On the Reactivity of N-<i>tert</i>-Butyl-1,2-Diaminoethane: Synthesis of 1-<i>tert</i>-Butyl-2-Imidazoline, Formation of an Intramolecular Carbamate Salt from the Reaction with <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.1996pt" id="M1" height="15.6076pt" version="1.1" viewBox="-0.0657574 -11.408 31.7722 15.6076" width="31.7722pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g187-68" d="M625 186C574 85 512 32 429 32C293 32 194 153 194 337C194 485 274 621 419 621C496 621 573 586 606 468L643 475C636 537 629 583 620 638C593 644 519 665 438 665C199 665 42 523 42 317C42 158 152 -15 418 -15C486 -15 578 5 604 11C621 46 647 122 660 171L625 186Z"/></g><g transform="matrix(.017,0,0,-0.017,11.79,0)"><path id="g187-80" d="M394 664C165 664 42 495 42 323C42 132 181 -15 381 -15C570 -15 725 116 725 332C725 529 576 664 394 664ZM374 622C491 622 571 503 571 304C571 120 494 27 399 27C271 27 196 171 196 343C196 516 274 622 374 622Z"/></g><g transform="matrix(.012,0,0,-0.012,25.027,4.134)"><path id="g187-243" d="M442 172C405 109 393 108 333 108H171L289 222C383 315 430 374 430 457C430 569 349 635 249 635C187 635 134 610 97 573L34 478L61 455C93 502 136 542 196 542C265 542 300 491 300 422C300 346 261 273 191 190C142 132 84 76 31 25V0H432C443 42 455 105 471 163L442 172Z"/></g></svg>,</span> and Generation of a Hydroxyalkyl-Substituted Imidazolinium Salt

Evans, Kieren J.; Potrykus, Ben; Mansell, Stephen M.

doi:https://doi.org/10.1155/2019/1094173

Heteroatom Chemistry

On this page

Abstract Introduction Results and Discussion Conclusions Experimental Data Availability Conflicts of Interest Acknowledgments Supplementary Materials References Copyright Related Articles

Research Article | Open Access

Volume 2019 | Article ID 1094173 | https://doi.org/10.1155/2019/1094173

On the Reactivity of N-tert-Butyl-1,2-Diaminoethane: Synthesis of 1-tert-Butyl-2-Imidazoline, Formation of an Intramolecular Carbamate Salt from the Reaction with , and Generation of a Hydroxyalkyl-Substituted Imidazolinium Salt

Kieren J. Evans,¹Ben Potrykus,¹and Stephen M. Mansell¹

Academic Editor: Oscar Navarro

Received09 Oct 2018

Accepted14 Jan 2019

Published05 Feb 2019

Abstract

N-tert-Butyl-1,2-diaminoethane was shown to react rapidly with atmospheric carbon dioxide to generate the zwitterionic ammonium carbamate salt CO₂N(H)C₂H₄NBu (1). Reaction of N-tert-butyl-1,2-diaminoethane with triethylorthoformate gave 1-tert-butyl-2-imidazoline (2) in 24% yield after fractional distillation, and the hydroxyalkyl-tethered imidazolinium salt [HOC(Me)₂CH₂NC₂H₄N(CH)^tBu][Cl] (3) was synthesised from the sequential reaction of N-tert-butyl-1,2-diaminoethane with isobutylene epoxide, HCl, and triethylorthoformate.

1. Introduction

1,2-Diamines, exemplified by ethylenediamine and its derivatives, are produced on a large scale and are used for many purposes including coordination chemistry [1] and CO₂ capture [2–6]. Chiral diamines are also well known and have been utilised in the production of various chiral catalysts [7–9]. N-substituted ethylenediamines can also function as precursors to 1-substituted-2-imidazolines (dihydroimidazoles) [10, 11], with the synthesis of unsymmetrical saturated N-heterocyclic carbenes (NHCs) one potential application for these compounds [12, 13]. Examples of 2-imidazolines that are widely used in the synthesis of unsymmetrical saturated NHCs include those with mesityl (2,4,6-Me₃C₆H₂) and 2,6-diisopropylphenyl (Dipp: 2,6-ⁱPr₂C₆H₃) substituents [12, 13]. 1-Ethyl-2-imidazoline and 1-benzyl-2-imidazoline are known compounds [14], but the tert-butyl derivative, to the best of our knowledge, has not been reported. If the N-3 position is subsequently substituted with a hydrocarbon linker terminating with a donor atom, then these compounds represent useful precursors to tethered saturated NHCs [15], which have been extensively explored by Arnold and coworkers [16–20]. We have recently reported on the use of N-substituted-1,2-diaminoethanes to form fluorenyl tethered diamines [21], which then acted as useful precursors to a tethered N-heterocyclic stannylene (NHSn) with a Dipp substituent [21]. During this research we noted the reactivity of N-tert-butyl-1,2-diaminoethane [22] with air, which encouraged us to explore the reactivity of this diamine further. In this publication, we characterise the reaction product of N-tert-butyl-1,2-diaminoethane with carbon dioxide, the synthesis of 1-tert-butyl-2-imidazoline, and the formation of a hydroxyalkyl imidazolinium salt with an N-tert-butyl substituent.

2. Results and Discussion

N-tert-Butyl-1,2-diaminoethane was synthesised as previously described [21, 22]; however, we noticed that it rapidly reacts with atmospheric CO₂ forming a zwitterionic alkylammonium carbamate (1, Scheme 1). This was confirmed by X-ray crystallographic analysis of a single crystal formed by the reaction of the parent diamine and showed the structure to be an intramolecular alkylammonium carbamate salt resulting from nucleophilic attack of CO₂ followed by the formal deprotonation of the NH₂ by the N(H)^tBu unit (Figure 1).

The solid-state structure of 1 shows dimeric units formed from H-bonding between the two H atoms of the two different N atoms towards O2 of the carbamate group. An (8) graph set ring motif is constructed from H-bonding between the remaining O atom of the carbamate group and the second H atom on N2. The C-O bond lengths are almost identical and C1 has a planar geometry. The molecular structure is similar to that observed for MeN(H)₂C₂H₄N(H)CO₂, which was observed to be H-bonding to additional water molecules [5]. Long and coworkers have structurally characterised several intramolecular ammonium carbamates based on N-substituted ethylene diamines from in situ reactions of CO₂ with a Mg-based metal-organic framework containing the bound diamine [6].

The synthesis of 1-tert-butyl-2-imidazoline (2) was achieved by the acid-catalysed reaction of the diamine with triethylorthoformate (Scheme 1). Careful fractional distillation yielded the product in low yield (24%). The H atom at the 2-position was observed at δ 7.03 ppm by ¹H NMR spectroscopy as a triplet due to coupling to one of the backbone CH₂ groups via coupling through the C=N bond. The ¹³C NMR spectroscopic resonance for C-2 was also observed at high frequency (154.6 ppm). Accurate mass spectrometry observed the parent molecular ion at 126.11510 Da. 2 reacts with moisture in the air so should be stored and handled under N₂. The attempted reaction with isobutylene epoxide (70°C, 5 days) did not yield the desired hydroalkyl-functionalised carbene (or the related zwitterionic alkoxy-imidazolinium tautomer that was seen with imidazoles) [23–27], so a different synthetic route to a substituted imidazolinium salt was attempted based on literature precedent (Scheme 1) [16]. In consecutive steps, isobutylene epoxide, HCl, and triethylorthoformate were reacted with N-tert-butyl-1,2-diaminoethane to yield an oil that was purified by crystallisation from acetone in low yield (12%). Unfortunately, changing the anion to [I]^- or [BF₄]^- did not aid crystallisation and did not result in an improved synthesis. The product was characterised by X-ray crystallography (Figure 2), multinuclear NMR spectroscopy, and elemental analysis. The molecular structure of 3 showed a 5-membered imidazolinium ring with a tert-butyl substituent and a hydroxyalkyl chain. The Cl counter anion is H-bonded to the imidazolinium C-H as well as the O-H, and there are several close contacts to other C-H atoms as well. The C-N bond lengths in the ring are similar (C1-N1 = 1.311(3) Å and C1-N2 = 1.323(3) Å) and C2-C3 is a single bond (1.530(4) Å). ¹H NMR spectroscopic analysis revealed the expected signals based on the X-ray structure, with the imidazolinium CH as a singlet at 9.54 ppm. The C-2 resonance was observed at δ 158.0 ppm by ¹³C NMR spectroscopy.

3. Conclusions

N-tert-Butyl-1,2-diaminoethane was found to be a convenient starting material for the synthesis of 1-tert-butyl-2-imidazoline (2) as well as the hydroxyalkyl-tethered imidazolinium salt 3. However, N-tert-butyl-1,2-diaminoethane was found to react with atmospheric CO₂ to give the alkylammonium carbamate 1, and 1-tert-butyl-2-imidazoline was also found to be unstable in the presence of atmospheric moisture, highlighting the greater reactivity of these compounds compared to related literature examples with N-aryl groups.

4. Experimental

All reactions were performed under an oxygen-free (H₂O, O₂ < 0.5 ppm) nitrogen atmosphere using standard Schlenk line techniques or by using an MBRAUN UNIlab Plus glovebox unless otherwise stated. Anhydrous toluene was obtained from an MBRAUN SPS-800 and diethyl ether was distilled from sodium/benzophenone; CDCl₃ was dried over molecular sieves (4 Å). All anhydrous solvents were degassed before use and stored over activated molecular sieves. N-tert-Butyl-1,2-diaminoethane was synthesised as previously described [21]. NMR spectra were recorded on Bruker AV300 or AVIII400 spectrometers at 25°C, and the chemical shifts δ are noted in parts per million (ppm) calibrated to the residual proton resonances of the deuterated solvent (CDCl₃ δ = 7.27 ppm). X-ray diffraction experiments were performed using a Bruker X8 APEXII diffractometer at 100 K on single crystals of the samples covered in inert oil and placed under the cold stream of the diffractometer, with exposures collected using Mo Kα radiation (λ = 0.71073 Å). Indexing, data collection, and absorption corrections were performed and structures were solved using direct methods (SHELXT) [28] and refined by full-matrix least-squares (SHELXL) [28] interfaced with the programme OLEX2 [29] (Table 1). H atoms were placed using a riding model except for those attached to N or O atoms, which were located in the electron density map and freely refined with a fixed isotropic parameter of 1.2x that of the atom they are attached to. CCDC deposition numbers were 1871407 (1) and 1871406 (3). Elemental analyses were conducted using an Exeter CE-440 elemental analyser at Heriot-Watt University by Dr. Koenraad Collart or by Mr. Stephen Boyer at London Metropolitan University. Electron ionization mass spectrometry (EIMS) was performed using a Finnigan (Thermo) LCQ Classic ion trap mass spectrometer at the University of Edinburgh.

4.1. Synthesis of 1

Freshly distilled N-tert-butyl-1,2-diaminoethane was exposed to air and a white solid formed rapidly. ¹H NMR (300 MHz, 25°C, D₂O): δ(ppm) 3.28 (2H, m, CH₂), 3.08 (m, 2H, CH₂), 1.31 (s, 9H, ^tBu). ¹³C NMR (75.5 MHz, 25°C, D₂O): δ(ppm) 164.86 (NCO₂), 56.53 (CH₂), 43.07 (CH₂), 38.46 (CMe₃) and 24.83 (CH₃).

4.2. Synthesis of 1-tert-butyl-2-Imidazoline (2)

N-tert-Butyl-1,2-diaminoethane (3.439 g, 29.6 mmol, 1 equiv.) was combined with triethylorthoformate (19.7 cm³, 118.4 mmol, 4 equiv.) and para-toluenesulfonic acid (281 mg, 1.48 mmol, 0.05 equiv.) and then heated under reflux for 16 h. NaOH (10 cm³ of a 5% solution in H₂O) was added and the mixture extracted with CHCl₃ (3 x 50 cm³). The organic layer was dried over MgSO₄ and CHCl₃ and EtOH were removed under reduced pressure. A short path distillation apparatus was used to fractionally distil the resulting liquid. Triethylorthoformate distilled at 50°C, 20 mbar (diaphragm pump) as the first fraction then 1-tert-butyl-2-imidazoline at 26 – 30°C at 5 x10 ⁻¹ mbar (rotary vane pump) as the second fraction yielding a moisture sensitive colourless liquid (960 mg, 7.6 mmol, 26%). ¹H NMR (300 MHz, 25°C, CDCl₃): δ(ppm) 7.00 (t, = 1.8 Hz, 1H, CH), 3.75 (td, = 9.9 Hz, = 1.8 Hz, 2H, CH₂N=CH), 3.23 (t, = 9.9 Hz, 2H, CH₂N^tBu), 1.23 (s, 9H, ^tBu). ¹³C NMR (75.5 MHz, 25°C, CDCl₃): δ(ppm) 154.57 (CH), 54.41 (CH₂), 51.91 (CMe₃), 44.32 (CH₂), 28.47 (CH₃). HRMS (EI-MS) m/z: [M]⁺ Calcd for C₇H₁₄N₂ 126.11515; Found 126.11510.

4.3. Synthesis of 3

N-tert-Butyl-1,2-diaminoethane (2.018 g, 17.4 mmol, 1 equiv.) was combined with isobutylene oxide (1.252g, 1.54 mL, 17.4 mmol, 1 equiv.) in an ampoule equipped with a Young’s tap and heated to 60°C for 16 h. Dry Et₂O (30 cm³) was then added to the resultant colourless oil and the solution transferred to a Schlenk vessel equipped with a large stirrer bar. 1 M HCl in Et₂O (17.2 cm³, 1 equiv.) was added at 0°C forming a white solid which was then stirred for 16 h at room temperature. The supernatant solution was removed by cannula filtration and the white solid dried under vacuum. Toluene (30 cm³) and triethylorthoformate (10 cm³) were added and the mixture was heated to 90°C for 7 h. Et₂O (50cm³) was added which caused a yellow oil to separate and the supernatant solution was removed by cannula. Acetone (ca. 10 cm³) was added to dissolve the oil, and storage at -25°C gave colourless crystals of the product (488 mg, 2.08 mmol, 12%).

¹H NMR (400 MHz, 25°C, CDCl₃): δ(ppm) 9.54 (s, 1H, C-H), 5.10 (s, 1H, OH), 4.18 (m, 2H, BuNCH₂CH₂N), 3.96 (m, 2H, BuNCH₂CH₂N), 3.69 (s, 2H, CH₂C(CH₃)₂), 1.44 (s, 9 H, Bu), 1.27 (s, 6 H, CH₂C(CH₃)₂). ¹³C NMR (75.5 MHz, 25°C, CDCl₃): δ(ppm) 158.0 (C-H), 69.8 (4°C), 57.5 (CH₂C(CH₃)₂), 56.7 (4°C), 51.3 (BuNCH₂CH₂N), 45.2 (BuNCH₂CH₂N), 28.3 (^tBu), 27.4 (C(CH₃)₂). Elemental analysis calculated for C₁₁H₂₃ClN₂O (%): C 56.28, H 9.88 N 11.93. Found (%): C 56.18, H 9.95, N 11.86.

Data Availability

In addition to the supporting information (available here), additional research data supporting this publication are available from Heriot-Watt University’s research data repository at DOI: 10.17861/ab6d5f14-ee8f-4be1-94c7-3c9fd0eea37a. CIF files for 1 and 3 have been deposited with the CCDC, deposition numbers: 1871407 (1) and 1871406 (3).

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

We thank the EPSRC UK National Crystallography Service at the University of Southampton for collecting an additional data set of compound 1. Financial support is gratefully acknowledged from the EPSRC (DTP studentship to Kieren J. Evans), the Royal Society (Research grant: RG130436), and Heriot-Watt University.

Supplementary Materials

The supporting information which the authors submitted with the paper gives NMR spectra for the new compounds described in the publication. (Supplementary Materials)

References

A. Ehnbom, S. K. Ghosh, K. G. Lewis, and J. A. Gladysz, “Octahedral Werner complexes with substituted ethylenediamine ligands: a stereochemical primer for a historic series of compounds now emerging as a modern family of catalysts,” Chemical Society Reviews, vol. 45, pp. 6799–6811, 2016.
View at: Google Scholar
C. Gouedard, D. Picq, F. Launay, and P. L. Carrette, “Amine degradation in CO₂ capture. I. A review,” International Journal of Greenhouse Gas Control, vol. 10, pp. 244–270, 2012.
View at: Publisher Site | Google Scholar
F. Zheng, D. N. Tran, B. J. Busche et al., “Ethylenediamine-modified SBA-15 as regenerable CO₂ sorbent,” Industrial & Engineering Chemistry Research, vol. 44, no. 9, pp. 3099–3105, 2005.
View at: Publisher Site | Google Scholar
A. Demessence, D. M. DAlessandro, M. L. Foo, and J. R. Long, “Strong CO₂ Binding in a Water-Stable, Triazolate-Bridged Metal−Organic Framework Functionalized with Ethylenediamine,” Journal of the American Chemical Society, vol. 131, pp. 8784–8786, 2009.
View at: Google Scholar
I. Tiritiris and W. Kantlehner, “Orthoamide und Iminiumsalze, LXX. Zur Fixierung von Kohlendioxid mit organischen Basen (Teil 1) – Reaktionen von Diaminen mit Kohlendioxid,” Zeitschrift für Naturforschung B, vol. 66, pp. 164–176, 2011.
View at: Google Scholar
R. L. Siegelman, T. M. McDonald, M. I. Gonzalez et al., “Controlling Cooperative CO₂ Adsorption in Diamine-Appended Mg₂(dobpdc) Metal–Organic Frameworks,” Journal of the American Chemical Society, vol. 139, p. 10526, 2017.
View at: Publisher Site | Google Scholar
C. Kouklovsky, Y. Langlois, E. Aguilar, J. M. Fernández-García, and V. Sikervar, “(1S,2S)-1,2-Diaminocyclohexane,” in Encyclopedia of Reagents for Organic Synthesis, 2014.
View at: Google Scholar
S. Pikul and E. J. Corey, “(1R,2R)-(+)- and (1S,2S)-(−)- 1,2-Diphenyl-1,2-Ethylenediamine[1,2-Ethanediamine, 1,2-Diphenyl-, [R-(R,R)]- and [S-(R,R)]-],” Organic Syntheses, vol. 71, p. 22, 1993.
View at: Publisher Site | Google Scholar
J. F. Larrow and E. N. Jacobsen, “(R,R)-N,N'-bis(3,5-di-tert-butylsalicylidene)-1,2cyclohexanediamino manganese(III) chloride, a highly enantioselective epoxidation catalyst [Manganese, chloro[[2,2'-[1,2-cyclohexanediylbis(nitrilomethylidyne)]-bis[4,6-bis (1,1-dimethylethyl)phenalato]](2-)-N,N',O,O']-, [SP-5-13-(1R-trans-]- ],” Organic Syntheses, vol. 75, p. 1, 1998.
View at: Publisher Site | Google Scholar
H. Liu and D.-M. Du, “Recent advances in the synthesis of 2‐imidazolines and their applications in homogeneous catalysis,” Advanced Synthesis & Catalysis, vol. 351, pp. 489–519, 2009.
View at: Publisher Site | Google Scholar
K. Murai, “Development and application of practical synthetic methods of imidazolines,” Yakugaku Zasshi, vol. 130, no. 8, pp. 1011–1016, 2010.
View at: Publisher Site | Google Scholar
C. Marshall, M. F. Ward, and J. M. S. Skakle, “Steric variations between the synthesis of a stable chiral C 2-symmetric diimidazolidinylidene and an electron-rich tetraazafulvalene,” Synthesis, no. 6, pp. 1040–1044, 2006.
View at: Google Scholar
M. Bessel, F. Rominger, and B. F. Straub, “Modular trimethylene-linked bisimidazol(in)ium salts,” Synthesis, no. 9, pp. 1459–1466, 2010.
View at: Google Scholar
B. Çetinkaya, E. Çetinkaya, P. B. Hitchcock, M. F. Lappert, and I. Özdemir, “Synthesis and characterisation of 1-alkyl-2-imidazoline complexes ofnoble metals; crystal structure oftrans-[PtCl2{[upper bond 1 start]N[double bond, length as m-dash]C(H)N(Et)CH2C[upper bond 1 end]H2}(PEt3)],” Journal of the Chemical Society, Dalton Transactions, p. 1359, 1997.
View at: Google Scholar
S. T. Liddle, I. S. Edworthy, and P. L. Arnold, “Anionic tethered N-heterocyclic carbene chemistry,” Chemical Society Reviews, vol. 36, p. 1732, 2007.
View at: Google Scholar
P. L. Arnold, I. J. Casely, Z. R. Turner, and C. D. Carmichael, “Functionalised Saturated‐Backbone Carbene Ligands: Yttrium and Uranyl Alkoxy–Carbene Complexes and Bicyclic Carbene–Alcohol Adducts,” Chemistry – A European Journal, vol. 14, pp. 10415–10422, 2008.
View at: Google Scholar
P. L. Arnold, Z. R. Turner, A. I. Germeroth, I. J. Casely, R. Bellabarba, and R. P. Tooze, “Lanthanide/actinide differentiation with sterically encumbered N-heterocyclic carbene ligands,” Dalton Transactions, vol. 39, no. 29, pp. 6808–6814, 2010.
View at: Publisher Site | Google Scholar
P. L. Arnold, Z. R. Turner, N. Kaltsoyannis, P. Pelekanaki, R. M. Bellabarba, and R. P. Tooze, “Covalency in Ce^IV and U^IV Halide and N‐Heterocyclic Carbene Bonds,” Chemistry – A European Journal, vol. 16, p. 9623, 2010.
View at: Google Scholar
P. L. Arnold, Z. R. Turner, R. Bellabarba, and R. P. Tooze, “Carbon–Silicon and Carbon–Carbon Bond Formation by Elimination Reactions at Metal N-Heterocyclic Carbene Complexes,” Journal of the American Chemical Society, vol. 133, p. 11744, 2011.
View at: Google Scholar
P. L. Arnold, Z. R. Turner, A. I. Germeroth et al., “Carbon monoxide and carbon dioxide insertion chemistry of f-block N-heterocyclic carbene complexes,” Dalton Transactions, vol. 42, p. 1333, 2013.
View at: Google Scholar
M. Roselló-Merino and S. M. Mansell, “Synthesis and reactivity of fluorenyl-tethered N-heterocyclic stannylenes,” Dalton Transactions, vol. 45, p. 6282, 2016.
View at: Google Scholar
K. Kormendy, “The reactions of polyamines with phthalimidoalkyl halides,” Acta Chimica Academiae Scientiarum Hungaricae, vol. 17, pp. 255–264, 1958.
View at: Google Scholar
P. L. Arnold, A. C. Scarisbrick, A. J. Blake, and C. Wilson, “Chelating alkoxy-N-heterocyclic carbene complexes of silver and copper,” Chemical Communications, p. 2340, 2001.
View at: Google Scholar
P. L. Arnold, M. Rodden, K. M. Davis, A. C. Scarisbrick, A. J. Blake, and C. Wilson, “Asymmetric lithium(I) and copper(II) alkoxy-N-heterocyclic carbene complexes; crystallographic characterisation and Lewis acid catalysis,” Chemical Communications, p. 1612, 2004.
View at: Google Scholar
P. L. Arnold and A. C. Scarisbrick, “Di- and trivalent ruthenium complexes of chelating, anionic N-heterocyclic carbenes,” Organometallics, vol. 23, no. 11, pp. 2519–2521, 2004.
View at: Publisher Site | Google Scholar
P. L. Arnold, M. Rodden, and C. Wilson, “Thermally stable potassium N-heterocyclic carbene complexes with alkoxide ligands, and a polymeric crystal structure with distorted, bridging carbenes,” Chemical Communications, p. 1743, 2005.
View at: Google Scholar
P. L. Arnold and C. Wilson, “Sterically demanding bi- and tridentate alkoxy-N-heterocyclic carbenes,” Inorganica Chimica Acta, vol. 360, p. 190, 2007.
View at: Google Scholar
G. M. Sheldrick, “A short history of SHELX,” Acta Crystallographica Section A: Foundations of Crystallography, vol. 64, pp. 112–122, 2008.
View at: Publisher Site | Google Scholar
O. V. Dolomanov, L. J. Bourhis, R. J. Gildea, J. A. K. Howard, and H. Puschmann, “OLEX2: a complete structure solution, refinement and analysis program,” Journal of Applied Crystallography, vol. 42, no. 2, pp. 339–341, 2009.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2019 Kieren J. Evans et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies

Views

1019

Downloads

1069

Citations