Introduction to Soft Matter

3SCMP

20 January, 2005

Lecture 1

Condensed Matter

• “Condensed matter” refers to matter that is not in the gas phase but is condensed as liquid or solid. (condensed denser!)

• Liquids and gases are separated by a meniscus; they differ only in density not structure (i.e. arrangement of molecules in space).

• Matter condenses when attractive intermolecular bond energies are comparable to or greater than thermal (i.e. kinetic) energy.

Soft Condensed Matter• Refers to condensed matter that exhibits

characteristics of both solids and liquids• The phrase “soft matter” was used by Pierre Gilles 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• A polymer is a large molecule, typically with

50 or more repeat units.

• A colloid is a sub-m particle of one phase dispersed in another.

• Types of colloids: A liquid in a liquid = emulsion; liquid/solid in a gas = aerosol; solid in a liquid = sol; gas in a liquid = foam

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

• 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).

• A surfactant contains both a hydrophobic and a hydrophilic component; reduces interfacial tension; used to make emulsions and to achieve “self assembly”.

Types of Soft Matter

“Side” view: “Top” view:

Acrylic Latex Paint Monodisperse Particle Size

Vertical scale = 200nm

(1) Length scales between atomic and macroscopic

Top view3 m x 3 m scan

Characteristics of Soft Matter (4 in total)

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 molecule: ~10 nm

• Diam. of a colloidal particle (e.g. in paint): ~200 nm• Bacteria cell: ~2 m• Diameter of a human hair: ~80 m

Surfactant bilayer adsorbed at the interface between a solid and liquid

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.

Physicist’s View of a Polymer Molecule

• Each “pearl” on the string represents a repeating group of atoms, linked together by strong covalent bonds.

• The composition of the “pearls” is not important.• Physics can predict the size and shape of the molecule;

the important parameter is the number of repeat units.

(2) The importance of thermal fluctuations and Brownian motion

Characteristics of Soft Matter (4 in total)

Thermal fluctuations• Soft condensed matter is not static but in

constant motion at the level of molecules and particles.

• Brownian motion is the result of a slight imbalance of momentum being transferred between liquid molecules and a colloidal particle.

• Thermal (kinetic) energy for a single monoatomic molecule is 3/2 kT (3 d.o.f.)

• 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.

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

Characteristics of Soft Matter (4 in total)

Copolymer molecules spontaneously form a pattern in a thin film.

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

Image from IBM (taken from BBC website)

Examples of Self-Assembly

Surfactants can assemble into spherical micelles, cylindrical micelles, bi-layers (membranes), or saddle surfaces in bicontinuous structures

From I.W. Hamley, Introduction to Soft Matter

Examples of Self-Assembly

• 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

(4) Short-range forces and interfaces are important.

Characteristics of Soft Matter (4 in total)

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.

From Materials World (2003)

Origin of Surface Tension (i.e. Interfacial Energy)

From I.W. Hamley,

Introduction to Soft Matter

• In reducing the interfacial area, more molecules are brought into close contact.

• Increasing the interfacial area requires the separation of neighbouring molecules.

MeniscusIncreasing density

• Force associated with neighbouring molecules = surface tension.

Importance of Interfaces• An interfacial energy is associated with any interface

between two phases (J m-2) (also called a surface tension: Nm-1)

• Free energy change: dF = dA • An increase in area raises the system’s free energy,

which is not thermodynamically favourable.• Surfaces become increasingly more important as

particles become smaller.• For a sphere, surface area:volume is

rr

rVA 3

344

3

2

==

r

Particle Coalescence

Surface area of N particles:

4Nr2

Surface area of particle made from coalesced particles:

4R2

Same polymer volume before and after coalescence:

Rr

Change in area, A = - 4r2(N-N2/3)In 1 L of latex (50% solids), with a particle diameter of 200 nm, N is ~ 1017 particles. Then A = -1.3 x 104 m2

With = 3 x 10-2 J m-2, F = - 390 J.

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.

What are these forces that operate over short distances and hold soft matter together?

Interaction Potentials

• Interaction between two atoms/molecules/ segments can be described by an attractive potential: watt(r) = -C/rn 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, . A simple repulsive potential: wrep(r) = (/r)

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

r

Simple Interaction Potentials

+

w(r)

-

Attractive potential

r

watt(r) = -C/rn

+

w(r)

-

Repulsive potential

rwrep(r) = (/r)

Simple Interaction Potentials

+

w(r)

-

Total potential:r

w(r) = watt + wrep

Minimum of potential = equilibrium spacing in a solid =

Potentials and Intermolecular Force

+

re = equilibrium spacing

• 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, F is at its maximum.• Force acts between all neighbouring molecules!

Interaction Potentials

r

How much energy is required to remove a central molecule?

Q: Does a central molecule interact with ALL the others?

nrCrw =)(

Applies to pairs

L

= molecular spacing

= #molec./vol.

Individual molecules

•

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 to L), E:

drrv 24=)(=)( drrrN 24

Lr

rnrn

CE

=

=)(=

3

13

4

24 +=)()(= nrCrNrwE

LEntire system

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

[ ]33 1

3

4 nn Ln

C)(

)(

E=

But L >>

Conclusions about E• There are two cases:• When n<3, then the exponent is negative. As

L>>, then (/L)n-3>>1 and is thus significant.• In this case, E varies with the size of the

system, L! • But when n>3, (/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 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

r

mm2

rmGm

rw 21=)(

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

r

QQ2

rQQ

rwo4

21=)(

• With Q1 = z1e, where e is the charge on the electron and z1 is an integer value.

• o is the permittivity of free space and is the relative permittivity of the medium between ions (can be vacuum with = 1 or can be a gas or liquid with > 1).

• The interaction potential is additive in crystals.

• When molecules are in close contact, w(r) is typically ~ 10-18 J, corresponding to about 200 to 300 kT at room temp

van der Waals Interactions

r

2

64 r

Crw

o )(=)(

u2 u1

• Interaction energy (and the constant, C) depends on the dipole moment (u) of the molecules and their polarisability ().

• 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!

• 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

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.

• H-bonding can lead to weak ordering in water.

HO

HH

HO

+

+

++

--

Hydrophobic Interactions

• “Foreign” molecules in water can cause local ordering - which decreases the entropy - thus it is unfavourable.

• Less ordering of the water is required if two or more of the foreign molecules cluster together: a type of attractive interaction.

• Can promote self-assembly.

A water “cage” around another molecule