DIFFUSION ….

Kausar Ahmad

Kulliyyah of Pharmacy, IIUM

http://staff.iium.edu.my/akausar

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Contents

• Diffusion process

Lecture 1

• Equations describing diffusion phenomena• Methods to study diffusion

Lecture 2

• Factors affecting diffusion process• Applications

Lecture 3

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Introduction

• Gas• Liquid• Solid

Diffusion occurs in

• The process by which a gas escapes from its container through a tiny hole into an evacuated space.

Effusion occurs in gas

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The Process of DiffusionMolecule migration from

region of HIGH to LOW concentration

Brownian movement of

solute molecule

Achieve equilibrium state

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Passive Diffusion of Ions or Molecules

dashed line is a membrane

red dots move out of membrane,

following their concentration gradient.

concentration of red dots inside/outside the same,

net diffusion ceases.

red dots still diffuse into and out of the membrane,

but the rates of the inward /diffusion the same 5

Rate of DiffusionGas > liquid > solide.g. distances between molecules are much shorter in a liquid than in a gas.

Collisions are much more frequent.

Migration becomes lesser.

Thus, diffusion is slower.

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Example

Atmospheric gases mix so well that the 80 km of air closest to Earth has a uniform composition

Much less mixing occurs in the oceans, and the differences in composition at various depths support different species.

Rocky solids intermingle so little that adjacent strata remain separated for millions of years.

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Al-Quran 35:27

Example: Pulmonary gas exchange

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Driven by passive diffusion. Substances move down a concentration

gradient.

Oxygen moves from the alveoli (high oxygen concentration) to the blood (lower oxygen

concentration, due to the continuous consumption of oxygen in the body).

Conversely, carbon dioxide is produced by metabolism and has a higher concentration

in the blood than in the air. Thus.

Diffusion in Polymers

• diffusion of small molecules (permeants)

through a polymer

Permeation

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Permeation through Polymers

Permeant molecule migrates through the

voids between the polymer chains.

Rate of diffusion depends on

the size of the permeant

relative to the gaps between the polymer

molecules.

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Effect of polymer crystallinity Size effect is strongest for crystalline polymers, where the material has a

rigid structure.

I n elastomers , movement o f t he

po l ymer mo lecu les can a l l ow f r ee

passage o f t he pe rmea t i ng spec ies ,

giving higher diffusion rates which are less dependent on permeant size.

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Diffusion in liquids

Similar to diffusion of gas molecules BUT

the mean free path is very short (ca. the

size of a molecule).

Lack rigid lattice. Thus individual

atoms/molecules can move more freely.

Usually high diffusion rates.

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End Lecture 1/3

Fick’s First Law of Diffusion

Amount of substance, dm,

diffusing in x direction,

in time dt,

across an area A,

Is proportional to concentration gradient dc/dx.

Thus, the diffusion rate is:

dm/dt = constant(A)(dc/dx)

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Constant is D, = diffusion coefficient (diffusivity)

Diffusion rate -> dm/dt= -DA(dc/dx)

‘D’ is not constant, varies slightly with concentration

‘D’ can be considered as mean value for concentration range covered

“-ve” because it is in the direction of decreasing concentration

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Fick’s Second Law of Diffusion

The concentration rate of change,

within diffusional field,

at a particular point,

is proportional to

rate of change in concentration gradient.

Dc/dt = D(d2c/dx2)

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Einstein’s Law of DiffusionFor diffusion of colloidal particles,

D = kT/f

f= friction coefficient

k = Boltzmann constant (1.38 x 10-23 JK-1)

T = absolute temperature (K)

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Stoke’s Law

For spherical particles, friction coefficient is:

f = 6r

= viscosity of medium

r = radius of particle

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Stoke-Einstein LawBoltzmann constant, k = R/N

R = gas constant (8.314 JK-1mol-1)N = Avogadro number (6.022 x 1023 mol-1)

From Einstein:D = kT/f

D = kT/ 6rD = RT/6Nr

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Measurement of DiffusionPorous disc method

m = -DA(c1 – c2)(t1 – t2)/L m = amount of solute diffused c1,c2 = solute concentration at either side of the

disc at time t1,t2

A = cross section of pores L= effective length of pores A/L is obtained by calibrating the cell in solute with

known D

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Solution: t1, c1

Path of a particle diffusing through porous disc

Solvent: t2, c2

A

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Limitation of Porous disc method

Calibration of cell with low molecular weight solute may not be valid for high molecular weight solutes. WHY????

Trapped air bubbles in pores.

Adsorption of molecules in pores.

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Diffusion through gels

Mt = Moe(-x2/4Dt)

ln Mt = ln Mo + (-x2/4Dt)

ln Mt = ln Mo - (x2/4Dt)

x2/4Dt = ln Mo - ln Mt

x2/t = 2.303 x 4D(log Mo - log Mt)

A plot of x2 against t gives a straight line,

Slope: 2.303 x 4D(log Mo - log Mt)

D can be calculated

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Solution: M0

Gel

x

x2

t

Continue Diffusion through gels

Applications

Cup plate method of assay of antibiotics Diffusion through agar gels seeded

with test organism Zone of growth inhibition proportional

to antibiotic potency

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Continue Diffusion through gels

Zone of growth inhibition proportional to antibiotic potency

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inhibition of growth zone

filled with antibiotic

Membrane Functions

A. Form selectively permeable

barriers

B. Transport phenomena• 1. Passive diffusion• 2. Mediated transport

• a. facilitated diffusion: carrier/channel proteins

• b. active transport

C. Cell communication and signaling

D. Cell-cell adhesion

and cellular attachment

E. Cell identity and antigenicity F. Conductivity

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Membrane allows separation of

small molecules from

big macromolecules

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Passive Diffusion

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Facilitated Diffusion

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Facilitated Diffusion

This animation illustrates protein mediated, facilitated diffusion out of a cell.

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Example: Diffusion across GIT

Absorption of weakly acidic/basic drugs

Passive diffusion of un-ionised molecule

across lipoidal membrane of GIT.

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Example: Purification by dialysis

Low MW impurities such as electrolytes are separated from colloidal particles.

Cellophane sac (Visking tube) containing the substance is immersed in large amount of water.

Pores of cellophane membrane are large enough for low MW solutes to pass through,but larger ones remain in the tube

Water into which the small solutes diffused, will be changed until the dialysate is free of electrolytes (monitored by change in conductivity).

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Diffusion through membrane

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Water renewed to establish

concentration gradient

Semi-permeable membraneSmall

molecules

Big molecule

Example: Diffusion from Dosage Form

Drugs are incorporated in insoluble matrix e.g. wax, fatty

alcohol, polymer

GIT fluid penetrate the

pores and drug particles are leached out.

The diffusion of drug through the insoluble liquid-filled matrix is achieved via a tortuous path.

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Rate of drug released from one surface of insoluble matrix (Higuchi,1963):

Q = DeCs(2A – eCs)t/t)1/2

Q= amount of drug released per unit area at time, t

D = diffusion coefficient

e = porosity of matrix

Cs = solubility of drug

A = concentration/amount of drug in the tablet

= tortuosity of matrix

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End Lecture 2 /3

Factors affecting DiffusionFick’s First Law: dm/dt= -DA(dc/dx), Stoke-Einstein Law: D = RT/6Nr

• As surface area /cross-sectional area of pores increases,amount of solutes diffused, dM or M,increases.• E.g. amount absorbed in small intestine is higher than

in stomach.

1) Area (A)

• As the concentration gradient (difference) increases, dM or M increases

2) Concentration gradient (dc/dx)

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Continue Factors affecting Diffusion

• As duration increases, dM or M increases,until saturation is obtained.

3) Time (t)

• As distance/thickness increases, dM or M decreases.• E.g. transdermal drug delivery depends on location due to

varying thickness of the skin: thigh, arm, chest, back, sole, palm, back of ear.

4) Distance or thickness (x or L)

• As temperature increases, diffusion coefficient, D,increases, dM or M increases

5) Temperature (T)

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Continue Factors affecting Diffusion

• As f increases, D decreases, dM or M decreases.

6) Frictional coeffiecient (f)

• f h and D 1/h, as h increases, dM or M decreases.

7) Viscosity (h)

• f r and D 1/r, as r increases, dM or M decreases.

8) Particle size (r)

• As porosity increases, dM or M increases.

9) Pore size or porosity

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Continue Factors affecting Diffusion

• As t increases, dM or M decreases.

10) Tortuosity

• Pore size of gel decreases.• Viscosity of liquid within the pores increases.• Affects network structure of gel.• Opposite charge of matrix ionised groups may result in

adsorption,thus retarding diffusion.• E.g. gelatin

11) Solute interaction with gel matrix or diffusion medium.

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Example of a membrane: Gelatin

Contain -NH2 (+) and -COOH (-) groups

pH influences ionisation

In acidic condition (+), gel is positively charged

In alkaline condition (-), gel is negatively charged

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Application of Diffusion

• E.g. D = kT/6rDetermine physical

parameters of particle

• Separation of molecules• Sample analysisChromatography

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Continue Application of Diffusion

• Isolation of impurities from colloidal particles• E.g. Removal of low MW

water-soluble proteins from natural rubber latex, a possible source of allergens

• Haemodialysis/purification of blood – remove small MW metabolic waste product while preserving high MW components.

Dialysis

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Continue Application of Diffusion

• Matrix system• Coating system• Transdermal system

Drug release from control-release preparations

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Continue Application of Diffusion

• Drugs release from carrierDrug release from ointment/cream

• Drugs pass through membraneGastro intestinal

absorption of drugs

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Continue Application of Diffusion

• Permeability coefficient for undissociated drugs

Transcorneal permeation

• Dissolution of drug in its vehicle• Diffusion of solubilised drug (solute) from

vehicle to surface of skin• Penetration of drug through layers of skin

esp. stratum corneum

Percutaneous absorption passage

through skin

• Drugs released from vehicle and absorbed through membraneBuccal absorption

• Drugs released from vehicle and absorbed through membraneSuppository

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Example in research: Lateral Diffusion of Proteins

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Source: http://bio.winona.msus.edu/berg/ANIMTNS/difusean.htm

Example in research:Diffusion of Membrane Proteins

Source: http://bio.winona.msus.edu/berg/ANIMTNS/Prot-dif.htm

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References

Rawlins, E. A. (1984). Bentley’s Textbook of Pharmaceutics 8th Ed.

Bailliere Tindall. Chapter 8

http://bio.winona.msus.edu/berg/ANIMTNS/Prot-dif.htm

http://cr.middlebury.edu/biology/labbook/diffusion//

http://www.d.umn.edu/~sdowning/Membranes/lecturenotes.html

http://www.biologycorner.com/bio1/diffusion.html#

Thank you to contributors for images used in this presentation.

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