J. CHEM. SOC. FARADAY TRANS., 1994, 90(2), 271-278 27 1 Fluorescence Anisotropy Decays and Viscous Behaviour of 2-Methyltetrahydrofuran Brian Brocklehurst" and Ronald N. Young Chemistry Department, The University of Sheffield, Sheffield, UK S3 7HF The decay of the fluorescence anisotropy has been measured for solutions in 2-methyltetrahydrofuran (MTHF) between -50 and -150°C.Solutes include both neutral species (perylene, tetracene, carbazole) and ion pairs (of carbazolyl-, 1,&diphenylallyl-and its vinylogues). The results lie between values calculated for ellipsoids using the 'stick' and 'slip' boundary conditions. In some cases, notably perylene, two-exponential decay is predicted but not observed, suggesting that the solvent-solute interaction is comparable with solventsolvent forces, contrasting with the hydrogen-bonded solvents used by other workers.The data are used to discuss cis-trans photo-isomerisation of diphenylallyl ions and to estimate the viscosity of MTHF, for which measure- ments cover eleven orders of magnitude. The Williams-Landel-Ferry (WLF) equation is obeyed well over the whole range with To = 81 K. MTHF forms a glass on cooling. The glass transition tem- perature is near 90 K so that it can form a rigid clear glass at the temperature of liquid nitrogen; this has been widely used to trap reactive species, especially radical anions, for spectro- scopic studies.'S2 The normal boiling point of MTHF is 80°C: its large liquid range makes it very useful for a variety of kinetic studies in which reaction may be initiated in the liquid state3 or by irradiation of glassy solutions followed by ~arming.~Since reactions of radicals etc.are generally diffusion-controlled, knowledge of the viscosity is important ; measurements have been made at high ( -75-+25 OC)' and low temperatures (92-108 K),6 ranging over some eleven orders of magnitude. As in the case of other glass-formers, the activation energy for viscous flow is not constant but increases with falling tem- perature; however, the WLF equation, provides a good fit over a very wide range; the characteristic temperature, To, lies a few degrees below the glass tran- ~ition.~ We have studied the temperature dependence of the fluo- rescence of 1,3-diphenylallyl anions (DPA) and related species' in MTHF.The excited-state behaviour of these species closely resembles that of 1,2-diphenylethene (stilbene);' cis-trans isomerisation competes with fluores-cence from the first excited singlet. As in the case of stilbene, isomerisation of excited trans,trans-DPA involves crossing an intrinsic energy barrier (ca. 20 kJ mol-'), but there appears to be no barrier in the case of the cispans form, probably as a result of steric repulsion. The fluorescence of cispans-DPA has not been observed. Methyl substitution on the central carbon of the ally1 group stabilises the ground state of the cis,trans form: fluorescence is then observed but only at very low temperatures. As in the case of cis-stilbeneg and other sterically crowded species,''-' ' isomerisation appears to be dependent on the viscosity of the solvent rather than the tem- perature.The use of the macroscopic (shear) viscosity to describe microscopic processes is debatable.' 3-15 Following the example of others,I5 we have used the decay of fluorescence anisotropy16 to measure the rate of overall rotation of a number of species in MTHF for comparison with the rate of internal rotation of DPA etc. However, with suitable scaling it is possible to calculate the viscosity approximately and for our data to fill the gap between previous measurements. Species studied are shown in Fig. 1. Measurement of both internal and overall rotation in a single system, such as cis,trans-2-methylDPA, is not feasible because of the rapid decay of fluorescence in the region of interest.The behaviour of trans,trans-DPA is complicated at higher temperatures by photo-isomerisation and changes in ion-pairing. However, at temperatures below -70 "C where fluorescence anisotropy becomes measurable, only loose ion-pairs are present for lithium and sodium salts in MTHF and isomerisation is rela- tively slow. Results are presented for Na+ DPA- and for the lithium salts of 1,5-diphenylpentadienyl anions (DPPD) and 1,7-diphenylheptatrienylanions (DPHT). For comparison with the photo-labile anions we have studied fluorescence of the rigid anion, carbazolyl,' and three neutral species : carbazole, for comparison with car-bazolyl, and perylene and tetracene which have been the sub- jects of a number of previous mainly in alcohols.Experimental MTHF was stirred over a sodium-potassium alloy under high vacuum in the presence of a little benzophenone. The development of a permanent blue colour due to the forma- tion of the anions of benzophenone indicated the absence of water or other protogenic impurities. The mixture was allowed to stand for 24 h before MTHF was distilled from it to ensure that all the benzophenone had been reduced to the involatile ions. 1 2 4 5 Fig. 1 Solutes used: 1, Carbazole; 2, carbazolyl lithium; 3, perylene; 4, n = 1, 1,3-diphenylallyl anion (DPA), n = 2, 1,Sdiphenyl-pentadienyl anion (DPPD), n = 3, 1,7-diphenylheptatrienylanion (DPHT); 5, tetracene.NB arrows denote the orientation of the tran- sition axis. Carbazole, perylene and tetracene were used as received. Preparation of DPA and its vinylogues has been described previ~usly.~*’~An early study concluded that DPPD is prob- ably entirely in the all-trans conformation;24 recent work has confirmed this and shown that DPHT is also all-tr~ns.’~ Lithium carbazolyl was prepared indirectly since the reaction between lithium and carbazole in MTHF gives a product contaminated by several by-products. A solution of the lithium salt of the dimeric dianion of a-methylstyrene was titrated into a solution of carbazole under high vacuum until equivalence was reached. The approach of this condition was indicated by the decreasing speed with which the red colour of the styryl ion was discharged; the precise end point was indicated by the disappearance of the carbazole absorption band at 338 nm.X-Ray crystallography has shown that, in the solid state, lithium carbazolyl is complexed with two mol- ecules of THF and is dimeric.26 Several related species have similarly been shown to be dimerised and in some cases NMR spectorscopy in solution has also revealed dimer- i~ation.~’Preliminary studies in this laboratory have shown that the electronic absorption spectrum of lithium carbazolyl in MTHF is virtually independent of concentration in the range lop4 to 5 x lop6 mol dmp3, suggesting that aggre- gation probably does not occur at this di1uti0n.I~ The cryostat’ and the use of visible and near-ultraviolet radiation from the Synchrotron Radiation Source (SRS) at SERC’s Darebury Laboratory (DL) to study of the decay of fluorescence and fluoresence anisotropy28 have been described previously.Temperatures quoted are believed accu- rate to 0.2”C. Our present apparatus limits us to excitation wavelengths above ca. 320 nm. The exciting light passes through a Spex 0.75 m vacuum monochromator and a pol- ariser. Fluoresence at right angles to the incident beam passes through a second, rotatable polariser and a filter (Table 1) before falling on a Mullard XP2020 or similar photomulti- plier. Conventional single-photon counting is used to record fluorescence polarised vertically (parallel) and horizontally (perpendicular) and also the ‘prompt ’, the instrument reponse function, measured by scattering light at the fluorescence wavelength from a dilute suspension of Ludox.Wavelengths used are listed in Table 1. Count rates were kept below 30 kHz. The timescale was adjusted to cover some 5-10 decay times; counting continued until the peak channel (of 1024) contained 20-50 OOO counts. Data were analysed on the DL Convex C220 computer using the programe ‘srd fluor’. The parallel and perpendicu- lar decays are first deconvolved from the instrument response using a series of eight exponentials to fit them. The anisot- ropy, r(t),defined as is calculated and then fitted to one or more exponentials. Since no emission monochromator is used, there should be J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 no inherent bias in the detection system towards one or other polarisation, i.e. the limiting value r(m) should be zero. To check for effects of errors of alignment, this quantity was treated as a variable. Values of 0-0.01 were obtained in most cases. The pulse width of the synchrotron is ca. 160 ps and the measured FWHM of the instrument reponse was 600-700 ps. Synchrotron radiation has the advantage over flash-lamps that the pulse shape is independent of wavelength, so decon-volution should give access to times < 100 ps. However, diffi- culties were sometimes experienced at short times, probably the result of small amounts of internal reflection in the appar- atus. Measurement of long times, much greater than the fluo- rescence decay time, is also difficult, or course.The denominator of eqn. (2) is the total emission, indepen- dent of polarisation. This quantity was analysed in terms of one or two exponential decays using non-linear squares deconvolution. Apart from tetracene which showed evidence of a small amount of an impurity with a longer lifetime, one exponential sufficed for all these systems in the temperature range of interest. Values of decay times are listed in Table 1. Theory Molecular Rotation The foundations of the subject were laid by Einstein29 and Perrin3* who used the hydrodynamic theory of Stokes to describe Brownian rotation of particles in suspension. For a sphere, the rotational correlation time, 7R,is given by 1 (3) where, the rotational diffusion constant, D,, is kTD,= -(4)6rlV In the absence of viscous drag, zR would equal zI, which cor- responds to purely inertial rotation and is given by3* For the molecules considered here T~ is a maximum of 1-2 ps, and can be neglected. For less symmetrical species, three dif- fusion coefficients, D,, D,, D,, are needed to describe the rotation.The axis perpendicular to the molecular plane is denoted by x throughout this paper: the transition moment defines the z direction (see Scheme 1). In the most general case, five exponentials are needed to describe the decay of fluorescence ani~otropy,~~ but, if the transition moments for absorption and emission are in the same direction (as in all the measurements reported here), the time-dependence of r Table 1 Experimental and molecular parameters lifetime/ns excitation filter dimensions/nm at -150°C wavelength/nm cut-off/nm 22 2Y tetracene 4.9 440 470” 1.420 0.730 perylene 4.64 430 470 1.133 0.888 carbazole 13.2 338 365” 0.684 1.133 Li carbazolyl-26.2 370 400 1.133 0.684 Na DPA 4.6 555 590 1.408 0.704 Li DPPD 2.75 550 610 1.649 0.704 Li DPHT 2.34 630 665 1.890 0.704 ~~ a 10 nm bandpass interference filter.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 simplifies to r(t) = (0.2 + a)exp( -(6D + 2A)t) + (0.2 -a) x exp{ -(6D -2A)t) (6) where u = 0.3 D = (D,+ D,+ D,)/3 A = J(D: + 0,’+ DI -D, D,-D, D, -D,D,) Eqn.(4) represents the ‘stick’ limiting condition. The solvent is treated as a continuum and it is assumed that a thin layer of solvent moves with the solute. This approach is found to be satisfactory in many cases and especially for very large molecule^.^ However, molecular rotation in liquids is generally faster than predicted, especially when the rotor is comparable in size with the solvent molecule^.^^^^^ Such behaviour is described as ‘slip’: in the limiting case, there is no frictional drag and D depends only on the need to displace solvent: a sphere can rotate freely (rR= 2,) and so can a spheroid rotating round its symmetry axis. The consequences for rotation about other axes have been treated theoretically for spheroids36 and ellipsoid^.^ Rotation times also depend on the solvent: e.g.trans-stilbene rotates more r pidly in alcohols than in alkanes of the same vis~osity.~’ In some cases,22.3 9 -42 ‘saturation’ of the rotation time is observed at high viscosities; the effect can be very large, a factor of 50 in the polyhydric alcohol^.^' Such behaviour is described as ‘sub-slip’ and has been interpreted in terms of the molecular structure of the solvent:43 such large effects must reflect the strong solvent-solvent interaction, which can leave the solute in a cavity larger than its molecular dimensions. These results demonstrate the danger of using the macroscopic viscosity to describe microscopic motion. Perrin3’ extended eqn. (4) to ellipsoids, bodies with ellip- tical cross-sections and unequal hemi-axes (x, y, z), for the stick condition.Youngren and Acrivos3’ used numerical methods to calculate friction coefficients for ellipsoids in the slip case. We have used their results to calculate values of D,, D, and D, for the molecules used in this work. The anions were treated as bare ions though in fact they are loose (solvent-separated) ion pairs; it was assumed that they were in the all-trans conformation (see Discussion). All the molecules were treated as rectangular blocks of dimensions 2x x 2y x 22; molecular dimensions used are listed in Table 1. The molecular thickness was taken to be 340 pm; 2y and 22 were put equal to the maximum length and width. The dimensions were then scaled to give those of an ellipsoid of the same volume, i.e.8xyz = (4x/3)x’y’z’.Values of the com- ponents of D were substituted in eqn. (6)to give eqn. (7): r(t)= r,(O)exp -+ r,(O)exp -(7)L:l {::I[r,(O)+ r2(0)= 0.41. These calculated rR values are probably too small for propeller-shaped molecules like DPA etc. which will displace large volumes of solvent than ellipsoids of the same volume. (For this reason, the maximum rather than the average width was used in the calculations.) Results of the calculations are presented in Table 2. Also listed are rR values calculated for a sphere of the same volume. The viscosity of the liquid has been measured down to -75 OC5 which overlaps the range accessible to us, so this temperature was chosen for comparison of theory and experi- ment.Results A typical anisotropy decay is shown in Fig. 2. In all cases, the decay could be fitted satisfactorily (0.9 < x2 < 1.1) by a single exponential; the measured lifetime is equated with the rota- tional correlation time, T~.Values of r(0)were in the ranges: 0.2-0.24 (tetracene), 0.32-0.35 (perylene), 0.155-0.18 (carbazole), 0.13-0.16 (carbazolyl), 0.33 (DPA; only two measurements), 0.33-0.34 (DPPD), 0.30-0.33 (DPHT). Experimental rR values at -75 “C are listed in Table 2 for comparison with theoretical calculations. Though the decay times are small, they are consistent with the more accurate measurements at lower temperatures: this can be seen in Fig. 3-5 which show the temperature dependences of the quantity ‘R a Table 2 Rotational correlation times/ns for MTHF at -75 “C calculated ellipsoid experimental sphere ‘stick’ ‘slip’ ‘stick ’ r(0) TR tR r(0) 511 r(0) TR tetracene 0.23 0.124 0.265 0.305 0.328 0.382 0.099 0.095 0.630 0.018 0.215 perylene 0.33 0.116 0.258 0.003 0.397 0.354 0.461 0.291 0.109 0.043 0.329 carbazole” 0.16 0.135 0.198 0.299 0.233 0.400 0.075 0.101 0.376 Li carbazolyl- 0.13 - 0.439 - -0.198’ 0.400’ - 0.376’ - -0.1006 -0.075’ 0.3006 0.1506 Na DPA 0.33 0.278 0.254 0.400 0.605 0.007’ 0.061‘ 0.393’ 0.199‘ Li DPPD 0.33 0.432 0.297 0.400 0.860 0.006 0.081 0.394 0.257 Li DPHT 0.31 0.686 0.341 0.400 1.178 0.002 0.077 0.398 0.309 ~ ~ a Transition taken to be short-axis polarised.Predictions for long-axis polarised transition (see text). Extrapolated value (see text). J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 -1 I 0 7 4 h rlns Fig. 2 Decay of fluorescence anisotropy of perylene in MTHF at -120°C; (-), data; (-), fitted single exponential; (---), (-. -), cal-culated curves using 'stick ' and 'slip' assumptions, respectively Fitting the previous viscosity mea~urements~~~ to eqn. (1) gives : 162 log(q/kg m- s-') = -3.986 + T/K -81 (8) The data are shown in Fig. 6 together with some of our data for perylene which have been converted to viscosities using eqn. (3) and (4) and scaled by multiplication by a factor of 2.5. + 1','0 I 1 I 4 7 h 8 9 103K/T Fig.3 Temperature dependence of the decay of fluorescence anisot- ropy: experimental results and curves calculated from eqn. (8), scaled to fit at -100°C: +, x ,(-), perylene (two series of experiments); 0,(---), tetracene t</ , I '11 4 7 6 8 9 103KjT Fig. 5 As for Fig. 3: +, (-), Li+DPPD; 0,(---), LifDPHT;0,Na'DPA For comparison with the zRT data, interpolated values of the viscosity, (scaled to fit the data at -100°C) are plotted in Fig. 3-5 ;these quantities should be proportional according to eqn. (4). The fit is generally good except at the lowest tem- peratures. This discrepancy appears to be real, but, unfor- tunately, measurements in this region are difficult: zRis much larger than zF and the solvent is liable to crystallise suddenly and violently, usually breaking the cell.zF values for DPA, DPPD and DPHT increase as the tem- perature is reduced because the rate of skeletal twisting 7723decreases.**' For tetracene, perylene and carbazole at 20"C, lifetimes of 5.04, 5.10 and 13.9 ns, respectively, were obtained; the perylene value lies within the range 4.8 to 6.9 ns reported for a variety of the tetracene value is lower than the 6.4 ns quoted for cyclohexane. zF for car- bazolyl ion pairs showed a small increase on cooling (23.5 ns at +2O"C, 25.1 at -51 "C, 26.1 at -140"C), presumably the result of a temperature-dependent internal conversion process, but perylene and neutral carbazole both show a small decrease in zF.Non-radiative processes commonly decrease in rate with falling temperature, so this effect must be due to changes in the radiative rate, A. In the case of perylene, this can be ascribed to the dependence of A on the refractive inde~,~~-~~ but for carbazole the effect is too large, suggesting a change in the solvent perturbation with tem-perat ure (below). 10 -,' + ,,,+ + ,'+8-'+ -+ +,+' h I 6-+ ,' v) + ,,' c I E m Y+7-e-v m-4' 0 0' 0' 0 20 u) ho 80 4 , h 8 103K/T 1O~K/(T-81 Fig. 4 As for Fig. 3: +, (-), neutral carbazole; 0,(---), Li+ Fig. 6 Temperature dependence of the viscosity of MTHF; 0,this carbazolyl-work (perylene; scaled-see text); x ,ref. 5; +, ref. 6; (---), eqn. (8) J. CHEM.SOC. FARADAY TRANS., 1994, VOL. 90 Discussion Transitions The fluorescence transition of perylene is strongly allowed but that of carbazole is considerably weaker as is shown by their purely radiative lifetimes, 6.5 and 44.2 ns at 20°C. The first excited state of carbazole has been assigned as 1Lb;47 transitions from such states in alternant hydrocarbons are 'accidentally forbidden' and become allowed partly by inter- action with a symmetrical vibrations and partly by solvent perturbations, the Ham The former are temperature independent but the latter may well increase with falling tem- perat ure. The values of r(0) will be discussed further below, but it is clear from Table 2 that they are ca. 0.3 with exceptions such as carbazole and its ion.The polarisation of the fluorescence transition of carbazole is predominantly short-axis (i.e. through the nitrogen atom), but contains long-axis and out-of-plane components The transition in the anion has not been assigned, apparently, but it is likely to be similar in nature, since deprotonation does not directly involve the 7t electrons. Theoretical calculations for both long-axis and short-axis components are included in Table 2: in principle, anisotropy decay measurements could distinguish the two cases, but this is not possible in MTHF, given the generally poor agreement between experiment and theory. The observed low values of r(0)in both ion and neutral molecule are probably due to this mixed polarisation.Similar results for tetracene can be explained in the same way.22 Rotational Difhsion Anisotropy decay times and r(0) values calculated from eqn. (6) and the parameters listed in Table 1 are compared with experimental results in Table 2: the approximation of molec- ular shapes to ellipsoids must be borne in mind. It is imme- diately clear that the experimental zR for the neutral species are much less than the 'stick' values calculated for either ellipsoids or spheres. Perylene In Fig. 2 calculated curves are compared with experiment at -120.2 "C.While the stick curve is essentially single expo- nential, the decay is too slow by a factor of 4; the slip curve is closer in position but has the wrong shape. A number of trials were made with two exponentials, essentially varying the D,D,, ratio.We estimate that this ratio must be less than two to fit our data; though a small proportion of a slow decay would be hard to detect, it is noteworthy that one exponential sufficed at all temperatures except possibly the lowest. Weber first suggested that molecules such as perylene could rotate much faster in plane than out of plane, on the basis of careful steady-state measurements and studies of the effect of wavelength and of substituents." This was con-firmed by time-resolved measurements of the anisotropy, which showed the presence of two decays: values of the ratio D, D,, (out of plane in plane) of 28 in propylene glycol,' 10 & 1 in paraffinlg and glycerolZo and 6.5 & 0.3 in glycerol- water mixtures2' were obtained.It is surprising therefore that only one exponential is observed for MTHF. It appears that perylene rotates like a sphere; this implies that some solvent rotates with the large solute molecule (weakly bound, above and below the molecular plane), i.e. friction between solvent molecules is comparable with that between solute and solvent. This is not true for the hydrogen-bonded solvents used elsewhere or for a paraffin with chains much longer than the solute. Perylene gives r(0) values in agreement with those in the literature;'8-2' DPA and its vinylogues which also have strongly allowed transitions (no significant vibronic interaction) give similar values, significantly less than the theoretical value of 0.4.Zinslilg found that this difference was temperature dependent for perylene in paraffin as did Viovy for dimethylanthracene in glyceryl tripr~pionate.~~ Both authors ascribe the effect to libration but Christensen et aLZ1 have cast doubt on this interpretation, putting forward alter- native explanations. We observe no consistent variation with temperature. Tetracene Wirth and ChouZ2 observed 'sub-slip' behaviour and double exponential decay for tetracene in long-chain alcohols; the ratio of the D values was found to be temperature dependent. Our data fit a single exponential over the whole range. Stick behaviour rather than slip is predicted to give two exponen- tials (Table 2), but the values are close enough that dis- tinguishing them would be difficult. The difference between experiment and theory is less in this case.Carbazole The behaviour of the neutral molecule parallels that of the hydrocarbons, single exponential decay at a rate between stick and slip, where theory predicts two decays, though the decay times are close in the stick case. As expected the rota- tion time is considerably longer for the carbazolyl ion pair. On could regard this as a switch from slip to stick behaviour, but in the light of the above, it is simpler to suppose that the effective size of the ion is larger due to the solvation. The counter-ion has not been included in the calculations in Table 2: it is noteworthy that in this case, molecular rotation must involve considerable movement of the lithium ion and its solvation shell: it is believed to lie in the molecular plane,50 where it is some distance from the rotation axes involved ; this contrasts with DPA etc.where the counter-ion is at the centre of the rotor. DPA, DPPD and DPHT For these long molecules, with transitions aligned along the long axis, single-exponential decay is expected (Table 2). Unlike carbazolyl, their rotation rates are faster than the stick values. The ratio is not constant, i.e. DPHT rotates more slowly than DPA even after allowing for its size. This is surprising insofar as interaction with the solvent might be expected to decrease with molecular size, the charge being more delocalised. However, it must be recalled that the departure from ellipsoidal shape is large for these molecules.Viscosity Fig. 6 shows collected data for the viscosity of MTHF. The value of To = 81 K is largely determined by the low temperature6 data, of course. The scatter shows that there is considerable uncertainty in To. The high-temperature data are more precise, but their range is not adequate for accurate determination of To;taken alone, they give a best fit to eqn. (1) with To = 40 K. The temperature dependence of our own data (Fig. 3-5) agrees well with the value of 81 K though the fit is not exact and differs slightly between solutes. Dainton and Salmon4 quote a value of 75 K for To for MTHF, presumably obtained by fitting their reaction rate data. The glass transition temperature, 7, lies higher than it is a kinetic rather than an equilibrium phenomenon, the temperature at which flow becomes very slow on the laboratory timescale.This is commonly taken to be 10l2 kg ,-1 s-l P). Eqn. (8) gives < = 91 K. Kato et aL3 extrapolated the low temperature viscosity data6 to obtain < = 88 K. The empirical equation, eqn. (l), has been interpreted in terms of free volume theory;" the activation step is supposed to involve creation of a space into which movement can take J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 temperatures (T9 To)the discrepancy is small, but in the light of the results obtained here, it is more appropriate to combine eqn. (1)and (9) and differentiate to give place. More sophisticated theories have follo~ed;~~*~~-~~ in E' is the activation energy obtained by applying the Arrhe- particular, Adam and GibbsS2 discussed dielectic relaxation behaviour near the glass transition in terms of the entropy involved in solvent movements, pointing out that the number of molecules involved increases rapidly as the glassy state is approached; Kivelson and Kivel~on~~ have described the two types of relaxation behaviour (fast movements within a fixed potential and slower changes in the potential itself) which are observed experimentally.The apparent saturation behaviour at low temperatures (Fig. 3, 5) is interesting in this context: possibly a change in the solvent structure is occurring, leaving a larger cavity for solute motion.In common with most other worker^,'^-^ '*33-35 we find that the rotational correlation time follows the viscosity quite closely at high temperatures, even though the proportionality constants vary from system to system. The fit is not exact (Fig. 3-9, imply-ing that the free volume for molecular rotation is larger than for viscous flow. GoldsteinS3 has warned against the difficulties of inter- preting measurements near the glass transition, but, given the wide range of viscosity data now available for MTHF, the plots in Fig. 3-5 must be regarded as satisfactory, vindicating the use of eqn. (1). To can be regarded as the temperature at which motion of the second kind stops completely. Photo-isomerisat ion In fluid solutions at normal temperatures, singlet excited aryl-alkenes decay rapidly by twisting from the planar to the perpendicular form which then decays back to the ground state of the original species or its cis or trans isomer.Mea- surements of fluorescence lifetimes, zF,give the rate constant of this process as (l/zF -l/zo) where zo here is the lifetime at low temperatures or in a solid where rotation cannot occur. The behaviour of stilbene has been studied in great detail in recent years.g The role of solvent viscosity has received par- ticular attention',' and in some cases the intrinsic '-14718*54 and solvent barriers have been distinguished by comparing rates in different solvents at the same viscosity. The same picture is appropriate to DPA and related compounds. In the trans,trans form, the barriers are ca.15-30 kJ mol-': we have now studied several s~lvents'~'~*~~ with the aim of eluci-dating the role of the nature of the ion pairings; the role of the viscosity cannot yet be separated. Isomerisation from cis to trans is simpler, in some respects: there is no intrinsic barrier, so that twisting is probably a simple one-dimensional process : for trans-stilbene simultaneous rotation round the central bond and round the carbon-phenyl bond has been suggested.5 In the case of a reaction with an intrinsic energy barrier, Ei, a convenient simple relation between the rate constant and the viscosity can be derived from free volume theory:' 1,54 A( -$exp( $)k = (9) where a can be regarded as the ratio of the free volumes required for reaction and for viscous flow : observed values are typically in the range 0.1.13 For most work in this field, the temperature dependence of viscosity has been expressed by the Andrade equation, i.e.T, is put equal to zero. At high nius equation. For MTHF, the viscosity parameters give con- tributions from the second term in eqn. (10) of 6.8, 8.8, 14.7 and 86 kJ mol-' at 250, 200, 150 and 100 K, respectively (a = 1). When the transition-state region is a broad maximum on the potential-energy surface, crossing it can be regarded as a diffusive process and a will be large; when it is a sharp peak, a will be small.' Since MTHF is a 'good' solvating solvent, DPA and its derivatives generally form loose ion pairs, especially at reduced temperature^.'^ Usually the decay of the excited state gives linear Arrhenius plots with activation energies of ca.20-25 kJ mol-' and the rate becomes negligible below 150 K.' For stilbene, solvent variation, e.g. among the n-alkanes,'TS4 has made possible the separation of viscosity and intrinsic barriers. Studies of carbanions are limited by the sol- vation requirement; viscosity is likely to contribute to E' but the linear Arrhenius plots' suggest that its role is fairly small. Steeper, sometimes curved, plots which can be studied at lower temperatures are given by tight ion pairs;' they give linear 1/(T -To)plots but it is necessary to use other sol- vents for which viscosities are not available.In MTHF, 2-aza derivatives of DPA also give curved Arrhenius but their behaviour is complicated: the curved portion lies at higher temperatures than is predicted by eqn. (10). In this case, isomerisation or deactivation may involve inversion at the nitrogen rather than twisting. The solvent displacement will then be small and viscosity less important. Fluorescence from cispans DPA has not been observed. Experimental measurements even on cispans 2-methyl DPA are difficult; though substitution in the central position sta- bilises the cis,trans form relative to trans,trans, the fluores- cence of the latter predominates until very low temperatures are reached: some preliminary for the range -120 to -155"C are shown in Fig.7. The rate constant for isom- erisation is ca. 1 ns-' at -150 "C;for comparison, the rate of overall rotation (for DPA) has the same value at -104 "C. The linear relationship between the twisting rate of cispans 2-methylDPA and 1/(T-81) shows that Ei is negligi- ble in this case, paralleling the behaviour of cis-stilbene. The slope corresponds to 1.56 kJ mol-', i.e. a = 0.50, a typical 103K/(7-81) ' ' Fig. 7 Temperature dependence of the rate (ns-') of skeletal twist- ing of Li' 2-methylDPA in MTHF J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 result for rotational deactivation processes. [The use of eqn. (1) should be recalled; use of an Arrhenius fit in this region would give a smaller value of a.] Calculation of the absolute value of the rate of these pro- cesses is very dificult.13 A simple formula has been given by RappS8 l/k = 4nxyzq/f (1 1) x, y and z are here the hemi-axes of the rotating group.Taking the rotational force-constant, f, to be 40 kJ mol-' rad -',a value taken from semi-empirical calculation^,'^ gives a rate constant, k, of 4.3 x 10' s-l at 150 K, compared to the experimental value of 4.7 x lo9 s-'. Fitting the rate in this way would require an implausibly large f value. An alterna- tive approach is to regard A in eqn. (9) as the limiting rate in the gas phase. The value of 1.9 x 1013 s-l is considerably larger than the 3 x lo'* s-l observed for ~is-stilbene,'~ con-firming that the driving force for twisting is very large. Tight ion pairs in dimethyltetrahydrofuran' and some loose ion pairs in amine solvents23 give very large pre-exponential factors: in all these cases, it appears necessary to postulate a positive entropy of activation due to changes in solvation.The rates of bimolecular reactions have been related to vis- cosity in much the same way. A square-root relation is often .~found,60 i.e. 01 = 0.5. Kato et ~1 measured the rate of ion recombination in MTHF solutions after radiolysis over nine orders of magnitude. Replotting their results against 1/( T-81) gives a straight line, but the slope corresponds to a value of o! of 1.26 which is puzzling. It disagrees with the value of 0.5 found for similar measurements over a smaller range in parafin. Conclusion The synchrotron operated in single bunch mode is a very convenient source for the study of fluorescence and fluores- cence anisotropy decays down to 100 ps.Access time avail- able is very limited which has prevented us from accumulating the large numbers of counts required to better characterise the decays better. Nonetheless it appears that at temperatures above -130-140°C all our data fit well to single-exponential decays. The disagreement with theory sug- gests that the conventional hydrodynamic approach is not appropriate to MTHF. Very tentatively, we suggest that there is some very weak complex formation, resulting in a rotor which is more nearly spherical and which can 'slip' relative to the rest of the solvent, However, it is also clear, that if appropriately scaled, the macroscopic viscosity is a good guide to the temperature dependence of both overall and intramolecular rotation rates.At temperatures below -140"C, the anisotropy decays are faster than expected; in this region there is some evidence for two exponentials, but the results are more uncertain because the decay of anisot- ropy is slower than the fluorescence decays. It is interesting that in this region intramolecular rotation can be treated in terms of the viscosity while molecular rotation cannot: this must be due to the large driving force in the former case, much greater than the random forces of thermal motion. Our main aim has been to characterise the dynamic pro- cesses occurring in MTHF. It should be noted that we are dealing with a racemic mixture; possibly this leads to local structure at low temperatures.Previous workers have usually used solvents with an intrinsic structure, insofar as they consist of long chains or they are hydrogen bonded. Further work on ethereal solutions appears to be worthwhile. We thank the Science and Engineering Research Council for providing facilities at Daresbury and Dr. C.E. Oliver, and Dr. D.A. Shaw, Dr. M. Behan-Martin and other members of the Daresbury Laboratory staff for their assistance. References 1 M. R. Ronayne, J. P. Guarino and W. H. Hamill, J. Am. Chem. SOC.,1962,84,4230. 2 W. H. Hamill, in Radical Ions, ed. E. T. Kaiser and L. Kevan, Wiley-Interscience, New York, 1968; T. Shida, The Electronic Absorption Spectra of Radical Ions, Elsevier : Amsterdam, 1988.3 N. Kato, T. Miyazaki, K. Fueki, S. Miyata and Y. Kawai, J. Phys. Chem., 1984,88, 1445. 4 F. S. Dainton and G. A. Salmon, Proc. R. SOC.,A, 1965,285, 319. 5 D. Nicholls, C. Sutphen and M. Szwarc, J. Phys. Chem., 1968, 72, 1021. 6 A. C. Ling and J. E. Willard, J. Phys. Chem., 1968, 72, 1918. 7 A. J. Barlow, J. Lamb and A. J. Matheson, Proc. R. SOC., A, 1966,292,322. 8 S. S. Parmar, B. Brocklehurst and R. N. Young, J. Photochem., 1987,40, 121. B. Brocklehurst, R. N. Young and S. S. Parmar, J. Photochem. Photobiol., A, 1988,41, 167. 9 D. H. Waldeck, Chem. Rev., 1991,91,415; D. C. Todd and G. R. Fleming, J. Phys. Chem., 1993,97,269. 10 H. Stegemeyer, Ber.Bunsernges. Phys. Chem., 1968,72, 335. 11 D. Gegiou, S. Sharafy and K. A. Muszkat, J. Am. Chem. SOC., 1968, 90, 12; S. Sharafy and K. A. Muszkat, J. Am. Chem. SOC., 1971,93,4119. 12 G. Fischer, G. Seger, K. A. Muszkat and E. Fischer, J. Chem. SOC., Perkin Trans. 2, 1975, 1569. 13 B. Bagchi, Int. Rev. Phys. Chem., 1987,6, 1. 14 J. Saltiel and Y-P. Sun, J. Phys. Chem., 1989, 93, 6246; J. Saltiel, A. S. Waller, D. F. Sears and C. 2. Garrett, J. Phys. Chem., 1993, 97, 25 16. 15 Y-P. Sun, J. Saltiel, N. S. Park, E. A. Hoburg and D. H. Waldeck, J. Phys. Chem., 1991,95, 10336. 16 Time-Resolued Fluorescence Spectroscopy in Biochemistry and Biology, ed. R. B. Cundall and R. E. Dale, Plenum, New York, 1983, NATO AS1 Series A, vol. 69. 17 C. E.Oliver, R. N. Young and B. Brocklehurst, J. Photochem. Photobiol., A, 1993, 70, 17. 18 W. W. Mantulin and G. Weber, J. Chem. Phys., 1977,66,4092. 19 P. E. Zinsli, Chem. Phys., 1977,20,299. 20 M. D. Barkley, A. A. Kowalczyk and L. Brand, J. Chem. Phys., 1981, 75, 3581; L. B-A. Johansson, J. Karolin, H. Langhals, S. Reichherzer, N. V. Fiiner and K. Polborn, J. Chem. SOC., Faraday Trans., 1993,-89, 49. 21 R. L. Christensen, R.C. Drake and D. Phillips, J. Phys. Chem., 1986,90, 5960. 22 M. J. Wirth and S-H. Chou, J. Phys. Chem., 1991,%, 1786. 23 R. N. Young, C. E. Oliver and B. Brocklehurst, unpublished work. 24 S. Brenner and J. Klein, Isr. J. Chem., 1969, 7, 735. 25 L. M. Tolbert and M. E. Ogle, J. Am. Chem. SOC., 1989, 111, 5958. 26 R.Hacker, E. Kaufmann, P. v. R. Schleyer, W. Mahdi and H. Dietrich, Chem. Ber., 1987, 120, 1533. 27 K. Gregory, M. Bremer, W. Bauer, P. v. R. Schleyer, N. P. Lorenzen, J. Kopf and E. Weiss, Organometallics, 1990,9, 1485. 28 I. H. Munro, D. Shaw, G. R. Jones and M. M. Martin, Anal. Instrum., 1985,14,465; B. Brocklehurst, Chem. Br., 1987,23,853. 29 A. Einstein, Ann. Phys., Ser. 4, 1905, 17, 549, 1906, 19, 371. 30 F. Perrin, J. Phys. Radium, 1934,5497. 31 F. J. Bartoli and T. A. Litowitz, J. Chem. Phys., 1972,56,413. 32 T. J. Chuang and K. B. Eisenthal, J. Chem. Phys., 1972,57,5094. 33 D. Ben-Amotz and J. M. Drake, J. Chem. Phys., 1988,89, 1019. 34 D. R. Bauer, J. I. Brauman and R. Pecora, J. Am. Chem. SOC., 1974, %, 6840. 35 D. Kivelson and P.A. Madden, Annu. Rev. Phys. Chem., 1980, 31, 532; J. L. Dote, D. Kivelson and R. N. Schwartz, J. Phys. Chem., 1981,85,2169. 36 C-M. Hu and R. Zwanzig, J. Chem. Phys., 1974,6Q, 4354. 37 G. K. Youngren and A. Acrivos, J. Chem. Phys., 1975,63,3846. 38 S. K. Kim and G. R. Fleming, J. Phys. Chem., 1988,92,2168. 39 S. A. Rice and G. A. Kenney-Wallace, Chem. Phys., 1980, 47, 161. 40 D. H. Waldeck and G. R. Fleming, J. Phys. Chem., 1981, 85, 26 14. 41 R. S. Moog, M. D. Ediger, S. G. Boxer and M. D. Fayer, J. Phys. Chem., 1982,86,4694. 278 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 42 S. Canonica, A. A. Schmid and U. P. Wild, Chem. Phys. Lett., 1985,122, 529. 52 53 G. Adam and J. H. Gibbs, J. Chem. Phys., 1965,43,139. M. Goldstein, J. Chem. Phys., 1969,51, 3728. 43 44 D. Kivelson and S. K. Kivelson, J. Chem. Phys., 1989,90,4464. J. B. Birks, Photophysics of Organic Molecules, Wiley-Interscience, London, 1970. 54 S. P. Velsko and G. R. Fleming, J. Chem. Phys., 1982, 76, 3553; S. P. Velsko, D. H. Waldeck and G. R. Fleming, J. Chem. Phys., 1983,78, 249. 45 46 47 R. B. Cundall and L. C. Pereira, J. Chem. SOC., Faraday Trans. 2,1972,68,1152. S. Hirayama and D. Phillips, J. Photochem., 1980,12, 139. S. Siege1 and H. S. Judeikis, J. Phys. Chem., 1966, 70, 2205; C. A. Pinkham and S.C. Wait, J. Mol. Spectrosc., 1968,27, 326. 55 56 57 N. Agmon and R. Kosloff, J. Phys. Chem., 1987,91, 1988. J. W. Burley and R. N. Young, J. Chem. SOC., Perkin Trans. 2, 1972,835. R. N. Young, B. Brocklehurst and D. A. Shaw, Particles and Waves Series; Synchrotron Radiation and Dynamic Phenomena, 48 49 J. S. Ham, J. Chem. Phys., 1953, 21, 756; A. Nakajima, Bull. Chem. SOC.Jpn., 1971,44, 3272; K. Kalyanasundaram and J. K. Thomas, J. Am. Chem. SOC., 1977,99,2039. J. L. Viovy, J. Phys. Chem., 1985,89,5465. 58 59 60 ed. A. Beswick, Am. lnst. Phys., New York, 1992,474. W. Rapp, Chem. Phys. Lett., 1974,27, 187. B. 1. Greene and R. C. Farrow, J. Chem. Phys., 1983,78,3336. J. Fuller, M. Peteleski, D. Ruppel and M. Tomlinson, J. Phys. 50 H. W. Vos, C. MacLean and N. H. Velthorst, J. Chem. SOC., Chem., 1970,74,3066. Faraday Trans. 2, 1976,72,63. 51 M. H. Cohen and D. Turnbull, J. Chem. Phys., 1959,31, 1164. Paper 3/04982E; Received 17th August, 1993