GHENT UNIVERSITY
FACULTY OF PHARMACY
Institut für Pharmazeutische Technologie und Biopharmazie
Düsseldorf, Germany
2008-2009
DETERMINATION OF SURFACE ENERGY USING
DIFFERENT APPROACHES
Bart CLAEYS
First master in pharmaceutical science
Promoter
Dr. M. Thommes
Co-promoter
Prof. Dr. C. Vervaet
Commissarissen
Prof. W. Baeyens
Dr. K. Remaut
GHENT UNIVERSITY
FACULTY OF PHARMACY
Insitute für Pharmazeutische Technologie und Biopharmazi
pharmaceutical technology
Düsseldorf, Germany
2008-2009
DETERMINATION OF SURFACE ENERGY USING
DIFFERENT APPROACHES
Bart CLAEYS
First master in pharmaceutical science
Promoter
Dr. M. Thommes
Co-promoter
Prof. Dr. C. Vervaet
Commissarissen
Prof. W. Baeyens
Dr. K. Remaut
Copyright
“The author and the promotor are giving their authorization to make this master thesis available
for consultation and to copy parts of it for personal use. Any other use is subject to the restrictions
of copyright, in particular with regard to the obligation to mention explicitly the source when
quoting the results from this master thesis.”
02/06/2009
Bart Claeys
Prof. Dr. C. Vervaet
Acknowledgements
Sincere thanks to my supervisor, Dr. M. Thommes, for his support,
guidance and knowledge throughout this entire work.
The assistance and the overall advice of Prof. Dr. C. Vervaet
is also greatly appreciated.
PhD-students and personnel from the Institute of Pharmaceutical Technology and
Biopharmacy, under supervision of Prof. Dr. P. Kleinebudde, thank you.
Finally, I would like to express my gratitude to my family,
in particular my parents and my oldest brother.
Without their assistance and loving support,
this adventure would be impossible.
Copyright
Acknowledgements
Index
Abbreviations
1
INTRODUCTION .....................................................................................................................1
1.1
GENERAL TERMS ........................................................................................................1
1.2
BIOAVAILABILITY ......................................................................................................1
1.2.1
Bioavailability of poorly soluble drugs ...................................................................1
1.2.2
Rate of dissolution ...................................................................................................2
1.3
SOLID DISPERSIONS ...................................................................................................3
1.3.1
Definition and benefits ............................................................................................3
1.3.2
Solid dispersion: an overview of different types .....................................................4
1.4
SURFACE ENERGY AND TENSION ..........................................................................5
1.4.1
General terms...........................................................................................................5
1.4.2
Surface energy determination of a solid sample......................................................8
1.4.2.1
Young ..................................................................................................................8
1.4.2.2
Owens & Wendt ................................................................................................10
1.4.3
Measuring approaches ...........................................................................................12
1.4.3.1
Du Nouy: Surface tension determination ..........................................................12
1.4.3.2
Wilhelmy plate method: Surface tension determination ...................................13
1.4.3.3
Lucas-Washburn’s method: Contact angle determination.................................15
1.4.3.4
Tensiometric approach of contact angle determination.....................................16
1.4.3.5
Goniometric: optical approach for contact angle determination .......................18
2
AIM OF THIS STUDY ...........................................................................................................21
3
EXPERIMENTAL...................................................................................................................22
3.1
MATERIALS ................................................................................................................22
3.2
METHODS ....................................................................................................................23
3.2.1
Wilhelmy plate ......................................................................................................23
3.2.2
Lucas-Washburn....................................................................................................23
3.2.3
Tensiometric contact angle determination.............................................................24
3.2.4
Goniometric contact angle determination..............................................................24
4
3.2.5
Tabletting...............................................................................................................25
3.2.6
Jet milling ..............................................................................................................25
RESULT AND DISCUSION ..................................................................................................26
4.1
LUCAS-WASHBURN..................................................................................................26
4.1.1
Contact angle of griseofulvin ................................................................................26
4.1.2
Contact angle of mannitol......................................................................................27
4.2
TENSIOMETRIC CONTACT ANGLE DETERMINATION .....................................28
4.2.1
Griseofulvin ...........................................................................................................28
4.2.2
Mannitol.................................................................................................................29
4.3
GONIOMETRIC: THE DROP SHAPE ANALYZER .................................................30
4.3.1
Preliminary studies ................................................................................................30
4.3.1.1
Tablet sides ........................................................................................................30
4.3.1.2
Drop kinetics......................................................................................................31
4.3.1.3
Powder vs. Tablets.............................................................................................31
4.3.2
Experimental design ..............................................................................................32
4.3.3
Griseofulvin tablets: contact angles.......................................................................35
4.3.3.1
Griseofulvin - Pure water ..................................................................................35
4.3.3.2
Griseofulvin – Diiodomethane ..........................................................................36
4.3.4
4.4
Mannitol tablets: contact angles ............................................................................36
4.3.4.1
Mannitol - Diiodomethane.................................................................................36
4.3.4.2
Mannitol - Pure water ........................................................................................36
PARAMETERS NEEDED TO CALCULATE THE SURFACE ENERGY................37
4.4.1
Surface tension ......................................................................................................37
4.4.2
Liquid polar and dispersive fractions ....................................................................38
4.4.3
Contact angles........................................................................................................39
4.4.4
Energy determinations...........................................................................................39
4.4.5
Evaluation of porosity effects................................................................................40
5
CONCLUSION .......................................................................................................................43
6
REFERENCES ........................................................................................................................44
Abbreviations
Ang
c
CIR
CO2
CV
DOE
DSA
DV
Fw
H-W
HA
HO
L
Light
Liq
R²
Q²
Tan 1
Tan 2
Y-L
θ
θA
θR
θLeft
θRight
∆θ
∆G
γD
γP
γLV
γSL
γSV
ρ
ŋ
Camera angle of the drop shape analysis system
Constant in the Lucas Washburn method
Circle fitting method
Carbon dioxide
Coefficient of variations
Design Of Experiment
Drop Shape Analyzer
Drop Volume
Wetting force
Height-Width drop fitting method
Alternative hypothesis
Null hypothesis
Wetted Length
Illumination strength with the drop shape analysis system
Liquid used with the drop shape analysis system
Coefficient of determination
Prediction Value
Tangent 1 drop fitting method
Tangent 2 drop fitting method
Young Laplace drop fitting method
Contact angle
Advancing Contact angle
Receding Contact angle
Contact angle on the left side of the drop
Contact angle on the right side of the drop
Contact angle hysteris (θA - θR)
Gibbs Free Energy
Dispersive fraction of surface energy
Polar fraction of surface energy
Liquid-vapor surface energy
Solid-liquid surface energy
Solid-vapor surface energy
Density
Viscosity
Determination of surface energy using different approaches
1
1.1
INTRODUCTION
GENERAL TERMS
The appearance and evolution of high-throughput screening significantly increases the
number of new candidate drugs. However, many of these new candidate drugs have a low
solubility leading to low plasma concentrations and therefore a low bioavailability.
Pharmaceutical research has been seeking for different approaches to deal with this
problem. Prodrug formation, drug conjugates, different chiral forms, binding to charged ligands
and use of nanoparticles are only some methods used to increase the solubility. In addition,
different solid dispersion methods are well known among research groups in order to overcome
the solubility problem. The approach that is the focus of this paper is called: the “Solid Crystal
Suspension”.
Considering the solid crystal suspension approach, a mathematical model is in
development to understand more about the thermodynamics and kinetics of this dosage form.
Thereby different parameters are considered (e.g. crystal energy, solubility, diffusivity, surface
energy…). The overall goal is the fundamental understanding of this technology in order to
recognize the advantages and limitations. This work considers only the determination of surface
energy, regardless from other evaluations.
1.2
1.2.1
BIOAVAILABILITY
Bioavailability of poorly soluble drugs
The bioavailability is defined as the amount and the speed of drug that reaches the
systemic circulation and is determined by four steps: dissolution, absorption, distribution and
elimination. Intravenously administrated drugs have a bioavailability of 100%, while other
administration routes (e.g. oral, subcutaneous, rectal) undergo an absorption process which can
decrease their bioavailability depending on several parameters (e.g. pharmaceutical formulations,
drug solubility, drug permeability...).
1
Determination of surface energy using different approaches
As the dissolution of poorly soluble drugs is limited, their absorption after oral
administration is insufficient and as a consequence their plasma concentration and bioavailability
are low.
1.2.2
Rate of dissolution
Noyes and Whitney determined in 1897 the rate of dissolution (eq 1.1). The diffusion
coefficient, the surface area and the concentration gradient are influencing the dissolution rate.
The height of the diffusion layer and liquid volume are also influential parameters. (Noyes and
Whitney, 1897)
dC DA(Cs − C )
=
dt
Vh
(equation 1.1)
EQUATION 1.1 - NOYES-WITHNEY EQUATION: DESCRIBING OF THE DISSOLUTION RATE. PARAMETERS: D= DIFFUSION COEFFICIENT, A= SURFACE AREA, Cs = CONCENTRATION OF THE
SATURATED SOLUTION AROUND THE PARTICLE, C= BULK CONCENTRATION, V= LIQUID VOLUME,
h= DIFFUSION LAYER HEIGHT
The immersion of a solid in a liquid (solvent) is a process that proceeds in four steps: (1)
surface wetting, (2) displacing the air around the particles with the solvent, (3) breaking chemical
bonds of the lattice, resulting in dissolution of the solid sample, and (4) prevention of
reaggregation. If wetting does not occur in this process, a discussion of how to improve the
following steps is useless. Therefore, it is important to determine the surface energy and the
Gibbs free energy (∆G) in order to understand the wetting thermodynamics. If the wetting is
unfavorable (∆G>0), there will never be any dissolution. (Parfitt, 1973)
Increasing the solubility can be done by several approaches. First, physical methods are
used with the goal of increasing the surface area. Examples in this approach are: micronizing by
pin-, bal- or jet-milling, spray drying, the application of ultrasound waves… Secondly, different
chemical methods (e.g. prodrug, solubility enhancers, altering administration route…) are
commonly used to overcome the solubility problem. Finally, several advanced formulation
2
Determination of surface energy using different approaches
methods (e.g. self-emulsifying delivery systems, micro-emulsions, use of cyclodextrines…) are
considered. One of these approaches is the formation of a solid dispersion. (Albers et al., 2008;
Thommes et al., 2009)
1.3
1.3.1
SOLID DISPERSIONS
Definition and benefits
Solid dispersions, solid-state dispersions or co-precipitates are similar terms referring to
the dispersion of one or more active ingredients in a matrix at solid state. They are prepared by
the melting, solvent or melting-solvent method with the objective of increasing the drug
dissolution rate. The reasons for the improved dissolution characteristics are described below.
(Vasconcelos et al., 2007)
Apolar substances (with low dissolution rates) tend to aggregate due their high surface
energy as they try to obtain the lowest energy condition as possible. This results in a lower
surface area which is negative for the dissolution rate. By inclosing the drug within a matrix, this
aggregation is prevented with higher surface areas and therefore faster dissolution rates.
(Goldberg et al., 1965; Chiou & Riegelman, 1971; Vasconcelos et al., 2007)
During production of solid dispersions the drug can crystallize in a metastabel condition
with a lower stability, resulting in a faster dissolution process. (Vasconcelos et al., 2007)
In a solid dispersion the poorly soluble drug is surrounded by a carrier and both are in a
solid state. When the carrier has a high water-solubility it will dissolve fast, resulting in fast
exposure of the drug to the solvent. By dissolution of the matrix that encloses the drug, the active
substance is instantly and entirely surrounded by the solvent which results in higher dissolution
rates. (Goldberg et al., 1965; Chiou & Riegelman, 1971; Vasconcelos et al., 2007)
3
Determination of surface energy using different approaches
1.3.2
Solid dispersion: an overview of different types
Tabel 1.1 presents the different types of solid dispersion approaches.
A solid solution is a solution of one or more solutes in a solvent where all substances are
in their solid state. It is still called a solution because the outcome remains a one phase system
and the crystal lattice of the solvent does not change due the addition of more substances. Two
possible theories are known to understand the logic behind this matter: substitution and
interstitutionality. The lattice of the solvent does not change on the grounds that the solute
particles are taking the place of the solvent particles in the crystal lattice (substitution) or due the
fact that the solute particles are filling the empty spots in the solvent lattice (interstitutionality).
When comparing the solid solution to the other solid dispersion approaches, the solid solution
method came out as the one with the fastest dissolution rate.
(Goldberg et al., 1965; Vasconcelos et al., 2007)
In a glass suspension an amorphous or crystallized drug is included in an amorphous
carrier. A very fast cooling process is needed to create an amorphous state as this prevents
molecules to form a crystal lattice. Immobilisation of the molecules at random positions is the
result. The use of this approach is limited as often the stability of the amorphous carrier is not
sufficient. (Goldberg et al., 1965; Vasconcelos et al., 2007)
Eutectic mixtures are obtained by the solidification of two completely miscible
components that are crystallizing simultaneously from the molten liquid solution. A two phase
system is the result. The biggest disadvantage of this method is that for each drug the right carrier
has to be founded in order to obtain simultaneous crystallization. (Goldberg et al., 1965;
Vasconcelos et al., 2007)
A fourth subdivision in the solid dispersion systems is the amorphous precipitation where
the drug remains in an amorphous state while the carrier crystallizes. Since an amorphous system
is in a higher energy form, dissolution rates are faster compared to the crystalline form. However,
the amorphous state can cause stability issues. (Goldberg et al., 1965; Vasconcelos et al., 2007)
4
Determination of surface energy using different approaches
TABEL 1.1 - SOLID DISPERSIONS: AN OVERVIEW - ADAPTED FROM THOMMES ET AL., 2009
Solid Solution
Glass Suspension
Phases
Drug
Carrier
1
molecularly dispersed
amorphous
molecularly dispersed
crystalline
amorphous
amorphous
crystalline
amorphous
2
Eutectic Mixture
2
crystalline
crystalline
Amorphous precipitation
2
amorphous
crystalline
Solid Crystal Suspension
2
particle dispersed
crystalline
A fifth and universal application is the solid crystal suspension. By dispersing the drug on
a particle level, instead of a molecular level, a wider range of drugs can be used. Since many of
the new drugs are complex and hydrophobic, finding for each of them a suitable carrier is
difficult. Consequently, this universal approach is gaining attention in the pharmaceutical
research. (Thommes et al., 2009)
In order to obtain a crystalline carrier, the selection of the carrier is essential in the solid
crystal suspension method (e.g. high stability, low toxicity, high solubility). If it has the right
properties, crystallization will occur during production resulting in a drug particle dispersed in a
crystalline matrix. (Thommes et al., 2009)
1.4
1.4.1
SURFACE ENERGY AND TENSION
General terms
The surface energy of a solid is the work required per unit area to create a new surface
(J/m²), while the surface tension of a liquid is the force required per unit length to stretch a preexisting surface (N/m). The surface energy has therefore two different dimensions: force per unit
length or energy per unit area. Both are changeable used in calculations since their units represent
the same as shown in equation 1.2. (Halldorsson, 2007)
5
Determination of surface energy using different approaches
1J 1N .m 1N
= 2 =
m2
m
m
(equation 1.2)
EQUATION 1.2 – SURFACE ENERGY UNITS (J/m²) REPRESENT THE SAME AS SURFACE TENSION
UNITS (N/m).
The difference relies on the fact that surface tension can only be used when considering
liquids, while surface energy can be used for liquids and solids. The surface energy of a solid
surface is the equivalent of the liquid surface tension. They are both a reflection of the amount
and strength of bonds that needs to be broken in order to create a new surface and are therefore
interchangeable used. (Halldorsson, 2007)
Molecules at a surface are different from molecules in the bulk. The latter are surrounded
on all sides by similar molecules and have a netto force that equals zero. Molecules at the surface
are exposed to unbalanced forces and therefore they possess additional energy. The surface
energy manifests itself as internal forces with the goal of reducing the surface area, and thus the
energy, to a minimum. Obtaining a more favorable and consequently lower energy condition is
the driving force behind this. (Shaw, 1992; Lazghab, 2005; Halldorsson, 2007)
Surface energy is a reflection for the amount of energy that is needed to enlarge the
surface. This energy is needed to overcome the interactions that exist between the different
molecules. Depending on the functional groups and the charge they carry, different interactions
occur between molecules. Hence, an intrinsic connection is found between surface energy and
attractive forces. Molecular interactions vary between ion-ion and induced dipole-induced dipole.
The latter (the London-interactions) are always present, while ion-ion interactions are only
present when both molecules carry charges. Possible interactions are described in Tabel 1.2.
(Halldorsson, 2007)
6
Determination of surface energy using different approaches
TABEL 1.2 - DESCRIPTION OF MOLECULAR INTERACTIONS. ION-ION INTERACTION BEING THE
STRONGEST.
LONDON-INTERACTION
BEING
THE
WEAKEST
-
TABEL
OBTAINED
FROM
HALLDORSON, 2007
Molecular Interaction
Definition
Ion-ion
Coulomb
Ion-dipole
Coulomb
Ion-induced dipole
Coulomb
Dipole-dipole
Keesom
Dipole-induced dipole
Debye
Induced dipole-induced dipole
London
The surface tension is an extremely sensitive indicator that provides a lot of information
about the characteristics (e.g. wetting, foaming, emulsification…) of a liquid. A high liquid
surface tension causes low wetting properties. A high solid surface energy (mostly hydrophilic),
on the other hand, means that the interfaces between the solid material and the air are not
favorable in a thermodynamic sense. Therefore, high surface energy solids are easily wetted by
liquids (fig 1.1). Wetting of a solid eliminates the solid-air interface in favor of the solid-liquid
interface. The interaction between the solid surface and the liquid results in a lower energy state
which is a more favorable state. (Shaw, 1992; Lazghab et al., 2005)
FIG 1.1 - WETTING OF HYDROPHILIC AND HYDROPHOBIC SAMPLES - OBTAINED FROM LAZGHAB
ET AL., 2005
7
Determination of surface energy using different approaches
The determination of the surface tension is a sensitive method: each dust particle or each
solute in the liquid is influencing the outcome as the attraction forces between two totally
different molecules are always smaller than between two similar ones. For example, by adding a
foreign dust particle to water, the surface tension will be lowered and the attraction forces that
attempt to reduce the surface are less due this foreign substance. Consequently, the forces needed
to overcome these attractive forces, in order to create new surfaces, are lowered.
An example, describing the importance of surface tension and surface energy, is found in
the beer foam. A foam is mostly formed by CO2 rising in the liquid, forming air bubbles
(surrounded by a thin liquid film) at the surface. A clean glass surface with high surface energy
results in a high foam stability since a high energy condition is not favorable. The glass reduces
its energy state by covering the surface with the air bubbles (that are surrounded by a thin liquid
film). The air-solid interface becomes as a consequence smaller with respect to a higher air-liquid
interface, creating a more favorable energy state which is the driving force behind this process.
On the other hand, if the glass has a dirty surface (e.g. fat and/or soap residues) the conditions are
less favorable to cover the glass surface with the liquid due to the lower energy state. Hence, the
tendency to increase the air-liquid interface in order to lower the surface energy is less, resulting
in a lower stability of beer foam. This explains as well why the beer foam in a plastic cup is less
stable than in glass as plastic has a lower surface energy than glass.
Another manner to explain this effect is that if the solid-liquid adhesive forces are
stronger than the liquid cohesive forces and solid-gas interactions, wetting occurs spontaneously,
resulting in a high foam stability. (Lazghab, 2005)
1.4.2
Surface energy determination of a solid sample
1.4.2.1 Young
The determination of the surface energy of a solid sample (γsv) is difficult since there is
no direct method to measure it. The result will remain an estimation of the actual value.
(Mykhalyk et al., 2003)
8
Determination of surface energy using different approaches
In 1805, Young described the relation between the contact angle and the different surface
tensions (fig 1.2 and eq 1.3). This equation is one of two equations used to calculate the surface
energy of a solid sample. The fundamentals of this theory rely on the mechanical equilibrium
between the working forces of a liquid drop on a solid sample (fig 1.2). In Young’s equation, two
parameters can be measured directly: the liquid surface tension (γLV) and the contact angle (θ).
The two other parameters (γSV and γSL) have to be derived. (Halldorson, 2007)
γ SV = γ SL + γ LV cos θ
(equation 1.3)
EQUATION 1.3 - YOUNG’S EQUATION: AN EXPRESSION OF DIFFERENT ENERGIES WORKING AT THE
THREE PHASE CONTACT POINT (SOLID, LIQUID, AIR) - γSV : SOLID-VAPOR SURFACE ENERGY, γSL :
SOLID-LIQUID SURFACE ENERGY, γSL : LIQUID-VAPOR SURFACE ENERGY, θ : CONTACT ANGLE AT
THREE PHASE CONTACT POINT
FIG 1.2 - THE WORKING ENERGIES AT THE THREE PHASE CONTACT POINT - FIGURE OBTAINED
FROM AHADIAN ET AL., 2009
Theoretically, the Young equation is correct, but as it is based on ideal surfaces
(homogeneous, pure, smooth) it is experimentally difficult to obtain. Considering this, a range of
contact angles is obtained, depending on the smoothness of the surface and with a maximum and
minimum possible value. The difference between the maximum contact angle (θA) and the
minimum or receding contact angle (θR) is referred as the contact angle hysteris (∆θ= θA - θR).
(Kamusewitz & Possart, 2003)
9
Determination of surface energy using different approaches
1.4.2.2 Owens & Wendt
Following the work that Fowkes pioneered in 1962, every surface energy (γSV, γSL and
γLV) can be split into two components: polar and dispersive fractions. Based on the assumption
that only the same type of interaction (polar and/or dispersive) can occur between both phases,
Owens & Wendt presented equation 1.4: the surface energy between two phases equals the
surface energy of each phase separately minus the interaction that they have with each other. In
other words, the force needed to extend the contact region between two immiscible phases relies
on the force needed to extend each phase separately minus the interaction that they have with
each other. Describing the interaction of two forces by taking the geometric mean of them is the
second assumption that is made in equation 1.4. (Fowkes, 1962; Owens & Wendt, 1969;
Rudawska & Jacniacka, 2008)
1
1
γ 12 = γ 1 + γ 2 − 2[(γ 1Dγ 2D ) 2 + (γ 1P γ 2P ) 2 ]
(equation 1.4)
EQUATION 1.4 – DESCRIBING THE INTERACTION BETWEEN TWO PHASES, BY OWENS & WENDT -
γ12 : SURFACE ENERGY OF CONTACT REGION BETWEEN PHASE 1 AND 2, γ1
ENERGY,
γ2
: PHASE 2 SURFACE ENERGY,
γD:
DISPERSIVE FRACTION,
γP:
: PHASE 1 SURFACE
POLAR FRACTION OF
THE SURFACE ENERGY
Thermodynamically this equation can be interpretated as follow: each substance is
seeking for the lowest energy possible. Since a surface has a higher energy state, each phase tries
to reduce its surface area. When two immiscible liquids are combined, a contact region is formed
between both. To extend this region, energy is needed. This energy depends on the energy needed
to break the bindings of each phase separately minus the interactions they have with each other.
This negative sign is explained since, by creating two new surfaces, new interactions between the
different phases will occur, causing a lower energy and therefore a more favorable state.
Considering equation 1.4, the equation 1.5 can be set up in order to describe the interaction of a
solid sample with a liquid. This equation is, next to the Young equation, the second equation
needed for calculating the surface free energy of a solid sample. (Fowkes, 1962; Owens & Wendt,
1969; Rudawska & Jacniacka, 2008)
10
Determination of surface energy using different approaches
1
1
D D
P
P
γ SL = γ SV + γ LV − 2[(γ SV
γ LV ) 2 + (γ SV
γ LV
) 2]
(equation 1.5)
EQUATION 1.5 - DESCRIBING THE INTERACTION BETWEEN A SOLID SAMPLE AND A LIQUID - γSL :
SOLID-LIQUID SURFACE ENERGY,
D
SURFACE ENERGY, γ
γSV
: SOLID-VAPOR SURFACE ENERGY,
γLV
: LIQUID-VAPOR
: DISPERSIVE FRACTION, γP: POLAR FRACTION OF THE SURFACE ENERGY
By combining equation 1.5 with the Young equation, a final mathematical statement (eq
1.6) can be made in order to calculate the surface energy of a solid sample (γSV). By linking both
equations, the surface energy of the solid liquid interface (γSL) and the solid vapor surface energy
(γSV) are excluded. Consequently a formula arises that only describes the influence of the liquid
vapor surface energy (γLV) and the contact angle (θ), that are both directly measurable, on the
dispersive and polar fractions of the solid and liquid surface energy. (Mykhalyk et al., 2003;
Rudawska & Jacniacka, 2008)
1
1
D D
P
P
γ LV (cosθ + 1) = 2[(γ SV
γ LV ) 2 + (γ SV
γ LV
) 2]
(equation 1.6)
EQUATION 1.6 - YOUNG EQUATION COMBINED WITH OWENS & WENDT EQUATION - γLV : LIQUIDVAPOR SURFACE ENERGY,
DISPERSIVE FRACTION, γ
θ: CONTACT ANGLE, γSV : SOLID-VAPOR SURFACE ENERGY, γD:
P
: POLAR FRACTION OF THE SURFACE ENERGY
By using a liquid that only interacts on a dispersive level (diiodomethane) with other
phases, equation 1.6 can be simplified by excluding the polar fractions (γP). The liquid vapor
surface energy and the contact angle can be directly determined. The dispersive fraction of the
D
liquid vapour surface energy ( γ LV
) of diiodomethane is equal to the total liquid vapor surface
energy ( γ LV ) since the polar interactions are zero. Consequently, the only unknown parameter
D
( γ SV
) can be calculated.
11
Determination of surface energy using different approaches
D
Extrapolating the γ SV
-value determined using the dispersive liquid (equation 1.6), and by
using a second liquid having dispersive and polar interactions with the solid sample, the only
P
) can be determined. The second used liquid is mostly water and its
unknown parameter ( γ SV
P
D
and γ LV
) can be determined by measuring the interaction that
polar and dispersive fraction ( γ LV
water has with a solid sample that only has dispersive fractions (Teflon plate).
P
D
and γ SV
) the total surface
Summing up both calculated fractions of the solid material ( γ SV
free energy of a solid sample can be determined.
Selected liquids need have suitable properties in order to interact in the best possible way
to determine the surface energy. Firstly, the liquids have to carry a wide range of intermolecular
interactions from polar to apolar. In addition, the liquid surface tension has to be higher than the
solid surface energy: the working forces on the surface of the solid sample are superior to the
forces needed to create the drop, resulting in a high wettability. The latter makes it impossible to
determine a contact angle. Finally, one liquid should at least have a surface tension close to the
solid surface energy. (Mykhalyk et al., 2002)
1.4.3
Measuring approaches
1.4.3.1 Du Nouy: Surface tension determination
Du Nouy described a method for the determination of a liquid surface tension/energy. A
ring is lowered into the liquid surface until it is completely wetted. Subsequently the ring is
carefully and progressively raised until contact with the liquid is broken. The force on the ring
(just before detachment) is measured and used to calculate the surface tension. Why the force on
the ring is used just before detachment can be explained referring to the definition of surface
tension. Since a liquid surface tension is a reflection of the strength of bonds that needed to be
broken in order to create a new surface, the force measured just before detachment is the best
value to calculate the surface tension of a liquid. (Lunkenheimer & Wantke, 1981)
12
Determination of surface energy using different approaches
The Du Nouy ring method is a dynamic method of determination, meaning that the ring
moves upwards during the measurements. This influences the liquid surface and therefore also its
surface tension. In addition, the ring has to be constantly parallel with the liquid surface and the
latter must remain motionless during the procedure. Furthermore, a correction factor must be
added to take into account the small amount of liquid that is lifted up together with the ring. The
only advantage is that this method can be used for liquids that have poor wetting properties on
the Wilhelmy plate. Consequently, obtaining accurate and representable data via this method is
difficult. (Lunkenheimer & Wantke, 1981; Ozcelik et al., 2000)
1.4.3.2 Wilhelmy plate method: Surface tension determination
A second method to measure the liquid surface tension involves the use of a pre-weighed
plate and the measurement of wetting forces. The level of the liquid is raised until contact
between the liquid surface and the plate is registered. Contact between the liquid and the plate
induces a netto change of working forces on the plate, which is measured by the tensiometer.
There are 3 forces acting on the plate: the force due to (1) gravity, (2) wetting and (3) buoyancy.
The latter force has a different direction then the first two. By using a pre-weighed plate, the
tensiometer can exclude the gravity force and by extrapolating the measured forces back to zero
depth of immersion, the buoyancy force can also be excluded. The only force left, the wetting
force (Fw), is then easily measured by the tensiometer. (Mykhaylyk et al.,2003; Gaonkar et al.,
1984)
A high energy platinum plate is used in this approach, with the assumption that the
contact angle (θ) liquid-platinum plate is 0° (fig 1.3). As a consequence, the liquid-vapor surface
tension can be calculated as follows: Fw = γlv L cos θ, where γlv is the liquid-vapor surface
tension, L the wetted length of the plate (= twice the width and length of the plate) and θ the
plate-liquid contact angle. (Mykhaylyk et al.,2003; Gaonkar et al., 1984)
13
Determination of surface energy using different approaches
FIG 1.3: THE WILHELMY PLATE METHOD USING A ROUGHENED PLATINUM PLATE WITH THE GOAL
OF LIQUID SURFACE TENSION DETERMINATION - OBTAINED FROM MANUAL TENSIOMETER K100
Its biggest advantage is that the liquid surface tension is analyzed at a fixed point,
resulting in a static determination method. After the plate is immersed in the liquid and
equilibrium has settled, there is no movement of the plate or liquid which results in a higher
accuracy. In contrast, in the Du Nouy ring method the surface is permanently renewed due to the
movement of the ring. Furthermore allows the Wilhelmy plate method to determine the surface
tension of viscous liquids. (Mykhaylyk et al.,2003; Gaonkar et al., 1984)
The mechanical sensitivity of this method and the cost of a single Wilhelmy plate are the
major disadvantages of this method. Careful handling of the plate is therefore required since a
Wilhelmy plate is small and very sensitive to deformation. In addition, since the perpendicular
entry of the plate in the liquid is decisive in this method, best practice is to place the tensiometer
on a shock absorbing device to exclude external influences. Finally, temperature affects the
measurement since high temperature liquids have a lower surface tension while bonds are then
more easily broken. (Mykhaylyk et al., 2003; Gaonkar et al., 1984)
14
Determination of surface energy using different approaches
1.4.3.3 Lucas-Washburn’s method: Contact angle determination
This approach is also known as the capillary rise method. It determines the contact angle
by analyzing the capillary rise of liquids into a porous powder. It is a very simple and universally
applicable method and is therefore commonly used.
The set up of the experiment is done by adding a porous powder to a glass tube with a
filter on the bottom. The glass tube with powder is densified and attached to the tensiometer. The
liquid with known density (ρ), viscosity (ŋ), and surface tension (γLV) is placed at the bottom of
the tensiometer and its level is subsequently raised until contact with the filter of the glass tube is
registered. Via capillary forces the liquid rises through the porous powder and the increase in
weight is measured by the tensiometer, resulting in a graph of the square mass plotted against the
time. The equation that fits this graph is presented in equation 1.7. (Dang-Vu & Hupka, 2005;
Kiesvaara & Yliruusi, 1993)
2
m =
cρ 2γ cosθ
η
t
(equation 1.7)
EQUATION 1.7 - WASHBURN’S EQUATION PRESENTS THE LINEAR DEPENDENCE BETWEEN THE
SQUARE MASS OF THE COLUMN VS THE TIME - C= CONSTANT DEPENDING ON THE MATERIAL, ρ=
LIQUID DENSITY,
γ=
LIQUID-VAPOR TENSION,
θ= CONTACT ANGLE, ŋ= LIQUID VISCOSITY, T=
TIME
Two parameters are still unknown in equation 1.7. In order to determine the contact angle
(θ), two liquids are required. These two liquids should have good wetting properties. One of these
is mostly hexane or heptane. Since the reference liquid (hexane or heptane) is wetting the solid
material entirely, the contact angle is close to zero (cosθ=1), and therefore negligible. Hence, the
constant parameter in the equation (c) can be calculated. Since the characteristics of the powder
(expressed as c) are determined in this way, the contact angle can be calculated between a second
selected liquid and the powder. (Dang-Vu & Hupka, 2005; Kiesvaara & Yliruusi, 1993)
15
Determination of surface energy using different approaches
Considering the use of two different liquids (one to determine the powder characteristics
and one to determine its contact angle with the powder) it is important that both experiments are
done under the same conditions. It is a comparative method, so adding precisely the same amount
of powder into each tube and accurate bed packing are needed to ensure the repeatability of the
experiment. It is also important that the powder is introduced to the column in one time. If not,
uneven packing will occur with higher bulk density for the lower layers due to more tapping.
Homogeneity of the powder is also important for obtaining good and repeatable results. Other
conditions for this experiment are: steady state laminar flow, no external pressure and negligible
gravitation differences. (Dang-Vu & Hupka, 2005; Kiesvaara & Yliruusi, 1993)
Benefits of this method are the simplicity and the fact that it is a universal applicable
approach, while the cleaning of the filter at the bottom of the tube is the biggest disadvantage.
The latter can be solved by using changeable paper filters.
1.4.3.4 Tensiometric approach of contact angle determination
Considering the Wilhelmy plate method, another method is proposed to determine contact
angles using the tensiometer. This theory uses the same principles as the Wilhelmy plate method,
but the wetted length (L) is altered and the liquid surface tension must be determined before
contact angle measurements. The experimental setup is shown in figure 1.4 with corresponding
equation (eq 1.8). The unknown parameter in this formula is the contact angle, whereas with the
Wilhelmy plate the surface tension was the only unknown parameter.
Fw = γLV L cos θ
(equation 1.8)
EQUATION 1.8 - TENSIOMETRIC CONTACT ANGLE DETERMINATION - Fw = WETTING FORCE, γLV =
LIQUID VAPOR SURFACE TENSION, L = WETTED LENGTH, θ = CONTACT ANGLE BETWEEN LIQUID
AND SOLID SAMPLE
16
Determination of surface energy using different approaches
1
2
3
FIG 1.4 -EXPERIMENTAL SETUP OF THE TENSIOMETRIC CONTACT ANGLE MEASUREMENT - (1)
WEIGHT SENSOR, (2) TABELT, (3) LIQUID IN ADJUSTABEL HOLDER
Lowering a tablet in the liquid allows to determine liquid-tablet interaction by plotting the
force on the tablet versus the depth of immersion. When the tablet is in contact with the liquid
surface, buoyancy forces result in a lower force needed to displace the tablet. Hence the force and
the immersion depth are inversely proportional. When the tablet exits the liquid again,
penetration and wetting of the liquid on the tablet has occurred, resulting in a higher weight and
therefore a higher force to adjust the position of the tablet. This is clearly shown on fig 1.5.
FIG 1.5 - CONTACT ANGLE DETERMINATION BY OWN TENSIOMETRIC APPROACH: FORCE VS
IMMERSION DEPTH - DOWNWARD MOVEMENT (PRESENTED BY ARROW) IS CONTINUED UNTIL AN
IMMERSION DEPTH OF 5MM WHICH IS THEN FOLLOWED BY AN UPWARD TABLET MOVEMENT WETTED FORCES (Fw) NEEDED IN EQUATION 1.8 ARE OBTAINED BY EXTRAPOLATING BOTH
GRAPHS TO AN IMMERSION DEPTH OF ZERO
17
Determination of surface energy using different approaches
Via two regression lines and extrapolating them to the point of zero immersion depth, two
wetting force (Fw) are determined. These wetting forces are subsequently used to calculate the
advanced (θA) and receding (θR) contact angle via equation 1.8.
Considering the goniometric approach several variables are making this procedure more
complicated. Hence, a benefit of the tensiometric contact angle determination is that only a
limited number of variables must be taken into account. In addition, the variability of sample
preparation which complicates the Lucas-Washburn method, is excluded since tablets are pressed
at a specific pressure. The precision is the greatest drawback of this method due to inaccuracy of
wetted length determination, the need for perpendicularly tablet entry and on the purity of the
liquid and tablet.
1.4.3.5 Goniometric: optical approach for contact angle determination
In this method the solid surface is wetted by single drops of the probe liquid. A highresolution camera captures the shape of the drop and processes this by image analyzing software.
Advantages of this optical approach are the precision and quickness. In addition, placing
drops at different positions gives the opportunity to explore the diversity of the surface. Solid
sample preparation, camera resolution, together with the investigation of only two contact points
are the disadvantages of this method. Especially the camera angle to obtain a perfect baseline
image is important. Baseline inaccuracy is the primary contributor of a lower repeatability.
(Lander et al., 1993)
Contact angle measurements are influenced by several factors. First, the shape of the drop
is an important influence. Measurement should take place immediately after the drop is placed on
the solid material. This should cover the errors made due to interaction with the material which
must be chemical and physical homogeneous. Secondly, surface roughness and surface impurities
are influential parameters. As a results the drop can have various metastable states, which
automatically influence the contact angle. Finally, the humidity and temperature are factors that
provide contact angle variance. (Rudawska & Jacniacka., 2009)
18
Determination of surface energy using different approaches
There is no universally suitable model for the drop shape analysis. Different fitting
procedures are used to determine the best shape of the drop and thus the correct contact angle:
(User manual Krüss V1.9-03, Drop Shape Analysis)
The circle method together with the height-width approach, are appropriate for small
contact angle measurements (between 0 and 20°). The circle-method shapes the drop in the form
of a circular arc, while the height-width-method determines the height and the width of a
rectangle that surrounds the drop. The disadvantage with this design is that only a few points are
taken into account, leading to a lower repeatability.
A third method, the tangent1-method or the conic section method, fits a conic section
equation on the drop shape where θ acts as the angle at the three-phase contact point. A benefit
here is that it the contact angle range is much wider (between 10 and 100°), and that the fitting
procedure does not assume that contact angles on both sides are equal, resulting in two different
contact angles (θLeft and θRigth).
Additional, the tangent2-method, is a form that can be used on any drop shape. There are
no geometrical requirements for the drop shape; even highly asymmetrical drops are possible to
evaluate. Reason for this is that only the phase contact region is evaluated. A drawback, on the
other hand, is that the procedure is more sensitive to interferences (e.g. dirty surfaces,
irregularities...). As with the tangent1-method, this polynomial or tangent2-method also provides
two different contact angles (θLeft and θRight).
Finally, the Young-Laplace method determines the drop shape through a sophisticated
method and by considering gravity. Therefore, it is necessary that the drop is symmetrical. This
approach has, together with the tangent2-method, the widest contact angle range. A summary of
the different approaches is given in tabel 1.3.
19
Determination of surface energy using different approaches
TABEL 1.3 - SUITABEL FITTING MODELS – CIR: CIRCLE METHOD; HW: HEIGHT WIDTH; TAN1:
TANGENT 1 METHOD; TAN2: TANGENT 2 APPROACH; YL: YOUNG LAPLACE
Contact
Contour shape that
Method
angle range
can be modelled
CIR
0-20°
symmetrical
shapes drop to circular arc
H-W
0-20°
symmetrical
makes rectangle around drop
Tan 1
10-100°
slightly asymmetrical
fits drop to equation
Tan 2
10-180°
very asymmetrical
only evaluates the phase contact region
Y-L
10-180°
symmetrical
fits drop to equation, taking gravity into account
20
Determination of surface energy using different approaches
2
AIM OF THIS STUDY
Improving drug solubility can be done by different solid dispersion approaches. In this
work, attention is given to the solid crystal suspension method. Dispersing the drug in a matrix on
a particle level makes this method universally applicable. Extensive research to find a perfect
drug-carrier match is therefore not needed anymore. Hence, different kind of drugs and excipients
can be used with the solid crystal suspension approach. This work has its focus on griseofulvin
and mannitol.
Considering the solid crystal suspension approach, a mathematical model is under
development to understand and validate the thermodynamics and kinetics of this dosage form.
Thereby different parameters are considered (e.g. crystal energy, solubility, diffusivity, surface
energy…). The overall goal is the fundamental understanding of this technology in order to
recognize the advantages and limitations. This work focuses on a limited part of this project: the
determination of surface energy.
The surface energy, which is a reflection of intermolecular interactions, is best described
by analyzing the interaction of the surface with carefully selected liquids. In this work, distilled
water and diiodomethane were used and surface energy was determined using the two-liquid
mathematical model, presented by Owens & Wendt.
21
Determination of surface energy using different approaches
3
EXPERIMENTAL
3.1
MATERIALS
Griseofulvin (C17 H17 Cl O6, MG = 352.8, fig. 3.1) is an orally administrated class-II- drug
that is given to patients suffering from tinea infections of the nails, skin and hair. It is practically
insoluble in water. Absorption from the gastro-intestinal tract is variable and incomplete, due to
low solubility, low wettability and high crystal energy. Consequently, this solid compound is
perfect as research topic. Micronized griseofulvin from Hawkins (Minneapolis, USA) was used
in this work.
(FIG. 3.1 – GRISEOFULVIN
FIG. 3.2– MANNITOL
Mannitol (C6 H14O6, MG=182.2, fig. 3.2) is a sugar-alcohol with 6 hydroxyl groups. It has
all the requirements (high stability, low toxicity and high solubility) needed to be a good
excipient for the solid crystal suspension approach. Mannitol was obtained from Roquette
(Lestrem, France).
Liquids used for these experiments were pure water, made via distillation (Muldestordevice, Wagner&Munz, München, Germany), and diiodomethane (Merck, Hohenbrunn,
Germany). Water has, due to hydrogen bonding, a very high surface polarity and forms, thanks to
its high surface tension, a measurable drop on a tablet (slow wettability). Diiodomethane interacts
only on a dispersive level with other compounds but has due its molecular symmetry also a high
surface tension.
22
Determination of surface energy using different approaches
3.2
METHODS
3.2.1
Wilhelmy plate
Liquid vapor surface tension was measured by a K100 Tensiometer (Krüss, Hamburg,
Germany) with the Labdesk 3.0 as software. A roughened platinum Wilhelmy plate (Krüss,
Hamburg, Germany) with a width, thickness and height of 19.9mm, 0.2mm and 10mm was
lowered into a liquid to determine its surface tension. Measurements were done with a measuring
speed of 3mm/min and a sensitivity of 0.001g. Immersion depth of the Wilhelmy plate was set at
3mm. The experiment ran for 90 seconds, each 9 seconds a value was obtained.
The tensiometric software gave a graph of the surface tension to time. After carefully
analyzing this graph, the last 8 or last 5 values were taken into account depending on whether the
liquid water or diiodomethane was.
3.2.2
Lucas-Washburn
Glass tubes from Krüss (Hamburg, Germany) with a diameter of 1 cm and a glass cinter
filter at the bottom were used in these experiments. They were filled with 250mg of powder and
densified in order to achieve a constant porosity and therefore a good and repeatable packing.
The liquid was added to the vial 5minutes before the experiment in order to reach equilibrium
state.
Powder density was analyzed by evaluating the rise of n-heptane (Baker, Deventer,
Holland), with a given density of 0.684g/cm³, viscosity of 0.409mPa.s and a surface tension of
20.4mN/m, in 1g densified griseofulvin during a 3-minutes period. A longer measurement was
needed to obtain an idea of the powder densification its repeatability.
The procedure for other Lucas Washburn experiments, was set at a measuring time of
60seconds with a fast acquisition data set during the first 5 seconds to have more accurate data at
the start. The amount of powder added was 250mg, linear curve fitting was used and
measurements were done at room temperature.
23
Determination of surface energy using different approaches
3.2.3
Tensiometric contact angle determination
Having knowledge of the liquid surface tension, contact angle measurements could be done
with the tensiometer K100 (Krüss, Hamburg, Germany).
Tablets were evaluated with a digital measuring device (Mitutoyo, Neuss, Germany) with
an accuracy of 0.001mm in order to accurately determine the diameter. The latter was very
important in order to obtain an accurate wetted length (L). Attachment of the tablet to the
measuring sensor of the tensiometerK100 was done with glue (Pritt tesa stick, Beiersdorf,
Hamburg, Germany). The tablets that were lowered at a measuring speed of 3mm/min, into a
liquid with known surface tension, for a period of 90seconds. All analyses were done at a room
temperature of 24°C.
3.2.4
Goniometric contact angle determination
The drop shape analysis system (DSA100, Krüss, Hamburg, Germany) was used for
optical determination of the contact angle between a tablet and a selected liquid.
The drop shape analyzer (DSA) determines the contact angle in two steps. First of all, the
drop image is subjected to a gray level analysis, resulting in an optically determined contour line
around the phase boundary. Secondly, the contact angle is determined from the angle between the
drop shape contour function and the sample surface. The latter is reflected by the surface baseline
which has an important influence on the contact angle determination.
A syringe with a blunt end (0.40 x 25 mm) from Braun (Melsungen, Germany) was used to
form symmetrical drops. Camera angle and drop volume were set at 2° and 0.75µL, respectively.
Illumination strength was set at 50 % to obtain a good drop perception. Contact angles on the
bottom and/or top surface of the tablet were determined. The circle approach and the YoungLaplace method were found to be the best fitting methods. All measurements were done at room
temperature (24°C).
Determining the polar and dispersive fractions of water was done using the goniometric
approach and a Teflon plate (polytetrafluorethyleen, Stintmann, Düsseldorf, Germany).
24
Determination of surface energy using different approaches
3.2.5
Tabletting
Tablets were made by a Flexitab tablet press (Röltgen marking systems, Seevetal,
Germany). Micronized griseofulvin and mannitol were weighed (250mg) with a Sartorius A200S
analytical balance (Sartorius, Garching, Germany).
Mannitol tablet production was causing problems due to capping of the powder with a
fragile and easily breakable tablet as a result. Therefore, mannitol powder was first reduced in
particle size (x50=8µm) and consequently tablets were made at a lower pressure. The main
objective of tablet production was to create flat and homogeneous surfaces.
Larger griseofulvin tablets (8mm x 13mm, 1.5g), needed for the tensiometric contact angle
determination were made with a manual hydraulic press (Perkin Elmer, Massachusetts, USA)
with a pressure of about 400 kN/m².
Production of large mannitol tablets was impossible with the manual hydraulic press.
Capping of the powder occurred, resulting in a fragile tablet at all pressures evaluated. As an
alternative, mannitol was melted and the liquid phase was poured into the tablet holder of the
manual hydraulic press. After a cooling process of 5 minutes, mannitol tablets with the same
diameter (13.04mm) as the griseofulvin tablets were obtained.
3.2.6
Jet milling
Mannitol was jet-milled in order to reduce the particle size to the same range of
griseofulvin (5-15µm). Jet-milling occurred with a Spiral Mill 50 AS (Hosokawe Alpine,
Augsburg, Germany) with a mill- and inject pressure of 3 and 5 bar, respectively.
25
Determination of surface energy using different approaches
4
RESULT AND DISCUSION
4.1
LUCAS-WASHBURN
4.1.1
Contact angle of griseofulvin
The packaging of the powder (powder densification) and therefore the repeatability is
tested. Ten measurements of 3 minutes are performed and no large differences in packing were
detected visually. The constants calculated by fitting a straight line through the linear ascending
part of the curve (before reaching the plateau) are listed in figure 4.1. The constant is on average
2.609 x10-6 cm5 with a standard deviation of 0.2455 x10-6 cm5. Hence the packaging method was
found to have a sufficient repeatability with the goal of contact angle determination.
Constant Determination
constant (x10^-6)
3,500
3,000
2,500
2,000
1,500
1,000
0,500
0,000
0
1
2
3
4
5
6
7
8
9
10
sample
FIG 4.1 - CONSTANT DETERMINATION MEASURED BY THE RISE OF N-HEPTANE THROUGH
GRISEOFULVIN POWDER WITH THE GOAL OF EVALUATING THE POWDER DENSIFICATION AND ITS
REPEATABILITY
Secondly, once the constant is known, contact angles can be calculated using a second
liquid. After packaging and lowering the device into the water, there appeared to be no sorption
due to the low wettability between griseofulvin and water. Hence the requirement of a contact
angle lower then 90° is not fulfilled, resulting in a inappropriate method.
In addition, proof of the low wettability effect is found by measuring the contact angle
between water and non-compressed powder in a petri-dish described in section 4.3.1.3. The
contact angles obtained with the powder are larger than the ones obtained with the tablets.
26
Determination of surface energy using different approaches
4.1.2
Contact angle of mannitol
Experiments are done with 250mg of powder and with a fast acquisition data for the first
five seconds. A sigmoid curve is obtained with heptane (reference liquid). However, the
difference of the increase in square mass between heptane and water is too large to be correct
(figure 4.2)
0,16
0,14
Mass² (g²)
0,12
0,1
Heptane
0,08
Water
0,06
0,04
0,02
0
0
10
20
30
40
50
60
70
Time (sec)
FIG 4.2 - INCREASE IN SQUARE MASS PLOTTED AGAINST THE TIME WITH THE GOAL OF CONTACT
ANGLE DETERMINATION BETWEEN MANNITOL AND WATER USING THE LUCAS WASHBURN
METHOD
The first reason that causes this problem can be the dissolution of mannitol into water.
Subsequently, experiments are done with mannitol-saturated water, but still the same problem
occurred. Extensive cleaning of the filters also did not help. A third reason could be that water is
not sufficiently wetting the powder. The wetting ability of water in mannitol is therefore tested
but is found to be sufficient. Based on information provided by Dr. Kirchner (Krüss, Hamburg,
Germany), the assumption is made that the used glass cinter filters are inappropriate for the
experiments with water. Probably hydrophilic liquids have difficulties to pass through the filter in
order to wet the powder. A solution could be to use changeable paper filters, but due the tight
time frame and the lack of appropriate equipment these experiments could not be done during this
project.
27
Determination of surface energy using different approaches
4.2
TENSIOMETRIC CONTACT ANGLE DETERMINATION
4.2.1
Griseofulvin
The tensiometric contact angle measurement is an independent method, meaning it is not
affected by measuring parameters. However this promising method is difficult to perform, when
the experiments are analysed.
Artefacts are detected on a regular base. In the graph force plotted against the immersion
depth, irregularities of force measurements are detected at the start. Cause of this effect is the
tablet entry into the liquid. A perpendicularly entry in the liquid is very important and since one
side of the tablet is wetted first, this results in irregularities at the start which influences the
following measurements.
Contact angles are measured by taking the inverse cosines of Fw / L γLV (see eq 1.8). If
this value changes with a factor of 0.1, the difference in calculated contact angle is at least 6°.
Considering this statement, the tensiometric contact angle determination is not accurate enough to
detect the small difference between the diiodomethane surface tension and the solid surface
energy. In several experiments the inverse cosine is as a result above 1 which is mathematically
impossible to calculate.
Water, on the other hand, has a higher surface tension and the inverse cosines is always
below one. Six measurements between water and griseofulvin (of ten in total) where no artefacts
were detected are listed in tabel 4.1. It can be noticed that the range of contact angle results is too
large and therefore the precision too low (standard deviation around 4°) to achieve repeatable
results. As a consequence, this method is found to be not suitable to determine the contact angle
of griseofulvin.
Considering the use of this method, the outcome is that in order to determine the contact
angle with griseofulvin, only a high surface tension liquid (e.g. water) can be used. The
difference between the diiodomethane surface tension and the griseofulvin surface energy is too
small to be detectable by this approach.
28
Determination of surface energy using different approaches
TABEL 4.1 –TENSIOMETRIC CONTACT ANGLE BETWEEN GRISEOFULVIN AND WATER
4.2.2
Sample
Cos θ
θ (°)
1
0,4966
60° 13’
2
0,4054
66° 05’
3
0,4201
65° 09’
4
0,5422
57°09’
5
0,5586
56° 02’
6
0,4865
60° 53’
Mannitol
Mannitol tablets could not be made with the manual hydraulic press. Capping of the
mannitol powder is resulting in fragile and easily breakable tablets. Therefore, tablets are made
by a melting and re-solidification process. Results of these experiments are presented in tabel 4.2.
The contact angle (θ) is calculated with the following equation: Fw = γlv L cos θ.
A disadvantage is that, due the melting and crystallisation, the material properties are
changed and the values are therefore incomparable with the contact angles obtained with the
goniometric approach (section 4.3.4). Again a low precision is detected (standard deviation of
around 3°)
TABEL 4.2 - CONTACT ANGLE BETWEEN MANNITOL AND DISTILLED WATER - DETERMINED BY
THE TENSIOMETRIC APPROACH
Fw: Wetting force (mN)
Cos (θA)
θA
1
2,7578
0,9312
21° 22’
2
2,8185
0,9517
17° 52’
3
2,7089
0,9147
23° 50’
29
Determination of surface energy using different approaches
4.3
4.3.1
GONIOMETRIC: THE DROP SHAPE ANALYZER
Preliminary studies
4.3.1.1 Tablet sides
The top and bottom surface of griseofulvin tablets are twice tested by an unpaired t-test
with a significance level of 0.05: no statistical difference appeared between both (Tabel 4.3).
Both time, the null hypothesis (HO) cannot be rejected since T < t with 95% of certainty. As a
consequence, the bottom and top surface of the tablets can be used in the experiments.
TABEL 4.3 - UNPAIRED T-TEST: TABELT SIDES (TOP AND BOTTOM) EVALUATION WITH RESPECT
TO THE CONTACT ANGLE AT A SIGNIFICANCE LEVEL OF 0.05 - WATER AND DIIODOMETHANE
WERE USED ON GRISEOFULVIN TABELTS
Null hypothesis (HO)
Mean top = mean bottom
Alternative hypothesis (HA)
Mean top ≠ mean bottom
(x A − xB )
T=
(
σ A2
nA
+
σ B2
nB
t
n A + n B − 2 ,
)
α
2
1
Water
CH2I
1.1300
0.7347
2.000
2.000
2
Furthermore, mannitol tablets are subjected to an unpaired t-test with a 0.05 significance
level. The obtained T-value is -23.92, resulting in a statistical significance difference between the
top and bottom of a mannitol tablet. The drop kinetic of a water drop on the top of a mannitol is
therefore different: it is more dependent on time. Proof is given by a higher contact angle
variance (higher standard deviation for the top side of the tablet) and a visual conformation of a
faster immersion into the top side of the tablet. Hence, only the bottom side is used in following
experiments.
30
Determination of surface energy using different approaches
4.3.1.2 Drop kinetics
As the behavior of a water drop on a griseofulvin tablet is not uniform, this complicated
the contact angle measurements. During the first seconds, the drop shape is influenced by a fast
wetting of the surface, resulting in a fast decrease (slope: -3.394) of the contact angle.
Subsequently to the fast wetting, immersion becomes more important which will cause, together
with the slow wettability, a more slightly decrease (slope: -0.3885) of the contact angle. The fast
wetting of the solid sample can be seen on fig 4.3 during the first two seconds, followed by an
immersion effect and a slow wettability that starts after two seconds and ends when the drop is
completely disappeared (only first 20seconds are provided in fig 4.3).
Contact Angle (°)
65
60
55
50
45
0
2
4
6
8
10
12
14
16
18
20
Time (sec)
FIG 4.3 - CONTACT ANGLE VS TIME – FIRST TWO SECONDS = FAST WETTING = FAST DECREASE IN
CONTACT ANGLE, FOLLOWED BY A MORE SLIGHTLY DECREASE EXPLAINED BY A SLOW
WETTING AND AN IMMERSION EFFECT.
4.3.1.3 Powder vs. Tablets
The fast wetting properties at the start (first two seconds in fig 4.3) can be explained using
the surface energy of griseofulvin. A high solid surface energy is unfavorable for a solid sample,
resulting in a high desire of reducing its solid-air interface. Hence, by placing a drop on the
surface, the powder reduces its solid-air interface by surrounding powder particles with liquid.
An image (fig 4.4) is taken a few milliseconds after a water drop has slightly touched loose
griseofulvin powder to have visual confirmation about this effect (water drop is completely
surrounded by powder). The same effect is recognized for mannitol.
31
Determination of surface energy using different approaches
FIG 4.4 - VISUAL CONFORMATION BETWEEN A DROP SURROUNDED BY POWDER (LEFT) AND A
PURE DROP WITH A SMOOTH DROP SHAPE (RIGHT)
4.3.2
Experimental design
A full factorial design with three quantitative factors on two levels and one center point is
set up. The entire model is repeated twice and done for water as well as diiodomethane
(qualitative factor), resulting in 54runs. The goal is to evaluate the influence of the drop volume
(DV), the camera angle (Ang), the illumination strength (Lig) and the type of liquid (Liq) on the
contact angle. The contact angle is determined using the circle fitting method or the YoungLaplace fitting approach (described in section 1.4.3.5). The design of experiment (DOE) is listed
in tabel 4.4.
TABEL 4.4 - DESIGN OF EXPERIMENT: FULL FACTORIAL DESIGN: FACTORS AND LEVELS
Factors
Abbreviation
-1
Level
0
1
Drop volume
(µL)
DV
0.50
0.75
1
Camera angle
(°)
Ang
1
2
3
Illumination
strength (%)
Lig
35
50
65
Type of Liquid
Liq
Water
-
Diiodomethane
32
Determination of surface energy using different approaches
The DOE-dataset is fitted to a MLR (Multiple Linear Regression), which presents a linear
relationship between the variables, resulting in equation 4.1. Considering the negligible influence
of the interaction coefficients, a backward regression on the given model is done. A simplified
equation (eq 4.2) is the result, its coefficients are presented in fig 4.5.
Y = Z. [DV] + Y . [Angle] + X . [LIQ] + W . [DV . Angle] +
(equation 4.1)
V . [DV . Liq] + U . [DV . Lig] + T . [Angle . Liq] +
S . [Angle Lig] + R . [Liq . Lig] + C
EQUATION 4.1 - MLR-MODEL - DV=DROP VOLUME, ANGLE= CAMERA ANGLE, LIQ= LIQUID, LIG=
ILLUMINATION STRENGTH (LIGHT), C= CONSTANT VALUE, Z-R= COEFFICIENTS
Y = Z. [DV] + Y . [Angle] + X . [LIQ] + C
(equation 4.2)
EQUATION 4.2 - MLR-MODEL AFTER BACKWARD REGRESSION - DV=DROP VOLUME, ANGLE=
CAMERA ANGLE, LIQ= LIQUID, LIG= ILLUMINATION STRENGTH (LIGHT)
FIG 4.5 - MAIN FACTOR COEFFICIENTS - DV= DROP VOLUME, ANGLE= CAMERA ANGLE, LIQ=
LIQUID, LIG= ILLUMINATION STRENGTH, YL= YOUNG-LAPLACE, CIR= CIRCLE FITTING METHOD
33
Determination of surface energy using different approaches
Concerning the data in fig. 4.5, it can be noticed that only the type of liquid plays an
important role in the determination of the contact angle. Confidence intervals (α=0.05) of the
three other main factors include zero indicating they have a negligible effect. The only exception
is the influence of the camera angle with the YL method. It has a 95% confidence interval of
[0.167 - 2.137], but compared to the liquid influence, this factor is also considered as negligible.
Furthermore, this effect is not noticeable with the circle fitting method. Hence, this main effect
has not been taken into account for the contact angle determinations.
The quality of the model can be characterized by four parameters presented in tabel 4.5.
These presented values are obtained after performing a backward regression where only the main
effects are taken into account (all interaction factors had considerably high p-values).
TABEL 4.5 – PARAMETERS THAT DESCRIBE THE QUALITY OF THE DOE – R²= COEFFICIENT OF
DETERMINATION, Q²= PREDICTION VALUE, P= P-VALUE , CV= COEFFICIENT OF VARIATIONS, YL=
YOUNG LAPLACE DROP SHAPE FITTING METHOD, CIR= CIRCLE FITTING METHOD
R²
CV
Q²
P-value
YL-method
0.9737
0.9709
0.9704
0.9500
CIR-method
0.9846
0.9857
0.9810
0.4877
The coefficient of determination (R²) is a number between zero and describes how good
the regression line represents the data. In this statistical design a R² of 0.9737 and 0.9846 is
calculated for the YL- and the CIR-method, respectively. Secondly, the variations coefficient
(CV) is a reflection of the model repeatability which was also sufficient (0.9709 and 0.9857 for
YL- and CIR-fitting method, respectively) in the DOE.
Q² is a value that analyses the predictability of the model. How well new obtained values
fit the DOE is expressed by Q². The higher this value is (between 0 and 1), the better a data point
can be predicted based on previous values. The presented values are found to be sufficient:
0.9704 (YL) and 0.9810 (CIR).
34
Determination of surface energy using different approaches
The p-value expresses the probability of obtaining a result at least as high as the one that
was actually observed, assuming that the H0-hypothesis is true. This p-value is compared to the
significance level (α). The H0 can be rejected if the p-values are lower then the significance level.
In this case, the p-values are 0.9500 for YL and 0,4877 for the CIR-method. Both of them are
clearly higher then 0.05, therefore the Ho-hypothesis is correctly rejected with 95% of certainty.
Regarding the parameters in tabel 4.5, it must be concluded that the model, fitted by a
multiple linear regression (MLR), is of a high quality.
Following the DOE described in section 4.3.2 experiments are done at center point
conditions. These conditions are selected while they are, thanks to the DOE, protected from
influences (e.g. camera angle, light, drop volume) on each possible side. Considering tabel 4.5
this means that all contact angle determinations are done at an illumination strength of 50%, a
camera angle of 2° and a drop volume of 0.75µL.
4.3.3
Griseofulvin tablets: contact angles
Considering the drop kinetics (see preliminary study results, section 4.3.1), contact angle
determinations are done after two seconds. Reason for this is exclusion of the time variance at the
start caused by a fast wetting process.
4.3.3.1 Griseofulvin - Pure water
Water drops with a volume 0.75µL are placed on several griseofulvin tablets at different
positions, resulting in a total of sixty measured
griseofulvin-distilled water interactions. Fitting is done
by the YL- or CIR-method after two seconds. The
obtained averages with YL and CIR are 54.7° and 53.0°
with the following 95% confidence intervals: [54.2° 55.2°] and [52.4° - 53.6°].
FIG 4.6 - WATER AND GRISEOFULVIN
35
Determination of surface energy using different approaches
4.3.3.2 Griseofulvin – Diiodomethane
Interactions between a griseofulvin tablet and
diiodomethane are more difficult to obtain since
diiodomethane has a lower surface tension and therefore a
faster wettability on the tablet. As a consequence, contact
angles are small with higher standard deviations and
larger confidence intervals. Furthermore, due the higher
wettability and therefore larger spreading over the
surface, more tablets needed to be made.
FIG 4.7 - DIIODOMETHANE AND GRISEOFULVIN
Data are obtained by placing diiodomethane drops on tablets at different positions,
resulting in a total of sixty contact angle determinations. Fitting is done by the YL- or CIRmethod after two seconds. The obtained averages with the YL- and CIR-method are 17.6° and
17.5° with the following 95% confidence intervals: [16.8° - 18.4°] and [16.8° - 18.2°].
4.3.4
Mannitol tablets: contact angles
4.3.4.1 Mannitol - Diiodomethane
Interaction of mannitol and diiodomethane is measured sixty times by taking a picture of
the event after two seconds. The obtained averages with the YL- and CIR-method were 15.6°
and 15.7° with the following 95% confidence intervals: [15.1° - 16.1°] and [15.2° - 16.2°].
4.3.4.2 Mannitol - Pure water
The droplet disappeared to quickly after placing it on the mannitol tablet due to (1) high
porosity (2) dissolution and (3) fast wettability. Consequently, the mannitol powder is introduced
into a jet milling two times in order to reduce the particle size and therefore decrease the porosity
with the goal of having measurable drops.
36
Determination of surface energy using different approaches
Since the contact angle is still decreasing very fast and since it was still important to
determine the interaction of water and mannitol after two seconds, another method is used
comparing to the previous experiments. A video with a special software that automatically
determines the baseline is used in this matter. Hence the precision of the contact angle
determinations is based on the precision of the baseline detection software. This latter is not
always sufficient, resulting in a higher standard deviation. Another disadvantage is that the
software is using only one drop shape fitting method. In this matter, choice is made in benefit of
the CIR-method, as it had the highest precision. In addition, the expected low contact angles
benefits the choice to the CIR-method as explained in tabel 1.3. Despite, the limitations this
method is still selected while it was important to determine the interaction with pure water after
two seconds exact.
Consequently sixty measurements are done with the CIR-method, resulting in an average
result of 23.4° and with a 95% confidence interval of: [22.2° - 24.7°]. As expected, this
experiment has by far the largest confidence interval. All results are, as a summary, listed in
section 4.4.3.
4.4
4.4.1
PARAMETERS NEEDED TO CALCULATE THE SURFACE ENERGY
Surface tension
The surface tension of pure water, determined with the Wilhelmy plate method, is 72.28
mN/m with a 95% confidence interval of [72.28 ± 0.02]. Diiodomethane, on the other hand, is
characterised with a surface tension of 48.95mN/m and a 95% confidence interval of [48.95 ±
0.03].
TABEL 4.6 - SURFACE TENSION OBTAINED BY THE WILHELMY PLATE METHOD WITH
CORRESPONDING STANDARD DEVIATION AND 95% CONFIDENCE INTERVAL
surface tension (mN/m)
Pure water
72.28
Diiodomethane
48.95
Standard deviation (mN/m)
0.11
0.21
95% Confidence interval
[72.28 ± 0.02]
n= 160
[48.95 ± 0.03]
n=180
37
Determination of surface energy using different approaches
4.4.2
Liquid polar and dispersive fractions
The total liquid surface tension is divided into the polar and the dispersive fractions.
A tetrafluoroethylene (Teflon) plate has, due its molecular structure, no dipole moment
and interacts therefore only on a dispersive level with other liquids. By measuring the interaction
that a liquid has with the Teflon-plate (expressed as the contact angle), calculations can be made
to determine the liquid dispersive fractions.
Contact angles are determined six times between Teflon and distilled water, resulting in
an average of 116,3° and a 95% confidence interval of [116,0 – 116,6]. Considering the Owens &
Wendt equation, this form can be simplified by excluding the polar fractions, resulting in
equation 4.3.
D D
γ LV (cosθ + 1) = 2(γ SV
γ LV )
1
2
(equation 4.3)
EQUATION 4.3 – SIMPLIFIED OWENS & WENDT METHOD - γLV : LIQUID-VAPOR SURFACE ENERGY,
θ: CONTACT ANGLE BETWEEN LIQUID AND SOLID SAMPLE, γSV : SOLID-VAPOR SURFACE
D
ENERGY, γ
: DISPERSIVE FRACTION
The only unknown parameter in the simplified Owens & Wendt equation, is the dispersive
D
fraction of the liquid-vapor surface energy ( γ LV
). The latter can therefore be easily calculated,
resulting in a value of 20.3mJ/m² or 20.3mN/m for water. Since the total surface tension of pure
water is known (72.28mN/m, tabel 4.6), the polar parts can also be calculated, with 52.0mN/m as
a result. Water used in these experiments interacts therefore for 28% on a dispersive level and for
72% on a polar level.
Diiodomethane has, due his structural symmetry, no polar fractions. The total liquid
surface tension of diiodomethane is therefore equal to the dispersive fraction of the liquid surface
tension, which is 48.95 mN/m (tabel 4.6).
38
Determination of surface energy using different approaches
4.4.3
Contact angles
TABEL 4.7 - GONIOMETRIC EXPERIMENTS: CONTACT ANGLES WITH THEIR 95% CONFIDENCE
INTERVAL - CH2I= DIIODOMETHANE, YL= YOUNG LAPLACE DROP SHAPE FITTING METHOD, CIR=
CIRCLE FITTING METHOD
4.4.4
Griseofulvin - water
YL (°)
54.7 ± 0.57
CIR (°)
53.0 ± 0.61
Griseofulvin - CH2I
17.6 ± 0.78
17.5 ± 0.73
Mannitol - CH2I
15.6 ± 0.44
15.7 ± 0.43
Mannitol - water
/
23.4 ± 1.25
Energy determinations
The Owens & Wendt equation (eq 4.4) is used as a mathematical basis to perform the
calculations needed to determine the total solid surface energy.
1
1
D D
P
P
γ LV (cosθ + 1) = 2[(γ SV
γ LV ) 2 + (γ SV
γ LV
) 2]
(equation 4.4)
EQUATION 4.4 – OWENS & WENDT METHOD - γLV : LIQUID-VAPOR SURFACE ENERGY, θ: CONTACT
ANGLE BETWEEN LIQUID AND SOLID SAMPLE,
DISPERSIVE FRACTION, γ
γSV
: SOLID-VAPOR SURFACE ENERGY,
γD:
P
: POLAR FRACTION OF THE SURFACE ENERGY
The liquid diiodomethane interacts only on a dispersive level, therefore the simplified
D
. Results
Owens & Wendt equation is used to calculate the unknown parameter, which now is γ SV
are 46.7 and 46.9 mJ/m² for griseofulvin and mannitol, respectively.
Water interacts with the solid surface on a polar and dispersive level. Hence, before
calculating this parameter, there should be knowledge of the dispersive solid fractions (see
paragraph above). Equation 4.1 is used with 14.1 and 28.5 mJ/m² as results for griseofulvin and
mannitol, respectively.
39
Determination of surface energy using different approaches
The total surface energy of griseofulvin and mannitol are calculated by summing up the
polar and dispersive fractions. In addition, based on the Young equation (eq. 1.2), the solid-liquid
interfacial tension (γSL) and the Gibbs free energy of immersion can be calculated. Results are
listed in tabel 4.8.
TABEL 4.8 – DIFFERENT ENERGIES OF GRISEOFULVIN AND MANNITOL CALCULATED USING THE
OWENS & WENDT EQUATION AND THE YOUNG EQUATION
Energies (mJ/m²)
Griseofulvin
Water
Water
60.8
Surface Energy (mJ/m²)
γSL (mJ/m²)
CH2I
Mannitol
CH2I
75.4
17.3
14.2
9.0
28.5
- 43.5
-46.7
-66.3
-46.9
Gibbs free
energy(mJ/m²)
Considering the results in the above tabel, it can be concluded that the dissolution of
mannitol in water is thermodynamically more favourable than griseofulvin. Dissolution of the
solid samples in diiodomethane is thermodynamically similar. A higher mannitol surface energy
is explained by the higher amount of polar fractions: 14.1 and 28.3mJ/m² for griseofulvin and
mannitol, respectively. Dispersive fractions are considered to be the same: 46.7 and 47.1mJ/m²
for griseofulvin and mannitol, respectively. By summing both polar and dispersive fractions, the
total solid surface energy can be calculated as listed in tabel 4.8.
4.4.5
Evaluation of porosity effects
With respect to drop kinetics (analysed in section 4.3.1.2), the tablet porosity is found to
have an important impact on the contact angle. The powder characteristics are therefore not
explained by tabel 4.8. It is only correct for a certain amount of porosity. Tablet porosity can be
seen as a mixture of air and powder. A higher porosity results in a higher solid-air interface
leading to a faster liquid immersion into the tablet and therefore smaller contact angles.
40
Determination of surface energy using different approaches
Excluding the porosity should give a better image of the solid-liquid interaction
(expressed as the contact angle between both phases). Tablets with different porosities are
therefore made and plotted against their contact angles (fig 4.8 and fig 4.9). A linear trend line is
added to determine the correlation between different data points. By extrapolating these trend
lines to the point of zero porosity, the true solid-liquid contact angle is obtained without the
influence of porosity (no air between different powder particles).
The contact angle on griseofulvin with water and diiodomethane is, based on this
approach, 73.2° and 26.1°. With respect to mannitol, values are determined at 48.5° and 37.4° for
tablets with zero porosity. Consequently, values in tabel 4.9 are changed and listed in tabel 4.9.
TABEL 4.9 - CORRECTION - SURFACE ENERGIES OF GRISEOFULVIN AND MANNITOL
Energies (mJ/m²)
Griseofulvin
Water
Mannitol
CH2I
Water
49.5
Surface Energy
CH2I
58.9
(mJ/m²)
γSL (mJ/m²)
28.5
5.5
11.0
20.0
- 20.9
-44.0
-47.9
-38.9
Gibbs free
energy(mJ/m²)
Excluding the porosity effect results in a lower solid surface energy. By decreasing the
solid-air interface, the wetting properties of the powders are lowered resulting in a less desire of
covering the surface with a liquid, leading to a lower contact angle and therefore a lower surface
energy. Griseofulvin its surface energy is lowered by 11.3mJ/m² while surface energy of
mannitol is lowered for 16.5mJ/m². The porosity effect on mannitol is larger compared to
griseofulvin. Mannitol particle size variance is found to be the reason for this effect.
41
Determination of surface energy using different approaches
70
y = -1.7833x + 73.18
R2 = 0.8689
Contact angle (°)
60
50
40
Water
30
Diiodomethane
20
10
y = -0.7733x + 26.083
R2 = 0.7635
0
0
3
6
9
12
15
18
21
Porosity (%)
FIG 4.8 - CONTACT ANGLE VS POROSITY: GRISEOFULVIN AND DIIODOMETHANE/DISTILLED
WATER. CONTACT ANGLE IS DETERMINED BY EXTRAPOLATING THE TREND LINE TO A POINT OF
ZERO POROSITY
y = -1.78x + 48.532
R2 = 0.8332
40
40
35
35
30
25
20
15
30
25
20
15
10
10
5
5
0
y = -1.22x + 37.418
R2 = 0.5717
45
Contact angle (°)
Contact angle (°)
45
0
0
3
6
9
12
15
18
0
3
6
Porosity (%)
FIG
4.9
-
CONTACT
ANGLE
9
12
15
Porosity (%)
VS
POROSITY
FOR
RESPECTIVELY
WATER
(LEFT)
AND
DIIODOMETHANE (RIGHT) ON A MANNITOL TABELT. CONTACT ANGLE IS DETERMINED BY
EXTRAPOLATING THE TREND LINE TO A POINT OF ZERO POROSITY
42
18
Determination of surface energy using different approaches
5
CONCLUSION
Three different methods were considered to determine the contact angle. Griseofulvin and
mannitol were used as model substances and were selected based on their high crystal energies
and different water solubilities.
The contact angle can be used to calculate the surface energy and Gibbs free energy which
are useful parameters for fundamental understanding of pharmaceutical processes. Distilled water
and diiodomethane were identified as suitable probes for characterizing Griseofulvin and
Mannitol because the contact angle was in a measurable range.
The tensiometric and the Lucas Washburn approaches were found to be less repeatable than
the drop shape analysis. Therefore, the latter approach was used for further investigations.
Nevertheless, the measuring parameters such as camera angle, drop volume and illumination
strength were evaluated systematically in the design of experiments. The effects of all three
parameters were negligible which indicates a robust method. Finally, the effect of the porosity on
the contact angle was studied: a linear correlation between the porosity and the contact angle was
observed.
Surface energy calculations were done with a two-liquid model, first presented by Owens &
Wendt and with respect to the evaluation of the porosity, correction calculations were considered.
The obtained parameters should be used in a mathematical model to simulate the drug
release from a solid crystal suspension to proof the mechanism. The suitability of the results from
this study was not proofed but they are considered in following studies.
43
Determination of surface energy using different approaches
6
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Determination of surface energy using different approaches
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Determination of surface energy using different approaches
47