F33ON1: Force and function at
the Nanoscale
James Sharp
Room C135
Mathematics and Physics building
Email: james.sharp@nottingham.ac.uk
Tel: 0115 9515142
Aims of the module
The module aims to provide an introduction to
the kinematics of nanoscale systems.
To develop an intuition of the origin of forces
on the nanoscale
To develop an appreciation of the role of
intermolecular, interparticle and surface forces
in nanoscale science, nanotechnology and
biology
Structure of the module
This is a 10 credit module that
runs ONLY in the Autumn
Semester
The module will consist of
~18-20 lectures
2 problems classes (weeks 6 and 11)
Content of the module
We will study the following topics;
1) Macroscopic and microscopic forces
2) Forces and potentials (2 lectures)
3) Van der Waals Interactions between atoms, molecules and macroscopic
bodies (3-4 lectures)
4) Measurement of nanoscale forces (2 lectures)
5) Surface Energy, Adhesion and Capillary forces (2 lectures)
6) Double layer forces and entropic repulsion forces (3 lectures)
7) Special interactions
8) Aggregation and self assembly
9) Micelles and membranes (3 lectures)
The textbook
The main text book for this course will
be
Intermolecular and Surface Forces:
2nd edition
Jacob Israelachvili, Academic Press,
1991
Library code QD485 ISR (5 copies)
Cost: £ 50-60 (Based on amazon.co.uk)
I will refer to other books as I go through
the module (also in the library)
Assessment
The module will be assessed as follows;
1.5 hour examination (80%) - January
Answer 3 (out of 5) 25 mark questions
2 sets of coursework (10% each)
Should be in your coursework book
The website
All this information and more can be
found on the website
http://www.nottingham.ac.uk/~ppzphy11/2ndoptions/modules/nanoscience/
Lecture 1:
Macroscopic and Microscopic
Forces
In this lecture…
1) Macroscopic forces
2) Microscopic and nanoscale forces
3) When do microscopic forces become
important?
4) Why is it important to understand
interactions at the nanoscale?
5) Energy scales
6) Motion on different length scales (viscosity
vs. Brownian motion)
Macroscopic forces: Gravity
Gravity is an important force which influences everything
around us on a macroscopic scale
Power law dependence
Gravity has a simple inverse square law dependence
GMm
FGravity   2
r
Where G is the gravitational constant 6.672 x 10-11 Nm2kg-2
, r is the separation between two objects (m)
M and m are the masses of the two objects (kg)
The force of gravity acts between all objects everywhere in
the universe
Microscopic and nanoscale
forces
Intermolecular and surface forces also act between objects
These are typically much shorter range than interactions
such as gravity
One class of intermolecular forces that we will meet in
future lectures are Van der Waals (dispersion) forces.
These forces act between all atoms and molecules
everywhere in the universe and are electrostatic in origin
6C
F  7
r
where C ~ 10-79 -10-77 Jm6
r
Importance of microscopic forces
Nanoscale forces hold materials together and they influence
the properties of a wide range of systems
Intermolecular and surface forces
(nanoscience experiments)
Nanoparticles, quantum dots and
ferrofluids (Nanotechnology)
Food
Biological cells,
molecules and
organisms
When do microscopic forces start
to become important?
If we equate the gravitational and dispersion forces we can
estimate the length scale at which the crossover between
these important forces occurs
1
5
or
GMm
6C
 2  7
r
r
 6C 
r 

 GMm 
For two Neon atoms we have G=6.67 x10-11 Nm2kg-2, C=3.9
x10-79 Jm6, M=m=3.2 x 10-26 kg
r ≈ 512 microns
In fact interatomic forces do not extend over these length
scales (usually less than 1 nm!)
What determines the range of
intermolecular and surface forces?
Although gravitational forces become less important on the
micron length scale, intermolecular and surface forces are
only significant over ranges of
0.2 nm
–
(weak interatomic/molecular)
This is because thermal
motion of the molecules
and particles has a
tendency to disrupt these
interactions on longer
length scales
100 nm
(micron sized particles)
The energy scale of thermal
motions
Consider an ideal gas, where all the internal energy is given
by kinetic energy of the atoms/molecules
PV  nRT
Ideal gas equation
Where P is the pressure (Nm-2), V, the volume (m3), n the
number of moles of gas, R, the molar gas constant (Jmol-1K-1)
and T is the temperature (Kelvin)
The left hand side of this equation has units of energy
P=Force/Area, PV= (Force x Volume)/Area = Force x distance
The relevance of kT
In the ideal gas law, nRT has units of energy, where
N
R
nRT 
RT  N
T  NkT
NA
NA
Where N is the number of atoms/molecules in the gas
and k is Boltzmann’s constant (1.38 x 10-23 JK-1 )
So
Thermal energies
 kT
As we will see in future lectures, thermal motions disrupt
interatomic/intermolecular interactions so much that they
only act on the sub-nm length scale
How big is kT?
Thermal energies are not negligible at room temperature
Taking Troom= 300K
kT= 4.14 x 10-21 J = 0.025 eV
If we compare this to the strength of Van der Waals
interactions between molecules at 0.2nm
For two Neon atoms C=3.9 x10-79 Jm6 putting r=0.2 nm
U VdW
C
 21
  6  6.110 J
r
Problem
Calculate an estimate of the distance above which
thermal effects dominate over
a) Gravitational interactions
b) Van der Waals interactions
between two methane molecules at room
temperature
G=6.67 x 10-11 Nm2kg-2
Cmethane=1.01 x 10-77 Jm6
Mmethane=2.56 x 10-26 kg
Motion on the microscopic scale
The motion of molecules on the micron and nanometre
length scale is determined by the thermal motion of
neighbouring atoms and molecules.
Atoms, molecules and small particles execute a random
walk. In a time t, the mean square displacement of an atom,
molecule or particle is given by
<x2>
~ Dt
where D is the diffusion coefficient (m2s-1)
kT
D
6a
a is the radius of the particle (m)
 is the viscosity of the
surrounding medium (Pas)
√<x2>
Summary of key concepts
Microscopic and nanoscale forces
are important in a number of
areas of nanoscience,
nanotechnology and biology
These forces start to become
important on the sub micron
length scale
The relevant energy scale on
these small length scales is the
thermal energy scale
U thermal  kT