Transcript Osmotic forces

Introduction to Statistical Thermodynamics
of Soft and Biological Matter
Lecture 5
Interactions
• Osmotic pressure.
• Depletion force.
• Hydrophobic interactions.
• Hydration force.
• Electrostatic interactions. Debye screening.
• DNA condensation by multivalent ions.
• van der Waals attraction.
• Phase separation.
Diffusion coefficient
Number of random steps N corresponds to time t:
From dimensional analysis:
Diffusion coefficient and dissipation
Einstein relation:
Friction coefficient:
Viscosity
Particle size
- velocity
Force
Osmotic pressure
Free energy of ideal gas:
N – number of particles
V - volume
concentration:
Pressure:
Osmotic forces:
Protein solution
Concentration difference induces
osmotic pressure
Semi-permeable membrane
(only solvent can penetrate)
Depletion force
R
Free energy gain:
A – surface area of contact
R – small particle radius
- small particles concentration
Depletion force
Molecular size asymmetry leads to aggregation of large molecules
Sometimes entropy can lead to order
Disordered Liquid
Ordered Solid
Hydrophobic interactions
• Amphiphiles (lipids): polar head-group and hydrophobic tail
Lipid
molecule
Self assembly
Hydrophobic interaction
is due to disruption of entropy of hydrogen bonding of water
chain (tail) (hate water)
polar head (love water)
Types of lipid molecules
Hydration repulsion
At small separations (<1 nm), there is a repulsion between
surfaces in water due to disruption of water molecular ordering
(layering) at the surfaces.
Hydration repulsion constitutes energetic barrier for
membrane fusion.
Electrostatic interactions
Two charges in medium with dielectric constant
R
Interaction energy:
Two charges in salt solution with dielectric constant
---
----+- - + - +
--- + R -
++ ++
+
+
+
+
++
Screened interactions:
Debye screening
----
----+- - + - +
--- + R -
++ ++
+
+
+
+
++
Screened interactions:
- Debye radius
DNA condensation by multivalent ions
Bacteriophage virus 100 nm
Mg Cl (salt)
++
Cl- Cl Mg
O. Lambert, L. Letellier , W. M. Gelbart, and J.-L. Rigaud* PNAS, 2000
DNA in solution
V. Bloomfield
I. Rouzina
DNA is condensed after addition of
multivalent salt
van der Waals attraction
• Always present between molecules:
- Usually attractive between same species
- Long range (power law)
van der Waals attraction between two atoms:
Hamaker constant
vdW attraction is due to fluctuations of electron clouds in atoms
Phase separation
Interactions can lead to phase separation:
Conclusions
Main Questions and Ideas
• How can living organisms be so highly ordered ?
• Equilibrium versus non-equilibrium systems. Living systems
are not at equilibrium, and they are open. Quasi equilibrium.
• Interactions can lead to a spontaneous ordering even
at equilibrium.
• Entropy can lead to a spontaneous ordering at equilibrium !
• Flow of information characterizes living organisms.
• Evolution is the biological “pressure”.
Living organisms are robust.
Thank you!