CC BY
5
Keywords:
benzene, metastable state, critical pressure point, melting
equilibrium curves of substances, plazma.
UDC 543.272.75:544.344.015.4
Phase transitions and the phase diagrams. A case of benzene
Beycan Ibrahimoglu1*, B.A. Grigoryev2, Berk Gokbel3, Beycan Ibrahimoglu jun.3
1 Ankara Science University, Qamlica Mah. Anadolu Bulvari No:16A/1 Yenimahalle, Ankara, Turkey
2 Gazprom VNIIGAZ LLC, Bld. 1, Estate 15, Proyektiruemyy proezd no. 5537, Razvilka village, Leninskiy district, Moscow Region, 142717, Russian Federation
3 Anadolu Plazma Teknoloji Enerji Merkezi, Gazi Universitesi Yerlefkesi Golbafi Kampusu Teknoplaza Binasi C Blok Zemin Kat No:27 Golbafi Ankara, Turkey
* E-mail: beycanibrahimoglu@yahoo.com
Abstract. In this study, the metastable state of benzene at high pressure and temperature was examined and a critical pressure point was determined on the melting equilibrium curve. In addition, with the application of the thermodynamic geometry system and the evaluation of the axiomatic method, the melting equilibrium curves of many organic and inorganic substances ending with a critical point has been shown. Location of plasma in single component system p-T phase diagram determined and modeled considering benzene atom.
Determination of the true critical pressure and density in p-t phase diagram
Based on the general laws of thermodynamics, certain physic laws were established using geometrical methods, different than the ordinary analytical methods. Therefore, it is very important from a thermodynamic point of view to use the axiomatics for constructing a mathematical theory. When applying geometrical thermodynamics to some parameters, axiomatic principles are accepted (axioms) and the rest are logically deduced. Axiomatic approach enables expressing geometric expressions that are not possible to prove.
Kelvin applied graphical method to p-T, V = const and V-T, p = const diagrams of the gas phase of substances, and the absolute temperature of substances in the solid phase was determined as T(K) = t(°C) + 273,15 °C with great accuracy (fig. 1). Even today, despite the technological developments, Kelvin's V = 0, t = -273,15 °C has not yet been reached experimentally. According to observations provided, in the gas and liquid phases the hydrogen behaves completely different [1-3].
Kelvin's method has started from the following postulates that are later accepted as the postulates of the ideal gas law:
(1)
There is a unique temperature where V = 0 for all substances at all pressures.
S ^
V
-273,15
0
100
t, °C
Fig. 1. Determination of absolute temperature in p-T, V = const diagram
T, K
Fig. 2. Determination of ionization temperature in the p-T, p = const diagram
Same method is used to determine the temperature of ionization and decomposition of the substance, using the p-p, T = const dependence on the gas phase of the substance, and the graph obtained is given in fig. 2 [4-10].
Studies revealed that the p-p, T = const dependence shows the ionization point in monatomic gases and the decomposition temperature in polyatomic gases.
Application of geometric method to liquid phase of substances
Density and viscosity tests of benzonitrile, medium-, meta- and para-toluidine at high pressures and temperatures were carried out [11-15]. When the graphical method was applied to p-p, T = const diagram, it was observed that at high pressure the isotherms merge into a point for liquid phase of hydrocarbons. For example, the geometric method was applied to the experimental results of benzonitrile (C6H5(CN)) provided in Table 1, and the presence of a point where isotherms intersect [9, 16] on the melting equilibrium curve at high pressure values was determined as shown in fig. 3. This point is considered as the real critical pressure:
| —I = const. (2)
Up )t ' '
Table 1
Experimental density (p) data for benzonitrile at high pressures and temperatures, kg/m3
p, MPa T, K
298 323 348 373 398 423 448 473 498 523
0,1 1001,2 980,1 957,5 935,8 911,8 885,1 859,8 832,6 - -
5 1004,2 982,8 962,1 940,9 917,4 893,8 866,8 842,3 816,5 791,2
10 1006,2 985,9 965,4 944,1 922,1 899,7 874,8 852,3 826,3 804,8
20 1010,8 990,9 969,9 949,8 927,6 907,1 884,8 862,2 839,6 818,2
30 1016,2 996,6 977,4 957,0 936,2 915,5 893,6 874,0 853,0 832,5
40 1020,2 1001,4 981,3 963,6 943,6 923,7 903,2 883,1 863,1 844,8
50 1022,6 1005,1 987,5 969,9 950,1 930,1 913,0 893,2 874,2 861,8
There exists a pressure where density of the fluid is zero for all temperatures. True critical pressure (pcr) and critical density (pcr) values for benzonitrile and some other hydrocarbons are presented in table 2.
| 290 ^250 210 170 130 90 50
T, K:
— 298
— 323
— 348
— 373
— 398
— 423
— 448
— 473
— 498
— 523
10 800
i
л
/ :;<////
✓ /'// '//// i i
/ / ' S / / /' /V/'/ '///
✓ ✓ / ' / ✓ ✓ / ' / / / / / / / / ' / V/
// ///
850 900 950
1000 1050 1100
p, kg/m3
Fig. 3. Point at p-p, T = const dependency, where the isotherms of benzonitrile intersect on the p axis (p = 270 MPa, p = 1100 kg/m3)
Table 2
Solid-liquid critical pressure value of some hydrocarbons
Matter Chemical formula Pcr, MPa Pcr, kg/m2
n-Decane c10h12 130 839
n-Nonan c9h20 150 826
n-Xylene c8h10 200 990
o-Xylene c8h10 205 1000
o-Toluidine c7h9n 150 1400
m-Toluidine c7h9n 140 1450
p-Toluidine c7h9n 200 1100
Benzonitrile c7h5n 185 1350
Benzene C6H6 210 1200
Liquid phase of the substance
The phase diagram of the pure substance provided in fig. 4 is visually plotted on the p-T-phase diagram based on pressure and temperature dependent experimental results. In the phase diagram, all three phases and the triple point where these phases are in equilibrium are present. In addition, a point on a liquid-gas equilibrium curve, commonly known as a critical point, is also available on the phase diagram.
In the conventional p-T-phase diagram being used today, there are only three phases and the boundary curves separating these phases from each other, the triple point where the three phases coexist at one point and the critical parameters where the liquid gas equilibrium curve ends (Tcr, pcr, pcr). Examining the diagram in fig. 5 which determines the pressure and temperature dependent boundary range of the liquid phase, it seems that pcr and pcr
in the classical phase diagram do not characterize the real critical pressure and density values.
Based on the high pressure and temperature experiments of the benzene metastable state, authors observed that there is a critical point on the melting equilibrium curve [17-19]. The existence of a critical point at high pressures on the liquid-solid equilibrium curve based on the laws of geometric thermodynamics will be discussed. For this purpose, it is important to examine the state of the boundary range of the liquid phase depending on temperature and pressure. In the diagram (see fig. 5), the temperature-dependent boundary interval of the liquid phase exists between the triple point TTP and the critical point Tcr. With the same approach, when the pressure range of the liquid phase is examined in the diagram, it is obvious that the triple point and critical point, pTP and pcr, do not determine the range limit of the liquid phase. Because the pj point in the diagram is the liquid phase below the critical pressure pcr, p2 and p3 points are in the liquid phase above the pcr. In this case, the presence of liquid phase above and below the pcr point indicates that the pcr point at fig. 5 does not characterize the critical pressure. This is the case also for the critical density pcr.
Benzene critical point found on melting equilibrium curve using experimental method
For determining the critical point, the metastable state of benzene at high pressure and temperature was investigated in experiments. Analysis of the benzene meta-stable state is an important problem of the modern science. Benzene is a prototype
^ A
Ptp
Critical point
^Superheated
Tt,
T
T
Fig. 4. Critical parameters shown on p-J-phase diagram
Pa-
Pi
pTP
Pi > Pi > Pcr > Pi
Ti Tcr Ti
Fig. 5. p-J-phase diagram determining the boundary range of the liquid phase
ci
aromatic hydrocarbon and is an object of numerous experimental and theoretical studies [20-27]. In literature, benzene pre-crystallization meta-stable state at normal pressures was mainly studied with the thermal pre-treatment of liquid benzene; this pre-treatment influenced the degree of overcooling AT- relative to melting temperature TL [28, 29]. At the same time, there are practically no studies of pressure effect on the liquid benzene pre-crystallization meta-stable state. The ice was broken by M. Azreg-Ai'nou, et al. [25], who described the technique of a similar research with the help of obtained data of volume and enthalpy changes at phase transformations under permanent external pressure and the benzene isobar in the T-V coordinates [30, 31]. It was diagramed with phase transformation taken into account. In the course of research, a necessity of studying a number of parameters of benzene meta-stable state under different pressures emerged.
By the way, a large number of metastable phases have been studied mostly on the evaporation equilibrium curves [24, 31-34].
Experiment setup and technique. With the help of the experimental facility provided [5, 9, 16], authors measured and controlled the following parameters of the benzene meta-stable state: pressure p, container temperature, freezing temperature Tb (i.e. crystallization temperature), temperature Tc in the low point of the meta-stable state, overcooling AT- = Tb - Tc relative to freezing temperature, pressure difference Ap at the initial stage of explosive crystallization, incubation period t1 of liquid benzene stay in the meta-stable (overcooled) state; t2 - the time of an abrupt
transition from the meta-stable state to the crystalline one; t3 - the time of isothermal freezing, the total time tE of solidification (tE = t1 + t2 + t3).
Experimental results. Two schematic thermograms of benzene cooling (fig. 6) with (I) and without (II) a meta-stable area of benzene of volume 10 cm3 at 0,1 atm were analysed.
The first thermogram characterizes an overcooling-free equilibrium crystallization (AT^ ~ 0). Such thermograms are fixed after a small pre-heating of liquid benzene and its cooling [29]. On the way a' ^ b a liquid phase cools down, and on the way b ^ e' the isothemal crystallization takes place at 278,5 K, this temperature coincides with benzene melting temperature TL [35]. On the way e' ^ f solid benzene cools down. Point b on the thermogram is conventionally called one of the boundaries of the meta-stable state at the minimum overcooling AT- = 0. In benzene cooling from higher temperature (with an overheating of about AT + > 5 K relative to TL), i.e. from point a > a' on thermogram II, another shape of the T-t curve is observed. Temperature approaches to the area of overcooled state along the way b ^ e. Assume that point c is the lower boundary of meta-stable state of liquid benzene and it corresponds to some temperature Tc = 258,5 K (i.e. to overcooling AT- = 20 K). Time t1 ~ 160 5 is an incubation period of the liquid phase stay in the meta-stable state. In a time t1 on the boundary of metastability, temperature starts rising quickly from point c to point d for a time t2 ~ 6 5. As this takes place, the rate of adiabatic process on the segment cd is ~4 K/s. Keeping in mind that the
Fig. 6. Schematic thermograms in the T-t coordinates recorded at p = 1 atm:
they characterise (I) the absence of a meta-stable state and equilibrium crystallization and (II) the availability of a meta-stable state and non-equilibrium-explosive crystallization
system cooling rate is ~0,14 K/s << 4 K/s, heat losses into the environment can be neglected and the equation of heat balance can be written as Qx ~ Q2, i.e. mxAHLS ~ cp^ATwhere mx is the mass of a solidified part of the sample after the termination of meta-stable state, m = 8,8 g is the mass of the whole sample of benzene, cp = 1759 Jmole'K1 is specific heat capacity, AHls = 128 kJ kg-1 is enthalpy of benzene melting [9]. From this formula one can calculate an initial fraction of volume (or mass) of the solidified benzene after it has falled in the meta-
m cp AT~
stable state: a = —^ = —-= 0,27. That is
m ahis
mx ~ 2,4 g. Then, on thermogram II the remaining part of benzene p = 1 - a = 0,73 freezes in a time t2 = 260 s (or 6,4 g) at temperature 278,5 K. Thus, the total time tE of the whole process of solidification was ~426 s. The relative concetration q of all crystal-like clusters in a meta-stable liquid phase was calculated from the formula q = xJx [30], in practice this concetration was in the range of 0,37 ± 1 at all pressures.
The thermograms like thermogram II were also obtained at other static pressures p up to 2300 atm (fig. 7). In table 3 the average values of singular points at 24 different pressures were provided. In this table there are also temperatures Tb, Tc, Td, Te corresponding to points b, c, d, e on the thermograms, pressures pc and pd in points c
and d, pressure differences Ap at a temperature transition from point c up to point d and time intervals t1, t2, t3, t4.
From this table, it is evident that as pressure increases the temperature of freezing Tb (or amin) increases and, as the natural result, the other parameters (AT-, Ap and time intervals t1, t2, t3, t) decrease.
To illustrate these changes, in fig. 8 separate thermograms are shown at pressures p = 1; 500; 1000; 1500 and 2200 atm. On the corresponding points of freezing one can write the equations of dependences Tb = f p); Tc = f p); AT - = f p); Ap = f( p); ti = f( p); tE = f( p):
Tb = Ai + Bi p + Cip2, (3)
where A1 = 278,5 K, B1 = 710 3 K atm1, C1 = 1,235 10 5 Katm2;
Tc = A2 + B2p + C2p\ (4)
where A2 = 258,5 K, B2 = 3,3 10 2 K atm1, C2 = 4,296 10 6 K^atm2;
AT - = Tb( p) - Tc( p); (5)
Ap = A3 - B3p + C3 p2, (6)
where A3 = 32 atm, B3 = 3,2102, C3 = 7,794 10 6 atm-1;
Table 3
Parameters of the meta-stable state of benzene and its freezing on the thermograms
p, atm Tb, K T, K AT-, K Td = T, K pc, atm Рф atm Ap, atm t1, s t2, s t3, s t, s
0,1 278,5 258,5 20,0 278,5 - - - 160 -6,0 260 426
100 279,0 267,0 13,0 279,0 100 68 32,0 131 -3,0 210 343
200 280,0 270,0 10,0 280,0 200 173 27,0 112 -2,5 180 294
300 282,8 274,6 8,2 282,8 300 277 23,0 97 -2,0 155 254
400 284,8 277,8 7,0 284,8 400 380 20,0 85 -2,0 135 222
500 286,7 280,7 6,0 286,7 500 482,5 17,5 72 -2,0 115 189
600 289,5 284,5 5,0 289,5 600 585 15,0 61 -1,5 97 159
700 291,2 287,2 4,0 291,2 700 687 13,0 53 -1,5 85 139
800 294,8 291,2 3,6 294,8 800 788,5 11,5 44 -1,5 70 115
900 297,0 293,8 3,3 297,0 900 890,5 9,5 37 -1,5 60 98
1000 299,5 296,6 2,9 299,5 1000 992 8,0 31 -1,0 50 82
1100 302,5 300,1 2,4 302,5 1100 1093,3 6,7 25 -1,0 40 66
1200 305,3 303,3 2,0 305,3 1200 1194,5 5,5 22 -1,0 35 58
1300 308,0 306,2 1,8 308,0 1300 1295,8 4,2 18 -1,0 30 49
1400 312,2 310,7 1,5 312,2 1400 1396,4 3,6 16 -1,0 25 42
1500 315,5 314,3 1,1 315,5 1500 1497,2 2,8 12 -1,0 19 32
1600 320,1 319,2 0,9 320,1 1600 1598,1 1,9 8 -1,0 14 23
1700 324,0 323,3 0,7 324,0 1700 1698,8 1,2 6 -0,5 10 16
1800 328,0 327,5 0,5 328,0 1800 1799,4 0,6 4 -0,5 6 10
1900 333,5 333,2 0,3 333,5 1900 1899,8 0,2 2 0,5 4 6
2000 340,5 340,4 0,1 340,5 2000 1999,9 0,1 1 -0,5 2 3
2100 347,0 347,0 0 347,0 2100 2100 0 0,5 0 1 1
2200 356,0 356,0 0 356,0 2200 2200 0 0 0 0 0
2300 368,0 368,0 0 368,0 2300 2300 0 0 0 0 0
ti = A 4 - BAp + C4p2, (7)
where A4 = 160 s, B4 = 0,179 satm1, C4 = 4,980 10 5 s'atm2;
tE=a5 - Bp + c5 p2, (8)
where A5 = 426 s, B5 = 0,480 satm1, C5 = 1,342 10 4 s'atm2.
Relying on these data one can conclude that curves Tb = fp) and Tc = fp) cross at a point P (see fig. 8) at which the meta-stable state parameters AT - t1 and tE become equal to zero.
Using the information provided in table 3 and fig. 7 it was possible to construct a graph similar to fig. 9 in order to determine a limiting value for a pressure beyond which there is no any coexistence of solid and liquid states. The value of this pressure is denoted as critical pressure of the liquid [16, 21-24]. This pressure determines the pressure-dependent boundary range of the liquid phase.
Based on the test results the critical pressure pcr = 2200 atm and the corresponding temperature Tcr = 356 K for benzene (see fig. 9).
The results of the graphical method applied to some substances and the experimental results obtained from the metastable state of benzene revealed the presence of pcr on the equilibrium curve and the presence of plasma in the p-T phase diagram (fig. 10).
Fig. 8. Types of curves
2200
49,2
0,48
Solid
i
Liquid
-ОТ
Gas
278,6
356
Fig. 9. Phase diagram for benzene: for liquid phase pcr = 2200 atm, Tcr = 356 K
л л
Ptc Ptp
P , P crcr
Solid \ Plasma
Liquid \ cr
T V tp
- Ci Gas
562,7 T, K
T„
T
T
T, K
" ds ~ TP ~ pc
Fig. 10. p-T-diagram showing the plasma phase
In fig. 10, besides the melting, condensation, sublimation equilibrium curves, the ionization equilibrium curve between the two critical points Tcr and pcr completes the phase diagram. Gibbs' phase rule determines the phase equilibrium conditions in a system. Gibbs' rule also indicates that there cannot be more than three phases at equilibrium states in a homogeneous system. Although the benzene phase diagram indicates that four phases (solid, liquid, gas and plasma) coexist, only three phases will always be in equilibrium.
Definition of single component systems with plasma included in phase diagram:
• in single component systems the degrees of freedom is only zero;
• the number of phases that can be in equilibrium varies from one to four.
Location of plasma in the phase diagram. Experimental results and graphs of metastable state of liquid benzene at high pressure and temperature were applied to benzene thermodynamic parameters, and the existence of a pcr point on the melting equilibrium curve have been provided. The Tcr point on the evaporation curve and the pcr points on the melting equilibrium curve determined the location of the plasma in the p-T phase diagram.
In addition, the position of the plasma in the phase diagram formed the ionization equilibrium curve between two critical points Tcr and pcr. In this case, the phase diagram consists of melting, evaporation, sublimation and ionization equilibrium curves. Studies on determining the
location of plasma in the phase diagram have been carried out for many years [36, 37] and research is still ongoing.
Atomic model
A model is a representation of a system in the real world. Models help us to understand systems and their properties. Atom is the smallest unit of any element maintaining its chemical and physical properties. Different models of the atom have been developed by famous physicists. The concept of another atomic model presented is an attempt to clarify some aspects of the structure of the atom due recent observations and scientific achievements.
Physical and chemical properties of atom. Each chemical element corresponds to a set of certain atoms. Physical properties are those that can be observed without changing the identity of the substance. General properties of a substance such as color, density, state of aggregation, melting points, boiling points, pcr, pcr, Tcr and hardness, etc., are examples of physical properties.
In order to simplify the complexity of the conventional phase diagram, due to atoms inheritance of physicochemical properties of a matter, atomic model is accepted as a model for phase diagram of pure substance. A pressure and temperature-dependent phase diagram of a single component substance has been drawn, provided in fig. 11.
Phase diagram of benzene and benzonitrile. Atoms carry the chemical and physical properties of the material, allowing all parameters to take part
л
cr
ds
Meltings Freezings
Critical field (p )
Metastable solid-liquid Triple field
Sublimation deposition
^Vaporization ^Condensation
Critical field (TJ
Metastable liquid-gas Metastable solid-gas
Critical field (pj Absolute temperature
Fig. 11. Thermodynamic surface of matter drawn based on the atomic model
Fig. 12. Benzene atom
in the phase diagram of that material. This property of the atom has led to the drawing of the phase diagram of the results we obtained in experimental and graphic studies of benzene.
In order to make the phase diagram of benzene, the atom of benzene (fig. 12) was proposed as a model and a phase diagram was made in the light of the results obtained by graphical and experimental methods.
The phase diagram for benzene and benzonitrile provided in fig. 13 containing all four phases (solid, liquid, gas and plasma), but yet there still exist only three phases at equilibrium conditions (TTP, pcr, Tcr) where the degree of freedom of the system is equal to zero. The thermodynamic symmetry conditions are provided in table 4.
2200
4,92 -1
0,152 0
2700
43
0,72
b
> - - ^ Plasma \ 4 \ Liquid \
/ Solid //
ИгТ Sy 1 1 X/ 1 /
1 /А 1 // 1 I /у 1 1 1 1 1 1 1 1 1 1 / 1 / Gas 1 / 1 / I у/ ^^' 1 1
vo
2
T, K
Fig. 13. Pressure and temperature p-T phase diagram of benzene (a) and benzonitrile (b)
1
0
Table 4
Thermodynamic symmetry state of benzene and benzonitrile in p-T-diagram
Substance Liquid-Solid-Gas (TTP) Liquid-Plasma-Gas (Tcr) Solid-Plasma-Liquid ( pcr)
Benzene p = 1 atm; T = 278,5 K p = 49,2 atm; T = 561,5 K p = 2200 atm; T = 347 K
Benzonitrile p = 1 bar; T = 260 K p = 43 bar; T = 700 K p = 2700 bar; T =375 K
***
Via applying graphs to thermodynamic parameters, it is possible to determine the equilibrium curves and critical points of all phases and improve the details of the p-T phase diagram. Critical pressure and critical density on the equilibrium curve are determined by applying (1/V-T)p = const diagram to the liquid phase of the substances. In addition, the investigation of the metastable state of benzene at high pressures revealed the critical pressure on the melting equilibrium curve by experiments.
The path followed and basic inferences regarding the determination of plasmas location on the phase diagram are given below.
1. The end point of the melting curve determines the limit range of the liquid phase depending on pressure and temperature.
2. The end point of the melting curve has determined the location of the true critical pressure pcr.
3. Combining the two critical points ( pcr, Tcr) with each other created a new ionization equilibrium curve.
4. The new phase diagram reveals that the degrees of freedom are zero and cannot be changed. (The number of phases that can be in equilibrium is between one and four.)
5. In addition, although there are four phases in the phase diagram, only three phases are in equilibrium.
6. The phase diagram p-T is drawn by applying the experimental pressure temperature data of benzene and benzonitrile to the atomic model.
References
1. IBRAHIMOGLU, B., T.N. VEZIROGLU, A. HUSEYNOV. Study of thermodynamic parameters of hydrogen gas by grapho-analytic method. International Journal
of Hydrogen Energy, 2005, vol. 30, pp. 515-519, ISSN 0360-3199.
2. IBRAHIMOGLU, B., N. VEZIROGLU,
A. HUSEYNOV, et al. Study of thermodynamic parameters of hydrogen gas by grapho-analytic method. In: Hydrogen Materials Science and Chemistry of Carbon Nanomaterials, 2004, pp. 225-232.
3. IBRAHIMOGLU, B., Q.K. DINDAR, H. EROL, et al. Determination of 1/V-T (p, constant) diagrams of hydrogen gases by graph-analytical methods. Journal of Thermal Engineering [online], 2017, vol. 3, no. 1,
pp. 1071-1077, ISSN 2148-7847.
4. IBRAHIMOGLU, B., G. TEKELI,
Z. YILMAZOGLU, et al. Investigation of hydrogen gas with graphical method. In: Proc. of 4th International Hydrogen Technologies Congress (IHTEC-2019), 20-23 June, Edirne.
5. FARZALIEV, B.I., A.M. RAGIMOV, A.T. HAJIYEV. Graphical definition
of the parameters of the triple equilibrium point [Graficheskoye opredeleniye parametrov troynoy tochki fazovogo ravnovesiya]. Izvestiya Vysshikh Uchebnykh Zavedeniy. Neft i Gaz, 1985, no. 12, pp. 57-59, ISSN 0445-0108. (Russ.).
6. FARZALIEV, B.I, N.F. ALIEV. Determination of melting line for gases by graphical analytic method [Opredeleniye linii plavlebiya gazov grafoanaliticheskim metodom]. In: Proc.
of a scientific conference in Tzerbaijan Technical University, 1992, Az TU, Baku, p. 21. (Russ.).
7. IBRAHIMOGLU, B. Grafoanalytical of critical pressure in gas. Finding with the method. Turkish Journal of Science and Technology, 1994, vol. 17, p. 2, ISSN 1308-9080.
8. IBRAHIMOGLU, B.I., O.E. ATAER. Determination of a node on the melting curve. In: 11th National Congress of Business Science and Technology (ULIBTK-97), Edirne, p. 33.
9. IBRAHIMOGLU, B., B. IBRAHIMOGLU jun. determination of liquid phase range of matters
by graphic-analytical method. SSRG International Journal of Thermal Engineering [online], 2018, vol. 4, no. 2, ISSN 2395-0250.
10. IBRAHIMOGLU, B., G. TEKELI. Application of graphic and graphic-analytic geometry systems on the liquid and gas phases of matter. Vesti Gazovoy Nauki. collected scientific technical papers. Moscow. Gazprom VNIIGAZ LLC, 2019, no. 1 (38). Actual issues in research
of bedded hydrocarbon systems, pp. 163-171. ISSN 2306-9849.
11. GUSEUNOV, S.O., B.I. FARZALIEV, Y.M. NAZIYEV. The density and dynamic viscosity of benzonitrile at high pressures and temperatures [Plotnost i dinamicheskaya vyazkost benzonitrila pri vysokikh davleniyakh i temperaturakh]. Izvestiya Vysshikh Uchebnykh Zavedeniy. Neft i Gaz, 1978, no. 12, p. 48, ISSN 0445-0108. (Russ.).
12. GUSEUNOV, S.O., B.I. FARZALIEV, Y.M. NAZIYEV. Investigation of dynamic viscosity of O-methylanil at high pressure and temperature [Issledovaniye dinamicheskoy vyazkosti O-metilanilina pri vysokikh davlenii i temperature]. Izvestiya Vysshikh Uchebnykh Zavedeniy. Neft i Gaz, 1979, no. 7, p. 52, ISSN 0445-0108. (Russ.).
13. GUSEINOV, S.O., B.I. FARZALIEV. Investigation of the density and dynamic viscosity of a P-toloudine under high pressures and temperatures [Issledovaniye plotnosti
i dinamicheskoy vyazkosti P-toloudina pri vysokikh davleniyakh i temperaturakh]. Izvestiya Vysshikh Uchebnykh Zavedeniy. Neft i Gaz, 1981, no. 6, p. 65-68, ISSN 0445-0108. (Russ.).
14. NAZIYEV, Y.M., S.O. GUSEYNOV,
B.I. FARZALIEV. Untersuchungen zur Dichte und dynamischen viskositat dev o-m und p-toluidine bei hohen Drücken und verschiedenen temperaturen. Chemische technik, 1983, vol. 35, p. 40-42, ISSN 0045-6519. (Germ.).
15. GRIGORYEV, B.A., A.A. GERASIMOV,
I.S. ALEKSANDROV. Thermophysical properties of oil hydrocarbons, gas condensates, natural and associated gases [Teplofizicheskiye svoystva uglevodorodov nefti, gazovykh kondensatov, prirodnogo i soputstvyyushchikh gazov]. Moscow; MphEI, 2019, vol. 1. (Russ.).
16. AZREG-AINOU, M., B. IBRAHIMOGLU. High-pressure eects on the benzene pre-crystallizationmetastable states. Eur. Phys. J.E, 2019, vol. 42, ISSN 1292-8941.
17. ALEXANDROV, V.D., B. IBRAGIMOGLU, A.E. POKINTELITSA. Pressure falling effects accompanying phase transformations
of benzene under the accession of comprehensive compression. Cynami ôydieenbHi Mamepianu, 2015, no. 1 (111), ISSN 1814-3296. (Ukr.).
18. IBRAHIMOGLU, B., C. KANBESH, I.M. AHMEDOV. Phase transformations
of benzene in terms of low temperatues and high pressures [Fazovyye prevrashcheniya benzola v usloviyakh nizkikh temperatur i vysokikh davleniy]. KimyaProblemleri, 2015, no. 4, pp. 367-371, ISSN 2221-8688. (Russ.).
19. FARZALIEV, B.I., N.F. ALIYEV. On benzene phase transitions at high pressures [O benzolnykh fazovykh perekhodakh pri vysokikh davleniyakh]. In. Thermodynamic and transport properties
of substances [Termodinamicheskiye i perenosnyye svoystva veshchestv]. collected book. Baku. Azerbaijan Polytechnic Institute named after Ch. Ildrym, 1989, pp. 61-65. (Russ.).
20. KNUNYANTS, I.L. Encyclopaedic dictionary in chemistry [Khimicheskiy entsiklopedicheskiy slovar]. Moscow. Bolshaya Sovetskaya Entsiklopediya, 1983, p. 792. (Russ.).
21. GLASSTONE, S. Theoretical chemistry. New York. Boston College, 1948.
22. Benzen [Benzin]. In. Encyclopaedic dictionary of Brockhaus and Ephron [Entsiklopedicheskiy slovar Brokgauza i Efrona]. 86 vols.
St. Petersburg, 1890-1907.
23. CIABINI, L., F.A. GORELLI, M. SANTORO,
et al. High-pressure and high-temperature equation of state and phase diagram of solid benzene. Phys. Rev. B, 2005, vol. 72, no. 094108-1, ISSN 2469-9950.
24. DEBCNEDETLI, P.G. Metastable liquids: concepts and principles. Princeton. Princeton University Press, 1996.
25. AZREG-AÏNOU, M., A. HÜSEYNOV,
B. IBRAHIMOGLU. Phase equilibrium and metastability of liquid benzene at high pressures. J. of Chemical Physics, 2006, vol. 124, no. 20, p. 204505, ISSN 0021-9606.
26. KALDIS, E. (ed.). Crystal growth of electronic materials. Amsterdam. North-Holland, 1985.
27. VINET, B., L. MAGNUSSON,
H. FREDRIKSSON et al. Correlations between surface and interface energies with respect to crystal nucleation. Journal of Colloid and Interface Science, 2002, vol. 255, no. 2, p. 363-374, ISSN 0021-9797.
28. ALEXANDROV, V.D. Kinetics of nucleation and mass crystallization of an overcooled liquid and amorphous media [Kinetika zarozhdeniya
i massovoy kristallizatsii pereokhlazhdennoi zhidkosti i amorfnykh sred]. Donetsk. Donbas, 2011. (Russ.)
29. ALEXANDROV, V.D., V.A. POSTNIKOV. Investigation of overcoolings in benzene crystallization [Issledovaniye pereokhlazhdeniy pri kristallizatsii benzola]. Укратський xiMiuHm журнал, 2004, vol. 70, no. 9-10. p. 104-109, ISSN 0041-6045. (Russ.).
34. PROZENKO, S.P., V.G. BAYDAKOV,
A.O. TIPEEV. Melting line, spinodal and end point of the melting line in a system with modified Lennard-Jones potential [Liniya plavleniya, spinodal i konechnaya tochka linii plavleniya v sisteme s modifizirovannym Lennard-Dzhonsonovskym potencialom]. Teplophizika i aeromekhanika, 2013, vol. 20, no. 1, p. 95-106, ISSN 0869-8635. (Russ.).
30. BRIDGMAN, P.W. Collected experimental papers. Cambridge, Massachusetts: Harvard University Press, 1964.
32. BAIDAKOV, V.G., S.P. PROTSENKO. Singular point of a system of Lennard - Jones particles at negative pressures. Phys. Rev. Lett., 2005, vol. 95, no. 015701, ISSN 1079-7114.
31. SKRIPOV, V.P. The concept of metastability and phase transitions. Thermo-physical properties of matter, 2002, no. 10.
35. NORMAN, G.E., A.N. STAROSTIN. Failure of classical description of nondegenerated dense plazma [Nesostoyatelnost klassicheskogo opisaniya nevyrazhdennoy plotnoy plazmy]. Teplofizika vysokikh temperatur, 1968, vol. 6, no. 3, pp. 410-415. ISSN 0040-3644. (Russ.).
33. SKRIPOV V.P., M.Z. FAIZULLIN. Phase transitions crystal-liquid-vapor [Fazovye perekhody kristall-zhidkost-par i termodinamicheskoe podobie]. Moscow: Phizmatlit, 2003, 160 p. (Russ.)
36. NORMAN, G.E., A.N. STAROSTIN. Thermodynamics of highly imperfect plasma [Termodinamika silno neidealnoy plazmy]. Teplofizika vysokikh temperatur, 1970, vol. 8, no. 2, pp. 381-408.
37. BRAZHKIN, V.V., A.G. LYAPIN. Universal viscosity growth in metallic melts at megabar pressures: the vitreous state of the Earth's inner core. Uspekhi Fizicheskikh Nauk, 2000, vol. 170, no. 5, pp. 535-551. ISSN 0042-1294.
Фазовые переходы и фазовые диаграммы на примере бензола
Б. Ибрагимоглы [Б.И. Фарзалиев]1*, Б.А. Григорьев2, Б. Гёкбел3, Б. Ибрагимоглы мл.3
1 Университет Анкары (Ankara Bilim Unversitesi), Турция, Анкара, Qamlica Mah.Anadolu Bulvari No:16A/1 Yenimahalle
2 ООО «Газпром ВНИИГАЗ», Российская Федерация, 142717, Московская обл., г.о. Ленинский, пос. Развилка, Проектируемый пр-д № 5537, зд. 15, стр. 1
3 Энергетический центр «Анатолийские плазменные технологии» (Anadolu Plazma Teknoloji Enerji Merkezi), Турция, Анкара, Университет Гази, Yerle^kesi Golba^i Kampusu Teknoplaza Binasi C Blok Zemin Kat No:27 Golba^i
* E-mail: beycanibrahimoglu@yahoo.com
Тезисы. Исследовано метастабильное состояние бензола в условиях высоких температур и давлений, на равновесной кривой плавления определена точка критического давления. Дополнительно с применением средств геометрической термодинамики и аксиоматики для многих органических и неорганических веществ показаны равновесные кривые плавления, оканчивающиеся критической точкой. Для однокомпонентной системы определено положение плазмы на фазовой диаграмме в координатах давления и температуры, соответствующая модель показана на примере атома бензола.
Ключевые слова: бензол, метастабильное состояние, критическое давление, равновесные кривые плавления веществ, плазма.
Список литературы
1. Ibrahimoglu B. Study of thermodynamic parameters of hydrogen gas by grapho-analytic method / B. Ibrahimoglu, T.N. Veziroglu, A. Huseynov // International Journal of Hydrogen Energy. -2005. - Т. 30. - С. 515-519.
2. Ibrahimoglu B. Study of thermodynamic parameters of hydrogen gas by grapho-analytic method / B. Ibrahimoglu, N. Veziroglu, A. Huseynov, et al. // Hydrogen Materials Science and Chemistry of Carbon Nanomaterials. - 2004. - С. 225-232.
3. Ibrahimoglu B. Determination of 1/V-T (p, constant) diagrams of hydrogen gases by graph-analytical methods / B. Ibrahimoglu, Q.K. Dindar, H. Erol, et al. // Journal of Thermal Engineering. - 2017. - Т. 3. -№ 1. - С. 1071-1077.
4. Ibrahimoglu B. Investigation of hydrogen gas with graphical method / B. Ibrahimoglu, G. Tekeli, Z. Yilmazoglu, et al. // Proc. of 4th International Hydrogen Technologies Congress (IHTEC-2019), 20-23 June, Edirne.
5. Фарзалиев Б.И. Графическое определение параметров тройной точки фазового равновесия / Б.И. Фарзалиев, А.М. Рагимов, А.Т. Гаджиев // Известия высших учебных заведений. Нефть и газ. - 1985. - № 12. - С. 57-59.
6. Фарзалиев, Б.И. Определение линии плавления газов графоаналитическим методом / Б.И. Фарзалиев, Н.Ф. Алиев // Материалы научной конференции АзТУ, Баку. - 1992. - с. 21.
7. Ibrahimoglu B. Grafoanalytical of critical pressure in gas. Finding with the method / B. Ibrahimoglu // Turkish Journal of Science and Technology. - 1994. - Т. 17. - С. 2.
8. Ibrahimoglu B.I. Determination of a node on the melting curve / B.I. Ibrahimoglu, O.E. Ataer // 11th National Congress of Business Science and Technology (ULIBTK-97), Edirne. - С. 33.
9. Ibrahimoglu B. determination of liquid phase range of matters by graphic-analytical method / B. Ibrahimoglu, B. Ibrahimoglu jun. // SSRG International Journal of Thermal Engineering. - 2018. - Т. 4. - № 2.
10. Ibrahimoglu, B. [Фарзалиев]. Application of graphic and graphic-analytic geometry systems on the liquid and gas phases of matter = Применение графических и графоаналитических геометрических систем для изучения жидкого и газообразного фазовых состояний вещества / Beycan Ibrahimoglu, Gözde Tekeli // Вести газовой науки: науч.-технический. сб. - М.: Газпром ВНИИГАЗ, 2019. - № 1 (38): Актуальные вопросы исследований пластовых систем месторождений углеводородов. - С. 163-171.
11. Гусейнов С.О. Плотность и динамическая вязкость бензонитрила при высоких давлениях и температурах / С.О. Гусейнов, Б.И. Фарзалиев, Ю.М. Назиев // Известия высших учебных заведений. Нефть и газ. - 1978. - № 12. - С. 48.
12. Гусейнов С.О. Исследование динамической вязкости О-метиланилина при высоких давлениях и температуре / С.О. Гусейнов, Б.И. Фарзалиев, Ю.М. Назиев // Известия высших учебных заведений. Нефть и газ. - 1979. - № 7. - С. 52.
13. Гусейнов С.О. Исследование плотности и динамической вязкости P-толоудина при высоких давлениях и температурах / С.О. Гусейнов, Б.И. Фарзалиев // Известия высших учебных заведений. Нефть и газ. -1981. - № 6. - С. 65-68.
14. Naziyev Y.M. Untersuchungen zur Dichte und dynamischen viskositat dev o-m und p-toluidine bei hohen Drücken und verschiedenen temperaturen / Y.M. Naziyev, S.O. Guseynov, B.I. Farzaliev // Chemische technik. - 1983. - Т. 35. - С. 40-42.
15. Григорьев Б.А. Теплофизические свойства углеводородов нефти, газовых конденсатов, природного и сопутствующих газов / Б.А. Григорьев, А.А. Герасимов, И.С. Александров. - М.: МЭИ, 2019. - Т. 1.
16. Azreg-Ainou M. High-pressure eects on the benzene pre-crystallizationmetastable states / M. Azreg-Ainou,
B. Ibrahimoglu // Eur. Phys. J.E. - 2019. - Т. 42.
17. Alexandrov V.D. Pressure falling effects accompanying phase transformations of benzene under the accession of comprehensive compression / V.D. Alexandrov, B. Ibragimoglu, A.E. Pokintelitsa // Сучаст будiвельнi Mamepianu. - 2015. - № 1 (111).
18. Ибрагимоглы Б. Фазовые превращения бензола в условиях низких температур и высоких давлений / Б. Ибрагимоглы, Ч. Канбеш, И.М. Ахмедов // KimyaProblemleri. - 2015. - № 4. - С. 367-371.
19. Фарзалиев Б.И. О бензольных фазовых переходах при высоких давлениях / Б.И. Фарзалиев, Н.Ф. Алиев // Термодинамические и переносные свойства веществ: c6. - Баку: Азерб. политехи. ин-т им. Ч. Ильдрыма, 1989. - С. 61-65.
20. Кнунянц И.Л. Химический энциклопедический словарь / И.Л. Кнунянц. - М.: Большая советская энциклопедия, 1983. - С. 792.
21. Glasstone S. Theoretical chemistry / S. Glasstone. - New York: Boston College, 1948.
22. Бензол // Энциклопедический словарь Брокгауза и Эфрона: в 86 т. - СПб., 1890-1907.
23. Ciabini L. High-pressure and high-temperature equation of state and phase diagram of solid benzene / L. Ciabini, F.A. Gorelli, M. Santoro, et al. // Phys. Rev. B. - 2005. - Т. 72. - № 094108-1.
24. Debcnedetli P.G. Metastable liquids: concepts and principles / P.G. Debcnedetli. - Princeton: Princeton University Press, 1996.
25. Azreg-Ainou M. Phase equilibrium and metastability of liquid benzene at high pressures / M. Azreg-Ainou, A. Hüseynov, B. Ibrahimoglu // J. of Chemical Physics. - 2006. - Т. 124. - № 20. - С. 204505.
26. Crystal growth of electronic materials / E. Kaldis (ed.). - Amsterdam: North-Holland, 1985.
27. Vinet B. Correlations between surface and interface energies with respect to crystal nucleation / B. Vinet, L. Magnusson, H. Fredriksson, et al. // Journal of Colloid and Interface Science. - 2002. - Т. 255. - № 2. -
C. 363-374.
28. Александров В.Д. Кинетика зарождения и массовой кристаллизации переохлажденной жидкости и аморфных сред = Kinetics of nucleation and mass crystallization of an overcooled liquid and amorphous media / В.Д. Александров. - Донецк: Donbas, 2011.
29. Александров В.Д. Исследование переохлаждений при кристаллизации бензола / В.Д. Александров, В.А. Постников // Украшський хiмiчний журнал. - 2004. - Т. 70. - № 9-10. - С. 104-109.
30. Bridgman P.W. Collected experimental papers / P.W. Bridgman. - Cambridge, Massachusetts: Harvard University Press, 1964.
31. Skripov V.P. The concept of metastability and phase transitions / V.P. Skripov // Thermo-physical properties of matter. - 2002. - № 10.
32. Baidakov V.G. Singular point of a system of Lennard - Jones particles at negative pressures / V.G. Baidakov, S.P. Protsenko // Phys. Rev. Lett. - 2005. - Т. 95. - № 015701.
33. Скрипов В.П. Фазовые переходы кристалл - жидкость - пар / В.П. Скрипов, М.З. Файзуллин. -М.: Физматлит, 2003. - 160 с.
34. Прозенко С.П. Линия плавления, спинодаль и конечная точка линии плавления в системе с модифицированным леннард-джонсоновским потенциалом / С.П. Прозенко, В.Г. Байдаков, А.О. Типеев // Теплофизика и аэродинамика. - 2013. - Т. 20. - № 1. - С. 95-106.
35. Норман Г.Э. Неостоятельность классического описания невыраженной плотной плазмы / Г.Э. Норман, А.Н. Старостин // Теплофизика высоких температур. - 1968. - Т.. 6. - № 3. - С. 410-415.
36. Норман Г.Э. Термодинамика сильно неидеальной плазмы / Г.Э. Норман, А.Н. Старостин // Теплофизика высоких температур. - 1970. - Т. 8. - № 2. - С. 381-408.
37. Brazhkin V.V. Universal viscosity growth in metallic melts at megabar pressures: the vitreous state of the Earth's inner core / В.В. Бражкин, А.Г. Ляпин // Успехи физических наук. - 2000. - Т. 170. - № 5. - С. 535-551.
