1. Introduction to Soft Matter
Soft Matter Physics
11 February, 2010
Lecture 1:
Introduction to Soft Matter

2. 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:

3. Phase diagram of water
Image:

4. Condensed Matter and the Origin of Surface Tension
Increasing density
Meniscus
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.

5. Interface with air = “surface”
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 = N/m
For water, G = N/m
For ethanol, G = N/m
Mercury has a very high surface energy!
What characteristics result from a high surface energy?
Image:

6. Hydrophobicity and Hydrophilicity
Fully wetting
water
solid
water
solid q
Hydrophilic
q is <90
water q
solid
Hydrophobic
q is >90

7. Contact Angle: Balance of Forces
Three interfaces: solid/water (sw); water/air (wa); solid/air (sa)
Each interface has a surface tension: Gsw; Gwa; Gsa
Gsa
Gwa
Gsw q
At equilibrium, lateral tensions must balance:
Contact angle measurements thus provide information on surface tensions.

8. 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, tissue, humans?

9. Types of Soft Matter: 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 Examples
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!

10. 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.
Consider a 1 cm3 phase dispersed in a continuous medium:
No. particles Particle volume(m3) Edge length (m) Total surface area(m2)

11. 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

12. 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.
Physicist’s view of a polymer:
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. 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.

13. 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:
This form of soft matter is interesting and useful because of its anisotropic optical and mechanical properties.

14. Example of colloidal particles
Characteristics of Soft Matter (4 in total)
(1) Length scales between atomic and macroscopic
Top view
3 mm x 3 mm scan
Vertical scale = 200nm
Acrylic Latex Paint
Monodisperse Particle Size
Example of colloidal particles

15. 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

16. Poly(ethylene) crystal
Typical Length Scales
Poly(ethylene) crystal
Crystals of poly(ethylene oxide)
15 mm x 15 mm
5 mm x 5 mm
Polymer crystals can grow up to millimeters in size!

17. Spider Silk: An Example of a Hierarchical Structure
Amino acid units
P. Ball, Nanotechnology (2002) 13, R15-R28

18. 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.

19. 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.

20. Thermal fluctuations Vz V Vy Vx
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, the thermal energy is 3/2 kT.
k = 1.38 x JK-1, so kT = 4 x 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.

21. 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 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.
100 mm x 30 mm x 2 mm X

22. 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.)

23. Polymer Self-Assembly
Poly(styrene) and poly(methyl methacrylate) copolymer
AFM image
Diblock copolymer
2mm x 2mm
Layers or “lamellae” form spontaneously in diblock copolymers.

24. 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

25. 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 Biochemistry

26. Colloidal particles (<1 mm)
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

27. Hydrophilically-driven self-assembly of particles
I. Karakurt et al., Langmuir 22 (2006) 2415

28. Colloidal Crystals Colloidal particles can have a +ve or -ve charge.
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.

29. Surfactants at Interfaces
emulsion
Work (W) is required to increase the interfacial area (A):
“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
Surfactants reduce G. Are used to make emulsions 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.

30. Examples of Self-Assembly
Spherical end is hydrophilic.
(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

31. Examples of Self-Assembly
The “plumber’s nightmare”
From RAL Jones, Soft Condensed Matter
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.

32. 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.
Surfactant micelles are packed together
SiO2 (silica) is grown around the micelles
P. Ball, Nanotechnology (2002) 13, R15-R28

33. 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 can dominate.
DF = DU - TDS
If the free energy decreases (DF < 0), then the process is spontaneous.
Entropy (S) increase is favourable
Internal Energy (U) decrease is favourable

34. Importance of Interfaces
Work associated with changing an interfacial area:
dW = GdA
Doing work on a system will raise its internal energy (U) 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 self-assembly.
An example is coalescence in emulsions.

35. r R Coalescence in Emulsions Change in area, DA = - 4pr2(N-N2/3)
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 = J.

36. 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.

37. 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

38. 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,

39. 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?

40. 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”!

41. 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.

43. What are the forces that operate over short distances and hold soft matter together?

44. 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 simple repulsive potential:
wrep(r) = (s/r)
The interaction potential w(r) = watt + wrep

45. Simple Interaction Potentials+
w(r) -
Attractive potential r
watt(r) = -C/rn +
w(r) -
Repulsive potential r s
wrep(r) = (s/r)

46. 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:

47. Potentials and Intermolecular Force+
re = equilibrium spacing

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

49. How much energy is required to remove a molecule from the condensed phase?
Individual molecules
Applies to pairs r L
s = molecular spacing
r = #molec./vol. • s
Q: Does a central molecule interact with ALL the others?

50. But L >> s! When can we neglect the term?
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: s L
Entire system
r -n+2=r -(n-2) dr E=
But L >> s! When can we neglect the term?

51. 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!
But when 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! E=

52. The Case of n = 3
s will be very small (typically 10-9 m), but lns is not negligible. L cannot be neglected in most cases.

53. 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?

54. Gravity: n = 1 G = 6.67 x 10-11 Nm2kg-1 m2 m1 r
When molecules are in contact, w(r) is typically ~ J
Negligible interaction energy!

55. Coulombic Interactions: n = 1Q1 Q2
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 ~ J, corresponding to about 200 to 300 kT at room temp
• The interaction potential is additive in crystals.

56. van der Waals Interactions (London dispersion energy): n = 6u2 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 ~ to 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.

57. 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.!

58. H O H O H H Hydrogen bonding d- d+ d- d+ d+ 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 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.

59. 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.