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Quantifying Solvophobic Effects in Non-polar Cohesive InteractionsLixu Yang, Catherine Adam, Scott L. Cockroft*EaStCHEM School of Chemistry, University of Edinburgh, Joseph Black Building, David Brewster Road, Edinburgh, EH9 3FJ, UK.Supporting Information PlaceholderABSTRACT:The hydrophobic effect plays a central role in determining the structure, activity and properties of biomolecules and materials. In contrast, the general manifestation of this phenomenon in other solvents -the solvophobic effect- although widely invoked, is currently poorly defined due to the lack of a universally accepted descriptor. Here we have used synthetic molecular balances to measure solvent effects on aromatic, aliphatic and fluorous non-polar interactions. Our solvent screening data combined with independent experimental measurements of supramolecular association, single-molecule folding and bulk phase transfer energies were all found to correlate well with the cohesive energy density of the solvent. Meanwhile, other measures of solvent cohesion, such as surface tension and internal pressure, gave inferior correlations. Thus, we establish cohesive energy density as a readily accessible, quantitative descriptor of solvophobic association in a range of chemical contexts.The hydrophobic association of non-polar solutes in aqueous solution demonstrates the intrinsic role that a solvent can play in driving self-assembly processes.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPkdy

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ADDIN EN.CITE.DATA 1b,2 the minimization of solvent-exposed non-polar surface area can be most simply rationalized as arising from the out-competition of solvent-solute interactions by cohesive solute-solute interactions.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPkh1

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ADDIN EN.CITE.DATA 1,3 The general manifestation of this phenomenon in other solvents can be referred to as the solvophobic effect, with solvent cohesion having both electrostatic and van der Waals dispersion contributions.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPkRh

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ADDIN EN.CITE.DATA 4 The solvophobic effect has been invoked as governing the rate and outcome of chemical reactions,PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPlNj

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ADDIN EN.CITE.DATA 8 and in ionic liquids, ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Greaves</Author><Year>2013</Year><RecNum>5422</RecNum><DisplayText><style face="superscript">9</style></DisplayText><record><rec-number>5422</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5422</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Greaves, Tamar L.</author><author>Drummond, Calum J.</author></authors></contributors><titles><title>Solvent nanostructure, the solvophobic effect and amphiphile self-assembly in ionic liquids</title><secondary-title>Chemical Society Reviews</secondary-title></titles><periodical><full-title>Chemical Society Reviews </full-title><abbr-1>Chem. Soc. Rev.</abbr-1></periodical><pages>1096-1120</pages><volume>42</volume><number>3</number><dates><year>2013</year></dates><publisher>The Royal Society of Chemistry</publisher><isbn>0306-0012</isbn><work-type>10.1039/C2CS35339C</work-type><urls><related-urls><url> but their role is less clear away from the immiscible extremes. For example, there have been contrasting views on whether solvophobic self-assembly requires solvents that form hydrogen-bond networks.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPlJh

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ADDIN EN.CITE.DATA 4b,9-10 Furthermore, the role of solvophobic effects may be further obscured by other non-covalent interactions, particularly those whose magnitudes scale with the size of molecular surface area contacts as is the case with dispersion interactions.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPkh1

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ADDIN EN.CITE.DATA 3b,6d,6f,11 As a result, most attributions of the solvophobic effect are qualitative, and only in a few notable cases are sufficient solvents examined to draw firm conclusions regarding the mechanistic origin of any observed behavior.2b,3b,5d,5e,6f,6l,6m,6o,8a,10,11a,11c,12h,18,20. Even then, there is no general agreement on the parameters that can be reliably used to identify solvophobic effects.Here we examine the utility of different parameters for quantifying solvophobic effects in multiple classes of non-polar molecular contacts. Solvophobic effects in aromatic edge-to-face, aliphatic and fluorous interactions were measured using Wilcox torsion balances (Figures 1 to 3), and the generality of the findings tested in a range of contexts: from the unfolding of single polymer molecules (Figure 4b), to supramolecular aromatic stacking interactions (Figure 4c), and bulk phase transfer energies (Figure 4d).Figure 1. Wilcox molecular torsion balances showing the conformational equilibria used to measure non-covalent interactions between non-polar functional groups. ?Gcontrols is the mean conformational free energy of the control balances.The ambiguity surrounding the significance of solvophobic effects, particularly in organic solvents, can be largely attributed to the scarcity of solvent screening data. For example, in some solvents the interactions between non-polar species such as those shown on the right of Figure 1 may be too weak to overcome the entropic cost associated with bimolecular association, ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Hunter</Author><Year>2004</Year><RecNum>4</RecNum><DisplayText><style face="superscript">1c</style></DisplayText><record><rec-number>4</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">4</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hunter, C. A.</author></authors></contributors><auth-address>Hunter, CA&#xD;Univ Sheffield, Dept Chem, Krebs Isnt Biomol Sci, Ctr Chem Biol, Sheffield S3 7HF, S Yorkshire, England&#xD;Univ Sheffield, Dept Chem, Krebs Isnt Biomol Sci, Ctr Chem Biol, Sheffield S3 7HF, S Yorkshire, England</auth-address><titles><title>Quantifying intermolecular interactions: Guidelines for the molecular recognition toolbox</title><secondary-title>Angew. Chem. Int. Ed.</secondary-title><alt-title>Angew Chem Int Edit</alt-title></titles><periodical><full-title>Angew. Chem. Int. Ed.</full-title><abbr-1>Angew. Chem. Int. Ed.</abbr-1></periodical><alt-periodical><full-title>Angewandte Chemie-International Edition</full-title><abbr-1>Angew Chem Int Edit</abbr-1></alt-periodical><pages>5310-5324</pages><volume>43</volume><number>40</number><keywords><keyword>formation enthalpy</keyword><keyword>hydrogen bonds</keyword><keyword>molecular recognition</keyword><keyword>solvent effects</keyword><keyword>statistical thermo-dynamics</keyword><keyword>host-guest complexes</keyword><keyword>hydrogen-bonded complexes</keyword><keyword>free-energy relationships</keyword><keyword>cation-pi interaction</keyword><keyword>theoretical prediction</keyword><keyword>protein-ligand</keyword><keyword>solvent size</keyword><keyword>binding</keyword><keyword>basicity</keyword><keyword>associations</keyword></keywords><dates><year>2004</year></dates><isbn>1433-7851</isbn><accession-num>ISI:000224592400005</accession-num><urls><related-urls><url>&lt;Go to ISI&gt;://000224592400005</url></related-urls></urls><language>English</language></record></Cite></EndNote>1c while in other cases solvophobic self-association may be so strong that the compounds of interest may not even dissolve. In addition, obtaining high-quality thermodynamic data using titration-based methods in many different solvents can be a particularly time-consuming process. Synthetic molecular torsion balances provide a means of overcoming some of the challenges associated with the measurement of non-covalent interactions.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPk1h

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ADDIN EN.CITE.DATA 6p,6q,12 Most molecular torsion balances possess defined folded and unfolded conformations in which functional groups are either exposed to the solvent or brought into contact. The structures shown in Figure 1 represent archetypal molecular torsion balances of the type originally derived by Wilcox and co-workers from a Tr?ger’s base scaffold.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPlBh

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ADDIN EN.CITE.DATA 13 Since the conformational population is sensitive to the magnitude of the intramolecular interactions and the effects of the solvent, then the position of a conformational equilibrium can be used as a direct measure of non-covalent interactions and solvent effects.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPk1h

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ADDIN EN.CITE.DATA 12a,14 Furthermore, rotation about the biaryl bond in the compounds shown in Figure 1 is slow on the NMR timescale (but rapid enough for equilibrium to be established in a convenient period of time). This means that the conformational free energy difference between the two conformers can be determined from a single NMR spectrum by integrating the distinct NMR peaks corresponding to each of the conformers, where ?G = ?RT ln[folded]/[unfolded]. Thus, molecular balances are particularly suited to examining the solvent effects on weak non-covalent interactions.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPk1h

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AG==

ADDIN EN.CITE.DATA 6l,6m,12hWe set out to screen for solvophobic effects on the cohesive self-association of the non-polar functional groups depicted in Figure 1. Despite numerous previous studies of aromatic edge-to-face interactions using Wilcox torsion balances, none have involved extensive solvent screens.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPlBh

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ADDIN EN.CITE.DATA 6n,13,15 To date, the general finding has been that both direct substituent-aryl and polar CH-aryl interactions make the largest contributions to the interaction energy in organic solvents. ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Gardarsson</Author><Year>2014</Year><RecNum>5406</RecNum><DisplayText><style face="superscript">15d</style></DisplayText><record><rec-number>5406</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5406</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Gardarsson, Haraldur</author><author>Schweizer, W. Bernd</author><author>Trapp, Nils</author><author>Diederich, Fran?ois</author></authors></contributors><titles><title>Structures and Properties of Molecular Torsion Balances to Decipher the Nature of Substituent Effects on the Aromatic Edge-to-Face Interaction</title><secondary-title>Chem. Eur. J.</secondary-title></titles><periodical><full-title>Chem. Eur. J.</full-title></periodical><pages>4608-4616</pages><volume>20</volume><number>16</number><keywords><keyword>aromatic edge-to-face interactions</keyword><keyword>dipole–dipole interactions</keyword><keyword>fluorine</keyword><keyword>molecular torsion balance</keyword><keyword>substituent effects</keyword><keyword>Tr?ger base</keyword></keywords><dates><year>2014</year></dates><publisher>WILEY-VCH Verlag</publisher><isbn>1521-3765</isbn><urls><related-urls><url> Thus, the unsubstituted Wilcox balance (±)-1E was used in the present study (Figure 1a), since any investigation of solvophobic effects on aromatic edge-to-face interactions should seek to minimize electrostatic contributions.To account for the multiple factors contributing to the position of the conformational equilibrium in each solvent,PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPkNv

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ADDIN EN.CITE.DATA 12a,14 the strength of the edge-to-face interaction, ?Gedge was estimated by subtracting the conformational free energy of the control compound (±)-2E (in which the aryl ring was replaced by a methyl group) from that of (±)-1E. ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Kim</Author><Year>1998</Year><RecNum>171</RecNum><DisplayText><style face="superscript">13b</style></DisplayText><record><rec-number>171</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">171</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Kim, Eun-il</author><author>Paliwal, Sunil</author><author>Wilcox, Craig S.</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Measurements of Molecular Electrostatic Field Effects in Edge-to-Face Aromatic Interactions and CH-</style><style face="normal" font="default" charset="161" size="100%">π</style><style face="normal" font="default" size="100%"> Interactions with Implications for Protein Folding and Molecular Recognition</style></title><secondary-title>J. Am. Chem. Soc.</secondary-title></titles><periodical><full-title>J. AM. CHEM. SOC.</full-title></periodical><pages>11192-11193</pages><volume>120</volume><number>43</number><dates><year>1998</year></dates><publisher>American Chemical Society</publisher><isbn>0002-7863</isbn><urls><related-urls><url>, ADDIN EN.CITE <EndNote><Cite><RecNum>0</RecNum><Note> Computational models of this compound support Wilcox’s previous assertion that the methyl group is not large enough to form significant dispersive contact or CH-aryl interactions in the folded conformation, but is still large enough to block solvation of the aromatic face in a similar manner as the phenyl ester in the folded conformation (Figure S2).{#171</Note><DisplayText><style face="superscript">16</style></DisplayText></Cite></EndNote>16 Similarly, non-polar alkyl-alkyl (?Galiphatic) and perfluoroalkyl-perfluoroalkyl interactions (?Gfluorous) were measured in Wilcox balances (±)-1H and (±)-1F against the control compounds shown in Figure 1b-c. ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Yang</Author><Year>2013</Year><RecNum>5374</RecNum><DisplayText><style face="superscript">6l,6m</style></DisplayText><record><rec-number>5374</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5374</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Yang, L.</author><author>Adam, C.</author><author>Nichol, G. S.</author><author>Cockroft, S. L.</author></authors></contributors><titles><title>How much do van der Waals dispersion forces contribute to molecular recognition in solution?</title><secondary-title>Nat. Chem.</secondary-title></titles><periodical><full-title>Nat. Chem.</full-title></periodical><pages>1006-1010</pages><volume>5</volume><dates><year>2013</year></dates><urls></urls></record></Cite><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Adam</Author><Year>2015</Year><RecNum>5401</RecNum><record><rec-number>5401</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5401</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Adam, Catherine</author><author>Yang, Lixu</author><author>Cockroft, Scott L.</author></authors></contributors><titles><title>Partitioning solvophobic and dispersion forces in alkyl and perfluoroalkyl cohesion</title><secondary-title>Angew. Chem. Int. Ed.</secondary-title></titles><periodical><full-title>Angew. Chem. Int. Ed.</full-title><abbr-1>Angew. Chem. Int. Ed.</abbr-1></periodical><pages>1164-1167</pages><volume>54</volume><number>4</number><dates><year>2015</year></dates><urls></urls><electronic-resource-num>10.1002/anie.201408982</electronic-resource-num></record></Cite></EndNote>6l,6m ?Gedge, ?Galiphatic, and ?Gfluorous were measured in 23 different solvents (Figure 2).All three classes of non-polar interaction examined were found to be weak, lying in the range of +1 to ?2 kJ mol–1. The aromatic edge-to-face interaction measured in chloroform was similar to that previously determined in other supramolecular model systems.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPk1h

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ADDIN EN.CITE.DATA 17 The preference for non-polar association in the aqueous and polar organic solvents compared to the apolar solvents was observed across all three data sets (Figure 2). This qualitative observation points to a role of cohesive solvent-solvent (solvophobic) effects in all three classes of non-polar association examined (aromatic edge-to-face, aliphatic and fluorous cohesion). Thus, it might be expected that parameters describing Figure 2. Bar graph showing non-polar cohesive interactions measured in a range of solvents using the compounds and equations shown in Figure 1. Deuterated solvents were used in place of all protic solvents. Solvent mixtures are quoted in v/v %. All data are tabulated in the SI.Figure 3. Correlations of ?Galiphatic,??Gedge, and ?Gfluorous (colored circles), and the average of all three ?Gnon-polar (black circles) as the cohesive energy density of the solvent is varied. For the purpose of clarity, the plots of ?Gfluorous, ?Gedge, ?Galiphatic are offset by ?2,???, and ?? kJ mol?1, respectively. All data are tabulated in the SI. A version of this graph in which the extrapolated water points (hollow circles) are excluded is shown in Figure S7a.solvent-solvent cohesive interactions may be useful for quantifying solvophobic association. Several different parameters have been proposed as describing cohesive solvent interactions: cohesive tension (?),PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPlRh

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ADDIN EN.CITE.DATA 3c,6o internal pressure (Pi), ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Dack</Author><Year>1975</Year><RecNum>5378</RecNum><DisplayText><style face="superscript">3b,4a</style></DisplayText><record><rec-number>5378</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5378</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Dack, M. R. J.</author></authors></contributors><titles><title>The importance of solvent internal pressure and cohesion to solution phenomena</title><secondary-title>Chem. Soc. Rev.</secondary-title></titles><periodical><full-title>Chem. Soc. Rev.</full-title></periodical><pages>211-229</pages><volume>4</volume><number>2</number><dates><year>1975</year></dates><publisher>The Royal Society of Chemistry</publisher><isbn>0306-0012</isbn><work-type>10.1039/CS9750400211</work-type><urls><related-urls><url> ExcludeAuth="1" ExcludeYear="1"><Author>Otto</Author><Year>2013</Year><RecNum>5373</RecNum><record><rec-number>5373</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5373</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Otto, Sijbren</author></authors></contributors><titles><title>The role of solvent cohesion in nonpolar solvation</title><secondary-title>Chem. Sci.</secondary-title></titles><periodical><full-title>Chem. Sci.</full-title></periodical><pages>2953-2959</pages><volume>4</volume><number>7</number><dates><year>2013</year></dates><publisher>The Royal Society of Chemistry</publisher><isbn>2041-6520</isbn><work-type>10.1039/C3SC50740H</work-type><urls><related-urls><url> the enthalpy of vaporization (?Hvap), cohesive energy density (ced),3b, 20 Hildebrand solubility parameter (?H) ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Hildebrand</Author><Year>1964</Year><RecNum>5486</RecNum><DisplayText><style face="superscript">18</style></DisplayText><record><rec-number>5486</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5486</key></foreign-keys><ref-type name="Book">6</ref-type><contributors><authors><author>Hildebrand, J. H.</author><author>Scott, R. L.</author></authors></contributors><titles><title>The Solubility of Nonelectrolytes</title></titles><edition>3rd Ed.</edition><dates><year>1964</year></dates><pub-location>New York</pub-location><publisher>Dover Publications</publisher><urls></urls></record></Cite></EndNote>18 and Abraham’s solvophobicity parameter (Sp). ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Abraham</Author><Year>1988</Year><RecNum>5386</RecNum><DisplayText><style face="superscript">11c</style></DisplayText><record><rec-number>5386</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5386</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Abraham, Michael H.</author><author>Grellier, Priscilla L.</author><author>McGill, R. Andrew</author></authors></contributors><titles><title>A quantitative measure of solvent solvophobic effect</title><secondary-title>J. Chem. Soc., Perkin Trans. 2</secondary-title></titles><periodical><full-title>J. Chem. Soc., Perkin Trans. 2</full-title><abbr-1>J. Chem. Soc., Perkin Trans. 2</abbr-1></periodical><pages>339-345</pages><number>3</number><dates><year>1988</year></dates><publisher>The Royal Society of Chemistry</publisher><isbn>0300-9580</isbn><work-type>10.1039/P29880000339</work-type><urls><related-urls><url> Several of the parameters are related as follows:?H2 = ced = (?Hvap – RT) / Vmwhere R is the gas constant, T is the temperature and Vm is the molar volume of the solvent.Among the independent parameters describing cohesive solvent-solvent interactions, cohesive energy density provided the best correlations with the non-polar interaction energies measured in the present study (Figure 3, data are offset in 2 kJ mol–1 increments for purposes clarity). This plot comprises over 200 experimental measurements of conformational free energies determined for the nine molecular balances shown in Figure 1 in 23 different solvents. However, these data correlated substantially less well with alternative descriptors of solvent cohesion such as surface tension and internal pressure (Figure S6). The result supports earlier suggestions that surface tension may not be an ideal descriptor for hydrophobic effects.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPlRh

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ADDIN EN.CITE.DATA 3c,19 Internal pressure has been shown to be more important in the solvation of very small solutes such as gases compared to the larger interaction interfaces examined in the present study. ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Otto</Author><Year>2013</Year><RecNum>5373</RecNum><DisplayText><style face="superscript">3b</style></DisplayText><record><rec-number>5373</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5373</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Otto, Sijbren</author></authors></contributors><titles><title>The role of solvent cohesion in nonpolar solvation</title><secondary-title>Chem. Sci.</secondary-title></titles><periodical><full-title>Chem. Sci.</full-title></periodical><pages>2953-2959</pages><volume>4</volume><number>7</number><dates><year>2013</year></dates><publisher>The Royal Society of Chemistry</publisher><isbn>2041-6520</isbn><work-type>10.1039/C3SC50740H</work-type><urls><related-urls><url> Indeed, the gradients of the correlations in Figure 4a reflect the qualitative ordering of the size of the interaction interfaces. The significant scatter associated with the correlations corresponding to individual interaction classes (colored circles in Figure 3) can be attributed to solvent-specific attenuation of dispersion and electrostatic interactions, in addition to the experimental errors associated with the measurement of very weak non-covalent interactions. ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Adam</Author><Year>2015</Year><RecNum>5401</RecNum><DisplayText><style face="superscript">6l</style></DisplayText><record><rec-number>5401</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5401</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Adam, Catherine</author><author>Yang, Lixu</author><author>Cockroft, Scott L.</author></authors></contributors><titles><title>Partitioning solvophobic and dispersion forces in alkyl and perfluoroalkyl cohesion</title><secondary-title>Angew. Chem. Int. Ed.</secondary-title></titles><periodical><full-title>Angew. Chem. Int. Ed.</full-title><abbr-1>Angew. Chem. Int. Ed.</abbr-1></periodical><pages>1164-1167</pages><volume>54</volume><number>4</number><dates><year>2015</year></dates><urls></urls><electronic-resource-num>10.1002/anie.201408982</electronic-resource-num></record></Cite></EndNote>6l Strikingly, taking the mean interaction energy across all three classes of non-polar contact reveals a common solvophobic driving force for non-polar association, providing a correlation with R2 = 0.95 (black circles in Figure 3, and R2 = 0.83 with water points excluded in Figure S7), which arises due to the minimization of errors, and the cancellation of dispersion contributions across the interaction types. Interestingly, the intercepts of the correlations in Figure 3 are close to zero (~0.5 kJ mol–1). Since the intercept corresponds to the situation where there is no solvophobic effect, the observation is consistent with a minimal contribution of electrostatic interactions and the generalized cancellation of dispersion forces in solution in the classes of interaction examined.3b, 6l, 6m, 11a,12kTo test the generality of cohesive energy densities as a scale for describing solvophobic association (Figure 4a), we have replotted experimental data previously obtained in a range of solvents for both the collapse of single polystyrene molecules (Figure 4b) ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Li</Author><Year>2010</Year><RecNum>5462</RecNum><DisplayText><style face="superscript">6o</style></DisplayText><record><rec-number>5462</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5462</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Li, Isaac T. S.</author><author>Walker, Gilbert C.</author></authors></contributors><titles><title>Interfacial Free Energy Governs Single Polystyrene Chain Collapse in Water and Aqueous Solutions</title><secondary-title>J. Am. Chem. Soc.</secondary-title></titles><periodical><full-title>J. AM. CHEM. SOC.</full-title></periodical><pages>6530-6540</pages><volume>132</volume><number>18</number><dates><year>2010</year><pub-dates><date>2010/05/12</date></pub-dates></dates><publisher>American Chemical Society</publisher><isbn>0002-7863</isbn><urls><related-urls><url> and supramolecular aromatic stacking interactions (Figure 4c). ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Cubberley</Author><Year>2001</Year><RecNum>5279</RecNum><DisplayText><style face="superscript">20</style></DisplayText><record><rec-number>5279</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5279</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Cubberley, Mark S.</author><author>Iverson, Brent L.</author></authors></contributors><titles><title>1H NMR Investigation of Solvent Effects in Aromatic Stacking Interactions</title><secondary-title>J. Am. Chem. Soc.</secondary-title></titles><periodical><full-title>J. AM. CHEM. SOC.</full-title></periodical><pages>7560-7563</pages><volume>123</volume><number>31</number><dates><year>2001</year><pub-dates><date>2001/08/01</date></pub-dates></dates><publisher>American Chemical Society</publisher><isbn>0002-7863</isbn><urls><related-urls><url> The data shown in Figure 4b represents the plateau force required to unfold a collapsed single polystyrene molecule in solution, which is directly proportional to the solvation free energy per monomer (?G). ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Li</Author><Year>2010</Year><RecNum>5462</RecNum><DisplayText><style face="superscript">6o</style></DisplayText><record><rec-number>5462</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5462</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Li, Isaac T. S.</author><author>Walker, Gilbert C.</author></authors></contributors><titles><title>Interfacial Free Energy Governs Single Polystyrene Chain Collapse in Water and Aqueous Solutions</title><secondary-title>J. Am. Chem. Soc.</secondary-title></titles><periodical><full-title>J. AM. CHEM. SOC.</full-title></periodical><pages>6530-6540</pages><volume>132</volume><number>18</number><dates><year>2010</year><pub-dates><date>2010/05/12</date></pub-dates></dates><publisher>American Chemical Society</publisher><isbn>0002-7863</isbn><urls><related-urls><url> This data had previously been plotted against solvent surface tension differences, giving a good, but notably lower quality correlation (Figure S8) than that shown in Figure 4b. Figure 4c shows a plot of experimental aromatic stacking interaction energies plotted against the cohesive energy density of the solvents examined. A subset of this data had previously been correlated against the ET(30) solvent polarity scale, ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Wheeler</Author><Year>2014</Year><RecNum>5379</RecNum><DisplayText><style face="superscript">21</style></DisplayText><record><rec-number>5379</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5379</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Wheeler, Steven E.</author><author>Bloom, Jacob W. G.</author></authors></contributors><titles><title>Towards a More Complete Understanding of Non-Covalent Interactions Involving Aromatic Rings</title><secondary-title>J. Phys. Chem. A</secondary-title></titles><periodical><full-title>J. Phys. Chem. A</full-title><abbr-1>J. Phys. Chem. A.</abbr-1></periodical><pages>6133–6147</pages><volume>118</volume><dates><year>2014</year></dates><publisher>American Chemical Society</publisher><isbn>1089-5639</isbn><urls><related-urls><url> yielding a correlation with R2 = 0.88 (Figure S9a). However, all three of the original data sets can now correlated against cohesive energy density giving R2 values ranging between 0.94 and 0.97 (Figure 4c). Contrasting with the correlations in Figure 3, the different intercepts in Figure 4c can be attributed to differences in electrostatic/dispersion interactions as the stacked complex was varied. Correlations of this data against Abraham’s solvophobicity parameter, Sp HYPERLINK \l "_ENREF_46" \o "Abraham, 1988 #5386" ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Abraham</Author><Year>1988</Year><RecNum>5386</RecNum><DisplayText><style face="superscript">11c</style></DisplayText><record><rec-number>5386</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5386</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Abraham, Michael H.</author><author>Grellier, Priscilla L.</author><author>McGill, R. Andrew</author></authors></contributors><titles><title>A quantitative measure of solvent solvophobic effect</title><secondary-title>J. Chem. Soc., Perkin Trans. 2</secondary-title></titles><periodical><full-title>J. Chem. Soc., Perkin Trans. 2</full-title><abbr-1>J. Chem. Soc., Perkin Trans. 2</abbr-1></periodical><pages>339-345</pages><number>3</number><dates><year>1988</year></dates><publisher>The Royal Society of Chemistry</publisher><isbn>0300-9580</isbn><work-type>10.1039/P29880000339</work-type><urls><related-urls><url> yielded equally pleasing correlations with R2 = 0.93-0.97 (Figure S9b). As was the case for the three non-polar contacts measured using Wilcox balances, the data for aromatic stacking did not correlate well with the surface tension nor the internal pressure of the solvent (Figure S9c-d). The general utility of cohesive energy densities in describing solvophobic effects was further demonstrated by the strong correlations with solvophobicity values, Sp (Figure 4d) ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Abraham</Author><Year>1988</Year><RecNum>5386</RecNum><DisplayText><style face="superscript">11c</style></DisplayText><record><rec-number>5386</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5386</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Abraham, Michael H.</author><author>Grellier, Priscilla L.</author><author>McGill, R. Andrew</author></authors></contributors><titles><title>A quantitative measure of solvent solvophobic effect</title><secondary-title>J. Chem. Soc., Perkin Trans. 2</secondary-title></titles><periodical><full-title>J. Chem. Soc., Perkin Trans. 2</full-title><abbr-1>J. Chem. Soc., Perkin Trans. 2</abbr-1></periodical><pages>339-345</pages><number>3</number><dates><year>1988</year></dates><publisher>The Royal Society of Chemistry</publisher><isbn>0300-9580</isbn><work-type>10.1039/P29880000339</work-type><urls><related-urls><url> and phase transfer free energies of hydrocarbons from water (Figure S10a). The quality of these relationships (R2 = 0.94-0.97) are notable given that cohesive energy density is directly related to the enthalpy of vaporization (see equation above),while the phase transfer energies (from which Sp values are determined) are oftenFigure 4. a) Scale of cohesive energy densities (ced) indicating the relative solvophobicities of common solvents. Solvent mixtures are quoted in v/v %. b) Previously reported plateau forces, FN for unfolding single polystyrene molecules,6o and c) aromatic stacking interaction energies, ?Gstack. ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Cubberley</Author><Year>2001</Year><RecNum>5279</RecNum><DisplayText><style face="superscript">20</style></DisplayText><record><rec-number>5279</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5279</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Cubberley, Mark S.</author><author>Iverson, Brent L.</author></authors></contributors><titles><title>1H NMR Investigation of Solvent Effects in Aromatic Stacking Interactions</title><secondary-title>J. Am. Chem. Soc.</secondary-title></titles><periodical><full-title>J. AM. CHEM. SOC.</full-title></periodical><pages>7560-7563</pages><volume>123</volume><number>31</number><dates><year>2001</year><pub-dates><date>2001/08/01</date></pub-dates></dates><publisher>American Chemical Society</publisher><isbn>0002-7863</isbn><urls><related-urls><url> replotted against the cohesive energy density of the solvents in which the measurements were made. d) Abraham’s solvophobicity parameter5e,11c versus cohesive energy density. All plotted data are tabulated in the SI. dominated by entropy. ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1" ExcludeYear="1"><Author>Frank</Author><Year>1945</Year><RecNum>5501</RecNum><DisplayText><style face="superscript">23</style></DisplayText><record><rec-number>5501</rec-number><foreign-keys><key app="EN" db-id="5ptpv0a5uvat59e0ff3v2wso92psfwr0aw5d">5501</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Frank, Henry S.</author><author>Evans, Marjorie W.</author></authors></contributors><titles><title>Free Volume and Entropy in Condensed Systems III. Entropy in Binary Liquid Mixtures; Partial Molal Entropy in Dilute Solutions; Structure and Thermodynamics in Aqueous Electrolytes</title><secondary-title>The Journal of Chemical Physics</secondary-title></titles><periodical><full-title>The Journal of Chemical Physics</full-title></periodical><pages>507-532</pages><volume>13</volume><number>11</number><dates><year>1945</year></dates><urls><related-urls><url> This relationship is likely to be a consequence of enthalpy-entropy compensation, and the existence of a mechanistic continuum between the two thermodynamic extremes of entropically versus enthalpically dominated solvophobic effects. Indeed, the manifestation of the hydrophobic effect at both thermodynamic extremes is well-recognized.PEVuZE5vdGU+PENpdGUgRXhjbHVkZUF1dGg9IjEiIEV4Y2x1ZGVZZWFyPSIxIj48QXV0aG9yPkJl

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ADDIN EN.CITE.DATA 1b,4b,24In summary, we have collated new and previously published experimental measurements of non-polar cohesive interactions to examine the utility of several quantitative solvophobic descriptors. The collated data comprised hundreds of aromatic stacking, aromatic edge-to-face, aliphatic and fluorous interaction energies measured in intramolecular, intermolecular, bulk and single-molecule contexts where solvent effects were systematically examined. All sets of solvent screening data correlated well with cohesive energy densities (the square of the Hildebrand parameter, ?H2), or Abraham’s Sp values.25 In contrast, alternative measures of solvent cohesion, such as surface tension and internal pressure provided substantially lower quality correlations. Thus, we propose that correlations of chemical properties against solvent cohesive energy densities provide a quantitative signature for characterizing solvophobic effects. ASSOCIATED CONTENTSupporting InformationTables of data, additional correlations, synthetic procedures and compound characterization data are provided in the Supporting Information. This material is available free of charge via the Internet at . AUTHOR INFORMATIONCorresponding Authorscott.cockroft@ed.ac.ukNotesThe authors declare no competing financial interests.ACKNOWLEDGMENT We thank Pfizer Ltd. and MTEM Ltd. for studentships to C.A. and L.Y. respectively, and Nicholas Dominelli-Whiteley for assistance with compound characterization.REFERENCES ADDIN EN.REFLIST (1) a) Granick, S.; Bae, S. C. Science 2008, 322, 1477; b) Biedermann, F.; Nau, W. M.; Schneider, H.-J. Angew. Chem. Int. Ed. 2014, 53, 11158; c) Hunter, C. A. Angew. Chem. Int. Ed. 2004, 43, 5310.(2) a) Marmur, A. J. Am. Chem. Soc. 2000, 122, 2120; b) Abraham, M. H.; Blandamer, M. J. J. Am. Chem. Soc. 2002, 124, 7853.(3) a) Lazaridis, T. Acc. Chem. Res. 2001, 34, 931; b) Otto, S. Chem. Sci. 2013, 4, 2953; c) Tanford, C. Proc. 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G.; Barcina, J. O.; Cerezo, A. D. Chem. Eur. J. 2001, 7, 1171; b) Carver, F. J.; Hunter, C. A.; Livingstone, D. J.; McCabe, J. F.;Seward, E. M. Chem. Eur. J. 2002, 8, 2847.(18) Hildebrand, J. H.; Scott, R. L. The Solubility of Nonelectrolytes; 3rd Ed.; Dover Publications: New York, 1964.(19) Crothers, D. M.; Ratner, D. I. Biochemistry 1968, 7, 1823.(20) Cubberley, M. S.; Iverson, B. L. J. Am. Chem. Soc. 2001, 123, 7560.(21) Wheeler, S. E.; Bloom, J. W. G. J. Phys. Chem. A. 2014, 118, 6133.(22) Frank, H. S.; Evans, M. W. J. Chem. Phys. 1945, 13, 507.(23) Contrasting with the correlations against Gibbs energy-related properties shown in Figures 4d and S10a, there is no correlation between ced and the enthalpy of phase transfer from water (Figure S10b).(24) a) Ben-Amotz, D.; Underwood, R. Acc. Chem. Res. 2008, 41, 957; b) Biela, A.; Nasief, N. N.; Betz, M.; Heine, A.; Hangauer, D.; Klebe, G. Angew. Chem. Int. Ed. 2013, 52, 1822; c) Meyer, E., A.; Castellano, R. K.; Diederich, F. Angew. Chem. Int. Ed. 2003, 42, 1210; d) Chen, L.-J.; Lin, S.-Y.; Huang, C.-C. J. Phys. Chem. B 1998, 102, 4350. (25) We propose that ced is the most useful parameter for quantifying solvophobic effects since: i. Linear free energy correlations require energies (or parameters that are directly proportional to energies) to be plotted against one another [cf. the Hildebrand parameter, which has units of (energy)1/2]. ii. Comprehensive data for Gibbs energies of phase transfer of standard solutes (from which Sp values are derived) are not easily sourced, while enthalpies of vaporization from which ced values are determined are widely reported (see Tables and associated references in the SI).Table of Contents Graphic ................
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