Diffusion

1
Diffusion

• Kausar Ahmad
• Kulliyyah of Pharmacy,IIUM
• http//staff.iiu.edu.my/akausar

2
Contents

• Lecture 1
• Diffusion process
• Lecture 2
• Equations describing diffusion phenomena
• Methods to study diffusion
• Lecture 3
• Factors affecting diffusion process
• Applications

3
Example

• Diffusion plays a key part in the movement of
  oxygen from lungs to blood.
• This is an example of diffusion of gas in liquid.
  

4
Pulmonary gas exchange

• 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.

5
Introduction

• Diffusion occurs in
• Gas
• Liquid
• Solid
• Effusion occurs in gas
• The process by which a gas escapes from its
  container through a tiny hole into an evacuated
  space.

6
The Process of Diffusion
Molecule migration from region of high to low
concentration
Brownian movement of solute molecule
Achieve equilibrium state
7
Passive Diffusion of Ions or Molecules

• The dashed line is a membrane that is permeable
  to the molecules or ions illustrated as red dots.
  
• Initially all of the red dots are within the
  membrane.
• As time passes, there is net diffusion of the red
  dots out of the membrane, following their
  concentration gradient.
• When the concentration of red dots is the same
  inside and outside of the membrane the net
  diffusion ceases.
• However, the red dots still diffuse into and out
  of the membrane, but the rates of the inward and
  outward diffusion are the same resulting in a net
  diffusion of zero.

8
Rate of Diffusion

• Gas gt liquid gt solid
• 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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atmosphere
Mountain Al-Quran 3527
Describe how these pictures can be related to the
diffusion process.
10
Environmental Flow

• The environment demonstrates beautifully the
  abilities of the three states to flow and
  diffuse.
• 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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Diffusion in Polymers

• permeation
• diffusion of small molecules (permeants) through
  a polymer
• polymer self-diffusion.

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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.

13
Effect of polymer crystallinity

• Size effect is strongest for crystalline
  polymers, where the material has a rigid
  structure.
• In elastomers, movement of thepolymer
  molecules can allow free passage of
  the permeating species, giving higher diffusion
  rates which are less dependent on permeant
  size.

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Self Diffusion of Polymers

• Occurs by threading of a molecule along its
  length - a process called reptation by analogy
  with the mechanism that a snake uses to move
  along the ground.
• In the polymer, a defect such as a kink in the
  chain can move at random along the chain, thereby
  driving the molecule through the material.

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Diffusion in liquids

• Diffusion in simple liquids is similar to the
  diffusion of gas molecules as described in
  kinetic theory,
• the mean free path is very short (approximately
  the size of a molecule).
• The lack of a rigid lattice means that individual
  atoms or molecules can move more freely, and
  diffusion in liquids is usually characterised by
  high diffusion rates.

End Lecture 1/3
16

• End of lecture 1 of 3

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Ficks 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 -gt 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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Ficks 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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Einsteins Law of Diffusion

• For 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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Stokes Law

• For spherical particles, friction coefficient is
• f 6??r
• ? viscosity of medium
• r radius of particle

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Stoke-Einstein Law

• Boltzmann 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/ 6??r
• D RT/6N??r

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Measurement of Diffusion

• Porous 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
A
Solvent t2, c2
Path of a particle diffusing through porous disc
A
t1,c2
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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
x

• 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

Solution M0
Gel
x2
t
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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

inhibition of growth zone
filled with antibiotic
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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.
• The protein is a uniporter, transporting one
  substrate across the membrane.
• In facilitated diffusion, the protein allows
  molecules or ions to enter or leave the cell
  moving DOWN their concentration gradient.
• The concentration of molecules or ions
  (illustrated by the red dots) is greater inside
  the cell than outside the cell. Thus, the protein
  carrier allows the red dots to leave, down their
  concentration gradient.
• If the concentration of red dots was higher
  outside of the cell than inside of the cell the
  protein would allow the dots to pass into the
  cell just as easily.

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e.g. 1) Diffusion through Membrane

• Absorption of weakly acidic/basic drugs
• Passive diffusion of un-ionised molecule across
  lipoidal membrane of GIT.

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e.g. 2) Diffusion through membrane

• 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 (MW cutoff point 50,000).
• 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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e.g. 3) Diffusion through membrane

• 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

End Lecture 2 /3
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• End of lecture 2 of 3

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Factors affecting DiffusionFicks First Law
dm/dt -DA(dc/dx), Stoke-Einstein Law D
RT/6N??r

• Area (A)
• 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.
• Concentration gradient (dc/dx)
• As the concentration gradient (difference)
  increases, dM or M increases

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Continue Factors affecting Diffusion

• Time (t)
• As duration increases, dM or M increases,until
  saturation is obtained.
• Distance or thickness (x or L)
• 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.
• Temperature (T)
• As temperature increases,diffusion
  coefficient,D,increases, dM or M increases

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Continue Factors affecting Diffusion

• Frictional coeffiecient (f)
• As f increases, D decreases, dM or M decreases.
• Viscosity (h)
• f ? h and D ? 1/h, as h increases, dM or M
  decreases.
• Particle size (r)
• f ? r and D ? 1/r, as r increases, dM or M
  decreases.
• Pore size or porosity
• As porosity increases, dM or M increases.

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Continue Factors affecting Diffusion

• Tortuosity
• As t increases, dM or M decreases.
• Solute interaction with gel matrix or diffusion
  medium.
• 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

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Continue Factors affecting Diffusion

• 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

• Determine physical parameters of particle
• E.g. D kT/6??r
• Chromatography
• Size exclusion chromatography - separate large
  molecules from small ones
• Sample analysis using HPLC

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Continue Application of Diffusion

• Dialysis
• Isolation of impurities from colloidal particles
• E.g. Removal of low MW water-soluble proteins
  from natural rubber latex, a possible source of
  allergens.
• Isolation of drugs from cream base
• Haemodialysis/purification of blood remove
  small MW metabolic waste product while preserving
  high MW components.

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Continue Application of Diffusion

• Drug release from control-release preparations
• Matrix system
• Coating system opacifier, taste-masking,
  control-release
• Transdermal system
• Reservoir system
• Matrix system control-release

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Continue Application of Diffusion

• Drug release from ointment/cream
• Gastro intestinal absorption of drugs
• Drugs pass through membrane can be either
  active or passive transport
• Passive transport simple diffusion driven by
  differences in drug concentration on the two
  sides of the membrane animation

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Continue Application of Diffusion

• Transcorneal permeation
• Permeability coefficient for undissociated drugs
• Percutaneous absorption passage through skin
• 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
• Buccal absorption
• Suppository (bioadhesive)

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Lateral Diffusion of Proteins

• The cell is gray.
• The green dots indicate fluorescently labeled
  antibodies which have bound to proteins on the
  surface of the cell.
• The green dots move across the surface of the
  cell.
• A tiny but intense laser beam is applied, which
  bleaches the flourescent labels in a small area
  on the surface of the cell.
• This photobleaching produces a patch of unlabeled
  cell surface that appears gray.
• With time, however, proteins with fluorescent
  labels that were not bleached diffuse back into
  the area which was bleached and the bleached
  proteins diffuse away.
• The bleached spot disappears and the cell is
  uniformly labeled again.
• This type of experiment has been used to provide
  evidence that proteins are free to diffuse
  laterally across the plane of the membrane.

http//bio.winona.msus.edu/berg/ ANIMTNS/difusean.
htm
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Diffusion of Membrane Proteins

• use antibodies to couple fluorescent dyes to
  specific membrane proteins.
• proteins of human cells were labeled with blue
  dye and the proteins of mouse cells were labeled
  with red dye.
• view cells with a fluorescence microscope and see
  the individual proteins diffusing on the human
  and mouse cells.
• the human and mouse cells were subjected to
  conditions which allowed the cells to fuse
  together forming a living hybrid cell with two
  nuclei.
• the fluorescently labeled proteins of the human
  and mouse cells diffuse across the plane of the
  membrane, intermingling together and completely
  randomizing their distribution in less than one
  hour.

• http//bio.winona.msus.edu/berg/ANIMTNS/Prot-dif.h
  tm

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References

• EA Rawlins, Bentleys Textbook of Pharmaceutics
  8th Ed., Bailliere Tindall (1984) Chapter 8
  Diffusion
• http//bio.winona.msus.edu/berg/ANIMTNS/Prot-dif.h
  tm
• http//cr.middlebury.edu/biology/labbook/diffusion
  //
• http//www.d.umn.edu/sdowning/Membranes/lectureno
  tes.html
• http//www.biologycorner.com/bio1/diffusion.html