A statistical investigation based on a Markov chain theory of polarity formation applied to channel-type inclusion compounds loaded with both dipolar A-π-D and non-polar N-π-N (N: A or D) guests is presented. The key parameters effecting polarity formation are identified and their effects are explored. A number of paradoxes are set out and an attempt to explain the mechanisms behind them is made: dependence of macroscopic polarity on orientational selectivity induced by intermolecular interactions, tuning of polarity through (i) the concentration of non-polar guest and (ii) growth temperatur

Batagiannis, Athanasios

Hulliger, Jürg

Wüst, Thomas

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J Math Chem (2009) 45:882–883DOI 10.1007/s10910-008-9469-1ERRATUMUniversality behaviour for polarity formationin channel-type inclusion compoundsAthanasios Batagiannis · Thomas Wüst ·Jürg HulligerPublished online: 25 September 2008© Springer Science+Business Media, LLC 2008Erratum to: J Math ChemDOI 10.1007/s10910-008-9433-0Table 1 in the original article is missing some text and characters. The table shouldread as follows:Table 1 Guest–guest andhost–guest interaction energies Eij Range (kJ mol−1)EAD −25.0 to 0.01EAA 0.01 to 10.0EDD −5.0 to 5.0ECj −5.0 to 5.0In Eq. 6, a subscript character is missing; the equation should appear as follows:Pi j = Xe−β(Ei j+EC j )Zi(6)Figures 3 and 8 appear in color in the online version of the article. Where dashesappear in the captions of the original, there should be written out the correspondingcolor terminology.Therefore the caption to Fig. 3 should read:The online version of the original article can be found under doi:10.1007/s10910-008-9433-0.A. Batagiannis · T. Wüst · J. Hulliger (B)Department of Chemistry and Biochemistry, University of Berne, Freiestrasse 3, 3012 Berne,Switzerlande-mail: publication.hulliger@iac.unibe.ch123J Math Chem (2009) 45:882–883 883Fig. 3 Net polarity Xnet , as a function of XN, the fraction of non-polar guests included in the crystal. Xnetis plotted for various values of Xg (dark blue line: Xg = 0.05, light blue line: Xg = 0.25, purple line:Xg = 0.5, yellow line: Xg = 0.75, green line: Xg = 0.95). Interactions energies were randomly chosenwithin the energy range given in Appendix 1. Dashed curves were obtained from calculations using anextended hypothetical energy range (−100 < Ei j < 100 kJ mol−1). The solid black lines show the upperlimits of Xnet as a function of XNFig. 8 The effect of temperature on polarity for various concentrations Xg (black line: Xg = 0, light blueline: Xg = 0.00001, red line: Xg = 0.0001, purple line: Xg = 0.0003, green line: Xg = 0.001, darkblue line: Xg = 0.01). The interaction energies used for the calculations were EAD = −25 kJ mol−1,EAA = 5 kJ mol−1 and EDD = −5 kJ mol−1. Surprisingly, a very small amount of neutral D–π–D mole-cules in the gas phase can have a strong effect on polarity as temperature is variedand the caption to Fig. 8 should read:In Appendix 1, “Substituting Eqs. 3 and 3” should read “Substituting Eqs. 3 and4”, and “Substituting Eq. 3 for the probabilities” should read “Substituting Eq. 6 forthe probabilities”.123

Universality behaviour for polarity formation in channel-type inclusion compounds

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Universality behaviour for polarity formation in channel-type inclusion compounds

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