Page 585 - Carrahers_Polymer_Chemistry,_Eighth_Edition

548 Carraher’s Polymer Chemistry

whereupon it acts as a solid protecting the wearer from the major impact. Kevlar is also being employed
to protect space craft and space men from discarded space junk and small meteors. Thus experimenta-
tion in body armor is being applied to additional areas where impact protection is essential.

16.11 BREAKAGE OF POLYMERIC MATERIALS
When a plastic is broken by a sharp blow or cut, are polymer chains broken? The important factors
include the nature of the polymer, chain length, and arrangement of the chains.
Sperling and coworkers looked at the question of how many chains are broken and the defi ning
factors related to this breakage when a polymeric material is cut or broken. They used various chain
lengths of PS and employed a dental drill as the cutting implement.
Pictorially, the problem can be described as looking at a robin pulling a worm out of a hole. Does
the robin get the entire worm or some fraction of the worm? The factors are similar and deal with the
length of the worm and how far into the hole it is. If it is largely within the hole then it can grasp
the dirt, roots, and so on about it to “hold on for dear life.” If not, then the entire worm is a meal for
the “early bird.”
It turns out that the question dealt with here is related to determining the critical length of fi bers

that are to be used in a composite. When determining the optimum fiber length of a fiber in a matrix,
measurements are made using fibers of differing lengths. If a fiber can be removed from the matrix

unbroken, then it is too short, and if the fi ber breaks before it can be removed, then the fi ber is too

long. Thus, fiber lengths should be such that the fiber just begins to be broken rather than allowing
it to be removed in tact. In a composite, the worm is the fiber and the soil is the matrix. For the plas-

tic, the worm is the individual chain and the soil is the remainder of the plastic. For the composite,

the fiber contains many individual polymer chains, while for the situation dealt with here individual
polymer chains will be examined.
The length of fiber or chain that can be removed without breaking is related to the frictional and

attractive energies between the fiber and the matrix or other polymer chains holding onto the chain.

Thus, if the strength holding together the polymer backbone is greater than the frictional energy
holding the chain in place, the polymer chain will be removed unbroken. In general, what was found
through calculations was that PS chains to 300 units in length are capable of being removed in
tact without breakage. This is in rough agreement with what Sperling found experimentally. Thus,
individual PS chains up to about 300 units in length are removed from the plastic without chain
breakage.
The relationship between chain length and chain breakage was found to be directly related to
the typical length of chain necessary to produce physical cross-links, that is, chain entanglements.
(This is probably due to the fact that chain entanglements greatly increase the “apparent” chain
length and frictional energy needed to overcome to move a chain.) Typically, at least one chain
entanglement is needed to guarantee some chain breakage. For many vinyl polymers, including
PS, one chain entanglement occurs for every 300 units. Experimentally it was found that as the
length of the PS chain increases so does the number of chain entanglements so that with a chain
length of about 2,000 (or an average of seven chain entanglements), 50% of the chains are broken
and when the chain length is about 4,000 (or an average of 13 entanglements), approximately 100%
of the chains break.
The production of chain entanglements is statically directly related to polymer length for linear
chains, and almost independent of the nature of the vinyl unit for many polymers.
Chain length and entanglement are also related to the strength of the polymeric material. As
chain length increases, the number of entanglements increases as does the strength. At about eight
entanglements, the relationship between number of entanglements (and chain length) and polymer
strength levels off with only small changes in polymer strength occurring as the chain length and
number of entanglements further increases as shown in Figure 16.12.

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