2.5 Memcapacitors and Meminductors: Properties and Signatures
79
In the next, an example of a generic memcapacitor is presented.
Example 2.28 (Memory Capacitance in Biomimetic Membranes) The work [43]
reports the first example of a volatile, voltage-controlled memcapacitor where
capacitive memory arises from reversible and hysteretic geometrical changes in a
lipid bilayer that mimics the composition and structure of biomembranes.
The system consists of an elliptical, planar lipid bilayer that forms at the interface
between two lipid-coated aqueous droplets (about 200 nL each; L denotes Liter) in
oil.
The charge is given by
q = C(R, W )v
where R(t) is the membrane radius, W (t) is the hydrophobic thickness, v is the
applied voltage, and C is the memcapacitance. For a parallel-plate capacitor with
planar ellipticity a, and equivalent dielectric constant ε (ε 0 is the vacuum dielectric
constant), we have
C(R, W ) =
εε 0 (aπ R 2 (t))
W (t)
.
The state variables R(t) and W (t) are governed by
dR(t)
dt
=
1
ξ ew
aεε 0
2W (t)
v
2 (t) − k ew (R(t) − R 0 )
and
dW (t)
dt
=
1
ξ ec
−aεε 0 πR 2 (t)
2W 2 (t)
v
2 (t) − k ec (W (t) − W 0 )
where ξ ew , k ew , ξ ec , k ec are positive physical parameters (defined in [43]).
Such biomimetic membrane actually falls into the class of generic memcapacitors and it exhibits volatile memory features. In fact, when power is off, i.e., we set
v = 0, then the state variables R(t) and W (t) tend to a unique steady state (R 0 , W 0 ).
The biomimetic membrane shows a pinched hysteresis loop in the (v, q) plane
at low and intermediate frequencies. Hysteretic and reversible changes in the
memcapacitance C(R, W ) yield complex nonlinear dynamical behaviors, including
capacitive short-term facilitation and depression. The biomimetic membrane is then
capable of adaptive signal processing and learning via synapse-like, short-term
capacitive plasticity. This is potentially useful to develop low-energy, biomolecular
neuromorphic mem-elements, which, in turn, could also serve as models to study
capacitive memory and signal processing in neuronal membranes. In addition to
their possible implementation as memcapacitive synapses for spike recurrent neural
networks supporting online learning and computation, biomimetic membranes are
79
In the next, an example of a generic memcapacitor is presented.
Example 2.28 (Memory Capacitance in Biomimetic Membranes) The work [43]
reports the first example of a volatile, voltage-controlled memcapacitor where
capacitive memory arises from reversible and hysteretic geometrical changes in a
lipid bilayer that mimics the composition and structure of biomembranes.
The system consists of an elliptical, planar lipid bilayer that forms at the interface
between two lipid-coated aqueous droplets (about 200 nL each; L denotes Liter) in
oil.
The charge is given by
q = C(R, W )v
where R(t) is the membrane radius, W (t) is the hydrophobic thickness, v is the
applied voltage, and C is the memcapacitance. For a parallel-plate capacitor with
planar ellipticity a, and equivalent dielectric constant ε (ε 0 is the vacuum dielectric
constant), we have
C(R, W ) =
εε 0 (aπ R 2 (t))
W (t)
.
The state variables R(t) and W (t) are governed by
dR(t)
dt
=
1
ξ ew
aεε 0
2W (t)
v
2 (t) − k ew (R(t) − R 0 )
and
dW (t)
dt
=
1
ξ ec
−aεε 0 πR 2 (t)
2W 2 (t)
v
2 (t) − k ec (W (t) − W 0 )
where ξ ew , k ew , ξ ec , k ec are positive physical parameters (defined in [43]).
Such biomimetic membrane actually falls into the class of generic memcapacitors and it exhibits volatile memory features. In fact, when power is off, i.e., we set
v = 0, then the state variables R(t) and W (t) tend to a unique steady state (R 0 , W 0 ).
The biomimetic membrane shows a pinched hysteresis loop in the (v, q) plane
at low and intermediate frequencies. Hysteretic and reversible changes in the
memcapacitance C(R, W ) yield complex nonlinear dynamical behaviors, including
capacitive short-term facilitation and depression. The biomimetic membrane is then
capable of adaptive signal processing and learning via synapse-like, short-term
capacitive plasticity. This is potentially useful to develop low-energy, biomolecular
neuromorphic mem-elements, which, in turn, could also serve as models to study
capacitive memory and signal processing in neuronal membranes. In addition to
their possible implementation as memcapacitive synapses for spike recurrent neural
networks supporting online learning and computation, biomimetic membranes are