The Interdisciplinary Laboratory
Pre-Lab
Assignment
#2 for Experiment #7:
Synthesis and
Characterization
of Liquid Crystals
Pre-Lab
Assignment
#2 for Experiment #7:
Synthesis and
Characterization
of Liquid Crystals
1. The following data were obtained for cholesteryl
nonanoate/cholesteryl
chloride mixtures with x = 0.46 mole fraction of cholesteryl
chloride.
Develop an equation for the line that represents the average refractive
index as a function of temperature in the range 40. to 70.
°C.
(Note this exercise is exactly what you did for PreLab #1, without the
need to average three values of n parallel and three values of n
perpendicular.)
| T/°C | n parallel | n perpendicular |
| 40.9 ± 0.2 | 1.5159 ± 0.0001 | 1.4925 ± 0.0002 |
| 46.0 ± 0.2 | 1.5143 ± 0.0003 | 1.4912 ± 0.0002 |
|
|
|
|
| 55.2 ± 0.2 | 1.5101 ± 0.0006 | 1.4887 ± 0.0003 |
| 65.0 ± 0.2 | 1.5057 ± 0.0005 | 1.4867 ± 0.0003 |
| Uncalibrated Values - No Calibration Data Available | ||
2. The following data are available for the selective reflection as
a function of temperature of a mixture of cholesteryl chloride and
cholesteryl
nonanoate with x = 0.46 (mole fraction) of cholesteryl chloride.
| T/°C | l/nm | %T |
| 45.0 ± 0.1 | 629 ± 1 | 63.5 ± 0.1 |
| 55.1 ± 0.1 | 644 ± 1 | 65.5 ± 0.1 |
| 60.0 ± 0.1 | 660. ± 1 | 67.8 ± 0.1 |
| 64.9 ± 0.1 | 681 ± 1 | 70.0 ± 0.1 |
| 69.8 ± 0.1 | 704 ± 1 | 72.3 ± 0.1 |
Using the line found in #1 and the data above, calculate the pitch of the cholesteric phase as a function of temperature in the range of 40 to 70 °C. Note: Pitch is not a linear function of temperature (nor is the peak transmission a linear function of temperature). A second-order polynomial should fit the data well. Read below for hints on the calculational method. BE SURE TO DESCRIBE YOUR CALCULATION PROCEDURE.
Hints on calculation procedure: Follow the instructions on p.
24 (Analysis) - do not worry about using/needing any isotropic
refractive
index data. (1) Calculate average refractive index values
using
equation 2. (2) Fit average refractive index as a linear function of
temperature.
(3) Fit the wavelength data above as a second-order polynomial in
temperature.
(By the way, %T is %Transmission. You do not need these data for
the pre-lab assignment.) (4) Now find average n and wavelength at
5 to10 set values of temperature (e.g., 40.0, 45.0, 50.0 degrees
Celsius,
etc.). (5) Calculate pitch at these 5 to10 temperatures using
equation
8. (6) Now fit the pitch values to a second-order polynomial in
temperature.
What are the units of pitch? What are the units of your fitting
coefficients?
Do you have any remaining questions about the background and/or protocol from the first week of the experiment?
Submit via e-mail the solutions to this pre-lab assignment to
Professor
Van Hecke (Gerald_VanHecke@hmc.edu)
by 7 p.m. on Monday, March 29 or 7 p.m. on Monday, April 19 (i.e.,
prior
to your second laboratory day).