Page 21 - Handbook of Adhesion Promoters

14 Mechanisms of Adhesion

⁄
(
⁄
χ t() = R t τ rep ) 14 [2.2]
g
where:
χ(t) displacement of center of mass during a time t
gyration radius of chain
R g
reptation time
τ rep
This equation shows that when the time of contact (diffusion time), t, equals the time
of reptation, τ , then the weld will reach cohesion strength of interphase. 15,16 In the non-
rep
isothermal fusion welding of ethylene polymers, the cohesion strength at interphase nearly
reached cohesion strength of bulk of the material (polyethylene) after less than 10 s of
16
contact time under infrared radiation. The reptation of the shortest chains contributed to
the restoration of the entanglement network of the longest chains within a timescale much
16
shorter than the reptation time of the longer chains. This shows that shorter chains dif-
fuse faster than the longer chains and it explains the frequent observation that the weld
interphase is somewhat weaker than the bulk because it preferentially contains shorter
chains.
The time of reptation can be calculated from the following equation:
3 4
ζN b
τ rep = ------------------ [2.3]
2
π kTa 2
where:
ζ friction coefficient of monomeric unit
N average length of chain given in number of random links
b length of random link (for example it has an average molar weight of 140 Da for
polyethylene chains)
k Boltzmann’s constant
T temperature
a diameter of reptation tube
This equation shows that the molecular weight of the polymer (chain length) has
very strong influence on the time of reptation (the third power of the chain length and the
fourth power of the chain link length).
The mechanism of diffusion-controlled adhesion has limited influence on overall
adhesion when substrate material is highly crystalline or crosslinked and when contact
8
between the two materials occurs well below their glass transition temperatures.
Figure 2.12 shows polyolefin surface (bottom) painted with thermoplastic polyure-
17
thane/olefin block copolymer paint (top). Between the paint and the substrate, there is an
interphase layer (top picture) which is expanded at the bottom picture because of forma-
17
tion of extension fibrils during paint delamination. The presence of these fibrils means
that polyurethane chains from the paint diffused into the blend substrate during painting
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and the subsequent drying step and entangled with TPU in the blend. The entanglement
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between the paint and the substrate generated a physical link that provided adhesion.
Raman spectroscopy was used for detection of interdiffusion in two-component
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injection molded parts. The two-component injection molded parts were made out of
combinations of five materials chosen from polypropylene, styrene-based thermoplastic
elastomer, polycarbonate, polystyrene and polymethylmethacrylate produced at varying
18
melt temperatures. Figure 2.13 shows an example of results. TPE is present between -5