Volumetric Dilatometry The ability to measure and characterize the volumetric behavior of new and existing materials as a function of temperature and time is of great importance. This is due to the fact that there are a variety of physical phenomena that result in dimensional change (i.e. crystallization, melting, glass formation, secondary transitions and physical aging). No where is this statement more valid than in the field of polymer science.[1] Thermal Expansion The coefficient of linear expansion, also known as expansivity, is the ratio of the change in lengt -h per ◦C to the length at 0◦C. The coefficient of volume expansion for solids is approximately three times the corresponding linear coefficient. The coefficient of volume expansion of a liquid is the ratio of the change in volume per degree, to the volume at 0◦C. The value of thecoefficient varies with temperature.The coefficient of volume expansion for a gas under constant pressure is nearly the same for all gases and temperatures, and is equal to 0.00367.[2] 1. Linear expansion in solids. A bar of length L0 at temperature T0 expands to a length L when heated to a temperature T. The change in length ΔL (i.e. L – L0) is related to the change in temperature ΔT (i.e.T – T0) and the original length L0 by a 1
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Volumetric Dilatometry
The ability to measure and characterize the volumetric behavior of new and existing materials
as a function of temperature and time is of great importance. This is due to the fact that there
are a variety of physical phenomena that result in dimensional change (i.e. crystallization,
melting, glass formation, secondary transitions and physical aging). No where is this statement
more valid than in the field of polymer science.[1]
Thermal Expansion
The coefficient of linear expansion, also known as expansivity, is the ratio of the change in lengt
-h per ◦C to the length at 0◦C. The coefficient of volume expansion for solids is approximately
three times the corresponding linear coefficient. The coefficient of volume expansion of a liquid
is the ratio of the change in volume per degree, to the volume at 0◦C. The value of thecoefficient
varies with temperature.The coefficient of volume expansion for a gas under constant pressure is
nearly the same for all gases and temperatures, and is equal to 0.00367.[2]
1. Linear expansion in solids. A bar of length L0 at temperature T0 expands to a length L when
heated to a temperature T. The change in length ΔL (i.e. L – L0) is related to the change in
temperature ΔT (i.e.T – T0) and the original length L0 by a constant that depends on the material.
This constant is the coefficient of linear expansion (also called the coefficient of thermal
expansion), α.
a. The change in length is directly proportional to the change in temperature: ΔL ∝ ΔT.
b. The change in length is directly proportional to the original length: ΔL ∝ L0.
c. The change in length is directly proportional to the coefficient of linear expansion: ΔL α.∝
d. Together, these proportionalities form the equation ΔL = αL0ΔT.
2. Volume expansion in solids and liquids. A volume V0 of solid or liquid at temperature T0
expands to a volume V when heated to a temperature T. The change in volume ΔV (i.e. V – V0) is
related to the change in temperature ΔT (i.e. T – T0) and the original volume V0 by a constant
that depends on the material. This constant is the coefficient of volume expansion, β.
a. The change in volume is directly proportional to the change in temperature: ΔV ∝ ΔT.
b. The change in volume is directly proportional to the original volume: ΔV ∝ V0.
c. The change in volume is directly proportional to the coefficient of volume expansion: ΔV β.∝
1
d. Together, these proportionalities form the equation ΔV = βV0ΔT.
e. For solids whose coefficient of linear expansion is known, the equation ΔV = 3αV0ΔT may be
used.
3. Volume expansion in gases. The volume V of a gas is related to its temperature and the
pressure at which it is contained. Raising the temperature of the gas from T0 to T increases the
volume from V0 to V if the pressure P is held constant (Charles’ Law). Reducing the pressure
from P0 to P of a gas increases the volume of a gas from V0 to V if the temperature is held
constant (Boyle’s Law). Taken together, these proportionalities form “Charboyle’s Law” (a. k. a.
The Ideal Gas Law): P0V0/T0 = PV/T.[10]
Methods for measurement of thermal expansion
Solids
-(Mechanical) Dilatometry
- Thermomechanical
Analyser
- Interferometry
- X-Ray diffraction
- Line-width camera
- Strain gauge technique
Liquids
- Magnetic suspension
- Rise of meniscus in capillary
Fig 1
Dilatometers (an early version is shown above)
are the most common measurement devices
for thermal expansion measurement.
Expansion measurement methods for solids
The most commonly used technique on a suitable test-piece is one based on mechanical
dilatometry – the change in length of a known length is recorded as a function of temperature by
a contacting push-rod. The movement of this push-rod is determined by one of several
2
techniques, including a simple dial gauge, a capacitance transducer, an LVDT or interferometer.
This technique works well from liquid helium temperature to over 2000 °C, provided that the
materials of the supporting system and the push-rod are stable. There are commercial
instruments that make direct measurements on individual test-pieces, or compare the movement
in an unknown with that in a reference material.
The accuracy of such instruments is
typically no better than ± 0.1 x 10-6 °C in
expansion coefficient or expansivity, for data
obtained over a 100 °C temperature interval. In
the polymer field, e Thermomechanical
Analyser is a simple form of dilatometer, but is
not capable of the same level of accuracy as
purpose-built dilatometers on materials of low
thermal expansion.
Fig 2
Commercial dilatometers are available
from various suppliers, like that shown
above .
The use of interferometry to measure length
change directly from the test-piece is less
common but potentially more accurate since it
is less reliant on mechanical contact
movements. The test-piece is placed on a
mirror, has a small mirror placed on top, and the
relative movement of the mirrors as the test-
piece is heated and cooled is determined by
multiple beam interferometry. Preferably, the
test-piece itself is made with mirror surfaces.
The accuracy of this type of arrangement is
perhaps an order of magnitude improvement
over mechical dilatometry,but is limited by
achievable temperature homogeneity. The
technique is also more expensive, more limited
in temperature range, and more restricted in
terms of test-piece type and geometry. Fig 3
3
Laser interferometer for expansion
measurement on pulse-heated samples at OGI,
Austria.
Direct optical expansion measurement is in use for high-expansion plastics materials and has
been used extensively in the past. In fact, certified reference materials have been calibrated using
this method. Fiducial marks are placed on a long test-piece and viewed laterally using a long
focal length microscope attached to an accurately calibrated length scale parallel to the test-piece.
As the test-piece is heated or cooled, the position of the fiducial marks are recorded manually.
Modern versions of this method involving analysis of video-images have also been employed for
complex structures.
There are a number of other techniques that have their place, but are less commonly used
for data generation, and they include:
X-ray diffraction – measures lattice cell expansion, but may not produce the same
results as whole body methods because the effects of local residual stresses may not be
taken into account
electrical heating with servo displacement – allows expansion to be measured when
subjected to a given force
line-width camera – useful for measuring size changes of very hot objects which can be
imaged, but where other direct dilatometric methods are not appropriate, but the accuracy
may be limited by resolution limitations
strain gauge – this technique has value for determining local behaviour of complex
bodies, such as composite structures, but the gauges have to be carefully calibrated for
their response with respect to changing temperature.
Expansion measurement methods for fluids
Techniques for the direct measurement of fluid volume are less well developed than for linear dim
-ensions. The volume of a known mass of liquid can be tracked as a function of temperature as its
meniscus rises up a capillary exiting from a filled rigid vessel.
4
More sophisticated magnetic suspension devices that operate over wide ranges of temperature
and pressure are available for accurate determinations.[3]
Dilatometers
dilatometers, measure the dimensional changes as a function of temperature. The instruments of
this family may differ in the way they measure dimensional changes of the sample. One very
relevant difference is if there is contact with the sample or not.
All the mechanical or electronic dilatometers use a push rod in touch with the sample to transfer
the dimensional change of the sample from the internal of the fumace to the transducer (dial