Determination of Wada Constant, Rao’ Constant, Compressibility Andviscosity of A Cholesteric Liquid Crystal Solution at Various Temperatures

Determination of Wada Constant, Rao’ Constant, Compressibility Andviscosity of A Cholesteric Liquid Crystal Solution at Various Temperatures

Determination of Wada Constant, Raos Constant, Compressibility Andviscosity of A Cholesteric Liquid Crystal Solution at Various Temperatures

Anita Kanwar and Pritee Mhatre

VES College of Arts, Science and Commerce, Department of Physics, Sindhi society, Chembur, Mumbai 400071.

ABSTRACT:

The ultrasonic waves having different frequencies propagate through the liquid crystal solution with different velocities at various temperatures. This fact helps in studying physical and chemical properties of Cholesteric liquid crystal (CLC) of different concentration at various temperatures. We in our laboratory have found out Acoustic Impedance, Raos constant, Adiabatic Compressibility,Wada constant,Van der Waals constant, Free Volume, Internal pressure andClassical Absorption Co-efficientof CLC solutionof different concentration. The measurements were made at various temperatures using Ultrasonic interferometer working at the frequencies 3MHz and 5MHz. The results so obtained are analyzedto see the effect temperature, concentration and transition of CLC into various mesophases. It is observed that when the miscibility is high and the solution is highly homogeneousthe values of the parameters change drastically showing the change in the mesophases at phase transition temperatures.

INTRODUCTION:

Cholesteryl Pelargonate (CP) a CLC [1] having molecular formula C36H62O2 and molecular weight of 526.88 g/mol as obtained from Sigma Aldrich is used in preparation of the samples. The phase transition temperatures of CLC, CP were obtained using the Fabryperot scattering studies (FPSS) technique [2]. Homogeneous mixture of Toluene and CP [3] having various concentration is used as a sample to study the effect of temperature and concentration on the physical and chemical parameters. We have determined the Wada constant, Raos constant, compressibility and viscosity [4-5] of the solution at various temperatures by varying concentration of the solution.

Ultrasonic velocities for the solutions of different concentrations were measured by varying the temperature using indigenously designed thermometer. The ultrasonic interferometer (Mittal enterprises, India; Model: F-80X) was used for the measurements of velocity of ultrasonic waves in the solvent and solution. It consists of a high frequency generator and a measuring cell and the measurements were made at two different frequencies viz3MHz and 5MHz. The least count of micrometer measuring cell is 0.01mm. The ultrasonic velocity has an accuracy of ± 0.5%. It is used to find the Acoustic Impedance, Raos constant, Adiabatic Compressibility,and Wada constant. The viscosity was measured by Oswaldsviscometer. It is used to find Van der Waals constant, Free Volume, Internal pressure andClassical Absorption Co-efficient of the five samples prepared in the laboratory.

Experimental details:

The phase transitions in CP using FPSS occurred at 331.6K, 337.8K, 344.5K and 357K respectively. Homogeneous mixture of Toluene and cholesteric liquid crystal Cholesteryl Pelargonate having various concentration is used as a sample to study the effect of temperature and concentration on the physical and chemical parameters. We have determined the Wada constant, Raos constant, compressibility and viscosity of the solution at various temperatures by varying concentration of the solution. Indigenously designed temperature controller using transducer and a digital thermometer was used to maintain the temperature constant and for the measurement with accuracy of 0.10C.

The following formulae were used for the calculation of various parameters.

1. Acoustic Impedance (A)= Ugm/cm2.sec (where U is ultrasonic velocity and is density)

2. Raos constant or Molar sound velocity(R) = 1/3cm10/ 3/sec1/ 3

   where M=M1W1+M2W2 (M1 and M2 are molecular weights of CP and toluene respectively and W1 and W2 are weight fractions of CP and toluene respectively in the solution.

   2

3. Adiabatic Compressibility (K) = 1

   cm2/dyne

4. Wada Constant or Molar compressibility (W) = [] x K-1/7cm 19/7/dyne 1/7

5. Viscous relaxation time (T) = 4

   3 2

   sec where is viscosity.

6. Van der Waals constant (b) = V 1 1 + 2

   1/2

   cm3/mole

   2

   3

   Where, R is the gas constant = 8.3143×107 erg × mol-1 ×K-1

   f

7. Free Volume (V ) =

3/2

8) Internal Pressure () = 1/2 2/3 where b=2 and K= (93.875+0.375T)x 10-8

9) Classical Absorption Co-efficient =

2

7/6

=

8 2

33

Observations:

The five sample solutions were prepared using Toluene (T) and Cholesteryl Pelargonate (CP) in the following proportionand analyzed to find above physical and chemical parameters. The Table 1 to Table 5 shows the calculated values of the parameters at 3MHz and 5MHz when the temperature is varied from 303K to 343K using above formulae.

1. 10ml T + 20 mg CP, Molecular Weight (MW)=710.2gm

2. 10ml T + 40 mg CP, Molecular Weight =720.7gm

3. 10ml T+ 60 mg CP, Molecular Weight =731.2 gm

4. 10ml T+ 80 mg CP, Molecular Weight =741.8gm

5. 10ml+ 100 mg CP, Molecular Weight = 752.3 gm

Table1 (a): Sample1: 10ml T + 20 mg CP, =0.761gm/cc, =1.206 dynes.sec/cm2

Table 1(b)

Table 2(b)

td>

2.292E-03

Table 3(b)

Table 4(b)

Table 5(a): Sample5: 10ml T + 100 mg CP, =0.769gm/cc, =1.298 dynes.sec/cm2

Table 5(b)

Figure1 shows the Optical Polarizing Microscope images of the sample1 to sample5 respectively at room temperature.

Figure1: Optical Polarizing Microscope images

Figure2 to Figure6 showsvariation of ultrasonic velocity with temperature at two different frequencies viz 3MHz and 5 MHz for sample1 to sample5 respectively.

Ultrasonic velocity

Figure2: Sample1

Variation of Velocity with temperature at different frequencies(10ml T + 20mg CP)

130500

130000

129500

129000

128500

128000

127500

127000

3 MHz

5 MHz

300 305 310 315 320 325 330 335 340 345

Temperature

Figure3: Sample2

Variation of Velocity with temperature at different frequencies(10ml T + 40mg CP)

130000

129000

128000

127000

126000

125000

124000

123000

122000

121000

120000

3 MHz

5 MHz

300 305 310 315 320 325 330 335 340 345

Temperature

Figure4: Sample3

Variation of Velocity with temperature at different frequencies (10ml T + 60mg CP)

142000

140000

Ultrasonic

Velocity

138000

136000

134000

132000

130000

128000

126000

3 MHz

5 MHz

300 305 310 315 320 325 330 335 340 345

Temperature

Figure5: Sample4

Variation of Velocity with temperature at different frequencies(10ml T + 80mg CP)

129000

128000

127000

126000

125000

124000

123000

3 MHz

5 MHz

300 305 310 315 320 325 330 335 340 345

Temperature

Figure6: Sample5

Variation of Velocity with temperature at different frequencies(10ml T + 100mg CP)

142000

140000

Ultrasonic

Velocity

138000

136000

134000

132000

130000

128000

126000

124000

122000

3 MHz

5 MHz

300 305 310 315 320 325 330 335 340 345

Temperature

Figure7 to Figure11 shows variation of Viscosity with temperature at two different frequencies viz 3MHz and 5 MHz for sample1 to sample5 respectively.

Figure7: Sample1

Variation of Classical absorption coefficient with temperature at different frequencies(10ml T+20mg CP)

43000

41000

39000

37000

35000

33000

31000

29000

3 MHz

5 MHz

300 305 310 315 320 325 330 335 340 345

Temperature

Figure8: Sample2

temp

Variation of Classical absorption coefficient with erature at different frequencies(10ml T+40mg CP)

50000

48000

46000

44000

42000

40000

38000

36000

34000

32000

3 MHz

5 MHz

Figure9: Sample3

300 305 310 315 320 325 330 335 340 345

Temperature

Variation of Classical absorption coefficient with temperature at different frequencies(10ml T+60mg CP)

45000

3 MHz

5 MHz

40000

35000

30000

25000

20000

300

305

310

315

320

325

330

335

340

345

Temperature

Figure10: Sample4

Variation of Classical absorption coefficient with temperature at different frequencies(10ml T+80mg CP)

45000

43000

41000

39000

37000

35000

33000

31000

3 MHz

5 MHz

300 305 310 315 320 325 330 335 340 345

Temperature

45000

40000

35000

30000

25000

Figure11: Sample5

Variation of Classical absorption coefficient with temperature at different frequencies(10ml T+100mg CP)

50000

3 MHz

5 MHz

300

305

310

315

320

325

330

335

340

345

Temperature

Results and Discussions:

Figure1 shows that as the amount of solute (CP) increases in the solvent (T) the density increases [6] and the effect of CP becomes more prominent in the solution. Table1 to Table5 and Figure2 to Figure6 show that ultrasonic velocity varies with temperature and variation is non linear. The non- linear variation in ultrasonic velocity and other acoustical parameters indicates that there is a strongmolecular interaction between CP in Toluenesolution [1, 4].The variation is much more prominent in case of 5MHz frequency than 3MHz. Acoustic impedance is directly proportional to ultrasonic velocity. Acoustic compressibility and viscous relaxation time varies inversely with square of ultrasonic velocity. These all nonlinear behaviour with molar concentration is may be attributed to molecular association and complex formation. This indicates that the solution is becoming more homogeneous with increasing temperature and such solution generally absorbs more ultrasonic energy [7-9]. The non linear variation in the parameters with temperature can also be related to mesophases of CP, because of which orientation and arrangement of the molecule changes. Internal pressure increases with increasing temperature here the variation is nearly linear [10, 11].Thisshows that binding forces between the CP and toluene insolution are becoming stronger which shows thatthere exists a strong molecular interaction.

Data above Table1 to table5 show that viscosity increases with rise in concentration. This indicates that there exists a stronginteraction between solute and solvent which is alsosupported by ultrasonic velocity [12].

It is found that vanderwalls constant [13] is decreasing with increasing temperature as shown in Table2 to table6. This shows that binding forces between the CP and solvent in solution are becoming weaker as the CP goes from Cholesteric phase to liquid phase.

Acknowledgement

The author is grateful to University grant commission, New Delhi for providing financial support to this work through Major research project letter F.No.41-836/2012 (SR)2012.

References:

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13. Jatinder Pal Singh, Rajesh Sharma, Variation of Wada Constant, Raos Constant and Acoustic Impedance of Aqueous Cholesteryl Oleyl Carbonate with Temperature, International Journal of Engineering Research and Development, e-ISSN: 2278-067X, p- ISSN: 2278-800X, Volume 5, Issue 11 (February 2013), PP. 48-51.