Effect of temperature and composition on the volumetric, acoustic and thermal properties of N,N-dimethylformamide + propan-1-ol mixture

Journal of Molecular Liquids 290 (2019) 111124

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Effect of temperature and composition on the volumetric, acoustic and thermal properties of N,N-dimethylformamide + propan-1-ol mixture Magdalena Tyczyńska ⁎, Małgorzata Jóźwiak, Marlena Komudzińska, Tomasz Majak Department of Physical Chemistry, Faculty of Chemistry, University of Lodz, Pomorska 165, 90-236 Lodz, Poland

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 12 February 2019 Received in revised form 27 May 2019 Accepted 3 June 2019 Available online 08 June 2019

The density (ρ), sound velocity (u) and specific heat capacity (cp) of a binary mixture of N,N-dimethylformamide and 1-propanol were measured over its entire composition range. The values of the obtained results were used to

Keywords: N,N-dimethylformamide + 1-propanol mixture Density Sound velocity Isobaric molar heat capacity Isochoric molar heat capacity

was based on consideration us in an aspect of intermolecular interactions resulting changes in the mixture structure. © 2019 Elsevier B.V. All rights reserved.

calculate the values of excess molar volume (V Em ), molar expansion volume coefficient (Ep,m), molar isentropic (KS,m) and isothermal (KT,m) compressibility, isobaric (Cp,m) and isochoric (CV,m) molar heat capacity as well as their excess functions (EEp;m ; K ES;m ; K ET;m ; C Ep;m ; C EV;m ; uE ). The analysis of changes in the physicochemical quantities

1. Introduction It is believed that the thermodynamic properties of mixed solvents are a good source of information about the interactions between solute molecules and solvent. In recent years, also the measurements of speed of sound have been appropriately used in understanding molecular nature of the systems as well as physicochemical properties [1–5]. A nonlinear course of the dependence of ultrasonic velocity, compressibility, and other thermodynamical parameters with an increasing content of one component of solution is attributed to the difference in size of molecules and the strength of interactions [4]. Furthermore, these properties allow one to indirectly draw information about the system structure. Amides constitute an interesting group of compounds which can play a role as model compounds of peptides to obtain information about protein systems. Good miscibility with various liquids such as water, alcohols, esters, ketones or even aromatic hydrocarbons guarantees the potential numerous industrial applications of N,Ndimethylformamide (DMF). DMF is used in the production of synthetic fibers, leathers, films and coatings [6]. The ability to form hydrogen bonds by DMF molecules makes it useful to study the interactions of molecules in biological systems, serving as a model substance for proteins [7]. Alcohol as a component of mixed solvent has been selected due to its wide use in organic synthesis as well as in the industry. DMF and

⁎ Corresponding author. E-mail address: [email protected] (M. Tyczyńska).

https://doi.org/10.1016/j.molliq.2019.111124 0167-7322/© 2019 Elsevier B.V. All rights reserved.

alkanols like 1-propanol (PrOH) are interesting liquid systems in the aspect of studying molecular interactions. The increasing use of monoalkanols like PrOH and their mixtures in pharmaceutical and cosmetics branches of industry [8,9] has greatly stimulated the need for extensive information about their properties. It is well known that amides interact with alcohols and form hydrogen bonded interactions or even more hetero-associates. Due to that fact amides and alcohols are the most common solvents used in industrial processes. Available data has shown that some volumetric properties of DMF and selected alkanols mixtures are presented and analyzed [10–18]. Available works have been mainly focused on short-chain aliphatic alcohols such as methanol [14–17], ethanol [10–12,14,16,17] and 1propanol [10,13,15–19], analyzing the changes taking place in the solution caused by the chain length of the aliphatic molecule. In the present paper we demonstrate the functions derived from density, the speed of sound and molar heat capacity of N,Ndimethylformamide + 1-propanol (DMF + PrOH) system at six temperatures. Moreover we determined thermal properties of the system by taking the attempts of measuring the isobaric specific heat capacity (cp). We calculated selected physicochemical quantities e.g. excess molar volume (V Em ), molar volume expansion (Ep,m), molar isentropic (KS,m) and isothermal (KT,m) compressibility, isobaric (Cp,m) and isochoric (CV,m) molar heat capacity as well as their excess values (EEp;m ; K ES;m ; K ET;m ; C Ep;m ; C EV;m ; uE ). A change in the structure of the mixed solvent causes changes in the course of the function depending on the composition and temperature. In the literature, only a few works on DMF + PrOH mixtures can be found [10,13,15–19] but they are focused around density

2

M. Tyczyńska et al. / Journal of Molecular Liquids 290 (2019) 111124

measurements and what is more the results turned out to be incoherent. However, there are no data presenting isobaric (Cp,m) and isochoric (CV,m) molar heat capacities of such system and what is the most important, in the available data there is no combination of so many physicochemical functions in a temperature range (293.15–318.15) K. Furthermore, the paper presents worth attention results in this field as evidenced by coherent results obtained by different experimental methods. 2. Experimental 2.1. Materials 1-propanol (PrOH) (Sigma-Aldrich, w = 0.995) was used as received. DMF (Aldrich, w = 0.99) was purified and dried according to the procedures described in the literature [19,20]. DMF was not used to prepare solutions immediately just after purchase. Due to the fact that this compound may decompose after some time we subjected it to distillation as a result of which we received a purity of 99.8%. DMF after purification was used immediately to prepare samples. DMF and PrOH were stored in dark-bottle. The purity of chemicals is presented in Table 1. 2.2. Measurements 2.2.1. Density and sound velocity The density and speed of sound of (DMF + PrOH) mixture within its whole concentration range were measured at temperatures T = (293.15, 298.15, 303.15, 308.15, 313.15, 318.15) K with the use of a DSA 5000 analyzer from Anton Paar. This device combines two miniaturized inline cells to simultaneously measure the density and sound speed of a liquid sample at ambient pressure. The density is measured using a cell with oscillatory U-tube, whose repeatability of density was ±1·10−3 kg·m−3 as declared by the manufacturer. Considering the formula for the combined standard uncertainty for the average of density measurements proposed by Fortin et al. [21], the estimated uncertainty was ±2·10−2 kg·m−3. The sound speed cell has a circular cylindrical cavity of 8 mm diameter and 5 mm thickness that is sandwiched between the transmitter and receiver. The speed of sound is determined by measuring the time-of-flight of signals between the transmitter and receiver [21]. The repeatability declared by the manufacturer of the speed of sound measurements as well as their estimated uncertainty [21] were ±0.1 m·s−1 and ±0.5 m·s−1, respectively. Both measurement cells are housed in a thermostated block, the temperature of which is controlled with a combination of thermoelectric Peltier elements and an integrated Pt-100 resistance thermometer. The manufacturer gives an operating temperature range of 273 K to 343 K. The temperature measured with an integrated Pt-100 thermometer gives the repeatability equal to ±0.001 K. In the densimeter and sound speed cells, an adjustment procedure was performed with ultra-pure Type 1 (MilliporeSigma™ Synergy™ Ultrapure Water Purification System), degassed water and air at 293.15 K and at 0,1002 MPa pressure. The value of water density and speed of sound amounting 998.203 kg·m−3 and 1482.66 m·s−1 at a temperature of 293.15 K is

similar to that reported in the literature [22]. The solutions of (DMF + PrOH) were prepared by weight using an analytical balance (RADWAG XA 60/220, Poland) with the precision ±1·10−5 g. In order to obtain a solution with a specific composition, suitable components were collected using a syringe. The solvents were degassed in an ultrasonic bath prior to use. Particular attention has been paid to degassing and the precise weighing of each sample. After the last digit on the analytical balance had been determined the sample was weighed until it gained three times the same value. For this purpose, a drying gel (Silica gel Blue, Merck) was placed inside the balance to maintain low humidity during weighing. After that samples were taken to the densimeter immediately. To make a measurement, liquid sample with defined mole fraction of DMF was injected into the instrument using a syringe. Careful cleaning of the sound speed cell with suitable solvents was found critical to avoid contamination and to ensure this level of performance. For the same reason, fresh samples of test liquids were injected for each temperature scan. Temperature scans were programmed from 45 to 20 °C in decrements of 5 °C. The data of solution densities and speeds of sounds obtained as a function of DMF mole fraction, xDMF and temperature, T are presented in Tables S1 and S2 (Supplementary material). The mentioned data obtained by us for pure DMF and PrOH are compared with literature data in Table 2. 2.2.2. Heat capacity The values of isobaric specific heat capacity cp of N,Ndimethylformamide with water mixture were measured by means of a high sensitivity differential scanning calorimeter (Micro DSC III, Setaram - France). The detailed description of the measurement procedure has been described by Góralski et al. [60]. Measurements were carried out in the temperature range 288.15–323.15 K with the scanning rate of 0.35 K/min. Continuous with reference method with n-heptane as a reference substance of known capacity [61] was used. For the measurements a batch-type cell of about 1 cm3 was applied. The uncertainty in the cp values can be estimated to be smaller than 0.2% with the error of the absolute temperature determination 0.05 K. The values of specific heat capacity as a function of DMF molar fraction are presented in Table S3 (Supplementary material). The data of calculated molar heat capacity obtained by us for pure DMF and PrOH are compared with literature data in Table 3. 3. Results and discussion 3.1. Densimetry As one can notice (Tables S1 and S2), the addition of DMF molecules to PrOH results in an increase in density and sound velocity of the mixture. The values of both of them decrease systematically with increasing temperature over the whole range of mixture compositions. The molar volume values of the (DMF + PrOH) mixture were calculated from the experimental values of mixture density according to the Eq. (1): Vm ¼

x1 m1 þx2 m2

ð1Þ

ρ

Table 1 Materials. Chemical name PrOH DMF a b c

Molecular mass g·mol−1 62.08760 73.09380

CAS number

Source

16504-75-9 Sigma-Aldrich 68-12-2 Aldrich

Declared by the supplier. After distillation the 1NMR was the analysis method of purity. Determined by Karl Fisher method.

Mole fraction purity N0.995a 0.998a

Purification method

Purification and distillation [19,20]

Mole fraction purity after purification

0.998b

Mass fraction of water 7·10−4c 2·10−4c

M. Tyczyńska et al. / Journal of Molecular Liquids 290 (2019) 111124

3

Table 2 Densities (ρ) and sound velocities (u) of PrOH and DMF at pressure p = 0.1002 ± 0.005 MPa.a T/K

PrOH

DMF

ρ(g ⋅ cm−3)

u (m·s−1)

ρ(g ⋅ cm−3)

u (m·s−1)

Exp.

Lit.

Exp.

Lit.

Exp.

Lit.

Exp.

Lit.

293.15

0.80362

0.80362 [15,23] 0.80387 [24,25] 0.80392 [26] 0.80363 [27] 0.800497 [28]

1223.8

1223.4 [25] 1223.9 [26] 1223.17 [38] 1227.3 [41]

0.94869

1477.2

298.15

0.79962

1206.6

1206.6 [16] 1206.3 [30] 1206.47 [38] 1207.03 [31] 1205.4 [29] 1205.64 [33] 1208.39 [37] 1209.9 [41]

0.94392

1458.0

1469.5 [54] 1457.69 [50] 1458.5 [55] 1457.49 [56] 1458 [57] 1457.13 [48]

303.15

0.79558

1189.5

1189.86 [38] 1189.03 [37] 1192.5 [41] 1195.2 [42]

0.93916

0.939201 [44] 0.939206 [45] 0.939196 [46] 0.939047 [50] 0.939073 [47] 0.939042 [49]

1438.7

1438.23 [50] 1440.2 [55] 1476.2 [58]

308.15

0.79149

1172.5

1172.3 [25] 1172.6 [26] 1172.04 [37] 1155.1 [25] 1175.1 [41]

0.93441

0.934425 [44] 0.934430 [45] 0.934420 [46] 0.934721 [50] 0.934298 [51] 0.934255 [49]

1419.2

1421.95 [50] 1420.8 [55] 1426.03 [59] 1464.6 [58]

313.15

0.78736

1155.6

1156.8 [30] 1155.15 [43] 1157.7 [33]

0.92965

0.929478 [50] 0.929458 [49]

1399.6

1395.69 [50]

318.15

0.78318

0.79956 [29,30] 0.80013 [31] 0.79941 [23] 0.79949 [32] 0.79947 [33] 0.79975 [34] 0.79948 [35] 0.79967 [36] 0.79962 [27] 0.799709 [37] 0.799666 [38] 0.79527 [23] 0.79689 [28] 0.795182 [24] 0.79558 [27] 0.795698 [37] 0.79546 [32] 0.79601 [39] 0.79179 [25] 0.79184 [26] 0.795649 [38] 0.78776 [34] 0.78744 [36] 0.79149 [27] 0.791627 [37] 0.78662 [23] 0.78907 [28] 0.78763 [40] 0.78737 [27] 0.787516 [37] 0.78728 [32] 0.78322 [27] 0.78336 [37]

0.948742 [44] 0.948747 [45] 0.948737 [46] 0.948611 [47] 0.948546 [48] 0.948584 [49] 0.943976 [44] 0.943981 [45] 0.943971 [46] 0.944290 [50] 0.943869 [51] 0.943817 [49] 0.944603 [57]

1138.8

1138.35 [37] 1140.3 [41]

0.92490

0.924683 [51] 0.92549 [52] 0.92404 [53]

1379.8

1453.5 [58]

a Standard uncertainties u are u(T) = 0.01 K, u(p) = 0.005 MPa, and the combined expanded uncertainty Uc are Uc(u) = 0.5 m·s−1 and Uc(ρ) = 2·10−5 g·cm−3 with 0.95 level of confidence (k ≈ 2).

where: ρ is the density of (DMF + PrOH) mixture, x1, x2 and M1, M2 are the mole fractions and molar masses of the mixture components, respectively, i.e. PrOH (1), DMF (2). The excess properties were calculated using the following expression

The values of excess volume of (DMF + PrOH) mixture were fitted to the polynomial of Redlich–Kister type: V Em ¼ x1 x2

n X

A j ð1−2x1 Þ j

ð4Þ

j¼0

Z E ¼ Z−Z id

ð2Þ

where ZE is the excess quantity of the property Z (Vm, Ep,m, KS,m, KT,m, Cp, id m, CV,m, u) and Z is the corresponding ideal value [66]. Using the data of Vm the values of excess molar volume, V Em , of the mixture within the whole concentration range of mixed solvent at temperature range of (293.15 to 318.15) K were calculated according to Eq. (3):
   V Em ¼ V m −V id m ¼ V m − x1 V 1 þx2 V 2

ð3Þ

where: Vm is the molar volume of (DMF + PrOH) mixture, V id m is the volume of ideal mixture, V 1 ; V 2 are the molar volume of pure compounds, i.e. PrOH (1), DMF (2). Excess molar volume as a function of molar fraction of DMF is presented in Fig. 1.

n X V Em ¼ A j ð1−2x1 Þ j x1 x2 j¼0

ð5Þ

where Aj is the polynomial coefficient calculated by the least-squares method using Eq. (5). The excess values were estimated to explain the intermolecular interactions occurring in the mixtures. Fig. 1 shows a small negative value of the molar excess volume over the range of mixture. Similar research has already been carried out but the results turned out to be incoherent [13,15–18]. One can clearly see that the V Em values for the system (DMF + PrOH) are negative over the whole composition and temperature range in all cases. The authors of above mentioned papers were focused mainly on one selected temperature. Nevertheless those values differ between each other. Zielkiewicz [18] presents the results of V Em that are very similar to the data obtained by us, although the investigations were performed only at 313.15 K.

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M. Tyczyńska et al. / Journal of Molecular Liquids 290 (2019) 111124

Table 3 Isobaric molar heat capacities (Cp, m) for PrOH and DMF at pressure p = 0.1002 ± 0.005 MPa. T/K

Cp,m/(J·mol−1·K−1) PrOH This paper

DMF Literature a

This paper

Literature 147.16 [73] 147.3 [61]a 147.5 [61]b 147.6c 148.0 [61]b 148.1 [61]a 148.15c 148.16 [64] 148.2 [64] 148.54 [55] 150.16 [63] 148.5 [61]b 148.7c 148.9 [61]a 150.41 [55] 151.3 [65] 153.32 [63] 149.1 [61]b 149.8 [61]a 152.65 [55] 149.7 [61]b 150.7 [61]a 152.9 [65] 150.4 [61]b 151.5 [61]a

293.15

141.4

141.4 [61] 141.5 [61]b 142.3 [62]

147.5

298.15

144.2

144.1 [61]a 144.26 [61]b 144.9 [62]

148.1

303.15

147.1

146.9 [61]a 147.2 [61]b 148.2 [62]

148.7

308.15

150.1

149.4

313.15

153.2

318.15

156.4

149.9 [61]a 150.2 [61]b 151.0 [62] 152.9 [61]a 153.3 [61]b 153.7 [62] 156.1 [61]a 156.6 [61]b 157.1 [62]

a b c

150.3

151.3

Data calculated from recommended values of parameters of quasi-polynomial equation. Data calculated from recommended values of parameters of cubic spline polynomials or parameters of regression polynomials. Data calculated using the experimental values of specific heat capacities from [62].

Fig. 1. Excess molar volume (V Em ) of (DMF + PrOH) mixtures: ■, T = 293.15 K; ●, T = 298.15 K; ▲, T = 303.15 K; ▼, T = 308.15 K; ♦, T = 313.15 K; ◄, T = 318.15 K. Solid lines are calculated using Redlich-Kister Eq. (4).

V Em values decrease with increasing DMF content in mixtures and reach the minimum value for xDMF = 0.5 at all measuring temperatures. The reduction in the excess molar volume with the increase in DMF content is probably related to interstitial accommodation of DMF molecules into the vacant spaces in the structural network of PrOH conditioned by existing of H-bonds. It is assumed that there are no hydrogen bonds –N– H⋯O=C in the structure of pure DMF. However, DMF is somewhat associated due to the dipole-dipole effects. Moreover, Jorgensen and Swenson [67] reveal that a significant order is observed in its liquid structure. According to the results obtained by scientists, this is because the amide particles form weak intermolecular interactions of formyl oxygen with hydrogen atoms of formyl groups –HCO⋯HCO– and hydrogen atoms of the methyl group –C–H⋯OCH–. Analyzes accomplished with various methods [68–70] confirm this tendency of interactions and demonstrate that DMF molecules can form a chain structure or a network of chain structures in which intermolecular interactions are easily broken [71]. On the other hand in PrOH rich region, the molecules of alcohol exist largely in associated form through H-bonding. Mixing DMF and PrOH will therefore cause volume changes observed in the mixtures. In this area of mixed solvent, DMF molecules are thought to be predominantly disassociated. Moreover, the –N–C=O group present in the DMF molecule implies the delocalization of the double-bond binding, which leads to the formation of resonance structures [72]. Consequently, there is a negative partial electron charge on the oxygen atom, therefore this atom is the best acceptor of hydrogen bonds. In accordance with the above mentioned information and despite the fact that there exists a certain extent steric hindrance because of –CH3 group attached to –N– atom of DMF, there probably still occurs a possibility to form some amount of hydrogen bonds between DMF and PrOH molecules. Due to the fact that DMF and monoalkanols have proton donor and proton acceptor groups leading to self and mutual association [73] this could be the reason for the effect of molar volume contraction. The negative V Em

M. Tyczyńska et al. / Journal of Molecular Liquids 290 (2019) 111124

5

values depict the existence of interactions created between the –OH groups and carbonyl oxygen of DMF (–C=O). In the opposite situation, however, when the amount of DMF starts to prevail in the solution (DMF rich region), disassociated alcohol molecules and much weaker dipolar interactions found in the structure of DMF (as compared to PrOH) probably contribute to the reduction in volume contraction with increasing DMF content in the mixture. In the area where DMF is dominant component, the loosening of the mixture structure becomes the reason of increase in the volume of the mixture or precisely, it causes the decrease of the negative values of V Em in DMF rich region. Such conclusions are supported by literature reports [74] on excess enthalpies, HE, showing positive values for (DMF + PrOH) mixture. The decrease in V Em values could be influenced by the disassociation of self-associated alkanols by DMF in PrOH rich region. The temperature impact on V Em values can be observed in Fig. 1. One can see that excess molar volumes become less negative with an increase in temperature. This is a reflection of the situation that at lower temperature due to slower thermal movements of molecules the negative value of VEm increases with decreasing temperature and with an increase in DMF content it simultaneously increases also (in the range 0 b xDMF ≤ 0.5). The interaction and the packing between the components become stronger. High precision density measurements allowed the determination of the volume expansion coefficient, αp, using Eq. (6): αp ¼

  1 ∂V m ∂ ln ρ ∂ρ ¼− ¼− V m ∂T p ∂T ρ∂T

ð6Þ

The values of Vm were described as a function of temperature using Eq. (7) [75] V m ¼ a2 ðT−273:15Þ2 þ a1 ðT−273:15Þ þ a0

ð7Þ

Based on presented results the values of αp were possible to obtain from Eq. (8) [75]:

Fig. 2. Molar volume expansion coefficients (Ep,m) of (DMF + PrOH) mixtures: ■, T = 293.15 K; ●, T = 298.15 K; ▲, T = 303.15 K; ▼, T = 308.15 K; ♦, T = 313.15 K; ◄, T = 318.15 K.

presented in Fig. 3:

2

αp ¼

2a2 ðT−273:15Þ þ a1 a2 ðT−273:15Þ2 þ a1 ðT−273:15Þ þ a0

ð8Þ

The values of molar expansion coefficient (Ep,m) were calculated using Eq. (9): Ep;m ¼ α p  V m

ð9Þ

The values of Ep,m for the whole concentration and temperature range are presented in Fig. 2. The Ep,m values increase with the increase DMF pass through maximum whose position changes with temperature. The Ep,m values increase with increasing temperature over the whole range of the mixture composition. In the case of the associated structure of pure PrOH, an increase in temperature causes greater changes in the volume expansion, which can be explained by the fact that hydrogen bonds are more easily broken at high temperature. The situation is opposite in DMF high content where the increase in temperature has a small influence on the expansion properties. In this composition range, the volumetric expansion under the influence of temperature changes slightly and the disassociate of PrOH molecules in DMF does not significantly affect the volume expansion of this range of the system. Small changes in the value of the molar volumetric expansion coefficient in DMF rich region show that the structure of this solvent remains only slightly associated by dipol-dipol interactions. The addition of DMF monomers to PrOH rapidly increases the volume expansion coefficient to the maximum value. The increase is possibly caused by the formation of new bonds between unlike molecules. The excess molar volume expansion coefficients EEp;m were calculated using Eqs. (10)–(12) [66] and the dependence EEp;m = f(xDMF) is

id id Eid p;m ¼ V m α p

ð10Þ

  α id p ¼ φ1 α p;1 þ φ2 α p;2

ð11Þ

EEp;m ¼ Ep;m −Eid p;m

ð12Þ

where φ1, φ2 are volume fraction and α1∗, α2∗ are the volume expansion of pure PrOH and DMF respectively. The EEp, m changes as a function of the mixture composition (Fig. 3) are characterized by a pronounced maximum which decreases with increasing temperature. The EEp;m value can be a reliable source of information about deviations of EEp;m coefficient for the solution under study from that for ideal system. The positive deviations from ideality indicate that as a result of changing in the nature of bonds, the mixture exhibits a greater tendency to expand the system in comparison to pure components. The intensity of the maximum diminishes with temperature and its position has not change. At the concentration indicated by the maximum position, changes in the structure of the solution cause that the system exhibit the greatest tendency to expand in this area in comparison to the pure components. 3.2. Sound velocity and heat capacity Experimental values of density and sound velocity collected in Tables S1 and S2, were used to determine the compressibility coefficients and molar compressibility coefficients using the following

6

M. Tyczyńska et al. / Journal of Molecular Liquids 290 (2019) 111124 id id K id T;m ¼ V m κ T

ð18Þ

  κ id T ¼ φ1 κ T;1 þ φ2 κ T;2

ð19Þ

K ES;m ¼ K S;m −K id S;m

ð20Þ

id id K id S;m ¼ V m κ S

ð21Þ

Based on specific heat capacities of the (DMF + PrOH) mixture obtained from the experiment (Table S3) the values of isobaric molar heat capacities (Cp,m) in the whole composition range of the mixture were calculated and presented in Table S5 in Supplementary material. According to those results the values of κid S were calculated:

id κ id S ¼ κT −

 2 id TV id m αp C id p;m

  C id p;m ¼ x1 C p;m;1 þ x2 C p;m;2

ð22Þ ð23Þ

where: K ET;m , K ES;m is the molar excess isothermal compressibility and id id id molar excess isentropic compressibility, κ id T ; κ S ; K T;m ; K S;m are the isothermal and isentropic compressibility and their molar values for ideal mixture respectively, φi is the volume fraction of the components, C p;1 ;

C p;2 are the values of the molar heat capacity of PrOH and DMF respectively, C id p;m is the isobaric molar heat capacity of ideal mixture. The comparison of the courses of excess compressibility coefficients K ES;m and Fig. 3. Excess molar volume expansion coefficient (EEp;m ) of (DMF + PrOH) mixtures: ■, T = 293.15 K; ●, T = 298.15 K; ▲, T = 303.15 K; ▼, T = 308.15 K; ♦, T = 313.15 K; ◄, T = 318.15 K. Solid lines are calculated using Redlich-Kister Eq. (4).

K ET;m , versus the composition of the mixture at T = 298.15 K is shown in Fig. 4. As can be seen, negative values are observed for both K ES;m

Eqs. (13) and (14):   1 ∂V m 1 ¼ κS ¼ − V m ∂p S u2 ρ

ð13Þ

K S;m ¼ V m κ S

ð14Þ

where κs is the isentropic compressibility coefficient, KS,m is the molar isentropic compressibility coefficient, u is the sound velocity of (DMF + PrOH) mixture, ρ is the experimental value of solution's density. The values of κS, are collected in Table S4. Changes in the value of the volumes examined are small but they depict that the structure become presumably more and more rigid with increase DMF amount in the mixture. The values of molar isothermal compressibility coefficients KT,m were calculated by means of Eqs. (15) and (16), using the values of isentropic coefficients of compressibility κs, volume expansion coefficients αp and the specific heat capacities cp of the mixture which are included in Table S3 (Supplementary material). κT ¼ κS þ

α 2p T cp ρ

K T;m ¼ V m κ T

ð15Þ ð16Þ

Using the values of compressibility coefficients collected in Table S4 (Supplementary material) and Eqs. (13)–(23) the values of excess molar isentropic (K ES;m ) and isothermal (K ET;m ) compressibility coefficients were calculated [66]: K ET;m ¼ K T;m −K id T;m

ð17Þ

Fig. 4. Excess molar compressibilities (K ES;m and K ET;m ) of (DMF + PrOH) mixtures: ■, isentropic; ● isothermal at 298.15 K. Solid lines are calculated using Redlich-Kister Eq. (4).

M. Tyczyńska et al. / Journal of Molecular Liquids 290 (2019) 111124

and K ET;m , nevertheless they are higher for excess isentropic coefficient. As one can notice the negative values of both excess coefficients are

(CV,m) were calculated by using the thermodynamic relation (24):

found when V Em values are negative too. Negative contribution to the

C V;m ¼ C p;m

V Em

values in the whole composition range of the mixture is partly the result of changes in the structure caused by the rupture of hydrogen bonds in pure PrOH occurring during mixing. Another negative contribution arise from interstitial accommodation of DMF in the hydrogen bonded structure of the PrOH (observed in the range 0 b xDMF b 0.5). The above analyze can explain the fact that mixtures become less compressible than pure liquids. As is seen, the course of the functions are decreases and passes through a deep minimum at xDMF ≈ 0.45 (Fig. 4). When we are looking at this from the point of view of donor-acceptor properties of DMF, the rupture of the associates present in pure liquids is responsible for the positive contribution to the excess molar enthalpy of the mixture discussed [74]. With the addition of DMF to the mixture, the excess compressibility rapidly decreases and achieves the minimum, which is confirmed by earlier results indicating the tendency of the system to the hydrogen bonds formation (–C=O⋯H–O–) between polar DMF and the hydroxyl group of PrOH molecules. Based on specific heat capacities of the (DMF + PrOH) mixture obtained from the experiment (Table S3) the values of isobaric molar heat capacities (Cp,m) in the whole composition range of the mixture were calculated and presented on Fig. 5. Values of Cp,m are increasing with increasing temperature. It is clearly seen that with the increase in temperature Cp,m increases much more for solutions in which predominates the amount of PrOH in comparison to solutions in DMF rich region. It can be seen that depending on the composition of the mixture, there are distinct differences in the bonds formed between the molecules. Based on Cp,m changes, one can observe the transition from strong hydrogen bonds in the structure of PrOH to weak intermolecular interactions in DMF rich region. The values of isochoric molar heat capacities

κS κT

7

ð24Þ

The obtained results of isobaric and isochoric molar heat capacities are presented in Table S5 (Supplementary material). The excess functions were calculated using Eqs. (25)–(28) [66]: C Ep;m ¼ C p;m −C id p;m

ð25Þ

C EV;m ¼ C V;m −C id V;m

ð26Þ

  C id p;m ¼ x1 C p;m;1 þ x2 C p;m;2

ð27Þ

κ id S κ id T

ð28Þ

id C id V;m ¼ C p;m

id where C id p;m ; C V;m is the isobaric and isochoric molar heat capacity of ideal mixture. The excess isobaric molar heat capacities are plotted in Fig. 6. It can be seen that Cp,m for the mixture is smaller than for pure components. The negative deviation from ideality is more visible with

increase in temperature. Moreover C Ep;m values decrease with DMF content in the mixture and achieve the minimum at xDMF = 0.5 just like for V Em values. The fact that PrOH molecules tend to form hydrogen bonds in pure state can explain that C Ep;m values become less negative in PrOH rich region. The reason of reduction of C Ep;m is forming of interactions occurring between DMF and PrOH molecules which are presumably

Fig. 6. Excess molar heat capacity (C Ep;m) of (DMF + PrOH) mixtures: ■, T = 293.15 K; ●, T Fig. 5. Isobaric molar heat capacity (Cp,m) of (DMF + PrOH) mixtures: ■, T = 293.15 K; ●, T = 298.15 K; ▲ T = 303.15 K; ▼, T = 308.15 K; ♦, T = 313.15 K; ◄, T = 318. 15 K.

= 298.15 K; ▲, T = 303.15 K; ▼, T = 308.15 K; ♦, T = 313.15 K; ◄, T = 318.15 K. Solid lines are calculated using Redlich-Kister Eq. (4).

8

M. Tyczyńska et al. / Journal of Molecular Liquids 290 (2019) 111124

weaker compared to the hydrogen bonds between the molecules of these compounds existing in their pure form. Based on the values of sound velocity (Table S2), u, the excess sound velocity have been calculated using Eqs. (29) and (30) [66]: uE ¼ u−uid " uid ¼ ðφ1 Þ2

ð29Þ C p;m;1

C V;m;1

!

id C id V;m =C p;m
 2 w1 u1

! þ ðφ2 Þ2

C p;m;2

C V;m;2

!

id C id V;m =C p;m
 2 w2 u 2

!#−1=2

ð30Þ where: u1∗, u2∗ are the sound velocity of pure PrOH and DMF respectively, w1, w2 are the mass friction of components, φi is the volume fraction of the components and C p;1 ; C p;2 are the values of the molar heat capacity of PrOH and DMF respectively, that have been presented in Table S5, id C id p;m ; C V;m are the isobaric and isochoric molar heat capacity of ideal mixture according to Eqs. (27) and (28). The function uE = f (xDMF) is presented in Fig. 7. The values of uE are positive, reach a maximum at a content of about xDMF = 0.5 and decrease with increasing temperature over the whole composition range of the mixture. This confirm interactions between unlike species and a reduction in the stiffness of the structure in the solution due to increase in temperature.

4. Conclusions In the presented paper the data of sound velocity (u), density (ρ) and heat capacity (cp) of (DMF + PrOH) mixture were included. Based on the data obtained by us and comparing the course of all the analyzed functions V Em = f(xDMF), EEp;m = f(xDMF), K ES;m = f(xDMF) and K ET;m = f

Fig. 7. Excess sound velocity (uE) of (DMF + PrOH) mixtures: ■, T = 293.15 K; ● T = 298.15 K; ▲, T = 303.15 K; ▼, T = 308.15 K; ♦ T = 313.15 K; ◄, T = 318.15 K. Solid lines are calculated using Redlich-Kister Eq. (4).

(xDMF), C Ep;m = f(xDMF) as well as uE = f(xDMF), one can notice an interesting observation connected with changes in the mixture structure caused by the presence of another solvent in the system. The results for the volumetric properties are consistent with the partial destruction of the hydrogen bonded structure of PrOH during the mixing process. The emerging minimum on the course of excess molar volume indicates probably the formation of weak interactions based on hydrogen bonding between unlike molecules. In this sense, interstitial accommodation of DMF molecules in hydrogen-bonded structure of PrOH or free volume effects seem to play significant role in this system. On the other hand energetic properties such as excess molar heat capacities reflect probably the randomness of the molecular distribution of DMF in the mixture. 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