Binding Forces Between Molecules , Solids and the Crystalline State , Phase Equilibria and the Phase Rule

1. STATES OF MATTER
PHYSICAL PHARMACY I
LEC 1
ASSISTANT LECTURER
DR AHMAD A YOSEF
MSC PHARMACEUTICAL SCIENCES
1

2.  Binding Forces Between
Molecules
 Solids and the Crystalline State
 Phase Equilibria and the Phase
Rule
STATES OF MATTER
2

3. OBJECTIVES
After completion of this chapter, the students should be
able to:
Describe the solid state , crystallinity, solvates and
polymorphism
Understand phase equilibria and phase transitions between the
three main states of matter
Understandthe phase rule and its application to different
systems containing multiple components.
3

4.  Gases are compressible fluids. Their molecules are widely separated.
 Liquids are relatively incompressible fluids. Their molecules are more tightly
packed.
 Solids are nearly incompressible and rigid. Their molecules or ions are in
close contact and do not move.
COMPARISON OF GASES, LIQUIDS AND SOLIDS
In order for molecules to exist in aggregates in gases, liquids
and solids Intermolecular forces must exist 4

5. 5

6.  As two atoms or molecules are brought
closer together, the opposite charges and
binding forces in the two molecules are
closer together than the similar charges
and forces, causing the molecules to
attract one another.
 The negatively charged electron clouds of
molecules (equilibrium) molecules largely
govern the balance forces between the
two
REPULSIVE AND ATTRACTIVE FORCES
6

7. IDEAL GAS EQUATION
1
Boyle’s law: P  V (at constant (n and T)
Charles’ law: V  T (at constant n and P)
Avogadro’s law: V  n (at constant P and T)
P1V1
T1
=
P2V2
T2
PV = nRT
R is the gas
constant
7

8.  The conditions 0 0C and 1 atm are called standard
temperature and pressure (STP).
 Experiments show that at STP, 1 mole of an ideal gas occupies
22.414 L.
PV = nRT
GASEOUS STATE
R
=
PV =
n
T
(1 atm)(22.414L)
(1mol)(273.15 K)
R =0.082057 L • atm / (mol • K) 8

9. 9
What is the volume (in liters) occupied by 49.8 g of HCl at STP?
PV =
nRT
V =
nR
T
P
T = 0 0C = 273.15 K
P = 1 atm
n = 49.8 g x
1 mol HCl
36.45 g HCl
= 1.37 mol
V =
1 atm
1.37 mol x 0.0821 L•atm
x 273.15 Kmol•K
V = 30.7 L
GASEOUS STATE
1 atm ≈760.001 mm-Hg
9

10. P1V1
T1
=
P2V2
T2
GASEOUS STATE
10

11.  The critical temperature (Tc) is the temperature above which the gas
cannot be made to liquefy, OR is the temperature above which the liquid
cannot longer exist
 The critical pressure (Pc) is the minimum pressure required to liquefy a
gas at
its critical temperature.
 critical temperature (Tc) of water is 374°C, or 647 K, and its critical
pressure is 218 atm,
LIQUEFACTION OF GASES
11

12. 12

13. SOLIDS & CRYSTALLINE STATE
PHARMACEUTICAL DRUGS: MORE THAN 80% ARE SOLID FORMULATIONS
13

14.  A crystalline solid possesses rigid and long-range
order.
 In a crystalline solid, atoms, molecules or ions
occupy (predictable) positions.
specific
 An amorphous solid does not possessa well-defined
arrangement and long-range molecular order.
SOLIDS AND THE CRYSTALLINE STATE
14

15. CLASSIFICATION OF SOLIDS
Crystalline Amorphous
 Amorphous
15

16. A UNIT CELL IS THE BASIC REPEATING STRUCTURAL UNIT
OF A CRYSTALLINE SOLID.
lattice
point
Unit Cell Unit cells in 3 dimensions
At lattice points:
• Atoms
• Molecules
• Ions
16

17. THE CRYSTAL LATTICE OF SODIUM CHLORIDE NACL
Na Cl

18. The various crystal forms are divide to basic 7 unit according to its
symmetry
NaCl urea
iodine
sucrose Boric acid
CRYSTAL FORMS
iodoform
Be3Al2(SiO3)6
18

19. CsCl Zn
S
CaF2
Ionic Crystals
• Lattice points occupied by cations and
anions
• Held together by electrostatic attraction
• Hard, brittle, high melting point
• Poor conductor of heat and electricity
TYPES OF CRYSTALS
19

20. diamond
graphite
carbon
atoms
COVALENT CRYSTALS
• Lattice points occupied by atoms
• Held together by covalent bonds
• Hard, high melting point
• Poor conductor of heat and
electricity
20

21. Cross Section of a Metallic Crystal
nucleus & inner shell e-
mobile “sea” of e-
METALLIC CRYSTALS
• Lattice points occupied by metal
atoms
• Held together by metallic bonds
• Soft to hard, low to high melting
point
• Good conductors of heat and
electricity
21

22.  Some elemental substance such as
C and S ,may exist in more than
one crystalline form and are said to
be allotropic, which is a special
case of polymorphism
 Polymorphism is the ability of a
substance to exist in more than one
crystal structure
POLYMORPHISM
22

23. Polymorphism is the ability of a substance to exist in more than
one crystal structure
 Polymorphs: when two crystals have the same chemical
composition
but different internal structure (molecular packing –molecular
conformation or / and inter or intra molecular
interactions)modifications or polymorphs or forms
Pseudo polymorphs : different crystal forms have molecules of the
same given substances and also contain molecules of solvent
incorporated into a unique structure (solvates or hydrates (water))
23

24. diamond graphite
carbon
atoms
High T and p
Diamond is metastable and converts very slowly to graphite
THE MOST COMMON EXAMPLE OF POLYMORPHISM
24

25. SOLID STATE : POLYMORPHS
Mono-component systems: Polymorphs
Multi-component systems
25

26. 26

27. COCRYSTAL
 The simplest definition of a cocrystal is a crystalline structure
made up of two or more components in a definite stoichiometric
ratio, where each component is defined as either an atom, ion,
or molecule.
27

28. PRINCIPLE OF POLYMORPHISM
 When the change from one form to another is reversible, it is
said to be enantiotropic.
 When the transition takes place in one direction only—for
example, from a metastable to a stable form—the change is
said to be monotropic.
28

29. SOLVATES
 Pharmaceutical synthesis include purification and crystallization,
 residual solvent can be trapped in the lattice.
 This result in the formation of cocrystal or solvate.
 The presence of residual solvent may affect dramatically the
crystalline structure of the solid depending on the type of inter.
molecular forces that the solvent may have with crystalline
solid
29

30. POLYMORPHISM
30

31. AMORPHOUS SOLIDS
Solids that don’t have a definite geometrical shape are known as Amorphous Solids.
1. In these solids particles are randomly arranged in three dimension.
2. They don’t have sharp melting points.
3. Amorphous solids are formed due to sudden cooling of liquid.
4. Amorphous solids melt over a wide range of temperature
AMORPHOUS SOLID
 An amorphous solid does not possess a well-defined arrangement and
long-range molecular order.
 Amorphous substances, as well as cubic crystal, are isotropic, that is,
they exhibit similar properties in all direction.
31

32.  The crystalline from of the antibiotic novobiocin acid is poorly
absorbed and has no activity, where the amorphous form is
readily absorbed and therapeutically active, due to different
dissolution rate.
AMORPHOUS OR CRYSTALLINE & THERAPEUTIC ACTIVITY
32

33. General crystallization conditions
Solvents –different polarities
Concentration of the solutions (super saturated, saturated, diluted)
Cooling speed (quenching, slow) Temperature (room or lower than
room temperature)
CRYSTALLIZATION
33

34. Final Form
Granulation
Drying
Compaction
Tableting
Drug Product
API
Crystallization
Filtration
Drying
Milling
Bulk API
Stability
POLYMORPHISM AND INDUSTRY/ PHARMACEUTICAL
34

35. POLYMORPHISM AND INDUSTRY/
PHARMACEUTICAL
 Fluoxetine HCl, the
active ingredient in the
antidepressant drug
Prozac.
 co crystal which will
have increased
solubility compared to
the crystalline form
35

36. CELECOXIB
 CELECOXIB is a nonsteroidal anti-inflammatory drug
 However it was found that the higher bioavailability was shown by the amorphous
state
 The downfall of the amorphous state was its stability.
 This was due to the structural relaxation.
 This was enhanced by mixing it with polymers like PVP, which helped in
stabilizing the amorphous system (Piyush Gupta et al. 2004, Piyush Gupta et al.
2005).
 A new solid state form was developed by Pharmacia
36

37. FUROSEMIDE
Two forms with significantly differing aqueous solubility and
dissolution rate
Oral bioavailability compromised
Giron lists >20 excipients that display polymorphism,
including
– Lactose (anhydrous; also monohydrate)
– Aspartame (anhydrous; hydrate forms)
– Magnesium stearate (can affect lubrication of tablets)
37

38. BIOAVAILABILITY
 The rate and extent to which the active ingredient or active
moiety is absorbed from a drug product and becomes available
at the site of action.
38

39. 39

40. 40

41. BIOEQUIVALENCE
 The absence of a significant difference in the rate and extent to
which the active ingredient or active moiety in pharmaceutical
equivalents or pharmaceutical alternatives becomes available
at the site of drug action when administered at the same molar
dose under similar conditions in an appropriately designed
study.
41

42. 42

43. CARBAMAZEPINE
43

44. CHLORPROPAMIDE
at least, six polymorphic white or almost white, crystalline powder. It
exhibits polymorphism. Practically insoluble in water soluble in
alcohol freely soluble in acetone and in dichlo- romethane dissolves
in dilute solutions of alkali hydroxides.
Protect from light.
blood-glucose-lowering drug
44

45. AIDS DRUG RITONAVIR
45

46.  Theobroma oil (cacao butter ) is a polymorphic natural
fat.
 Theobroma oil can exist in 4 different polymorphic forms
of which only one is Stabile
1. Unstable gamma form melting at 18°C
2. Alpha form melting at 22°C
3. Beta prime form melting at 28°C
4. Stable beta form melting at 34.5°C
 This is important in the preparation of
theobroma suppositories.
 If the oil is heated to a point where it is completely
liquified (about 35 C), the crystals of the stable
polymorph are destroyed & the mass does not crystallize
until it is cooled to 15 C.
 The crystals that form are unstable & the suppositories
melt
at 24 C.
 Theobroma suppositories must be prepared below 33 C.
POLYMORPHISM AND INDUSTRY/ PHARMACEUTICAL
46

47. POLYMORPHISM AND INDUSTRY/ PHARMACEUTICAL
Anhydrates together with salts form the majority of all drug
formulations About a half of all APIs used today are salts
Salts are stable and well soluble in polar solvents (first of all in water), because they contain ionic
bond. There is one more essential advantage of salts – their solubility is a function of pH. Since pH
in the gastrointestinal tract (GIT) vary between 1-7,5
atorvastatin calcium trihydrate
Each tablet contains Atorvastatin Calcium
Trihydrate equivalent to Atorvastatin 20
mg.
47

48. PHASE EQUILIBRIA & THE PHASE RULE
48

49. Phase
diagram –
Water
49

50.  Phase Equilibrium: A stable phase structure with lowest free-energy
(internal energy) of a system, and also randomness or disorder of the
atoms or molecules (entropy).
 Any change in Temperature, Composition, and Pressure causes an
increase in free energy and away from Equilibrium thus forcing a move to
another ‘state’
PHASE EQUILIBRIA & THE PHASE RULE:
DEFINITIONS
50

51.  A phase is defined as any homogeneous and physically distinct part of a system
which is separated from other parts of the system by interfaces.
 A part of a system is homogeneous if it has identical physical properties and
chemical
composition throughout the part.
A phase may be gas, liquid or solid.
A gas or a gaseous mixture is a single phase.
Totally miscible liquids constitute a single phase.
In an immiscible liquid system, each layer is counted as a separate phase.
Every solid constitutes a single phase except when a solid solution is formed.
A solid solution is considered as a single phase.
Each polymorphic form constitutes a separate phase.
PHASE DEFINITION
51

52. • Examples
1. Liquid water, pieces of ice and water vapour are present together.
The number of phases is 3 as each form is a separate phase. Ice in the system is a single
phase even
if it is present as a number of pieces.
2.Calcium carbonate undergoes thermal
decomposition. The chemical reaction is: CaCO3(s) 
CaO(s) + CO2 (g)
Number of phases = 3 : This system consists of 2 solid phases, CaCO3 and CaO and one
gaseous
phase, that of CO2.
3. Ammonium chloride undergoes thermal decomposition. The chemical reaction is:
 NH4Cl(s) NH3 (g) + HCl (g) Number of phases = 2
 This system has two phases, one solid, NH4Cl and one gaseous, a mixture of NH3 and
HCl.
52

53.  The number of components of a system at equilibrium is the
smallest number of independently varying chemical
constituents using which the composition of each and every
phase in the system can be expressed.
COMPONENTS
53

54. • Examples
 Counting the number of components
1. The sulphur system is a one component system. All the
phases, monoclinic, rhombic, liquid and vapour – can be
expressed in terms of the single constituent – sulphur.
2. A mixture of ethanol and water is an example of a two
component system. We need both ethanol and water to
express its composition.
54

55. An example of a system in which a reaction occurs and an equilibrium is
established is the thermal decomposition of solid
CaCO3.
In this system, there are three distinct phases:
Solid CaCO3
Solid CaO
Gaseous CO2
Though there are 3 species present, the number of components is only two, because of the
equilibrium:
 CaCO3 (s)  CaO(s) + CO2(g)
 Any two of the three constituents may be chosen as the components.
 If CaO and CO2 are chosen, then the composition of the phase CaCO3 is expressed as
one mole of component CO2 plus one mole of component CaO.
 If, on the other hand, CaCO3 and CO2 were chosen, then the composition of the phase
CaO would be described as one mole of CaCO3 minus one mole of CO2.
55

56. DEGREES OF FREEDOM (OR
VARIANCE)
 The degreesof freedom or varianceof a systemis defined as
the minimum number of variables such as:
temperature
pressure
concentration
which must be fixed in order to define the system completely.
F = C  P + 2
56

57. • Examples
1. A gaseous mixture of CO2 and N2.
Three variables: pressure, temperature and composition are required to define this
system. This is, hence, a trivariant system.
2. A system having only liquid water has two degrees of freedom or is bivariant.
Both
temperature and pressure need to be mentioned in order to define the system.
3. If to the system containing liquid water, pieces of ice are added and this system
with 2 phases is allowed to come to equilibrium, then it is an univariant
system.
Only one variable, either temperature or pressure need to be specified in order to
define
the system.
If the pressure on the system is maintained at 1 atm, then the temperature of the
system gets automatically fixed at 0oC, the normal melting point of ice. 57

58. PHASE EQUILIBRIA & THE
PHASE RULE
 A phase diagram (Equilibrium Phase
Diagram) summarizes the conditions at which a
substance exists as a solid, liquid, or gas.
 OR : It isa “map”of theinformation about the control
of phase structure of a particular material system.
 Therelationships between temperature and the
compositions and the quantities of phases present at
equilibrium are represented.
58

59. F = C  P + 2The phase rule
THE PHASE
RULE
 J.W. Gibbs formulated the phase rule, which is a general
relation between the variance, F, the number of component,
C, and the number of phases P, at equilibrium , for a system
of any composition:
 For a system in
equilibrium
 F : degree of freedom, the least number of intensive variable
that must be fixed (known) to describe the system completely
59

60.  Phase Rule relation to determine the least number of intensive
variable, that can be changed without changing the equilibrium
state of the system, or, alternately,
The least number required to define the state of the system,
which is called degree of freedom F.
 Intensive variable independent variable that do not depend on
the volume or the size, e.g.Temp., pressure
60

61.  Independent chemical species which comprise the
system: These could be: Elements, Ions,
Compounds
E.g. Au-Cu system : Components → Au,
Cu Ice-water system : Component
→ H2O
Al2O3 – Cr2O3 system : Components → Al2O3, Cr2O3
 Component the smallest number of constituent by which the
composition of each phase in the system at equilibrium can be
expressed in form of chemical formula or equation
PHASE EQUILIBRIA & THE PHASE RULE
Components of a system
61

62. THE NUMBER OF PHASES IN A SYSTEM IS DENOTED P
(a) A gas, or a gaseous mixture is a single phase. P=1
(b)For a solid system, an alloy of two metals is a two-phase system (P=2) if the metals
are immiscible, but a single-phase system (P=1) if they are miscible---a homogeneous
mixture of the two substances---is uniform on a molecular scale.
(c)For a liquid system, according to the solubility to decide whether a system consists of
one phase or of two.
For example, a solution of sodium chloride in water is a single phase.
A pair of liquids that are partially miscible or immiscible is a two-phase system(P=2)
Oil in water
62

63. Degrees of Freedom = What you can control What the system controls
F = C + 2 P
Can control the no. of
components added and P & T
System decided how many
phases to produce given the
conditions
A WAY OF UNDERSTANDING THE GIBBS PHASE RULE:
THE DEGREES OF FREEDOM CAN BE THOUGHT OF AS THE DIFFERENCE BETWEEN
WHAT YOU (CAN) CONTROL AND
what the system controls
63

64.  F : degree of freedom, the least number of intensive variable that must be
fixed (known) to describe the system completely
 Degree of freedom (or variance) F is the number of variables (T, p,
and/or composition) that can be changed independently without changing
the phases of the system
a) At the triple point:
P = 3 (solid, liquid, and
gas) C= 1
(water)
P + F = C + 2
F = 0 (no degree of
freedom)
b) liquid-solid
curve P =
2
2+F = 1 + 2
F= 1
One variable (T or P) can be
changedc) Liquid
P =1
So F =2
Two variables (T and P) can be varied independently
and the system will remains a single phase
64

65. ONE-COMPONENT SYSTEMS
Phase diagram of
water
P(atm)
Critical point
374
1
=100=0O--Triple point
0.006
218
Curve O -C
Sublimatio
n
Deposition
Curve O-A
Vaporization
Condensation
Curve O -B
Melting
Freezing
F = C  P + 2
65

66. F = C  P + 2
66

67. PHASE DIAGRAM OF CARBON
DIOXIDE
67

68.  Condensed system: System in which the vapor phase is ignored
and only the solid and/or liquid phases are considered.
Two component system
 For two component system F can be 3, (3D model is needed), e.g. T,
p and concentration , usually we fix p = 1atm , the vapor phase is
neglected, and F is reduced to 2
 For three component system the pressure and temperature are fixed
68

69. 69

70. Phenol water phase diagram
70

71. e.g. for point d (24%)
TWO COMPONENT SYSTEM CONTAINING
LIQUID PHASE
 Tie Line : bc line: The line at which the
system at equilibrium will separate into
phases of constant composition, termed
‘conjugate phases’
 Lever Rule: a way to calculate the proportions of
each phase present on a phase diagram in a two
phase field (at a given temperature and
composition).
71

72. E.G. FOR POINT D
(24%)
For every 10 g of liquid system
in equilibrium in point d
7.5 g phase A
2.5 g phase B
Example:
Mixed 24g phenol +76g water , T 50°C,
equilibrium
75 g phase A 25 g phase B
11% phenol 63 % phenol
0.11× 75 g=8.25 g
phenol
0.63× 25 g=15.75 g
phenol
water rich phase
contains water+ phenol(11%)
Phenol rich phase
contains Phenol (63%)+ water
72

73. THE CRITICAL SOLUTION
TEMPERATURE: CST
 Is the maximum temperature at which
the 2-phase region exists (or upper
consolute temperature).
 In the case of the phenol-water
system, this is 66.8oC (point h)
 All combinations of phenol and water
> CST are completely miscible and
yield 1- phase liquid systems.
73

76. A :salol B: thymol
53%
TWO COMPONENT SYSTEM CONTAINING SOLID AND
LIQUID PHASE (EUTECTIC MIXTURES)
76

77. A :salol B: thymol
77

78.  EMLA® (lidocaine 2.5% and prilocaine 2.5%) Cream
 EMLA Cream (lidocaine 2.5% and prilocaine 2.5%) is an emulsion in
which the oil phase is a eutectic mixture of lidocaine and prilocaine in a
ratio of 1:1 by weight. This eutectic mixture has a melting point below
room temperature and therefore both local anesthetics exist as a liquid oil
rather than as crystals
EUTECTIC MIXTURE : PHARMACEUTICAL
APPLICATION
78

79. Triangular Diagrams for three –
component
systems
THREE COMPONENT
SYSTEM
79

80. Birzeit University Physical Pharmacy PHAR 323 Dr. Hani
Shtaya 80

81. 1. Binding Forces Between Molecules
2. Repulsive and Attractive Forces
3. The Gaseous State
 The Ideal Gas Law
 Liquefaction of Gases
 Aerosols
4. Solids and the Crystalline State
 Crystalline Solids
 Polymorphism
 Solvates
 Amorphous Solids
5. Phase Equilibria and the Phase Rule
 Phase Rule
 Systems Containing One Component
 Condensed System
 Two-Component Systems Containing Liquid Phases
 Two-Component Systems Containing Solid and Liquid Phases : Eutectic
Mixtures
 Rules Relating to Triangular Diagrams
TOPICS THAT WE HAVE
COVERED:
81

82. 82