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Diffusion Parameters

Presented to: Presented by:

Dr. Yasmin Sultana mam Sameea Ahmed Khan


I Sem


 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

 Free diffusion of the substance through liquids, solids and the
membranes are f special interest in designing of a dosage

 Studying the diffusion parameters will help us to understand
the PERMEATION AND DISTRIBUTION of drug molecules in
living systems.


General representation of drug


The need to study diffusion

 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

 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= 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

Driving force Example

Concentration Passive diffusion

Pressure Osmotic drug release

Temperature lyophilization

Electric potential electrophoresis


Techniques for determination of
 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


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

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


 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-



 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