State of matter (Physical Pharmacy)

 Binding Forces Between Molecules
 Solids and the Crystalline State
 Phase Equilibria and the Phase Rule
States of Matter

Objectives of the lecture
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
Understand the phase rule and its application to different systems
containing multiple components.

 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

 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 largely govern the balance
(equilibrium) forces between the two
molecules
Repulsive and Attractive Forces

Ideal Gas Equation
Boyle’s law: P a (at constant n and T)
1
V
Charles’ law: V a T (at constant n and P)
Avogadro’s law: V a n (at constant P and T)
P1V1
T1
=
P2V2
T2
PV = nRT
R is the gas
constant

 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
nT
=
(1 atm)(22.414L)
(1 mol)(273.15 K)
R = 0.082057 L • atm / (mol • K)

9
What is the volume (in liters) occupied by 49.8 g of HCl at STP?
PV = nRT
V =
nRT
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 x 273.15 KL•atm
mol•K
V = 30.7 L
Gaseous state
1 atm ≈ 760.001 mm-Hg

P1V1
T1
=
P2V2
T2
Gaseous state

 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

SOLIDS & CRYSTALLINE STATE
Pharmaceutical Drugs: more than 80% are solid formulations

 A crystalline solid possesses rigid and long-range order.
 In a crystalline solid, atoms, molecules or ions occupy specific
(predictable) positions.
 An amorphous solid does not possess a well-defined arrangement
and long-range molecular order.
Solids and the crystalline state

Classification of Solids
Crystalline Amorphous
 Amorphous

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

The crystal lattice of sodium chloride NaCl
Na Cl

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

CsCl ZnS 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

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

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

 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

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))

diamond graphite
carbon
atoms
High T and p
Diamond is metastable and converts very slowly to graphite
The most common example of polymorphism

Solid State : Polymorphs
Mono-component systems: Polymorphs
Multi-component systems

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.

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.

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

Melting point
Vapor pressure
Hardness
Optical, electrical magnetic
properties
Color
IR spectra
NMR spectra
Photochemical reactivity
Thermal stability
Filtration and drying characteristics
Dissolution rate
Bioavailability
Physical and chemical stability
Solubility and melting point are very important in pharmaceutical
processes including dissolution and formulation.
Polymorphism

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.

 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

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

Final Form
Granulation
Drying
Compaction
Tableting
Drug Product
API
Crystallization
Filtration
Drying
Milling
Bulk API
Stability
Polymorphism and Industry/ Pharmaceutical

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

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

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)

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.

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.

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

 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.

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.

Phase Equilibria & The Phase Rule

 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

 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

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.
4. A solution of NaCl in water Number of phases = 1
• Examples

 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

 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.
• Examples

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.

 The degrees of freedom or variance of a system is defined as the
minimum number of variables such as:
temperature
pressure
concentration
which must be fixed in order to define the system completely.
Degrees of freedom (or variance)
F = C  P + 2

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.
• Examples

 A phase diagram (Equilibrium Phase Diagram) summarizes the
conditions at which a substance exists as a solid, liquid, or gas.
 OR : It is a “map” of the information about the control of phase
structure of a particular material system.
 The relationships between temperature and the compositions and
the quantities of phases present at equilibrium are represented.

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

 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

 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
Components of a system

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

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

 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 changed
c) Liquid
P =1
So F =2
Two variables (T and P) can be varied independently
and the system will remains a single phase

One-component systems
Phase diagram of water
P(atm)
Critical point
374
1
=100=0O--Triple point
0.006
218
Curve O -C
Sublimation
Deposition
Curve O-A
Vaporization
Condensation
Curve O -B
Melting
Freezing
F = C  P + 2

Phase Diagram of Carbon Dioxide

 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

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).

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

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.

Systems Showing a Decrease in Miscibility with
Rise in Temperature
 A few mixtures, exhibit a lower critical
solution temperature (low CST), e.g.
triethylamine plus water. The miscibility
with in temperature.

Systems Showing Upper and Lower CSTs
The miscibility with temp.
a certain temperature miscibility
starts to again with further in
temperature.
Closed-phase diagram, i.e.
nicotine-water system.

A :salol B: thymol
53%
Two component system containing solid
and liquid phase (Eutectic Mixtures)

 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

Triangular Diagrams for three – component
systems
Three component system

Birzeit University Physical Pharmacy PHAR 323 Dr. Hani
Shtaya

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
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State of matter (Physical Pharmacy)

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