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Surface tension correlation of carboxylic acids from liquid viscosity data
Accepted Manuscript Surface tension correlation of carboxylic acids from liquid viscosity data Mariano Pierantozzi, Giovanni Di Nicola PII:
S0378-3812(18)30474-6
DOI:
https://doi.org/10.1016/j.fluid.2018.11.015
Reference:
FLUID 12002
To appear in:
Fluid Phase Equilibria
Received Date: 28 August 2018 Revised Date:
5 November 2018
Accepted Date: 14 November 2018
Please cite this article as: M. Pierantozzi, G. Di Nicola, Surface tension correlation of carboxylic acids from liquid viscosity data, Fluid Phase Equilibria (2018), doi: https://doi.org/10.1016/j.fluid.2018.11.015. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Surface Tension Correlation of Carboxylic Acids from Liquid Viscosity Data
SAAD, Università degli studi di Camerino, Ascoli Piceno, Italy 2
DIISM, Università Politecnica delle Marche, Ancona, Italy
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1
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Mariano Pierantozzi,1, Giovanni Di Nicola2
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Abstract
This study presents a method to calculate the surface tension of a wide variety of organic carboxylic-based acids molecules starting from the experimental data of the liquid viscosity. The first step of this research was a data collection and then an accurate selection of experimental sources for the calculation of surface tension.
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Besides, in order to build two different but comparable databanks, the experimental points were regressed with simple equations at the same reduced temperature range, spanning from 0.35 to 0.75.
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As a final step, the original relationship of Pelofsky between the natural logarithm of surface tension and the inverse of viscosity was changed to better describe the property under investigation.
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The simple modification of adding the reduced temperature as parameter allowed to achieve an AAD of 1.24% for the whole dataset that contains 22 fluids with 170 surface tension data and 379 liquid viscosity experimental data.
Keywords: surface tension; liquid viscosity; DIPPR; acids.
1. Introduction
1
ACCEPTED MANUSCRIPT An acid is a substance which donates hydrogen ions. The most popular organic acids are composites including a carboxyl group, –COOH, defined carboxylic acids. Organic acids are widely adopted in many fields: they are used as food additives, in medicines and
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in the manufacture of various chemicals. Furthermore, biological systems create many complex organic acids that contain carboxyl groups, like amino acids and nucleic acids. Higher fatty acids are used in the manufacture of soaps.
Recover some acids like formic, propionic, and acetic from aqueous mixtures is economically
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important in industries that employ these kinds of acids as solvents and raw materials for reactions.
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For example, formic acid is adopted in the skin and textile industries, aqueous solutions of acetic acid are used in the composition of textile fibers, and vinyl acetate generation. Another use of acid is the propionic acid that is used as a catalyst in the manufacture of polyester resins [1,2]. The knowledge of the surface tension is crucial to predict and correlate the phase transitions of acids and for the description of technical processes like boiling and condensation. Moreover, the
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physical properties of this particular family are heavily linked to their capacity to produce hydrogen bonds, which can occur between two molecules of acid producing a dimer and doubling the size of
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the molecules [3].
Our research group developed different correlations to estimate viscosity and surface tension [4–9].
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One of them especially adapted to the family of acids [7]. In particular, we proposed the following formula oriented explicitly to acids: =
⋅ 1−
⋅ 1+
(1)
where σ is the surface tension (N/m), σ0 is a scaled factor = (kB·Tc)/Gr2, Tr is the reduced temperature, kB is the Boltzmann’s constant (J/K), Gr is the radius of gyration (m), Φ is an adimensional term = NA·ρc·Gr3, NA is the Avogadro’s number (mol-1), ρc is the critical density (mol·m-3). During the data elaboration, the authors divided the dataset into two subgroups: a first 2
ACCEPTED MANUSCRIPT containing the n-aliphatic acids (excluding the methanoic acid) and other aliphatic acids (excluding the cyclopropane carboxylic acid), a second containing the aromatic carboxylic acids, the levulinic acid, the methanoic acid and the cyclopropane carboxylic acid.
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Up to now, several estimation methods have been proposed in literature [10–19] to connect viscosity to surface tension. The most relevant models will be listed in Section 3. Generally, they are empirical or semi-empirical correlations with three or four adjustable coefficients relating the natural logarithm of the surface tension to the reciprocal viscosity, but none of these equations is
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explicitly oriented to acids.
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In the present work, following the same approach of a recent paper devoted to silanes [19] and introducing the reduced temperature as an independent variable in the model, a new equation to estimate surface tension of selected organic acids from the knowledge of viscosity data is presented. In a fact, as already done for the family of silanes in a similar way, the proposed model presents a set of coefficients for each acid, giving very accurate results in a wide reduced temperature range
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(0.35-0.75). In Section 2, we describe the dataset creation while in Section 3 the new correlation together with the literature ones are presented and discussed. And finally, the conclusions are
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2. Data analysis
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presented in Section 4.
Both the experimental dataset of viscosity and surface tension were gathered from the DIPPR database [20] and then examined. The more recent version of DIPPR database includes a total of 170 surface tension data and 379 liquid viscosity experimental data of a standard group of 22 acids. In this work, the smoothed and predicted points presented in the DIPPR database were not considered during the collection and only the experimental data were included in the final dataset. In the case of fluids, for which fewer experimental points are available in literature, most of those data have to be extrapolated and this could influence the final results. Thus, in order to extend the 3
ACCEPTED MANUSCRIPT reduced temperature ranges of the dataset and limit the extrapolations as much as possible, 12 additional data points for acids were taken from the DECHEMA database [21]. Table 1 summarizes a review of the number of points considered, the range of the experimental
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values of liquid viscosity and for the surface tension, and the critical temperature. In Figure 1, the experimental data ranges of reduced temperatures of both surface tension and liquid viscosity are illustrated. From the figure, it is evident that data are generally measured at reduced temperatures between 0.4 and 0.6 and that for some acids for which additional data in the
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DECHEMA database [21] were not found (i.e. 1-eicosanoic and nonanoic acid) the measurement
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ranges are very narrow.
After defining the definitive dataset, the available surface tension data were regressed through the original Van der Waals equation [22]:
σ = σ 0 (1 − Tr )n
(2)
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where Tr=T/TC is the reduced temperature and Tc (K) is the critical temperature, while σ0 (mN·m-1) and n are empirical constants.
Five-constant Daubert and Danner [23] equation was also applied to regress the liquid viscosity
ln
=
+
+
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experimental data: ⋅ ln
+
⋅
(3)
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Both the previous regressions were restricted in the reduced temperature range (from 0.35 to 0.75) in order to obtain a more stable description of the gathered experimental data. Tables 2 and 3 contain the coefficients and the AAD performed by the regressions for both the surface tension and the viscosity, determined as follows:
AAD( σ ) =
1 n σ exp − σ calc ⋅100 ∑ n i =1 σ exp
(4)
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ACCEPTED MANUSCRIPT AAD(η ) =
1 n ηexp − ηcalc ∑ n i =1 ηexp
⋅ 100
(5)
Analyzing the AAD, it is clear that proposed regressions represent quite well the whole set of
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experimental data of the surface tension, while in the case of viscosity some AAD values higher than 3% are obtained, reaching a 6.7% in the case of oleic acid in the chosen range of reduced temperatures. The experimental and the regressed points for oleic acid are reported in Figure 2.
the points are not influencing the final regression.
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From the figure it is evident that the higher deviations are caused by few scattered points. However,
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It has to be pointed out that the databases with original surface tension and viscosity data generally contain a limited number of points both in the low-reduced temperature range (between 0.40 and 0.45) and in the high-reduced temperature range (between 0.6 and 0.7), owning most of data in a narrow range (between 0.45 and 0.6). In addition, only one fluid (namely oleic acid) shows a point
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below 0.4 and no experimental data were found between 0.7 and 0.75. In spite of these limitations that lead the model to extrapolate at reduced temperatures both down to 0.35 and up to 0.75, the generated equations demonstrated to well represent the thermophysical properties in the entire range
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of analysis.
In Figure 3, an example of the regression is reported for dodecanoic acid together with the
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experimental data, both for the surface tension (right) and the viscosity (left). The limited distribution of the experimental data of dodecanoic acid well represents the general situation for both databases and the need of an extrapolation in the region where experimental data are not available.
As a final step, using Equation (2) and (3) and the corresponding coefficients, two virtual sets of data were generated at the same reduced temperatures (ranging from 0.35 to 0.75 with a step of 0.01), for both the surface tension and the liquid viscosity of organic acids. When the reduced 5
ACCEPTED MANUSCRIPT temperature ranges of the experimental data are not matching with the ones of the virtual set of data, the fitting procedure was extended outside the investigated temperature range. The created dataset is the starting point for the surface tension estimation of acids, beginning from the liquid viscosity
3. Surface tension-viscosity correlations for liquids
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data, precisely as carried out in a previous paper for the silanes [19].
In 1966, Pelofski [10] introduced an empirical equation containing two adjustable parameters, A
= ln
+
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ln
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and B, as follows:
(6)
The Pelofski equation was employed for n-alkanes [13] and their mixtures, reaching poorer results only close the critical region. The same equation was also used for some ionic [14,15] compounds
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where a third additional parameter was added.
The following modified Pelofski equation [16] was suggested for fifty-four substances, including rare gases, simple hydrocarbons, refrigerants, and some other substances such as carbon dioxide,
ln
=
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water or ethanol obtained from REFPROP software [24]:
+[
"#
$
(7)
Equation (7) includes four adjustable parameters, A4, B4, C4 and m, for the prediction of the surface tension from the viscosity data, available in the same range of temperatures.
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ACCEPTED MANUSCRIPT Recently, a 4-coefficient correlation was introduced for a collection of 40 fluids in an extended range of temperatures [17], giving the lowest overall deviations for 32 out of the 40 substances considered.
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In the present research, the original Pelofski equation (6) and its modification, Equation (7), were examined for the set of data generated as before shown. Table 4 contains the outcomes and the adjustable coefficients expressly regressed for the dataset under consideration. Deviations were found to be acceptable, with the exception of four fluids (benzoic acid, decanoic acid, tetradecanoic
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acid and isovaleric acid), for which they were higher than 15%. The mean AAD of equation 6 was
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7.68%. Lower deviations were obtained with Equation (7) with an average deviation of 5.59%. In the present research, we slightly modify the equation in order to increase the general surface tension description through the liquid viscosity:
= ln[
%
1−
$+
&
(8)
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ln
Equation (8), already recommended for the silanes [19], is still a simple equation, including only
parameter.
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two adjustable parameters, and requires the information of the reduced temperature as an extra
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Table 4 shows the results obtained with equation (8), together with the A5 and B5 coefficients. Deviations are always well within 5%, and the proposed model well describes even the fluids that showed high deviations for the other models. The mean AAD is 1.24%. Furthermore, Table 4 also contains the original results obtained by an artificial neural networkgroup contribution approach [25] recently suggested to represent/predict the surface tension of pure chemical fluids. This model was built considering a huge number of fluids and a wider range of
7
ACCEPTED MANUSCRIPT reduced temperatures. However, it has to be pointed out that, even if experimental data are coming from the same source [7], they could be not exactly the same. Figure 4 and 5 report the two acids for which the best results were obtained, namely oleic acid and
as in Equation (9), versus the reduced temperature. % =(
)*+ , -./)*+
0 ⋅ 100
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o-toluic acid. For a better understanding, these figures also include the relative deviations calculated
(9)
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The plot with AD denotes an s-shaped trend of deviations within the considered range of reduced temperatures, always well within ±1%.
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From the figures, it is possible to see that the reduced temperature ranges of the experimental data are not matching with the ones of the virtual set of data. Nevertheless, in both cases the final results in terms of deviations are good.
Figures 6 and 7 report the two acids with the poorest behavior, namely tetradecanoic acid and 1-
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eicosanoic acid. The plot with AD denotes again higher deviations within the considered range of reduced temperatures. For the case of Figure 6, the tetradecanoic acid shows strong deviations especially at high-reduced temperatures (above Tr=0.6), where the model does not seem to be able
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to describe the fluid’s behavior. For the case of Figure 7, the reduced temperature ranges of the experimental data of 1-eicosanoic acid are rather narrow. For this acid, the low number of data
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available could influence on the final results and the higher deviations seem to be due to the extrapolated data outside the temperature range where experimental data are available. As stated above, to obtain a higher number of experimental data and to enlarge their reduced temperature ranges, dataset was enriched by data from DECHEMA database when possible. In particular, additional experimental data were collected for 4 acids, namely acetic acid, octadecanoic acid, octanoic acid and pentanoic acid, for a total of 12 points, as reported in Table 1.
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ACCEPTED MANUSCRIPT Experimental data for octadecanoid acid from both DIPPR and DECHEMA sources are reported as example in Figure 8. Here it is evident how the DECHEMA data were useful to enrich databank at lower surface tension points.
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To provide a better view of the overall performance of each model, Table 5 lists the number of fluids for which the AAD values are less than some given value taken as reference.
It is worth to notice that the new model represents the data with AADs below 1% for 13 fluids, whereas the other models do this for a maximum of 11 acids. It is also noticeable that for the
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majority of the fluids equation (8) gives AAD values below 4% and with just one acid giving
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deviations below 5%.
Table 4 presents the results achieved with Equation (1) adopting the coefficients listed in the original paper. For the fluids in common between the two research, it is possible to remark that Equation (8) always works better than Equation (1), except for the following fluids: 1-eicosanoic acid, decanoic acid, heptadecanoic acid and tetradecanoic acid.
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Finally, Table 6 reports as comparison the prediction of different literature equations that can be adopted to calculate the surface tension of organic acids from the corresponding states principle.
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From the table it is evident that the Sastri and Rao equation [26] generally better performs, also considering that is the only equation that gives specific coefficients for organic acids.
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According to the results reported in Tables 4 and 6, when viscosity data are available, the use of Equation (8) should be preferred while, when viscosity data are not available, Equation (1) should be preferred. Of course, it is worth noting that Equation (1) is a general formula valid for all the acids (based on the corresponding states principle and requiring up to 4 parameters for the calculation), while Equation (8) requires the knowledge of liquid viscosity data and has coefficients regressed for each fluid.
4. Conclusions 9
ACCEPTED MANUSCRIPT In this paper, the modified version of the Pelofsky empirical equation has been extended to estimate the surface tension of 22 organic acids. The model is based on the knowledge of the liquid viscosity data that was adopted as input parameter together with the reduced temperature, following the same
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approach of a recent paper dedicated to the inorganic family of silanes. To calculate surface tension, we built two virtual sets of data at the same reduced temperature using reliable correlations. When the reduced temperature ranges of experimental data of surface tension and viscosity are not coinciding or in case of a limited number of experimental points, data were
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extrapolated. The range of validity of the proposed equation spans from 0.35 to 0.75 of reduced
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temperature.
The new method reaches very low deviations when compared with the existing methods in the literature. Analyzing the deviations from comparable models in the literature (AAD of 7.75% and AAD of 5.57% for Eqs. 7 and 8, respectively), the introduction of reduced temperature as additional
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(AAD of 1.24%).
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parameter clearly improves the description of the surface tension of the organic acids under analysis
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Table 1. Summary of the data collected for surface tension and liquid viscosity.
O-toluic Acid 1-eicosanoic Acid Acetic Acid Butyric Acid Decanoic Acid Dodecanoic Acid Formic Acid Heptadecanoic Acid Heptanoic Acid Hexadecanoic Acid Hexanoic Acid Nonanoic Acid Octadecanoic Acid Octanoic Acid Pentanoic Acid Tetradecanoic Acid Cyclopropane Carboxylic Acid Isobutyric Acid Isovaleric Acid Oleic Acid
118-90-1 506-30-9 64-19-7 107-92-6 334-48-5 143-07-7 64-18-6 506-12-7 111-14-8 57-10-3 142-62-1 112-05-0 57-11-4 124-07-2 109-52-4 544-63-8 1759-53-1 79-31-2 503-74-2 112-80-1
751
5
751 820 591.95 615.7 722.1 743 588 792 677.3 785 660.2 710.7 803 694.26 639.16 763 671 605 629.09 781
7 4 12 10 3 17 12 6 9 13 5 5 8 6 8 16 4 15 7 4
25.7-31.7
3
3 3 3
Tr range
Viscosity N° Points
range (mPa·s) Tr range
0.55-0.63
7 0.808433-1.60133
0.55-0.63
27-31.21
0.54-0.59
7 1.062-1.67
0.53-0.56
25.7-31.7 27.6-29 16.16-27.57 20.32-27.32 25.1-29.17 20.8-28.71 31.8-38.2 22.5-27.9 24.02-29.84 22.1-28.6 23-28.1 27.87-29.7 22.9-28.9 22-29.2 21.29-27.83 21.3-28.8 27.64-34.29 15.39-25.61 12.6-26.6 21.6-32.8
0.55-0.63 0.43-0.45 0.48-0.68 0.47-0.59 0.42-0.49 0.43-0.56 0.49-0.59 0.43-0.52 0.4-0.51 0.43-0.54 0.44-0.53 0.41-0.44 0.43-0.53 0.42-0.52 0.45-0.56 0.43-0.55 0.47-0.62 0.48-0.67 0.46-0.71 0.38-0.58
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65-85-0
6
σ range (mN/m)
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Benzoic Acid
754
N° Points [21]
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99-04-7
Tc (K)
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3-methylbenzoic Acid
Family Aromatic carboxylic Aromatic carboxylic Aromatic carboxylic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic Other aliphatic Other aliphatic Other aliphatic Other aliphatic
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Fluid
N° Points [20]
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Surface tension Cas N
7 2 58 40 3 17 24 3 20 19 31 10 18 10 23 8 6 34 6 26
0.85678-1.3974 3.2-9.78 0.297-1.314 0.3267-2.1257 2.563-4.34 0.25-7.3 0.549-2.385 4.03-9.26 0.819-5.53 1.02-7.8 0.9135-3.56 1.73-8.3 1.14-9.87 1.3-6.09 0.753-2.41 3.67-7.93 0.448-3.574 0.317-1.885 1.967-2.731 1-39.1
0.55-0.63 0.43-0.52 0.49-0.68 0.45-0.7 0.45-0.48 0.43-0.74 0.48-0.63 0.43-0.48 0.42-0.58 0.44-0.6 0.44-0.56 0.41-0.51 0.43-0.59 0.42-0.52 0.45-0.57 0.44-0.48 0.44-0.65 0.45-0.7 0.46-0.48 0.38-0.6
14
ACCEPTED MANUSCRIPT Table 2. Coefficients for Equation (2) and deviations calculated according to Equation (4). AAD (σ)
σ0 [mN·m-1]
n
3-methylbenzoic Acid
0.74
0.072
1.043
Benzoic Acid
1.10
0.072
1.084
O-toluic Acid
1.68
0.071
1.026
1-eicosanoic Acid
0.08
0.069
Acetic Acid
0.72
0.059
Butyric Acid
0.46
0.057
Decanoic Acid
0.69
Dodecanoic Acid
0.48
Heptadecanoic Acid Heptanoic Acid
1.112
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1.178 1.280
0.057
1.225
0.35
0.065
0.786
0.47
0.055
1.198
0.85
0.054
1.125
0.28
0.057
1.219
0.14
0.057
1.222
Nonanoic Acid
0.17
0.057
1.230
Octadecanoic Acid
1.00
0.055
1.160
Octanoic Acid
1.02
0.063
1.399
Pentanoic Acid
0.23
0.057
1.188
Tetradecanoic Acid
0.49
0.058
1.253
Cyclopropane Carboxylic Acid
0.25
0.051
0.631
Isobutyric Acid
0.84
0.053
1.143
Isovaleric Acid
0.83
0.052
1.147
Oleic Acid
0.38
0.053
1.035
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Hexanoic Acid
EP
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Hexadecanoic Acid
1.528
0.059
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Formic Acid
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Fluid
Table 3. Coefficients for Equation (3) and deviations calculated according to Equation (5). 15
ACCEPTED MANUSCRIPT
AAD (η)
A2
B2
C2
D2
E2
3-methyl Benzoic Acid
1.83
-12.87
2238.33
0.23
-1.66
-0.25
Benzoic Acid
1.43
-19.06
-1.87
2.48
0.001
-13.88
O-toluic Acid
1.49
-67.67
6391.19
9.96
-22.49
-0.07
1-eicosanoic Acid
0.00
28.77
0.63
-5.47
-0.06
0.52
Acetic Acid
3.44
10.51
330.33
-3.23
0.28
-26.47
Butyric Acid
2.26
-11.16
1459.76
-0.04
-4.06
-1.70
Decanoic Acid
0.43
1.48
0.13
-0.25
-0.01
1.19
Dodecanoic Acid
3.39
8.56
1269.92
-3.03
2.03
-13.67
Formic Acid
2.29
-62.81
4082.06
7.49
-8.76
-143.92
Heptadecanoic Acid
1.21
38.86
1.30
-7.47
1.02
-0.64
Heptanoic Acid
0.84
-38.17
3210.95
3.83
2.73
-23.73
Hexadecanoic Acid
2.72
-26.96
3379.29
2.10
1.32
-22.91
Hexanoic Acid
1.01
-45.74
3441.87
5.07
-0.78
-0.06
1.22
-50.83
4196.79
5.58
-2.62
-1.25
3.84
-23.33
3274.27
1.57
1.25
-23.55
3.54
-50.93
4098.06
5.60
-3.63
-161.54
Pentanoic Acid
1.76
-32.01
2590.47
3.00
-1.06
-26.02
Tetradecanoic Acid
1.69
-211.34
12931.96
28.86
12.21
-217.40
Cyclopropane Carboxylic Acid
2.16
-19.76
2240.84
1.14
25.11
-22.14
Isobutyric Acid
0.63
-11.50
1365.71
0.04
-1.34
-6.15
Isovaleric Acid
0.00
-278.64
13667.39
39.78
5.67
-132.19
Oleic Acid
6.27
-52.85
4852.62
5.80
2.53
-43.95
Octadecanoic Acid
AC C
EP
Octanoic Acid
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Nonanoic Acid
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Fluid
16
ACCEPTED MANUSCRIPT Table 4. Coefficients adopted for Equation (8) together with deviations for Equation (1), (6), (7), (8), and for [25]. AAD Fluid
A5
AAD
AAD
AAD
AAD
B5
Eq. (6) Eq. (7) Eq. (8)
Eq. (1)
[25]
0.070304892
-0.000016
3.37
0.15
0.14
1.60
-
Benzoic Acid
0.067186685
0.000002
26.85
26.34
1.99
6.50
1.3
O-toluic Acid
0.069717884
-0.000014
4.13
3.91
0.10
2.70
1.4
1-eicosanoic Acid
0.050261082
-0.000153
10.88
0.61
3.78
2.50
-
Acetic Acid
0.05564577
-0.000023
Butyric Acid
0.052442898
-0.000043
Decanoic Acid
0.048722283
-0.000010
Dodecanoic Acid
0.050009805
Formic Acid
0.071821959
Heptadecanoic Acid
0.048313106
Heptanoic Acid
0.050455097
Hexadecanoic Acid
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3-methylbenzoic Acid
0.54
0.38
4.30
1.1
2.56
1.02
0.39
0.80
0.8
15.64
17.95
3.43
1.40
1.1
-0.000052
7.21
0.05
1.33
2.60
0.7
0.000064
1.86
0.78
0.51
1.20
0.4
-0.000027
10.35
0.06
1.72
1.60
2.8
-0.000038
2.10
0.54
0.23
1.30
1.2
0.050634099
-0.000077
4.45
0.31
0.80
1.60
0.7
Hexanoic Acid
0.051860039
-0.000074
2.39
2.39
0.43
2.80
0.4
Nonanoic Acid
0.050790103
-0.000073
2.64
2.29
0.50
2.00
0.6
Octadecanoic Acid
0.050063596
-0.000055
4.65
0.25
0.64
1.20
1.4
0.051458047
-0.000114
2.99
2.62
0.86
2.40
0.5
0.051994737
-0.000052
1.87
1.72
0.30
3.40
0.6
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AC C
Pentanoic Acid
EP
Octanoic Acid
SC 3.74
Tetradecanoic Acid
0.050378855
-0.000222
26.06
31.51
4.79
2.10
0.8
Cyclopropane Carboxylic Acid
0.061536498
0.000088
1.71
0.12
1.01
5.90
1.6
Isobutyric Acid
0.049905892
-0.000035
1.90
1.01
0.24
2.90
1.1
Isovaleric Acid
0.046597467
-0.000014
29.04
28.14
3.52
6.90
2.0
Oleic Acid
0.052237425
-0.000015
2.50
0.68
0.09
9.90
1.1
Overall AAD
-
-
7.68
5.59
1.24
3.1
1.1
17
ACCEPTED MANUSCRIPT
Table 5. Numbers of fluids in different AAD (%) ranges for each correlation model. AAD%<=1
1< AAD%<=2 2< AAD%<=3 3< AAD%<=4 4< AAD%<=5 AAD%>5
Tot
0
4
6
2
2
8
22
AAD Eq. (7)
11
3
3
1
0
4
22
AAD Eq. (8)
13
5
0
3
1
0
22
AAD Eq. (1)
1
7
8
1
1
4
22
AAD [25]
9
9
2
0
0
0
20
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AAD Eq. (6)
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Table 6. Prediction of different literature equations for the organic acids. AAD
AAD
AAD
Fluids
[26]
[27]
[28]
[29]
1-eicosanoic Acid
9.86
8.50
38.56
32.53
14.88
15.09
13.02
52.72
27.44
46.98
23.97
4.49
3.13
55.25
13.20
21.00
18.23
42.40
17.92
16.25
10.17
24.83
13.35
10.13
12.76
17.01
22.77
19.20
34.91
10.48
15.91
22.65
13.76
4.23
36.99
31.06
7.22
40.48
2.30
2.45
15.11
5.55
34.70
30.06
Hexanoic Acid
4.62
47.10
5.56
8.44
Isobutyric Acid
5.21
44.91
8.42
22.39
Isovaleric Acid
1.77
56.28
12.33
24.78
Nonanoic Acid
9.19
29.30
8.46
6.50
15.54
2.00
39.72
34.53
4.62
44.40
4.41
4.95
3-methylbenzoic Acid
27.61
Acetic Acid
3.80 22.62
Butyric Acid
3.62
Decanoic Acid Dodecanoic Acid Formic Acid Heptadecanoic Acid
AC C
Heptanoic Acid
EP
Cyclopropane Carboxylic Acid
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Benzoic Acid
Hexadecanoic Acid
Octadecanoic Acid Octanoic Acid
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AAD
18
ACCEPTED MANUSCRIPT Oleic Acid
19.17
4.62
43.71
36.32
O-toluic Acid
28.16
12.36
15.55
13.10
4.47
50.48
8.57
13.78
Tetradecanoic Acid
13.93
10.47
30.59
25.29
Mean
13.02
27.37
19.09
19.93
EP
TE D
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Pentanoic Acid
AC C
Figure 1. A summary of the experimental data temperature ranges of surface tension (green) and liquid viscosity (orange).
19
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ACCEPTED MANUSCRIPT
AC C
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Figure 2. Liquid viscosity experimental data for oleic acid.
20
ACCEPTED MANUSCRIPT Fig. 3 Regression using Equation (3) and (4) for dodecanoic acid together with the experimental data, both for the surface tension (circles, right) and the viscosity (triangles, left). The dashed lines
AC C
EP
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represent the range of application of the regression.
21
ACCEPTED MANUSCRIPT
AC C
EP
TE D
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Fig. 4 Surface tension and AD (%) values for oleic acid.
Fig. 5 Surface tension and AD (%) values for o-toluic acid. 22
AC C
EP
TE D
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Fig. 6 Surface tension and AD (%) values for tetradecanoic acid.
23
AC C
EP
TE D
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Fig. 7 Surface tension and AD (%) values for 1-eicosanoic acid.
24
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Fig. 8. Experimental versus calculated surface tension for the fluid octadecanoic acid. The red
AC C
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dashed line is y=x.
25
S0378-3812(18)30474-6
DOI:
https://doi.org/10.1016/j.fluid.2018.11.015
Reference:
FLUID 12002
To appear in:
Fluid Phase Equilibria
Received Date: 28 August 2018 Revised Date:
5 November 2018
Accepted Date: 14 November 2018
Please cite this article as: M. Pierantozzi, G. Di Nicola, Surface tension correlation of carboxylic acids from liquid viscosity data, Fluid Phase Equilibria (2018), doi: https://doi.org/10.1016/j.fluid.2018.11.015. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Surface Tension Correlation of Carboxylic Acids from Liquid Viscosity Data
SAAD, Università degli studi di Camerino, Ascoli Piceno, Italy 2
DIISM, Università Politecnica delle Marche, Ancona, Italy
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1
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Mariano Pierantozzi,1, Giovanni Di Nicola2
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Abstract
This study presents a method to calculate the surface tension of a wide variety of organic carboxylic-based acids molecules starting from the experimental data of the liquid viscosity. The first step of this research was a data collection and then an accurate selection of experimental sources for the calculation of surface tension.
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Besides, in order to build two different but comparable databanks, the experimental points were regressed with simple equations at the same reduced temperature range, spanning from 0.35 to 0.75.
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As a final step, the original relationship of Pelofsky between the natural logarithm of surface tension and the inverse of viscosity was changed to better describe the property under investigation.
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The simple modification of adding the reduced temperature as parameter allowed to achieve an AAD of 1.24% for the whole dataset that contains 22 fluids with 170 surface tension data and 379 liquid viscosity experimental data.
Keywords: surface tension; liquid viscosity; DIPPR; acids.
1. Introduction
1
ACCEPTED MANUSCRIPT An acid is a substance which donates hydrogen ions. The most popular organic acids are composites including a carboxyl group, –COOH, defined carboxylic acids. Organic acids are widely adopted in many fields: they are used as food additives, in medicines and
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in the manufacture of various chemicals. Furthermore, biological systems create many complex organic acids that contain carboxyl groups, like amino acids and nucleic acids. Higher fatty acids are used in the manufacture of soaps.
Recover some acids like formic, propionic, and acetic from aqueous mixtures is economically
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important in industries that employ these kinds of acids as solvents and raw materials for reactions.
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For example, formic acid is adopted in the skin and textile industries, aqueous solutions of acetic acid are used in the composition of textile fibers, and vinyl acetate generation. Another use of acid is the propionic acid that is used as a catalyst in the manufacture of polyester resins [1,2]. The knowledge of the surface tension is crucial to predict and correlate the phase transitions of acids and for the description of technical processes like boiling and condensation. Moreover, the
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physical properties of this particular family are heavily linked to their capacity to produce hydrogen bonds, which can occur between two molecules of acid producing a dimer and doubling the size of
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the molecules [3].
Our research group developed different correlations to estimate viscosity and surface tension [4–9].
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One of them especially adapted to the family of acids [7]. In particular, we proposed the following formula oriented explicitly to acids: =
⋅ 1−
⋅ 1+
(1)
where σ is the surface tension (N/m), σ0 is a scaled factor = (kB·Tc)/Gr2, Tr is the reduced temperature, kB is the Boltzmann’s constant (J/K), Gr is the radius of gyration (m), Φ is an adimensional term = NA·ρc·Gr3, NA is the Avogadro’s number (mol-1), ρc is the critical density (mol·m-3). During the data elaboration, the authors divided the dataset into two subgroups: a first 2
ACCEPTED MANUSCRIPT containing the n-aliphatic acids (excluding the methanoic acid) and other aliphatic acids (excluding the cyclopropane carboxylic acid), a second containing the aromatic carboxylic acids, the levulinic acid, the methanoic acid and the cyclopropane carboxylic acid.
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Up to now, several estimation methods have been proposed in literature [10–19] to connect viscosity to surface tension. The most relevant models will be listed in Section 3. Generally, they are empirical or semi-empirical correlations with three or four adjustable coefficients relating the natural logarithm of the surface tension to the reciprocal viscosity, but none of these equations is
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explicitly oriented to acids.
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In the present work, following the same approach of a recent paper devoted to silanes [19] and introducing the reduced temperature as an independent variable in the model, a new equation to estimate surface tension of selected organic acids from the knowledge of viscosity data is presented. In a fact, as already done for the family of silanes in a similar way, the proposed model presents a set of coefficients for each acid, giving very accurate results in a wide reduced temperature range
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(0.35-0.75). In Section 2, we describe the dataset creation while in Section 3 the new correlation together with the literature ones are presented and discussed. And finally, the conclusions are
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2. Data analysis
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presented in Section 4.
Both the experimental dataset of viscosity and surface tension were gathered from the DIPPR database [20] and then examined. The more recent version of DIPPR database includes a total of 170 surface tension data and 379 liquid viscosity experimental data of a standard group of 22 acids. In this work, the smoothed and predicted points presented in the DIPPR database were not considered during the collection and only the experimental data were included in the final dataset. In the case of fluids, for which fewer experimental points are available in literature, most of those data have to be extrapolated and this could influence the final results. Thus, in order to extend the 3
ACCEPTED MANUSCRIPT reduced temperature ranges of the dataset and limit the extrapolations as much as possible, 12 additional data points for acids were taken from the DECHEMA database [21]. Table 1 summarizes a review of the number of points considered, the range of the experimental
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values of liquid viscosity and for the surface tension, and the critical temperature. In Figure 1, the experimental data ranges of reduced temperatures of both surface tension and liquid viscosity are illustrated. From the figure, it is evident that data are generally measured at reduced temperatures between 0.4 and 0.6 and that for some acids for which additional data in the
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DECHEMA database [21] were not found (i.e. 1-eicosanoic and nonanoic acid) the measurement
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ranges are very narrow.
After defining the definitive dataset, the available surface tension data were regressed through the original Van der Waals equation [22]:
σ = σ 0 (1 − Tr )n
(2)
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where Tr=T/TC is the reduced temperature and Tc (K) is the critical temperature, while σ0 (mN·m-1) and n are empirical constants.
Five-constant Daubert and Danner [23] equation was also applied to regress the liquid viscosity
ln
=
+
+
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experimental data: ⋅ ln
+
⋅
(3)
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Both the previous regressions were restricted in the reduced temperature range (from 0.35 to 0.75) in order to obtain a more stable description of the gathered experimental data. Tables 2 and 3 contain the coefficients and the AAD performed by the regressions for both the surface tension and the viscosity, determined as follows:
AAD( σ ) =
1 n σ exp − σ calc ⋅100 ∑ n i =1 σ exp
(4)
4
ACCEPTED MANUSCRIPT AAD(η ) =
1 n ηexp − ηcalc ∑ n i =1 ηexp
⋅ 100
(5)
Analyzing the AAD, it is clear that proposed regressions represent quite well the whole set of
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experimental data of the surface tension, while in the case of viscosity some AAD values higher than 3% are obtained, reaching a 6.7% in the case of oleic acid in the chosen range of reduced temperatures. The experimental and the regressed points for oleic acid are reported in Figure 2.
the points are not influencing the final regression.
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From the figure it is evident that the higher deviations are caused by few scattered points. However,
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It has to be pointed out that the databases with original surface tension and viscosity data generally contain a limited number of points both in the low-reduced temperature range (between 0.40 and 0.45) and in the high-reduced temperature range (between 0.6 and 0.7), owning most of data in a narrow range (between 0.45 and 0.6). In addition, only one fluid (namely oleic acid) shows a point
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below 0.4 and no experimental data were found between 0.7 and 0.75. In spite of these limitations that lead the model to extrapolate at reduced temperatures both down to 0.35 and up to 0.75, the generated equations demonstrated to well represent the thermophysical properties in the entire range
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of analysis.
In Figure 3, an example of the regression is reported for dodecanoic acid together with the
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experimental data, both for the surface tension (right) and the viscosity (left). The limited distribution of the experimental data of dodecanoic acid well represents the general situation for both databases and the need of an extrapolation in the region where experimental data are not available.
As a final step, using Equation (2) and (3) and the corresponding coefficients, two virtual sets of data were generated at the same reduced temperatures (ranging from 0.35 to 0.75 with a step of 0.01), for both the surface tension and the liquid viscosity of organic acids. When the reduced 5
ACCEPTED MANUSCRIPT temperature ranges of the experimental data are not matching with the ones of the virtual set of data, the fitting procedure was extended outside the investigated temperature range. The created dataset is the starting point for the surface tension estimation of acids, beginning from the liquid viscosity
3. Surface tension-viscosity correlations for liquids
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data, precisely as carried out in a previous paper for the silanes [19].
In 1966, Pelofski [10] introduced an empirical equation containing two adjustable parameters, A
= ln
+
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ln
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and B, as follows:
(6)
The Pelofski equation was employed for n-alkanes [13] and their mixtures, reaching poorer results only close the critical region. The same equation was also used for some ionic [14,15] compounds
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where a third additional parameter was added.
The following modified Pelofski equation [16] was suggested for fifty-four substances, including rare gases, simple hydrocarbons, refrigerants, and some other substances such as carbon dioxide,
ln
=
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water or ethanol obtained from REFPROP software [24]:
+[
"#
$
(7)
Equation (7) includes four adjustable parameters, A4, B4, C4 and m, for the prediction of the surface tension from the viscosity data, available in the same range of temperatures.
6
ACCEPTED MANUSCRIPT Recently, a 4-coefficient correlation was introduced for a collection of 40 fluids in an extended range of temperatures [17], giving the lowest overall deviations for 32 out of the 40 substances considered.
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In the present research, the original Pelofski equation (6) and its modification, Equation (7), were examined for the set of data generated as before shown. Table 4 contains the outcomes and the adjustable coefficients expressly regressed for the dataset under consideration. Deviations were found to be acceptable, with the exception of four fluids (benzoic acid, decanoic acid, tetradecanoic
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acid and isovaleric acid), for which they were higher than 15%. The mean AAD of equation 6 was
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7.68%. Lower deviations were obtained with Equation (7) with an average deviation of 5.59%. In the present research, we slightly modify the equation in order to increase the general surface tension description through the liquid viscosity:
= ln[
%
1−
$+
&
(8)
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ln
Equation (8), already recommended for the silanes [19], is still a simple equation, including only
parameter.
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two adjustable parameters, and requires the information of the reduced temperature as an extra
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Table 4 shows the results obtained with equation (8), together with the A5 and B5 coefficients. Deviations are always well within 5%, and the proposed model well describes even the fluids that showed high deviations for the other models. The mean AAD is 1.24%. Furthermore, Table 4 also contains the original results obtained by an artificial neural networkgroup contribution approach [25] recently suggested to represent/predict the surface tension of pure chemical fluids. This model was built considering a huge number of fluids and a wider range of
7
ACCEPTED MANUSCRIPT reduced temperatures. However, it has to be pointed out that, even if experimental data are coming from the same source [7], they could be not exactly the same. Figure 4 and 5 report the two acids for which the best results were obtained, namely oleic acid and
as in Equation (9), versus the reduced temperature. % =(
)*+ , -./)*+
0 ⋅ 100
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o-toluic acid. For a better understanding, these figures also include the relative deviations calculated
(9)
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The plot with AD denotes an s-shaped trend of deviations within the considered range of reduced temperatures, always well within ±1%.
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From the figures, it is possible to see that the reduced temperature ranges of the experimental data are not matching with the ones of the virtual set of data. Nevertheless, in both cases the final results in terms of deviations are good.
Figures 6 and 7 report the two acids with the poorest behavior, namely tetradecanoic acid and 1-
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eicosanoic acid. The plot with AD denotes again higher deviations within the considered range of reduced temperatures. For the case of Figure 6, the tetradecanoic acid shows strong deviations especially at high-reduced temperatures (above Tr=0.6), where the model does not seem to be able
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to describe the fluid’s behavior. For the case of Figure 7, the reduced temperature ranges of the experimental data of 1-eicosanoic acid are rather narrow. For this acid, the low number of data
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available could influence on the final results and the higher deviations seem to be due to the extrapolated data outside the temperature range where experimental data are available. As stated above, to obtain a higher number of experimental data and to enlarge their reduced temperature ranges, dataset was enriched by data from DECHEMA database when possible. In particular, additional experimental data were collected for 4 acids, namely acetic acid, octadecanoic acid, octanoic acid and pentanoic acid, for a total of 12 points, as reported in Table 1.
8
ACCEPTED MANUSCRIPT Experimental data for octadecanoid acid from both DIPPR and DECHEMA sources are reported as example in Figure 8. Here it is evident how the DECHEMA data were useful to enrich databank at lower surface tension points.
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To provide a better view of the overall performance of each model, Table 5 lists the number of fluids for which the AAD values are less than some given value taken as reference.
It is worth to notice that the new model represents the data with AADs below 1% for 13 fluids, whereas the other models do this for a maximum of 11 acids. It is also noticeable that for the
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majority of the fluids equation (8) gives AAD values below 4% and with just one acid giving
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deviations below 5%.
Table 4 presents the results achieved with Equation (1) adopting the coefficients listed in the original paper. For the fluids in common between the two research, it is possible to remark that Equation (8) always works better than Equation (1), except for the following fluids: 1-eicosanoic acid, decanoic acid, heptadecanoic acid and tetradecanoic acid.
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Finally, Table 6 reports as comparison the prediction of different literature equations that can be adopted to calculate the surface tension of organic acids from the corresponding states principle.
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From the table it is evident that the Sastri and Rao equation [26] generally better performs, also considering that is the only equation that gives specific coefficients for organic acids.
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According to the results reported in Tables 4 and 6, when viscosity data are available, the use of Equation (8) should be preferred while, when viscosity data are not available, Equation (1) should be preferred. Of course, it is worth noting that Equation (1) is a general formula valid for all the acids (based on the corresponding states principle and requiring up to 4 parameters for the calculation), while Equation (8) requires the knowledge of liquid viscosity data and has coefficients regressed for each fluid.
4. Conclusions 9
ACCEPTED MANUSCRIPT In this paper, the modified version of the Pelofsky empirical equation has been extended to estimate the surface tension of 22 organic acids. The model is based on the knowledge of the liquid viscosity data that was adopted as input parameter together with the reduced temperature, following the same
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approach of a recent paper dedicated to the inorganic family of silanes. To calculate surface tension, we built two virtual sets of data at the same reduced temperature using reliable correlations. When the reduced temperature ranges of experimental data of surface tension and viscosity are not coinciding or in case of a limited number of experimental points, data were
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extrapolated. The range of validity of the proposed equation spans from 0.35 to 0.75 of reduced
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temperature.
The new method reaches very low deviations when compared with the existing methods in the literature. Analyzing the deviations from comparable models in the literature (AAD of 7.75% and AAD of 5.57% for Eqs. 7 and 8, respectively), the introduction of reduced temperature as additional
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(AAD of 1.24%).
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parameter clearly improves the description of the surface tension of the organic acids under analysis
10
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References R.P. Lowry, A. Aguilo, Acetic Acid Today, Hydrocarb. Process. 53 (1974) 103–113.
[2]
A. Aguilo, T. Horlenko, Formic acid, Hydrocarb. Process. 59 (1980) 120–130.
[3]
R.J. Ouellette, J.D. Rawn, R.J. Ouellette, J.D. Rawn, Carboxylic Acids, Org. Chem. (2018)
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[1]
625–663. doi:10.1016/B978-0-12-812838-1.50021-9. [4]
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RI PT
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AC C
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AC C
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13
ACCEPTED MANUSCRIPT
Table 1. Summary of the data collected for surface tension and liquid viscosity.
O-toluic Acid 1-eicosanoic Acid Acetic Acid Butyric Acid Decanoic Acid Dodecanoic Acid Formic Acid Heptadecanoic Acid Heptanoic Acid Hexadecanoic Acid Hexanoic Acid Nonanoic Acid Octadecanoic Acid Octanoic Acid Pentanoic Acid Tetradecanoic Acid Cyclopropane Carboxylic Acid Isobutyric Acid Isovaleric Acid Oleic Acid
118-90-1 506-30-9 64-19-7 107-92-6 334-48-5 143-07-7 64-18-6 506-12-7 111-14-8 57-10-3 142-62-1 112-05-0 57-11-4 124-07-2 109-52-4 544-63-8 1759-53-1 79-31-2 503-74-2 112-80-1
751
5
751 820 591.95 615.7 722.1 743 588 792 677.3 785 660.2 710.7 803 694.26 639.16 763 671 605 629.09 781
7 4 12 10 3 17 12 6 9 13 5 5 8 6 8 16 4 15 7 4
25.7-31.7
3
3 3 3
Tr range
Viscosity N° Points
range (mPa·s) Tr range
0.55-0.63
7 0.808433-1.60133
0.55-0.63
27-31.21
0.54-0.59
7 1.062-1.67
0.53-0.56
25.7-31.7 27.6-29 16.16-27.57 20.32-27.32 25.1-29.17 20.8-28.71 31.8-38.2 22.5-27.9 24.02-29.84 22.1-28.6 23-28.1 27.87-29.7 22.9-28.9 22-29.2 21.29-27.83 21.3-28.8 27.64-34.29 15.39-25.61 12.6-26.6 21.6-32.8
0.55-0.63 0.43-0.45 0.48-0.68 0.47-0.59 0.42-0.49 0.43-0.56 0.49-0.59 0.43-0.52 0.4-0.51 0.43-0.54 0.44-0.53 0.41-0.44 0.43-0.53 0.42-0.52 0.45-0.56 0.43-0.55 0.47-0.62 0.48-0.67 0.46-0.71 0.38-0.58
SC
65-85-0
6
σ range (mN/m)
M AN U
Benzoic Acid
754
N° Points [21]
TE D
99-04-7
Tc (K)
EP
3-methylbenzoic Acid
Family Aromatic carboxylic Aromatic carboxylic Aromatic carboxylic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic n-aliphatic Other aliphatic Other aliphatic Other aliphatic Other aliphatic
AC C
Fluid
N° Points [20]
RI PT
Surface tension Cas N
7 2 58 40 3 17 24 3 20 19 31 10 18 10 23 8 6 34 6 26
0.85678-1.3974 3.2-9.78 0.297-1.314 0.3267-2.1257 2.563-4.34 0.25-7.3 0.549-2.385 4.03-9.26 0.819-5.53 1.02-7.8 0.9135-3.56 1.73-8.3 1.14-9.87 1.3-6.09 0.753-2.41 3.67-7.93 0.448-3.574 0.317-1.885 1.967-2.731 1-39.1
0.55-0.63 0.43-0.52 0.49-0.68 0.45-0.7 0.45-0.48 0.43-0.74 0.48-0.63 0.43-0.48 0.42-0.58 0.44-0.6 0.44-0.56 0.41-0.51 0.43-0.59 0.42-0.52 0.45-0.57 0.44-0.48 0.44-0.65 0.45-0.7 0.46-0.48 0.38-0.6
14
ACCEPTED MANUSCRIPT Table 2. Coefficients for Equation (2) and deviations calculated according to Equation (4). AAD (σ)
σ0 [mN·m-1]
n
3-methylbenzoic Acid
0.74
0.072
1.043
Benzoic Acid
1.10
0.072
1.084
O-toluic Acid
1.68
0.071
1.026
1-eicosanoic Acid
0.08
0.069
Acetic Acid
0.72
0.059
Butyric Acid
0.46
0.057
Decanoic Acid
0.69
Dodecanoic Acid
0.48
Heptadecanoic Acid Heptanoic Acid
1.112
SC
1.178 1.280
0.057
1.225
0.35
0.065
0.786
0.47
0.055
1.198
0.85
0.054
1.125
0.28
0.057
1.219
0.14
0.057
1.222
Nonanoic Acid
0.17
0.057
1.230
Octadecanoic Acid
1.00
0.055
1.160
Octanoic Acid
1.02
0.063
1.399
Pentanoic Acid
0.23
0.057
1.188
Tetradecanoic Acid
0.49
0.058
1.253
Cyclopropane Carboxylic Acid
0.25
0.051
0.631
Isobutyric Acid
0.84
0.053
1.143
Isovaleric Acid
0.83
0.052
1.147
Oleic Acid
0.38
0.053
1.035
AC C
Hexanoic Acid
EP
TE D
Hexadecanoic Acid
1.528
0.059
M AN U
Formic Acid
RI PT
Fluid
Table 3. Coefficients for Equation (3) and deviations calculated according to Equation (5). 15
ACCEPTED MANUSCRIPT
AAD (η)
A2
B2
C2
D2
E2
3-methyl Benzoic Acid
1.83
-12.87
2238.33
0.23
-1.66
-0.25
Benzoic Acid
1.43
-19.06
-1.87
2.48
0.001
-13.88
O-toluic Acid
1.49
-67.67
6391.19
9.96
-22.49
-0.07
1-eicosanoic Acid
0.00
28.77
0.63
-5.47
-0.06
0.52
Acetic Acid
3.44
10.51
330.33
-3.23
0.28
-26.47
Butyric Acid
2.26
-11.16
1459.76
-0.04
-4.06
-1.70
Decanoic Acid
0.43
1.48
0.13
-0.25
-0.01
1.19
Dodecanoic Acid
3.39
8.56
1269.92
-3.03
2.03
-13.67
Formic Acid
2.29
-62.81
4082.06
7.49
-8.76
-143.92
Heptadecanoic Acid
1.21
38.86
1.30
-7.47
1.02
-0.64
Heptanoic Acid
0.84
-38.17
3210.95
3.83
2.73
-23.73
Hexadecanoic Acid
2.72
-26.96
3379.29
2.10
1.32
-22.91
Hexanoic Acid
1.01
-45.74
3441.87
5.07
-0.78
-0.06
1.22
-50.83
4196.79
5.58
-2.62
-1.25
3.84
-23.33
3274.27
1.57
1.25
-23.55
3.54
-50.93
4098.06
5.60
-3.63
-161.54
Pentanoic Acid
1.76
-32.01
2590.47
3.00
-1.06
-26.02
Tetradecanoic Acid
1.69
-211.34
12931.96
28.86
12.21
-217.40
Cyclopropane Carboxylic Acid
2.16
-19.76
2240.84
1.14
25.11
-22.14
Isobutyric Acid
0.63
-11.50
1365.71
0.04
-1.34
-6.15
Isovaleric Acid
0.00
-278.64
13667.39
39.78
5.67
-132.19
Oleic Acid
6.27
-52.85
4852.62
5.80
2.53
-43.95
Octadecanoic Acid
AC C
EP
Octanoic Acid
SC
M AN U
TE D
Nonanoic Acid
RI PT
Fluid
16
ACCEPTED MANUSCRIPT Table 4. Coefficients adopted for Equation (8) together with deviations for Equation (1), (6), (7), (8), and for [25]. AAD Fluid
A5
AAD
AAD
AAD
AAD
B5
Eq. (6) Eq. (7) Eq. (8)
Eq. (1)
[25]
0.070304892
-0.000016
3.37
0.15
0.14
1.60
-
Benzoic Acid
0.067186685
0.000002
26.85
26.34
1.99
6.50
1.3
O-toluic Acid
0.069717884
-0.000014
4.13
3.91
0.10
2.70
1.4
1-eicosanoic Acid
0.050261082
-0.000153
10.88
0.61
3.78
2.50
-
Acetic Acid
0.05564577
-0.000023
Butyric Acid
0.052442898
-0.000043
Decanoic Acid
0.048722283
-0.000010
Dodecanoic Acid
0.050009805
Formic Acid
0.071821959
Heptadecanoic Acid
0.048313106
Heptanoic Acid
0.050455097
Hexadecanoic Acid
RI PT
3-methylbenzoic Acid
0.54
0.38
4.30
1.1
2.56
1.02
0.39
0.80
0.8
15.64
17.95
3.43
1.40
1.1
-0.000052
7.21
0.05
1.33
2.60
0.7
0.000064
1.86
0.78
0.51
1.20
0.4
-0.000027
10.35
0.06
1.72
1.60
2.8
-0.000038
2.10
0.54
0.23
1.30
1.2
0.050634099
-0.000077
4.45
0.31
0.80
1.60
0.7
Hexanoic Acid
0.051860039
-0.000074
2.39
2.39
0.43
2.80
0.4
Nonanoic Acid
0.050790103
-0.000073
2.64
2.29
0.50
2.00
0.6
Octadecanoic Acid
0.050063596
-0.000055
4.65
0.25
0.64
1.20
1.4
0.051458047
-0.000114
2.99
2.62
0.86
2.40
0.5
0.051994737
-0.000052
1.87
1.72
0.30
3.40
0.6
M AN U
TE D
AC C
Pentanoic Acid
EP
Octanoic Acid
SC 3.74
Tetradecanoic Acid
0.050378855
-0.000222
26.06
31.51
4.79
2.10
0.8
Cyclopropane Carboxylic Acid
0.061536498
0.000088
1.71
0.12
1.01
5.90
1.6
Isobutyric Acid
0.049905892
-0.000035
1.90
1.01
0.24
2.90
1.1
Isovaleric Acid
0.046597467
-0.000014
29.04
28.14
3.52
6.90
2.0
Oleic Acid
0.052237425
-0.000015
2.50
0.68
0.09
9.90
1.1
Overall AAD
-
-
7.68
5.59
1.24
3.1
1.1
17
ACCEPTED MANUSCRIPT
Table 5. Numbers of fluids in different AAD (%) ranges for each correlation model. AAD%<=1
1< AAD%<=2 2< AAD%<=3 3< AAD%<=4 4< AAD%<=5 AAD%>5
Tot
0
4
6
2
2
8
22
AAD Eq. (7)
11
3
3
1
0
4
22
AAD Eq. (8)
13
5
0
3
1
0
22
AAD Eq. (1)
1
7
8
1
1
4
22
AAD [25]
9
9
2
0
0
0
20
RI PT
AAD Eq. (6)
SC
Table 6. Prediction of different literature equations for the organic acids. AAD
AAD
AAD
Fluids
[26]
[27]
[28]
[29]
1-eicosanoic Acid
9.86
8.50
38.56
32.53
14.88
15.09
13.02
52.72
27.44
46.98
23.97
4.49
3.13
55.25
13.20
21.00
18.23
42.40
17.92
16.25
10.17
24.83
13.35
10.13
12.76
17.01
22.77
19.20
34.91
10.48
15.91
22.65
13.76
4.23
36.99
31.06
7.22
40.48
2.30
2.45
15.11
5.55
34.70
30.06
Hexanoic Acid
4.62
47.10
5.56
8.44
Isobutyric Acid
5.21
44.91
8.42
22.39
Isovaleric Acid
1.77
56.28
12.33
24.78
Nonanoic Acid
9.19
29.30
8.46
6.50
15.54
2.00
39.72
34.53
4.62
44.40
4.41
4.95
3-methylbenzoic Acid
27.61
Acetic Acid
3.80 22.62
Butyric Acid
3.62
Decanoic Acid Dodecanoic Acid Formic Acid Heptadecanoic Acid
AC C
Heptanoic Acid
EP
Cyclopropane Carboxylic Acid
TE D
Benzoic Acid
Hexadecanoic Acid
Octadecanoic Acid Octanoic Acid
M AN U
AAD
18
ACCEPTED MANUSCRIPT Oleic Acid
19.17
4.62
43.71
36.32
O-toluic Acid
28.16
12.36
15.55
13.10
4.47
50.48
8.57
13.78
Tetradecanoic Acid
13.93
10.47
30.59
25.29
Mean
13.02
27.37
19.09
19.93
EP
TE D
M AN U
SC
RI PT
Pentanoic Acid
AC C
Figure 1. A summary of the experimental data temperature ranges of surface tension (green) and liquid viscosity (orange).
19
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
Figure 2. Liquid viscosity experimental data for oleic acid.
20
ACCEPTED MANUSCRIPT Fig. 3 Regression using Equation (3) and (4) for dodecanoic acid together with the experimental data, both for the surface tension (circles, right) and the viscosity (triangles, left). The dashed lines
AC C
EP
TE D
M AN U
SC
RI PT
represent the range of application of the regression.
21
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
Fig. 4 Surface tension and AD (%) values for oleic acid.
Fig. 5 Surface tension and AD (%) values for o-toluic acid. 22
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Fig. 6 Surface tension and AD (%) values for tetradecanoic acid.
23
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Fig. 7 Surface tension and AD (%) values for 1-eicosanoic acid.
24
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
Fig. 8. Experimental versus calculated surface tension for the fluid octadecanoic acid. The red
AC C
EP
TE D
dashed line is y=x.
25