o-xylene

The results of an experimental study of the refractive index of solutions of fullerene C 60 in PW of 52...54 °C melting point at the ranges of С 60 content of 0...0.052 wt. %and temperatures of 41…65 °С are presented in the study. The complex character of the concentration dependence of the refractive index on isotherms for the studied thermodynamic systems has been registeredboth in liquid and solid phases.Data on the effect of the C 60 content in PW on the temperatures of the start and finish of its phase transition is presented. At C 60 content in PW of 0…0.01 wt. % the temperatures of the start and finish of the phase transition decreased, at C 60 content of 0.01…0.04 wt. % they increased more than the pure PW temperatures and at C 60 content more than 0.04 wt. % they decreased again. The obtained effects of a decrease and increase in the refractive index on the isotherms and temperatures of start and finish of PWcrystallizationcan be explained by structural transformations in PW caused by C 60 presence. In the authors' opinion, the reason for the extreme behavior of concentration dependence of the refractive index of objects of study is the effect of C 60 on the density fluctuations and the quasi-crystalline structure of the liquid and solid phases.These structural transformations in PW cause a similar change inthe concentration dependencies of the temperatures of the start and finish of the phase transition of objects of study.

1. Introduction.The paraffin wax (PW) utilized as phase change material (PCM) is very promising for thermal energy storage systems.These materials have a wide range of fusion temperatures and are appropriate for medium-temperature thermal energy storage applications [1,2,3].However, the application of PW as PCM is limited by low thermal conductivity.
The fullerene C 60 adding in PW can help to eliminate this problem [2,3].The advantage of fullerene С 60 is that form a time-stable molecular solution with PW [4].However, nowadays there are very few papers devoted to studying the PCM containing fullerene.In [2] the thermal conductivity enhancement of composite PW/C 60 vs. pure PW was shown.The expediency of adding the fullerene С60 in PCM (binary carbonate eutectic salts) was studied in [5], however, the thermal conductivity enhancement was not recorded.Fullerene has been chosen as nanoadditives into poly(ethylene oxide), and obtained by melt-solidification method composite was investigated for thermal energy storage applications in [6].The higher heat of melting in comparison to theoretical values has been observedfor the blend with fullerene.Al-so, it has been found that for the crystallization of samples, the incorporation of fullerene lowers the activation energy of nucleation.Therefore, further study of the properties of PW/C 60 solutions for use as PCM is currently important.
Within the comprehensive studies of the thermophysical properties of composite PCMs, the use of simple methods of experimental study of the nanoparticles' effect on the phase transition parameters of these materials is of interest.Conventional methods for studying the phase transitions of n-alkanes are adiabatic and differential scanning calorimetry [3,6].In addition, optical methods are often applied to studying the parameters of phase transitions of various substances due to their simplicity and precision [7,8,9,10].The temperatures of phase transitions (melting, crystallization, rotator phases) were determined for a number of individual n-alkanes from C 19 H 40 to C 28 H 58 by the optical method based on dynamic light scattering [9].However, alkanes were studied as an emulsion in water [9].In the authors' opinion, it is practical to use the refractometry method to determine the phase transition temperatures, since it provides the high accuracy of the refractive index measurement and allowsto registerof the structural transformations in the studying samples [7,8,10].
It is known that the temperature dependence of the refractive index n D (t) exhibits a discontinuity (an abrupt change in n D ) or a break (an abrupt change in dn D /dt) atthe phase transition point for pure substances.An abrupt change in n D (t) dependence is typical for the melting point of a pure substance, and a break in the n D (t) dependence is observed during second-order phase transitions [7].For n-alkanes (components of industrial PW) a considerable "jump" in n D during the phase transition is typical [8].This circumstance makes refractometry a sufficiently accurate technique for studying the phase transition temperatures in this class of substances.
The promise of the method for determining the phase transition temperatures by the refractive index temperature dependence is confirmed by the presence of recent studies that propose devices and methods for the express determination of phase transition temperatures for various substances [10].A single-mode-no-core-single-mode (SNS) fiber optical sensor for the detection of solid-liquid and liquid-solid phase changes in n-octadecane is proposed in [10].А large discontinuous change of the noctadecane's refractive index during its phase transition leads to the corresponding step-like change in the transmitted optical power that can reliably indicate the phase change of the sample in the vicinity of the sensor.
The purpose of the present paper is to study the effect of the fullerene C 60 in industrial PW on the refractive index and phase transition temperaturesby applying the refractometry method.
The first step of the composite PCMs pre aration containing C 60 consists of C molten PW and mechanical stirring 55±5 °С.
During the second step, PCM containing C 60 was kept for 15 days in the liquid phase at a temperature of about 60 °an air thermostat.This is necessary because it takes considerable time to reach the saturation equilibrium, from several hours to several days [4].The obtained solution has been founded as supersaturated because of the presence of the undissolved crystals of fullerene C precipitate.The precipitate with crystals of C was carefully removed after PW/C pitate was washed repeatedly by n ty in n-pentane 0.005 mg•ml difference in mass of the dry filter with C ment allowed us to obtain the mass of C tion mass fractions of C 60 in PW at 60…65 °C is Composite PCM samples for further studies were obtained by diluting the sat rated solution of PW/C 60 with pure PW.The required quantity of components was measured using the Model GR 300 electronic balance with an instrument error of 0.5 mg.The C 60 mass fraction uncertainties were evaluated as 1.0 %.
The list of samples that were used for in The first step of the composite PCMs prepconsists of C 60 mixing in molten PW and mechanical stirring at about During the second step, the composite was kept for 15 days in the temperature of about 60 °С in an air thermostat.This is necessary because it takes considerable time to reach the saturation equilibrium, from several hours to several days ].The obtained solution has been founded as supersaturated because of the presence of the undissolved crystals of fullerene C 60 in form of a precipitate.The precipitate with crystals of C 60 was carefully removed after PW/C 60 crystallization.The removed PW with C pitate was washed repeatedly by n-pentane to remove PW (С 60 has very low solubil pentane 0.005 mg•ml -1 at 20 °C [11]) and filtered through a paper filter.The difference in mass of the dry filter with C 60 crystals and the filter b ment allowed us to obtain the mass of C 60 that was not dissolved in PW.The satur in PW at 60…65 °C is 0.000746 g•g −1 -Fig. 1. Composite PCM samples for further studies were obtained by diluting the sat with pure PW.The required quantity of components was measured using the Model GR 300 electronic balance with an instrument error of 0.5 mass fraction uncertainties were evaluated as 1.0 %.The list of samples that were used for the refractive index measurement is given in Table .1.The image of PW samples with various content of C 60 is shown in Fig. 2. PW with C 60 precihas very low solubiliat 20 °C [11]) and filtered through a paper filter.The crystals and the filter before the experithat was not dissolved in PW.The satura-Fig. 1. Composite PCM samples for further studies were obtained by diluting the satuwith pure PW.The required quantity of components was measured using the Model GR 300 electronic balance with an instrument error of 0.5 the refractive index measurement is given is shown in Fig. 2. 2.2 Experiment technique.AnИРФ-454Б Abbe type refractometer was used in the study.The index of refraction, relative to the air, at a wavelength of 589 nm (sodium D line) was measured.It was revealed in [12,13] that fullerene C 60 in solutions of tetralin and o-xylene at low content does not absorb light of 589 nm wavelength.Convergence of readings of the refractive index is no more than ±5•10 -4 .A circulation thermostat was used to maintain a constant temperature during the refractive index measuring.The water thermostat was equipped with automatic temperature control.Temperature deviations in the thermostat from the set value did not exceed ±0.02 °C.The uncertainty of measured temperature in the temperature-controlled part of the refractometer did not exceed 0.05 °C.
PW is a multicomponent solution, thus, after the crystallization of molten PW, the compositions of the solid sample on the surface and in the volume may differ slightly.This effect is caused by different crystallization temperatures of the PW components and thermal diffusion processes.The previously performed experimental analysis revealed that the refractive index of the samples taken in the solid state from different parts of large-volume objects of study can vary within 0.001.To eliminate the methodological error, the samples for measurements were taken from the liquid phase of the object of study, and the refractive index was measured from a higher temperature to a lower one.

Results.
The measured values of the refractive index of the objects of study are presented in Fig. 3. Additionally measured values of the refractive index and the temperatures of the start and finish of the crystallization are presented in Table A.1 of the Appendix.
The data obtained reveal that the effects of small amounts of fullerene C 60 in PW on the refractive index variation are insignificant in absolute value.Therefore, it is advisable to analyze the concentration dependence n D =f(w) at T = const after the experimental data fitting to reduce the influence of the random component of uncertainty.
The obtained experimental data were fitted by Eq. ( 1).The coefficients of Eq. ( 1) and its range of application are given in Table 2. Deviations of experimental data from fitting ones are presented in Fig. 4. The performed analysis reveals that the expanded uncertainty in measuring the refractive index of PW/C 60 samples did not exceed 5.52•10 -4 for liquid phase and 6.57•10 -4 for solid phase.

Discussion.
As follows from the given in Fig. 3 information, the temperature dependencies of the refractive index of composite PCMs PW/C 60 represent a series of almost equidistant straight lines.Curvetting of the linear dependencies of the refractive index n D (t) in the solid phase is observed only at temperatures below 44°C.Since industrial PW is a multi-component mixture of high molecular alkanes (from C 19 and  above), this curvature reflects the effects of structural transformations of some co ponents in the solid phase.
During slow PW cooling with achieving the liquid peratures, a second total internal reflection boundary was observed at refractometry.In the authors' opinion, its presence is explained by the appearance of a new phase (Fig. 3).There are reasons to suppose [7] that under conditions of a low rate of fo mation of crystallization centers in PW and a strong increase in viscosity of PW the glassy state of the substance can form.dex of this phase differs significantly from the refractive index of PW in the liquid and solid crystalline statessolid phase formed during cooling.With a further decrease in temperature, the glassy state transforms into a solid state.During slow PW cooling with achieving the liquid-solid phase transition te peratures, a second total internal reflection boundary was observed at refractometry.In the authors' opinion, its presence is explained by the appearance of a new phase There are reasons to suppose [7] that under conditions of a low rate of fo ation of crystallization centers in PW and a strong increase in viscosity of PW the glassy state of the substance can form.The data obtained reveal that the refractive i dex of this phase differs significantly from the refractive index of PW in the liquid -Fig.3.PW in the glassy state is in equilibrium with the solid phase formed during cooling.With a further decrease in temperature, the glassy state transforms into a solid state.
Fig. 5 presents the concentration dependences of the refractive index corre ponding to various isotherms in the liquid and solid phases.
The analysis of the results revealed the existence of variousregions with two e tremes on the concentration dependencies of the refractive index of the system .The minimum points on the dependenc confirmation with the previously obtained data for other systems [13 above), this curvature reflects the effects of structural transformations of some comsolid phase transition temperatures, a second total internal reflection boundary was observed at refractometry.

In the authors' opinion, its presence is explained by the appearance of a new phase
There are reasons to suppose [7] that under conditions of a low rate of foration of crystallization centers in PW and a strong increase in viscosity of PW the The data obtained reveal that the refractive index of this phase differs significantly from the refractive index of PW in the liquid Fig. 3.PW in the glassy state is in equilibrium with the solid phase formed during cooling.With a further decrease in temperature, the glassy s of the refractive index corresregions with two exes of the refractive index of the system .The minimum points on the dependenciesn D (w) have its confirmation with the previously obtained data for other systems [13][14][15][16][17][18][19][20].
Deviations of experimental data on the refractive index from fitting ones: а -liquid Concentration dependences of the refractive index in the liquid (57…62 °C) and nding to various isotherms Obviously, the complex behavior of the concentration dependencies of the refractive index of the PW/C 60 liquid and solid phases should have a thermodynamic substantiation.Since the thermophysical properties of substances and the refractive index are related [7], the presence of extrema should also manifest itself in the concentration dependencies of other thermophysical properties.
Up to now a lot of studies devoted to investigating the effect of fullerene on the thermophysical properties of liquids were published [4,11,[13][14][15][16][17][18][19][20].However, the principles of thermodynamic modeling of the nanofluids properties, including properties of solutions of PW/C 60 (the molecule C 60 in the solution can be considered both a nanoparticle and a large molecule [4]), remain developed insufficiently [13,15,21,22].In the opinion of some authors [18][19][20][21][22], the current situation is caused by the absence of an approach for the correct evaluation of the nanoparticles' effect on structural changes in the base fluids.It should be emphasized, that mentioned above concerns not only the formation of an interfacial phase around nanoparticles in a nanofluid but also structural changes in base fluidat the distance from the nanoparticles.
According to the mentioned, the study of the properties of fullerene solutions in hydrocarbons is of considerable interest.The interfacial layer of base liquid molecules around C 60 molecules is absent in these solutions.At the same time, fullerene C 60 solutions exhibit unusual optical, thermodynamic, kinetic, and other properties [4,11,[13][14][15][16][17][18][19][20]: complex temperature dependence of the solubility of fullerenes in some solvents was revealed in [4,11,16], non-linear nature of the change in some thermophysical properties with concentration at low content of fullerene in solutions was revealed in [13][14][15][17][18][19][20].
There are several hypotheses of anomalous variation in the base liquids' properties with the presence of fullerene in low content.Thus, the authors of the study [17] assume the presence of two shells around fullerene molecule in solution, first a "loose" lyophobic one, second a lyophilic one (the dense layer of base liquid).
The mentioned features of the fullerene C 60 behavior in solutions are explained by the recently predicted theoretically and discovered experimentally phenomenon of the formation of structural anomalies in solutions [17][18][19][20].The dissolution of fullerene C 60 in aromatic solvents is typicallyfollowed by heat release and entropy decrease, which indicates structural transformations in the liquid phase of the solvent.
The most comprehensive explanation of the described phenomena is given in the studies of Ginzburg with coauthors [17][18][19], where the hypothesis about the appearance of regions with "zero" density in the liquid phase of aromatic hydrocarbons during the fullerene dissolving is formulated.The model of fullerene C 60 solutions in aromatic hydrocarbons assumes the formation of a shell with zero density around C 60 molecules [17].The volume of this shell in the solution cannot be filled with liquid, since the shell's size is smaller than the size of liquid molecules.The formation of this volume by adding a low amount of fullerene C 60 cancontribute to a decrease in the density of aromatic hydrocarbons.
A new thermodynamic hypothesis that explained the causes of fullerene C 60 admixtures'effect on the variation of thermophysical properties of aromatic hydrocarbons was proposedin studies [13][14][15].According to the hypothesis, a low amountof fullerene admixtures C 60 contribute to an anomalous variation in fluctuations of density and volume, as well as variation in the activation energy of aromatic hydrocarbon molecules.As a result, the saturated vapor pressure, density, and viscosity of the liquid significantly change.The obtained data on the refractive index of the liquid phase of composite PCM PW/C 60 allow us to state that the hypothesis on the effect of fullerene admixtures on fluctuations of the thermodynamic functions is also valid for high-molecular n-alkanes.
This conclusion is confirmed by the concentration dependencies of the refractive index -Fig.5.The refractive index values are related to the density by the Lorentz-Lorenz equation.Therefore, the decreasing refractive index in the range of fullerene concentrations of 0…0.01 wt.% is concerned with increasing the density fluctuations [13].According mentioned above, the obtained data on the refractive index of PW/C 60 is thermodynamically justified.The increasing refractive index in the concentration range of 0.01...0.035 is probably concerned with the destruction of the long-range order between the molecules of the PW components (clusters), which is typical for liquids with parameters close to the triple point [23].
Refractive index values obtained in the temperature range of phase transition allow us to accurately determine the temperatures of the start and finish of melting for the PW/C 60 .The studying breaks of the dependencies of n D (t) is an effective method to register the phase transformations in the objects of study.The obtained concentration dependencies of the temperatures of the start and finish of the phase transition are shown in Fig. 6.
An analysis of data presented in Fig. 6 reveals that fullerene C 60 admixture changes the temperatures of the phase transition of the objects of study.Repeated experiments state that the melting points of the same PW/C 60 sample can vary within 0.5...1 °C.This effect has a random character and is typical for systems with abroken metastable state (the supercooled liquid phase transforms into a solid phase).The concentration dependence of the start and finish of the phase transition is complex.At C 60 content in PW of 0…0.01 wt.% the temperatures of the start and finish of the phase transition decreased, at C 60 content of 0.01…0.04wt.% they increased more than the pure PW temperatures and at C 60 content more than 0.04 wt.% they decreased again.It should be noted that the concentration dependencies of the phase transition temperatures and concentration dependencies of the refractive index are similar in shape and location of the extrema points -Figs.5-6.

Conclusion.
The purpose of the paper was to study the effect of the fullerene C 60 in industrial PW on the refractive index and phase transition temperatures by applying the refractometry method.
The values of the refractive index of solutions of fullerene C 60 in PW of 52...54 °C melting point at the ranges of С 60 content of 0...0.052 wt.% and temperatures of 41…65 °С were obtained.The expandeduncertainty of the experimental data did not exceed 5.52•10 -4 for liquid phase and 6.57•10 -4 for solid phase.The complex character of the concentration dependence of the refractive index on isotherms for system PW/C 60 has been registered both in liquid and solid phases.Data on the effect of the C 60 content in PW on the temperatures of the start and finish of its phase transition was obtained.At C 60 content in PW of 0…0.01 wt.% the temperatures of the start and finish of the phase transition decreased, at C 60 content of 0.01…0.04wt.% they increased more than the pure PW temperatures and at C 60 content more than 0.04 wt.% they decreased again.The obtained effects of a decrease and increase in the refractive index on the isotherms and temperatures of start and finish of PW crystallizationcan be explained by structural transformations in PW caused by C 60 presence.In the authors' opinion, the reason for the extreme behavior of concentration dependence of the refractive index of objects of study is the effect of C 60 on the density fluctuations and the quasi-crystalline structure of the liquid and solid phases.These structural transformations in PW cause a similar change in the concentration dependencies of the temperatures of the start and finish of the phase transition of objects of study.

Fig. 3 .
Fig. 3.Temperature dependence of the refractive index for objects of study

Fig. 5 13 a 4 .Fig 5 .
Fig 5.Concentration dependences of the refractive index in the liquid (57…62 °C) and solid (43…51 °C) phases correspo Deviations of experimental data on the refractive index from fitting ones: а phase, b -solid phase Concentration dependences of the refractive index in the liquid (57…62 °C) and solid (43…51 °C) phases corresponding to various isotherms
Table. 1.The image of PW samples with various content of C