Page 405 - Mechanical Engineers' Handbook (Volume 4)

394 Cooling Electronic Equipment

interface materials, it is important to measure it exclusively. Separation of the contact resis-
tance and bulk resistance will also help researchers to model the contact resistance and the
bulk resistance separately.
61
Equations (50) and (51) by Fletcher, show that the thermal resistance of any interface
material depends on both the bond line thickness and thermal conductivity of the material.
As a consequence, for materials with relatively low bulk conductivity, the resistance of the
added interstitial layer may dominate the thermal behavior of the interface and may result
in an overall interfacial thermal resistance that is higher than that of the bare solid–solid
contact. Thus, both the conductivity and the achievable thickness of the interstitial layer must
be considered in the selection of an interfacial material. Indeed, while the popular ‘‘phase-
change’’ materials have a lower bulk thermal conductivity (at a typical value of 0.7W/mK)
than the silicone-based greases (with a typical value of 3.1 W/mK), due to thinner ‘‘phase-
change’’ interstitial layers, the thermal resistance of these two categories of interface mate-
rials is comparable.
To understand the thermal behavior of such interface materials, it is useful to separate
the contribution of the bulk conductivity from the interfacial resistance, which occurs where
the interstitial material contacts one of the mating solids. Following Prasher, who studied
62
the contact resistance of phase-change materials (PCM) and silicone-based thermal greases,
can be
the thermal resistance associated with the addition of an interfacial material, R TIM
expressed as
R R R (52)
R TIM bulk co 1 co 2
where R bulk is the bulk resistance of the thermal interface material, and R co is the contact
resistance with the substrate and subscripts 1 and 2 refer to substrate 1 and 2. Prasher 62
rewrote Eq. (52) as

A

A

R TIM 1 nom 2 nom (53)
k TIM 2k TIM A real 2k TIM A real
where R TIM is the total thermal resistance of the thermal interface material, the bond-line
the thermal conductivity of the interface material, and are the roughness
thickness, k TIM 1 2
is the nominal area, and A is the real area of contact
of surfaces 1 and 2, respectively, A nom real
of the interface material with the two surfaces. Equation (53) assumes that the thermal
conductivity of the substrate is much higher compared to that of the thermal interface ma-
terial. The first term on right hand side of Eq. (53) is the bulk resistance and other terms
are the contact resistances.
Figure 11 shows the temperature variation at the interface between two solids, in the
presence of a thermal interface material, associated with Eq. (53). Unlike the situation with
the more conventional interface materials, the actual contact area between a polymeric ma-
terial and a solid is determined by capillary forces, rather than the surface hardness, and an
, in Eq. (53). Modeling each of the relevant
alternative approach is required to determine, A real
surfaces as a series of notches, and including the effects of surface roughness, the slope of
the asperities, the contact angle of the polymer with each the substrates, the surface energy
of the polymer, and the externally applied pressure, a surface chemistry model was found
to match very well with the experimental data for PCM and greases at low pressures. 62
Unfortunately, it has not been possible, as yet, to determine the contact area with a closed
form expression. It is also to be noted that Eq. (53) underpredicts the interface thermal
resistance data at high pressures.