Phase Transitions in Some Phase Changing Organic Materials Studied by Nuclear Magnetic Resonance Relaxometry

Using nuclear magnetic resonance relaxometry and calorimetry methods were studied phase transitions in isoparaffin i-C22H46 and paraffin added bitumen. They can be used as a phase-changing materials (PCM) and so as heat accumulating/emitting thermal electric energy storage. For studies of phase transitions time and temperature dependences on protons was used relaxometer NMR 09/PC on resonance frequency νо = 9,2 МГц. Were received data on structure-dynamical NMR-parameters, determining properties of studied organic materials. Was discovered prolonged complex form of phase transition through many stage crystallization process, which does not satisfy the criteria of phase transitions of I or II order.


Introduction
Investigations on direct electric energy production using phase transition (PT) of phase-changing materials (PCM) is of great technology relevance. Solution of the problem gives an opportunity for use of temperature changes during 24 hours, especially in the regions with sharp continental climate. Such materials are named thermal energy storage (TES) systems, widely used in air conditioning systems for its benefits on energy conservation [1][2][3]. Phase transitions can be also used for power generation -transformation of heat of fusion/crystallization in electric current power as a most convenient form of energy. For this purpose can be used the thermoelectric Seebek effect of electricity production using temperature over fall during the process of PT at heating and cooling. [4]. But phase transitions are not studied completely and is a complicated phenomena. Noble laureate V.L.Ginsburg put it on the seventh place among physic problems, that are needed to be solved.
Spin-echo amplitudes А е envelopes dependences in Hahn and CPMG-methods after the amplitude detection had forms, which can be described by equations: Relaxation function can be approximated by the sum of exponents if T 1,2i difference is large enough [14]. Tyat is so, and for relaxation times determination we used graph-analytical method of spin-echo envelopes dependences decomposition, described earlier in [7].
Molecular motion activation energies Е а of the linear parts of Т 1 and Т 2 were defined from reverse temperatures (10 3 /Т) temperature dependences using program Advanced Grafer. For Arrenius form of correlation times dependence τ с = τ о ехр(Е а /RT) (where τ о period of atom oscillation, R = 8,314 J/mol -universal gas constant) at high temperature approximation 2πν о τ с << 1, relaxation times are equal T 1 = T 2 , and for intramolecular contribution in relaxation the activation energy Е а can be determined from T 1,2 (2) и T 1,2 (1) for temperatures T (1) and T (2) using [13]: Error of Е а determination is the sum of instrumental. relaxation times and temperature errors: and equal to γ Е = ± (1,4 + 3,5 + 0,4) ≈ ± 5 %. Analysis techniques used to study phase transitions are conventional calorimetric, differential scanning calorimetric (DSC) and differential thermal analysis (DTA). As it is mentioned by Gibbs [3], there is considerable uncertainty about the property values provided by manufacturers. Yinping [3] reviewed conventional calorimetric methods and pointed out their limitations such as: a) too small quantities of sample can be analyzed (1-10 mg), but some properties depend on sampler volume; b) phase changes cannot be visually observed. According to [14] error of DTA reach ± 3% at measurement range ends. Following [3] recommendations calorimetric we elaborated design, which combine common and differential calorimetric and additionally determine Seebeck thermoelectric tension U(mV) and current I(mcA) of endo/xothermic effects. Small was used. One solder of thermo element TEMO-7 (40x60 mm) is connected with heat conducting plate immersed in paraffin or bitumen. Another solder is connected with radiator freeze by cooler or ice. Usually point of melting is determined during 15 minutes. We controlled cooling process during 100-180 minutes in the sample of volume ≈ 100 ml. Temperatures in sample and water were measured by thermo resistors of the II class of precision (∆t = ± (0,30 + 3,5⋅10 -3 t) in the temperature range -50 о С ≤ T ≤ +180 о С with resistivity R = 50 Ohm, maintained with Winston (bridge) power. Resistivity is determined from equation R t = R o (1 + αT), where α = 4,26⋅10 -3 К -1 . Temperature measurement error was ± 0.1%.
iii) For relaxation times Т 2А of А proton phase in the range 10 3 /Т = 3,155-3,37 (43 -24 о С) the decrease of Т 2А with three clear extremes (minimums) of Т 2А are observed. Probably they are connected with three-stage process of precrystallization ordering of -CH 2 -CH 3 -groups. After that at the range 10 3 /Т = 3,356-3.39 (25 -22 о С) we observe oscillation process with the amplitude of Т 2А oscillations from 89 ms to 126 ms. Fluctuations ends at 22 о С by the full crystallization of the proton phase А and sharp fall of Т 2А to value 7.6 ms and only this temperature may be named as "rigid lattice" state of paraffin.
iiii) In the melt state of paraffine proton phase A population (corresponding to the end CH 3 -groups) has value P 2А = 65%. At the temperature of the full cooling its value reach value Р 2А = 98%, which is interpreted as that at low temperatures main contribution in relaxation comes from the end chains. Molecular fragments of B phase …CH 2 -CH 2 -CH 2 -… …CH 2 -CH 2 -CH 2 -…have reached already the solid crystallized (ordered) state.
So, the conclusion can be made, that full crystallization at cooling process does not end at Т = 30,4 о С (as it is indicated by literature data [5]), but goes up on till 22 о С, passing through formation of temporal ordered structures, which gradually increase their degree of ordering and decrease Т 2i as it followes from eq. (7). But this ordered forms has intermediate melt states with higher relaxation times before ne order formation. This process gives oscillations of Т 2i as it is following from (7) before final crystallization.
Ordering from melt in the temperature range 10 3 /Т = 3,15-3,38 (44.5 -23 о С) can be attributed to metastable state before ordering. But this temperature range differs for А and В proton phases. For proton phase В it is 44.5-34 о С, for А it is 25-22 о С, i.e. more mobile protons need higher degree of cooling. Range 10 3 /Т = 3,16-3.39 (43 -22 о С), correspond to unstable intermediate state and can be named structure-dynamical phase transition (SDPT). At the end of this range, before the transition to ordered (crystal) state, expenditure of the heat is needed. Physically it need additional energy for transformation molecular fragments in the more ordered state. According to classical thermodynamics this situation can be expressed by Nernst law: where ∆F, ∆Q and ∆S are changes of free energy F, heat content Q and entropy S at temperature T. According the law all substances aspire to the minimum of free energy and the most stable substance has minimal F. For i-С 22 Н 46 free energy of formation is F =12.5 kcal/mol, for most stable substance graphite F =0 kcal/mol. In the case, when F decreases more rapidly, then Q, entropy S will also decrease, i.e. substance will come to more ordered form, and this will lead to decrease of Т 2i . The most stable solid state will be reached only at 22 о С, not 30.4 о С [5].
Solidification processes for i-С 22 Н 46 two proton phases end not only at different temperatures Т К , but also at different times t к ( fig.2) which depend from molecular motions restrictions. For proton phase В they are Т К = 34 о С and t к = 76 min, for А they are Т К = 22 о С and t к = 156 min. with the end of phase transition of paraffin i-С 22 Н 46 to crystal state.
For verification of the made conclusions alternative calorimetric method is used and were received time dependences, presented at fig.3. Considering calorimetric temperature curve of i-С 22 Н 46 we can see, that at 12-th minute is observed sharp break, corresponding to Т = 44 о С of allotroph transition. In the time interval t = 12-180 minutes three local extremes are observed, named exotherms Ехt1, Ехt2 and Ехt3. The initial of Ехt1 (44 о С) coincide with the start of pre-crystallization process in proton phase В, which ends at 49-th minute at temperature 35 о С (10 3 /Т = 3,246). Start of Ехt2 we attribute to warming of phase B molecular motion for overcoming activation barrier for start of the several stages of structure-dynamical processes finishing by crystallization of phase B at 34 о С on 75-th minute.
At the same time on 47-th minute initiated pre-crystallization of proton phase А. So to the exotherm Ехt2 contribute simultaneously В and А, and this Ехt2 is the sum of at least three peaks, corresponding to 82 Phase Transitions in Some Phase Changing Organic Materials Studied by Nuclear Magnetic Resonance Relaxometry pre-crystallization stages (three minimums of Т 2А at fig.1, 2). Start Ехt3 at 136-th minute correspond to local warming for overcoming of the potential barrier to start orering, preceding final crystallization of i-С 22 Н 46 at 156-th minute, when Т 2А sharply falls to 7,6 -8,3 ms., corresponding "rigid lattice".
Approximately at the same temperatures, the extremes on the tension dependence of U TE (mV) (curve 4) on thermo-element are observed. It is clearly seen, that extremes, approximately coincide with the temperature peaks of exothermic processes at temperature at fig.3.
Time dependence of relaxation times at cooling at fig.3 support conclusions, made from fig.1 and 2. Really, Ехt1 corresponds to decrease (protons ordering) of Т 2В . Ехt2 characterize three stage pre crystallization (the minimums of Т 2А ) of А proton phase. Ехt3 corresponds to final crystallization of proton phase A and i-С 22 Н 46 in whole.

Bitumen
Вitumen, used for study contain sufficient amount of paraffins-12.4 %. Experimental slopes of spin-echo amplitudes Ае in CPMG-method after amplitude detection is described by the sum of three components with relaxation times Т2А, Т2В and Т2С, corresponding to proton phases А, В and С. They are can be attributed: А -to dispersion media of light paraffins and naphtens with high reorientation velosities of CH3 groups and cis-trans configuration motion of …-CH2-CH2-CH2… chains; В -to resins and С -to asphaltenes -most heavy molecular polar aromatic structures. Attribution is conventional, because protons of high mobile fragments of phases В and С can contribute in Т2А of А proton phase, and on the contrary fragments of А -phase with low mobility of linear paraffins, contribute in relaxation with Т2В and Т2С. In scientific literature is used term "structure unit" (SU) [7] for description of disperse phase elements in oils. SU are phase fractal particles, which can be described on the basis of dynamical phenomenon of the fractal cluster, composed from aggregated asphaltene (or paraffin) molecules, attracted to each other and forming SU core. Solvate envelope of SU is formed mainly from resin and aromatics molecules. SU are sediment in the medium of hydrocarbons of phase A [5].
As it can be seen from temperature dependences of Т2А, Т2В and Т2С in fig. 4, relaxation times reduce with temperature decrease, but the times drop is dependent from temperature. It is the indication of the activation energies EА increase with temperature fall. Use of high temperature approximation is also substantiated in the case of bitumen. In [15] was shown, that in colloid systems intermolecular contribution is much less, then intramolecular.
At the same time at the curves 1-3 at fig.4 observed several temperature ranges, manifesting sharp jumps of relaxation times Т 2i , exceeding the experimental error several times. This changes of Т 2i with the negative slopes at high temperature side (and, consequently with negative local activation energies Е АSD ) can not be attributed neither to phase transitions of the second order, because no heat emission at this temperatures are observed ( fig.6, curve 2), nor to PT of the first order, because no transition in another aggregate state takes place. We connect this peculiarities in Т 2i behavior with structure-dynamical phase transitions (SDPT), which appear as a result of temporary (dynamical) formation and following melting of the clusters of supermolecular structures on the paraffin base. In our case SDPT are accompanied by the structure ordering with decreasing of R ij in SU and which is the cause of Т 2С and Т 2В decrease according to eq(7) as a result of the ordering. This process is exothermic, resulting to the negative Е АСД and is the manifestation of open dissipative systems aspiration to the minimum of the free energy and entropy. More sufficient decrease of the enthalpy H contribution in the Е АSD than the entropy S decrease (∆H < 0, ∆S < 0, |∆H} > |∆S|) gives negative Е АSD : As it was mentioned in [16], during bitumen cooling «occur imposition of plural number of structure and phase transitions. Bitumen with high concentration of asphaltenes (up to 40%) and paraffin-naphtens (up to 35%) aggregative unstable and their heterogenization goes during 2 days. Concentration of disperse phase arise by the molecules, detained in dispersion media due to viscosity". Temporal dependence of Т 2А in bitumen sample on fig.5 demonstrate oscillations, which with coefficient α = 510 can approximately be described by equation: Т 2А = cos(αt)[exp(-t/6000) + 11.4exp(-t/400) (10) Oscillating character of relaxation times at fig.5, curves 1,2 can also be explained by SDPT. Extremes of temperatures on thermogramm ( fig.6, curve 2) and dependence of voltage on thermoelement ( fig.6, curve 1) closely coincide with SDPT at fig.5. This is connected with absorbance of energy, necessary for transformation and ordering of the new ordered structure and is the evidence of many stage solidification process in bitumen.
It was interesting to study the influence of laser irradiation of the sample. As it is known, energy Е i of the molecule is a sum of electronic energy and energies of oscillation, rotation and translation types of motion. Irradiation lead to absorption of electromagnet energy and to transition from energy level i to more high energetic level j with the change on the value: ∆Е ij = Е i -Е j = hν = hc/λ ∼ 1,2⋅10 5 /λ (11) ∆Е ij expressed in kJ/mol, λ -wave length in nm, c -light velocity.