entropy in SOFT MATTER PHYSICS

1. entropy in SOFT MATTER PHYSICS Author: Tim Verbovšek Mentor: doc. dr. Primož Ziherl

2. Overview • Entropy • Polymers • Depletion potential • Experiment • Liquid crystals • Simulation Entropy in soft matter physics

3. Entropy • 2nd Law of thermodynamics • In equilibrium, the system has maximal entropy • Written in mathematical form by Rudolf Clausius • Free energy • Hard-core interactions Entropy in soft matter physics

4. In Statistical Physics • Macrostate: propertyof the system • Microstate: state of a subunit of the system • Ω statistical weight • Different sets of microstates for a given macrostate • if all sets of microstates are equally probable Entropy in soft matter physics

5. In Statistical Physics Entropy in soft matter physics

6. Polymers • Long chains • Random walk • Real polymer chains • Entropic spring Entropy in soft matter physics

7. Ideal Polymer Chains • Random walk • Persistence length • Approximate length at which the polymer loses rigidity • Gaussian probability distribution of the end-to-end vector size • exp() • Configurational entropy: • Free energy: Entropy in soft matter physics

8. Ideal Polymer Chain Entropy in soft matter physics

9. Real Polymer Chains • Correlation of neighbouring bonds • Finite bond angle • Excluded volume • Self-avoiding walk; the polymer cannot intersect itself • The coil takes up more space Entropy in soft matter physics

10. Depletion Potential • Macrospheres and microspheres • Exclusion zone • Asakura-Oosawa model (1954) • The result of overlapping exclusion zones is an attractive force between macrospheres Microscopic image of milk. Droplets of fat can be seen. Entropy in soft matter physics

11. Depletion Zone An excluded zone appears around the plate submerged in a solution of microspheres Entropy in soft matter physics

12. Depletion Zone Exclusion zones overlap, leading to a larger available volume for the microspheres Entropy in soft matter physics

13. Depletion Potential • Ideal gas of microspheres • Free energy is • Entropic force: • Two spheres: • ) • Wall-sphere: • Short ranged interactions Entropy in soft matter physics

14. Measuring the Forces • Silica beads were suspended in a solution of λ-DNA polymers • Measurement of the positions of the beads gives the probability distribution P(r) Entropy in soft matter physics

15. Measuring the Forces • Optical tweezers hold the beads in place • The potential as a result of optical tweezers was found to be parabolic Entropy in soft matter physics

16. Measuring the Forces Entropy in soft matter physics

17. Measuring the Forces • Experiment gives a good fit to the Asakura-Oosawa model • The range of the depletion potential was found to be • Depth of the potential increases linearly with polymer concentration • ) Entropy in soft matter physics

18. Liquid Crystals • Isotropic phase • Nematic phase • Director • Positions of the centers of mass are isotropic • Smectic phase • Layers • Smectic A • Smectic C • Columnar • Disk-shaped molecules Entropy in soft matter physics

19. Phase Transitions • Onsager theory (1949) • Solid rod model • - orientational entropy • Has a maximum in the isotropic phase • - packing entropy • It is maximised when the molecules are parallel • The same role as the depletion potential in colloidal dispersions • It is a linear function of the concentration of rods Entropy in soft matter physics

20. The Simulation • Lyotropic liquid crystals: Phase changes occur by changing the molecule concentration (T = const.) • Computer simulations for hard spherocylinders • Shape anisotropy parameter • Length-to-width ration Entropy in soft matter physics

21. The Results Entropy in soft matter physics

22. Summary • Entropy • With hard spheres and constant temperature, the free energy depends only on entropy • Polymers • Entropic spring • Depletion potential • Short-range attraction between colloids • Experiment • Liquid crystals • Phase transitions • Simulation Entropy in soft matter physics