Data on 85%/15% w/w cyclohexylbromide/decalin

Dandan Chen, Andrew Levitt & Eric Weeks -- <weeks(at)physics.emory.edu>
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85% cyclohexylbromide / 15% decalin (by weight!)
• Viscosity eta: 2.18 mPa s at 22 deg C (about 2.18 times larger than water)
• Viscosity changes by -0.03 mPa s/deg C, that's about 1.3% per degree
• Density: 1.23249 g/cm^3
• Index of refraction: 1.495 (Scott Franklin, 5-1-07)

• Oct 26, 2015: Carlos says a density of 1.227 g/cm^3 works better for density matching, this is about 83.5% CXB and 16.5% DCL.

Solvent viscosity is measured using a glass Cannon-Fenske kinematic viscometer. This device relates a liquid's viscosity to the time it takes for the liquid to fall a given distance through a skinny tube. This time is called the efflux time. By multiplying the efflux time by the viscometer constant for the appropriate temperature and the solvent density, one obtains the viscosity in millipascal seconds (centipoise).

 These are the viscometer constants for our Cannon-Fenske viscometer no. 50 Y871: .004407 mm^2/s^2 at 40 deg. Celsius .004385 mm^2/s^2 at 100 deg. Celsius.

Dandan Chen's data from June 2009:

• Note: Alumina absorption was used to get rid of bromine ions before these measurements. Also, the solvent was filtered with a 0.2 micron filter.
• We believe room temperature in our lab is 22 degrees C. If you care about the viscosity in your sample, then you should probably check what room temperature is the day you're doing your experiment.
T flux time constant bulk viscosity eta
20 C(412.10+412.62)/2= 412.360 s0.0044143 2.24348 mPa s
22 C(400.77+ 400.54)/2=400.655 s0.0044136 2.17945 mPa s
24 C(389.78+389.67)/2=389.725 s0.0044129 2.11965 mPa s
26 C(378.49+378.16)/2=378.325 s0.0044121 2.05728 mPa s
28 C(367.93+368.28)/2= 368.105 s0.0044114 2.00139 mPa s
30 C(358.90+359.27)/2=359.085 s0.0044107 1.95204 mPa s
• note: bulk viscosity of water 1.002 mPa s at 20 deg C
• mPa s = milli Pascal seconds
• Pre June 2009 value: 2.24941 mPa s (Click here for details), not measured with temperature control.

Density

• June 2009 (Dandan Chen): Density measured to be 1.23249 g/cm^3 for a solvent mixture 84.991% CX B, 15.009% decalin.
• pre June 2009 (Andrew Levitt): Density of 1.23397 g/cm^3
• Note: The viscometer measurement, from the efflux time, really provides the kinematic viscosity "nu". To find the bulk viscosity "eta", you have to multiply by density. Thus the numbers in the June 2009 table above used the June 2009 density.

Einstein says:

dx^2(dt) = 2D*dt

where dx is one-dimensional RMS particle displacement in some time dt. D is:

(kB)T/6(pi)va

where (kB) is Boltmann's constant, T is temperature in Kelvin, v is bulk viscosity as above, and a is particle radius. Take a lot of data of diffusive motion of your particles, in a dilute sample where the particles don't bump into each other much. There should be ~100 particles per image. The MSD will be linear; this is the function listed in the first equation above. Find the slope of this graph; this is equal to 2D. If you use data from x^2 + y^2, then the slope is equal to 4D. Slope = 2(kB)T/6(pi)va, a = 2(kB)T/[6(pi)v*Slope]. Presto.

kB is 1.381e-23 in MKS
T = 295 in the lab
v = 2.25e-3 in MKS
slope = slope of MSD in microns^2 per second times 10^-12 to get MKS

The result should be something like 1.1e-6 (a is the radius, not diameter). We've used this webpage for many years, so if you don't get this result, you probably made a mistake. Keep in mind that if you only know temperature to within the nearest degree, that's a 0.3% uncertainty for T but a 1.3% uncertainty for eta. Thus, lack of temperature control results in about a 1% uncertainty of the particle size.