Science - USA (2020-10-02)

array are 150 and 300mm, respectively. The
effective through-plane thermal conductivity
in the region of the vias is about 85.7 W/(m·K)
based on a finite-element simulation in
COMSOL, assuming 400 W/(m·K) as the ther-
mal conductivity of electroplated copper and
0.29 and 0.81 W/(m·K), respectively, as the
through-plane and in-plane thermal conduc-
tivities of FR-4 ( 44 ). The MLCCs are assembled
onto the ATC plates to form the top and bot-
tom EC modules (Fig. 3A), which contained
five and four MLCCs, respectively. The bottom
module has an aluminum plate-fin heat sink
at each end to facilitate achieving stable tem-
peratures when required. The modules are
seated in a 3D-printed VeroClear housing filled
with polyurethane foam insulation with a ther-
mal conductivity of 0.04 W/(m·K). The housing
(Fig. 3B) provides structural support and mini-
mizes heat leakage. We attached a miniature
fan to one end to flow air across the hot-end
heat sink. We connected the top housing to a
spring-returned single-acting linear solenoid
actuator with a maximum stroke length of
12.7 mm and a contraction force of 7.2 N at
50% stroke. Application of 12-V dc to the ac-
tuator draws the top module toward the actu-
ator. When the voltage is returned to zero, the
solenoid relaxes and a spring returns it to its
original position. The extents of actuation in
each direction are set by adjusting the position
of the actuator and an adjustable buffer. The
EC module housing provides vertical pressure
through a set of wheels to enhance the ther-
mal contact between the two modules without
hindering sliding. Control software synchro-
nizes the actuation of the top module layer
with the application of electric fields to the EC
capacitors ( 43 ).
We operated the MLCCs under an EC Brayton
cycle, with two isoelectric and two isentropic
stages(Fig.1D).Tomeasurethemaximum
temperature span, we fully insulated both
ends of the device. The heat sinks are filled
with silicon paste to prevent air flow, the fan is
removed, and the hot end is enclosed in foam
insulation. Thermistors for measurement of
thehotandcoldendtemperatures,ThandTc,
respectively, were fitted into bore holes in the
aluminum heat sinks. The variation in offset
between the two thermistors was measured to
be less than 0.1°C, allowing accurate measure-
ment of small temperature lifts. We measured
hot-end and cold-end temperatures with the
cooler operated at a 400-V polarizing voltage
(equivalent to ~10.5-MV/m electric field) and a
0.2-Hz switching frequency (5-s period) with a
50% duty cycle and negligible transition time
(Fig. 4A). We also determined the maximum
temperature liftDT=Th−Tcfor several differ-
ent operating cycle periods, all with a polariz-
ing voltage of 400 V (Fig. 4B). We achieved a
maximum temperature span of 5.2°C at an
operation frequency of 0.15 Hz (6.7-s period).

This is equivalent to a ~0.09°C/mm temper-

ature gradient along the heat pumping axis.

To measure the cooling power, we attached

a 1-mm–by–2-mm 100-ohm chip resistor to the

cold end and used it as an electric heater. The

fan provides air flow across the uninsulated

hot-end heat sink to maintainThnear ambient

temperature. We characterized the system by

varying the current through the heater resistor

and allowing the temperature liftDTto stabi-

lize (Fig. 4, C and D). Because the coupling to

ambient temperature is imperfect, over the

course of the experiments, the heat sink temper-

ature,Th, increases slightly as heat is pumped

to the hot end. The cold end temperature,Tc,

changes in discrete steps as the heater power

is varied. Because the temperature difference

between the heater and the environment is

small and the insulation is very good, heat

leakage is negligible, and the heat pumped by

the cooler is well approximated by the applied

heater power. The measurement results show

a linear relationship between the cooling power

and temperature lift. We achieved a maximum

heat power of ~85 mW with no temperature

lift. This value is equivalent to a heat flux of

~135 mW/cm^2 ,giventhe0.63-cm^2 active cool-

ing area of the MLCC. The specific cooling

power normalized to the volume of the active

electrocaloric material is ~116 mW/cm^3. We

also calculated the cooling power normalized

to the total volume and to the total mass—each

including the inactive material of the MLCC,

the ATC plate, and the insulating material—to

be ~29.2 mW/cm^3 and ~6.8 mW/g, respec-

tively. The equivalent heat flux in the heat

pumping direction is ~156 mW/cm^2 , given the

0.54-cm^2 cross-sectional area normal to the

heat flow direction.

A key determinant of the efficiency of a heat

switch–based EC cooling system is the effec-

tive thermal contrast ratioK′, defined as the

ratio of“effective”on and off conductivity,kh′

andkl′( 45 ).We can model our system as a

cascaded heat switch–based architecture ( 43 ).

In an otherwise ideal heat switch–based sys-

tem operating under a Carnot cycle, theCOPis

given by

COPK′¼

Qc

WECE

¼COPr;K′COPCar

¼

ffiffiffiffiffi

K′

p


 1

ffiffiffiffiffi

K′

p

þ 1

! 2

COPCar ð 1 Þ

whereWECEis the work required to move

heat through actuation of the ECE,K′is the

effective heat-switch contrast ratio,Qcis

the heat collected from the cold side of the

device, andCOPCar¼Tc=ðTh
TcÞis the maxi-

mum thermodynamic (Carnot)COP.COPr,K′

is the maximumCOPrelative toCOPCarfor a

heat switch–based system with effective ther-

mal contrast ratioK′( 33 ). Assuming a nec-

essarily imperfect charge recovery, system

efficiency is given by

COPC¼Qc=Wtot

¼Qc=½WECEþWelecð 1 
hECRފ

¼helecCOPK′ ð 2 Þ

whereWelecis the additional electrical work

associated with charging and discharging the

EC capacitor, andhECRis the electrical charge

recovery (ECR) efficiency, or the portion of

electrical energy recovered each cycle. This

work is often disregarded in thermodynamic-

cycle efficiency calculations that assume that

input work and net cycle work are equivalent,

leading to unrealistically high efficiency esti-

mates. We did not observe measurable frictional

or Joule heating in the system. Additionally, the

mechanical work required to move the recip-

rocating system is orders of magnitude smaller

than other work terms ( 43 ).Thus, we can neg-

lect this term as well as the electrical work

required to drive the actuator, assuming a

reasonably efficient actuator. The electrical

efficiency factorhelecis given by

helec¼

WECE

WECEþWelecð 1 
hECRÞ

ð 3 Þ

and can be approximated as

helec¼

1

1 þrTceE DDTE


 2

ð 1 
hECRÞ

ð 4 Þ

for given electrical permittivitye, material den-

sityr, and heat capacity at constant electric

fieldcE(43).As detailed in ( 43 ), this approx-

imation is based on a number of simplifying

assumptions to allow analytical insight. A more

complete thermodynamic model is required for

an accurate calculation ofhelecand systemCOP

( 46 ). Operating on a Brayton cycle instead of a

Carnot cycle, theCOPis reduced by the ratio of

the temperature difference between the heat

source and heat sink to the maximum temper-

ature difference internal to the device,D/d

( 45 ), giving the system relativeCOP(sometimes

termed efficiency):

COPr¼

D

d

COPC

COPCar

¼

D

d

1

1 þrTceE DDTE


 2

ð 1 
hECRÞ

ffiffiffiffiffi

K′

p


 1

ffiffiffiffiffi

K′

p

þ 1

! 2

ð 5 Þ

We determinedhelecas a function ofhECR

for the partially ordered PST material used in

this work (fig. S5) and the material parame-

ters (table S2). As the material ECE improves

relative to the permittivity, the impact of ECR

132 2 OCTOBER 2020•VOL 370 ISSUE 6512 sciencemag.org SCIENCE

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