The temperature jump method is a technique used in

chemical kinetics Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in ...

for the measurement of very rapid reaction rates. It is one of a class of chemical relaxation methods pioneered by the German physical chemist

Manfred Eigen Manfred Eigen (; 9 May 1927 – 6 February 2019) was a German biophysical chemist who won the 1967 Nobel Prize in Chemistry for work on measuring fast chemical reactions. Eigen's research helped solve major problems in physical chemistry and ...

in the 1950s. In these methods, a reacting system initially at equilibrium is perturbed rapidly and then observed as it ''relaxes'' back to equilibrium.Atkins P. and de Paula J. ''Atkins' Physical Chemistry'' (8th ed., W.H.Freeman 2006) p.805, Steinfeld J.I., Francisco J.S. and Hase W.L., ''Chemical Kinetics and Dynamics'' (2nd ed., Prentice-Hall 1998) p.140-3, In the case of temperature jump, the perturbation involves rapid heating which changes the value of the

equilibrium constant The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...

, followed by relaxation to equilibrium at the new temperature. The heating usually involves discharging of a capacitor (in the kV range) through a small volume (< 1 mL) of a conducting solution containing the molecule/reaction to be studied. In some versions of the apparatus used, the solution is heated instead by the output of a pulsed laser which emits in the near infra-red. When laser heating is employed, the solution need not be conducting. In both cases, the temperature of the solution is caused to rise by a small amount in microseconds (or less in the case of laser heating). This allows the study of the shift in equilibrium of reactions that equilibrate in milliseconds (or microseconds with laser temperature jump), these changes most commonly being observed using

absorption spectroscopy Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating fi ...

fluorescence spectroscopy Fluorescence spectroscopy (also known as fluorimetry or spectrofluorometry) is a type of electromagnetic spectroscopy that analyzes fluorescence from a sample. It involves using a beam of light, usually ultraviolet light, that excites the electro ...

. Due to the small volumes involved the temperature of the solution returns to that of its surroundings in minutes. The fractional extent of the reaction (''i.e.'' the percentage change in concentration of a measurable species) depends on the molar enthalpy change (Δ''H''°) between the reactants and products and the equilibrium position. If ''K'' is the equilibrium constant and ''dT'' is the change in temperature then the enthalpy change is given by the

Van 't Hoff equation The Van 't Hoff equation relates the change in the equilibrium constant, , of a chemical reaction to the change in temperature, ''T'', given the standard enthalpy change, , for the process. It was proposed by Dutch chemist Jacobus Henricus van ' ...

: :

= .\frac

where ''R'' is the

universal gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per ...

and ''T'' is the

absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic w ...

. When a single step in a reaction is perturbed in a temperature jump experiment, the reaction follows a single exponential decay function with

time constant In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system.Concretely, a first-order LTI system is a s ...

(\tau)

equal to a function of the forward (k_a) and reverse (k_b) rate constants. For the perturbation of a simple equilibrium A <=> B which is first order in both directions, the reciprocal of the time constant equals the sum of the two rate constants :

1/\tau = k_a + k_b

The two rate constants can be determined from the values of

(\tau)

and the equilibrium constant :

K = k_a / k_b

, yielding two equations for two unknowns. In more complex reaction networks, when multiple reaction steps are perturbed, then the reciprocal time constants are given by the

eigenvalue In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted ...

s of the characteristic rate equations. The ability to observe intermediate steps in a reaction pathway is one of the attractive features of this technology. Related chemical relaxation methods include pressure jump,Espenson J.H. ''Chemical Kinetics and Reaction Mechanisms'' (2nd ed., McGraw-Hill 2002) p.256 electric field jump and pH jump.Gutman, M. and Huppert, D.J. (1979) Biochem. Biophys. Methods 1, 9-19

References

{{reflist Chemical kinetics