Fluctuation aspects of isotope theory - III. Isotopic phase similarity in the set of deuterated methanes CHxD4-x

Abstract

We have proposed the new principle of isotopic phase similarity (IPS) in the previous works I, II, of this series. The fundamental Born-Oppenheimer approximation maintains separately its applicability within each isotopic phase. The fluctuation-thermodynamic formalism is based on the developed earlier predictive model of CVL (congruent vapor-liquid) – diagram. It changes the mean-field concept of the macroscopic VLE (vapor-liquid equilibrium) – diagram to describe adequately the mesoscopic scale of volumes and time-intervals for a fluid state. The well-established by CVL-diagram fluctuation boundaries of the boil- Pb(T)- and dew-Pd(T)-pressures are important ones. They form the essential mesoscopic expansion of the single Pv(T)- vapor-pressure curve postulated by VLE- diagram. This mesoscopic peculiarity of a non-mean-field phase transition was revealed earlier for any one-component fluids. It provides the new insight into the classic theory of isotope effects. In the first instance the conventional interpretation of the vapor-pressure isotope effect (VPIE) and the molar-volume isotope effect needs an independent consideration by the comparison of CVL-diagrams for isotopes. In two previous works I, II we have introduced the undimensional fluctuation calibration complex Zoc=P0M/(RT0ρc) (P0=101.325kPa, T0=1K, M g/mol – molar mass of isotope, ρc - its critical density of mass) which provides the separation of VPIEs for the variety of isotopic families on two main types: (n) normal (Zocn<1) and (i) inverse (Zoci>1) at low temperatures. In this work III we have applied the same IPS-methodology to the set of partially deuterated methanes CHxD4-x of i-type. The set of exclusively n-type pairs {H2O/D2O/T2O; 36Ar/40Ar; 235U/238U} was considered in works I, II. The reasonable predictive capability of IPS-principle determines systematic shifts in the critical parameters of heavier isotopes if only those for the basic lighter isotope (CH4) are known. The most impressive confirmation of IPS-principle is the reasonable concordance of its dew-pressure isotope effect (DPIE)-predictions with the experimental absolute differences between small vapor pressures of isotopes ΔPv=Pv′−Pv. We have proposed and corroborated the concept of two coupled crossover Bancroft'sTbB and Clapeyron'sTlgC-points. They offer the study of the difference between the vaporization enthalpies of isotopes without virial correction for non-ideality of v-phase.