TABLE V : Zero-Point and Thermal Energy Contributions to Vibrational Energies (kcal/mol) Calculated with and without Scaling for the Reactions X + H,O + H,OX AE,O va
0.9va
A ( AEy)298
va
0.9vQ
total va
0.9va
+8.3 + 7 . 7 b + 0 . 2 + 0 . 2 b + 8 . 5 + 7 . g b H,O+ H,OLi+ + 2 . 1 + 1 . 9 t 0 . 4 +0.5 +2.5 t2.4 +1.9 +2.1 +4.1 t 4 . 1 +2.2 t2.0 (H,O), a Calculated from Hartree-Fock 6-31G*frequencies ( U ) or from 0.9 times these values ( 0 . 9 ~ ) . See ref 10. Umbrella mode for H,O+unscaled.
kcal/mol. It is noteworthy that this is similar in magnitude but opposite in sign to the contribution due to the loss of translational and rotational degrees of freedom (-1.8 kcal mol). The final computed enthalpy of dimerization is -3.7 kcal/mol for H20,and -3.9 kcal/mol for D20. The computed deuterium isotope effect on the dimerization enthalpy is -0.6 kcal/mol at 0 K, and -0.2 kcal/mol at 298 K. Thus, the effect of the smaller zero-point energy in (D20)*is partially offset at 298 K by the increased thermal population of the dimer low-frequency modes. Curtiss, Frurip, and Blander have measured the enthalpies of dimerization of H 2 0 and D 2 0 at 373 K, and obtained values of -3.6 and -3.7 kcal/mol, respe~tive1y.l~ At this same temperature, the corresponding calculated (19) L. A. Curtiss, D. J. Frurip, and M. Blander, J. Chem. Phys., 71, 2703 (1979).
Validity of the Brunauer-Emmett-Teller Carbon Black
enthalpies of dimerization AIP73for both H 2 0 and D20 are -3.9 kcal/mol. General Comments The results of these hydration studies show that if hydration forms a complex that is strongly bound, the new vibrational modes have high frequencies, and will contribute only to the zero-point vibrational energy term, M: in eq 5. If, however, the complex is weakly bound, the new modes will have lower frequencies (-600 cm-l or less), and will also contribute to the thermal population term A(AEv)298. In such cases, it is necessary to evaluate both AE: and A(Mv)298. Finally, it is interesting to note that although HartreeFock vibrational frequencies are generally overestimated by about 12% ,lo this error makes little difference in the computed enthalpies at 298 K. This is illustrated in Table V, where the vibrational energy contributions to the hydration reaction enegies are energies from the HartreeFock frequencies, and from these frequencies scaled by 0.9. For H20Li+and (H20),, the lower zero-point energy obtained with the reduced frequencies is about equally compensated by the increased thermal population of these modes at 298 K. Even in H30" where there is no such compensation, the difference is only 0.6 kcal/mol.
Acknowledgment. This work was supported in part by NSF Grant CHE81-01061-01. Registry No. D2,7782-39-0; Li+, 17341-24-1; H+,12408-02-5.
Equation near the Monolayer for Krypton on
D. E. Hoggarty, Woon-Sun Ahn,+ and 0. D. Halsey' Department of Chemistfy, University of Washington, Seaft/e,Washington 98 195 (Receivscl:November 29, 1982)
The general BET theory is applied to the absorption of krypton on graphitized carbon black in the region near the completion of a monolayer (point B) and is shown to give an inadequate account of the existing data over an extended temperature range. The data are adequately explained by the model of a compressible monolayer without appreciable second-layer formation. This layer appears to change gradually from registered to nonregistered as a function of spreading pressure.
Introduction The adsorption of rare gases and other simple molecules on graphite and similar surfaces has been extensively studied.' In recent years, particular attention has been given to the more or less abrupt changes in the amount of adsorption that can be identified with phase changes. For the case of graphite as the substrate, two-dimensional phase changes identified with gas-liquid-solid condensation phenomena, and registry-disregistry transitions, have been discovered.2 Quite naturally, less attention has been paid to the featureless regions of the adsorption isotherm that are relatively flat, that is, where the quantity adsorbed is changing slowly as the pressure is increased. Here we will be concerned with the region of the isotherm near the completion of a monolayer, for the par+ Department of Chemistry, Sung Kyun Kwan University, Seoul, Korea.
0022-3654l83/2087-328z$ol.50/0
ticular case of the adsorption of kyrpton on graphitized carbon black, which has been studied over a range of temperatures by Putnam and Fort.3 The features identified with phase changes are less easy to discern, but the relatively large surface area of the material makes the accurate measurement of small changes in adsorption that are necessary for our study possible. We also will make use of older data for other rare gases obtained on a similar graphitic substrate by Prenzlow and Halsey.4 In addition, Professor Pierotti has provided us with some unpublished data of a similar naturea5 (1)R. A. Pierotti and H. E. Thomas in 'Surface and Colloid Science", 1971, p 93. (2) S. C. Fain and M. D. Chinn, J.Phys. (Paris),Colloq., 38, C4-99 (1977). (3) F. A. Putnam and T. Fort, Jr., J. Phys. Chem., 79, 459 (1975). (4) C. F. Prenzlow and G. D. Halsey, Jr., J. Phys. Chem. 61, 1158 (1957).
Vol. IV, E. Matejevic, Ed., Wiley-Interscience, New York,
0 1983 American Chemlcal Soclety
Krypton on Carbon Black
The Journal of Physical Chemistry, Vol. 87, No. 17, 1983
3283
The monolayer region is of particular interest because an estimate of the numbers of moles in the completed monolayer, coupled with a knowledge of the area per adatom, allows the surface area to be calculated. This procedure is the basis of the Brunauer-Emmett-Teller (BET) method, and we will begin our analysis with this model for multilayer adsorption.
BET Description of the Monolayer Region The BET model for monolayer adsorption is based on a sitewise Langmuir adsorption in each of several layers. It is insufficiently complex to allow for the details of the actual monolayer formation, which may involve 2-D phase changes during its formation, and in the multilayer region it gives an inadequate account of lateral interactions. However, it may be nearly applicable to the monolayer region where for a type I1 isotherm the first layer is nearly full, with a few lattice vacancies, and the second layer is nearly empty and thus in a Henry's law region. In this region, adsorption in the third and higher layers can be neglected. Thus, we have the equations for dynamic adsorption on the first and second layers kl(P/PO)(l - 01) - k-1(01 - 02) = 0 (la) k2(P/P0)(4- 02) - k-2(02) = 0 Ob) to solve for the total coverage 0 = O1 + d2. In the region with which we are concerned, where dl is very close to unity and O2 is very small, these equations lead to the limiting result 0 = 1 - [Kl(P/P0)]-'+ K z ( P / P o ) (2) where K 1 = k l / k - l and K 2 / k - , are the binding constants in the first and second layers and PIPo the relative pressure. The number of moles adsorbed can be expressed as n = n,[l - (1/Ki)(P/Po)-' + KdP/Po)I (3) The constant n, is the number of moles in a monolayer, and, in the region where this expression may be valid, the second and third terms in the brackets are small and nearly compensate each other, The constants K 1 and K 2 are temperature dependent and have the form K 1 = ule"1lRT and K 2 = u2ehE2/RT. Anticipated Values for t h e Constants The interaction energy AEl is composed of three terms: the interaction energy of the adatom with the graphite surface, plus the lateral interaction with the six neighbors around the site, minus the reference enthalpy of vaporization of the adsorbate. The later two terms approximately cancel each other, so the anticipated value of AE1/R should be of the order of the energy determined from the interaction of krypton atoms with the nearly bare surface, or 1500-2000 K.6 The interaction energy AEz is composed of the interaction energy of the adatom with the first adsorbed layer (nearly complete) minus the reference enthalpy. The first term should be of the order of half the reference enthalpy and so AE2 is expected to be (minus) about half the energy of vaporization of the solid reference state,' or for krypton about 2650 cal divided by -2R or -675
K. It is more difficult to make estimates of ul and u2,which reflect standard entropy changes between the bulk and the (5) D. S. Newsome, Ph.D. Dissertation, Georgia Institute of Technology, Atlanta, GA, 1972. (6) J. R. S m , G. Constabaris, and G. D. Halsey,J.Phys. Chem., 64, 1689 (1960). (7) W. T. Ziegler, D. W. Yarbrough, and J. C. Mullins, 'Calculation of the VaDor Pressure and Heats of Sublimation of Liauids and Solids Below One Atmosphere Pressure. IV. Krypton",Techhal Report No. 1, Project A-764, Georgia Institute of Technology, Atlanta, GA, 1964.
0.999
0.05
0
0.10
P/Po Figure 1. Krypton isotherms calculated for 8 of lo-', a 2 of 10, A€, of 1400 K, and AE2 of -700 K. P o is the bulk saturation vapor pressure.
TABLE I: Parameters for the Putnam and Fort Krsuton Data temp, K Kl K2 104.49 2.0 x 103 0.55 99.34 5.1 x 103 0.62 94.72 1.3 x 103 0.70 n, = 1.22x mol/g Q 1 = 3.3 x 10-5 0.053 A E , = 1873 K A E , = 244.3 K
a2 =
adsorbate. However, one would expect ul to be somewhat less than unity, as the entering adatom somewhat restricts its new neighbors; on the other hand, u2 would be expected to be greater than unity to reflect the greater lateral freedom of an isolated atom in the second layer relative to the bulk phase. In the simple BET formulation al = u2 = 1 and AE2 = 0. The remaining constant AEl determines the BET shape factor c, which then is equal to exp(AE,/RT). Isotherm shapes at a single temperature often yield values of c of the order of 100. This value in turn implies (at 100 K) an unrealistic value for AE1/R of about 500 K. Isotherms are plotted in Figure 1 that show the effect of the assignments. Qualitatively, the results are satisfactory. The isotherms cross on a PIPoplot and become "sharper" at lower temperatures. Qualitatively, however, K 2 is much too small, the crossing is at too low a partial pressure, and the "sharpening" is too extreme. The BET line with very large AEl is almost perpendicular near the vertical axis on the scale of this diagram. BET isotherms at all temperatures approach this line as an asymptote. A fifth constant n, is required in order to analyze real data, measured in mol/(g of adsorbent). The relation giving the moles adsorbed is n = n,0 where n, is the number of moles in the monolayer or, equivalently, it can be expressed as the monolayer volume at STP u, of the BET theory. Unless a thermal expansion terms is included, u, should be independent of temperature. Constants Evaluated from the Data The krypton data of Putnam and Fort can be accomodated within the BET framework only if the constants in K 1 and K 2 are given values quite different from those anticipated. The values are given in Table I and the fitted points' shown in Figure 2. The value of u, is consistent with that selected by Putnam and Fort and the value of
3284
The Journal of Physical Chemistry, Vol. 87,No. 17, 1983
Heggarty et al.
TABLE 11: Values for the Virial Treatment of the Second Layer
145
temp, K
Po,mm
K,
157.7 81.3 42.23 1.62 0.72
Krypton 0.55 695-540 0.62 1450-1125 0.70 3000-2335 0.35 31790-24725 0.34 77745-60470
I40
104.49' 99.34' 94.72' 77.00b 73.50'
1
135 0) 0 -
E 130 i
z o = 3.5 x 10-'-4.5 x l o w 8cm A = 11.4 x l o 4 cmz n , = 1.22 X mol/g; 1.43 x
E
125
c*/k, K 850-820 885-860 920-895 935-915 960-945
mol/g at 73.50 K
, 0 A
115
B,s/Az,
0
0.10
99.34 K 104.49 K
0.20
I
Argon o n One-Layer Xenon 348.4 0.27 100-75 240.0 0.24 125-95 154.1 0.21 160-125 104.8 0.20 220-170 10-8-4.5 x l o - * cm
81.06d 78.47d 75.72d 73.54d z o = 3.5 x A = 11.4 x l o 4 cm2 n, = 1.00 x mol/g
0.30
P/ Po
Flgure 2. Adsorptlon isotherms fttted to observed data. Data are from Put"and Fort, Newsome and Pierotti, and Singleton and Halsey. P o is the bulk saturation vapor pressure.
AEl is acceptable. However, the value of ul,so far removed from unity, reflects a large entropy difference between the bulk and adsorbed phase (approximatelySIR = -10) which is not acceptable. The positive value of AE2 is also difficult to accept. This value, which implies that the energy of adsorption in the second layer is greater than the bulk condensation value, would be acceptable only after the onset of lateral interaction in the second layer. An acceptable value would be in the region of half the energy of condensation plus a small contribution from the underlying solid. The value of u2 is less than unity rather than greater, and also contrary to expectation. If we attempt to extend the temperature range of the fit by inclusion of the data of Newsome and Pierotti: on a similar but no identical sample, we can no longer maintain a constant value of n,. (A few points from the early measurements of Singleton and Halseg are in substantial agreement with the data of Newsome and Pierotti.) We thus conclude that the extended BET treatment of the monolayer region is not valid. Virial Expansion for the Second Layer In our treatment of the monolayer region, the constant K2 can be recognized as a Henry's law constant for the independent adsorption of atoms in a second layer over a completed first layer or
e2 = n2/nm= K2(P/Po)
(4)
We will treat this adsorption on the basis of the virial constant expansion for adsorption (ref 1, eq IV.9)
n2 = BAS(P/RT) + C f i s ( P / R T ) 2+ ...
(5)
where for the moment we neglect the term in (P/RT)2. Values of the dimensionless function (BAs/Azo)are available for simple models. For example, for the Lennard-Jones 3-9 potentiall
BAs/AzO = 0.579(kT / E*)
lJ2er*JkT
(6)
where zo and E* are the interaction parameters for the potential and A is the area. Thus K2 = (A / n,) ( P o / R T ) ~ o ( B/Azo) As
(7)
From estimated values of K2 and the parameters, the en(8)J. H.Singleton and G. D.Halsey, Jr., J. Phys. Chem. 58, 1011 (1954).
' Data from ref 5.
3. Data from ref 8. Data from ref 4.
490-460 495-470 500-475 510-490
Data from ref
ergy t*/k can be evaluated. The values so determined are not sensitive to the choice of parameters, or to the exponents in the Lennard-Jones potential. They are given in Table 11. We have evaluated the energy for two cases: the "second layer" of krypton as defiied by our BET analysis, and for argon adsorbed on a monolayer of xenon.4 Only the latter case corresponds to what is clearly a second layer. The results show that a 25% variation in zo has only a minor effect on the energy, which would also apply to similar uncertainties in the other parameters and K2 itself. If we assume that the principal source of interaction energy is the triple contact of argon with the underlying xenon atoms, we can use a simple averaging rule to calculate the value of t * / k
( f * ~ r - h /)k(t*xe-xe / k ) I 1'2 (8) we find, for an argon parameter of 120 K and a xenon parameter of 220 K that t*/k = 487 K, consistent with the results given. An equivalent calculation for the krypton on krypton second layer gives (3)(170 K) = 510 K, which is clearly not consistent. If, on the other hand, we use the value of 510 K to calculate K2,we find values that range from 0.014 at 94.72 K to 0.031 at 104.49 K. These values imply an adsorption in the second layer of n2 of the order of 1 pmol, at PIPo 20.2, which is essentially negligible or within the experimental accuracy of the adsorption measurements. We can thus conclude that, if the interaction energy in the second layer is near the reasonably expected value, there is essentially no second layer present in the region of the krypton isotherms we have been analyzing. e* / k = 3
Higher Order Terms We can make a crude estimate of the coefficient C f i s by total neglect of correction terms in eq IV.lOb, IV.82, and IV.84 of ref 1. Thus, in terms of the two-dimensional virial coefficient &d CAAS -(2B~s~/A)Bzd (9) What matters is the ratio r of adsorption due to the term in P2 to the linear term or r = (CAAS/BAS)(P/RT)= -2(BAS/A)B2d(P/RT) = -(Po/R r )(BAS/Azo) (~obo)B*m( T*)(P/Po) (10)
The reduced coefficient B*,(T*) has been tabulated? and
The Journal of Physical Chemistry, Vol. 87, No. 17, 1983
Krypton on Carbon Black
TABLE 111: Data f o r the Spreading Pressure Plot temp, K
PI,,,
“
no,Cmol/g
compressibility, cm2/erg
1.12 x 10-4 1.14 X 1.16 x 10-4 1.14 X
2.9 x 10-3 2.8 X 10.’ 2.4 x 10-3 4.5 X
I
-
8
140
3285
.
I
135
~~
104.49’ 99.34’ 94.72a 73.50b
0.272 0.110 0.043 0.000232
‘ Data from ref
3.
Data from ref 5.
t
8
f
Extrapolated
to 0 spreading pressure.
the area factor bo = (1/2)N7ru2 cm2/mol, where u is the molecular diameter. We have calculated the ratio r for the adsorption of argon on a monolayer of xenon. With the argon-argon interaction e*/k = 170 K and u = 3.7 X cm the value of r at PIPo= 0.1 is approximately 0.1. Experimentally, this layer undergoes 2-D condensation shortly thereafter, at about PIPo = 0.15; whereas the second layer of krypton on krypton condenses at about 0.4. I t is clear that this correction is not important for either case. Monolayer Density as a Function of Spreading Pressure From the preceding analysis, we conclude that secondlayer formation is not an important factor in the linear region above point B that we have characterized by K p In this region, where the coverage is not changing rapidly, the spreading pressure can be readily approximated. From the definition of spreading pressure in the differential form (gas-phase ideal) d 4 = r dp = RT(n/A)d In P (11) it can be evaluated by integration over the isotherm from P = 0 to P. If however coverage r = n/A rises abruptly to a nearly constant value r0 = nm/A, a convenient approximation for the spreading pressure takes the formlo 4 = RT(nm/A) In (P/Pl/z) (12) where Pl/zis the pressure of half-monolayer coverage. This equation is exact for stepwise formation of the monolayer, and nearly exact for Langmuir or similar isotherms. The values of the spreading pressure calculated this way from the data of Putnam and Fort are in agreement with those estimated from their plots of 4A/RT. Moles adsorbed are plotted against the spreading pressure in Figure 3. Table I11 gives estimated compressibilities for the linear region of these curves as well as the surface densities at zero pressure and temperature by extrapolation. The thermal expansion coefficient in the region of 30 dyn/cm was found to be 2.4 X 10-3/K, which compares with 8.0 X 10-3/K at 60 K obtained by Webb and co-workers,ll for krypton on silver, which is considered to be a “structureless” surface. All the data extrapolate to approximately the same value of 115 pmol/g at zero spreading pressure, and therefore the thermal expansion extrapolates to zero at that pressure. A possible explanation of this behavior is suggested. If small regions of registered and disregistered molecules are interspersed,’O then, as spreading pressure increases, a larger proportion of regions would be disregistered. Then only the disregistered portions would show thermal expansion, and so the average thermal expansion would show a variation similar to that shown in Figure 3. This behavior (9)L.J. Slutaky and G. D. Halsey, Jr. in ‘Physical Chemistry: An Advanced Treatise”, Vol. 11, H. Eyring, D. Henderson, and W. Jost, Eds., Academic Press, New York, 1967,p 479. (10)G.D.Halsey, J.Phys. Chem., 81,2076 (1977). (11)J. Unguria, L. W. Bruch, E. R. Moog,and M. B. Webb, Surf. Sci., 109,522 (1981).
H
r
0
A
*
I15
6
8””
2120
t-
0
9 73 74 94
60 50 60 72
K K K K
0 99 3 4 K o I O 4 49 K
.e,
1
1
1
I
IO
20
30
40
4
50
(erg/cm2)
Figure 3. Moles adsorbed vs. spreading pressures calculated from Putnam and Fort and Newsome and Pierotti data. Least-squares lines are shown through points below 4 = 37 erg/cm2. Dashed lines are extrapolations to zero spreading pressure. Arrows correspond to spreading pressures at the onset of in-registry to outsf-registry soiid-solid transition on the basal plane of graphite at 73.5 and 100 K estimated from Fain and Chinn, ref 2.
is contrasted to the abrupt change in thermal expansion that would be expected if a first- or second-order phase change occurred between large areas of registered and disregistered adatoms. The approximate spreading pressures where such a transition takes place2 on the basal plane of graphite are indicated by arrows in Figure 3. The extrapolated coverage at zero spreading pressure is approximately 115 pmol/g. If the registered area per molecule (0.1574 nm2 (ref 3) is applied to this figure, an area of 10.9 m2/g is realized. For comparison, the BET area of the original sample was given as 12.5 m2/g,12and Putnam and Fort have selected the value 11.4, which is the value used in our calculations. Conclusions It appears that the general BET treatment does not give an adequate account of the monolayer or point B regions of these isotherms. That is, the filling of lattice vacancies is not an important factor in this region. At one temperature, the BET treatment gives apparent agreement, but with artificial values of the constants, and in particular with an unreasonably low value of the c constant, as compared with the value determined by the relative energy of adsorption estimated from high-temperature data (see ref 1). The low estimate of second-layer coverage is based on choices of parameters and potential function; however, the numerical constant in eq 6 is not affected enough by the choice of potential to cause significant increase in the second-layer adsorption. We have shown that a reasonable range of zo values has only a minor effect on E*. In addition, the experimental data for adsorption of argon on xenon support the results of the calculations. The data are adequately explained by a compressible monolayer, but not one on a structureless surface where one would expect a relatively constant coefficient of thermal expansion. The several sets of data seem to fit together and thus indicate that the graphitized carbon samples are similar. This is particularly true of the plot against spreading pressure which suggests a suitable method of verifying registry and thus estimating surface area, when the extrapolation is independent of temperature. We (12)M. H.Polley, W. D. Schaeffer, and W. R. Smith, J.Phys. Chem., 57, 469 (1957).
also note that the surface area so estimated is closer to that from high-temperature gas-solid interaction measurements’ and thus helps close the gap between these two methods of measurement. Acknowledgment. We gratefully acknowledge support of this project through a grant, No. DMR 8111111, from
the Division of Materials Research, Metallurgy Polymers and Ceramic section of the National Science Foundation. We are extremely indebted to Professor Pierotti for allowing us to use his data prior to publication. We also thank Professor S. Fain for pointing out several errors. Registry No. Kr, 7439-90-9.
Picosecond Fluorescence Anisotropy Decay in the Ethldlum/DNA Complex Douglas Magde,” Marlna Zappala, Wayne H. Knox, and Thomas M. Nordlund Department of Physics and Astronomy, Institute of Optics, and Department of Radietion Biology and Blophysics, University of Rochester, River Station, Rochester, New York 14627 (Received: November 15, 1982)
Ethidium bromide intercalated into calf thymus or salmon sperm DNA exhibits fluorescence anisotropy relaxation due to torsional motion (and, at long times, bending) of the DNA which is well described by the elastic continuum model for times greater than 0.5 ns. A fast component of amplitude 0.025 f 0.01 and characteristic time 100 (-50, +loo) ps is present at short times and is affected very weakly or not at all by solution viscosity. Such fast relaxation may be attributed to “wobbling”of the dye within a binding site, although it is not completely certain that all other possibilities have been rigorously excluded.
Introduction Deoxyribonucleic acid (DNA) is a double-stranded linear polymer which codes genetic information in higher organisms. Both replication and transcritpion of DNA imply subtle control of motion of the polymer. Ethidium bromide (EB) is a fluorescent dye probe which intercalates between adjacent base pairs of the DNA helix. The time dependence of fluorescence depolarization of EB can be monitored in order to determine the local torsional flexibility of DNA. We report here the extension of such anisotropy decay measurements down to the true picosecond regime. Our time resolution is improved by a factor of ten or more over earlier studies.’-5 Wahl and his group were the first to observe this behavior,’ although their data had only limited time resolution and their original interpretive model has been superceded. Barkley and Zimm (BZ) proposed a different theoretical treatment.6 Schurr and co-workers introduced a CW mode-locked laser with single-photon correlation to improve the measurement2 and proposed their own theoretical analysis,’ which was independent of but largely equivalent to that of BZ. At almost the same time, Zewail and his group3 also studied anisotropy decay over times from below 1 to about 100 ns, using the BZ formulation to analyze their results. They have since refined their analyses and extended somewhat their measurement^.*#^ Their last paper5 (MRZ) will constitute the takeoff point for our analyses, since it describes very succinctly the issues left unresolved by the nanosecond studies. In particular, all workers agree that an extrapolation of their nanosecond data back to an initial anisotropy implies small but significant “missing amplitude”. Instead of the theoretically expected value of 0.4, MRZ can account for only about 0.36; other workers found somewhat larger discrepancies, which could, so far as one can tell from published reports, be partly instrumental. More recently, Schurr and co-
* Author to whom correspondence should be addressed at the Department of Chemistry, University of California, La Jolla, CA 92093
worker^*^^ have extended the theory further. In particular, they consider large angles of reorientation, rather than the small angles assumed by BZ. This matters for long time behavior, including even that of MRZ. However, it is irrelevant for the issue treated here. Experimental Section Single-photon correlation offers excellent linearity and sensitivity with good, but not picosecond, time resolution. To reach shorter times, we have combined a very stable, mode-locked and Q-switched, Nd3+:YAG laser with a highly sensitive jitter-free streak camera to form a system capable of extensive signal averaging. This instrumentation has been thoroughly described previously10and has been utilized in applications which challenge its time resolution and its sensitivity for weak emission. The present application tests its ability to distinguish a very small, possibly very fast component of a multiple decay process. This is a difficult task and only the outstanding performance of the jitter-free streak system tempted us to undertake the effort. In order to facilitate comparison with earlier work, many of our measurements were made on calf-thymus DNA, chopped to molecular weight 100000. In order to have some evidence for the generality of the results, measurements were also carried out on salmon sperm DNA. Both (1)D.Genest and Ph. Wahl, Biochim. Biophys. Acta, 521,502(1978). (2)J. C. Thomas, S. A. Allison, C. J. Appellof, and J. M. Schurr, Biophys. Chem., 12,177 (1980). (3)D. P. Millar, R. J. Robbins, and A. H. Zewail, h o c . Natl. Acad. Sci. U.S.A., 77,5593 (1980). (4)D.P. Millar, R. J. Robbins, and A. H. Zewail, J. Chem. Phys., 74, 4200 (1981). (5)D.P.Millar, R. J. Robbins, and A. H. Zewail, J. Chem. Phys., 76, 2080 (1981). ( 6 ) M. D. Barkley and B. H. Zimm, J. Chem. Phys., 70,2991 (1979). (7)S. A. Allison and J. M. Schurr, Chem. Phys., 41,35 (1979). (8)S.A. Allison, J. H. Shibata, J. Wilcoxon, and J. M. Schurr, Biopolymers, 21,729 (1982). (9)J. M. Schurr, Chem. Phys., 65, 417 (1982). (10)W. Knox and G. Mourou, Opt. Commun., 37, 203 (1981).
@ 1983 American Chemical Society
