Clasificación de los paralelogramos.
VOLUMEN DE CUBOS, PRISMAS Y PIRÁMIDES RECTOS
http://dx.doi.org/10.1071/CH12452
Journal compilation!CSIRO 2013 www.publish.csiro.au/journals/ajc
species by the polymer propagating radical, and at the same time readily re-initiate polymerisation by adding to monomer. These requirements are sometimes in tension in that a good leaving group is typically more stabilised than the propagating radical, a property that can then hinder its ability to re-initiate polymeri- sation.[8]To overcome this, one typically exploits differences in polar or other stereoelectronic effects in reactivity of a radical R! towards monomer versus control agent.[9]For instance, cyano- isopropyl is an effective leaving group in RAFT polymerisation, even for propagating radicals that are more stabilised than itself, because polar and anomeric effects help to promote its prefer- ential fragmentation from the RAFT intermediate radical.[10] Nonetheless, for simple carbon-centred leaving groups, the scope for such optimisation is still limited; for example, cyano- isopropyl, although excellent for widely used classes of monomer, is only partially effective for certain monomers at the reactivity extremes. Moreover, the cyanoisopropyl end- group that is transferred to the polymer chain on re-initiation is not the most synthetically useful starting point for post- functionalisation of the polymer chain in cases where functio- nalisation is desired at the opposite end to the thiocarbonyl.
A potentially more productive approach to developing uni- versal leaving groups, already pioneered in ATRP,[11,12]would be to utilise non-carbon-centred radicals and thereby take advantage of the more substantial differences in the strengths of the covalent bonds that certain heteroatoms make with the dormant species (i.e. R–SC(Z)¼S in RAFT and R–ONR2in NMP) versus the propagating radical. Sulfur-centred radicals are promising as, compared with C-centred radicals, they form weaker bonds both with sulfur (as in RAFT dormant species, e.g. typical bond dissociation energy (BDE)(RS–SR)¼260– 270 kJ mol#1 versus BDE(RS–CH
2R).300 kJ mol#1) and oxygen (as in NMP dormant species, e.g. BDE(HO–SCH3)¼ 305 kJ mol#1 versus BDE(HO–CH2CH3)¼393 kJ mol#1).[13] Indeed, since the seminal works of Kharasch,[14] sulfonyl radicals have been widely used as radical initiators owing to their fast and reversible addition to carbon–carbon double bonds,[15,16]and sulfonyl halides are known as highly effective universal initiators in transition metal-catalysed ATRP of styrene and acrylate monomers,[11,17,18]and also acrylonitrile.[19] Such initiation involves generation of sulfonyl radicals and their subsequent addition to the monomer, and proceeds with close to 100 % efficiency in styrene, acrylates, and methacrylate poly- merisations.[11]The relative rates of sulfonyl radical additions have been measured for a range of vinyl monomers at varying conditions, and appear to follow an order styrene.methyl methacrylate.methyl acrylate.vinyl acetate.[20]Not surpris- ingly, addition to vinyl acetate is the least favoured as the resulting propagating radical is the least stabilised of these species, but even in this case, addition is still observed.
Given their universal ability to initiate radical polymerisa- tion, and their success as universal initiators in ATRP, we wondered if sulfonyl radicals might function as universal initiating species in other controlled radical polymerisations, and specifically in RAFT polymerisation. Finding such a uni- versal leaving group would offer potential synthetic efficiencies – particularly when combined with a universal RAFT agent. More significantly, the use of such a leaving group would impart the synthetically useful sulfonyl end-group on the majority of polymer chains.[11,21] In the present work, we studied the performance of the sulfonyl group as the R-group in RAFT. We considered the control agents S-methyl-trithiocarbonates and compared the performance of methyl- and phenylsulfonyl
with that of a commonly used cyanoisopropyl group at 608C for four polymer systems, modelled as monomeric units: polyeth- ylene, polystyrene (STY), polymethyl methacrylate, and poly- vinyl acetate (Fig. 1).
Computational Procedures
Standardab initiomolecular orbital theory and density func- tional theory (DFT) calculations were carried out using
Gaussian 09,[22]Molpro 2009.1,[23]Q-Chem 3.2,[24]andADF
2010.01.[25]Calculations on radicals were performed with an
unrestricted wave function except in cases designated with an ‘R’ prefix, where a restricted open-shell wave function was used. For all species, either full systematic conformational searches (at a resolution of 1208) or, for more complex systems, energy-directed tree searches[26] were carried out to ensure global, and not merely local minima were located. All confor- mational searches were performed in toluene solution using the M06-2X/6-31G(d) method in conjunction with the Conductor Polarised Continuum Model (CPCM)[27] and scaled UAKS radii.[28]Geometries of all species were then fully optimised at the M06-2X/6-31G(d) level of theory and frequencies were also calculated at this level and scaled by recommended scale fac- tors.[29]Interestingly, we found that the RAFT radical inter- mediates are not stable (and cannot be localised even from a starting optimised M06-2X geometry) in the gas-phase energy landscapes obtained with the popular B3LYP/6-31G(d) method, which emphasises the importance of dispersion forces (imple- mented into the M06-2X functional) in these species[30]and, methodologically, of the choice of an appropriate method for geometry optimisations.
Accurate energies for all species at 608C (333.15 K) were then calculated using the high-level compositeab initio G3 (MP2)-RAD[31]procedure that approximates URCCSD(T) cal- culations with a large triple-zbasis from calculations with a double-zbasis set, via basis-set corrections carried out at the R(O)MP2 level. Calculations on large species (.20 heavy atoms; in the present work, the reaction between STY and phenylsulfonyl RAFT agent) were performed using a double- layer ONIOM-type method. The core layer was calculated at the G3(MP2)-RAD[31]level of theory, whereas R(O)MP2 with a GTMP2Large basis set was applied to the full system.
O O O O Monomers (P) S O O S O O R-groups ET SO2Me SO2Ph STY VA MMA RAFT agent S S S R N CNiPr TTC
Fig. 1. Structures and abbreviations of the studied monomers, leaving groups and reversible addition–fragmentation chain transfer (RAFT) agents. ET, polyethylene; STY, polystyrene; VA, polyvinyl acetate; MMA, poly- methyl methacrylate.
Equilibrium constantsKeqof the studied reactions were then
calculated using the following equation: Keqð Þ ¼ ðT coÞDnexp $D
Gsoln
RT
! "
;
wherecois the standard unit of concentration and is equal to 1 mol L$1in solution,Dnis the change in moles upon reaction,T is the temperature (333.15),Ris the universal gas constant, and
DGsolnis the reaction Gibbs free energy in toluene solution.
In calculatingDGsoln, values ofDGsolnfor each species were
obtained as the sum of the corresponding gas-phase free energy and the free energy of solvation, including a phase-change correction term RT(lnV), where V is the molar volume. In calculating the gas-phase free energies, entropies and thermal corrections were calculated using standard textbook formu- lae[32]for the statistical thermodynamics of an ideal gas under the harmonic oscillator approximation in conjunction with the optimised geometries and scaled frequencies. The free energies of solvation in toluene were computed using the COSMO-RS (COnductor-like Screening MOdel for Realistic Solvents) method.[33]The COSMO-RS model uses a scaled conductor boundary condition for the calculation of the polarisation charges of a molecule in a continuum, and further performs a statistical thermodynamics post-processing of the results. The ADF[25]package was used to compute COSMO-RS solvation free energies on the solution-phase CPCM-UAKS/M06–2X/ 6–31G(d) geometries (obtained as described above) at the BP/TZVP level of theory, and the remaining parameters (e.g. atomic cavity radii, radius of the probing sphere, and cavity construction) were kept as default values for toluene.[34]
Results
In order to assess the potential of a sulfonyl group as an initial leaving group in RAFT polymerisation, we calculated the energetics of the addition–fragmentation equilibria (Scheme 2) under relevant experimental conditions. The core process is the addition of a propagating radical P%to a RAFT agent, yielding a radical intermediate that then fragments, releasing R%. Calcu- lations were performed at 608C for a trithiocarbonate RAFT agent with a reference cyanoisopropyl and investigated methyl- and phenylsulfonyl R-groups for four monomers, namely eth- ylene, styrene, vinyl acetate, and methyl methacrylate (Fig. 1). We chose these four monomers in order to assess the perfor- mance of the sulfonyl groups across the full range of propagating radical stabilities – from the relatively unstable (ethylene and vinyl acetate) to the relatively stable (styrene and methylacry- late). At the same time, this test set covers a range of steric properties – from primary (ethylene) through to tertiary (methyl methacrylate) radicals, and polarities – from the electron- donating (vinyl acetate) through to electron-accepting (methyl
methacrylate). The trithiocarbonate system was chosen as representing a synthetically relevant class of RAFT agents with an intermediate reactivity relative to the other main families. Preliminary calculations conducted on some of these other families (including simple dithioesters and xanthates) suggest that the qualitative trends in leaving group (R) ability are rela- tively unaffected by the nature of the thiocarbonyl substituent (Z in S¼C(Z)SR). More generally, we have shown in our studies of linear free energy relationships that, except where very spe- cific interactions (such as hydrogen bonding) between R and Z occur, the effects of Z and R on the RAFT process are largely additive.[9]Calculated equilibrium constants are collected in Table 1, while Fig. 2 illustrates the thermodynamics of these equilibria with respect to the reference and examined initial leaving groups.
Discussion
The success of reversible addition–fragmentation radical poly- merisation is highly dependent on the stability of a radical intermediate, formed by the addition of a propagating radical P% to a RAFT agent (Scheme 2). On one hand, its formation must be favoured thermodynamically, i.e. it should be stable with respect to the initial reactants (positive, or high log(KP-RAFT)).
On the other hand, it should be unstable enough to easily undergo fragmentation via release of the leaving group R% (negative, or low log(KR-RAFT)). We evaluated the thermo-
dynamics of these processes for a typical RAFT agent, S-methyltrithiocarbonate, containing the cyanoisopropyl (our reference R-group) or sulfonyl group (which we aim to test) under relevant experimental conditions (Table 1 above). We also calculated the RAFT agent stabilities and chain-transfer efficiencies[35]in order to quantify their performance in RAFT compared with a common reference CH3group (Table 2).
Our results indicate the superior performance of sulfonyl compared with cyanoisopropyl for all four considered mono- mers. In contrast to cyanoisopropyl, where addition of STY%to the RAFT agent is slightly endoergic, addition to sulfonyl RAFT agent is almost 30 kJ mol$1(with R¼SO2Me) and 50 kJ mol$1 (with R¼SO2Ph) downhill for STY%and even more favoured for other propagating radicals. Furthermore, subsequent frag- mentation of the intermediate radical is nearly thermoneutral for ethylene and methacrylate adducts with cyanoisopropyl RAFT agent, but becomes more feasible thermodynamically with
S ! ! S S R KP-RAFT P S S S P R S S S P R KR-RAFT