Jean-François Dufrêche
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1 Jean-François Dufrêche! Entropy and Temperature A fifth force in the nature? E TS Rudolf Clausius (Koszalin, Bonn, 1888) Entropy = η τροπη = the transformation
2 Thermodynamics In mechanics Equilibrium : E minimum E = potential energy Belleville roller coaster (1817)! modern roller coaster! In thermodynamics (T constant) : valid only at T = 0 K Equilibrium : E - TS minimum Interpretation Sunivers maximum S univers = S syst + S ext $ ext S ext E ext ext ext & S = S (Etot E) S (Etot ) + ( E ) = S0 with % E T & S syst = S ' External environment! Thermostat! system! E! gives T! S univers E = S (+S0ext ) T minimization of the energy = maximization of the entropy of the external environement
3 Competition between S and E Equilibria : minimisation of F = E TS! V(r) = potential energy between two molecules! (= -TSuniverse)! V(r)! repulsion! attraction!!! σ $12! σ $6 $ typically, V (r) = 4ε ### & # & && r % r % % r! distance between the molecules! ε! σ! Solid! U predominant! atoms at fixed distance! Low T! Gas! S predominant! desorder! High T! ε: depth of the attraction! σ : size of the molecules! Liquid! U TS???! Intermediate T!
4 Hard spheres and entropy a (crystalline) solid phase can have a higher entropy than a liquid phase! solid! liquid (or dense fluid)!
5 Hard spheres and entropy a (crystalline) solid phase can have a higher entropy than a liquid phase! solid! liquid (or dense fluid)!
6 Hard spheres and entropy a (crystalline) solid phase can have a higher entropy than a liquid phase! solid! liquid (or dense fluid)!
7 Hard spheres and entropy a (crystalline) solid phase can have a higher entropy than a liquid phase! solid! liquid (or dense fluid)! A high density, an organized phase (solid) gives more space for every molecules, because it can move in relatively large site!
8 Hard spheres and entropy a (crystalline) solid phase can have a higher entropy than a liquid phase! solid! liquid (or dense fluid)! A high density, an organized phase (solid) gives more space for every molecules, because it can move in relatively large site! Solid phases entropically favourable at high pressure T! Hard spheres phase diagram F! S + F S (fcc)! 0.494! 0.545! 0.740! Φ (packing fraction)! (exception: water)!
9 Liquid crystals Liquid crystal: long rigid molecules! Isotropic liquid phase! rot : L trans: L! Ex: MPPA! Nematic! Smectic top view! top view! rot : S trans: L! Crystal solid phase! rot : S trans: 1/3S+2/3L! Competition of translational and rotational entropy top view! rot : S trans: S!
10 Liquid crystals Liquid crystal: Ex: MPPA! long rigid molecules! Isotropic liquid phase! 2 P / kbar! Nematic! Smectic solid phase! So! Octylcyanobiphényl (8CB)! Shashidhar et Venkatesh! J. Phys. Coll. (1979)! N! 1 top view! Sm! rot : L trans: L! rot : S trans: L! Crystal L! top view! rot : S trans: 1/3S+2/3L! T / oc! 80! 40! Competition of translational and rotational entropy top view! rot : S trans: S!
11 Micelles theory for dummies Amphiphilic molecule hydrophobic tail / hydrophilic head Law of attraction : like attracks like
12 Micelles theory for dummies Amphiphilic molecule hydrophobic tail / hydrophilic head Law of attraction : like attracks like Completly wrong with electrostaic forces! one interaction is missing Entropy! chains! solvent (solvation)
13 EntropyN ooft e the solvation t e c hsolvent n i q u e D Rfor CP/S CPS/2008/21 Page 37/50 Born model for solvation εr!! 1 molal Ze! 2RBorn! 2 molal Δ solvg 0 Z 2e2 # 1 & = % 1( 8πε 0 RBorn $ εr ' 0 3 molal solvation entropy stantanées Corresponding représentant les deux premières sphères de coordination des chlorures % T εr ( Δ solvg Z 2e2 TΔ solv S = T = ' * 8πε 0εr Rsphère εr coordina T ) &de cules d eau et des chlorures dans la première T et la deuxième Born s pour chaque 23). Forconcentration water at 25o(Tableau C T εr 1.36 Δ solv Saqueuse < 0 à 300 K étés dynamiques des molécules d eau et=des ions Cl- en solution εr T s de UO2Cl2. résidence Solvation (TMR) des: molécules d eau dans la première sphère (TMR(1)WAT ) etless la translation decrease of the solvent entropy (less rotation and (2) 2+ TMR WAT) de coordination de UO2 (en ps). of solvent molecules) résidence (TMR) des Cl- dans la première sphère (TMR(1)Cl-) et la deuxième sphère ination de UO22+ (en ps).
14 Micelles theory and solvent entropy Dissociated molecules A lot of solvating solvent molecules Low solvent entropy Associated molecules Less solvating solvent molecules Higher solvent entropy For the solute entropy, it is the contrary (see lesson 1)!
15 Van der Waals forces with rotation Keesom! Dipole mobile / Dipole mobile p12 p22 V (r) = 3(4πε 0 )2 kbtr 6 < kt (weak) but water p1! p2! p 2Q 2 V (r) = 6(4πε 0 )2 kbtr 4 < kt (weak) but water Debye! Dipole mobile / Ion Q! p! Potential : free energy of the pair of particles f (r) V (r) = T F E TS = T = F F = E TS = E F = T 2 The entropic contribution is unfavourable (lost rotation) and is it is half of the energetic one!
16 Depletion 0 Mixture of big and small hard spheres - Big hard spheres (ex: colloid) - Small hard spheres (ex: polymer) Purely repulsive system but an attraction is measured! Possible explanation P! 0 depletion domain! P!
17 Depletion Entropic interpretation Asakura et Oosawa - excluded volume of the small spheres When the colloids come together - overlapping of the excluded volumes - more volume for the small spheres - more important entropy - favourable configuration attraction
18 Depletion Entropic interpretation Asakura et Oosawa Z = N βv dr e = (V Vexclu ) N F(x )= kt ln Z = F id +Veff (r) r! Hence πd3 % 3r r3 ( Veff (r) /kt = ρ + '1 * 6 & 2D 2D3 ) Effective potential potential averaged over the solvent configurations 2R < r < 2R + σ = D Veff (r ) attraction
19 Depletion Phase separations Nature, 416, 801 (2002)! Direct measurement Phys. Rev. Lett., 81, 4004 (1998)!
20 Interfacial depletion Big solutes are attracted to an interface just because they are big Entropy of the solvant Similar to Asakura et Oosawa Forbidden domain for the solvent! Smaller forbidden domain if the particle is at the surface! Bigger entropy! stability! Brazilian Nuts effect!
21 Conclusion Entropy = a force in the nature Important parameter: temperature Driving phenomenon: excluded volumes +!
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