entropy in SOFT MATTER PHYSICS

ENTROPY IN SOFT MATTER PHYSICS

Author: Tim VerbovšekMentor: doc. dr. Primož Ziherl

Entropy in soft matter physics

Overview Entropy Polymers Depletion potential

Experiment Liquid crystals

Simulation


Entropy 2nd Law of thermodynamics

In equilibrium, the system has maximal entropy Written in mathematical form by Rudolf Clausius

Free energy

Hard-core interactions


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


In Statistical Physics


Polymers Long chains Random walk Real polymer

chains Entropic spring


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:


Ideal Polymer Chain


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


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.


Depletion Zone

An excluded zone appears around the plate submerged in a solution of microspheres


Depletion Zone

Exclusion zones overlap, leading to a larger available volume for the microspheres


Depletion Potential Ideal gas of microspheres

Free energy is Entropic force: Two spheres:

) Wall-sphere:

Short ranged interactions


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)


Measuring the Forces Optical tweezers hold

the beads in place The potential as a

result of optical tweezers was found to be parabolic


Measuring the Forces


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 )


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


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


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


The Results


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

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entropy in SOFT MATTER PHYSICS