phase diagrams and phase transitions of unary systems

(Equilibrium) Phase Diagram H2O

Phase diagrams and phase transitions

of unary systems

•Phase transitions

•Phase boundaries

•Phase transition temperature

•Melting point

•Boiling point

•Triple point

•Critical point

•Polymorphic forms

•Thermodynamics vs kinetics

•Metastable phases

Solid

1

1 bar

2

Phase diagrams and phase transitions of unary systems


Solid

Tfus = Tcryst = 273.15 K H-bonding

1 bar

3



Solid

1 bar

Tvap = 373.15 K

l

g

4



Solid

1 bar

Triple point

273.16 K

611 Pa

0.006 bar

5



Solid

Super critical sc 1 bar

Triple point

Critical point 220.6 bar

647.1 K

6



Solid

Critical point

T

7


l l

g g

super

critical

l l

g g

super

critical

Critical point

T

T < Tc(ritical) T > Tc

Critical

point

220.6 bar

647.1 K H2O

8


H-bonding

1 bar

Triple point

Critical point

9



Solid

1 bar

10

Polymorphic forms

for the solids



Solid

* OHO

H3C

N

CH3

H3C

c c c

b

T < 40 ºC T > 40 ºC T > 60 ºC (Tfus = 70 ºC) Venlafaxine

Polymorphic (solid state) phase transitions 11


sub

CO2 4He

1 bar

1 bar

sublimation point

at 1 bar

ambient conditions “dry

ice”

12


13

Phase boundary lines in diagrams of unary systems

1 bar

Tvap = 373.15 K

l

g

14 (Equilibrium) Phase Diagram H2O


Solid

l

g

15

The chemical potential of phase i (i = l,g)

Equilibrium between phases gl OHOH 22

0idn

i

i

idnSdTVdPdG

ijnTPi

in

G

,,

lg nn

Note: we are dealing with a unary system

m,ii G (pure compound)


(Study guide p.11-13)

l

g

16

Importance of the chemical potential:

ggll dndnSdTVdPdG

Equilibrium between phases gl OHOH 22

Equilibrium 0, PTdG

gl dndn

gl




Triple point

gl

gs I

ls I

Solid

III ss

ls VII



Triple point

m,m, gl GG

m,m,I gs GG

m,m,I ls GG Solid

m,m, III ss GG

m,m,VII ls GG

pure compound: m,ii G



Triple point

m,m, gl GG

Solid

Along phase boundary line:

m,m, gl dGdG

dTSdPVdG iii m,m,m,

dTSdPVdTSdPV ggll m,m,m,m,



Triple point

m,m, gl GG

Solid


m,m, gl dGdG

m

m

V

S

dT

dP

gl

gl

0m Ggl

m

m

VT

H

dT

dP

glgl

gl

Clapeyron equation:

dTSdPVdG iii m,m,m,


22



dTVT

HdP

glgl

gl

m

m

Clapeyron equation:

Triple point

Solid

Perfect gas: RTPV m

P

RTVV ggl m,m

dTRT

H

P

dP

gl

gl

2

m

dT

RT

H

P

dP

gl

gl

2

m

23



Triple point

Solid

T

T

glP

P

dTRT

H

P

dP

gl

2

m

T*

P*

P

T

mm )( HTH glgl

T

T

glP

PT

dT

R

H

P

dP2

m

TTR

H

P

P gl 11ln

m

24



Triple point

Solid

T*

P*

P

T

TTR

H

P

P gl 11ln

m

expPP

TTR

H 11mvap

Clausius-Clapeyron equation:

Clausius-Clapeyron equation

VT

H

V

S

T

P

trstrs

trs

trs

trs

d

d

Clapeyron

VT

H

T

P

fusfus

fus

d

d

*

fus

*

fus*

*

fus

fus* ln TTVT

HP

T

T

V

HPP

VT

H

T

P

subsub

sub

d

d

2

sub

RTd

lnd H

T

P

*

sub* 11

Rexp

TT

HPP

VT

H

T

P

vapvap

vap

d

d

2

vap

RTd

lnd H

T

P

Clausius-Clapeyron

*

vap* 11

Rexp

TT

HPP

25

Phase boundary lines in phase diagrams of unary systems

Exercise 5-8

Phase transitions in phase diagrams of unary systems

26

m

P

ST

m

T

VP

s

m

l

m VV

s

m

l

m VV

(H2O)

TSPVG mmm dddd

27


s

m

l

m VV

(H2O)

(H2O)

28

TSPVG mmm dddd

m

P

ST


3

m

T

VP

TSPVG mmm dddd

(H2O) 273.16 K 273.15 K

0.006 bar

1 bar

29

s

m

l

m VV

(H2O)

(H2O)

m

T

VP


Ehrenfest classification of phase transitions transitions

T

T P

T

TP

2

2

First order Second order Exercise 9

* OHO

H3C

N

CH3

H3C

c c c

b

T < 40 ºC T > 40 ºC T > 60 ºC (Tfus = 70 ºC) Venlafaxine

Polymorphic (solid state) phase transitions

32

Polymorphic forms characterized using

X-Ray Powder Diffraction 33

Polymorphic solid state phase transitions

Characterized using Differential Scanning Calorimetry 34

Polymorphic solid state phase transitions

Kinetic roughening transition for naphthalene crystals in a toluene solution

35 ad: increasing driving force for crystallization

36

Gibbs phase rule: multicomponent phases

37

Triple point

m,m, gl GG

m,m,I gs GG

m,m,I ls GG Solid

m,m, III ss GG

m,m,VII ls GG

(pure compound)

What about mixtures of compounds in the phases?


38

Importance of the chemical potential:

Equilibrium between phases OHOH 22

in equilibrium:

Equilibrium between phases of component i in mixtures

,, ii in equilibrium:

phase α

phase β


phases α, β

components i

39

,, ii in equilibrium: phases α, β

components i

unary phase diagram

P phases in mutual equilibrium

1P

2P

3P


40

Equilibrium between phases of components i in mixtures


components i

C components in the mixtures

# independent variables CxxTPF C 2,, 1

whole

system

for each

phase


P

j

ji

C

i

ji dnSdTVdPdG

,

1

,

j

j

ii

n

nx

mole fraction

41



components i


P phases in mutual equilibrium


whole

system

for each

phase


P

j

ji

C

i

ji dnSdTVdPdG

,

1

,

42



components i


P phases PCF 2

for each

phase


P

j

ji

C

i

ji dnSdTVdPdG

,

1

,

43



components i


P phases

j

j

ii

n

nxfor each phase

mol fraction

1i

ix

PCF 2

# independent variables )1(2 CPF


44



components i

PCCC

P

P

,,,

,2,2,2

,1,1,1

P phases in

mutual equilibrium

2)1()1(2 PCCPCPF

(P −1)C times

an “=” sign


45

Equilibrium between P phases of C components in mixtures


components i


P phases in mutual equilibrium 2 PCF


Gibbs phase rule

F = 2

F: # degrees of freedom

C: # components

P: # phases

46

Gibbs phase rule: unary phase diagrams

2 PCF

P = 1

unary phase diagram

C = 1

47

Gibbs phase rule

F = 1

2 PCF

P = 2 C = 1

unary phase diagram


48

Gibbs phase rule

F = 0

2 PCF

P = 3 C = 1

unary phase diagram


49

Gibbs phase rule

F = −1

2 PCF

P = 4 C = 1

unary phase diagram


phase diagrams and phase transitions of unary systems

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