Author: Tim Verbovšek Mentor: doc. dr. Primož Ziherl

ENTROPY IN SOFT MATTER PHYSICS

Author: Tim Verbovšek

Mentor: 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)



Optical tweezers hold the beads in place

The potential as a result of optical tweezers was found to be parabolic





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

Documents

Author: Tim Verbovšek Mentor: doc. dr. Primož Ziherl