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Welcome To Research
Below are photos and descriptions of materials used for gun cleaning,
and in them you can find how we make recommendations.
Filament Types and Recommendations
The three most common types of filaments used for gun-cleaning are
phosphor bronze, nylon, and stainless steel.  While brass is an alloy of
copper and zinc, phosphor bronze is an alloy of copper and tin with
some phosphorous.

On the Mohs scale of hardness, phosphor bronze at value 4 is not as
abrasive as stainless steel at value range 5 to 8.5.  While nylon has a
lower coefficient of friction than phosphor bronze and stainless steel,
when nylon become embedded with carbon, its coefficient of friction
rises.  It rises because on the Mohs scale, carbon is at the maximum
value 10.  When nylon filaments are embedded with carbon, it follows
that thicker ones since they are stiffer have a higher coefficient of
friction than thinner ones since they are more flexible.

It is common to use solvents containing ammonia to clean copper
fouling from the rifling since ammonium ions react with copper fouling to
dissolve it.  In the ammonia environment, nylon filaments are used since
nylon does not give a false indication of dirty.  The reason for it is that
nylon does not react with ammonium ions.  It means nylon would let you
know when the bore is free from copper fouling since the patches would
come out clean and not discolored.  On the other hand, phosphor
bronze brushes give a false dirty  since ammonium ions react with
metal filaments.  That is, even though a bore is free from copper fouling
and patches should come out clean, they do not.  The patches may
come out discolored due to ammonium ions reacting with phosphor
bronze filaments, making you think the bore is still copper fouled, when,
in reality, it is clean.

However, nylon has its disadvantage.  Nylon is more porous than
metals, which means it is more likely to collect carbon particulates from
a dirty bore.  When nylon becomes embedded with carbon particulates,
it acts as a severe abrasive for the bore.  To remove carbon
particulates from nylon bristles, we recommend washing a nylon brush
vigorously in warm soapy water.

Nylon filaments have better memory than metallic ones, which means
nylon brushes last longer in terms of bristle remaining at right angles to
the twisted wire core.  Aluminum is softer than phosphor bronze, so
while it would appear to be a good filament wire choice, its
disadvantage is its poor memory.

Photos below show close ups of filament surfaces, and we can see
nylon is more porous than metals.
Fabric Types
Common types of fabrics used as gun-cleaning patches are cotton
flannel, cotton knit, cotton twill, and petroleum-based synthetic.

Cotton flannel is more absorbent than cotton knit since cotton flannel is
100% bleached cotton while cotton knit is not.  Cotton knit is cotton
threads running one direction, and nylon threads running in the
perpendicular direction.   Because cotton knit contains some nylon
threads, cotton knit stretches in the direction where the nylon threads
run.  Cotton flannel, having cotton threads in both directions, does not
stretch.  Cotton knit sheds less threads than cotton flannel.

Cotton flannel is made using a plain weave.  Thin threads run in one
direction, and thick yarns run in the perpendicular direction.  When a
thread goes over one yarn, then it goes under the next yarn.  The over
and under occurs in singles.  Cotton twill uses an over-and-under weave
like cotton flannel, but a thread goes under more than one yarn at a
time.  For example, when under and over occurs in doubles, a thread
goes under two yarns, and then over two yarns.

Synthetics are a conglomeration of non-woven fibers.  They do not shed
threads, and are less absorbent than cottons.
Connector Types
When choosing the metal-type for a connector, there is a trade off.  
Aluminum is softer than brass, so it is less likely to scratch deeply or to
wear down a bore's rifling.  But being softer, the threads of aluminum
are more likely to strip, making the connector, and cleaning element to
which it is mounted, no longer usable.

On the Mohs hardness scale, aluminum is at 2 to 2.9, while brass is at 3
to 4.  You can verify it yourself.  Use a nail to scratch an aluminum
connector and a brass connector.  Use a magnifier to see that the
scratch into the aluminum connector is wider and deeper than the
scratch into the brass one.  The alloy of aluminum for connectors is not
a hard aluminum like alloys of it used for other purposes, such as for
aircraft parts.
Wire Core Types
When choosing the metal-type for the twisted-wire core of a spiral bore
brush, there are trade offs.

Brass is softer than carbon steel, so it is less likely, than carbon steel,
to scratch cut-grooved rifling.  However, a brass core is more likely to
bend under stress due longitudinal force along its twisted-wire core
when pushing a brush into or through a bore.  A bent brush is no longer
useable, and if exposed to rifling, a brass core, which is massive, can
damage rifling.

Brass' greater likelihood to bend under stress of a longitudinal force is
due to its lower flexural modulus or modulus of elasticity.   Brass'
modulus of elasticity at 15 million psi is half that of carbon steel's which
is at 30 million psi.

Carbon steel has a greater fracture toughness, aka resistance to
fracturing, than brass, and it is especially true at lower temperatures
near 0 degrees Celsius.  It means a carbon steel core is less likely to
crack than is a brass core when twisted during brush manufacture or
when using the brush in a near freezing environment.                                  

Being more likely to crack during manufacture means there are more
faulty brass core brushes discarded during manufacture, and that
increases cost.  Another factor making brass cores more expensive is
that brass wire costs more than carbon steel wire.

Because carbon steel wire has a higher flexural modulus than brass,
when twisted it crimps bristles tighter than brass.  Better crimping
means carbon steel cores are less likely to let bristles loosen and fall
out of the brush.

Aluminum is not desirable for core wire because it is brittle and not
sufficiently malleable.  Both factors add up to bristles being more likely
to fall out of aluminum core wires.
phosphor bronze photo with 400 micrometer width
nylon photo with 100 micrometer width
phosphor bronze photo with 1200 micrometer width
brass photo with 250 micrometer width