Towards the Equation of State for Neutral (C H ), Polar (H ...downloads.hindawi.com/journals/jther/2014/496835.pdf · properly by this RPP-model. In contrast with the discrete LG-model,

Research ArticleTowards the Equation of State for Neutral (C2H4) Polar (H2O)and Ionic ([bmim][BF4] [bmim][PF6] [pmmim][Tf2N]) Liquids

Vitaly B Rogankov and Valeriy I Levchenko

Department of Physics Odessa State Academy of Refrigeration Dvoryanskaya Street 13 Odessa 65082 Ukraine

Correspondence should be addressed to Vitaly B Rogankov vrogankovyandexua

Received 5 August 2014 Accepted 4 November 2014 Published 16 December 2014

Academic Editor Pedro Jorge Martins Coelho

Copyright copy 2014 V B Rogankov and V I Levchenko This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Despite considerable effort of experimentalists no reliable vapor-liquid coexistence at very small pressures and liquid-solidcoexistence at high pressures have been until now observed in the working range of temperature 290 lt 119879119870 lt 350 for ionic liquidsThe measurements of high-pressure properties in low-temperature stable liquid are relatively scarce while the strong influenceof their consistency on the phase equilibrium prediction is obvious In this work we discuss the applicability of fluctuational-thermodynamic methodology and respective equation of state to correlate the properties of any (neutral polar ionic) liquids sinceour ultimate goal is the simple reference predictive model to describe vapor-liquid liquid-liquid and liquid-solid equilibria ofmixtures containing above components It is shown that the inconsistencies among existing volumetric measurements and thestrong dependence of the mechanical and especially caloric derived properties on the shape of the functions chosen to fit theexperimental data can be resolved in the framework of fluctuational-thermodynamic equation of state To illustrate its results thecomparison with the known experimental data for [bmim][BF

4] and [bmim][PF

6] as well as with the lattice-fluid equation of state

and the methodology of thermodynamic integration is represented It corroborates the thermodynamic consistency of predictionsand excellent correlation of derived properties over the wide range of pressures 0 lt 119875MPa lt 200

1 Introduction

Behavior of low-melting organic salts or ionic liquids (ILs)[1ndash6] in the region of phase transitions is qualitatively similarto that either for high-temperature nonorganic molten saltsor long-hydrocarbon-chain organic solvents and even forpolymer systems Such characteristic features as negligiblevapor pressure 119875

120590(119879) undefined critical parameters 119875

119888 120588119888

119879119888for vapor-liquid (V 119897)-transition split of liquid-solid (ls)-

boundary onto melting 119875119898(119879) and freezing 119875

119891(119879) branches

existence of glassy states make the problem of metastabilityto be quite complex but vital for many potential uses ofILs In particular thermodynamic modeling and computersimulation of the phase behavior in mixtures formed byILs with water and low-molecular organic solvents such asethylene can be of great importance for the further tuning oftheir operational parameters If one proceeds from a pure to amixed fluid it is especially advantageous to develop the sameformat of reference equation of state (EOS) and the common

format of reference pair potential (RPP) for each componentand mixture

As a first step toward consistent modeling of thephase behavior of IL and its solution we demonstrate inthis work how the fluctuational-thermodynamic (FT)EOS [7ndash12] and the relevant finite-range Len-nard-Jones (LJ) RPP can be applied to model the underlyingstructure and properties of low-molecular (C

2H4 H2O)

and imidazolium-based (1-butyl-3-methylimidazoliumtetrafluoroborate ([bmim][BF

4]) 1-butyl-3-methylimida-

zolium hexafluorophosphate ([bmim][PF6]) 23-dimethyl-

1-propylimidazolium bis(trifluoromethylsulfonyl)imide([pmmim][Tf

2N])) solvents For any pure component FT-

model is based either on the measurable coexistence-curveinput data 119875

120590(119879) 120588V(119879) 120588119897(119879) (if they are achievable as

for C2H4and H

2O) or on the also measurable one-phase

density of liquid at atmospheric pressure 120588 (1198750asymp 01MPa

T) for ILs This methodology becomes purely predictive fordensity 120588(119875 119879) in any one-phase V 119897 119904-regions including

Hindawi Publishing CorporationJournal of ermodynamicsVolume 2014 Article ID 496835 15 pageshttpdxdoiorg1011552014496835

2 Journal of Thermodynamics

their metastable extensions Only the measurable isobaricheat capacity data 119862

119875(1198750 119879) have to be added to the set

of input data for prediction of other caloric properties(isochoric heat capacity 119862V(119875 119879) speed of sound 119882(119875 119879)and Gruneisen parameter Gr(119875 119879)) at higher pressures119875 gt 119875

0and lower 119879 lt 119879

119898or higher 119879 gt 119879

119887temperatures

where 119879119887is the hypothesized normal boiling temperature

119879119887(1198750) Its existence itself is a debatable question because the

thermal decomposition 119879119889may be former 119879

119889lt 119879119887

Such approachwas proposed recently [7 8] to reconstructthe hypothetical (V 119897)-diagram of any ILs in its stable andmetastable regions on the base of only standard reference dataon density 120588(119879) at119875

0[1ndash4] and one free parameter an a priori

unknown value of the excluded volume 1198870 To our knowledge

this is first attempt to predict simultaneously the wholeset of one-phase and two-phase properties for ILs withoutthe fit at any other pressures including the negative ones Itwas argued that the particular low-temperature variant ofthe most general FT-EOS [9ndash12] should be used to obtainthe consistent prediction of volumetric properties and thestandard response functions 119886

119875 120573119879 120574120588

= 119886119875120573119879by the

following equations

119875 =120588119877119879

1 minus 1198870120588minus 119886 (119879) 120588

2 (1)

120573119879=

(1 minus 1198870120588)2

2119875 (1 minus 1198870120588)2

+ 120588119877119879 (21198870120588 minus 1)

gt 0 (2)

120572119875=

(1 minus 1198870120588) lfloor120588119877 minus 120588

2(1 minus 119887

0120588) 119889119886119889119879rfloor

2119875 (1 minus 1198870120588)2

+ 120588119877119879 (21198870120588 minus 1)

(3)

120574120588=120588119877 minus 120588

2(1 minus 119887

0120588) 119889119886119889119879

(1 minus 1198870120588)

(4)

where 1198870is the excluded molecular volume and 119886(119879) is

the 119879-dependent effective cohesive energy The derivative119889119886119889119879 affects the thermal expansion 120572

119875and the thermal-

pressure coefficient 120574120588while the isothermal compressibility

120573119879depends only on 119887

0-value at the given pressure The

changeable sign of two thermal derivatives 120572119875 120574120588offers

a possibility to predict the properties of anomalous low-temperature substances (such aswater for example) too [7 8]

Fortunately we have obtained now [13ndash19] a possibilityto test our predictions not only by the direct experimentalone-phase data [14 16 18 19] on 120588(119875 119879)- and 119882(119875 119879)-surfaces Another possibility is offered by comparison of thepredictions obtained by FT-EOS for the critical parametersof ILs ([bmim][BF

4] 119879119888= 9623 K 119875

119888= 35039 kPa 120588

119888=

438565 kgsdotmminus3 with those predicted here by the Sanchez-Lacombe EOS for lattice fluid (LF) [15] 119879

119888= 88501 K

119875119888= 2829 kPa 120588

119888= 248565 kgsdotmminus3 as well as with those

simulated by GEMC-methodology [6] 119879119888= 1252K 119875

119888=

390 kPa 120588119888= 181 kgsdotmminus3 It seems that the relatively close

location of (119879119888 119875119888)-parameters predicted by both EOSs is

some guarantee of their reliability while119879119888and119875119888from [6] are

significantly overestimated and underestimated respectivelyInterestingly the known descriptive factor of compressibility

119903119905= 119875119888(120588119905119877119879119888) estimated by Guggenheim [20] in the vicinity

of triple point 119879119905for argon as 119903

119905= 0108 is equal to close

values 119903119905= 0082 for FT-EOS and 119903

119905= 0072 for LF-

EOS but only to very small value 119903119905= 0007 for result

of GEMC-simulations if the common realistic estimate (seebelow) 120588

119905asymp 120588119897= 5350646molsdotdmminus3 at T = 290K is used

Moreover it will be shown that the characteristic dimensionalparameters 119875lowast

119888 119879lowast119888 120588lowast119888and another compressibility factor

119903lowast

119888= 119875lowast

119888(120588lowast

119888119877119879lowast

119888) obtained by Machida et al [14] by

the fit to (119875 120588 119879)-experimental data for [bmim][BF4] and

[bmim][PF6] provide the structural estimates of hard-core

volume number of lattice sites in a cluster and energyof near-neighbor pair interactions which are surprisinglyclose to ones independently predicted by the FT-model of acontinuum substance

Taking into account the compatibility of above results itis important to consider the presumable similarity betweenthe square-well fluid (which may be thought of as a con-tinuum analogue of the lattice-gas (LG) or lattice-fluid (LF)systems) on the one hand and the LJ-fluid of finite-rangeinteractions (RPP) on the other This conceptual analogy hasbeen pointed out long ago for the critical region by Widom[21] who suggested that it is the propagation of attractivecorrelations in the LG which determines the peculiarities ofcriticality However such unphysical LG-predictions at lowtemperatures of the (120588 119879)-plane as the nonexistence of a (119897 119904)-transition suggest that repulsive forces are not being treatedproperly by this RPP-model In contrast with the discreteLG-model it seems that both attractive and repulsive forcesare being dealt with properly in the square-well continuumfluid because it exhibits both (V 119897)- and (119897 119904)-transitionsThe serious restriction of latter is however evident sinceany singularities of RPP imply an artificial jump of pair-distribution isotropic function 119892(119903) at the point of cutoffradius 119903

119888for attractive interactions

In this context only the shifted and smoothed at 119903119888-

point LJ-potential [5 6] seems to be appropriate as RPP fora continuum system Of course the algebraic form of therespective reference EOS is essential too In accordance withthe statistical-mechanical arguments presented by Widom[21] there are the set of alternative forms including theoriginal vdW-EOS and the LG-EOS in thewell-knownBragg-Williams approximation which share the common restrictivefeature Onemay suppose that the probability of finding someprescribed value of the potential energy 119880( 119903) at an arbitrarypoint in the fluid is independent of 119879 at fixed 120588 119880( 119903 120588)Another simplifying assumption is that such EOS supposesonly two types of fluid structure one of the excluded (or hard-core) volume 119873V

0where the singular hard-sphere branch of

potential is infinite and one of free volume (119881 minus 119873V0) where

the potential is uniform weak and unrestricted (an infinite-range rectilinear well) It should be directly proportional todensity 119890 = 119880119873 = minus119886120588 where 119880 is the total configurationalenergy and 119886 is the constant vdW-coefficientThese historicalnotes are important to explain how one can go beyond theabove restriction of119879-independency by adoption of linear 120588-dependence for a generalized specific or molar energy (seealso (8) below) Consider

Journal of Thermodynamics 3

119886 (119879) = minus(120597119890

120597120588)

119879

(5)

Another aim of the developed FT-EOS follows from thepossibility [7] to estimate the effective LJ-parameters withoutany fit Indeed their general T-dependent values

120590 (119879) = [3119887 (119879)

(2120587119873119860)]

13

(6a)

120576 (119879)

119896= 119879 (1 minus 119885

119897) (6b)

are determined simply in the low-temperature range of allILs where 119887

0is constant in ((1)ndash(4)) while the compressibility

factor of saturated liquid 119885119897= 119875120590(120588119897119877119879) becomes negligible

as well as the vapor pressure 119875120590(119879) trends to zero Taking into

account this asymptotic behavior it is especially importantto study the possible correlations of these parameters in theRPP-model of an effective LJ-potential for ILs as the functionsof total molecular weight 119872 This concept is unusual forthe conventional consideration of a separate influence of theanionrsquos 119872

119886and cationrsquos 119872

119888components It may provide in

principle the useful insight the nature of (V 119897)-transition inILs by effective capturing underlying pair interactions

The distinction of both FT-EOS and LF-EOS [14] fromthe conventional hard-sphere reference EOS is crucial toprovide the quantitative description of one-phase liquid Theformers include the quadratic in density contribution whichis dominating at high pressures along the isotherms Thelatter considers this term as a small vdW-perturbation for thehard-sphere EOS Such perturbation approach is not directlyapplicable to associating fluids such as water and alcoholsfor which presence of hydrogen bonding anisotropic dipolar11199033 or coulombic 1119903 interactions in addition to isotropic

dispersive 11199036 attractions is inconsistent with the main

assumption of the perturbation methodology that the struc-ture of a liquid is dominated by repulsive forces [15]

The FT-model promotes the more flexible approach inwhich the above factors of attraction and clustering can beeffectively accounted by the 119886(119879)-dependence It was firstlyconfirmed by Longuet-Higgins and Widom and then bymany authors that a combination of Carnahan-Starling EOSfor example with the vdW-perturbation 1198861205882 is a reasonableapproximation for the 119897- and 119904-phases but not the V-phaseGuggenheim [20] has concluded its applicability only to aliquid when large clusters are more important than smallclusters (ie at low temperatures 119879

119898lt 119879 lt 119879

119887) In

contrast with this observation the general FT-EOS providesthe adequate representation of entire subcritical range 119879

119898lt

119879 lt 119879119888including the critical region and (V 119897)-phase transition

[9ndash12] It will be shown below by FT-model without unduecomplexity of calculations

2 Universal FT-EOS for AnyLow-Temperature Fluids

21 General Form of FT-EOS for Subcritical Temperatures Itis often claimed that the original van der Waals (vdW)-EOS

with two constant coefficients 119886 119887 determined by the actualcritical-point properties 120588

119888 119879119888is only an approximation at

best and cannot provide more than qualitative agreementwith experiment even for spherical molecules However itwas proved recently [9ndash12] that the general FT-EOS withthree 119879-dependent coefficients

119875 =120588119877119879 [1 minus 119888 (119879)]

1 minus 119887 (119879) 120588minus 119886 (119879) 120588

2 (7)

is applicable to any types of fluids including ILs The mea-surable volumetric data of coexistence curve (CXC) havebeen used for evaluation of 119879-dependences without any fitConsider

119886 (119879) =119875120590(119860120590minus 1)

120588119897120588119892

= minus

(119890119897minus 119890119892)

(120588119897minus 120588119892)

(8)

119887 (119879) =119860120590minus 2

(120588119897+ 120588119892) (119860120590minus 1)

(9)

1 minus 119888 (119879) = 119885119897lfloor1 +

120588119897(119860120590minus 1)

120588119892

rfloor (1 minus 119887120588119897) (10)

where the reduced slope 119860120590(119879) of 119875

120590(119879)-function is defined

by the thermodynamic Clapeyronrsquos equation

119860120590(119879) =

119879

119875120590

119889119875120590

119889119879=

119879 (119904119892minus 119904119897) 120588119897120588119892

119875120590(120588119897minus 120588119892)

(11)

This fundamental ratio of the (V 119897)-latent heat to the ther-modynamic work of (V 119897)-expansion is the main parameterof FT-coefficients determined by ((8)-(9)) It should be calcu-lated separately in each of high-temperature (119879

119887le 119879 le 119879

119888)

[9ndash12] v- and l-phases to obtain the reasonable quantitativeprediction of one-phase thermophysical propertiesThegeneralFT-EOS is applicable to the entire subcritical range (119879

119905le 119879 le

119879119888) but it can be essentially simplified to the form of (1) if

(119879119905le 119879 le 119879

119887)

22 Particular Form of FT-EOS for Low Temperatures Anabsence of input CXC-data 119875

120590(119879) 120588

119892(119879) 120588

119897(119879) for ILs

is the serious reason to develop the alternative methodfor the evaluation of T-dependent FT-coefficients Thethermodynamically-consistent approach has been proposedin [7 8] for the particular form of FT-EOS (1) applicable inthe low-temperature range from the triple 119879

119905(or melting 119879

119898)

point up to the 119879119887-point Former one is usually known for

ILs while the latter one is as a rule more than temperatureof thermal decomposition 119879

119887gt 119879119889sim 650K The method-

ology was tested on two low-molecular-weight substances(C2H4 H2O) and two imidazolium-based ILs ([bmim][PF

6]

[pmmim][Tf2N]) with the promising accuracy of predictions

even for the isothermal compressibility 120573119879up to the pressure

P = 200MPaTo illuminate the distinction between the particular

(reference) and general form of FT-EOS let us discuss in briefthemain steps of the proposed procedure Its detailed analysiscan be found elsewhere [7 8] The algorithm is as follows


Step 1 At the chosen free parameter 119879119887one determines the

orthobaric molar densities 120588119897(119879119887) = 120588(119879

119887 1198750) 120588119892(119879119887) =

1198750119877119879119887to solve the transcendent equation

120588119892

120588119897

=1 + 119910 (119909) 119890

minus119909

1 + 119910 (119909) 119890119909 (12)

for the reduced entropy (disorder) parameter 119909(119879119887) and the

respective molar heat 119903120590(119879119887) of vaporization Consider

119909 =

(119904119892minus 119904119897)

2119877 (13a)

119903120590= ℎ119892minus ℎ119897= 2119877119879

119887119909 (119879119887) (13b)

Step 2 The universal CXC-function 119910(119909) in (12) is deter-mined by equalities

119910 (119909) =sh119909 ch 119909 minus 119909119909 ch 119909 minus sh119909

sh119909 = 119890119909minus 119890minus119909

2 ch119909 = 119890

119909+ 119890minus119909

2

(14)

and it provides the possibility to estimate a preliminary valueof 1198870

1198870=

[119909 (119879119887) minus 1]

120588119897(119879119887) [119909 (119879

119887) minus 12]

(15)

as well as to evaluate the orthobaric densities at any 119879 if thefunction 119909(119879) is known Consider

120588119892= 1198870lfloor1 + 119910(119909)119890

119909rfloorminus1

(16a)

120588119897= 1198870lfloor1 + 119910(119909)119890

minus119909rfloorminus1

(16b)

Step 3 (119860-variant of 119909(119879)-prediction [7 8]) To calculate itsvalues one must obtain two densities 120588plusmn (at the assumption119875120590asymp 0) from equation

120588plusmn=

1

21198870

[1 plusmn radic1 minus41198870120588 (1 minus 119887

0120588)

1 minus 1198850(1 minus 119887

0120588)] (17)

where 120588 = 120588(119879 1198750) 1198850

= 1198750120588119877119879 and the 120588

+(119879)-

function provides the preliminary estimate of 119909(119879) for thelow-temperature range (at the consistent assumption 120588+ ≫120588119892asymp 0) Consider

119909 (119879) =1 minus 1198870120588+2

1 minus 1198870120588+ (18)

Step 4 One substitutes 119909(119879) from (18) in ((13a) (13b) (16a)(16b)) to calculate 119903

120590(119879) 120588

119892(119879) 120588

119897(119879) respectively

Step 5 A preliminary value of 1198860(119879) may be estimated then

by the more restrictive assumption 1198750asymp 0 (used also in

the famous Flory-Orwoll-Vrij EOS developed for heavy n-alkanes) Consider

1198860(119879) =

119877119879

120588119897(1 minus 119887

0120588119897) (19)

Table 1 Coefficients of FT-EOS (1) for neutral (C2H4) and polar(H2O) substances

1198870[dm3mol] 119886 [Jsdotdm3mol2] 119879 [K]

C2H4 H2O1198870= 004181 119887

0= 001658

119879 119886 119879 119886

10399 155712 27316 517162105 145976 27815 527171110 112730 28315 534941115 935490 28815 540955120 812151 29315 545767125 725634 29815 548270130 661817 30315 549648135 613602 30815 549424140 575528 31315 548755145 545191 31815 547172150 520785 32315 544760155 500788 32815 541609160 484652 33315 537810165 471466 33815 53345516935 462006 34315 529044

34815 52460535315 51978935815 51467636315 50967436815 50448037315 499159

Step 6 (119861-variant of 119909(119879)-prediction) To control the con-sistency of methodology one may use instead of Step 3 (119860-variant) the same equation (17) with the approximate equality120588119897(119879) asymp 120588

+(119879) to solve (16b) at the a priori chosen 119887

0-value for

determination of alternative 119909(119879) and so forth (Steps 4 and5) Just this approach (B-variant) has been used below in thelow-temperature range of [bmim][BF4]

Step 7 The self-consistent prediction of a hypothetical(V 119897)-diagram requires the equilibration of CXC-pressures119875120590(119879 120588119892) = 119875120590(119879 120588119897) by FT-EOS (1) with the necessary final

change in 1198860(119879)-value from (19) to satisfy the equality

119886 (119879) = 1198860(119879) minus

119875120590(119879 120588119892)

1205882

119897

(20)

Only in the low-temperature range119879 le 119879119887the distinction

between the preliminary definition (18) and its final form(19) for 119886(119879)-values is not essential at the prediction of vaporpressure 119875

120590(119879 120588119892)

3 Reference Equation of State Effective PairPotential and Hypothetical Phase Diagram

To demonstrate universality of approach and for convenienceof reader we have collected the coefficients of FT-EOS (1) forneutral (C

2H4) and polar (H

2O) fluids [7 8] in Table 1 and


Table 2 Coefficients of FT-EOS (1) for ILs [bmim][PF6] [pmmim][Tf2N] and [bmim][BF4]

1198870 [dm3mol] 119886 [Jsdotdm3mol2] 119879 [K]

[bmim][PF6] [pmmim][Tf2N] [bmim][BF4]1198870 = 01953 1198870 = 02711 1198870 = 0178

119879 119886 119879 119886 119879 119886

285 843352 28815 117248 290 94700290 821424 29515 122245 300 89009295 801504 30425 122790 310 84350300 783344 31365 117289 320 80475305 766734 32435 113084 330 77208310 751497 33515 106723 340 74422315 737483 34465 100511 350 72026320 724564 35015 970950325 712631330 701589335 691355340 681859345 673037350 664836

added in Table 2 to other ILs ([bmim][PF6] [pmmim][Tf

2N]

[7 8]) the data for [bmim][BF4] obtained in this work

(Table 3) When temperature is low 119879119898lt 119879 lt 119879

119887FT-model

follows a two-parameter (120576(119879) 1205900) correlation of principle of

corresponding states (PCS) on molecular level as well as atwo-parameter (119886(119879) 119887

0) correlation of PCS on macroscopic

levelOne the most impressed results of FT-methodology is

shown in Figure 1 where the comparison between suchdifferent high- and low-molecular substances as ILs andC2H4 H2O is represented The results based on the coeffi-

cients of Tables 1 and 2 demonstrate that the proposed low-temperature model provides the symmetric two-value repre-sentation of vapor pressure plusmn119875

119904(119879) similar to that observed

for the ferromagnetic transition in weak external fieldsTo estimate the appropriate excluded molar volume 119887

0

(M = 22582 gmol) of FT-model we consider that it belongsto the range [V

0= 119872120588

0asymp 162 V

119897= 119872120588

119897asymp

187 cm3mol] The extrapolated to zero temperature T = 0Kldquocoldrdquo volume V

0= 162 cm3mol follows from (27) The fixed

value 1198870= 178 cm3mol (119887

0asymp 11V

0) has been used in

this work to demonstrate the main results of the proposedmethodology Such choice for [bmim][BF

4] on the ad hoc

basis is in a good correspondence with the respective values1198870= 1953 cm3mol for [bmim][PF

6] and 119887

0= 2711 cm3mol

for [pmmim][Tf2N] where the empirical relationship 119887

0asymp

11V0was also observed [7 8] Our estimates of the effective

LJ-diameters by (6a) for ILs 120590([bmim][BF4]) = 5208 A

120590([bmim][PF6]) = 5371 A and 120590([pmmim][Tf

2N]) = 5992 A

can be tested by comparison with the independently deter-mined values [13] for anions 120590

119886([BF4]) = 451 A 120590

119886([PF6])

= 506 A We have verified Berthelotrsquos combining rule forspherical molecular ions (21a) and van der Waalsrsquo combining

25

75

125

100 140 180 220 260 300 340

Ps(kPa)

minus25

minus75

minus125

C2H4 H2O

Ps[25]Ps[23]

Pgs

Pgs

Pminusl Pminusl

T (K)

(a)

0

05

1

15

280 295 310 325 340

Ps(kPa)

T (K)

[pmmim][Tf2N]

[bmim][PF6]

minus05

minus1

minus15

Pgs

Pminusl

Pgs

Pminusl

(b)

Figure 1 (a) Comparison of the predicted two-value vapor-pressures plusmn119875119892

119904(minus119875119892

119904≃ 119875minus

119897) with the tabular 119875

119904(119879)-data for ethy-

lene [23] and water [24] (b) predicted two-value vapor-pressuresplusmn119875119892

119904(minus119875119892

119904≃ 119875minus

119897) for [bmim][PF

6] and [pmmim][Tf

2N]

rule for chain molecules (21b) usually considered by van derWaalsrsquo-type of EOS for mixtures [22] Consider

120590 =120590119888+ 120590119886

2 (21a)

1198870=119887119888+ 119887119886

2 (21b)

The predicted by former rule of LJ-diameter for the same[bmim]-cation were close but still different 5906 A and5682 A For the latter rule their values and distinctionbecome even smaller 5757 A and 5651 A As a result thechain rule (21b) seems preferable for ILs and its averagevalue for 120590

119888[bmim] = 5704 A can be used to estimate the

LJ-diameter of [Tf2N]-anion 120590

119886[Tf2N] = 6254 A taking into

account the equality119872119888[bmim] =119872

119888[pmmim] = 139 gmol


Table 3 Predicted hypothetical (V 119897)-transition in the low-temperature range for FT-model of [bmim][BF4] based on the experimental data[1 2] treated by FT-EOS (119861-variant of 119909(119879)-prediction)

119879 (K) 120588119897(moldm3) 120588

119892(moldm3) 119875

120590(kPa) 119903

120590(Jmol) 119886 (Jsdotdm3mol2) 120576119896 (K)

290 5350646 309E minus 08 745E minus 05 53082 94700 290300 5322170 21E minus 07 524E minus 04 49866 89009 300310 5293693 101E minus 06 0002 47230 84350 30999320 5265215 374E minus 06 0009 45032 80475 31999330 5236735 113E minus 05 0031 43175 77208 32999340 5208254 292E minus 05 0082 41587 74422 33999350 5179771 661E minus 05 0192 40216 72026 34999360 5151287 0000135 0404 39022 69946 35999370 5122802 0000253 0778 37974 68130 36998380 5094315 0000441 1393 37048 66535 37996390 5065828 0000725 2347 36225 65127 38994400 5037338 0001131 3754 35488 63878 39991410 5008848 0001689 5740 34826 62766 40986420 4980355 0002428 8446 34228 61774 41979430 4951862 0003379 12017 33684 60887 42970440 4923367 0004569 16604 33188 60091 43959450 4894871 0006027 22359 32733 59376 44945460 4866373 0007778 29432 32314 58732 45927470 4837873 0009843 37968 31926 58154 46905480 4809372 0012244 48105 31566 57632 47879490 4780869 0014997 59977 31230 57163 48849500 4752365 0018119 73704 30914 56741 49813510 4723859 0021622 89400 30618 56361 50772511 4721008 0021993 91082 30589 56325 50867512 4718157 0022369 92785 30561 56290 50963513 4715307 0022748 94509 30532 56254 51058514 4712456 0023132 96254 30504 56220 51154515 4709605 0023519 98020 30476 56186 51249516 4706754 0023910 99806 30448 56152 51344517 4703903 0024306 101615 30420 56118 51440

Table 4 Effective LJ-diameters of FT-model for ILs determined by(6a) (6b) and (21b) on the base of estimates [7 13] and the choice1198870 = 178 cm3mol for [bmim][BF4] in this work

IL 119872 (gmol) 120590 (A) 119872119888119872119886

120590119888120590119886

[bmim][BF4] 22582 5208 1398682 5757451 [13][bmim][PF6] 284 5371 [7] 139145 5651506 [13][pmmim][Tf2N] 4191 5992 [7] 1392801 57046254

The collected in Table 4 effective LJ-diameters are linearfunctions of 119872

119886in the set of ILs with different anions and

cations if the molecular weight of latters119872119888is the same one

Since the low-temperature compressibility factor 119885119897(119879) is

very small for all discussed liquids their dispersive energies120576(119879) (molecular attractionrsquos parameters) are comparable inaccordance with (6b) However the differences in cohesiveenergies 119886(119879) (collective attractionrsquos parameters) between thelow-molecular substances (C

2H4 H2O) and ILs are striking

as it follows from Tables 1 and 2 The physical nature of such

distinction can be at the first glance attributed to omittedin the reference LJ-potential influence of intramolecularforce-field parameters and anisotropic (dipole-dipole andcoulombic) interactions At the same time one must accountthe collective macroscopic nature of 119886(119879)-parameter It cor-responds to the scales which are compatible or larger thanthe thermodynamic correlation length 120585(120588 119879) FT-model[9ndash12] provides an elegant and simple estimation of thiseffective parameter based on the concept of comparabilitybetween energetic and geometric characteristic of force fielddetermined by the given RPP Consider

1205853=119886 (119879)

119896119861119879minus120576 (119879)

120588119896119861119879=

1198870

1 minus 1198870120588 (22)

Taking into account the above results and the coefficientsfrom Tables 1ndash3 we have used (22) at T = 300K (119879lowast =

119896119861119879120576 asymp 1) to compare the thermodynamic correlation

length predicted for [bmim][BF4] (a = 89009 Jsdotdm3mol2

1198870= 178 cm3mol 120588= 5322294moldm3) and atT = 29815 K

for water (a = 54827 Jsdotdm3mol2 1198870

= 1658 cm3mol


100

300

500

700

900

1100

1300

0 1 2 3 4 5 6

T(K

)

120588 (moldm3)

Figure 2 Comparison of the GEMC-simulated (black triangles)(V 119897)-diagram [6] for [bmim][BF

4] with the HPD-predicted coex-

istence of orthobaric densities (lines with black squares) the char-acteristic (119879

119888 119879119887) points are emphasized as well as the distinction

of respective rectilinear [6] and strongly-curved (HPD) diametersThe input low-temperature experimental 120588

119897(119875119900 119879)-data [1 2] are

represented by white diamonds Location of classical spinodal andits critical point (◻) predicted by LF-EOS [14] is shown by dashedline

0

20

40

60

80

200 400 600 800 1000 1200 1400

r 120590(kJm

ol)

T (K)

Figure 3 Enthalpy of vaporization for [bmim][BF4] calculated

by different methodologies (GEMC-simulated [6] ( 998771) FT-EOS-predicted at 119879 le 119879

119887(◼zz) HPD-predicted (ndash◼-◼) tabular data for

water [24] (ndashQndashQ))

120588 = 55444moldm3) [24] The dimensional and reduced(120585lowast= 120585120590) values for former are respectively 120585 = 1777 A

120585lowast = 3412 while for latter 120585 = 6986 A 120585lowast = 2945 No moreneed be said to confirm the universality of FT-model

One may note that our estimates of correlation lengthare significantly larger than those usually adopted for thedimensional or reduced cutoff radius (119903

119888or 119903lowast119888= 119903119888120590) of

direct interactions at computer simulations As a result thestandard assumption 120585lowast

119888asymp 119903lowast

119888may become questionable in

the comparatively small (mesoscopic) volumes of simulation1198713lt 120585(120588 119879)

3 At this condition the simulated propertiesare mesoscopic although their lifetime may be essentiallylarger than its simulated counterpart The key point here isthe same as one near a critical point where the problem of

0

1

2

3

4

5

200 400 600 800 1000 1200 1400T (K)

P(M

Pa)

Figure 4 Comparison of the GEMC-simulated [6] pressures ofcondensation ( 998771) with the HPD-predicted pressures of boiling(ndash◼-◼) for [bmim][BF

4] The characteristic (119879

119888 119879119887) points are

emphasized tabular data for water [24] (ndashQndash) The location ofspinodal predicted by LF-EOS [14] is shown by dashed line

consistency between the correlation length for statics and thecorrelation time for dynamics becomes crucial In any casethe computer study of possible nongaussian nature of localfluctuations within the thermodynamic correlation volume1205853 may be quite useful The relevant inhomogeneities inthe steady spacial distributions of density and enthalpy canaffect first of all the simulated values of volumetric (120572

119875 120573119879)

and caloric (119862119901 119862V) derived quantities Simultaneously an

account of internal degrees of freedom and anisotropy by theperturbed RPP may change the correlation length itself

The above described by ((12)ndash(20)) FT-methodology hasbeen used to reconstruct the hypothetical phase diagram(HPD) for [bmim][BF

4] shown in Figures 2 3 and 4 and

represented in Table 3 Both (119879 120588) (Figure 2) and (119875 119879)(Figure 4) projections contain also the branches of classi-cal spinodal calculated by the LF (Sanchez-Lacombe)-EOSobtained in [14] Its top is the location of a respective criticalpoint It seems that the relatively close (119875

119888 119879119888)-parameters

predicted independently by FT-EOS and by LF-EOS (seeSection 1) are reasonable

The FT-model provides a possibility to estimate sep-arately the coordination numbers of LJ-particles in theorthobaric liquid 120588

119897(119879)- and vapor 120588

119892(119879)-phases An ability

to form the respective ldquofriablerdquo (119873119897119892+ 1)-clusters is defined

by the ratio of effective cohesive anddispersivemolar energiesat any subcritical temperature Consider

119873119897119892=

119886119897119892(119879) 120588119897119892

119877119879 (1 minus 119885119897) (23)

The term ldquofriablerdquo is used here to distinguish the clustersformed by the unbounded LJ-particles at the characteristicdistance 119897lowast = 119897120590 asymp

3radic2 gt 1 from the conventional

ldquocompactrdquo ones with the bonding distance 119897lowast lt 1 studiedin particular by the GEMC-methodology [25] to model ofmolecular association It is straightforwardly to obtain thelow-temperature estimates based on the assumptions


0

5

10

15

20

25

30

250 450 650 850 1050

Nl

T (K)

Figure 5 Comparison of two coordination numbers 119873119897predicted

by FT-EOS to characterize the clustering in an orthobaric liquid of[bmim][BF

4] at 119879 le 119879

119887(◼zz) and in the entire (V 119897)-range of HPD

(ndash◼-◼) FT-EOS predictions for water are shown as ndashQ at119879 le 373K

119885119897≪ 119885119892asymp 1

119873119897asymp

1

1 minus 1198870120588119897

(24a)

119873119892asymp

1198870120588119892

1 minus 1198870120588119892

(24b)

and to find the critical asymptotics based on the differenceof classical (1198860 1198870 1198880) and nonclassical (119886 119887 119888) 119879-dependentFT-EOSrsquo coefficients [9ndash12] Consider

119873119888

119897=

3119885119888

1 minus 119885119888

(25a)

119873119888

119892=

119885119888

1 minus 119885119888

[

119860119888(1 minus 119887

0

119888120588119888)

1 minus 119887119888120588119888

minus 1] (25b)

The crucial influence of excluded-volume in (24a) andits relative irrelevance in (24b) for 119873

119897119892-predictions are illus-

trated by Figure 5 where119873119897(119879) function is shown also for the

entire l-branch based on the evaluated in the present workHPD For comparison the low-temperature ability to formthe (119873

119897+ 1)-clusters in liquid water [7 24] is represented in

Figure 5 tooIn according with ((25a) (25b)) the ldquofriablerdquo clusters

can exist only as dimers in the classical critical liquid phase(119873119888

119897asymp 1) It is not universal property in the meaning

of scaling theory but it corresponds to the PCS-concept ofsimilarity between two substances (H

2O and [C

4mim][BF

4]

eg) if their 119885119888-values are close On the other side the

scaling hypothesis of universality is confirmed by the FT-EOSrsquo estimates in the nonclassical critical vapor phase Forthe set of low-molecular-weight substances studied in [9](Ar C

2H4 CO2 H2O) for example one obtains by (25b)

the common estimate (119873119888119892asymp 25) which shows a significant

associative near-mean-field behaviorIt is worthwhile to note here the correspondence of

some FT-EOSrsquo-estimates with the set of GEMC-simulated

results One may use the approximate estimate of criticalslope 119860

119888asymp 786 [9] for [bmim][BF

4] based on the similarity

of its 119885119888-value with that for H

2O [24] In such case the

respective critical excluded volume 119887119888

asymp 220 cm3molbecomes much more than vdW-value 13120588

119888= 1198870

119888asymp 1198870asymp

178 cm3mol Another observation seems also interestingAuthors [25] have calculated (see Figure 3 in [25]) for theldquocompactrdquo clusters at 119897lowast = 07 05 045 the (119879lowast 120588lowast)-diagramof simple fluids One may note that only the value 119897lowast =

07 corresponds to the shape of strongly-curved diametershown in Figure 2 for the HPD while the smaller values119897lowast= 05 045 give the shape of HPD and the nearly rectilinear

diameter strongly resembling those obtained by the GEMC-simulations [6] for the complex ILrsquos force-field If this corre-spondence between the ldquofriablerdquo and ldquocompactrdquo clustering isnot accidental one obtains the unique possibility to connectthe measurable thermophysical properties with the bothcharacteristics of molecular structure in the framework ofFT-EOS

4 Comparison with the Empirical Tait EOSand Semiempirical Sanchez-Lacombe EOS

The empirical Tait EOS is based on the observation thatthe reciprocal of isothermal compressibility 120573minus1

119879for many

liquids is nearly linear in pressure at very high pressuresConsider

1 minus120588 (1198750 119879)

120588 (119875 119879)= 119862 (119879) ln [ 119861 (119879) + 119875

119861 (119879) + 1198750

] (26)

where some authors [14 19] omit the T-dependence incoefficient 119862 and ignore the value 119875

0asymp 0 [14] Such

restrictions transform the Tait EOS into the empirical formof two-parameter (119861(119879) 119862) PCS because the sets of 119862-values for different ILs become close one to another Forexample Machida et al [14] have found the sets C = 009710for [bmim][PF

6] C = 009358 for [bmim][BF

4] and C =

008961 for [bmim][OcSO4] which is rather close to the set

obtained by Matkowska and Hofman [19] C = 0088136 for[bmim][BF

4] and C = 00841547 for [bmim][MeSO

4] At

the same time Gu and Brennecke [3] have reported themuch larger T-dependent values 119862(298 2K) = 0 1829 and119862(323 2K) = 0 1630 for the same [bmim][PF

6]

Two other reasons of discrepancies in the Tait method-ology is the different approximations chosen by authors forthe reference input data 120588(119875

0 119879) and for the compound-

dependent function 119861(119879) Some authors [4 14 18] preferto fit the atmospheric isobars 120588(119875

0 119879) and 119862

119901(1198750 119879) with

a second-order or even third-order polynomial equationwhile the others [1 2 16 19] use a linear function for thisaim As a result the extrapolation ability to lower andhigher temperatures of different approximations becomesrestricted


In this work we have used for [bmim][BF4] the simplest

linear approximation of both density and heat capacity

120588 (1198750 119879)

= 1205880(1 minus

119879

1198790

)

= 139465 (1 minus 119879

217044) kgsdotmminus3

(27)

119862119901(1198750 119879)

= 1198620

119901(1 +

119879

1198790

)

= 27365 (1 + 9537 sdot 10minus4119879) Jsdotmolminus1 sdotKminus1

(28)

taken from [1] The extrapolated to zero of temperature value1205880(0 K) = 139465 kgsdotmminus3 [1] is in a good correspondence

with that from [14] 1205880(0 K) = 139392 kgsdotmminus3 in reasonable

correspondence with that from [19] 1205880(0 K) = 141603 kgsdotmminus3

and that from [16] 1205880(0 K) = 1429 kgsdotmminus3 but its distinction

fromvalue1205880(0 K) = 1476277 kgsdotmminus3 reported by authors [18]

is rather large The similar large discrepancy is observablebetween 119862

0

119901(0 K) = 27365 JmolsdotK from [1] and 1198620

119901(0 K) =

464466 JmolsdotK from [18]The different choices of an approximation function for

119861(119879) (so authors [14] have used the exponential form whileauthors [19] have preferred the linear form) may distortthe derivatives 120573

119879and 120572

119875calculated by the Tait EOS (26)

The problem of their uncertainties becomes even morecomplex if one takes into account the often existence ofsystematic distinctions of as much as 05 between thedensities measured by different investigators even for thesimplest argon [23] Machida et al [14] for example pointedout the systematic deviations measured densities from thosereported by the de Azevedo et al [18] and Fredlake et al[1] for both [bmim][BF

4] and [bmim][PF

6] Matkowska and

Hofman [19] concluded that the discrepancies between thedifferent sets of calculated 120573

119879- and 120572

119875-derivatives increase

with increasing of 119879 and decreasing of 119875 due not only toexperimental differences in density values but also result fromthe fitting equation used The resultant situation is that theexpansivity 120572

119875of ILs reported in literature was either nearly

independent of T [18] or noticeably dependent of T [3 19]We can add to these observations that the linear in

molar (or specific) volume Tait Eos (26) is inadequate inrepresenting the curvature of the isotherm 119875(120588) at lowpressures It fails completely in description of (V 119897)-transitionwhere the more flexible function of volume is desirableHowever this has been clearly stated and explained by Streettfor liquid argon [23] that the adjustable T-dependence ofempirical EOS becomes the crucial factor in representing theexpansivity 120572

119875and especially heat capacities 119862

119875 119862V at high

pressures even if the reliable input data of sound velocity119882(119875 119879) were used

From such a viewpoint one may suppose that the linearin temperature LF-EOS proposed by Sanchez and Lacombe

119875 = minus1205882minus 119879[ln (1 minus 120588) + (1 minus 1

119873119897

)120588] (29)

is restricted to achieve the above goal but can be used as anyunified classical EOS common for both phases to predict theregion of their coexistence Such conjecture is confirmed bythe comparison of FT-EOSwith LF-EOS presented in Figures2 and 4 and discussed belowTheobvious advantage of formeris themore flexibleT-dependence expressed via the cohesive-energy coefficient 119886(119879) On the other hand the LF-EOS istypical form of EOS (see Section 1) in which the constraintof T-independent potential energy 119880( 119903 120588) is inherent [21]

Onemay consider it as the generalized variant of the well-known Bragg-Williams approximation for the ordinary LGpresented here in the dimensional form

119875 = minus1198861205882minus119896119861119879

V0

ln (1 minus 120588V0) (30)

Such generalization provides the accurate map of phe-nomenological characteristic parameters 119879lowast 119875lowast 120588lowast whichdetermine the constant effective number of lattice sites 119873

119897

occupied by a complex molecule

119873119897=

119875lowast119872

120588lowast119877119879lowast=

119872

Vlowast120588lowast=119872119875lowast

120576lowast120588lowast (31)

into the following set of molecular characteristic parametersfor a simple molecule (119873

119897= 1)

120588lowast=1

V0

119875lowast=119911120576

2V0

119879lowast=

119911120576

2119896119861

(32)

where V0is the volume of cell and 119911 is the coordination

number of lattice in which the negative 120576 is the energy ofattraction for a near-neighbor pair of sites In the polymerterminology 120576lowast from (31) is the segment interaction energyand Vlowast is the segment volume which determines the charac-teristic hard core per mole119872120588

lowast (excluded volume 119887 in thevdW-terminology)

Another variant of described approach is the knownperturbed hard-sphere-chain (PHSC) EOS proposed by Songet al [15] for normal fluids and polymers

119875

120588119896119861119879= 1 + 119892 (119889) 119887119873

2

119897120588 minus [119892 (119889) minus 1] (119873

119897minus 1) minus

1198861198732

119897120588

119896119861119879

(33)

where 119892(119889) = (1 minus 1205782)(1 minus 120578)3 is the pair radial distributionfunction of nonbonded hard spheres at contact and the termwith (119873

119897minus 1) reflects chain connectivity while the last term

is the small perturbation contribution Though the PHSC-EOS has the same constraint of the potential energy field119880( 119903 120588) authors [15] have introduced two universal adjustable


Φ119886(119879)- andΦ

119887(119879)-functions to improve the consistency with

experiment The vdW-type coefficients were rescaled as

119886 (119879) = (2120587

3) 1205903120576Φ119886(119879

119904) (34a)

119887 (119879) = (2120587

3) 1205903Φ119887(119879

119904) (34b)

where 119904(119873119897) is the additional scaling function for 119879lowast = 120576119896

119861

It provides the interconnection of molecular LJ-type param-eters (120576 120590) with the phenomenological vdW-ones (119886 119887) Theresultant reduced form of PHSC is [15]

119875 = minus1205882Φ119886(119879

119904)

minus 119879lfloorminus120588 minus 119892 (119889)Φ119887(119879

119904)1205882+ (1 minus

1

119873119897

)119892 (119889) 120588rfloor

(35)

where the following characteristic and reduced variables areused

120588 =21205871205903

3119873119897120588 =

120588

120588lowast 119879 =

119896119861119879

120576=119879

119879lowast

119875 =119875

119896119861119879lowast120588lowast119873119897

=119875

119875lowast

(36)

It was compared with the simpler form of LF-EOS (29)Their predictions of the low-temperature density at saturation120588119897(119879) are comparable but unfortunately inaccurate (overesti-

mated) even for neutral low-molecular liquidsThe respectivepredictions of the vapor pressure 119875

120590(119879) are reasonable [15]

excepting the region of critical point for both EOSs Ourestimates based on the LF-EOS [14] shown in Figures 2 and 4are consistent with these conclusions

The comparison of volumetricmeasurements andderivedproperties [14 18] with the purely predictive (by the FT-EOS)and empirical (by the Tait EOS and LF-EOS) methodologiesused for [bmim][BF

4] is shown in Figures 6ndash9 Evidently

that former methodology is quite promising Machida et al[14] have reported two correlations of the same (119875 120588 119879)-data measured for [bmim][BF

4] at temperatures from 313 to

473 and pressures up to 200MPa To examine the trends inproperties of ILs with the common cation [bmim] the Taitempirical EOS was preliminarily fitted as the more appropri-ate model The estimate of its extrapolation capatibilities for(119875 120588 119879)-surface in the working range (290 lt 119879K lt 350)follows from the compatibility of experimental points (wherethose measured by de Azevedo et al [18] in the range oftemperature 298 lt 119879K lt 333 and pressure (01 lt 119875MPa lt60) were also included) with the thick curves in Figure 6 It isnoticeable for example that the extrapolated Taitrsquos isothermT = 290K coincides practically with isotherm T = 29834Kfrom [18] because the measured densities of latter source aresystematically higher than those from [14] Density data ofFredlake et al [1] for [bmim][BF

4] (not shown in Figure 6)

are also systematically shifted from measurements [14]

1160

1180

1200

1220

1240

1260

1280

0 50 100 150 200 250

120588(kgmiddotmminus3)

290K290K

290K

350K350K

350K

P (MPa)

Figure 6 Comparison of experimental densities for [bmim][BF4]

(l-29834 [18] ◻-31301 [18] -32285 [18] -33273 [6] ◼-3131[14]Q-3326 [14]998771-3526 [14]) with those calculated (a) by the TaitEOS [14] (in a working range 290 lt 119879K lt 350 via the interval10 K thick continuous curves) (b) by the Sanchez-LacombeEOS [14](thick dashed curves) (c) by the FT-EOS (thin continuous curves)

152

253

354

455

556

657

0 50 100 150 200 250

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K

120572P(times10

4Kminus

1)

Figure 7 Comparison of isobaric expansivities for [bmim][BF4]

calculated (a) by theTait EOS [14] (b) by the Sanchez-LacombeEOS[14] (c) by the FT-EOS

The consequence of such discrepancies is also typical forany simple liquids (Ar Kr Xe) [23] at moderate and highpressures It is impossible to reveal an actualT-dependence ofvolumetric (mechanical) derived functions 120572

119875 120574120588due to sys-

tematic deviations between the data of different investigatorsIn such situation an attempt ldquoto take the bull by the hornsrdquoand to claim the preferable variant of EOS based exclusivelyon volumetric data may be erroneous Indeed since the TaitEOS is explicit in density while the LF-EOSmdashin temperaturethe direct calculation of 120572

119875 120573119879-derivatives for former and

120572119875 120574120588-derivatives for latter are motivated To illustrate the

results of these alternative calculations we have used inFigures 6ndash9 the coefficients of LF-EOS reported by Machidaet al [14] for the restricted range of moderate pressures01 lt 119875MPa lt 50 The thick dashed curves represent


0

1

2

3

4

5

0 50 100 150 200 250

120573T

(times10

7kP

aminus1)

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K

Figure 8 Comparison of isothermal compressibilities for [bmim][BF4] calculated (a) by the Tait EOS [14] (b) by the Sanchez-

Lacombe EOS [14] (c) by the FT-EOS

1

15

2

25

3

35

0 50 100 150 200 250P (MPa)

(a)

(c)

290K

350K350K340K330K320K

310K

300K

290K

120574120588(M

PamiddotK

minus1)

Figure 9 Comparison of thermal pressure coefficient for [bmim][BF4] calculated (a) by the Tait EOS [14] (c) by the FT-EOS

the boundaries of working range where the extrapolation toT = 290K is again assumed One may notice the qualitativesimilarity of FT-EOS (the thin curves) and LF-EOSwhich canbe hypothesized as an existence of certain model substanceat the extrapolation to higher pressures 119875MPa gt 50 Itdemonstrates the smaller compressibility 120573

119879(Figure 8) and

expansivity 120572119875(Figure 7) than those predicted by the Tait

EOSwhile the value of thermal-pressure coefficient 120574120588for FT-

EOS (Figure 9) becomes larger It determines the distinctionsin the calculated internal pressure The choice of the FT-modelrsquos substance as a reference system for the perturbationmethodology provides the set of advantages in comparisonwith the LF-EOS

It follows from Figure 6 that at moderate pressures119875MPa lt 50 the predictive FT-EOS is more accurate than thefitted semiempirical LF-EOS [14] although the discrepanciesof both with the empirical Tait EOS [14] become signifi-cant at the lowest (extrapolated) temperature T = 290K

120

125

130

135

140

145

150

0 50 100 150 200 250

C(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K

310K

300K

290K

Figure 10 Comparison of predicted by FT-EOS isochoric heatcapacity for [bmim][BF

4] (lines) with that evaluated by de Azevedo

et al [18] (points) on the base of speed velocity and density inputdata

The Taitrsquos liquid has no trend to (V 119897)-transition (as well aspolymers) in opposite to the clear trends demonstrated byFT-EOS and LF-EOS One may suppose [26] a competitionbetween vaporization of IL (primarily driven by the isotropicdispersive attraction 1119903

6 in RPP) and chain formation(driven mainly by the anisotropic dipolar interactions 11199033)reflected by the Tait EOS fitted to the experimental data Ofcourse such conjecture must be at least confirmed by thecomputer simulations and FT-model provides this possibilityby the consistent estimate of RPP-parameters (120576 120590) at eachtemperature

The differences of calculated expansivity 120572119875in Figure 7

are especially interesting FT-EOS predicts even less variationof it with temperature than that for the Tait EOS This resultand crossing of 120572

119875(119875)-isotherms are qualitatively similar to

those obtained by de Azevedo et al [18] although the pressuredependence of allmechanical (120572

119875 120573119879 120574120588) and caloric (119862

119875 119862V)

derivatives (see Figures 10 11 and 12) is always more signifi-cant for the FT-EOSpredictions It seems that the curvature ofthe 120588(119879)-dependence following from the LF-EOS (29) is notsufficient to predict the 120572

119875(119875) behavior (Figure 7) correctly

The strong influence of the chosen input120588(1198750 119879)-dependence

is obvious from Figures 7ndash9The prediction of caloric derivatives (119862

119901 119862V 119862119901119862VGr)

is the most stringent test for any thermal (119875 120588 119879) EOSIt should be usually controlled [23] by the experimental(119882120588 119879)-surface to use the thermodynamical identities

119862119901= 119862V +

119879120572119875120574120588

120588 (37)

119882 = radic

119862119901

119872(119862119901120573119879120588 minus 119879120572

2

119875)

(38)

Gr = 1198721198822120572119875

119862119901

=1

119879120572119875

(

119862119901

119862Vminus 1) (39)


140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K

Figure 11 Comparison of predicted by FT-EOS isobaric heatcapacity for [bmim][BF



105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)

Figure 12 Comparison of predicted by FT-EOS ratio of heatcapacities for [bmim][BF

4] (thin lines) with that evaluated by de

Azevedo et al [18] on the base of speed velocity and density inputdata (thick lines)

in addition to the chosen input 119862119901(1198750 119879)-dependence de

Azevedo et al [18] applied this strategy to comprise theapproximated by the Pade-technique measured speed ofsound data for [bmim][PF

6] and [bmim][BF

4] (Figure 13)

with the evaluated at high pressures heat capacitiesOur predictive strategy is based [17] on the differentiation

of 119886(119879)-dependence to evaluate directly the most subtle(119862V 119875 119879)-surface in a low-temperature liquid

119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)

where the influence of the consistence for the chosen input120588(1198750 119879)- and 119862

119901(1198750 119879)-dependences (via (37) used for esti-

mate of 119862V(1198750 119879) at the atmospheric pressure 1198750) becomes

crucial The use of first derivative 119889119886119889119879 (even by its roughapproximation in terms of finite differences Δ119886Δ119879) to

1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)

Figure 13 Comparison of predicted by FT-EOS speed of sound for[bmim][BF

4] (thin lines) with that (points) used by de Azevedo et

al [18] as the input data (see also Figure 5 for density used by deAzevedo et al [18] as the input data at evaluations)

calculate simultaneously by ((3) (4) (37) (40)) all volumetricand caloric derivatives is the important advantage over thestandard integration of thermodynamic identities

(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)

To illustrate such statement it is worthwhile to remind thesituation described by the Streett [23] for liquid argon Sinceisotherms of 120572

119875(119875) cross over formany simple liquids (Ar Kr

Xe) this author concludes that the sign of (1205972V1205971198792)119875changes

also from positive to negative at the respective pressureThis conclusion is not valid because to change the sign ofderivative (120597120572

119875120597119879)119875it is enough to account for the exact

equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)

119875can be always positive In this case

one would expect the monotonous decrease of 119862119901with

increasing119875 in accordance to ((41a) (41b))while the presenceof extremum (minimumormaximumof119862

119901(119875)-dependence)

seems to be artificialThere is the variety of pressures reported by different

investigators as a presumable cross-point for the same ILsMachida et al [14] have estimated it to be about 10MPa onthe base of Tait EOS for [bmim][PF

6] but have not found it

(Figure 7) for [bmim][BF4] For latter our estimate by the FT-

EOS is P = 206MPa de Azevedo et al [18] have reported themild decrease of 120572

119875(119879)-dependence and the sharp decrease

120572119875(119875)-dependence while a presumable cross-point is located

between about 100 and 120MPa for [bmim][BF4] Taking

into account the above distinction in the evaluated (120572119875 119875 119879)-

surface it is interesting to consider their consequences for


Table 5 Comparison of excluded volumes (119872120588lowast [14] and 119887

0) characteristic interaction energy (120576lowast [14] and 120576) and effective number of

bonded units (119872119875lowast119877119879lowast120588lowast [14 15] and119873

119897) (see text)

Compound 119872120588lowast

(cm3mol)1198870

(cm3mol)120576lowast

(Jmol)120576

(Jmol) 119872119875lowast119877119879lowast120588lowast

119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181

Table 6 Comparison of internal pressure (120597119890120597V)119879for [bmim][BF4] based on the LF-EOS [14] and FT-EOS (this work) with the values

estimated [16] by experimental data on speed of sound119882 density 120588 and isobaric heat capacity 119862119901

119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731

caloric (119862V 119875 119879)-(119862119901 119875 119879)- and 119862V119862119901-surfaces shown inFigures 10ndash12

The remarkable qualitative and even quantitative (lt8)correspondence between the predicted by FT-EOS 119862V-valuesand those reported by de Azevedo et al [18] follows fromFigure 10 At the same time although the discrepanciesbetween 119862

119901-values [18] and those predicted by the FT-

EOS are again within acceptable limits (lt10) the formersdemonstrate the weak maximum and very small pressuredependence for [bmim][BF

4] (for [bmim][PF

6] this 119862

119901(119875)-

dependence is monotonous as well as that predicted by theFT-EOS) It seems that the resultant ratio of heat capacity119862119901119862V shown in Figure 12 which demonstrates the irregular

crossing of isotherms [18] is questionable It suggests thattheir pressure dependence either needs the more accurateapproximation or reflects the realistic distinction of referenceFT-EOS from the actual behavior of [bmim][BF

4]

The lock of noticeable variations in pressure is thecommon feature of integration methodology [18] based onthe given (119882119875 119879)- and (120588 119875 119879)-surfaces The unavoidableaccumulation of uncertainties at each stage of calculationsin the set 119882 minus 119862

119901minus 119862V may cause the unplausible behavior

of adiabatic exponent 119862119901119862V in liquid The same is true for

the set 119862V minus 119862119901 minus 119882 used in the FT-methodology It is themost appropriate explanation of significant discrepancies for119882(119875)-dependence shown in Figure 13 Let us remind alsothat the precise mechanical measurements of speed velocity[18] in the very viscous IL cannot be attributed exactly to thecondition of constant entropy

Thus strictly speaking the measured (119882119875 119879)-surfacereflects the strong dispersive properties of media andmust beless than its thermodynamic counterpart in the ideal (withouta viscosity) liquid

5 Conclusions

There are the structure-forming factors related to the above-discussed thermodynamic characteristic Despite the certaindiscrepancies between the predicted and derived propertiesfor FT-EOS and LF-EOS both ones provide the close esti-mates of structure factors represented in Table 5

Our aim here is to show that the thermodynamically-consistent predictions of thermodynamical properties by theFT-EOS yields also the molecular-based parameters whichare at least realistic (see also Table 3) The estimate ofaverage T-dependent well-depth 120576 by (6b) as well as estimateof average value 119873

119897by (24a) is related to the middle of

temperature range T = 320K The distinction of 120576 from therespective 120576lowast-parameters of LF-EOS [14] can be attributedto the difference between nonbonded interactions in thediscrete (LF-EOS) and continuum (FT-EOS) models of fluidOur estimate of cohesive-energy density 120576coh by equality

120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)

represented in Table 6 seems also physically plausible Mag-inn et al [5 6] have determined it within the frameworkof GEMC-simulations by the knowledge of 120588(119875

0 119879) and


the internal energy difference between an ideal-gas ion pairand the average internal energy of an ion pair in the liquidstate

Such definition indicates that cohesive energy densitiesof many ILs are on the order of 500ndash550 Jcm3 (see forcomparison Table 6) and demonstrate a slight decrease astemperature increases

Another relevant characteristic is the internal pressuredetermined by the derivative of molar (or specific) internalenergy

(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)

which is compared to ones calculated by different authors [1416] for [bmim][BF

4] in Table 6 As in the other cases the FT-

EOS predicts the much faster change of both cohesive energydensity 120576coh and internal pressure (120597119890120597V)

119879as temperature

increasesOne should collect a large number of precise exper-

imental measurements to reconstruct the thermodynamicsurface of a substance FT-methodology provides a possibilityof preliminary reliable estimates of relevant macroscopicandmolecular-based correlations Its thermodynamic consis-tency provides the serious advantage in comparison with thepurely empiric treatment of any volumetric measurements atthe description of derived heat capacities

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] C P Fredlake J M Crosthwaite D G Hert S N V K Aki andJ F Brennecke ldquoThermophysical properties of imidazolium-based ionic liquidsrdquo Journal of Chemical and Engineering Datavol 49 no 4 pp 954ndash964 2004

[2] C Cadena J L Anthony J K Shah T I Morrow J FBrennecke and E J Maginn ldquoWhy is CO

2so soluble in

imidazolium-based ionic liquidsrdquo Journal of the AmericanChemical Society vol 126 no 16 pp 5300ndash5308 2004

[3] ZGu and J F Brennecke ldquoVolume expansivities and isothermalcompressibilities of imidazolium and pyridinium-based ionicliquidsrdquo Journal of Chemical and Engineering Data vol 47 no2 pp 339ndash345 2002

[4] B Gonzalez E Gomez A Domınguez M Vilas and E TojoldquoPhysicochemical characterization of new sulfate ionic liquidsrdquoJournal of Chemical and Engineering Data vol 56 no 1 pp 14ndash20 2011

[5] C Cadena Q Zhao R Q Snurr and E J Maginn ldquoMolecularmodeling and experimental studies of the thermodynamic andtransport properties of pyridinium-based ionic liquidsrdquo TheJournal of Physical Chemistry B vol 110 no 6 pp 2821ndash28322006

[6] N Rai and E J Maginn ldquoVapor-liquid coexistence and criticalbehavior of ionic liquids via molecular simulationsrdquo Journal ofPhysical Chemistry Letters vol 2 no 12 pp 1439ndash1443 2011

[7] V B Rogankov ldquoEquation of state for ionic liquidsrdquo HighTemperature vol 47 no 5 pp 656ndash663 2009

[8] V B Rogankov V I Levchenko and Y K Kornienko ldquoFluc-tuational equation of state and hypothetical phase diagram ofsuperheated water and two imidazolium-based ionic liquidsrdquoJournal of Molecular Liquids vol 148 no 1 pp 18ndash23 2009

[9] V B Rogankov and L Z Boshkov ldquoGibbs solution of the vander Waals-Maxwell problem and universality of the liquid-gascoexistence curverdquo Physical Chemistry Chemical Physics vol 4no 6 pp 873ndash878 2002

[10] V A Mazur and V B Rogankov ldquoA novel concept of symmetryin the model of fluctuational thermodynamicsrdquo Journal ofMolecular Liquids vol 105 no 2-3 pp 165ndash177 2003

[11] V B Rogankov O G Byutner T A Bedrova and T VVasiltsova ldquoLocal phase diagramof binarymixtures in the near-critical region of solventrdquo Journal of Molecular Liquids vol 127no 1ndash3 pp 53ndash59 2006

[12] V B Rogankov ldquoAsymmetry of heterophase fluctuations innucleation theoryrdquo in Nucleation Theory and Applications J WP Schmelzer G Ropke and V Priezshev Eds chapter 22 pp227ndash241 Joint Institute for Nuclear Research Dubna Russia2011

[13] A B McEwen H L Ngo K LeCompte and J L GoldmanldquoElectrochemical properties of imidazolium salt electrolytes forelectrochemical capacitor applicationsrdquo Journal of the Electro-chemical Society vol 146 no 5 pp 1687ndash1695 1999

[14] H Machida Y Sato and R L Smith Jr ldquoPressure-volume-temperature (PVT) measurements of ionic liquids ([bmim+][PFminus6] [bmim+][BFminus

4] [bmim+][OcSOminus

4]) and analysis with the

Sanchez-Lacombe equation of staterdquo Fluid Phase Equilibria vol264 no 1-2 pp 147ndash155 2008

[15] Y Song S M Lambert and J M Prausnitz ldquoA PerturbedHard-Sphere-Chain equation of state for normal fluids and polymersrdquoIndustrial amp Engineering Chemistry Research vol 33 no 4 pp1047ndash1057 1994

[16] A Kumar ldquoEstimates of internal pressure and molar refractionof imidazolium based ionic liquids as a function of tempera-turerdquo Journal of Solution Chemistry vol 37 no 2 pp 203ndash2142008

[17] L P N Rebelo J N C Lopes JM S S Esperanca and E FilipeldquoOn the critical temperature normal boiling point and vaporpressure of ionic liquidsrdquo The Journal of Physical Chemistry Bvol 109 no 13 pp 6040ndash6043 2005

[18] R G de Azevedo J M S S Esperanca V Najdanovic-Visak et al ldquoThermophysical and thermodynamic propertiesof 1-Butyl-3-methylimidazolium tetrafluoroborate and 1-Butyl-3-methylimidazolium hexafluorophosphate over an extendedpressure rangerdquo Journal of Chemical amp Engineering Data vol50 no 3 pp 997ndash1008 2005

[19] D Matkowska and T Hofman ldquoHigh-pressure volumetricproperties of ionic liquids 1-butyl-3-methylimidazoliumtetrafluoroborate [C

4mim][BF

4] 1-butyl-3-methylimid-

azolium methylsulfate [C4mim][MeSO

4] and 1-ethyl-3-meth-

ylimidazolium ethylsulfate [C2mim][EtSO

4]rdquo Journal of

Molecular Liquids vol 165 pp 161ndash167 2012[20] E A Guggenheim ldquoThe new equation of state of Longuet-

Higgins andWidomrdquoMolecular Physics vol 9 no 1 pp 43ndash471965

[21] B Widom ldquoSome topics in the theory of fluidsrdquoThe Journal ofChemical Physics vol 39 pp 1808ndash1812 1963

[22] R L Scott and P H van Konynenburg ldquoStatic properties ofsolutions van der Waals and related models for hydrocarbon


mixturesrdquo Discussions of the Faraday Society vol 49 pp 87ndash971970

[23] W B Streett ldquoThermodynamic properties of liquid argon athigh pressures calculated from PVT and sound-velocity datardquoPhysica vol 76 no 1 pp 59ndash72 1974

[24] A Saul andWWagner ldquoInternational equations for the satura-tion properties of ordinary water substancerdquo Journal of Physicaland Chemical Reference Data vol 16 pp 893ndash901 1987

[25] F Bresme E Lomb and J L F Abascal ldquoInfluence of associationon the liquid-vapor phase coexistence of simple systemsrdquo TheJournal of Chemical Physics vol 106 no 4 pp 1569ndash1575 1997

[26] R van Roij ldquoTheory of chain association versus liquid conden-sationrdquo Physical Review Letters vol 76 no 18 pp 3348ndash33511996

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


Superconductivity


Statistical MechanicsInternational Journal of


GravityJournal of


AstrophysicsJournal of


Physics Research International


Solid State PhysicsJournal of

Computational Methods in Physics

Journal of



Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


Journal of

Biophysics


ThermodynamicsJournal of


their metastable extensions Only the measurable isobaricheat capacity data 119862

119875(1198750 119879) have to be added to the set

of input data for prediction of other caloric properties(isochoric heat capacity 119862V(119875 119879) speed of sound 119882(119875 119879)and Gruneisen parameter Gr(119875 119879)) at higher pressures119875 gt 119875

0and lower 119879 lt 119879

119898or higher 119879 gt 119879

119887temperatures

where 119879119887is the hypothesized normal boiling temperature

119879119887(1198750) Its existence itself is a debatable question because the

thermal decomposition 119879119889may be former 119879

119889lt 119879119887

Such approachwas proposed recently [7 8] to reconstructthe hypothetical (V 119897)-diagram of any ILs in its stable andmetastable regions on the base of only standard reference dataon density 120588(119879) at119875

0[1ndash4] and one free parameter an a priori

unknown value of the excluded volume 1198870 To our knowledge

this is first attempt to predict simultaneously the wholeset of one-phase and two-phase properties for ILs withoutthe fit at any other pressures including the negative ones Itwas argued that the particular low-temperature variant ofthe most general FT-EOS [9ndash12] should be used to obtainthe consistent prediction of volumetric properties and thestandard response functions 119886

119875 120573119879 120574120588

= 119886119875120573119879by the

following equations

119875 =120588119877119879

1 minus 1198870120588minus 119886 (119879) 120588

2 (1)

120573119879=

(1 minus 1198870120588)2

2119875 (1 minus 1198870120588)2

+ 120588119877119879 (21198870120588 minus 1)

gt 0 (2)

120572119875=

(1 minus 1198870120588) lfloor120588119877 minus 120588

2(1 minus 119887

0120588) 119889119886119889119879rfloor

2119875 (1 minus 1198870120588)2

+ 120588119877119879 (21198870120588 minus 1)

(3)

120574120588=120588119877 minus 120588

2(1 minus 119887

0120588) 119889119886119889119879

(1 minus 1198870120588)

(4)

where 1198870is the excluded molecular volume and 119886(119879) is

the 119879-dependent effective cohesive energy The derivative119889119886119889119879 affects the thermal expansion 120572

119875and the thermal-

pressure coefficient 120574120588while the isothermal compressibility

120573119879depends only on 119887

0-value at the given pressure The

changeable sign of two thermal derivatives 120572119875 120574120588offers

a possibility to predict the properties of anomalous low-temperature substances (such aswater for example) too [7 8]

Fortunately we have obtained now [13ndash19] a possibilityto test our predictions not only by the direct experimentalone-phase data [14 16 18 19] on 120588(119875 119879)- and 119882(119875 119879)-surfaces Another possibility is offered by comparison of thepredictions obtained by FT-EOS for the critical parametersof ILs ([bmim][BF

4] 119879119888= 9623 K 119875

119888= 35039 kPa 120588

119888=

438565 kgsdotmminus3 with those predicted here by the Sanchez-Lacombe EOS for lattice fluid (LF) [15] 119879

119888= 88501 K

119875119888= 2829 kPa 120588

119888= 248565 kgsdotmminus3 as well as with those

simulated by GEMC-methodology [6] 119879119888= 1252K 119875

119888=

390 kPa 120588119888= 181 kgsdotmminus3 It seems that the relatively close

location of (119879119888 119875119888)-parameters predicted by both EOSs is

some guarantee of their reliability while119879119888and119875119888from [6] are

significantly overestimated and underestimated respectivelyInterestingly the known descriptive factor of compressibility

119903119905= 119875119888(120588119905119877119879119888) estimated by Guggenheim [20] in the vicinity

of triple point 119879119905for argon as 119903

119905= 0108 is equal to close

values 119903119905= 0082 for FT-EOS and 119903

119905= 0072 for LF-

EOS but only to very small value 119903119905= 0007 for result

of GEMC-simulations if the common realistic estimate (seebelow) 120588

119905asymp 120588119897= 5350646molsdotdmminus3 at T = 290K is used

Moreover it will be shown that the characteristic dimensionalparameters 119875lowast

119888 119879lowast119888 120588lowast119888and another compressibility factor

119903lowast

119888= 119875lowast

119888(120588lowast

119888119877119879lowast

119888) obtained by Machida et al [14] by

the fit to (119875 120588 119879)-experimental data for [bmim][BF4] and

[bmim][PF6] provide the structural estimates of hard-core

volume number of lattice sites in a cluster and energyof near-neighbor pair interactions which are surprisinglyclose to ones independently predicted by the FT-model of acontinuum substance

Taking into account the compatibility of above results itis important to consider the presumable similarity betweenthe square-well fluid (which may be thought of as a con-tinuum analogue of the lattice-gas (LG) or lattice-fluid (LF)systems) on the one hand and the LJ-fluid of finite-rangeinteractions (RPP) on the other This conceptual analogy hasbeen pointed out long ago for the critical region by Widom[21] who suggested that it is the propagation of attractivecorrelations in the LG which determines the peculiarities ofcriticality However such unphysical LG-predictions at lowtemperatures of the (120588 119879)-plane as the nonexistence of a (119897 119904)-transition suggest that repulsive forces are not being treatedproperly by this RPP-model In contrast with the discreteLG-model it seems that both attractive and repulsive forcesare being dealt with properly in the square-well continuumfluid because it exhibits both (V 119897)- and (119897 119904)-transitionsThe serious restriction of latter is however evident sinceany singularities of RPP imply an artificial jump of pair-distribution isotropic function 119892(119903) at the point of cutoffradius 119903

119888for attractive interactions

In this context only the shifted and smoothed at 119903119888-

point LJ-potential [5 6] seems to be appropriate as RPP fora continuum system Of course the algebraic form of therespective reference EOS is essential too In accordance withthe statistical-mechanical arguments presented by Widom[21] there are the set of alternative forms including theoriginal vdW-EOS and the LG-EOS in thewell-knownBragg-Williams approximation which share the common restrictivefeature Onemay suppose that the probability of finding someprescribed value of the potential energy 119880( 119903) at an arbitrarypoint in the fluid is independent of 119879 at fixed 120588 119880( 119903 120588)Another simplifying assumption is that such EOS supposesonly two types of fluid structure one of the excluded (or hard-core) volume 119873V

0where the singular hard-sphere branch of

potential is infinite and one of free volume (119881 minus 119873V0) where

the potential is uniform weak and unrestricted (an infinite-range rectilinear well) It should be directly proportional todensity 119890 = 119880119873 = minus119886120588 where 119880 is the total configurationalenergy and 119886 is the constant vdW-coefficientThese historicalnotes are important to explain how one can go beyond theabove restriction of119879-independency by adoption of linear 120588-dependence for a generalized specific or molar energy (seealso (8) below) Consider


119886 (119879) = minus(120597119890

120597120588)

119879

(5)


120590 (119879) = [3119887 (119879)

(2120587119873119860)]

13

(6a)

120576 (119879)

119896= 119879 (1 minus 119885

119897) (6b)













119898lt 119879 lt 119879

119887) In


119898lt








119875 =120588119877119879 [1 minus 119888 (119879)]

1 minus 119887 (119879) 120588minus 119886 (119879) 120588

2 (7)


119886 (119879) =119875120590(119860120590minus 1)

120588119897120588119892

= minus

(119890119897minus 119890119892)

(120588119897minus 120588119892)

(8)

119887 (119879) =119860120590minus 2

(120588119897+ 120588119892) (119860120590minus 1)

(9)

1 minus 119888 (119879) = 119885119897lfloor1 +

120588119897(119860120590minus 1)

120588119892

rfloor (1 minus 119887120588119897) (10)




119860120590(119879) =

119879

119875120590

119889119875120590

119889119879=

119879 (119904119892minus 119904119897) 120588119897120588119892

119875120590(120588119897minus 120588119892)

(11)


119887le 119879 le 119879

119888)


119905le 119879 le


(119879119905le 119879 le 119879

119887)


120590(119879) 120588

119892(119879) 120588

119897(119879) for ILs


119905(or melting 119879

119898)





6]








119887 1198750) 120588119892(119879119887) =


120588119892

120588119897

=1 + 119910 (119909) 119890

minus119909

1 + 119910 (119909) 119890119909 (12)



119909 =

(119904119892minus 119904119897)

2119877 (13a)

119903120590= ℎ119892minus ℎ119897= 2119877119879

119887119909 (119879119887) (13b)



sh119909 = 119890119909minus 119890minus119909

2 ch119909 = 119890

119909+ 119890minus119909

2

(14)


1198870=

[119909 (119879119887) minus 1]

120588119897(119879119887) [119909 (119879

119887) minus 12]

(15)


120588119892= 1198870lfloor1 + 119910(119909)119890

119909rfloorminus1

(16a)

120588119897= 1198870lfloor1 + 119910(119909)119890


(16b)


120588plusmn=

1

21198870


0120588)

1 minus 1198850(1 minus 119887

0120588)] (17)

where 120588 = 120588(119879 1198750) 1198850

= 1198750120588119877119879 and the 120588

+(119879)-


119909 (119879) =1 minus 1198870120588+2

1 minus 1198870120588+ (18)


120590(119879) 120588

119892(119879) 120588





1198860(119879) =

119877119879

120588119897(1 minus 119887

0120588119897) (19)



C2H4 H2O1198870= 004181 119887

0= 001658

119879 119886 119879 119886

10399 155712 27316 517162105 145976 27815 527171110 112730 28315 534941115 935490 28815 540955120 812151 29315 545767125 725634 29815 548270130 661817 30315 549648135 613602 30815 549424140 575528 31315 548755145 545191 31815 547172150 520785 32315 544760155 500788 32815 541609160 484652 33315 537810165 471466 33815 53345516935 462006 34315 529044

34815 52460535315 51978935815 51467636315 50967436815 50448037315 499159



0-value for




119886 (119879) = 1198860(119879) minus

119875120590(119879 120588119892)

1205882

119897

(20)



120590(119879 120588119892)



2H4) and polar (H






119879 119886 119879 119886 119879 119886

285 843352 28815 117248 290 94700290 821424 29515 122245 300 89009295 801504 30425 122790 310 84350300 783344 31365 117289 320 80475305 766734 32435 113084 330 77208310 751497 33515 106723 340 74422315 737483 34465 100511 350 72026320 724564 35015 970950325 712631330 701589335 691355340 681859345 673037350 664836


2N]



119887FT-model









0


0= 119872120588

0asymp 162 V

119897= 119872120588

119897asymp



value 1198870= 178 cm3mol (119887

0asymp 11V

0) has been used in


4] on the ad hoc


6] and 119887

0= 2711 cm3mol


0asymp




2N]) = 5992 A


119886([BF4]) = 451 A 120590

119886([PF6])


25

75

125

100 140 180 220 260 300 340

Ps(kPa)

minus25

minus75

minus125

C2H4 H2O

Ps[25]Ps[23]

Pgs

Pgs

Pminusl Pminusl

T (K)

(a)

0

05

1

15

280 295 310 325 340

Ps(kPa)

T (K)

[pmmim][Tf2N]

[bmim][PF6]

minus05

minus1

minus15

Pgs

Pminusl

Pgs

Pminusl

(b)


119904(minus119875119892

119904≃ 119875minus


119904(119879)-data for ethy-


119904(minus119875119892

119904≃ 119875minus


6] and [pmmim][Tf

2N]


120590 =120590119888+ 120590119886

2 (21a)

1198870=119887119888+ 119887119886

2 (21b)






119888[pmmim] = 139 gmol



119879 (K) 120588119897(moldm3) 120588

119892(moldm3) 119875

120590(kPa) 119903




IL 119872 (gmol) 120590 (A) 119872119888119872119886

120590119888120590119886










1205853=119886 (119879)

119896119861119879minus120576 (119879)

120588119896119861119879=

1198870

1 minus 1198870120588 (22)






= 1658 cm3mol


100

300

500

700

900

1100

1300

0 1 2 3 4 5 6

T(K

)

120588 (moldm3)






119897(119875119900 119879)-data [1 2] are


0

20

40

60

80

200 400 600 800 1000 1200 1400

r 120590(kJm

ol)

T (K)








119888or 119903lowast119888= 119903119888120590) of






0

1

2

3

4

5

200 400 600 800 1000 1200 1400T (K)

P(M

Pa)



119888 119879119887) points are



119875 120573119879)






119888 119879119888)-parameters



119897(119879)- and vapor 120588




119873119897119892=

119886119897119892(119879) 120588119897119892

119877119879 (1 minus 119885119897) (23)





0

5

10

15

20

25

30

250 450 650 850 1050

Nl

T (K)



4] at 119879 le 119879



119885119897≪ 119885119892asymp 1

119873119897asymp

1

1 minus 1198870120588119897

(24a)

119873119892asymp

1198870120588119892

1 minus 1198870120588119892

(24b)


119873119888

119897=

3119885119888

1 minus 119885119888

(25a)

119873119888

119892=

119885119888

1 minus 119885119888

[

119860119888(1 minus 119887

0

119888120588119888)

1 minus 119887119888120588119888

minus 1] (25b)










2O and [C

4mim][BF

4]














119888= 1198870







119879for many


1 minus120588 (1198750 119879)

120588 (119875 119879)= 119862 (119879) ln [ 119861 (119879) + 119875

119861 (119879) + 1198750

] (26)


0asymp 0 [14] Such


6] C = 009358 for [bmim][BF

4] and C =




4] At


6]




0 119879) and 119862

119901(1198750 119879) with





120588 (1198750 119879)

= 1205880(1 minus

119879

1198790

)

= 139465 (1 minus 119879


(27)

119862119901(1198750 119879)

= 1198620

119901(1 +

119879

1198790

)


(28)







0


119901(0 K) =



119879and 120572



4] and [bmim][PF

6] Matkowska and


119879- and 120572







119875 119862V at high




119873119897

)120588] (29)



119875 = minus1198861205882minus119896119861119879

V0

ln (1 minus 120588V0) (30)


119897


119873119897=

119875lowast119872

120588lowast119877119879lowast=

119872




119897= 1)

120588lowast=1

V0

119875lowast=119911120576

2V0

119879lowast=

119911120576

2119896119861

(32)





119875

120588119896119861119879= 1 + 119892 (119889) 119887119873

2

119897120588 minus [119892 (119889) minus 1] (119873


1198861198732

119897120588

119896119861119879

(33)





Φ119886(119879)- andΦ



119886 (119879) = (2120587

3) 1205903120576Φ119886(119879

119904) (34a)

119887 (119879) = (2120587

3) 1205903Φ119887(119879

119904) (34b)


119861


119875 = minus1205882Φ119886(119879

119904)


119904)1205882+ (1 minus

1

119873119897

)119892 (119889) 120588rfloor

(35)


120588 =21205871205903

3119873119897120588 =

120588

120588lowast 119879 =

119896119861119879

120576=119879

119879lowast

119875 =119875

119896119861119879lowast120588lowast119873119897

=119875

119875lowast

(36)



120590(119879) are reasonable [15]









1160

1180

1200

1220

1240

1260

1280

0 50 100 150 200 250


290K290K

290K

350K350K

350K

P (MPa)



152

253

354

455

556

657

0 50 100 150 200 250

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K

120572P(times10

4Kminus

1)




119875 120574120588due to sys-






0

1

2

3

4

5

0 50 100 150 200 250

120573T

(times10

7kP

aminus1)

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K



1

15

2

25

3

35

0 50 100 150 200 250P (MPa)

(a)

(c)

290K

350K350K340K330K320K

310K

300K

290K

120574120588(M

PamiddotK

minus1)








120

125

130

135

140

145

150

0 50 100 150 200 250

C(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K

310K

300K

290K










119875 120573119879 120574120588) and caloric (119862

119875 119862V)





119901 119862V 119862119901119862VGr)


119862119901= 119862V +

119879120572119875120574120588

120588 (37)

119882 = radic

119862119901

119872(119862119901120573119879120588 minus 119879120572

2

119875)

(38)

Gr = 1198721198822120572119875

119862119901

=1

119879120572119875

(

119862119901

119862Vminus 1) (39)


140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K




105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)






6] and [bmim][BF

4] (Figure 13)



119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)





1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)





(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)






equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)




119901(119875)-dependence)















119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




119886 (119879) = minus(120597119890

120597120588)

119879

(5)


120590 (119879) = [3119887 (119879)

(2120587119873119860)]

13

(6a)

120576 (119879)

119896= 119879 (1 minus 119885

119897) (6b)













119898lt 119879 lt 119879

119887) In


119898lt








119875 =120588119877119879 [1 minus 119888 (119879)]

1 minus 119887 (119879) 120588minus 119886 (119879) 120588

2 (7)


119886 (119879) =119875120590(119860120590minus 1)

120588119897120588119892

= minus

(119890119897minus 119890119892)

(120588119897minus 120588119892)

(8)

119887 (119879) =119860120590minus 2

(120588119897+ 120588119892) (119860120590minus 1)

(9)

1 minus 119888 (119879) = 119885119897lfloor1 +

120588119897(119860120590minus 1)

120588119892

rfloor (1 minus 119887120588119897) (10)




119860120590(119879) =

119879

119875120590

119889119875120590

119889119879=

119879 (119904119892minus 119904119897) 120588119897120588119892

119875120590(120588119897minus 120588119892)

(11)


119887le 119879 le 119879

119888)


119905le 119879 le


(119879119905le 119879 le 119879

119887)


120590(119879) 120588

119892(119879) 120588

119897(119879) for ILs


119905(or melting 119879

119898)





6]








119887 1198750) 120588119892(119879119887) =


120588119892

120588119897

=1 + 119910 (119909) 119890

minus119909

1 + 119910 (119909) 119890119909 (12)



119909 =

(119904119892minus 119904119897)

2119877 (13a)

119903120590= ℎ119892minus ℎ119897= 2119877119879

119887119909 (119879119887) (13b)



sh119909 = 119890119909minus 119890minus119909

2 ch119909 = 119890

119909+ 119890minus119909

2

(14)


1198870=

[119909 (119879119887) minus 1]

120588119897(119879119887) [119909 (119879

119887) minus 12]

(15)


120588119892= 1198870lfloor1 + 119910(119909)119890

119909rfloorminus1

(16a)

120588119897= 1198870lfloor1 + 119910(119909)119890


(16b)


120588plusmn=

1

21198870


0120588)

1 minus 1198850(1 minus 119887

0120588)] (17)

where 120588 = 120588(119879 1198750) 1198850

= 1198750120588119877119879 and the 120588

+(119879)-


119909 (119879) =1 minus 1198870120588+2

1 minus 1198870120588+ (18)


120590(119879) 120588

119892(119879) 120588





1198860(119879) =

119877119879

120588119897(1 minus 119887

0120588119897) (19)



C2H4 H2O1198870= 004181 119887

0= 001658

119879 119886 119879 119886

10399 155712 27316 517162105 145976 27815 527171110 112730 28315 534941115 935490 28815 540955120 812151 29315 545767125 725634 29815 548270130 661817 30315 549648135 613602 30815 549424140 575528 31315 548755145 545191 31815 547172150 520785 32315 544760155 500788 32815 541609160 484652 33315 537810165 471466 33815 53345516935 462006 34315 529044

34815 52460535315 51978935815 51467636315 50967436815 50448037315 499159



0-value for




119886 (119879) = 1198860(119879) minus

119875120590(119879 120588119892)

1205882

119897

(20)



120590(119879 120588119892)



2H4) and polar (H






119879 119886 119879 119886 119879 119886

285 843352 28815 117248 290 94700290 821424 29515 122245 300 89009295 801504 30425 122790 310 84350300 783344 31365 117289 320 80475305 766734 32435 113084 330 77208310 751497 33515 106723 340 74422315 737483 34465 100511 350 72026320 724564 35015 970950325 712631330 701589335 691355340 681859345 673037350 664836


2N]



119887FT-model









0


0= 119872120588

0asymp 162 V

119897= 119872120588

119897asymp



value 1198870= 178 cm3mol (119887

0asymp 11V

0) has been used in


4] on the ad hoc


6] and 119887

0= 2711 cm3mol


0asymp




2N]) = 5992 A


119886([BF4]) = 451 A 120590

119886([PF6])


25

75

125

100 140 180 220 260 300 340

Ps(kPa)

minus25

minus75

minus125

C2H4 H2O

Ps[25]Ps[23]

Pgs

Pgs

Pminusl Pminusl

T (K)

(a)

0

05

1

15

280 295 310 325 340

Ps(kPa)

T (K)

[pmmim][Tf2N]

[bmim][PF6]

minus05

minus1

minus15

Pgs

Pminusl

Pgs

Pminusl

(b)


119904(minus119875119892

119904≃ 119875minus


119904(119879)-data for ethy-


119904(minus119875119892

119904≃ 119875minus


6] and [pmmim][Tf

2N]


120590 =120590119888+ 120590119886

2 (21a)

1198870=119887119888+ 119887119886

2 (21b)






119888[pmmim] = 139 gmol



119879 (K) 120588119897(moldm3) 120588

119892(moldm3) 119875

120590(kPa) 119903




IL 119872 (gmol) 120590 (A) 119872119888119872119886

120590119888120590119886










1205853=119886 (119879)

119896119861119879minus120576 (119879)

120588119896119861119879=

1198870

1 minus 1198870120588 (22)






= 1658 cm3mol


100

300

500

700

900

1100

1300

0 1 2 3 4 5 6

T(K

)

120588 (moldm3)






119897(119875119900 119879)-data [1 2] are


0

20

40

60

80

200 400 600 800 1000 1200 1400

r 120590(kJm

ol)

T (K)








119888or 119903lowast119888= 119903119888120590) of






0

1

2

3

4

5

200 400 600 800 1000 1200 1400T (K)

P(M

Pa)



119888 119879119887) points are



119875 120573119879)






119888 119879119888)-parameters



119897(119879)- and vapor 120588




119873119897119892=

119886119897119892(119879) 120588119897119892

119877119879 (1 minus 119885119897) (23)





0

5

10

15

20

25

30

250 450 650 850 1050

Nl

T (K)



4] at 119879 le 119879



119885119897≪ 119885119892asymp 1

119873119897asymp

1

1 minus 1198870120588119897

(24a)

119873119892asymp

1198870120588119892

1 minus 1198870120588119892

(24b)


119873119888

119897=

3119885119888

1 minus 119885119888

(25a)

119873119888

119892=

119885119888

1 minus 119885119888

[

119860119888(1 minus 119887

0

119888120588119888)

1 minus 119887119888120588119888

minus 1] (25b)










2O and [C

4mim][BF

4]














119888= 1198870







119879for many


1 minus120588 (1198750 119879)

120588 (119875 119879)= 119862 (119879) ln [ 119861 (119879) + 119875

119861 (119879) + 1198750

] (26)


0asymp 0 [14] Such


6] C = 009358 for [bmim][BF

4] and C =




4] At


6]




0 119879) and 119862

119901(1198750 119879) with





120588 (1198750 119879)

= 1205880(1 minus

119879

1198790

)

= 139465 (1 minus 119879


(27)

119862119901(1198750 119879)

= 1198620

119901(1 +

119879

1198790

)


(28)







0


119901(0 K) =



119879and 120572



4] and [bmim][PF

6] Matkowska and


119879- and 120572







119875 119862V at high




119873119897

)120588] (29)



119875 = minus1198861205882minus119896119861119879

V0

ln (1 minus 120588V0) (30)


119897


119873119897=

119875lowast119872

120588lowast119877119879lowast=

119872




119897= 1)

120588lowast=1

V0

119875lowast=119911120576

2V0

119879lowast=

119911120576

2119896119861

(32)





119875

120588119896119861119879= 1 + 119892 (119889) 119887119873

2

119897120588 minus [119892 (119889) minus 1] (119873


1198861198732

119897120588

119896119861119879

(33)





Φ119886(119879)- andΦ



119886 (119879) = (2120587

3) 1205903120576Φ119886(119879

119904) (34a)

119887 (119879) = (2120587

3) 1205903Φ119887(119879

119904) (34b)


119861


119875 = minus1205882Φ119886(119879

119904)


119904)1205882+ (1 minus

1

119873119897

)119892 (119889) 120588rfloor

(35)


120588 =21205871205903

3119873119897120588 =

120588

120588lowast 119879 =

119896119861119879

120576=119879

119879lowast

119875 =119875

119896119861119879lowast120588lowast119873119897

=119875

119875lowast

(36)



120590(119879) are reasonable [15]









1160

1180

1200

1220

1240

1260

1280

0 50 100 150 200 250


290K290K

290K

350K350K

350K

P (MPa)



152

253

354

455

556

657

0 50 100 150 200 250

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K

120572P(times10

4Kminus

1)




119875 120574120588due to sys-






0

1

2

3

4

5

0 50 100 150 200 250

120573T

(times10

7kP

aminus1)

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K



1

15

2

25

3

35

0 50 100 150 200 250P (MPa)

(a)

(c)

290K

350K350K340K330K320K

310K

300K

290K

120574120588(M

PamiddotK

minus1)








120

125

130

135

140

145

150

0 50 100 150 200 250

C(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K

310K

300K

290K










119875 120573119879 120574120588) and caloric (119862

119875 119862V)





119901 119862V 119862119901119862VGr)


119862119901= 119862V +

119879120572119875120574120588

120588 (37)

119882 = radic

119862119901

119872(119862119901120573119879120588 minus 119879120572

2

119875)

(38)

Gr = 1198721198822120572119875

119862119901

=1

119879120572119875

(

119862119901

119862Vminus 1) (39)


140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K




105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)






6] and [bmim][BF

4] (Figure 13)



119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)





1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)





(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)






equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)




119901(119875)-dependence)















119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






119887 1198750) 120588119892(119879119887) =


120588119892

120588119897

=1 + 119910 (119909) 119890

minus119909

1 + 119910 (119909) 119890119909 (12)



119909 =

(119904119892minus 119904119897)

2119877 (13a)

119903120590= ℎ119892minus ℎ119897= 2119877119879

119887119909 (119879119887) (13b)



sh119909 = 119890119909minus 119890minus119909

2 ch119909 = 119890

119909+ 119890minus119909

2

(14)


1198870=

[119909 (119879119887) minus 1]

120588119897(119879119887) [119909 (119879

119887) minus 12]

(15)


120588119892= 1198870lfloor1 + 119910(119909)119890

119909rfloorminus1

(16a)

120588119897= 1198870lfloor1 + 119910(119909)119890


(16b)


120588plusmn=

1

21198870


0120588)

1 minus 1198850(1 minus 119887

0120588)] (17)

where 120588 = 120588(119879 1198750) 1198850

= 1198750120588119877119879 and the 120588

+(119879)-


119909 (119879) =1 minus 1198870120588+2

1 minus 1198870120588+ (18)


120590(119879) 120588

119892(119879) 120588





1198860(119879) =

119877119879

120588119897(1 minus 119887

0120588119897) (19)



C2H4 H2O1198870= 004181 119887

0= 001658

119879 119886 119879 119886

10399 155712 27316 517162105 145976 27815 527171110 112730 28315 534941115 935490 28815 540955120 812151 29315 545767125 725634 29815 548270130 661817 30315 549648135 613602 30815 549424140 575528 31315 548755145 545191 31815 547172150 520785 32315 544760155 500788 32815 541609160 484652 33315 537810165 471466 33815 53345516935 462006 34315 529044

34815 52460535315 51978935815 51467636315 50967436815 50448037315 499159



0-value for




119886 (119879) = 1198860(119879) minus

119875120590(119879 120588119892)

1205882

119897

(20)



120590(119879 120588119892)



2H4) and polar (H






119879 119886 119879 119886 119879 119886

285 843352 28815 117248 290 94700290 821424 29515 122245 300 89009295 801504 30425 122790 310 84350300 783344 31365 117289 320 80475305 766734 32435 113084 330 77208310 751497 33515 106723 340 74422315 737483 34465 100511 350 72026320 724564 35015 970950325 712631330 701589335 691355340 681859345 673037350 664836


2N]



119887FT-model









0


0= 119872120588

0asymp 162 V

119897= 119872120588

119897asymp



value 1198870= 178 cm3mol (119887

0asymp 11V

0) has been used in


4] on the ad hoc


6] and 119887

0= 2711 cm3mol


0asymp




2N]) = 5992 A


119886([BF4]) = 451 A 120590

119886([PF6])


25

75

125

100 140 180 220 260 300 340

Ps(kPa)

minus25

minus75

minus125

C2H4 H2O

Ps[25]Ps[23]

Pgs

Pgs

Pminusl Pminusl

T (K)

(a)

0

05

1

15

280 295 310 325 340

Ps(kPa)

T (K)

[pmmim][Tf2N]

[bmim][PF6]

minus05

minus1

minus15

Pgs

Pminusl

Pgs

Pminusl

(b)


119904(minus119875119892

119904≃ 119875minus


119904(119879)-data for ethy-


119904(minus119875119892

119904≃ 119875minus


6] and [pmmim][Tf

2N]


120590 =120590119888+ 120590119886

2 (21a)

1198870=119887119888+ 119887119886

2 (21b)






119888[pmmim] = 139 gmol



119879 (K) 120588119897(moldm3) 120588

119892(moldm3) 119875

120590(kPa) 119903




IL 119872 (gmol) 120590 (A) 119872119888119872119886

120590119888120590119886










1205853=119886 (119879)

119896119861119879minus120576 (119879)

120588119896119861119879=

1198870

1 minus 1198870120588 (22)






= 1658 cm3mol


100

300

500

700

900

1100

1300

0 1 2 3 4 5 6

T(K

)

120588 (moldm3)






119897(119875119900 119879)-data [1 2] are


0

20

40

60

80

200 400 600 800 1000 1200 1400

r 120590(kJm

ol)

T (K)








119888or 119903lowast119888= 119903119888120590) of






0

1

2

3

4

5

200 400 600 800 1000 1200 1400T (K)

P(M

Pa)



119888 119879119887) points are



119875 120573119879)






119888 119879119888)-parameters



119897(119879)- and vapor 120588




119873119897119892=

119886119897119892(119879) 120588119897119892

119877119879 (1 minus 119885119897) (23)





0

5

10

15

20

25

30

250 450 650 850 1050

Nl

T (K)



4] at 119879 le 119879



119885119897≪ 119885119892asymp 1

119873119897asymp

1

1 minus 1198870120588119897

(24a)

119873119892asymp

1198870120588119892

1 minus 1198870120588119892

(24b)


119873119888

119897=

3119885119888

1 minus 119885119888

(25a)

119873119888

119892=

119885119888

1 minus 119885119888

[

119860119888(1 minus 119887

0

119888120588119888)

1 minus 119887119888120588119888

minus 1] (25b)










2O and [C

4mim][BF

4]














119888= 1198870







119879for many


1 minus120588 (1198750 119879)

120588 (119875 119879)= 119862 (119879) ln [ 119861 (119879) + 119875

119861 (119879) + 1198750

] (26)


0asymp 0 [14] Such


6] C = 009358 for [bmim][BF

4] and C =




4] At


6]




0 119879) and 119862

119901(1198750 119879) with





120588 (1198750 119879)

= 1205880(1 minus

119879

1198790

)

= 139465 (1 minus 119879


(27)

119862119901(1198750 119879)

= 1198620

119901(1 +

119879

1198790

)


(28)







0


119901(0 K) =



119879and 120572



4] and [bmim][PF

6] Matkowska and


119879- and 120572







119875 119862V at high




119873119897

)120588] (29)



119875 = minus1198861205882minus119896119861119879

V0

ln (1 minus 120588V0) (30)


119897


119873119897=

119875lowast119872

120588lowast119877119879lowast=

119872




119897= 1)

120588lowast=1

V0

119875lowast=119911120576

2V0

119879lowast=

119911120576

2119896119861

(32)





119875

120588119896119861119879= 1 + 119892 (119889) 119887119873

2

119897120588 minus [119892 (119889) minus 1] (119873


1198861198732

119897120588

119896119861119879

(33)





Φ119886(119879)- andΦ



119886 (119879) = (2120587

3) 1205903120576Φ119886(119879

119904) (34a)

119887 (119879) = (2120587

3) 1205903Φ119887(119879

119904) (34b)


119861


119875 = minus1205882Φ119886(119879

119904)


119904)1205882+ (1 minus

1

119873119897

)119892 (119889) 120588rfloor

(35)


120588 =21205871205903

3119873119897120588 =

120588

120588lowast 119879 =

119896119861119879

120576=119879

119879lowast

119875 =119875

119896119861119879lowast120588lowast119873119897

=119875

119875lowast

(36)



120590(119879) are reasonable [15]









1160

1180

1200

1220

1240

1260

1280

0 50 100 150 200 250


290K290K

290K

350K350K

350K

P (MPa)



152

253

354

455

556

657

0 50 100 150 200 250

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K

120572P(times10

4Kminus

1)




119875 120574120588due to sys-






0

1

2

3

4

5

0 50 100 150 200 250

120573T

(times10

7kP

aminus1)

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K



1

15

2

25

3

35

0 50 100 150 200 250P (MPa)

(a)

(c)

290K

350K350K340K330K320K

310K

300K

290K

120574120588(M

PamiddotK

minus1)








120

125

130

135

140

145

150

0 50 100 150 200 250

C(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K

310K

300K

290K










119875 120573119879 120574120588) and caloric (119862

119875 119862V)





119901 119862V 119862119901119862VGr)


119862119901= 119862V +

119879120572119875120574120588

120588 (37)

119882 = radic

119862119901

119872(119862119901120573119879120588 minus 119879120572

2

119875)

(38)

Gr = 1198721198822120572119875

119862119901

=1

119879120572119875

(

119862119901

119862Vminus 1) (39)


140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K




105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)






6] and [bmim][BF

4] (Figure 13)



119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)





1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)





(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)






equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)




119901(119875)-dependence)















119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics







119879 119886 119879 119886 119879 119886

285 843352 28815 117248 290 94700290 821424 29515 122245 300 89009295 801504 30425 122790 310 84350300 783344 31365 117289 320 80475305 766734 32435 113084 330 77208310 751497 33515 106723 340 74422315 737483 34465 100511 350 72026320 724564 35015 970950325 712631330 701589335 691355340 681859345 673037350 664836


2N]



119887FT-model









0


0= 119872120588

0asymp 162 V

119897= 119872120588

119897asymp



value 1198870= 178 cm3mol (119887

0asymp 11V

0) has been used in


4] on the ad hoc


6] and 119887

0= 2711 cm3mol


0asymp




2N]) = 5992 A


119886([BF4]) = 451 A 120590

119886([PF6])


25

75

125

100 140 180 220 260 300 340

Ps(kPa)

minus25

minus75

minus125

C2H4 H2O

Ps[25]Ps[23]

Pgs

Pgs

Pminusl Pminusl

T (K)

(a)

0

05

1

15

280 295 310 325 340

Ps(kPa)

T (K)

[pmmim][Tf2N]

[bmim][PF6]

minus05

minus1

minus15

Pgs

Pminusl

Pgs

Pminusl

(b)


119904(minus119875119892

119904≃ 119875minus


119904(119879)-data for ethy-


119904(minus119875119892

119904≃ 119875minus


6] and [pmmim][Tf

2N]


120590 =120590119888+ 120590119886

2 (21a)

1198870=119887119888+ 119887119886

2 (21b)






119888[pmmim] = 139 gmol



119879 (K) 120588119897(moldm3) 120588

119892(moldm3) 119875

120590(kPa) 119903




IL 119872 (gmol) 120590 (A) 119872119888119872119886

120590119888120590119886










1205853=119886 (119879)

119896119861119879minus120576 (119879)

120588119896119861119879=

1198870

1 minus 1198870120588 (22)






= 1658 cm3mol


100

300

500

700

900

1100

1300

0 1 2 3 4 5 6

T(K

)

120588 (moldm3)






119897(119875119900 119879)-data [1 2] are


0

20

40

60

80

200 400 600 800 1000 1200 1400

r 120590(kJm

ol)

T (K)








119888or 119903lowast119888= 119903119888120590) of






0

1

2

3

4

5

200 400 600 800 1000 1200 1400T (K)

P(M

Pa)



119888 119879119887) points are



119875 120573119879)






119888 119879119888)-parameters



119897(119879)- and vapor 120588




119873119897119892=

119886119897119892(119879) 120588119897119892

119877119879 (1 minus 119885119897) (23)





0

5

10

15

20

25

30

250 450 650 850 1050

Nl

T (K)



4] at 119879 le 119879



119885119897≪ 119885119892asymp 1

119873119897asymp

1

1 minus 1198870120588119897

(24a)

119873119892asymp

1198870120588119892

1 minus 1198870120588119892

(24b)


119873119888

119897=

3119885119888

1 minus 119885119888

(25a)

119873119888

119892=

119885119888

1 minus 119885119888

[

119860119888(1 minus 119887

0

119888120588119888)

1 minus 119887119888120588119888

minus 1] (25b)










2O and [C

4mim][BF

4]














119888= 1198870







119879for many


1 minus120588 (1198750 119879)

120588 (119875 119879)= 119862 (119879) ln [ 119861 (119879) + 119875

119861 (119879) + 1198750

] (26)


0asymp 0 [14] Such


6] C = 009358 for [bmim][BF

4] and C =




4] At


6]




0 119879) and 119862

119901(1198750 119879) with





120588 (1198750 119879)

= 1205880(1 minus

119879

1198790

)

= 139465 (1 minus 119879


(27)

119862119901(1198750 119879)

= 1198620

119901(1 +

119879

1198790

)


(28)







0


119901(0 K) =



119879and 120572



4] and [bmim][PF

6] Matkowska and


119879- and 120572







119875 119862V at high




119873119897

)120588] (29)



119875 = minus1198861205882minus119896119861119879

V0

ln (1 minus 120588V0) (30)


119897


119873119897=

119875lowast119872

120588lowast119877119879lowast=

119872




119897= 1)

120588lowast=1

V0

119875lowast=119911120576

2V0

119879lowast=

119911120576

2119896119861

(32)





119875

120588119896119861119879= 1 + 119892 (119889) 119887119873

2

119897120588 minus [119892 (119889) minus 1] (119873


1198861198732

119897120588

119896119861119879

(33)





Φ119886(119879)- andΦ



119886 (119879) = (2120587

3) 1205903120576Φ119886(119879

119904) (34a)

119887 (119879) = (2120587

3) 1205903Φ119887(119879

119904) (34b)


119861


119875 = minus1205882Φ119886(119879

119904)


119904)1205882+ (1 minus

1

119873119897

)119892 (119889) 120588rfloor

(35)


120588 =21205871205903

3119873119897120588 =

120588

120588lowast 119879 =

119896119861119879

120576=119879

119879lowast

119875 =119875

119896119861119879lowast120588lowast119873119897

=119875

119875lowast

(36)



120590(119879) are reasonable [15]









1160

1180

1200

1220

1240

1260

1280

0 50 100 150 200 250


290K290K

290K

350K350K

350K

P (MPa)



152

253

354

455

556

657

0 50 100 150 200 250

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K

120572P(times10

4Kminus

1)




119875 120574120588due to sys-






0

1

2

3

4

5

0 50 100 150 200 250

120573T

(times10

7kP

aminus1)

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K



1

15

2

25

3

35

0 50 100 150 200 250P (MPa)

(a)

(c)

290K

350K350K340K330K320K

310K

300K

290K

120574120588(M

PamiddotK

minus1)








120

125

130

135

140

145

150

0 50 100 150 200 250

C(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K

310K

300K

290K










119875 120573119879 120574120588) and caloric (119862

119875 119862V)





119901 119862V 119862119901119862VGr)


119862119901= 119862V +

119879120572119875120574120588

120588 (37)

119882 = radic

119862119901

119872(119862119901120573119879120588 minus 119879120572

2

119875)

(38)

Gr = 1198721198822120572119875

119862119901

=1

119879120572119875

(

119862119901

119862Vminus 1) (39)


140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K




105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)






6] and [bmim][BF

4] (Figure 13)



119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)





1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)





(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)






equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)




119901(119875)-dependence)















119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





119879 (K) 120588119897(moldm3) 120588

119892(moldm3) 119875

120590(kPa) 119903




IL 119872 (gmol) 120590 (A) 119872119888119872119886

120590119888120590119886










1205853=119886 (119879)

119896119861119879minus120576 (119879)

120588119896119861119879=

1198870

1 minus 1198870120588 (22)






= 1658 cm3mol


100

300

500

700

900

1100

1300

0 1 2 3 4 5 6

T(K

)

120588 (moldm3)






119897(119875119900 119879)-data [1 2] are


0

20

40

60

80

200 400 600 800 1000 1200 1400

r 120590(kJm

ol)

T (K)








119888or 119903lowast119888= 119903119888120590) of






0

1

2

3

4

5

200 400 600 800 1000 1200 1400T (K)

P(M

Pa)



119888 119879119887) points are



119875 120573119879)






119888 119879119888)-parameters



119897(119879)- and vapor 120588




119873119897119892=

119886119897119892(119879) 120588119897119892

119877119879 (1 minus 119885119897) (23)





0

5

10

15

20

25

30

250 450 650 850 1050

Nl

T (K)



4] at 119879 le 119879



119885119897≪ 119885119892asymp 1

119873119897asymp

1

1 minus 1198870120588119897

(24a)

119873119892asymp

1198870120588119892

1 minus 1198870120588119892

(24b)


119873119888

119897=

3119885119888

1 minus 119885119888

(25a)

119873119888

119892=

119885119888

1 minus 119885119888

[

119860119888(1 minus 119887

0

119888120588119888)

1 minus 119887119888120588119888

minus 1] (25b)










2O and [C

4mim][BF

4]














119888= 1198870







119879for many


1 minus120588 (1198750 119879)

120588 (119875 119879)= 119862 (119879) ln [ 119861 (119879) + 119875

119861 (119879) + 1198750

] (26)


0asymp 0 [14] Such


6] C = 009358 for [bmim][BF

4] and C =




4] At


6]




0 119879) and 119862

119901(1198750 119879) with





120588 (1198750 119879)

= 1205880(1 minus

119879

1198790

)

= 139465 (1 minus 119879


(27)

119862119901(1198750 119879)

= 1198620

119901(1 +

119879

1198790

)


(28)







0


119901(0 K) =



119879and 120572



4] and [bmim][PF

6] Matkowska and


119879- and 120572







119875 119862V at high




119873119897

)120588] (29)



119875 = minus1198861205882minus119896119861119879

V0

ln (1 minus 120588V0) (30)


119897


119873119897=

119875lowast119872

120588lowast119877119879lowast=

119872




119897= 1)

120588lowast=1

V0

119875lowast=119911120576

2V0

119879lowast=

119911120576

2119896119861

(32)





119875

120588119896119861119879= 1 + 119892 (119889) 119887119873

2

119897120588 minus [119892 (119889) minus 1] (119873


1198861198732

119897120588

119896119861119879

(33)





Φ119886(119879)- andΦ



119886 (119879) = (2120587

3) 1205903120576Φ119886(119879

119904) (34a)

119887 (119879) = (2120587

3) 1205903Φ119887(119879

119904) (34b)


119861


119875 = minus1205882Φ119886(119879

119904)


119904)1205882+ (1 minus

1

119873119897

)119892 (119889) 120588rfloor

(35)


120588 =21205871205903

3119873119897120588 =

120588

120588lowast 119879 =

119896119861119879

120576=119879

119879lowast

119875 =119875

119896119861119879lowast120588lowast119873119897

=119875

119875lowast

(36)



120590(119879) are reasonable [15]









1160

1180

1200

1220

1240

1260

1280

0 50 100 150 200 250


290K290K

290K

350K350K

350K

P (MPa)



152

253

354

455

556

657

0 50 100 150 200 250

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K

120572P(times10

4Kminus

1)




119875 120574120588due to sys-






0

1

2

3

4

5

0 50 100 150 200 250

120573T

(times10

7kP

aminus1)

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K



1

15

2

25

3

35

0 50 100 150 200 250P (MPa)

(a)

(c)

290K

350K350K340K330K320K

310K

300K

290K

120574120588(M

PamiddotK

minus1)








120

125

130

135

140

145

150

0 50 100 150 200 250

C(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K

310K

300K

290K










119875 120573119879 120574120588) and caloric (119862

119875 119862V)





119901 119862V 119862119901119862VGr)


119862119901= 119862V +

119879120572119875120574120588

120588 (37)

119882 = radic

119862119901

119872(119862119901120573119879120588 minus 119879120572

2

119875)

(38)

Gr = 1198721198822120572119875

119862119901

=1

119879120572119875

(

119862119901

119862Vminus 1) (39)


140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K




105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)






6] and [bmim][BF

4] (Figure 13)



119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)





1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)





(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)






equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)




119901(119875)-dependence)















119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




100

300

500

700

900

1100

1300

0 1 2 3 4 5 6

T(K

)

120588 (moldm3)






119897(119875119900 119879)-data [1 2] are


0

20

40

60

80

200 400 600 800 1000 1200 1400

r 120590(kJm

ol)

T (K)








119888or 119903lowast119888= 119903119888120590) of






0

1

2

3

4

5

200 400 600 800 1000 1200 1400T (K)

P(M

Pa)



119888 119879119887) points are



119875 120573119879)






119888 119879119888)-parameters



119897(119879)- and vapor 120588




119873119897119892=

119886119897119892(119879) 120588119897119892

119877119879 (1 minus 119885119897) (23)





0

5

10

15

20

25

30

250 450 650 850 1050

Nl

T (K)



4] at 119879 le 119879



119885119897≪ 119885119892asymp 1

119873119897asymp

1

1 minus 1198870120588119897

(24a)

119873119892asymp

1198870120588119892

1 minus 1198870120588119892

(24b)


119873119888

119897=

3119885119888

1 minus 119885119888

(25a)

119873119888

119892=

119885119888

1 minus 119885119888

[

119860119888(1 minus 119887

0

119888120588119888)

1 minus 119887119888120588119888

minus 1] (25b)










2O and [C

4mim][BF

4]














119888= 1198870







119879for many


1 minus120588 (1198750 119879)

120588 (119875 119879)= 119862 (119879) ln [ 119861 (119879) + 119875

119861 (119879) + 1198750

] (26)


0asymp 0 [14] Such


6] C = 009358 for [bmim][BF

4] and C =




4] At


6]




0 119879) and 119862

119901(1198750 119879) with





120588 (1198750 119879)

= 1205880(1 minus

119879

1198790

)

= 139465 (1 minus 119879


(27)

119862119901(1198750 119879)

= 1198620

119901(1 +

119879

1198790

)


(28)







0


119901(0 K) =



119879and 120572



4] and [bmim][PF

6] Matkowska and


119879- and 120572







119875 119862V at high




119873119897

)120588] (29)



119875 = minus1198861205882minus119896119861119879

V0

ln (1 minus 120588V0) (30)


119897


119873119897=

119875lowast119872

120588lowast119877119879lowast=

119872




119897= 1)

120588lowast=1

V0

119875lowast=119911120576

2V0

119879lowast=

119911120576

2119896119861

(32)





119875

120588119896119861119879= 1 + 119892 (119889) 119887119873

2

119897120588 minus [119892 (119889) minus 1] (119873


1198861198732

119897120588

119896119861119879

(33)





Φ119886(119879)- andΦ



119886 (119879) = (2120587

3) 1205903120576Φ119886(119879

119904) (34a)

119887 (119879) = (2120587

3) 1205903Φ119887(119879

119904) (34b)


119861


119875 = minus1205882Φ119886(119879

119904)


119904)1205882+ (1 minus

1

119873119897

)119892 (119889) 120588rfloor

(35)


120588 =21205871205903

3119873119897120588 =

120588

120588lowast 119879 =

119896119861119879

120576=119879

119879lowast

119875 =119875

119896119861119879lowast120588lowast119873119897

=119875

119875lowast

(36)



120590(119879) are reasonable [15]









1160

1180

1200

1220

1240

1260

1280

0 50 100 150 200 250


290K290K

290K

350K350K

350K

P (MPa)



152

253

354

455

556

657

0 50 100 150 200 250

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K

120572P(times10

4Kminus

1)




119875 120574120588due to sys-






0

1

2

3

4

5

0 50 100 150 200 250

120573T

(times10

7kP

aminus1)

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K



1

15

2

25

3

35

0 50 100 150 200 250P (MPa)

(a)

(c)

290K

350K350K340K330K320K

310K

300K

290K

120574120588(M

PamiddotK

minus1)








120

125

130

135

140

145

150

0 50 100 150 200 250

C(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K

310K

300K

290K










119875 120573119879 120574120588) and caloric (119862

119875 119862V)





119901 119862V 119862119901119862VGr)


119862119901= 119862V +

119879120572119875120574120588

120588 (37)

119882 = radic

119862119901

119872(119862119901120573119879120588 minus 119879120572

2

119875)

(38)

Gr = 1198721198822120572119875

119862119901

=1

119879120572119875

(

119862119901

119862Vminus 1) (39)


140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K




105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)






6] and [bmim][BF

4] (Figure 13)



119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)





1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)





(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)






equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)




119901(119875)-dependence)















119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0

5

10

15

20

25

30

250 450 650 850 1050

Nl

T (K)



4] at 119879 le 119879



119885119897≪ 119885119892asymp 1

119873119897asymp

1

1 minus 1198870120588119897

(24a)

119873119892asymp

1198870120588119892

1 minus 1198870120588119892

(24b)


119873119888

119897=

3119885119888

1 minus 119885119888

(25a)

119873119888

119892=

119885119888

1 minus 119885119888

[

119860119888(1 minus 119887

0

119888120588119888)

1 minus 119887119888120588119888

minus 1] (25b)










2O and [C

4mim][BF

4]














119888= 1198870







119879for many


1 minus120588 (1198750 119879)

120588 (119875 119879)= 119862 (119879) ln [ 119861 (119879) + 119875

119861 (119879) + 1198750

] (26)


0asymp 0 [14] Such


6] C = 009358 for [bmim][BF

4] and C =




4] At


6]




0 119879) and 119862

119901(1198750 119879) with





120588 (1198750 119879)

= 1205880(1 minus

119879

1198790

)

= 139465 (1 minus 119879


(27)

119862119901(1198750 119879)

= 1198620

119901(1 +

119879

1198790

)


(28)







0


119901(0 K) =



119879and 120572



4] and [bmim][PF

6] Matkowska and


119879- and 120572







119875 119862V at high




119873119897

)120588] (29)



119875 = minus1198861205882minus119896119861119879

V0

ln (1 minus 120588V0) (30)


119897


119873119897=

119875lowast119872

120588lowast119877119879lowast=

119872




119897= 1)

120588lowast=1

V0

119875lowast=119911120576

2V0

119879lowast=

119911120576

2119896119861

(32)





119875

120588119896119861119879= 1 + 119892 (119889) 119887119873

2

119897120588 minus [119892 (119889) minus 1] (119873


1198861198732

119897120588

119896119861119879

(33)





Φ119886(119879)- andΦ



119886 (119879) = (2120587

3) 1205903120576Φ119886(119879

119904) (34a)

119887 (119879) = (2120587

3) 1205903Φ119887(119879

119904) (34b)


119861


119875 = minus1205882Φ119886(119879

119904)


119904)1205882+ (1 minus

1

119873119897

)119892 (119889) 120588rfloor

(35)


120588 =21205871205903

3119873119897120588 =

120588

120588lowast 119879 =

119896119861119879

120576=119879

119879lowast

119875 =119875

119896119861119879lowast120588lowast119873119897

=119875

119875lowast

(36)



120590(119879) are reasonable [15]









1160

1180

1200

1220

1240

1260

1280

0 50 100 150 200 250


290K290K

290K

350K350K

350K

P (MPa)



152

253

354

455

556

657

0 50 100 150 200 250

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K

120572P(times10

4Kminus

1)




119875 120574120588due to sys-






0

1

2

3

4

5

0 50 100 150 200 250

120573T

(times10

7kP

aminus1)

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K



1

15

2

25

3

35

0 50 100 150 200 250P (MPa)

(a)

(c)

290K

350K350K340K330K320K

310K

300K

290K

120574120588(M

PamiddotK

minus1)








120

125

130

135

140

145

150

0 50 100 150 200 250

C(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K

310K

300K

290K










119875 120573119879 120574120588) and caloric (119862

119875 119862V)





119901 119862V 119862119901119862VGr)


119862119901= 119862V +

119879120572119875120574120588

120588 (37)

119882 = radic

119862119901

119872(119862119901120573119879120588 minus 119879120572

2

119875)

(38)

Gr = 1198721198822120572119875

119862119901

=1

119879120572119875

(

119862119901

119862Vminus 1) (39)


140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K




105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)






6] and [bmim][BF

4] (Figure 13)



119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)





1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)





(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)






equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)




119901(119875)-dependence)















119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






120588 (1198750 119879)

= 1205880(1 minus

119879

1198790

)

= 139465 (1 minus 119879


(27)

119862119901(1198750 119879)

= 1198620

119901(1 +

119879

1198790

)


(28)







0


119901(0 K) =



119879and 120572



4] and [bmim][PF

6] Matkowska and


119879- and 120572







119875 119862V at high




119873119897

)120588] (29)



119875 = minus1198861205882minus119896119861119879

V0

ln (1 minus 120588V0) (30)


119897


119873119897=

119875lowast119872

120588lowast119877119879lowast=

119872




119897= 1)

120588lowast=1

V0

119875lowast=119911120576

2V0

119879lowast=

119911120576

2119896119861

(32)





119875

120588119896119861119879= 1 + 119892 (119889) 119887119873

2

119897120588 minus [119892 (119889) minus 1] (119873


1198861198732

119897120588

119896119861119879

(33)





Φ119886(119879)- andΦ



119886 (119879) = (2120587

3) 1205903120576Φ119886(119879

119904) (34a)

119887 (119879) = (2120587

3) 1205903Φ119887(119879

119904) (34b)


119861


119875 = minus1205882Φ119886(119879

119904)


119904)1205882+ (1 minus

1

119873119897

)119892 (119889) 120588rfloor

(35)


120588 =21205871205903

3119873119897120588 =

120588

120588lowast 119879 =

119896119861119879

120576=119879

119879lowast

119875 =119875

119896119861119879lowast120588lowast119873119897

=119875

119875lowast

(36)



120590(119879) are reasonable [15]









1160

1180

1200

1220

1240

1260

1280

0 50 100 150 200 250


290K290K

290K

350K350K

350K

P (MPa)



152

253

354

455

556

657

0 50 100 150 200 250

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K

120572P(times10

4Kminus

1)




119875 120574120588due to sys-






0

1

2

3

4

5

0 50 100 150 200 250

120573T

(times10

7kP

aminus1)

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K



1

15

2

25

3

35

0 50 100 150 200 250P (MPa)

(a)

(c)

290K

350K350K340K330K320K

310K

300K

290K

120574120588(M

PamiddotK

minus1)








120

125

130

135

140

145

150

0 50 100 150 200 250

C(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K

310K

300K

290K










119875 120573119879 120574120588) and caloric (119862

119875 119862V)





119901 119862V 119862119901119862VGr)


119862119901= 119862V +

119879120572119875120574120588

120588 (37)

119882 = radic

119862119901

119872(119862119901120573119879120588 minus 119879120572

2

119875)

(38)

Gr = 1198721198822120572119875

119862119901

=1

119879120572119875

(

119862119901

119862Vminus 1) (39)


140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K




105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)






6] and [bmim][BF

4] (Figure 13)



119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)





1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)





(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)






equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)




119901(119875)-dependence)















119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




Φ119886(119879)- andΦ



119886 (119879) = (2120587

3) 1205903120576Φ119886(119879

119904) (34a)

119887 (119879) = (2120587

3) 1205903Φ119887(119879

119904) (34b)


119861


119875 = minus1205882Φ119886(119879

119904)


119904)1205882+ (1 minus

1

119873119897

)119892 (119889) 120588rfloor

(35)


120588 =21205871205903

3119873119897120588 =

120588

120588lowast 119879 =

119896119861119879

120576=119879

119879lowast

119875 =119875

119896119861119879lowast120588lowast119873119897

=119875

119875lowast

(36)



120590(119879) are reasonable [15]









1160

1180

1200

1220

1240

1260

1280

0 50 100 150 200 250


290K290K

290K

350K350K

350K

P (MPa)



152

253

354

455

556

657

0 50 100 150 200 250

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K

120572P(times10

4Kminus

1)




119875 120574120588due to sys-






0

1

2

3

4

5

0 50 100 150 200 250

120573T

(times10

7kP

aminus1)

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K



1

15

2

25

3

35

0 50 100 150 200 250P (MPa)

(a)

(c)

290K

350K350K340K330K320K

310K

300K

290K

120574120588(M

PamiddotK

minus1)








120

125

130

135

140

145

150

0 50 100 150 200 250

C(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K

310K

300K

290K










119875 120573119879 120574120588) and caloric (119862

119875 119862V)





119901 119862V 119862119901119862VGr)


119862119901= 119862V +

119879120572119875120574120588

120588 (37)

119882 = radic

119862119901

119872(119862119901120573119879120588 minus 119879120572

2

119875)

(38)

Gr = 1198721198822120572119875

119862119901

=1

119879120572119875

(

119862119901

119862Vminus 1) (39)


140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K




105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)






6] and [bmim][BF

4] (Figure 13)



119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)





1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)





(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)






equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)




119901(119875)-dependence)















119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0

1

2

3

4

5

0 50 100 150 200 250

120573T

(times10

7kP

aminus1)

(a)

(b)

(c)

P (MPa)

290K290K

290K

350K

350K

350K



1

15

2

25

3

35

0 50 100 150 200 250P (MPa)

(a)

(c)

290K

350K350K340K330K320K

310K

300K

290K

120574120588(M

PamiddotK

minus1)








120

125

130

135

140

145

150

0 50 100 150 200 250

C(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K

310K

300K

290K










119875 120573119879 120574120588) and caloric (119862

119875 119862V)





119901 119862V 119862119901119862VGr)


119862119901= 119862V +

119879120572119875120574120588

120588 (37)

119882 = radic

119862119901

119872(119862119901120573119879120588 minus 119879120572

2

119875)

(38)

Gr = 1198721198822120572119875

119862119901

=1

119879120572119875

(

119862119901

119862Vminus 1) (39)


140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K




105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)






6] and [bmim][BF

4] (Figure 13)



119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)





1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)





(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)






equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)




119901(119875)-dependence)















119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




140

145

150

155

160

165

170

0 50 100 150 200 250

Cp(JkgmiddotK)

32315K31815K31315K30815K30315K29815K

P (MPa)

350K340K330K320K310K300K290K




105107109111113115117119121123125

0 50 100 150 200 250

CpC

v 29815K

32315K

350K340K330K320K310K300K290K

P (MPa)






6] and [bmim][BF

4] (Figure 13)



119862V (119875 119879) = 119862V (1198750 119879) minus119889119886

119889119879[120588 (119875 119879) minus 120588 (119875

0 119879)] (40)





1300

1600

1900

2200

2500

2800

3100

3400

3700

4000

0 50 100 150 200 250

W(m

s)

28315K32315K

350K340K330K320K310K300K290K

P (MPa)





(120597119862V

120597V)

119879

= 119879(1205972119875

1205971198792)

V (41a)

(

120597119862119901

120597119875)

119879

= minus119879(1205972V1205971198792)

119875

(41b)






equality

(120597120572119875

120597119879)

119875

= minus1205722

119875+1

V(1205972V1205971198792)

119875

(42)

in which (1205972V1205971198792)




119901(119875)-dependence)















119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics







119897) (see text)


(cm3mol)1198870


(Jmol)120576


119873119897

[bmim][BF4] 1753 178 5642 2661 176 170[bmim][PF6] 1962 1953 5658 2661 188 181



119879 [14](K)

(120597119890120597V)119879

(MPa)119879 [16](K)

(120597119890120597V)119879

1015840

(MPa)119879 [FT](K)

(120597119890120597V)119879

(MPa)120576coh

(Jcm3)3131 48278 28315 45991 290 74376 555153326 47150 28815 45931 310 57316 486413526 46035 29315 45920 330 46391 437853727 45011 29815 45779 350 38861 401573928 44000 30315 45576 370 33384 373354129 42923 30815 45373 390 29227 350674326 41935 31315 45120 410 25966 331944523 40884 31815 44806 430 23340 316134722 39919 32315 44664 450 21177 30252

32815 44461 470 19364 2906033315 44309 490 17819 2800133815 44168 510 16676 2704634315 43975 517 16241 26731





4] (for [bmim][PF

6] this 119862

119901(119875)-



4]






5 Conclusions





120576coh = 1205882(1198750 119879) 119886 (119879) + 120588

119897(119879) 119903120590(119879) (43)


0 119879) and





(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics







(120597119890

120597V)

119879

= 119879(120597119875

120597119879)

120588

minus 119875 = 119879120572119875

120573119879

minus 119875 (44)









References



2so soluble in






















4mim][BF





4]rdquo Journal of
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics














FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



Documents

Towards the Equation of State for Neutral (C H ), Polar (H ...downloads.hindawi.com/journals/jther/2014/496835.pdf · properly by this RPP-model. In contrast with the discrete LG-model,