Phase Transitions: Liquid- Liquid Unmixing– Equilibrium Phase Diagram Soft-Condensed Matter...
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Transcript of Phase Transitions: Liquid- Liquid Unmixing– Equilibrium Phase Diagram Soft-Condensed Matter...
Phase Transitions: Liquid-Liquid Unmixing– Equilibrium Phase Diagram
Soft-Condensed MatterDepartment of Physics,Tunghai-University
Phase Transition and Order Parameters Order parameter: change from a more ordered
state to a less ordered state, and vice versa → order parameters are necessary to describe the change of the states
First order transition: order parameter changes discontinuously between zero and finite values
Second order transition: order parameter changes continuously between zero and finite values
Phase Transition in Soft Matter
The self-assembled process The states of soft matters are usually very
complex A transition means the atoms of the system to
rearrange themselves → usually takes longer time to reach the equilibrium
If the time scale for the rearrangement is too long, we may observe the non-equilibrium states
Liquid-Liquid Unmixing Problem
A B
A+B
Regular Solution Model: A Mean-Field Approach Change of free energy of mixing: Fmix = FA+B – (FA+
FB)
A and B can mix if Fmix < 0, phase separation for F
mix > 0 Assume the liquids are incompressible Assume the molecules are located at lattice points
with coordinate number = z Ф: volume fractions
BA
BABA VV
V
,
,
Regular Solution Model (Conti.): Entropy part Mean-field approximation: the neighboring
sites are independent of each other Boltzmann formula:
In this case:
i iiB ppkS ln
BBAABmix kS lnln
Regular Solution Model (Conti.): Energy part Assume only n.n. interactions Assume the interactions are pairwise additive Mean-field approximation: there are zФA A molec
ules and zФB B molecules at the neighbors of each site (no matter the site is occupied by A or B)
єAA, BB, AB are the contact energies for AA, BB, and AB n.n. contacts
Regular Solution Model (Conti.): Energy part
Free Energy for mixing
Stable and Unstable Cases
Phase Separation
For Fig.3.3 (b), the mixed state is unstable and the system will become a phase-separated state
Metastable State
Unstable
Metastable
Phase Diagram
Interface between Phases and Interfacial Tension For phase separated liqui
ds, there is an interface The interface costs free e
nergy → Surface tension The force needed to kee
p the interface: F=γL
Interfacial Tension
The definition is performed under the constant temperature condition, i. e., isothermal rather than adiabatic
The interfacial tension is an interfacial free energy rather than internal energy
For ideal sharp interface: