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.
