PH3-SM (PHY3032)

Soft Matter Physics

4 October, 2010

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

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 ExamplesL/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!

Interfacial Area of Colloids

r

For a spherical particle, the ratio of surface area (A) to volume (V) is:

rr

rVA 1

≈3

44

=3

2

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

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

Colloidal Flow Properties

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.

• 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.

Physicist’s view of a polymer:

Terminology of Polymers• A “plastic” is a more 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.

Chain network in an elastomer.Strain

Stress Elastic

Plastic

• 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).

Types of Soft Matter: (3) Liquid Crystals

This form of soft matter is interesting and useful because of its anisotropic optical and mechanical properties.

Image: http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html

Flows easily in the aligned direction.

Elastic in the normal direction.

Acrylic Latex Paint Monodisperse Particle Size

Edge length = 1 mmVertical scale = 200 nm

(1) Relevant length scales between the atomic and the macroscopic

Top view3 mm x 3 mm 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 “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

15 mm x 15 mm

Poly(ethylene) crystal Crystals of poly(ethylene oxide)

5 mm x 5 mm

Polymer crystals can grow up to millimeters in size!

Typical 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.

(2) Weak short-range forces and interfaces are important.

Characteristics of Soft Matter

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)

• 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.

Chemical Bonds in Soft Matter

• 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

From I.W. Hamley,

Introduction to Soft Matter

• 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.

MeniscusIncreasing density

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

Mercury has a very high surface energy!

Image: http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html

What characteristics result from a high surface 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

Interfacial Energy

F

qG

dF cos

d

liquid

solid

q

Contact Angle: Balance of Forces

Three interfaces: solid/liquid (SL); liquid/air (LA); solid/air (SA)

Each interface has a tension (energy): GSL; GLA; GSA

Contact angle measurements thus provide information on surface tensions.

At equilibrium, lateral tensions must balance:

cos-

⇒cos

LA

SLSALASLSA

GLA

GSAGSL

SA energy is equivalent to ½ of the energy to cleave the solid

Imagine a 10 mL drop of liquid on a solid. (No effect of g.)

Hydrophobicity and Hydrophilicity

water

solid

qHydrophilic

water

solid

q

Hydrophobic

q is <90

q is >90

solid

water Fully wetting

http://scottosmith.com/2007/10/03/water-beads/

Laser-patterned surface

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.

Lotus Leaf Inspired Synthetic Super-hydrophobic Surfaces

Lotus leaf: low surface energy plus textured.

(3) The importance of thermal fluctuations and Brownian motion

Characteristics of Soft Matter

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).• kT is a useful “gauge” of bond energy.

Vx

Vy

Vz V

The kinetic energy for a particle of mass, m, is 1/2 mv2 = 3/2 kT. When m is small, v becomes significant.

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 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!

X100 mm x 30 mm x 2 mm

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

Characteristics of Soft Matter

Diblock 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)Two “blocks” in one

polymer chain

Poly(styrene) and poly(methyl methacrylate) copolymer

2mm x 2mm

Layers or “lamellae” form spontaneously in diblock copolymers.

Diblock copolymer

Polymer Self-Assembly

AFM image

Spider Silk: An Example of a Hierarchical Structure

Amino acid units

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

ATCGAT TAGCTA

Example of DNA sequence:

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.

DNA Base Pairs Drive the Self-Assembly of Helices

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

MRS Bulletin,

Feb 2004, p. 86

Particles Can Assemble into Colloidal Crystals

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.

Colloidosomes: Self-assembled colloidal particles

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

Liquid B

Liquid A

Colloidal particles (<1

mm)

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

Hydrophilically-driven self-assembly of particles

Interfacial tension, GTypical G values for interfaces with water - carbon tetrachloride: 45 mN/m; benzene: 35 mN/m; octanol: 8.5 mN/m

Work (W) is required to increase the

interfacial area (A):

∫= dAW

“oil”

water

Surfactants at Interfaces

Surfactants reduce G. Are used to make emulsions using less W and to achieve “self assembly” (i.e. spontaneous organisation)

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!

emulsion

Examples of Surfactant Self-Assembly

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.

From I.W. Hamley, Introduction to Soft Matter

(a) (b)

(c) (d)

Spherical end is hydrophilic. Tail is hydrophobic.

Surfactantwater

Examples of Surfactant 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

The “plumber’s nightmare”

Materials with controlled structure obtained through self-assembly

Surfactant micelles (soft “nano-objects”) are packed together

SiO2 (silica) is grown around the micelles

Micelles are removed to leave ~ 10 nm spherical

holes. Structure has low refractive index. Can be

used as a membrane.

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

Competitions in Self-Assembly

• 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.

DF = DU - TDS

If a process decreases the free energy (DF < 0) of a system, then the process happens spontaneously.

Entropy (S) increase is favourable

Internal Energy (U) decrease is favourable

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

Surface area of N particles:

4Npr2

Surface area of droplet made from

coalesced droplets: 4pR2

Liquid droplet volume is the same before and after coalescence:

Rr

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.

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

http://physicsworld.com/cws/article/print/19961K Eric Drexler/Institute for Molecular Manufacturing, www.imm.org.

(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.

Key Limitations for Nanorobots and Nanodevices

Why not make use of the length scales and self assembly of soft matter?

vaRe

V = velocitya

h = viscosity of the continuous medium

r = density of the continuous medium

Reynolds’ Number:

When Re is low, the viscosity dominates over inertia. There is no “coasting”!

Viscous Limitation for “Nanorobot Travel”

(Compares the effects of inertia (momentum) to viscous drag)

Alternative Vision of a Nano-Device

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.

Closed state: K+ cannot pass through Open state: K+

can pass through

http://physicsworld.com/cws/article/print/19961