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Decoupling the Contribution of Dispersive and Acid-Base Components of Surface
Energy on the Cohesion of Pharmaceutical Powders
Umang V. Shaha, Dolapo Olusanmib, Ajit S. Narangb, Munir A. Hussainb, Michael J. Tobync, Jerry Y. Y. Henga*
a Surfaces and Particle Engineering Laboratory (SPEL), Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.
b Bristol-Myers Squibb Pharmaceuticals, 1 Squibb Drive, New Brunswick, NJ 08903, USAc Bristol-Myers Squibb Pharmaceuticals, Reeds Lane, Moreton, Wirral CH46 1QW, UK
*Corresponding Author: [email protected]: +44-(0)207-594-0784. Fax: +44-(0)207-594-5700 Web: www.imperial.ac.uk/spel
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Abstract
This study reports an experimental approach to determine the contribution from two different
components of surface energy on cohesion. A method to tailor the surface chemistry of mefenamic acid
via silanisation is established and the role of surface energy on cohesion is investigated. Silanisation was
used as a method to functionalise mefenamic acid surfaces with four different functional end groups
resulting in an ascending order of the dispersive component of surface energy. Furthermore, four
halogen functional end groups were grafted on to the surface of mefenamic acid, resulting in varying
levels of acid-base component of surface energy, while maintaining constant dispersive component of
surface energy. A proportional increase in cohesion was observed with increases in both dispersive as
well as acid-base components of surface energy. Contributions from dispersive and acid-base surface
energy on cohesion were determined using an iterative approach. Due to the contribution from acid-base
surface energy, cohesion was found to increase ~11.7× compared to the contribution from dispersive
surface energy. Here, we provide an approach to deconvolute the contribution from two different
components of surface energy on cohesion, which has the potential of predicting powder flow behaviour
and ultimately controlling powder cohesion.
Key Words: dispersive surface energy, acid-base surface energy, silanisation, de-coupling, cohesion
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1. Introduction
Inter-particle interaction is argued to be governed by the material surface properties. Mechanisms for
inter-particle interaction can be classified as two broad categories, physical and chemical interactions.
Chemical interactions involves mainly covalent, ionic, metallic or electrostatic bonds, whereas physical
interactions are a result of intermolecular forces, for example van der Waals and hydrogen bonding
(Kendall, 1994). In addition to chemical and physical interactions, mechanical interlocking and
diffusion are other two mechanisms widely discussed in the literature (Maeda et al., 2002). In industrial
particle processing, instantaneous formation of menisci in capillaries between adhered particles is
unavoidable and in such scenarios capillary forces of adhesion and inter-particle contact area becomes
increasingly important (Rabinovich et al., 2002). For the purpose of this study, the discussion is focused
on different intermolecular forces based on inter-particle interaction mechanisms. Furthermore, the
analysis is limited to the surface energetic heterogeneity/ homogeneity not taking into consideration role
of any structural or compositional heterogeneity.
In the current literature, focusing on the cohesion of pharmaceutical materials, a number of reports have
considered the role of surface energy on cohesion and powder flow properties (Barra et al., 1996; Barra
et al., 1998; Bhandari and Howes, 2005; Chen et al., 2010; Deng and Davé, 2013; Han et al., 2013; Jallo
et al., 2011; Kilbury et al., 2012; Moreno-Atanasio et al., 2005; Spillmann et al., 2008; Traini et al.,
2005; Young et al., 2003, 2004). Barra et al. investigated the effect of the surface energy and cohesion
parameters proposed by Wu (Wu, 1973) and Rowe (Rowe, 1989a, b) to predict the maximum value of
interaction parameters or strength of interaction between particles of binary mixture. Furthermore they
also studied the influence of polar and dispersive fractions of two interacting materials on prediction
(Barra et al., 1996; Barra et al., 1998). Moreno-Atanasio et al. used distinct element method (DEM) to
simulate the effect of surface energy on unconfined yield stress (UYS), revealing that an increase in
surface energy by an order of magnitude produced similar increase in simulated UYS (Moreno-Atanasio
et al., 2005). Traini et al. used atomic force microscopy as a tool to investigate adhesion-cohesion
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balance in pressurised metered dose inhalers, demonstrating a linear correlation between theoretical
work of cohesion/adhesion calculated from contact angle, inverse phase gas chromatography and atomic
force microscopy measurements (Traini et al., 2005). Chen et al. and Jallo et al. used surface
modification, either using silanisation of aluminium particles or using dry-coating method to coat
surface using silica particles, to reduce cohesion. Reduction in cohesion was attributed to the reduction
in surface energy; silanisation of aluminium was found to result in a reduction of the surface energy, and
subsequently measured cohesion values of silanised aluminium were observed to be lower, compared to
unsilanised aluminium (Chen et al., 2010; Jallo et al., 2011). On the basis of the findings of Chen et al.,
Han et al. investigated effect of dry coating on passivating the high energy sites of micronised ibuprofen
for improving flowability recently. Surface energy heterogeneity was observed to reduce as a result of
dry-coating and the surface energy follows a descending trend with increasing coating resulting in
reduction in cohesion (Han et al., 2013).
It is apparent from the current literature that surface energy has a major role to play in controlling
cohesion. However, whilst recent literature reports have suggested that a higher surface energy may
result in higher cohesion and suggested routes to passivate higher surface energy sites, no fundamental
understanding on the contribution from surface energy on cohesion compared to other surface attributes
have been reported. Recently methodology for de-coupling roles of different surface properties,
particularly, particle shape, surface area and surface energy has been established (Shah et al., 2014a;
Shah et al., 2014b). Considering that different components of surface energy can contribute towards
cohesion on the basis of contribution from intermolecular forces, this study focuses on developing an
approach for de-coupling the contribution from dispersive and acid-base component of surface energy
on cohesion.
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2. Materials
Mefenamic acid (2-(2, 3-dimethylphenyl) amino benzoic acid) (99.0%), n-heptane (99.0), n-octane
(99.0%), n-nonane (99.0%), n-decane (99.0%), dichlorodimethylsilane (>99.5%,), dodecyl
triethoxysilane (technical grade), vinyltrimethoxysilane (>97.0%), triethoxyphenylsilane (>98.0%), (3-
iodopropyl)trimethoxysilane (95.0%), (3-bromopropyl)trimethoxysilane (97.0%) and
trimethoxy(3,3,3-trifluoropropyl)silane (97.0%) were purchased from Sigma Aldrich, Dorset, UK.
Methanol (>99.5%), ethyl acetate (>99.5%), dichloromethane (>99.0%), n-hexane (>99.0%), and
cyclohexane (>99.0%) were received from VWR BDH Prolabo, Lutterworth, UK and (3-
chloropropyl)trichlorosilane (>97.0%) was received from Alfa Aesar, Heysham, UK. All chemicals
were used as received.
3. Methods
3.1 Silanisation of milled mefenamic acid
Milled mefenamic acid powders were silanised using a protocol reported in the literature (Al-Chalabi et
al., 1990). In a typical process, 500 mg of mefenamic acid powder was added to a 50 mL 5% (v/v)
solution of appropriate silane in cyclohexane. The mixture was refluxed at 80 oC for 24 hours. Then, the
reaction mixture is allowed to cool down to room temperature and filtered using general-purpose
laboratory filter paper (Whatman, UK) followed by drying in a vacuum oven at 80 oC for 4 hours. Post
silanisation, the silanised mefenamic acid powders were stored in a glass vial at ambient conditions.
3.2 Surface energy analysis
Surface Energy Analyser (SEA, Surface Measurement Systems Ltd., London, UK) was used for surface
energy heterogeneity characterisation. Approximately 300 mg of mefenamic acid was packed in pre-
silanised iGC columns (Surface Measurement Systems Ltd., London, UK) and conditioned for 2 hours
at 30 oC followed by pulse injection measurements. Methane was used to determine the column dead
time. Helium at a flow rate of 10 sccm was used as a carrier gas for all injections for the columns
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packed with un-silanised mefenamic acid, whereas 3 sccm helium flow rate was used for columns
packed with silanised mefenamic acid. A series of dispersive n-alkane probes (hexane, heptane, octane,
nonane and decane) at a range of concentrations were injected in order to achieve target surface
coverages (n/nm) ranging from 0.7% to 10%. Net retention volumes were calculated using the commonly
applied Schultz method (Schultz et al., 1987). Mono-polar probes (dichloromethane and ethyl acetate)
were injected at the same concentrations to determine non-dispersive interactions. The surface energy
due to the non-dispersive interactions was calculated using the vOCG method reported in the literature
(Das et al., 2010; Van Oss et al., 1988). Principles of the techniques and a review of currently literature
including theory, can be found elsewhere (Ho and Heng, 2013).
3.3 Uniaxial compression test
A uniaxial compression test was used for powder cohesion measurements. Cylindrical compacts of 5mm
diameter were prepared using an evacuable IR die (Specac Ltd., Slough, UK) at a minimum of three
different consolidation loads (10 N, 20N and, 40N). Post consolidation, confinements were removed and
yield load was measured using SMS texture analyser TA.XT2i (Stable Micro Systems Ltd., Godalming,
UK) equipped with a 5 kg load cell in a displacement compression mode, with compression speed of
0.02 mms-1. Consolidation and yield load values were divided by the contact area to convert into
consolidation and yield stress, respectively. Yield stress obtained was plotted as a function of
consolidation stress. A linear regression line can be plotted for yield stress as a function of consolidation
stress. Linear regression line was extrapolated to find intercept with y-axis showing yield load at zero
consolidation load, which is cohesion. Theoretical principles of this test are detailed elsewhere (Head,
1994; Wang, 2013).
4. Results and Discussion
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4.1 Isolating the effect of different components of surface energy on cohesion
4.1.1 Contribution of acid-base component of surface energy on cohesion
Dispersive (d) and acid-base (AB) surface energy heterogeneity profiles for mefenamic acid silanised
with four different haloalkane functional end groups, chloropropyl, trifluoropropyl, bromopropyl and
iodopropyl are presented in Figures 1 and 2 respectively. Post silanisation, the surface energies (both d
and AB) of mefenamic acid powders remained constant with increasing fractional surface coverage,
suggesting energetic homogeneity. For surface energy measurements to be representative of the entire
material surface properties, typical fractional coverages used for analysis ranges from n/nm=0.02 to 0.05
(Gamble et al., 2013; Gamble et al., 2012; Shah et al., 2014a; Shah et al., 2014b). The analysis of
energetically homogeneous surfaces remains similar for different fractional surface coverages.
Considering the range of fractional surface coverages typically used to provide material representative
surface energy, n/nm=0.02 was selected for analysis of both silanised and unsilanised materials.
d profiles for mefenamic acid silanised with different haloalkane functional groups were found to have
very similar surface energy values at different fractional surface coverages (40.00.3 mJ/m2). All
haloalkanes selected for this study have a propyl chain attached to the halogen atoms as a spacer and can
provide very similar dispersive interactions.
The acid-base component of surface energy was found to decrease in the order of -Cl > -F > -Br > -I
functional groups. For fractional surface coverage n/nm=0.02, the acid-base components of surface
energy for chloropropyl, trifluoropropyl, bromopropyl and iodopropyl are 7.7 mJ/m2, 5.2 mJ/m2, 3.9
mJ/m2, and 2.2 mJ/m2, respectively. The order of decrease in the acid-base surface energy observed in
this study can be explained by the functional end group properties, due to the electronegativity of
haloalkanes.
Unconfined yield stress was measured for powders silanised with haloalkane functional end groups and
the data is shown in Figure 3. Cohesion values were calculated from unconfined yield stress
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measurements following the method reported by Head, and plotted as a function of acid-base surface
energy (Figure 4) (Head, 1994). Cohesion was found to increase linearly with increasing acid-base
surface energy. The dispersive component of the surface energy for the powders silanised with
haloalkanes is very similar (40.00.3 mJ/m2), hence this increase in total surface energy is solely
attributed to the increase in the acid-base component of the surface energy. Considering the linear
relationship between cohesion and acid-base of surface energy, the intercept of the best fit line for
cohesion as a function of acid-base surface energy (when AB = 0 mJ/m2), will be attributed to the
dispersive surface energy. The cohesion (9.0 kPa) at the intercept of best fit line for cohesion as a
function of acid-base surface energy is net cohesion due to the dispersive surface energy at 40.0 mJ/m2
(Figure 4). By subtracting the cohesion due to the dispersive component (9.0 kPa) from the total
cohesion, the contribution of AB on cohesion can be determined as shown using dotted line in Figure 4.
4.1.2 Contribution of dispersive component of surface energy on cohesion
d heterogeneity profiles, before and after silanisation of mefenamic acid, are presented Figure 5. d
remained constant with increasing surface coverages for mefenamic acid silanised with different
functional end groups, whereas the d for unsilanised milled mefenamic acid was observed to decrease.
Therefore, it can be suggested that silanisation results in an energetically homogenous surfaces. d for
silanised mefenamic acid was observed in the ascending order from methyl, dodecyl, phenyl and vinyl
functional end groups. Acid base surface energy for surfaces silanised with vinyl and phenyl functional
groups were found to be higher compared to that of surfaces functionalised with methyl and dodecyl
functional groups. Variations here could be due to distribution of charge density and dipole moments.
Surface energy for mefenamic acid silanised with methyl functional groups was found to vary
minimally within the error bars from 32.7 mJ/m2 to 31.6 mJ/m2 with increasing fractional surface
coverage from 0.7% to 10%. Dichlorodimethylsilane is the silane used for grafting methyl functional
end group on to the surface. This molecule has no spacer and the methyl moiety is directly attached to
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the terminal end group, such that it provides no molecular flexibility to the functional end group.
Therefore the grafted (or deposited) methyl functional end group, which is known to be unreactive, is
very stable. Dodecyltriethoxysilane ((OC2H5)3-Si-CH2(CH2)10CH3) was used for grafting. Mefenamic
acid grafted with dodecyl end group has -CH2(CH2)10CH3 functional group attached to -Si without any
spacer. Dodecyl is a long chain functional end group and results in relatively higher dispersive surface
energy compared to methyl functional group, i.e. surface energy heterogeneity profile varies from 36.6
mJ/m2 to 34.9 mJ/m2 with increasing fractional surface coverage from 0.7% to 10%. Mefenamic acid
silanised with phenyl and vinyl functional groups resulted in surface energy heterogeneity profiles
ranging from 40.2 mJ/m2 to 40.5 mJ/m2 and 42.9 mJ/m2 to 42.8 mJ/m2 respectively for fractional surface
coverage ranging from 0.7% to 10%, thus demonstrating homogeneity. Considering the isostere at 2%
fractional surface coverage, dispersive component of surface energy was found to be 32.7 mJ/m2 for
methyl, 36.3 mJ/m2 for dodecyl, 40.7 mJ/m2 for phenyl and 42.3 mJ/m2 for vinyl silanised surfaces, and
46.4 mJ/m2 for un-silanised surfaces. The acid-base component of surface energy at an isostere of 2%
fractional surface coverage was calculated to be 0.4 mJ/m2 for methyl, 0.8 mJ/m2 for dodecyl, 3.0 mJ/m2
for phenyl and 3.0 mJ/m2 for vinyl silanised surfaces (Figure 6).
Uniaxial compression test was used for measurements of unconfined yield stress at three different
consolidation stresses for the silanised mefenamic acid and results are presented in Figure 7. With a
decrease in the dispersive component of the surface energy, a decrease in unconfined yield stress was
observed for 2040 kPa and 1020 kPa consolidation stress. For 510 kPa consolidation stress unconfined
yield stress for surfaces silanised with phenyl and vinyl are within experimental errors, and decrease in
unconfined yield stress was observed in the order of the surfaces silanised with phenyl vinyl >
dodecyl > methyl. Cohesion values calculated for methyl silanised surface was 10.3 kPa, dodecyl
functionalised surface was 12.1 kPa, vinyl functionalised surface was 16.0 kPa and phenyl
functionalised surface was 15.4 kPa. A proportional increase in cohesion as a function of dispersive
component of the surface energy was observed.
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To de-couple the contribution of the dispersive surface energy on cohesion from the acid-base
component, the correlation developed in section 4.1.1, was used to calculate net cohesion due to the
acid-base component of surface energy. However, the correlation developed between acid-base surface
energy and cohesion is only specific to the mefenamic acid. The approach reported here can be applied
to establish correlation for other systems. The total cohesion calculated is attributed to the total surface
energy, which has two components – the acid-base component and the dispersive component. To
calculate the cohesion due to dispersive surface energy, the cohesion due to acid-base surface energy
calculated previously was subtracted from the total cohesion.
A linear regression line was fitted to the net cohesion (due to dispersive surface energy calculated) as a
function of dispersive surface energy. As this regression line represent net cohesion due to dispersive
surface energy, it was fitted with a zero intercept, suggesting at zero dispersive surface energy,
calculated cohesion is also zero. An iterative approach was adopted to converge regression lines of net
cohesion as a function of acid-base and dispersive surface energy. Using the linear regression for the net
cohesion (due to dispersive surface energy) as a function of dispersive energy, cohesion due to the
dispersive energy at 40.0 mJ/m2 was calculated and the obtained cohesion was used to set intercept of
linear fit for total cohesion as a function of acid base surface energy. Such iterations were continued
until the cohesion value due to dispersive surface energy at 40.0 mJ/m2 calculated using both linear
regressions (net cohesion as a function of acid-base and dispersive surface energy), converged (9.03
kPa). Figure 4 shows the linear regression fits obtained as a result of iterative approach, showing the
correlation between net cohesion and dispersive as well as acid-base surface energy.
Net cohesion calculated due to the dispersive component of surface energy was found to be 9.2 kPa for
surfaces silanised with methyl, 10.0 kPa for surfaces silanised with dodecyl, 7.8 kPa for surface
silanised with phenyl and 8.3 kPa for surface silanised with vinyl functional end groups. Considering
the approach adopted here to calculate net cohesion due to the dispersive component only, a linear
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correlation, intersecting at the origin, for cohesion as a function of dispersive surface energy was
established and represented by an equation y = 0.226x (i.e. when dispersive surface energy is zero,
cohesion is zero as net cohesion is only due to dispersive surface energy). The correlation between
dispersive surface energy and cohesion is only specific to mefenamic acid.
For the model system investigated, the contribution from AB was found to result in ~11.7× higher
cohesion compared to contributions from d. i.e. when contributions from d was eliminated as a factor
in cohesion for material with same surface area, the remaining cohesion can be estimated from AB.
Furthermore, relationships between dispersive as well as acid-base surface energy and net cohesion due
to contribution from dispersive as well as acid-base surface energy were established.
The role of different components of surface energy on cohesion is system specific and also depends on
intrinsic properties of the material. In addition, the contribution from the dispersive and acid-base
components of surface energy on cohesion can be different for different materials and also depend on
the experimental conditions. The approach presented in this study shows the potential for developing a
fundamental understanding of contributions from different surface energy components on cohesion,
which will permit controlling cohesion by engineering particle surface properties either via appropriate
processing methods or crystal engineering.
5. Conclusion
Here, an approach for de-coupling the different components of surface energy has been demonstrated.
Silanisation was used as a tool to tailor surface energies of mefenamic acid. Methyl, dodecyl, phenyl
and vinyl functional groups were grafted on the mefenamic acid surface to investigate role of d,
whereas a series of haloalkanes functional groups were grafted to study role of AB on cohesion. Powder
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cohesion was found to increase in linear correlation with surface energy. A linear correlation between
AB and total cohesion was developed and used for determining contribution from d on cohesion. An
iterative approach was employed to converge the relationship between net cohesion (due to d) and
dispersive surface energy, and total cohesion and acid-base surface energy. For the model system
investigated, contribution from d and AB on cohesion was decoupled and correlation between net
cohesion (due to the d and AB) was established. Increase in cohesion was found to be ~11.7 × higher
due to contribution from AB compared to that of d. Findings of this study not only provided
fundamental understanding on effect of surface energy on cohesion but also can be used for
quantification of contributions from different components of surface energy.
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List of Figures
Figure 1 γd profiles for milled mefenamic acid silanised with –Cl, –F, –Br, and –I functional end groups.
Figure 2 γAB profiles for milled mefenamic acid silanised with –Cl, –F, –Br, and –I functional end groups.
Figure 3 Unconfined yield stress as a function of consolidation stress for mefenamic acid silanised –Cl, –F, –Br, and –I functional end groups.
Figure 4 Cohesion as a function of acid-base component of surface energy.
Figure 5 γd profiles for milled mefenamic acid silanised with methyl, vinyl, phenyl, and dodecyl functional end groups.
Figure 6 γAB profiles for milled mefenamic acid silanised with methyl, vinyl, phenyl, and dodecyl functional end groups.
Figure 7 Unconfined yield stress as a function of consolidation stress for mefenamic acid silanised with methyl, vinyl, phenyl, and dodecyl functional end groups.
15
1234
56
78
9101112
1314
1516
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.125
30
35
40
45
50
55
60
65Milled MA - Un-SilanisedMilled MA - Silanised – (-F) groupMilled MA-Silanised - (-Cl) groupMilled MA - Silanised – (-Br) groupMilled MA - Silanised – (-I) group
Fractional Surface Coverage (n/nm) (-)
Disp
ersiv
e Su
rfac
e E
nerg
y (γ
d) (m
J/m
2)
Figure 1 γd profiles for milled mefenamic acid silanised with –Cl, –F, –Br, and –I functional end groups.
16
1
2
3
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
1
2
3
4
5
6
7
8
9
10 Milled MA - Un-SilanisedMilled MA - Silanised – (-F) groupMilled MA - Silanised – (-Cl) groupMilled MA - Silanised – (-Br) groupMilled MA - Silanised – (-I) group
Fractional Surface Coverage (n/nm) (-)
Aci
d-B
ase
Surf
ace
Ene
rgy
(γA
B) (
mJ/
m2)
Figure 2 γAB profiles for milled mefenamic acid silanised with –Cl, –F, –Br, and –I functional end groups.
17
1
2345
6
400 600 800 1000 1200 1400 1600 1800 2000 22000
20
40
60
80
100
120
140
160
180Milled MA - Un-SilanisedLinear (Milled MA - Un-Silanised)Milled MA - Silanised – (-F) group
Consolidation Stress (kPa)
Unc
onfin
ed Y
ield
Str
ess (
kPa)
Figure 3 Unconfined yield stress as a function of consolidation stress for mefenamic acid silanised –Cl, –F, –Br, and –I functional end groups.
18
1
2345
6
0 5 10 15 20 25 30 35 40 45
0 5 10 15 20 25 30 35 40 45
0
5
10
15
20
25
30
f(x) = 0.226008602574528 x
f(x) = 2.63792529446778 xR² = 0.980700383281023
f(x) = 2.63802550270293 x + 9.0304R² = 0.980698075618403
Total cohesion (due to acid-base and dispersive surface energy)Linear (Total cohesion (due to acid-base and dispersive surface energy))
Acid-Base Surface Energy (AB )(n/nm=0.02) (mJ/m2)
Coh
esio
n (k
Pa)
Dispersive Surface Energy (d)(n/nm=0.02) (mJ/m2)
Figure 4 Cohesion as a function of acid-base component of surface energy.
19
1
2
34
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.125
30
35
40
45
50
55
60
65 Milled MA - Un-SilanisedMilled MA - Silanised - Methyl groupMilled MA - Silanised - Vinyl groupMilled MA - Silanised - Phenyl groupMilled MA - Silanised - Dodecyl group
Fractional Surface Coverage (n/nm) (-)
Disp
ersiv
e Su
rfac
e E
nerg
y (γ
d) (m
J/m
2)
Figure 5 γd profile for milled mefenamic acid silanised with methyl, vinyl, phenyl, and dodecyl functional end groups.
20
1
234
5
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0Milled MA - Un-SilanisedMilled MA - Silanised – Methyl groupMilled MA - Silanised – Vinyl groupMilled MA - Silanised – Phenyl groupMilled MA - Silanised – Dodecyl group
Fractional Surface Coverage (n/nm) (-)
Aci
d-B
ase
Surf
ace
Ene
rgy
(γA
B) (
mJ/
m2)
Figure 6 γAB profiles for milled mefenamic acid silanised with methyl, vinyl, phenyl, and dodecyl functional end groups.
21
1
2345
6
400 600 800 1000 1200 1400 1600 1800 2000 22000
20
40
60
80
100
120
140
160 Milled MA - Un-SilanisedLinear (Milled MA - Un-Silanised)Milled MA - Silanised - Methyl groupLinear (Milled MA - Silanised - Methyl group)
Consolidation Stress (kPa)
Unc
onfin
ed Y
ield
Str
ess (
kPa)
Figure 7 Unconfined yield stress as a function of consolidation stress for mefenamic acid silanised with methyl, vinyl, phenyl, and dodecyl functional end groups.
22
1
234