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Decoupling the Contribution of Dispersive and Acid-Base Components of Surface
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Energy on the Cohesion of Pharmaceutical Powders
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Umang V. Shaha, Dolapo Olusanmib, Ajit S. Narangb, Munir A. Hussainb, Michael J. Tobync, Jerry Y. Y.
Henga*
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a
Surfaces and Particle Engineering Laboratory (SPEL), Department of Chemical Engineering, Imperial
College London, South Kensington Campus, London SW7 2AZ, UK.
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b
Bristol-Myers Squibb Pharmaceuticals, 1 Squibb Drive, New Brunswick, NJ 08903, USA
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c
Bristol-Myers Squibb Pharmaceuticals, Reeds Lane, Moreton, Wirral CH46 1QW, UK
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*Corresponding Author: jerry.heng@imperial.ac.uk
Phone: +44-(0)207-594-0784. Fax: +44-(0)207-594-5700 Web: www.imperial.ac.uk/spel
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Abstract
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This study reports an experimental approach to determine the contribution from two different
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components of surface energy on cohesion. A method to tailor the surface chemistry of mefenamic acid
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via silanisation is established and the role of surface energy on cohesion is investigated. Silanisation was
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used as a method to functionalise mefenamic acid surfaces with four different functional end groups
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resulting in an ascending order of the dispersive component of surface energy. Furthermore, four
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halogen functional end groups were grafted on to the surface of mefenamic acid, resulting in varying
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levels of acid-base component of surface energy, while maintaining constant dispersive component of
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surface energy. A proportional increase in cohesion was observed with increases in both dispersive as
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well as acid-base components of surface energy. Contributions from dispersive and acid-base surface
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energy on cohesion were determined using an iterative approach. Due to the contribution from acid-base
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surface energy, cohesion was found to increase ~11.7× compared to the contribution from dispersive
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surface energy. Here, we provide an approach to deconvolute the contribution from two different
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components of surface energy on cohesion, which has the potential of predicting powder flow behaviour
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and ultimately controlling powder cohesion.
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Key Words: dispersive surface energy, acid-base surface energy, silanisation, de-coupling, cohesion
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1. Introduction
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Inter-particle interaction is argued to be governed by the material surface properties. Mechanisms for
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inter-particle interaction can be classified as two broad categories, physical and chemical interactions.
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Chemical interactions involves mainly covalent, ionic, metallic or electrostatic bonds, whereas physical
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interactions are a result of intermolecular forces, for example van der Waals and hydrogen bonding
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(Kendall, 1994). In addition to chemical and physical interactions, mechanical interlocking and diffusion
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are other two mechanisms widely discussed in the literature (Maeda et al., 2002). In industrial particle
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processing, instantaneous formation of menisci in capillaries between adhered particles is unavoidable
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and in such scenarios capillary forces of adhesion and inter-particle contact area becomes increasingly
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important (Rabinovich et al., 2002). For the purpose of this study, the discussion is focused on different
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intermolecular forces based on inter-particle interaction mechanisms. Furthermore, the analysis is
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limited to the surface energetic heterogeneity/ homogeneity not taking into consideration role of any
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structural or compositional heterogeneity.
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In the current literature, focusing on the cohesion of pharmaceutical materials, a number of reports have
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considered the role of surface energy on cohesion and powder flow properties (Barra et al., 1996; Barra
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et al., 1998; Bhandari and Howes, 2005; Chen et al., 2010; Deng and Davé, 2013; Han et al., 2013; Jallo
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et al., 2011; Kilbury et al., 2012; Moreno-Atanasio et al., 2005; Spillmann et al., 2008; Traini et al.,
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2005; Young et al., 2003, 2004). Barra et al. investigated the effect of the surface energy and cohesion
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parameters proposed by Wu (Wu, 1973) and Rowe (Rowe, 1989a, b) to predict the maximum value of
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interaction parameters or strength of interaction between particles of binary mixture. Furthermore they
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also studied the influence of polar and dispersive fractions of two interacting materials on prediction
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(Barra et al., 1996; Barra et al., 1998). Moreno-Atanasio et al. used distinct element method (DEM) to
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simulate the effect of surface energy on unconfined yield stress (UYS), revealing that an increase in
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surface energy by an order of magnitude produced similar increase in simulated UYS (Moreno-Atanasio
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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
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work of cohesion/adhesion calculated from contact angle, inverse phase gas chromatography and atomic
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force microscopy measurements (Traini et al., 2005). Chen et al. and Jallo et al. used surface
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modification, either using silanisation of aluminium particles or using dry-coating method to coat surface
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using silica particles, to reduce cohesion. Reduction in cohesion was attributed to the reduction in
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surface energy; silanisation of aluminium was found to result in a reduction of the surface energy, and
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subsequently measured cohesion values of silanised aluminium were observed to be lower, compared to
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unsilanised aluminium (Chen et al., 2010; Jallo et al., 2011). On the basis of the findings of Chen et al.,
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Han et al. investigated effect of dry coating on passivating the high energy sites of micronised ibuprofen
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for improving flowability recently. Surface energy heterogeneity was observed to reduce as a result of
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dry-coating and the surface energy follows a descending trend with increasing coating resulting in
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reduction in cohesion (Han et al., 2013).
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It is apparent from the current literature that surface energy has a major role to play in controlling
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cohesion. However, whilst recent literature reports have suggested that a higher surface energy may
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result in higher cohesion and suggested routes to passivate higher surface energy sites, no fundamental
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understanding on the contribution from surface energy on cohesion compared to other surface attributes
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have been reported. Recently methodology for de-coupling roles of different surface properties,
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particularly, particle shape, surface area and surface energy has been established (Shah et al., 2014a;
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Shah et al., 2014b). Considering that different components of surface energy can contribute towards
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cohesion on the basis of contribution from intermolecular forces, this study focuses on developing an
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approach for de-coupling the contribution from dispersive and acid-base component of surface energy on
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cohesion.
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2. Materials
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Mefenamic acid (2-(2, 3-dimethylphenyl) amino benzoic acid) (99.0%), n-heptane (99.0), n-octane
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(99.0%), n-nonane (99.0%), n-decane (99.0%), dichlorodimethylsilane (>99.5%,), dodecyl
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triethoxysilane (technical grade), vinyltrimethoxysilane (>97.0%), triethoxyphenylsilane (>98.0%), (3-
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iodopropyl)trimethoxysilane
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trimethoxy(3,3,3-trifluoropropyl)silane (97.0%) were purchased from Sigma Aldrich, Dorset, UK.
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Methanol (>99.5%), ethyl acetate (>99.5%), dichloromethane (>99.0%), n-hexane (>99.0%), and
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cyclohexane (>99.0%) were received from VWR BDH Prolabo, Lutterworth, UK and (3-
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chloropropyl)trichlorosilane (>97.0%) was received from Alfa Aesar, Heysham, UK. All chemicals were
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(95.0%),
(3-bromopropyl)trimethoxysilane
(97.0%)
and
used as received.
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3. Methods
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3.1 Silanisation of milled mefenamic acid
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Milled mefenamic acid powders were silanised using a protocol reported in the literature (Al-Chalabi et
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al., 1990). In a typical process, 500 mg of mefenamic acid powder was added to a 50 mL 5% (v/v)
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solution of appropriate silane in cyclohexane. The mixture was refluxed at 80 oC for 24 hours. Then, the
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reaction mixture is allowed to cool down to room temperature and filtered using general-purpose
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laboratory filter paper (Whatman, UK) followed by drying in a vacuum oven at 80 oC for 4 hours. Post
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silanisation, the silanised mefenamic acid powders were stored in a glass vial at ambient conditions.
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3.2 Surface energy analysis
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Surface Energy Analyser (SEA, Surface Measurement Systems Ltd., London, UK) was used for surface
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energy heterogeneity characterisation. Approximately 300 mg of mefenamic acid was packed in pre-
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silanised iGC columns (Surface Measurement Systems Ltd., London, UK) and conditioned for 2 hours at
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30 oC followed by pulse injection measurements. Methane was used to determine the column dead time.
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Helium at a flow rate of 10 sccm was used as a carrier gas for all injections for the columns packed with
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un-silanised mefenamic acid, whereas 3 sccm helium flow rate was used for columns packed with
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silanised mefenamic acid. A series of dispersive n-alkane probes (hexane, heptane, octane, nonane and
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decane) at a range of concentrations were injected in order to achieve target surface coverages (n/nm)
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ranging from 0.7% to 10%. Net retention volumes were calculated using the commonly applied Schultz
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method (Schultz et al., 1987). Mono-polar probes (dichloromethane and ethyl acetate) were injected at
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the same concentrations to determine non-dispersive interactions. The surface energy due to the non-
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dispersive interactions was calculated using the vOCG method reported in the literature (Das et al.,
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2010; Van Oss et al., 1988). Principles of the techniques and a review of currently literature including
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theory, can be found elsewhere (Ho and Heng, 2013).
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3.3 Uniaxial compression test
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A uniaxial compression test was used for powder cohesion measurements. Cylindrical compacts of 5mm
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diameter were prepared using an evacuable IR die (Specac Ltd., Slough, UK) at a minimum of three
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different consolidation loads (10 N, 20N and, 40N). Post consolidation, confinements were removed and
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yield load was measured using SMS texture analyser TA.XT2i (Stable Micro Systems Ltd., Godalming,
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UK) equipped with a 5 kg load cell in a displacement compression mode, with compression speed of
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0.02 mms-1. Consolidation and yield load values were divided by the contact area to convert into
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consolidation and yield stress, respectively. Yield stress obtained was plotted as a function of
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consolidation stress. A linear regression line can be plotted for yield stress as a function of consolidation
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stress. Linear regression line was extrapolated to find intercept with y-axis showing yield load at zero
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consolidation load, which is cohesion. Theoretical principles of this test are detailed elsewhere (Head,
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1994; Wang, 2013).
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4. Results and Discussion
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4.1 Isolating the effect of different components of surface energy on cohesion
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4.1.1 Contribution of acid-base component of surface energy on cohesion
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Dispersive (d) and acid-base (AB) surface energy heterogeneity profiles for mefenamic acid silanised
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with four different haloalkane functional end groups, chloropropyl, trifluoropropyl, bromopropyl and
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iodopropyl are presented in Figures 1 and 2 respectively. Post silanisation, the surface energies (both d
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and AB) of mefenamic acid powders remained constant with increasing fractional surface coverage,
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suggesting energetic homogeneity. For surface energy measurements to be representative of the entire
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material surface properties, typical fractional coverages used for analysis ranges from n/nm=0.02 to 0.05
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(Gamble et al., 2013; Gamble et al., 2012; Shah et al., 2014a; Shah et al., 2014b). The analysis of
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energetically homogeneous surfaces remains similar for different fractional surface coverages.
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Considering the range of fractional surface coverages typically used to provide material representative
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surface energy, n/nm=0.02 was selected for analysis of both silanised and unsilanised materials.
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d profiles for mefenamic acid silanised with different haloalkane functional groups were found to have
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very similar surface energy values at different fractional surface coverages (40.00.3 mJ/m2). All
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haloalkanes selected for this study have a propyl chain attached to the halogen atoms as a spacer and can
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provide very similar dispersive interactions.
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The acid-base component of surface energy was found to decrease in the order of -Cl > -F > -Br > -I
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functional groups. For fractional surface coverage n/nm=0.02, the acid-base components of surface
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energy for chloropropyl, trifluoropropyl, bromopropyl and iodopropyl are 7.7 mJ/m 2, 5.2 mJ/m2, 3.9
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mJ/m2, and 2.2 mJ/m2, respectively. The order of decrease in the acid-base surface energy observed in
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this study can be explained by the functional end group properties, due to the electronegativity of
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haloalkanes.
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Unconfined yield stress was measured for powders silanised with haloalkane functional end groups and
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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
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energy (Figure 4) (Head, 1994). Cohesion was found to increase linearly with increasing acid-base
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surface energy. The dispersive component of the surface energy for the powders silanised with
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haloalkanes is very similar (40.00.3 mJ/m2), hence this increase in total surface energy is solely
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attributed to the increase in the acid-base component of the surface energy. Considering the linear
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relationship between cohesion and acid-base of surface energy, the intercept of the best fit line for
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cohesion as a function of acid-base surface energy (when AB = 0 mJ/m2), will be attributed to the
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dispersive surface energy. The cohesion (9.0 kPa) at the intercept of best fit line for cohesion as a
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function of acid-base surface energy is net cohesion due to the dispersive surface energy at 40.0 mJ/m2
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(Figure 4). By subtracting the cohesion due to the dispersive component (9.0 kPa) from the total
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cohesion, the contribution of AB on cohesion can be determined as shown using dotted line in Figure 4.
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4.1.2 Contribution of dispersive component of surface energy on cohesion
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d heterogeneity profiles, before and after silanisation of mefenamic acid, are presented Figure 5. d
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remained constant with increasing surface coverages for mefenamic acid silanised with different
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functional end groups, whereas the d for unsilanised milled mefenamic acid was observed to decrease.
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Therefore, it can be suggested that silanisation results in an energetically homogenous surfaces. d for
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silanised mefenamic acid was observed in the ascending order from methyl, dodecyl, phenyl and vinyl
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functional end groups. Acid base surface energy for surfaces silanised with vinyl and phenyl functional
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groups were found to be higher compared to that of surfaces functionalised with methyl and dodecyl
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functional groups. Variations here could be due to distribution of charge density and dipole moments.
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Surface energy for mefenamic acid silanised with methyl functional groups was found to vary minimally
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within the error bars from 32.7 mJ/m2 to 31.6 mJ/m2 with increasing fractional surface coverage from
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0.7% to 10%. Dichlorodimethylsilane is the silane used for grafting methyl functional end group on to
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the surface. This molecule has no spacer and the methyl moiety is directly attached to the terminal end
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group, such that it provides no molecular flexibility to the functional end group. Therefore the grafted
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(or deposited) methyl functional end group, which is known to be unreactive, is very stable.
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Dodecyltriethoxysilane ((OC2H5)3-Si-CH2(CH2)10CH3) was used for grafting. Mefenamic acid grafted
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with dodecyl end group has -CH2(CH2)10CH3 functional group attached to -Si without any spacer.
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Dodecyl is a long chain functional end group and results in relatively higher dispersive surface energy
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compared to methyl functional group, i.e. surface energy heterogeneity profile varies from 36.6 mJ/m2 to
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34.9 mJ/m2 with increasing fractional surface coverage from 0.7% to 10%. Mefenamic acid silanised
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with phenyl and vinyl functional groups resulted in surface energy heterogeneity profiles ranging from
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40.2 mJ/m2 to 40.5 mJ/m2 and 42.9 mJ/m2 to 42.8 mJ/m2 respectively for fractional surface coverage
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ranging from 0.7% to 10%, thus demonstrating homogeneity. Considering the isostere at 2% fractional
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surface coverage, dispersive component of surface energy was found to be 32.7 mJ/m2 for methyl, 36.3
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mJ/m2 for dodecyl, 40.7 mJ/m2 for phenyl and 42.3 mJ/m2 for vinyl silanised surfaces, and 46.4 mJ/m2
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for un-silanised surfaces. The acid-base component of surface energy at an isostere of 2% fractional
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surface coverage was calculated to be 0.4 mJ/m2 for methyl, 0.8 mJ/m2 for dodecyl, 3.0 mJ/m2 for phenyl
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and 3.0 mJ/m2 for vinyl silanised surfaces (Figure 6).
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Uniaxial compression test was used for measurements of unconfined yield stress at three different
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consolidation stresses for the silanised mefenamic acid and results are presented in Figure 7. With a
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decrease in the dispersive component of the surface energy, a decrease in unconfined yield stress was
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observed for 2040 kPa and 1020 kPa consolidation stress. For 510 kPa consolidation stress unconfined
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yield stress for surfaces silanised with phenyl and vinyl are within experimental errors, and decrease in
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unconfined yield stress was observed in the order of the surfaces silanised with phenyl  vinyl > dodecyl
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> methyl. Cohesion values calculated for methyl silanised surface was 10.3 kPa, dodecyl functionalised
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surface was 12.1 kPa, vinyl functionalised surface was 16.0 kPa and phenyl functionalised surface was
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15.4 kPa. A proportional increase in cohesion as a function of dispersive component of the surface
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energy was observed.
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To de-couple the contribution of the dispersive surface energy on cohesion from the acid-base
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component, the correlation developed in section 4.1.1, was used to calculate net cohesion due to the
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acid-base component of surface energy. However, the correlation developed between acid-base surface
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energy and cohesion is only specific to the mefenamic acid. The approach reported here can be applied
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to establish correlation for other systems. The total cohesion calculated is attributed to the total surface
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energy, which has two components – the acid-base component and the dispersive component. To
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calculate the cohesion due to dispersive surface energy, the cohesion due to acid-base surface energy
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calculated previously was subtracted from the total cohesion.
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A linear regression line was fitted to the net cohesion (due to dispersive surface energy calculated) as a
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function of dispersive surface energy. As this regression line represent net cohesion due to dispersive
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surface energy, it was fitted with a zero intercept, suggesting at zero dispersive surface energy,
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calculated cohesion is also zero. An iterative approach was adopted to converge regression lines of net
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cohesion as a function of acid-base and dispersive surface energy. Using the linear regression for the net
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cohesion (due to dispersive surface energy) as a function of dispersive energy, cohesion due to the
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dispersive energy at 40.0 mJ/m2 was calculated and the obtained cohesion was used to set intercept of
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linear fit for total cohesion as a function of acid base surface energy. Such iterations were continued until
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the cohesion value due to dispersive surface energy at 40.0 mJ/m2 calculated using both linear
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regressions (net cohesion as a function of acid-base and dispersive surface energy), converged (9.03
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kPa). Figure 4 shows the linear regression fits obtained as a result of iterative approach, showing the
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correlation between net cohesion and dispersive as well as acid-base surface energy.
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Net cohesion calculated due to the dispersive component of surface energy was found to be 9.2 kPa for
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surfaces silanised with methyl, 10.0 kPa for surfaces silanised with dodecyl, 7.8 kPa for surface silanised
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with phenyl and 8.3 kPa for surface silanised with vinyl functional end groups. Considering the approach
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adopted here to calculate net cohesion due to the dispersive component only, a linear correlation,
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intersecting at the origin, for cohesion as a function of dispersive surface energy was established and
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represented by an equation y = 0.226x (i.e. when dispersive surface energy is zero, cohesion is zero as
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net cohesion is only due to dispersive surface energy). The correlation between dispersive surface energy
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and cohesion is only specific to mefenamic acid.
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For the model system investigated, the contribution from AB was found to result in ~11.7× higher
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cohesion compared to contributions from d. i.e. when contributions from d was eliminated as a factor
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in cohesion for material with same surface area, the remaining cohesion can be estimated from AB.
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Furthermore, relationships between dispersive as well as acid-base surface energy and net cohesion due
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to contribution from dispersive as well as acid-base surface energy were established.
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The role of different components of surface energy on cohesion is system specific and also depends on
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intrinsic properties of the material. In addition, the contribution from the dispersive and acid-base
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components of surface energy on cohesion can be different for different materials and also depend on the
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experimental conditions. The approach presented in this study shows the potential for developing a
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fundamental understanding of contributions from different surface energy components on cohesion,
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which will permit controlling cohesion by engineering particle surface properties either via appropriate
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processing methods or crystal engineering.
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5. Conclusion
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Here, an approach for de-coupling the different components of surface energy has been demonstrated.
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Silanisation was used as a tool to tailor surface energies of mefenamic acid. Methyl, dodecyl, phenyl and
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vinyl functional groups were grafted on the mefenamic acid surface to investigate role of d, whereas a
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series of haloalkanes functional groups were grafted to study role of AB on cohesion. Powder cohesion
6
was found to increase in linear correlation with surface energy. A linear correlation between AB and total
7
cohesion was developed and used for determining contribution from d on cohesion. An iterative
8
approach was employed to converge the relationship between net cohesion (due to d) and dispersive
9
surface energy, and total cohesion and acid-base surface energy. For the model system investigated,
10
contribution from d and AB on cohesion was decoupled and correlation between net cohesion (due to
11
the d and AB) was established. Increase in cohesion was found to be ~11.7 × higher due to contribution
12
from AB compared to that of d. Findings of this study not only provided fundamental understanding on
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effect of surface energy on cohesion but also can be used for quantification of contributions from
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different components of surface energy.
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18
14
1
2
3
4
List of Figures
Figure 1
γd profiles for milled mefenamic acid silanised with –Cl, –F, –Br, and –I functional end
groups.
5
6
Figure 2
γAB profiles for milled mefenamic acid silanised with –Cl, –F, –Br, and –I functional end
groups.
7
8
Figure 3
Unconfined yield stress as a function of consolidation stress for mefenamic acid silanised
–Cl, –F, –Br, and –I functional end groups.
9
10
11
12
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.
13
14
Figure 6
γAB profiles for milled mefenamic acid silanised with methyl, vinyl, phenyl, and dodecyl
functional end groups.
15
16
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
1
Dispersive Surface Energy (γd) (mJ/m2)
65
Milled MA - Un-Silanised
Milled MA - Silanised – (-F) group
Milled MA-Silanised - (-Cl) group
Milled MA - Silanised – (-Br) group
Milled MA - Silanised – (-I) group
60
55
50
45
40
35
30
25
0
2
3
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Fractional Surface Coverage (n/nm) (-)
0.08
0.09
0.1
Figure 1 γd profiles for milled mefenamic acid silanised with –Cl, –F, –Br, and –I functional end groups.
16
1
Milled MA - Un-Silanised
Milled MA - Silanised – (-F) group
Milled MA - Silanised – (-Cl) group
Milled MA - Silanised – (-Br) group
Milled MA - Silanised – (-I) group
Acid-Base Surface Energy (γAB) (mJ/m2)
10
9
8
7
6
5
4
3
2
1
0
0
2
3
4
5
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Fractional Surface Coverage (n/nm) (-)
0.08
0.09
0.1
Figure 2 γAB profiles for milled mefenamic acid silanised with –Cl, –F, –Br, and –I functional end
groups.
6
17
1
200
Milled MA - Un-Silanised
Milled MA - Silanised – (-F) group
Milled MA - Silanised – (-Cl) group
Milled MA - Silanised – (-Br) group
Milled MA - Silanised – (-I) group
Unconfined Yield Stress (kPa)
180
160
140
120
100
80
60
40
20
0
0
2
3
4
5
500
1000
1500
Consolidation Stress (kPa)
2000
2500
Figure 3
Unconfined yield stress as a function of consolidation stress for mefenamic acid silanised
–Cl, –F, –Br, and –I functional end groups.
6
18
1
0
5
Dispersive Surface Energy (d)(n/nm=0.02) (mJ/m2)
10
15
20
25
30
35
40
45
35
Total cohesion (due to acid-base
and dispersive surface energy)
Net Cohesion (due to acid-base
surface energy)
Net Cohesion (due to dispersive
surface energy)
30
Cohesion (kPa)
25
y = 2.64x + 9.03
R² = 0.75
y = 2.64x
R² = 0.75
20
15
10
5
y = 0.23x
0
0
1
2
3
4
5
6
7
8
9
Acid-Base Surface Energy (AB )(n/nm=0.02) (mJ/m2)
2
3
4
Figure 4
Cohesion as a function of acid-base component of surface energy.
19
1
Dispersive Surface Energy (γd) (mJ/m2)
65
Milled MA - Un-Silanised
Milled MA - Silanised - Methyl group
Milled MA - Silanised - Vinyl group
Milled MA - Silanised - Phenyl group
Milled MA - Silanised - Dodecyl group
60
55
50
45
40
35
30
25
0
2
3
4
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Fractional Surface Coverage (n/nm) (-)
0.08
0.09
0.1
Figure 5 γd profile for milled mefenamic acid silanised with methyl, vinyl, phenyl, and dodecyl
functional end groups.
5
20
1
Acid-Base Surface Energy (γAB) (mJ/m2)
5.0
Milled MA - Un-Silanised
Milled MA - Silanised – Methyl group
Milled MA - Silanised – Vinyl group
Milled MA - Silanised – Phenyl group
Milled MA - Silanised – Dodecyl group
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
2
3
4
5
Figure 6
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Fractional Surface Coverage (n/nm) (-)
0.09
0.1
γAB profiles for milled mefenamic acid silanised with methyl, vinyl, phenyl, and dodecyl
functional end groups.
6
21
1
160
Milled MA - Un-Silanised
Milled MA - Silanised - Methyl group
Milled MA - Silanised - Vinyl group
Milled MA - Silanised - Phenyl group
Milled MA - Silanised - Dodecyl group
Unconfined Yield Stress (kPa)
140
120
100
80
60
40
20
0
0
2
3
4
Figure 7
500
1000
1500
2000
2500
Consolidation Stress (kPa)
Unconfined yield stress as a function of consolidation stress for mefenamic acid silanised
with methyl, vinyl, phenyl, and dodecyl functional end groups.
22