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Figure 7. First coefficients of the spherical harmonic expansion of g(r,., @,, @). (—— refer ence system (5) for L* = 1-0 at T* = 1-0, --—- hard spherocylinders with L* = 1-0).

Figure 7 First coefficients of the spherical harmonic expansion of g(r,., @,, @). (—— refer ence system (5) for L* = 1-0 at T* = 1-0, --—- hard spherocylinders with L* = 1-0).

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‘igure 1. Illustration of the dependence of the shortest distances between cores on the orientation of the particles. properties of Kihara models with molecular cores modelled as rods. Boublik has already proposed several perturbation treatments [6-8] for the study of Kihara models, but in all of them a semiempirical approximation for the structure of the reference system must be used. The Percus-Yevick (PY) equation has been recently solved [11] for hard spherocylinders and for a purely repulsive Kihara model [12]. The numerical procedure in both cases is too complex to serve as a practical means of evaluating the structure of the reference eystem in a perturbation scheme, and so we used Fischer 1] approximation to evaluate g°. ry np 14 ce. me < a aa a ee a ee oe
‘igure 1. Illustration of the dependence of the shortest distances between cores on the orientation of the particles. properties of Kihara models with molecular cores modelled as rods. Boublik has already proposed several perturbation treatments [6-8] for the study of Kihara models, but in all of them a semiempirical approximation for the structure of the reference system must be used. The Percus-Yevick (PY) equation has been recently solved [11] for hard spherocylinders and for a purely repulsive Kihara model [12]. The numerical procedure in both cases is too complex to serve as a practical means of evaluating the structure of the reference eystem in a perturbation scheme, and so we used Fischer 1] approximation to evaluate g°. ry np 14 ce. me < a aa a ee a ee oe
Figure 2. Free Helmholtz energy data at reduced temperatures 0-85, 1-075 and 1-35 (—— tl work, -~-- Boublik predictions [6], ---- experimental data).
Figure 2. Free Helmholtz energy data at reduced temperatures 0-85, 1-075 and 1-35 (—— tl work, -~-- Boublik predictions [6], ---- experimental data).
The best agreement between our theoretical results and the experimental dat: appears in the intermediate range of packing fractions. The source of errors in the lov density range seems to be obvious: the convergence of the perturbation expansion i this range is slow. It should, therefore, be expected that more than two terms ar needed for an accurate description of the thermodynamic properties of the fluid. O: the other hand, in the high-density range, a first-order perturbation expansion shoul be enough to predict thermodynamic properties, so in this range the main source o errors seems to be the evaluation of the reference system properties. As is shown i [9] the approximation used to obtain A° overestimates its value in the high densit range. An alternative equation of state [18] was used in order to evaluate A°, but w did not find any significant improvement. Furthermore, as will be discussed below approximation (17) for 2°(r,2, @,, @)) worsens as the density increases. Fioure 3 dienlave the Ronbhhk recuite and aur awn nredictiane far exceee interna
The best agreement between our theoretical results and the experimental dat: appears in the intermediate range of packing fractions. The source of errors in the lov density range seems to be obvious: the convergence of the perturbation expansion i this range is slow. It should, therefore, be expected that more than two terms ar needed for an accurate description of the thermodynamic properties of the fluid. O: the other hand, in the high-density range, a first-order perturbation expansion shoul be enough to predict thermodynamic properties, so in this range the main source o errors seems to be the evaluation of the reference system properties. As is shown i [9] the approximation used to obtain A° overestimates its value in the high densit range. An alternative equation of state [18] was used in order to evaluate A°, but w did not find any significant improvement. Furthermore, as will be discussed below approximation (17) for 2°(r,2, @,, @)) worsens as the density increases. Fioure 3 dienlave the Ronbhhk recuite and aur awn nredictiane far exceee interna
Figure 5. Compressibility factor data for L* = 0-29 at T* = 1-075 (——) theoretical predic tions using EOS from [6] (- - —)id. using EOS from reference [18]; (C1) semitheoretica predictions (see text); (A) simulation data [9].
Figure 5. Compressibility factor data for L* = 0-29 at T* = 1-075 (——) theoretical predic tions using EOS from [6] (- - —)id. using EOS from reference [18]; (C1) semitheoretica predictions (see text); (A) simulation data [9].
Table 2. Compressibility factor of a Kihara model with L* = 1-0. derive Irom approximation |! /}. For this model, therelore, the main source of errors in the liquid densities range, where a first-order perturbation theory should reproduce the thermodynamic properties of the model, seems to be the approximation for A°. In general, we can say that our theory gives a better agreement with simulations than Boublik’s theory. To further clarify this point, we checked how sensitive the results of our theory are to the choice of a set of parameters [4, 8] and we found no meaningful differences between the two models, since the results are expressed in terms of reduced magnitudes and the value of L* is about the same for both models. When theoretical results are compared with each corresponding set of experimental data, it is found, however, that theoretical predictions with Kihara parameters [4] show better agreement with experimental data. Furthermore, A“ /NkT appears to be more sensitive to the choice of parameters of the potential than E*°/NkT and pV|NKT. The very general conclusion that simulations are the only correct way to decide in which extension a theory is valid, is strengthened here once again. In this sense the theory presented here is a clear improvement on the Boublik results [6].
Table 2. Compressibility factor of a Kihara model with L* = 1-0. derive Irom approximation |! /}. For this model, therelore, the main source of errors in the liquid densities range, where a first-order perturbation theory should reproduce the thermodynamic properties of the model, seems to be the approximation for A°. In general, we can say that our theory gives a better agreement with simulations than Boublik’s theory. To further clarify this point, we checked how sensitive the results of our theory are to the choice of a set of parameters [4, 8] and we found no meaningful differences between the two models, since the results are expressed in terms of reduced magnitudes and the value of L* is about the same for both models. When theoretical results are compared with each corresponding set of experimental data, it is found, however, that theoretical predictions with Kihara parameters [4] show better agreement with experimental data. Furthermore, A“ /NkT appears to be more sensitive to the choice of parameters of the potential than E*°/NkT and pV|NKT. The very general conclusion that simulations are the only correct way to decide in which extension a theory is valid, is strengthened here once again. In this sense the theory presented here is a clear improvement on the Boublik results [6].
Figure 6. Compressibility data for L* = 1-0 at T* = 1-0. (- - -) theoretical predictions using EOS from reference [6]; (- - —)id. using EOS from reference [18]; (GQ) semitheoreti- cal predictions (see text); (A) simulation data [8].
Figure 6. Compressibility data for L* = 1-0 at T* = 1-0. (- - -) theoretical predictions using EOS from reference [6]; (- - —)id. using EOS from reference [18]; (GQ) semitheoreti- cal predictions (see text); (A) simulation data [8].
in figure 9; the results for g},,(r) are not displayed because its value is comparatively too small. In general, the theoretical results show the correct shape. For 47 = 0-2 the agreement is quantitative. As the density increases, however, the orientational corre- lations appear to be correctly described at smaller values of r but underpredicted at large and intermediate r values; in general they are short ranged. br. oF , eS, Ae, ee, eS oy 2h 2.42 Wk 0 Me 448s igs: meee bow ent
in figure 9; the results for g},,(r) are not displayed because its value is comparatively too small. In general, the theoretical results show the correct shape. For 47 = 0-2 the agreement is quantitative. As the density increases, however, the orientational corre- lations appear to be correctly described at smaller values of r but underpredicted at large and intermediate r values; in general they are short ranged. br. oF , eS, Ae, ee, eS oy 2h 2.42 Wk 0 Me 448s igs: meee bow ent
discrepancies with simulation data in the whole range of r. In order to improve the theoretical results for models with large elongation like L* = 1-0, it seems to be necessary to introduce more information about the orientational correlations in the fluid in the approximation for the reference system structure.
discrepancies with simulation data in the whole range of r. In order to improve the theoretical results for models with large elongation like L* = 1-0, it seems to be necessary to introduce more information about the orientational correlations in the fluid in the approximation for the reference system structure.
Figure 10. gooo(r), 2300(r), S320(r) and g%,(r) for L* = 1-0 at T* = 1-0 at three packing fractions. (a) 4 = 0-196; (b) 7 = 0.289; (c) 47 = 0.4. ( ) theory; (@) go(r) from simulation [19], (GQ) g%o(r) from simulation [19]; (©) g%o(r) from simulation [19]; (A) g%)(r) from simulation [19].
Figure 10. gooo(r), 2300(r), S320(r) and g%,(r) for L* = 1-0 at T* = 1-0 at three packing fractions. (a) 4 = 0-196; (b) 7 = 0.289; (c) 47 = 0.4. ( ) theory; (@) go(r) from simulation [19], (GQ) g%o(r) from simulation [19]; (©) g%o(r) from simulation [19]; (A) g%)(r) from simulation [19].
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Molecular PhysicsThermodynamicsTHEORETICAL AND COMPUTATIONAL CHEMISTRYReference Systems
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