MN¼
SHi
SHi=Mi(2.25)
In recent years, the technology of mass spectroscopy has been well developed.
The matrix-assisted Laser desorption/ionization time-of-flight mass spectrometry
(MALDI-TOF MS) can be applied to measure the molecular weights of
macromolecules (up to one million Dalton) due to its high sensitivity and its wide
response range. In combination with the distribution of fragment lengths, it can be
used to characterize those bio- and synthetic macromolecules with complicated
molecular architectures.
2.5 Topological Architectures
Polymers are not only simply linear chains, but also the building blocks to construct
topologically more complicated three-dimensional macromolecules. Some typical
cases are listed below.
- Linear polymers.Linear structure is the basic topological shape of polymer
chains, as shown in Fig.2.6a. The assembly of linear polymers normally
contains a specific distribution of chain lengths. - Ring polymers.The ring contains no chain end, as shown in Fig.2.6b. Since
ring polymers cannot make entanglement with each other, their mobility is much
higher than the linear polymers with the same chain lengths. - Branched polymers.There can be multiple branches on the linear chains,
characterized by the degree of branching. There are several typical cases. The
comb-like polymers contain all the branches derived from the same backbone
chain, as shown in Fig.2.7a. If the branches of comb-like polymers are chemi-
cally different from the backbone chain, we have the graft copolymers. A
famous example for the random branching is the amylopectin (branched starch).
The hyper-branched polymers (more often called dendrimers) may contain
several levels of branching at the chain ends, like a Cayley tree, as shown in
Fig.2.7b. Chain branching destroys the sequence regularity of polymer chains,
hindering crystallization and thus depressing the mechanical performance.
Fig. 2.6 Illustration of (a) linear polymers and (b) ring polymers
2.5 Topological Architectures 27