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Evolution of a Polydisperse Ensemble of Spherical Particles in a Metastable Medium with Allowance for Heat and Mass Exchange with the Environment. CRYSTALS 2022. [DOI: 10.3390/cryst12070949] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Motivated by a wide range of applications in various fields of physics and materials science, we consider a generalized approach to the evolution of a polydisperse ensemble of spherical particles in metastable media. An integrodifferential system of governing equations, consisting of a kinetic equation for the particle-size distribution function (Fokker–Planck type equation) and a balance equation for the temperature (concentration) of a metastable medium, is formulated. The kinetic equation takes into account fluctuations in the growth/reduction rates of individual particles, the velocity of particles in a spatial direction, the withdrawal of particles of a given size from the metastable medium, and their source/sink term. The heat (mass) balance equation takes into account the growth/reduction of particles in a metastable system as well as heat (mass) exchange with the environment. A generalized system of equations describes various physical and chemical processes of phase transformations, such as the growth and dissolution of crystals, the evaporation of droplets, the boiling of liquids and the combustion of a polydisperse fuel. The ways of analytical solution of the formulated integrodifferential system of equations based on the saddle-point technique and the separation of variables method are considered. The theory can be applied when describing the evolution of an ensemble of particles at the initial and intermediate stages of phase transformation when the distances between the particles are large enough, and interactions between them can be neglected.
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2
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Ivanov AA, Alexandrov DV, Alexandrova IV. Dissolution of polydisperse ensembles of crystals in channels with a forced flow. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190246. [PMID: 32279642 PMCID: PMC7202765 DOI: 10.1098/rsta.2019.0246] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 11/06/2019] [Indexed: 05/18/2023]
Abstract
A non-stationary integro-differential model describing the dissolution of polydisperse ensembles of crystals in channels filled with flowing liquid is analysed. The particle-size distribution function, the particle flux through an arbitrary cross-section of the channel, the particle concentration profile, as well as the disappearance intensity of particles are found analytically. It is shown that a nonlinear behaviour of solutions is completely defined by the source term of particles introduced into the channel. In particular, the model approximately describes the processes of dissolution and transport of drug microcrystals to the target sites in a living organism, taking into account complex dissolution kinetics of drug particles. This article is part of the theme issue 'Patterns in soft and biological matters'.
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Giese CC, King HE, van den Ende MP, Plümper O, ten Kate IL, Tielens AG. In Situ Nanoscale Investigation of Step Retreat on Fluoranthene Crystal Surfaces. ACS EARTH & SPACE CHEMISTRY 2018; 2:1301-1311. [PMID: 30662975 PMCID: PMC6326534 DOI: 10.1021/acsearthspacechem.8b00120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/26/2018] [Revised: 10/25/2018] [Accepted: 11/02/2018] [Indexed: 06/09/2023]
Abstract
Fluoranthene, a polycyclic aromatic hydrocarbon, has been detected on Earth as well as in asteroids and meteorites and may have played a role in the formation of life. Increasing the ionic strength of aqueous solutions has been observed to lower the fluoranthene solubility, but it is unclear how solution composition controls the release rate of fluoranthene to an aqueous solution. To elucidate this, we performed in situ atomic force microscopy experiments in which we characterized the sublimation and dissolution behavior of fluoranthene crystal surfaces. From this, we quantify the step retreat rate upon exposure to air, deionized water, and a 0.4 M NaCl or 0.1 M MgSO4 solution. Surface roughness is the main factor that determines the dissolution or sublimation rate. The results imply that during fluoranthene remediation or breakdown in meteorites and asteroids, ionic strength will be more important than chemical composition for controlling fluoranthene release into solution.
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Affiliation(s)
- Claudia-Corina Giese
- Leiden
Observatory, Faculty of Science, Leiden
University, 2300 RA Leiden, The Netherlands
- Department
of Earth Sciences, Faculty of Geosciences, Utrecht University, 3584 CB Utrecht, The Netherlands
| | - Helen E. King
- Department
of Earth Sciences, Faculty of Geosciences, Utrecht University, 3584 CB Utrecht, The Netherlands
| | - Martijn P.A. van den Ende
- Department
of Earth Sciences, Faculty of Geosciences, Utrecht University, 3584 CB Utrecht, The Netherlands
- Géoazur, Université Côte
d’Azur, 06560 Valbonne, France
| | - Oliver Plümper
- Department
of Earth Sciences, Faculty of Geosciences, Utrecht University, 3584 CB Utrecht, The Netherlands
| | - Inge Loes ten Kate
- Department
of Earth Sciences, Faculty of Geosciences, Utrecht University, 3584 CB Utrecht, The Netherlands
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Guo M, Wang K, Qiao N, Fábián L, Sadiq G, Li M. Insight into Flufenamic Acid Cocrystal Dissolution in the Presence of a Polymer in Solution: from Single Crystal to Powder Dissolution. Mol Pharm 2017; 14:4583-4596. [DOI: 10.1021/acs.molpharmaceut.7b00712] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Affiliation(s)
- Minshan Guo
- School
of Pharmacy, De Montfort University, Leicester LE1 9BH, U.K
| | - Ke Wang
- School
of Pharmacy, De Montfort University, Leicester LE1 9BH, U.K
| | - Ning Qiao
- College
of Materials Science and Engineering, North China University of Science and Technology, Tangshan, 063210 Hebei, China
| | - László Fábián
- School
of Pharmacy, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, U.K
| | - Ghazala Sadiq
- The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, U.K
| | - Mingzhong Li
- School
of Pharmacy, De Montfort University, Leicester LE1 9BH, U.K
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5
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In Silico Prediction of Growth and Dissolution Rates for Organic Molecular Crystals: A Multiscale Approach. CRYSTALS 2017. [DOI: 10.3390/cryst7100288] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
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6
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Chan EJ. On the use of molecular dynamics simulation to calculate X-ray thermal diffuse scattering from molecular crystals. J Appl Crystallogr 2015. [DOI: 10.1107/s1600576715013242] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
The use of molecular dynamics simulations to calculate the thermal diffuse scattering from X-ray diffraction experiments on molecular crystals is described, using the crystal structure of aspirin form I as an example system. Parameter settings that do not affect the actual simulation are varied in order to examine the effect on the final calculated diffraction pattern, and thus roughly determine a range for general settings that might be used in further experiments targeted at tailoring parameters associated with the functional forms for dispersion interaction terms commonly used in molecular simulation force fields. The proposed method is compared with that of the more widely accepted Monte Carlo technique, and possible advantages and drawbacks for the use of either method are discussed.
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Schneider J, Zheng C, Reuter K. Thermodynamics of surface defects at the aspirin/water interface. J Chem Phys 2014; 141:124702. [DOI: 10.1063/1.4895906] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Affiliation(s)
- Julian Schneider
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Chen Zheng
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Karsten Reuter
- Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
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Greiner M, Elts E, Briesen H. Insights into pharmaceutical nanocrystal dissolution: a molecular dynamics simulation study on aspirin. Mol Pharm 2014; 11:3009-16. [PMID: 25090160 DOI: 10.1021/mp500148q] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The presented molecular dynamics simulations are the first simulations to reveal dynamic dissolution of a pharmaceutical crystal in its experimentally determined shape. Continuous dissolution at constant undersaturation of the surrounding medium is ensured by introducing a plane of sticky dummy atoms into the water slab. These atoms have a strong interaction potential with dissolved aspirin molecules, but interactions with water are excluded from the calculations. Thus, the number of aspirin molecules diffusing freely in solution is kept at a low value and continuous dissolution of the aspirin crystal is monitored. Further insight into face-specific dissolution is drawn. The dissolution mechanism of receding edges is found for the (001) plane. These findings are in good agreement with experimental results. While the proposed dissolution mechanism for the (100) plane is terrace sinking on a rough surface, no pronounced dissolution of the perfectly flat face is seen in the present work. Molecular simulations of pharmaceuticals in their experimentally obtained structure therefore have shown to be especially suited for the investigation of dissolving faces, where the edges have a pronounced effect. In contrast to previous studies a propagation of the dissolution front into the crystal face is reported, and the crystal bulk is stable over the whole simulation time of 150 ns.
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Affiliation(s)
- Maximilian Greiner
- Chair for Process Systems Engineering, Technische Universität München , Freising 85354, Germany
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9
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Kinnear SL, McKelvey K, Snowden ME, Peruffo M, Colburn AW, Unwin PR. Dual-barrel conductance micropipet as a new approach to the study of ionic crystal dissolution kinetics. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2013; 29:15565-72. [PMID: 24224979 DOI: 10.1021/la403630u] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
A new approach to the study of ionic crystal dissolution kinetics is described, based on the use of a dual-barrel theta conductance micropipet. The solution in the pipet is undersaturated with respect to the crystal of interest, and when the meniscus at the end of the micropipet makes contact with a selected region of the crystal surface, dissolution occurs causing the solution composition to change. This is observed, with better than 1 ms time resolution, as a change in the ion conductance current, measured across a potential bias between an electrode in each barrel of the pipet. Key attributes of this new technique are: (i) dissolution can be targeted at a single crystal surface; (ii) multiple measurements can be made quickly and easily by moving the pipet to a new location on the surface; (iii) materials with a wide range of kinetics and solubilities are open to study because the duration of dissolution is controlled by the meniscus contact time; (iv) fast kinetics are readily amenable to study because of the intrinsically high mass transport rates within tapered micropipets; (v) the experimental geometry is well-defined, permitting finite element method modeling to allow quantitative analysis of experimental data. Herein, we study the dissolution of NaCl as an example system, with dissolution induced for just a few milliseconds, and estimate a first-order heterogeneous rate constant of 7.5 (±2.5) × 10(-5) cm s(-1) (equivalent surface dissolution flux ca. 0.5 μmol cm(-2) s(-1) into a completely undersaturated solution). Ionic crystals form a huge class of materials whose dissolution properties are of considerable interest, and we thus anticipate that this new localized microscale surface approach will have considerable applicability in the future.
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Affiliation(s)
- Sophie L Kinnear
- Department of Chemistry and ‡MOAC Doctoral Training Centre, University of Warwick , Gibbet Hill Road, Coventry CV4 7AL, United Kingdom
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Thakuria R, Eddleston MD, Chow EHH, Lloyd GO, Aldous BJ, Krzyzaniak JF, Bond AD, Jones W. Use of In Situ Atomic Force Microscopy to Follow Phase Changes at Crystal Surfaces in Real Time. Angew Chem Int Ed Engl 2013. [DOI: 10.1002/ange.201302532] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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11
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Thakuria R, Eddleston MD, Chow EHH, Lloyd GO, Aldous BJ, Krzyzaniak JF, Bond AD, Jones W. Use of in situ atomic force microscopy to follow phase changes at crystal surfaces in real time. Angew Chem Int Ed Engl 2013; 52:10541-4. [PMID: 23955996 DOI: 10.1002/anie.201302532] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2013] [Revised: 07/10/2013] [Indexed: 11/07/2022]
Abstract
AFM of cocrystals: Atomic force microscopy can be used to observe phase changes at crystal surfaces where the transformation is accompanied by a change in the spacing between layers of molecules. The conversion of a metastable polymorph of the caffeine-glutaric acid cocrystal into the thermodynamically stable form was analyzed continuously in situ using intermittent-contact-mode atomic force microscopy.
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Affiliation(s)
- Ranjit Thakuria
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (UK); Department of Chemical Sciences, Tezpur University, Napaam, Tezpur-784 028, Assam (India)
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Cassidy AM, Gardner CE, Auffret T, Aldous B, Jones W. Decoupling the Eeffects of Esurface Chemistry and Humidity on Solid-State Hydrolysis of Aspirin in the Presence of Dicalcium Phosphate Dihydrate. J Pharm Sci 2012; 101:1496-507. [DOI: 10.1002/jps.23038] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2011] [Revised: 11/16/2011] [Accepted: 12/13/2011] [Indexed: 11/08/2022]
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13
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Chow EHH, Bučar DK, Jones W. New opportunities in crystal engineering – the role of atomic force microscopy in studies of molecular crystals. Chem Commun (Camb) 2012; 48:9210-26. [DOI: 10.1039/c2cc32678g] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
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14
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Synergic Effects of Polymeric Additives on Dissolution and Crystallization of Acetaminophen. Pharm Res 2007; 25:349-58. [DOI: 10.1007/s11095-007-9468-0] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2007] [Accepted: 10/01/2007] [Indexed: 10/22/2022]
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15
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Heng JYY, Bismarck A, Lee AF, Wilson K, Williams DR. Anisotropic surface chemistry of aspirin crystals. J Pharm Sci 2007; 96:2134-44. [PMID: 17238200 DOI: 10.1002/jps.20841] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
The wettability of the (001), (100), and (011) crystallographic facets of macroscopic aspirin crystals has been experimentally investigated using a sessile drop contact angle (theta) method. theta for a nonpolar liquid was very similar for all three facets, though significant theta differences were observed for three polar probe liquids. The observed hydrophobicity of the (001) and (100) facets is ascribed to a reduced hydrogen bonding potential at these surfaces, whilst the observed hydrophilicity of facet (011) may be attributed to presence of surface carboxylic functionalities as confirmed by X-ray photoelectron spectroscopy (XPS). The dispersive component of the surface free energy (gamma(s)(d)) was similar for all three facets (35 +/- 2 mJ/m2). The total surface energy, gammas varied between 46 and 60 mJ/m2 due to significant variations in the polar/acid-base components of gamma for all facets. Surface polarity as determined by gamma measurements and XPS data were in good agreement, linking the variations in wettability to the concentration of oxygen containing surface functional groups. In conclusion, the wettability and the surface energy of a crystalline organic solid, such as aspirin, was found to be anisotropic and facet dependant, and in this case, related to the presence of surface carboxylic functionalities.
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Affiliation(s)
- Jerry Y Y Heng
- Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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16
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Wen H, Morris KR, Park K. Study on the interactions between polyvinylpyrrolidone (PVP) and acetaminophen crystals: partial dissolution pattern change. J Pharm Sci 2006; 94:2166-74. [PMID: 16136578 DOI: 10.1002/jps.20383] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
The objective of the study was to investigate the interactions between polyvinylpyrrolidone (PVP) and acetaminophen crystal especially on crystal surface. The effects of PVP on the etching pattern change of the acetaminophen (010) face, solubility enhancement as well as the intrinsic dissolution rate (IDR) of acetaminophen crystals have been studied. The etching patterns of the acetaminophen (010) face in the presence of PVP have stable ledges in the direction of a-axis, but deviate from c-axis, which shows that the dissolution on the (010) face has been affected by the adsorbed PVP especially in the direction of c-axis through van der Waals interactions rather than hydrogen bonding interactions. Even though PVP(K30) can enhance the solubility of acetaminophen in concentration higher than 1 mg/mL, the IDR of acetaminophen in diluted PVP solutions was lower than in water. Because the viscosity of those diluted PVP(K30) solutions were the same as water viscosity, the lowered IDR of acetaminophen cannot be explained simply by the viscosity effects of PVP solutions. Overall, the study suggests that the PVP molecules adsorbed on the surface of acetaminophen crystals play an important role in etching pattern change as well as the intrinsic dissolution rate change.
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Affiliation(s)
- Hong Wen
- Department of Industrial and Physical Pharmacy, Purdue University, West Lafayette, Indiana 47907-1336, USA.
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17
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Wen H, Morris KR, Park K. Hydrogen bonding interactions between adsorbed polymer molecules and crystal surface of acetaminophen. J Colloid Interface Sci 2005; 290:325-35. [PMID: 16153902 DOI: 10.1016/j.jcis.2005.04.049] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2004] [Revised: 03/05/2005] [Accepted: 04/14/2005] [Indexed: 11/24/2022]
Abstract
The objective of this work was to investigate whether or not the hydrogen bonding interaction between polymer and crystal surface can be detected by the etching pattern changes in the presence of polymers. The (010) face of acetaminophen single crystal was used as a model solid surface. The etching patterns on the (010) face of acetaminophen crystal by water are in the directions of a- and c-axes, which are the same as the directions of the dominant attachment energies on the (010) face. In the presence of polymer, the hydrogen bonding interactions between adsorbed polymer and crystal surface can affect surface diffusion of acetaminophen molecules and change the etching patterns in the direction of a-axis, i.e., the direction of one hydrogen bond chain. Studies with 2-hydroxyethyl cellulose (HEC), hydroxypropyl cellulose (HPC), hydroxypropyl methylcellulose (HPMC) and poly(vinyl alcohol) (PVA) showed that polymers, which can form hydrogen bonds with acetaminophen crystal surface, can change etching patterns in the direction of a-axis. Study with Dextran suggested that if a polymer cannot form hydrogen bonds with crystal surface due to steric repulsion, it will not change the etching pattern in the direction of a-axis. Studies with poly(ethylene glycol) (PEG) and poly(propylene glycol) (PPG) further confirmed that only if a polymer can form hydrogen bonds with acetaminophen on crystal surface, the etching patterns in the direction of a-axis will be affected. The study results suggest that in the presence of polymers, the etching pattern change in the direction of hydrogen bond chain, the a-axis of acetaminophen crystals, can be used to indicate the existence of the hydrogen bonding interactions between adsorbed polymers and acetaminophen crystal surface.
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Affiliation(s)
- Hong Wen
- Department of Industrial and Physical Pharmacy, Purdue University, West Lafayette, IN 47907-1336, USA.
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18
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Cao X, Sun C, Thamann TJ. A Study of Sulfamerazine Single Crystals Using Atomic Force Microscopy, Transmission Light Microscopy, and Raman Spectroscopy. J Pharm Sci 2005; 94:1881-92. [PMID: 16052565 DOI: 10.1002/jps.20402] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Sulfamerazine (SMZ) Form I and II single crystals were prepared from aqueous dispersions of SMZ bulk samples and studied using several microscopic and spectroscopic techniques. Transmission light microscopy and Raman spectroscopy were used to observe and identify single crystals. The results indicated that Form I single crystals tended to be rectangular laths while Form II ones tended to be hexagonal laths. Surface morphology of individual single crystals was further investigated by atomic force microscopy (AFM). AFM images revealed a smooth top surface, a uniform height, and sharp edges for both forms of single crystals. Both height and phase images showed crystalline terraces with different step heights for the top surface of Form I. Surface properties of single crystals were evaluated using AFM force measurements. Experimental results indicated that the top surface of Form I single crystals was more hydrophilic than that of Form II. Theoretical calculations predicted a dominant crystal face of (020) for the Form I single crystals and (002) for the Form II ones. The correlations between calculation predictions and experimental results were discussed.
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Affiliation(s)
- Xiaoping Cao
- Pfizer Global Research and Development, 7000 Portage Road, Kalamazoo, Michigan 49001, USA.
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