soft matter physics 11 february , 2010 lecture 1: introduction to soft matter
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Soft Matter Physics 11 February , 2010 Lecture 1: Introduction to Soft Matter. What is Condensed Matter?. Phase diagram of carbon dioxide. I mage : http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html. - PowerPoint PPT PresentationTRANSCRIPT
Soft Matter Physics
11 February, 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
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Phase diagram of water
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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, more 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!
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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
dFG qcos
d
Hydrophobicity and Hydrophilicity
watersolid
qHydrophilic
water
solidq
Hydrophobic
q is <90
q is >90
solidwater Fully wetting
http://scottosmith.com/2007/10/03/water-beads/
Contact Angle: Balance of ForcesThree interfaces: solid/water (sw); water/air (wa); solid/air (sa)
Each interface has a surface tension: Gsw; Gwa; Gsa
Gsa
Gwa
Gsw
q
Contact angle measurements thus provide information on surface tensions.
At equilibrium, lateral tensions must balance:
qq cos-⇒cos GGG
GGGwa
swsawaswsa
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?
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 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:
rrr
VA 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
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. 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:
• 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: Liquid Crystals
This form of soft matter is interesting and useful because of its anisotropic optical and mechanical properties.
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Acrylic Latex Paint Monodisperse Particle Size
Vertical scale = 200nm
(1) Length scales between atomic and 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 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
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
Spider Silk: An Example of a Hierarchical Structure
Amino acid units
P. Ball, Nanotechnology (2002) 13, R15-R28
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) The importance of thermal fluctuations and Brownian motion
Characteristics of Soft Matter
Brownian motion can be though 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 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 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 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.
X100 mm x 30 mm x 2 mm
(3) 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”
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
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
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 42 7259-7269
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
MRS Bulletin,
Feb 2004, p. 86
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.
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 G
“oil”
water
Surfactants at Interfaces
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.
emulsion
Examples of Self-Assembly
Surfactants can assemble into (a) spherical micelles, (b) cylindrical micelles, (c) bi-layers (membranes), or (d) saddle surfaces in bicontinuous structures
From I.W. Hamley, Introduction to Soft Matter
(a) (b)
(c) (d)Spherical end is hydrophilic.
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
The “plumber’s nightmare”
Materials with controlled structure obtained through self-assembly
Surfactant micelles 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• 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
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.
Coalescence in Emulsions
Surface area of N particles: 4Nr2 Surface area of droplet made from
coalesced droplets: 4R2
Liquid droplet volume before and after coalescence:
Rr
Change in area, DA = - 4r2(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.
(4) 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.
• 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.
• At nm distances, they become significant. r
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
= viscosity of the continuous medium
= 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
What are the 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/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
r
s
Simple Interaction Potentials+
w(r)
-
Attractive potential
r
watt(r) = -C/rn
+
w(r)
-
Repulsive potential
rswrep(r) = (s/r)
Simple Interaction Potentials+
w(r)
-Total potential:
rw(r) = watt + wrep
s
Minimum of potential = equilibrium spacing in a solid = s
The force acting on particles with this interaction energy is:
drdwF
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, attractive F is at its maximum.• Force acts between all neighbouring molecules!
Interaction Potentials
r
How much energy is required to remove a molecule from the condensed phase?
Q: Does a central molecule interact with ALL the others?
nrCrw =)(
Applies to pairs
L
s = molecular spacing
= #molec./vol.
Individual molecules
•
s
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:
drrv 24=)(=)( drrrN 24
Lr
rnrn
CE
s
3
13
4)(
[ ]33 1
34 n
n LnC
)()(
ss
E=
But L >> s! When can we neglect the term?
24 +=)()(= nrCrNrwE s
LEntire system
r -n+2=r -(n-2) dr
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!
[ ] 33
3 )3(4
≈)(1)3(
4n
nn n
CLn
Css
s
E=
The Case of n = 3
3)( Crrw
drrrN 24)(
s
s
lnln44
LCrCdrE
Lr
r
s will be very small (typically 10-9 m), but lns is not negligible. L cannot be neglected in most cases.
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: n = 1
r
m1m2
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: n = 1
r
Q1Q2 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
Sign of w depends on whether charges are alike or opposite.
van der Waals Interactions (London dispersion energy): n = 6
ra1
a264 r
Crw
o )(=)(
u2 u1
• 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.
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.!
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.
• 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.
HO
HH
HO
d+
d+
d+d+
d-d-
Hydrophobic Interactions
• “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.
A water “cage” around another molecule