11827
J. Phys. Chem. 1994, 98, 1 1827- 11831
Time-Resolved Determination of Picosecond Lifetimes of Weak Hydrogen Bonds in Liquids Gerhard Seifert and Heinrich Graener* Physics Department, University of Bayreuth, 0-95440 Bayreuth, Germany Received: June 11, 1994; In Final Form: August 25, 1994@
Using conventional absorption and picosecond double-resonance spectroscopy in the infrared the reaction kinetics of weak hydrogen bonds in liquids has been studied. By combination of the two methods the dissociation rate of hydrogen bonds formed between the components of binary mixtures can be determined. It is shown that the vibrational relaxation of such systems is characterized by two concentration-dependent decay constants. Experimental data for the liquid system CHBr&D5OD are presented and discussed. A hydrogen bond dissociation rate of k~ = (0.25 f 0.10) ps-’ is obtained for weak hydrogen bonds between the components of this system.
Introduction It is widely accepted that spectroscopic methods are well suited for the study of hydrogen bonding in liquids.‘ Especially Raman and IR techniques have, due to their extraordinarily high sensitivity to the presence of hydrogen bonds, been applied in many investigations concerning structure and association features of hydrogen-bonded liquid On the other hand it has been shown that time-resolved techniques on the picosecond time scale allow one to gain information about time constants characterizing dissociation or association processes.6,’ In this paper we demonstrate that a combination of conventional IR absorption spectra and the results of time-resolved picosecond measurements may provide a direct measure of the dissociation rate of weak hydrogen bonds in liquids. In addition the association rates of the investigated solutions can be determined from the data. The idea of the investigation is, briefly, the following: imagine a binary liquid mixture, where two spectroscopically distinguishable species (here specifically monomeric (“M’) and hydrogen-bonded (“B”)) of one molecular component exist. It will be shown that the formation and breakage of hydrogen bonds strongly influences the observed vibrational dynamics of the system. Furthermore concentration-dependent studies of vibrational relaxation may yield direct information about the hydrogen bond dynamics of the system.
with monomeric and bonded molecules k A and kD represent the association and dissociation constants; and characterize relaxation within a vibrational manifold. For illustration an excitation pulse is symbolized by an arrow.
Theoretical Description The influence of hydrogen bond dynamics on the time evolution of a vibrational population can be considered in general for a binary system composed of a proton donor (D) and a proton acceptor (A): in the following the concentrations of monomeric and bonded species of the donor are denoted by [DM]and [DB],respectively; the concentrations of the acceptor are given by [Af] (not bonded to D) and [AB], where the condition [AB]= [DB]must hold. The equilibrium reaction of interest can be written as
According to the mass action law (eq 2) the association rate k~[Af]can be replaced by ~D[DB]/[&] (in the following the abbreviation X = [DB]/[DM]will be used). The solution of eq 3 is easily written:
A
k? monomeric bonded Figure 1. Relaxation scheme for vibrational excitation of a system
tionally excited system. The relaxation times and characterize relaxation within the vibrational manifold of the corresponding species; dissociation and association rates are assumed to be equal in ground and excited states. The following coupled rate equations describe the time evolution of a given vibrational population (an asterisk marks vibrational excitation):
[D,*](t) = C, exp
[DB*l(t)= , C , exp( Square brackets indicate a concentration in moles per liter. The mass action law gives the ratio of the rate constants of association and dissociation, kA and kD:
Figure 1 shows the considered relaxation scheme for a vibra-
t)+
k)
(4b)
The time constants z, (slow) and tf(fast) occurring in eq 4 are given by
([+-.:
+ kD(l - x)]’ + 4 k 3 ) ” ’
@Abstractpublished in Advance ACS Abstracts, October 15, 1994.
0022-365419412098-11827$04.50/0
a&, exp( -
0 1994 American Chemical Society
(5)
Seifert and Graener
11828 J. Phys. Chem., Vol. 98, No. 46, 1994
The negative (positive) sign in front of the square root refers to ts (tf). The amplitudes Cs and Cf of the corresponding exponentials in eq 4 depend on the initial conditions; the amplitude prefactors a,,fin eq 4b are given by
T+ 1
kDas,f= - k&
1
-tS,f
Though being straightforward the above results have quite interesting consequences: time-resolved measurements of vibrational population in hydrogen-bonded binary mixtures will in general contain two time constants. For rather long-lived hydrogen bonds (Le., k~ -=
