Older solvent info: Click here for most up-to-date info

Andrew Levitt & Prof. Eric Weeks -- <weeks(at)physics.emory.edu>
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Quick answers:
Using measured values of solvent viscosity, particularly the 85% CXB / 15% DEC mixture, and information about the diffusion of particles in that solvent, particle radii can be determined. This webpage contains viscometry data (measured viscometer efflux times, solvent density measurements) and equations relating diffusion time to particle radius.

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.
  • Extrapolation to 22 deg. gives a constant of .0044136.

The efflux times that I measured for the CXB/DEC mixture in question are:
  • 413.380 seconds
  • 414.740 seconds
  • 410.940 seconds
  • avg = 413.020 s
    stddev = 1.92540 s

These are my weight measurements for 25 mL of solvent measured into a volumetric flask.
  • 30.8895 g
  • 30.8344 g
  • 30.8317 g
  • 30.8411 g
  • avg=30.8492 g
    stddev = .0271721 g

These return a density of:
  • 1.23397 g/cm^3

Multiplying the viscometer constant by the efflux time returns a kinematic viscosity nu of:

  • 1.82291 cSt = 0.0182291 cm^2/s
  • (note: kinematic viscosity of water ~1 cSt = 0.01 cm^2/s)
Multiplying the viscometer constant by the efflux time and the density returns a bulk viscosity eta of:
  • 2.24941 mPa s
  • (milli-Pascal seconds)
  • (note: bulk viscosity of water 1.002 mPa s at 20 deg C)

Einstein says:

dx^2(dt) = 2D*dt

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


where K 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 frame. 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 = 2KT/6(pi)va, a = 2KT/[6(pi)v*Slope]. Presto.

K 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.