On the Actinometric Measurement of Absolute Luminescence Quantum Yields

The theory of the measurement of luminescent quantum yields using chemical actinometry is described. The sample’s emission intensity is measured by nearly completely surrounding the sample with an actinometer solution, and the excitation intensity is directly measured with the same type of actinometer. The ratio of the measured sample emission intensity corrected for the fraction escaping through the excitation ports to the measured excitation intensity is the absolute luminescence yield. Equations, a suitable cell design, and computer calculated correction factors for different cell dimensions and optical densities are given. The absolute yield of the actinometer is not needed, only its relative response with wavelength. New quantum-flat actinometers which should greatly simplify the measurements are described.


Introduction
The meas ure me nt of absolute lumin escence quantum yields is a n important but experimentally difficult area [1 , 2, 3]. t Most yield measurements are made relative to a luminesce nce standard rather than by an "absolute" method. It is thu s imperative for good accuracy that the luminescent standards be accurately calibrated. To date, these standards have bee n derived almost exclusively from calorimetry or by reference to a standard scatterer, usually with a luminescent quantum counter detector.
The history of quantum yield measure ments has demonstrated quite painfully that it is exceedingly difficult to detect and eliminate all systematic errors. Thus, materials selected for standards should be tested by as many independent and presumably reliable "absolute" methods as possible and r ec hec ked as new techniques beco me available.
We describe here the theo ry of a co nce ptually new "absolute" me thod for measurin g lumin escence quantum yields based on c he mical actinometers. The tec hnique avoids many of the intrinsic error sources of th e other me thods and thu s promises to be a useful c hec k on existin g and new s tandards. Th e c urre nt availability of numerous lasers with both hi gh intensites and a wide range of wavelen gth s ranging from < 250 nm to > 800 nm coupled with new broadband , quantum-flat actinometers make the actin ometri c method most attractive. In addition to the theory we present a s uitable cell desi gn, tabular correction factors, and des cribe s uitable actinometers.

Theory
The actinometric approac h for de terminin g yields measures the exci tation intensity and th e sample e mission intensity by c hemical actinom e try; th e ratio of th e emission to excitation intensity, both corrected for the fra ction of the excitation beam a bsorbe d, is th e absolute quantum yield. Th e total e mitted inte nsity is measured by nearl y completely s urroundin g the sa mple with the actinometer solution except for a s mall excitation port and correctin g for the s mall port losses. The same type of actinometer is th e n used to measure the excitation beam intensity.
For the actinometer monitoring the emission in· tensity of the luminescent unknown , the amount of reaction in the actinometer, Dx (mol of produ ct), is given by where 10 (einstein/s) is the incident excitation intensity, tAs) is the irradiation time, F x is the fraction of incident excitation light absorbed by the unknown, T is the effective transmittance of the entrance window, A x is the absorbance of the solution to the excitation beam, f/ J is the sample's absolute luminescence efficiency, F ~ is the fraction of emitted light captured by the actinometer, and e x(mol/einstein) is the actinometer's effective photochemical quantum yield for the emission band. It is assumed that the excitation beam is monochromatic, all of the emission passing into the actinometer is absorbed, and reabsorptionreemission corrections are negligible. ex is given by (2) where lJ is energy in cm -I, F(v) (relative quanta/cm -1 of bandwidth) is the corrected relative emission spectrum and exe;;) (mol/einstein) is the variation of the actinometer yield with excitation energy.
In the measurement of the excitation beam intensity, the amount of reaction in the actinometer, Ds(mol), is giver. by where tis) is the irradiation time, F s is the fraction of the excitation beam absorbed by the actinometer, T is the same as eq 1, As is the absorbance of the actinometer solution to the laser, and es (mol/einstein) is the actinometer's yield at the excitation wavelength. The absolute luminescence quantum yield is then given by The D's, A's and t's are directly measurable and F; can be evaluated from geometric considerations (see below). At first it might appear that this method can be no more accurate than the absolute accuracy of the e valuation of the actionometer's yield, e (lJ), a process which is rarely good to better thanJ-O percent. In reality since eq 4 uses the ratio of e s to e x , only the variation of f/J (lJ) with lJ need be known accurately. As long as data from the same workers are used, this error is likely to be substantially smaller than 10 percent and quite possibly less than 5 percent. Also, as we shall show, actinometers with intrinsically quantum-flat res29nses are becoming available which will make es/e x = l.000 within ~ 1-2 percent, regardless of how accurately the absolute yield is known. The Model Figure 1 shows an easily fabricated cell suitable for measuring absolute yields by actinometry. The cell, built much like a reflux condenser, has a long, central irradiation volume with a small diameter filling stem. The outer jacket contains the actinometer solution which intercepts and absorbs a large fraction of the emitted light. The two filling ports on the actinometer jacket facilitate filling and permit the use of flow actinometers.
This cell design has numerous advantages. The system is only suitable for use with laser excitation; therefore, the monochromatic laser light eliminates, in virtually all solution cases, the need for effective absorbance corrections arising from variation of absorbance over the excitation band [4]. Questionable refractive index corrections are also eliminated. The high symmetry and entering and exiting excitation ports simplify evaluation of F x and F~; further, the exit port removes unabsorbed excitation light from the system so that it cannot affect the actinometer. By silvering the ends of the actinometer jacket, radiation light piped down the glass walls can be directed back into the actinometer. By making L/R large, F~ can be made to approach unity as closely as desired. By choosing a large L/ R, one can easily absorb a large fraction of the exciting light and still keep the reabsorptionreemission correction small. Thus, the system combines some of the best features of the optically dense and dilute approaches.

Evaluation of FE
To evaluate F~ we make several assumptions , all of which will be quite accurate or will introduce negligible errors in a well-designed cell. These assumptions are: (1) the laser beam is centered and its diameter is small compared to R, (2) all emission not directly striking the windows is absorbed by the actinometer, (3) all of the emission transmitted by the cell windows is lost, (4) reabsorption-reemission corrections are negligible, and (5) the windows and cell walls are nonabsorbing.
F~ is divided into two terms, a geometric factor for direct capture of the emitted light and a correction for th e em itted li ght re fle cted by the windows back into th e cell which is subsequently absorbed by the actinometer. Fk is given by where FE is the fraction of primary emission that would be absorbed if the windows were perfectly transparent with no reflection losses, r eff is the frac tion of primary e mitted radiation reflected back into the cell by th e windows, and F RA is that fraction of thi s re fl ec ted radiation which is eventually absorbed by th e actinometer, th e remainder eventually escapin g_ FE can be evaluated by +cos [arctan CL~t' »)]} Adt' (6)

B=I-exp [-In (1 0)ECL]
where E is th e sa mpl e's molar extin cti on coefficie nt at the excitation wavelength a nd C is the sample co ncentration , The first a nd seco nd cosin e ter ms acco unt for the fraction of radiation strikin g the e ntrance and exit windows respectively as a fun ction of position in th e celL The A term acco unts for th e decrease in emission intensity along th e tube ca used by absorption, Th e B term corrects for the total fraction of excitation li ght absorbed in the celL For a very large L/R and not too hi gh an opti cal density , FE will approach unity, For extre mely hi gh opti cal densities, however, the e mi ss ion front s urfaces at the e ntran ce window where half the radiation could escape, and FE approaches 0_5, Equation 6 has n o obvious analytical soluti on and was evaluated numerically using Simpson's rule, Because of the discontinuities in the integrand at t' =o and t' =L, the evaluation limits were just set very near both windows, Initiall y calc ulations were done on a Hewlett Packard 2000 2 sys te m in tim e sharin g BASIC, but its -6 -7 sign ificant figures proved in adequate, All calc ulation s presented here were don e on a Hewlett Packard 9100 B programmable desk calcula tor which has 10-12 significant figures; the re were no problems with co nvergence, Integrati on was performed over the ra nge t'IL= 10-5 to 0,99999 with 200 s ubdivi s ions, In creasing the numb er of divisions to 1000 ca used no c han ges in the fifth significant figure, Our calc ulated FE'S are thus acc urate to be tter than 0,1 percent. Calc ulated res ults for Fe's as a fun ction of LI Rand A x are given in table L 2 1n ord er to desc ribe material s and experi me ntal procedures adequa tel y. it is occasionally necessa ry to id e ntify commercial products by manufac ture r's name or label. In no ins tance does suc h identifica ti on imply e nd orse me nt b y the Na tional Bureau of Standards. nor docs it imp ly Ih ul th e parti c ular product or equipm ent is necessaril y the best ava il able for that purpose.  As a practical cons ide ration FE s hould be as close as possible to unit y. Fortunately thi s is not difficult. Even for a cell which is onl y 2.5 times longer than its In the evaluation of 0, F~, rather th a n Fe' is actually req uired. We have not done a quantitative a nalys is for Fk because r eff and F R A a re quite difficult to eval uate, but in a well-designed cell the error associated with replacing Fk by FE is quite s mall. For exa mpl e, in a cell with a large LI R , most of the em ission in cide nt on the cell windows will b e at near normal incidence; thus , we can us e r eff ~ 0,04 for a glass-air inte rface,

Discussion
For FE =90 percent, Fk will be < 0.5 percent greater than FE, and the error falls for larger FE'S, Until rece ntly the potential c hoices of actinometers were limited to ferrioxalate a nd R ein ec ke's salt. Th e ferrioxalate actinometer will yield total absorption of the e mitted radiation up to ~ 480 nm usin g a 5 c m thi ck actinometer solution (0. 15 F). The yield is not stron gly wavelength depe nd ent from 254 nm to 480 nm, and calibration is su ffi cie ntly detailed to permit accurate evaluation of 8 , X'.
Reinec ke's salt offers muc h d ee per red penetration , ~ 610 nm for 2 X 1O-2 M solution and a 5 c m minimum cell le ngth. The yield is more nearly constant th an ferrioxalate over the 390-620 nm range. Unfortunately Rein ec ke's salt has senous disadvantages. The yield c hanges sharply below 390 nm, and detailed data in this region are lacking. The complex is difficult to dissolve at high concentrations and undergoes a relatively rapid thermal reaction (-0.6%/h). Although it is about an order of magnitude less sensitive than ferrioxalate, this is not likely to be a problem with a high intensity laser excitation source.
New photosensitized actinometers promise to eliminate the previous difficulties. For example, the tris-(2,2-bipyridine)ruthenium(n) photo oxidation of tetramethylethylene has been developed as an actinometer for high power lasers [5]-The system should be intrinsically quantum flat, because the lowest excited state is responsible for the sensitization; luminescence experiments have verified that the efficiency of population of the emitting state is constant to -± 2 percent over this region [6]. A solution 1O-3M in the ruthenium co mplex will absorb all radiation below -520 nm in a 2 em pathle ngth. By using similar osmium(n) complexes as the sensitizer [6,7,8], total absorption of the emission and a quantum flat response below -700 nm should be realized. These systems use volumetric monitoring of th e consumed O 2 and are thus not very sensitive, but laser excitation supplies adequate intensity. Finally, because the consumed O 2 must be replaced and inhomo ge neity of the reactants can be a problem in a static syste m, these actinometers must be operated in a flow syste m.
An analogous sys tem whi c h also s hows promise is the methylene blue sensitized photooxidation of tetramethylethylene. Solutions can easily be made totally absorbing to beyo nd 700 nm in a 1 em pathlength , and the yield is comparable to the RU(Il ) and Os(n ) sys tems. The quantum yields may, however, not be perfectly flat , and minor corrections may be re quired.
In summary, we feel that the actinometric method, although too co mplex for routine measure me nts, will prove especially useful in developing primary luminescence quantum yield standards. This method eliminates mos t of the error sources inhere nt in other absolute technique s, and thus s upplies a valuable c heck. The technique is c urre ntly feasible for compounds e mitting below 520 nm , and with the natural evolution of actinometry, operation to 700 nm and beyond s hould soon be feasible.