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Soft Matter Physics


22 January, 2009

Lecture 1:

Introduction to Soft Matter

What is Condensed Matter?

Phase diagram of carbon dioxide


  • “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 water



Increasing density

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.

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)





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?


soft condensed matter
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 (measurable viscosity)
  • Soft matter can bear stress (elastic deformation)
  • Viscoelastic behaviour = viscous + elastic
  • Examples: rubbers, gels, pastes, creams, paints, soaps, liquid crystals, proteins, cells
types of soft matter colloids
Types of Soft Matter: Colloids
  • A colloid has 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 phase can consist of either a solid (S), liquid (L), or gas (G):

Dispersed PhaseContinuousNameExamples

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

Physicist’s view of a polymer:

Types of Soft Matter: 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; biomolecules, such as proteins and starch.
  • Each “pearl” on the string represents a repeat unit of atoms, linked together by strong covalent bonds. For instance, in a protein molecule the repeat units are amino acids.
  • 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.
Types of Soft Matter: 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).


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




Interfacial tension,G

Typical G values for interfaces with water - carbon tetrachloride: 45 mN/m; benzene: 35 mN/m; octanol: 8.5 mN/m

Hydrophobicity and Hydrophilicity







Fully wetting


qis <90




qis >90

Contact Angle: Balance of Forces





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.

Characteristics of Soft Matter (4 in total)

(1)Length scales between atomic and macroscopic

Top view

3 mm x 3 mmscan

Vertical scale = 200nm

Acrylic Latex Paint

Monodisperse Particle Size

Example of colloidal particles

typical length scales
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 molecule: ~10 nm
  • Diam. of a colloidal particle (e.g. in paint): ~200 nm
  • Bacteria cell: ~2 mm
  • Diameter of a human hair: ~80 mm
Poly(ethylene) crystal

Crystals of poly(ethylene oxide)

15 mm x 15 mm

5 mm x 5 mm

Spider Silk: An Example of a Hierarchical Structure

Amino acid units

P. Ball, Nanotechnology (2002) 13, R15-R28

intermediate length scales
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) 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.


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 1/2kT of thermal energy.
  • For a colloidal particle able to undergo translation in the x, y and z directions, 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).
  • kT is a useful “gauge” of bond energy.
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?
  • For AFM applications, the cantilever beam typically has a spring constant, kS, of ~ 10 N/m.
  • The energy required for deflection of the beam by a distance X is E = ½ kSX 2.
  • At a temperature of 300 K, the thermal energy, E, is on the order of kT = 6 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.

100 mm x 30 mm x 2 mm


Characteristics of Soft Matter

(3)Tendency to self-assemble into hierarchical structures (i.e. ordered on size scales larger than molecular)

Image from IBM (taken from BBC website)

Two “blocks”

Diblock copolymer molecules spontaneously form a pattern in a thin film.

(If one phase is etched away, the film can be used for lithography.)

Poly(styrene) and poly(methyl methacrylate) copolymer

Polymer Self-Assembly

AFM image

Diblock copolymer

2mm x 2mm

Layers or “lamellae” form spontaneously in diblock copolymers.

DNA Base Pairs

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:


Designed Nanostructures from DNA

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

Colloidosomes: Self-assembled colloidal particles

Colloidal particles (<1 mm)

Liquid B

Liquid A

A.D. Dinsmore et al., “Colloidosomes: Selectively Permeable Capsules Composed of Colloidal Particles,” Science, 298 (2002) p. 1006.

Hydrophilically-driven self-assembly of particles

I. Karakurt et al., Langmuir 22 (2006) 2415

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.

Examples of Self-Assembly





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

examples of self assembly
Examples of Self-Assembly

The “plumber’s nightmare”

  • 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.

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

competitions in self assembly
If free energy decreases (DF < 0), then the process is spontaneous.


Internal Energy (U) decrease is favourable

Entropy (S) increase is favourable

Competitions in Self-Assembly
  • Molecules often segregate at an interface to LOWER the interfacial energy - 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 that dominate.
importance of interfaces
Importance of Interfaces
  • Free energy change: dF = GdA
  • An increase in area raises the system’s free energy, which is not thermodynamically favourable.
  • So, sometimes interfacial tension opposes and destroys self-assembly.
  • An example is coalescence in emulsions.
Coalescence in Emulsions

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

(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

• 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?

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,

Key Limitations for Nanorobots and Nanodevices

(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”

Reynolds’ Number:

(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

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.

interaction potentials
Interaction Potentials



  • Interaction between two atoms/molecules/ segments can be described by an attractive potential: watt(r) = -C/r n where C and n are constants
  • There is a repulsion because of the Pauli exclusion principle: electrons cannot occupy the same energy levels. Treat atoms/molecules like hard spheres with a diameter, s. A simplerepulsive potential:

wrep(r) = (s/r)

  • The interaction potential w(r) = watt + wrep



Repulsive potential



wrep(r) = (s/r)

Simple Interaction Potentials




Attractive potential


watt(r) = -C/rn

Simple Interaction Potentials




Total potential:



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


re = equilibrium spacing

interaction potentials1
Interaction Potentials
  • When w(r) is a minimum, dw/dr = 0.
  • Solve for r to find equilibrium spacing for a solid, where r = re.
  • Confirm minimum by checking curvature from 2nd derivative.
  • The force between two molecules is F = -dw/dr
  • Thus, F = 0 when r = re.
  • If r < re, F is compressive (+).
  • If r > re, F is tensile (-).
  • When dF/dr = d2w/dr2 =0, attr.F is at its maximum.
  • Force acts between all neighbouring molecules!
Individual molecules

s = molecular spacing

Applies to pairs



r= #molec./vol.


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


r -n+2=r-(n-2)



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?

conclusions about e
E=Conclusions about E
  • There are two cases:
  • When n<3, then the exponent is negative. As L>>s, then (s/L)n-3>>1 and is thus significant.
  • In this case, E varies with the size of the system, L!
  • Butwhen n>3, (s/L)n-3<<1 and can be neglected. Then E is independent of system size, L.
  • When n>3, a central molecule is not attracted strongly by ALL others - just its closer neighbours!
interaction potentials2
Interaction Potentials
  • Gravity: acts on molecules but negligible
  • Coulomb: applies to ions and charged molecules; same equations as in electrostatics
  • van der Waals: classification of interactions that applies to non-polar and to polar molecules (i.e. without or with a uniform distribution of charge). IMPORTANT in soft matter!
  • We need to consider: Is n>3 or <3?
Gravity: 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!




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

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













  • In a covalent bond, an electron is shared between two atoms.
  • Hydrogen possesses only one electron and so it can covalently bond with only ONE other atom.
  • The proton is unshielded and makes an electropositive end to the bond: ionic character.
  • Bond energies are usually stronger than v.d.W., typically 25-100 kT.
  • The interaction potential is difficult to describe but goes roughly as r-2, and it is somewhat directional.
  • H-bonding can lead to weak structuring in water.
Hydrophobic Interactions

A water “cage” around another molecule

  • “Foreign” molecules in water can increase the local ordering - which decreases the entropy. Thus their presence is unfavourable.
  • Less ordering of the water is required if two or more of the foreign molecules cluster together: a type of attractive interaction.
  • Hydrophobic interactions can promote self-assembly.