Diffusion

							         Diffusion
          Dr. Sakina Sultana
  Ph.D (King’s College London. UK
    M.S (U-SA, South Australia)
            M.Pharm (DU)
        B.Pharm (Hons.) (DU)
               Proessor
      Department of Pharmacy
     Jahangirnagar University
             Savar, Dhaka
E mail : sultana_s2003@yahoo.co.uk
                          Definition
Diffusion is a spontaneous process. In this process there occurs
transfer of anisotropic materials (matters with the same structural
and diffusional properties in all directions) from a region of higher
conc. to a region of lower conc. through a semi permeable
membrane until equillibrium state is reached. The process is
characteristically selective. For example
- protein molecules, gums, starch can’t undergo diffusion. These
are non diffusible; while particles of colloidal size range exhibiting
Brownian movement undergoes diffusion

- movement of solute is unidirectional i.e. in one direction
- movement involves no expenditure of energy and the process is
automatic and slow. Moreover migration occurs in absence of
influence of any external force
- this can give a measure of escaping tendency of solute



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- movement occurs against conc. gradient i.e. from a region of
higher concentration (liquid area adjacent to solid surface) to a
region of lower concentration (liquid area distant to solid surface)
and as such the direction of movement is negative.
- transfer continues unless a state of equillibrium is attained. At this
level conc. grad approaches to zero.
- lastly the process is unlike osmosis and dialysis. Here materials
means solute molecules. So transfer occurs with solute molecules
only.

Note : Osmosis involves the transfer of solvent molecules across a
semi permeable membrane (separating solutions of unequal
concentration) to that side where solution is concentrated. Here
transfer of solvent molecules dilutes the solution.
- In ‘dialysis’ there occurs passage of solvent and solute molecules
in an unequal rate across a semi porous membrane in such a
manner that solvent containing smaller solute molecules are passed
out and solutes of larger dimensions are retained (1).


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Diffusion process
        Boundary
        layer    Solid in bulk
                        Lo conc




   Solid in liquid layer very
   adjacent to the solid i.e.
   boundary layer
   Hi conc




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                     Importance of Diffusion
                       or Purpose of study

Diffusion is a common process that occurs in in - vivo, in vitro even in drug
delivery system.
Diffusion in in –vivo :
In biological system diffusion aids absorption of weak acidic or basic drugs.
In GI tract salicylic acid remains undissociated and is absorbed through bio
membrane. (i.e gastric wall). Actually these bio membranes are not compact
structures. These have pores which are channel like structures. These
structures are un-uniform, tortuous and at random. Through these
networked channels solute molecules pass (on their own) from a higher
conc region to lower conc region and ultimately absorbed and is circulated.
Through circulation ultimately reaches the site of action and drug response
occurs. Orally administered drugs like salicylates (weakly acidic drugs) and
amino pyrine (weakly basic drugs) are absorbed in this manner.Thus
diffusion phenomenon prevails in drug action.

Note that mucous membrane is more permeable to acidic drugs and weakly
basic drug



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                 Importance of Diffusion
                   or Purpose of study
In vivo :
Case 2 : Drug applied topically involves diffusion process. Skin is a
multilayer organ. Skin has several layers of cells, separate
membranes, different cell contents. Drug to be absorped through the
skin needs penetration though them. Among them two factors are
important and these are i. nature of barrier and ii. State of hydration
of skin. Each barrier has its own thickness and offers resistance
against permeation of drug molecule. Here resistance is reciprocal
of permeability co efficient P.
And P = (Diffusion coeff X partition co efficient) / thickness of
membrane
And lastly resistance R = reciprocal of permeability
                                =1/P




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             Importance of Diffusion
               or Purpose of study

In vitro :
Passing of small solutes across ‘gelatuin’ gel and ‘agar
gel’ diffusion occurs. Gelatin or agar is a partial water
soluble agents. So in water these molecules swells up
(here some part of the molcule is soluble, some are not).
Such swelling is due to the formation of 3-D structure
within which water molecules are entrapped in a large
amount. This water fraction is immobile and forms a
continuous phase through which solute molecules
diffuses out. Such passing of solute molecules is
because of formation of conc grad in and outside the
structure.

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                  Importance of Diffusion
                    or Purpose of study
In Pharma field:
In sustained release formulations
the release of drug involves           Q = [d E Cs (2A – E Cs) t] / 
diffusion phenomenon. In the           where
formulation drug is taken inside an
insoluble matrix (e.g. plastic         Q = drug released / unit surface area
resins, waxes, fatty alcohol etc).     D = diffusion co.eff. of drug in elution
As the formulation upon                    media
administration comes in contact        E = porosity of the matrix
with GI fluid then fluid slowly        Cs = drug solubility in elution media
penetrates the pores of tablets
and thee occurs slow release of         (tou) = tortuosity of matrix
solid particles from tablet surface    A = drug conc. In tablet
(erosion) and that constitutes a        = initial loading dose of drug in matrix
conc grad. Diffusion thus occurs
and we can quantify the quantuty
according to the equation



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                           Laws
Experimental evidences              Fick’s 1st law of diffusion
supports      that     mass         If dm = solute mass diffusing in
transfer follows a rule             time dt
which states that amount            A = Cross sectional area
                                    dC = concentration gradient
of solid transferred per            X = space coordinate measured
unit area of a section in           normal to the surface. Then rate
unit time (i.e. flux) is            of transfer of mass per unit
proportional to the conc            area in unit time what is called
grad measured normal to             ‘flux’ will be proportional to the
the section.                        concentration change taking place
This rule is lateron has            along the space normal to the
been expressed by a                 surface.
mathematical model for              If , flux is represented as J
quantification     and the          Then J = rate of transfer of mass per
model is recognized as              unit area in unit time
                                    And rate of transfer of mass per
Fick’s 1st law of diffusion.        unit area in unit time = dm / dt / A

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   So J = dm / dt / A
   i.e. dm / dt / A is  to - dC/dx
   or J  - dc / dx
   i.e. J = - D dc / dx
- = negative sign means that diffusion takes place in the
   direction of decreasing conc.
   D = constant of proportionality
   = diffusion coefficient
   It is because this D is not a constant and is not a fixed
   quantity. It varies with temperature, concentration,
   pressure, solvent properties and chemical nature of the
   diffusant. So D is called as coefficient rather than a
   constant.
   Aulton, pp . 73 and 506

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                                                    The second law of diffusion
    Fick’s 2nd law of diffusion :
                                                    is the polynomial derivation of the first
    Fick’s 1st law gives an emphasis on             law. The second law is
    transport of mass across a barrier                  dc / dt = Dd2C / dx2
    including 3 variables like flux term j,         Here,
    mass term m and space coordinate                dc / dt = rate of change in
    measured normal to the surface x. This          conc. at any time at a
    emphasis has been reduced by replacing          definite location rather
    ‘m ’ by concentration term and
                                                    than the mass diffusing
    minimising the involvement of other
                                                    across a unit area of barrier
    variables. So the law has taken a second
                                                    in unit time.
    form where mass term has been
                                                    Here if conc. term is
    eliminated. This modified expression is
    called Fick’s 2nd law of diffusion.
                                                    expressed in g / cm3 then D
                                                    will be in cm2 /sec
    Aulton pp 19, 73, 506
    Martin pp 324
    Bently pp 119
    Remington pp 700



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            Derivation of 2nd law
During diffusion there occurs a change in
concentration. Such change is
due to the difference in in - flow and out flow across
a particular volume of element. The conc of
diffusant in the volume element changes with time
that is C / t which is the flux or the amount
diffusing changes with distance i.e. J / x in the x
direction where j = flux and x = distance. Or
 C / t = - J / x differentiating the equation with
respect to x it becomes - J / x = D 2C / x2 = C / t
Thus C / t = D 2C / x2 represents 2nd law of
Fick’s occurring along x direction.




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Flux = amount M of material passing through a unit cross section S of a
barrier in unit time t is known as flux and is represented as J.
then j = dM / s.dt
Which in turn is dependent on conc grad. Thus
j = - D dc / dx where x = distance (cm) of movement perpendicular to the
surface of the barrier.

Explanation of diffusion :

Solids or individual particles (which are aniosotropic) when in a at random
motion in a liquid shows diffusion. Here a liquid according to the crystal
lattice theory is postulated to be composed of a number of pseudocrystalline
chambers and inside the chambers there are void spaces. Solids move on
and get into the first chamber and then goes to the next and so on. Thus
diffusion sometimes is visualised as jumping of solid molecules in liquid
chambers one after another




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                     Measurement of D
Porous disc method :
The process involves using a specially made container fitted with a
sintered disc which looks like a funnel and it is filled with a solution.
One end is closed with a stopper. It is now inverted and is dipped in
a solution which is also contained in a beaker. The liquid in the
sintered area is immobile. So only the diffusional force works here
and it is conc grad. After a period of time certain condition will
prevail where conc becomes the same across the disc. Now the rate
of diffusion is determined by using the following equation
m = - DA (C1-C2) (t1 – t2)/ L
where m = solute mass diffused
C1 and C2 = solute conc on either side at time t1 & t2
A = cross section of pores
L = effective length of pores
However A and L are not directly measurable; but A / L can be by
calibrating the cell with a standard solute of known D i.e. KCl

Note : please consult Bently’s book pp 98, 121-122
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     Factors affecting the rate
• D is not a fixed quantuty. It varies withn
   temperature, conc., pressure, solvent
   properties and chemical nature of
   diffusant. So D is called as coefficient than
   a constant and its value is dependent on –
 - sieve like structure of membrane
- pH of gel
- Viscosity of the medium
- Presence of ions
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EXTRAS :
Membranes = a film separating the phases and
material passes by passive, active and facilitated
transport across the membrane (1)
Barrier = the term applies in a more general
sense to the region or regions that offers
resistance to passage of a diffusing material and
the total barrier is the sum of individual
resistances of membranes lying between a
donor and a receptor chamber (1)


1. Physical pharmacy – A Martin. Pp 324.

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