Diffusion

Diffusion

Contents of This Chapter

•Definition and concept of diffusion

•Concept of steady state diffusion and the laws involved with it

•Methods and procedures of conducting diffusion studies

•Applications of diffusion

Learning Objectives

• At the end of this lecture, student will be able to

– Explain the concept of diffusion

– Explain steady state and sink condition

– Explain the different laws involved in the process of diffusion

– Explain the different methods and procedures to conduct the in vitro diffusion experiment

Diffusion-Definition and Concept

• Diffusion is defined as a process of mass transfer of individual molecules of a substance from a region of higher concentration to a region of lower concentration along a concentration gradient

• The process of diffusion occurs across a barrier

• Barrier is a region or regions that offers resistance to the passage of materials

• The material that undergoes the transport is known as diffusant or penetrant or permeant

WHAT IS DIFFUSION?

• 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

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.

DIFFUSION BASED PROCESS

• Drug absorption

• Drug elimination

• Drug release

• Osmosis

• Ultra filtration

• Dialysis Membrane

STEADY STATE DIFFUSION

• 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’.

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, and the solute diffuses through the central barrier from solution to solvent side.

Steady State Diffusion

• The diffusion of molecules is estimated using a transport cell shown below.

• Steady state- a system is said to be steady state, if the conditions do not vary with time

• In case of diffusion, the mass transfer remains constant with time i.e., dc/dt or dM/dt is constant

• If the condition vary with time the system is under unsteady state

• During the diffusion process, the concentrations of solute in the donor and acceptor compartments must be maintained constant

• Both the compartments are connected to large reservoirs of solutions and recirculated

• Sink condition – It is a state in which the concentration in the receptor compartment is maintained at a lower level compared to the concentration in the donor compartment

• During diffusion study, the donor compartment acts as a source and the receptor compartment acts as a sink

• This condition is maintained by connecting the receptor compartment to a large reservoir from which the solution is recirculated

• It is easy to maintain sink condition rather than steady state, because recirculation in one compartment is sufficient.

• Sink condition is employed in practice and mass transfer is approximated as steady state

Fick’s First Law

• In diffusion, molecules (mass) get transported from one compartment to another over a period of time i.e., rate of mass transfer (dM/dt).This is expressed as flux

• Flux is equal to the rate of mass transfer across a unit surface area of a barrier

• The flux J, can be mathematically expressed as:

𝟏 𝒅𝑴

J= -- ----- ……………….(1)

𝑺 𝒅t

Where, dM=change in the mass of material, g

S=barrier surface area,cm2

dt=change in time, sec

• The units for flux are g.cm-2sec-1

• In SI units, it can be expressed as kilogram.meter-2.time-1

• Time may be given in minutes, hours or days

• Fick’s first law states that the flux is directly proportional to the concentration gradient

• Fick’s law can be expressed as:

𝒅𝑪

J= -D----- ………………..(2)

𝒅x

Where, dC=change in concentration of material, g/cm3

D=diffusion coefficient of a penetrant, cm2/sec dx=change in distance, cm

• Flux is a positive quantity and increases continuously during the process

• The dx is perpendicular to the surface of the barrier

• Combining equations (1) and (2) we get:

𝒅𝑴 𝒅𝑪

----- = -DS -------- …………. (3)

𝒅𝒕 𝒅x

• Equation (3) represents the rate of mass transfer as per Fick’s first law

• The diffusion coefficient, D, may change in its value with high concentration

• The diffusion coefficient, D, is affected by temperature, pressure, solvent properties and chemical nature of diffusant.

• ‘D’ is not a constant but a coefficient

Fick’s Second Law

• Fick’s second law states that the change in concentration with time in a particular region is proportional to the change in the concentration gradient at that point of time

• The second law explains the change in the concentration with time at a definite location with respect to x, y and z axes

• In a particular volume element, the concentration, C, changes as a result of net flow of molecules into and outside the region

• dC is due to difference in the input and output, at the same time dC also changes with time i.e., (ΔC/ Δt)

• Change in dC is as a result of flux or amount of diffusing molecules changes with distance, (ΔJ/ Δx) in the x direction.

• This relationship can be expressed as:

δ C δ J

------ = − ----- ……….(4)

δt δx

Considering Fick’s first law expression from equation (2)

J= -D----

d𝑥

And differentiating the equation with respect to x gives:

δJ δ²C

---- = −D ------- …………………(5)

δx δx²

δ C δ J

Substituting the ---- in equation (5) for -----, we get

δt δx

δ C δ ²C

------- = D ------- …………….(6)

δt δx²

• Equation (6) represents diffusion in x-direction only.

• Extending the equation (6) in all the coordinates, Fick’s second law can be given by:

Methods and Procedures

• For the diffusion studies, two compartment cells are used.

1. Horizontal transport cell

2. DIFFUSION CELL FOR PERMEATION THROUGH STRIPPED SKIN LAYERS

It is developed by wurster et al. to study the diffusion through stratum corneum of various permeants , including gases, liquids and gels.

3. Vertical transport cell

• Horizontal cells are designed to study the skin permeation of drugs. This systems are used as in vitro models for drug absorption

• Vertical cells are used for diffusion of gases and liquids. The diffusion of drugs from ointments, transdermal drug delivery systems can be studied using these cells

• The diffusion cells are made up of glass, plexiglass, pyrex or plastic

• The cells are jacketed and thermostated in order to maintain the temperature

Applications of Diffusion Studies

• It is used for the interpretation of the release of drugs from the different dosage forms.

• Molecular weight of polymer can be estimated from diffusion studies

• The transport of drugs (absorption) from GIT, skin, etc., can be predicted

• The diffusion of drugs into tissues and their excreation through kidneys can be anticipated

• The processes such as dialysis, microfiltration, ultrafiltration, haemodialysis, osmosis etc., use the principles of diffusion

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)

PH-partition Hypothesis

• Biologic membranes are predominantly lipophlic, and drugs penetrated these 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.

Transport of a drug by diffusion across a membrane such as the gastrointestinal mucosa is governed by Ficks law

Gut compartment has high conc. and a large volume compared to Cp, Cg becomes constant and Cp relatively small. Equation becomes

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

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

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

Modification of pH-partition Hypothesis

PH 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

• 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.

Summary