118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. 118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions any particular point on the rigid surface becoming in turn negative neutral and positive these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Ultra-Violet Polarization Ratios in Anthracene-Tetracene Mixed Crystals BY C.D. AKON AND D. P. CRAIG William Ramsay and Ralph Forster Laboratories University College London Received 31st August 1966 The visible absorption and emission spectra of tetracene in anthracene host crystal have been re-investigated and values of polarization ratio and crystal intensification factors recorded with the help of measured crystal thickness and tetracene concentration. The results are compared with theoretical expectations based on solution oscillator strengths and estimates of higher transition multipoles. The trend is correctly accounted for and the agreement for polarization ratios and intensification factors is reasonably good. Experiments on mixed crystals in which a host molecule is replaced by a guest with the same orientation of axes are of importance for theories of intermolecular inter- actions in molecular crystals.Difficulties over the treatment of electromagnetic retardation of the dipole-dipole interactions which are severe in pure crystals appear in mixed crystals in a much weakened form and there are experimental advantages from the fact that measurements can be made with relatively thick crystals in which the guest is present in high dilution. Mixed crystals of tetracene in anthracene provide a favourable example because the ultra-violet spectra of both host and guest are well known and adequate theoretical models are available. Advances in technique have made it necessary to record new measurements of the polarization properties of fluorescence and absorption in these systems.Some of the present results have already been briefly reported in part 1 and compared with previously available values3 The host anthracene crystals belong to space group P21/a and both fluorescence and absorption are measured with the electric vector of the light parallel and per- pendicular to the b crystal axis and the direction of propagation perpendicular to the ab plane. The extinction coefficient in absorption is different for the two directions of polarization of the light. The polarization ratio is defined as PR(b/a) = where ~b and are extinction coefficients for the band maxima with light polarized parallel and perpendicular to the b crystal axis. Similarly in fluorescence PR(b/a) = &/Ea where E is the intensity of the light emitted with the indicated polarization directions.Corresponding quantities integrated over the whole bands are of more fundamental significance. The definitions are then modified by replacing E or E by S&(ij)dij or SE(ij)dij where i j is the energy of absorption or fluorescence. In absorption the polarization ratio is then the ratio of oscillator strengths for absorption of the two electric vector directions of the light. With the assumptions that tetracene replaces anthracene by a simple substitution at a lattice site and that the directions of the corresponding molecular axes are exactly preserved we may calculate the oriented-gas polarization ratio for a transition of any given molecular polarization property. For the first absorption system of tetracene in which the absorbed light is polarized parallel to the shorter in-plane molecular axis the oriented-gas polarization ratio is 7.7 1 with the stronger com- ponent along the b crystal axis.Evidence in support of the assumption that the mixed 56 C. D. AKON AND D. P . CRAIG 57 crystal of tetracene in anthracene forms by precise molecular substitution is lacking but in a number of other and similar mixed crystals the correctness of the assumption has been shown by spin resonance studies of the triplet state of the impurity molecule.3 Measurements of polarization ratios for ultra-violet absorption and fluorescence give values different from the oriented-gas ratio both in pure and mixed crystals and the character and extent of these departures from expectation are the subject of the present investigation. EXPERIMENTAL The spectral measurements were made with a specially constructed single-beam recording spectrophotometer based on a Hilger-Miiller monochromator with photo-multiplier detection.Fluorescence spectra were recorded continuously across the spectrum but in absorption were obtained with point-by-point measurements. The device as a whole was linear with respect to light intensity within the limits used. The apparatus was calibrated in spectral response with a standard light source. Light was polarized by passage through a Glan prism with collimation to ensure that the divergence of the light beam was less than 4" of arc. The purity of the emerging polarized light was checked by the insertion of an accurately oriented second polarizing prism. Mixed single crystals were grown from dimethyl formamide by the method of Lipsett 4 by adding about 10-3 mole of tetracene for each mole of anthracene in solution.The anthracene used was B.D.H. blue fluorescence-grade zone-refined in 70 passes ; tetracene was repeatedly re-crystallized from benzene. Its extinction coefficient in cyclohexane at 275 mp was found to be 2.94 f0.05 x 105 in excellent agreement with a recent measurement in dioxane.5 Earlier literature reports invariably give a lower extinction coefficient probably on account of oxygen contamination. The crystals used were all of approximately the same thickness and were free from imperfections under microscopic examination. All had developed ub crystal faces. Crystal thickness was measured from the difference in height between the focal planes at the upper and lower surfaces of the crystal measured microscopically and corrected to true thickness using the refractive indices of anthracene of Sundararajan.6 Crystals about 200 p thick were used throughout the thickness measurement being accurate to about 5 %.The tetracene concentration was estimated spectrophotometrically by dissolving a known mass of the crystal in cyclohexane and measuring the optical densities of the solution at 310 and 275 mp. From the values of the extinction coefficients of tetracene and anthracene at the two wavelengths the percentage tetracene to anthracene can be calculated (for anthracene E at 275 mp 3-08 f 0 . 1 5 ~ 102 and at 310 mp 1-26 &O-04 x 103 ; for tetracene E at 275 mp as already quoted and at 310 mp 6 1/50 E of tetracene at 275 mp). The concentrations so found are accurate to about f8 %.Otherwise measurements of fluorescence and ab- sorption polarization ratios were made by standard methods. The polarizing prism and other optical components were not moved during the experiments. In order to eliminate errors due to polarization discrimination within the optics different polarization directions were observed by rotating the crystal between runs through 90" on a microscope stage. RESULTS A typical absorption spectrum is shown in fig. 1 and a table of results in table 1. The values quoted in table 1 are means of results obtained on two crystals each measured four times. The imperfect agreement between values obtained from band maxima and integrated band areas is mainly to be ascribed to the difficulty of allowing for background absorption which was troublesome even in apparently perfect crystals.The ratios of extinction coefficients measured at band maxima are therefore probably the more reliable. Values at 430mp are the least satisfactory on account of the absorption tail of the anthracene host crystal. The results in table 1 are compared with those of Choudhury and Ganguly2 for &b. The new values are higher; the agreement for the weaker absorption in the direction is within 10-20 % in extinction 58 ULTRA-VIOLET POLARIZATION I N CRYSTALS coefficient. Probably Choudhury and Ganguly's values were low on account of penetration of the crystal by a small component of light with the " wrong " polariza- tion. This can have a large effect on measurements of the intensities of strongly absorbing systems and must be avoided by rigorous experimental precautions to ensure that the incoming light is completely polarized._- 4 0 $-r h 3.0 3 4 73 2 0 0 .- $-r n I 0 0 2 2 0 0 0 23000 2 4 0 0 0 20000 21000 frequency (cm-1) FIG. 1 .-Typical absorption spectrum of tetracene in anthracene host crystal. Tetracene concentra- tion 1-03 x 10-3 mole/mole &8 % ; crystal thickness 176 p. TABLE 1 .-ABSORPTION BY TETRACENE IN ANTHRACENE SINGLE CRYSTAL l(w) v(cm-1) 'Xt fb't 'bIEa fblf 490 20,410 2 8 8 x 104 (2.23 x 104) 0.024 4-0 3.6 459 21,790 2-27 x 104 (1.72X 104) 0.023 3.9 3.7 430 23,260 1 . 0 5 ~ 104 ( 1 . 1 5 ~ 104) 0.012 3.1 3.1 * The uncertainty in the extinction coefficients and oscillator strengths is about f 12 %. Polariza- tion ratios in which the errors due to crystal thickness and concentration measurements do not arise should be better than A10 %.Bracketed values are those of Choudhury and Ganguly.2 ** oscillator strength. j- Values revised from those given in a preliminary communication 1 to take account of new values of extinction coefficients of rigorously oxygen-free anthracene solution on which the estimation of crystal concentration depends. We are indebted to Dr. Gad Fischer for new measurements. 0 il - 17000 18000 19000 20000 2lOOO frequency (cm-1) PIG. 2.-Fluorescence emission spectrum of tetracene in anthraame host. C. D. AKON AND D. P . CRAIG 59 Fig. 2 and table 2 show the results obtained in fluorescence. The values quoted are means of a large number of determinations carried out on several different crystals. A comparison with the results of Choudhury and Ganguly given in table 2 discloses values that are lower and closer to those obtained in absorption.TABLE 2.-FLUORESCENCE OF TETRACENE IN ANTHRACENE CRYSTAL mw) v(cm-1) EblE $Ebdvl$E,dv 532 18,800 4.6 f0-2 4.7 A10.2 (5.2) 57 1 17,510 5.0 f0.2 5.6 f0.2 (5.7) 495 20,200 4.4 f0.2 ** 4-9f0.2 ** (5.7) * ratio of maximum intensities. ** affected by re-absorption ; bracketed values are those of Choudhury and Ganguly.2 COMPARISON WITH THEORY A general understanding of the results may be had with the help of theoretical studies of the mixing of states of the guest molecule with those of the host by inter- molecular forces.7-9 Let us suppose that the guest-host interactions are the same as those of host and host implying not only accurate alignment of the guest on a site left vacant by a host molecule but also equal host and guest transition moments for corresponding transitions.Then if w is the difference between the excitation energy of the lowest transitions of guest and host i.e. the trap depth the transition energies in the mixed crystal are given by the values of E solving eqn. (l) where N is the number of lattice sites in the finite crystal block used to calculate the pure host energy spectrum e&) k being the wave vector. The N sites in the mixed crystal are occupied by N - 1 host molecules and one guest. The lowest of the energy levels from eqn. (1) applies to an excitation essentially localized in the guest (trap level) and the other solutions apply to delocalized or free excitons in the host. Presently we are concerned only with the trap level here well separated from all the others.We now re-write eqn. (1) with the energy variable e referring to the centre of gravity of the host band er where e(k) = e' + I&) 4 In expressions (2) Vpg is the interaction energy between the guest molecule at site p and hosts at sites q. For the trap level assumed widely separated from the host band we expand in powers of Z&)/e W = 1 - -z{ 1 + I@)/e + (I(k)/e)2 + . . .>. Ne k (3) Application of the closure properties of sums over the wave vector k gives for the leading term e = w+CVk/e+. . . which may be written approximately for large e e = w+cV&/w+. . . 4 4 (4) 60 ULTRA-VIOLET POLARIZATION I N CRYSTALS This agrees with the result of a straightforward application of perturbation theory in ref. (9) but depends on the assumed equality of the host-guest and host-host inter- actions.In the limit of perturbation theory result (4) applies with no such restriction. The appearance of the sum of squared interactions in expression (4) shows that the host-guest coupling falls off rapidly with distance and retardation effects can be neglected. For the same reason however consideration of higher multipole inter- actions should be included a problem not considered in earlier work. The calculation of polarization ratio depends upon the wave function for the guest molecule. These are obtained as in ref. (9) by consideration of the mixing of the first two excited states of the host with the guest. In table 3 the results of calculations are compared with experimental results ; the dipole calculations are those of ref.(9) while the effects of including higher multipole moments have been newly worked out by Dr. T. Thirunamachandran.10 Table 3 includes values for the intensiJication factors not so far defined. They are the ratios of the measured oscillator strengths to those calculated from the solution spectrum with the oriented gas assumption. They are thus indices of the degree to which intensity transfers are induced between different free molecule transitions under the influence of intermolecular forces. They depend upon the measurement of absolute absorption strengths in the crystal and are less accurately known than the ratio of measured intensities given by the polarization ratio. TABLE 3 .-CALCULATED AND EXPERIMENTAL POLARIZATION RATIOS AND INTENSIFICATION FACTORS PR PR 1 1 1 member (expt.1 pR (calc.A)* (calc. B)* (exp t .I (calc. A) (calc. B)* n = O 3.6 2.77 4.17 2.2 1.7 2-36 n = 1 3.7 2-68 4-10 1-5 1.5 2.42 n = 2 3.1 2.57 4.0 1.8 1.8 2.50 * calculation A based upon solution values of transition dipole moment and zero values of calculation B solution values of transition dipole moment and values of tetracene octupole progression higher multipoles. moment to fit the crystal spectrum of pure tetracene viz. 01 = 4eA3 03s = - 130eA3. t see table 1. The experimental intensification factors in table 3 have been calculated from the crystal intensities in table 1 and solution values of oscillator strengths for the successive absorption maxima of 0.0291 0.0398 and 0.0224. The experimental results fall between those calculated on the basis of purely dipole coupling and the basis including realistic values of higher moments.The agreement is generally satisfactory while however not favouring one or other basis decisively. The work has been sponsored in part by Air Force Cambridge Research Labora- tories OAR through the European Office of Aerospace Research (OAR) United States Air Force. C . D. A. acknowledges the award of a postgraduate travelling Fellowship by Messrs. I.C.I.A.N.Z. 1 C. D. Akon and D. P. Craig J. Chem. Phys. 1964,41,4000. 2N. K. Choudhury and S. C. Ganguly Proc. Roy. SOC. A 1960,259,419. 3 C. A. Hutchison and B. W. Mangum J. Chem. Phys. 1961,34,908. 4 F. R. Lipsett Can. J. Phys. 1957 35 284. 5 R. S. Becker I. S. Sin& and E. A. Jackson J. Chem. Phys. 1963,38,2144. 6 I. K. S. Sundararajan Z. Krist. 1936,93 238. 7 G. F. Koster and J. C. Slater Phys. Reus. 1954 95 1167. * D. P. Craig and M. R. Philpott Proc. Roy. SOC. A 1966 293,213. 9 D. P. Craig and T. Thirunamachandran Proc. Roy. Suc. A 1963,271,207. 10 T. Thirunamachandran 1966 private communication.