Diffusion Parameters

Presented to: Presented by:

Dr. Yasmin Sultana mam Sameea Ahmed Khan

M.Pharm,Pharmaceutics

I Sem

Definition-

Diffusion is a process of the mass transfer of the individual

molecule of a substance brought about by random molecular

motion associated with a driving force like concentration

gradient i.e. generally from higher concentration to lower

concentration.

Free diffusion of the substance through liquids, solids and the

membranes are f special interest in designing of a dosage

form.

Studying the diffusion parameters will help us to understand

the PERMEATION AND DISTRIBUTION of drug molecules in

living systems.

General representation of drug

diffusion-

The need to study diffusion

parameters:

In controlled release systems.

Whether or not the tablet matrix disintegrates, the rate

at which solvent penetrates the matrix influences in

terms of the drug release rate as well as the total drug

released

The solvent/water penetration rate into the tablet often

correlates well with the disintegration rate

For ex- A swelling gel layer, formed during the

penetration and acting as a diffusion barrier for active

ingredients, may also affect their dissolution rate.

Fick’s Law of Diffusion-

The amount of material, M of materialflowing through aa unit

cross section, S, of a barrier in a unit time, t, is known as flux,

j;

J= dM/ (S.dt)

The flux, in unit turn, is proportional to the concentration

gradient, dC/dx;

J= -D. (dC/dx)

Where D is the diffusion coefficient in cm2/sec.

C is the concentration in g/cm3

D is affected by the concentration ,temp., pressure, solvent

property, and chemical nature of diffusant.

• If diffusion is the rate determining step, then we can use

Fick’s first law of diffusion to describe the overall process.

Fick’s Second law of diffusion-

Fick’s second law of diffusion forms the basis for

most mathematical models of diffusion processes.

One often wants to examine the rate of change of

mass transport that emphasizes the change in

concentration with time at a definite location rather

than the mass diffusing across a unit area of

barrier in unit time is known as fick’s second law.

Fick’s Second law of diffusion-

Driving forces that facilitate

diffusion-

Driving force Example

Concentration Passive diffusion

Pressure Osmotic drug release

Temperature lyophilization

Electric potential electrophoresis

Techniques for determination of

diffusion:

A number of experimental techniques have been developed

for diffusion studies in polymers, consisting of two basic

types of investigation:

1. the diffusion front rates

2. the concentration profile measurements.

Time-dependent solvent concentration profiles can provide

more complete information about the diffusion mechanism

but are difficult to obtain and require quite sophisticated and

expensive techniques such as nuclear magnetic resonance

imaging, light and electron microscopy etc.

Ultrasound method offers the possibility of continuous

measurement of both the swelling and eroding fronts.

A newer technique of practical nature for solvent diffusion

tracking is by visualizing the penetration process using digital

video image processing.

it facilitates a fast diffusion rate estimation and comparison

in multiple tablets of different formulations or process

parameters. This technique is especially suitable for

immediate release tablets that show relatively fast solvent

penetration rate. It works well with commonly prepared

tablets (i.e., compressed using a rotary tablet press).

It should be noted, that in some studies, the sorption ability of

tablets is determined by measuring the absorbed

mass M with time t using standard tensiometers. Then, a

velocity constant K is obtained by fitting the experimental

data to the Washburn-like equation.

M*M= k*t

There are several theories/models of the non-Fickian

diffusion that can be used to interpret/fit the experimental

penetration data. One such theory, developed by Thomas

and Windle, recognizes that the kinematics of the penetration

is controlled by the rate at which the polymer structure

rearranges or relaxes due to the solvent moving in.

An alternative approach for describing the penetration

process is that the diffusion rate is mainly controlled by the

resistance of the polymer matrix to the solvent flow, which is

put forward in the molecular sorption model proposed by

Vesely.

This model visualizes the polymer matrix as

a porous media containing voids filled by

the solvent with the molecular interactions

between the polymer and solvent

molecules resulting in an internal pressure,

similar to the capillary pressure.

Thus, the penetrant motion is driven by the

capillary pressure with the contact angle θ,

opposed by the viscous resistance forces.

Diffusion limited model or film

theory-

The first dissolution experiments were conducted by

Noyce and Whitney and found that the dissolution

rate(dC/dt), is a linear function of the difference

between the bulk concentration at time t and the

saturation solubility.

dC/dt= k(Cs-Cb)

Where k is the dissolution rate constant.

Later on, Nernst and Brunner showed that k is a composite

constant being proportional to the diffusion coefficient, D and

the surface area of the dissolving body, S. thus the modified

equation is called as the Nernst and Brunner eq.

dC/ dt=D.S(Cs-Cb) / Vh

where h designates the thickness of the boundary layer and V

is the volume of the dissolution medium.

Diagram representing diffusion

through stagnant layer-

Variables in the Diffusion process-

1. Surface area, A:

The surface area per gram (or per dose) of a solid drug can

be changed by altering the particle size. For example, a cube

3 cm on each side has a surface area of 54 cm2. If this cube

is broken into cubes with sides of 1 cm, the total surface area

is 162 cm2. Actually if we break up the particles by grinding

we will have irregular shapes and even larger surface areas.

Generally as A increases the dissolution rate will also

increase. Improved bioavailability has been observed with

griseofulvin, digoxin, etc.

2. Diffusion layer thickness, h:

This thickness is determined by the agitation in the bulk

solution. In vivo we usually have very little control over this

parameter. It is important though when we perform in

vitro dissolution studies because we have to control the agitation

rate so that we get similar results in vitro as we would in vivo.

The apparent thickness of the stagnant layer can be reduced

when the drug dissolves into a reactive medium. For example,

with a weakly basic drug in an acidic medium, the drug will react

(ionize) with the diffusing proton (H+) and this will result in an

effective decrease in the thickness of the stagnant layer.

The effective thickness is now h’ not h. Also the bulk

concentration of the drug is effectively zero. For this reason

weak bases will dissolve more quickly in the stomach.

Plot of concentration versus

distance in medium-

3. Diffusion coefficient, D:

The value of D depends on the size of the molecule and the

viscosity of the dissolution medium. Increasing the viscosity

will decrease the diffusion coefficient and thus the dissolution

rate. This could be used to produce a sustained release

effect by including a larger proportion of something like

sucrose or acacia in a tablet formulation.

4.Drug solubility, Cs:

Solubility is another determinant of dissolution rate. As Cs

increases so does the dissolution rate. We can look at ways

of changing the solubility of a drug.

Additional parameters related to

diffusion in DRUG RELEASE-

1. Considering the sink condition, the factor affecting the

apparent rate of the release of the core molecule.

2. the diffusion path length.

3. Molecular collision radius of the diffusing substance.

4. Viscosity of the diffusing environment.

5. Surface area of the dosage form in contact.

6. Concentration difference between the start of the

molecular diffusion and sink condition.

Diffusion in rate controlled drug

delivery systems-

In these systems, the release rate of a drug is determinedby

its diffusion through an inert membrane barrier, usually n

insoluble polymer.

There are 2 types-

1. Reservoir devices

2. Matrix devices

1. RESERVOIR TYPE-

The release is governed by Fick’s first law. Diffusion reservoir

devices are developed using techniques like

microencapsulation and film coating.

1. Diffusion from reservoir type-

2.Diffusion from polymer matrix-

References-

Patricks J., Martins physical pharmacy and pharmaceutical

sciences, 5th edition, Lippincott Williams and Wilkins, New

Delhi,2008, 301-317

Leon Lachman, Lieberman A., Joseph Kanig, The theory and

practice of industrial pharmacy, 3rd edition, Varghese

publishing house,Mumbai, pg-158-159

www.pharmascience.com

www.researchgate.net

www.ncbi.nlm.nih.gov

THANK YOU!