The Water Molecule with Conjoint Translational, Rotational and Spin Degrees of Freedom in the Gas and Liquid Phases

V.K Konyukhov

doi:10.13189/ujpa.2014.020604

Abstract

The theoretical model of water molecule is created which gives an opportunity to understand what happen with translational, rotational and spin degrees of freedom when molecule makes transitions from gas into liquid phase and vice versa. Translational degrees of freedom are considered classically but rotational and spin degrees of freedom are treated according to quantum-mechanical rules. The model is based on the mathematical techniques of geometric algebras over the field of real numbers. Unusual properties of water molecules with conjoint degrees of freedom compared to usual or free molecules are predicted and denoted as latent in future. The latent molecules have not the full rotational spectrum but possess three isolated rotational levels only. The latent molecules are capable of moving along straight lines at finite distances in 3D-space. The latent molecules conserve all their degrees of freedom during the transition from gas into liquid phase.

Highlights

Water molecules continue to attract an permanent attention of scientists due to an exceptionally significant role that this molecule plays in the existence of living things and technological processes
The given degrees of freedom integrate with the corresponding degrees of freedom of condensed matter while electronic and vibrational degrees of freedom continue to belong to a single molecule. If we take this point of view and suppose that it is right for the rotational degrees of freedom of water molecule we have a problem: how an ortho-molecule transfers into adsorbed state with losing rotational angle momentum? Note, that the quantum number of angle momentum of ortho-molecule in ground state is equal to 1, while the momentum number of para-molecule in the ground state is equal to 0 and we have not any problem with adsorption of this isomer
This means that the translational, rotational and spin degrees of freedom are unified by one mathematical construction based on geometric algebra G(R3,0)

Summary

Introduction

Water molecules continue to attract an permanent attention of scientists due to an exceptionally significant role that this molecule plays in the existence of living things and technological processes. The Water Molecule with Conjoint Translational, Rotational and Spin Degrees of Freedom in the Gas and Liquid Phases the subalgebra G+(R3,1) and G(R3,0) algebra to transform coordinates of bivectors to the elements of reference system (see Appendix A). We will have to consider the elements x0x1e1, x0x2e2, x0x3e3 as positions of molecule on straight lines in 3D-space directed by e1, e2, e3 vectors It should be noted, that there are three different operations, namely (i) the reverse rotation replaces the direct rotation, (ii) the conjugation of quaternion, (iii) the inversion on 3D-space have the identical mathematical form that variables x1, x2, x3 obtain an opposite sign. The elements x0x1e1, x0x2e2, x0x3e3 behave as vectors under operations while the elements x2x3e23, x1x3e31, x1x2e12 behave as angular momentums

Spin states of molecule

Physical properties of latent molecules

Discussion of results

Conclusion