QED coherence and electrolyte solutions
Introduction
The answer has now been sought for nearly two centuries to the following simple question: what is the nature of the virtue (or vis as our forefathers used to call it) of water and other polar liquids which compensates for the high stability of ionic lattices so as to produce electrolyte solutions?
We observe that the lattice energy and dynamics of such solids are interpreted presently in terms of the generally accepted electrostatic picture of matter. The formation of strong electrolytes has then been attributed (since the time of Arrhenius [1]) to the ionic character of the salts themselves coupled to the high dielectric constant, e.g. of water (ϵ=80 at 300 K). It is assumed that the Coulombic forces in the lattice are reduced by a factor ϵ thereby allowing a separation of the ions with only negligible changes of enthalpy (e.g. see Nernst and Thomson [2], [3], [4]). However, the dielectric constant is a purely phenomenological observable describing the bulk properties of the medium. While it is certainly true that two charges separated by several layers of water will interact with a force ϵ times smaller than in vacuo the Nernst–Thomson argument has to circumvent the difficulty that the ionic lattice is not immersed in water but in a vacuum. We then need to explain the way in which we can surmount an energy barrier of the order of 5 eV in order to insert a single layer of water (thickness≈3.2 Å) between the ions.
We need to ask: what physically reasonable interaction is there in water to offset such large energy imbalances? Modern molecular dynamists might be tempted (and, indeed, have been) to invent all manner of two-body potentials between the water molecules and ions to explain such phenomena. However, such explanations are physically unmotivated for they rely on a panoply of two- and three-body potentials, whose common feature is a large electric polarisability of the water molecule in the ground state. We maintain, instead, that such a crucial feature is totally baseless for the following reason: second order perturbation theory ties the polarisability of H2O in the ground state to its spectrum and to the transition probabilities (oscillator strengths) between the ground state and the excited states. A rapid survey of both kinds of experimental information shows that the hardness of the spectrum (the first excited state being at 7.6 eV) and the smallness of the oscillator strengths [5], make the H2O molecule a very stiff object, totally at variance with the polarisability required by the potentials used in molecular dynamics. Thus the only electrostatic interactions that H2O in the ground state is capable of exerting are related to its rather modest electric dipole (corresponding to two unit charges separated by 0.38 Å), which thus cannot compensate the attractive force between two opposite charges at the same distance.
We have to conclude that the Coulombic attraction can be damped out by the dielectric constant of water only after an energy barrier of approximately 5 eV has been surmounted, a phenomenon which cannot be explained by electrostatics. In this paper we shall show how the basic question can be answered in a natural and simple manner by adopting the concepts of QED [6].
Section snippets
The short-time dissociation process
As a first step in the overall processwe consider the highly endothermic transition to neutral specieswhose energy deficit Δ(AB→A+B) can be obtained from standard thermodynamic data (Table 1). In view of the large value of Δ(AB→A+B) (≈6 eV for most strong electrolytes) such transitions can be only virtual and, consequently, can last only for the time given by the Heisenberg principle unless there is a further transition from such a virtual
The Debye–Hückel coherent plasmas
The short time dynamics of the dissociation process leads us to the conclusion that a salt can dissolve to form an electrolyte solution only, provided the ions A+ and B−, once separated by a layer of water molecules, undergo a dynamical process which provides an energy loss comparable to the large barrier Δ(AB→A+B). If this is not the case, then energy conservation would require that the ions should fall back to their initial, stable, configuration. This is the basic reason why the formation of
Discussion and conclusions
We need to consider first of all the qualitative differences between the conventional Debye–Hückel theory and the model which we have outlined in the previous sections. In the conventional theory, the interaction between the ions in solution is discussed in the framework of classical electrostatics and such a formulation gives a well-defined variation of the interaction energy (the minor term) with the concentration. The critically important question of why lattices should dissolve in the first
List of symbols
ϵ dielectric constant dw electric dipole moment of the water molecule=1.83 Debyes=1.15×10−9 cm (in ‘natural’ units) T absolute temperature (1 K=4.31 cm−1 in ‘natural’ units) kB Boltzmanns constant (kB=1 in ‘natural’ units) N/V number density of molecules or ions ρ charge density e electron charge (e=0.3, adimensional in ‘natural’ units) a ionic radius 1/κ Debye–Hückel length ω=2πν angular velocity, proportional to the frequency ν. In ‘natural’ units 3×1010 Hz=1 cm−1, since the speed of light c=1 g2 plasma coupling
Acknowledgements
We wish to thank Professor Roger Parsons for directing us through the ‘archaeology’ of electrolyte solutions.
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