2
Precise coexistence curves are reported for the liquid–liquid phase transition of binary solutions of the room temperature ionic liquid (RTIL) 1-methyl-3-hexylimidazolium tetrafluoroborate (C6mim+BF4−) in a series of alcohols (1-butanol, 1-pentanol, 2-butanol, and 2-pentanol).
Type: Object |
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3
The phase diagrams are determined by measuring the temperature dependence of the refractive index in the two phases of samples of critical composition.
Type: Method |
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Novelty: New |
ConceptID: Met1
4
The critical data of the systems are in the region predicted for the model fluid of equal-sized, charged, hard spheres in a dielectric continuum, the so-called restricted primitive model (RPM).
Type: Background |
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ConceptID: Bac1
5
Therefore, the phase transition can be classified as essentially driven by Coulomb interactions.
Type: Conclusion |
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ConceptID: Con1
6
The effective exponents βeff determined are close to the universal Ising value, where the deviations are found to be negative, when the volume fraction or the mass fraction are chosen as concentration variable.
Type: Conclusion |
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ConceptID: Con2
7
The negative values of the first Wegner correction indicate non-uniform crossover from Ising to mean-field criticality.
Type: Conclusion |
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ConceptID: Con3
8
The diameter of the coexistence curves shows the non-analytic temperature dependence typical for Ising systems.
Type: Result |
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ConceptID: Res1
Introduction
9
Recently we have reported a survey on the location of the liquid–liquid phase transition1 in binary solutions of room temperature ionic liquids (RTIL) in water and in a series of alcohols.
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10
The RTILs considered contain a 1-methyl-3-alkylimidazolium cation (Cnmim+, n = 4, 6, 8) and the PF6− or BF4− anion.
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ConceptID: Bac2
11
A first detailed investigation of critical properties of such systems concerned the viscosity in binary mixtures of the RTIL C6mim+BF4− with 1-pentanol.2
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ConceptID: Bac3
12
Ising criticality with crossover to regular behaviour was observed in accordance with viscosity measurements on other solutions of low melting salts.3–5
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13
In this work, we continue investigating critical properties of binary mixtures of RTILs with non-ionic fluids analysing coexistence curves of solutions in alcohols.
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14
While in ref. 1, separation temperatures were determined by visual inspection when cooling down homogenous mixtures, in this work, we investigate flame sealed samples of critical composition by a laser technique.
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ConceptID: Met1
15
We determine the refractive index of the coexisting phases and of the one-phase region as function of the temperature applying the minimum beam deflection method.
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ConceptID: Met1
Type: Method |
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ConceptID: Met1
17
Coexistence curves of solutions of RTILs are of technical interest in view of applications in chemical engineering as reaction media and in separation processes.14,15
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18
Reactions have been proposed that, taking advantage of phase transitions, enable elegant separation of products, catalyst and solvent by small changes of temperature or composition.16
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19
Clearly, the knowledge of coexistence curves is essential for designing such processes.
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ConceptID: Mot1
20
From a scientific point of view, RTILs are of interest for studies of the nature of the critical point in liquid–liquid phase transitions driven by Coulomb interactions.
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ConceptID: Mot2
21
We recall that Ising criticality, generally observed in fluid phase transitions,30 requires short-range r−n interactions with n > 4.97 (ref. 17,18) as driving potential.
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ConceptID: Bac6
22
Different critical behaviour is expected when long-range interactions17–20 drive the phase transition.
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23
Mean field criticality of the van der Waals (vdW) type was conjectured in the case of Coulomb forces.21
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Type: Background |
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ConceptID: Bac7
25
However, later experiments on this system, using samples that were tempered for some days before the measurement, did not confirm the observations of mean field criticality4,7 but reported Ising behaviour.
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ConceptID: Bac8
Type: Background |
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ConceptID: Bac9
27
With the exception of the work refs. 22 and 23 all experiments3–5,7,8 and most simulations30–33 indicate that phase transitions driven by Coulomb interactions also belong to the Ising universality class.
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28
Nevertheless, this matter is still under discussion.34,35
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29
The salts investigated have a rather low melting point if compared to typical inorganic salts.
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30
The critical temperatures Tc of the solutions are near room temperature.
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31
Thus, mK-accuracy can be achieved easily.
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32
For a review, see .refs. 36–38
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33
However, all experiments remain suspect, because of the limited chemical stability of the organic salts.
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34
The so-called Pitzer salt N2226+B2226− is a notoriously unstable compound.4,7
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ConceptID: Bac11
35
Consequently; rather different figures for Tc have been reported.
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ConceptID: Bac11
36
Instability of Tc during the measurements may also cause erroneous conclusions.7
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ConceptID: Bac12
37
The solutions of the picrates (NR4+Pic−) also cannot expected to be perfectly stable, because, after all, the picrates are explosives.
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38
The EAN–octanol solution decomposes already 20 K above the consolute temperature.27
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ConceptID: Bac12
39
Therefore, it is worthwhile to investigate the critical properties of solutions of RTILs, which now are commercially available in good quality, chemically stable, and therefore well suited for accurate measurements.
Type: Motivation |
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ConceptID: Mot3
40
Corresponding states analysis of the location of the consolute point enables to distinguish phase transition that are driven by Coulomb interactions from those determined by solvophobic interactions.39
Type: Background |
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ConceptID: Bac13
41
We have carried out such an analysis of the location of the consolute point based on a survey of more than 200 mixtures of RTILs.1
Type: Background |
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ConceptID: Bac2
42
The reduced variables are defined by the restricted primitive model (RPM), a model fluid of equal sized, charged, hard spheres in a dielectric continuum.
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ConceptID: Bac1
43
Phase transitions with reduced critical data near the RPM figures are termed Coulombic, because the phase transitions are expected to be driven by Coulomb forces.36,39
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ConceptID: Bac14
44
The energy scale defining the reduced temperature T* is set by the Coulomb energy of the charges q± at the contact separation σ in a continuum with the dielectric constant ε.
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ConceptID: Bac15
45
The reduced density is defined by the total number density of the ions ρ = (N+ + N−)/V and the volume σ3.
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ConceptID: Bac15
46
Monte Carlo simulations, which are accompanied by finite-size scaling techniques, yield the critical point of the RPM at Tc* = 0.049, ρc* = 0..0830–33
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ConceptID: Bac16
47
Binary solutions of organic salts in solvents of small ε, e.g. in higher alcohols have their consolute point in that region.
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ConceptID: Bac17
48
In water, where the phase transition is driven by hydrophobic interactions, which are short-range, the reduced critical data (Tc* = 0.6 and ρc* =0.1) become much larger, which is in the region typical for phase transitions driven by solvophobic interactions.1,24,36,39
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49
Similar values apply for phase transitions of non-ionic systems,24 where vdW forces set the energy scale.
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ConceptID: Bac19
50
The remarkable result in ref. 1 was a nearly linear relation between Tc* and ε of the solvents.
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ConceptID: Bac20
51
Including water and higher alcohols, this observation suggests a continuous change from Coulomb phase transitions to such driven by solvophobic interactions with ε as the determining parameter.
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ConceptID: Bac20
52
The nature of the critical point in ionic systems is a puzzling problem.
Type: Motivation |
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ConceptID: Mot4
53
To start with, the thermodynamic limit does not exist in systems with particles interacting by r−1 Coulomb forces.
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ConceptID: Bac21
54
The thermodynamic limit exists only for r−n potentials with n > .317
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Type: Background |
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ConceptID: Bac22
Type: Background |
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ConceptID: Bac22
57
Ising critical behaviour is also obtained for the general primitive model, where both, size and charges of the ions may be different.43,44
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ConceptID: Bac23
58
However, in ionic solutions other long-range interactions may influence the criticality.
Type: Hypothesis |
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ConceptID: Hyp1
59
Charge-induced dipole interactions and the so-called charge cavity interactions that vary as r−4 are present.45
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60
In 2.1 we will outline that in cases when long-range r−n interactions with 3 < n < 5 determine the phase transition the critical exponents will deviate from the Ising values.
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ConceptID: Mod1
61
However, Debye–Hückel charge ordering can be expected to shield all electrostatic interactions, so that all long-range interactions, e.g. the mentioned charge-induced dipole interactions may become effectively short range.40,41
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62
Therefore, the conservative expectation is: Ising criticality with crossover to vdW mean field behaviour at larger separation from the critical point.26,46,47
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63
The crossover is determined by the Ginzburg temperature.48
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64
Theory predicts a Ginzburg temperature for Coulomb phase transitions, which is large if compared to non-ionic systems and therefore implies a non-classical Ising region that is even larger than in non-ionic systems.49,50
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65
In variance to this prediction, experiments indicate a crossover to vdW mean field criticality in a smaller temperature region above the critical temperature than in normal non-ionic systems.26
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ConceptID: Bac27
66
Semi-empirical crossover theory allows describing the experiments,46–49 but a physical explanation is not available.
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ConceptID: Mot5
67
A hypothesis, which could explain the reported crossover at rather small separation from the critical point, is a scenario involving a tricritical point.
Type: Hypothesis |
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ConceptID: Hyp2
68
A tricritical point arises, when a line of second order transitions cuts the coexistence curve at the critical consolute point.17,51
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69
Even if this condition is not exactly met, the coupling of the two fluctuations is expected to change critical properties, e.g. the shape of the coexistence curve.52
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ConceptID: Bac28
70
In ionic fluids, order transitions between an insulating and a conducting state or between a uniform fluid and a charge ordered state53 might be thought of.
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71
Therefore, precise measurements of coexistence curves are required to judge the validity of those theoretical reasoning.
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ConceptID: Mot6
72
In this work, we present measurements of the coexistence curves of solutions of C6mim+BF4− in the alcohols 1-butanol, 1-pentanol, 2-butanol and 2-pentanol.
Type: Goal |
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ConceptID: Goa1
73
In samples of critical composition we determine the refractive index in the homogeneous phase above Tc and in the two phases below Tc using the minimum beam deflection method.6
Type: Method |
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ConceptID: Met1
74
The coexistence curves are calculated from the refractive index data and compared with the results obtained by determining the separation temperatures in a set of mixtures of given concentration1.
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ConceptID: Goa1
Theoretical background
Critical exponents for long-range potentials
75
The power n of r−n potentials may be written n = d + s, where d is the dimension of the system.
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ConceptID: Mod2
76
For s ≥ 2 − ηsr the potential is termed short range and phase transitions determined by such potential belong to the Ising universality class17,51.η is the so-called Fisher exponent, which corrects the classical Ornstein–Zernicke correlation function and assumes the value ηsr = 0.03 in (d = 3)-Ising systems.
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77
The common scenario for fluid phase transitions driven by short-range interactions is Ising criticality in the asymptotic region with crossover to vdW mean field behaviour at large separations from the critical point.48
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78
For s < 0 the thermodynamic limit does not exist.17
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79
Potentials with 0 < s < 2 − ηsr are termed long-range potentials.
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80
Theory predicts for potentials with 0 < s < d/2 the following set of critical exponents19,20ν = 1/s, η = 2 − s, γ = 1,which are termed mean field exponents.
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ConceptID: Mod3
81
The exponents ν and γ determine the temperature dependence of correlation length ξ and susceptibility χ, respectively.
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ConceptID: Mod3
82
The vdW mean field exponents, conventionally called mean field exponents, result from a mean field theory for fluids with particles interacting by a short-range potential.
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ConceptID: Mod3
83
The exponents given in eqn. (2) become identical with the vdW mean field exponents for s = 2.
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ConceptID: Mod3
84
Based on the hypothesis that thermodynamic functions are homogeneous functions, relations between the various critical exponents have been derived,17,51 which served as a guide in the development of renormalisation group theory of critical phenomena.
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85
For convenience, we give the four relations and apply them to calculate the other mean field exponents:γ = (2 − η)ν, γ = β(1 − δ), γ = 2 − α − 2β, dν = 2 − α.
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ConceptID: Mod4
86
The last relation of eqn. (3), termed the hyperscaling relation, applies only for d ≤ 4.
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ConceptID: Mod4
87
Therefore, d = 4 is termed critical dimension dc.
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ConceptID: Mod4
88
The critical exponent of the specific heat is denoted by α, the exponent δ relates the field to the order parameter at critical temperature.
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ConceptID: Mod4
89
In the context of the phase transitions of fluids, the exponent δ determines the divergence of the osmotic susceptibility χ, when, at critical temperature, the variable X of the composition approaches the critical value:χ ∼ |X − Xc|1−δ.
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ConceptID: Mod5
90
The osmotic susceptibility can be determined by measuring the scattering intensity.
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ConceptID: Bac32
91
The mean field exponents (eqns. (2)) satisfy the relation γ = (2 − η)ν.
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ConceptID: Mod6
92
The other two relations determining γ and the hyperscaling relation can be used to calculate the exponents α, β and δ yieldingα = 2 − d/s, β = (d − s)/2s, δ = (d + s)/(d − s).For s = d/2 the exponents α, β, γ, and δ agree with the vdW mean field coefficients 0, 1/2, 1, 3, respectively.
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ConceptID: Mod7
93
Only if d = 4 the exponents ν and η also agree with the vdW mean field values.
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ConceptID: Mod7
94
However, theoretical analysis requires that for long-range interactions the critical dimension dc depends also on the power of the potential according dc = 2s.17
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ConceptID: Mod8
95
Furthermore, the dimension d in the hyperscaling relation has to be replaced by the critical dimension.
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ConceptID: Mod8
96
With this setting, the coefficients α, β, γ and δ agree with the vdW mean field values whenever long-range interactions drive a phase transition, while ν, η assume the vdW mean field values only for s = 2.
Type: Model |
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ConceptID: Mod8
97
First simulations54,55 of fluids with long range potentials 0 < s < 2 yield β/ν = 0.8 for s = 1 and d = 3.
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98
This result is between the estimates β/ν = 1 resulting from eqns. (5) and β/ν = 1/2 obtained with dc = 2, while the Ising value is β/ν = 0.515.
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ConceptID: Bac33
The power laws and corrections to scaling
99
Phase transitions in fluids that are driven by short-range interactions belong to the Ising universality class.
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ConceptID: Mod9
100
However, the simple power laws involving the universal critical Ising exponents are valid only in the asymptotic region near the critical point.
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ConceptID: Mod9
101
In general a crossover theory48 should be applied to analyse the date in a wide temperature region.
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ConceptID: Bac34
102
In fluid mixtures the asymptotic power laws commonly hold in the region τ = |T − Tc|/Tc < 10−3.
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ConceptID: Mod10
103
In the region 10−3 < τ < 10−2 corrections to scaling56,57 by power series in τ may suffice.
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ConceptID: Bac35
104
Considering the coexistence curve, the difference ΔX of the composition in the two coexisting phases vanishes as the critical temperature Tc is approached according to the following scaling law termed Wegner expansion:|Xu − Xl| = Bτβ (1 + B1τΔ + B2τ2Δ + ⋯).
Type: Model |
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ConceptID: Mod11
105
Xu and Xl represent the compositions in the upper and in the lower phase, respectively.
Type: Model |
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ConceptID: Mod11
106
While the exponents β = 0.325 and Δ = 0.51 are universal for an Ising critical point, the amplitudes B of the coexistence curve and the amplitudes of the correction terms are specific to the system, but not independent.
Type: Model |
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ConceptID: Mod11
107
There are rather strict conditions on size and sign of the terms in the Wegner expansion.
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ConceptID: Mod11
108
However, regular terms, which are not part of the Wegner expansion, may also contribute to the fits of the experimental data.47,54,55
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ConceptID: Bac36
109
Therefore, we apply the expansion (6) just as a tool to fit the data and do not claim to get Wegner coefficients in its strict sense from the data analysis.
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Novelty: New |
ConceptID: Met2
110
The diameter Xm = (Xl + Xu)/2 is also a non-linear function of τ and may be represented56,57 by the seriesXm − Xc = Aτ + Cτ2β + Dτ1−α (1 + D1τΔ + …)involving the critical exponent α of the specific heat with α = 0.11.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod12
111
Note, that in a vdW mean field system with α = 0 and β = 1/2 the diameter becomes a linear function of τ, thus satisfying the rule of the rectilinear diameter.
Type: Model |
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ConceptID: Mod12
112
The temperature dependence of the diameter has been a matter of controversy for a long time.58
Type: Background |
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ConceptID: Bac37
113
The 2β term is commonly regarded as a spurious contribution, which occurs when a “wrong” concentration variable56,57 is chosen for the data analysis.
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ConceptID: Bac37
114
This qualification of the 2β term, however, has been questioned recently.59
Type: Background |
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ConceptID: Bac37
115
Furthermore; the deviation from rectilinear diameter is often small and not observable in many cases.
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ConceptID: Mod12
116
Therefore, it is difficult to determine uniquely the various coefficients in eqn. (7) in a numerical analysis of experimental data.
Type: Background |
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ConceptID: Bac38
The composition variable
117
On experimental grounds, many choices for the composition variable X may be used with equal validity e.g. the mole fraction x, the mass fraction w or the volume fraction φ.
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ConceptID: Bac39
118
There is no a priory reason to choose one variable over the other.
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ConceptID: Bac39
119
Japas and Levelt Sengers named some criteria for selecting the best variable:60 simple scaling laws should hold over the largest range, where β assumes the Ising value; the critical composition should be near 0.5 and the coexistence curve should be almost symmetrical.
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ConceptID: Bac39
120
The asymmetry should be determined by the (1 − α) anomaly only.
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ConceptID: Mod13
121
Therefore, in the data analysis various choices of the concentration variables may be considered.
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ConceptID: Bac39
122
If, e.g. the coexistence curve is determined by measuring the transition temperatures in a series of samples of given composition, the mole fraction x or the mass fraction w are known and appear to be the natural choices to represent the composition.
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ConceptID: Bac40
123
In general, any concentration variable X can be transformed into a certain desired new variable Y by a transformation61 of the formIf the mole fraction x is transformed into the mass fraction w, the parameter p becomes p = M2/M1, where M1 is the molar weight of the compound with mole fraction x.
Type: Model |
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ConceptID: Mod14
124
In general the parameter p may depend on temperature and composition as, e.g., in the transformation of the mole fraction x into the volume fraction φ, where p = V2/V1 is the ratio of the partial molar volumes.
Type: Model |
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ConceptID: Mod14
125
As an approximation to the volume fraction an ideal volume fraction φ0 may be defined, in which the excess volume is neglected and p = V20/V10 is given by the molar volumes of the pure components.
Type: Model |
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ConceptID: Mod14
126
The transformation eqn. (8) may also be applied to construct a symmetrical coexistence curve represented in terms of a new variable.
Type: Model |
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ConceptID: Mod14
127
The transformation of the mole fraction x into a variable, which fixes the critical composition to Y = 0.5 requires p = xc/(1 − xc).
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod14
128
The thermodynamic analysis of Anisimov et al62. appears to remove the arbitrariness of the composition variable.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac41
129
In the Landau theory the free energy density is expanded.
Type: Background |
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Novelty: None |
ConceptID: Bac42
130
In this thermodynamic potential, the variable is the density and the corresponding field is the chemical potential.
Type: Background |
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Novelty: None |
ConceptID: Bac42
131
Therefore, in mixtures the number density (concentration) of one of the components should be chosen as variable, which is ρ1 = φ1/V10.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod15
132
Because in the investigated temperature range the molar volume V10 is changing very little, the volume fraction is also an appropriate concentration variable.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod15
133
The density is not identical with the order parameter M.
Type: Model |
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Novelty: None |
ConceptID: Mod15
134
The order parameter M is a linear combination of density and entropy density, where the (1 − α) term in eqn. (7) represents the entropy density2Mu,l = ±Bτβ (1 + B1τΔ + …) − Aτ − Dτ1−α.Eqns.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod16
135
(6) and (7) result as difference or sum of the two branches given by eqn. (9).
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod16
136
The order parameter M is the variable in the crossover theory.47,48
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac43
137
The application of this rather involved approach is outside the scope of this work.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac44
Determination of the composition from refractive index data
138
If the phase diagrams are determined by measurements of the refractive index of the phases in the sample, the refractive index n or the Lorenz–Lorentz function (n2 − 1)/(n2 + 2) may directly be taken as measure for the composition.
Type: Model |
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ConceptID: Mod17
139
Otherwise, the Lorenz–Lorentz relation can be used to determine the concentration.
Type: Model |
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Novelty: None |
ConceptID: Mod17
140
The Lorenz–Lorentz relation connects the averaged polarizability 〈αi〉 and the number densities ρi = Ni/V of the components of a mixture to the refractive index, where Ni is the number of particles of the component labelled i.
Type: Model |
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Novelty: None |
ConceptID: Mod17
141
For a binary mixture we have
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod18
142
The averaged polarizabilities 〈α1〉 and 〈α2〉 are nearly independent of composition and temperature.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod18
143
With the total number density ρ = ∑iNi/V and ρi = xiρ the Lorenz–Lorentz relation may be reformulated in terms of the mole fractions xi or in terms of the volume fractions φi = ρiVi.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod19
144
For a binary mixture the Lorenz–Lorentz relation reads in terms of the mole fraction x of the component labelled 1The density may be written in terms of the partial molecular volumes vi = Vi/Ni asFor pure compounds eqn. (10) becomeswhere 〈α1〉0 and vi0 denote the average molecular polarizability and the volume per molecule in the pure components, respectively.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod20
145
In many applications, the Lorenz–Lorentz function eqn. (10) is identified with the ideal expression based on the parameters of the pure compounds:
Type: Model |
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ConceptID: Mod21
146
In our analysis, it turns out to be necessary to supplement the ideal expression by an excess term, which takes care of excess volume and excess contributions to the polarizabilties.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod22
147
With the Porter-Ansatz for the excess function and the assumption that the excess function assumes their maximum value at critical composition we getK = Kid[1 + 4Y (1 − Y)(Kc − Kcid)/Kcid],where Kc is the value of the Lorenz–Lorentz function at critical composition.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod22
148
The variable Y was defined in eqn. (8), where p = xc/(1 − xc).
Type: Model |
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Novelty: None |
ConceptID: Mod22
149
Eqn. (15) is used in the final data analysis.
Type: Model |
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Novelty: None |
ConceptID: Mod22
Experimental
Sample preparation
150
Samples of critical composition were prepared for solutions of the RTIL C6mim+BF4− in alcohols (1-butanol, 2-butanol, 1-pentanol and 2-pentanol).
Type: Experiment |
Advantage: None |
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ConceptID: Exp1
151
The alcohols with certified purity (1-pentanol (Fluka) > 99%, 1-butanol (Fluka) (HPLC), 2-butanol (Fluka) > 99.5%, and 2-pentanol (Sigma-Aldrich) > 99%) were used without further purification.
Type: Experiment |
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ConceptID: Exp1
152
The ionic liquid C6mim+BF4− was purchased from Solvent Innovation.
Type: Experiment |
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Novelty: None |
ConceptID: Exp1
153
Standard NMR-, MS- and chromatographic analysis did not show impurities.
Type: Background |
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Novelty: None |
ConceptID: Bac45
154
Traces of water were removed from the salt by keeping it for three days at 60 °C under oil-pump vacuum and storing it in a desiccator.
Type: Experiment |
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ConceptID: Exp2
155
Solutions were made up by weight with a precision of ±0.1 mg.
Type: Experiment |
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Novelty: None |
ConceptID: Exp3
156
The critical compositions for the systems have been determined before and are given in .ref. 1
Type: Background |
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Novelty: None |
ConceptID: Bac46
157
The samples were prepared in standard square 10 mm cells (Hellma, PY 221).
Type: Experiment |
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Novelty: None |
ConceptID: Exp4
158
The critical solutions were filled into the cells using a syringe and a septum in order to prevent condensation of moisture in the sample.
Type: Experiment |
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Novelty: None |
ConceptID: Exp4
159
The samples were flame sealed under vacuum after a pump and freeze procedure.
Type: Experiment |
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Novelty: None |
ConceptID: Exp4
160
The criticality of the samples was checked employing the equal-volume criterion.
Type: Experiment |
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Novelty: None |
ConceptID: Exp4
161
The cloud points were determined visually by repeated cooling the homogeneous solution in a thermostat (Schott) with glass windows filled with water.
Type: Experiment |
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Novelty: None |
ConceptID: Exp5
162
The temperature was determined with an accuracy of 0.01 °C using a Quartz thermometer (Hereus QUAT200).
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp6
Refractive index measurements
163
The refractive index was measured in the uniform phase above the critical temperature and in the two-phase region by means of the minimum beam deflection method.6
Type: Method |
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Novelty: Old |
ConceptID: Met3
164
The coexistence curves of the system were determined from the refractive indices of the upper and of the lower phase.
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp7
165
The optical arrangement and further details are described in .refs. 7–9
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met4
166
In order to prevent the formation of meta-stable states the temperature steps were increased when lowering the temperature in the two-phase region.
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp8
167
A waiting time of about 8 h was necessary to achieve a complete phase separation.
Type: Experiment |
Advantage: None |
Novelty: None |
ConceptID: Exp8
168
Equilibrium was assumed when the two phases were no longer opalescent, and the position of the laser beam on the screen did not change any more.
Type: Experiment |
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Novelty: None |
ConceptID: Exp8
169
By checking the critical temperatures before and after the refractive index measurements, we tested the stability of the critical temperatures.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met1
170
A shift of the critical temperatures of −8 × 10−8 K s−1 was observed during the measuring time and taken into account in the data evaluation.
Type: Observation |
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ConceptID: Obs1
171
As the critical temperature, we choose the average between the last measurement in the homogeneous phase and the first point in the two-phase region, which limits the accuracy of the critical temperature to 0.005 K. The data analysis was carried out using the Origin 6 and Mathematica 4 program packages.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met1
Experimental results and data evaluation
Phase diagrams with the Lorenz–Lorentz function as variable
172
The coexistence curves of the binary solutions of C6mim+BF4− in 1-butanol, 2-butanol, 1-pentanol, and 2-pentanol were obtained by refractive index measurements.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met1
173
In addition, the refractive index of the pure compounds was determined by the same method.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met1
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs2
175
The small differences of the refractive indices between salt and solvents limit the relative accuracy of the measurements.
Type: Method |
Advantage: No |
Novelty: New |
ConceptID: Met1
176
In fact, the refractive indices of the alcohols and of the salts are so similar that it is difficult to see the meniscus.
Type: Method |
Advantage: No |
Novelty: New |
ConceptID: Met1
177
The coexistence curves obtained from the refractive index measurements are shown in Fig. 1.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs3
178
The reduced temperature τ is plotted as function of K − Kc.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met5
179
We employ the Lorenz–Lorentz function K as variable instead of the often-used refractive index8,22 because it is more directly related to thermodynamic quantities than the refractive index.
Type: Method |
Advantage: Yes |
Novelty: New |
ConceptID: Met5
180
At first, we check the accuracy of the critical composition deduced from the equal volume criterion.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met5
181
It can be seen that the Lorenz–Lorentz function K in the homogeneous phase and the diameter Km, which is the mean of the K values in the coexisting phases, meet at the critical temperature.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs3
182
No offset is noticeable, which proves that our samples have the critical composition.
Type: Method |
Advantage: Yes |
Novelty: New |
ConceptID: Met1
183
The coexistence curves with K as composition variable are strongly skewed like the top of a banana.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs3
184
Due to the banana shape, two temperatures correspond to the same K value.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs3
185
In the upper phase (alcohol-rich phase with the lower refractive index), the variation of K with the temperature is very small.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs4
186
The variation of the refractive index in the salt-rich, lower phase is much larger.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs4
187
The coexistence curves of the solutions in 1- and 2-butanol are wider than those in 1- and 2-pentanol.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs5
188
Obviously, the more polar alcohol can mix with the salt better.
Type: Conclusion |
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Novelty: None |
ConceptID: Con4
189
There is little difference between the isomers; the width of the coexistence curves of the secondary alcohols is only slightly larger than that of the primary alcohols.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs6
190
In the one-phase region, the Lorenz–Lorentz function is reduced linearly with increasing temperature.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs7
191
This can be expected from the linear decrease of the density with temperature raise.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac47
192
No indication of a non-analytic critical contribution63 can be seen.
Type: Result |
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Novelty: None |
ConceptID: Res2
193
In contrast, the diameter shows a marked nonlinear temperature dependence: the rectilinear diameter rule clearly does not apply.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res2
194
Estimates of the critical composition based on the rectilinear diameter rule are necessarily far off.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac48
195
The slope of the diameter has the same sign as the slope in the one-phase region.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs8
196
The temperature dependence of the diameter is slightly stronger than the temperature dependence of K in the homogeneous phase.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res3
197
Both, the temperature variation of K in the one phase region and of Km are almost the same for different mixtures.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res3
198
The curves, which concern the mixture with 1-butanol, are the best fits using eqns. (6) and (7), which will be dicussed in what follows.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res4
199
In Table 1, we give parameters obtained from fitting different functions to the experimental data of the coexistence curve.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs9
200
As a routine we apply first a simple power law, where the exponent βeff is a free parameter, and then use the Wegner-type expansions for the fit with up to two coefficients.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6
201
In the expansion the exponents β and Δ are fixed, while the amplitudes B, B1, and B2 are the fitting parameters.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6
202
The effective exponents βeff are found to be smaller than the Ising value, which may be taken as indication of non-monotonous crossover to mean field criticality.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res5
203
Accordingly, the first correction term in the Wegner-type expansion comes out negative.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs10
204
However, conclusions based on the size of the coefficients are difficult, because their values change, when the second correction is included into the fit.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs11
205
The statistical error estimated for the parameters becomes then unduly large, which shows that the parameters are not independent.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res6
206
Hence, the expansion with two correction terms is not appropriate, therefore not included in Table 1.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac49
207
Comparing the deviations from the asymptotic Ising behaviour for the different alcohols no obvious systematic can be seen.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs12
208
The diameters Km of the coexistence curves are analysed by fitting different approximants of eqn. (7) to the data, where the amplitudes A, C, D and Kc are the fitting parameters, while the exponents are fixed to their universal values.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6
209
At first, we employ one-term expansions with Kc and one of the amplitudes A, C, or D as fit-parameters.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6
210
In a next step, a two-term expansion is used containing the linear term A and either the 1 − α term D or the 2β terms C.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6
211
The relevant results of the fits are given in Table 2.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs13
212
The fits, which consider only the 1 − α term, are already rather good.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res7
213
Including the linear term improves the fit although the statistical uncertainty becomes too large.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res7
214
The value of the corresponding parameter D changes only little when the linear term is included in the fit.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res7
215
The fits which include the linear and the 2β term are not as good as those, which include the linear and the 1 − α term and in most cases even worse than those that involve the 1 − α term only.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res7
216
In Fig. 2a we show the log–log plots of ΔK = Kl − Kuvs. the reduced temperature τ for the four systems.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs14
217
The sets of data points are shifted by an offset for visual clarity.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6
218
The points appear to follow straight lines.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs15
219
Deviations for τ < 10−4 are due to the rather small difference of the refractive index between the phases and due to the limited accuracy of the critical temperature, which was only ±0.005 K. Above τ = 10−4 no change of the direction can be seen although the measurements cover a temperature range up to 10 K from the critical point.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res8
220
The lines in Figs. 2a and 1 represent the best fits obtained with eqn. (6) with one Wegner correction.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs16
221
Fig. 2b shows the diameters of all investigated samples as function of the reduced temperature τ in a logarithmic scale.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs17
222
Again, the curves are shifted by arbitrary factors for a better view.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6
223
The curves in Figs. 1 and 2b are the fits with Kc, A and D as fitting parameter.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met6
Phase diagrams with thermodynamic concentration variables
224
The banana shape of the coexistence curves obtained shown in Fig. 1 indicates that K is not a good choice of a variable.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res9
225
Furthermore, in the homogeneous phase the refractive index varies with temperature, although the relative composition of the components is unchanged.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res9
226
Therefore, composition variables, which are constant in the homogeneous phase, like the mole fraction x or the mass fraction w appear more appropriate.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res9
227
From the theoretical point of view, the volume fraction φ is the best choice of a concentration variable.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res9
228
Dividing by the molar volume, which is almost independent of temperature in the critical region, it can easily be transformed into the density required in the advanced theoretical analysis.47,48
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac50
229
In order to investigate the influence of the choice of the variables on the parameters in eqns. (6) and (7), we transform the refractive index data into the concentration variables x, w, and φ.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met7
230
The data are reanalysed in terms of those variables.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met7
231
For estimating the mole fraction of a mixture from refractive index data it is necessary to know the refractive indices and the densities of the pure components.
Type: Motivation |
Advantage: None |
Novelty: None |
ConceptID: Mot7
232
The refractive indices of the pure components were also determined by the minimum deflection method.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met7
233
Density data of the alcohols are collected from standard sources.64
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac51
234
The densities of the salt have been measured using a pycnometer.2
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac51
235
The resulting molar volume of the salt is Vs = (224.76 + 0.13324 ΔT) cm3 mol−1 agrees rather well with Vs = (227.116 + 0.1575ΔT) cm3 mol−1 (ΔT = T − 318.15 K) obtained by linear interpolation of the volumes of the salts C4mim+PF6−, C8mim+PF6− and C8mim+BF4−,65 which was assumed in the analysis in .ref. 1
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res10
236
The data of the pure compounds required for the transformations are summarized in Table 3.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs18
237
In the table, we give the refractive index n298, the polarizability α298, the mass densities ρm298, and the linear temperature coefficients n1, α1 and ρ1 of the pure compounds.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs18
238
In order to check the accuracy of the transformation, we calculate the value of K at the critical point assuming ideal mixing properties and vice versa recalculate the mole fraction of the critical sample from the refractive index data.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met7
239
As can be seen in Table 4, the relative accuracy of the estimate of K is 0.001, while relative accuracy of the mole fraction is only 0.1.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs19
240
Both figures are not sufficient for our purpose.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac52
241
In order to achieve the required accuracy it is necessary to take into account the excess of the mole refraction.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met7
242
Therefore we apply the correction for non-ideal contributions as given in eqn. (15), which ensures consistent figures for Kc and xc within the accuracy of the measurements.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met7
243
The excess of the Lorenz–Lorentz function is positive, while pycnometric measurements2 point towards a positive excess volume, which would account for a negative excess of the Lorenz–Lorentz function.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res11
244
This observation indicates a positive excess of the averaged polarizabilities that overcompensates the effect of the small but noticeable positive excess volume.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res11
245
Finally we compare the coexistence curves, which are based on the estimates for the composition obtained from the refractive index measurements with the phase diagrams, which are obtained by direct observation of the appearance of the meniscus in samples of given concentration.1
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met7
246
Fig. 3 shows the phase diagrams of the investigated systems with the weight fraction as concentration variable.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs20
247
As can be seen, there is no substantial difference between the separation curves obtained by the two methods.1
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs20
248
This proves not only the reliability of our analysis, but it shows also that the compounds are sufficiently pure: The maximum of the phase diagram, determined by visual observation of the phase separation in a set of samples of different composition, is identical with the critical concentration.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res12
249
In three-component systems, this is usually not the case.9
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac53
250
We mention that preliminary measurements with salts, which were not dried, yielded a critical point different from the maximum of the phase diagram.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs21
251
In Fig. 3, we have included data of other solutions (water, 1-propanol and 1-hexanol) that were obtained by the visual method1 to emphasize the corresponding-state similarity of the phase diagrams.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs22
252
The coexistence curves in terms of the new variables are shown in Figs. 4.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs23
253
Representing the coexistence curves in terms of the variables x, w, and φ the banana shape that was found in the representation in terms of the Lorenz–Lorentz relation, see Fig. 1, disappears.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res13
254
The representation in terms of the mole fraction is still rather skewed, while the mass fraction gives the most symmetrical shape.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs24
255
In all figures, the coexistence curves of all four systems are very similar.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs25
256
Only a minor difference between the solutions in the 1-alcohols and the 2-alcohols is noticeable.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs25
257
The curves of the mixtures with the 1-alcohols appear slightly more narrow and symmetrical than those of the mixtures with the secondary alcohols.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs25
258
The coexistence curves represented by the concentration variables mole fraction x, weight fraction w and the volume fraction φ are analysed in the same way as done in Section 4.1, where the Lorenz–Lorentz function was the concentration variable.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met5
259
The results of the fits are given in Table 5.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs26
260
In the fits, the critical temperatures Tc were fixed to the experimental values.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met7
261
We start with a fit to a simple exponential with the exponent βeff as a fitting parameter.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met7
262
With the exception of the temperature dependence of Δx, the analysis of the coexistence curves in terms of the other variables (Δw or Δφ) yield values for the exponent β that are smaller than the Ising value.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res14
263
When the coexistence curves are represented by the mole fraction, we get figures slightly above or below the Ising value.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res14
264
The results of the fits by a Wegner-type expansion with one correction term correspond to this analysis: small positive or negative values of B1, when x is the variable, or larger negative figures of B1 when w or φ is chosen.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res14
265
As can be seen in Table 5, the fits to a single exponential, where the exponent β is a free parameter and to a one-term Wegner expansion with fixed exponents are equally good.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs27
266
No systematic is noticeable, when the deviations from the Ising value are compared for the different solvents.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs28
267
The representation of the coexistence curve by the mass fraction requires larger corrections than the volume fraction.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs28
268
Fits involving two Wegner corrections are not included in the table because of the large uncertainty of the parameters obtained.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac54
269
In Fig. 5a, we show the log–log plots of Δφ drawn as function of τ for the investigated systems.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs29
270
The data follow straight lines that are almost parallel.
Type: Observation |
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Novelty: None |
ConceptID: Obs29
271
This indicates a very good representation of the data by an effective exponent, which is used to draw the lines.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res15
272
It remains to analyse, how the choice of the variables influences the diameter of the coexistence curves.
Type: Goal |
Advantage: None |
Novelty: None |
ConceptID: Goa2
273
As can be seen in Figs. 3 and 4 the diameters (Xu + Xl)/2 of the coexistence curves clearly show a nonlinear temperature dependence.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs30
274
Again, the curves are not detailed enough to allow free fits of all the coefficients in eqn. (7).
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac55
275
Therefore, we start with one correction assuming either an exponent 2β or 1 − α.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met7
276
As in the analysis of Km, the critical compositions Xc are treated as parameter in the fits.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac56
277
In Table 6, we display the results of the fits with D as parameters and the fits with the two parameters A and D.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs31
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res16
279
Two terms were required to yield a reasonable fit.
Type: Result |
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Novelty: None |
ConceptID: Res16
280
In almost all cases, the combination of the linear term with the 1 − α term is superior to that with the 2β term, although the difference is not impressive.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res16
281
The linear term is always negative.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res16
282
The linear and the 1 − α term are always of the same order of magnitude but differ in the sign, which indicates that in the fit the parameters are coupled.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res16
283
In fact, in the two-parameter fit the amplitude D is always about four times of that obtained in the one-parameter fit.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res16
284
The Fig. 5b shows the diameter with the fit function when the volume fraction is chosen as concentration variable.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs32
285
Concluding, we state that, independent of the concentration variable; the temperature dependence of the diameter is consistent with the assumption of a linear term and a non-analytic contribution with an exponent 1 − α.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con5
286
The additional presence of a non-analytic 2β term cannot be excluded.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con5
Discussion
287
In this work we have investigated the coexistence curves of solutions of the RTIL C6mim+BF4− in 2-pentanol, 1-pentanol, 2-butanol, and 1-butanol.
Type: Object |
Advantage: None |
Novelty: New |
ConceptID: Obj1
288
For this purpose, we have measured the refractive index in critical samples of critical composition by applying the minimum beam deflection method.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met1
289
Measurements on mixtures with higher alcohols turned out to be unfeasible because the difference between the refractive indices of the RTIL C6mim+BF4− and the alcohols became too small to allow for reliable measurements.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs33
290
We first discuss the location of the critical points of the investigated solutions in the RPM phase diagram.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac57
Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp3
292
Using the reduced variables of the RPM, the values for the reduced critical temperature Tc* vary from 0.09 to 0.14.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod23
293
We find a monotonous increase with the dielectric permittivity ε of the solvents, which is 10.2, 12.6, 15.2, and 16.6 for the alcohols 2-pentanol, 1-pentanol, 2-butanol, and 1-butanol, respectively.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res17
294
The figures estimated for Tc* are above the value of 0.049, predicted by simulations of the RPM.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res18
295
However, they are much below 0.65, found for this salt in water, where the phase transition is caused by hydrophobic interactions.1
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res18
296
Therefore, we expect that the phase transition is mainly driven by Coulomb interactions.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con1
297
We note, that the variation of Tc* is in agreement with the first simulation results on ionic solutions.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs34
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac58
299
Considering the reduced density, we find figures below the RPM value of ρc* = 0.08.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res19
300
No simple correlation exists between the critical density and the dielectric permittivity of the solvents.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res20
301
The primary and secondary alcohols form a group, where the critical reduced density is higher for the n-alcohols (1-pentanol: 0.063, 1-butanol: 0.065); the corresponding figures for the secondary alcohols are 0.056, and 0.060, respectively.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res20
302
This indicates that packing effects modify the interactions of the ions with the solvent and influence the location of the critical point.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con6
303
Such dependence on the structure of the solvent was already noted in the investigation of solutions of N4444+Pic− in alcohols.8
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac59
304
We now turn to a discussion of the nature of the critical point.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac60
305
The investigation of the coexistence curve is particularly appropriate for this purpose as, the relative change of the exponent β is larger than for the exponents ν or γ, when going from mean field to Ising behaviour.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod24
306
Therefore, it appears promising to investigate the coexistence curve in order to trace eventual differences in the critical properties of ionic and non-ionic systems.
Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp4
307
For our systems, we find effective exponents βeff for the coexistence curve that are near to the Ising value.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res21
308
Within the accuracy of our measurements, we see no change of βeff with temperature.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res21
309
The log-log plots Figs. 2a and 5a appear perfectly linear.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs35
310
No curvature or change of the slope can be seen indicating a sharp crossover within a small temperature range.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs35
311
A quantitative analysis of the corrections to scaling depends on the choice of the variable chosen to represent the coexistence curve.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac61
312
Therefore, we will discuss this matter using the criteria given by Japas and Levelt Sengers.60
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac62
313
The mass faction is the variable, which yields critical points near w = 0.3, which is the value nearest 0.5 obtained for the set of variables considered.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac63
314
The mole fraction gives the most asymmetric location of the critical point, which is xc = 0.11 for 2-butanol and 0.14 for 1-pentanol.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac63
315
With K as variable, the critical compositions are Kc = 0.24 for all alcohols.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac63
316
The volume fraction yields similar figures.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac63
317
Clearly, the symmetry criterion supports the mass fraction, where wc = 0.3.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac63
318
Judging, however, by the value found for the effective exponent βeff the mole fraction appears to be the best choice followed by the mass fraction.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac63
319
The quantitative analysis of the diameter anomaly also rests on the chosen variable.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac63
320
Here, the best choice appears to be the Lorenz–Lorentz function, because in the fit with one variable, the 1 − α term gives by far the best representation of the data and, furthermore, the amplitude D is almost unchanged when the linear temperature dependence of the diameter is taken into account.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con4
321
From the phenomenological point of view, it can be said, there is no clear evidence why one of the variables should be preferred.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con7
322
However, according to the theoretical analysis of Anisimov et al62. there is no ambiguity about the choice of the variable: The density of one component is the appropriate variable, which is the volume fraction divided by the molar volume.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac64
323
Because the molar volume is changing very little in the investigated temperature range, it is trivial matter to transform the fit results for the volume fraction into such of the concentration.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac64
324
Unfortunately, the analysis in terms of the crossover theory47,48 is not trivial and merits a separate paper.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac65
325
Accepting the volume fraction as the best variable βeff is found to be significantly smaller than the Ising value.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res6
326
The figures are in general agreement with the behaviour observed on the alcohol solutions of N4444+Pic−.8 However, for solutions of N4444+Pic− in long-chain alcohols like tetradecanol positive deviations from the Ising value were found, which became smaller with increasing value of ε and negative for 2-propanol.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res6
327
2-propanol was the only alcohol with chain length <10 considered in this investigation.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac66
328
In the work reported here, the polarities of the alcohols are between that considered in ref. 8 but near to that of 2-propanol.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac67
329
Accordingly, we find negative deviations when the variables K, w, or φ are used.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res22
330
Negative deviations indicate non-uniform crossover to mean field behaviour at higher temperatures.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con2
331
No regular variation of βeff with the dielectric permittivity ε of the solvent can be observed.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res23
332
Quite likely, the ε-range of the solvents used in this work is too small to establish such dependence.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac68
333
The non-analytic temperature dependence of the diameter of the coexistence curves is a general property of phase transitions in fluids belonging to the Ising universality class.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac69
334
The amplitude, however, depends on specific properties of the system.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac69
335
In many systems, the amplitude is too small to be seen.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac69
336
Substantial deviations from the rectilinear diameter rule are common in systems where the intermolecular interactions themselves depend on the density.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac69
337
This is the case, e.g. in liquid-gas phase transition of metals, where one phase is an insulator and the other a molten metal.70
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res23
338
In a fluid of charged hard spheres the low-density phase can be pictured as a gas of ion pairs while the high-density phase appears as an expanded melt containing essentially free ions.53
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac70
339
In this picture the effective interactions are indeed density dependent, which may explain the observed irregularity.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con8
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac71
341
A substantial diameter anomaly appears to be a signature of ionic systems.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac71
342
Concluding, we state that the coexistence curves of the investigated systems agree remarkably well in the corresponding state representation.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con9
343
We state Ising critical behaviour for a set of new nearly Coulomb systems and confirm the earlier results obtained on systems with rather limited chemical stability.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con10
344
The coexistence curves show Ising critical behaviour with deviations.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con1
345
No indication of a second maximum in the coexistence curves is noticeable, which is predicted for phase transition with strong coupling to a tricritical point.52
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs36
346
The deviations of the exponent βeff from the Ising value depend on the choice of the order parameter chosen for the analysis.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res24
347
With the exception of the mole fraction, the analysis in terms of all other possible variables yields a negative deviation from Ising criticality, which may be taken as an indication of non-monotonous crossover.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res6
348
Deviations from the asymptotic Ising exponent are noticeable in the complete temperature range investigated and not only in the region with τ > 10−2, where deviations from Ising critical behaviour are common.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res6
349
A sharp crossover, reported from the turbidity measurements58 of solutions of picrates in alcohols, is not observed in the phase diagrams.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs37
350
Measurements of higher accuracy in the mK-region are desirable, which are expected to show the change of the effective critical exponent from the asymptotic Ising value to the region with negative deviations, while investigations in a wider temperature range should show the increase of βeff towards the vdW mean field value.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac72
351
Finally, we mention a result, which may be important in respect to applications of the RTILs in separation processes.
Type: Motivation |
Advantage: None |
Novelty: None |
ConceptID: Mot1
352
Already 10 K below the critical points the refractive index of the alcohol-rich phase is almost identical with that of the pure solvent.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res25
353
Using the coefficients obtained for describing the coexistence curve, we estimate that the salt content is below 1%, while the equilibrium concentration of the alcohol in the salt-rich phase is substantial.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res26