Diffusion• Diffusion is defined as a process of mass

transfer of individual molecules of a substance • Diffusion is Migration of solute molecules

from higher concentration to lower concentration to achieve equilibrium

• In case of osmosis escaping tendency of solvent molecules is measured

• In case of diffusion escaping tendency of solute molecule is measured

• In pharmacy diffusion through natural barrier or polymeric barrier is important

• membrane is film separating the phases which may be porous or non porous

• Diffusant or permeant orpenetrant is The material that undergoes the transport by passive diffusion

Application • Controlled and sustained release follows

diffusion controlled• Molecular weight of polymer can be

estimated• Transport of drug from GIT can be predicted

through diffusion studies

• Diffusion of drugs into tissues and their excretion through kidney can be studied through diffusion

• Dialysis,micronisation,ultrafiltration,haemodialysis,osmosis use the principle of diffusion

STEADY STATE DIFFUSION

• At Steady state - conditions do not vary with time

• In case of diffusion mass transfer remains constant with time OR mass transfer takes place at constant rate through the study and diffusion process is not allowed to attain equilibrium

• If condition vary with time then the system is under unsteady state

Transport cell

• Transport cell is used to study the diffusion• Which consists of donor and receptor

compartment separated by membrane• Permeant dissolved in solvent and placed in

donor compartment• Vehicle is placed in receptor compartment• The permeant get transported in to receptor

comportment through membrane• At steady state mass transfer remains constant

SINK CONDITION

• It is the state in which the concentration in the receptor compartment is maintained at lower level compared to its concentration in the donor compartment

• This can be maintained by connecting receptor compartment to a large reservoir from which solution is reticulated

• It is easy to maintain sink condition than steady state condition due to maintaining constant gradient in donor compartment is difficult

• Rate of mass transfer (dM/dt) expressed as of flux(J)

• Flux (J) is rate of mass transfer across unit surface area of a barrier and mathematically expressed as:

dt

dM

SJ

1

dM = change in mass of material, gS = surface area.cm2d t = change in time.sec

Units for flux are g.cm -2sec -1 OR kg .meter -2sec -1

Flux

Flux is always positive quantity because it increases continuously during process

timeareaatomsJ //

• Fick’s first law states that the flux is directly proportional to the concentration gradient

OR

Combining equation and i.e.

dx

dcJ

flow statesteady in flux

2...dx

dcDJ

dc=change in conc. of material g/cm3.D=diffusion coefficient of a penetrant, cm/sec2.Dx=change in the distance, cm.

Negative sign indicates a decrease in concentrationBut flux is positive quantity

dt

dM

SJ

1

dx

dcDJ

3...dx

dcDS

dt

dM

dx

dcD

dt

dM

SJ

1

Eqn 3 explains Rate of mass transfer as per fick’s first lawWe get

D is effected by temperature, pressure etc hence it is not constant it is coefficient

gradientionconcentrattimeareaatomsJ //

Fick’s I law

Fick’s I law

dx

dcDS

dt

dM

No. of atoms crossing area A

per unit time

Cross-sectional area

Concentration gradient

Mass transport is down the concentration gradient

Diffusion coefficient/ diffusivity

AFlow direction

Application of fick’s first law

• Used to explain drug diffusion across biomembranes with desirable parameters

• Applied in the design of sustained and controlled release systems

It explains the change in conc. at definite location with respect to x , y and z axes(or direction)

Fick’s Second Law ; Non-steady state Diffusion

J x

J y

J z x

y

z

Fick’s second law states that the change in concentration With time in a particular region is proportional to the change In the concentration gradient at that point of time

The concentration i.e. changes with time due to

change in amount or flux i.e. of diffusing

molecules with in the x direction

c

t

c

J

x

J

• The relationship can be expressed w.r.t -x ,y and z as:

x

J

t

c

y

J

t

c

z

J

t

c

Partial derivatives notation used due to concentration is a function of both x or y or z and t

dx

dcDJ

dz

dcDJ

dy

dcDJ

Differentiating above equation w.r.t x ,y and z respectively

2

2

x

CD

x

J

2

2

y

CD

y

J

2

2

z

CD

z

J

and, and, zJ

yJ

xJforequationaboveint

Ct

Ct

Cforngsubstituti

2

2

x

CD

t

C

2

2

y

CD

t

C

2

2

z

CD

t

C

2

2

2

2

2

2

z

C

y

C

x

CD

t

C

Fick’s second law refers to change in concentration of diffusant with time at any distance x i.e. non steady state flow

DIFFUSION CONTROLLED RELEASEHIGUCHI’S EQUATION

• Sustained and controlled release of a drug form a table has been obtained by incorporating the drug in insoluble matrix such as plastic ,resin, wax and fatty alcohol

• In this matrix model ,outside layer of the drug is exposed to the bathing solution

• Then the drug diffuses out of the matrix• The rate of dissolution of drug particle within

the matrix must be faster than that of diffusion rate of drug leaving the matrix

1........20sCdxC

dt

dM

matrix in the drug theof conc saturatedC

matrix in the eunit volumin drug ofamount totalC

drug of depletedbeen hasat th

matrix of zone theof thicknessin the changedx

unit timeper released drug ofamount in the changedM

where

s

0

The rate of release of drugs dispersed in an inert matrix system has been derived by higuchi

2........dtx

CDdM sm

21

2 0 tCCDCM sms

3......2 21

0tCDCM ms

21

ktM

From diffusion theory

Where Dm is diffusion coefficient in the matrix

Equating eqn 1 and 2 ,integrating and solving for x gives

When the amount of drug in excess of saturation concentrationthat is Co>Cs

Eqn 3 indicates that the amount drug released is a function of square root time

OR

Methods and procedures• Two types• A) horizontal transport cell wurester cell Viles chein permeation cell• B) vertical transport cell Aquair and weiner diffusion cell biber

and rhodes cell franz diffusion cell

Horizontal Transport Cell wurester cell

Receptor and donor compartment made of pyrex glass materialAnimal or human skin acts as semi permeable cell and barrier may be supported on a perforated plateDrug sample solution taken in donor compartment and solvent in the receptor compartmentWhole set up placed in constant temperature bath to maintain the temp of 37±0.2The liquid in receptor stirred by using magnetic beads to obtain uniform distribution

vertical Transport Cell

Viles chein skin permeation cellReceptor and donor compartment made of pyrex glass or glass or plexi glass materialAnimal or human skin acts as semi permeable cellThis system used for as in vitro models for drug absorption and used to test drug diffusion from ointments ,transdermal patches etcDrug sample solution taken in donor compartment and solvent in the receptor compartmentWhole set up placed in constant temperature bath to maintain the temp of 37±0.2

The liquid in receptor stirred by using magnetic beads to obtain uniform distribution

Horizontal Transport Cell

Aquair and weiner diffusion cellReceptor and donor compartment made of pyrex glass or plastic materialAnimal or human skin acts as semi permeable cell and barrier may be supported on a perforated plateDrug sample solution taken in upper compartment and solvent in the lower compartmentWhole set up placed in constant temperature bath to maintain the temp of 37±0.2The liquid in receptor stirred by using magnetic beads to obtain uniform distribution

Horizontal Transport Cell biber and rhodes cell

This is three compartment cellTwo Receptor and one donor compartmentSynthetic or isolated biological membrane can be usedDrug sample solution allowed to diffuse from two donor compartment to inner receptor compartment

liquid in receptor stirred by using magnetic beads to obtain uniform distribution

Horizontal Transport Cell scheuplein cell

Receptor and donor compartment made of pyrex glass materialAnimal or human skin acts as semi permeable cell and barrier may be supported on a perforated plateDrug sample solution taken in donor compartment and solvent in the receptor compartmentWhole set up placed in constant temperature bath to maintain the temp of 37±0.2The liquid in receptor stirred by using magnetic beads to obtain uniform distribution

Horizontal Transport Cell franz diffusion cell

modified version of different cell for in-vitro studiesExcised human cell membrane acts as semi permeable membraneAnimal or human skin acts as semi permeable cell and barrier may be supported on a perforated plateDrug sample solution filled in donor compartment and solvent in the receptor compartmentWhole set up placed in constant temperature bath to maintain the temp of 37±0.2

The liquid in receptor stirred by using magnetic beads to obtain uniform distribution

Transport across GI tract

• Most of drugs ,when administered ,have to pass through GI membrane to reach blood• The structure and nature of GI tract decide

the transport of drugs• These barrier are highly complex structure

composed of lipids ,proteins , lipoproteins and polysaccharides and lipoidal in nature

Proteins

Polar heads love water & dissolve.

Non-polar tails hide from water.

Carbohydrate cell markers

Fluid Mosaic Model of the

cell membrane

Types of diffusion • Passive diffusion• Active transport• Facilitated diffusion• pinocytosis

NEXT CHAPTER

RHEOLOGY

Answer any Four QuestionsEach question carries 5 marks

1) List out the method to determine interfacial tension explain any one method

2) Write a note on factors influencing rate of reaction3) What are chelates give its application4) What are adsorption isotherms explain different

types5) Explain chemical degradation by oxidation6) Write a note on size distribution curves7) Explain-how particle sizes are expressed 8) Define and differentiate order and molecularity of a

reaction