<s>
A	O
force-sensing	B-Algorithm
resistor	I-Algorithm
is	O
a	O
material	O
whose	O
resistance	O
changes	O
when	O
a	O
force	O
,	O
pressure	O
or	O
mechanical	O
stress	O
is	O
applied	O
.	O
</s>
<s>
They	O
are	O
also	O
known	O
as	O
force-sensitive	B-Algorithm
resistor	I-Algorithm
and	O
are	O
sometimes	O
referred	O
to	O
by	O
the	O
initialism	O
FSR	O
.	O
</s>
<s>
The	O
technology	O
of	O
force-sensing	B-Algorithm
resistors	I-Algorithm
was	O
invented	O
and	O
patented	O
in	O
1977	O
by	O
Franklin	O
Eventoff	O
.	O
</s>
<s>
Force-sensing	B-Algorithm
resistors	I-Algorithm
consist	O
of	O
a	O
conductive	B-Algorithm
polymer	I-Algorithm
,	O
which	O
changes	O
resistance	O
in	O
a	O
predictable	O
manner	O
following	O
application	O
of	O
force	O
to	O
its	O
surface	O
.	O
</s>
<s>
They	O
are	O
normally	O
supplied	O
as	O
a	O
polymer	O
sheet	O
or	O
ink	B-Application
that	O
can	O
be	O
applied	O
by	O
screen	O
printing	O
.	O
</s>
<s>
As	O
with	O
all	O
resistive	O
based	O
sensors	O
,	O
force-sensing	B-Algorithm
resistors	I-Algorithm
require	O
a	O
relatively	O
simple	O
interface	O
and	O
can	O
operate	O
satisfactorily	O
in	O
moderately	O
hostile	O
environments	O
.	O
</s>
<s>
Force-sensing	B-Algorithm
capacitors	I-Algorithm
offer	O
superior	O
sensitivity	O
and	O
long	O
term	O
stability	O
,	O
but	O
require	O
more	O
complicated	O
drive	O
electronics	O
.	O
</s>
<s>
There	O
are	O
two	O
major	O
operation	O
principles	O
in	O
force-sensing	B-Algorithm
resistors	I-Algorithm
:	O
percolation	O
and	O
quantum	O
tunneling	O
.	O
</s>
<s>
Although	O
both	O
phenomena	O
actually	O
occur	O
simultaneously	O
in	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
,	O
one	O
phenomenon	O
dominates	O
over	O
the	O
other	O
depending	O
on	O
particle	O
concentration	O
.	O
</s>
<s>
More	O
recently	O
,	O
new	O
mechanistic	O
explanations	O
have	O
been	O
established	O
to	O
explain	O
the	O
performance	O
of	O
force-sensing	B-Algorithm
resistors	I-Algorithm
;	O
these	O
are	O
based	O
on	O
the	O
property	O
of	O
contact	O
resistance	O
occurring	O
between	O
the	O
sensor	O
electrodes	O
and	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
.	O
</s>
<s>
The	O
contact	O
resistance	O
,	O
,	O
plays	O
an	O
important	O
role	O
in	O
the	O
current	O
conduction	O
of	O
force-sensing	B-Algorithm
resistors	I-Algorithm
in	O
a	O
twofold	O
manner	O
.	O
</s>
<s>
However	O
,	O
under	O
a	O
scanning	O
electron	O
microscope	O
,	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
is	O
irregular	O
due	O
to	O
agglomerations	O
of	O
the	O
polymeric	O
binder	O
.	O
</s>
<s>
Up	O
to	O
date	O
,	O
there	O
is	O
not	O
a	O
comprehensive	O
model	O
capable	O
of	O
predicting	O
all	O
the	O
non-linearities	O
observed	O
in	O
force-sensing	B-Algorithm
resistors	I-Algorithm
.	O
</s>
<s>
The	O
multiple	O
phenomena	O
occurring	O
in	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
turn	O
out	O
to	O
be	O
too	O
complex	O
such	O
to	O
embrace	O
them	O
all	O
simultaneously	O
;	O
this	O
condition	O
is	O
typical	O
of	O
systems	O
encompassed	O
within	O
condensed	O
matter	O
physics	O
.	O
</s>
<s>
However	O
,	O
in	O
most	O
cases	O
,	O
the	O
experimental	O
behavior	O
of	O
force-sensing	B-Algorithm
resistors	I-Algorithm
can	O
be	O
grossly	O
approximated	O
to	O
either	O
the	O
percolation	O
theory	O
or	O
to	O
the	O
equations	O
governing	O
quantum	O
tunneling	O
through	O
a	O
rectangular	O
potential	O
barrier	O
.	O
</s>
<s>
The	O
percolation	O
phenomenon	O
dominates	O
in	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
when	O
the	O
particle	O
concentration	O
is	O
above	O
the	O
percolation	O
threshold	O
.	O
</s>
<s>
A	O
force-sensing	B-Algorithm
resistor	I-Algorithm
operating	O
on	O
the	O
basis	O
of	O
percolation	O
exhibits	O
a	O
positive	O
coefficient	O
of	O
pressure	O
,	O
and	O
therefore	O
,	O
an	O
increment	O
in	O
the	O
applied	O
pressure	O
causes	O
an	O
increment	O
in	O
the	O
electrical	O
resistance	O
,	O
For	O
a	O
given	O
applied	O
stress	O
,	O
the	O
electrical	O
resistivity	O
of	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
can	O
be	O
computed	O
from	O
:	O
</s>
<s>
where	O
matches	O
for	O
a	O
prefactor	O
depending	O
on	O
the	O
transport	O
properties	O
of	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
and	O
is	O
the	O
critical	O
conductivity	O
exponent	O
.	O
</s>
<s>
Quantum	O
tunneling	O
is	O
the	O
most	O
common	O
operation	O
mode	O
of	O
force-sensing	B-Algorithm
resistors	I-Algorithm
.	O
</s>
<s>
A	O
conductive	B-Algorithm
polymer	I-Algorithm
operating	O
on	O
the	O
basis	O
of	O
quantum	O
tunneling	O
exhibits	O
a	O
resistance	O
decrement	O
for	O
incremental	O
values	O
of	O
stress	O
.	O
</s>
<s>
The	O
quantum	O
tunneling	O
operation	O
implies	O
that	O
the	O
average	O
inter-particle	O
separation	O
is	O
reduced	O
when	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
is	O
subjected	O
to	O
mechanical	O
stress	O
,	O
such	O
a	O
reduction	O
in	O
causes	O
a	O
probability	O
increment	O
for	O
particle	O
transmission	O
according	O
to	O
the	O
equations	O
for	O
a	O
rectangular	O
potential	O
barrier	O
.	O
</s>
<s>
In	O
order	O
to	O
operate	O
on	O
the	O
basis	O
of	O
quantum	O
tunneling	O
,	O
particle	O
concentration	O
in	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
must	O
be	O
held	O
below	O
the	O
percolation	O
threshold	O
.	O
</s>
<s>
By	O
re-arranging	O
the	O
aforesaid	O
equation	O
,	O
it	O
is	O
possible	O
to	O
obtain	O
an	O
expression	O
for	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
resistance	O
,	O
where	O
is	O
given	O
by	O
the	O
quotient	O
according	O
to	O
the	O
Ohm	O
's	O
law	O
:	O
</s>
<s>
When	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
is	O
fully	O
unloaded	O
,	O
the	O
following	O
relationship	O
can	O
be	O
stated	O
between	O
the	O
inter-particle	O
separation	O
at	O
rest	O
state	O
,	O
the	O
filler	O
volume	O
fraction	O
and	O
particle	O
diameter	O
:	O
</s>
<s>
where	O
is	O
the	O
Young	O
's	O
modulus	O
of	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
.	O
</s>
<s>
has	O
been	O
widely	O
accepted	O
by	O
many	O
authors	O
,	O
it	O
has	O
been	O
unable	O
to	O
predict	O
some	O
experimental	O
observations	O
reported	O
in	O
force-sensing	B-Algorithm
resistors	I-Algorithm
.	O
</s>
<s>
When	O
subjected	O
to	O
dynamic	O
loading	O
,	O
some	O
force-sensing	B-Algorithm
resistors	I-Algorithm
exhibit	O
degradation	O
in	O
sensitivity	O
.	O
</s>
<s>
where	O
is	O
the	O
resistance	O
of	O
the	O
conductive	O
nano-particles	O
and	O
,	O
are	O
experimentally	O
determined	O
factors	O
that	O
depend	O
on	O
the	O
interface	O
material	O
between	O
the	O
conductive	B-Algorithm
polymer	I-Algorithm
and	O
the	O
electrode	O
.	O
</s>
<s>
Force-sensing	B-Algorithm
resistors	I-Algorithm
are	O
commonly	O
used	O
to	O
create	O
pressure-sensing	O
"	O
buttons	O
"	O
and	O
have	O
applications	O
in	O
many	O
fields	O
,	O
including	O
musical	O
instruments	O
(	O
such	O
as	O
the	O
Sensel	O
Morph	O
)	O
,	O
car	O
occupancy	O
sensors	O
,	O
artificial	O
limbs	O
,	O
foot	O
pronation	O
systems	O
,	O
and	O
portable	O
electronics	O
.	O
</s>
<s>
They	O
are	O
also	O
used	O
in	O
mixed	B-General_Concept
or	O
augmented	B-General_Concept
reality	I-General_Concept
systems	O
as	O
well	O
as	O
to	O
enhance	O
mobile	O
interaction	O
.	O
</s>
