Physical Pharmacy: Dosage Forms

Physical Pharmacy Overview

• Physical pharmacy leads to a proper understanding of pharmaceutics and pharmaceutical technology.
• Physical pharmacy integrates math, physics, and chemistry for pharmaceutical dosage form development.
• Enables pharmacists to make rational decisions on the scientific basis concerning the art and technology of making tablets solutions, suspensions, emulsions, etc.
• Provides the basis for understanding the chemical and physical phenomena that govern the in vivo and in vitro actions of pharmaceutical products.

Properties of Pharmaceutical Dosage Forms

• Micromerotics
• Rheology
• Interfacial phenomena

Micromeretics

• Most drug substances are chosen for final product development in powder form.
• Solid-state materials' technical properties are important in formulation and manufacture.
• Compression characteristics are essential for tablet formation.
• Flow properties are essential in capsule and tablet production.
• Micromeritics is the science or study of small particles.
• Powder is made of particles obtained by crashing, grinding, or filtration.

Relevant Micromeritics Parameters

• Particle Shape
• Particle Size
• Particle Size Distribution
• Number of Particles Per Gram
• Surface Area
• Density
• Porosity
• Flowability

Particle Shape

• Particle shapes vary.
• Shapes should be related to a spherical shape for measurements.

Particle Size

• Asymmetry of particles increases the difficulty of expressing size.
• Recourse is made to use equivalent spherical diameter.
• Equivalent spherical diameter relates the size of a particle to the diameter of a sphere having the same surface area, volume, or diameter.

Particle Size Distribution

• A collection of particles is usually polydisperse.
• Knowledge of the size of particles and how many of the same size exist in the sample is necessary.
• Particle size distribution and average particle size for a sample estimate are required.

Classification of Powders by Size

• Microfine (25 micrometers): Injection
• Extra Fine (90 micrometers)
• Very Fine (125 micrometers): Oral Suspension
• Fine (250 micrometers): Capsules
• Semi Fine (500 micrometers)
• Coarse (1250 micrometers): Tablets

Mean Equivalent Diameter

• Arithmetic Mean:
  • d = (d₁ + d₂ +...d₁₂) / (n₁ + N₂ + ...nn)
  • d = Σ(nd) / Σn
  • d stands for diameter
  • n stands for particles in range

Statistical Diameters

• Arithmetic diameters*

• dln 20.56
• dsn 21.68
• dsl 22.87
• dvn 22.79
• dvs 25.17

Graphing Method

• Distribution curve with log (d) on x axis.
• Distribution curve with Diameter (micron) on x axis.

Graphing Method of % Undersize and Oversize

• Graph using nd number.
• Graph using nd3 weight.
• Standard deviation σ= dg(50%) / dg(16%) undersize
• Standard deviation σ = dg(84%) / dg(50%) uppersize

Linearisation of Graphing Method

• Use Log-probit scale.
• Plot probit nd against log d.
• Plot probit nd3 against log d.

Methods for Determining Particle Size

• Optical Microscopy
• Sieving
• Sedimentation
• Electronic Methods

Optic Microscope

• Particles of diameter > 0.2 micron.
• Minimum 300 particles.
• Exhaustive for the eye.
• Photomicrograph is more convenient.
• Eyepiece with micrometer to estimate the size (for particle size between 0.2µm and 100µm)
• Particles are measured along an arbitrarily fixed line across the center.
• Electronic scanner has been developed to avoid visual observation.
• Disadvantages:
  • Diameter is obtained from only 2 dimensions of particle.
  • Around 300 to 500 particles to obtain good estimation.
  • Used when other methods are used because of the presence of agglomerates.

Sieving Method

• Sieving uses decreasing sizes of meshed sieves.
• Limit of 37 micron equivalent to 400 mesh US
• High performance sieves reach 5 micron size.
• Easy to use.

• A defined mass of sample (e.g.100g) is placed on the proper sieve in a mechanical shaker.
• Powder is shaken for a defined period.
• The material that passes filters is collected and weighed.
• Powder is assigned to the opening of the screen. Percent by weight of powder retained is plotted on a probability scale. Arithmetic mean size is plotted with the opening logs of 2 successive screens.
• Ensure reproducible techniques are employed (sieve loading, duration, intensity of agitation).

Undersize Representation of Particles Distribution

Sedimentation Method

• Sedimentation obeys Stocke's law.
• Measured by Stokes' diameter.
• Use aqueous or lipid suspension at 1%.
• Withdraw and weight sediment at regular intervals.

Anderson Apparatus

• 500ml vessel contains a 10 ml pipette sealed into a ground stopper.
• Using a 1 or 2% suspension of particles in a medium containing a deflocculating agent.
• The suspension is introduced into the vessel and brought to the 550 ml mark.
• The stoppered vessel which is shaken to disturb the particles.
• The apparatus is clamped securely in a constant-temperature bath.
• 10ml samples are withdrawn at time intervals, then evaporated and weighed.
• Particle diameter is calculated from Stockes' law.

Stokes' Law

• V = h/t = d² (ρ- ρ₀)g / 18η

  • V = rate of settling
  • η = Liquid viscosity
  • p = Powder density
  • P₀ = Liquid density
  • g = gravity constant
  • h = Fall height
  • t = Fall time

• dst = 18.η.h / (ρ-ρ₀).g.t

• The equation holds exactly for spheres falling freely without hindrance and at a constant rate.

• The diameter obtained is a relative particle size equivalent to that sphere.

• Particles must not be aggregated in suspension using a defloculating agent.

• Stokes' law is applicable if the flow of dispersion medium around particles as it sediments is laminar or streamline.

• The rate of sedimentation of particles must not be so rapid that turburence is set up; indicated by Reynolds number, Re.

Reynolds Number

• Use Reynolds number to correct turbulence effect.
• Re = V.dst.ρ₀ / η
• V = Reη / dst ρ₀ = h / t = ds²t(ρ- ρ₀)g / 18η
• dst = ³√18η²Re / ρ₀(ρ- ρ₀)g
• Stokes' law cannot be used if Re is greater than 0.2 because of turbulance.

Electrical Sensing Zone Method

• Known as the Coulter counter.
• Determines size and quantity of particles.
• This method applies Coulters Principle.
• The instrument operates on the principal that when a particle is suspended in conducting liquid passes through a small orifice, on either side of which are electrodes, a change in electric resistance occurs.
• If a constant voltage is applied, as the particle travels through the orifice, it displaces its own volume of electrolyte.
• This results in an increased resistance between the two electrodes.
• This generates a voltage pulse that is amplified and fed to a pulse height analyzer calibrated in terms of particle size.
• Particles suspended in a weak electrolyte solution are drawn through a small aperture.
• This separates two electrodes between which an electric current flows.
• Voltage applied across the aperture creates a "sensing zone".
• Particles passing through the aperture then displace their own volume of electrolyte, momentarily increasing the impedance of the aperture.
• Changes in impedance create a pulse that is digitally processed in real time.
• Pulse analysis enables a size distribution to be acquired and displayed in volume.
• "Coulter Principle states that the ration of pulse is directly proportional to the temple dimensional volume of the particle that produced it”.

Surface Area of Particles

• Surface area of a solid object is a measure of the total area that the surface of the object occupies.
• Sphere surface
  • Ssphere = πd vs²
• Sphere amount
  • Vsphere = πd vs³ / 6
• Surface
  • Sν = 6πd vs² / πd vs³ = 6 / d vs
• Quantity
  • Sw = 6 / p dvs

Measurement of Surface Area

• Gas Adsorption

Adsorption Method

• Particles with a large specific surface are good adsobents of gases or solutes from solution
• Measurement of volume of gas adsorbed per gram of adsorbent plotted against the pressure of gas at constant temperature
• Adsorbed layer is monomolecular at low pressures and multimolecular at high pressure
• The completion of monolayer of nitrogen may be observed on a graph plotting (P/Po vs volume of gas N₂ adsorbed).
• Measured with a quantasorb device

Quantasorb

• Sw = Vm * AmN / M/ρ = (16,2.10⁻¹⁶ ст²)(6,02.10²³) / 22,414x10⁴ * XVm
• Sw(m²g⁻¹) = 4.35xVm
• N₂ (P) and Helium Vector (Po) measure:
  • M/p=molar volume of the gas
  • N= Avogadro's number
  • Am= area of a single close-packed nitrogen molecule adsorbed as a monolayer on the surface of the particle
  • Sw= specific surface

Air Permeability Method

• Resistance to fluid flow like air through compacted powder is its surface area.
• The greater the area per gram the greater resistance to flow.
• Permeability for a given pressure drop across the plug is inversely proportional to specific surface area.
• Measures to provide means of estimating this parameter.
• A plug of powder has internal surfaces functions of particle area.
• If V is volume of air flowing, d internal diameter, I length of plug, ΔP pressure difference and t seconds, Poiseuille equation may be applied.

Hysteresis

• Hysteresis detects porous materials.
• Open hysteresis loop of an isotherm is due to materials having “ink-bottle" pores.
• The hysteresis surface is proportional to the porosity.
• In a perfect non-porous powder, the two curves would superpose each other.

Density and Porosity

• Volume occupied has:
  • V0=Vi+Ve
    • Intraparticles voids (Vi)
  • Interparticles voids Ve
  • Actual Volume
    • Va = Vr +V0

Types of Rhombohedral and Cubic Packing

• Rhombohedral packing 26% of voids
• Cubic packing 48% of voids
• High presure compaction High pressure compaction 1% of voids

Densities of Particles

• True density: exclusive of the voids and intraparticles pores
• Granule density: the deplacement of mercury does not penetrates into pores at ordinary pressures
• Bulk density: determined from bulk volume and the weight of a dry powder in graduated cylinder

Porosity Calculation

• Va =Vr +Vi +Ve
• Vo =Vi+Ve
• Vg =Vr+Vi
• Porosity of gas
  • Pg = mass / Vg
• Porosity
  • Pr = mass / Vr
• Volume
  • Va =Vr +Vo
  • ε=Va-Vr / Va
  • ε% =100×( 1- (Vr/Va))
  • Va =Vr +Vi +Ve
  • ε granular = 1 - ( Pg /Pr)
  • ε total = 1- Vr/Va= 1-(Pa/Pr)

Flowability of Powders

• Powder may be free flowing or cohesive.
• Factors that increase cohesiveness
  • Particle Shape
  • Surface texture
  • Size
  • Density
  • Static electricity
  • Friction forces
  • Moisture content
• Methods to improve flow
  • Fixed base cone
  • Fixed height cone
  • Rotating cylinder
• NOTE: Small particles less than 10µm are mostly cohesive.
• NOTE: Poor flow may result from the presence of moisture
• NOTE: Powder with high density and low internal porosity tend to be free flowing
• NOTE: Free flow powders are characterized by dustibility
• NOTE: Pooleying powder may cause difficulties to pharmaceutical industry.

Fixed Funnel Method

• tg (α) = h/r
• α =arctg (h/r)
• Used in Determination of angle of repose-

Flow Property Angle

Carr's Index

• Frequently used in pharmaceutics as an indication of powder compressability.
• Calculated by by considering bulk density and tapped density.
• In a free-flowing powder bulk density and tapped density be close in value.

% Compressibility and Flowability

• Formula: Carr Index (CI) =pt- pB / pt * 100

Hausner Ratio and Flow Characteristics

• Hausner Ratio =(Ptapped / Pbulk)
• Compressibility Index = 100 * (Ptapped-Pbulk / Ptapped)

Angle of Repose, Ratio and Properties

Improve Flow Properties

• Granulation is for small particles.
• Glidants may be added to granular powder 1% or less. (magnesium stearate, starch, and talc)
• Control relative humidity.
• Control shape and size of particles.

Liquid Preparations

• Solutions, Dispersions and Emulsions

Solutions Preparations

• Solutions have great importance in many areas of pharmaceutical formulation.
• Solutions are homogeneous one phase systems consisting of two or more components drug.
• The drug is uniformly distributed throughout the preparation.
• Solute is the component which is dispersed as molecules or ions in solvent.
• Solute shall be a liquid or solid.
• Solutions of gases in liquid are characteristic of pressurized aerosols.
• It is essential to understand the properties of solutions and the factors that affect the solubility and the process of dissolution.

Liquid Preparation Manufacturing

• Raw materials with specifications of identity, purity, and uniformity.
• Raw materials should be free from microbial contaminations.
• Preformulation study and additional processing may be necessary for desirable property.
• Active ingredients nature/structure must be known.
• Non Active Ingredients will be added.
• Water is the mostly important constituent in a liquid product.
• Pharmaceutical water, by distillation, ion-exchange, reverse osmosis
• Water for injection (pyrogen free and sterile), de-ionized water.
• Non-aqueous solutions: alcohols, polyhydric alcohols, fixed oil of vegetable oils (fatty esters of glycerol), liquid paraffin, miscellaneous solvents.

Disperse Systems

• A disperse consists of one component disperse phase dispersed as particles or droplets.
• A disperse consists of another component called continuous phase.
• Dispersions in which the size of dispersed particles is within the range of Inm to about 1µm are termed colloidal
• The upper limit of droplets size may exceed 1µm, but the system shows many properties of colloidal systems.
• Dispersions may be coarse such as suspensions, emulsions, aerosols or fine dispersion such as micellar systems

Colloidal Preparation

• Colloids are micro-heterogeneous dispersed systems.
• Dispersed phases’ particles is within the range 1 - 1000 nm.
• The colloids phases cannot be separated undergravity, centrifugal or other forces.
• Dispersed phase of colloids may be separated from the dispersion medium by micro-filtration. Examples:
  • Milk is an emulsion of fat
  • Fog is an aerosol of water micro-droplets in air

Suspensions

• Suspension qualities are dependent on particle and liquid
• Acceptable suspension characteristics
  • Particles with settle slowly, but not rapidly.
  • Settled particles must redisperse readily with agitation
  • Particles shall not form a hard mass
• Thickened products reduce the settling rate but maintain a viscosity
• Suspension must remain homogenous for proper time

Emulsions

• When two immiscible liquids are mechanically agitated
• Both phases initially tend to form droplets.
• When agitation is stopped the drops quickly coalesce and liquids separate.
• Addition of an emulsifier increases the droplets.
• Internal disperse discontinuous phase is surrounded by external continuous phase.
• Most emulsions droplets have a diameter of 0.1 -100 μm.
• An emulsifier stabilizes the droplet form globules internal phase, with both hydrophilic and hydrophobic portions.
• Droplets determine the emulsion appearance:
  • Opaque emulsion > usually white (0.25 and 10µm)
  • Less than 120nm is transparent or micellar emulsions (5-20nm)
• Lipids and micelles possess a spherical shape
• Can act like solubilized oils

Rheology of Fluids

• General info on flow of fluids

Objective of Rheology

• Describe the flow and behavior of liquids
• Describe the deformation of solids

Rheologic Properties

• Newtonian Systems
• Non-Newtonian Systems
• Thixotropy
• Viscoelasticity
• Psychorheology
• Applications to Pharmacy
• Rheology is used to describe the flow of liquids and the deformation of solids
• Viscosity: resistance of a fluid to flow
• Rheology has an application in pharmacy in formulation and analysis of pharmaceutical products such as emulsions, pastes, suppositories and tablets coatings
• Rheology is involved in the mixing and packing of materials in containers and their removal prior the use through tubes/needles
• Consistency from fluid to semisolid, to solid can affect patient acceptability, physical stability and biologic availability

Fundamental Rheology Parameters

• Shearing Stress
• Velocity Gradient
• Rate of Shear
• Viscosity
• Fluidity
• Mobility.

Newton's Law of Flow

• Considers a block of liquid consisting of parallel plates of moelcules.
• Includes properties of:
  • Force (F)
  • Are ((A)
  • Velocity (dV)
  • Incremental Distance (dX)
• The bottom layer is considered to be fixed in place.
• The top plane of liquid is moved at a constant velocity, each lower layer with will move with a velocity directly proportional to its distance from the stationary bottom layer.

Newtons law of Systems

• The difference of velocity between two planes of liquid separated by an infinitesimal distance is the velocity gradient or rate of shear.
• The force per unit area required to bring about flow is called the shearing stress.
• The higher the viscosity of a liquid, the greater the force per unit area required to produce a constant rate of shear.

General Rheologic Equation

• t(dyne.cm⁻²) = F/S Shearing stress
• ɛ(s⁻¹) = dV/dX Rate of shear
• τ=f(ε) Rheologic equation

Types of Rheologic Flow

• Newtonian Flow
• Non Turbulent Flow
• Non-Newtonian Flow
• Turbulent Flow
  • Plastic
  • Pseudoplastic
  • Dilatant

Newtonian Bodies Qualities

• A fluid system presents a laminar flow which means a flow without turbulence.
• Laminar flow is movement that is strictly coordinated and stratified without mixing
• Layers flow without exchange of substance from one layer to the other.

Rheological Equation for Newton Systems

• τ=μ.ε
• μ = τ/ε = Dynamic viscosity
• 1p = dyne.s.cm² = pascal.s
• V = μ/ρ =Kinematic viscosity (stokes)
• 1 st = cm²s-1
• Φ= 1/μ =Fluidity NOTE: The rate of shear is directly proportional to the shearing stress

Effect of Temperature on Viscosity

• μ = A.e/RT
• Arrhenius equation where A is a constant depending on the molecular weight and molar volume of the fluid, and Ev is an activation energy required to initiate flow between the molecules
• The Viscosity of a gas increases with temperature but decreases a liquid when temperature is raised.
• Fluidity of a liquid increases with temperature
• The rate of diffusion increases exponentially with temperature

Reynolds's number

• REYNOLDS NUMBER PREDICTS THE LIMIT OF NEWTONIAN BEHAVIOR
• Re = p.d.v/ μ
  • p: Density of the fluid
  • d: Size of the flowing tube
  • v: Flow rate μ: Dynamic viscosity of the flu
• Where Re < 2000 the system shows Newton behavior
• Re > 2000 Non Newton behavior