Collapse of polymer brushes grafted onto planar ... - Wageningen UR

10-50 Å, which increases with the block length. Both experiments and theory reveal evidence for the
existence of three regimes regarding the configuration of the dangling blocks: a “wet brush” regime, a
“mushroom” regime, and a broad transition regime in between.
SCF calculations can serve as a starting point for predicting mechanical failure at interfaces subjected to
large-scale deformations. A hierarchical simulation approach has been designed for this purpose. Using as
input the chemical constitutions and relative amounts of chain species present at the interface, the
composition profiles and conformational characteristics for all these species are first calculated by SCF
theory (Terzis 2000a). The statistical weights derived from the model are then used within a Monte Carlo
procedure to generate large ( ≈ 0.1 µm-sized) three-dimensional computer “specimens” of the interfacial
region. In these specimens the material is represented, in a coarse-grained sense, as a network of
entanglement points. Each entanglement point is shared by two chains. Each chain is defined by the
positions of its ends and of all entanglement points it traverses, as well as by its contour lengths between
these points (Terzis 2000b). A coarse-grained free energy function incorporating excluded volume, dispersion
attraction, and conformational entropy contributions is written for the network. An efficient numerical
procedure is invoked for finding local minima of this free energy function with respect to the positions of all
chain ends and entanglement points, and thereby imposing the condition of mechanical equilibrium.
Deformation of the network to fracture (Figure 1) at prescribed temperature and strain rate is simulated
through a kinetic Monte Carlo procedure, which tracks elementary events of chain slippage across
entanglements, chain disentanglement, chain reentanglement, and chain rupture (Terzis 2002). This
hierarchical procedure has been applied to study interfaces between polypropylene (PP) and polyamide 6
(PA6) compatibilised with the reaction product between maleic anhydride-functionalised PP (PP-g-MA) and
PA6. Such interfaces can be viewed as consisting of a homopolymer (free PP) next to an impenetrable solid
surface (PA6), onto which are grafted chains of the same chemical constitution as the homopolymer (endgrafted
PP). The effects of the surface density of grafted PP and of the molecular weight distribution of free
PP and grafted PP have been explored. It is clearly seen that increasing the surface grafting density does not
necessarily enhance adhesion. For high surface grafting densities, a “brush” of grafted PP builds up next to
the PA6 surface; as a consequence, the region over which grafted and free PP chains interentangle is of
limited width. For monodisperse grafted PP of molar mass 40 kg/mol in a free PP matrix of molar mass 60
kg/mol, optimal adhesion (a maximum in the work required to destroy the interface) is seen at 0.1 grafted
chains/nm 2 .
TRUE STRESS (MPa)
250
200
150
100
50
1% per sec
10% per sec
0
1 2 3 4
DRAW RATIO
Figure 1: Shapshots and stress-draw ratio curves from tensile deformation computer experiments carried out on
network specimens modelling the PP/PP-g-MA/PA6 interface. Grafted and free PP chains are shown in red and
green, respectively. The stress-strain curves have been obtained at two strain rates for a surface grafting density of
0.10 chains/nm 2 . The specimen, of initial dimensions 45 nm × 45 nm × 70 nm, contained 1300 chains.