Physical Pharmacy

Frank M. EtzlerLECOM Fall 2012

Introduction

• Instructor Contact Info– Room A4-354– 814-860-5184– fetzler@lecom.edu

• 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.

REVIEW OF BASIC CONCEPTSPhysical Pharmacy Fall 2012

Greek Alphabet

It is expected that you will be familiar with the Greek alphabet used in mathematics.

Review of Basic ConceptsSI Units (International System of Units)

Base UnitsName Symbol Quantity Symbol

meter m Length lkilogram kg Mass msecond s Time tkelvin K Thermodynamic

temperatureT

mole mol Amount of substance

n

ampere A Electric current Icandela 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 ConceptsSI Units (International System of Units)

Prefixes

Prefix Factor Prefix Factorc 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 ConceptsSI Units (International System of Units)

Derived QuantitiesDerived 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

3

3 3

1000.900 900.1

1000.831 831.1

1000 100985. 0.9851 1

mgg mgg

gmg gmg

kg g cm gmm kg m cm

You should be able dimensional analysis in problem solving

Review of Basic ConceptsLogarithms

10

10

10

log { ; 0; 1}

Bases of 2, , and 10 are commonly used.Changing base of log.

logloglog

log ( )ln log e 2.71828log (2.71828)

ln 2.30259log ( )

x

b

kb

k

e

y b

y x b R b b

e

xxb

xx x

x x

Review of Basic ConceptsFormulas from Geometry

2

2

3

2 Circle

2 ( ) Closed Cylinder

4

Perimeter

Surface Area

V Sphere

Retangular prism

Cylinder4 Sphere3

olume

P r

A r h r

A r

V l w h

V r h

V r

Review of Basic ConceptsPlotting Data

Linear Plot

Review of Basic ConceptsPlotting Data

ln lnbxy Ae y A bx

Log Graph Paper

Review of Basic ConceptsSignificant 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 ConceptsSignificant 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 ConceptsSignificant Figures

• Examples.

• 32.451 x 10.02 =325.15902 ~ 325.2

• 4.2500 + 10.1 = 14.3500 ~ 14.3

pH1410

log

wK H OH

pH H

0 14

Acid Base

7

Neutral

Temperature Dependence of Kw

Water temperature Kw / 10−14 pKw

0°C 0.1 14.9210°C 0.3 14.5218°C 0.7 14.1625°C 1.2 13.9230°C 1.8 13.7550°C 8.0 13.1060°C 12.6 12.9070°C 21.2 12.6780°C 35 12.4690°C 53 12.28100°C 73 12.14

Thermodynamic Principles

Energy, E - Sum of all kinetic and potiential energy in a system This is the first law of thermodynamics

positive if heat absorbed by the system positive is work done on t

dE q wq heatw work

he sytem

Enthalpy, H - applies to constant pressure processes

When processes are carried out at constant pressure some PV work also occurs.This property is otherwise similar to E.

pq H

H E PV

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

Entropy increases on going from s

trtr

HST

olid to liquid to gas.

Free Energy

or at constant temperature

0 for a spontaneous process at equlibrium

G H TS

G H T S

GG

Free Energy

0

reactants

Consider a reactionaA + bB cC + dDFor a perfect gas

lnFor a moles of A

ln and

products

G G RT p

aG aG aRT p

G G G

0

0

ln

At equilibrium G = 0

ln

these presures are equilibrium pressures

c dC Da bA B

c dC Da bA B

p pG G RT

p p

G RT K

p pK

p p

Basic Thermodynamic Relations

0 for spontaneous process0 at equlibrium

i ii

i ii

i ii

i ii

G H T SGG

dG SdT VdP dn

dA SdT PdV dn

G A PV

dH TdS PdV dn

dE TdS VdP dn

H E PV

,

ii

i T P

Gn

Basic Thermodynamic Relations

,

1

1

i

TT n

pP

PP

VV P

HCT

VV T

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

CHAPTER 1 - SOLIDSPhysical Pharmacy Fall 2011

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)

2. monoclinic (1 diad)

simple base-centered

3. orthorhombic (3 perpendicular diads)

simple base-centered body-centered face-centered

4. rhombohedral (trigonal) (1 triad)

5. tetragonal (1 tetrad)

simple body-centered

Fundamental Bravis Lattices

6. hexagonal (1 hexad)

7. cubic (4 triads)

simple (SC) body-centered (bcc) face-centered (fcc)

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 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.

3

Miller Index

Miller directions

Miller Index

1 1 1, , intercept intercept interceptx y z

Miller Indices for Crystal Planes in Cubic Lattice

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

{110}

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

2

2

2

4

4 ( )For Circle: 1(2 )

ACircularity A Area P PerimeterP

rCircularityr

widthAspect Ratiolength

Wulff Theorem

• 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.

i jj

G A

What is Particle Size?

The size of a sphere can be described by a single number, r

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 2x1x0.5 1x1x10 1x1x20 10x10x1

da 0.56 0.8 1.78 2.52 5.64dp 0.63 0.96 3.51 6.68 6.37dsa 0.69 0.75 1.83 1.83 4.37dv 0.62 0.62 1.34 1.68 2.88

da = projected area dp= perimeter dsa = surface area

dv = volume (mass)

Presentation of Particle Size Data

0 .1 1 1 0 1 0 0P a rtic le D iam e te r

0

0 .1

0 .2

0 .3

0 .4

Prob

abili

ty

N u m b e rV o lu m eS u rfa ce A re a

0 .1 1 1 0 1 0 0P a rt ic le D ia m e te r

0

0 .2

0 .4

0 .6

0 .8

1

P(d'

<d)

Data can be presented as number, volume(mass) or surface area distributions

Data can be presented as histogram, cumulative or differential distribution

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)

• 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.

G GA

s

T P

FHG IKJ

,

Contact Angle, Wettability and Young’s Equation

SV SL LV cos( )Young’s Equation:

0 completely wettable 90 not wettableo o Young’s eqn. relates surface free energies to contact angle.

Spreading and Surface Free Energy

• 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.

FHG IKJ

GA

SB Area

B A A B AB/

Zisman Critical Surface Tension

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.

2 0 3 0 4 0 5 0 6 0 7 0 8 0L (m N /m )

-0 .5

0

0 .5

1

cos ()

co s ()= 1

c = L

Zisman Critical Surface Tensions of PolymersPolymer γc

mN/mSurface Type

Polyhexaflouropropylene 16.2 flourocarbonPolytetraflouroethylene 18.5 flourocarbonPolyethylene 31 hydrocarbonPolystyrene 33 hydrocarbonPoly(vinyl alcohol) 37 Polar groupsPoly(ethylene teretphhalate)

43 Polar groups

Poly(hexamethylene adipamide)

46 Polar groups

W.A. Zisnan, in Contact Angle Wettability and Adhesion, American Chem. Soc., Washington , DC 1964

Washburn Equation

• The Washburn equation describes the penetration of liquid into cylindrical pores.

• Critical variables are liquid viscosity and contact angle.

v d ld t

rl

L

cos( )4

0 if 90 and 0 if 90dl dldt dt

Poor wetting prevents liquids from penetrating into porous media.

Washburn Equation

Hydrophobic Sand

Water Drop

High contact angle thus no liquid penetration

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

( )

rate of dissolution

surface area of solid concentration of material in bulk media saturation soubility of material

Diffusion Coffecient Diffusion layer thickness.

s

s

DA C Cdmdt L

dmdtACCDL

Noyes-Whitney Equation and Dissolution

L

C

CCs

L

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.