DIFFUSION 1

Diffusion is a process of migration of solute molecules from a region of higher concentration to a region of lower concentration and is brought by random molecular motion. Movement from one side of membrane to another side. Diffusion is a time dependent process. Movement is based on kinetic energy(speed), charge, and mass of molecule WHAT IS DIFFUSION ? 2

DIFFUSION It is defined as a process of mass transfer of individual molecules of a substance brought about by random molecular motion and associated with a driving force such as a concentration gradient. 3

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DIFFUSION BASED PROCESS Drug absorption Drug elimination Drug release Osmosis Ultra filtration Dialysis Mambrane Barrire 5

A system is said to be steady state, if the condition do not vary with time dc/dt or dm/dt should be constant for diffusion To described steady state diffusion fick ’ s I and II laws should be described Fick’s first law gives flux in a steady state of flow. Thus it gives the rate of diffusion across unit cross section in the steady state of flow. Second law refers to the change in concentration of diffusant with time ‘t’ at any distance ‘x’. STEADY STATE DIFFUSION 6

Consider the diffusant originally dissolved in the left hand compartment of the cell, solvent alone is placed on the right hand side of the barrier, the solute diffuses through the central barrier from solution to solvent side. 7

FICK´S I LAW The amount “M” of material flowing through a unit cross section “S” of a barrier in unit time “t” is known as the flux “J” The flux, in turn, is proportional to the concentration gradient, dc/dx: 8

No. of atoms crossing area A per unit time Cross-sectional area Concentration gradient Matter transport is down the concentration gradient Diffusion coefficient/ diffusivity A Flow direction As a first approximation assumed D ≠ f(t) 9

Fick’s first law 10

FICKS SECOND LAW An equation for mass transport that emphasizes the change in concentration with time at a definite location rather than the mass diffusing across a unit area of barrier in unit time is known as Fick’s second law 11 Differentiating the first law expression with respect to x one obtains

Its represents diffusion only in x direction substituting Dc/dt From the above equation Its represents diffusion in three dimensions 12

STEADY STATE The solution in the receptor compartment is constantly removed and replaced with fresh solvent to keep the concentration at low level. This is know as “ SINK CONDITION ”. The left compartment is source and right compartment is sink. The diffusant concentration In the left compartment falls and rises in the right compartment until equilibrium is attained, based on the rate of removal of diffusant from the sink and nature of barrier. 13

When the system has been in existence a sufficient time, the concentration of diffusant in the solution at the left and right compartments becomes constant, but obviously not same. Then within each compartment the rate of change of concentration dc/dt will be zero and by second law. Concentration will not be constant but rather is likely to vary slightly with time, and then dc/dt is not exactly zero. The conditions are referred to as a “QUASI STATIONARY STATE” and little error is introduced by assuming steady state under these conditions. 14

Diffusion through membranes Steady Diffusion Across a Thin Film and Diffusional Resistance steady Diffusion across a thin film of thickness “h”, the concentration of both sides cd&cr kept constant, Diffusion occurs in the direction the higher concentration(Cd) to lower concentration(Cr) the concentration of both sides cd&cr kept constant, after sufficient time steady state is achieved and the concentrations are constant at all points, At steady state (dc/dt=0), ficks second law becomes 15

The term h/D is called deffusional resistance “R” the flux equation can be written as Integrating above equation twice using the conditions that at z=0,c=Cd and at z=h, C=Cr yields the fallowing equation after sufficient time steady state is achieved and the concentrations are constant at all points at steady state (dc/dt=0), ficks second law becomes 16 Permeability

If a diaphragm separates the two compartments of a diffusion cell, the first law of fick’s may be written as Where, S=cross sectional area H=thickness c 1,c 2= concentration on the left and right sides of the membrane (c 1 -c 2 )/h within the diaphragm must be assumed to be constant for quasi-stationary state to exist. The concentrations c1,c2 can be replaced by partition coefficient multiplied by the concentration Cd on the donor side or Cr on receiver side. 17

If sink condition in the receptor compartment P=permeability coefficient P is obtained from slope of a linear plot permeant (M) vs. t. 18

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SIMPLE DIFFUSION CELL The diffusion chambrer constructed in a simple way 20

It is developed by wurster et al. to study the diffusion through stratum corneum of various permeants, including gases, liquids and gels. DIFFUSION CELL FOR PERMEATION THROUGH STRIPPED SKIN LAYERS: A-glass stopper B-glass chamber C-aluminum collar D-mambrane & sample holder 21

BIOLOGIC DIFFUSION Gastrointestinal absorption of drugs Drug pass through living membranes according to two main classes of transport 1) passive transfer It involves a simple diffusion driven by differences in drug concentration on the two sides of the membrane. 2)carrier mediated This is 2types a)active transport (requires energy) b)facilitated diffusion(does not depend on energy ) 22

pH-partition Hypothesis Biologic membranes are predominantly lipophlic, and drugs penetrated theses barriers mainly in their molecular, undissociated form. drugs are absorbed from the gastrointestinal tract by passive diffusion depending on the fraction of undissociated drug at pH of the intestines. pH-partition principle has been tested in a large number of in vitro and in vivo studies, and it is only partly applicable in real biologic systems. 23

Gut compartment has high conc. and a large volume compared to Cp, Cg becomes constant and Cp relatively small. Equation becomes Transport of a drug by diffusion across a membrane such as the gastrointestinal mucosa is governed by Ficks law Where, M= amount. Of drug in gut compartment at time ‘t’ Dm=diffusivity in intestinal membrane S= area of the membrane K= partition coefficient h= membrane thickness Cg=conc. of drug in intestinal compartment Cp=conc. of drug in plasma compartment 24

Cg, Pg are the concentration And permeability coefficient for drug passage from intestine to plasma for reverse passage of drug from plasma to intestine Cg and V are constants the left hand side converted in to concentration units, C(mass/unit volume) x V(volume). On the right hand side of the diffusion constant, membrane area, partition coefficient, and membrane thickness are combined to yield a permeability coefficient. These changes leads to the pair of equations

P H partition principle is only approximate, assuming drugs that absorbed through intestinal mucosa, in nondissociated form alone. For Small, ionic and nonionic following complicating factors must be considered 1. Metabolism of drugs in the gastrointestinal membrane 2. Absorption in micellar form 3. Enterohepatic circulatory effects Modification P H -partition Hypothesis 26

Applications Release of drugs from dosage forms diffusion controlled like sustained and controlled release products. Molecular weight of polymers can be estimated from diffusion process. The transport of drugs from gastrointestinal tract, skin can be predicted from principal of diffusion. 27

Processes such as dialysis, micro filtration, ultra filtration, hemodialysis, osmosis use the principal of diffusion. Diffusion of drugs into tissues and excretion through kidney can be estimated through diffusion studies. 28

References  ‘SINKO.J PATRICK’, “Martin’s physical pharmacy and pharmaceutical sciences”, 5th edition, pp no.301 to 337.  ‘SUBRAMANYAM.C.V.S’, “A text book of physical pharmaceutics”, pp no.-110 to 127.  The theory and practice of industrial pharmacy,leo lachmann,heberta. Liberman,joseph L. Kanio:3rd edition,pg no- 158 to 159.  Encyclopedia of pharmaceutical technology, 2 nd edition,volume -2: pg no to 1247 ; edited by james swarbrick,james C.Boylan.  29