Scaled Particles' Models And Thermodynamic Properties Of

The possibility of the usage of the scaled particles' models for the description of elastic and thermal properties of n-alkanes is analyzed. It is shown that the scaled particles' models describe the dependence of coeecient of compression and elastic module on the n-alkanes' density qualitatively correctly, at the same time quantitative divergence increases as density increases. The dependence of the elastic and thermal properties of n-alkanes on thermodynamic parameters is determined by the whole potential curve particularities (not only by its repulsive part for elastic properties or only by its attractive part for thermal properties).


Introduction
Existence of the connection between the physical properties of liquids and their molecular structure follows from the statistical theory of the liquids.However the problem of determination of this connection is solved for limited number of cases (for simple, isotropic or slightly anisotropic liquids) because of the impossibility of the correct description of intermolecular interaction and the mathematical di culties while solving integral equations which can not be completely removed by using numerical methods.For majority of practically important molecular liquids the statistical theory is not developed.Therefore, we have to nd the connection between physical properties of liquids and their molecular structure experimentally.
Finding the equation of state which allows to describe the dependence of the equilibrium properties of the complex molecular liquids consisting of nonspherical particles not only on the thermodynamic parameters but also on their microcharacteristics is a part of the mentioned above problem.

Experiment
The group of n-alkanes, from n-hexane to n-pentadecane, was taken as object of investigations.For the discussion we also used data on CO 2 1] and Ar 2].The PVT data were obtained by the metal bellows method.The apparatus and the experimental procedure were described in 3].The speci c volumes were measured in the temperature range from 313 to 413 K and in the pressure range from 0.1 to 245.25 MPa.In addition to PVT data we have studied the ultrasonic velocity in the same temperature and c I.Adamenko, Ya.Skirda, 1997 ISSN 0452{9910.Condensed Matter Physics 1997 No 9 (13{18) 14 I.Adamenko, Ya.Skirda pressure ranges by the direct pulse-echo method of the xed distance with frequency 5 MHz 4].Previously we had checked that there was no dispersion of ultrasonic velocity in the frequency range 1.25{10 MHz within the indicated limits of the thermodynamic parameters' change.The errors of measurement of speci c volume and ultrasonic velocity were 0.2% and 0.3%, respectively.To determine the parameters of scaled particles we used X-ray investigation data about the C-C and C-H bond length and bond angles 5].
Barker and Henderson have shown 13] that the consideration of the particles' attraction in the shape of rectangular well leads to the appearance of the additional term A "=k B T in the equation of state of scaled particles where A is constant with the value dependent on the width of the rectangular well Q: Lebowits and Rowlinson have shown 14] that consideration of the power character of the repulsive potential dependence on the distance between particles preserves the form of the state equation, but the diameter of particles turns out to be decreasing function of temperature d =dT = ?3=k B T: Thermodynamic properties of N-alkanes 15 Therefore for soft spherecylinder we supposed that l = l 0 293 T 1=n ; (7) l 0 is the length of the molecule at T = 273 K.
Because the statistical theory is well developed only for the simple liquids it is interesting to study Ar | the liquid with spherical shape of molecules, and CO 2 | one of the simplest liquids with nonspherical shape of molecules.We obtained the coe cient of the thermal dilatation and PV=RT of Ar in a wide range of temperatures (from T critical to T triple point) and pressures (from 0:2P critical to 2P critical ) for soft particles with and without consideration of the attractive force (in a form of rectangular potential well).The best correlation with experimental data is given by the model of the soft spheres with attraction.If we use the hard attractive model, P is higher than the experimental value and PV=RT is lower.
For liquid CO 2 we used the following X-ray data to calculate the parameters of models 11] : R C?O =0.113 nm, R C = 0:180 nm, R O = 0:136 nm, = 1:576.The values of PV=RT calculated by equations ( 1), ( 2), ( 6) and determined experimentally for CO 2 in the undercritical and overcritical regions of thermodynamic parameters changie are given in table 1 Comparison of these values shows that equations ( 1), ( 2), and (6) describe the character of the dependence of the coe cient of compression of CO 2 on temperature on the undercritical isobar (2.8 MPa) correctly, but quantitative deviation between the experimental and calculated data sometimes reaches several orders.In the overcritical region (8 MPa), the experimental isobar of the compression coe cient increases.None of the examined models describes this fact correctly.When the temperature is higher than the critical for CO 2 in 3{4 times the quantitative deviation between experimental and calculated values of PV=RT is approximately equal to 5%.However the experimental function PV=RT of T for CO 2 is increasing up to 1 and all calculated functions PV=RT of T is decreasing to 1.For n-hexane and n-pentadecane the bond length and factor are equal, respectively, to: l = 7:9 A and = 4:7; l = 19:65 A and = 12:2.The dependence of pressure on the numeral density in a system of spherecylinder for n-hexane and n-pentadecane qualitatively correlates with the experimental one.Quantitative agreement can not be obtained.The comparison between the experimental values of elastic module of n-hexane and n-pentadecane with those calculated for the hard spherecylinder model demonstrates that the model describes the behaviour of this dependence qualitatively correctly.Quantitative distinction of elastic module is large.The value of (K T exper -K T theor ) increases with density for n-alkanes.Theoretical value of the coe cient of thermal dilatation for n-alkanes decreases as temperature increases both in the region of high pressures and in the region of low pressures.Experimental dependence of P on temperature is quite di erent: it increases with temperature under low pressures and it decreases under high pressures (see table 2).The model of spherecylindrical particles can not be considered as appropriate for quantitative description of the coe cient of compression of n-alkanes.The consideration of the softness of particles in the form of (7) in this model does not lead to the improvement of correlation between the theoretical and experimental values of the coe cient of compression.The alteration of the power of repulsive force potential n from 12 to 36 has no in uence on the behavior and values of PV=RT.It can be caused by the leading role of the attractive force in the studied regions of pressures and temperatures.

Conclusion
Comparison of the results of the calculations of elastic and thermal properties of n-alkanes, CO 2 and Ar using the models for hard and soft particles and with consideration of attraction or without it shows that equilibrium properties of liquids are determined by the geometry of molecules.The signi cance of the potential energy for the description of the thermodynamic properties of model system increases as temperature and density increase.virno opisu t~zale nist~faktora stisnenn i modul prunosti vid gustini n-parafiniv, pri c~omu kil~kisne rozhod enn zrosta z rostom gustini.Harakter zale nosti pru nih tateplovih vlastivoste n-parafiniv vid termodinamiqnih parametriv viznaqa t~s osoblivost mi vs potencial~no krivo , a ne til~ki vidxtovhu qo qastini (dl pru nih vlastivoste ) abo osoblivost mi potencialu prit gann (dl teplovih vlastivoste ).

Table 1 .
. Comparison of the values of PV=RT for CO 2 calcu-

Table 2 .
Coe cient of the thermal dilatation of n-hexane calculated on the basis of the hard spherecylinder model and obtained from the experimental results.