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Heat capacity of dowanols within a temperature range of (275.15–339.15) K. Measurements and prediction
Fluid Phase Equilibria 430 (2016) 13e18
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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Heat capacity of dowanols within a temperature range of (275.15e339.15) K. Measurements and prediction ralski*, Mariola Tkaczyk, Katarzyna Łudzik Paweł Go dz, Pomorska Street 165, 90-236 Ło dz, Poland Department of Physical Chemistry, University of Ło
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 June 2016 Received in revised form 31 August 2016 Accepted 1 September 2016 Available online 2 September 2016
The saturation heat capacities of seven dowanols, i.e. polyoxy(iso)propylene glycol mono-alkyl ethers (CnPm) and two dimethyl ethers; C1P1C1 and C1P2C1 were measured by the calorimetric (DSC) method. The measurements were performed within the temperature range of (275.15e339.15) K by means of a Micro DSCIII (Setaram) calorimeter. Assuming that the molar heat capacity (Cp,m) shows an additive character, the contributions to the Cp,m values of particular functional groups forming the compounds of CnPm series were calculated. Two models differing in the manner of molecule division into functional groups, i.e. first- and second-order additivity group contribution approach were used. In the latter, not only the type of functional group but also its position and the closest neighborhood were taken into account. The average relative deviations (ARD) between the experimental values of Cp,m and those estimated on the basis of the group contributions for the compounds of the series under investigation were calculated. Furthermore, the effect of hydrogen bond association on Cp,m values was also estimated and discussed. © 2016 Elsevier B.V. All rights reserved.
Keywords: Dowanols Polyoxypropylene glycol monoalkyl ethers Heat capacity DSC Group additivity Hydrogen bonds
1. Introduction Solvosurfactants are compounds, whose properties are characteristic of typical surfactants and solvents. They include, among others, monoalkyl ether of polyoxyalkylene glycols with general formula: CnH2nþ1[OR]mOH, where n is the number of carbon atoms in the hydrophobic chain of “tail”, while m is the number of oxyalkylene groups in the hydrophobic chain of “head”. Depending on the molecular structure, these compounds can be used as: solvents, co-solvents, surfactants or co-surfactants [1e4]. Pure monoalkyl ethers of polyoxyalkylene glycols undergo association due to the formation of intermolecular hydrogen bonds [5e9]. Thanks to the presence of the ether oxygen atoms and the terminal hydroxyl group, they also form intramolecular hydrogen bonds. In aqueous solutions, these compounds can create clusters, ‘micelle-like’ structures or micelles [10e14]. Monoalkyl ethers of polyoxyethylene glycols [where R ¼ CH2CH2] and polyoxypropylene glycols or dowanols [where R ¼ CH(CH2)CH2] have found their use in industrial practice. Owing to their interesting properties they are used in many fields of chemical, cosmetic or pharmaceutical
* Corresponding author. ralski). E-mail address: [email protected] (P. Go http://dx.doi.org/10.1016/j.fluid.2016.09.002 0378-3812/© 2016 Elsevier B.V. All rights reserved.
industry. Because of their low toxicity, dowanols more and more frequently replace, in various products, the ether derivatives of polyoxyethylene glycols that show adverse effects on living organisms [3]. The physicochemical properties of compounds belonging to the derivatives of polyoxyethylene glycols have been frequently studied. In the case of dowanols, the number of such works is very limited. In practice, dowanols are most often used in the form of aqueous solutions, therefore researchers pay most attention to the mixtures of dowanols with water. Most commonly the phenomenon of limited miscibility, i.e. the range of the occurrence of miscibility gap (composition/temperature) was investigated [4,15e18]. Literature reports only a few experimental data concerning the physicochemical and especially thermochemical properties of pure dowanols or their mixtures. The growing interest in these compounds increases the demand for this type of data. Their analysis makes it possible to describe the intermolecular interactions in pure dowanols and their mixtures. One of the basic thermodynamic quantities used in chemical engineering is the molar heat capacity under constant pressure (Cp,m). The analysis of changes in this quantity caused by temperature or mixture composition provides valuable information about the structural changes of a liquid [10e12,19,20]. The molar heat capacity is often considered to be an additive quantity. The
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determination of the contributions made by particular groups makes it possible to estimate the value of Cp,m of a compound, whose experimental data are absent in literature. The systematic studies of heat capacity carried out by us concern the homological series of various types of liquid compounds [21e25]. Our recent study concerns the Cp of polyoxyethylene glycol monoalkyl ethers (abbreviation: CnEm) [26]. In this work, several monoalkyl ethers of poly(iso)propylene glycols (CnPm) with general formula: CH3-(CH2)n-1-[O-CH(CH3)-CH2)]m-OH, namely CnP1 (n ¼ 3,4), CnP2 (n ¼ 1,3,4), CnP3 (n ¼ 1,3), and two dimethyl ethers: CH3-[O-CH(CH3)-CH2)]m-OCH3, m ¼ 1,2 are investigated. The saturation molar heat capacities of pure compounds were determined by the DSC method with the temperature range of (275.13e339.15) K. 2. Experimental 2.1. Chemicals The names, source, CAS number and purities of all chemicals are reported in Table 1. Before measurements, all the compounds were dried during several days with activated molecular sieves (type 4 A from Lancaster) and degassed in an ultrasonic stream. Water used as a Cp reference was firstly triple distilled and then degassed by heating under vacuum. The samples and measuring cells were filled and stored in a dry-box dried by phosphorus pentoxide. 2.2. Apparatus and procedure The saturation molar heat capacities were measured by means of a high sensitivity differential scanning calorimeter (Micro DSC III e Setaram) based on the Tian-Calvet principle. The so-called continuous with reference method (with water as a reference) was used. The values of specific heat capacity of water were taken from literature [27]. The details of the measuring procedure was described previously [21,26]. Due to the low vapor pressure of the liquids in the temperature range studied, the measured values of the saturation heat capacity can be considered as isobaric heat capacity (Csat ¼ Cp). The method used allows one to obtain the heat capacity data with the apparatus error being at a level of 0.15%. In reality, the total error is higher, and is mainly connected with the type and quantity of impurities present in the substances under investigation. Therefore we estimate that the total measurement error for the compounds with purity degree 0.99 amounts to 0.4%
and for the remaining ones 0.6% [26]. The sample mass was determined by a Sartorius RC 210D balance with an accuracy of 2 105 g. As literature reports no Cp data of the compound under investigation at 298.15 K, it was impossible to make any comparison with the results of other authors. Only possible comparison relates to the Cp data of C1P2C1 [28] in the temperature range (312.57e339.15) K. Agreement of Cp values for the given temperature range is about 0.4%. 3. Results and discussion 3.1. Specific and molar heat capacity At the temperature ranging from 275.13 to 339.15 K, the continuous method applied by us gives a set of 2560 values of Cp for each temperature scan. To obtain of reliable data, the experiments were repeated usually 2 or 3 times, both for heating and cooling sequences. Each time, the content of the measuring cell was replaced. Usually two sequences of heating and two sequences of cooling whose results did not differ more than 0.15% were chosen for averaging. A complete set of data (10240 points) were described with a common polynomial expressing the temperature dependence of molar heat capacity: Cp,m ¼ A0þ A1(T/100)þA2(T/100)2
(1)
The coefficients of Eq. (1) and mean deviations (dCp,m) of the experimental values from the calculated with polynomial are listed in Table 2. The Cp,m values with a 1.5 K step (and additionally at 298.15 K) averaged by above equation are listed in Table 3 and presented in Fig. 1. As is seen, for all the dowanols studied, the function Cp,m ¼ f(T) is almost rectilinear with a similar slope. The mutual location of the curves in the diagram results from the growing number of functional groups present in the molecule (growing molar mass). Considerably more information can be obtained from the interpretation of the temperature dependence of specific heat capacity, shown in Fig. 2. The numerical data of specific heat at (275.13e339.15) K for all the compounds are listed in Supplementary Materials - Table S1. As is seen in Fig. 2, the courses of function Cp ¼ f(T) are grouped at three levels, each of which represents a group of dowanols with identical length of the polyoxypropylene chain m. A change in the hydrocarbon chain length n in the limits 4 n 1 does not exert any considerable effect. There is only a small drop in the heat capacity with increasing chain
Table 1 Chemical names, source and purity of the polyoxy(iso)propylene glycol mono- and dialkyl ethers under investigation. Abbreviation Chemical name C3P1a C4P1 C1P2a C3P2a C4P2a C1P3a C3P3a C1P1C1 C1P2C1a a
propylene glycol monopropyl ether; 1-propoxypropan-2-ol propylene glycol monobutyl ether; 1-butoxypropan-2-ol dipropylene glycol monomethyl ether; 2-(2-methoxypropoxy) propan-1-ol
Supplier CAS number
Aldrich 1569-01-3 Aldrich 5131-66-8 Aldrich 34590-948 dipropylene glycol monopropyl ether; 1-(1-methyl-2-propoxyethoxy)propan-2-ol Aldrich 29911-274 dipropylene glycol monobutyl ether; 1-[(1-butoxy-2-propoanyl)oxy]propan-2-ol Aldrich 29911-282 tripropylene glycol monomethyl ether; 2-[1-(1-methoxypropan-2-yloxy)propan-2-yloxy] Aldrich 25498-49propan-1-ol 1 tripropylene glycol monopropyl ether; 1-[1-methyl-2-(1-methyl-2- propoxyethoxy)ethoxy]- Aldrich 96077-042-propanol 2 propylene glycol dimethyl ether; 1,2-dimethoxypropane Aldrich 7778-85-0 dipropylene glycol dimethyl ether; 1-methoxy-2-(2-methoxypropoxy)propane Aldrich 11110977-4
Mixture of isomers.
Molar mass/ g mol1
Mass fraction purity
118.17 132.20 148.20
0.99 0.99 0.99
176.25
0.985
190.28
0.99
206.28
0.975
234.33
0.995
104.15 162.23
0.99 0.991
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Table 2 Coefficients of the polynomial (equation (1)) and mean deviation from the regression line. Substance C3P1 C4P1 C1P2 C3P2 C4P2 C1P3 C3P3 C1P1C1 C1P2C1 P d ¼ n1i Cpcalc Cpexp ; i ¼ 10240.
A0/J mol1 K1
A1/J mol1 K2
A2/J mol1 K3
dCp,m/J mol1 K1
41.331 42.186 194.90 193.10 203.98 285.27 301.85 153.54 285.27
112.59 129.16 41.397 71.958 80.979 39.205 58.537 17.730 11.566
10.503 12.579 1.1425 2.2028 3.0211 3.6707 2.0343 1.1315 7.9887
0.28 0.20 0.23 0.23 0.28 0.29 0.23 0.29 0.12
i
Table 3 Saturated molar heat capacities (Cp,m/J mol1 K1) of examined liquid compounds for T ¼ (275.13e339.15) K and p ¼ 0.1 MPa.a T/K
C3P1
C4P1
C1P2
C3P2
C4P2
C1P3
C3P3
C1P1C1
C1P2C1
275.15 276.65 278.15 279.65 281.15 282.65 284.15 285.65 287.15 288.65 290.15 291.65 293.15 294.65 296.15 297.65 298.15 299.15 300.65 302.15 303.65 305.15 306.65 308.15 309.65 311.15 312.65 314.15 315.65 317.15 318.65 320.15 321.65 323.15 324.65 326.15 327.65 329.15 330.65 332.15 333.65 335.15 336.65 338.15 339.15
271.6 272.4 273.2 274.0 274.8 275.6 276.4 277.2 278.0 278.8 279.6 280.3 281.1 281.9 282.6 283.4 283.6 284.1 284.9 285.6 286.4 287.1 287.8 288.5 289.2 290.0 290.7 291.4 292.1 292.8 293.4 294.1 294.8 295.5 296.1 296.8 297.5 298.1 298.8 299.4 300.0 300.7 301.3 301.9 302.4
302.3 303.2 304.1 305.0 305.9 306.8 307.6 308.5 309.3 310.2 311.0 311.9 312.7 313.5 314.4 315.2 315.5 316.0 316.8 317.6 318.4 319.2 320.0 320.7 321.5 322.3 323.0 323.8 324.5 325.3 326.0 326.8 327.5 328.2 328.9 329.6 330.3 331.0 331.7 332.4 333.1 333.8 334.4 335.1 335.5
317.5 318.2 318.9 319.6 320.3 321.0 321.8 322.5 323.2 323.9 324.6 325.4 326.1 326.8 327.5 328.2 328.5 329.0 329.7 330.4 331.1 331.9 332.6 333.3 334.0 334.8 335.5 336.2 337.0 337.7 338.4 339.1 339.9 340.6 341.3 342.1 342.8 343.5 344.3 345.0 345.7 346.5 347.2 347.9 348.4
374.4 375.3 376.2 377.1 378.0 378.9 379.8 380.7 381.6 382.5 383.3 384.2 385.1 386.0 386.9 387.8 388.1 388.6 389.5 390.4 391.3 392.2 393.0 393.9 394.8 395.7 396.5 397.4 398.3 399.2 400.0 400.9 401.8 402.6 403.5 404.4 405.2 406.1 406.9 407.8 408.7 409.5 410.4 411.2 411.8
403.9 404.9 405.9 406.8 407.8 408.7 409.7 410.6 411.6 412.6 413.5 414.5 415.4 416.4 417.3 418.3 418.6 419.2 420.1 421.1 422.0 423.0 423.9 424.8 425.8 426.7 427.6 428.6 429.5 430.4 431.3 432.3 433.2 434.1 435.0 436.0 436.9 437.8 438.7 439.6 440.5 441.4 442.4 443.3 443.9
420.9 421.8 422.7 423.6 424.5 425.4 426.3 427.2 428.1 429.0 429.9 430.8 431.7 432.7 433.6 434.5 434.8 435.4 436.3 437.2 438.2 439.1 440.0 440.9 441.9 442.8 443.7 444.7 445.6 446.5 447.5 448.4 449.4 450.3 451.2 452.2 453.1 454.1 455.0 456.0 456.9 457.9 458.9 459.8 460.5
478.3 479.4 480.4 481.5 482.5 483.6 484.6 485.7 486.7 487.8 488.8 489.9 490.9 492.0 493.0 494.1 494.5 495.2 496.2 497.3 498.4 499.4 500.5 501.5 502.6 503.7 504.8 505.8 506.9 508.0 509.0 510.1 511.2 512.3 513.3 514.4 515.5 516.6 517.6 518.7 519.8 520.9 522.0 523.1 523.8
210.9 211.3 211.6 212.0 212.3 212.7 213.1 213.4 213.8 214.1 214.5 214.9 215.2 215.6 216.0 216.3 216.5 216.7 217.1 217.4 217.8 218.2 218.5 218.9 219.3 219.7 220.0 220.4 220.8 221.2 221.5 221.9 222.3 222.7 223.0 223.4 223.8 224.2 224.5 224.9 225.3 225.7 226.1 226.4 226.7
313.9 314.4 314.9 315.4 315.9 316.4 316.9 317.4 317.9 318.4 319.0 319.5 320.0 320.6 321.1 321.6 321.8 322.2 322.7 323.3 323.8 324.4 324.9 325.5 326.1 326.6 327.2 327.8 328.4 328.9 329.5 330.1 330.7 331.3 331.9 332.5 333.1 333.8 334.4 335.0 335.6 336.2 336.9 337.5 337.9
a Standard uncertainty u is u(T) ¼ 0.03 K. The combined uncertainty Uc is Uc(Cp,m) ¼ 0.004 Cp,m for C3P1, C4P1, C1P2, C4P2, C3P3, C1P1C1, C1P2C1 and Uc(Cp,m) ¼ 0.006 Cp,m for C3P2, C1P3 (0.95 level of confidence).
length n (see numerical values, Table S1). The increase in the polyoxypropylene chain length m from 1 to 3 abruptly decreases the values of specific heat capacity and (to some extent) the curve slope. A similar phenomenon have been observe previously [26] in the case of heat capacities of polyoxyethylene ethers (CnEm). It was
Fig. 1. Molar heat capacities of the polyoxy(iso)propylene glycol monoalkyl ethers as a function of temperature. - e C3P1, A e C4P1, : e C1P2, ; e C3P2, > e C4P2, + e C1P3, , e C3P3.
Fig. 2. Temperature dependence of specific heat capacity (Cp) of the polyoxy(iso) propylene glycol monoalkyl ethers.
interpreted as an effect of breaking of hydrogen bonds formed by the molecules of liquid containing both proton-donor (hydroxyl) and proton-acceptor (ethereal oxygen) groups. The number of such H-bonds per mass unit is the highest in CnP1 compounds. The possibility of their breaking (with rising temperature by 1 )
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Table 4 Coefficients of group contributions of heat capacity (equation (3)) for different model used.a Model
CH3-
SM
B0 B1 B0 B1 B0 B1 B0 B1
SOM1 SOM2 SOM3 a
O-CH3
C-CH3
-CH2-
27.926 6.5675 38.013 e 27.071 6.8197 32.552 5.8559
30.699 6.3694 33.990 6.4626
29.994 e
9.9417 6.8051
28.389 e
11.868 6.4397
-CH
-O-
-OH
11.608 e 2.0951 e 11.497 e e 5.2778
16.140 e 11.816 e 15.220 e 9.6047 e
e 23.611 e 26.910 e 22.723 e 21.486
Unites: B0/J mol1 K1, B1/J mol1 K2.
Compound
SM ARD
PD
ARD
PD
ARD
PD
ARD
PD
C3P1a C4P1a C1P2a C3P2b C4P2a C1P3a C3P3a C1P1C1a C1P2C1b Database compounds Test compounds Number of group Number of parameters
0.14 0.36 0.18 0.31 0.21 0.15 0.05 0.08 0.17 0.17 0.24 5 7
0.37 0.50 0.38 0.37 0.28 0.20 0.14 0.17 0.57 0.50 0.57
0.15 0.33 0.18 0.27 0.24 0.14 0.06 0.14 0.11 0.17 0.19 6 7
0.64 0.47 0.34 0.40 0.40 0.23 0.18 0.18 0.44 0.64 0.44
0.28 0.26 0.11 0.12 0.03 0.05 0.07 0.04 0.27 0.12 0.19 6 9
0.56 0.39 0.28 0.19 0.12 0.14 0.12 0.10 0.41 0.56 0.41
0.13 0.13 0.13 0.15 0.05 0.06 0.07 0.09 0.43 0.10 0.29 7 10
0.57 0.21 0.35 0.20 0.18 0.09 0.18 0.20 0.57 0.57 0.57
a
C-CH2-C
17.636 4.1831
Table 5 Average relative deviation (ARD/%, equation (4)) and maximum percent deviation (PD/%) of Cp,m estimation by different models. T ¼ (275.15e339.15) K.
b
O-CH2-C
18.581 3.8938
SOM1
SOM2
SOM3
Compounds forming the database of calculation. Compounds used as a test of estimation.
increases the liquid heat capacity. With the increase in the number of large oxypropylene groups (volume- and mass-wise), there occurs a peculiar ‘dilution’ of the number of hydrogen bonds per mass unit. It causes a decrease in the energy needed for their breaking. This probably results in an abrupt decrease in specific heat capacity of dowanols with increase in the number of oxypropylene groups in the compound. 3.2. Group contributions of molar heat capacity Based on extensive experimental database of molar heat capacity as a function of temperature, the values of group contributions Cp,m made by particular functional groups of dowanols can be calculated. The knowledge of these contributions makes it possible to predict the value of molar heat capacity of the compounds belonging to the same homological series that have not been investigated up to now. As we shown previously [21,29] the group contributions determined for a particular, narrow group of compounds of homological series more precisely predict the Cp,m values than the universal models based on the data for compounds of various properties. According to the additivity rule, the molar heat capacity of each of the compounds can be presented at the given temperature as follows:
Cp;m ¼
X
ni Cp;i
(2)
i
where n1 defines the number of particular groups, Cp,i - its group contribution. In the simple model (SM) five basic functional groups forming the molecules of the compound under investigation: CH3, CH2, CH, -O- and eOH were distinguish. The advantage of this model is its
simplicity and a low number of adjustable parameters describing the molar heat capacity. This model does not take into account the fact that the group heat capacity may depend on its neighborhood in the molecule. Therefore so-called second order models (SOM) that takes into account the vicinity of individual groups was also analyzed. In SOM models, independent groups: O-CH3 (methyl group connected with oxygen atom), C-CH3 (methyl group connected with carbon atom) and O-CH2-C and C-CH2-C groups can be isolated. The neighborhood of the remaining groups is the same in all the compounds. Three variants of the SOM model were analyzed. In the first one (SOM1), only the difference of vicinity for CH2 group were took into account. The heat capacity of CH3 group does not depend on its neighborhood. In SOM2 model, the dissimilarity of OCH3 and C-CH3 but equality of heat capacity of both differently located CH2 groups were assumed. In the last model tested, SOM3, the different heat capacity of each group forming the compound was considered. The contribution of each group was presented as a function of temperature according to analogous to equation (1) dependence: Cp,i ¼ B0þB1(T/100)þB2(T/100)2
(3)
The database of Cp,m ¼ f(T) values measured for the nine investigated compound was divided into two sets. The first one, comprising seven compounds (omitting C1P2C1 and C3P2) constituted the basis for calculating the group contributions of heat capacity. The second one included Cp,m data for C1P2C1 and C3P2 was used to verify the compatibility of the values estimated by particular models with experimental data. The values of coefficient Bi of equation (3) calculated for particular groups and models are listed in Table 4. Despite the fact that Cp,m ¼ f(T) for particular compounds was described with quadratic equation (Eq. (1), Table 2), the group contributions are only linearly dependent on temperature. The values of coefficients B2 have turned out to be insignificant. The correctness of estimating Cp,m values on the basis of group contributions for particular models was assessed on the basis of average relative deviation (ARD) between the calculated (estimated) and experimental values:
C calc C exp X p;m p;m 100 ARD=% ¼ exp ni i Cp;m
(4)
and maximal percentage deviation of the Cp,m value calculated from calc C exp Þ=C exp . experimental value: PD=% ¼ 100½ðCp;m p;m p;m The ARD and PD values calculated with the use of all the models for all particular compounds are listed in Table 5. This table contains also the average values of ARD of ‘database compounds’ and those used for testing - ‘test compounds’. Presented data do not provide explicit answer which of the model is the “best” one. The most developed model (SOM3), in
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Table 6 Estimated molar heat capacity at 298.15 K and coefficients of polynomial (1) for the temperature dependence of (Cp,m/J mol1 K1) of several liquid polyox(iso)propylene glycol monoalkyl ethers. Temperature range (275e340) K. Abbreviation
Chemical name
Cp,m/J mol1 K1
A0/J mol1 K1
A1/J mol-1 K2
a
C2P1 C2P2 C1P3 C2P3 C4P3 C2P1C2 C3P1C3 C2P2C2 C3P2C3 C1P3C1 C2P3C2 C3P3C3
propylene glycol ethyl ether dipropylene glycol ethyl ether tripropylene glycol methyl ether tripropylene glycol ethyl ether tripropylene glycol butyl ether propylene glycol diethyl ether propylene glycol dipropyl ether dipropylene glycol diethyl ether dipropylene glycol dipropyl ether tripropylene glycol dimethyl ether tripropylene glycol diethyl ether tripropylene glycol dipropyl ether
253.5 359.6 434.5 465.7 526.5 278.6 339.4 384.7 445.5 428.5 490.8 551.6 calc model P P ðCp;m Cp;m Þ 100
129.14 201.98 249.90 274.83 303.86 195.68 224.72 268.53 297.56 291.52 341.37 370.40
41.700 52.844 61.934 63.988 74.642 27.840 38.494 38.985 49.638 46.020 50.129 60.783
0.26 0.18 0.07 0.27 0.31 0.69 0.68 0.68 0.67 0.32 0.67 0.66
a Average relative deviation of Cp,m among different models “i”: ARD=% ¼ 275.15 to 339.15 K.
ni;j
j
i
j
which the highest number of different functional groups and adjustable B1 parameters is distinguished, well describes Cp,m ¼ f(T) for the database compounds. For the compound used for testing (C3P2 i C1P2C1), the correctness of estimation does not significantly differ from that of the remaining models. For any of the model, the value of average deviation of ARD does not exceed 0.5%, and that of the maximal deviation (PD) 0.7%. It seems that for the prediction of
calc Cp;m
ARD/%
j; i ¼ 4 (number of models), j ¼ 64 (number of different temperatures from
the molar heat capacity of compounds belonging to the homological series of CnPm and CnPmCn, it would be appropriate to use all the models analyzed and averaging the values obtained. Table 6 contains the predicted values of heat capacity at 298.15 K and the coefficients of equation (1) describing Cp,m ¼ f(T) within the temperature range 275e340 K for the so far no studied compounds. The calculations concern homologues with n and m chain length from one to three. The values of Ai coefficients given in the table are averaged values obtained with the use of all the models described. The mean deviation (ARD) between Cp,m values estimated on the basis of coefficient Ai and calculated from the group contributions of each model separately are also presented. Low ARD values for dowanols CnPm (on average about 0.2%) indicate that all additivity models provide mutually coherent results. In the case of diethers CnPmCn, where the ARD value amounts to about 0.6%, the deviation between the models used is higher. Therefore we believe that the values of Cp,m can be predicted on the basis of the data listed in Table 6 with an accuracy better than 1% for dowanols CnPm, while that of diethers CnPmCn below 1.5%.
3.3. Effect of hydrogen bonds on the heat capacity of dowanols
Fig. 3. Heat capacity of isomers of polyoxalkylene glycol mono- and diethers of different molar mass. Effect of hydrogen bonding. Solid line e hydrogen bonded compounds, dashed line e non-hydrogen bonded compounds. D e C1E1C1, e Pr2O, *e C1P1C1, B e C1E1C3, 2 e Bu2O, , e C1E2C1, V e C3E1C3, > e C2P2C1, K e C2P2C2, : e C2E1, e HxOH, + e C2P1, C e C4E1, 3 e OcOH, - e C2E2, ; e C6E1, A e C3P2, J e C4P2.
An intermolecular interaction via hydrogen bonds and consequently the molecule association influences the value of heat capacity of the compounds. The values of Cp of associating compounds are higher since an additional energy is required for breaking some hydrogen bonds. Quantitatively, the effect of such interactions on the value of Cp,m is difficult to make a precise assessment. The compounds of monoalkyl ethers of polyoxyalkylene glycols with general formula CnH2þ1[OR]mOH, investigated by us now and previously, are characterized by the possibility of forming both
Table 7 Molar heat capacities of several mono- and di-polyoxyalkylene ethers as a function of its molar mass (298.15 K). Compounds associated by H-bonds
M/g mol1
Compounds non-associated by H-bonds
Compound
Cp,m/J mol1 K1
Source
Compound
Cp,m/J mol1 K1
Source
C2P1 C3P2 C4P2 C2E1 C4E1 C6E1 C2E2 HxOH OcOH
253.5 388.1 418.6 211.1 273.0 332.6 301.7 242.5 304.0
estimated, this work experimental, this work experimental, this work ref. [26] ref. [26] estimated ref. [26] ref. [26] ref. [30] ref. [30]
C1P1C1 C2P2C1 C2P2C2 C1E1C1 C1E1C3 C3E1C3 C1E2C1 Pr2O Bu2O
216.5 354.2 384.7 191.5 248.9 309.0 279.6 221.5 279.0
experimental, this work estimated, this work estimated, this work ref. [31] ref. [32] ref. [32] ref. [33] ref. [34] ref. [35]
104.15 176.25 190.28 90.12 118.18 146.23 134.18 102.18 130.23
18
ralski et al. / Fluid Phase Equilibria 430 (2016) 13e18 P. Go
inter- and intramolecular hydrogen bonds [5e9]. The influence of such interactions on the values of heat capacity was suggested by us above (Fig. 2). To show the effect of hydrogen bonds on the molar heat capacities of the compounds under investigation, we compared the values of Cp,m of several pairs of the compounds formed by isomers: monoether þ diether. In the case of the later, a lack of hydroxyl group excludes the formation of both intra- and intermolecular hydrogen bonds. The comparison is shown in Fig. 3 containing the values of Cp,m of various compounds of CnPm and CnEm series and its diether equivalents, as a function of molar mass of these compounds. Numerical data of Cp,m and molar mass are presented in Table 7. The comparison also includes two aliphatic alcohols and corresponding ether isomers. As is seen in the case of the ethers that cannot form hydrogen bonds, the trend line of Cp,m ¼ f(M) is located below the line of the compounds forming such bonds. It is characteristic that the compounds of the series of CxPy, CxEy and even simple aliphatic alcohols are on one common line. In turn, on the second line are their ether isomers that do not form hydrogen bonds. The difference in the values of Cp,m for both types of compounds (the distance of both straight lines) amounts to (24e30) J$mol1$K1. Taking into account the fact that the average values of the enthalpy of alcohol association through hydrogen bonds amount [36] to 26.7 kJ mol1, this would correspond to breaking about 0.1% of hydrogen bonds with increasing temperature by 1 K.
4. Conclusions Experimental values of saturation heat capacities of seven dowanols have been reported in this paper. Assuming an additive character of the molar heat capacity (Cp,m), the contributions to the Cp,m values of particular functional groups forming the compounds of CnPm series were calculated. Average relative deviations (ARD) between the experimental values of Cp,m and those estimated on the basis of the group contributions do not exceed 0.4% for the compounds under investigation. The group contributions made it possible to predict the molar heat capacity of analogous mono- and di-ethers within the investigated temperature range with an average error of about 1%. For twelve compounds, whose molar heat capacities are unknown, the Cp,m values have been estimated. Pure mono-alkyl ethers of polyoxyalkylene glycols have the ability to form both inter- and intramolecular hydrogen bonds which affects the value of heat capacity. The effect of hydrogen bond association on Cp,m values was estimated to be about 27 ± 3 J mol1 K1. It corresponds to breaking of about 0.1% of hydrogen bonds with increasing temperature by 1 K.
Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.fluid.2016.09.002.
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Contents lists available at ScienceDirect
Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Heat capacity of dowanols within a temperature range of (275.15e339.15) K. Measurements and prediction ralski*, Mariola Tkaczyk, Katarzyna Łudzik Paweł Go dz, Pomorska Street 165, 90-236 Ło dz, Poland Department of Physical Chemistry, University of Ło
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 June 2016 Received in revised form 31 August 2016 Accepted 1 September 2016 Available online 2 September 2016
The saturation heat capacities of seven dowanols, i.e. polyoxy(iso)propylene glycol mono-alkyl ethers (CnPm) and two dimethyl ethers; C1P1C1 and C1P2C1 were measured by the calorimetric (DSC) method. The measurements were performed within the temperature range of (275.15e339.15) K by means of a Micro DSCIII (Setaram) calorimeter. Assuming that the molar heat capacity (Cp,m) shows an additive character, the contributions to the Cp,m values of particular functional groups forming the compounds of CnPm series were calculated. Two models differing in the manner of molecule division into functional groups, i.e. first- and second-order additivity group contribution approach were used. In the latter, not only the type of functional group but also its position and the closest neighborhood were taken into account. The average relative deviations (ARD) between the experimental values of Cp,m and those estimated on the basis of the group contributions for the compounds of the series under investigation were calculated. Furthermore, the effect of hydrogen bond association on Cp,m values was also estimated and discussed. © 2016 Elsevier B.V. All rights reserved.
Keywords: Dowanols Polyoxypropylene glycol monoalkyl ethers Heat capacity DSC Group additivity Hydrogen bonds
1. Introduction Solvosurfactants are compounds, whose properties are characteristic of typical surfactants and solvents. They include, among others, monoalkyl ether of polyoxyalkylene glycols with general formula: CnH2nþ1[OR]mOH, where n is the number of carbon atoms in the hydrophobic chain of “tail”, while m is the number of oxyalkylene groups in the hydrophobic chain of “head”. Depending on the molecular structure, these compounds can be used as: solvents, co-solvents, surfactants or co-surfactants [1e4]. Pure monoalkyl ethers of polyoxyalkylene glycols undergo association due to the formation of intermolecular hydrogen bonds [5e9]. Thanks to the presence of the ether oxygen atoms and the terminal hydroxyl group, they also form intramolecular hydrogen bonds. In aqueous solutions, these compounds can create clusters, ‘micelle-like’ structures or micelles [10e14]. Monoalkyl ethers of polyoxyethylene glycols [where R ¼ CH2CH2] and polyoxypropylene glycols or dowanols [where R ¼ CH(CH2)CH2] have found their use in industrial practice. Owing to their interesting properties they are used in many fields of chemical, cosmetic or pharmaceutical
* Corresponding author. ralski). E-mail address: [email protected] (P. Go http://dx.doi.org/10.1016/j.fluid.2016.09.002 0378-3812/© 2016 Elsevier B.V. All rights reserved.
industry. Because of their low toxicity, dowanols more and more frequently replace, in various products, the ether derivatives of polyoxyethylene glycols that show adverse effects on living organisms [3]. The physicochemical properties of compounds belonging to the derivatives of polyoxyethylene glycols have been frequently studied. In the case of dowanols, the number of such works is very limited. In practice, dowanols are most often used in the form of aqueous solutions, therefore researchers pay most attention to the mixtures of dowanols with water. Most commonly the phenomenon of limited miscibility, i.e. the range of the occurrence of miscibility gap (composition/temperature) was investigated [4,15e18]. Literature reports only a few experimental data concerning the physicochemical and especially thermochemical properties of pure dowanols or their mixtures. The growing interest in these compounds increases the demand for this type of data. Their analysis makes it possible to describe the intermolecular interactions in pure dowanols and their mixtures. One of the basic thermodynamic quantities used in chemical engineering is the molar heat capacity under constant pressure (Cp,m). The analysis of changes in this quantity caused by temperature or mixture composition provides valuable information about the structural changes of a liquid [10e12,19,20]. The molar heat capacity is often considered to be an additive quantity. The
ralski et al. / Fluid Phase Equilibria 430 (2016) 13e18 P. Go
14
determination of the contributions made by particular groups makes it possible to estimate the value of Cp,m of a compound, whose experimental data are absent in literature. The systematic studies of heat capacity carried out by us concern the homological series of various types of liquid compounds [21e25]. Our recent study concerns the Cp of polyoxyethylene glycol monoalkyl ethers (abbreviation: CnEm) [26]. In this work, several monoalkyl ethers of poly(iso)propylene glycols (CnPm) with general formula: CH3-(CH2)n-1-[O-CH(CH3)-CH2)]m-OH, namely CnP1 (n ¼ 3,4), CnP2 (n ¼ 1,3,4), CnP3 (n ¼ 1,3), and two dimethyl ethers: CH3-[O-CH(CH3)-CH2)]m-OCH3, m ¼ 1,2 are investigated. The saturation molar heat capacities of pure compounds were determined by the DSC method with the temperature range of (275.13e339.15) K. 2. Experimental 2.1. Chemicals The names, source, CAS number and purities of all chemicals are reported in Table 1. Before measurements, all the compounds were dried during several days with activated molecular sieves (type 4 A from Lancaster) and degassed in an ultrasonic stream. Water used as a Cp reference was firstly triple distilled and then degassed by heating under vacuum. The samples and measuring cells were filled and stored in a dry-box dried by phosphorus pentoxide. 2.2. Apparatus and procedure The saturation molar heat capacities were measured by means of a high sensitivity differential scanning calorimeter (Micro DSC III e Setaram) based on the Tian-Calvet principle. The so-called continuous with reference method (with water as a reference) was used. The values of specific heat capacity of water were taken from literature [27]. The details of the measuring procedure was described previously [21,26]. Due to the low vapor pressure of the liquids in the temperature range studied, the measured values of the saturation heat capacity can be considered as isobaric heat capacity (Csat ¼ Cp). The method used allows one to obtain the heat capacity data with the apparatus error being at a level of 0.15%. In reality, the total error is higher, and is mainly connected with the type and quantity of impurities present in the substances under investigation. Therefore we estimate that the total measurement error for the compounds with purity degree 0.99 amounts to 0.4%
and for the remaining ones 0.6% [26]. The sample mass was determined by a Sartorius RC 210D balance with an accuracy of 2 105 g. As literature reports no Cp data of the compound under investigation at 298.15 K, it was impossible to make any comparison with the results of other authors. Only possible comparison relates to the Cp data of C1P2C1 [28] in the temperature range (312.57e339.15) K. Agreement of Cp values for the given temperature range is about 0.4%. 3. Results and discussion 3.1. Specific and molar heat capacity At the temperature ranging from 275.13 to 339.15 K, the continuous method applied by us gives a set of 2560 values of Cp for each temperature scan. To obtain of reliable data, the experiments were repeated usually 2 or 3 times, both for heating and cooling sequences. Each time, the content of the measuring cell was replaced. Usually two sequences of heating and two sequences of cooling whose results did not differ more than 0.15% were chosen for averaging. A complete set of data (10240 points) were described with a common polynomial expressing the temperature dependence of molar heat capacity: Cp,m ¼ A0þ A1(T/100)þA2(T/100)2
(1)
The coefficients of Eq. (1) and mean deviations (dCp,m) of the experimental values from the calculated with polynomial are listed in Table 2. The Cp,m values with a 1.5 K step (and additionally at 298.15 K) averaged by above equation are listed in Table 3 and presented in Fig. 1. As is seen, for all the dowanols studied, the function Cp,m ¼ f(T) is almost rectilinear with a similar slope. The mutual location of the curves in the diagram results from the growing number of functional groups present in the molecule (growing molar mass). Considerably more information can be obtained from the interpretation of the temperature dependence of specific heat capacity, shown in Fig. 2. The numerical data of specific heat at (275.13e339.15) K for all the compounds are listed in Supplementary Materials - Table S1. As is seen in Fig. 2, the courses of function Cp ¼ f(T) are grouped at three levels, each of which represents a group of dowanols with identical length of the polyoxypropylene chain m. A change in the hydrocarbon chain length n in the limits 4 n 1 does not exert any considerable effect. There is only a small drop in the heat capacity with increasing chain
Table 1 Chemical names, source and purity of the polyoxy(iso)propylene glycol mono- and dialkyl ethers under investigation. Abbreviation Chemical name C3P1a C4P1 C1P2a C3P2a C4P2a C1P3a C3P3a C1P1C1 C1P2C1a a
propylene glycol monopropyl ether; 1-propoxypropan-2-ol propylene glycol monobutyl ether; 1-butoxypropan-2-ol dipropylene glycol monomethyl ether; 2-(2-methoxypropoxy) propan-1-ol
Supplier CAS number
Aldrich 1569-01-3 Aldrich 5131-66-8 Aldrich 34590-948 dipropylene glycol monopropyl ether; 1-(1-methyl-2-propoxyethoxy)propan-2-ol Aldrich 29911-274 dipropylene glycol monobutyl ether; 1-[(1-butoxy-2-propoanyl)oxy]propan-2-ol Aldrich 29911-282 tripropylene glycol monomethyl ether; 2-[1-(1-methoxypropan-2-yloxy)propan-2-yloxy] Aldrich 25498-49propan-1-ol 1 tripropylene glycol monopropyl ether; 1-[1-methyl-2-(1-methyl-2- propoxyethoxy)ethoxy]- Aldrich 96077-042-propanol 2 propylene glycol dimethyl ether; 1,2-dimethoxypropane Aldrich 7778-85-0 dipropylene glycol dimethyl ether; 1-methoxy-2-(2-methoxypropoxy)propane Aldrich 11110977-4
Mixture of isomers.
Molar mass/ g mol1
Mass fraction purity
118.17 132.20 148.20
0.99 0.99 0.99
176.25
0.985
190.28
0.99
206.28
0.975
234.33
0.995
104.15 162.23
0.99 0.991
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15
Table 2 Coefficients of the polynomial (equation (1)) and mean deviation from the regression line. Substance C3P1 C4P1 C1P2 C3P2 C4P2 C1P3 C3P3 C1P1C1 C1P2C1 P d ¼ n1i Cpcalc Cpexp ; i ¼ 10240.
A0/J mol1 K1
A1/J mol1 K2
A2/J mol1 K3
dCp,m/J mol1 K1
41.331 42.186 194.90 193.10 203.98 285.27 301.85 153.54 285.27
112.59 129.16 41.397 71.958 80.979 39.205 58.537 17.730 11.566
10.503 12.579 1.1425 2.2028 3.0211 3.6707 2.0343 1.1315 7.9887
0.28 0.20 0.23 0.23 0.28 0.29 0.23 0.29 0.12
i
Table 3 Saturated molar heat capacities (Cp,m/J mol1 K1) of examined liquid compounds for T ¼ (275.13e339.15) K and p ¼ 0.1 MPa.a T/K
C3P1
C4P1
C1P2
C3P2
C4P2
C1P3
C3P3
C1P1C1
C1P2C1
275.15 276.65 278.15 279.65 281.15 282.65 284.15 285.65 287.15 288.65 290.15 291.65 293.15 294.65 296.15 297.65 298.15 299.15 300.65 302.15 303.65 305.15 306.65 308.15 309.65 311.15 312.65 314.15 315.65 317.15 318.65 320.15 321.65 323.15 324.65 326.15 327.65 329.15 330.65 332.15 333.65 335.15 336.65 338.15 339.15
271.6 272.4 273.2 274.0 274.8 275.6 276.4 277.2 278.0 278.8 279.6 280.3 281.1 281.9 282.6 283.4 283.6 284.1 284.9 285.6 286.4 287.1 287.8 288.5 289.2 290.0 290.7 291.4 292.1 292.8 293.4 294.1 294.8 295.5 296.1 296.8 297.5 298.1 298.8 299.4 300.0 300.7 301.3 301.9 302.4
302.3 303.2 304.1 305.0 305.9 306.8 307.6 308.5 309.3 310.2 311.0 311.9 312.7 313.5 314.4 315.2 315.5 316.0 316.8 317.6 318.4 319.2 320.0 320.7 321.5 322.3 323.0 323.8 324.5 325.3 326.0 326.8 327.5 328.2 328.9 329.6 330.3 331.0 331.7 332.4 333.1 333.8 334.4 335.1 335.5
317.5 318.2 318.9 319.6 320.3 321.0 321.8 322.5 323.2 323.9 324.6 325.4 326.1 326.8 327.5 328.2 328.5 329.0 329.7 330.4 331.1 331.9 332.6 333.3 334.0 334.8 335.5 336.2 337.0 337.7 338.4 339.1 339.9 340.6 341.3 342.1 342.8 343.5 344.3 345.0 345.7 346.5 347.2 347.9 348.4
374.4 375.3 376.2 377.1 378.0 378.9 379.8 380.7 381.6 382.5 383.3 384.2 385.1 386.0 386.9 387.8 388.1 388.6 389.5 390.4 391.3 392.2 393.0 393.9 394.8 395.7 396.5 397.4 398.3 399.2 400.0 400.9 401.8 402.6 403.5 404.4 405.2 406.1 406.9 407.8 408.7 409.5 410.4 411.2 411.8
403.9 404.9 405.9 406.8 407.8 408.7 409.7 410.6 411.6 412.6 413.5 414.5 415.4 416.4 417.3 418.3 418.6 419.2 420.1 421.1 422.0 423.0 423.9 424.8 425.8 426.7 427.6 428.6 429.5 430.4 431.3 432.3 433.2 434.1 435.0 436.0 436.9 437.8 438.7 439.6 440.5 441.4 442.4 443.3 443.9
420.9 421.8 422.7 423.6 424.5 425.4 426.3 427.2 428.1 429.0 429.9 430.8 431.7 432.7 433.6 434.5 434.8 435.4 436.3 437.2 438.2 439.1 440.0 440.9 441.9 442.8 443.7 444.7 445.6 446.5 447.5 448.4 449.4 450.3 451.2 452.2 453.1 454.1 455.0 456.0 456.9 457.9 458.9 459.8 460.5
478.3 479.4 480.4 481.5 482.5 483.6 484.6 485.7 486.7 487.8 488.8 489.9 490.9 492.0 493.0 494.1 494.5 495.2 496.2 497.3 498.4 499.4 500.5 501.5 502.6 503.7 504.8 505.8 506.9 508.0 509.0 510.1 511.2 512.3 513.3 514.4 515.5 516.6 517.6 518.7 519.8 520.9 522.0 523.1 523.8
210.9 211.3 211.6 212.0 212.3 212.7 213.1 213.4 213.8 214.1 214.5 214.9 215.2 215.6 216.0 216.3 216.5 216.7 217.1 217.4 217.8 218.2 218.5 218.9 219.3 219.7 220.0 220.4 220.8 221.2 221.5 221.9 222.3 222.7 223.0 223.4 223.8 224.2 224.5 224.9 225.3 225.7 226.1 226.4 226.7
313.9 314.4 314.9 315.4 315.9 316.4 316.9 317.4 317.9 318.4 319.0 319.5 320.0 320.6 321.1 321.6 321.8 322.2 322.7 323.3 323.8 324.4 324.9 325.5 326.1 326.6 327.2 327.8 328.4 328.9 329.5 330.1 330.7 331.3 331.9 332.5 333.1 333.8 334.4 335.0 335.6 336.2 336.9 337.5 337.9
a Standard uncertainty u is u(T) ¼ 0.03 K. The combined uncertainty Uc is Uc(Cp,m) ¼ 0.004 Cp,m for C3P1, C4P1, C1P2, C4P2, C3P3, C1P1C1, C1P2C1 and Uc(Cp,m) ¼ 0.006 Cp,m for C3P2, C1P3 (0.95 level of confidence).
length n (see numerical values, Table S1). The increase in the polyoxypropylene chain length m from 1 to 3 abruptly decreases the values of specific heat capacity and (to some extent) the curve slope. A similar phenomenon have been observe previously [26] in the case of heat capacities of polyoxyethylene ethers (CnEm). It was
Fig. 1. Molar heat capacities of the polyoxy(iso)propylene glycol monoalkyl ethers as a function of temperature. - e C3P1, A e C4P1, : e C1P2, ; e C3P2, > e C4P2, + e C1P3, , e C3P3.
Fig. 2. Temperature dependence of specific heat capacity (Cp) of the polyoxy(iso) propylene glycol monoalkyl ethers.
interpreted as an effect of breaking of hydrogen bonds formed by the molecules of liquid containing both proton-donor (hydroxyl) and proton-acceptor (ethereal oxygen) groups. The number of such H-bonds per mass unit is the highest in CnP1 compounds. The possibility of their breaking (with rising temperature by 1 )
ralski et al. / Fluid Phase Equilibria 430 (2016) 13e18 P. Go
16
Table 4 Coefficients of group contributions of heat capacity (equation (3)) for different model used.a Model
CH3-
SM
B0 B1 B0 B1 B0 B1 B0 B1
SOM1 SOM2 SOM3 a
O-CH3
C-CH3
-CH2-
27.926 6.5675 38.013 e 27.071 6.8197 32.552 5.8559
30.699 6.3694 33.990 6.4626
29.994 e
9.9417 6.8051
28.389 e
11.868 6.4397
-CH
-O-
-OH
11.608 e 2.0951 e 11.497 e e 5.2778
16.140 e 11.816 e 15.220 e 9.6047 e
e 23.611 e 26.910 e 22.723 e 21.486
Unites: B0/J mol1 K1, B1/J mol1 K2.
Compound
SM ARD
PD
ARD
PD
ARD
PD
ARD
PD
C3P1a C4P1a C1P2a C3P2b C4P2a C1P3a C3P3a C1P1C1a C1P2C1b Database compounds Test compounds Number of group Number of parameters
0.14 0.36 0.18 0.31 0.21 0.15 0.05 0.08 0.17 0.17 0.24 5 7
0.37 0.50 0.38 0.37 0.28 0.20 0.14 0.17 0.57 0.50 0.57
0.15 0.33 0.18 0.27 0.24 0.14 0.06 0.14 0.11 0.17 0.19 6 7
0.64 0.47 0.34 0.40 0.40 0.23 0.18 0.18 0.44 0.64 0.44
0.28 0.26 0.11 0.12 0.03 0.05 0.07 0.04 0.27 0.12 0.19 6 9
0.56 0.39 0.28 0.19 0.12 0.14 0.12 0.10 0.41 0.56 0.41
0.13 0.13 0.13 0.15 0.05 0.06 0.07 0.09 0.43 0.10 0.29 7 10
0.57 0.21 0.35 0.20 0.18 0.09 0.18 0.20 0.57 0.57 0.57
a
C-CH2-C
17.636 4.1831
Table 5 Average relative deviation (ARD/%, equation (4)) and maximum percent deviation (PD/%) of Cp,m estimation by different models. T ¼ (275.15e339.15) K.
b
O-CH2-C
18.581 3.8938
SOM1
SOM2
SOM3
Compounds forming the database of calculation. Compounds used as a test of estimation.
increases the liquid heat capacity. With the increase in the number of large oxypropylene groups (volume- and mass-wise), there occurs a peculiar ‘dilution’ of the number of hydrogen bonds per mass unit. It causes a decrease in the energy needed for their breaking. This probably results in an abrupt decrease in specific heat capacity of dowanols with increase in the number of oxypropylene groups in the compound. 3.2. Group contributions of molar heat capacity Based on extensive experimental database of molar heat capacity as a function of temperature, the values of group contributions Cp,m made by particular functional groups of dowanols can be calculated. The knowledge of these contributions makes it possible to predict the value of molar heat capacity of the compounds belonging to the same homological series that have not been investigated up to now. As we shown previously [21,29] the group contributions determined for a particular, narrow group of compounds of homological series more precisely predict the Cp,m values than the universal models based on the data for compounds of various properties. According to the additivity rule, the molar heat capacity of each of the compounds can be presented at the given temperature as follows:
Cp;m ¼
X
ni Cp;i
(2)
i
where n1 defines the number of particular groups, Cp,i - its group contribution. In the simple model (SM) five basic functional groups forming the molecules of the compound under investigation: CH3, CH2, CH, -O- and eOH were distinguish. The advantage of this model is its
simplicity and a low number of adjustable parameters describing the molar heat capacity. This model does not take into account the fact that the group heat capacity may depend on its neighborhood in the molecule. Therefore so-called second order models (SOM) that takes into account the vicinity of individual groups was also analyzed. In SOM models, independent groups: O-CH3 (methyl group connected with oxygen atom), C-CH3 (methyl group connected with carbon atom) and O-CH2-C and C-CH2-C groups can be isolated. The neighborhood of the remaining groups is the same in all the compounds. Three variants of the SOM model were analyzed. In the first one (SOM1), only the difference of vicinity for CH2 group were took into account. The heat capacity of CH3 group does not depend on its neighborhood. In SOM2 model, the dissimilarity of OCH3 and C-CH3 but equality of heat capacity of both differently located CH2 groups were assumed. In the last model tested, SOM3, the different heat capacity of each group forming the compound was considered. The contribution of each group was presented as a function of temperature according to analogous to equation (1) dependence: Cp,i ¼ B0þB1(T/100)þB2(T/100)2
(3)
The database of Cp,m ¼ f(T) values measured for the nine investigated compound was divided into two sets. The first one, comprising seven compounds (omitting C1P2C1 and C3P2) constituted the basis for calculating the group contributions of heat capacity. The second one included Cp,m data for C1P2C1 and C3P2 was used to verify the compatibility of the values estimated by particular models with experimental data. The values of coefficient Bi of equation (3) calculated for particular groups and models are listed in Table 4. Despite the fact that Cp,m ¼ f(T) for particular compounds was described with quadratic equation (Eq. (1), Table 2), the group contributions are only linearly dependent on temperature. The values of coefficients B2 have turned out to be insignificant. The correctness of estimating Cp,m values on the basis of group contributions for particular models was assessed on the basis of average relative deviation (ARD) between the calculated (estimated) and experimental values:
C calc C exp X p;m p;m 100 ARD=% ¼ exp ni i Cp;m
(4)
and maximal percentage deviation of the Cp,m value calculated from calc C exp Þ=C exp . experimental value: PD=% ¼ 100½ðCp;m p;m p;m The ARD and PD values calculated with the use of all the models for all particular compounds are listed in Table 5. This table contains also the average values of ARD of ‘database compounds’ and those used for testing - ‘test compounds’. Presented data do not provide explicit answer which of the model is the “best” one. The most developed model (SOM3), in
ralski et al. / Fluid Phase Equilibria 430 (2016) 13e18 P. Go
17
Table 6 Estimated molar heat capacity at 298.15 K and coefficients of polynomial (1) for the temperature dependence of (Cp,m/J mol1 K1) of several liquid polyox(iso)propylene glycol monoalkyl ethers. Temperature range (275e340) K. Abbreviation
Chemical name
Cp,m/J mol1 K1
A0/J mol1 K1
A1/J mol-1 K2
a
C2P1 C2P2 C1P3 C2P3 C4P3 C2P1C2 C3P1C3 C2P2C2 C3P2C3 C1P3C1 C2P3C2 C3P3C3
propylene glycol ethyl ether dipropylene glycol ethyl ether tripropylene glycol methyl ether tripropylene glycol ethyl ether tripropylene glycol butyl ether propylene glycol diethyl ether propylene glycol dipropyl ether dipropylene glycol diethyl ether dipropylene glycol dipropyl ether tripropylene glycol dimethyl ether tripropylene glycol diethyl ether tripropylene glycol dipropyl ether
253.5 359.6 434.5 465.7 526.5 278.6 339.4 384.7 445.5 428.5 490.8 551.6 calc model P P ðCp;m Cp;m Þ 100
129.14 201.98 249.90 274.83 303.86 195.68 224.72 268.53 297.56 291.52 341.37 370.40
41.700 52.844 61.934 63.988 74.642 27.840 38.494 38.985 49.638 46.020 50.129 60.783
0.26 0.18 0.07 0.27 0.31 0.69 0.68 0.68 0.67 0.32 0.67 0.66
a Average relative deviation of Cp,m among different models “i”: ARD=% ¼ 275.15 to 339.15 K.
ni;j
j
i
j
which the highest number of different functional groups and adjustable B1 parameters is distinguished, well describes Cp,m ¼ f(T) for the database compounds. For the compound used for testing (C3P2 i C1P2C1), the correctness of estimation does not significantly differ from that of the remaining models. For any of the model, the value of average deviation of ARD does not exceed 0.5%, and that of the maximal deviation (PD) 0.7%. It seems that for the prediction of
calc Cp;m
ARD/%
j; i ¼ 4 (number of models), j ¼ 64 (number of different temperatures from
the molar heat capacity of compounds belonging to the homological series of CnPm and CnPmCn, it would be appropriate to use all the models analyzed and averaging the values obtained. Table 6 contains the predicted values of heat capacity at 298.15 K and the coefficients of equation (1) describing Cp,m ¼ f(T) within the temperature range 275e340 K for the so far no studied compounds. The calculations concern homologues with n and m chain length from one to three. The values of Ai coefficients given in the table are averaged values obtained with the use of all the models described. The mean deviation (ARD) between Cp,m values estimated on the basis of coefficient Ai and calculated from the group contributions of each model separately are also presented. Low ARD values for dowanols CnPm (on average about 0.2%) indicate that all additivity models provide mutually coherent results. In the case of diethers CnPmCn, where the ARD value amounts to about 0.6%, the deviation between the models used is higher. Therefore we believe that the values of Cp,m can be predicted on the basis of the data listed in Table 6 with an accuracy better than 1% for dowanols CnPm, while that of diethers CnPmCn below 1.5%.
3.3. Effect of hydrogen bonds on the heat capacity of dowanols
Fig. 3. Heat capacity of isomers of polyoxalkylene glycol mono- and diethers of different molar mass. Effect of hydrogen bonding. Solid line e hydrogen bonded compounds, dashed line e non-hydrogen bonded compounds. D e C1E1C1, e Pr2O, *e C1P1C1, B e C1E1C3, 2 e Bu2O, , e C1E2C1, V e C3E1C3, > e C2P2C1, K e C2P2C2, : e C2E1, e HxOH, + e C2P1, C e C4E1, 3 e OcOH, - e C2E2, ; e C6E1, A e C3P2, J e C4P2.
An intermolecular interaction via hydrogen bonds and consequently the molecule association influences the value of heat capacity of the compounds. The values of Cp of associating compounds are higher since an additional energy is required for breaking some hydrogen bonds. Quantitatively, the effect of such interactions on the value of Cp,m is difficult to make a precise assessment. The compounds of monoalkyl ethers of polyoxyalkylene glycols with general formula CnH2þ1[OR]mOH, investigated by us now and previously, are characterized by the possibility of forming both
Table 7 Molar heat capacities of several mono- and di-polyoxyalkylene ethers as a function of its molar mass (298.15 K). Compounds associated by H-bonds
M/g mol1
Compounds non-associated by H-bonds
Compound
Cp,m/J mol1 K1
Source
Compound
Cp,m/J mol1 K1
Source
C2P1 C3P2 C4P2 C2E1 C4E1 C6E1 C2E2 HxOH OcOH
253.5 388.1 418.6 211.1 273.0 332.6 301.7 242.5 304.0
estimated, this work experimental, this work experimental, this work ref. [26] ref. [26] estimated ref. [26] ref. [26] ref. [30] ref. [30]
C1P1C1 C2P2C1 C2P2C2 C1E1C1 C1E1C3 C3E1C3 C1E2C1 Pr2O Bu2O
216.5 354.2 384.7 191.5 248.9 309.0 279.6 221.5 279.0
experimental, this work estimated, this work estimated, this work ref. [31] ref. [32] ref. [32] ref. [33] ref. [34] ref. [35]
104.15 176.25 190.28 90.12 118.18 146.23 134.18 102.18 130.23
18
ralski et al. / Fluid Phase Equilibria 430 (2016) 13e18 P. Go
inter- and intramolecular hydrogen bonds [5e9]. The influence of such interactions on the values of heat capacity was suggested by us above (Fig. 2). To show the effect of hydrogen bonds on the molar heat capacities of the compounds under investigation, we compared the values of Cp,m of several pairs of the compounds formed by isomers: monoether þ diether. In the case of the later, a lack of hydroxyl group excludes the formation of both intra- and intermolecular hydrogen bonds. The comparison is shown in Fig. 3 containing the values of Cp,m of various compounds of CnPm and CnEm series and its diether equivalents, as a function of molar mass of these compounds. Numerical data of Cp,m and molar mass are presented in Table 7. The comparison also includes two aliphatic alcohols and corresponding ether isomers. As is seen in the case of the ethers that cannot form hydrogen bonds, the trend line of Cp,m ¼ f(M) is located below the line of the compounds forming such bonds. It is characteristic that the compounds of the series of CxPy, CxEy and even simple aliphatic alcohols are on one common line. In turn, on the second line are their ether isomers that do not form hydrogen bonds. The difference in the values of Cp,m for both types of compounds (the distance of both straight lines) amounts to (24e30) J$mol1$K1. Taking into account the fact that the average values of the enthalpy of alcohol association through hydrogen bonds amount [36] to 26.7 kJ mol1, this would correspond to breaking about 0.1% of hydrogen bonds with increasing temperature by 1 K.
4. Conclusions Experimental values of saturation heat capacities of seven dowanols have been reported in this paper. Assuming an additive character of the molar heat capacity (Cp,m), the contributions to the Cp,m values of particular functional groups forming the compounds of CnPm series were calculated. Average relative deviations (ARD) between the experimental values of Cp,m and those estimated on the basis of the group contributions do not exceed 0.4% for the compounds under investigation. The group contributions made it possible to predict the molar heat capacity of analogous mono- and di-ethers within the investigated temperature range with an average error of about 1%. For twelve compounds, whose molar heat capacities are unknown, the Cp,m values have been estimated. Pure mono-alkyl ethers of polyoxyalkylene glycols have the ability to form both inter- and intramolecular hydrogen bonds which affects the value of heat capacity. The effect of hydrogen bond association on Cp,m values was estimated to be about 27 ± 3 J mol1 K1. It corresponds to breaking of about 0.1% of hydrogen bonds with increasing temperature by 1 K.
Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.fluid.2016.09.002.
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