Soft Matter Physics 3SM 22 January, 2009 Lecture 1: Introduction to Soft Matter. What is Condensed Matter?. Phase diagram of carbon dioxide. Image : http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html.
22 January, 2009
Introduction to Soft Matter
Phase diagram of carbon dioxide
Condensed Matter and Origin of Surface Tension
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, more molecules are forced below the surface, where they are completely surrounded by neighbours.
• Force associated with separating neighbouring molecules = surface tension.
An interfacial energy G is associated with the interface between two phases (units of Jm-2) (also called an interfacial tension: Nm-1)
Interface with air = “surface”
For mercury, G = 0.486 N/m
For water, G = 0.072 N/m
For ethanol, G = 0.022 N/m
Mercury has a very high surface energy!
What characteristics result from a high surface energy?
L/S G aerosol fog, hair spray; smoke
G L/S foam beer froth; shaving foam; poly(urethane) foam
L L (S) emulsion mayonnaise; salad dressing
S L sol latex paint; tooth paste
S S solid suspension pearl; mineral rocks
There is no “gas-in-gas” colloid, because there is no interfacial tension between gases!
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
Interfacial Area of Colloids
For a spherical particle, the ratio of surface area (A) to volume (V) is:
Thus, with smaller particles, the interface becomes more significant. A greater fraction of molecules is near the surface.
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: Polymers
• 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).
This form of soft matter is interesting and useful because of its anisotropic optical and mechanical properties.
Work (W) is required to increase the interfacial area (A):
A surfactant (surface active agent) molecule has two ends: a “hydrophilic” one (attraction to water) and a “hydrophobic” (not attracted to water) one.
Surfactants reduce G. Are used to make emulsions and to achieve “self assembly” (i.e. spontaneous organisation)
Types of Soft Matter: Surfactants
Typical G values for interfaces with water - carbon tetrachloride: 45 mN/m; benzene: 35 mN/m; octanol: 8.5 mN/m
At equilibrium, lateral tensions must balance:
Three interfaces: solid/water (sw); water/air (wa); solid/air (sa)
Each interface has a surface tension:Gsw; Gwa; Gsa
Contact angle measurements thus provide information on surface tensions and the effect of surfactants.
(1)Length scales between atomic and macroscopic
3 mm x 3 mmscan
Vertical scale = 200nm
Acrylic Latex Paint
Monodisperse Particle Size
Example of colloidal particles
Crystals of poly(ethylene oxide)
15 mm x 15 mm
5 mm x 5 mm
Amino acid units
P. Ball, Nanotechnology (2002) 13, R15-R28
(2) The importance of thermal fluctuations and Brownian motion
Brownian motion can be though of as resulting from a slight imbalance of momentum being transferred between liquid molecules and a colloidal particle.
The kinetic energy for a particle of mass, m, is 1/2 mv2 = 3/2 kT. When m is small, v becomes significant.
100 mm x 30 mm x 2 mm
(3)Tendency to self-assemble into hierarchical structures (i.e. ordered on size scales larger than molecular)
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.)
2mm x 2mm
Layers or “lamellae” form spontaneously in diblock copolymers.
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:
Strands of DNA only bind to those that are complementary. DNA can be designed so that it spontaneously creates desired structures.
N C Seeman 2003 Biochemistry42 7259-7269
Colloidal particles (<1 mm)
A.D. Dinsmore et al., “Colloidosomes: Selectively Permeable Capsules Composed of Colloidal Particles,” Science, 298 (2002) p. 1006.
I. Karakurt et al., Langmuir 22 (2006) 2415
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.
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
The “plumber’s nightmare”
From RAL Jones, Soft Condensed Matter
Materials with controlled structure obtained through self-assembly
Micelles are removed to leave ~ 10 nm spherical holes. Structure has low refractive index. Can be used as a membrane.
Micelles are packed together
SiO2 (silica) is grown around the micelles
P. Ball, Nanotechnology (2002) 13, R15-R28
If free energy decreases ( self-assemblyDF < 0), then the process is spontaneous.
DF = DU - TDS
Internal Energy (U) decrease is favourable
Entropy (S) increase is favourableCompetitions in Self-Assembly
Coalescence in Emulsions self-assembly
Liquid droplet volume before and after coalescence:
Surface area of droplet made from coalesced droplets:4pR2
Surface area of N particles:4Npr2
Change in area, DA = - 4pr2(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.
Characteristics of Soft Matter self-assembly
(4) Short-range forces and interfaces are important.
From 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 self-assembly
• 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.
• Hence, bonds are easily broken and re-formed.
• The strength of molecular interactions (e.g. charge attractions) decays with distance, r.
• At nm distances, they become significant.
Nanotechnology Science Fact or fiction? self-assembly
A vision of “nanorobots” travelling through the a blood vessel to make repairs (cutting and hoovering!).
An engine created by down-scaling a normal engine to the atomic level
K Eric Drexler/Institute for Molecular Manufacturing, www.imm.org.
Key Limitations for Nanorobots and Nanodevices self-assembly
(1) Low Reynolds number, Re : viscosity is dominant over inertia.
(2) Brownian and thermal motion: there are no straight paths for travel and nothing is static! (Think of the AFM cantilever beam.)
(3) Attractive surface forces: everything is “sticky” at the nano-scale. Is not easy to slide one surface over another.
Why not make use of the length scales and self assembly of soft matter?
Viscous Limitation for “Nanorobot Travel” self-assembly
(Compares the effects of inertia (momentum) to viscous drag)
V = velocity
h= viscosity of the continuous medium
r= density of the continuous medium
When Re is low, the viscosity dominates over inertia. There is no “coasting”!
Alternative Vision of a Nano-Device self-assembly
Closed state: K+ cannot pass through
Open state: K+ can pass through
A channel that allows potassium ions to pass through a cell membrane but excludes other ions. The nanomachine can be activated by a membrane voltage or a signalling molecule.
Flexible molecular structure is not disrupted by thermal motion.
What are the forces that operate over short distances and hold soft matter together?
wrep(r) = (s/r)
+ hold soft matter together?
wrep(r) = (s/r)
Simple Interaction Potentials
watt(r) = -C/rn
Simple Interaction Potentials hold soft matter together?
w(r) = watt + wrep
Minimum of potential = equilibrium spacing in a solid =s
The force acting on particles with this interaction energy is:
Potentials and Intermolecular Force hold soft matter together?
re = equilibrium spacing
Individual molecules hold soft matter together?
s = molecular spacing
Applies to pairs
How much energy is required to remove a molecule from the condensed phase?
Q: Does a central molecule interact with ALL the others?
Entire system hold soft matter together?
Total Interaction Energy, E
Interaction energy for a pair: w(r) = -Cr -n
Volume of thin shell:
Number of molecules at a distance, r :
Total interaction energy between a central molecule and all others in the system (from s to L), E:
But L >>s! When can we neglect the term?
E= hold soft matter together?Conclusions about E
Gravity: hold soft matter together?n = 1
G = 6.67 x 10-11 Nm2kg-1
When molecules are in contact, w(r) is typically ~ 10-52 J
Negligible interaction energy!
Q hold soft matter together?2
Coulombic Interactions: n = 1
Sign of w depends on whether charges are alike or opposite.
• With Q1 = z1e, where e is the charge on the electron and z1 is an integer value.
• eo is the permittivity of free space and e is the relative permittivity of the medium between ions (can be vacuum with e = 1 or can be a gas or liquid with e > 1).
• When molecules are in close contact, w(r) is typically ~ 10-18 J, corresponding to about 200 to 300 kT at room temp
• The interaction potential is additive in crystals.
van der Waals Interactions (London dispersion energy): n = 6
• Interaction energy (and the constant, C) depends on the dipole moment (u) of the molecules and their polarisability (a).
• When molecules are in close contact, w(r) is typically ~ 10-21 to 10-20 J, corresponding to about 0.2 to 2 kT at room temp., i.e. of a comparable magnitude to thermal energy!
• v.d.W. interaction energy is much weaker than covalent bond strengths.
Covalent Bond Energies dispersion energy):
From Israelachvili, Intermolecular and Surface Forces
1 kJ mol-1 = 0.4 kT per molecule at 300 K
Homework: Show why this is true.
Therefore, a C=C bond has a strength of 240 kT at this temp.!
Hydrogen bonding dispersion energy):
Hydrophobic Interactions dispersion energy):
A water “cage” around another molecule