Diffusion v2
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- Diffusion is the spontaneous movement of molecules from a region of higher concentration to lower concentration driven by the concentration gradient until equilibrium is reached. - It plays an important role in processes like drug release from dosage forms, absorption of drugs from the gastrointestinal tract, distribution of drugs in tissues, and excretion of drugs through organs like the kidneys. - Fick's first law quantifies diffusion as being directly proportional to the concentration gradient, while Fick's second law describes how the concentration changes over time at different locations during diffusion. - Steady state diffusion refers to a constant rate of diffusion over time when the concentration gradient remains unchanged, such as in a diffusion cell experiment.
![Fick`s Second Law
• From Ficks first law
• J= -D . dC/dx
• Differentiating wrt x
• - dJ/dx = D d2C/dx2
• But, - dJ/dx = dC/dt
• dC/dt = D d2C/dx2
• Above equation represent diffusion in x
direction only. Extending this to 3
coordinates x y and z
dC/dt = D [d2C/dx2 + d2C/dy2 + d2C/dz2]](https://image.slidesharecdn.com/diffusionv2-200310145108/85/Diffusion-v2-19-320.jpg)
![Permeability
• If membrane separate two compartments of
diffusion cell of cross-sectional area S and
thickness h
• If concentration on donor and receptor
sides are C1 and C2 respectively, Ficks first
law (J= dM/Sdt & dM/dt = DS . dC/dx ) will
become
• J = dM/Sdt
= D [(C1-C2)/h]](https://image.slidesharecdn.com/diffusionv2-200310145108/85/Diffusion-v2-31-320.jpg)
![Permeability (P)
• We know, dM/Sdt = D [(C1-C2)/h]
• dM/dt = DSK (Cd-Cr) /h
• If sink condition hold in receptor Cr = 0
• dM/dt = DSKCd/h = PSCd
• P= DK/h](https://image.slidesharecdn.com/diffusionv2-200310145108/85/Diffusion-v2-34-320.jpg)
Diffusion v2
- 1. Diffusion (Dr.) Mirza Salman Baig Assistant Professor (Pharmaceutics) AIKTC, School of Pharmacy,New Panvel Affiliated to University of Mumbai (INDIA)
- 2. Defination • Diffusion is the processes of mass transfer of molecules of a substance because of random molecular motion (Brownian motion) and associated with driving force such as concentration gradient.
- 3. Diffusion • Diffusion is spontaneous movement of molecules from higher concentration region to lower concentration region till equilibrium is established
- 4. Application • Release of drug from dosageform in diffusion controlled system...SR • Molecular wt of polymer can be estimated • Transport of drug (absorption) from GIT • Diffusion of drug in tissues (distribution) and excretion through kidnies • Dialysis/ Microfiltration/ultrafiltration
- 5. Application Dissolution of drug from • Tablet • Powder • Granules • Ointment • Suppositories
- 6. Diffusion through biological membranes • Dissolution of drug in polymeric membrane then simple molecular diffusion • Drug + Solvent transport across skin • Steriodal molecule with hydrophilic group pass through hair follicles • Diffusant may pass through pores • Diffusion play important role in transport of drug in kidney, brain and liver
- 7. • Diffusion through lipoidal membrane (BBB) is known as transcellular diffusion • Paracellular diffusion occurs through the space between cells • In addition to drugs, nutrients also pass through biological membranes Diffusion through biological membranes
- 8. • Energy dependent carrier mediated diffusion through biological membrane (Active transport) • Energy independent carrier mediated diffusion through biological membrane (Facilitated diffusion) Diffusion through biological membranes
- 9. • Membrane transporters are specialized proteins that facilitate drug transport • Active transport • Facilitated diffusion Diffusion through biological membranes
- 11. • Concentration gradient • Osmotic pressure • Temperature • Electrical potential Driving force for Diffusion
- 12. Measurement of Diffusion • Diffusion of molecules is estimated using diffusion cell • Solute is dissolved in solvent is placed in donor compartment • Solvent is placed in receptor compartment
- 13. Valia chien diffusion cell
- 14. Diffusion cell • Made up of glass or clear plastic • Easy to assemble and clean • May be thermostated • Automatic sample collection from receptor • Analysis can be done using chromatography/ Spectrometry
- 15. Flux (J) • Flux (J): Is the amount, M, of material flowing through a unit cross section area, S, of a barrier (membrane) in unit time, t. • J= dM/Sdt ....(1) • dM= change in mass, gm • dt= change in time, sec • S= surface area, cm2
- 16. Fick`s First Law • States that • ‘Flux is directly proportional to the concentration gradient’ • J= - D . dC/dx ...(2) • D= diffusion coeff, cm2 /sec • C= concn, gm/cc • x= distance in cm of movement perpendicular to the surface of the barrier • dC/dx= concentration gradient
- 17. Fick`s First Law • Negative sign represent decrease in concentration from donor compartment • From eqn (1) and (2) we get • dM/Sdt = -D . dC/dx • dM/dt = -DS . dC/dx
- 18. Fick`s Second Law • Emphasize on change in concentration with time at definite location
- 19. Fick`s Second Law • From Ficks first law • J= -D . dC/dx • Differentiating wrt x • - dJ/dx = D d2C/dx2 • But, - dJ/dx = dC/dt • dC/dt = D d2C/dx2 • Above equation represent diffusion in x direction only. Extending this to 3 coordinates x y and z dC/dt = D [d2C/dx2 + d2C/dy2 + d2C/dz2]
- 21. Steady state diffusion • System is said to be steady state if conditions (concentration in donor and receptor compartment) do not vary with time • Mass transfer remain constant with time • To achieve this both the compartments are connected to reservoirs of solute/diffusant (maintained at respective concentration) and recirculated. • Concentration gradient remain constant.
- 22. Steady state (Sink condition) • Concentration in receptor compartment is maintained at lower level compare to concentration in the donor compartment. • Donor compartment act as source and receptor compartment act as sink. • Receptor compartment is connected to large reservoirs and solution is recirculated.
- 23. Steady state Within each diffusional slice perpendicular to direction of flow of diffusant, the rate of change of concentration, dC/dt = 0
- 24. Steady state • Within each diffusional slice perpendicular to direction of flow of diffusant, the rate of change of concentration, dC/dt = 0 • dC/dt = D d2C/dx2 =0 • But D ≠ 0, • Hence, d2C/dx2 =0 • dC/dx is constant indicating a linear relation between concentration,C, and distance, x
- 25. Driving forces for diffusion in pharmaceutical systems Driving Force Example Description Concentration Passive diffusion Mass transfer due to random motion of molecule , across concn gradient Drug dissolution Disintegration --> Deaggregation --> Fine particles--> Diffusion of drug from small particles--> Dissolution --> Absorption Pressure Osmotic pressure Osmotic pressure cause controlled release of drug, osmotic core coated with semipermiable membrane, orifice for drug release Pressure driven jets High velocity jet (>100m/s) penetrate skin and deliver drug subcutaneously or intramuscularly without needle
- 26. Driving Force Example Description Temperature Lyophilization Freeze-Drying, of frozen aqueous solution containing drug. Water vapor diffusion across pore pathlength of dry matrix under low pressure. Microwave Assisted Extraction (MAE) Microwave radiation-> Moisture get heated up –> heated solvent in contact with powder sample cause partitioning of analytes from sample. Rapid heating of solvent is attributed to MAE –> mass transfer from sample matrix Electrical Potential Iontophoretic dermal drug delivery It is used to enhance transdermal delivery by applying little electric current. One electrode (having charge same as that of drug molecule) is placed in between drug reservoir and skin and other electrode with oppositely charged near it. Charged ion of drug pass through skin. Electrophoresis Movement of charged particles across membrane under the influence of applied potential difference. When potential applied across electrodes particles migrate toward oppositely charged electrode.
- 28. Electrophoresis
- 29. Diffusion through film • At steady state diffusion Fick`s second law become • dC/dt = D d2C/dx2 =0 • Integrating above equation twice, x=0 to h, C1=Cd, C2= Cr • J= D/h (C1-C2) • Flux equation can be written as- • J= (C1-C2)/R …. R= h/D • Resistance and permeability are inversely related
- 31. Permeability • If membrane separate two compartments of diffusion cell of cross-sectional area S and thickness h • If concentration on donor and receptor sides are C1 and C2 respectively, Ficks first law (J= dM/Sdt & dM/dt = DS . dC/dx ) will become • J = dM/Sdt = D [(C1-C2)/h]
- 32. Quasi-stationary state (nearly equal to steady state) Where, • (C1-C2)/h ≈ dC/dx
- 33. Permeability • C1 and C2 can be replaced by partition coefficient multiplied by concentration on donor (Cd) and receptor (Cr) side • K= C1/Cd = C2/Cr
- 34. Permeability (P) • We know, dM/Sdt = D [(C1-C2)/h] • dM/dt = DSK (Cd-Cr) /h • If sink condition hold in receptor Cr = 0 • dM/dt = DSKCd/h = PSCd • P= DK/h
- 35. P= Permeability • P= DK/h • P= Permeability • K= Distribution coeff • h= Barrier thickness