CHARACTERIZATION OF RHEOLOGICAL PROPERTIES OF SEMISOLID MATERIALS USED AS THERMAL INTERFACES . PART II : EXPERIMENTAL TESTS

The paper presents the proposed experimental methodologies employed in testing thermal greases. The data obtained from static tests, shearing test and filament stretching tests are used in estimating the parameters required for theoretical modelling of the material. Newtonian, viscoelastic and viscoplastic models were considered in correlating the experimental results to theoretical models necessary in interpreting and planning the material behaviour.


INTRODUCTION
The thermal paste must fulfil as any thermal interface material, some main characteristics, like sufficiently low thermal resistance to maintain the operating temperature in its target range, reduced electrical resistance, good adhesion and consistent thermal performance, temperature cycling and moisture resistance, and good spreadable properties.
A thermal interface material consists in the conductive filler and the fluid matrix.Suppliers have employed many different polymer technologies in thermal interface materials, including polyimides, epoxies, siloxanes and acrylates.A wide range of conductive fillers has been used to achieve the thermal conductance of the composite.These fillers include ceramics-alumina and boron nitride, or metals -silver and copper [1].From the characteristics of the constituents, the resulting material, the interface thermal paste is a semisolid that, besides sought functional properties presents mechanical and rheological characteristics influencing the workability and life time.
The paper presents some test made in our laboratory, aiming didactical methodologies for finding the viscosity of semisolids and a starting point for modelling according to rheological models.

EXPERIMENTAL PROCEDURES
There were tested commercial thermal pastes filled with silver particles, with no mentions of viscosity or other mechanical or elastic characteristics.Concern upon thermal conductivity and thermal resistance for improving heat transfer is prevalent [2], but viscosity also affects the workability and capacity of filling the voids and is the first parameter sought after.
During the work, a methodology was set for experimental procedures intending to find the main mechanical and rheological parameters of some thermal greases and the following succession of test was proposed:  Estimation of the surface tension by measuring the wetting contact angle by sessile drops and the stalagmites method by weigthing and analysing a drop of liquid;  Finding dynamic viscosity by the coaxial cylinders method using Rheotest 2 equipment.Finding the viscosity using the sliding plate method, presented as principle in part I of the work;  Studying the behaviour during filament stretching tests.
Surface tension measurements by sessile drop method were intended by setting material on a finished flat steel surface.It was observed that, due to high viscosity, the material did not drop from the syringe and after depositing it, it did not form a drop and remained unchanged in shape, as seen in Figure 1.
After long time periods, days respectively, it still had the same indefinite but steady shape.As the drop is not formed, the contact angle cannot be measured.
The stalagmite method also could not be applied due to the consistency of the semisolid thermal paste.As a future direction, a method for finding the surface tension is an objective.The Rheotest 2 equipment requires large quantities of sample for materials of high viscosity, 17 grams when using the coaxial cylinders method -as the cone and plate devices were not available.
The samples existing in our laboratory are commercial products, 2-3 g each and thus, the method was abandoned and shear sliding plates tests were made.
Thermal paste was set on aluminium blades, on both faces, as a central line, Figure 2.a.The blade was then pressed Figure 2.b between other two blades from the same material, obtaining thus a sandwich pack, Figure 2c.
Three similar packs were made, and they were tested by traction with an imposed force upon the central blade.Shear occurred in the two films of thermal paste.The tests were video recorded and the movies were processed using software, analysing the images frame by frame.
The recorded displacement at different moments is presented in Figure 3, for the three packs tested at an interval of one hour and at interval of 15 minutes, presented in Figure 4. From displacement results, the velocity and viscosity were computed and the dependence is presented in Figure 5 and Figure 6.The tests were made at intervals of one hour and respectively of a quarter of hour.
The velocities for the first sliding pack are lower than the velocities for the next packs.After 15 minutes of being applied, the thermal paste becomes stiffer.For low values of velocity, the viscosity presents values approximately constant.The velocity is proportional with the shearing rate of the sample.
From the plot in Figure 5, values of viscosities of an order 50-150 Pa·s resulted, for sliding velocities lower than 0.01 m/s, and after that, a sudden increase of viscosity is observed.This corresponds to a rheological behaviour of shear thickening material [3,4].
For semisolids like mayonnaise, mustard, honey, peanut butter the viscosity ranges is around hundreds of Pa·s, then it can be concluded the order of magnitude obtained is correct [5].
From the plot in Figure 6 it is observed first that the viscosity decreases with increasing velocity, a plateau follows and at increased velocities, a sudden increase of viscosity occurs.
The behaviour is then, first shear thinning and at the end, shear thickening material.This is in very good agreement with the suspensions behaviour [6].It can be concluded that, from qualitative point of view, the tests showed that the thermal paste presents a shear thickening behaviour [7].A quantity of thermal paste was set between two cylinders, as in Figure 7.The upper cylinder was then moved on axial direction (vertically) at a given distance and then maintained.The photos and measurements made showed that there was no change in the shape of the filament.It remained symmetric, with the neck shape, and maintained its shape even a few minutes.The material does not flow under its own weight.The shape of the filament indicates Newtonian, [8] but plastic behaviour is also more probable than a viscoelastic one, depending on time.The minimum diameter of the filament is d=1.8 mm, and the maximum distance between cylinders L=8 mm.The volume of paste sample is V=78 mm 3 .T=0 T=10 s T=310 s T=660 s Fig. 7. Frames of the movie recording the uniaxial traction test, at different moments T.
The second test was performed moving the upper cylinder at constant speed, and the filament formed between the two cylinders was measured from captured movie decomposed into frames with dedicated software, with the results given in Table 1.From the shape the sample takes during uniaxial traction, the material does not behave viscoelastic [8].
The results are plotted in Figure 9 and Figure 10.The deformation velocity imposed is constant and the dependency of filament length versus time, L-t is linear.The variation of the minimum diameter of the filament is approximated in Mathcad, using a linfit function.
In Figure 11

CONCLUSIONS
Thermal pastes are widely used in electronic devices and optimisation of contact interface is a necessity.The workability, spreadability and contact pressure are only a few features dependent on rheological properties of constituents.The thermal greases performances as thermal interface depend on the filler volume fraction but the higher the filler content, the higher the viscosity.The optimum is sought, and for the semisolid obtained the rheological behaviour is analysed.
Common rheometry test applied for fluids cannot be used for semisolids and the sliding plate method and filament stretching were finally made.
From sliding plate tests it was observed that the viscosity is influenced by the shear rate, proportional to sliding velocity.At low sliding velocities, the viscosity values are similar to other semisolids.For higher velocities, the viscosity increases showing a shear thickening behaviour.This is a qualitative aspect that should be considered for future work, from quantitative point of view.
There is a change of viscosity for samples kept at laboratory temperature, namely, for the thermal paste from the same pack, for tests made after an hour, the displacements were lower than the initial ones.The paste should be applied after opening the tube, or else, its viscosity increases.The shearing rate influences the viscosity, and the spread of the paste should be made at slow velocities because at high velocities, the viscosity increases.
A rheological model can be fitted, like Bingham plastic or power law shear thickening [9], but supplementary experimental data are needed.Large quantities of thermal paste are necessary for complete sets of measurements and this is a potential work direction.
From filament stretching tests, the shape of the filament suggested a time-independent behaviour.The sliding tests showed more, proposing plastic and shear thickening behaviour.From both methods, it resulted that the viscoelastic behaviour can be overlooked, and a time-independent model aimed.The mathematical expression for filament diameter variation obtained by approximating the experimental data can be used for future modelling the behaviour of the material.

Fig. 2 .
Sliding pack methodology: a) Thermal paste line on aluminium blades, both faces; b) Assembled pack of blades; c) Pack pressed by the same weight.

Fig. 3 .
Fig. 3. Displacement-time dependency, for the three packs, tested at one hour interval.

Fig. 5 .
Fig. 5. Viscosity variation with sliding velocity, for tests performed at one hour interval.

Fig. 6 .
Fig.6.Viscosity variation with sliding velocity, for tests performed at 15 minutes interval Next, filament stretching test were made, following the principle presented in Part I.A quantity of thermal paste was set between two cylinders, as in Figure7.The upper cylinder was then moved on axial direction (vertically) at a given distance and then maintained.The photos and measurements made showed that there was no change in the shape of the filament.It remained symmetric, with the neck shape, and maintained its shape even a few minutes.The material does not flow under its own weight.The shape of the filament indicates Newtonian,[8] but plastic behaviour is also more probable than a viscoelastic one, depending on time.The minimum diameter

8 .
there are presented the sequence of program of approximation function and the plot of the proposed function comparatively with the experimental points.The square deviation is computed (Figure 11.a) and a very good value results, 1.347, showing a very good approximation of experimental values by the hyperbolic proposed function.Sequences (a, b, c) from the filament stretching movie.

Fig. 9 .
Fig. 9. Filament length function of time for a traction velocity v=0.04 mm/s

Table 1 .
Test parameters.L is length of filament and d is minimum diameter of the filament at the moment t.