Dilatometer 1. The Basic principle Dilatometer is a measuring instrument that quantifies thermal expansion and dil ation in solids and liquids. It uses the basic principles of dilatometry. Dilatometric method utilizes either transformational strains or thermal strain. The basic data generated using dilatometer are in the form of curves of dimension against time and temperature. The Tg can be calculated as shown in the figure:
2. The important terms:
2.1.
Fig 1.1
Glass Transition temperature:
The Glass transition temperature, Tg, is the temperature at which the molecular motion in an amorphous solid, such as glass or a polymer, ceases after a certain temperature on going from l iquid to solid state. In other words, T g, is the temperature at which an amorphous solid, such as glass or a polymer, becomes brittle on cooling, or soft on heating. More specifically, it defines a pseudo second order phase transition in which a supercooled melt yields, on cooling, a glassy structure and properties similar to those of crystalline materials.
Tg is usually applicable to wholly or partially amorphous solids such as common glasses and plastics (organic polymers) Below the glass transition temperature, Tg, amorphous solids are in a glassy state and most of their joining bonds are intact. Above T g glasses and organic polymers become soft and capable of plastic deformation without fracture.
2.2.
Amorphous solid:
An amorphous solid is a solid in which there is no long-range order of the positions of the atoms.
2.3.
Second order phase transition: transition:
The variation of Gibbs energy with temperature and pressure for an amorphous material is a smooth curve. Thus, a discontinuity is observed in the second derivatives of the Gibbs free energy. Three possible second derivatives can be used to provide a basis for the experimental measurement of Tg.
Since entropy is not an experimentally measurable quantity, eq. 1 may be recast into more useful form in terms of specific heat at constant pressure, Cp.
Substitution of eq.2 in eq.1 indicates that a second order transition should occur as a discontinuity in specific heat. Specific heat is measured by calorimetric techniques.
Fig 2.1
3. Pre-design research:
3.1.
List of polymers and their T g values:
List of Polymers
Polyethylene
low density (LDPE) Polyethylene
high density (HDPE) Poly(vinyl acetate)
(PVAc) Poly(vinyl alcohol) (PVA) Poly(vinyl chloride)
(PVC) Polystyrene
(PS) Poly(methyl methacrylate)
(PMMA, Lucite, Plexiglas)
Tg values (°C)
-105 -30 28 69 82 95 105
Poly carbonate
145
Poly norbornene
215
With most of the important polymers with their T g values in the range of 25 to 250 °C, We decided to raise the temperature in our apparatus to a maximum of 350 °C.
3.2.
Basic design selection:
3.2.1.
Principle of measurement: As provided in the theory above, there were two basic properties that could be utilized to design the system:
1. Longitudinal strain (Pushrod dilatometers) 2. Volumetric expansion 3.2.1.1. Pushrod dilatometers: In the longitudinal strain design, the polymer is inserted in the form of a solid which on heating extends longitudinally. The longitudinal strain is measured with the help of a pressure transducer. All pushrod dilatometers – having either one or two pushrods – measure relative to a reference material with known thermal expansion as a function of temperature. A graph can be plotted between the (linear expansion/initial length, ∆L/L₀) to the temperature. The Tg value of the material can be calculated easily from the above plot.
Fig 3.1.1
Fig 3.1.2 3.2.1.2. Volumetric expansion: In the Volumetric expansion method, the polymer samples are embedded in a fluid medium and the change of volume of the material along with the fluid is measured with the rise in the capillary tube. We plot a graph between the (change in volume/initial volume, ∆V/V₀) to the temperature and use the above shown technique to calculate the T g value of the material.
Generally the dilatometers are connected to a computer which specific sets of equations that uses the observed volumetric expansion data, after taking in account the expansion of the specimen holder or medium to plot a ∆V curve. It then automatically calculates the T g values from the graph.
Sudden increase in volume
Fig 3.2 Computer generated graph We looked after the various possible designs of the dilatometer among the ones those are presently used and then did our own modifications. 3.2.2.
Some of the dilatometer designs:
3.2.2.1 Pushrod dilatometers: They work on the principle of longitudinal strain and measures pressure developed by an expanding solid material.
a.
High temperature pushrod dilatometer (Austrian Foundry Research Institute, Leoben)
Fig 3.3 b. Double specimen pushrod dilatometer
Fig 3.4 c.
Differential dilatometer (NETZSCH-Geraetebau GmbH)
Fig 3.5
Fig 3.5
3.2.2.2. Volumetric measurements based dilatometer: a.
Gnomix pvT High Pressure Dilatometer
Fig 3.6 The Gnomix PVT Apparatus generates pressure-specific volume-temperature measurements using high-pressure dilatometry. b. Water submerged volumetric expansion
Fig 3.7
The design that we selected is based on the principle of measuring the volumetric expansion of the polymer submerged in a fluid medium. The volumetric expansion of the polymer is plotted with temperature and Tg is calculated from the graph. Criteria of selecting the design: 1. This is the only method where the shape of the specimen does not matter and any strain that may be presented to the specimen, acts on all sides of it uniformly and equally. 2. The design is comparatively simpler and can be easil y studied. 3. The accuracy levels are not much compromised which is the only loss with this design.
4. Initial Design:
Design 1: Our initial design consisted of a cylindrical container fitted with a B-29 cap and a long capillary tube fitted over it. Our motive was to submerge the polymer sample in a fluid medium inside the cylindrical container and then on heating measure the volume rise in the capillary tube.
Base container
Capillary tube
Complete assembly
Fig 4.1 Design 1
Errors with Design1: Error 1: When we took the design to the Glass blowing lab incharge and discussed about the
experimental conditions he suggested us that the material used should be Quartz as on heating the borosilicate glass may soften and the capillary tube may be deformed.
Modification 1: Thus, we decided to use Quartz as the glass material. Error 2: But there was an error of using the complete set up made up of quartz too as the minimum ID available for a quartz tube is 6 mm. Such a large diameter could reduce the sensitivity of the apparatus to small volume change which are commonly observed during the process in the
experiment. Modification 2: Thus we decided to use capillary part made of Borosilicate glass and bottom container of Quartz. Thus the section of the instrument in direct contact with the heat source may be
protected from softening. Error 3: The heat source was supposed to be cylindrical coil or depressed heater that would surround
the glass container. The heat transfer to the borosilicate capillary tube is quite high and thus the problem of softening sustained.
Design 2: The significant features of the new design are: 1. The bottom cylindrical container is made of Quartz, to wi thstand high temperatures of heating. 2. The top capillary part is made up of borosilicate glass with a standard capillary tube of 3.94 mm diameter. 3. A middle section made up of Quartz is introduced between the top capillary and bottom base. The purpose of this section is to insulate the borosilicate capillary tube from high temperatures and thus avoiding any possibility of softening in borosilicate capillary tube. The bottom section could also be elongated or enlarged but then volume may also have increased. 4. The observed rise in the height of medium in the capillary is the result of volume expansion in medium fluid and the sample. There is no contact of the fluid medium with air. 5. The middle section contains a quartz tube with the ID exactly equal to the OD of the capillary tube. They can be further be sealed by applying vacuum grease. 6. There is a small projection at the bottom of the middle section to avoid the polymer to rise in the capillary tube. 7. The dimensions of the sections are based on some assumptions and calculations. 8. For calibration of the capillary tube a graph sheet is pasted along the tube.
The following designs were given for manufacturing: Base
Final Assembly
Middle section
Capillary tube
Fig 4.2 Design 2
5. Final apparatus Design: There was some anomaly with the final apparatus that was built to the final design that was given. Base
Middle section
Capillary tube
Final Assembly
5.1.
Design features of the final apparatus:
1. The bottom and the middle section are made of Quartz while the capillary tube is made of borosilicate glass. 2. The air gap in the middle section is filled with cotton and then M seal was out over it. It should have not been present according to the design, but due to manufacturer fault, it was formed which created errors of extra rise due to air expansion. 3. The ID of the quartz tube in the middle section and OD of the capillary tube didn’t match perfectly. We melted the borosilicate glass inside the quartz tube and sealed the air g ap. 4. The dimensions dimensions of all the sections sections are based based on some assumptions assumptions and calculations.
5.2.
Material selection
Section
Material
Use
Bottom container
Quartz
Container for the sample and the fluid medium
Middle section
Quartz
Insulates capillary tube from heat
Capillary tube
Borosilicate glass
Measures the volume change
Medium fluid
Linseed oil
Durable, very less variation of cheap
Thermocouple
Standard
To measure the temperature fall
Heater
Standard, depressed
To provide uniform heating at the base container
Sealant
Cotton with M Seal
To avoid any contact between fluid medium and air
α
with T,
5.2.1. Glass material property: As the temperature we are supposedly working is in the range of 25-250 °C, the glass material to be used must be able to withstand the temperature well up to 350 °C in case of an uncontrolled rise in temperature.
Thus we had the choice of 2 materials: 1. Borosilicate glass (High temperature durable) 2. Quartz glass As per our discussion at the Glass blowing workshop, it was realized that if we use a borosilicate glass the temperature rise may soften it and the capillary tube may get g et bend or deformed. Thus the bottom section was decided to be made up of Quartz. The middle section was also made up of quartz as it may al so experience considerable amount of heat by the heater. The capillary section was decided to be of borosilicate glass as it is cheap and also in quartz we don’t get capillaries of diameters less than 6 mm.
5.2.2. Fluid medium The criteria of selection of fluid medium are: 1. Low thermal coefficient of expansion. 2. Low variation of coefficient of expansion with temperature. 3. Availability, cost and convenience in handling. 4. Non reactive with the polymers. The choices of fluid media that we had were Glycerine, Ethanol, Olive oil, Linseed oil, Mercury. Of all these we chose to have Linseed oil as it best suited our requirements.
6. Experimental process: 1. We follow the following steps while observing the readings: 2. The volume of the polymer sample is calculated though submerging them in water and measuring the difference in volume. 3. The polymer sample is fed into the bottom container. 4. The container if filled with linseed oil upto the neck. 5. The upper section is tightened and the a pparatus is placed inside the heater for heating. 6. We heat the polymer samples sam ples a little above their glass g lass transition temperatures. 7. Now the heating is stopped and the thermocouple is placed around the bottom container. 8. Equilibrium is allowed to achieve.
9. After equilibrium is attained, subsequent readings are taken in alternate periods of time. We record the temperature and the height of the fluid in the capillary tube as the temperature falls. 10. After some time the temperature in the thermocouple stops to drop further. The final reading of temperature is taken as T0. 11. We feed the data in the excel sheet that already has requisite formula that finally gives us a plot of the Change in volume with respect to the temperature. 12. By using the graph we calculate the T g values.
7. Apparatus extension: The apparatus basically plots the volumetric change with temperature. The data can not only be used for calculating the glass transition temperatures but also can be used to measure Coefficient of Thermal Expansion (CTE), softening point, curie point, crystalline transformation, phase transition, shrinkage, warping, bloating, sintering rate, isothermal creep, stress relaxation.
Also the same apparatus can be used for calculating the reaction coefficients in case of polymer reactions by using the principle of volume contraction on polymerization reaction.
