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Aggregate elasticity, crystal structure and tableting performance for p-aminobenzoic acid and a series of its benzoate esters. Aditya B. Singaraju, Kyle Nguyen, Abhay Jain, Rahul V. Haware, and Lewis L Stevens Mol. Pharmaceutics, Just Accepted Manuscript • DOI: 10.1021/acs.molpharmaceut.6b00598 • Publication Date (Web): 10 Oct 2016 Downloaded from http://pubs.acs.org on October 11, 2016
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Molecular Pharmaceutics
Aggregate elasticity, crystal structure and tableting performance for p-aminobenzoic acid and a series of its benzoate esters. Aditya B. Singaraju1, Kyle Nguyen1, Abhay Jain2, Rahul V. Haware2 and Lewis L. Stevens1,* 1. Division of Pharmaceutics and Translational Therapeutics, College of Pharmacy, The University of Iowa, Iowa City, IA 52242 2. Division of Pharmaceutical Sciences, College of Pharmacy & Health Sciences, Campbell University, Buies Creek, NC 27506
ABSTRACT The tableting performance for p-aminobenzoic acid (PABA) and a series of its benzoate esters with increasing alkyl chain length (methyl-, ethyl- and n-butyl) was determined over a broad range of compaction pressures. The crystalline structure of methyl benzoate (Me-PABA) exhibits no slip systems and does not form viable compacts under any compaction pressure. The ethyl (Et-PABA) and n-butyl (Bu-PABA) esters each have a similar, corrugated-layer structure that displays a prominent slip plane and improves material plasticity at low compaction pressure. The compact tensile strength for Et-PABA is superior to Bu-PABA; however, neither material achieved a tensile strength greater than 2 MPa over the compression range studied. Complementary studies with powder Brillouin light scattering (BLS) show the maxima of the shear wave, acoustic frequency distribution red shift in an order consistent with both the observed tabletability and attachment energy calculations. Moreover, zero-porosity aggregate elastic moduli are determined for each material using the average acoustic frequency obtained from specific characteristics of the powder BLS spectra. The Young’s moduli for Et- and BuPABA is significantly reduced relative to PABA and Me-PABA and this reduction is further evident in tablet compressibility plots. PABA, however, is distinct with high elastic isotropy as interpreted from the narrow and well-defined powder BLS frequency distributions for both the shear and compressional acoustic modes. The acoustic isotropy is consistent with the quasiisotropic distribution of hydrogen bonding for PABA. At low compaction pressure, PABA tablets display the lowest tensile strength of the series; however, above a compaction pressure of ca. 70 MPa PABA tablet tensile strength continues to increase while that for Et- and Bu-PABA plateau. PABA displays lower plasticity relative to the either ester and this is consistent with its crystalline structure and high yield pressure determined from in-die Heckel analysis. Overall the complementary approach of using both structural and the acoustic inputs uniquely provided from powder BLS is anticipated to expand our comprehension of the structure-mechanics relationship and its role in tableting performance. Keywords: molecular crystals, powders, Brillouin scattering, structure-mechanics, tabletability, compressibility
* Corresponding author. Tel: (319)-335-8823; e-mail:
[email protected] 1 ACS Paragon Plus Environment
Molecular Pharmaceutics
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1. INTRODUCTION The tableting process involves a complex interplay of powder bed deformation to reduce porosity, reorganize grain orientation and redistribute interparticulate bonding. To develop a mechanistic description of tablet formation and to enable active pharmaceutical ingredient (API) phase selection for optimum processability, the mechanical properties of the API are chiefly important. [1, 2, 3, 4] A significant challenge that remains for improving our capacity for modeling the tableting process is the development of an unambiguous structure-mechanics relationship. Progress in addressing this challenge has predominantly focused on identifying those structural motifs that empirically exhibit improved tabletability as gauged by an increase in compact tensile strength. Flat-layered crystal structures have previously been reported for multiple systems to display superior tableting performance. [5, 6, 7] The packing polymorphism of acetaminophen is routinely used to illustrate the influence of crystal structure on tabletability. Form I, the more stable modification of acetaminophen, exhibits a herringbone structure that frustrates slip-mediated plasticity and provides poor compacts when compared with Form II of acetaminophen. The structure of acetaminophen Form II displays extended, two-dimensional sheets that facilitate plastic deformation under load and improve tabletability. [7] These twodimensional sheets typically exhibit strong intra-planar interactions, e.g. extended hydrogen bonding, yet individual sheets are connected by weak van der Waals or π-π interactions. This molecular organization naturally provides a predominant slip system that facilitates plastic deformation. The physical stability of Form I, however, supports its selection for manufacturing despite its mechanical disadvantage. Routine solutions to overcoming this disadvantage include the introduction of excipients and binders to provide mechanical integrity to the tablet formulation. [8] Selection of the appropriate excipient(s) is a trial-and-error process that requires a significant time and material investment. This is not ideal practice in early development stage, where quantity of the API is often limited. Moreover, the possibility of adverse chemical instabilities increases through the introduction of API-excipient(s) interactions. With the identification of specific structural elements that predispose a material to exhibit desirable mechanical characteristics, an opportunity becomes available for crystal engineering, e.g. co-crystallization, whereby a co-former is crystallized with the parent compound to deliberately enhance a specific material property. [9, 10, 11] With respect to tabletability, multiple co-crystals have demonstrated improved performance relative to the individual parent materials. A crystal-structure motif that repeatedly demonstrated superior tabletability is flatlayered with strong, extended hydrogen-bonding interactions conserved within the molecular sheets. [12] Selection of the appropriate co-former must satisfy this criterion for extended hydrogen-bonding, however, beyond the expectation for specific, local synthon formation the overall supramolecular organization is not guaranteed a priori and remains an empirical process. Significant research is further needed to realize the full potential of crystal engineering for designing materials to support a specific performance attribute. Both plasticity and elasticity are integral components to the tableting process. [13] While traditional interpretations of tabletability emphasize plasticity, there is a growing interest in crystal elasticity and its role in tablet formation and strength. [14, 15, 16] The strength and orientation of intermolecular interactions has clear influence on the bulk material mechanics. While co-crystallization in an effective strategy for redistributing intermolecular interactions in an effort to modify material mechanics, for those molecules with an ionizable functionality, salt formation is an alternative approach. Both strategies were recently employed to tune the mechanical properties of voriconazole as assessed using AFM nanoindentation. [17] Voriconazole salts displayed higher hardness and higher Young’s moduli relative to pure voriconazole and this was interpreted through the introduction of strong ionic bonds that arise from salt formation. Co-crystals of voriconazole consistently displayed a lower hardness, however, Young’s moduli remained higher relative to the pure material. The consistently higher modulus for the co-crystals was rationalized by their higher number of intermolecular 2 ACS Paragon Plus Environment
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Molecular Pharmaceutics
interactions and their relative orientation to the direction of indentation. The authors suggest that the isotropic character, i.e. the spatial distribution of the intermolecular interactions, is important to connecting material elasticity with crystal structure. For a general three-dimensional body the linear elasticity relationship may be expressed as,
σij =Cijkl εkl
(1)
with the second-rank stress tensor (σij) related to the second-rank strain tensor (εkl) through the fourth-rank elasticity tensor (Cijkl) with repeated indices in Eq. 1 indicating summation per Einstein’s convention. [18] With a complete elasticity tensor, calculation of all engineering moduli is straightforward. [19] Furthermore, those moduli with directional sensitivity, e.g. a Young’s modulus, their anisotropy may be characterized with a full Cijkl, as demonstrated Ortiz et al. for a series of metal-organic frameworks. [20] Multiple techniques are available for determining the elasticity tensor for single crystals: e.g., pulse-echo ultrasound, resonant ultrasound spectroscopy (RUS) and Brillouin light scattering (BLS). [21, 22, 23] Both pulse-echo ultrasound and RUS require large, single-crystal samples that are manufactured to a specific geometry. However, crystal growth at the mm scale in all dimensions is challenging and limits application of these techniques. [24] BLS is an optical method and may be applied to small, micron-scale samples but for low-symmetry materials several independent scattering geometries are required to accurately solve for the elastic constants. Overall, these practical challenges have led to the limited elasticity database for organic molecular crystals and further limits the use of elasticity data for interpreting tabletability. [25] Indeed from the preceding discussion on voriconazole, to analyze the nanoindentation results a Poisson’s ratio was assumed to be 0.3 for all materials. [17] However, as reported by Mazel et al., the Poisson’s ratio varied significantly when comparing acetaminophen, ibuprofen, mannitol and microcrystalline cellulose. [26] Therefore, the assumption of a constant Poisson’s ratio can potentially introduce a significant source of error. In this report, we introduce the use of powder BLS for determining aggregate elastic moduli. We performed an initial validation of the aggregate moduli determined from powder BLS using acetylsalicylic acid as a model compound. We further applied this spectroscopic approach to the previously reported paraben series [27] and our own PABA series to provide mechanical data supporting the interpretation of their respective tableting performance. Overall, this method offers many potential advantages: (1) no special sample preparation (apart from sieving to reduce particle size), (2) it is material sparing with 20 - 50 mg samples being typical and (3) spectra may be acquired in 15 – 20 minutes. The continued validation of this approach will allow the incorporation of both structural and mechanical data for insight into the tableting process. The model compounds chosen for this study are p-aminobenzoic acid (PABA) and a series of its benzoate esters with increasing alkyl chain length. The molecular structure is shown in Figure 1. The selection of this series permits the observation of both structural and mechanical modification with minor changes to the parent compound. A similar approach was reported for multiple independent studies for a series of n-alkyl-4-hydroxybenzoates (parabens). [28, 27, 29, 30] All parabens except for the methyl-substituted paraben exhibited a layered crystalline structure. The reported tabletability from Feng et al. over a compaction range of ca. 20 – 60 MPa demonstrated an alkyl-paraben rank order of ethyl > n-buytl > n-propyl > methyl. [28] Calculated attachment energies followed the same rank-order and supported a slipmediated plasticity that improved tabletability. For reference in this study, the individual PABA esters are referred to as Me-PABA, EtPABA and Bu-PABA to respectively discriminate the pendant alkyl group: methyl-, ethyl- and n3 ACS Paragon Plus Environment
Molecular Pharmaceutics
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butyl. The parent molecule, p-aminobenzoic acid, will be referred to as PABA. The primary molecular distinction between the paraben and PABA series is the para-positioned hydroxyl group is substituted with an amine group. Despite a similar molecular homology with paraben, none of the PABA materials exhibit crystal structures with a thin, flat-layered organization. [31, 32, 33, 34] Previous solution NMR of aniline, phenol and thiophenol rank ordered the strength of interaction as phenol >> aniline > thiophenol as determined from concentration dependent proton chemical shifts. [35] Thus, it is expected the alternative hydrogen bonding character of the phenylamine, distinct from that of phenol, consequently contributes to the observed structural differences and will equally provide mechanical discrimination. 2. EXPERIMENTAL 2.1 Materials. Purchased materials, PABA (Aldrich, >99%), Me-PABA (Alfa Aesar, >98%), Et-PABA (Aldrich, >99%) and Bu-PABA (Aldrich, >98%) were used without further purification. Raw powders were all sieved through a 250 µm sieve (Advantech, Inc.) and stored in an ambercolored, cabinet desiccator to maintain a consistent storage environment; however, per vendor recommendation, the PABA powder was stored in the refrigerator (2 – 8 oC) after sieving. Sieves were washed and air-dried between samples to avoid cross contamination. Typical relative humidity values inside the desiccator ranged from 14 – 19% and the room humidity was recorded before each compaction study. Particle size distributions (PSDs) were determined for all PABA materials using a sieve analysis. [36] The results of this analysis are shown in Figure 2 and all four materials have similar D50 and D90 values, which we determined for PABA, Me-PABA, Et-PABA and Bu-PABA to be respectively (D50, D90): (138, 198), (117, 182), (151, 213) and (145, 207) µm. 2.2 Thermal Analysis. Differential scanning calorimetry (DSC) scans were performed using a TA instruments Q20 calibrated with an indium standard. The melting point and enthalpy for the indium reference were found to be 155.93 0C and 28.29 J/g respectively. Approximately 3-5 mg of powders were used in the study. All powders were heated in a closed pan from ambient to approximately 20 oC above the observed melt transition at a rate of 10 oC per minute under a nitrogen purge of 20 mL/minute. Obtained thermograms were analyzed using the Universal Analysis software package provided from TA Instruments. Thermograms for all the materials in this study are provided as supporting information, however, melting points are collected in Table I for PABA and the ester series. 2.3 Powder X-ray Diffraction. Powder patterns were collected using a Siemens D5000 diffractometer. The source of X-rays was Cu Kα X-rays with λ = 1.5418 Å. Room-temperature powder patterns were collected at 2θ values ranging from 7o to 45o with a step size of 0.02o and a dwell time of 0.75 seconds. All obtained PXRD patterns are available as supporting information to this report. Moreover, the Cambridge Structural Database reference codes for entries with predicted powder patterns that matched our experimental results are collected in Table I. These specific structures we will make reference to for interpreting the influence of crystal structure on the tabletability and powder BLS spectra. A summary of the crystallographic parameters for the PABA series are further collected in Table I. 2.4 Tableting and Tensile Strength.
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Molecular Pharmaceutics
A Model C Carver press (Carver, Inc.) was used for tableting. Flat-faced tablets with ca. 8mm diameter were prepared with a stainless-steel punch and die. After placing the lower punch, 295 – 304 mg of powder was loaded into the die. The punch and die assembly was centered on the lower platen and the pressure was carefully increased in order to achieve the desired compaction pressures. For a consistent comparison among each material studied in this report, a five-minute dwell time was selected. During the course of this dwell time the piston pressure would relax to a steady value that was ca. 10-15% lower than the peak pressure observed. This steady-state value is reported as the compaction pressure. To avoid damage to the compacts, the tablets were ejected by removing the lower punch and applying light pressure to the upper punch until the tablet could be removed from the die. Ejected compacts were stored in a cabinet desiccator at room temperature for 24 hours to allow for elastic recovery. After this period, all compacts were evaluated for thickness, diameter and mass. Particle densities were determined in triplicate with a helium micropycnometer (MPY-2, Quantachrome) and the results are recorded in Table I. Using this particle density, the tablet porosity was determined. For all pressure points, three replicate samples were prepared and all reported error bars represent the standard deviation of the measurement. Heckel analysis was performed as previously reported. [37] Tensile strength of the compacts was determined using a Universal Stress Strain analyzer. (QTestII, MTS Systems Corporation) A strain rate of 0.01 mm/sec was used. The compacts were placed between two steel plates and the platens were covered with a thin sheet of paper to minimize shear at the contact points. The peak force at which the tablet underwent diametrical failure was recorded and the diametrical tensile strength (σ) was calculated using Equation 2, σ =
2F π DT
(2)
with the peak breaking force, tablet diameter and tablet thickness respectively shown as F, D and T. [38] 2.5 Powder Brillouin Light Scattering. The mechanical properties of the powders were evaluated using powder BLS. The demonstration of powder BLS was previously reported by Hernandez et al. in application to four model compounds: salol, lysozyme, NaCl and powdered glass. [39] Their theoretical treatment began with the Brillouin shift equation for isotropic materials,
ν=
θ V sin λo 2
2n
(3)
which relates the measured Brillouin frequency shift (ν ) to the material refractive index (n), incident laser wavelength (λo), sound velocity (V) and the scattering angle (θ ). [40] For a given bulk, isotropic material then the maximum ν would be expected for a backscattering geometry (θ = 180o) and a sharp, single resonance at this frequency (νmax) would be observed. For powder samples, however, the incident laser light undergoes multiple reflections at each particle-air interface and thereby generates a distribution of scattering angles. The resultant spectrum is a superposition of these multiple scattering events each with a Brillouin scattering frequency consistent with Eq. 3. A model illustration to contrast bulk and powder BLS spectra for an isotropic material is shown in Figure 3 for polystyrene. In Fig. 3 the νmax appears as a sharp cutoff frequency and the multiple-scattering contribution results in a broad tailing toward the 5 ACS Paragon Plus Environment
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central Rayleigh line. If particle orientation is homogeneously distributed throughout the scattering volume, this low-frequency tailing is smooth; however, if the particle size were too large then no longer can homogeneity be assumed over the scattering volume and the observed powder spectra is overlaid with various discrete modes. To minimize potential particle-size effects, all powders for the BLS studies were sieved through a 150 µm sieve (Advantech, Inc.) prior to recording the spectra. All experiments were performed in a backscattering geometry with our custom BLS spectrometer and a block diagram of the instrumental set-up is shown in Figure 4. The light source is a diode pumped, visible CW laser (Excelsior, Spectra Physics) operating at λ = 532 nm. Typical laser power at the sample was approximately 25 mW. The focusing lens (L1 in Fig. 4) focused the incident laser light onto the powdered sample and the scattered light was collected through the same lens. A second lens (L2 in Fig. 4) focused the scattered light onto the entry pinhole of a six-pass tandem Fabry-Perot interferometer (TFP-1, JRS Scientific Instruments). All measurements were performed with a mirror spacing of either 5, 6 or 7 mm to allow adjustment of the free spectral range (FSR). For certain materials in this study, the larger mirror spacing, which corresponds to a smaller FSR, allowed separation of the low-frequency transverse modes from the Rayleigh line. Scattered light was detected with a single-photon counting module (COUNT® BLUE Series, Laser components) operating near 70% quantum efficiency at 532 nm. Approximately 2000 scans were collected for all the powdered samples, which amounts to a total scan time of approximately 15 - 20 minutes. 3. RESULTS AND DISCUSSION 3.1 Initial validation of powder BLS: Aggregate elastic moduli for acetylsalicylic acid To provide an initial validation for our powder BLS approach, we chose acetylsalicylic acid because its anisotropic elasticity tensor has been fully determined by both pulse-echo and resonant ultrasound spectroscopy. [41] A complete elasticity tensor permits straightforward calculation of all mechanical moduli for comparison to our powder BLS results. [42] Our observed powder BLS spectra displayed two frequency distributions corresponding to the longitudinal and transverse acoustic waves and their angular dispersion. Here we extend upon our previous work by determining the aggregate elastic moduli from the powder BLS spectra. For anisotropic materials the sound velocity shown in Eq. 3 depends on the direction of propagation and thus depending upon the extent of acoustic anisotropy the frequency distributions become broader. To aid a consistent analysis of powder BLS spectra, we identify three easily measured features that are shown in the acetylsalicylic acid powder BLS model spectrum in Figure 5. First, the high-frequency cut-off (νLmax) represents the maximum longitudinal frequency, i.e. a backscattering geometry with the acoustic wavevector propagating along the stiffest direction of elasticity. Second, the mid-frequency, local minimum in the powder Brillouin scattering intensity represents the frequency gap (νsep) that separates longitudinal from transverse modes. We make the approximation that this frequency of separation represents the minimum possible longitudinal frequency and the maximum possible transverse frequency. Last, the frequency corresponding to the peak intensity in the transverse distribution we assign as the minimum transverse frequency (νTmin). We support these characteristic frequencies using the acoustic frequency distributions calculated from the Christoffel determinant using experimentally reported elastic constants and a large population of randomly sampled propagation directions (q). The results of this frequency analysis are shown in Fig. 5. Further details of this calculation have been reported previously by Singaraju et al. [37] Using this analysis, we take the average of νLmax and νsep to be the aggregate longitudinal frequency for the powdered material and similarly, the average of νsep and νTmin to be the aggregate transverse frequency. Using these aggregate frequencies and Eq. 3, the 6 ACS Paragon Plus Environment
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Molecular Pharmaceutics
longitudinal and transverse sound velocities are determined and respectively allow direct calculation of the longitudinal (M) and shear (G) moduli using [42],
M = ρν L2,agg
(4)
G = ρν T2,agg
(5)
with ρ being the density and νL,agg and νT,agg being respectively the aggregate longitudinal and transverse acoustic frequency. From these two moduli, all remaining moduli may be determined under the assumption that the powdered material is composed of randomly oriented grains and may be modeled as isotropic. [42] For the model spectrum shown in Fig. 5, we determined νTmin, νsep and νLmax to be respectively 7.5, 10.8 and 20.8 GHz. Using these frequencies, the reported crystal density (ρ = 1.40 g/mL) and an average refractive index (n = 1.55) the aggregate elastic moduli were calculated and reported in Table II. [43] For comparison, the Voigt-Reuss-Hill aggregate moduli were further determined using the elastic constants reported by Bauer et al. using both pulseecho ultrasound and resonant ultrasound spectroscopy (RUS). [41] Further comparison is drawn for the Young’s modulus of acetylsalicylic acid determined using rectangular powder compacts and a 3-point beam bending experiment. [44] The value reported in Table II for the beam-bending experiment is the extrapolated value for Young’s modulus at zero porosity. Comparison of our powder BLS results with those calculated from the elasticity tensors reported by Bauer et al. yielded an average percent difference of 17%. The largest discrepancy is seen for the bulk modulus (K) comparison which is approximately 27% lower than the K calculated from either the pulse-echo ultrasound or RUS determined elastic constants. As we have previously noted, this powder BLS measurement is not performed on compacts but rather loose powdered lightly tamped into a sample holder. The good correspondence between our evaluation and that for the single-crystal indicates the powder BLS measurement is a zeroporosity determination. We would expect this behavior because the acoustic waves sampled in BLS have a wavelength nominally of 200 nm (calculated from ν/V in Eq. 3) which is at least one to two orders of magnitude smaller than the typical expected particle size. For isotropic materials, the bulk modulus can be determined from [19], 4 K =M − G 3
(6)
Our assignment of νTmin as the peak intensity in the transverse distribution may overestimate the average shear velocity (and therefore the shear modulus) for some materials and result in a lower determination of K. Illustrated in Fig. 5 are the aggregate longitudinal and shear frequencies calculated from the frequency analysis (red dashed line) compared with those determined from our assignment of the characteristic frequencies, νTmin, νsep and νLmax, and shown with the green dashed line. The average percent difference between these separate determinations is 6.2%. As will be discussed for other materials, the transverse frequency distribution can display low frequencies near the Rayleigh line and would prevent the consistent assignment of a lower νTmin across all material types. Therefore, to aid an unbiased determination of powder mechanical properties we opt for frequency assignments, i.e. νTmin, νsep and νLmax, that are consistently and reproducibly identifiable. Overall enhancements to our calculation of aggregate elastic moduli will require an improved modeling of powder BLS for acoustic and optically anisotropic materials coupled with complementary single-crystal elasticity data. These improvements are ongoing and will be reported in follow-on studies. 7 ACS Paragon Plus Environment
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The relative standard deviation in the determination of the characteristic frequencies and the bulk densities for all powders studied in this report is better than ± 2%. Since the refractive indices are predicted values, we estimate ±10% relative standard deviation as the error for refractive index. Thus, for nominally n = 1.5, this estimation of error would account for n = 1.35 – 1.65, which reasonably bounds typical refractive indices for organic molecules of C, H, N and O composition. [45] Using these estimates of error and performing a propagation of error analysis, we estimate the relative standard deviation for the moduli determined using powder BLS at ±21%. It is noteworthy that the refractive index constitutes the primary contribution to this error analysis and would be substantially reduced with measured refractive indices at the incident wavelength (λ = 532 nm). For the following discussion on the paraben series and the PABA ester series we would not reasonably expect the refractive index to vary substantially within a given homologous series and thus the relative differences in their mechanical properties presumably remain significant. 3.2 Crystal elasticity and the tabletability of the paraben series. To further support the application of powder BLS for the present study, the powder BLS spectra were recorded for the homologous paraben series to provide mechanical data for interpreting their previously reported tableting performance. [27] To first confirm adequate sample homogeneity was established, powder BLS spectra were recorded for n-butyl-paraben at five different sample locations. These raw powder BLS spectra are overlaid in Figure 6 and despite small variation in absolute intensities, our chosen frequency assignments are highly reproducible. There are multiple influences to the scattering intensity for BLS from single crystal: scattering geometry, polarization of the incident and scattered light, and the photoelastic constants. [46] For powder BLS, these single-crystal intensity considerations remain operative; however, for powdered samples, grain orientation and particle size also significantly contribute. If particle size is too large, then discrete Brillouin-scattering components appear on top the distribution and significant sample-to-sample intensity variation is displayed. For all materials in this report, passing the powdered samples through a 150 µm sieve alleviated this concern, however, it is likely that with further particle size reduction the sampling variation in scattering intensity would improve further. Note that νTmin is not shown in Fig. 6 as a smaller free spectral range (FSR) is required to resolve the peak intensity of the transverse distribution from the central Rayleigh line, however, the same reproducibility in νTmin was observed as well. One free spectral range FSR was not adequate to fully capture both the longitudinal and transverse acoustic mode distributions while maintaining sufficient separation from the Rayleigh line to observe the transverse distribution maxima. Two FSRs were used (by adjusting the mirror spacing of the interferometer) to highlight the longitudinal and transverse frequency distributions separately shown in Figure 7. Referring to Fig. 7b., for all parabens except for the methyl ester, the longitudinal distribution is bimodal. We would anticipate this to result from the two-dimensional, flat-layered structures prominent with the ethyl-, n-propyl- and n-butylparabens. For those longitudinal modes propagating within layered sheets, the restoring forces are strengthened by intra-planar hydrogen bonding and thus result in a higher frequency shift. Alternatively, those longitudinal modes propagating along inter-planar directions supported by weak, dispersive interactions would expectedly show a reduced frequency shift. This splitting is not observed for the methyl-paraben since the hydrogen-bonding is three-dimensional with no pronounced directional preference and the crystalline structure is not layered. The powder BLS frequency assignments obtained from Fig. 7 are shown in Table III. Using the densities previously reported by Feng et al. and a refractive index of 1.54, both M and G were respectively calculated from the aggregate BLS longitudinal and transverse frequencies and the Young’s modulus (E) was calculated from the standard relationship for isotropic materials [19, 47], 8 ACS Paragon Plus Environment
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Molecular Pharmaceutics
E=
G (3 M − 4G ) M −G
(7)
Our determination of the mechanical moduli for the n-alkyl-paraben series are shown in Table III. Young’s moduli for the n-alkyl paraben series has previously been reported by both Newton et al. and Pedersen et al. using respectively a 4-point bending experiment and a compaction simulator. [29, 30] In the bending experiment, rectangular compacts were prepared at different solid fractions and the zero-porosity Young’s modulus (Eo) was then determined by extrapolation. These results were compared by Newton et al. to theoretical predictions of the Young’s modulus (ET) based on cohesive energy densities. [30] The results of these previous works are compared with those obtained in this work in Table IV. The four determinations of E for ethyl-paraben show a large spread ranging from 3.2 – 10.0 GPa. From powder BLS, E is most consistent with that reported by Newton et al. for ethyl-paraben; however, this agreement does not extend to the other materials. The theoretical values (ET) are consistently the highest prediction of E with exception for methyl-paraben. Our work finds the rank-order of E as, methyl- >> n-propyl > n-butyl > ethyl-paraben, while Eo from Newton et al. follows as, methyl- > ethyl- >> n-butyl ≈ n-propyl. Methyl-paraben displayed the highest E for all reports and this agrees with the quasiisotropic distribution of hydrogen bonding in all three dimensions as described by Feng et al. [28] The remaining paraben esters adopt a flat-layered structure with weak intermolecular forces connecting the separate planes of molecules. Without the reinforcement provided from a 3D distribution of hydrogen bonding, the stiffness of these of materials would be expected to decrease, i.e. more compressible, certainly along a stress direction perpendicular to the molecular sheets. However, only a modest decrease in Eo was observed for ethyl-paraben in the beam-bending experiments, followed by a significant decrease for the propyl- and butylparabens. Our powder BLS results confirm a reduction in E for the layered paraben structures; however, relative differences within this series (ethyl-, propyl- and butyl-) are less pronounced. The similarity of the powder BLS spectra shown in Fig. 7 is particularly evident when comparing the ethyl- and butyl-paraben. Even though this report marks the first evaluation of aggregate elastic moduli using powder BLS and our approach may certainly be refined, the relative difference between ethyl- and butyl-paraben is expected to be small, which is contrary to that reported by Newton et al. [30] The challenges with accurately determining elastic moduli through beam-bending experimentation have been previously noted. Variations in particle size, porosity and beam dimensions may all contribute to deviations in the reported values. Moreover, the compressibility plots reported by Feng et al. compare favorably with the mechanical data provided from powder BLS. Their reported rank-order of compressibility is, butyl- > ethyl > propyl >> methyl-paraben. Considering the Young’s modulus as a measure of material resistance to compression, our results reflect the observed compressibilities for the paraben series, i.e. methyl-paraben is distinctly higher than the remaining three esters. Of these remaining esters, ethyl-paraben is most compressible consistent with the smallest Young’s modulus found from powder BLS. The transverse frequency distributions offer further interpretation of the previously reported paraben tabletability. The maxima in the transverse frequency distributions (νTmin), shown in Fig. 7 and Table III, show a clear rank-order: ethyl- < n-propyl < n-butyl-
