# Effect of Solvents on the Ultrasonic Velocity and Acoustic Parameters of Polyvinylidene Fluoride Solutions

Authors: S. S. Kulkarni; U. V. Khadke
Journal: Indian Journal of Materials Science
 (2016)

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## Abstract

Ultrasonic studies provide a wealth of information in understanding the molecular behavior and intermolecular interaction of polymer solvent mixtures. Attempts were made to measure ultrasonic velocity, density, and viscosity for the mixture of polyvinylidene fluoride (PVDF) in acetone and dimethylformamide (DMF) of various stoichiometric ratios at 300 K using crystal controlled ultrasonic interferometer (Mittal make), pyknometer (specific gravity bottle), and Ostwald viscometer, respectively. The acoustic parameters adiabatic compressibility (β), intermolecular free path length (Lf), acoustic impedance (Z), relative association (RA), ultrasonic attenuation (α/f2), and relaxation time (τ) have been estimated using experimental data with well-known techniques. The variation of these acoustic parameters is explained in terms of solute-solvent molecular interaction in a polymer solution.


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## Body

## 1. Introduction

Ultrasonic studies in polymeric solutions have drawn the attention of many researchers in the recent years [1–4]. The extensive use of polymeric materials in technology has necessitated investigations of the molecular interactions of polymers and solvents [5–9]. The ultrasonic technique is a powerful and effective tool for investigation of polymer solutions and behavior of polymer chain in an ultrasonic field.Polyvinylidene fluoride (PVDF) is a semicrystalline polymer that has a simple chemical structure[-(CH2-CF2)-]n. It is the first ferroelectric polymer and unique among many inorganic and organic ferroelectric substances [10, 11]. The PVDF exists in four crystalline forms, namely, α,  β,  γ, and δ, depending upon preparation conditions. It has attracted researchers due to its piezo-, pyro-, and ferroelectric characteristics [12]. These properties are useful for device application such as ultrasound transducers, nonvolatile memory, sensors, actuators, sonar instruments, and solar cells. The scarcity of knowledge regarding the ultrasonic studies of solutions of PVDF in the literature has promoted us to understand the effect of concentration and nature of solvents on the molecular interactions in the polymer solution. The physical properties of this ferroelectric polymer can be understood better by the study of molecular interaction.In our experimental investigation, we used the ultrasonic technique to find the acoustic parameters such as adiabatic compressibility (β), intermolecular free path length (Lf), acoustic impedance (Z), relative association (RA), ultrasonic attenuation, and relaxation time to correlate with the physical properties.


## 2. Materials and Methods

AR grade (99.8% pure) ferroelectric polymer PVDF in powder form is procured from Sigma Aldrich, Bangalore, India. Figure1 shows the X-ray diffraction pattern of the procured PVDF. The diffraction peak observed at 2θ = 18.09°, 19.58° confirms the β-phase of the powder sample. This PVDF powder is mixed with different concentrations of acetone (AR grade 99.5%) and DMF (AR grade 99.5%), both the solvents procured from High-Media Laboratories Pvt. Ltd., Mumbai, India. The solution was magnetically stirred for 2 hours, so that the powder dissolves completely. The acoustic properties are studied in this prepared solution.Figure 1
XRD pattern of virgin PVDF powder confirming the phase formation.


### 2.1. Experimental Technique

Ultrasonic interferometer, specific gravity bottle, and Ostwald viscometer are used to measure ultrasonic velocity, density, and viscosity, respectively.Ultrasonic velocity was measured using a single-crystal interferometer (Mittal Enterprises, New Delhi) operating at 1 MHz with an accuracy of ±1.0 m/s. The experimental procedures are standard and described elsewhere [13]. Densities of the solutions were measured using a 25 mL specific gravity bottle and the weight of the liquid was measured using an electronic balance (Model Shimadzu AX200). The measurement was repeated thrice for the same solution to obtain better accuracy. Accuracy in the measurement of densities of the solutions is ±0.1 kg/m3. The viscosity was measured with Ostwald’s viscometer and the flow time with a digital stopwatch. The measurements were repeated thrice to confirm the accuracy of results. The time flow is measured using digital stopwatch capable of registering time accurate to ±0.1 s.The acoustic parameters were computed as follows.The ultrasonic velocity is calculated as(1)v=fλ,where “f” is the frequency of the ultrasonic waves and “λ” is the measured wavelength value of ultrasonic waves in a given solution.The viscosity of the solution is calculated using(2)η=dltldwtwηw,where dl and tl are density and time flow of liquid, whereas dw and tw are density and time flow of water. The density of the solution is taken as mass per unit volume.The following equations are used to compute the acoustic parameters: adiabatic compressibility (β), intermolecular free path length (Lf), acoustic impedance (Z), relative association (RA), ultrasonic attenuation (α/f2), and relaxation time (τ).


### 2.2. Theoretical Calculations

(1)
Adiabatic compressibility (β) has been calculated from the ultrasonic velocity “v” and the density “ρ” of the solution using the Newton-Laplace equation [14]:(3)β=1ρv2.
(2)
Intermolecular free path length (Lf) has been determined as follows [15]:(4)Lf=Kβ1/2,
whereK is the temperature dependent Jacobson’s constant (K=205.35×10-8 at 300 K) and β is the adiabatic compressibility.
(3)
Acoustic impedance (Z) is given as follows:(5)Z=ρv,
whereρ and v are the density and velocity of the solution, respectively.
(4)
Relative association (RA) is as follows:(6)RA=ρρovov,
whereρo and vo are the density and velocity of the solvent.
(5)
Ultrasonic attenuation (α/f2) and relaxation time (τ) were calculated using the following [16]:(7)αf2=8π2ηρv3,τ=4η3ρv2,
whereη is the viscosity of the solution.


## 2.1. Experimental Technique

Ultrasonic interferometer, specific gravity bottle, and Ostwald viscometer are used to measure ultrasonic velocity, density, and viscosity, respectively.Ultrasonic velocity was measured using a single-crystal interferometer (Mittal Enterprises, New Delhi) operating at 1 MHz with an accuracy of ±1.0 m/s. The experimental procedures are standard and described elsewhere [13]. Densities of the solutions were measured using a 25 mL specific gravity bottle and the weight of the liquid was measured using an electronic balance (Model Shimadzu AX200). The measurement was repeated thrice for the same solution to obtain better accuracy. Accuracy in the measurement of densities of the solutions is ±0.1 kg/m3. The viscosity was measured with Ostwald’s viscometer and the flow time with a digital stopwatch. The measurements were repeated thrice to confirm the accuracy of results. The time flow is measured using digital stopwatch capable of registering time accurate to ±0.1 s.The acoustic parameters were computed as follows.The ultrasonic velocity is calculated as(1)v=fλ,where “f” is the frequency of the ultrasonic waves and “λ” is the measured wavelength value of ultrasonic waves in a given solution.The viscosity of the solution is calculated using(2)η=dltldwtwηw,where dl and tl are density and time flow of liquid, whereas dw and tw are density and time flow of water. The density of the solution is taken as mass per unit volume.The following equations are used to compute the acoustic parameters: adiabatic compressibility (β), intermolecular free path length (Lf), acoustic impedance (Z), relative association (RA), ultrasonic attenuation (α/f2), and relaxation time (τ).


## 2.2. Theoretical Calculations

(1)
Adiabatic compressibility (β) has been calculated from the ultrasonic velocity “v” and the density “ρ” of the solution using the Newton-Laplace equation [14]:(3)β=1ρv2.
(2)
Intermolecular free path length (Lf) has been determined as follows [15]:(4)Lf=Kβ1/2,
whereK is the temperature dependent Jacobson’s constant (K=205.35×10-8 at 300 K) and β is the adiabatic compressibility.
(3)
Acoustic impedance (Z) is given as follows:(5)Z=ρv,
whereρ and v are the density and velocity of the solution, respectively.
(4)
Relative association (RA) is as follows:(6)RA=ρρovov,
whereρo and vo are the density and velocity of the solvent.
(5)
Ultrasonic attenuation (α/f2) and relaxation time (τ) were calculated using the following [16]:(7)αf2=8π2ηρv3,τ=4η3ρv2,
whereη is the viscosity of the solution.


## 3. Results and Discussion

The experimentally obtained values of density, viscosity, and ultrasonic velocity of PVDF with different concentrations of acetone and DMF are reported in Tables1 and 2, respectively. Due to specific molecular interactions such as association, expansion, and unfolding the variation of η and v with c is considerably more than that of ρ. Molecular interactions depend on the strength of the repulsive forces acting among solvent and solute molecules and hence intermolecular motion is affected accordingly. Attractive forces result into molecular association (solvation), that is, modification of the PVDF molecule. Molecular association leads to change in apparent molecular volume as well as mass and hence density changes accordingly. Under a set of experimental conditions the values of ρ, η, and v are affected by molecular interaction. Vander Waals, H-bonding, dipolar, and London types forces between solvent and solute molecules result in the aggregation of solvent molecules around solute molecules. It shows that the density, viscosity, and ultrasonic velocity of the solution increase with increase in concentration. This linear increase of ρ, η, and v with concentration confirms an increase of cohesive forces because of strong molecular interactions [17]. The values of density, viscosity, and ultrasonic velocity of the solution increased by ~1%, ~7.1% , and  0.5% and 0.7%, 69%,  and 2%, respectively, for the 50% concentration of PVDF in acetone and DMF. The least square equations along with regression coefficients are reported in Table 3. A fairly good to excellent correlation between given parameters and concentration was observed in acetone and DMF solvents. The observed correlation between ρ,  η,  and v with concentration is R2 = 0.929–0.992, 0.949–0.961, and 0.90–0.987, respectively. The obtained values of R2 support linear dependence of ρ,  η, and v with concentration.Table 1
Variation of density, viscosity, and ultrasonic velocity of PVDF with different concentrations of acetone at 300 K.
Concentrationc mass%
Densityρ kg/m3
Viscosityη 10−3 Nsm−2
Ultrasonic velocityv m/s
0.00
783.00
0.3635
1165.00
0.10
783.56
0.3665
1165.90
0.20
784.10
0.3672
1166.50
0.30
784.68
0.3747
1168.00
0.40
787.76
0.3836
1169.00
0.50
790.36
0.3893
1170.80
Compounded uncertainty in measurement of density (Uρ) = ±0.52, viscosity (Uη) = ±0.0188, and ultrasonic velocity (Uv) = ±0.20 with level of confidence is 95%.Table 2
Variation of density, viscosity, and ultrasonic velocity of PVDF with different concentrations of dimethylformamide at 300 K.
Concentrationc mass%
Densityρ kg/m3
Viscosityη 10−3 Nsm−2
Ultrasonic velocityv m/s
0.00
934.20
0.7921
1454.00
0.10
934.92
0.9084
1474.00
0.20
937.04
0.9156
1478.00
0.30
938.16
1.0505
1482.50
0.40
939.04
1.0818
1485.00
0.50
940.88
1.3422
1486.60
Compounded uncertainty in measurement of density (Uρ) = ±0.52, viscosity (Uη) = ±0.0188, and ultrasonic velocity (Uv) = ±0.20 with level of confidence is 95%.Table 3
The least square equations and regression coefficients for PVDF solution in acetone and DMF.
Parameters
Regression coefficients (R2)
Acetone
DMF
ρ kg/m3
14.28
c
+
782.00
0.929
13.394
c
+
934.024
0.992
η   10−3 Nsm−2
5.257
×
10
-
5
c
+
3.611
×
10
-
4
0.961
9.685
×
10
-
4
c
+
7.7219
×
10
-
4
0.949
v
m/s
11.37
c
+
1164.69
0.987
57.285
c
+
1462.36
0.890
β 10−10 m2/N
-
0.35097
c
+
9.42638
-
0.968
-
0.45354
c
+
5.0065
-
0.916
Z 106 kgm2s−1
0.02309
c
+
0.91106
0.971
0.07346
c
+
1.36582
0.940
L
f 10−11 m
-
0.11817
c
+
6.31044
-
0.968
-
0.21003
c
+
4.59886
-
0.917
RA
2.2614
×
10
-
5
c
+
2.3064
×
10
-
14
0.957
2.207
×
10
-
14
c
+
2.095
×
10
-
14
0.931
τ 10−13 s
4.913
×
10
-
14
c
+
4.534
×
10
-
13
0.962
5.1685
×
10
-
13
+
5.7522
×
10
-
13
0.938
α
/
f
2 10−14 s2m−1
0.96994
c
+
8.95398
0.962
2.207
×
10
-
14
c
+
2.0959
×
10
-
14
0.931In order to understand the effect of concentration and nature of solvent on PVDF polymeric solution, the acoustic parameters such as adiabatic compressibility (β), intermolecular free pathlength (Lf), acoustic impedance (Z), relative association (RA), ultrasonic attenuation (α/f2), and relaxation time (τ) were determined using standard equations and are correlated with concentration as shown in Figures 2, 3, 4, 5, 6, and 7. The least square and regression coefficients of these acoustic parameters are shown in Table 3.Figure 2
Variation of adiabatic compressibility with concentration of PVDF in acetone and DMF at 300 K.Figure 3
Variation of intermolecular free path length with concentration of PVDF in acetone and DMF at 300 K.Figure 4
Variation of acoustic impedance with concentration of PVDF in acetone and DMF at 300 K.Figure 5
Variation of ultrasonic attenuation with concentration of PVDF in acetone and DMF at 300 K.Figure 6
Variation of relative association with concentration of PVDF in acetone and DMF at 300 K.Figure 7
Variation of relaxation time with concentration of PVDF in acetone and DMF at 300 K.Ultrasonic speed in the solutions depends on intermolecular free path length. When ultrasonic waves are present in the solution, the molecules get perturbed. Due to some elasticity of the medium, perturbed molecules regain their equilibrium positions. When a solute is added to a solvent, its molecules attract certain solvent molecules towards them. The phenomenon is known as compression and also as limiting compressibility. The aggregation of solvent molecules around solute molecules supports powerful solvent-solute interactions. Because of solvent-solute interactions, the structure of the solute is modified to the considerable extent. The adiabatic compressibility and intermolecular free path length decrease from those of pure solution by ~2% and 1% and 5% and 2.5%, respectively, in acetone and DMF. Decrease ofLf with concentration supports solvent-solute interactions. However, acoustic impedance, relative association, ultrasonic attenuation, and relaxation time increase by 1.2%, 0.7%, 4.5%, and 5.05% and 3%, 0.027%, 57%, and 61% with respect to those in pure solution of acetone and DMF, respectively. This indicates a strong intermolecular interaction between solute and solvent molecules in the system at higher concentration of PVDF and suggests more association between solute and solvent molecules in the system.The variation of ultrasonic velocity in a solution depends on the intermolecular free length on mixing. On the basis of a model for sound propagation proposed by Kincaid and Eyring [18] ultrasonic velocity increases with decrease of free path length and vice versa.The property which can be studied to understand the interaction is relative association (RA). It can be explained by two factors [19]: (1) the breaking up of solvent molecules on addition of solute to it and (2) solvation of the solute molecule. The former leads to decrease and the latter to the increase of relative association. In our study the values of RA increase with increase in the solute concentration due to solvation of the solute molecule.


## 4. Conclusion

The ultrasonic technique is a powerful and effective tool for the investigation of polymer solutions and behavior of polymer chain in an ultrasonic field. The present study describes the acoustic properties that confirm the molecular interaction of PVDF polymer powder with a acetone and DMF. The acoustic parameters like adiabatic compressibility (β), intermolecular free path length (Lf), acoustic impedance (Z), relative association (RA), ultrasonic attenuation (α/f2), and relaxation time (τ) have been estimated using experimental data. The variations in the acoustic parameters suggest that there are strong polymer-solvent interactions at higher concentration.



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