Data on 85%/15% w/w cyclohexylbromide/decalin
Dandan Chen, Andrew Levitt
& Eric Weeks --
Lab Home --
Experimental facilities --
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)
- Click here for older data (pre June
- 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%
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
- 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.
||bulk viscosity eta|
|20 C||(412.10+412.62)/2= 412.360 s||0.0044143
||2.24348 mPa s|
|22 C||(400.77+ 400.54)/2=400.655 s||0.0044136
||2.17945 mPa s|
|24 C||(389.78+389.67)/2=389.725 s||0.0044129
||2.11965 mPa s|
|26 C||(378.49+378.16)/2=378.325 s||0.0044121
||2.05728 mPa s|
|28 C||(367.93+368.28)/2= 368.105 s||0.0044114
||2.00139 mPa s|
|30 C||(358.90+359.27)/2=359.085 s||0.0044107
||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.
- 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
- 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.
dx^2(dt) = 2D*dt
where dx is one-dimensional RMS particle displacement in some time dt.
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.