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A combined modelling and experimental study of the surface energetics of α-lactose monohydrate
A Combined Modelling and Experimental Study of the Surface Energetics of a-Lactose Monohydrate A. SAXENA,1 J. KENDRICK,2 I.M. GRIMSEY,1 R. ROBERTS,3 P. YORK1 1
Drug Delivery Group, Institute of Pharmaceutical Innovation, School of Pharmacy, University of Bradford, Bradford, UK
2
The Computational Group, Institute of Pharmaceutical Innovation, School of Pharmacy, University of Bradford, Bradford, UK 3
Product Development, Pharmaceutical & Analytical R&D, AstraZeneca, Macclesfield, UK
Received 16 April 2009; accepted 28 May 2009 Published online 7 August 2009 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.21864
ABSTRACT: The surface energy of a-lactose monohydrate measured by inverse gas chromatography (IGC) is reported along with a dynamic molecular modelling study of the interaction of the various molecular probes with different surfaces of a-lactose monohydrate. The IGC results show that a-lactose monohydrate is acidic in nature. Using quantitative calculations of the energy of adsorption, the acidic nature of the surface is confirmed and the calculated values agree closely with the experimentally measured values. Along with the acidic nature, dynamic molecular modelling also reveals that the presence of a channel and water molecules on a surface affects the surface energetics of that face. The presence of water on the surface can decrease or increase the surface energy by either blocking or attracting a probe molecule, respectively. This property of water depends on its position and association with other functional groups present on the surface. The effect of a channel or cavity on the surface energy is shown to depend on its size, which determines whether the functional groups in the channel are assessable by probe molecules or not. Overall molecular modelling explains, at the molecular level, the effect of different factors affecting the surface energy of individual faces of the crystal. ß 2009 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 99:741–752, 2010
Keywords: molecular modelling; hydrate; physicochemical properties; surface chemistry; chromatography; materials science
INTRODUCTION Most of the materials come in contact with water during processing, formulation, or even storage. The presence of water can affect the physical and chemical properties of some of these materials. It can alter the crystal growth and dissolution,
A. Saxena’s present address is Department of Pharmaceutics, University of Minnesota, 9-125, WDH, 308 Harvard Street SE, Minneapolis, MN 55455. Correspondence to: A. Saxena (Telephone: 8062207698; Fax: 6126262125; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 99, 741–752 (2010) ß 2009 Wiley-Liss, Inc. and the American Pharmacists Association
wettability, dispersibility, flowability, lubricity, compactability, hardness and even rates of chemical degradation. Most of these properties are directly or indirectly influenced by the surface energetics of the material, which is again affected by the presence of the water. Water can associate with solids in number of ways. It can interact with the surface of the solid (adsorption) or it can penetrate the bulk solid substrate (absorption) or it can be present as the water of crystallisation. It is necessary to know both the location and mobility of the water as well as its physical state, in order to have a better understanding of its effect on the surface energetics and properties of a solid.
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A number of studies have been reported on the surface energetics of a material as a function of humidity. Ohta and Buckton1 studied changes in the acidic and basic properties of amorphous cefditoren pivoxil powder using inverse gas chromatography (IGC) under various relative humidities (RHs). The basicity of the powder surface decreased with the increasing RH. Newell et al.2 assessed the effect of RH on the surface energy of the amorphous lactose and found that at high humidity the dispersive energy was reduced to a value comparable to that of crystalline lactose. Goss and Schwarzenbach3 found that the trend in electron donor/acceptor properties of three mineral surfaces (quartz, calcium carbonate and a-aluminium oxide) changes between 90% and 100% RH. They concluded that the change is probably connected to the orientation of the adsorbed water molecules. Balard et al.4 used IGC at infinite dilutions conditions and observed a strong decrease in the dispersive component of the surface energy of clay due to water molecules shielding the highest energy sites. Sunkersett et al.5,6 used IGC to study the surface energetics of selected pharmaceutical materials under dry conditions and at an ambient relative (47%) humidity. There was either no, or very small, change in the dispersive component, whereas the specific component of the free energy of adsorption remained constant, increased, or decreased at the increased RH, depending on the material and the probe. They demonstrated, with the help of molecular modelling, that the effect of water on the surface energy depends upon the interaction sites occupied by water and probe molecules. The significant limitation of this modelling work was that a single adsorbent molecule was considered representative of the whole surface. All the above determined the effect of atmospheric RH on the surface energy of different materials. Similarly, it is important to know how the water of crystallisation, present in the crystal lattice of many materials, can affect the surface energy, if it is present on the surface of the crystal. In this work, IGC is used to measure the surface energetics. A powder sample is packed into a column and its surface properties are analysed by measuring the retention behaviour of known vapour probes. Molecular modelling methods are used to understand the nature of the interactions between the probes and the surface at a molecular level. This combination of techniques has been applied in pharmaceutical and nonJOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 2, FEBUARY 2010
pharmaceutical applications to provide knowledge of the orientation and exposure of molecular groups on the crystal surfaces.7–10 Allington et al.11,12 compared the simulated results with the experimental data on nonpharmaceutical materials obtained from IGC. a-Lactose monohydrate crystal is used as a model compound in this study and four of its most important morphological surfaces are modelled by using the protocol developed previously.13 These four surfaces show a variation in the availability and position of the water of crystallisation. According to the protocol, molecular dynamic simulations were used to calculate the adsorption energy of the probe on these different surfaces. These simulated results for the different surfaces are compared to determine the effect of the presence of water on the surface energetics.
MATERIALS AND METHODS Materials a-Lactose monohydrate B.P. (>98% pure), a common excipient, was supplied by DMV International (Middlesex, UK). The probes used for IGC were: hexane (BDH Chemical, Poole, UK), heptane (Sigma Aldrich, Dorset, UK), octane (Aldrich Chemical, Milwaukee, WI), nonane (Aldrich Chemical), tetrahydrofuran (Riedel -de Haen, Seelze, Germany) and chloroform (Fisher Scientific, Loughborough, UK).
Methods Inverse Gas Chromatography IGC was used to measure the surface energy of a-lactose monohydrate. The experimental procedure for IGC was obtained from the previously published work by Ticehurst et al.14 Two presilanised columns of dimensions, 1 m (one loop) 6 mm (outer diameter) 3 mm (inner diameter) were packed with a-lactose monohydrate. Each column was analysed twice at room temperature, at 308C and 0% RH, using dry nitrogen gas as the carrier. A series of nonpolar (n-alkanes, hexane to nonane) and polar probes (THF and chloroform) were injected and retention time (tr) was meaSP sured. The dispersive (g D S ) and specific (DGA ) components were measured by the method of Schultz and Lavielle.15 Details of the calculations, are given in Saxena et al.13 DOI 10.1002/jps
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A distance-dependent dielectric constant was not used. No specific hydrogen bonding term was used.
Four crystal structures of a-lactose were found in the Cambridge Structural Database (Cambridge Crystallographic Data Centre, Cambridge, UK, CSD version 5.27, November 2005) using ConQuest version 1.8.16 Details of all these four structures, including their CSD reference code, are given in Table 1.
In the Dreiding force field, the exponential-6 potential function is given by 6 ! 6 j R jð1R=R0 Þ D0 e (1) j6 j 6 R0
Calculation of Partial Charges. From Table 1, the low temperature, most recently submitted crystal structure, LACTOS11, with a reasonably low R factor, was selected for molecular modelling calculations. A single molecule of a-lactose was extracted from LACTOS11 and was geometry optimised using the General Atomic and Molecular Electronic Structure System-UK (GAMESSUK) molecular orbital package21 using Hartree– Fock theory with a 6-31G basis set. Hartree–Fock calculations using a 6-31G basis set were then used to calculate the electrostatic potential around the optimised a-lactose molecule. Partial charges for the molecule optimised from LACTOS11 were derived from the surrounding electrostatic potential using a least-squares fit of the charges to the ab initio calculated potential.22 The partial charges for water and probe molecules were calculated in a similar manner, but the lowest energy conformation of each probe molecule, determined by energy minimisation was used for further modelling work.
where j was kept at 13.772 to maintain a function that is similar to the Lennard-Jones function at the minimum, and the parameters D0 and R0 of all hydrogen atoms involved in hydrogen bonding were adjusted to improve the agreement between predicted minimised structure and experiment. Crystal Morphology. Cerius2 was used to apply the Bravais–Freidel–Donnay–Harker (BFDH) method to predict the crystal morphology. This method is based on a geometrical calculation that uses the crystal lattice and symmetry to generate a list of possible growth faces and their relative growth rates. This approach calculates the interplanar spacing, dhkl, of the different crystal faces. Those faces with the lowest growth rates have the greatest dhkl. So the most morphologically important faces will be with the slowest growth rates and largest surface area.24 Cerius2 was used to generate the molecular arrangement of these surfaces.
Force Field. The DREIDING II force field,23 modified for D-b-mannitol in our previously published work,13 was used as the starting point for the present study on a-lactose monohydrate. This modified force field as implemented in Cerius2 (Molecular Simulations, Inc., San Diego, CA) uses the following options:
Molecular Dynamics. The protocol developed previously13 was used for molecular dynamics (MD) simulations of the probe molecules on the surface of a-lactose monohydrate in Cerius2. A slab was created from the surface, whose thickness was large enough so that the energy of lower surface should not affect the energy of upper surface. The surface energy of the slab was calculated using the following formula:
An exponential-6 potential for the van der Waals interaction. Coulombs interactions were calculated by Ewald method.
Surface energy ¼
slab energy bulk energy 2 surface area
(2)
Table 1. Details of Crystal Structures of a-Lactose Monohydrate Obtained from CSD
CSD Reference Code LACTOS01 LACTOS03 LACTOS10 LACTOS11 DOI 10.1002/jps
Space Group
R-Factor (%)
Measurement Temperature
References
P21 P21 P21 P21
15.0 3.4 2.7 3.32
RT RT RT 150 K
Beevers and Hensen17 Noordik et al.18 Fries et al.19 Smith et al.20
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where slab energy is the energy of a twodimension slab of a particular thickness, and bulk energy is the energy of one molecule multiplied by total number of molecules present in the slab. The slab was minimised (relaxed) and the molecules in the slab were then kept fixed during the MD simulation of the probe molecule on the surface. NVE MD simulations were performed for 50 ps with an integration step of 1 fs. The initial temperature of the simulation was 300 K. Equilibration was determined by examination of the change in average potential energy as a function of time. Twenty to 25 structures were randomly selected from the trajectory after equilibration and minimised. The average minimised energy was used as the energy of the system. The energy of the isolated probe molecules was calculated in the same way. The adsorption energy Eads is defined from Esystem ¼ Eprobe þ Esurface Eads
(3)
where Esystem is the average minimised energy of the system (probe/surface interaction), Eprobe the average minimised energy of isolated probe, Esurface the average minimised energy of surface (the energy of the surface is taken to be 0 as the surface was fixed during simulation).
RESULTS AND DISCUSSION Inverse Gas Chromatography The experimental adsorption energy measured by IGC is shown in Figure 1. Tetrahydrofuran (THF), a basic probe, has a high net retention volume (Vn) on a-lactose monohydrate as compared to chloroform (an acidic probe). The surface of a-lactose monohydrate crystal is clearly acidic in nature.
Molecular Modelling Force Field Starting from the experimental LACTOS11 experimental structure, the modified force field was used to minimise the lattice energy with respect to all lattice parameters and the molecular geometry. After examination of the modified force field, van der Waals parameters (original R0 ¼ ˚ and D0 ¼ 0.01520 kcals/mol) for hydro3.1950 A gen, capable of forming hydrogen bonding, were replaced by an improved set of parameters with ˚ and 0.01288 kcals/mol, respecvalues 1.5558 A tively. The result obtained by minimising the energy of the experimental crystal structure of a-lactose monohydrate (LACTOS11) using the
Figure 1. The experimental adsorption energy of different probes on a-lactose monohydrate measured by inverse gas chromatography. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 2, FEBUARY 2010
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Table 2. Comparison Between Experimental and Minimised Lattice Parameters by Applying the Modified Dreiding Force Field With Original and Improved R0 and D0 Values Modified Dreiding Force Field With Improved R0 and D0
Modified Dreiding Force Field With Original R0 and D0 CSD Reference Code Lactose 11 A B C B
Experimental Lattice ˚) Parameters (A
Minimised Lattice ˚) Parameters (A
% Difference
Minimised Lattice ˚) Parameters (A
% Difference
4.783 21.54 7.76 105.91
4.725 21.375 7.296 99.05
1.21 0.77 5.98 6.48
4.599 20.798 7.41 104.88
3.85 3.44 4.51 0.97
modified force field with new R0 and D0 values is shown in Table 2. Table 2 shows that with the default van der Waals parameters, the maximum absolute errors for angle b are unacceptably high, whereas with the improved parameters the largest deviation is within an acceptable limit of 5%. Because of the ability of the modified force field with improved van der Waals parameters, to predict a better
crystal structure, it was selected for the further study of adsorption on to the surface of a-lactose monohydrate. Crystal Morphology Figure 2 shows the crystal morphology predicted by Cerius2 using BFDH method, which is similar to the morphology obtained under the scanning electron microscope (Fig. 3).
Figure 2. Predicted morphology of a-lactose monohydrate crystal faces by BFDH method using Cerius2. DOI 10.1002/jps
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related, as can be seen in the crystal morphology, shown in Figure 2. We will, however, use the notation to distinguish between surfaces which have been generated by cleavage through different parts of the unit cell. Cleavage to produce the (0 2 0) and ð0 2 0Þ faces produced different surface compositions as did cleavage to produce the (0 0 1) and ð0 0 1Þ faces. These four surfaces are the morphological important faces for a-lactose monohydrate. So the molecular arrangement of these four faces has considerable influence on the surface energetics of the whole crystal. Molecular Arrangement of a-Lactose Monohydrate Faces
Figure 3. The crystal morphology of a-lactose monohydrate observed under the scanning electron microscope.
In the predicted morphology the (0 2 0) face has the maximum surface area, followed by the (0 0 1) face. The actual surface composition is dependent on where the unit cell is cleaved. The (0 2 0)/ð0 2 0Þ and the (0 0 1)/ð0 0 1Þ surfaces are symmetry
The bulk structure was sliced along the required hkl planes to visualise the (0 2 0), ð0 2 0Þ, (0 0 1) and ð0 0 1Þ faces (Figs. 4–7, respectively). Figures 4–7 show the molecular arrangement of these relaxed faces, respectively, which shows that all these four faces have hydroxyl (–OH) groups on the surface. This agrees with IGC measurements, which show that a-lactose monohydrate crystals are acidic in nature. The molecular arrangement of all these four faces also clarifies the basicity of the surface measured by IGC, which can be due to the presence of different
Figure 4. Molecular arrangement of the (0 2 0) face of a-lactose monohydrate. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 2, FEBUARY 2010
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Figure 5. Molecular arrangement of the (0 2 0) face of a-lactose monohydrate.
negatively charged oxygen atoms or the delocalised electrons on the ring structure, present on the surface. There are two important points concerning the molecular arrangement of all these faces. Firstly,
there is a difference in the channel width, created by the molecular arrangement of lactose molecules on the (0 2 0) and (0 0 1) faces (Figs. 4 and 6, respectively). The (0 0 1) face has a larger channel width compared to the (0 2 0) face. A similar
Figure 6. Molecular arrangement of the (0 0 1) face of a-lactose monohydrate. DOI 10.1002/jps
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Figure 7. Molecular arrangement of the (0 0 1) face of a-lactose monohydrate.
difference is in their related counterparts (Figs. 5 and 7). This width determines the total area of the surface exposed for the probes and what size of probe molecule can interact with the functional groups deep inside the channel. Secondly, the water molecules are present at different position on all four different faces (Figs. 4–7). The (0 2 0) and (0 0 1) faces have the water molecule deep in the channel, whereas on the ð0 2 0Þ and ð0 0 1Þ faces water is present on the surface. This difference in water molecules’ position can directly affect the probes interaction with other functional groups present on the surface. Molecular Dynamics In the MD simulations, all four faces were separately represented by four unit cell thick slabs. These slabs were relaxed and the molecules in the slab were then kept fixed during MD
simulation. The surface energy of these four slabs was calculated using Eq. (2) and summarised in Table 3. The surface with lower energy will be more stable and likely to appear in the crystal structure. Table 3 shows that faces with water on the surface (ð0 2 0Þ and ð0 0 1Þ) are more stable than the (0 2 0) and (0 0 1) faces. MD simulations of probe molecules on all four slabs were performed within the NVE ensemble. The average temperature over the equilibrated trajectories was around 300 K. The average, minimised energy of 15–25 randomly selected structures after the equilibration time was used to calculate the energy of the system. In the same way, the energy of the isolated probe was calculated but without the lactose surface. The adsorption energies for n-alkanes and polar probes on all four faces were calculated using Eq. (3) and summarised in Tables 4–7.
Table 3. The Calculated Surface Energy of Different Faces of a-Lactose Monohydrate
Faces
Slab Energy (kcal/mol)
Bulk Energy (kcal/mol)
Surface ˚) Area (A
Surface Energy ˚ 2) (kcal/mol/A
(0 2 0) ð0 2 0Þ (0 0 1) ð0 0 1Þ
1242.54 1219.86 1239.26 1217.84
1148.68 1148.68 1126.02 1126.02
34.14 34.14 95.65 95.65
1.38 1.04 0.59 0.48
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Table 4. The Calculated Adsorption Energy of Probes on the (0 2 0) Surface of a-Lactose Monohydrate
Probes n-Alkane Pentane Hexane Heptane Octane Polar probe THF Chloroform
Average Energy of Probe (kJ/mol)
Average Energy of Probe on Surface (kJ/mol)
Adsorption Energy (kJ/mol)
ag1/2 (nm2 mJ1/2/m)
6.2 4.9 72.0 30.3
21.3 25.9 37.7 6.8
27.5 30.8 34.3 37.1
1.84 2.2306 2.5682 2.9076
35.0 0.0
0.1 31.8
35.1 31.8
2.1345 2.2392
Table 5. The Calculated Adsorption Energy of Probes on the ð0 2 0Þ Surface of a-Lactose Monohydrate
Probes n-Alkane Pentane Hexane Heptane Octane Polar probe THF Chloroform
Average Energy of Probe (kJ/mol)
Average Energy of Probe on Surface (kJ/mol)
Adsorption Energy (kJ/mol)
ag1/2 (nm mJ1/2/m)
6.2 4.9 72.0 30.3
21.6 25.7 38.6 5.0
27.8 30.6 33.4 35.5
1.84 2.2306 2.5682 2.9076
35.0 0.0
2.0 31.2
33.0 31.2
2.1345 2.2392
2
Table 6. The Calculated Adsorption Energy of Probes on the (0 0 1) Surface of a-Lactose Monohydrate
Probes n-Alkane Pentane Hexane Heptane Octane Polar probe THF Chloroform
Average Energy of Probe (kJ/mol)
Average Energy of Probe on Surface (kJ/mol)
Adsorption Energy (kJ/mol)
ag1/2 (nm2 mJ1/2/m)
6.2 4.9 72.0 30.3
38.6 44.1 20.3 24.1
44.8 49.0 51.7 54.4
1.84 2.2306 2.5682 2.9076
35.0 0.0
20.6 51.3
55.6 51.3
2.1345 2.2392
Table 7. The Calculated Adsorption Energy of Probes on the ð0 0 1Þ Surface of a-Lactose Monohydrate
Probes n-Alkane Pentane Hexane Heptane Octane Polar probe THF Chloroform DOI 10.1002/jps
Average Energy of Probe (kJ/mol)
Average Energy of Probe on Surface (kJ/mol)
Adsorption Energy (kJ/mol)
ag1/2 (nm mJ1/2/m)
6.2 4.9 72.0 30.3
17.8 23.3 41.2 1.9
24.0 28.2 30.8 32.2
1.84 2.2306 2.5682 2.9076
35.0 0.0
8.2 35.7
43.3 35.7
2.1345 2.2392
2
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Figure 8. The calculated adsorption energy of different probes on the (0 2 0) and (0 2 0) surfaces.
From Tables 4 and 5, a graph of adsorption energy against area and square root of surface tension of vapour probes was plotted for the (0 2 0) and ð0 2 0Þ faces (Fig. 8), whereas for the (0 0 1) and ð0 0 1Þ faces, a similar graph was plotted (Fig. 9) from Tables 6 and 7, using a similar approach as for the experimental determination of the surface energies by IGC (Fig. 1). Comparison of Inverse Gas Chromatography and Molecular Modelling Results Table 8 summaries both the IGC and molecular modelling results. The results show that the
dispersive and specific energy calculated by molecular modelling is in quantitative agreement with the energy measured by IGC. The molecular modelling results also agree with the surface energy calculated in Table 3, where the ð0 2 0Þ and ð0 0 1Þ faces had lower surface energy and greater stability compared to the (0 2 0) and (0 0 1) faces. A similar comparison is shown in Table 8, where the dispersive energy of the (0 2 0) and (0 0 1) faces are more than their related counterpart faces. The main reason for this difference in the dispersive energy is due to the different position of water molecules on these faces. On the (0 2 0) and (0 0 1) faces water was
Figure 9. The calculated adsorption energy of different probes on the (0 0 1) and (0 0 1) surfaces. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 2, FEBUARY 2010
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Table 8. Comparison of Dispersive Energy and Specific Component of Free Energy Calculated by IGC and Molecular Modelling DGSP A (kJ/mol) Method Inverse gas chromatography Molecular modelling
Face
2 gD S (mJ/m )
THF
Chloroform
(0 2 0) ð0 2 0Þ (0 0 1) ð0 0 1Þ
45.5 ( 0.18) 58.4 35.6 54.8 41.9
6.6 ( 0.26) 5.0 3.0 7.9 16.4
1.8 ( 0.04) 0.7 0.4 2.6 7.9
present in the bulk or close to the surface, whereas on the ð0 2 0Þ and ð0 0 1Þ faces water molecules were present on the surface and blocking the interaction of probes with the surface functional groups. The (0 2 0) face has a high specific interaction with polar probes as compared to the ð0 2 0Þ face because of the similar water-blocking effect. On the contrary, the (0 0 1) face has less specific energy compared to the ð0 0 1Þ face, because on the ð0 0 1Þ face, instead of blocking the interaction, water on the surface acts as an active molecule to interact with polar probes and increases overall specific interaction. Similar results were obtained by Sunkersett et al.,5,6 where they found, in a qualitative study, that the presence of water can decrease or increase the probe–molecule interaction, depending on the position of water molecule. The effect of channel size is less evident for the dispersive interaction because the n-alkanes, which are larger in size (compared to the polar probes), cannot interact with the functional groups present in the channel of any of the faces. Whereas polar probes have more interactions with the larger channel (0 0 1) face compared to the (0 2 0) face.
CONCLUSION This article shows that the adsorption energy measured by IGC and calculated by molecular modelling is in quantitative agreement with each other. It also shows that molecular modelling helps in understanding the dispersive and specific nature of the surface at the molecular level by relating to the functional groups present on the surface. This application of molecular modelling gives valuable knowledge about the interaction mechanisms underlying the measured values. It also demonstrates the effect of water and channel width on the surface energetics. Modelling shows DOI 10.1002/jps
that when water molecule is present on the surface, it can either decrease the interaction of the probe molecule by blocking the surface functional groups or in some cases it may itself attract the probe molecules, if it is available for interaction. Molecular modelling also revealed that the presence of channel on the surface can affect the surface energy depending on its size.
ACKNOWLEDGMENTS We acknowledge AstraZeneca and University of Bradford for supporting this work by providing a studentship for A. Saxena.
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salbutamol sulfate by inverse gas-chromatography. Int J Pharm 111:241–249. Schultz J, Lavielle L, Martin C. 1987. The role of the interface on carbon fiber-epoxy composites. J Adh 23:45–60. Allen FH. 2002. The Cambridge structural database: A quarter of a million crystal structures and rising. Acta Crystallogr B 58:380–388. Beevers CA, Hensen HN. 1971. Structure of alphalactose monohydrate. Acta Crystallogr B 27:1323. Noordik JH, Beurskens PT, Bennema P, Visser RA, Gould RO. 1984. Crystal-structure, polarity and morphology of 4-O-b-D-galactopyranosyl-a-D-glucopyranose monohydrate (a lactose monohydrate)— A redetermination. Z Kristallogr 168:59–65. Fries DC, Rao ST, Sundaralingam M. 1971. Structural chemistry of carbohydrates III. Crystal and molecular structure of 4-O-b-D-galactopyranosyl-aD-glucopyranose monohydrate (a lactose monohydrate). Acta Crystallogr 27:994. Smith JH, Dann SE, Elsegood MRJ, Dale SH, Blatchford CG. 2005. a-Lactose monohydrate: A redetermination at 150 K. Acta Crystallogr 61: 2499–2501. Guest MF, Bush IJ, Van Dam HJJ, Sherwood P, Thomas JMH, Van Lenthe JH, Havenith RWA, Kendrick J. 2005. The GAMESS-UK electronic structure package: Algorithms, developments and applications. Mol Phys 103:719–747. Kendrick J, Fox M. 1991. Calculation and display of electrostatic potentials. J Mol Graph 9:182– 187. Mayo SL, Olafson BD, Goddard WA. 1990. Dreiding—A generic force-field for molecular simulations. J Phys Chem 94:8897–8909. Coombes DS, Catlow C, Richard A, Gale JD, Hardy MJ. 2002. Theoretical and experimental investigations on the morphology and pharmaceutical crystals. J Pharm Sci 91:1652–1658.
DOI 10.1002/jps
Drug Delivery Group, Institute of Pharmaceutical Innovation, School of Pharmacy, University of Bradford, Bradford, UK
2
The Computational Group, Institute of Pharmaceutical Innovation, School of Pharmacy, University of Bradford, Bradford, UK 3
Product Development, Pharmaceutical & Analytical R&D, AstraZeneca, Macclesfield, UK
Received 16 April 2009; accepted 28 May 2009 Published online 7 August 2009 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.21864
ABSTRACT: The surface energy of a-lactose monohydrate measured by inverse gas chromatography (IGC) is reported along with a dynamic molecular modelling study of the interaction of the various molecular probes with different surfaces of a-lactose monohydrate. The IGC results show that a-lactose monohydrate is acidic in nature. Using quantitative calculations of the energy of adsorption, the acidic nature of the surface is confirmed and the calculated values agree closely with the experimentally measured values. Along with the acidic nature, dynamic molecular modelling also reveals that the presence of a channel and water molecules on a surface affects the surface energetics of that face. The presence of water on the surface can decrease or increase the surface energy by either blocking or attracting a probe molecule, respectively. This property of water depends on its position and association with other functional groups present on the surface. The effect of a channel or cavity on the surface energy is shown to depend on its size, which determines whether the functional groups in the channel are assessable by probe molecules or not. Overall molecular modelling explains, at the molecular level, the effect of different factors affecting the surface energy of individual faces of the crystal. ß 2009 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 99:741–752, 2010
Keywords: molecular modelling; hydrate; physicochemical properties; surface chemistry; chromatography; materials science
INTRODUCTION Most of the materials come in contact with water during processing, formulation, or even storage. The presence of water can affect the physical and chemical properties of some of these materials. It can alter the crystal growth and dissolution,
A. Saxena’s present address is Department of Pharmaceutics, University of Minnesota, 9-125, WDH, 308 Harvard Street SE, Minneapolis, MN 55455. Correspondence to: A. Saxena (Telephone: 8062207698; Fax: 6126262125; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 99, 741–752 (2010) ß 2009 Wiley-Liss, Inc. and the American Pharmacists Association
wettability, dispersibility, flowability, lubricity, compactability, hardness and even rates of chemical degradation. Most of these properties are directly or indirectly influenced by the surface energetics of the material, which is again affected by the presence of the water. Water can associate with solids in number of ways. It can interact with the surface of the solid (adsorption) or it can penetrate the bulk solid substrate (absorption) or it can be present as the water of crystallisation. It is necessary to know both the location and mobility of the water as well as its physical state, in order to have a better understanding of its effect on the surface energetics and properties of a solid.
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A number of studies have been reported on the surface energetics of a material as a function of humidity. Ohta and Buckton1 studied changes in the acidic and basic properties of amorphous cefditoren pivoxil powder using inverse gas chromatography (IGC) under various relative humidities (RHs). The basicity of the powder surface decreased with the increasing RH. Newell et al.2 assessed the effect of RH on the surface energy of the amorphous lactose and found that at high humidity the dispersive energy was reduced to a value comparable to that of crystalline lactose. Goss and Schwarzenbach3 found that the trend in electron donor/acceptor properties of three mineral surfaces (quartz, calcium carbonate and a-aluminium oxide) changes between 90% and 100% RH. They concluded that the change is probably connected to the orientation of the adsorbed water molecules. Balard et al.4 used IGC at infinite dilutions conditions and observed a strong decrease in the dispersive component of the surface energy of clay due to water molecules shielding the highest energy sites. Sunkersett et al.5,6 used IGC to study the surface energetics of selected pharmaceutical materials under dry conditions and at an ambient relative (47%) humidity. There was either no, or very small, change in the dispersive component, whereas the specific component of the free energy of adsorption remained constant, increased, or decreased at the increased RH, depending on the material and the probe. They demonstrated, with the help of molecular modelling, that the effect of water on the surface energy depends upon the interaction sites occupied by water and probe molecules. The significant limitation of this modelling work was that a single adsorbent molecule was considered representative of the whole surface. All the above determined the effect of atmospheric RH on the surface energy of different materials. Similarly, it is important to know how the water of crystallisation, present in the crystal lattice of many materials, can affect the surface energy, if it is present on the surface of the crystal. In this work, IGC is used to measure the surface energetics. A powder sample is packed into a column and its surface properties are analysed by measuring the retention behaviour of known vapour probes. Molecular modelling methods are used to understand the nature of the interactions between the probes and the surface at a molecular level. This combination of techniques has been applied in pharmaceutical and nonJOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 2, FEBUARY 2010
pharmaceutical applications to provide knowledge of the orientation and exposure of molecular groups on the crystal surfaces.7–10 Allington et al.11,12 compared the simulated results with the experimental data on nonpharmaceutical materials obtained from IGC. a-Lactose monohydrate crystal is used as a model compound in this study and four of its most important morphological surfaces are modelled by using the protocol developed previously.13 These four surfaces show a variation in the availability and position of the water of crystallisation. According to the protocol, molecular dynamic simulations were used to calculate the adsorption energy of the probe on these different surfaces. These simulated results for the different surfaces are compared to determine the effect of the presence of water on the surface energetics.
MATERIALS AND METHODS Materials a-Lactose monohydrate B.P. (>98% pure), a common excipient, was supplied by DMV International (Middlesex, UK). The probes used for IGC were: hexane (BDH Chemical, Poole, UK), heptane (Sigma Aldrich, Dorset, UK), octane (Aldrich Chemical, Milwaukee, WI), nonane (Aldrich Chemical), tetrahydrofuran (Riedel -de Haen, Seelze, Germany) and chloroform (Fisher Scientific, Loughborough, UK).
Methods Inverse Gas Chromatography IGC was used to measure the surface energy of a-lactose monohydrate. The experimental procedure for IGC was obtained from the previously published work by Ticehurst et al.14 Two presilanised columns of dimensions, 1 m (one loop) 6 mm (outer diameter) 3 mm (inner diameter) were packed with a-lactose monohydrate. Each column was analysed twice at room temperature, at 308C and 0% RH, using dry nitrogen gas as the carrier. A series of nonpolar (n-alkanes, hexane to nonane) and polar probes (THF and chloroform) were injected and retention time (tr) was meaSP sured. The dispersive (g D S ) and specific (DGA ) components were measured by the method of Schultz and Lavielle.15 Details of the calculations, are given in Saxena et al.13 DOI 10.1002/jps
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A distance-dependent dielectric constant was not used. No specific hydrogen bonding term was used.
Four crystal structures of a-lactose were found in the Cambridge Structural Database (Cambridge Crystallographic Data Centre, Cambridge, UK, CSD version 5.27, November 2005) using ConQuest version 1.8.16 Details of all these four structures, including their CSD reference code, are given in Table 1.
In the Dreiding force field, the exponential-6 potential function is given by 6 ! 6 j R jð1R=R0 Þ D0 e (1) j6 j 6 R0
Calculation of Partial Charges. From Table 1, the low temperature, most recently submitted crystal structure, LACTOS11, with a reasonably low R factor, was selected for molecular modelling calculations. A single molecule of a-lactose was extracted from LACTOS11 and was geometry optimised using the General Atomic and Molecular Electronic Structure System-UK (GAMESSUK) molecular orbital package21 using Hartree– Fock theory with a 6-31G basis set. Hartree–Fock calculations using a 6-31G basis set were then used to calculate the electrostatic potential around the optimised a-lactose molecule. Partial charges for the molecule optimised from LACTOS11 were derived from the surrounding electrostatic potential using a least-squares fit of the charges to the ab initio calculated potential.22 The partial charges for water and probe molecules were calculated in a similar manner, but the lowest energy conformation of each probe molecule, determined by energy minimisation was used for further modelling work.
where j was kept at 13.772 to maintain a function that is similar to the Lennard-Jones function at the minimum, and the parameters D0 and R0 of all hydrogen atoms involved in hydrogen bonding were adjusted to improve the agreement between predicted minimised structure and experiment. Crystal Morphology. Cerius2 was used to apply the Bravais–Freidel–Donnay–Harker (BFDH) method to predict the crystal morphology. This method is based on a geometrical calculation that uses the crystal lattice and symmetry to generate a list of possible growth faces and their relative growth rates. This approach calculates the interplanar spacing, dhkl, of the different crystal faces. Those faces with the lowest growth rates have the greatest dhkl. So the most morphologically important faces will be with the slowest growth rates and largest surface area.24 Cerius2 was used to generate the molecular arrangement of these surfaces.
Force Field. The DREIDING II force field,23 modified for D-b-mannitol in our previously published work,13 was used as the starting point for the present study on a-lactose monohydrate. This modified force field as implemented in Cerius2 (Molecular Simulations, Inc., San Diego, CA) uses the following options:
Molecular Dynamics. The protocol developed previously13 was used for molecular dynamics (MD) simulations of the probe molecules on the surface of a-lactose monohydrate in Cerius2. A slab was created from the surface, whose thickness was large enough so that the energy of lower surface should not affect the energy of upper surface. The surface energy of the slab was calculated using the following formula:
An exponential-6 potential for the van der Waals interaction. Coulombs interactions were calculated by Ewald method.
Surface energy ¼
slab energy bulk energy 2 surface area
(2)
Table 1. Details of Crystal Structures of a-Lactose Monohydrate Obtained from CSD
CSD Reference Code LACTOS01 LACTOS03 LACTOS10 LACTOS11 DOI 10.1002/jps
Space Group
R-Factor (%)
Measurement Temperature
References
P21 P21 P21 P21
15.0 3.4 2.7 3.32
RT RT RT 150 K
Beevers and Hensen17 Noordik et al.18 Fries et al.19 Smith et al.20
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where slab energy is the energy of a twodimension slab of a particular thickness, and bulk energy is the energy of one molecule multiplied by total number of molecules present in the slab. The slab was minimised (relaxed) and the molecules in the slab were then kept fixed during the MD simulation of the probe molecule on the surface. NVE MD simulations were performed for 50 ps with an integration step of 1 fs. The initial temperature of the simulation was 300 K. Equilibration was determined by examination of the change in average potential energy as a function of time. Twenty to 25 structures were randomly selected from the trajectory after equilibration and minimised. The average minimised energy was used as the energy of the system. The energy of the isolated probe molecules was calculated in the same way. The adsorption energy Eads is defined from Esystem ¼ Eprobe þ Esurface Eads
(3)
where Esystem is the average minimised energy of the system (probe/surface interaction), Eprobe the average minimised energy of isolated probe, Esurface the average minimised energy of surface (the energy of the surface is taken to be 0 as the surface was fixed during simulation).
RESULTS AND DISCUSSION Inverse Gas Chromatography The experimental adsorption energy measured by IGC is shown in Figure 1. Tetrahydrofuran (THF), a basic probe, has a high net retention volume (Vn) on a-lactose monohydrate as compared to chloroform (an acidic probe). The surface of a-lactose monohydrate crystal is clearly acidic in nature.
Molecular Modelling Force Field Starting from the experimental LACTOS11 experimental structure, the modified force field was used to minimise the lattice energy with respect to all lattice parameters and the molecular geometry. After examination of the modified force field, van der Waals parameters (original R0 ¼ ˚ and D0 ¼ 0.01520 kcals/mol) for hydro3.1950 A gen, capable of forming hydrogen bonding, were replaced by an improved set of parameters with ˚ and 0.01288 kcals/mol, respecvalues 1.5558 A tively. The result obtained by minimising the energy of the experimental crystal structure of a-lactose monohydrate (LACTOS11) using the
Figure 1. The experimental adsorption energy of different probes on a-lactose monohydrate measured by inverse gas chromatography. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 2, FEBUARY 2010
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Table 2. Comparison Between Experimental and Minimised Lattice Parameters by Applying the Modified Dreiding Force Field With Original and Improved R0 and D0 Values Modified Dreiding Force Field With Improved R0 and D0
Modified Dreiding Force Field With Original R0 and D0 CSD Reference Code Lactose 11 A B C B
Experimental Lattice ˚) Parameters (A
Minimised Lattice ˚) Parameters (A
% Difference
Minimised Lattice ˚) Parameters (A
% Difference
4.783 21.54 7.76 105.91
4.725 21.375 7.296 99.05
1.21 0.77 5.98 6.48
4.599 20.798 7.41 104.88
3.85 3.44 4.51 0.97
modified force field with new R0 and D0 values is shown in Table 2. Table 2 shows that with the default van der Waals parameters, the maximum absolute errors for angle b are unacceptably high, whereas with the improved parameters the largest deviation is within an acceptable limit of 5%. Because of the ability of the modified force field with improved van der Waals parameters, to predict a better
crystal structure, it was selected for the further study of adsorption on to the surface of a-lactose monohydrate. Crystal Morphology Figure 2 shows the crystal morphology predicted by Cerius2 using BFDH method, which is similar to the morphology obtained under the scanning electron microscope (Fig. 3).
Figure 2. Predicted morphology of a-lactose monohydrate crystal faces by BFDH method using Cerius2. DOI 10.1002/jps
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related, as can be seen in the crystal morphology, shown in Figure 2. We will, however, use the notation to distinguish between surfaces which have been generated by cleavage through different parts of the unit cell. Cleavage to produce the (0 2 0) and ð0 2 0Þ faces produced different surface compositions as did cleavage to produce the (0 0 1) and ð0 0 1Þ faces. These four surfaces are the morphological important faces for a-lactose monohydrate. So the molecular arrangement of these four faces has considerable influence on the surface energetics of the whole crystal. Molecular Arrangement of a-Lactose Monohydrate Faces
Figure 3. The crystal morphology of a-lactose monohydrate observed under the scanning electron microscope.
In the predicted morphology the (0 2 0) face has the maximum surface area, followed by the (0 0 1) face. The actual surface composition is dependent on where the unit cell is cleaved. The (0 2 0)/ð0 2 0Þ and the (0 0 1)/ð0 0 1Þ surfaces are symmetry
The bulk structure was sliced along the required hkl planes to visualise the (0 2 0), ð0 2 0Þ, (0 0 1) and ð0 0 1Þ faces (Figs. 4–7, respectively). Figures 4–7 show the molecular arrangement of these relaxed faces, respectively, which shows that all these four faces have hydroxyl (–OH) groups on the surface. This agrees with IGC measurements, which show that a-lactose monohydrate crystals are acidic in nature. The molecular arrangement of all these four faces also clarifies the basicity of the surface measured by IGC, which can be due to the presence of different
Figure 4. Molecular arrangement of the (0 2 0) face of a-lactose monohydrate. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 2, FEBUARY 2010
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Figure 5. Molecular arrangement of the (0 2 0) face of a-lactose monohydrate.
negatively charged oxygen atoms or the delocalised electrons on the ring structure, present on the surface. There are two important points concerning the molecular arrangement of all these faces. Firstly,
there is a difference in the channel width, created by the molecular arrangement of lactose molecules on the (0 2 0) and (0 0 1) faces (Figs. 4 and 6, respectively). The (0 0 1) face has a larger channel width compared to the (0 2 0) face. A similar
Figure 6. Molecular arrangement of the (0 0 1) face of a-lactose monohydrate. DOI 10.1002/jps
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Figure 7. Molecular arrangement of the (0 0 1) face of a-lactose monohydrate.
difference is in their related counterparts (Figs. 5 and 7). This width determines the total area of the surface exposed for the probes and what size of probe molecule can interact with the functional groups deep inside the channel. Secondly, the water molecules are present at different position on all four different faces (Figs. 4–7). The (0 2 0) and (0 0 1) faces have the water molecule deep in the channel, whereas on the ð0 2 0Þ and ð0 0 1Þ faces water is present on the surface. This difference in water molecules’ position can directly affect the probes interaction with other functional groups present on the surface. Molecular Dynamics In the MD simulations, all four faces were separately represented by four unit cell thick slabs. These slabs were relaxed and the molecules in the slab were then kept fixed during MD
simulation. The surface energy of these four slabs was calculated using Eq. (2) and summarised in Table 3. The surface with lower energy will be more stable and likely to appear in the crystal structure. Table 3 shows that faces with water on the surface (ð0 2 0Þ and ð0 0 1Þ) are more stable than the (0 2 0) and (0 0 1) faces. MD simulations of probe molecules on all four slabs were performed within the NVE ensemble. The average temperature over the equilibrated trajectories was around 300 K. The average, minimised energy of 15–25 randomly selected structures after the equilibration time was used to calculate the energy of the system. In the same way, the energy of the isolated probe was calculated but without the lactose surface. The adsorption energies for n-alkanes and polar probes on all four faces were calculated using Eq. (3) and summarised in Tables 4–7.
Table 3. The Calculated Surface Energy of Different Faces of a-Lactose Monohydrate
Faces
Slab Energy (kcal/mol)
Bulk Energy (kcal/mol)
Surface ˚) Area (A
Surface Energy ˚ 2) (kcal/mol/A
(0 2 0) ð0 2 0Þ (0 0 1) ð0 0 1Þ
1242.54 1219.86 1239.26 1217.84
1148.68 1148.68 1126.02 1126.02
34.14 34.14 95.65 95.65
1.38 1.04 0.59 0.48
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Table 4. The Calculated Adsorption Energy of Probes on the (0 2 0) Surface of a-Lactose Monohydrate
Probes n-Alkane Pentane Hexane Heptane Octane Polar probe THF Chloroform
Average Energy of Probe (kJ/mol)
Average Energy of Probe on Surface (kJ/mol)
Adsorption Energy (kJ/mol)
ag1/2 (nm2 mJ1/2/m)
6.2 4.9 72.0 30.3
21.3 25.9 37.7 6.8
27.5 30.8 34.3 37.1
1.84 2.2306 2.5682 2.9076
35.0 0.0
0.1 31.8
35.1 31.8
2.1345 2.2392
Table 5. The Calculated Adsorption Energy of Probes on the ð0 2 0Þ Surface of a-Lactose Monohydrate
Probes n-Alkane Pentane Hexane Heptane Octane Polar probe THF Chloroform
Average Energy of Probe (kJ/mol)
Average Energy of Probe on Surface (kJ/mol)
Adsorption Energy (kJ/mol)
ag1/2 (nm mJ1/2/m)
6.2 4.9 72.0 30.3
21.6 25.7 38.6 5.0
27.8 30.6 33.4 35.5
1.84 2.2306 2.5682 2.9076
35.0 0.0
2.0 31.2
33.0 31.2
2.1345 2.2392
2
Table 6. The Calculated Adsorption Energy of Probes on the (0 0 1) Surface of a-Lactose Monohydrate
Probes n-Alkane Pentane Hexane Heptane Octane Polar probe THF Chloroform
Average Energy of Probe (kJ/mol)
Average Energy of Probe on Surface (kJ/mol)
Adsorption Energy (kJ/mol)
ag1/2 (nm2 mJ1/2/m)
6.2 4.9 72.0 30.3
38.6 44.1 20.3 24.1
44.8 49.0 51.7 54.4
1.84 2.2306 2.5682 2.9076
35.0 0.0
20.6 51.3
55.6 51.3
2.1345 2.2392
Table 7. The Calculated Adsorption Energy of Probes on the ð0 0 1Þ Surface of a-Lactose Monohydrate
Probes n-Alkane Pentane Hexane Heptane Octane Polar probe THF Chloroform DOI 10.1002/jps
Average Energy of Probe (kJ/mol)
Average Energy of Probe on Surface (kJ/mol)
Adsorption Energy (kJ/mol)
ag1/2 (nm mJ1/2/m)
6.2 4.9 72.0 30.3
17.8 23.3 41.2 1.9
24.0 28.2 30.8 32.2
1.84 2.2306 2.5682 2.9076
35.0 0.0
8.2 35.7
43.3 35.7
2.1345 2.2392
2
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Figure 8. The calculated adsorption energy of different probes on the (0 2 0) and (0 2 0) surfaces.
From Tables 4 and 5, a graph of adsorption energy against area and square root of surface tension of vapour probes was plotted for the (0 2 0) and ð0 2 0Þ faces (Fig. 8), whereas for the (0 0 1) and ð0 0 1Þ faces, a similar graph was plotted (Fig. 9) from Tables 6 and 7, using a similar approach as for the experimental determination of the surface energies by IGC (Fig. 1). Comparison of Inverse Gas Chromatography and Molecular Modelling Results Table 8 summaries both the IGC and molecular modelling results. The results show that the
dispersive and specific energy calculated by molecular modelling is in quantitative agreement with the energy measured by IGC. The molecular modelling results also agree with the surface energy calculated in Table 3, where the ð0 2 0Þ and ð0 0 1Þ faces had lower surface energy and greater stability compared to the (0 2 0) and (0 0 1) faces. A similar comparison is shown in Table 8, where the dispersive energy of the (0 2 0) and (0 0 1) faces are more than their related counterpart faces. The main reason for this difference in the dispersive energy is due to the different position of water molecules on these faces. On the (0 2 0) and (0 0 1) faces water was
Figure 9. The calculated adsorption energy of different probes on the (0 0 1) and (0 0 1) surfaces. JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 2, FEBUARY 2010
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Table 8. Comparison of Dispersive Energy and Specific Component of Free Energy Calculated by IGC and Molecular Modelling DGSP A (kJ/mol) Method Inverse gas chromatography Molecular modelling
Face
2 gD S (mJ/m )
THF
Chloroform
(0 2 0) ð0 2 0Þ (0 0 1) ð0 0 1Þ
45.5 ( 0.18) 58.4 35.6 54.8 41.9
6.6 ( 0.26) 5.0 3.0 7.9 16.4
1.8 ( 0.04) 0.7 0.4 2.6 7.9
present in the bulk or close to the surface, whereas on the ð0 2 0Þ and ð0 0 1Þ faces water molecules were present on the surface and blocking the interaction of probes with the surface functional groups. The (0 2 0) face has a high specific interaction with polar probes as compared to the ð0 2 0Þ face because of the similar water-blocking effect. On the contrary, the (0 0 1) face has less specific energy compared to the ð0 0 1Þ face, because on the ð0 0 1Þ face, instead of blocking the interaction, water on the surface acts as an active molecule to interact with polar probes and increases overall specific interaction. Similar results were obtained by Sunkersett et al.,5,6 where they found, in a qualitative study, that the presence of water can decrease or increase the probe–molecule interaction, depending on the position of water molecule. The effect of channel size is less evident for the dispersive interaction because the n-alkanes, which are larger in size (compared to the polar probes), cannot interact with the functional groups present in the channel of any of the faces. Whereas polar probes have more interactions with the larger channel (0 0 1) face compared to the (0 2 0) face.
CONCLUSION This article shows that the adsorption energy measured by IGC and calculated by molecular modelling is in quantitative agreement with each other. It also shows that molecular modelling helps in understanding the dispersive and specific nature of the surface at the molecular level by relating to the functional groups present on the surface. This application of molecular modelling gives valuable knowledge about the interaction mechanisms underlying the measured values. It also demonstrates the effect of water and channel width on the surface energetics. Modelling shows DOI 10.1002/jps
that when water molecule is present on the surface, it can either decrease the interaction of the probe molecule by blocking the surface functional groups or in some cases it may itself attract the probe molecules, if it is available for interaction. Molecular modelling also revealed that the presence of channel on the surface can affect the surface energy depending on its size.
ACKNOWLEDGMENTS We acknowledge AstraZeneca and University of Bradford for supporting this work by providing a studentship for A. Saxena.
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DOI 10.1002/jps