hierarchical functions at different levels of polymer assembly. Protein folding can be
regarded as a typical example of this case.The chain simultaneously contains various
specific interactions, and adjusts its complex hierarchical self-assembly structure with
the change of the local environment for maintaining its living functions. Such a
function is also known as the “robust stability”.
One kind of inter-chain interaction can even play multiple roles in determining
the physical behavior of a polymer. The local anisotropy of chain-like structures
endows polymers a typical character. Along the backbone of the polymer chain,
each chain unit connects its two neighbors with strong chemical bonds. However, if
we look at the direction normal to the chain, each chain unit interacts with other
neighboring units with relatively weaker sub-valence bonds. For example, in the
fully-extended-chain polyethylene crystal, the theoretical tensile strength along
the chain direction originating from the covalent bonds is as high as 350 GPa;
while the theoretical tensile strength normal to the chain coming from the van der
Waals interactions is as low as 10 GPa. Such anisotropy also makes the thermal
conductivity of polymer crystals along the chain direction much higher than that
normal to the chain. Therefore, the local anisotropy of chain-like structures makes
the local inter-chain interactions behave as the interactions between rigid-rod
molecules. If the common van der Waals interactions can be separated into the
short-range strong repulsive interactions and the long-range weak attractive
interactions, we can further split each kind of interaction into isotropic and aniso-
tropic parts for such rod-like molecules.
The van der Waals interactions are one of the important driving forces for the
physical behavior in polymer assembly states. On the one hand, the packing
structure of molecules in the liquid phase is dominated by the isotropic part of
volume repulsive interactions between polymer chains, especially the combinato-
rial entropy for liquid mixtures. Such kind of inter-molecular spatial combination
can be well represented by the lattice model. This is the reason why the lattice
model can successfully describe the statistical thermodynamics of multi-component
systems containing polymers. The hydrodynamic volume-exclusion interactions of
rigid-rod molecules can be regarded as effective anisotropic interactions, which
result in an entropy change driving the lyotropic liquid crystal ordering. In addition,
the combinatorial entropy of bond orientations at the neighboring positions of each
chain unit can be employed to explain the screening effect of the repulsive
interactions along a polymer chain due to the interpenetration of other polymer
chains. The screening effect makes polymer chains exhibit the scaling behavior of
unperturbed chain conformations in the melt phase. On the other hand, the isotropic
contributions of attractive interactions play a determinant role in driving mixing or
demixing in multi-component polymer systems. The anisotropic attractive
interactions will drive the thermotropic liquid crystal ordering in the bulk phase
via the enthalpy change. In addition, the local anisotropic attractive interactions
between chains can be utilized to describe molecular driving forces for spontaneous
crystallization of polymers.
22 2 Structure–Property Relationships