
or interactions between two particles without regard to the presence of
any other particles that could interact. However, in dense systems relevant to nanoscience, such as liquids, solids, and colloids, these interactions are affected by the presence of their neighbors. These complex
interactions can be treated by three major approaches: (a) averaging
these interactions into a simple parameter, (b) running computer simulations that contain many interacting particles, and/or (c) explicitly
modeling these interactions using potentials involving three or more
particles. We will focus on the first approach; the latter two approaches
are beyond the scope of the present text.
When molecules are exposed to an electric field, E, whether that field is
external (e.g., a beam of light or a voltage applied to a pair of electrodes)
or internal (e.g., other molecules/ions in the system), the molecules
reorient and polarize to minimize their energy of interaction with the
field. Figure 5.7 shows how water molecules can reorient in response to
the presence of either ions (left) or charged surfaces (right). The alignment of the permanent and induced dipoles of the other molecules in the
system produces an electric field that counteracts the applied field. This
field is known as the polarization field, P, and is defined as
P = e − 1
ð
Þe 0 E
(5.12)
The dielectric constant (or relative permittivity), e, is a dimensionless
quantity that reflects the system’s ability to polarize, and can be experimentally determined from the electrical capacitance of a material sandwiched between two parallel electrodes as
e =
Cd
A
=
Qd
VA
(5.13)
where C is the capacitance, A is the area of the plates, Q is the total charge
on each plate, V is the electrostatic potential (voltage) between the plates,
and d is the distance between the plates. Figure 5.7 (right side) shows how
when the dipoles of water align between two charged plates, they produce
an electric field in the opposite direction of their dipole moments that
reduces the total electric field between the plates by a factor of e. The
dielectric constant can be determined from either measuring the voltage
INTERMOLECULAR FORCES AND SELF-ASSEMBLY 145
The interactions that we have discussed thus far are electrostatic in origin,
involving charged species (ions) and either permanent or induced
dipoles. We have discussed these interactions in terms of pair potentials,
or interactions between two particles without regard to the presence of
any other particles that could interact. However, in dense systems relevant to nanoscience, such as liquids, solids, and colloids, these interactions are affected by the presence of their neighbors. These complex
interactions can be treated by three major approaches: (a) averaging
these interactions into a simple parameter, (b) running computer simulations that contain many interacting particles, and/or (c) explicitly
modeling these interactions using potentials involving three or more
particles. We will focus on the first approach; the latter two approaches
are beyond the scope of the present text.
When molecules are exposed to an electric field, E, whether that field is
external (e.g., a beam of light or a voltage applied to a pair of electrodes)
or internal (e.g., other molecules/ions in the system), the molecules
reorient and polarize to minimize their energy of interaction with the
field. Figure 5.7 shows how water molecules can reorient in response to
the presence of either ions (left) or charged surfaces (right). The alignment of the permanent and induced dipoles of the other molecules in the
system produces an electric field that counteracts the applied field. This
field is known as the polarization field, P, and is defined as
P = e − 1
ð
Þe 0 E
(5.12)
The dielectric constant (or relative permittivity), e, is a dimensionless
quantity that reflects the system’s ability to polarize, and can be experimentally determined from the electrical capacitance of a material sandwiched between two parallel electrodes as
e =
Cd
A
=
Qd
VA
(5.13)
where C is the capacitance, A is the area of the plates, Q is the total charge
on each plate, V is the electrostatic potential (voltage) between the plates,
and d is the distance between the plates. Figure 5.7 (right side) shows how
when the dipoles of water align between two charged plates, they produce
an electric field in the opposite direction of their dipole moments that
reduces the total electric field between the plates by a factor of e. The
dielectric constant can be determined from either measuring the voltage
INTERMOLECULAR FORCES AND SELF-ASSEMBLY 145