Stochastic theory for rate constants of chemical reactions in liquid solution

The stochastic model of irreversible processes is developed in a fashion that yields expressions for the magnitudes and temperature dependences of chemical reaction rate constants. The model is sufficiently abstract to encompass reactions in liquids as well as those in gases. For liquid reactions both the general point of view and one feature of the results (the “frequency factor”) are apparently new. For gas reactions the viewpoints and the results are compatible with (though not as detailed as) those of well-established collision theory. An approximation (to the effect that nonreactive but energy-redistributing transitions are much more frequent than reactive ones) may limit the quantitative, though not the schematic, application of this development to reactions in the presence of an excess of inert diluent. The traditional assumption to the effect that reactants are in equilibrium with “activated complexes” (whether or not such exist in the sense of possessing well-defined microstates) is avoided. As in previous discussion of sufficient conditions for an Arrhenius rate law, in which certain complicating features (treated here) of the case of chemical reactions were ignored, the method used here involves taking explicit account of the role of those (rapidly equilibrating via frequent nonreactive transitions) degrees of freedom that serve as the activation-energy-supplying (and temperature defining) “reservoir” by use of an especially detailed form of stochastic master equation. A concise form for the master equation facilitates (1) the appropriate extension of the previously described steady state treatment of the case in which a “transition state” lasts sufficiently long to be internally equilibrated and (2) the treatment of the probably more realistic case in which reactants undergo transitions directly to products without a definable intermediate and in which “transition state” can only be defined in terms of an energy threshold in the reaction transition probability. The latter case is a generalization to arbitrary density of that originally treated by Ross and Mazur within the framework of collision theory for bimoleculear dilute gas reactions. The familiar exponential dependence on “free energy of activation” is obtained for both cases, but the physical basis for it is different (in both cases) from that provided by the classical version of transition state theory. The “frequency factor” is not in either case simplykT/h but rather is dependent on the fundamental couplings within the system. It is also dependent on an effective “number of states” of reactants, products, and reservoir. A brief discussion of the possible significance of this latter feature in both enzymatic catalysis and heterogeneous catalysis is presented.     

An assessment of the measurement of impedance by analysis of a pulse using an on-line computer

It is demonstrated that the analysis, in the frequency plane, of an i-t transient in response to a small amplitude constant potential perturbation can be successfully carried out. This contradicts the statements of D.E. Smith and co-workers on this method. The analysis, as the impedance, represents a compromise due mainly to truncation errors in the input current transient. However, these errors are of the same order as those observed in the measurement of a.c. impedance using a sinusoidal perturbation. This method has the advantage of being rapid.     

Pulse structure studies and absolute cavity length determination for a synchronously pumped picosecond dye laser

Second harmonic cross correlation functions of a pulse with its near neighbor have been studied in a synchronously pumped cw dye laser. Measurements were made both as a function of dye laser cavity length mismatch and the number of cavity round trips separating the correlated pulses. The pulse envelope is found to have a characteristic interpulse frequency determined by the pump laser, whereas the pulse substructure has a characteristic frequency determined by the dye laser cavity length. The cross correlation measurements allow experimental determination of the dye laser length corresponding to exact synchrony. In contrast to theoretical predictions the length of exact synchrony corresponds to optimum pulse shape and duration. Our results are discussed in terms of a simple model which leads to pulse duration estimates as much as twice those obtained by conventional analysis of autocorrelation traces.     

The fluorescence lifetime of tetracene vapour

The fluorescence lifetimes of tetracene vapour as a function of excess vibrational energy in the first excited singlet state have been measured under collision free conditions. A very marked decrease in lifetime with increasing energy has been observed. We attribute this behaviour to enhanced internal conversion from vibrationally excited levels.     

Reactivity of muonium atoms in aqueous solution

A beam of surface muons (4.1 MeV) was used to generate thermalised muonium atoms (μ⁺e^?) in aqueous solutions. From measurements of the muonium atom relaxation time in the presence of various solutes, bimolecular rate constants were determined and compared with the corresponding reactions of the much heavier isotope, the hydrogen atom.