Depolarized Rayleigh Spectroscopy Studies of Orientational Relaxation in Solutions of the Xylenes W. BEER AND ROBERT BY CHARLES PECORA" Department of Chemistry Stanford University Stanford California 94305 U.S.A. Received 17th September 1976 Depolarized Rayleigh spectroscopy measurements of orientational relaxation of the three xylenes in solution are presented. The viscosity dependences of the single molecule reorientation times are obtained from the directly measured collective reorientation times by varying the solution concentra- tion. It is found that within experimental error all three xylenes have the same single particle re- orientation time viscosity dependence Values of the effective static and dynamic correlation factors are however quite different for the three xylenes.Studies of the para-xylene-CBr4 complex are also presented. Measurements of the intensity and spectrum of depolarized scattered light may be used to obtain information about the dynamics of molecular reorientation of optically-anisotropic molecules in the liquid state. Among the quantities that may be studied are the collective reorientation times and their relation to single-particle reorientation times as well as the viscosity dependence of the single-molecule reorien- tation time~.l-~ In this article we present measurements of these quantities for the three xylenes in solution and as neat liquids. We also discuss complexes of para-xylene with CBr as an illustration of how information about chemical interactions of molecules in solution may be obtained from light scattering.Previous measurements have shown that the reorientation times determined by light scattering and various other techniques such as carbon-1 3 nuclear magnetic relaxation nuclear quadrupole relaxation and Raman scattering do not agree even when the time being measured is about the same molecular axis. The difference is attributable to the fact that light scattering measures a different reorientation time from these other techniques. If 5'" is a given component of a laboratory-fixed second rank tensor associated with the orientation of molecule i in the fluid then light scattering measures quantities associated with the time-correlation function of where the sum is over all relevant molecules in the fluid.Thus in light scattering information is obtained about the time correlation function Clearly if light scattering experiments are performed in dilute solution and the results extrapolated to infinite dilution the second term on the right hand side of t Present address E. I. Dupont De Nemours Experimental Station Wilmington Delaware 19898. CHARLES W. BEER AND ROBERT PECORA eqn (1) will be negligible and only the first term will contribute to the light scattering. The other techniques mentioned above usually measure quantities associated with (c(l)(t)c(l)(0))even in concentrated solutions and neat liquids. Thus only in the limit of infinite dilution would reorientation times obtained from light scattering results be expected to agree with those obtained from the other techniques.We call the relaxation time obtained from the light scattering measurement the “collective ” reorientation time and those of (c(l)(t)c(l)(O))the “single molecule ” reorientation times. The differences between these times are as may be seen from eqn (l) due to the time-displaced correlations between the orientations of different molecules (c(1)(oc(2)(o)). One experimental strategy for studying both the single-molecule and collective orientation times is to perform light scattering measurements to measure the collective time and other types of experiments to measure the single-molecule The difficulty with this procedure however is that for non-spherical molecules the different techniques often also measure reorientation rates about different molecular axes or more often differently weighted combinations of reorientation rates.In favourable circumstances this difficulty may be turned to advantage and several experiments may be performed to obtain reorientation rates about separate molecule- fixed axes.3 Recent observations have shown however that for certain classes of solutions of optically anisotropic molecules both the collective and single molecule reorientation times are linear functions of solution viscosity if the solute concentration is kept constant.1*2 The particular solvent used makes little difference to the measured reorientation times. Thus by performing light scattering measurements of the collective reorientation time as a function of viscosity for a series of concentrations and then extrapolating to infinite dilution the viscosity dependence of the single- molecule reorientation time may be obtained.Since the single molecule time depends very weakly on solute concentration the single-molecule reorientation time in the neat liquid (or concentrated solutions) could then be estimated from knowledge of the solution viscosities. In order to interpret the results of our experiments on the xylenes we shall use a simplified language first developed to interpret experiments on reorientation of sym- metric top molecules.6 The collective reorientation time zLs of the molecular sym- metry axis is related to the single molecule time z, about this same axis by the relation wherefand g are respectively known as the static and dynamic orientation correlation factors.The quantityfis a measure of the tendency of the molecular axes of a pair of molecules to be aligned parallel (f positive) or perpendicular (fnegative). It is proportional to (~c1)(0)~(2)(O)) mentioned in eqn (1) above. The quantity f may be measured independently of zLsby studying the integrated depolarized intensity IHv as a function of concentration. I& is given by where n is the refractive index of the solution and p is the molecular optical aniso-tr~py.~ Spectral studies at infinite dilution then give z, (since zLs= z,J and integrated intensity studies [eqn (3)] give$ The dynamic correlation factor g may be estimated from eqn (2). DEPOLARIZED RAYLEIGH SPECTROSCOPY STUDIES Since the xylenes are not symmetric top molecules the values of f and g obtained from this procedure should be treated as experimental parameters that describe differences between zLs and qP.A more complete theoretical treatment for asymmetric tops is simple to perform but contains many parameters and is thus difficult to compare with experiment. Our main object however is to obtain the viscosity dependences of the single molecule reorientation times. This objective is not affected by uncertainties in the physical interpretation off and g. EXPERIMENTAL All spectra were recorded using a 488081 laser source and a piezoelectrically scanned Fabry-Perot interferometer described previously.2 The xylenes used in this study were either obtained from Aldrich (0-and m-xylene 99%pure) or MCB (p-xylene).The xylenes were distilled prior to use. The solvents used in this study were isopentane (reagent grade) cyclohexane and carbon tetrachloride (spectroquality grade) and cyclo-octane (distilled prior to use). The solutions were prepared on a volume-to-volume basis and fdtered through 0.2 Alpha Metricel filters to remove dust. Viscosities were measured using a Cannon-Ubbelohde viscometer thermostatted in a constant temperature bath. The tempera- tures at which the individual spectra were obtained were recorded and the viscosities of the solutions were determined at the same temperature. All measurements were made at 21.5 f2 "C. Total intensities were measured for the neat xylenes and their solutions using a method described previ~usly.~ Carbon tetrachloride which gives a much lower depolarized back- ground than most hydrocarbon solvents was used as the solvent in the intensity measurements.The measured intensities were corrected to remove the contribution from collision-induced s~attering.~ The dependence of the total intensity upon the refractive index of the solution was also taken into account using eqn (3).' The p-xylene-CBr4 complex was prepared by heating equimolar portions of CBr (MCB sublimed) and p-xylene until the CBr dissolved. The solution solidified upon cooling yielding the solid complex which was used to prepare the solutions used in this study. Since CBr4 is unstable to sunlight solutions were prepared and used as quickly as possible. RESULTS The recorded spectra were digitized and fitted to a single Lorentzian plus a base-line with a nonlinear least squares program.8 The half-width at half-height found by the program was then corrected for instrumental broadening and used to deter- mine zLs.Plots of zLs against solution viscosity for 0- m-,and p-xylene are shown in fig. 1,2 and 3. The line-width and zLsfor all three xylenes were found to depend upon the concentration of the xylene in solution as well as the viscosity of the solution. This is especially apparent for p-xylene as shown in fig. 3. TABLEME MEASURED AND DERIVED QUANTITLESFOR THE NEAT XYLENES u-x ylene rn-x ylene p-xylene dCP" 0.769 0.594 0.638 %SIPS 10.10 7.70 1 1.06 single particle slope C,,/ps cp-l single particle intercept z',od/ps single particle reorientation time %,IPS fN gN 6.57 rt 0.13 2.05 & 0.09 7.10 rt 0.14 0.03 f0.13 -0.27 & 0.09 6.62 f0 33 2.05 f0.03 5.98 f0.20 -0.31 f0.10 -0.46 -f 0.09 6.79 f0.30 1.99 f0.09 6.32 f0.21 0.68 f 0.15 -0.04 & 0.11 a Measured at 23.5 "Cfor 0-and m-xylene 21 "C for p-xylene.* zLsmeasurement error estimate is &S%. CHARLES W. BEER AND ROBERT PECORA The total intensity data (corrected for collision-induced scattering and refractive index dependence) were fitted to a parabolic equation as a function of concentration [eqn (3)]. The regression coefficients were then used to determine.fN for the neat xylenes and their solutions. The total intensity data for the three xylenes are shown in fig. 4 and the values offlv are given in table 1.The quantity z, has been found to be a linear function of viscosity q and is given by1 =sp - G,V 3-z\?* (4) The single molecule slope Csp,for each xylene was found from the experimentally determined slopes of fig. 1 2 and 3 as follows for p-xylene where most of the concentration dependence of the slope was believed to arise from fN,the experi-I 1 8 1" I "'1 I. $1 0 0.5 1.0 1.5 q/cP FIG.1.-Collective reorientation time 7 against solution viscosity for ortho-xylene. 0 15% (v/v) 0-xylene 0 30% o-xylene 0 50% o-xylene A 70% o-xylene x 85% o-xylene + neat o-xylene. 0 0.5 1.o 1.5 q/cP FIG.2.-Collective reorientation time 7 against solution viscosity for rneta-xylene. Symbolsdenote the same concentrations as in fig. 1. DEPOLARIZED RAYLEIGH SPECTROSCOPY STUDIES ,-~.~--,-,-..,-,-I-I* 0 05 1 .o 1.5 IpP FIG.3.-ColIective reorientation time z against solution viscosity for para-xylene.010%p-xylene 0 20%p-xylene 030%p-xylene V 45%p-xylene 0 60%p-xylene A 80%p-xylene x 90%p-xylene, +neat p-xylene. l,,,,,,,,, 20 4 0 60 80 100 % xylene (v/v) FIG.4.4ntegrated intensity against % xylene (v/v) Elp-xylene 0o-xylene and A m-xylene. mentally determined slopes were fitted as a function of concentration to a straight line 11. -1 * . .1 1 1 .1 1 111 1. PY least squares. ine intercept was taKen to pe tne single molecule slope ana is given in table 1. For 0-and m-xylene,fN is either nearly zero or negative. However the slopes of the lines in fig. 1 and 2 increase with concentration indicating that gN is fairly large and negative.Hence a' linear extrapolation to zero concentration is not justified. To obtain an accurate extrapolation for Cspfor o-and rn-xylene zLs/(l + fN)was calciilated and the Tz,,/ll 4-fN\. viscnsitvl data were fitted tn R straight line CHARLES W. BEER AND ROBERT PECORA by least squares. Plots of zLs/(l +fN) against viscosity for m-and p-xylene are shown in fig. 5 and 6. All of the p-xylene data regardless of concentration fit a single line of slope 6.97 0.19 ps cP-l to within experimental error. This is in good agreement with the value of 6.79 5 0.30 ps cP-l given in table 1 thus reinforcing our earlier hypothesis that most of the concentration dependence of Csp for p-xylene arises from 1 +flv.For 0-and m-xylene the reciprocals of the slopes of zLs/(1 +flv) against q predicted by least squares were plotted as a function of concentration. The reciprocals of the intercepts predicted by least squares analyses are the single molecule slopes which are given in table 1 for 0-and rn-xylene. The values of the single molecule slopes for the three xylenes agree with one another to within experimental error. The values of the zero viscosity intercepts z(O) in fig. 1,2 and 3 do not exhibit much concentration dependence hence we took the variance-weighted average as z:? for 0 0.5 1.0 1.5 q/cP FIG.S.-z/( 1 +fN)against solutionviscosity for meta-xylene. Symbols denote the concentrations asin fig. 2. i,,,,,,,,,,,,,,,~,,, 0 0.5 1.0 1.5 2.0 ?) /cP FIG.6.-2 /(1 +fN)against solution viscosity forp-xylene symbols denote the same concentrations as in fig.3.DEPOLARIZED RAYLEIGH SPECTROSCOPY STUDIES each xylene. These values which are listed in table 1 agree to within experimental error. Using the values of Cspand of table 1 and measured values of the viscosi- ties allows one to calculate z, for the neat xylenes and their solutions. The zsp values for the neat xylenes are listed in table 1 ; differences between the values reflect differences in the viscosities of the neat xylenes. The gN for the neat xylenes and their solutions are calculated from zsp, fN and measured values of zLs,using eqn (2). The values of gN for the neat xylenes are listed in table 1. The value of gN for neat p-xylene is nearly zero while the value for neat rn-xylene is negative and has the largest magnitude yet observed for a neat liquid.The spectra of the p-xylene-CBr complexes were fitted to a single Lorentzian. The solutions used in this study contained either 11 %p-xylene (v/v) at a 1 :1 p-xylene/-CBr molar ratio or 23% p-xylene (v/v) at a 2 1 p-xylene/CBr molar ratio. A plot of zLs against y for the 11 % p-xylene (1 :1 molar ratio) and 23% p-xylene (2 1 molar ratio) solutions is shown in fig. 7. For comparison the least squares lines for 0 0.5 1.0 1.5 2.0 q fCP FIG.ir.-Collective reorientation time z against solution viscosity for p-xylene-CBr solutions and p-xylene solutions. 0 1 :1 p-xylene-CBr4 (1 1% (v/v) p-xylene) 0 2:1 p-xylene-CBr4 (23% (v/v) p-xylene,--10%p-xylene,-.--20% p-xylene.the 10% and 20%p-xylene solutions of fig. 3 are also included (dashed lines). The slopes and intercepts of the 11 % and 23 %p-xylene-CBr solutions and the 10% and 20%p-xylene solutions are given in table 2. The slopes and intercepts of thep-xylene- CBr solutions clearly differ from those of the p-xylene solutions at comparable concentration. The difference is particularly striking in the case of the 11 % (1 :1) p-xylene-CBr solution as compared with the 10% p-xylene solution. As more p-xylene is added the slope and intercept of the 23 % (2 1)p-xylene-CBr solution become quite similar to those of the 20%p-xylene solution. These observations suggest the pre- sence of a long-lived 1 :1 complex formed between p-xylene and CBr in solution.* * In fitting the 1 :1 p-xylene-CBr4 solutions to a single Lorentzian we assumed that the complex remains 100%associated in solution.This assumption may not be unreasonable since it is possible quantitatively to sublime the solid complex indicating that it remains associated in the gas phase. CHARLES W. BEER AND ROBERT PECORA 2.-Vrscosm DEPENDENCEOF SOLUTIONS OF p-XYLENE TABLE AND OF p-m~m-CBr,COMPLEXES slope/ps cP1 intercept /ps ~ ~ ~~ ~ ~~~ ~~ ~~ 1 :1 p-xylene-CBr [11% p-xylene (v/v)] 2:1 p-xylene-CBr [23% p-xylene (v/v)]10%p-xylene (vlv) 20%p-xylene (v/v) 4.80 0.31 7.35 f 0.11 8.57 f.0.36 7.60 f 0.22 6.80 f 0.28 3.26 f 0.16 1.78 f 0.14 1.99 f 029 When a second mole of p-xylene is added as in the 2 1p-xylene-CBr case the slope and intercept take on values intermediate between those of the 1:1p-xylene-CBr case and the 20%p-xylene solution.This implies that the second mole of p-xylene does not interact appreciably with the complex already in solution and we simply observe the average linewidth. Had we performed a two Lorentzian fit at the proper viscosity we might have observed two Lorentzians a narrow one corresponding to the 1:1 complex in solution and a broader one corresponding to the free xylene. DISCUSSION The collective reorientation times of the three xylenes in concentrated solution or the neat liquid have very different viscosity dependences while the single molecule times have identical viscosity dependences within experimental error. We note that the collective time is always greater than the single molecule time.The molecular shapes and sizes are apparently not different enough to give rise to appreciable differences in the single molecule viscosity dependence^,^ but the inter- actions between the xylenes are sufficiently different to give rise to different fand g values. Since the xylenes are not symmetric tops and there are uncertainties as to the proper refractive index correction to the depolarized intensities these fand g values must be cautiously interpreted. More data are needed to clarify these points. The fact that the xylene with no electric dipole moment para-xylene has the largest value offN while that with the largest dipole moment has fN N” 0 probably means that dipolar forces are not the dominant influence in determining the orienta- tional correlations in these liquids.It is probable that the molecular shape and hence the short range repulsive interactions are the dominant influence. Para-xylene the most symmetrical molecule has the greatest tendency to orient with the axes passing through the methyl substituents parallel. This work was supported by a grant from the National Science Foundation (USA). We wish to thank Mr. Jason Chang for performing the viscosity measurements and Dr. Q.-H. Lao for performing some of the integrated intensity measurements. G. R. Alms,D. R. Bauer J. I. Brauman and R. Pecora J. Chem. Phys. 1973,58,5570. G. R. Alms D. R. Bauer J. I. Brauman and R. Pecora J. Chem. Phys. 1973,59,5310,5321. D.R. Bauer G. R. Alms J. I. Brauman and R. Pecora J. Chem. Phys. 1974,61,2255. ‘D. R. Bauer J. I. Brauman and R. Pecora J. Amer. Chem. SOC.,1974,96 6840. ’D. R. Bauer J. I. Brauman and R. Pecora J. Chem. Phys. 1975,63 53. T.Keyes and D. Kivelson J. Chem. Phys. 1972,56 1057. ’The refractive index contribution to IHvis currently a matter of great controversy. In eqn (3) we have used an especially simple form for this factor so that caution must be exercised in interpreting the values off obtained. See for example A. K. Burnham G. R. Alms and W. H. Flygare J. Chem. Phys. 1975,62,3289; T. Keyes J. Chem. Phys. 1975,63,815; G. D. Patterson J. Chem. Phys. 1975 63,4032. R. I. Shrager MODELAIDE A Computer Graphics Program for Evaluation of Mathematical Models Tech. Rep. No. 5 (U.S.Department of Health Education and Welfare 1970).