Investigations on direct electric energy production using phase transition (PT) heat accumulation/emission is of great technology relevance. Solution of the problem gives an opportunity to use sustainable temperature changes during 24 hours. Phase transitions in materials named thermal energy storage (TES) systems, can be used for power generation - transformation of heat of fusion/crystallization in electric current power through thermoelectric Seebeck effect during the process of PT at cooling [1,2].

For phase transitions study was used  isoparaffin i-C₂₂H₄₆ (docozan) of density r = 774,9 kg/m³, molecular weight M = 310.6, temperature of melting T_m = 44^oC, temperature and heat of allotropy transformation T_A = 43^oC, temperature of crystallization T_cr = 30,4^oC with heat of DH_C =  11,7 kcal/mol. For measurements of NMR-relaxation structure-dynamical parameters (SDP) - spin-lattice T_1i, spin-spin T_2i relaxation times - the NMR relaxometer NMR-10/PC was used. It has resonance frequency ν_o = 9,2 МHz and is described in our paper [3]. Temperature of samples was maintained with accuracy  ± 0,2 ^о by thermo stabilization unit of our patent [4]. Spin-lattice T_1i relaxation times were determined using spin-echo recovery sequence 90-t-90^о-t₀-180^о. For spin-spin T_2i relaxation times measurements 90^о-t- (180⁰-2t-)_N sequence was used. Experimental error of measurements was: for relaxation times ± 3¸4 %, for NMR-signal amplitudes recurrence ± 2 %, and could be reduced (n)^1/2 times using n accumulations.

It was established, that solidification processes for i-С₂₂Н₄₆ two proton phases end not only at different temperatures Т_К, but also at different times t_к (fig.2) which depends from molecular motions restrictions. For proton phase В they are  Т_К = 34 ^оС and t_к = 76 min, for А they are Т_К = 22 ^оС and t_к = 156 min. with the end of phase transition of paraffin i-С₂₂Н₄₆ to crystal state. It was considered, that in high-temperature approximation relaxation rate (Т_1,2)^-1 have two types of contributions: - intramolecular (Т_1,2)^-1_int, which characterize relaxation from reorientations of CH₃ groups and cis-trans configuration motion of ...-CH₂-CH₂-CH₂... chains:

(Т_1,2)_int^-1 = 3g⁴h²t_R/8p²R_ij⁶                                                           (1)

 and intermolecular (Т_1,2)^-1_tr from translational forms of motions in melt of i-C₂₂H₄₆ [8]:

(Т_1,2)_tr^-1 = pg⁴h² N_It_D(1 + 2a_o/5Dt_D)/4a_o³                                      (2)

where  g/2p = 4256/sеc×gauss - gyromagnetic ratio for protons, h = 6,626×10^-34J/s - Plank constant, N_I = 6,75×10²⁸ m^-3 - number of spins in cm³, a_o - average molecular diameter, R_ij - average distance between protons (nm), t_R and t_D - correlation times of rotational and translational motions (t_D = a_o/12D), D - self diffusion coefficient. In colloid systems (Т_2i)_int^-1 is sufficiently greater, than  (Т_2i)_tr^-1, for instance even for compact benzol molecule (interproton distance R_ij = 0.257 nm) is equal to 4,5% from the full relaxation rate, so eq(4) can be rewritten:

                                Т_1,2В^-1 = (3g⁴h²/4p²R_ij⁶)t_оexp(E_А/RT)                                  (3)

where E_А - activation energy, from which inter-proton distances R_ij can be calculated, which changed from R_ij = 0.26 nm to R_ij = 0.23 nm at phase transition of crystallization.

2. Zalba B., Marin J.M., Cabeza L.F., Mehling H. (2003) Applied Thermal Engineering 23, 251.

3. Каshaev R.S.-H., Idiatullin Z.Sh., Temnikov A.N. Device for sample thermostabilization in in relaxometer NMR (2006) Patent of Russian Federation on invention # 2319138.

4. Kashaev R.S., Faschiev N.R. (2011) Applied Magnetic Resonancе, 41, i.1, 31-43.