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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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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 • “Condensed matter” refers to matter that is not in the gas phase but is condensed as a liquid or solid. (condenseddenser!) • Matter condenses when attractive intermolecular bond energies are comparable to or greater than thermal (i.e. kinetic) energy ~ kT.
Phase diagram of water Image: http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_10.html
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.
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 • 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 • 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!
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.
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
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.
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.
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
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
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.
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 • 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
Poly(ethylene) crystal Crystals of poly(ethylene oxide) 15 mm x 15 mm 5 mm x 5 mm
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.
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.
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.
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
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.)
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.
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
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
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.
Hydrophilically-driven self-assembly of particles I. Karakurt et al., Langmuir 22 (2006) 2415
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.
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 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
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
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 • 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.
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.
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.
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
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.
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?
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”!
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
What are the forces that operate over short distances and hold soft matter together?
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
+ w(r) - Repulsive potential r s wrep(r) = (s/r) Simple Interaction Potentials + w(r) - Attractive potential r watt(r) = -C/rn
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:
Potentials and Intermolecular Force + re = equilibrium spacing
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!
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?
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?
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!