Introduction to Soft Matter 3SCMP 19 January, 2006 Lecture 1

Condensed Matter “Condensed matter” refers to matter that is not in the gas phase but is condensed as liquid or solid. (condensed denser!) Liquids and gases are separated by a meniscus; they differ only in density not structure (i.e. arrangement of molecules in space). Matter condenses when attractive intermolecular bond energies are comparable to or greater than thermal (i.e. kinetic) energy.

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 A polymer is a large molecule, typically with 50 or more repeat units. A colloid is a sub-mm particle of one phase dispersed in another. Types of colloids: A liquid in a liquid = emulsion; liquid/solid in a gas = aerosol; solid in a liquid = sol; gas in a liquid = foam

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 • 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). “Side” view: “Top” view: • A surfactant contains both a hydrophobic and a hydrophilic component; reduces interfacial tension; used to make emulsions and to achieve “self assembly”.

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

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

Surfactant bilayer adsorbed at the interface between a solid and liquid

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.

Physicist’s View of a Polymer Molecule Each “pearl” on the string represents a repeating group of atoms, linked together by strong covalent bonds. The composition of the “pearls” is not important. Physics can predict the size and shape of the molecule; the important parameter is the number of repeat units.

Characteristics of Soft Matter (4 in total) (2) The importance of thermal fluctuations and Brownian motion

Thermal fluctuations Soft condensed matter is not static but in constant motion at the level of molecules and particles. Brownian motion is the result of a slight imbalance of momentum being transferred between liquid molecules and a colloidal particle. Thermal (kinetic) energy for a single monoatomic molecule is 3/2 kT (3 d.o.f.) 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.

Characteristics of Soft Matter (4 in total) (3) Tendency to self-assemble into hierarchical structures (i.e. ordered on large size scales) Image from IBM (taken from BBC website) Copolymer molecules spontaneously form a pattern in a thin film. (If one phase is etched away, the film can be used for lithography.)

Examples of Self-Assembly From I.W. Hamley, Introduction to Soft Matter Surfactants can assemble into spherical micelles, cylindrical micelles, bi-layers (membranes), or saddle surfaces in bicontinuous structures

Examples of Self-Assembly 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.

Characteristics of Soft Matter (4 in total) (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.

Origin of Surface Tension (i.e. Interfacial Energy) Increasing density Meniscus From I.W. Hamley, Introduction to Soft Matter • Increasing the interfacial area requires the separation of neighbouring molecules. • In reducing the interfacial area, more molecules are brought into close contact. • Force associated with neighbouring molecules = surface tension.

Importance of Interfaces An interfacial energy g is associated with any interface between two phases (J m-2) (also called a surface tension: Nm-1) Free energy change: dF = gdA An increase in area raises the system’s free energy, which is not thermodynamically favourable. Surfaces become increasingly more important as particles become smaller. For a sphere, surface area:volume is r

Particle Coalescence r R Same polymer volume before and after coalescence: r R Surface area of particle made from coalesced particles: 4pR2 Surface area of N particles: 4Npr2 Change in area, DA = - 4pr2(N-N2/3) In 1 L of latex (50% solids), with a particle 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 = - 390 J.

Hydrophobicity and Hydrophilicity water Fully wetting solid water solid q Hydrophilic q is small water q solid Hydrophobic q is large

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, tensions must balance: Contact angles thus provide information on surface tensions and the effect of surfactants.

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.

What are these 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/rn 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

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

Simple Interaction Potentials + w(r) - Total potential: s r w(r) = watt + wrep Minimum of potential = equilibrium spacing in a solid = s

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!

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

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) E= But L >> s!

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=

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 m2 m1 r 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 Q1 Q2 • 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 ~ 10-18 J, corresponding to about 200 to 300 kT at room temp • The interaction potential is additive in crystals.

van der Waals Interactions u2 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 ~ 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! • Interaction energy is much weaker than covalent bond strengths.

1 kJ mol-1 = 0.4 kT per molecule at 300 K Covalent Bond Energies From Israelachvili, Intermolecular and Surface Forces 1 kJ mol-1 = 0.4 kT per molecule at 300 K Therefore, a C=C bond has a strength of 240 kT at this temp.!

Hydrogen bonding H O H O H H 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. H-bonding can lead to weak ordering in water.

Hydrophobic Interactions A water “cage” around another molecule “Foreign” molecules in water can cause local ordering - which decreases the entropy - thus it is unfavourable. Less ordering of the water is required if two or more of the foreign molecules cluster together: a type of attractive interaction. Can promote self-assembly.