Citethis:Phys. Chem. Chem. Phys.2011 13 ,1672816734 PAPER

Downloaded by Ben Gurion University of Negev on 12 September 2011Published on 22 August 2011 on http://pubs.rsc.org doi:10.1039/C1CP21719DView OnlineFig. 1 Nanoconfined nucleotide dimerization. Top: schematics of a base pair inside organic pillared coordination cages (after Sawada, Yoshizawa,Sato and Fujita5). (a) Mononucleotide dimerization reaction: AMP denotes 5 0 -adenosine monophosphate and UMP—5 0 -uridine monophosphate.(b) Dinucleotide dimerization: TA—thymidylyl-(3 0 -5 0 )-2 0 -deoxyadenosine. Bottom: the NCECE-induced dimer stabilization: (c) log K vs. DE /kTfor dimer formation inside the molecular cages (solid line) compared to the thermodynamic limit levels (dashed line). The vertical columns mark theresults for 300 K and hydrogen-bond energetics in a pyridine environment (Table 1). (d) The corresponding reaction extents.and entropic driving forces should contribute concomitantlyto the observed dimer stabilization, and the computationresults given below reflect their relative importance inthis case. While the statistical–mechanical derivation presented above is pretty straightforward, the issue of chemicalenvironment/solvent effects on H-bond energetics is rathercomplex, and quantitative predictions often remain at anelementary level.9 Thus, since specific energetic data for thepresent caged dimers are lacking, we adapted data fromexperimental studies of H-bonded model compounds inpyridine (Table 1). This seems to furnish a rough, but realisticestimate for the bonding energetics of the caged base pairs.zThe H-bond energies estimated for the dinucleotide base pairare about twice larger (Table 1) because of the doublednumber of hydrogen-bonds (Fig. 1b). The NCECE effectsare evaluated using these data, while taking into account thetwo equivalent binding sites of the nucleotides at the triazinepanels, as well as the cage 3-fold symmetry (Fig. 1a and b).z In comparison, for a strictly hydrophobic benzene environment,bond energies of model compounds yield estimated 6.7 kcal mol 1mononucleotide dimer H-bond energy, which as expected is significantly larger than in pyridine.16730Phys. Chem. Chem. Phys., 2011, 13, 16728–16734Regardless of the exact energetics, first we compare NCECEequilibrium constants to the corresponding TL values by usingthe reduced inverse temperature, DE /kT (Fig. 1c). A majorfinding concerns the extra stabilization of the dimers inducedby the NCECE, well above the KTL values. In particular, theplot of log K2,2 vs. DE /kT has a doubled slope for both themono- and dinucleotide dimerizations, and correspondinglymuch larger equilibrium constants. Using the estimatedenergetics (Table 1), the marked value (for 300 K) exhibitsB1.5 order of magnitude NCECE induced enhancementof KTL for the mononucleotides, compared to B3 for thedinucleotides due to the doubled H-bond energy. However, asrevealed by reaction extent computations (Fig. 1d) the effect ismuch more significant for the mononucleotide dimers. Inparticular, the in-cage equilibrated reaction is shifted by about50% towards dimer formation, compared to a macroscopicsystem of these bases. This seems to signify the non-negligiblerole of the NCECE in the observed dimer stabilization.These unequivocal results raise another question: is theNCECE effect alone sufficient to stabilize the nucleotide dimerformation even under a confined aqueous environment? Thecomputations summarized in Fig. 2a and b indicate that thisis quite probable, namely, confinement of the two reactantThis journal iscthe Owner Societies 2011

Downloaded by Ben Gurion University of Negev on 12 September 2011Published on 22 August 2011 on http://pubs.rsc.org doi:10.1039/C1CP21719DView OnlineFig. 2 (a) Equilibrium constants and (b) reaction extents vs. estimated range of mononucleotide dimer formation energies for an aqueousenvironment inside the cage (300 K). The vertical line indicates the onset energy for the NCECE-induced increase of the reaction extent beyond 0.5.small system reaction, the NCECE effect depends similarly onthe nano-system and nanospace sizes.2.3 Deuterium exchange reactions on interstellar dust grainsurfacesFig. 3 The nanospace size effect and the system-size effect on chemical equilibrium predicted for the indicated dimerization reaction of nmononucleotides in hypothetical molecular cages having N bindingsites, as compared to the thermodynamic limit (TL, dashed line).The NCECE effect modelling uses hydrogen-bond energetics corresponding to a pyridine environment (Table 1).molecules to a small space together with water molecules shouldresult in a considerable increase of the small TL equilibriumconstants (associated with the low DE values, Table 1). Moreover, the corresponding extent rises for a certain DE range froma TL value of xTL o 0.5 to x 4 0.5 (Fig. 2b), thus shifting theequilibrated macro-system reaction from dominant separatenucleotides to dimer dominance under the nanoconfinement.The reported presence of some water molecules in the vicinity ofcage confined nucleotide base-pairs forming crystallized chains(ref. 5) suggests that the actual equilibrium constant value at300 K should be somewhat lower than that presented in Fig. 1c.In order to get new insights into the role of the nanospacesize (and of the system size) in the NCECE effect, we madenumerical computations for hypothetical increasingly largercages based on the statistical–mechanical derivation given inSection 2.1. A quite remarkable dependence of Kn,N on n andN is shown for the mononucleotide dimerization reaction inFig. 3. Thus, for larger n and larger N the computed plotsgradually approach the TL values. At relatively low temperatures and coverages the equilibrium constant is found toobey a simple dependence that reads Kn,N E (KTL)2/(nN).Thus, beyond the dominant slope doubling in this type ofThis journal iscthe Owner Societies 2011Astrochemical observations10 have clearly shown that theabundance of deuterium atoms in many types of interstellarmolecules is much enhanced over the cosmic D/H ratio,B1.5 10 5. Some models attributed this D enrichment(or fractionation) to H–D exchange reactions on cold tinydust grain surfaces, generally driven by small zero-pointenergy differences7 making deuterium bonding stronger thanhydrogen, and proceeding by quantum tunnelling.10–12 Manyof these studies try to explain the results on the basis ofcomplex reaction kinetics, often assuming non-equilibriumconditions.13 However, given the interstellar environmentaldiversity and wide ranges of relevant physical parameters, theestablishment of chemical equilibrium on surfaces of tinyinterstellar dust grains cannot be ruled out, as is shown by acomparison of pertinent time scales. Thus, under common fluxconditions, gas-phase species are accumulated at an averagerate of one species per day or slower, which is much longerthan the migration rate of light species on the surface, so thatthe ‘‘accretion-limited’’ regime seems to be characteristic tosurface chemistry in interstellar clouds.11 Furthermore, theaverage residence time of molecular hydrogen in ice grainmantles, for example, can vary at 10 K from 100 days up to109 years depending on the actual coverage.12 As far asreaction equilibration is concerned, experiments carried outfor example on solid formaldehyde exposed to D and H atomsat 10 K showed reversible H–D exchange tunnellingreactions.7 Thus, while it appears that conditions of chemicalequilibrium between very few adsorbed molecules under agrain surface confinement are feasible for interstellar reactions, the possible role of the NCECE effect in the observeddeuterium fractionation has not been addressed so far.The energetics of the chosen simple deuteration reactionsthat enter the statistical–mechanical modelling are givenin Table 1. Besides the major part stemming from smallzero-point energy differences (DEintra) associated with massrelated intra-molecular vibration frequencies, even smallercontributions to the deuteration reaction energy originatefrom variations in the frequency of oscillation (libration) ofPhys. Chem. Chem. Phys., 2011, 13, 16728–1673416731

Downloaded by Ben Gurion University of Negev on 12 September 2011Published on 22 August 2011 on http://pubs.rsc.org doi:10.1039/C1CP21719DView Onlinereactant and product species physisorbed on the surface(DEads). The latter depends on the adsorption energy andthe species mass, and can be estimated in the harmonicoscillator approximation.14 Temperature programmed desorption (TPD) measurements for silica-based (olivine) surfaces, asa model for interstellar dust, yielded Eads E 450 K for H/Datoms and 320 K for H2/HD/D2 molecules.15 Due to therelatively small values of the total reaction energies, DE(Table 1), isotope exchange reactions are expected to satisfythe essential condition for occurrence of a considerable effecton the reaction extent, namely a small or moderate KTL value.Since in these reactions the coverage is preserved, no nanospace size effect is expected, namely the NCECE effect shouldbe independent of the grain surface area (for a given numberof reactant species), unlike the above addition reactions inmolecular cages. In particular, the low-temperature equilibrium constant for the 2HD H2 D2 reaction type isgiven by Kn E (KTL)2/(n/2)2 and does not depend on thenumber of binding sites. For the first three reactions (Table 1)according to the statistical–mechanical analysis x/xTL reachesa maximal value (Fig. 4), which for n 2 corresponds to 21%NCECE-induced extra deuteration (6-fold increase in theequilibrium constant). The computed plots of x/xTL vs. Texhibit this maximal value at moderate temperatures (betweenB100–300 K). On the other hand, the energy of the 2HD H2 D2 reaction is much lower, leading to a maximal extradeuteration value of about 11% (5-fold increase in the equilibrium constant), which corresponds to a quite low temperature of B25 K (Fig. 4). Like in the case of the nucleotidedimerization reactions (Fig. 1), plots of log Kn vs. 1/T exhibitlow temperature slopes that are double the TL value (Fig. 5).The plots approach the TL line with increased number ofmolecules in the reaction mixture, and the system-size effectnearly disappears for n E 50 molecules (at B10 K). Due tothe high-temperature moderate values of KTL, the predictedbackward shift in K (Fig. 5) corresponds to a considerablereduction effect of the reaction extent ((x xTL)/xTL E 0.3).The TL line almost coincides with recently reportedexperimental data for the same hydrogen–deuterium exchangeFig. 5 Equilibrium constants computed for the 2HD H2 D2grain surface reaction involving n molecules (stoichiometric composition). Upper inset: the time dependence of the reaction quotient, Q,computed for n 2. It coincides with the K2 values in the limit oflong times (dotted arrows). Lower inset: magnification of the hightemperature region together with experimental points measured forthe same reaction on microcrystalline palladium powder.33reaction on microcrystalline palladium powder (Fig. 5, lowerinset), and with statistical–mechanical values of the gaseousreaction, especially for T 4 100 K.16In view of relationships between chemical equilibrium andkinetics, one can anticipate a reflection of the NCECE effecton the reaction kinetics of small systems. Due to the smallnumber of molecules involved, a proper modelling of the latternecessitates the use of master equations.17 This is done for2HD H2 D2 as a single elementary step, namely the timeevolutions of the reactant state and of the product stateprobabilities are evaluated. The computations yield thequotient of the reaction, which coincide in the long time limitwith the equilibrium constant computed values (upper inset inFig. 5). Thus, confinement effects on the kinetics of thisreaction are consistent with the NCECE effect.2.4 The origin of the NCECE effectFig. 4 The NCECE reaction extent relative to the TL value computed for the four indicated exchange reactions on surfaces of interstellar grains. (The image of a few micron interplanetary silica-based(olivine) particle is taken from Windows to the Universe, http://www.windows.ucar.edu/.)16732Phys. Chem. Chem. Phys., 2011, 13, 16728–16734The extra stabilization of intermediates or products in nanospaces, such as cavitands,2 has been attributed to geometricalshape constraints and to guest–host interactions5,18 leadingpossibly also to variations in the reaction energetics. Beyondthese factors, the NCECE origin, related solely to the smallness of a closed reaction mixture, is elucidated by inspectingthe probability distribution function of the reaction extent(Fig. 6a–d). As the number of molecules in the systemdecreases, the quite sharp probability distribution of the reaction extent (Fig. 6a) first broadens with increasing fluctuations(Fig. 6b) and becomes highly asymmetric (Fig. 6c). The slopedoubling (e.g., for n 8 at T E 20 K, Fig. 5) is associated withThis journal iscthe Owner Societies 2011

View OnlineDownloaded by Ben Gurion University of Negev on 12 September 2011Published on 22 August 2011 on http://pubs.rsc.org doi:10.1039/C1CP21719Don the entire set of available system microstates, the NCECEeffect should be affected by off-stoichiometry of the reactionmixture, as well as by the reaction mechanism in general. Thus,off-stoichiometric increase of the nanosystem size (e.g. by extraH2 or D2 molecules) can reduce to a lesser extent the NCECEstabilizing effect, as compared to an identical stoichiometricincrease. As far as the role of the reaction mechanism isconcerned, possible intermediate reaction steps are expectedto give rise to additional intermediate microstates that diminishthe NCECE-induced enhancement of the equilibrium constant.3. ConclusionsFig. 6 Elucidation of the NCECE effect origin: the probabilitydistribution function of the equilibrium reaction extent and its average computed for different system sizes, n (at T 20 K). Note: invalue (x)the limiting case of n 2 (d) the shifted x almost coincides with x 1(pure products) and mixed states are entirely absent.these variations. Moreover, the concomitant reduction in thenumber of mixed reactant–product microstates for smaller nreveals the entropic nature of the NCECE effect (see also theESIw). Thus, in the macroscopic TL, a gaseous or surfacereaction never goes to completion because of mixing entropycontributions to the free-energy, related to the large number ofhighly degenerated reactant–product mixed x levels (e.g.,Fig. 6a). As the number of the mixed microstates decreasesfor smaller n mixtures, the average reaction extent (denoted shifts towards the pure products (Fig. 6b and c),here by x)until for n 2, namely the reaction smallest system,reactant–product mixed states are entirely absent and thereaction goes almost to completion (Fig. 6d). This remarkableeffect accounts for the general extra product stabilizationreflected in all previous figures. The reduction in the numberof reactant–product mixed microstates in a small reactionmixture is reflected in the related mixing entropy, which isnonextensive and decreases with the total number of moleculesuntil its complete disappearance in the case of n 2 (the ESIw,Fig. S2). It can be further noted that originating from variations in the probability distribution function while dependingThis journal iscthe Owner Societies 2011Chemical equilibrium is affected remarkably when a smallnumber of reaction mixture molecules is segregated fromsurrounding molecules (constituting a ‘‘nanosystem’’ withtypically few to several tens of molecules). These NCECEeffects are demonstrated here for two entirely different typesof reaction systems, namely nucleotide dimerization insidemolecular cages and surface H–D exchange, furnishingnew insights also into nanospace size effects operative formost reactions, except those preserving the overall numberof molecules, like the exchange reaction. Furthermore, asintroduced in the previous section the extra stabilization ofexothermic reaction products originates largely from thereduction in the number of reactant–product mixed microstates in a small reaction mixture, as reflected in the distribution function of the fluctuating reaction extent and in therelated mixing entropy. Besides the system size, the magnitudeof the NCECE effect depends on the reaction energy and thereactant stoichiometric coefficients, in accordance with ourrecent preliminary theoretical work.1 It can depend also onthe reaction mechanism, and varies for off-stoichiometricreaction mixtures. Thus, the corresponding nanoequilibrium‘‘constant’’ is actually not constant.Most remarkable effects on the reaction extent are predictedfor moderate values of the thermodynamic equilibrium constant (KTL between B1 and B10), i.e., when the reactionenergy is relatively low and comparable to the molecularthermal energy, such as in the formation of relatively weakhydrogen bonds at room temperature, or in H–D exchange atcryogenic temperatures due to zero-point energy differences.The formation of charge-transfer complexes (e.g., I2/benzene)falls into this category and is a potential candidate fordedicated experiments for quantitative verification of theNCECE theory accuracy. Other nanospaces for small systemreactions include sealed carbon nanotubes,19 fullerenes,20,21Fe–ligand tetrahedral,22 Ga–ligand tetrahedral,18 and Mo-oxidebased spherical molecular capsules,23–26 as well as mesoporousmaterials.3,4As emphasised above, this intrinsic NCECE effect ofentropic nature should be distinguished from other possibleconfinement effects of energetic origin, such as host–guestinteractions. Fully quantitative assessment of the magnitudeof such effects compared to the NCECE effect is desirable, aswell as going beyond the ideal gas model by employingimproved energetics. Evaluation of trends in catalysis-relatedquasi-equilibrated nano-mixtures, capable of weak matterexchange with the environment, is currently underway.Phys. Chem. Chem. Phys., 2011, 13, 16728–1673416733

View OnlineReturning to the main question posed above regarding theorigin of the experimental observations, the positive answerprovided by the present findings substantially strengthens thevalidity of the NCECE effect. Finally, this effect is expected tobe important in the growing nanotechnological utilization ofchemical reactions conducted within confined nanospaces, aswell as in theoretical physical chemistry in general, due to thefundamental deviations from classical thermodynamics ofmacroscopic systems.Downloaded by Ben Gurion University of Negev on 12 September 2011Published on 22 August 2011 on http://pubs.rsc.org doi:10.1039/C1CP21719DNotes and references1 M. Polak and L. Rubinovich, Nano Lett., 2008, 8, 3543–3547.2 T. Iwasawa, R. J. Hooley and J. Rebek, Science, 2007, 317,493–496.3 A. Thomas, S. Polarz and M. Antonietti, J. Phys. Chem. B, 2003,107, 5081–5087.4 S. Polarz and A. Kuschel, Chem.–Eur. J., 2008, 14, 9816–9829.5 T. Sawada, M. Yoshizawa, S. Sato and M. Fujita, Nat. Chem.,2009, 1, 53–56.6 J. A. Thomas, Nat. Chem., 2009, 1, 25–26.7 N. Watanabe and A. Kouchi, Prog. Surf. Sci., 2008, 83, 439–489.8 V. Garcı́a-Morales, in Handbook of Nanophysics: Principles andMethods, ed. K. D. Sattler, CRC Press Inc, Boca Raton, FL, USA,2011.9 J. L. Cook, C. A. Hunter, C. M. R. Low, A. Perez-Velasco andJ. G. Vinter, Angew. Chem., Int. Ed., 2007, 46, 3706–3709.10 H. Roberts and T. J. Millar, Astron. Astrophys., 2000, 361,388–398.11 T. Henning, Chem. Soc. Rev., 1998, 27, 315–321.12 L. Amiaud, J. H. Fillion, S. Baouche, F. Dulieu, A. Momeni andJ. L. Lemaire, J.

This ournal is c the Owner Societies 2011 Phys. Chem. Chem. Phys.,2011,13,1672816734 16729 constant given by KTL E exp[ (DE TDS/kT)], with the same reaction energy, DE, and the molecular-configurational entropy change,DS.Thesystemsize and nanospacesizeeffects,