ph3-sm (phy3032) soft matter physics 4 october, 2011 lecture 1: introduction to soft matter
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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 (CO2)
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 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 elastomerStrain
Stress Elastic
Plastic
Bond between
chains
• 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 Particles - Monosized
Edge length = 1 mmVertical scale = 200 nm
(1) Intermediate 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.
Work of A. Geim, highlighted in 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
solidq
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 interfacial 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.)
air
Hydrophobicity and Hydrophilicity
water
solid
qHydrophilic q is <90
solid
water Fully wetting
water
solid
q
Hydrophobic q is >90
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 very small, then 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
T. P. J. Knowles and M. J. Buehler, Nature Nanotech (2011) 6, 469
The hierarchical structure of
amyloid materials
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.
Phase Equilibria in Colloidal Dispersions
V. Prasad, D. Semwogerere and Eric R. Weeks, J. Phys.: Condens. Matter 19 (2007) 113102 (25pp)
Mono-sized particles can become ordered into crystals at f = 0.54 while still in the “wet” state.
RCP = random close-packing;
HCP = hexagonal close-packing
(Volume %)
Equilibrium:
Non-equilibrium:
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
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.
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”
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
Surface area per molecule, a
Free energy, F
Repulsive energy: K/a
Attractive energy: Ga
Total energy
a0
F Ga + K/a
Optimum area, a0, of molecule in a surfactant structure is found at the free energy minimum
At equilibrium each head group of the molecule will occupy an area of “a0”
a0
How would you find a0?
Israelachvili, Intermolecular & Surface Forces, Ch. 17, p. 366
Molecular Geometry Also Determines Whether Surfactant Micelles are Favourable
Spherical Micelle Cross-Sectional View
R
To pack densely into a sphere, the molecules should be conical in shape
Area, a0
R Lc
Lc is the hydrophobic chain length
V is the volume of the cone (molecule)
N molecules in total in micelle= Area sphere/area of molecule
= Volume sphere/ volume of molecule
vR
aR
N3
44 3
0
2
cLav
R 0
3
31
0
cLa
vIsraelachvili, Ch. 17, p. 366
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)
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