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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.

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slide1
Soft Matter Physics

3SM

22 January, 2009

Lecture 1:

Introduction to Soft Matter

slide2
What is Condensed Matter?

Phase diagram of carbon dioxide

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

  • “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.
slide3
Phase diagram of water

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

slide4
Meniscus

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.

slide5
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)

F

d

G

q

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?

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

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!

slide8
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:

r

Thus, with smaller particles, the interface becomes more significant. A greater fraction of molecules is near the surface.

slide9
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

slide10
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.
slide11
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).

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.

slide12
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

emulsion

“oil”

water

Interfacial tension,G

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

slide13
Hydrophobicity and Hydrophilicity

q

water

solid

Hydrophilic

solid

solid

Fully wetting

water

qis <90

water

q

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

Hydrophobic

qis >90

slide14
Contact Angle: Balance of Forces

Gwa

q

Gsa

Gsw

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.

slide15
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
slide17
Poly(ethylene) crystal

Crystals of poly(ethylene oxide)

15 mm x 15 mm

5 mm x 5 mm

slide18
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.
slide20
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.

slide21
Vz

V

Vy

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

Vx

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.
slide22
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

X

slide23
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.)

slide24
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.

slide25
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:

ATCGAT TAGCTA

slide26
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

slide27
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.

slide28
Hydrophilically-driven self-assembly of particles

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

slide29
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.

slide30
Examples of Self-Assembly

(b)

(a)

(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

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

slide32
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.

DF = DU - TDS

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.
slide35
Coalescence in Emulsions

Liquid droplet volume before and after coalescence:

r

R

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.

slide36
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.

slide37
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.

r

slide38
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/19961

K Eric Drexler/Institute for Molecular Manufacturing, www.imm.org.

slide39
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?

slide40
Viscous Limitation for “Nanorobot Travel”

Reynolds’ Number:

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

a

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”!

slide41
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.

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

interaction potentials
Interaction Potentials

s

r

  • 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
slide44
+

w(r)

-

Repulsive potential

r

s

wrep(r) = (s/r)

Simple Interaction Potentials

+

w(r)

-

Attractive potential

r

watt(r) = -C/rn

slide45
Simple Interaction Potentials

+

w(r)

-

Total potential:

s

r

w(r) = watt + wrep

Minimum of potential = equilibrium spacing in a solid =s

The force acting on particles with this interaction energy is:

slide46
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!
slide48
Individual molecules

s = molecular spacing

Applies to pairs

r

s

r= #molec./vol.

L

How much energy is required to remove a molecule from the condensed phase?

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

slide49
Entire system

L

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

s

E=

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:

dr

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?
slide52
Gravity: n = 1

m2

m1

r

G = 6.67 x 10-11 Nm2kg-1

When molecules are in contact, w(r) is typically ~ 10-52 J

Negligible interaction energy!

slide53
Q2

Q1

r

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.

slide54
van der Waals Interactions (London dispersion energy): n = 6

u2

u1

a2

a1

r

• 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.

slide55
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.!

slide56
Hydrogen bonding

d-

H

O

d+

d-

H

O

H

d+

d+

H

d+

  • 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.
slide57
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.
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