L. D. COLLEGE OF ENGINEERING

RUBBER TECHNOLOGY

Sub:- THERMODYNAMICS OF ELASTOMERS &

POLYMERS

The Phase Rule & Phase Diagram

Some basic concepts

• Phase– A homogeneous region with distinct structure

and physical properties– In principle, can be isolated– Can be solid, liquid or gas

• Phase Diagram– Representation of phases present under a set of

conditions (P, T, Composition etc.)

F = C - f + 2F = # degrees of freedom

The number of intensive parameters that must be specified in order to completely determine the system

f = # of phasesphases are mechanically separable constituents

C = minimum # of components (chemical constituents that must be specified in order to define all phases)

The Phase Rule

Gibbs Phase RuleFor a closed, homogeneous system of constant composition (e.g., an ideal gas), we require twoparameters of state (for example, T and p) in order to describe it. For a heterogeneous systemin equilibrium, consisting of one component (e.g., water substance) and two phases (e.g., liquidand vapour), we require only one parameter of state (for example, T).

This example may be expressed more generally in terms of Gibb’s phase rule:

where =number of independent state variables at equilibrium c=number of components =number of phasesWe assume here that the masses of the components and phases are specified. As an example, For equilibrium between a pure plane surface of water and its vapour, we require only one state

Gibb’s Phase Rule

P + F = C + 2 P=number of phasesC=number of componentsF=number of degrees of freedom (number of independent variables)

Modified Gibbs Phase Rule (for incompressible systems)

P + F = C + 1

Pressure is a constant variable

F = C - P + 2

F = C - P + 1

Application of the phase rule

At triple point, P=3, C=1, F=0i.e. this is an invariant point

At phase boundary, P=2, C=1, F=1

In each phase, P=1, C=1, F=2

The Phase Rule

There are two types of phase components as per below;

=> One Component Systems

=> Two Component Systems

1 - C Systems

1. The system SiO2

1 - C Systems

2. The system H2O

2 - C Systems1. Plagioclase (Ab-An, NaAlSi3O8 - CaAl2Si2O8)

2-C Eutectic Systems Example: Diopside - Anorthite

No solid solution

A simple phase diagram

Triple point(Invariant point)

Solid

Liquid

Vapor

Pressure

Temperature

Phase boundary

System: H2O

Construction of a simple phase diagram

• Conduct an experiment• Take 10 metal samples(pure Cu, Cu-10%Ni,

Cu-20%Ni, Cu-30%Ni………, pure Ni)• Melt each sample and then let it solidify• Record the cooling curves• Note temperatures at which phase

transformations occur

Results

L

S

L S

t

T

L

L + S

TL

TS S

L

L + S

TL

TS

Pure CuCu-10%Ni

Cu-20%Ni

L

L S

Pure Ni

S

TNi

TCu

The Eutectic Phase Diagram

T

A BWt%B

L

a+Lb+L

a+b

E

TE

CE

ab

LiquidusSolidusSolvus

L a + (b TE, CL=CE)

Thank You