diffusion Diffusion: Fick's laws Steady state diffusion Diffusion cell and applications Prepared by Dr.k.Jaya raj Kumar

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Diffusion: mass transfer (individual molecule movement) from higher concentration to lower concentration through a Semipermeable membrane. Generally due to Brownian motion In absence of external force Drug through barrier – synthetic or natural membrane (film) Material undergoes transport (diffusant)

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Application of diffusion Release of drugs from dosage forms is diffusion controlled (SR,CRDS) Molecular Weight of polymers can be estimated from diffusion process The transport of drugs (absorption) from gastro intestinal tract , skin etc… The diffusion of drugs into tissue and their excretion through kidneys Process such as dialysis, microfiltration, ultrafiltration,heamodialysis,osmosis …use principles of diffusion.

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Diffusion is a direct result of Brownian motion . Molecule diffuse spontaneously from a region of higher concentration to a region of lower concentration until diffusion Equilibrium is established Diffusant dissolved in a solvent and placed in donor compartment The vehicle is placed in a receptor compartment Diffusant gets transported from donor to accepter compartment Based on two laws of fick’s law

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Steady state diffusion : Condition do not very with time (constant) Mass transfer remain constant with time dc/dt (or) dm/dt The concentration of solute in the donor and acceptor compartment must be Constant. Both compartment are connected to large reservoirs of solution are recirculated. Therefore, Conc gradient is maintained constant Mass transfer takes place at constant rate throughout the study donor receptor time concentration Steady state curve

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Sink condition: Which the conc. in the receptor comportment is maintained at a lower level compared to its concentration in the donor comportment. donor receptor It is easy to maintain sink conditions rather than study state Un steady state diffusion : Condition very with time Withdraw of sample

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In diffusion molecule (mass) get transported from one compartment to another compartment over a period of time. i.e Rate of mass transfer (dm/ dt ) – expressed as flux Flux is equal to the rate of mass transfer (dm/ dt ) across a unit surface area of a barrier (S). Flux J can be expressed as: 1 dm S Flux, J = dt * dm-change in the mass of material S-barrier surface area dt-change in time eqn.1 Fick’s first law

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Fick’s first law state that the flux is directly proportional to the concentration gradient. Flux, J = -D dx dc dc- change in Conc. of material D- diffusion coefficient of a penetrant dx- change in distance eqn.2 Negative sign…decrease in conc. but flux is always positive…..increase continuously during process. the dx Perpendicular to the surface area of the barrier.

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Combining equ…1 and 2 gives = -DS dx dc dm dt eqn.3 dc = change in Conc. D = Diffusion Coefficient of diffusant dx = change in distance D is affected by temperature,pressure,solvent properties and chemical nature of diffusant Fick’s first law extensively applied in pharmacy-SR and CRS Flux, J = -D dx dc 1 dm S Flux, J = dt *

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FICK’S SECOND LAW Concentration of diffusing molecules change with time ,(∆C/∆t) flux or diffusing molecules changes with distance (∆J/∆x) in the x direction. eqn.4 ∆C/∆t= - ∆J/∆x Fick’s second law state that the Conc. with time in a particular region is proportional to the change in the Conc. Gradient at that point of time. The concentration is a function of both x and t. similarly flux is also a function of x and t.

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Fick’s second law refers to change in concentration of diffusant with time , at any distance x y z

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Flux, J = - D dx dc eqn.2 Consider fick’s first law expression i.e Differentiating equation- 2 with respect to x gives ∆J/∆X= - D ∆²c /∆x 2 eqn….5 Substituting the (∆C/∆t) in eqn (5) for ∆J/∆x, we get ∆C/∆t= D ∆ 2 C/∆x 2 eqn….6 Represents diffusion in x-direction only ∆C ∆t = D ∆ 2 C ∆ 2 C ∆ 2 C ∆x 2 ∆y 2 ∆z 2 eqn….7 Represents diffusion in x,y and z-direction only

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donor acceptor Water bath 37ºc Horizontal transport cell To study the skin permeation of drugs Used as in vitro model for drug absorption.

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Diffusion cells are made of glass, plexi glass, pyrex or plastic. Donor and receptor compartment assembled in Horizontal manner The cells are jacketed and thermostated in order to maintain the temperature. Barriers: Stripped skin of the forearm Buccal mucosa Human skin, cardavar skin (from dead bodies) Polyvinyl chloride (CRDDS) Polyvinyl acetate (CRDDS) Sampling: The diffusant in the form of a solution placed in donor compartment Ex. Ointment, gel, cream Solvent alone placed in accepter compartment Stirring rate and temperature are closely monitored at constant rate 37°c at 50 rpm Assemble:

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During process, the diffusant penetrate through the membrane and reaches the solvent (horizontal position) The concentration of diffusant in the donor compartment decrease continuously and in the acceptor compartment increase. After some time ,equilibrium state reaches, wherein the concentration of diffusant remain same in both sides. (study state diffusion) Periodically samples are withdrawn from the receptor compartment and concentration of diffusant is analyzed by a suitable method. time concentration

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donor acceptor Water bath 37ºc lid sample membrane (b) vertical transport cell

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Sampling: The diffusant in the form of a solution placed in donor compartment Ex. Ointment, gel, cream Solvent alone placed in accepter compartment Stirring rate and temperature are closely monitored at constant rate 37°c at 50 rpm During process, the diffusant penetrate through the membrane and reaches the solvent (vertical position) The concentration of diffusant in the donor compartment decrease continuously and in the acceptor compartment increase. After some time ,equilibrium state reaches, wherein the concentration of diffusant remain same in both sides. (study state diffusion) Periodically samples are withdrawn from the receptor compartment and concentration of diffusant is analyzed by a suitable method.

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