Transcript Physical Pharmacy

Physical Pharmacy
Frank M. Etzler
LECOM
Fall 2012
Introduction
• Instructor Contact Info
– Room A4-354
– 814-860-5184
– [email protected]
• Exams
– 2 Exams (100 pts ea.)
– 1 Final Exam (100 pts)
• Classroom conduct
– Distractions from cell phones, computers, newspapers, etc. are
disrespectful to the instructor and your classmates.
Textbook
Suggested Reading
Purpose
• Provide a basic knowledge of physical pharmacy,
pharmaceutics and biopharmaceutical principles as they apply
to the development and assessment of various types of drug
delivery systems .
• Develop critical thinking and problem solving required to
address related to dosage form design and effective use.
• Acquire technical vocabulary to discuss pharmaceutical
problems.
Physical Pharmacy Fall 2012
REVIEW OF BASIC CONCEPTS
Greek Alphabet
It is expected that you will be familiar with the Greek alphabet used in mathematics.
Review of Basic Concepts
SI Units (International System of Units)
Base Units
Name
Symbol
Quantity
Symbol
meter
m
Length
l
kilogram
kg
Mass
m
second
s
Time
t
kelvin
K
Thermodynamic
temperature
T
mole
mol
Amount of
substance
n
ampere
A
Electric current
I
candela
cd
Luminous
Intensity
lv
N.B. Names are not
capitalized. Symbols
are capitalized only
for units named after
a person.
All other units are
derived from these
base units.
Review of Basic Concepts
SI Units (International System of Units)
Prefixes
Prefix
Factor
Prefix
Factor
c centi
10-2
k kilo
103
m mili
10-3
M mega
106
µ micro
10-6
G giga
109
n nano
10-9
T Tera
1012
p pico
10-12
Review of Basic Concepts
SI Units (International System of Units)
Derived Quantities
Derived Dimensions
Dimensional Symbol
SI Unit
Area (A)
l2
m2
Volume (V)
l3
m3
Density (ρ)
m l-3
kg m3
Velocity (v)
l t-1
m s-1
Acceleration (a)
l t-2
m s-2
Force (f)
m l t-2 = mA
kg m s-1 = N (newton)
Pressure (p)
m l-1 t-2 = f/A
N m-2 = Pa (Pascal)
Energy (E)
m l2 t2 =Fx
N m = J (Joule)
Unit Conversions
You should be able dimensional analysis in problem solving
Review of Basic Concepts
Logarithms
y  bx
log b y  x
{b  R; b  0; b  1}
Bases of 2, e, and 10 are commonly used.
Changing base of log.
log b x 
log k x
log k b
ln x  log e x 
log10 ( x)
log10 (2.71828)
ln x  2.30259 log10 ( x)
e  2.71828
Review of Basic Concepts
Formulas from Geometry
Perimeter
P  2 r Circle
Surface Area
A  2 r (h  r ) Closed Cylinder
A  4 r 2 Sphere
Volume
V  l  w  h Retangular prism
V   r 2 h Cylinder
4 3
V   r Sphere
3
Review of Basic Concepts
Plotting Data
Linear Plot
Review of Basic Concepts
Plotting Data
y  Ae
bx
 ln y  ln A  bx
Log Graph Paper
Review of Basic Concepts
Significant Figures
• The number of significant figures represent the approximate
error of the measurement.
• In performing a series of calculations it is best to retain at least
an extra digit then rounding appropriately the final answer.
Number
Number of Sig. Figs.
53.
2
530.0
4
0.00053
2
5.0030
5
5.30 x 10-3
3
53,000
unknown
Review of Basic Concepts
Significant Figures
• Addition and Subtraction
– Include only as many figures to the right of the decimal point as the
number with the least such figures.
– 442.78+58.4+2.684 = 503.9
• Multipilcation and Division
– The number with the least number of significant digits determines the
number of significant figures in the result.
– 2.67 x 3.2 = 8.5
• Rounding rule
– If first insignificant digit is less than 5 last significant digit is not
changed; if greater than 5 then last significant digit is increased by 1.
– If exactly five then digit increased if last significant digit is odd.
Review of Basic Concepts
Significant Figures
• Examples.
• 32.451 x 10.02 =325.15902 ~ 325.2
• 4.2500 + 10.1 = 14.3500 ~ 14.3
pH


14




K w   H  OH   10
pH   log  H  
Acid
Neutral
0
7
Base
14
Temperature Dependence of Kw
Water
temperature
Kw / 10−14
pKw
0°C
0.1
14.92
10°C
0.3
14.52
18°C
0.7
14.16
25°C
1.2
13.92
30°C
1.8
13.75
50°C
8.0
13.10
60°C
12.6
12.90
70°C
21.2
12.67
80°C
35
12.46
90°C
53
12.28
100°C
73
12.14
Thermodynamic Principles
Energy, E - Sum of all kinetic and potiential energy in a system
dE   q   w This is the first law of thermodynamics
 q  heat positive if heat absorbed by the system
 w  work positive is work done on the sytem
Enthalpy, H - applies to constant pressure processes
qp  H
H  E  PV
When processes are carried out at constant pressure
some PV work also occurs.
This property is otherwise similar to E.
Thermodynamic Principles
Entropy, S, is a measure of the randomness of a system.
Increasing the the temperature or volume
of the system increases the randomness.
For a phase transition
Str 
H tr
T
Entropy increases on going from solid to liquid to gas.
Free Energy
G  H  TS
or at constant temperature
G   H  T  S
G  0 for a spontaneous process
G  at equlibrium
Free Energy
Consider a reaction
aA + bB
cC + dD
pCc pDd
 G  G  RT ln a b
p A pB
0
For a perfect gas
At equilibrium G = 0
G  G 0  RT ln p
 G 0   RT ln K
For a moles of A
aG  aG  aRT ln p
pCc pDd
K a b
p A pB
and
these presures are equilibrium pressures
G   G products   Greactants
Basic Thermodynamic Relations
G  H  T S
G  0 for spontaneous process
G  0 at equlibrium
dG   SdT  VdP   i dni
i
dA   SdT  PdV   i dni
i
G  A  PV
dH  TdS  PdV   i dni
i
dE  TdS  VdP   i dni
i
H  E  PV
 Gi 
i  

 ni T , P
Basic Thermodynamic Relations
1  V 
T   

V  P T ,n
i
 H 
Cp  

 T  P
1  V 
P  

V  T  P
Things you need to know
•
•
•
•
•
•
•
Recognize greek characters
SI units / perform unit conversions
Logarithms - define and convert between bases
Significant figures
pH and Kw definitions
Define basic thermodynamic functions E,H,S and G
Know the value of ΔG for and equlibrium and spontaneous
process.
• The relation between ΔG and K
Physical Pharmacy Fall 2011
CHAPTER 1 - SOLIDS
Crystal Structure
• All crystalline materials composed of repeating units called
unit cells.
• There are 7 types of primitive unit cells. Some of these cells
can be divided into sub classes bringing the total number of
types of cells to 14.
• Various planes in the crystal are described by Miller indices
Fundamental
Bravis Lattices
The 7 lattice systems
(From least to most
symmetric)
The 14 Bravais Lattices
1. triclinic
(none)
simple
base-centered
simple
base-centered
simple
body-centered
2. monoclinic
(1 diad)
3. orthorhombic
(3 perpendicular diads)
4. rhombohedral (trigonal)
(1 triad)
5. tetragonal
(1 tetrad)
body-centered
facecentered
Fundamental Bravis Lattices
6. hexagonal
(1 hexad)
simple (SC) body-centered (bcc) face-centered (fcc)
7. cubic
(4 triads)
Miller Index
Miller indices are a notation system in crystallography for
planes and directions in crystal (Bravais) lattices.
In particular, a family of lattice planes is determined by three
integers ℓ, m, and n, the Miller indices. They are written
(hkl), and each index denotes a plane orthogonal to a
direction (h, k, l) in the basis of the reciprocal lattice vectors.
By convention, negative integers are written with a bar, as
3 in for −3. The integers are usually written in lowest terms,
i.e. their greatest common divisor should be 1. Miller index
100 represents a plane orthogonal to direction ℓ; index 010
represents a plane orthogonal to direction m, and index 001
represents a plane orthogonal to n.
Miller Index
Miller directions
Miller Index
 1

1
1
,
,


 x intercept y intercept z intercept 
Miller Indices for Crystal
Planes in Cubic Lattice
Crystal Habit
In nature perfect crystals are rare. The faces that develop on a crystal
depend on the space available for the crystals to grow. If crystals grow
into one another or in a restricted environment, it is possible that no
well-formed crystal faces will be developed. However, crystals
sometimes develop certain forms more commonly than others, although
the symmetry may not be readily apparent from these common forms.
The term used to describe general shape of a crystal is habit.
Some Common Crystal Habits
Some common crystal habits are as follows.
•Cubic - cube shapes
•Octahedral - shaped like octahedrons, as described
above
•Tabular - rectangular shapes.
•Equant - a term used to describe minerals that have all
of their boundaries of approximately equal length.
•Fibrous - elongated clusters of fibers.
•Acicular - long, slender crystals.
•Prismatic - abundance of prism faces.
•Bladed - like a wedge or knife blade
•Dendritic - tree-like growths
•Botryoidal - smooth bulbous shape
Quantitative Methods for Describing Particle
Shape
4 A
Circularity  2 A  Area P  Perimeter
P
4 ( r 2 )
For Circle: Circularity 
1
2
(2 r )
width
Aspect Ratio 
length
Wulff Theorem
G    i Aj
j
• Crystal shape is determined by minimizing the ΔG for forming
the crystal faces. This is done by adjusting areas of the faces to
minimize ΔG
• The shape can be influenced by degree of saturation, solvent,
and adsorption of surfactants or other substances on crystal
surfaces.
What is Particle Size?
r
The size of a sphere can be described by a single number, r
What is Particle Size?
Irregular Particles
Size no longer described by single number.
Equivalent sphere diameter used to describe size.
Equivalent sphere diameters may be based on volume, surface area,
mass or linear dimension.
Various calculated equivalent diameters are only equal for spheres
These diameters differ to a greater degree when the particle shape
deviates more from that of a sphere.
Comparison of Various Measures of
Particle Size
Shape
1x1x1
da
dp
dsa
dv
da = projected area
2x1x0.5
0.56
0.63
0.69
0.62
1x1x10
0.8
0.96
0.75
0.62
dp= perimeter
dv = volume (mass)
1.78
3.51
1.83
1.34
1x1x20
10x10x1
2.52
6.68
1.83
1.68
dsa = surface area
5.64
6.37
4.37
2.88
Presentation of Particle Size Data
1
0.4
Number
Volume
Surface Area
0.8
P(d'<d)
Probability
0.3
0.2
0.6
0.4
0.1
0.2
0
0.1
1
10
Particle Diameter
100
0
0.1
1
10
Particle Diameter
Data can be presented as number, volume(mass) or surface area distributions
Data can be presented as histogram, cumulative or differential distribution
100
Particle Size Analysis
• Particle size is expressed as an equivalent spherical diameter.
• There a number of different ways to calculate equivalent
diameters each giving a different result.
• Particle size distributions may be number, surface area or
volume (mass) weighted.
• Various methods for determining particle size exist. These are
divided into two classes ensemble methods (e.g. sieves, light
scattering) and number counting methods ( e.g. microscopy)
• When comparing particle sizes the same type of distribution
and method must be used.
Pharmaceutical Importance of
Particle Size and Shape
• Particle size and shape influence a number of parmaceutical
processes.
–
–
–
–
Powder flow (smaller size worse flow)
Aerosolization (dry powder inhalers)
Dissolution (small size better)
Mixing and blending.
Crystal Forms and Polymorphism
Polymorphism – The ability of a solid to exist with more than one
crystal structure. (e.g. ROY)
Pseudopolymorphs- hydrates or solvates that have their own
crystal structure.
Allotropes – solid chemical elements which exist in different
crystalline forms. ( diamond, graphite and fullerenes are
allotropes of carbon)
Crystal Forms and Polymorphism
• Other crystal forms
– Salts ( often exhibit improved solubility)
– co-crystals - crystalline solids composed of at least two components
that form a unique crystal structure. Salts differ from cocrystals in the
complete proton transfer occurs in the case of salts.
Factors Affecting Which Polymorph is Formed
• Various factors affect which polymorph is formed.
• These factors include:
–
–
–
–
–
Choice of solvent
Level of supersaturation
Presence of impurities
Temperature
Stirring conditions.
Pharmaceutical Importance of Polymorphism
• Polymorphs have different properties including melting point and
solubility, dissolution rate, bioavailability and mechanical
properties. The most stable polymorph has the lowest solubility.
• Upon storage or handling a polymorph may convert to another form.
• Polymorphic forms are patentable.
• A polymorph initially formed may dissappear and never again be
made in a given facility. If this occurs after production starts a
product may have to be withdrawn.
Surface Free Energy (Surface Tension)
G
s
G I
F
 G J
HA K
T ,P
• Surface free energy is the extra free energy resulting from
creation of a surface.
• When liquids are studied surface free energy is referred to as
surface tension.
Contact Angle, Wettability and Young’s Equation
Young’s Equation:
 SV   SL   LV cos( )
  0o completely wettable
  90o not wettable
Young’s eqn. relates surface free energies to contact angle.
Spreading and Surface Free Energy
F
G I
G J
HA K
B
 SB / A   A   B  
AB
Area
• Spreading of a liquid B over a surface A is spontaneous if the
spreading coefficient, SB/A , is positive.
• γAB is called the interfacial tension between A and B.
Zisman Critical Surface Tension
cos()=1
cos ()
1
0.5
A Zisman Plot.
The critical surface tension is found
where the linear fit to the data
intersects and is about 26 mN/m
in this instance.
0
c = L
-0.5
20
30
40
50
60
L (mN/m)
70
80
Zisman Critical Surface Tensions of Polymers
γc
mN/m
Surface Type
Polyhexaflouropropylene
16.2
flourocarbon
Polytetraflouroethylene
18.5
flourocarbon
Polyethylene
31
hydrocarbon
Polystyrene
33
hydrocarbon
Poly(vinyl alcohol)
37
Polar groups
Poly(ethylene
teretphhalate)
43
Polar groups
Poly(hexamethylene
adipamide)
46
Polar groups
Polymer
W.A. Zisnan, in Contact Angle Wettability and Adhesion, American Chem. Soc., Washington , DC 1964
Washburn Equation
d l r L cos( )
v

dt
4l
• The Washburn equation describes the penetration of liquid into
cylindrical pores.
• Critical variables are liquid viscosity and contact angle.
dl
 0 if   90
dt
dl
and
 0 if   90
dt
Poor wetting prevents liquids from penetrating into porous media.
Washburn Equation
High contact angle thus no
liquid penetration
Water Drop
Hydrophobic Sand
Some Pharmaceutical Consequences of Wetting
• Good wetting is required for dispersion of powders in liquid
media and for the penetration of liquid into tablets.
• Wetting problems can often be solved by the inclusion of
surfactants into formulations.
• Surface free energies of particles along with the mechanical
properties of the particles determines the hardness of tablets.
• Adhesion of powders is in part influenced by surface free
energy.
Noyes-Whitney Equation and Dissolution
dm DA(Cs  C )

dt
L
dm
 rate of dissolution
dt
A  surface area of solid
C  concentration of material in bulk media
Cs  saturation soubility of material
D  Diffusion Coffecient
L  Diffusion layer thickness.
Noyes-Whitney Equation and Dissolution
C
L
L
Cs
C
Factors Affecting Dissolution Rate
• Increasing viscosity of medium decreases diffusion coefficient
and decreases dissolution rate.
• Decreasing particle size increases surface area and increases
dissolution rate.
• Increasing agitation decreases L and increases dissolution rate
• Cs can be changed by changes in pH for a weak electrolyte.
What you need to know
•
•
•
•
•
Recognize 7 types of unit cells.
Miller indices – identify crystal planes for cubic lattice
Crystal habit –factors affecting
Particle size – volume and number weighting.
Crystal forms –polymorphs, pseudopolymorphs, allotropes,
salts, co-crystals
• Contact angle – Zisman critical surface tension, Washburn
equation. Wulff theorem
• Noyes-Whitney equation – factors affecting dissolution rate.