Theories of dissolution

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THEORIES OF

DISSOLUTIONPRESENTED BY:

SAMIKSHA SAWANT M.PHARM(IP), 1st SEM

GUIDED BY : SHRUTI SHRIKHANDE

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WHAT IS DISSOLUTION?

WHAT IS DISSOLUTION?

Dissolution is a process in which a solid substance solubilises in a given solvent i.e mass transfer from the solid surface to the liquid phase

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WHAT IS DISSOLUTION RATE?

It is defined as the amount of solute dissolved in a given solvent under standard conditions of temperature, pH , solvent composition and constant solid surface area.

Solute-solvent adhesive forces should overcome solute-solute cohesive forces.

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To show that the release of drug from the tablet is close to 100%

To show that batch to batch rate of drug release is uniform

To show that release is equivalent to those batches proven to be bioavailable

WHY DISSOLUTION STUDIES?

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DISINTEGRATION AND DISSOLUTION

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MECHANISMS OF DRUG RELEASE1.) Diffusion method: Molecules intermingle as a result of their

kinetic energy.Based on Fick’s first law of diffusion J= -D(dc/ dx) where, J is the amount of drug passing through the

surface per unit timeD is the diffusion coefficientdc/dx is the concentration gradient

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2.) Zero order release:• Zero order refers to the process of constant drug release from a drug

delivery device such as oral osmotic tablets, transdermal systems, matrix tablets with low soluble drugs

Drug release from pharmaceutical dosage forms that donot disaggregate and release the drug slowly can be represented by the following equation

W0 – Wt = K .t ------------------- 1 W0 = initial amount of drug in the dosage form.Wt = amount of drug in the pharmaceutical dosage form at time tK = proportionality constant. Dividing this equation by W0 and simplifying ft = K0 .t where ft = 1-(Wt/W0)Ft = fraction of drug dissolved in time t and Ko the zero order release

constant.A graphic of the drug dissolved fraction versus time will be linear

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3.) First order release: If the amount of drug Q is decreasing at a rate that is

proportional to he amount of drug Q remaining ,then the rate of release of drug Q is expressed as

dQ/dt = -k.Q -----------------1Where k is the first order rate constant.Integration of above equation gives, ln Q = -kt + ln Q0 ---------------- 2The above equation is aslo expressed as Q = Q0 e-kt ------------------------ 3Because ln=2.3 log, equation (2) becomes log Q = log Q0 + kt/2.303 ---------------------(4)This is the first order equationA graphic of the logarithm of released amount of drug versus

time will be linear.

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4.) Korsmeyer and Peppas model Also called as Power law

To understand the mechanism of drug release and to compare the release profile differences among these matrix formulations ,the percent drug released time versus time were fitted using this equation

Mt / M∞ = k. tn

Mt / M∞ = percent drug released at time t k= constant incorporating structural and geometrical

characteristics of the sustained release device. n = release exponential which characterizes

mechanism of drug release

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RELEASE EXPONENT

RATE AS A FUNCTION OF

TIME0.5 t raise to -0.5

0.5<n<1 t raise to (n-1)

1 Zero order release

>1 t raise to (n-1)

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THEORIES OF DISSOLUTION

Diffusion layer

model/film theory

Danckwert’s model/surface

renewal theory

Interfacial barrier theory

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DIFFUSION LAYER MODEL/FILM THEORY

The theory is based on absence of any reactive or chemical forces.

It consist of two consecutive steps:1)Formation of stagnant film or diffusion layer

2)Diffusion of soluble solute from the stagnant layer to the bulk of the solution(rate determining step).

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Transport of solute into bulk is slower than solvent-solute

interaction

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dC/dt= dissolution rate of the drugk= dissolution rate constantCs= concentration of drug in the stagnant layerCb= concentration of drug in the bulk of the solution at time t.

Based on Fick’s first law of diffusion:

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Nerst and Brunner modified Noyes-Whitney equation to:

dC/dt =D.A.Kw/o (Cs –Cb)\ v.h dC/dt = dissolution rate of the drug. D = diffusion coefficient of the drug. A = surface area of the dissolving solid Kw/o = water/oil partition coefficient of drug V = volume of dissolution medium h = thickness of stagnant layer (Cs- Cb)= concentration gradient for

diffusion of drugs

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PARAMETERS SYMBOL INFLUENCE ON DRUG DISSOLUTION

Diffusion coefficient D Greater the value, faster is the dissolution rate

Surface area of solid A Greater the surface area, faster the dissolution rate

Water/oil partition coefficient

Kw/o Higher the value, faster the dissolution rate

Concentration gradient Cs-Cb Greater the value, faster the dissolution rate

Thickness of stagnant layer

h More the thickness, lesser is the diffusion and dissolution rate

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Noyes-Whitney equation represents first order dissolution rate process where (Cb-Cs) acts as the driving force .

Dissolution is in non-sink conditions, this is true in case of in-vitro dissolution in limited dissolution medium.

Dissolution slows down as concentration in the bulk builds up.

In-vivo dissolution is always faster than in-vitro dissolution, as Cb=0.

No concentration build up, hence no retarding force on dissolution rate.

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Cs>>Cb, thus sink conditions are maintained.

Equation reduces to dC/dt =K

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IN VITRO-IN VIVO CORRELATIONS

The relation can be improved by:Bathing the dissolving solid in fresh

solvent.Increasing the volume of dissolution fluid.Partitioning dissolved drug from aqueous

phase to organic phase.Adding water-miscible solvent to the

dissolution fluid.Adding adsorbent to remove the dissolved

drug.

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Noyes-Whitney equation assumes that the surface area of the dissolving solid remains constant which is practically impossible for dissolving solids.

To account for particle size decrease and change in surface area, Hixson and Crowell’s c Equation:

w01/3 – w1/3 = k .t

W=mass of drug remaining to be dissolved at time t

k=dissolution rate constant W =original mass of the drug

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Hixon-crowell cube root law Hixon Crowell cube root equation for dissolution kinetics is based on assumption that:

a) Dissolution occurs normal to the surface of the solute particles

b) Agitation is uniform all over the exposed surfaces and there is no stagnation.

c) The particle of solute retains its geometric shape The particle (sphere) has a radius r and surface area 4Π r2

Through dissolution the radius is reduced by dr and the infinitesimal volume of section lost is

dV = 4Π r2 . dr ------------------(1) For N such particles, the volume loss is dV = 4N Π r2 dr ----------------------------(2) The surface of N particles is S = 4 N Π r2 -----------------------------(3) Now ,the infinitesimal weight change as represented by he Noyes –

Whitney law ,equation is dW = k.S.Cs.dt ---------------------------(4) The drugs density is multiplied by the infinitesimal volume change

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ρ.dV, can be set equal to dW, ρ.dV = k.S.Cs.dt --------------------------- (5)Equations (2) and (3) are substituted into equation (5) , to yield -4 ρ N Π r2 . dr = 4 N Π r2 . K .Cs .dt -------------(6)Equation 6 is divided through by 4 N Π r2 to give - ρ . Dr = k Cs.dt -------------------------(7) Integration with r = ro at t= 0produces the expression r = ro – kCs .t/ ρ -----------------------------(8)The radius of spherical particles can be replaced by the weight

of N particles by using the relationship of volume of sphere W = N ρ(Π/6)d3 ----------------------------(9)Taking cube root of the equation (9) yield, W 1/3 = [ N ρ(Π/6)]1/3. d. ----------------------------(10) The diameter d from equation (10) ,is substituted for 2r into

equation 8 to give

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W01/3 - W1/3 =k t ------------------(11)

Where k = [ N ρ(Π/6)]1/3.2 k Cs/ρ.Wo is the original weight of drug particles .Equation (11) is known as Hixson- Crowell

cube root law ,and k is the cube root dissolution rate constant.

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DANCKWERT’S MODEL

Disapproved the existence of a stagnant layer at solid- liquid interface.

There exist turbulence in the dissolution medium at the solid-liquid interface.

Mass of eddies or packets reach the solid- liquid interface due to eddy currents.

Absorb solute by diffusion and carry it back into bulk solution.

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DANCKWERT’S MODEL

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DANCKWERT’S MODEL

As the packets are continuously replaced with new packets of fresh solvent, the concentration at interface never reaches Cs.

Since solvent packets are exposed to new solid surface each time, the theory is also known as surface renewal theory.

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DANCKWERT’S MODEL

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DANCKWERT’S MODEL

The Danckwert model is expressed by the equation:

V.dC/dT= dm/dt = A ( Cs-Cb). (ү.D)1/2

Where, m=mass of solid dissolved y= rate of surface renewal

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Diffusion and Danckwert’s model is based on two assumptions:

The rate limiting steps that controls dissolution is the mass transport.

Solid- solution equilibrium is achieved at the solid- liquid interface

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INTERFACIAL BARRIER MODEL

In this model it is assumed that the reaction at solid

surface is not instantaneous i.e. the reaction at solid

surface and its diffusion across the interface is slower than diffusion across liquid film.

Therefore the rate of solubility of solid in liquid film becomes

the rate limiting than the diffusion of dissolved

molecules

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In the interfacial barrier model, it is assumed that the reaction at the solid/liquid interface is not instantaneous due to a high activation free energy barrier which has to be surmounted before the solid can dissolve.

The rate of diffusion in the static layer is relatively fast in comparison with the surmounting of the energy barrier, which therefore becomes rate limiting in the dissolution process.

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Equation : dm/dt = Ki (Cs – Cb) Where Ki = effective interfacial transport rate

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CONCLUSIONThe Quantitative interpretation of the

values obtained in dissolution assays is easier using mathematical equations which describe the release profile in function of some parameters related with the pharmaceutical dosage forms

As dissolution is an important qc procedure, it is necessary to understand the basic mechanisms and theories of the process

Only then its easier to interpret the results and understand IVIVC

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REFERENCESTheories of dissolution by Oluwatoyin A

Odeku(http://www.pharmainfo.net/tablet-evaluation-tests/dissolution/theories-dissolution)

D.M.Brahmankar, Biopharmaceutics and pharmacokinetics- A Treatise, Vallabh Prakashan, pg no. 20-31

Leon Shargel, Applied Biopharmaceutics and Pharmacokinetics, 4th edition, pg no. 132-136

Shobha Rani R. Hiremath, Textbook of Biopharmaceutics and Pharmacokinetics

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REFERENCESMichael E. Alton, Alton’s Pharmaceutics- The

design and manufacturing of medicines” , pg no. 21-22

Dr. H.P. Tipnis and Dr. Amrita Bajaj, Principle and application of Biopharmaceutics and Pharmacokinetics

Remington, The science and practice of Pharmacy, 21st edition, volume 1

www.google images.com

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Theories of dissolution