PH3-SM (PHY3032)
Soft Matter Physics
4 October, 2011
Lecture 1:
Introduction to Soft Matter
What is Condensed Matter?
•
•
“Condensed matter” refers to matter that is not in the gas phase but is condensed as
a liquid or solid. (condensed denser!)
Matter condenses when attractive intermolecular bond energies are comparable to
or greater than thermal (i.e. kinetic) energy ~ kT.
Phase diagram of carbon dioxide (CO2)
Image: http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html
Phase Diagram of Water
Image: http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html
Soft (Condensed) Matter
• Refers to condensed matter that exhibits characteristics of
both solids and liquids.
• The phrase “soft matter” was used by Pierre de Gennes as
the title of his 1991 Nobel Prize acceptance speech.
• Soft matter can flow like liquids (has a measurable
viscosity).
• Soft matter can bear stress and recover its original shape
after deformation (i.e. is elastic).
• Viscoelastic behaviour = viscous + elastic
• Examples: rubbers, gels, pastes, creams, paints, soaps,
liquid crystals, proteins, cells, tissue, humans(?)
Types of Soft Matter: (1) Colloids
• A colloid consists of sub-mm particles (but not single molecules) of one phase
dispersed in a continuous phase.
• The size scale of the dispersed phase is between 1 nm and 1 mm.
• The dispersed phase and the continuous phases can consist of either a solid
(S), liquid (L), or gas (G):
Dispersed Phase Continuous
Name
Examples
L/S
G
aerosol
fog, hair spray; smoke
G
L/S
foam
beer froth; shaving foam;
poly(urethane) foam
L
L (S)
S
L
S
S
emulsion
sol
solid suspension
mayonnaise; salad dressing
latex paint; tooth paste
pearl; mineral rocks
There is no “gas-in-gas” colloid, because there is no interfacial tension
between gases!
Interfacial Area of Colloids
For a spherical particle, the ratio of surface area (A) to
volume (V) is:
A 4r 2
1
V
=
4 r 3
3
≈
r
r
Thus, with smaller particles, the interface becomes more significant. A
greater fraction of molecules is near the surface.
Consider a 1 cm3 phase dispersed in a continuous medium:
No. particles
“Particle” volume(m3) Edge length (m)
Total surface area(m2)
1
10-6
10-2
0.0006
103
10-9
10-3
0.006
106
10-12
10-4
0.06
109
10-15
10-5
0.6
1012
10-18
10-6
6.0
1015
10-21
10-7
60
1018
10-24
10-8
600
Colloidal Flow Properties
Shear thickening behaviour of a polymer colloid (200 nm particles
of polymers dispersed in water):
At a low shear rate: flows like a liquid
At a high shear rate: solid-like behaviour
Types of Soft Matter: (2) Polymers
• A polymer is a large molecule, typically with 50 or more repeat units. (A
“unit” is a chemical group.)
• Examples include everyday plastics (polystyrene, polyethylene); rubbers (also
called “elastomers”); biomolecules, such as proteins and starch.
Physicist’s view of a
polymer:
•
•
•
Each “pearl” on the string represents a “repeat unit” of several atoms, linked
together by strong covalent bonds. For instance, in a protein molecule, the repeat
units are amino acids. Starch consists of repeat units of sugar.
The composition of the “pearls” is not important (for a physicist!).
Physics can predict the size and shape of the molecule; the important parameter is
the number of repeat units, N.
Examples of Repeat Units
Terminology of Polymers
• A “plastic” is a solid-like polymer. When it is deformed beyond a certain
limit, the deformation becomes permanent, and it is called plastic
deformation.
• When polymers are at higher temperatures, the molecules move with
greater mobility, and flow is possible.
• When polymer chains are “tied together” by chemical bonds, the polymer
remains deformable, but it obtains elastic properties. When stress is
released, the material recovers its initial size and shape. This type of
polymer is a called a rubber or an elastomer.
• Polymers can be dissolved in a liquid (called a solvent) to make a solution.
Stress
Elastic
Bond
between
chains
Plastic
Chain network in an elastomer
Strain
Types of Soft Matter: (3) Liquid Crystals
• A liquid crystal is made up of molecules that exhibit a level of
ordering that is intermediate between liquids (randomly
arranged and oriented) and crystals (three-dimensional array).
Flows easily in the
aligned direction.
Elastic in the normal
direction.
Image: http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html
This form of soft matter is interesting and useful because of its
anisotropic optical and mechanical properties.
Characteristics of Soft Matter (4 in total)
(1) Intermediate length scales between the atomic
and the macroscopic
Top view
3 mm x 3 mm scan
Edge length = 1 mm
Vertical scale = 200 nm
Acrylic Latex Particles Monosized
Example of colloidal
particles
Typical Length Scales
• Atomic spacing: ~ 0.1 nm
• “Pitch” of a DNA molecule: 3.4 nm
• Diameter of a surfactant micelle: ~6-7 nm
• Radius of a polymer “chain” molecule: ~10 nm
• Diam. of a colloidal particle (e.g. in emulsion paint): ~200 nm
• Bacteria cell: ~2 mm
• Diameter of a human hair: ~80 mm
Typical Length Scales
Poly(ethylene) crystal
15 mm x 15 mm
Crystals of poly(ethylene oxide)
5 mm x 5 mm
Polymer crystals can grow up to millimeters in size!
Intermediate Length Scales
• Mathematical descriptions of soft matter can ignore the
atomic level.
• “Mean field” approaches define an average energy or
force imposed by the neighbouring molecules.
• Physicists usually ignore the detailed chemical make-up
of molecules; can treat molecules as “strings”, rods or
discs.
Characteristics of Soft Matter
(2) Weak short-range forces and interfaces are important.
Work of A. Geim, highlighted in Materials World (2003)
The structure of a gecko’s foot has been mimicked to create an adhesive. But the
attractive adhesive forces can cause the synthetic “hairs” to stick together.
Chemical Bonds in Soft Matter
• In “hard” condensed matter, such as Si or Cu, strong covalent
or metallic bonds give a crystal strength and a high cohesive
energy (i.e. the energy to separate atoms).
• In soft matter, weaker bonds - such as van der Waals - are
important. Bond energy is on the same order of magnitude as
thermal energy ~ kT. (k is Boltzmann’s constant: 1.38 x 10-23 J/K)
• Hence, bonds are easily broken and re-formed.
• The strength of molecular interactions (e.g.
charge attractions) decays with distance, r,
between molecules or particles.
• At distances less than 10 nm, they start to
become significant.
r
Condensed Matter and the Origin of
Surface Tension
Meniscus
Increasing
density
From I.W. Hamley,
Introduction to Soft Matter
Liquids and gases are separated by a meniscus; they differ only in
density but not structure (i.e. arrangement of molecules in space).
• Molecules at an interface have asymmetric forces around them.
• In reducing the interfacial area, molecules are forced below the surface, where they
are completely surrounded by neighbours.
• Force associated with separating neighbouring molecules = surface tension.
Interfacial Energy
An interfacial energy G is associated with the interface between two phases
(units of Jm-2) (also called an interfacial tension: Nm-1)
G cosq  F
F
d
d
Gq
Interface with air = “surface”
For mercury, G = 0.486 N/m
Mercury has a very high surface energy!
For water, G = 0.072 N/m
For ethanol, G = 0.022 N/m
What characteristics result from a high surface energy?
Image: http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html
Contact Angle: Balance of Forces
Imagine a 10 mL drop of liquid on a solid. (No effect of g.)
GLA
air
GSL
liquid
q
GSA
solid
SA energy is
equivalent to ½ of the
energy to cleave the
solid
Three interfaces: solid/liquid (SL); liquid/air (LA); solid/air (SA)
Each interface has a tension (energy): GSL; GLA; GSA
At equilibrium, lateral tensions must balance:
G -G
GSA  GSL  GLA cos q ⇒ SA SL  cos q
GLA
Contact angle measurements thus provide information on interfacial
tensions.
Hydrophobicity and Hydrophilicity
water
Fully wetting
solid
water
q
Hydrophilic
solid
water
solid
q is <90
q
http://scottosmith.com/2007/10/03/water-beads/
Hydrophobic
q is >90
Lotus Leaf Inspired Synthetic Super-hydrophobic Surfaces
Laser-patterned surface
Lotus leaf: low surface energy
plus textured.
DOI: 10.1117/2.1200901.1441
V. Zorba, et al., Biomimetic artificial surfaces quantitatively reproduce the water repellency of a lotus
leaf, Adv. Mater. (2008) 20, pp. 4049-4054.
M. Barberoglou, et al., Bio-inspired water repellent surfaces produced by ultrafast laser structuring of
silicon, Appl. Surf. Sci. (2009) 255, pp. 5425-5429.
Characteristics of Soft Matter
(3) The importance of thermal fluctuations and
Brownian motion
Brownian motion can be thought of as resulting from a slight imbalance of
momentum being transferred between liquid molecules and a colloidal particle.
Thermal fluctuations
• Soft condensed matter is not static but in constant motion at the level of
molecules and particles.
• The “equipartition of energy” means that for each degree of freedom of
a particle to move, there is kT/2 of thermal energy.
• For a colloidal particle able to undergo translation in the x, y and z
directions, the thermal energy is 3/2 kT.
• k = 1.38 x 10-23 JK-1, so kT = 4 x 10-21 J per molecule at room temperature
(300 K).
Vz
V
• kT is a useful “gauge” of bond energy.
Vy
The kinetic energy for a particle of mass, m, is
1/2 mv2 = 3/2 kT. When m is very small, then
v becomes significant.
Vx
Thermal motion of a nano-sized beam
• In atomic force microscopy, an ultra-sharp tip on the end of a silicon
cantilever beam is used to probe a surface at the nano-scale. By how
much is the beam deflected by thermal motion?
100 mm x 30 mm x
2 mm
X
• For AFM applications, the cantilever beam typically has a spring
constant, kS, of ~ 10 N/m.
• The potential energy required for deflection of the beam, Ed, by a
distance, X is Ed = ½ kSX 2.
• At a temperature of 300 K, the thermal energy, E, is on the order of
kT = 4 x10-21 J.
• This energy will cause an average deflection of the beam by
X = (2E/kS)0.5  1 x 10-7 m or 100 nm.
•Polymers and membranes can have an even lower spring constant!
Characteristics of Soft Matter
(4) Tendency to self-assemble into hierarchical structures (i.e.
ordered on size scales larger than molecular)
Two “blocks” in one
polymer chain
Image from IBM
(taken from BBC
website)
Diblock copolymer molecules spontaneously form a pattern in a thin film.
(If one phase is etched away, the film can be used for lithography.)
Polymer Self-Assembly
AFM image
Diblock copolymer
2mm x 2mm
Poly(styrene) and poly(methyl
methacrylate) copolymer
Layers or “lamellae” form spontaneously in diblock copolymers.
Spider Silk: An Example of a Hierarchical Structure
Amino acid units
P. Ball, Nanotechnology (2002) 13, R15-R28
The
hierarchical
structure of
amyloid
materials
T. P. J. Knowles and
M. J. Buehler,
Nature Nanotech
(2011) 6, 469
DNA Base Pairs Drive the Self-Assembly of Helices
Adenine (A) complements
thymine (T) with its two H bonds
at a certain spacing.
Guanine (G) complements
cytosine (C) with its three H
bonds at different spacings.
Example of DNA sequence:
ATCGAT
TAGCTA
Designed Nanostructures from DNA
Strands of DNA only bind to those that are complementary.
DNA can be designed so that it spontaneously creates desired
3-D structures.
N C Seeman (2003) Biochemistry, 42, 7259-7269
Particles Can Assemble into Colloidal Crystals
MRS Bulletin,
Feb 2004, p. 86
Colloidal particles can have a +ve or -ve charge.
In direct analogy to salt crystals of +ve and -ve ions, charge attractions
can lead to close-packing in ordered arrays.
Phase Equilibria in Colloidal Dispersions
Equilibrium:
Non-equilibrium:
(Volume %)
RCP = random
close-packing;
HCP = hexagonal
close-packing
Mono-sized particles can become ordered into crystals at f =
0.54 while still in the “wet” state.
V. Prasad, D. Semwogerere and Eric R. Weeks, J. Phys.: Condens. Matter 19 (2007) 113102 (25pp)
Hydrophilically-driven self-assembly of particles
I. Karakurt et al., Langmuir 22 (2006) 2415
Surfactants at Interfaces
Emulsion
“oil”
water
Interfacial tension, G
Work (W) is required to increase the
Typical G values for interfaces with water carbon tetrachloride: 45 mN/m; benzene: 35
mN/m; octanol: 8.5 mN/m
interfacial area (A):
∫
W = GdA
A surfactant (surface active agent) molecule
has two ends: a “hydrophilic” one (attraction
to water) and a “hydrophobic” (not attracted
to water) one. Commonly known as soap!
Surfactants reduce G. Are used to make
emulsions using less W and to achieve “self
assembly” (i.e. spontaneous organisation)
Importance of Interfaces
• There is thermodynamic work (W) associated with
increasing or decreasing the interfacial area, A, of a
substance:
dW = GdA
• Doing work on a system will raise its internal energy (U;
dU = dW + dQ)) and hence its free energy (F).
• An increase in area raises the system’s free energy, which is
not thermodynamically favourable.
• So, sometimes interfacial tension opposes and destroys the
formation of small phases.
• An example is coalescence in emulsions.
Coalescence in Emulsions
Liquid droplet volume is the same before and after coalescence:
r
Surface area of N particles:
4Nr2
R
Surface area of droplet made from
coalesced droplets: 4R2
Change in area, DA = - 4r2(N-N2/3)
In 1 L of emulsion (50% dispersed phase), with a droplet diameter of 200 nm, N is
~ 1017 particles. Then DA = -1.3 x 104 m2
With G = 3 x 10-2 J m-2, DF =GDA = - 390 J.
Examples of Surfactant Self-Assembly
water
(a)
Surfactant
(b)
Spherical end is hydrophilic. Tail is hydrophobic.
(c)
(d)
From I.W. Hamley, Introduction to Soft Matter
Surfactants can assemble into (a) spherical micelles, (b) cylindrical
micelles, (c) bi-layers (membranes), or (d) saddle surfaces in
bicontinuous structures depending on their concentration and the
balance between their hydrophobic and hydrophilic components.
Examples of Surfactant Self-Assembly
The “plumber’s
nightmare”
From RAL Jones, Soft Condensed Matter
• Surfactants can create a bi-continuous surface to separate an oil phase and
a water phase.
• The hydrophilic end of the molecule orients itself towards the aqueous
phase.
• The oil and water are completely separated but both are CONTINUOUS
across the system.
Competitions in Self-Assembly
If a process decreases the free energy (DF < 0) of a system,
then the process happens spontaneously.
DF = DU - TDS
Internal Energy (U)
decrease is favourable
Entropy (S) increase is
favourable
• Surfactant molecules segregate at an interface in order to LOWER
the interfacial energy (U) - leading to an ordering of the system.
• This self-assembly is opposed by thermal motion that disrupts the
ordering.
• Self-assembly usually DECREASES the entropy, which is not
favoured by thermodynamics.
• But there are attractive and repulsive interactions between
molecules (lowering U) that can dominate.
Optimum area, a0, of molecule in a surfactant structure is
found at the free energy minimum
a0
At equilibrium each
head group of the
molecule will occupy
an area of “a0”
F  Ga + K/a
Total energy
Free
energy, F
Attractive energy:  Ga
How would you find a0?
Repulsive energy:  K/a
a0
Surface area per molecule, a
Israelachvili, Intermolecular
& Surface Forces, Ch. 17,
p. 366
Molecular Geometry Also Determines Whether
Surfactant Micelles are Favourable
To pack densely into a sphere, the molecules
should be conical in shape
Area, a0
R
R  Lc
Lc is the hydrophobic chain length
V is the volume of the cone (molecule)
Spherical Micelle CrossSectional View
N molecules in total in micelle
= Area sphere/area of molecule
= Volume sphere/ volume of molecule
4R 2 4R 3
N

a0
3v
3v
 R   Lc
a0
v
1


a0Lc 3
Israelachvili, Ch.
17, p. 366
Colloidosomes: Self-assembled colloidal particles
Liquid
B
Colloidal
particles (<1
mm)
Liquid A
A.D. Dinsmore et al., “Colloidosomes: Selectively Permeable Capsules Composed of
Colloidal Particles,” Science, 298 (2002) p. 1006.
Materials with controlled structure obtained
through self-assembly
Surfactant micelles
(soft “nano-objects”)
are packed together
SiO2 (silica) is grown
around the micelles
P. Ball, Nanotechnology (2002) 13, R15-R28
Micelles are removed to
leave ~ 10 nm spherical
holes. Structure has low
refractive index. Can be
used as a membrane.