04 Partitioning

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    The effective surface area

    The effective surface areaA is lower than the total surface:

    not all of the total surface is wetted

    Wetting the surface is the first step in dissolution

    The wettability may be estimated from the contact angle, height

    of a drop on the surface etc.

    The effective surface areaA is proportional to the specific

    surface area Sv:

    vSMA

    163

    Contact Angle

    The contact angle is

    a measure of the wetting of a liquid on a solid surface

    is expressed in degrees, with 0 degrees being complete wetting and

    180 degrees being absolute non-wetting

    Contact angles on surfaces are influenced by many phenomena

    interfacial tensions (viscosity of the fluid)

    surface roughness (shape and size of the pores)

    chemical heterogeneity

    swelling

    partial solution of low-molecular constituents in the polymer

    material

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    Contact Angle:

    Methods of Measurement

    Goniometry

    a drop of the wetting liquid is placed on the solid sample

    the image of the drop shape is investigated with the contact angle

    being the tangent between the drop edge and the solid surface

    Tensiometry

    a sample of the solid is hung on a force balance and brought intocontact with the wetting liquid

    the change in forces when the solid contacts the liquid are used to

    calculate contact angles

    good wetting

    bad wetting

    165

    Specific surface area

    The specific surface area of solid particles

    is given in m2/g

    increases with decreasing diameter of the particles

    smaller particles exhibit higher dissolution rates

    example: Griseofulvin absorption was supposed to be limited by dissolution rate

    absorption of particles with a diameter of 2.7 m (2.5 m2/g) was twice

    that of particles with a diameter of 10 m (0.4 m2/g)

    0.5 1 1.5 2 2.5

    1.0

    1.5

    2.0

    2.5

    relativea

    bsorbedamount

    specific surface / (m2/g)

    0.0 0.5 1.0 1.5 2.0 2.5 3.0

    1.0

    1.5

    2.0

    2.5

    relativea

    bsorbedamount

    specific surface / (m2/g)

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    Specific surface area

    The specific surface area Sv may change for spherical particles

    according to

    or may remain nearly constant for needle-like particles

    3/1= MkSv

    constvS

    167

    The extended Noyes-Whitney equation

    The effective surface areaA may be expressed as

    with:

    M: mass remaining to dissolve

    t: time

    z: parameter describing size change of particles

    n: polydispersity proportional to the inverse of the width of the

    size distribution curve;

    for monodisperse particles: n = 1

    for polydisperse systems: n < 1, n changes with time

    Thus, the Noyes-Whitney equation becomes

    1= nz tMkA

    ( ) 1= nzs tMcckdt

    dM

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    Drug release

    Controlled release dosage forms:

    drug release is the rate-limiting step (i.e., slower than drug

    absorption)

    sustained and controlled drug release

    used for per oral, topical administration as well as in implants

    169

    Membrane controlled drug release

    Assumptions:

    drug concentration in solution c < cs

    drug concentration in the dosage form < cs

    Note:

    If the resistance of the unstirred layer is considerably larger than

    the resistance of the membrane, the diffusion through the unstirred

    layer will be rate limiting

    cons=

    =

    =

    sP

    s

    cAk

    chDAP

    dtdM

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    Matrix controlled release

    Matrix controlled release occurs if the matrix is not degraded

    during release

    Matrix controlled release is observed for ointments, matrix

    tablets

    The embedded drug may be

    completely dissolved

    mainly suspended

    within the matrix

    171

    Non-degradable porous matrix

    The total mass Mfreleased from the matrix is given by

    with

    A: effective surface area

    D: diffusion coefficient

    V: volume of the matrix

    M0: mass of the drug in the matrix at time t= 0

    : tortuosity

    tAkM rf =

    =

    VMDkr

    02

    H. Lapidus and N. Lordi.J. Pharm. Sci. 57:1292 (1968)

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    Non-degradable, homogeneous matrix

    173

    Non-degradable, homogeneous matrix

    Drug fully dissolved in matrix

    Drug suspended in matrix

    and forctotal>> cs:

    with c0: initial concentration in matrix

    D: diffusion coefficient in matrixcs: solubility in matrix

    DtAcMf = 02

    tccDM stotalf = 2

    ( ) tcccDAM stotalsf = 2

    T. Higuchi.J. Soc. Cosm. Chem. 11:85 (1960) & T. Higuchi.J. Pharm. Sci. 50:874 (1961)

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    The Weibull model

    General empirical equation by Weibull (1951)

    Adapted later to dissolution processes (1972)

    Commonly used in dissolution studies

    Disadvantages no kinetic fundament

    no relation between parameters and dissolution rate

    ( )

    =

    a

    TtMM

    b

    f exp10

    a: time scale of the process, b: shape parameter,

    T: location parameter

    175

    Partitioning

    G. Camenisch, G. Folkers, and H. van de Waterbeemd. Review of theoretical passive drug

    absorption models: Historical background, recent developments and limitations. Pharm.

    Acta Helv. 71(5):309-327, 1996

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    Membrane permeation

    Diffusion through

    lipid bilayer (hydrophobic molecules)

    pores (small, hydrophilic molecules)

    Active transport (molecules with affinity to carrier)

    Pinocytosis/Phagocytosis, cell drinking (large molecules)

    177

    Membrane permeation by diffusion

    I. Small

    hydrophobic

    molecules

    II. Small

    hydrophilic

    molecules

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    Partitioning

    Example 1: partition coefficient = 1

    aqueousphase,

    c0

    aqueousphase,

    c = c0

    lipoidalmembrane

    c

    1 1 0,5 0,5

    179

    Example 2: partition coefficient = 10

    Remember: flux is proportional to concentration gradient!

    Assuming steady-state conditions:

    Partitioning

    aqueous

    phase

    aqueous

    phase

    lipoidal

    membrane

    cpartition

    coefficient

    = 10 1 0,5

    10

    5

    cl

    DPJ WatMembr = /.

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    Partitioning

    n2, v2, c2

    n1, v1, c1n1,0 = ntotal,

    v1, c1,0

    181

    Nernst distribution law

    If two liquids (or solids) a and b are partially immiscible and if

    there is a third component i present in both phases which behaves

    individually as an ideal solute (i.e., if it is sufficiently dilute), the

    ratio of its concentration c is independent of the individual values

    ofc.

    ( )( )

    constic

    ic

    b

    a =

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    Example: Nernst distribution law

    ( )

    21

    11

    210,1

    1

    212

    1

    2

    2

    1

    1

    21

    1

    1

    2

    2

    1

    2

    21

    21

    1

    Pvv

    v

    n

    v

    Pvv

    n

    c

    c

    Pvv

    n

    Pv

    nn

    v

    n

    Pv

    n

    P

    cc

    n

    v

    v

    n

    c

    cP

    vvv

    nnn

    total

    total

    totaltotal

    total

    total

    +=

    +=

    +=

    ==

    =

    ==

    +=

    +=

    183

    Example: Nernst distribution law

    The ratio of concentration before and after extraction is:

    Example 1:

    P= 10, v1 = 200 ml, v2 = 100 ml

    Example 2:

    P= 10, v1 = 200 ml, v2 = 200 ml

    21

    1

    0,1

    1

    Pvv

    v

    c

    c

    +=

    17.01200

    200

    10ml100ml200

    ml200

    0,1

    1 =+

    =c

    c

    09.02200

    200

    10ml200ml200

    ml200

    0,1

    1 =+

    =c

    c

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    Partitioning

    In equilibrium state:

    DrugOctanol DrugWater

    Partitioning is a dynamic process (resulting from a dynamic

    equilibrium)

    POct: Partition coefficient

    Usually given:POct

    or logPOct

    But:

    water is not a physiological medium!

    ( )( )

    [ ]Oct

    Water

    Octanol

    Water

    Octanol

    ]Drug[

    Drug

    Drug

    DrugP

    c

    c==

    185

    Partition coefficient

    The partition coefficient is the constant ratio of the

    concentrations of the same molecular species in the two phases

    of a heterogeneous system in equilibrium.

    Most widespread predictor of drug absorption

    Routinely determined for new chemical entities

    In natural sciences, there are numerous partition coefficients:

    Octanol / water ( =POct )

    Cyclohexane / water

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    Dependence of the partition coefficient on chemical

    structure

    Partition coefficients encode two major terms

    cavity formation energies V

    solute-solvent interaction energies

    Example:

    In the octanol/water system, includes

    dipole-dipole interactions

    H-bonding capacity of the solute

    aVP =log

    187

    Partition coefficient

    Chemical potential of a solute:

    with i0

    = activityai = mole fraction

    i = activity coefficient, i < 1; ideal solution: i = 1

    ci = mole fraction

    Partitioning of a solute between two phases is defined by the

    chemical potential difference

    At equilibrium: chemical potential in both phases is equal

    iii

    iii

    cRT

    aRT

    ln

    ln

    0

    0

    +=

    +=

    WatWat

    0

    WatOctOct

    0

    Oct lnln cRTcRT +=+

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    Partition coefficient

    Partition coefficient based on activities:

    Partition coefficient based on concentrations:

    Partition coefficient based on solubility:

    ===RTa e

    c

    c

    a

    aK

    0Wat

    0Oct

    WatWat

    OctOct

    Wat

    Oct

    ===RTc e

    a

    a

    c

    cK

    0Wat

    0Oct

    Oct

    Wat

    WatOct

    OctWat

    Wat

    Oct

    Wat

    Oct

    s

    sKs =

    189

    Correlation between partition coefficients from

    different solvent systems

    logPvalues from different solvent pairs are linearly

    correlated [1,2]:

    This is only valid, if the organic solvents have similar physical

    properties!

    Taking into account the hydrogen bonding capacity of the

    solute:

    1. R. Collander. The distribution of organic compounds between iso-octanol and water.

    Acta Chem. Scand. 4:1085-1098, 1950

    2. R. Collander. The partition of organic compounds between higher alcohols and water.

    Acta Chem Scand 5:774 780 1951

    dPbP

    PdPb

    +=

    =

    Octsolv

    Octsolv

    loglog

    ++= HOctcyclohex loglog IdPbP