NONERGODICITY OF TRANSIENT OPEN CHAIN-ASSOCIATION IN LIQUIDS

In liquid alcohols there are a definite number N-hb of H-bonds for a given number N-a of molecules. The ratio r(f) = 1 - (N-hb/N-a) can be deduced from the IR spectrometric data of Luck. However the NMR results show that these H-bonds perpetually jump from one over time that a given molecule, taking partner to another. The chance (sic)(non-bonded) over time that a given molecule, taking advantage of these jumps, become free from H-bonding is equal to r(f). This agrees with the vapor pressure data. However, it can be shown that the fraction alpha(OH) of the molecules in the ensemble which are completely free from H-bonding, acting neither as donor nor as acceptor is of the order of r(f)(2), and thus much smaller than the time fraction (sic)(non-bonded). This non-ergodic behaviour can be explained by the fact that only molecules which are completely inserted in a chain, acting at the same time in H-bonding as proton donor and as proton acceptor (fraction alpha(-OH-)) are in full possession of the energy of an H-bond, Delta H-h-bond/L. One cannot attribute this energy to all the molecules which form only an H-bond on one side (fractions alpha(-OH) and alpha(OH-) because this would not fit the energy balance. These states have to be considered as transient ones during the lifetime of which the energy. Delta H-h-bond/L passes from the medium to the molecule or vice-versa. As a consequence, in the ensemble, the energy of these states cannot be defined, but this is quite possible in a time schedule, such molecules being then considered during half of their life-time as possessing the energy Delta H-h-bond/L, and during the remaining half as free. This means that the ensemble fraction alpha(-OH) contributes half to the time fraction (sic)(non-bonded), half to the time fraction (sic)(bonded). Non-ergodicity will be observed for all the liquid systems where in the ensemble states are found to which the energy of an ephemeral cohesion bond cannot unambiguously be attributed, because they have to be considered as transient forms during the non-negligible life-time of which this energy is transferred from the medium to the molecule or vice-versa. This will be the case for the molecules at the head or at the tail of all open transient chains. In such non-ergodic systems the thermodynamic probability has to be calculated, not on the basis of ensemble fractions, but on the basis of the time fractions during which the energy of the ephemeral bonding can be attributed or not to a given molecule. The use of time fractions for calculating the thermodynamic probability was already proposed by Einstein in 1911. The consequences of the non-ergodicity for the statistical thermodynamics of H-bonding are discussed. The correctness of the non-ergodic thermodynamics of hydrogen bonded Liquids, based on time fractions, is demonstrated by the fact that the derived equations allow to predict correctly, without any adjustable parameter, the solubilities of the alkanes in alcohols and in water. Here, the classical theories completely fail.