Soft Condensed Matter Flashcards
Examples of soft matter
Polyers - chain of molecultes
Colloids - solid particles suspended in a liquid
Foams, emulsion - liquid/gas droplets in liquid
Liquid crystals - liquid formed of particles that can be orientated
Supramolecular self-assemlies - ordered structures without bonds eg humans
Repulsive forces
Strong, short range, stop matter from collapsing. Pauli repulsion between e- orbitals of neighbouring molecules
Attractive forces
Weakest to strongest Van der waals Hydrophobic interactions Hydrogen bonds Ionic interactions Covalent bonds
Solid v Liquid v Gas
Solid
Uattract > kBT
stays in place, long range order, ordered packing
Liquid
Uattract ~ kBT
stay together after collision, correlation (local), random packing
Gas
Uattract < kBT
Occasional collisions, little correlation, no packing
Gibbs phase rule
F = N - P + 2
F = no. degrees freedom N = no. species present P = no. phases
Hookean solids
Solid that has perfectly elastic behaviour. Only true for perfect solids, ok approx for most ‘hard’ solids. Applying stress results in proportional sheer strain, proportionality is shear modulus G.
sigma = F/A stress e = delta x / y sigma = Ge
Newtonian liquids
Chartered by viscosity, water is example. Applied stress produces flow with constant shear strain rate edot. Stress proportional to shear rate and proportionality constant is viscosity.
Viscoelasticity
Many materials behave in way that combines viscous and elastic response depending on timescale - viscoelasticity.
t vs sigma plots:
Ideal hookean essentially straight across
Newtonian: y = x graph
Viscoelastic: starts like ideal hookean solid going up then across then goes up as liquid
Transition between liquid and glass
As temperature decreases. Glass transition. Not a true TD transition because glass is a kinetically trapped state and hence not at thermodynamic equilibrium. Happens at glass transition temperature, which depends on rate at which cooling experiment is done. If experiment occurs at slower cooling rate, resulting T will be lower. Cannot be arbitrary lower, Ku\mann temperature is when supercooled liquid has same entropy as that of equivalent crystalline solid.
Gibbs free energy if T and P are constant
Gibbs free energy determines outcome of process:
delta G < 0 spontaneous
delta G = 0 equilibrium
delta G > 0 disfavoured
In mixing: delta G < 0 spontaneous mixing
delta G > 0 demix
Solid liquid gas transitions
First order transitions, characterised by discontinuity in density and entropy. By definition of FOT this is a discontinuity on first derivative of free energy (curves in notes).
Entropy/ enthalpy when mixing
When mixing liquids entropy always increases - delta S > 0 is driving force for mixing to proceed.
Mixing ideal gas no change in enthalpy because of assumption there is no interaction. Not true for most liquids. This is displayed graphically in notes.
delta K > 0 disfavours mixing
delta K < 0 favours mixing
Stability of mixture
Not just if delta G is < = > 0, get it from shape of free energy curve. Concave: unstable, net decrease of G. Convex: metastable, net incrase in free energy.
Mixture in metastable region is stable to small change in conc.
In mixability gap
d2Gmix/dphi2 < 0 spinodal decomposition, unstable region
d2Gmix/dphi2 > 0, metastable, nucleation
Demixing result
In metastable, demixing of two components into combo of more stable compositions would bring the system to lower free energy.
Demixing beginning
Drop with composition corresponding to energy minima must appear despite initial increase of free energy it causes, and grow until free enegy starts to decrease again - must overcome energy barrier: nucleation energy. HOMOGENOUS NUCLEATION - originates from thermal fluctuations.
Where does initial cost in free energy opposing nucleation come from?
Comes from new interface created betweeen the nucleous of composition phi min and surrounding solution of composition phi.
Liquid systems, molecules arrange in drop so interface energy and thus area is minimized.
Heterogeneous nucleation
Nucleation occurs most around contaminants such as dust, particle nucleates phase separation reducing interfacial energy, as I.E between particle and lidquid is lower than liquids together.
Spinodal decomposition
Unstable region, fluctuation of mixture composition is sufficient to induce spontaneous demixing of components. Fluctuations occur naturally at equilibrium, process is continuous.
Optimum fluctuation wavelength
Too large wavelength requires molecules to diffuse over relatively long distances.
Too small can increase interfacial area and thus total free energy of sytem.
Growth
Once phase separation has begun, through SD or nucleation, phase domains start to grow. Smaller drops with higher radius of curvature less stable than larger ones. Larger particles grow at expense of smaller ones: Ostwald ripening.
Freezing
Liquid-solid transition example of nucleation process. When cooled, sytem undergoes first order phase transition - derivatives wrt TD variables exhibit discontinutity. When cooled beyond freezing temp, transformation occurs by nucleation of small solid clusters or nanoparticles. Formation of domains cost free energy - can prevent freezing of liquid event at lower temp, undercooled liquid - only ocurs in very pure liquid as impurity acts as catalyst.
Surface definition
Topological defect - region of medium where atomic/molecular bonds are under-coordinated - induce excess of free energy to system.
Surface free energy
Proportionality factor (gamma) in dG surface = gamma dA Corresonds to half the reversible work that is needed to create surface of unit area at constant T/P.
Dupre equation
gamma12 = gamma1 + gamma2 - W12
Where gamma12 is interfacial energy. W12 is reversible work of adhesion.
Work of adhesion
Work needed to separate two media, adhesion energy between both media. Sign of work of adhesion is opposite to that of interfacial energy.
Liquid droplet on surface of solid in air
Wlvs = gamma sv + gamma lv - gamma sl
Young equation
gamma lv cos theta = gamma sv - gamma sl
Can often use gamma sv ~ gamma s and gamma lv ~ gamma l
gamma s»_space; gamma l,
W sl ~ gamma l
Wetting
theta < 90 deg - strong wetting
theta > 90 deg - weak wetting
Corrections for real surfaces
Robert Wenzel (first is measured second is true) cos theta0 = cos theta . r
Larger holes can trap air, need to use Cassie eq:
cos theta0 = rfcos theta + f - 1
f is fraction of surface in contact with liquid
Capillary forces
Originate from surface tension of liquids in contact with solids. Drop of liquid in contact with two solids can for capillary bridge with a net force. Always attractive - but usually given positive sign.
Sum of surface tension-induced force and pressure induced force at any point.
Young Laplace eq. for pressure difference
delta P = P in - P out = gamma l (1/r1 + 1/r2)
Implications: if we know shape of liquid we can calculate pressure diffrence. In absence of fields such as g, pressure is the same everywhere or it would flow- curvature same too. Can calculate equilibrium shape of liquid.
With hydrostatic pressure:
delta P = gamma l (1/r1 + 1/r2) + rho g h.
Vapour pressure
Effectively describes ease with which a liquid will evaporate: high pressure is strong tendance to evaporate. Kelvin eq. describes how liquid curvature changes tendancy for evaporation.
Kelvin eq.
kg T ln(P/P0) = gamma l vm (1/r1 + 1/r2)
Tells us large liquid drops are more stable than smaller ones. Opposite true for bubbles.
Capillary rise
Tube inserted vertically through surface of liquid, liquid inside appears to go up or down with tube.
h = (2 gamma l cos theta)/ (rc g rho)
If liquid does not wet well, liquid is effectively expelled.
Small/ large particles
Small: gravity/ buoyancy can be neglected in comparison with brownian motion.
On water: small p - contact angle of 0, particle sinks, larger than zero, particle positions itself so contact angle is satisfied without inducing curvature of surface.
Large p - if gravity has ability to move particle, surface of liquid is deformed.
Spreading
Liquid-liquid interactions. Spreading coeff: Sabc = gamma ab - gamma ac - gamma bc S > 0 - spreading S < 0 - lense
DVLO forces
Occur between solids immersed inside a liquid that contains ions, in their simplest form, sum of attractive vdw and so called double layer repulsive forces.
Colloids
Small solid particles in a liquid, enormous total interface area, which comes at cost in free energy, need forces that prevent them from coalescing.
Van de Waals sum of 3 main contributions
Keesom Interactions - two freely rotating permanent dipoles tend to attract each other, as they preferentially oreint with opposite charges facing one another.
Debye Interactions - molecule with static dipole will interact with a polarizable molecule by inducing dipole moment.
London dispersion interactions - considering local charge density fluctuations (QM) non-polar molecules also experience net attractive force. Each atom thus has dipole moment and can experience attractive force.
You go Danni
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Double layer forces
Occur between charged solids immersed in liquid containing ions. Charges in liquid tend to accumulate close to surface of solid with opposite charge to ensure global neutrality.
Stability of colloidal solutions
When bringing two charge objects inside a solution together, they experience repulsive force as their double layer overlap. Net force decays exponentially over Debye length. Combo of vdw and double layers forces determines stability.
Grafted polymers
Colloids can be further stabilised by polymer molecules grafted to their surface. To come close together must compress the spring like polymer.
Qualitative remarks about mechanism
Solubility of polymer, elastic (good solvent) or globule (poor)
Interaction range regulated by polymer extension length.
Polymer colloid interaction energy Ep must be larger than thermal energy.
Depletion interactions
Adding third type of molecules to solvent can create net attractive force between colloids, occurs when particles added are soluble, they have intermediate size, they cannot adsorb to surface of colloids and are repelled.
Origin of attractive force comes from absense of paricles in overlapping depletion zone.
Controling/modifying interactions
Add salt or decrease T to reduce Debye length.
Add solvent in which grafted polymer is poorly soluble.
Physical or chemical removal of grated polymers from series of colloids.
Adding non-adsorbing polymer to create depletion interaction.
Four situations colloid behaviour
Inter-colloidal forces repulsive at all scales
Colloids with long ranged repulsion
colloids with weakly attractive interactions
Colloids withs trongly attractive interactions
Colloids repulsive at all scales
Hard sphere colloids, if colloids repulsive at all scales, solution is stable. If particles are same sizesphere, increasing conc. leads to phase transition from liquid-like to crystalline. Exist naturally in Opal. Entropy of system drives crystallisation
Colloids with long-range repulsion
If colloids experience repulsion, deviation from first case because range of forces is smaller than size of colloids when in solution.
Colloids with wealy attractive interactions
If interactions are weakly attractive, expected to behave like liquid. As interaction becomes stronger, system will trasnition to solid like.
Colloids with strongly attractive interactions
E»_space; kbT
Increasingly difficult to form equilibrium structures, not possible to do phase diagram. If rearrangement is possible aggregate can be relatively compact, otherwise it forms fractal structures (eg DLCA RLCA).
Stokes’ law
Fs = 6 pi a neta v
Brownian motion
Originates from random colllisions between thermally agitated liquid molecules and the particle. Averaged over time, zero net force on particle. Random walk.
Polymers
Can be syynthetic (glue etc) or natural (DNA)
Molecule made up of many repeat units covalently joined in chain.
Homopolymer - one type of molecule
Copolymer - two or more repeat units (properties of this depend on whether the molecules are random or not)
Sequenced polymers (proteins) may appear random, arrangement of units completely determines 3D structure.
Degree of polymerisation
Number of repeat units in a chain.
At a given temperature polmers are in one of what states?
Liquid - usually viscous liquid with viscoelastic properties
Glass - common due to difficulty crystallising them
Crystalline - not usually complete with small crystals in amorphous matrix
Liquid crystalline - Kevlar, rigid polymers lined up to form liquid crystalline phases.
Freely jointed chain
Assumes polymer molecule to be chain of N links, each of length a. DIfferent links have independent, uncorrelated orientation - random walk.
= Na^2
Real polymer chains
Consecutive polymer units are not completely uncorrelated due to molecular constraints - effective monomer size such that = Nb^2
Actually self-avoiding alk, cannot intersect itself - reduces volume available and therefor gives more streched configuration: root = a N ^v (v=3/5)
Behaviour of polymer depending on chi (X)
X < kbT/2 - chain expands r~N^3/5 “good solvent”
X = kbT/2 - behaves as gel r~N^1/2 “theta condition”
X > kbT/2 - interfacial energy > entropy “globule”
Polymers at interfaces - grafting
If surface functionalization is needed - medical bio-chips etc - polymers are grafted to solid surface and attatched at one extremity.
Rubber
Polymer melt with cross links placed randomly between adjacent chains - thus any deformation imposed macroscopically is proportionally reflected at microscopoic level.
In first approx, rubber is incompressible. Free energy elastic work done during deformation
Measureing viscoelasticity in polymers
Stress relaxation function G(t) describes evolution of stress in system after a small strain
Strain relaxation function J(t) (creep compliance) describes eveolution of strain in system after applied stress.
Gel
Material made of sub-units (polymers colloids etc) that can form bonds with each other so as to create a network of macroscopic dimensions. If subunits are isolated they behave like a liquid - a sol, gel when they bind.
Classes of gel
Chemical: characterised by chemical bonds between sub-units, typically covalent.
Physical: interactions holding gels together do not involve chemical bonds and are hence usually weaker. Typically thermoreviserible into a liquid, examples are jelly.
Theories of gelation
Percolation model: bonds are added one by one randomly between molecules, progressively forming clusters that grow, when cluster spans entire space available, we assume gelation has occured. Classical model (Flory-Stockmayer): assumes clusters grow as Cayley trees from a given point. fc is percolation threshold.
Percolation threshold
ffc, infinite cluster, a gel.
