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2-diethylethanolamine at different temperatures
Physica B 515 (2017) 1–7
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Physica B journal homepage: www.elsevier.com/locate/physb
Study of parameter of nonlinearity in 2-chloroethanol with 2dimethylethanolamine/2-diethylethanolamine at different temperatures
MARK
⁎
Anjali Awasthia, Aashees Awasthib, a b
Faculty of Engineering & Technology, Dr. Shakuntala Misra National Rehabilitation University, Lucknow 226 017, Uttar Pradesh, India Material Science Research Laboratory, Department of Physics, University of Lucknow, Lucknow 226 007, Uttar Pradesh, India
A R T I C L E I N F O
A BS T RAC T
Keywords: Non-linearity parameter Temperature and pressure derivatives of sound velocity Molecular properties Phase shift parameter
The acoustic non-linearity parameter (B/A) for binary mixtures of 2-chloroethanol with 2-dimethylethanolamine (2-DMAE) and 2-diethylethanolamine (2-DEAE) are evaluated using Tong Dong, Beyer and Beyer-Tong Dong coefficients at varying concentrations and temperatures ranging from 293.15 to 313.15 K. The nonlinearity parameter is used to calculate various molecular properties such as internal pressure, cohesive energy density, Van der waals’ constant, distance of closest approach, diffusion coefficient and rotational correlation time. Additionally, the intermediate quantities like temperature and pressure derivatives of sound velocity and phase shift parameter as a function of temperature are also deduced. The extent of intermolecular interactions, anharmonicity and structural configuration of the binaries under investigation are discussed in terms of excess non-linearity parameter (B/A)E.
1. Introduction The Beyer nonlinearity parameter (B/A) is a basic measure of nonlinearity of a medium and is interesting in a number of areas ranging from underwater acoustics to medicine, in case of modern medical applications of ultrasound like ultrasonic diagnostics, tissue characterization, lithotripsy etc. [1–4]. The nonlinearity parameter must be known for accurate modeling and understanding of the interactions between an ultrasonic wave and a sample. The B/A parameter determine the nonlinear correction to the velocity due to the influence of nonlinear effects caused by the propagation of finite amplitude wave. Moreover, it can be related to the molecular dynamics of the medium and it can provide information about structural properties of medium, internal pressures, clustering, inter- and intramolecular spacing, etc. [5,6]. Importance of the B/A parameter increases with the advent of high pressure technologies of food processing and preservation. B/A is significant in diagnostic and therapeutic applications of ultrasound. The diagnosis requires the knowledge of B/A for designing and optimization of the ultrasound imaging devices. For therapy, B/A predicts the temperature in the tissues during ultrasonic treatment. B/ A is widely used in ultrasonic techniques for the characterization of different media such as liquids [7] and tissues [8–11]. The present paper aims to study the effect of acoustic non-linearity parameter (B/A) on binary mixtures of 2-chloroethanol with dimethylethanolamine (2-
⁎
Corresponding author. E-mail address: aasheesawasthi@rediffmail.com (A. Awasthi).
http://dx.doi.org/10.1016/j.physb.2017.03.045 Received 23 July 2016; Received in revised form 14 March 2017; Accepted 27 March 2017 Available online 30 March 2017 0921-4526/ © 2017 Published by Elsevier B.V.
DMAE) and diethylethanolamine (2-DEAE) using Tong Dong [12], Beyer [13] and Beyer-Tong Dong [14] at varying concentrations and temperatures ranging from 293.15 to 313.15 K. 2-chloroethanol consists of both an alkyl chloride and alcohol functional groups. It is a versatile solvent used in many industrial areas. Halogenoalcohols like 2-chloroethanol are possess an additional proton-accepting group other than the hydroxyl group. This is significant as they are potentially able to act not only as bi-functional hydrogen bonding solvent but also as a strong proton-donating acid. The protein denaturation ability of halogenoalcohols is much higher than that of aliphatic alcohols. 2DMAE has been shown to remarkably enhance brain function when used as a supplement in clinical studies and also used in anti-aging formulation. 2-DEAE is used as a corrosion inhibitor in steam and condensate lines by neutralizing carbonic acid and scavenging oxygen. 2-DEAE is also used for the synthesis of local anesthetics, in antirust compounds and in photographic emulsions. B/A values are used to determine the molecular properties such as internal pressure, cohesive energy density, Van der waals’ constant, distance of closest approach, diffusion coefficient and rotational correlation time [5,7,15] Apart from this, certain intermediate quantities like temperature derivatives of sound velocity (∂u /∂T )P and pressure derivatives of sound velocity (∂u /∂P )T and phase shift parameter (δφ) as a function of temperature are also deduced. The extent of intermolecular interactions, anharmonicity and structural configuration of the binaries under investigation are discussed in terms of excess non-linearity parameter (B/A)E. The
Physica B 515 (2017) 1–7
A. Awasthi, A. Awasthi
experimental values of density and ultrasonic velocity needed for the determination of B/A and related parameters are taken from our earlier work [16].
li =
∑
Xi ρi n
∑
Si L i
Xi ρi
i =1
(10)
2.2.1.2. Beyer and Tong-Dong coefficients. The pressure and temperature derivatives of sound velocity are calculated by TongDong method as [12]:
The propagation of ultrasonic waves is an adiabatic process hence acoustic nonlinearity parameter B/A is also a result of an adiabatic equation of state. B/A values are evaluated using three different methods namely Tong-Dong, Beyer and Beyer-Tong Dong. 2.1. Tong-Dong method Tong-Dong method uses Schaaffs relation [17] of sound velocity for the determination of B/A as:
⎛ ∂u ⎞ uβ ⎜ ⎟ = T J (x ) ⎝ ∂P ⎠T 2
(11)
⎛ ∂u ⎞ ⎤ uα ⎡ 1 − J (x ) ⎥ ⎜ ⎟ = ⎢ ⎦ ⎝ ∂T ⎠P 2 ⎣ Tα
(12)
2.3. To obtain the B/A values using Beyer and Tong-Dong method
(1)
B / A = J (0) + J (x )
To obtain the B/A values using Beyer and Tong-Dong method, the coefficients are evaluated by substituting Eqs. (11) and (12) in Eq. (7). The excess values of nonlinearity parameter (B / A)E are calculated by the relation [7,20,21]:
where,
⎛ 1 ⎞ u2ρβT J (0) = ⎜1 − ⎟ γ ⎠ Tα ⎝
x=
and θi =
i =1
2. Theory
J (x ) =
Si L i n
2(3 − 2x )2 3(x − 1)(6 − 5x )
V b
(2)
(B / A)E = (B / A)mix − (B / A)ideal
where, (B/A)mix is obtained by Tong Dong method and (B/A)ideal is obtained from its pure components as:
(3)
n
(4)
⎡ ⎤ ⎞ γRT ⎢ ⎛ Mu2 M ⎜⎜ V= − + 1 ⎟⎟ − 1⎥ ⎥⎦ ρ ρu2 ⎢⎣ ⎝ γRT ⎠
(B / A)ideal =
∑ Xi (B /A)i i =1
(14)
where, Xi is the mole fraction of pure components. The various molecular properties are calculated using the Sehgal's relation [8]:
(5)
Here, γ is specific heat, βT is the isothermal compressibility, x is the real volume of the molecules and b is van der Waals’ constant. The values of isobaric expansivity (α) are calculated from the temperature dependence of the density data of pure liquids by using the following relation [18]:
α = (−1/ ρ)(∂ρ /∂T )P
(13)
2.3.1. Internal pressure (Pi) It is the measure of the forces of attraction and repulsion between the molecules within a liquid medium. It is defined as the summation of the dispersive and repulsive forces, ionic and dipolar interactions.
(6)
Pl =
ρu2 (B / A + 1)
(15)
2.2. Beyer 2.3.2. Cohesive energy (∆A ) It is a measure of the total molecular cohesion and represents the change in internal energy of a liquid as it experiences a small isothermal expansion. It also represents the total strength or stiffness of the solvent structure [5,7].
Beyer [13] deduced non linearity parameter on the basis of thermodynamic parameters as:
⎛ ∂u ⎞ 2αTu ⎛ ∂u ⎞ B / A = 2ρu ⎜ ⎟ + ⎜ ⎟ ⎝ ∂P ⎠T CP ⎝ ∂T ⎠P
(7)
where, the specific heat at constant pressure (Cp) values for the pure liquids at the required temperatures has been calculated using group contribution method [18,19].
ΔA = −
2.2.1.1. Beyer coefficients. The intermediate quantities like temperature derivatives of sound velocity (∂u /∂T )P and pressure derivatives of sound velocity (∂u /∂P )T are deduced from the relation: n
∑ i =1
⎛ θi lV⎞ ⎤ ⎜ − i i ⎟ αi ⎥ Vai ⎠ ⎥⎦ ⎝2
a=
ρu2V 2 (B / A + 1)
b=V−
RT (B / A + 1) ρu2
(17)
(18)
(8) 2.3.4. Distance of closest approach of molecules (d) It explains as to how efficiently and closely the neighbouring molecules in a mixture are packed together.
where, τ is a constant obtained by the linear interpolation method.
⎛ n lV ⎛ ∂u ⎞ θ⎞ ⎜ ⎟ = u ⎜⎜∑ i i − i ⎟⎟ βTi ⎝ ∂P ⎠T 2⎠ ⎝ i =1 Vai
(16)
2.3.3. Effective van der Waal's constants (a and b) It is a measure of the force of attraction between the molecules and the effective volume of the molecule within the mixture.
2.2.1. Computation of temperature derivatives of sound velocity (∂u /∂T )P and pressure derivatives of sound velocity (∂u /∂P )T
⎡ ⎛ ∂u ⎞ ⎜ ⎟ = u ⎢τ + ⎝ ∂T ⎠P ⎣⎢
⎛ 82.051Tρ ⎞ Mu2 ln ⎜ ⎟ ⎠ (B / A + 1) ⎝ M
⎛ 3b ⎞1/3 d=⎜ ⎟ ⎝ 2N0 π ⎠
(9)
where, 2
(19)
Physica B 515 (2017) 1–7
A. Awasthi, A. Awasthi
2.3.5. Diffusion coefficient or diffusivity (D) It is the constant of proportionality between the flux and potential. The higher value of diffusivity is attributed to more readily the molecules diffuse into each other within a mixture.
⎛ 2N ⎞1/3 kT D = ⎜ 02 ⎟ ⎝ 81π ⎠ ηb1/3
Table 1 Nonlinearity parameter B/A of 2-chloroethanol (1) +2-DMAE/2-DEAE (2). 2-Chloroethanol (1)+2-DMAE (2) X1
(20)
2.3.6. Rotational correlation time (τ ) It is defined as the average time between molecular collisions and is the time taken by the molecules to be in a particular state of motion [22].
τ=
ηb 4N0 kT
(21)
2.3.7. Phase shift parameter (δϕ) The phase shift parameter is an independent parameter which is sensitive to the temperature and change in the molecular structure of the liquid mixtures.
δφ =
B /A 2ρu3
(22)
3. Results and discussion The acoustic non linearity parameter B/A is a quantity which represents the magnitude of hardness of the liquids. The values of acoustic non-linearity parameter (B/A) for binary mixtures of 2chloroethanol with 2-DMAE and 2-DEAE evaluated using Tong Dong, Beyer and Beyer & Tong-Dong methods at varying concentrations and temperatures ranging from 293.15 to 313.15 K are listed in Table 1. The temperature and pressure derivative of sound velocity for both the liquid mixtures are comparatively shown in Table 2. The molecular properties of both the mixtures, deduced from the nonlinearity parameter are given in Tables 3 and 4, respectively. The variations of excess non-linearity parameter (B/A)E as a function of mole fraction of 2-chloroethanol, for both the solvent systems are shown in Figs. 1 and 2, respectively. It is seen from the Table 1 that, at a specific temperature, the acoustic non linearity parameter B/A decreases linearly with an increase in the concentration of the 2-chloroethanol for both the liquid mixtures using Tong Dong and Beyer and Tong-Dong methods. In contrast, Beyer method shows a non-linear variation in the B/A values with an increase in concentration of 2-chloroethanol for both the liquid mixtures, indicating the presence of molecular interactions. A close inspection shows a peak in the B/A values at a concentration x1=0.5001 for 2-chloroethanol+DMAE mixture and x1=0.3893 for 2-chloroethanol+DEAE mixture, where the peak of ultrasonic velocity occurred in our earlier work [16]. The plausible reason for this could be the maximum association of 2-DMAE/2-DEAE breaking up into its monomers and the hydrogen bond formation between the hydrogen atom of 2-chloroethanol and the oxygen atom of 2-DMAE/2-DEAE. But, above these concentrations, it is also probable that the 2-DMAE/2DEAE molecules may remain in the associated form. The bulkier nature of these associated molecules over 2-chloroethanol molecules may cause steric hindrance, resulting in the deterioration of the strength of the intermolecular forces. Hence, a decrease in the B/A values occurs above 0.5001 and 0.3893 concentrations for the respective systems [21,23]. The molecular interaction may involve the association due to hydrogen bonding, dipole–dipole interaction or formation of charge-transfer complexes. This phenomenon may escort strong interactive forces [16,24,25]. It is quite interesting to note that the peak of B/A values using Beyer shifts towards a lower concentration for 2-chloroethanol+2-DEAE rather than 2-chloroethanol+2-DMAE
B/A
2-Chloroethanol (1)+2-DEAE (2) X1
B/A Tong Dong
Beyer
Beyer and Tong Dong
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
9.38 9.33 9.28 9.24 9.20 9.18 9.17 9.19 9.22 9.27 9.36
11.80 12.23 12.76 13.23 13.41 13.30 13.07 12.71 12.26 11.63 10.75
11.40 11.24 11.09 10.94 10.82 10.72 10.65 10.61 10.60 10.62 10.70
12.14 11.88 11.65 11.39 11.16 10.98 10.88 10.84 10.82 10.82 10.84
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
9.29 9.25 9.20 9.16 9.13 9.13 9.15 9.19 9.25 9.34 9.48
11.63 12.11 12.66 13.16 13.32 13.21 12.99 12.63 12.15 11.49 10.58
11.30 11.15 11.00 10.85 10.75 10.67 10.63 10.62 10.65 10.71 10.84
12.57 12.23 11.91 11.58 11.33 11.12 11.02 11.00 11.00 11.03 11.09
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
9.29 9.24 9.18 9.14 9.12 9.15 9.20 9.27 9.37 9.50 9.69
11.47 12.02 12.62 13.14 13.34 13.23 12.99 12.61 12.10 11.39 10.43
11.31 11.15 10.99 10.84 10.74 10.70 10.69 10.73 10.79 10.90 11.09
Tong Dong
Beyer
Beyer and Tong Dong
293.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
9.89 9.78 9.68 9.57 9.47 9.40 9.36 9.34 9.34 9.35 9.36
11.89 12.23 12.56 12.92 13.21 13.28 13.11 12.71 12.14 11.45 10.75
11.89 11.68 11.48 11.27 11.08 10.92 10.82 10.76 10.72 10.70 10.70
303.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
10.04 9.91 9.78 9.64 9.52 9.43 9.39 9.40 9.41 9.44 9.48
11.70 12.07 12.43 12.81 13.14 13.23 13.06 12.60 12.02 11.31 10.58
313.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
10.34 10.15 9.96 9.77 9.64 9.54 9.50 9.52 9.56 9.61 9.69
11.54 11.95 12.35 12.79 13.07 13.17 12.99 12.54 11.93 11.19 10.43
system. This may be due to the more acidic nature of 2-chloroethanol in comparison to 2-DMAE/2-DEAE molecules. Since, Cl- group of 2chloroethanol has -Inductive effect, while CH3/ C2H5 group of 2DMAE/2-DEAE have +Inductive effect, therefore, 2-DEAE reacts with 2-chloroethanol more rapidly, giving rise to the peak of B/A at a lower concentration than with 2-DMAE mixture. The values of B/A using Beyer method are slightly higher than those for Tong-Dong and Beyer-Tong Dong methods. The increase in temperature causes B/A values to increase using Tong-Dong and Beyer and Tong-Dong method while decreases using Beyer method. The variations of acoustic nonlinearity parameter using Tong-Dong and Beyer-Tong Dong methods show a different trend as compared to the non-monotonous behaviour revealed by the Beyer method. TongDong considered liquid as a system of rigid balls and expressed it as a function of molecular radii of the chosen liquid. Tong-Dong and BeyerTong Dong methods provide a reasonable approach towards estimation of B/A for small molecules but completely fails in prediction involving longer molecules. The inaccuracy in predicting B/A values using TongDong and Beyer-Tong Dong methods may be a result of overestimation of molecular radii based on the hypothesis of spherically symmetric larger molecules. From the Figs. 1 and 2, B/AE is found to be negative and non-linear indicating the presence of specific interactions between 2-chloroetha3
Physica B 515 (2017) 1–7
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Table 2 Pressure and temperature coefficients of 2-chloroethanol (1) +2-DMAE/2-DEAE (2). 2-Chloroethanol (1)+DMAE (2) X1
2-Chloroethanol (1)+DEAE (2)
Beyer
Beyer and Tong-Dong
(∂u/∂P)T (10−6 m3/sN)
(∂u/∂T)P (m/sK)
(∂u/∂P)T (10−6 m3/sN)
(∂u/∂T)P (m/sK)
293.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
4.92 4.83 4.76 4.67 4.56 4.40 4.23 4.01 3.77 3.51 3.26
−0.73 −0.74 −0.74 −0.74 −0.74 −0.74 −0.74 −0.73 −0.72 −0.71 −0.70
4.92 4.62 4.36 4.08 3.83 3.62 3.49 3.40 3.33 3.28 3.25
−3.07 −3.05 −3.04 −3.03 −3.02 −3.02 −3.01 −3.01 −3.01 −3.02 −3.02
303.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
5.02 4.94 4.87 4.79 4.68 4.52 4.34 4.11 3.85 3.57 3.31
−0.90 −0.90 −0.90 −0.91 −0.92 −0.92 −0.91 −0.90 −0.89 −0.88 −0.87
5.21 4.87 4.57 4.26 3.98 3.75 3.62 3.54 3.47 3.42 3.39
313.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
5.13 5.06 5.01 4.93 4.81 4.65 4.46 4.21 3.94 3.65 3.36
−1.04 −1.05 −1.06 −1.07 −1.07 −1.07 −1.07 −1.06 −1.05 −1.04 −1.02
5.60 5.19 4.83 4.47 4.17 3.93 3.79 3.70 3.64 3.60 3.58
X1
Beyer
Beyer and Tong-Dong
(∂u/∂P)T (10−6 m3/sN)
(∂u/∂T)P (m/sK)
(∂u/∂P)T (10−6 m3/sN)
(∂u/∂T)P (m/sK)
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
4.89 4.83 4.80 4.74 4.64 4.47 4.29 4.07 3.84 3.58 3.26
−1.29 −1.27 −1.25 −1.23 −1.19 −1.13 −1.07 −1.00 −0.91 −0.82 −0.70
4.72 4.44 4.17 3.92 3.75 3.60 3.50 3.40 3.33 3.27 3.25
−3.42 −3.38 −3.35 −3.31 −3.26 −3.18 −3.12 −3.07 −3.04 −3.02 −3.02
−3.28 −3.26 −3.23 −3.21 −3.19 −3.18 −3.18 −3.18 −3.19 −3.20 −3.22
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
5.00 4.96 4.92 4.87 4.76 4.58 4.40 4.18 3.93 3.64 3.31
−1.45 −1.44 −1.42 −1.40 −1.36 −1.30 −1.24 −1.17 −1.08 −0.99 −0.87
4.86 4.57 4.28 4.02 3.85 3.71 3.61 3.52 3.45 3.40 3.39
−3.48 −3.45 −3.42 −3.40 −3.35 −3.29 −3.24 −3.21 −3.19 −3.20 −3.22
−3.57 −3.51 −3.47 −3.42 −3.39 −3.37 −3.37 −3.38 −3.40 −3.43 −3.46
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
5.16 5.14 5.11 5.06 4.95 4.76 4.56 4.32 4.05 3.73 3.36
−1.58 −1.58 −1.57 −1.55 −1.52 −1.46 −1.40 −1.32 −1.24 −1.14 −1.02
5.09 4.77 4.45 4.17 3.99 3.85 3.76 3.68 3.62 3.58 3.58
−3.56 −3.53 −3.51 −3.48 −3.45 −3.41 −3.38 −3.37 −3.38 −3.40 −3.46
the range 1–1.5. Hence,(∂u /∂T )P < 0 ,(∂u /∂P )T > 0 and B/A > 8 [29]. It was found that the values of temperature derivatives and pressure derivatives of sound velocity, at constant temperature decreases slowly with the increasing concentration of 2-chloroethanol using Beyer and Beyer-Tong Dong methods. A close inspection shows that (∂u /∂P )T for Beyer-Tong Dong is slightly higher than that obtained by Beyer method. The increase in temperature causes the pressure derivatives to increase by both the methods for the liquid mixtures under investigation. Moreover, the pressure derivatives for 2-chloroethanol +2-DEAE are slightly more than 2-chloroethanol+2-DMAE system using Beyer method. This may be ascribed to an increase of carbon chain in 2-DEAE as compared to 2-DMAE. The value of temperature derivatives (∂u /∂T )P is almost insignificant in terms of increasing concentrations of 2-chloroethanol for both the liquid mixtures. As the temperature increases, there is a distinctive increase in the values of temperature derivatives. The temperature derivatives are higher for 2-chloroethanol+2-DEAE than 2-chloroethanol+2-DMAE systems. The value of temperature derivatives of sound velocity (∂u /∂P )T using Beyer method is comparatively higher than Beyer- Tong Dong method for both the binary liquid mixtures, at all temperatures. As the temperature is raised, the values of (∂u /∂P )T is found to increase for both Beyer and Beyer-Tong Dong methods. It is observed that the value of (∂u /∂P )T using Beyer method is higher for 2-chloroethanol+2-DEAE than 2chloroethanol+2-DMAE systems. The value of temperature derivatives
nol +2-DMAE/2-DEAE systems. A similar trend was observed in terms of excess acoustic parameters discussed in our earlier work [21]. The nonlinear behaviour of (B/A)E indicates the presence of intermolecular interactions between the unlike molecules [26,27]. When 2-chloroethanol molecules are mixed with 2-DMAE/2-DEAE molecules, it may induce mutual dissociation of the hydrogen bonded structure present in the pure forms following the creation of new hydrogen bonds between 2-chloroethanol and 2-DMAE/2-DEAE molecules, resulting in a decrease in the B/A values of the mixture and hence negative B/AE values are observed. The B/AE values become more negative with increase in temperature of the mixture. As the temperature is increased, thermal energy helps the breaking of bonds between the associated molecules of 2-chloroethanol+2-DMAE/2-DEAE into their monomers, resulting in further decrease in the B/AE values. The position of maxima of excess B/A does not change with an increase in temperature. The interactions between the components of the liquid mixtures may be attributed to effects like hydrogen bonding, chargetransfer, dipole-dipole interactions etc. It is seen from the Table 2 that the temperature derivatives of sound velocity (∂u /∂T )P are negative and pressure derivatives of sound velocity (∂u /∂P )T are positive [20,28]. At atmospheric temperature and room temperature, for most of the organic liquids, the thermal expansion coefficient is within a range of 0.5–1.7×10−3 K, adiabatic compressibility is of the order of 10−1 m2 N−1 and specific heat capacity ratio in
4
Physica B 515 (2017) 1–7
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Table 3 Molecular properties of 2-Chloroethanol (1) +2-DMAE (2). Pi (MPa)
ΔΑ (KJ/mole)
a (l2 atm/mole2)
b (l/mole)
d (Å)
D (10−9 m2 s−1)
τ (ps)
δφ (10–12 s3 kg−1)
293.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
151.25 160.54 169.97 181.22 193.05 203.27 209.59 213.22 215.55 217.33 218.10
−83.23 −84.68 −86.45 −88.54 −90.55 −91.58 −91.44 −90.31 −88.83 −87.31 −85.96
14.78 14.14 13.70 13.25 12.78 12.20 11.64 11.03 10.43 9.89 9.48
0.084 0.080 0.077 0.073 0.070 0.067 0.064 0.062 0.059 0.057 0.056
4.06 3.99 3.94 3.88 3.82 3.75 3.70 3.66 3.61 3.57 3.54
1.15 1.17 1.18 1.20 1.21 1.24 1.29 1.36 1.43 1.51 1.57
0.415 0.406 0.402 0.398 0.393 0.382 0.369 0.351 0.333 0.316 0.303
2.20 2.07 1.94 1.80 1.68 1.59 1.54 1.52 1.51 1.51 1.51
303.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
140.19 149.57 159.17 170.71 182.99 193.22 199.28 201.87 203.67 205.02 205.19
−78.21 −80.11 −82.24 −84.78 −87.26 −88.48 −88.41 −86.95 −85.33 −83.63 −81.98
13.96 13.48 13.14 12.80 12.43 11.90 11.37 10.72 10.12 9.55 9.09
0.083 0.080 0.076 0.073 0.070 0.067 0.064 0.062 0.059 0.057 0.055
4.04 3.98 3.93 3.87 3.81 3.75 3.70 3.66 3.61 3.56 3.53
1.27 1.29 1.30 1.30 1.30 1.34 1.38 1.46 1.54 1.63 1.71
0.374 0.369 0.367 0.367 0.365 0.356 0.344 0.326 0.309 0.292 0.278
2.44 2.27 2.12 1.95 1.80 1.70 1.65 1.64 1.63 1.63 1.64
313.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
128.13 137.99 148.18 160.62 171.69 181.90 187.62 190.09 191.16 191.68 190.83
−72.48 −75.00 −77.77 −81.07 −83.26 −84.74 −84.67 −83.23 −81.38 −79.35 −77.27
13.01 12.71 12.53 12.35 11.98 11.52 11.00 10.36 9.74 9.13 8.61
0.082 0.079 0.076 0.073 0.070 0.067 0.064 0.061 0.059 0.057 0.055
4.02 3.97 3.92 3.87 3.81 3.75 3.70 3.65 3.60 3.55 3.51
1.42 1.43 1.42 1.40 1.41 1.44 1.49 1.57 1.67 1.77 1.88
0.334 0.334 0.336 0.340 0.337 0.331 0.319 0.303 0.285 0.268 0.253
2.75 2.53 2.33 2.12 1.96 1.84 1.78 1.77 1.77 1.78 1.81
X1
decrease in both the systems. The cohesive energy is found to exhibit a nonlinear variation with peak obtained at the same concentration of 2-chloroethanol where peak of B/A values using Beyer were obtained for 2-chloroethanol+2DMAE system, at a given temperature. The cohesive energy for 2chloroethanol+2-DEAE decreases with increasing concentration. On increasing the temperature, cohesive energy decreases in both the binary systems [33]. The variation of cohesive energy confirms the formation of intermolecular hydrogen bonding between 2-chloroethanol and 2-DMAE/2-DEAE molecules [16,33]. The effective van der Waal's constant ‘a’ and ‘b’ follows a decreasing trend with increasing mole fractions of 2-chloroethanol for both the systems. A close examination shows that the values of van der Waals’ constant are higher in case of 2-chloroethanol+2-DEAE than 2-chloroethanol+2-DMAE systems. With an increase in temperature, van der Waals’ constant ‘a’ also decreases gradually but the effect on constant ‘b’ is found to be almost insignificant. The distance of closest approach of molecules ‘d’ decreases for the binary liquid systems with the increase in the concentration of 2chloroethanol. It not only depends upon how close the neighbouring molecules are, but also on how efficiently they are packed together. The variations in the values of the distance of the closest approach of molecules follows the same variations as that of ‘a′ and ‘b′. When the temperature is increased, d values are found to decrease gradually with the concentration. This indicates strong intermolecular interactions to occur between 2-chloroethanol and 2-DMAE/2-DEAE molecules. The values of d are greater for 2-chloroethanol+2-DEAE than 2Chloroethanol+2-DMAE systems.
(∂u /∂T )P is almost insignificant in terms of increasing concentrations of 2-chloroethanol for both the liquid mixtures. As the temperature increases, there is a gradual increase in the values of temperature derivatives. The temperature derivatives are higher for 2-chloroethanol +2-DEAE than 2-chloroethanol+2-DMAE systems. Thus, the dependence of B/A on pressure derivatives is more than that on temperature, specifying a decreasing trend in case of pressure and being upto reasonable extent temperature independent. It also depicts the fact that B/A is mainly dependent on pressure derivatives of sound velocity which signifies an increase in phase velocity brought about by pressure while temperature derivatives of sound velocity gives an increase due to temperature [30]. In the estimation process of B/A, pressure derivatives are calculated more accurately than the temperature derivatives. Hence, uncertainty due to pressure derivative dominates temperature derivative as it is affected by the goodness of (∂u /∂P )T . The accuracy for the determination of B/A using Beyer's method is approximately 5% [31,32]. Molecular properties evaluated using Sehgal's relation are advantageous in a sense that they reveal some distinctive physical features of liquids and resolution rate in medical imaging. It is seen from the Tables 3 and 4 that at given temperature, the internal pressure increases progressively with increasing concentrations of 2-chloroethanol for both the liquid mixtures. This behaviour of the internal pressure indicates stronger molecular interactions between the contributory binaries, in both the systems. It is also visible that internal pressure values are slightly higher for 2-chloroethanol+2DEAE than 2-chloroethanol+2-DMAE systems, at a particular temperature. The rise in temperature causes internal pressure is to 5
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Table 4 Molecular properties of 2-chloroethanol (1)+2-DEAE (2). Pi (MPa)
ΔΑ (KJ/mole)
a (l2 atm/mole2)
b (l/mole)
d (Å)
D (10−9 m2 s−1)
τ (ps)
δφ (10–12 s3 kg−1)
293.15 K 0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
159.02 168.09 179.11 190.52 198.20 203.42 207.07 210.84 214.30 217.31 218.10
−109.61 −109.04 −109.56 −109.75 −108.23 −104.47 −100.79 −96.86 −93.30 −89.77 −85.96
27.05 24.61 22.69 20.83 19.00 16.79 15.00 13.27 11.84 10.58 9.48
0.117 0.108 0.101 0.093 0.087 0.080 0.075 0.069 0.064 0.060 0.056
4.53 4.41 4.31 4.20 4.10 3.99 3.90 3.80 3.71 3.62 3.54
0.54 0.58 0.62 0.67 0.73 0.84 0.95 1.09 1.23 1.39 1.57
0.889 0.816 0.764 0.710 0.648 0.567 0.501 0.438 0.387 0.342 0.303
2.08 1.96 1.82 1.70 1.63 1.59 1.58 1.55 1.53 1.51 1.51
303.15 K 0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
150.56 159.77 170.71 182.01 189.12 193.89 197.23 200.55 203.14 205.06 205.19
−105.36 −105.36 −106.19 −106.62 −105.02 −101.25 −97.63 −93.67 −89.88 −86.03 −81.98
26.16 23.98 22.19 20.42 18.61 16.43 14.67 12.95 11.51 10.22 9.09
0.117 0.109 0.101 0.094 0.087 0.081 0.075 0.069 0.064 0.059 0.055
4.53 4.42 4.31 4.21 4.11 4.00 3.90 3.80 3.70 3.61 3.53
0.59 0.63 0.67 0.72 0.79 0.90 1.02 1.17 1.33 1.51 1.71
0.810 0.751 0.706 0.659 0.602 0.526 0.466 0.407 0.359 0.316 0.278
2.25 2.11 1.95 1.81 1.74 1.71 1.68 1.66 1.65 1.64 1.64
313.15 K 0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
138.83 148.47 159.57 170.68 177.82 182.31 185.08 187.75 189.92 191.23 190.83
−98.60 −99.46 −100.87 −101.57 −100.27 −96.68 −93.05 −89.07 −85.35 −81.42 −77.27
24.64 22.82 21.26 19.61 17.91 15.81 14.10 12.42 11.02 9.75 8.61
0.117 0.108 0.101 0.094 0.087 0.080 0.075 0.069 0.064 0.059 0.055
4.52 4.41 4.31 4.20 4.11 3.99 3.90 3.79 3.70 3.60 3.51
0.67 0.71 0.75 0.80 0.87 0.99 1.12 1.28 1.45 1.65 1.88
0.714 0.672 0.638 0.598 0.548 0.481 0.426 0.372 0.328 0.289 0.253
2.53 2.34 2.15 1.98 1.90 1.86 1.84 1.82 1.80 1.80 1.81
X1
Fig. 2. Plot of (B/A)E versus mole fraction of 2-Chloroethanol in 2-Chloroethanol (1) +2DEAE (2) mixtures.
Fig. 1. Plot of (B/A)E versus mole fraction of 2-Chloroethanol in 2-Chloroethanol (1) +2DMAE (2) mixtures.
The rotational correlation time ‘τ ’ is defined as the average time between molecular collisions and is the time taken by the molecules to be in a particular state of motion [22]. The correlation time decreases with concentration as well as temperature for both the binary liquid mixtures. This means that the motion of the molecules becomes faster showing strong intermolecular interactions in both the liquid mixtures. However, the values of correlation time for 2-chloroethanol+2-DEAE
The diffusion coefficient ‘D’ increases steadily for both the binary systems with increasing mole fractions of 2-chloroethanol, at a particular temperature. As the temperature increases, it causes the diffusion coefficient to increase. This means that greater the value of diffusivity, the faster the molecules diffuse into each other within a mixture leading to strong intermolecular interactions. 6
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Am. 65 (1979) 1392–1397. [7] J. Jugan, M.A. Khadar, Acoustic non-linearity parameter B/A and related molecular properties of binary organic liquid mixtures, J. Mol. Liq. 100 (2002) 217. [8] C.M. Sehgal, R.C. Bahn, J.F. Greenleaf, Measurement of the acoustic nonlinearity parameter B/A in human tissues by a thermodynamic method, J. Acoust. Soc. Am. 76 (4) (1984) 1023–1029. [9] F. Dong, E.L. Madsen, M.C. MacDonald, J.A. Zagzebski, Nonlinearity parameter for tissue-mimicking materials, Ultrasound Med. Biol. 25 (5) (1999) 831–838. [10] C.M. Sehgal, G.M. Brown, R.C. Bahn, J.F. Greenleaf, Measurement and use of acoustic nonlinearity and sound speed to estimate composition of excised livers, Ultrasound Med. Biol. 12 (1986) 865–874. [11] A.P. Sarvazyan, T.V. Chalikian, Acoustic nonlinearity parameter B/A of aqueous solutions of amino acids and proteins, J. Acoust. Soc. Am. 88 (3) (1990) 1555–1561. [12] J. Tong, Y. Dong, Expressions of acoustic parameters in organic liquid derived from Schaaff's theory, J. Acoust. Soc. Am. 93 (1993) 291–296. [13] R.T. Beyer, S.V. Letcher, Physical Ultrasonics (ch.7), Acad. Press, New York, USA, 1969, p. 202. [14] T. Jie, D. Yan wu, T. Tian-Kui, Theoretical study on temperature and pressure coefficients of ultrasonic speed in organic liquids, Chin. Sci. Bull. 34 (1989) 1262. [15] A.B. Coppens, R.T. Beyer, Parameter of Nonlinearity in Fluids. III. Values of Sound Velocity in Liquid Metals. J. Ballou, J. Acoust. Soc. Am. 41 (1967) 1443. [16] P.K. Pandey, A. Awasthi, A. Awasthi, Intermolecular interactions in binary mixtures of 2-Chloroethanol with 2-Dimethylaminoethanol and 2-Diethylaminoethanol at different temperatures, Chem. Phys. 423 (2013) 119–126. [17] W. Schaaffs, Bemerkungen zur Berechnung des Molekülradius aus Molvolumen und Schallgeschwindigkeit, Z. Phys. 115 (1940) 69. [18] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids, McGraw Hill Inc, New York, 1987, p. 139. [19] F.A. Missenard, Methode additive pour la determination de la. Chaleur Molaire de Liquides, C. R. Acad. Sci. Paris 260 (1965) 5521–5523. [20] Y. Lu, Y. Zhang, Y. Dong, Nonlinear ultrasonic nature of organic liquid and organic liquid mixture, Ultrasonics 44 (2006) e1419. [21] J. Jugan, R. Abraham, M. Abdulkhadar, Theoretical calculation of acoustic nonlinearity parameter B/A of binary mixtures, Pramana 45 (1995) 221. [22] F.A. Bovey, P.A. Mirau, NMR of Polymers, Academic Press, USA, 1996. [23] A. Awasthi, M. Rastogi, J.P. Shukla, Ultrasonic and IR study of molecular association process through hydrogen bonding in ternary liquid mixtures, Fluid Phase Equilib. 215 (2004) 119. [24] A. Awasthi, J.P. Shukla, Ultrasonic and IR study of intermolecular association through hydrogen bonding in ternary liquid mixtures, Ultrasonics 41 (2003) 477. [25] F. Kawaizumi, M. Ohno, Y. Miyahara, Ultrasonic and volumetric investigation of aqueous solutions of amides, Bull. Chem. Soc. Jpn. 50 (1977) 2229. [26] A. Awasthi, A. Awasthi, Acoustic, volumetric, and spectroscopic studies of formamide with 2-alkoxyethanols at different temperatures, J. Chem. Thermodyn. 53 (2012) 144. [27] R.J. Fort, W.R. Moore, Adiabatic compressibilities of binary liquid mixtures, Trans. Faraday Soc. 61 (1965) 2102. [28] A.B. Coppens, R.T. Beyer, M.B. Seiden, J. Donohue, R.H. Hodson, C. Townsend, Parameter of Nonlinearity in Fluids. II, J. Acoust. Soc. Am. 38 (1965) 797. [29] D.E. Gray, American Institute of Physics Handbook, 3rd ed., McGraw Hill, New York, USA, 1972. [30] I. Rudnick, On the attenuation of finite amplitude waves in a liquid, J. Acoust. Soc. Am. 30 (1958) 564–567. [31] W.K. Law, L.A. Frizzell, F. Dunn, Determination of the nonlinearity parameter B/A of biological media, Ultrasound Med. Biol. 11 (1985) 307–318. [32] E.C. Everbach, R.E. Apfel, An interferometric technique for B/A measurement, J. Acoust. Soc. Am. 98 (1995) 3428–3438. [33] A. Awasthi, A. Awasthi, Intermolecular interactions in formamide +2-alkoxyethanols: viscometric study, Thermochim. Acta 537 (2012) 57. [34] Z. Lu, B. Lagourette, J.L. Daridon, Acoustic Nonlinearity Parameter of Liquid Alkanes as a Function of Temperature, Chain Length and Isomerism, Phys. Chem. Liq. 39 (2001) 255.
are more than 2-chloroethanol+2-DMAE systems. The higher the temperature lower is the correlation time which means that at higher temperatures the average time of collision drops causing strong interactions to occur at an earlier stage. The variation of B/A parameter is not very considerable in lieu of increase in chain length (i.e. number of carbon atoms). Hence, in order to explain the molecular and structural changes, phase shift parameter (δφ) is effectively used. According to Lu et al. [34] like the pressure derivative of sound speed, the phase shift parameter also decreases rapidly with the increasing concentration of 2-chloroethanol. The rate of decrease for the phase shift parameter is even faster than that of the pressure derivatives of sound velocity. The phase shift parameter increases rapidly with temperature. The phase shift parameter is lower for 2-chloroethanol+2-DEAE than 2-chloroethanol+2-DMAE systems. Due to an increase of carbon chain in 2-DEAE molecule, a change of molecular structure is expected. The phase shift parameter emerged as an independent parameter which is sensitive to the temperature and change in the molecular structure of the liquid mixtures. 4. Conclusions The study of behaviour of 2-chloroethanol+2-DMAE/2-DEAE systems at various temperatures and concentration in terms of nonlinear ultrasonics and molecular properties provides interesting results. The present work focuses on establishing a bridge between the real behaviour of the pressure and temperature derivatives of sound velocity and acoustic nonlinearity parameter. The excess nonlinearity parameter (B/AE) confirms the presence of intermolecular interactions in both the binary systems. Among all the three methods discussed in the present work, Beyer's method is found to be most suitable for studying the intermolecular interactions in liquid mixtures. Therefore, the acoustic nonlinearity parameter can be used as a promising parameter for the characterization in ultrasonic biomedicine. Acknowledgement This work is not supported by any funding agency. References [1] R.T. Beyer, Parameter of nonlinearity in fluids, J. Acoust. Soc. Am. 32 (1960) 719–721. [2] L. Bjorno, Forty years of nonlinear ultrasound, Ultrasonics 40 (2002) 11–17. [3] X. Jacob, C. Barriere, D. Royer, Acoustic nonlinearity parameter measurements in solids using the collinear mixing of elastic waves, Appl. Phys. Lett. 82 (2003) 886–888. [4] F.A. Duck, Nonlinear acoustics in diagnostic ultrasound, Ultrasound Med. Biol. 28 (2002) 1–18. [5] C.M. Sehgal, Non-linear ultrasonics to determine molecular properties of pure liquids, Ultrasonics 33 (1995) 155–161. [6] B. Hartman, Potential energy effects on the sound speed in liquids, J. Acoust. Soc.
7
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Physica B journal homepage: www.elsevier.com/locate/physb
Study of parameter of nonlinearity in 2-chloroethanol with 2dimethylethanolamine/2-diethylethanolamine at different temperatures
MARK
⁎
Anjali Awasthia, Aashees Awasthib, a b
Faculty of Engineering & Technology, Dr. Shakuntala Misra National Rehabilitation University, Lucknow 226 017, Uttar Pradesh, India Material Science Research Laboratory, Department of Physics, University of Lucknow, Lucknow 226 007, Uttar Pradesh, India
A R T I C L E I N F O
A BS T RAC T
Keywords: Non-linearity parameter Temperature and pressure derivatives of sound velocity Molecular properties Phase shift parameter
The acoustic non-linearity parameter (B/A) for binary mixtures of 2-chloroethanol with 2-dimethylethanolamine (2-DMAE) and 2-diethylethanolamine (2-DEAE) are evaluated using Tong Dong, Beyer and Beyer-Tong Dong coefficients at varying concentrations and temperatures ranging from 293.15 to 313.15 K. The nonlinearity parameter is used to calculate various molecular properties such as internal pressure, cohesive energy density, Van der waals’ constant, distance of closest approach, diffusion coefficient and rotational correlation time. Additionally, the intermediate quantities like temperature and pressure derivatives of sound velocity and phase shift parameter as a function of temperature are also deduced. The extent of intermolecular interactions, anharmonicity and structural configuration of the binaries under investigation are discussed in terms of excess non-linearity parameter (B/A)E.
1. Introduction The Beyer nonlinearity parameter (B/A) is a basic measure of nonlinearity of a medium and is interesting in a number of areas ranging from underwater acoustics to medicine, in case of modern medical applications of ultrasound like ultrasonic diagnostics, tissue characterization, lithotripsy etc. [1–4]. The nonlinearity parameter must be known for accurate modeling and understanding of the interactions between an ultrasonic wave and a sample. The B/A parameter determine the nonlinear correction to the velocity due to the influence of nonlinear effects caused by the propagation of finite amplitude wave. Moreover, it can be related to the molecular dynamics of the medium and it can provide information about structural properties of medium, internal pressures, clustering, inter- and intramolecular spacing, etc. [5,6]. Importance of the B/A parameter increases with the advent of high pressure technologies of food processing and preservation. B/A is significant in diagnostic and therapeutic applications of ultrasound. The diagnosis requires the knowledge of B/A for designing and optimization of the ultrasound imaging devices. For therapy, B/A predicts the temperature in the tissues during ultrasonic treatment. B/ A is widely used in ultrasonic techniques for the characterization of different media such as liquids [7] and tissues [8–11]. The present paper aims to study the effect of acoustic non-linearity parameter (B/A) on binary mixtures of 2-chloroethanol with dimethylethanolamine (2-
⁎
Corresponding author. E-mail address: aasheesawasthi@rediffmail.com (A. Awasthi).
http://dx.doi.org/10.1016/j.physb.2017.03.045 Received 23 July 2016; Received in revised form 14 March 2017; Accepted 27 March 2017 Available online 30 March 2017 0921-4526/ © 2017 Published by Elsevier B.V.
DMAE) and diethylethanolamine (2-DEAE) using Tong Dong [12], Beyer [13] and Beyer-Tong Dong [14] at varying concentrations and temperatures ranging from 293.15 to 313.15 K. 2-chloroethanol consists of both an alkyl chloride and alcohol functional groups. It is a versatile solvent used in many industrial areas. Halogenoalcohols like 2-chloroethanol are possess an additional proton-accepting group other than the hydroxyl group. This is significant as they are potentially able to act not only as bi-functional hydrogen bonding solvent but also as a strong proton-donating acid. The protein denaturation ability of halogenoalcohols is much higher than that of aliphatic alcohols. 2DMAE has been shown to remarkably enhance brain function when used as a supplement in clinical studies and also used in anti-aging formulation. 2-DEAE is used as a corrosion inhibitor in steam and condensate lines by neutralizing carbonic acid and scavenging oxygen. 2-DEAE is also used for the synthesis of local anesthetics, in antirust compounds and in photographic emulsions. B/A values are used to determine the molecular properties such as internal pressure, cohesive energy density, Van der waals’ constant, distance of closest approach, diffusion coefficient and rotational correlation time [5,7,15] Apart from this, certain intermediate quantities like temperature derivatives of sound velocity (∂u /∂T )P and pressure derivatives of sound velocity (∂u /∂P )T and phase shift parameter (δφ) as a function of temperature are also deduced. The extent of intermolecular interactions, anharmonicity and structural configuration of the binaries under investigation are discussed in terms of excess non-linearity parameter (B/A)E. The
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experimental values of density and ultrasonic velocity needed for the determination of B/A and related parameters are taken from our earlier work [16].
li =
∑
Xi ρi n
∑
Si L i
Xi ρi
i =1
(10)
2.2.1.2. Beyer and Tong-Dong coefficients. The pressure and temperature derivatives of sound velocity are calculated by TongDong method as [12]:
The propagation of ultrasonic waves is an adiabatic process hence acoustic nonlinearity parameter B/A is also a result of an adiabatic equation of state. B/A values are evaluated using three different methods namely Tong-Dong, Beyer and Beyer-Tong Dong. 2.1. Tong-Dong method Tong-Dong method uses Schaaffs relation [17] of sound velocity for the determination of B/A as:
⎛ ∂u ⎞ uβ ⎜ ⎟ = T J (x ) ⎝ ∂P ⎠T 2
(11)
⎛ ∂u ⎞ ⎤ uα ⎡ 1 − J (x ) ⎥ ⎜ ⎟ = ⎢ ⎦ ⎝ ∂T ⎠P 2 ⎣ Tα
(12)
2.3. To obtain the B/A values using Beyer and Tong-Dong method
(1)
B / A = J (0) + J (x )
To obtain the B/A values using Beyer and Tong-Dong method, the coefficients are evaluated by substituting Eqs. (11) and (12) in Eq. (7). The excess values of nonlinearity parameter (B / A)E are calculated by the relation [7,20,21]:
where,
⎛ 1 ⎞ u2ρβT J (0) = ⎜1 − ⎟ γ ⎠ Tα ⎝
x=
and θi =
i =1
2. Theory
J (x ) =
Si L i n
2(3 − 2x )2 3(x − 1)(6 − 5x )
V b
(2)
(B / A)E = (B / A)mix − (B / A)ideal
where, (B/A)mix is obtained by Tong Dong method and (B/A)ideal is obtained from its pure components as:
(3)
n
(4)
⎡ ⎤ ⎞ γRT ⎢ ⎛ Mu2 M ⎜⎜ V= − + 1 ⎟⎟ − 1⎥ ⎥⎦ ρ ρu2 ⎢⎣ ⎝ γRT ⎠
(B / A)ideal =
∑ Xi (B /A)i i =1
(14)
where, Xi is the mole fraction of pure components. The various molecular properties are calculated using the Sehgal's relation [8]:
(5)
Here, γ is specific heat, βT is the isothermal compressibility, x is the real volume of the molecules and b is van der Waals’ constant. The values of isobaric expansivity (α) are calculated from the temperature dependence of the density data of pure liquids by using the following relation [18]:
α = (−1/ ρ)(∂ρ /∂T )P
(13)
2.3.1. Internal pressure (Pi) It is the measure of the forces of attraction and repulsion between the molecules within a liquid medium. It is defined as the summation of the dispersive and repulsive forces, ionic and dipolar interactions.
(6)
Pl =
ρu2 (B / A + 1)
(15)
2.2. Beyer 2.3.2. Cohesive energy (∆A ) It is a measure of the total molecular cohesion and represents the change in internal energy of a liquid as it experiences a small isothermal expansion. It also represents the total strength or stiffness of the solvent structure [5,7].
Beyer [13] deduced non linearity parameter on the basis of thermodynamic parameters as:
⎛ ∂u ⎞ 2αTu ⎛ ∂u ⎞ B / A = 2ρu ⎜ ⎟ + ⎜ ⎟ ⎝ ∂P ⎠T CP ⎝ ∂T ⎠P
(7)
where, the specific heat at constant pressure (Cp) values for the pure liquids at the required temperatures has been calculated using group contribution method [18,19].
ΔA = −
2.2.1.1. Beyer coefficients. The intermediate quantities like temperature derivatives of sound velocity (∂u /∂T )P and pressure derivatives of sound velocity (∂u /∂P )T are deduced from the relation: n
∑ i =1
⎛ θi lV⎞ ⎤ ⎜ − i i ⎟ αi ⎥ Vai ⎠ ⎥⎦ ⎝2
a=
ρu2V 2 (B / A + 1)
b=V−
RT (B / A + 1) ρu2
(17)
(18)
(8) 2.3.4. Distance of closest approach of molecules (d) It explains as to how efficiently and closely the neighbouring molecules in a mixture are packed together.
where, τ is a constant obtained by the linear interpolation method.
⎛ n lV ⎛ ∂u ⎞ θ⎞ ⎜ ⎟ = u ⎜⎜∑ i i − i ⎟⎟ βTi ⎝ ∂P ⎠T 2⎠ ⎝ i =1 Vai
(16)
2.3.3. Effective van der Waal's constants (a and b) It is a measure of the force of attraction between the molecules and the effective volume of the molecule within the mixture.
2.2.1. Computation of temperature derivatives of sound velocity (∂u /∂T )P and pressure derivatives of sound velocity (∂u /∂P )T
⎡ ⎛ ∂u ⎞ ⎜ ⎟ = u ⎢τ + ⎝ ∂T ⎠P ⎣⎢
⎛ 82.051Tρ ⎞ Mu2 ln ⎜ ⎟ ⎠ (B / A + 1) ⎝ M
⎛ 3b ⎞1/3 d=⎜ ⎟ ⎝ 2N0 π ⎠
(9)
where, 2
(19)
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A. Awasthi, A. Awasthi
2.3.5. Diffusion coefficient or diffusivity (D) It is the constant of proportionality between the flux and potential. The higher value of diffusivity is attributed to more readily the molecules diffuse into each other within a mixture.
⎛ 2N ⎞1/3 kT D = ⎜ 02 ⎟ ⎝ 81π ⎠ ηb1/3
Table 1 Nonlinearity parameter B/A of 2-chloroethanol (1) +2-DMAE/2-DEAE (2). 2-Chloroethanol (1)+2-DMAE (2) X1
(20)
2.3.6. Rotational correlation time (τ ) It is defined as the average time between molecular collisions and is the time taken by the molecules to be in a particular state of motion [22].
τ=
ηb 4N0 kT
(21)
2.3.7. Phase shift parameter (δϕ) The phase shift parameter is an independent parameter which is sensitive to the temperature and change in the molecular structure of the liquid mixtures.
δφ =
B /A 2ρu3
(22)
3. Results and discussion The acoustic non linearity parameter B/A is a quantity which represents the magnitude of hardness of the liquids. The values of acoustic non-linearity parameter (B/A) for binary mixtures of 2chloroethanol with 2-DMAE and 2-DEAE evaluated using Tong Dong, Beyer and Beyer & Tong-Dong methods at varying concentrations and temperatures ranging from 293.15 to 313.15 K are listed in Table 1. The temperature and pressure derivative of sound velocity for both the liquid mixtures are comparatively shown in Table 2. The molecular properties of both the mixtures, deduced from the nonlinearity parameter are given in Tables 3 and 4, respectively. The variations of excess non-linearity parameter (B/A)E as a function of mole fraction of 2-chloroethanol, for both the solvent systems are shown in Figs. 1 and 2, respectively. It is seen from the Table 1 that, at a specific temperature, the acoustic non linearity parameter B/A decreases linearly with an increase in the concentration of the 2-chloroethanol for both the liquid mixtures using Tong Dong and Beyer and Tong-Dong methods. In contrast, Beyer method shows a non-linear variation in the B/A values with an increase in concentration of 2-chloroethanol for both the liquid mixtures, indicating the presence of molecular interactions. A close inspection shows a peak in the B/A values at a concentration x1=0.5001 for 2-chloroethanol+DMAE mixture and x1=0.3893 for 2-chloroethanol+DEAE mixture, where the peak of ultrasonic velocity occurred in our earlier work [16]. The plausible reason for this could be the maximum association of 2-DMAE/2-DEAE breaking up into its monomers and the hydrogen bond formation between the hydrogen atom of 2-chloroethanol and the oxygen atom of 2-DMAE/2-DEAE. But, above these concentrations, it is also probable that the 2-DMAE/2DEAE molecules may remain in the associated form. The bulkier nature of these associated molecules over 2-chloroethanol molecules may cause steric hindrance, resulting in the deterioration of the strength of the intermolecular forces. Hence, a decrease in the B/A values occurs above 0.5001 and 0.3893 concentrations for the respective systems [21,23]. The molecular interaction may involve the association due to hydrogen bonding, dipole–dipole interaction or formation of charge-transfer complexes. This phenomenon may escort strong interactive forces [16,24,25]. It is quite interesting to note that the peak of B/A values using Beyer shifts towards a lower concentration for 2-chloroethanol+2-DEAE rather than 2-chloroethanol+2-DMAE
B/A
2-Chloroethanol (1)+2-DEAE (2) X1
B/A Tong Dong
Beyer
Beyer and Tong Dong
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
9.38 9.33 9.28 9.24 9.20 9.18 9.17 9.19 9.22 9.27 9.36
11.80 12.23 12.76 13.23 13.41 13.30 13.07 12.71 12.26 11.63 10.75
11.40 11.24 11.09 10.94 10.82 10.72 10.65 10.61 10.60 10.62 10.70
12.14 11.88 11.65 11.39 11.16 10.98 10.88 10.84 10.82 10.82 10.84
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
9.29 9.25 9.20 9.16 9.13 9.13 9.15 9.19 9.25 9.34 9.48
11.63 12.11 12.66 13.16 13.32 13.21 12.99 12.63 12.15 11.49 10.58
11.30 11.15 11.00 10.85 10.75 10.67 10.63 10.62 10.65 10.71 10.84
12.57 12.23 11.91 11.58 11.33 11.12 11.02 11.00 11.00 11.03 11.09
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
9.29 9.24 9.18 9.14 9.12 9.15 9.20 9.27 9.37 9.50 9.69
11.47 12.02 12.62 13.14 13.34 13.23 12.99 12.61 12.10 11.39 10.43
11.31 11.15 10.99 10.84 10.74 10.70 10.69 10.73 10.79 10.90 11.09
Tong Dong
Beyer
Beyer and Tong Dong
293.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
9.89 9.78 9.68 9.57 9.47 9.40 9.36 9.34 9.34 9.35 9.36
11.89 12.23 12.56 12.92 13.21 13.28 13.11 12.71 12.14 11.45 10.75
11.89 11.68 11.48 11.27 11.08 10.92 10.82 10.76 10.72 10.70 10.70
303.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
10.04 9.91 9.78 9.64 9.52 9.43 9.39 9.40 9.41 9.44 9.48
11.70 12.07 12.43 12.81 13.14 13.23 13.06 12.60 12.02 11.31 10.58
313.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
10.34 10.15 9.96 9.77 9.64 9.54 9.50 9.52 9.56 9.61 9.69
11.54 11.95 12.35 12.79 13.07 13.17 12.99 12.54 11.93 11.19 10.43
system. This may be due to the more acidic nature of 2-chloroethanol in comparison to 2-DMAE/2-DEAE molecules. Since, Cl- group of 2chloroethanol has -Inductive effect, while CH3/ C2H5 group of 2DMAE/2-DEAE have +Inductive effect, therefore, 2-DEAE reacts with 2-chloroethanol more rapidly, giving rise to the peak of B/A at a lower concentration than with 2-DMAE mixture. The values of B/A using Beyer method are slightly higher than those for Tong-Dong and Beyer-Tong Dong methods. The increase in temperature causes B/A values to increase using Tong-Dong and Beyer and Tong-Dong method while decreases using Beyer method. The variations of acoustic nonlinearity parameter using Tong-Dong and Beyer-Tong Dong methods show a different trend as compared to the non-monotonous behaviour revealed by the Beyer method. TongDong considered liquid as a system of rigid balls and expressed it as a function of molecular radii of the chosen liquid. Tong-Dong and BeyerTong Dong methods provide a reasonable approach towards estimation of B/A for small molecules but completely fails in prediction involving longer molecules. The inaccuracy in predicting B/A values using TongDong and Beyer-Tong Dong methods may be a result of overestimation of molecular radii based on the hypothesis of spherically symmetric larger molecules. From the Figs. 1 and 2, B/AE is found to be negative and non-linear indicating the presence of specific interactions between 2-chloroetha3
Physica B 515 (2017) 1–7
A. Awasthi, A. Awasthi
Table 2 Pressure and temperature coefficients of 2-chloroethanol (1) +2-DMAE/2-DEAE (2). 2-Chloroethanol (1)+DMAE (2) X1
2-Chloroethanol (1)+DEAE (2)
Beyer
Beyer and Tong-Dong
(∂u/∂P)T (10−6 m3/sN)
(∂u/∂T)P (m/sK)
(∂u/∂P)T (10−6 m3/sN)
(∂u/∂T)P (m/sK)
293.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
4.92 4.83 4.76 4.67 4.56 4.40 4.23 4.01 3.77 3.51 3.26
−0.73 −0.74 −0.74 −0.74 −0.74 −0.74 −0.74 −0.73 −0.72 −0.71 −0.70
4.92 4.62 4.36 4.08 3.83 3.62 3.49 3.40 3.33 3.28 3.25
−3.07 −3.05 −3.04 −3.03 −3.02 −3.02 −3.01 −3.01 −3.01 −3.02 −3.02
303.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
5.02 4.94 4.87 4.79 4.68 4.52 4.34 4.11 3.85 3.57 3.31
−0.90 −0.90 −0.90 −0.91 −0.92 −0.92 −0.91 −0.90 −0.89 −0.88 −0.87
5.21 4.87 4.57 4.26 3.98 3.75 3.62 3.54 3.47 3.42 3.39
313.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
5.13 5.06 5.01 4.93 4.81 4.65 4.46 4.21 3.94 3.65 3.36
−1.04 −1.05 −1.06 −1.07 −1.07 −1.07 −1.07 −1.06 −1.05 −1.04 −1.02
5.60 5.19 4.83 4.47 4.17 3.93 3.79 3.70 3.64 3.60 3.58
X1
Beyer
Beyer and Tong-Dong
(∂u/∂P)T (10−6 m3/sN)
(∂u/∂T)P (m/sK)
(∂u/∂P)T (10−6 m3/sN)
(∂u/∂T)P (m/sK)
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
4.89 4.83 4.80 4.74 4.64 4.47 4.29 4.07 3.84 3.58 3.26
−1.29 −1.27 −1.25 −1.23 −1.19 −1.13 −1.07 −1.00 −0.91 −0.82 −0.70
4.72 4.44 4.17 3.92 3.75 3.60 3.50 3.40 3.33 3.27 3.25
−3.42 −3.38 −3.35 −3.31 −3.26 −3.18 −3.12 −3.07 −3.04 −3.02 −3.02
−3.28 −3.26 −3.23 −3.21 −3.19 −3.18 −3.18 −3.18 −3.19 −3.20 −3.22
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
5.00 4.96 4.92 4.87 4.76 4.58 4.40 4.18 3.93 3.64 3.31
−1.45 −1.44 −1.42 −1.40 −1.36 −1.30 −1.24 −1.17 −1.08 −0.99 −0.87
4.86 4.57 4.28 4.02 3.85 3.71 3.61 3.52 3.45 3.40 3.39
−3.48 −3.45 −3.42 −3.40 −3.35 −3.29 −3.24 −3.21 −3.19 −3.20 −3.22
−3.57 −3.51 −3.47 −3.42 −3.39 −3.37 −3.37 −3.38 −3.40 −3.43 −3.46
0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
5.16 5.14 5.11 5.06 4.95 4.76 4.56 4.32 4.05 3.73 3.36
−1.58 −1.58 −1.57 −1.55 −1.52 −1.46 −1.40 −1.32 −1.24 −1.14 −1.02
5.09 4.77 4.45 4.17 3.99 3.85 3.76 3.68 3.62 3.58 3.58
−3.56 −3.53 −3.51 −3.48 −3.45 −3.41 −3.38 −3.37 −3.38 −3.40 −3.46
the range 1–1.5. Hence,(∂u /∂T )P < 0 ,(∂u /∂P )T > 0 and B/A > 8 [29]. It was found that the values of temperature derivatives and pressure derivatives of sound velocity, at constant temperature decreases slowly with the increasing concentration of 2-chloroethanol using Beyer and Beyer-Tong Dong methods. A close inspection shows that (∂u /∂P )T for Beyer-Tong Dong is slightly higher than that obtained by Beyer method. The increase in temperature causes the pressure derivatives to increase by both the methods for the liquid mixtures under investigation. Moreover, the pressure derivatives for 2-chloroethanol +2-DEAE are slightly more than 2-chloroethanol+2-DMAE system using Beyer method. This may be ascribed to an increase of carbon chain in 2-DEAE as compared to 2-DMAE. The value of temperature derivatives (∂u /∂T )P is almost insignificant in terms of increasing concentrations of 2-chloroethanol for both the liquid mixtures. As the temperature increases, there is a distinctive increase in the values of temperature derivatives. The temperature derivatives are higher for 2-chloroethanol+2-DEAE than 2-chloroethanol+2-DMAE systems. The value of temperature derivatives of sound velocity (∂u /∂P )T using Beyer method is comparatively higher than Beyer- Tong Dong method for both the binary liquid mixtures, at all temperatures. As the temperature is raised, the values of (∂u /∂P )T is found to increase for both Beyer and Beyer-Tong Dong methods. It is observed that the value of (∂u /∂P )T using Beyer method is higher for 2-chloroethanol+2-DEAE than 2chloroethanol+2-DMAE systems. The value of temperature derivatives
nol +2-DMAE/2-DEAE systems. A similar trend was observed in terms of excess acoustic parameters discussed in our earlier work [21]. The nonlinear behaviour of (B/A)E indicates the presence of intermolecular interactions between the unlike molecules [26,27]. When 2-chloroethanol molecules are mixed with 2-DMAE/2-DEAE molecules, it may induce mutual dissociation of the hydrogen bonded structure present in the pure forms following the creation of new hydrogen bonds between 2-chloroethanol and 2-DMAE/2-DEAE molecules, resulting in a decrease in the B/A values of the mixture and hence negative B/AE values are observed. The B/AE values become more negative with increase in temperature of the mixture. As the temperature is increased, thermal energy helps the breaking of bonds between the associated molecules of 2-chloroethanol+2-DMAE/2-DEAE into their monomers, resulting in further decrease in the B/AE values. The position of maxima of excess B/A does not change with an increase in temperature. The interactions between the components of the liquid mixtures may be attributed to effects like hydrogen bonding, chargetransfer, dipole-dipole interactions etc. It is seen from the Table 2 that the temperature derivatives of sound velocity (∂u /∂T )P are negative and pressure derivatives of sound velocity (∂u /∂P )T are positive [20,28]. At atmospheric temperature and room temperature, for most of the organic liquids, the thermal expansion coefficient is within a range of 0.5–1.7×10−3 K, adiabatic compressibility is of the order of 10−1 m2 N−1 and specific heat capacity ratio in
4
Physica B 515 (2017) 1–7
A. Awasthi, A. Awasthi
Table 3 Molecular properties of 2-Chloroethanol (1) +2-DMAE (2). Pi (MPa)
ΔΑ (KJ/mole)
a (l2 atm/mole2)
b (l/mole)
d (Å)
D (10−9 m2 s−1)
τ (ps)
δφ (10–12 s3 kg−1)
293.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
151.25 160.54 169.97 181.22 193.05 203.27 209.59 213.22 215.55 217.33 218.10
−83.23 −84.68 −86.45 −88.54 −90.55 −91.58 −91.44 −90.31 −88.83 −87.31 −85.96
14.78 14.14 13.70 13.25 12.78 12.20 11.64 11.03 10.43 9.89 9.48
0.084 0.080 0.077 0.073 0.070 0.067 0.064 0.062 0.059 0.057 0.056
4.06 3.99 3.94 3.88 3.82 3.75 3.70 3.66 3.61 3.57 3.54
1.15 1.17 1.18 1.20 1.21 1.24 1.29 1.36 1.43 1.51 1.57
0.415 0.406 0.402 0.398 0.393 0.382 0.369 0.351 0.333 0.316 0.303
2.20 2.07 1.94 1.80 1.68 1.59 1.54 1.52 1.51 1.51 1.51
303.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
140.19 149.57 159.17 170.71 182.99 193.22 199.28 201.87 203.67 205.02 205.19
−78.21 −80.11 −82.24 −84.78 −87.26 −88.48 −88.41 −86.95 −85.33 −83.63 −81.98
13.96 13.48 13.14 12.80 12.43 11.90 11.37 10.72 10.12 9.55 9.09
0.083 0.080 0.076 0.073 0.070 0.067 0.064 0.062 0.059 0.057 0.055
4.04 3.98 3.93 3.87 3.81 3.75 3.70 3.66 3.61 3.56 3.53
1.27 1.29 1.30 1.30 1.30 1.34 1.38 1.46 1.54 1.63 1.71
0.374 0.369 0.367 0.367 0.365 0.356 0.344 0.326 0.309 0.292 0.278
2.44 2.27 2.12 1.95 1.80 1.70 1.65 1.64 1.63 1.63 1.64
313.15 K 0.0000 0.1009 0.1885 0.2862 0.3887 0.5001 0.5982 0.7005 0.8044 0.9098 1.0000
128.13 137.99 148.18 160.62 171.69 181.90 187.62 190.09 191.16 191.68 190.83
−72.48 −75.00 −77.77 −81.07 −83.26 −84.74 −84.67 −83.23 −81.38 −79.35 −77.27
13.01 12.71 12.53 12.35 11.98 11.52 11.00 10.36 9.74 9.13 8.61
0.082 0.079 0.076 0.073 0.070 0.067 0.064 0.061 0.059 0.057 0.055
4.02 3.97 3.92 3.87 3.81 3.75 3.70 3.65 3.60 3.55 3.51
1.42 1.43 1.42 1.40 1.41 1.44 1.49 1.57 1.67 1.77 1.88
0.334 0.334 0.336 0.340 0.337 0.331 0.319 0.303 0.285 0.268 0.253
2.75 2.53 2.33 2.12 1.96 1.84 1.78 1.77 1.77 1.78 1.81
X1
decrease in both the systems. The cohesive energy is found to exhibit a nonlinear variation with peak obtained at the same concentration of 2-chloroethanol where peak of B/A values using Beyer were obtained for 2-chloroethanol+2DMAE system, at a given temperature. The cohesive energy for 2chloroethanol+2-DEAE decreases with increasing concentration. On increasing the temperature, cohesive energy decreases in both the binary systems [33]. The variation of cohesive energy confirms the formation of intermolecular hydrogen bonding between 2-chloroethanol and 2-DMAE/2-DEAE molecules [16,33]. The effective van der Waal's constant ‘a’ and ‘b’ follows a decreasing trend with increasing mole fractions of 2-chloroethanol for both the systems. A close examination shows that the values of van der Waals’ constant are higher in case of 2-chloroethanol+2-DEAE than 2-chloroethanol+2-DMAE systems. With an increase in temperature, van der Waals’ constant ‘a’ also decreases gradually but the effect on constant ‘b’ is found to be almost insignificant. The distance of closest approach of molecules ‘d’ decreases for the binary liquid systems with the increase in the concentration of 2chloroethanol. It not only depends upon how close the neighbouring molecules are, but also on how efficiently they are packed together. The variations in the values of the distance of the closest approach of molecules follows the same variations as that of ‘a′ and ‘b′. When the temperature is increased, d values are found to decrease gradually with the concentration. This indicates strong intermolecular interactions to occur between 2-chloroethanol and 2-DMAE/2-DEAE molecules. The values of d are greater for 2-chloroethanol+2-DEAE than 2Chloroethanol+2-DMAE systems.
(∂u /∂T )P is almost insignificant in terms of increasing concentrations of 2-chloroethanol for both the liquid mixtures. As the temperature increases, there is a gradual increase in the values of temperature derivatives. The temperature derivatives are higher for 2-chloroethanol +2-DEAE than 2-chloroethanol+2-DMAE systems. Thus, the dependence of B/A on pressure derivatives is more than that on temperature, specifying a decreasing trend in case of pressure and being upto reasonable extent temperature independent. It also depicts the fact that B/A is mainly dependent on pressure derivatives of sound velocity which signifies an increase in phase velocity brought about by pressure while temperature derivatives of sound velocity gives an increase due to temperature [30]. In the estimation process of B/A, pressure derivatives are calculated more accurately than the temperature derivatives. Hence, uncertainty due to pressure derivative dominates temperature derivative as it is affected by the goodness of (∂u /∂P )T . The accuracy for the determination of B/A using Beyer's method is approximately 5% [31,32]. Molecular properties evaluated using Sehgal's relation are advantageous in a sense that they reveal some distinctive physical features of liquids and resolution rate in medical imaging. It is seen from the Tables 3 and 4 that at given temperature, the internal pressure increases progressively with increasing concentrations of 2-chloroethanol for both the liquid mixtures. This behaviour of the internal pressure indicates stronger molecular interactions between the contributory binaries, in both the systems. It is also visible that internal pressure values are slightly higher for 2-chloroethanol+2DEAE than 2-chloroethanol+2-DMAE systems, at a particular temperature. The rise in temperature causes internal pressure is to 5
Physica B 515 (2017) 1–7
A. Awasthi, A. Awasthi
Table 4 Molecular properties of 2-chloroethanol (1)+2-DEAE (2). Pi (MPa)
ΔΑ (KJ/mole)
a (l2 atm/mole2)
b (l/mole)
d (Å)
D (10−9 m2 s−1)
τ (ps)
δφ (10–12 s3 kg−1)
293.15 K 0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
159.02 168.09 179.11 190.52 198.20 203.42 207.07 210.84 214.30 217.31 218.10
−109.61 −109.04 −109.56 −109.75 −108.23 −104.47 −100.79 −96.86 −93.30 −89.77 −85.96
27.05 24.61 22.69 20.83 19.00 16.79 15.00 13.27 11.84 10.58 9.48
0.117 0.108 0.101 0.093 0.087 0.080 0.075 0.069 0.064 0.060 0.056
4.53 4.41 4.31 4.20 4.10 3.99 3.90 3.80 3.71 3.62 3.54
0.54 0.58 0.62 0.67 0.73 0.84 0.95 1.09 1.23 1.39 1.57
0.889 0.816 0.764 0.710 0.648 0.567 0.501 0.438 0.387 0.342 0.303
2.08 1.96 1.82 1.70 1.63 1.59 1.58 1.55 1.53 1.51 1.51
303.15 K 0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
150.56 159.77 170.71 182.01 189.12 193.89 197.23 200.55 203.14 205.06 205.19
−105.36 −105.36 −106.19 −106.62 −105.02 −101.25 −97.63 −93.67 −89.88 −86.03 −81.98
26.16 23.98 22.19 20.42 18.61 16.43 14.67 12.95 11.51 10.22 9.09
0.117 0.109 0.101 0.094 0.087 0.081 0.075 0.069 0.064 0.059 0.055
4.53 4.42 4.31 4.21 4.11 4.00 3.90 3.80 3.70 3.61 3.53
0.59 0.63 0.67 0.72 0.79 0.90 1.02 1.17 1.33 1.51 1.71
0.810 0.751 0.706 0.659 0.602 0.526 0.466 0.407 0.359 0.316 0.278
2.25 2.11 1.95 1.81 1.74 1.71 1.68 1.66 1.65 1.64 1.64
313.15 K 0.0000 0.0994 0.1957 0.2966 0.3893 0.4984 0.5950 0.7014 0.8020 0.9024 1.0000
138.83 148.47 159.57 170.68 177.82 182.31 185.08 187.75 189.92 191.23 190.83
−98.60 −99.46 −100.87 −101.57 −100.27 −96.68 −93.05 −89.07 −85.35 −81.42 −77.27
24.64 22.82 21.26 19.61 17.91 15.81 14.10 12.42 11.02 9.75 8.61
0.117 0.108 0.101 0.094 0.087 0.080 0.075 0.069 0.064 0.059 0.055
4.52 4.41 4.31 4.20 4.11 3.99 3.90 3.79 3.70 3.60 3.51
0.67 0.71 0.75 0.80 0.87 0.99 1.12 1.28 1.45 1.65 1.88
0.714 0.672 0.638 0.598 0.548 0.481 0.426 0.372 0.328 0.289 0.253
2.53 2.34 2.15 1.98 1.90 1.86 1.84 1.82 1.80 1.80 1.81
X1
Fig. 2. Plot of (B/A)E versus mole fraction of 2-Chloroethanol in 2-Chloroethanol (1) +2DEAE (2) mixtures.
Fig. 1. Plot of (B/A)E versus mole fraction of 2-Chloroethanol in 2-Chloroethanol (1) +2DMAE (2) mixtures.
The rotational correlation time ‘τ ’ is defined as the average time between molecular collisions and is the time taken by the molecules to be in a particular state of motion [22]. The correlation time decreases with concentration as well as temperature for both the binary liquid mixtures. This means that the motion of the molecules becomes faster showing strong intermolecular interactions in both the liquid mixtures. However, the values of correlation time for 2-chloroethanol+2-DEAE
The diffusion coefficient ‘D’ increases steadily for both the binary systems with increasing mole fractions of 2-chloroethanol, at a particular temperature. As the temperature increases, it causes the diffusion coefficient to increase. This means that greater the value of diffusivity, the faster the molecules diffuse into each other within a mixture leading to strong intermolecular interactions. 6
Physica B 515 (2017) 1–7
A. Awasthi, A. Awasthi
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are more than 2-chloroethanol+2-DMAE systems. The higher the temperature lower is the correlation time which means that at higher temperatures the average time of collision drops causing strong interactions to occur at an earlier stage. The variation of B/A parameter is not very considerable in lieu of increase in chain length (i.e. number of carbon atoms). Hence, in order to explain the molecular and structural changes, phase shift parameter (δφ) is effectively used. According to Lu et al. [34] like the pressure derivative of sound speed, the phase shift parameter also decreases rapidly with the increasing concentration of 2-chloroethanol. The rate of decrease for the phase shift parameter is even faster than that of the pressure derivatives of sound velocity. The phase shift parameter increases rapidly with temperature. The phase shift parameter is lower for 2-chloroethanol+2-DEAE than 2-chloroethanol+2-DMAE systems. Due to an increase of carbon chain in 2-DEAE molecule, a change of molecular structure is expected. The phase shift parameter emerged as an independent parameter which is sensitive to the temperature and change in the molecular structure of the liquid mixtures. 4. Conclusions The study of behaviour of 2-chloroethanol+2-DMAE/2-DEAE systems at various temperatures and concentration in terms of nonlinear ultrasonics and molecular properties provides interesting results. The present work focuses on establishing a bridge between the real behaviour of the pressure and temperature derivatives of sound velocity and acoustic nonlinearity parameter. The excess nonlinearity parameter (B/AE) confirms the presence of intermolecular interactions in both the binary systems. Among all the three methods discussed in the present work, Beyer's method is found to be most suitable for studying the intermolecular interactions in liquid mixtures. Therefore, the acoustic nonlinearity parameter can be used as a promising parameter for the characterization in ultrasonic biomedicine. Acknowledgement This work is not supported by any funding agency. References [1] R.T. Beyer, Parameter of nonlinearity in fluids, J. Acoust. Soc. Am. 32 (1960) 719–721. [2] L. Bjorno, Forty years of nonlinear ultrasound, Ultrasonics 40 (2002) 11–17. [3] X. Jacob, C. Barriere, D. Royer, Acoustic nonlinearity parameter measurements in solids using the collinear mixing of elastic waves, Appl. Phys. Lett. 82 (2003) 886–888. [4] F.A. Duck, Nonlinear acoustics in diagnostic ultrasound, Ultrasound Med. Biol. 28 (2002) 1–18. [5] C.M. Sehgal, Non-linear ultrasonics to determine molecular properties of pure liquids, Ultrasonics 33 (1995) 155–161. [6] B. Hartman, Potential energy effects on the sound speed in liquids, J. Acoust. Soc.
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