Thermally conductive liquid materials for electronics packaging
y
osit
y
V
isc
osit Shear Thinning
V
isc
0
Increased
Filler loading
φ
Filler Loading
max
10-20% rods
20-40% plates
Shear Rate
> 60% spherical
Figure 5. Viscosity model. Figure 6. Shear thinning dispersions.
Rheology 2b through 2e). or drum, flows at high shear rate during
Various excellent reviews of rheology of Equations 2b through 2e represent the pumping and dispensing and again experi-
dispersions are available
8-10
. The rheologi- ‘low shear’ viscosity of dispersions, in other ences no shear once it has been dispensed
cal models for particulate dispersions have words they apply to dispersions under very in the application.
been around for some time starting with slow deformation. Typical trends for these Long chain polymers, either entangled
the simple Einstein type model for the models are shown in Figure 5. or crosslinked, tend to be viscoelastic—i.e.
relative viscosity of very dilute dispersions
11
The structure of particulate disper- show both elastic and viscous behavior
(Equation 2a). sions can be very sensitive to shear rate. under various time dependent stress or
However, thermally conductive liquids Typically as shear rate is increases the strain regimes. More elastic under higher
are rarely dilute. Several other models are viscosity decreases - these fluids are non- frequency and more viscous under low
available for such dispersions
12-15
(Equations Newtonian. Typically the shear dependent frequency or steady shear. The relative
behavior of such liquids can be modeled as magnitude of these behaviors are repre-
a power law
10,16
(Equation 3). sented by the storage modulus G' and loss
While mostly one observes shear thin- modulus G". These typically represent the
Equation 2a
ning behavior, at high particle packing and energy stored elastically or lost through
high shear rate there can be a shear thick- viscous dissipation per strain cycle. Typical
Where η is the viscosity of the dispersion
ening as particles get jammed into each thermally conductive dispersions do not
and η
0
is the viscosity of the polymer liquid
other and unable to slip past fast enough. have long chain polymer but do show some
in which the particles are dispersed.
An understanding of the shear thin- viscoelastic behavior due to the structure
ning behavior can be critical in applica- induced by hydrodynamic interactions
tions where the fluid goes through a gamut between particles. One such model due to
of shear rates. It is at rest in the package Faulkner and Schmidt
17
is seen in Equa-
tions 4a and 4b. The subscript R denotes
reduced, i.e. normalized to the properties
of the polymer liquid matrix.
Equation 2b
Lets add a word of caution on the
common usage of terminology. The terms
Equation 3
thixotropic and rheopectic describe respec-
tively thinning and thickening behavior
Where
Equation 2c
over time—i.e. it describes time dependent
K is a constant, is the shear rate and n
behavior rather than steady shear behav-
is a constant indicative of shear depen-
ior. In the industry the term ‘thixotropic’
dent behavior (n < 1 for shear thinning
is commonly used to describe the shear
fluids, n = 1 for Newtonian fluids, n > 1
thinning behavior—typical behavior of
for dilatant or shear thickening fluids).
particulate dispersions. In this paper we
Equation 2d
use the latter common usage.
Bondline—interface thickness
An important factor in the ultimate
Equation 4a
thermal performance and reliability of an
adhesive, paste or cure-in-place gasket, is
Equation 2e
the bondline. This is the thickness of the
interface after the manufacturing opera-
Here φ
m
is the maximum packing tion.
fraction.
Equation 4b
Sometimes the bondline is dictated by
the mechanical and electrical requirements
20 – Global SMT & Packaging – December 2008 www.globalsmt.net
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