J. C. POWERS, J R . , W. R. HELLER,J KUMA~VOTO, A N D l V E. DONATH
1004 HMaq)
+ -\"-(as)
=
%.-(as)
+ HL(aq)
(3)
where subscripts s and u indicate substituted and unsubstituted phenol Previous investigations'? have shown t h a t AH3' may be expressed as the sum of two terms representing solute-solvent interactions (AHext) and "internal" effects These considerations have led to the equation AH?' = A N , , t
+ j3AS3"
( B = 280")
(1)
for reactions of type 3 Experimental enthalpy and entropy changes are represented by AH3' and ASj' while A H , , t represents the part of the total AH3' that is associated with breaking and forming 0-H bonds as affected by resonance, inductive effects, etc Combination of 4 with AF,' = AH3' - 7'5S3' leads to AF3" = 1 + ( ~ 3 - T,AS," ~ _ _ and t.hen, because
(P
(5)
AHd
.1H,,t
-
7Xs3'
------
- be explained by assuming t h a t a Stark shift occurs. % . shift of 12 c m . - ' a t 9 X 1Oj v . / c m . is observed on t h e band edge a t 6800 b.,a n d this corresponds t o an actual shift of 15 cm - l when an intensity change correction is applied. A method for treating d a t a t o determine true band shifts in the presence of a simultaneous change in intensity is derived.
Phenol blue (I) has been of interest for some time because of the sensitivity of the position of its absorption "CH, N q - J - N ~ O
I
maximum to the polarity of a solvent. Brooker' found the maximum to be a t 5520 fL. in cyclohexane and 6680 A. in water. He rationalized this effect as due to a lowering of energy of the charged resonance forms, 11, in a more polar solvent resulting in increased resonance stabilization of the molecule. Bayliss and McRae? and Platt3 have used this concept of solvent(1) L. G. S Brooker and R H . Sprague, J . A m . Chem. SOC.,63, 3214 (1941). (2) S S Bayliss and E. G . McRae, J , Phys. Chem., 68, 1002 (1954). (3) J , R . P l a t t , J . Chem Phys., 2 6 , 80 (1956).
March 20. 1964
STARKEFFECTOF PHENOL BLUE
1005
I \ Fig. 1.-Randoin
+.O
dipoles in a unidirectional field.
solute dipole interactions to account for general solvent effects in spectra. Brooker was unable to correlate his data with a macroscopic solvent property (the dielectric constant), and later measurements by LeKosen and Reid4 showed that the effect of solvent could not be correlated with the index of refraction of the solvent. rl general theory of solvent effects on electronic spectra has been worked out by O o ~ h i k a ,Longuet~ Higgins,fi and McRae' by means of perturbation theory. (Here the solvent field interaction with the solute dipoles is taken as the perturbation.) McRae7 was able to fit the existing data for phenol blue in relatively nonpolar solvents by an equation involving only first-order corrections; he estimated the excited state dipole moment to be between i . 5 and 9.1 D . , an increase of about 2.3 D. from the reported ground state8 value of 3.SO D. Recently, Kosowerg has shown that the solvent effects on the position of the maximum in phenol blue correlate with Z,Io a universal solvent parameter, and he estimated the dipole moment in the first excited state of phenol blue to be a t least 10.2 D. in polar solvents. Figure 1 shows schematically how the energy of a molecular lexrel with fixed dipole moment varies with orientation when an external electric field is applied. The effect of an electric field on an isolated, rigidly held dye molecule (methyl red) has been recently reported. ' I In that study, an electrochromic shift of the absorption spectrum was observed and the hypothesis offered t h a t the shift was due to changes in electronic polarizability between the ground and excited state. 11.ork by Labhart" shows, however, that this cannot be the only important effect and that changes in dipole moment and in transition moment must be taken into account, including changes due to the action of the static electric field in displacing the nuclei (before the absorption actj. ,lccordingly, we can write the expression for the energy of a given state, as perturbed by an external field, only if the description of the state specifies nuclear as well as electronic coordinates. I t appears t h a t a semiclassical treatment of the excited state is sufficient, and hence one can predict that the absorption band of a given molecule can be discussed in terms of changes in the whole band. In addition, one must average over all the orientations of the molecule relative to the polarization vector of the incident light. Such a treatment predicts a change in center frequency, a change in integrated intensity (i.c, oscillator strength), and a broadening of the (4) A 1,. I.eliosen a n d C E . Reid, J Chpm Phys , 20, 238 (19.52j. ( 5 ) Y Ooshika, J P h y s SOC.Jnpnlz, 9 , 594 ( 1 9 5 4 ) . ( 6 ) H C 1,onguet~Higginsa n d J A Pople, J . C k r m P h y s . , 27, 192 (19.57) ( 7 ) I( G hlcRae, . I . P h y s . [ h e m , 61, 562 (1967). ( 8 ) C P S m y t h . "Ilielectic Behavior a n d Structure," SlcGraw-Hill Book C o , Inc , Z e w Y o r k , S Y . , 195.5, p 348 (9) E hl Kosuwer. J A m . C h e w S o c , 8 0 , :326l ( l s J 3 E j . ( I O ) E JI Kosower, ibzd , 8 0 , 32.53 (19.58). (11) J K u m a m o t o . J C P o w e r s , Jr , a n d W. I< Heller. J Chein P h y s , 36, 28!U (1962). (12) H L a b h a r t , Helo C h i m A c t a , 4 4 , 4 5 i (1961).
/
20-
0'
I
I
5000
6000
x(a)
10
7000
Fig. %.---The observed shifts along t h e band edge. T h e dots are t h e displacements in cni.-l (left scale). The solid-line shows t h e absorption band in O . D . (right scale).
observed absorption band, all three changes being proportional to the square of the applied electric field. I t appears that the broadening effect is difficult to determine experimentally because it involves the second moment of the absorption line, and hence is subject to errors due largely to uncertain contributions from the wings of the line. [Ye show in Appendix I an appzoximate method treating the data obtained a t 100 -1.intervals along the absorption band of phenol blue. In Appendix 11 we indicate a method for checking the approximate method as well as deriving the mean shift and the mean change i n intensity of the band. Experimental Phenol Blue.--Phenol blue was prepared by t h e method of Fieser'3; after recrystallization from ethyl acetate it melted a t 159-160'. Polystyrene.-Lustres (clear polystyrene) was used as such in t h e majority of t h e esperiments. Purification by precipitation from benzene with methanol and drying a t 60" did not alter a n y results. Preparation of Samples.-Ten grams of polystyrene was dissolved in approximately 200 mi. of benzene a n t i the requisite amount of phenol blue (0.05 i o 0.15 g.) dissolved in benzene was added. T h e solution was poured into large Petri dishes and allowed t o evaporate. T h e resultant polymeric mass was pressed into thin films b y heat molding a t 160'. T h e spectrum of phenol blue (-0.02 molal) in a thin film (0.065 m m . ) of polystyrene is shown in Fig. 2 (solid line). Electrodes.-Transparent electrodes were made by coating ordinary 2 X 3 in. microscope slides with a conducting film of tin oxide following t h e method of Gnmer." Contacts for the connecting wires were made with du Pont colloidal silver paint. T h e size of the cell was such t h a t it could be placed in t h e light path of a Cary spectrophotometer. In t h e experiments reported here, t h e sample was placed a i right angles t o t h e light path. Instruments.-.% Cary Model 14 spectrophotometer was used for the optical measurements. % . Sorenson Model 230-6P high voltage d.c. power supply was used with a constant voltage transformer on t h e power line side. Low Temperature Cell.--.$ cell of t h e t y p e dexribed by \Vagner and Hornigl5 was equipped with quartz w i n d o w . T h e sample was placed between tin oxide coated quartz plates and electrical connections were made with colloidal silver paint.
Results
A. The Effect of a Constant Applied Field Over the Total Band.-A typical spectrum of phenol blue in polystyrene is shown in Fig. 2 (solid line). The change in optical density, AO.D., caused by the application of a constant field was deterrninqd by a point-bypoint method a t intervals of 100 A. These are pre(IX) I, F. Fieser a n d H T Thrrmpson J A m Chem Solarch 20, 1964
5000
6000
7000
1007
.,
x (A) Fig. 3.-Intensity
change correction 1
5
15,370
1
T h e circles are t h e displacements in c m - ' (left scale). T h e solid line shows t h e absorption band in O.D. (right scale).
data, with no significant changes in the numerical values. B. Electric Field Dependence of the Shift.-The chang$s in optical density a t a fixed wave length, 6300 A , , on the band edge were studied with varying applied fields. Corresponding measure7ients were made on the opposite band edge a t 5100 A. -2 representative sample using a more concentrated film (0.066 molal) is shown in Fig. 1 and the data are given in Table IT. These results are plotted in Fig. 3 with a linear and a quadratic field dependence. It is clear t h a t an adequate fit with the quadratic field dependence is found. Additional studies were carried out on films containing 0.02 molal phenol blue as well as the pure material melted into a sandwich between mylar sheets. The results were essentially the same as described above. C. Measurements Made at Low Temperature.The apparent shift measured with liquid nitrogen in the cell was dependent on the square of the applied field and of the same magnitude as t h a t a t room temperature. Since the band shifts as the temperature decreases, it was difficult to compare equivalent points on the spectrum, but the shift is approximately the same with liquid nitrogen as a t room temperature. Discussion I t is clear from the data observed t h a t band broadening makes no significant contribution. T h e presence of both a band shift to the red and a band broadening should make the observed shift appear smaller on the blue edge and larger on the red edge. In fact, just the reverse is shown in Fig. 2 . \Then the small loss in intensity is taken into account (eq. 10, Appendix I) there is satisfactory agreement among all the points for a simple band translation, Fig. 3. Since the derivation shown in Appendix I contains a simplifying assumption about the intensity effect and neglects higher terms in expansions, a tnore rigorous derivation was made (Appendix 11) and was used in a machine calculation and found to agree with the values given in Table I. Conclusion The results of this study show that the niajor effect of an external electric field on a rigidly held matrix iso-
z 0
,
3
8
0
r
:
15,360
15,350
1
8
'
15,340A
'
'
I
2
3
4
5
'
6
KV
Fig. 5a.-Field
dependence a t 6500 L$ plotted with linear field
8
15,380::
t
15,370 -
I 0
15.360 -
0 15.350
4
,
I
I
I
0
Fig. Jb.-Field
dependence a t 6500 .I. plotted with the square of t h e field.
lated molecule of phenol blue is a band shift to the red. The absence of any temperature effect on the shift makes i t seem unlikely t h a t these molecules are being reoriented in the matrix by the field. (Such an orientation change could in principle give rise to the observed effect.) The failure t o detect any systematic trend in the shifts along the band edges in Fig. 3 indicates t h a t the expected band broadening is difficult to observe. This would be the case if the broadening is small relative to the band width.
1008
J C POWERS, J R , I\7 R HELLER, J KUMOIOTO, WD W E D O X ; ~ T H 1
19,600 1
I
t 19,600 p
0
so
Yo1
0 0
19,575
19.575
1
i *
19,525
I
-
0
i
19,525
1
c 0
,
19,5000-
1
2
’
’ 4
3
’
5
6
’
’
7
~
8
19,500
,
IO
,
20
,
30
/
40
,
SO
60
,
70
KV
(KV)‘
Fig.
;IC --Field
dependelice a t 5100 .!.
plotted with linear field.
I t appears that the general explanation for the solvent sensitivity of phenol blue in terms of a solutedipole solvent-field interaction” is not complete and should include a contribution from the second-order term. This quadratic field dependent effect can be rationalized as arising from a mixing of excited states induced by the external electric field. This sort of behavior has been known for a long time in atomic spectra and is the classical Stark effect.]’ Acknowledgments.---M-e wish to thank D r . H . L. Friedman and Dr. IV.L. Peticolas for encouragement and critical discussions and Dr. IT7.E. Bron for his cooperation in performing the experiments. Appendix I X broad band which has shifted an amount lv may be described in terms of its extinction coefficient e(.) as e(u
+ Av)
C (aeiav)Au
= e(u)
+ (,a2e/au2)Auz
(1)
If we assume t h a t a uniform change in intensity occurs, we can relate the new extinction coefficient ~ ’ ( v with ) E’(
v) = (1
+ G)e( v )
(2)
where G is defined in terms of the oscillator strength of the bandf as G
Fig. 5ti.--Ficld
dependence a t 5100 A . plotted with t h e square of the field.
Substituting in eq. T we can relate the experimentally determined shift to the actual shift Av(Ac/Av’) = Ae - G e ( u )
(9)
and
and 1 6 6 = L0.D. O . D , where 0 D. is the observed optical density. Appendix I1 Deduction of change in a single broad optical absorption band due to external influence (stress, electric field, etc ) is given. If we assume that the band absorption can be represented as an extinction or absorption co efficient which vanishes sufficiently rapidly a t infinity that the first and second moments exist, we may make the following definitions : Define
(3)
= Af/.f
and it follows that e’(u)
-
B(U)
=
J: . l e ( u ) d u
=
G
J: e ( v ) c l u
(1)
llsing expressions 1 and 2 to allow for a shift Lu and a simultaneous change in intensity G we have
+
=
i i -t G ! I e ( d
(aeldi).b
+
.
!
(5)
For small shifts and small changes in intensity we may neglect the higher terms. A’t(v) = e ‘ j u
+ Av)
- ~ ( v = )
Ge(u)
+ (be/8u).lv
(6)
liearranging terms gives
In terms of an actual observed shift of the band
Av’ we may write (17) Fix a recent review, see A I K i p r i a n o v . R t d ~ s .C h r m R a , ‘29, 618 (1960) (18) I< U Condon and G. H. Shortley. “ T h e T h e o r y of A t o m i c Spectra,’ Cambridge I-nir. Press, Cambridge, 1!)37, C h a p t e r X V 1 I , p p 3C47-117.
Define m e a n frc.quency shzlft by
Define mean broadening by B
F ) ) - /L?(O)\ = 4 J e ( u , F ) ( u - rue) - A c u ) ) 2 d u / ( l
= iL2(
+ G ) $ - ( ~ ‘ ( 0 ) )(61
Equations 1 , 2 , and 5 may be manipulated to give
