Viscosity and Self-Diffusion Coefficients of Dialkyl Adipates: A

Article pubs.acs.org/jced

Viscosity and Self-Diffusion Coefficients of Dialkyl Adipates: A Correlation Scheme with Predictive Capabilities Helena M. N. T. Avelino,†,‡ Joaõ C. F. Diogo,† Fernando J. P. Caetano,†,§ and Joaõ M. N. A. Fareleira*,† †

Centro de Química Estrutural, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001 Lisboa, Portugal Á rea Departamental de Engenharia Química, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emídio Navarro, 1, 1959-007 Lisboa, Portugal § Universidade Aberta, R. da Escola Politécnica, 147, 1269-001 Lisboa, Portugal ‡

ABSTRACT: A correlation and predictive scheme for the viscosity and self-diffusivity of liquid dialkyl adipates is presented. The scheme is based on the kinetic theory for dense hard-sphere fluids, applied to the van der Waals model of a liquid to predict the transport properties. A “universal” curve for a dimensionless viscosity of dialkyl adipates was obtained using recently published experimental viscosity and density data of compressed liquid dimethyl (DMA), dipropyl (DPA), and dibutyl (DBA) adipates. The experimental data are described by the correlation scheme with a root-mean-square deviation of ± 0.34 %. The parameters describing the temperature dependence of the characteristic volume, V0, and the roughness parameter, Rη, for each adipate are well correlated with one single molecular parameter. Recently published experimental self-diffusion coefficients of the same set of liquid dialkyl adipates at atmospheric pressure were correlated using the characteristic volumes obtained from the viscosity data. The roughness factors, RD, are well correlated with the same single molecular parameter found for viscosity. The root-mean-square deviation of the data from the correlation is less than 1.07 %. Tests are presented in order to assess the capability of the correlation scheme to estimate the viscosity of compressed liquid diethyl adipate (DEA) in a range of temperatures and pressures by comparison with literature data and of its self-diffusivity at atmospheric pressure in a range of temperatures. It is noteworthy that no data for DEA were used to build the correlation scheme. The deviations encountered between predicted and experimental data for the viscosity and self-diffusivity do not exceed 2.0 % and 2.2 %, respectively, which are commensurate with the estimated experimental measurement uncertainty, in both cases.

1. INTRODUCTION Dialkyl adipates are currently considered as green solvents and are used in an extensive range of applications, including in many process engineering industries.1−9 In fact, several properties of these liquids make them suitable for a large number of applications such as low temperature greases, fuel additives, plasticizers, solvents, lubricants, gear and automotive engine oils and hydraulic fluids, and even fuel additives.1−9 The diffusion of plasticizers in polymers is an important and complex phenomenon.10 Moreover, in the view of the authors, their use as industrial viscosity standards, with low viscosity, is also an interesting possibility.11 Obviously, the application of these liquids in industrial processes requires knowledge of their thermophysical properties, such as density and viscosity. Viscosity, in particular, is of paramount importance for equipment design and research of chemical process engineering. Density is also an important parameter, and, additionally, it is essential to correlate the transport properties, in particular the viscosity, of dense fluids. It is noteworthy that the densities of dialkyl adipates, at the same temperature and at atmospheric pressure, decrease with increasing molar mass, while, on the contrary, their viscosities © 2015 American Chemical Society

show the inverse trend. In fact, although the adipates with lower molar mass have more compact equilibrium structures, their viscosities increase with increasing molar mass,12 unlike other systems such as the n-alkanes. The main goal of the present work is the development of a correlation method for viscosity and self-diffusion coefficients of liquid dialkyl adipates, with an uncertainty commensurate with the experimental uncertainty of their measurement. In particular, a correlation scheme was developed on the basis of recent viscosity, η, and density, ρ, data of dimethyl (DMA), dipropyl (DPA), and dibutyl (DBA)11,13,14 adipates in a range of temperatures and pressures. Moreover, a scheme was developed that enables the estimation of the viscosity of compressed liquid diethyl adipate (DEA), which was not used to construct the correlation. The estimated values were compared with independent literature viscosity data.15 Special Issue: Memorial Issue in Honor of Anthony R. H. Goodwin Received: July 23, 2015 Accepted: November 12, 2015 Published: November 30, 2015 3696

DOI: 10.1021/acs.jced.5b00622 J. Chem. Eng. Data 2015, 60, 3696−3702

Journal of Chemical & Engineering Data

Article

Furthermore, recent measurements12 of the self-diffusivities, D, of DMA, DEA, DPA, and DBA, in the temperature range (293 to 339) K, at 0.1 MPa, have made possible to assess the consistency of the method. Extension of the correlation scheme was performed by incorporation of the self-diffusivity results for three of those adipates, namely, DMA, DPA, and DBA. Tests were made in order to assess the ability of the scheme to estimate the self-diffusivity data for DEA.

of a particle upon collision, it is found that the rough hardsphere coefficient, ηRHS, is directly related to the smooth hardsphere coefficient, ηSHS:28 η ≈ ηRHS ≈ CηSHS

(3)

with C ≥ 1. For some fluids, e.g., for normal alkanes, it has been found that the coupling factor C could be taken as equal to one.18 In the case of self-diffusivity for polyatomic molecules there is the possibility of changes in angular momentum as well as in translational momentum upon collision. Chandler28 showed that coupling between translational and rotational motions led to the result that the diffusion coefficient for a rough hardsphere fluid was related to that for a smooth hard-sphere fluid:27,28

2. CORRELATION MODEL The technique used to build the present correlation scheme is based on a semiempirical method proposed by Li et al.,16 which is a heuristic development of the kinetic theory for dense hardsphere fluids, applied to the van der Waals model of a liquid.17 The method is thus ultimately based on the theory of transport of hard-sphere fluids as developed by Dymond.17 An important characteristic of the van der Waals theory of transport properties is that it is equivalent to a hard-spheres theory, provided that the core sizes are allowed to decrease as the temperature increases, to reflect the somewhat soft repulsive potential of real molecular systems. This is a successful approximate theory for the dense fluid state which considers the molecules to interact through a weak long-range attractive potential and possessing a hard-core repulsive potential. Therefore, in this model, the molecules interact with a hardcore repulsion at a particular distance, and otherwise they move in a uniform attractive field. The development of the present scheme for the family of dialkyl adipates has followed the general procedures described by Assael et al. for the transport properties of n-alkanes18 and, later, for other families of compounds.19 The present correlation scheme was used previously in our group for correlation of viscosity data for DMA,13 DPA and DBA,14 2,2,4trimethylpentane,20 HFC-134a,21 toluene,22 HFC-143a and HFC-125,23 R507A,24 and tris(2-ethylhexyl) trimellitate25 and for constructing a reference correlation for the viscosity of toluene26 in wide ranges of temperature and pressure. A dimensionless viscosity, η*, is defined which, using SI units, is written as17,18

D ≈ DRHS ≈ ADSHS

(4)

with A ≤ 1. Those studies justify the use of Rη and RD appearing in eqs 1 and 2. These parameters were assumed to have a constant value for each dialkyl adipate, being temperature and density independent. Therefore, the dimensionless viscosity and diffusivity defined by eqs 1 and 2, obtained from experimental property data as a function of temperature and pressure, can be represented as a function of the molar volume as follows:

⎛V ⎞ η* = fη ⎜ m ⎟ ⎝ V0 ⎠

(5)

⎛V ⎞ D* = fD ⎜ m ⎟ ⎝ V0 ⎠

(6)

(2)

respectively. In the previous equations, V0 represents closepacked hard-spheres characteristic volumes that are made slightly temperature dependent. This temperature dependence is interpreted as providing the ability to correct for the finite gradient of the repulsive potential of real molecules. V0 for a fluid at each temperature is determined by the overlap of the isothermal curve from eq 5, as described in the following section. For consistency, V0(T) for each fluid should be the same for the different transport properties, in particular, for viscosity and self-diffusivity. In the present work, the available viscosity data as a function of temperature and pressure were used to calculate the characteristic volumes for each dialkyl adipate. These characteristic volumes were subsequently used to correlate the coefficients of self-diffusion, available at atmospheric pressure.

In eqs 1 and 2, M is the molar mass, R is the gas constant, T is the temperature, Vm is the molar volume, and Rη and RD are roughness coefficients. On this scheme, it is assumed that the reduced transport coefficients, given by eqs 1 and 2, depend, only on Vm /V0, where V0 is a characteristic molar volume which is assumed to be a weak function of the temperature. In the case of approximately spherical molecules, the viscosity and the diffusivity coefficients are directly proportional to the smooth hard-spheres values. Rη and RD are supposed to take into account the transfer between internal and external degrees of freedom in polyatomic systems, i.e., accounting for molecular nonsphericity.18,27,28 The roughness factors are assumed to be independent of both the temperature and density.18 When the effect of changes in the angular momentum is taken into account, as well as changes in the linear momentum

3. CORRELATION AND PREDICTIVE SCHEME OF VISCOSITY 3.1. Correlation of the Viscosity. In order to develop the present correlation scheme, eq 1 has first been employed to evaluate η* for all of the experimental data for DMA,13 DPA,14 and DBA14 along each isotherm. This procedure was used to construct a series of curves of the type of eq 5, one for each isotherm, in (η*,logV) space. Therefore, it was possible to obtain a single curve of η* as a function of log(Vm/V0) adjusting the value of V0 for each temperature. This was done by performing horizontal shifts along the log(Vm/V0) axis, in order to superimpose the curve for each isotherm on a reference isotherm, having a characteristic volume V0,ref = V0(Tref) obtained by an independent method. This procedure,

⎛ 1 ⎞1/2 η ⎟ η* = 6.035 × 108⎜ (Vm)2/3 ⎝ MRT ⎠ Rη

(1)

Analogously, a dimensionless diffusivity, D*17,18 is defined as ⎛ M ⎞1/2 D ⎟ D* = 5.030 × 108⎜ (Vm)−1/3 ⎝ RT ⎠ RD

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was first described by Li et al.16 and was used extensively by our group with success for a variety of liquids.12,13,20−26 In the present work, an equation of the form 1 = η*

⎛ Vm ⎞i ∑ ai⎜ ⎟ V i=0 ⎝ 0 ⎠

The resulting curve representing all of the viscosity data for DMA, DPA, and DBA may be described by a fitting equation of the type of

3

1 = η*

(7)

was used to fit η* as a function of the molar volume for each dialkyl adipate. The amount by which log(Vm/V0) has to be shifted to achieve superposition on the reference isotherm leads to the value V0(T)/V0(Tref) and hence gives a measure of the temperature effect on the characteristic volume. In this way the V0 dependence on the temperature has been described by a fitting equation of the form

NA

* − η * )2 ∑ (ηexp, i cal, i i=1

(10)

(11)

where η*exp,i is calculated by eq 1 and η*cal,i is determined by eq 10. The fitting coefficients Ai of eq 10, with the corresponding RMSD, bias and MD (maximum deviation) of the correlation, are listed in Table 2, The values of the parameter Rη for each adipate are listed in Table 3. Figure 3 shows the deviations of viscosity data for the three adipates; DMA, DPA, and DBA, from the correlation eq 8 and eq 10, with parameters from Tables 1, 2, and 3, as a function of the density, ρ. The RMSD of the correlation eq 10 is 0.34 %, which is commensurate with the repeatability of the viscosity measurements, and the bias is essentially zero. The maximum deviation of the viscosity data from the correlation does not exceed ± 1 %. These results show that using a single correlation equation for the three adipates did not introduce any significant loss of rigor in the description of the original correlation equations developed for the single liquids, as described in the respective literature sources.13,14 The correlation scheme can be used to interpolate or extrapolate viscosity data of the dialkyl adipates that entered in the development of the method. All of the data were determined at pressures above 0.1 MPa. Therefore, a first test of the scheme consists of using the correlation to perform the small extrapolations to atmospheric pressure and to compare the viscosity data measured in our laboratory, using Ubbelohde capillaries.13,14 This comparison is shown in Figure 4. The extrapolated data agree with the capillary data within ± 0.63 % for DMA,13 within ± 1.01 % for DPA, and within ± 1.42 % for DBA.14 All of the deviations are within the estimated uncertainty limit for the vibrating-wire and capillary data sets. The comparisons show that using eq 10 enables the extrapolation of the source data to atmospheric pressure with the same level of uncertainty as the individual correlation equations. However, Figure 4 compares also the viscosity data for DMA, obtained by Comuñas et al.34 at atmospheric pressure, with an Anton Paar Stabinger SVM 3000 from (283 to 373) K, with a claimed uncertainty of 1 %, with the present correlation equation. We note that the results reported by Comuñas et al.34 for DMA increase systematically with decreasing viscosity; this has previously been observed and discussed.13 3.2. Predictive Scheme for Viscosity. It is possible to expand the aforementioned correlation scheme to incorporate the ability to estimate the viscosity of a dialkyl adipate not used to construct the correlation, namely, diethyl adipate (DEA). This can be done in the following way. First, the characteristic reference volume, V0,X,ref, at the same temperature, Tref, for any of the dialkyl adipates studied, X, can be correlated with its molar mass, MX, by eq 12.

(8)

20.5

i=0

n

φ=

In the present work, a value of V0,ref = V0(Tref) has been calculated at 303.15 K for each dialkyl adipate, assuming it would be equivalent to the volume of close-packing of hardspheres, calculated from the hard-sphere diameter, σHS, as given by29 σHS3

⎛ Vm ⎞i ⎟ ⎝ V0 ⎠

In order to obtain the best fitting of all of the data, the parameters Rη in eq 1 are optimized simultaneously with the fitting parameters (eq 10), through the minimization of the objective function:

106V0(T )/(m 3· mol−1) = V0,ref + l(T − Tref ) + m(T − Tref )2

V0 =

3

∑ Ai ⎜

(9)

The hard-sphere diameter, σHS, was calculated from the Lennard-Jones potential parameters using the correlation proposed by Hammonds and Heyes.30 The Lennard-Jones parameters were estimated by the method described by Chung et al.31 The critical temperature, Tc, and critical volume, Vc, used in the estimation of the Lennard-Jones parameters, were obtained using the method of Marrero-Marejón and PardilloFontdevila32 as described in ref 33. The molar volumes used in the present work were calculated by the modified Tait equations proposed by Diogo et al. for DMA13 and for DPA and DBA.11 The curves of η* versus log(Vm/V0) obtained for the three dialkyl adipates (DMA, DPA, and DBA) by eqs 7 and 8 are shown in Figure 1. The reference volumes, V0,ref, and the fitting parameters l and m in eq 8 are listed in Table 1, as well as the statistical data of the fitting for each dialkyl adipate. The three curves are themselves superimposable on each other, by performing vertical shifts along the log(η*) axis, thus determining Rη for each dialkyl adipate. The result is shown in Figure 2.

Figure 1. Dimensionless viscosity, η*, curves of three adipates as a function of log(Vm/V0): ◇, DMA; ○, DPA; + , DBA. 3698



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Table 1. Reference Volumes and Fitting Parameters l and m of Equation 8 for Each Dialkyl Adipate Vo,ref/(cm3·mol−1)

fluid DMA DPA DBA

l/K−1 −1

− 1.054 × 10 − 1.416 × 10−1 − 1.630 × 10−1

133.9611 195.3295 224.3809

Figure 2. Dimensionless viscosity, η*, curve of three dialkyl adipates as a function of log(Vm/V0): ◇, DMA; ○, DPA; + , DBA; , eq 10 with parameters from Tables 1, 2 and 3.

Rη 1.832 2.080 2.369

V0, X(Tref ) V0,DBA(Tref )

(13)

The values of the roughness coefficients, Rη,X of adipate X, can thus be obtained by the following correlation with the molar mass: R η , X = 3.88903 − 2.38715 × 10−2MX + 6.9929 × 10−5MX 2 (14)

The parameters of eq 14 are determined from the values for Rη (in Table 3) of each adipate as a function of its molar mass. Therefore, eqs 12, 13, and 14, together with the corresponding fitting parameters, form a correlation scheme for the viscosity of all three alkyl adipates studied. Furthermore, this correlation can be applied to estimate the viscosity of other liquid dialkyl adipates, not used in construction of the correlation, using eq 10 provided the density is known. The utilization of this prediction scheme for viscosity comprises five main steps, involving the calculation of the following quantities: (i) V0,ref (at Tref = 303.15 K), using eq 12; (ii) V0(T), using eq 13; (iii) Rη, using eq 14; (iv) η*, for adipate X, using eq 10; (v) η, for adipate X, using eq 1. 3.3. Application of the Predictive Scheme: Viscosity of Diethyl Adipate. The accuracy of the prediction was tested with diethyl adipate (DEA), since its viscosity data have not been included in the viscosity correlation. Density and viscosity data for diethyl adipate (DEA) along eight isotherms from (303.15 to 373.15) K and at pressures up to 20 MPa were measured by Meng et al.15 The measurements of both properties were performed simultaneously using a vibrating-wire instrument, and their overall nominal uncertainties are ± 2 % for viscosity and ± 0.2 % for density.

Figure 3. Deviation of viscosity data from the correlation eq 10, as a function of the density, ρ: ◇, DMA; ●, DPA; +, DBA.

V0, X ,ref = 1.0771MX − 53.439

− 0.0052 0.0002 − 0.0009

V0, X(T ) = V0,DBA(T )

Table 3. Roughness Coefficients, Rη, for the Three Dialkyl Adipates Studied fluid

bias/%

0.19 0.22 0.32

From the correlation of the pure adipates, the variation with temperature of V0 (T) for adipate X can be calculated by relating the values of the characteristic volumes for DBA, V0,DBA(T), at the same temperature, according to the following equation:

0.54074 − 1.00066 0.368779 0.182570 − 0.087467 0.34 − 0.0001 − 0.97

DMA DPA DBA

RMSD/%

3.187 × 10−4 5.079 × 10−4 3.523 × 10−4

Figure 4. Relative deviations of viscosity data obtained at atmospheric pressure with an Ubbelohde capillary from the extrapolated data evaluated by the correlation scheme: ◇, DMA;13 ●, DPA;14 +, DBA.14 The deviations of the data obtained for DMA by Comuñas et al.34, □, are also shown.

Table 2. Fitting Parameters of Equation 10 Representing the Viscosity Data for the Liquid Dialkyl Adipates Studied A0 A1 A2 A3 A4 RMSD/% bias/% MD %

m/K−2

(12)

The parameters of eq 12 are obtained by fitting of V0,ref(Tref) (in Table 1) for each adipate as a function of its molar mass. 3699



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together with the RMSD, bias, and MD, for the correlation, are listed in Table 5.

The density of the DEA was calculated by the modified Tait equation with the parameters given by Meng et al.15 The deviations of the original experimental data from the present predictive scheme are shown in Figure 5.

Table 4. Roughness Coefficients, RD, for the Three Dialkyl Adipates fluid

RD

DMA DPA DBA

1.053 0.702 0.557

Table 5. Fitting Parameters of Equation 15, RMSD, Bias, and MD Representing the Diffusivity Data for the Liquid Dialkyl Adipates Studied B0 B1 B2 B3 RMSD/% bias/% MD %

Figure 5. Deviations of viscosity data for DEA reported by Meng at al.15 from the estimation made by means of the present predictive scheme: ●, 303 K; ◇, 313 K; □, 323 K; Δ, 333 K; + , 343 K; ○, 353 K; ⧫, 363; × , 373 K.

The experimental data reported by Meng et al.15 deviates from our predictions by (− 1.0 to + 1.9) %, within the estimated uncertainty of their viscosity measurements, which is an excellent agreement.

Figure 6 shows the deviations of the self-diffusivity data for DMA, DPA, and DBA, from the correlation eq 15, with

4. SELF-DIFFUSIVITY The self-diffusion coefficients of four dialkyl adipates (DMA, DEA, DPA, and DBA) have recently been measured by the PGSE-NMR spin−echo method in the temperature range (293 to 339) K, under atmospheric pressure.12 4.1. Correlation of Self-Diffusivity. The self-diffusion coefficients of the dialkyl adipates used to develop the viscosity correlation scheme, namely, DMA, DPA, and DBA, were correlated using the method described in section 2. The diffusivity data were used to calculate the dimensionless selfdiffusion coefficients, as defined in eq 2, which were correlated with the molar volume by the following equation: ⎛ Vm ⎞i D* = ∑ Bi ⎜ ⎟ V i=0 ⎝ 0 ⎠

Figure 6. Relative deviations of self-diffusivity data obtained at atmospheric pressure from the correlation scheme: ◇, DMA; ●, DPA; +, DBA.

3

(15)

parameters from Tables 4 and 5, as a function of log(Vm/V0) . The RMSD of correlation eq 15 is 1.07 %, which is within the estimated uncertainty of the measurements of the self-diffusion coefficients, and the bias is essentially zero. The maximum deviation of the self-diffusivity data from the correlation does not exceed ± 1.4 %. 4.2. Estimation of the Self-Diffusion Coefficients for Diethyl Adipate. The self-diffusion coefficients of DEA were estimated using eq 15 with the parameters in Table 5. The molar volume of DEA used in the correlation was determined by the modified Tait equation published by Comuñas et al.,35 and the characteristic volumes were the same as those used in the calculation of viscosity; i.e., they were calculated by eqs 12 and 13. RD are well correlated with the same single molecular parameter found for viscosity, the molar mass:

The molar volumes of DMA, DPA, and DBA used in the correlation were determined by the modified Tait equations reported by Diogo et al.11,13 V0 were calculated by eq 8, with the parameters given in Table 1. It should be pointed out that these parameters were obtained using viscosity (and density) data only. The curves of D* versus log(Vm/V0) for these dialkyl adipates were superimposed by vertical shifts along the D* axis in order to determine the roughness coefficients for selfdiffusivity, RD, of each substance. RD, in eq 2, were obtained simultaneously with the fitting parameters of eq 15, by the minimization of the objective function: n

φ=

* i − Dcal, * i)2 ∑ (Dexp, i=1

13.45536 − 4.95834 − 21.20617 10.65112 1.07 − 0.008 1.37

(16)

RD = 2.69291 − 11.7869M + 13.62671M2

where D*exp,i stands for the value of D* calculated by eq 2, using experimental data from ref 12 and Dcal,i * is determined by eq 15. RD are listed in Table 4, and the fitting coefficients Bi of eq 15,

(17)

Equation 17 was used to estimate RD = 0.866 for DEA. Subsequently, the estimated values for the self-diffusion 3700



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coefficients for DEA were obtained at several temperatures, using eqs 2 and 15. The estimated values, Dpred, were compared with the experimental values.12 The corresponding deviations are plotted in Figure 7.

This work was supported by the Strategic Project PEst-OE/ QUI/UI0100/2013, funded by Fundaçaõ para a Ciência e a Tecnologia (FCT), Portugal. J.C.F.D. also thanks FCT, Portugal, for his Ph.D. grant (SFRH/BD/66736/2009). Notes

The authors declare no competing financial interest.

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(1) New, N. H.; Schmaus, R. H. Performance of adipate diester synthetic lubricant in the hydrodynamic regime. Proceedings of the 12th Turbomachinery Symposium; Turbomachinery Laboratory, Texas A&M University: College Station, TX, USA, 1983; pp 139−144. (2) Balafas, D.; Shaw, K. J.; Whitfeld, F. B. Phthalate and adipate esters in Australian packaging materials. Food Chem. 1999, 65, 279− 287. (3) Berg, R. W.; Otero, A. D. Analysis of adipate ester contents in poly(vinyl chloride) plastics by means of FT-Raman Spectroscopy. Vib. Spectrosc. 2006, 42, 222−225. (4) Ren, Y.; Huang, Z.; Miao, H.; Jiang, D.; Zeng, K.; Liu, B.; Wang, X. Combustion and emission characteristics of a direct injection diesel engine fuelled with diesel-diethyl adipate blends. Energy Fuels 2007, 21, 1474−1482. (5) Esters in Synthetic Lubricants, http://www.bobistheoilguy.com/ esters-in-synthetic-lubricants/, Accessed Jul. 3, 2015. (6) Exxon Mobile. Esterex Adipate Esters, Product Data Sheet; http:// doc.ccc-group.com/spec/414024.pdf, Accessed Jul. 3, 2015. (7) Zhu, R.; Cheung, C. S.; Huang, Z.; Wang, X. Experimental Investigation on Particulate Emissions of a Direct Injection Diesel Engine Fueled with Diesel-Diethyl Adipate Blends. J. Aerosol Sci. 2011, 42, 264−276. (8) Zhu, R.; Cheung, C. S.; Huang, Z.; Wang, X. Regulated and Unregulated Emissions from a Diesel Engine Fueled with Diesel Fuel Blended with Diethyl Adipate. Atmos. Environ. 2011, 45, 2174−2181. (9) Meng, X.; Wu, J. Viscosity modeling of some oxygenated fuels. Fuel 2013, 107, 309−314. (10) Rahman, M.; Brazel, C. S. Review: An Assessment of Traditional Plasticizers and Research Trends for Development of Novel Plasticizers. Prog. Polym. Sci. 2004, 29, 1223−1248. (11) Diogo, J. C. F.; Avelino, H. M. T.; Caetano, F. J. P.; Fareleira, J. M. N. A. Density measurements of compressed dipropyl, dibutyl, bis(2-ethyhexyl) adipates from (293 to 373 K) at pressures up to about 68 MPa. Fluid Phase Equilib. 2014, 374, 9−19. (12) Ascenso, J. R.; Guilherme, R.; Diogo, J. C. F.; Avelino, H. M. N. T.; Caetano, F. J. P.; Fareleira, J. M. N. A. Self-Diffusivity Measurements of Dimethyl, Diethyl, Dipropyl, Dibutyl, Bis(2ethylhexyl) Adipates from (293 to 339) K by a PGSE-NMR Technique. Fluid Phase Equilib. DOI: 10.1016/j.fluid.2015.11.020. (13) Diogo, J. C. F.; Caetano, F. J. P.; Fareleira, J. M. N. A. Viscosity and density measurements of compressed liquid dimethyl adipate using oscillating body techniques. Fluid Phase Equilib. 2014, 367, 85− 94. (14) Diogo, J. C. F.; Avelino, H. M. N. T.; Caetano, F. J. P.; Fareleira, J. M. N. A. Viscosity Measurements of Compressed Liquid Dipropyl and Dibutyl Adipates. Fluid Phase Equilib. 2015, 395, 26−32. (15) Meng, X. Y.; Zheng, P. J.; Wu, J. T.; Liu, Z. G. Density and Viscosity Measurements of Diethyl Adipate from (303 to 373) K and up to 20 MPa. J. Chem. Eng. Data 2008, 53, 1474−1478. (16) Li, S. F. Y.; Trengove, R. D.; Wakeham, W. A.; Zalaf, M. The Transport Coefficients of Polyatomic Liquids. Int. J. Thermophys. 1986, 7, 273−284. (17) Dymond, J. H. Hard-sphere Theories of Transport Properties. Chem. Soc. Rev. 1985, 14, 317−356. (18) Assael, M. J.; Dymond, J. H.; Papadaki, M.; Patterson, P. M. Correlation and Prediction of Dense Fluid Transport Coefficients. I. nAlkanes. Int. J. Thermophys. 1992, 13, 269−281.

Figure 7. Deviations in self-diffusivity data for DEA reported by Ascenso et al.12 from data obtained using the predictive scheme presented in this work.

The self-diffusivity data calculated using the predictive scheme deviates within (1.02 to 2.25) % from the experimental data.12 These deviations are commensurate with the estimated expanded uncertainty of the measurements of the self-diffusion coefficients, which is a very good agreement.

5. CONCLUSION Dialkyl adipates have a large range of applications and are also considered as green solvents. Knowledge of their thermophysical properties, and, therefore, the capability to predict properties such as the viscosity and self-diffusivity, is of great importance. A correlation and predictive scheme based on a hard-sphere model was presented to describe the viscosity and the selfdiffusion coefficients of dialkyl adipates. It is noteworthy that the scheme is based on experimental viscosity and density data of three dialkyl adipates (DMA, dimethyl adipate; DPA, dipropyl adipate; DBA, dibutyl adipate), which are correlated with a root-mean-square deviation of ± 0.34 %, and enabling its use to perform small extrapolations of viscosity data. Moreover, a scheme was developed that enables the estimation of the viscosity of diethyl adipate (DEA), which was not used to construct the scheme, in a range of temperatures and pressures, from (303.15 to 373.15) K and up to 20 MPa, with deviations within ± 2 %. Furthermore, V0 obtained for the development of the viscosity correlation scheme were used to correlate the selfdiffusion coefficients of the same three adipates, which have been recently measured at atmospheric pressure in a range of temperatures (293 to 339) K. Self-diffusion coefficients are correlated with a root-mean-square deviation of ± 1.07 %. A scheme was also developed that enabled the estimation of the self-diffusivity of DEA with a maximum deviation ± 2.2 %, from the literature data. It is noteworthy that both estimation procedures yield results with uncertainties within the experimental uncertainties of the measurements.

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Viscosity and Self-Diffusion Coefficients of Dialkyl Adipates: A

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