entropy in soft matter physics
DESCRIPTION
entropy in SOFT MATTER PHYSICS. Author: Tim Verbovšek Mentor: doc. dr. Primož Ziherl. Overview. Entropy Polymers Depletion potential Experiment Liquid crystals Simulation. Entropy. 2nd Law of thermodynamics In equilibrium, the system has maximal entropy - PowerPoint PPT PresentationTRANSCRIPT
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ENTROPY IN SOFT MATTER PHYSICS
Author: Tim VerbovšekMentor: doc. dr. Primož Ziherl
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Entropy in soft matter physics
Overview Entropy Polymers Depletion potential
Experiment Liquid crystals
Simulation
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Entropy in soft matter physics
Entropy 2nd Law of thermodynamics
In equilibrium, the system has maximal entropy Written in mathematical form by Rudolf Clausius
Free energy
Hard-core interactions
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Entropy in soft matter physics
In Statistical Physics Macrostate: property of 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
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Entropy in soft matter physics
In Statistical Physics
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Entropy in soft matter physics
Polymers Long chains Random walk Real polymer
chains Entropic spring
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Entropy in soft matter physics
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:
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Entropy in soft matter physics
Ideal Polymer Chain
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Entropy in soft matter physics
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
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Entropy in soft matter physics
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.
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Entropy in soft matter physics
Depletion Zone
An excluded zone appears around the plate submerged in a solution of microspheres
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Entropy in soft matter physics
Depletion Zone
Exclusion zones overlap, leading to a larger available volume for the microspheres
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Entropy in soft matter physics
Depletion Potential Ideal gas of microspheres
Free energy is Entropic force: Two spheres:
) Wall-sphere:
Short ranged interactions
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Entropy in soft matter physics
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)
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Entropy in soft matter physics
Measuring the Forces Optical tweezers hold
the beads in place The potential as a
result of optical tweezers was found to be parabolic
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Entropy in soft matter physics
Measuring the Forces
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Entropy in soft matter physics
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 )
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Entropy in soft matter physics
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
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Entropy in soft matter physics
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
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Entropy in soft matter physics
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
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Entropy in soft matter physics
The Results
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Entropy in soft matter physics
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