ASPECT RATIO DETERMINATION THROUGH SURFACE AREA ANALYSIS
FOR MICA
This method utilizes surface area measurement with sample volume
information generated during the surface area analysis to determine
average flake thickness (t). The calculated t is ratioed with mean
particle size values as determined by both mass and particle number
distributions for two different aspect ratio values.
The total surface area of a flake is the total of the top, bottom and
four edge surfaces. This method assumes that the sample flakes are
sufficiently thin so that the surface area of the edge surfaces is
negligible. The top and bottom surfaces are also assumed to be equal,
making the measured surface area approximately 2A.
The volume of a flake which has equal top and bottom surfaces would be
equal to the top surface area multiplied by the flake thickness - At.
With these assumptions, the surface area to volume ratio would be 2A/At
or 2/t.
In determining the surface area, the analyzer uses helium to determine
sample container free space or conversely, sample volume. If the
specific gravity of the sample is known, the volume can be calculated
from the sample weight. The surface area measurement is expressed as
square meters per gram and should be
multiplied by the sample weight for strictly an area value.
Area
-----Volume
gravity)
t
=
2
--t
=
(measured surface area) x (sample weight)
---------------------------------------------------(measured volume) or (sample weight)/(specific
=
2 x (measured volume)
----------------------------------------(measured surface area) x (sample weight)
=
2
-------------------------------------------(measured surface area) x (specific gravity)
or
t
For mica samples with thick or poorly delaminated flakes, volume per unit
weight of sample will not change, but the surface area will decrease
significantly. The V/A ratio will increase, thereby increasing the
calculated t.
With the calculated thickness, the particle size distribution can be used
to further describe the sample. The ratio of the measured mean particle
size to t would give the aspect ratio based upon the mass distribution.
The Microtrac mass distribution can be entered into Lotus and defined by
particle size interval (mass by interval). Using the assumption that the
flakes are square and using the average interval diameter, the minimum
number of flakes per interval can be computed. The relative particle
number distribution can easily be determined and data regression analysis
is used to determine the mean particle size diameter from this
distribution. This mean particle size will be considerably smaller than
the mass mean, but the ratio of the number mean to t gives an aspect
ratio based upon the relative number of flakes throughout the size range.
Eric Westbrook
July 1992