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Silicon vs Carbon in Prismanes: Reversal of a Mechanical Property by Fluorine Substitution Nir Pour,‡ Eli Altus,§ Harold Basch,‡ and Shmaryahu Hoz*,‡ Department of Chemistry, Institute of Nanotechnology and AdVanced Materials, Bar-Ilan UniVersity, Ramat-Gan 52900, Israel, and Faculty of Mechanical Engineering, Technion, Israel Institute of Technology, Haifa, 32000 Israel ReceiVed: March 4, 2010; ReVised Manuscript ReceiVed: May 11, 2010
Poisson’s ratio is the measure of the extent by which the lengthening of a rod induces its thinning and vice versa. Prismanes are the only molecular system that exhibits a negative Poisson’s ratio (Auxetic effect). On the basis of the Thorpe-Ingold effect, which underlines the auxetic effect in prismanes, it is expected that silicon-based prismane will manifest a smaller Poisson’s ratio than carbon-based prismanes and that fluorine substitution on the terminal rings will also diminish the effect. Stretching and compressing experiments show that indeed the auxetic effect is significantly reduced upon going from carbon to silicon and moreover that fluorine substitution reverts the behavior of silicon-based prismanes from showing a negative Poisson’s ratio to a positive one. This is probably the first example of a substituent-induced reversal of the mechanical property of a chemical system. CHART 1
1. Introduction Poisson’s ratio is a parameter of prime importance in material engineering.1 It is the measure of the extent by which the lengthening of a rod induces its thinning and vice versa. The cork stopper used in wine bottles is an example of a material having a near-zero Poisson ratio. This characteristic is important because, otherwise, when incipiently inserted into the neck of a bottle, the cork would become thicker, making the seal of the bottle impossible. A negative Poisson’s ratio, namely, auxetic behavior, is observed when the lengthening is accompanied, counterintuitively, by a thickening of the rod.2 Needless to say longitudinal compression will result in the rod’s thinning. We have recently reported that carbon-based [n]prismanes display an auxetic behavior.3 That is, except for the terminal rings on both ends of the rod which contract, the inner rings expand upon stretching. The previously known examples for auxetic behavior were based on the geometry (structure) of the matter but were not a molecular property.2b,4 The simplest demonstration of such a structure-based effect, in two dimensions, can be viewed in the letter Z. By pulling the two horizontal parallel lines apart, the central diagonal line will become vertical expanding the structure in the perpendicular direction. Auxetic materials are found in unusual places. These range from white dwarf cores and neutron star outer crusts5 to cow teats.6 To the best of our knowledge, prismanes are the only molecules known to exhibit an auxetic behavior. We have shown7 that this behavior stems from the angular distortion in the ground state of the prismane and the Thorpe-Ingold effect.8 This could be easily demonstrated with biprismanes. In an ideal biprismane the two interlayer bonds of the central ring carbon are collinear as shown in structure a in Chart 1. To reduce the angular strain, the middle ring shrinks and the external rings expand resulting in the bowtie structure (b in * To whom correspondence should be addressed. ‡ Bar-Ilan University. § Israel Institute of Technology.
Chart 1). Stretching the prismane weakens the interlayer bonds thus reducing the angular strain. As a result, the inequality of the internal and external rings is reduced. That is to say, the middle ring will expand (the auxetic effect) and the terminal ones will exhibit a normal Poisson’s ratio. Since silicon differs from carbon in many aspects and is less sensitive to angular strain,9 we examined the effect of replacing the carbon in the carbon-based prismanes (CBP) by silicon. Silicon-based prismanes (SiBP) are expected to show a reduction in the auxetic effect. In addition, we report in this paper the effect of replacing the terminal hydrogen atoms by fluorine. The study focuses on bi- and triprismanes. 2. Methodology The equilibrium structure and the effect of stretching and compressing various prismanic rods were computed with quantum mechanics. In a preceding paper we have shown that the same behavior is obtained using a variety of computational levels.3 In the present paper, for CBP we used the B3LYP/631G* level whereas the computations on the SiBP were performed at the B3LYP/CEP/6-31G* level with the Gaussian03 program.10 In the first step, the structure of the prismanes was fully optimized. Then, the distance between the corresponding carbon atoms on the two capping rings carbon atoms were fixed at a given length, either shorter (compression) or longer (stretching), and all other degrees of freedom were reoptimized with respect to the energy.
10.1021/jp101966c 2010 American Chemical Society Published on Web 05/21/2010
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TABLE 1: Bond Lengths for Silicon-Based Biprismanes ring bond length Å ring size [3] [4] [5] [6] a
terminal
internal
ratio
2.454 2.449 2.463
2.397 2.376 2.365
1.024 1.031 1.041
Instead of the expected symmetric structure of the CBP analogue, structure 2 was obtained.
a
Collapsed.
TABLE 2: Bond Lengths for Carbon-Based Biprismanes ring bond length Å ring size
terminal
internal
ratio
[3] [4] [5] [6]
1.54 1.605 1.604 1.616
1.493 1.525 1.501 1.49
1.031 1.052 1.069 1.085
3. Results and Discussion We have calculated the structure of prismanes ranging from triangular to hexagonal bases. In the nomenclature of prismanes, the number in brackets indicates the number of atoms in the circumference (ring) and the prefix denotes the number of elementary prismanes face-fused together.11 Thus for example, bi[4]prismanes implies two cubanes face-fused to each other. Because we are describing herein four types of prismanes, throughout this paper we will use the following notations: the first number in the name denotes the number of rings the prismane is made up of. The symbol C or Si following it indicates whether it is CBP or SiBP, the number in square brackets denotes, as before, the number of atoms in the ring, and the letter at the end (H or F) represents the substituents at the terminal rings. Thus, for example, 3-Si[6]F stands for structure 1 shown below.
In this respect we find the comment made by Nagase12 and Earley13 highly relevant to the case at hand. They ascribed the behavior of cage Si compounds to the conflict between the strain which decreases upon descending the column in the Periodic Table and the accompanying decrease in bond strength. In our case the conflict is due to the relief of the angular strain around Si2 and Si3 at the cost of increasing it for Si1 (by rendering the latter an inverted silicon) in addition to a considerable stretching of bonds. It is interesting to note that the other SiBP ([4], [5], and [6]) gave upon optimization the expected symmetric structure. This is apparently because relieving the strain on two silicon atoms at the cost of increasing the strain on one is energetically beneficial, whereas in the wider prismanes, the ratio of the favored vs the nonfavored geometry changes is reduced from 2/1 in the present case to 1/1, 3/2, and 3/3 in [4], [5], and [6] prismanes. We have tried to attain the stable structure by using different basis sets (see Table S5, Supporting Information). All our attempts to find a stable symmetric structure for the cyclopropane-based prismanes failed. Surprisingly, substitution of the terminal hydrogen atoms by fluorine atoms stabilizes the symmetric structure of 2 (3-Si[3]F). TABLE 3: Poisson’s Ratio for the Inner Rings no. of rings biprismanes
The energies and geometrical data for all the systems studied are given in Tables S1-S4 (Supporting Information). We will begin the analysis by focusing first on some important structural aspects. It is well-known that in spite of the tetravalency common to carbon and silicon, they differ markedly in their chemical behavior.9 A distinct difference between carbon and silicon was observed when attempting to optimize 3-Si[3]H.
triprismanes
a
Collapsed.
prismane type
[3]
[4]
[5]
[6]
C Si CF SiF C Si CF SiF
-0.071 -a -0.016 0.004 -0.081 -a -0.057 -0.066
-0.066 -0.001 0.000 0.065 -0.079 -0.075 -0.033 -a
-0.115 -0.049 -0.032 0.026 -0.131 -0.110 -0.093 -0.051
-0.133 -0.066 -0.073 0.011 -0.156 -0.136 -0.096 -0.056
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On the other hand, 4-Si[4]H was found to be stable in the classical symmetric structure, yet its fluorinated derivative (3) was not.
In the Introduction we suggested that due to the different sensitivities of carbon and silicon to angular deformation, the SiBPs will exhibit a smaller tendency to adopt the bowtie structure and therefore also a lower Poisson’s ratio. We first focus on the biprismanes. Tables 1 and 2 give the bond lengths of the outer rings and the inner rings and their ratios. Since the bowtie structure of biprismanes is a response to angular stress and since this is less important in silicon than in carbon, it is expected that the bond length ratio, which is indicative of the extent of the bowtie structure, will be smaller for silicon than it is for carbon. The data in Tables 1 and 2 show that the fractional difference between the external and internal rings is indeed more than twice that in carbon-based than that in silicon-based prismanes. We have previously pointed out6 that, due to the Thorpe-Ingold effect,8 the bowtie structure will be accentuated as the ring size increases. This is undoubtedly true also for the Si-based prismanes as the differences in bond lengths between inner and outer rings almost doubles as we move from bi[4]prismane to bi[6]prismane. We turn now to the Poisson’s ratio of the various prismanes. The Poisson’s ratio was usually calculated on the basis of three points: compression to 97%, the optimal length (100%), and a stretch to 105%. The reason for not going below 97% is that in several cases the molecule collapsed and did not retain the symmetric structure, for example, compression of 3-Si[4] to 93% yielded 4 as the optimized structure. Similarly, stretching
Pour et al. resulted sometimes in a nonprismane structure as was observed for 4-Si[4] at 110% stretch. These correspond to non-elastic deformations of the molecular system which are beyond the scope of this paper.
Given in Table 3 are the Poisson’s ratios for the inner rings in the various bi- and triprismanes (3 and 4 rings). The results for the CBPs are taken from refs 3 and 7. The behavior observed for CBP is replicated in the SiBPs although the magnitude of the effect is largely attenuated. For example, while for the range bi[4] to bi[6] CBPs the negative Poisson’s ratio for the internal rings ranges from ca. 7% to 13%, in the corresponding SiBPs, the values were between 0 and 7%. Replacing the hydrogen by fluorine atoms in the CPB resulted also in the attenuation of the auxetic effect on the average, by ca. 50%. Fluorine substitution in SiBPs results in two unanticipated outcomes. The first one, structure stability/instability, was discussed above. However, a much more profound effect of fluorine substitution is the reversal of the auxetic phenomenon. In all cases, fluorine substitution reduced the auxetic effect. The reduction in the effect is on the average 7((1)%. As can be seen from the data for the three ring SiBPs, the Poisson’s ratio for the 3-Si[4,5,6] prismanes was less than 7%. Thus, further reduction of the auxetic effect by ca. 7%, due to fluorine substitution, moves the Poisson’s ratio from the negative into the positive side of the scale. In the four ring SiBPs, the initial Poisson’s ratio is larger (in absolute values) than 7% and therefore, in spite of the attenuation of the effect, the sign does not change from negative to positive. The terminal rings follow closely the behavior of the internal ones (Table 4). Again, Poisson’s ratio is decreased upon going from CBP to SiBP and fluorine substitution diminishes the effect even further. In the case of the SiBP the effect of fluorine again causes the Poisson’s ratio values to cross the border to the other side, converting a normal Poisson’s ratio to an auxetic one. The conversion of the Poisson’s ratio from normal to auxetic for the terminal rings in F-capped SiBPs implies that the bowtie nature of the SiBPs increases upon stretching. These results
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TABLE 4: Poisson’s Ratio for the Terminal Rings no. of rings biprismanes
triprismanes
a
prismane type
[3]
[4]
[5]
[6]
C Si CF SiF C Si CF SiF
0.049 -a 0.033 -0.091 0.064 -a 0.063 -0.160
0.071 0.005 0.047 -0.091 0.099 0.082 0.093 -a
0.093 0.010 0.024 -0.091 0.177 0.072 0.106 -0.142
0.122 0.023 0.061 -0.061 0.178 0.092 0.128 0.015
Collapsed.
persist even at a larger basis set (B3LYP/TZP+2df, see Tables S6 and S7, Supporting Information). This increase results mainly from the expansion of the terminal rings as given in Table S3 (Supporting Information), whereas in CBPs, the bowtie feature is diminished under the same stretching. This demonstrates again that drawing an analogy between the two tetravalent atoms, carbon and silicon, is not always justified.14 4. Summary and Conclusions In conclusion, we have shown the following: (a) Some siliconbased prismanes are unstable whereas the carbon analogues are stable. (b) In some cases this instability could be “healed” by replacement of the terminal hydrogen atoms by fluorine. However, in other cases, the introduction of fluorine cause instability. (c) The Poisson’s ratio displayed by carbon-based prismanes is attenuated upon going to silicon-based prismanes as well as by replacing the terminal hydrogen atoms by fluorines. (d) Combination of the two, namely, SiBP with fluorine substitution, causes a complete reversal of the Poisson’s ratio, i.e., the terminal rings exhibit an auxetic behavior whereas the inner rings display a normal Poisson’s ratio. This is probably the first example of a substituent-induced reversal of the mechanical property of a chemical system. Acknowledgment. This work was supported by the Israeli Science Foundation. Supporting Information Available: Tables S1-S7 giving energies and bond lengths of silicon bi- and triprismanes. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) CRC Handbook of Chemistry and Physics, 67th ed.; CRC: Boca Raton, FL, 1986-1987; p F97. (2) (a) Lakes, R. S. Science 1987, 235, 1038. (b) Evans, K. E.; Nkansah, M. A.; Hutchinson, I. J.; Rogers, S. C. Nature 1991, 353, 124. (c) Evans, K. E.; Nkansah, M. A.; Hutchinson, I. J. Acta Metall. Mater. 1994, 2, 1289. (d) Choi, J. B.; Lakes, R. S. J. Compos. Mater. 1995, 29, 113. (e) Smith, C. W.; Grima, J. N.; Evans, K. E. Acta Mater. 2000, 48, 4349. (f) Evans, K. E.; Caddock, B. D. J. Phys. D: Appl. Phys. 1989, 22, 1883. (g) Alderson, A.; Evans, K. E. J. Mater. Sci. 1997, 32, 2797. (h) Alderson, K. L.; Alderson, A.; Webber, R. S.; Evans, K. E. J. Mater. Sci. Lett. 1998, 17, 1415. (i) Baughman, R. H.; Galvao, D. S. Nature 1993, 365, 735. (j) Grima, J. N.; Williams, J. J.; Evans, K. E. Chem. Commun. 2005, 4065. (k) Baughman, R. H.; Shacklette, J. M.; Zakhidov, A. A.; Stafstrom, S. Nature 1998, 392,
362. (l) Yeganeh-Haeri, A.; Weidner, D. J.; Parise, J. B. Science 1992, 257, 650–652. (m) Alderson, A.; Alderson, K. L.; Evans, K. E.; Grima, J. N.; Williams, M. J. Metastable. Nanocryst. Mater. 2005, 23, 55. (n) Grima, J. N.; Gatt, R.; Alderson, A.; Evans, K. E. Mater. Sci. Eng., A 2006, 423, 219. (o) Kimizuka, H.; Ogata, S.; Shibutani, Y. Phys. Status Solidi B 2007, 244, 900. (p) Grima, J. N.; Gatt, R.; Zammit, V.; Williams, J. J.; Evans, K. E.; Alderson, A.; Walton, R. I. J. Appl. Phys. 2007, 101, 086102 (1-3). (q) Williams, J. J.; Smith, C. W.; Evans, K. E.; Lethbridge, Z. A. D.; Walton, R. I. Chem. Mater. 2007, 19, 2423. (3) Pour, N.; Itzhaki, L.; Hoz, B.; Altus, E.; Basch, H.; Hoz, S. Angew. Chem. Int. Ed. 2006, 45, 5981. (4) Evans, K. E.; Nkansah, M. A.; Hutchinson, I. J.; Rogers, S. C. Nature 1991, 353, 124. (5) Baughman, R. H.; Dantas, S. O.; Stafstro¨m, S.; Zakhidov, A. A.; Mitchell, T. B.; Dubin, D. H. E. Science 2000, 288, 2018. (6) (a) Lees, C.; Vincent, J. F. V.; Hillerton, J. E. Bio-Med. Mater. Eng. 1991, 1 (19-23), 1. (b) Van Horn, H. M. Science 1991, 252, 384. (7) Pour, N.; Altus, E.; Basch, H.; Hoz, S. J. Phys. Chem. C 2009, 113, 3467. (8) (a) Beesley, R. M.; Ingold, C. K.; Thorpe, J. F. J. Chem. Soc. 1915, 107, 1080. (b) Ingold, C. K. J. Chem. Soc. 1921, 119, 305. In its origin, the effect relates to ring closure enhancement by substitution. Put differently, this effect reads: in a tetrahedral arrangement, contraction of one angle will cause enlargement of the opposite angle. (9) (a) Kutzelnigg, W. Angew. Chem., Int. Ed. Engl. 1984, 23, 272. (b) Karni, M.; Apeloig, Y.; Kapp, J.; Schleyer, P. v. R. Chem. Org. Silicon Compounds 2001, 3, 1. (c) Corey, J. Y. The Chemistry of Organic Silicon Compounds; Patai, S., Rappoport, Z., Eds.; John Wiley & Sons: Chichester, UK, 1989; Chapter 1, p 1. (d) Sekiguchi, A.; Nagase, S. The Chemistry of Organic Silicon Compounds; Rappoport, Z., Apeloig, Y., Eds.; John Wiley & Sons: Chichester, UK, 1998; Vol. 2, Chapter 3, p 119. (e) Sekiguchi, A.; Lee, V. Y. Cage compounds of heavier group 14 elements. In Chemistry of Organic Germanium, Tin and Lead Compounds; Wiley: New York, 2002; Vol. 2, Part 2, p 935. (10) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision B.04; Gaussian, Inc., Pittsburgh, PA, 2003. (11) Minyaev, R. M.; Minkin, V. I.; Gribanova, T. N.; Starikov, A. G.; Hoffmann, R. J. Org. Chem. 2003, 68, 8588. (12) (a) Nagase, S. Angew. Chem., Int. Ed. Engl. 1989, 28, 329. (b) Nagase, S. Acc. Chem. Res. 1995, 28, 469. (13) Earley, C. W. J. Phys. Chem. A 2000, 104, 6622. (14) A referee has suggested that the fluorine-enhanced expansion of the terminal rings upon stretching results from the fact that the distance between neighboring fluorine atoms is diminished. Namely, as the prismane is stretched, the interlayer bonds are weakened, resulting in the strengthening and shortening of the bonds to F. Consequently, the distance between two vicinal fluorines will be reduced, resulting in a repulsion that will induce an expansion of the bonds within the ring. It turns out that the C-F and Si-F bonds are, indeed, slightly shortened (for 3-Si[3]F and 3-C[3]F by 0.001 and 0.004 Å). However, the distance between two fluorines in 3-Si[3]F prismane is 4.65 Å and it is shortened to 4.60 Å upon 5% stretching, and for 3-C[3]F it is 3.265 Å and shortens upon stretching to 3.236 Å, while the van der Waals radius of F is 1.47 Å. Thus, the steric repulsion cannot be the cause for the terminal ring expansion.
JP101966C
