Soft Matter Physics 11 February, 2010 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. (condensed denser!) • 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 the 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 Gis 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
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.
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 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. 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.
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.
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
Typical Length Scales Crystals of poly(ethylene oxide) Poly(ethylene) crystal 15 mm x 15 mm 5 mm x 5 mm Polymer crystals can grow up to millimeters in size!
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, 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.
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 kSX2. • 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
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)complementsthymine (T) with its two H bonds at a certain spacing. Guanine (G)complementscytosine (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. Dinsmoreet 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.
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) Surfactants at Interfaces 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
Examples of Self-Assembly (b) (a) 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
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. Surfactant micelles are packed together SiO2 (silica) is grown around the micelles P. Ball, Nanotechnology (2002) 13, R15-R28
If the 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 can dominate.
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 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, attractive Fis 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?