# Barocaloric effect of elastomers and plastic crystals: an outlook

V. M. Andrade<EMAIL_ADDRESS>IFIMUP - Institute of Physics for
Advanced Materials, Nanotechnology and Photonics of University of Porto,
Portugal  Faculty of Engineering of University of Porto, Portugal  L. S.
Paixão<EMAIL_ADDRESS>‘Gleb Wataghin’ Institute of Physics, State
University of Campinas (UNICAMP), Campinas-SP, Brazil  A. M. G. Carvalho
<EMAIL_ADDRESS>Mechanical Engineering Department, Maringá State
University, 87020-900, Maringá, PR, Brazil  Chemical Engineering Department,
São Paulo Federal University, 09913-030, Diadema, SP, Brazil  V. Franco
<EMAIL_ADDRESS>Dpto. Física de la Materia Condensada. Universidad de Sevilla.
P.O. Box 1065. 41080-Sevilla, Spain  M. S. Reis<EMAIL_ADDRESS>Dpto. Física
de la Materia Condensada. Universidad de Sevilla. P.O. Box 1065.
41080-Sevilla, Spain  Institute of Physics, Fluminense Federal University, Av.
Gal. Milton Tavares de Souza s/n, Niteroi-RJ, Brazil

###### Abstract

The urge for efficient and environmentally friendly alternatives for the
current gas-based refrigeration is becoming more critical due to global
warming and overpopulation. Among the main candidates, solid-state-based
cooling technology is appealing to substitute the conventional systems.
Recently, attention has been turned to the barocaloric effect in advanced
materials, namely, plastic crystals and elastomers, with reports revealing
great caloric responses around room temperature for a series of materials. In
this sense, this review has the goal of collecting, organizing and comparing
the results from the literature to provide an outlook on the subject.

barocaloric effect; solid state cooling; polymers; plastic crystals;
elastomers

##  I Introduction

Conventional gas compression/decompression refrigeration relies on harmful
substances with high global warming potential. In view of the huge
environmental challenges humankind faces nowadays, eco-friendly technologies
are of utter importance. Another disadvantage of conventional refrigeration is
its difficulty to scaling down to small sizes aiming its use for electronic
components. In this scenario, solid-state-based cooling is considered a viable
alternative refrigeration technology, mainly for its environmental
friendliness appeal.

Solid-state cooling is based on caloric effects, which are thermal responses
of materials induced by external stimuli. Depending on the applied field, the
effect is named: magnetocaloric, when induced by magnetic fields;
electrocaloric, by applying electric fields; and mechanocaloric, when the
material is under mechanical stresses. The mechanocaloric effect encompasses
the elastocaloric and the barocaloric effects, induced by uniaxial stress and
hydrostatic pressure, respectively.

In the last decades, a number of reports appeared describing new materials
with increasing caloric performances; however, further performance improvement
is needed to make an economically viable alternative for household
refrigeration [1]. In recent years, elastomers and plastic crystals are
classes of materials that received considerable interest due to their
impressive optical, mechanical, and barocaloric properties [2, 3, 4, 5]. From
the environmental point of view, besides contributing to the reduction of
greenhouse gas emissions (characteristic of the solid-state technology),
elastomers showed a recycling appeal, through the possibility of blending with
rubber waste materials [6].

Therefore, the present review aims to summarize and compare recent results
from the literature on the barocaloric properties of elastomers and plastic
crystals. We review the appropriate experimental techniques and the results
thereby obtained.

##  II Materials survey

###  II.1 Plastic Crystals (PC)

Plastic crystals (PC) are molecular materials with distinct and remarkable
features, being in a mesophase between liquid crystal (LC) and ordered crystal
(OC) [7]. The main distinction of PCs over LC and OC is regarding the degree
of freedom for the molecules inside the structures. For LC, there is no
formation of lattices, allowing translational and rotational motion of
molecules, which show weak van der Waals interactions and long-range
orientational ordering [8]. Distinctly, OC implies the formation of a lattice
with no accessible rotation and translation modes for the molecules,
presenting a long-range order and high inter- and intra-molecular
interactions. In between, the PC molecules are orientationally disordered in a
well-defined lattice, with low inter- and intra- molecular interactions of
long-range kind, giving rise to the observation of high plasticity for these
materials.

The classical PC is made of molecules with regular shapes (globular or
cylindrical), i. e., symmetrical around their center of mass or by rotation
around an axis. The exploitation of PC dates from the early 1960s with the
studies of materials comprising simple neutral molecular systems like
chloroform, cyclohexane, alkanes, cycloalkanes, certain terpenoids, pivalic
acid, pentaerythritol and its derivatives [3]. Further investigations on
binary compositions of anionic and cationic species, the so-called ionic PC,
revealed that cylindrical and disk shape molecules can also lead to the
formation of such interesting systems [9]. However, techniques to predict if a
material will form a PC or not is still under debate within the community [7,
10]. The development of novel PC materials and the understanding of their
properties is essential for applications in photonics, optics, energy and
memory devices, just to name a few [3].

J. Timmermans was the first to identify the peculiarities of PC during the
preparation of a data survey for organic crystalline compounds, as described
in his review written in 1961 [11]. For a set of compositions of simple
constituents, a low entropy of fusion/melting ($\Delta S_{f}$) below 20 J/kgK
was observed for systems composed of globular molecules, like methane, carbon
tetrachloride and cyclohexane. This was the first empirical criterion to
consider a material as PC: low $\Delta S_{f}$ and globular molecular shape.
Currently, due to the advances in these systems, to be considered a PC, the
material should present other features like plastic flow under stress, high
self-diffusion, high compressibility and high vapour pressures close to their
high melting temperature (above 350 K) [3]. For this reason, more recent
studies have demonstrated that a PC can be formed even exceeding the limit
established by Timmerman for $\Delta S_{f}$, i.e., with non-globular molecular
shape structures [9]. For the case of cylindrical and disk-like molecular
shapes, there is a reduced number of accessible rotation modes that depend on
the size and noncovalent interactions inside the structure, leading to $\Delta
S_{f}$ values of 70 J/kgK - broadening the possibility of a system to form a
PC. Materials with constrained available modes, namely OC, present $\Delta
S_{f}$ higher than 80 J/kgK, which is the upper limit to classify a molecular
arrangement as PC. These reduced $\Delta S_{f}$ values for plastic crystals
are due to the highest degrees of freedom accessed by the molecules, which is
also the reason for the crystalline arrangement presented by these structures.

A general curve of heat flow vs. temperature is given in Fig. 1(a), where the
lower contribution, located at a higher temperature, arises from the melting
process.

Figure 1: (a) An illustration of the temperature dependence of the heat flow
for a plastic crystal, revealing that the contribution at the fusion
temperature is lower than that at the order-disorder transition. Scheme of the
plastic crystals (b) at the ordered phase at low temperature, where the
molecules present a preferred orientation and (a) at the disordered phase with
the reorientation modes available for the molecules above the transition
temperature.

Additionally to the properties mentioned above, the main characteristic of PCs
is to present one or more solid-solid phase transitions from an ordered to a
disordered state before melting, preferably reversible [3]. Some PC systems
can present successive order-to-disorder phase transitions, such as the
trimorphic quinuclidium perrhenate that shifts from a cubic ordered phase to a
pseudo-rhombohedral phase and then to an orthorhombic phase with lower
symmetry [12]. The system presents a higher symmetry state with preferred
orientations for the molecules at low temperatures, as given in Fig. 1(b),
usually hexagonal and cubic phases. By increasing the temperature, the
possible rotational modes of the molecules can be accessed, and an anharmonic
lattice deformation shifts the structure to a lower symmetry state, such as
rhombohedral and monoclinic ones. During the symmetry change process, in a
first-order transition, a large enthalpy change is observed due to the
activation of the rotational modes by the molecules, as highlighted in figure
1(c). Although the plastic deformations are very isotropic, the molecular
interactions can lead to irreversibility during the phase change during the
application of stress [13]. Close to the fusion temperature (Tf), a high
plasticity behavior and diffusion constant occur for PC due to the higher
degrees of freedom and long-range orientational correlations for the
molecules. As for the melting (fusion) process, lower enthalpy changes are
associated, since the higher degree of freedom was already achieved by the
system. In other words, the energy cost for the transition from an ordered to
a disordered phase is higher than during the material melting, leading to
greater entropy changes at the solid-solid phase transitions [3]. This is one
of the main reasons for the great potential of PCs as barocaloric materials,
as will be further described in this review.

###  II.2 Elastomers

Polymers have a variety of features and, consequently, these materials can be
classified based on their source (natural/synthetic), structure, chemistry,
connectivity (or tacticity) and spatial arrangements [14]. These features rank
the polymers as elastomers, plastics and fibers. Plastics are materials with
high molar weight and may be divided into thermoplastic and thermosetting. The
former, having no cross-linked chains, is easily molded by heating, while the
second presents hardening after heating due to the cross bond of the polymer
chains. Fibers present higher structural organization, leading to less
elasticity, higher intermolecular forces and a geometrical condition of
length/diameter ratio higher than 100 [14]. A scheme about the type of
polymers is given in Fig. 2, where these are aligned regarding to their
mechanical properties (softness and hardness). Depending on the type of
process to produce the polymers, they can present amorphous and crystalline
phases, being, in reality, semicrystalline materials. Considering the Young’s
modulus dependence with temperature for an amorphous polymer, the system will
present a rigid glassy state at low temperatures. As the temperature
increases, a rubbery behavior occurs above the so-called glass transition
temperature (TG). The region of interest for the barocaloric effect relies on
the rubbery state, i.e., the region between TG and the melting temperature
(T${}_{M})$; which should be wide enough for practical use of the material.
Above the glass transition [14], their flexibility increases, reducing the
Young’s modulus. For this reason, considering flexibility as the requirement
for applications, TG well below room temperature are preferable for amorphous
elastomers. Among the mentioned polymer’ classes, elastomers present higher
elasticity and, for this reason, are the ones with higher barocaloric
response, as will be further discussed.

Figure 2: Classification of polymers according to their Young’s modulus: from
soft (left) to the hard (right).

Elastomers belong to the particular category of polymers that gave high
failure strain, low Young’s modulus and weak intermolecular forces - Coulomb
and van der Waals interactions - being the main characteristics responsible
for their rubber-like behavior. These materials can be classified as: natural,
when originated from plants and some fungi species; semi-synthetic, when
processed from other materials to improve resistance and elasticity [15]; and
synthetic, as petroleum or silicon-based products. In particular, natural
rubber was used by ancient cultures of Mesoamerica as early as 1600 B.C. [16];
however, it only became popular after the development of the vulcanization
process. These semi-synthetic polymers are commonly obtained by curing the
sticky extracted rubber with sulfur, peroxides, bisphenol and carbon black to
improve their mechanical strength, elasticity and durability [15]. Their large
molecules may be cross-linked, as in the case of vulcanized natural rubber, or
not, as in the case of raw (non vulcanized) natural rubber. Given this,
elastomers became essential products for the modern world, as they are used in
a vast range of industries due to their lightweight, flexibility, non-
toxicity, low cost and sustainability, just to name a few advantages.

These materials present lower molecular weight and none or few cross-linked
chains that are randomly oriented, having the freedom to rotate and translate
in the structure. For this reason, the elastomers can be reversibly extended
at room temperature up to twice their size without breaking [17], being of
interest for mechanocaloric applications. Furthermore, it should be pointed
out that at some conditions of temperature and pressure, the elastomers can
rearrange their chains and, thus, present a crystalline structure [18]. Upon
cooling, below the liquid flow region, the material presents a crystalline
phase with lower symmetry and volume, being called the plastic phase. At the
transition temperature, the system undergoes a first-order solid-state
transition in which its molecules exhibit preferred orientations and,
consequently, an ordered phase. The phase transition can be driven either by
decreasing temperature, as mentioned above, or by increasing pressure, as it
also limits the movement of the molecules and makes them ordered. Such
behavior is observed through the appearance of characteristic peaks in X-ray
diffraction measurements. This is the case of acetoxy silicone rubber (ASR),
where a crystalline ordering occurs around 250 K, contributing to an extra
increase in the barocaloric effect in this material[19]. However, it was
recently shown through simulations that the rising of great BC response in
elastomers originates at the molecular level. These aspects will be presented
in more detail later in this review article.

##  III Theoretical basis

###  III.1 Thermodynamics

The first law of thermodynamics, written in terms of the strain tensor
$\epsilon_{ik}$ (which is dimensionless) and the stress tensor $\sigma_{ik}$
(which has the dimension of pressure), reads as
$dE=TdS+V_{0}\sigma_{ik}d\epsilon_{ik}$, where the last term comprises a sum
over the repeated indexes $i$ and $k$; and $V_{0}$ represents the volume of
the unstressed material. From the Gibbs free energy $G=E-TS-
V_{0}\sigma_{ik}\epsilon_{ik}$, it is possible to write:

$dG=-SdT-V_{0}\epsilon_{ik}d\sigma_{ik}$ (1)

and, consequently, for an isothermal process ($dT=0$):

$\left.\frac{\partial G}{\partial\sigma_{ik}}\right|_{T}=-V_{0}\epsilon_{ik}.$
(2)

In a similar fashion, for an isobaric process ($d\sigma_{ik}=0$), the relation

$\left.\frac{\partial G}{\partial T}\right|_{\sigma}=-S$ (3)

holds and then it is possible to obtain an important Maxwell relation:

$\left.\frac{\partial
S}{\partial\sigma_{ik}}\right|_{T}=V_{0}\left.\frac{\partial\epsilon_{ik}}{\partial
T}\right|_{\sigma}.$ (4)

The Helmholtz free energy $F=E-TS$ is also an important potential for the
thermodynamic description of the caloric materials. Analogously to equation 1,
it is possible to write:

$dF=-SdT+V_{0}\sigma_{ik}d\epsilon_{ik}$ (5)

and, consequently, for an isothermal process, the following equation for the
stress tensor holds:

$\left.\frac{\partial F}{\partial\epsilon_{ik}}\right|_{T}=V_{0}\sigma_{ik}.$
(6)

###  III.2 Caloric potentials

For the case of uniaxial stress, i.e., for elastocaloric studies, the
corresponding tensor is $\sigma_{ik}=\sigma\delta_{iv}\delta_{kv}$, where $v$
is the direction of the applied pressure. For this uniaxial case, $\sigma>0$
means tension and $\sigma<0$ means compression. On the other hand,
$\sigma_{ij}=-p\delta_{ij}$ describes the barocaloric effect due to
hydrostatic pressure. From these definitions, we are able to write different
caloric potentials, focusing on the barocaloric effect.

####  III.2.1 Isothermal entropy change

Considering the barocaloric effect, equation 4 can be rewritten as:

$-\frac{\partial S}{\partial p}=V_{0}\frac{\partial\gamma}{\partial T}$ (7)

where $\gamma=\epsilon_{ll}=\text{Tr}\\{\epsilon_{ik}\\}=\Delta V/V_{0}$.
After integration, the isothermal entropy change, for a given pressure change,
is given by:

$\Delta S(T,\Delta p)=-V_{0}\int_{p_{1}}^{p_{2}}\frac{\partial\gamma}{\partial
T}dp.$ (8)

Around first-order transitions, a sharp change in the entropy takes place,
often associated with a sharp change in the sample volume. This change across
the transition ($\Delta S_{t})$ is given by the Clausius-Clapeyron equation

$\Delta S_{t}(T,\Delta p)=\Delta V_{t}\left(\frac{dT_{t}}{dp}\right)^{-1},$
(9)

where $\Delta V_{t}$ is the volume change of the material across the
transition and $T_{t}$ is the transition temperature. This relation gives the
entropy change induced by the transition. For materials presenting other
relevant contributions to the entropy change, this approach does not retrieve
the total entropy change.

####  III.2.2 Adiabatic temperature change

In order to write the other caloric potential, namely, the adiabatic
temperature change, we start considering the entropy as a function of
temperature and stress tensor: $S=S(T,\sigma_{ik})$. Thus, it is possible to
write:

$dS=\left.\frac{\partial S}{\partial T}\right|_{\sigma}dT+\left.\frac{\partial
S}{\partial\sigma_{ik}}\right|_{T}d\sigma_{ik}.$ (10)

The adiabatic condition imposes $dS=0$ and therefore:

$dT=-V_{0}\frac{T}{c_{\sigma}}\left.\frac{\partial\epsilon_{ik}}{\partial
T}\right|_{\sigma}d\sigma_{ik},$ (11)

where we have used equation 4 and the definition of specific heat as
$c_{\sigma}=T\ \partial S/\partial T|_{\sigma}$. From the equation above, the
adiabatic temperature change can be obtained for the barocaloric case:

$\Delta T(T,\Delta
p)=V_{0}\int_{p_{1}}^{p_{2}}\frac{T}{c_{p}}\left.\frac{\partial\gamma}{\partial
T}\right|_{p}dp.$ (12)

An interesting and useful relationship emerges from equations 8 and 12.
Considering the specific heat $c_{p}$ has a weak dependence with the applied
pressure, it is possible to verify the following equation:

$\Delta T(T,\Delta p)\approx-\frac{T}{c_{p}}\Delta S(T,\Delta p).$ (13)

###  III.3 Landau approach

####  III.3.1 Equation of state

The free energy can be expressed as a power function of the strain tensor
(provided that its elements are small enough):

$\displaystyle F(T)=$ $\displaystyle
F_{0}(T)-KV_{0}\alpha(T-T_{0})\epsilon_{ll}$ $\displaystyle+\mu
V_{0}\left(\epsilon_{ik}-\frac{1}{3}\delta_{ik}\epsilon_{ll}\right)^{2}+\frac{1}{2}KV_{0}\epsilon_{ll}^{2},$
(14)

where the second term is related to the thermal expansion, the third is the
shear term and the last one is the Hook’s term. $K$ is known as the bulk
modulus, $\mu$ is the shear modulus, $V_{0}$ is the volume of the unstressed
material, T0 is a reference temperature where the sample experiences no
thermal deformation and, finally, $\alpha$ is the thermal expansion
coefficient.

From equations 6 and 14, a general expression for the stress tensor can be
obtained:

$\displaystyle V_{0}\sigma_{ik}=\frac{\partial F}{\partial\epsilon_{ik}}=$
$\displaystyle-KV_{0}\alpha(T-T_{0})\delta_{ik}$ (15) $\displaystyle+2\mu
V_{0}\left(\epsilon_{ik}-\frac{1}{3}\delta_{ik}\epsilon_{ll}\right)+KV_{0}\epsilon_{ll}\delta_{ik}.$
(16)

Considering only an isothermal process, in which the temperature of the
material is kept constant, i.e., $T=T_{0}$, the first term above is null and
therefore:

$\sigma_{ik}=K\epsilon_{ll}\delta_{ik}+2\mu\left(\epsilon_{ik}-\frac{1}{3}\delta_{ik}\epsilon_{ll}\right).$
(17)

Conversely, the strain tensor can be written as:

$\epsilon_{ik}=\frac{\sigma_{ll}\delta_{ik}}{9K}+\frac{1}{2\mu}\left(\sigma_{ik}-\frac{1}{3}\sigma_{ll}\delta_{ik}\right).$
(18)

Let us write these equations in terms of more convenient parameters, the Young
modulus $Y$ and Poisson ratio $\nu$, which relate to the shear and bulk moduli
as

$\mu=\frac{Y}{2(1+\nu)}\;\;\;\text{and}\;\;\;K=\frac{Y}{3(1-2\nu)}.$ (19)

In terms of the Young modulus and Poisson’s ratio, the general equations 17
and 18 can be rewritten as:

$\sigma_{ik}=\frac{Y}{1+\nu}\left[\epsilon_{ik}+\frac{\nu}{(1-2\nu)}\epsilon_{ll}\delta_{ik}\right]$
(20)

and

$\epsilon_{ik}=\frac{1}{Y}\left[(1+\nu)\sigma_{ik}-\nu\sigma_{ll}\delta_{ik}\right].$
(21)

####  III.3.2 Isotermal entropy change

Considering the free energy (equation 14), the entropy of the system can be
derived as:

$S(T,p)=-\frac{\partial F}{\partial T}=S_{0}(T)+KV_{0}\alpha\epsilon_{ll}.$
(22)

As we are interested in an isothermal process ($T=T_{0}$), the entropy change
due to a pressure change, can be written as:

$\displaystyle\Delta S(T,\Delta p)$ $\displaystyle=S(T,p)-S(T,p_{0})$
$\displaystyle=KV_{0}\alpha\epsilon_{ll},$ (23)

where the final result depends on how the compression is achieved. In this
way, we can differentiate two cases: uniaxial vs. isotropic compression.

Uniaxial compression: This case corresponds to a rod compressed along the
$z$-axis, whose $x$ and $y$ sides are fixed. For this case, all strain
components are zero, except $\epsilon_{zz}$. From equation 20, the stress
components of the tensor can be written as:

$\sigma_{zz}^{uni}=\frac{Y(1-\nu)}{(1+\nu)(1-2\nu)}\epsilon_{zz}^{uni}$ (24)

and

$\sigma_{xx}^{uni}=\sigma_{yy}^{uni}=\frac{Y\nu}{(1+\nu)(1-2\nu)}\epsilon_{zz}^{uni}.$
(25)

Considering $\sigma_{zz}^{uni}=-p$, the non-null strain component can be
written in terms of the applied pressure $p$:

$\epsilon_{zz}^{uni}=-\frac{(1+\nu)(1-2\nu)}{Y(1-\nu)}p$ (26)

If we place the above result into equation 23, the isothermal entropy change
is obtained for this specific case:

$\Delta S^{uni}(T,\Delta p)=-\frac{\alpha}{3}\frac{(1+\nu)}{(1-\nu)}pV_{0}.$
(27)

Isotropic compression: This case is characterized by equal stresses along with
the diagonal components of the tensor
$\sigma_{xx}^{iso}=\sigma_{yy}^{iso}=\sigma_{zz}^{iso}=-p$, while the off-
diagonal components are zero. From equation 21 it is possible to write:

$\epsilon_{xx}^{iso}=\epsilon_{yy}^{iso}=\epsilon_{zz}^{iso}=-\frac{p}{Y}(1-2\nu).$
(28)

Analogously to before, moving the above result into equation 23 the following
expression emerges:

$\Delta S^{iso}(T,\Delta p)=-\alpha pV_{0}.$ (29)

####  III.3.3 Uniaxial compression vs. isotropic compression

Isotropic compression can also occur from the uniaxial compression discussed
before. From equations 24 and 25, the following relation reads:

$\sigma_{zz}^{uni}=\sigma_{xx}^{uni}\frac{1-\nu}{\nu},$ (30)

When the Poisson coefficient approaches 0.5, the equation above reads as
$\sigma_{zz}^{uni}\to\sigma_{xx}^{uni}$; i.e., the uniaxial compression
effectively works as an isotropic compression. We can also compare the strain
tensor for uniaxial and isotropic compression from equations 26 and 28,
obtaining:

$\epsilon_{zz}^{uni}=\epsilon_{zz}^{iso}\frac{1+\nu}{1-\nu}.$ (31)

Again, in the limit $\nu\to 0.5$, the equation above reads as
$\epsilon_{zz}^{uni}=3\epsilon_{zz}^{iso}$. For the uniaxial compression, the
sample is constrained to deform in only one direction (which we assume as the
$z$ direction). Thus, the deformation is 3 times larger than the case of
isotropic compression, where the sample is free to deform in all 3 directions.

In fact, for materials with Poisson coefficient close to 0.5, as is the case
of elastomers and natural rubbers, the BC of an uniaxial compression (equation
27) recovers the BC of an isotropic compression (equation 29). Thus, the
isotropic compression and the unilateral compression (for materials with
$\nu\sim 0.5$), described above, are basic configurations for measuring
barocaloric effects.

##  IV Experimental techniques for the barocaloric effect

It has been used two experimental methods to obtain the caloric parameters in
plastic crystals and polymers. The first one depends on indirect entropy
change calculation using calorimetric data under applied pressure. From these
results, equation 13 has been used to estimate the adiabatic temperature
change. The second procedure uses a direct approach to measure the adiabatic
temperature change upon cooling/heating and load/unloading the sample. A
strain-gauge coupled to the setup allows the collection of strain versus
stress data, to indirectly calculate the entropy change through equation 8.
Each well established procedure and its advantages/disadvantages is described
below.

Indirect measurements. Obtaining caloric properties through heat capacity
measurements is a well-established method for the community, being the first
method commonly reported in the literature to estimate the barocaloric effect
in different classes of materials. The procedure uses differential scanning
calorimetry data and, in some reports, is complemented using temperature-
dependent XRD data for the crystalline phases [4, 13]. It is claimed that the
lattice parameter vs. temperature data is necessary to correct the isothermal
entropy change obtained from calorimetric data [4]. In order to build the
entropy change curves, a series of parameters are required: specific heat of
ordered and disordered phases ($C_{o}$ and $C_{d}$, respectively), heat flow
($dQ/dT$) and the entropy change due to the volumetric expansion $\Delta
S_{vol}(p)=-[(\partial V/\partial T)_{p_{o}}]p$, with $(\partial V/\partial
T)_{p_{o}}$ considered as pressure independent - note that $p_{o}$ corresponds
to the ambient pressure. The total $S^{\prime}(T,p)=S(T,p)-S(T_{o},p_{o})$
equation, where $T_{o}$ is the reference temperature, reads then as [4]:

$S^{\prime}(T,p)=\left\\{\begin{array}[]{ll}\int_{T_{o}}^{T}\frac{C_{o}(T^{\prime})}{T^{\prime}}dT^{\prime}+\Delta
S_{vol}(p)&T<T_{i}\\\
S(T_{i},p)+\int_{T_{i}}^{T}\left[C_{o-d}(T^{\prime})+\left|\frac{dQ(T^{\prime},p)}{dT^{\prime}}\right|\right]dT^{\prime}+\Delta
S_{vol}(p)&T_{i}<T<T_{e}\\\
S(T_{e},p)+\int_{T_{e}}^{T}\frac{C_{d}(T^{\prime})}{T^{\prime}}dT^{\prime}+\Delta
S_{vol}(p)&T>T_{e}\end{array}\right.$ (32)

where $C_{o-d}=(1-x)C_{o}+xC_{d}$ corresponds to the intermediate specific
heat regarding to the disordered phase fractions ($x$) obtained from XRD
analysis, $T_{i}$ and $T_{e}$ are the temperatures corresponding to the start
and end of the ordered to disordered transformation, respectively, and
$S(T_{i},p)$ and $S(T_{e},p)$ the corresponding values of entropy at those
specific temperatures. An example of the constructed $S^{\prime}(T,p)$ for
neopentylglycol (NPG) is given in Fig. 3(a)(b), obtained on heating and
cooling with the corresponding applied pressures ranging from 0 GPa to 0.57
GPa. Thus, by subtracting the isobaric curves, the isothermal entropy change
on loading (0$\rightarrow$p) and unloading (p$\rightarrow$0) can be obtained,
as shown in Fig. 3(c). In principle, the extra term $\Delta S_{vol}$ takes
care of the differences observed in $\Delta S$ data in two different papers
for the same plastic crystal (NPG) [4, 20]. Nevertheless, it may be an
indicative of an issue with the indirect method of obtaining $\Delta S$. In
fact, the extra term $\Delta S_{vol}$ may not be necessary since calorimetric
data should contain all the contributions to $\Delta S$.

Figure 3: Entropy curves for neopentylglycol (NPG) calculated using equation
32 and calorimetric measurements on (a) heating/unloading and (b)
cooling/loading. (c) The isothermal entropy change $\Delta S$ calculated from
the loading/cooling curve in (b), with positive signal, and unloading/heating
process in (a), with negative signal. This image is reprinted from reference
[4] with permission of Nature Publishing Group.

Direct measurements. A scheme of a homemade setup is depicted in Fig. 4, where
the pressure chamber consists of a cylindrical steel block, with a hole in the
center to accommodate the sample and the moving piston. A thermocouple is
coupled to the sample in order to monitor its temperature. The temperature of
the system is changed using a thermostatic bath or liquid nitrogen. The load
cell put underneath the apparatus registers the applied force; and the value
of the pressure is obtained from standard equations. Note that the pressure is
applied along one direction; however, according to equation 31, for materials
with the Poisson coefficient of 0.5, the uniaxial compression/decompression
corresponds to an isotropic BC. In addition, from this experimental setup, the
application/release of pressure occurs quasi-adiabatically and the adiabatic
temperature change $\Delta T(p)$ of the sample is directly acquired.

Figure 4: Experimental setup for the measurement of BC containing a
cooling/heating system, pressure chamber, thermocouples to directly measure
the temperature change on loading/unloading pressure, and a length gauge to
acquire the strain curves $\gamma(T,p)$. Reprinted from reference 21 with
permission of American Chemical Society.

As can be seen in Fig. 4, a length gauge is also connected to the piston to
measure the sample strain during the compression/decompression and the
heating/cooling processes. The data is acquired by increasing and reducing the
sample temperature under constant stress to obtain a map of the strain
$\gamma(T,P)=(V-V_{0})/V_{0}$. An example of the obtained curves is given in
Fig. 5 for the Nitrile Butadiene Rubber (NBR) acquired by isobaric heating
protocol [21]. Thus, it is possible to indirectly obtain the entropy change
through the Maxwell relation (see equation 8). For this, the measurement
should be taken by varying the temperature in a constant step $\Delta
T=T_{i+1}-T_{i}$ at each pressure to numerically evaluate equation 8 as
follows:

$\footnotesize\Delta S(T,\Delta p)=\frac{-V_{0}\Delta
p}{2}\sum_{i=0}^{n}\left[\left(\frac{\Delta\gamma_{i}}{\Delta
T_{i}}\right)_{p_{i}}+\left(\frac{\Delta\gamma_{i+1}}{\Delta
T_{i}}\right)_{p_{i}+1}\right]$ (33)

where $\Delta p=p_{i+1}-p_{i}$ is the difference between two isobaric curves
under consideration and $n$ is the number of points for each curve. For better
visualization, all the quantities are represented in Fig. 5(a) and the
resulting isothermal entropy change curves are given in Fig. 5(b) for the
elastomer nitrile butadiene rubber (NBR). Nevertheless, it should be
highlighted that $\Delta S(T,p)$ can only be obtained from the procedure using
the method of Fig. 4 if the material presents a Poisson coefficient $\nu\sim
0.5$. For plastic crystals or other systems with $\nu\neq 0.5$, this method
would result in the evaluation of the mechanocaloric, being neither elasto- or
barocaloric effects.

Figure 5: (a) Strain isobaric map $\gamma(T,p)$ measurements obtained by
unloading and heating a nitrile butadiene rubber (NBR) elastomer using the
homemade setup from reference 21 and (b) the calculated isothermal entropy
change ($\Delta S$). The hatched area gives the reversible isothermal entropy
change. Reprinted from reference [21] with the permission of Americal Chemical
Society.

Finally, Zhang et al. [22] published in-situ measurements in carboranes using
thermocouples and double-toroidal tungsten carbide anvil cells. The
pressure/depressurization are performed through an automatic hydraulic pump to
control different pressure increase rates.However, there is no complete
information regarding the experimental methodology and, for this reason, it
will not be approached here.

##  V Plastic barocaloric materials: recent findings

###  V.1 Plastic crystals

####  V.1.1 Motivation

Recent findings for the colossal barocaloric effect in neopentylglycol (NPG)
[20, 4] have turned the community’s attention to study plastic crystals. An
adiabatic temperature change ($\Delta T_{ad}$) of 30 K for an applied pressure
of 0.57 GPa was observed around the order-disorder transition for this
material, as listed in Table 1. This result is among the highest reported
values for this class of material, accompanied by maximum isothermal entropy
change ($\Delta S_{max}$) of 550 J/kg.K. This $\Delta S_{max}$ value is close
to the one for R134a refrigerant of 520 J/kg.K [23], used nowadays in
conventional gas-based refrigerators, as demonstrated by Lloveras et al. [4].
A latter report on modified neopentane plastic crystal revealed even higher
values of 690 J/kg.K and 600 J/kg.K for AMP and TRIS, respectively, for an
applied pressure of 0.25 GPa [13]; however, these are irreversible, which is a
drawback for practical applications. More recently, Aznar et al. [24] observed
a colossal BC response in 1-X-adamantane with X = Br and Cl (Br-ada and Cl-
ada, respectively), where a reversible process occurs for these PCs around
room temperature for a moderately applied pressure of 0.24 GPa with a working
range temperature of $\sim$ 40 K, opening the possibility of using these
materials in devices. However, each PC system presents its peculiarities and,
for this reason, an overview of their barocaloric properties should be
performed to organize the potential of these materials to be applied as
refrigerant for solid-state cooling devices.

####  V.1.2 State of the art

A list of the reported barocaloric properties in plastic crystals is given in
Table 1, where the maximum values were collected from the isothermal entropy
change and adiabatic temperature change data. The listed values were acquired
from the data obtained on heating and removing stress, except for NPG1[20],
where the available data is only on cooling and loading. It is worth noting
the discrepancies found for the caloric potentials of NPG[4, 20]. There are
some reasons for this occurrence: (i) Lloveras et al. [4] included corrections
using X-ray diffraction data to analyze the entropy change; (ii) the use of
approximation in equation 13 can also be a reason and, finally, (iii) the use
of different values for $C_{p}$ by those authors. For the barocaloric effect
in plastic crystals, there is still a lack of a standard protocol to obtain
the caloric potentials.

A further study performed by the same group of Lloveras has shown that
neopentane [C(CH3)4] derivatives also present great barocaloric
potentials[13]. However, these have a melting temperature above room
temperature for most of the materials given in Table 1. Namely, the systems
selected by Aznar et al. were: (NH2)(CH3)C(CH2OH)3
[2-amino-2-methyl-1,3-propanediol, AMP]; (NH2)C(CH2OH)3
[2-amino-2(hydroxymethyl)propane-1,3-diol, TRIS]; (CH3)C(CH2OH)3
[2-hydroxymethyl-2-methyl-1,3-propanediol, PG] and; (CH3)3C(CH2OH)
[2,2-dimethyl-1-propanol, NPA]. For the particular case of NPA, the working
temperature for the barocaloric effect (TFWHM) is higher than NPG for a
comparable value of applied pressure. This might be due to the lowest
transition temperature of NPA, where it becomes disorientated around room
temperature and, consequently, the entropy curves become broader. Another set
of PCs, presenting large BC responses are the adamantane (C10H16) with the
substitution of one H atom by Cl (C10H15Cl, Cl-ada) and Br (C10H15Br, Br-ada)
where a high TFWHM of $\sim$ 40 K is observed for an applied pressure of 0.24
GPa [24]. The slightly higher entropy change values for Br-ada is related to
two successive ordered-disordered transitions from cubic to orthorhombic
structure at 282 K, becoming a monoclinic phase at 308 K [25]. The larger
contribution rises from the room temperature transition, being the one
depicted in Table 1 [24] with the higher pressure-induced temperature
transition rate ($dT_{t}/dP$) among the adamantanes.

Material | Type |  | $C_{p}$
---
(J/kg K)
| $|\Delta T_{max}|$
---
(K)
| $|\Delta S_{max}|$
---
(J/kg K)
| $|\Delta P|$
---
(GPa)
| $T_{FWHM}$
---
(K)
| $T_{t}$
---
(K)
| $dT_{t}/dP$
---
(K/GPa)
| $\Delta T_{hyst}$
---
(K)
| $P_{rev}$
---
(GPa)
Ref.
NPG1 | PC | 1940 | 64a | 390 | 0.09 | 15 | 313 | 130 | 18 |  |  20
NPG2 |  |  | 10 | 410 | 0.09 | 17 | 313 | 130 | 24 | 0.15 |  4
|  |  | 42 | 550 | 0.57 | 48 |  |  |  |  |  4
Neopentane AMP | PC | 1790 | 15b | 690b | 0.24 | 23 | 353 | 80 | 50 |  |  13
Neopentane TRIS | PC | 1800 | 8b | 600b | 0.24 | 21 | 407 | 30 | 64 |  |  13
Neopentane PG | PC | 1920 | 10 | 490 | 0.24 | 30 | 354 | 90 | 4 | 0.04 |  13
Neopentane NPA | PC | 2790 | 42 | 470 | 0.59 | 61 | 232 | 170 | 35 | 0.19 |  13
Cl-ada | PC |  | 48 | 220 | 0.24 | 44 | 245 | 270 | 10 | 0.03 |  24
Br-ada | PC |  | 57 | 235 | 0.24 | 40 | 308 | 350 | 4 | 0.04 |  24
p-carb | PC | 1590 | 19a | 98 | 0.06 | 20 | 308 | 380 | 11 | 0.01 |  22
o-carb | PC | 1590 | 14a | 80 | 0.06 | 18 | 277 | 330 | 8 | 0.01 |  22
|  |  | 9d |  | 0.30 |  |  |  |  |  |  22
m-carb | PC | 1590 | 13a | 72 | 0.06 | 19 | 286 | 330 | 9 | 0.01 |  22
PDMS | EL | 1350 | 28c | 140 | 0.39 |  | 150 |  |  |  |  26
VNR | EL | 1930 | 25c | 154 | 0.39 |  |  |  |  |  |  27
ASR | EL |  | 41c |  | 0.39 |  | 2 | 250 |  |  |  19
NBR | EL | 1350 | 16c | 68 | 0.39 |  |  |  |  |  |  21
PU | EL | 1350 | 13c | 96 | 0.22 |  |  |  |  |  |  28

  * a

calculated using $|\Delta T|=T|\Delta S|/C_{P}$.

  * b

Irreversible BC [13].

  * c

measured directly with the setup of Figure 4.

Table 1: Barocaloric response and physical parameters of plastic crystals (PC)
and elastomers (EL). $C_{p}$: heat capacity at room temperature, $|\Delta
T_{max}|$: maximum adiabatic temperature change, $|\Delta S_{max}|$: maximum
isothermal entropy change, $|\Delta P|$: applied pressure, $T_{FWHM}$: full
width at half maximum of the entropy curve, $T_{t}$: transition temperature,
being the melting for PC and glass transition temperature for EL at ambient
pressure, $dT_{t}/dP$: shift of the temperature change under applied pressure
obtained on cooling, $\Delta T_{hyst}$: thermal hysteresis obtained from DSC
measurements and Prev which correspond to the minimum applied pressure to
achieve reversible BC. The values were collected for $|\Delta S_{max}|$ and
$|\Delta T_{max}|$ curves obtained by unloading (p$\to$atmospheric pressure)
and heating.

Considering practical use of barocaloric materials, greater $dT_{t}/dP$ values
are desirable since it is related to higher working range temperature for the
BC with lower hysteresis losses. More recently, Zhang et al. [22] obtained
high $dT_{t}/dP$ values for three positional isomers of carborane (C2B10H12),
namely: ortho-carborane (o-carb), meta-carborane (m-carb) and para-carborane
(p-carb). The three materials present an orthorhombic to tetragonal structural
transition and the distinction between these carboranes relies on the B
occupation in the structure, where the highest symmetry occurs when B are
positioned at the icosahedron opposite vertices (p-carb). As given in Table 1,
this group of PC also presents low thermal hysteresis ($T_{hyst}$), with
p-carb being the one with improved BC responses due to its higher symmetry. In
addition, the minimum applied pressure required for reversibility ($P_{rev}$),
where there is an overlap between the entropy change curves on heating and on
cooling, is the lowest for carboranes among the PCs reported in the
literature. The improved BC response of p-carb is related to the higher
symmetry over o-carb and m-carb where boron occupies the vertices of the
icosahedron formed by the atoms. Although reducing hysteresis losses are
desirable for practical applications, the carboranes present low entropy
change values. Moreover, the temperature change obtained from in-situ
measurements is also obtained by the authors and, as can be noted, is below
the calculated from the entropy change (see Table 1). This is due to the lack
of thermal insulation during the measurement; however, there is no complete
information on the procedure in Ref. [22]. In this regard, Br-ada BC
properties are favorable for its use as a refrigerant, considering it presents
the lowest $T_{hyst}$. Thus, further investigation on how to improve symmetry
and successive phase transitions might be a path to select the best PC.

As can be noted from Table 1, the broad range of applied pressures used by
different authors makes difficult the comparison of the BC among materials. In
order to deepen this analysis, we normalized both entropy change and
temperature change by the applied pressure: $|\Delta S_{max}/\Delta P|$ and
$|\Delta T_{max}/\Delta P|$. For a reasonable comparison between the
properties of these materials, the data were collected for applied pressures
around 0.1 GPa, taking into account the values related to reversible processes
and might be underestimated. Except for AMP and TRIS, for which the processes
are irreversible for this range of applied pressure as highlighted in Table 1.
Materials presenting large $|\Delta S_{max}/\Delta P|$, with the highest
associated temperature change $|\Delta T_{max}/\Delta P|$, are better for
barocaloric applications. It becomes clear that plastic crystals present the
largest normalized entropy changes in comparison to the elastomers. In
particular, NPA and NPG2 are the ones with better properties. However, as
discussed below, for practical applications, the process should be reversible
and, for NPA, applied pressure above 0.30 GPa is required for the
reversibility. In this case, among the plastic crystals, we should classify
NPG2 as the material with the best reversible BC around this range of applied
pressure.

Figure 6: (a) Normalized $|\Delta S^{max}/\Delta P|$ vs $|\Delta T/\Delta P|$
values for plastic crystals (yellow region) and elastomers (green region).
This diagram was made for an applied pressure of ca. 0.1 GPa and the materials
highlighted with ∗ corresponding to irreversible processes. (b) Normalized
maximum Refrigerant Capacity (NRCmax) vs $\Delta T_{h-c}=T_{hot}-T_{cold}$
(hot and cold reservoir temperature difference) for plastics crystals and
elastomers. All the values presented here were acquired from the curves
obtained on heating and unloading. The values of applied pressure are:
o-,m-,p-carb $|\Delta P|$ = 0.06 GPa; NPA $|\Delta P|$ = 0.08 GPa; ASR, PDMS,
VNR, NBR, PU, and NPG1,2 $|\Delta P|$ = 0.09 GPa; AMP, PG, Br-ada and Cl-ada
$|\Delta P|$ = 0.10 GPa; TRIS $|\Delta P|$ = 0.11 GPa.

For a further analysis of these materials, we have calculated the normalized
maximum refrigerant capacity:

$NRC^{max}=\frac{|\int_{T_{hot}}^{T_{cold}}\Delta SdT|}{\Delta P}$ (34)

obtained from the entropy curves around 0.1 GPa, as a function of the
temperature difference between cold and hot reservoirs. Similar to the
previous graph, the entropy curves for the NRC calculation were acquired from
heating and releasing pressure curves, except for NPG1 data. Given the reduced
temperature range of reversible processes, the NRC was acquired from the
irreversible entropy change curves to extend the $\Delta T_{h-c}$ to 60 K for
most systems, as shown in figure 6(b). Although the plastic crystals present
the higher NRCmax values among all the presented materials, as $\Delta
T_{h-c}$ increases, the curves tend to saturate. As an example, see the
corresponding curves for NPG2 and NPA, which from Fig. 6(a) presents the
higher normalized entropy and temperature changes. The saturation of NRCmax
reveals the limitation on the barocaloric performance of these materials. In
contrast, although presenting lower normalized entropy change, the NRCmax of
Br-ada overcomes all the PCs at $\Delta T_{h-c}$ = 40 K, revealing that it can
be used in devices that require a large range of temperature operations.
Nevertheless, distinctly from the observations of figure 6(a), the materials
presenting the highest NRCmax values are AMP, TRIS and Br-ada. Although these
seem to be the best materials, we should emphasize that AMP and TRIS do not
present reversibility across the transition, which is an issue for practical
applications.

####  V.1.3 Microscopic scenario

The isothermal entropy change $\Delta S$ for plastic crystals has two main
contributions during transition: (i) volumetric ($\Delta S_{V}$) and (ii)
configurational ($\Delta S_{C}$) terms [4, 13]. Through X-ray diffraction and
calorimetry data[13], Aznar et al. calculated both contributions for
neopentane AMP, TRIS, PG and NPA and adamantine Br-ada and Cl-ada plastic
crystals to compare with the endothermic entropy change obtained during the
materials disordered-ordered transition at atmospheric pressure, denoted as
$\Delta S_{d\rightarrow o}(p_{o})$ in Table 2. The volumetric contribution
(due to lattice distortions) was calculated considering [13]:

$\Delta
S_{V}\approx\frac{\langle\alpha\rangle}{\langle\kappa_{V}\rangle}\Delta V_{t}$
(35)

where $\langle\alpha\rangle$ and $\langle\kappa_{V}\rangle$ are the average
thermal expansion and average isothermal compressibility, respectively, for
the two phases, and $\Delta V_{t}$ is the volumetric change across the phase
transition. Equation 35 is an approximation and must be used with caution
[29]. This evaluation found that the fraction of $\Delta S_{V}$ is around 15%
for TRIS, PG and AMP neopentane and 40% for NPA in relation to the total
entropy obtained from DSC measurements [13]. For the particular case of Br-
ada, the high volumetric entropy change contribution of 73% rises from the
remaining orthorhombic phase across the disordered monoclinic to ordered cubic
transition. This finding reveals that the main contribution for the large BC
observed in these materials comes from the configurational entropy. It is
worth mentioning that the volumetric contribution for the NPA material is due
to the high unit cell volume of the triclinic phase at low temperatures [30].
For the configurational entropy, Raman spectroscopy analysis was used and this
term was estimated through the relation:

$\Delta S_{C}=\frac{R}{M}\ln\left(\frac{N_{I}}{N_{II}}\right)$ (36)

with $R$ standing for the universal gas constant, $M$ the molar mass and
$N_{I}$ and $N_{II}$ the number of molecular conformations in the disordered
and ordered phases, respectively. All the calculated values obtained by Aznar
et al. are listed on Table 2, along with their corresponding fractions related
to the total value of $\Delta S_{exo}(p_{0})$ obtained at atmospheric pressure
($p_{0}$). In particular, for NPA, the fraction of $\Delta S_{C}$ is more than
50% larger than the experimental value of the entropy. This is because the
orientational disorder for these molecular arrangements is smaller than
predicted. Although the calculated values show that the main contribution to
the entropy change arises from the molecular contribution, these results are
overestimated due to the inaccessibility to all possible configurations.
Therefore, a more accurate understanding of the microscopic origins of the
entropy still lacks in the literature.

Material |  | $\Delta S_{d\rightarrow o}(p_{o})$
---
(J/kg.K)
| $\Delta S_{V}$
---
(J/kg.K)
| Frac.
---
(%)
| $\Delta S_{C}$
---
(J/kg.K)
| Frac.
---
(%)
PG | 485 | 80 | 13 | 325 | 67
NPA | 204 | 52 | 39 | 321 | 157
TRIS | 682 | 90 | 13 | 287 | 42
AMP | 632 | 100 | 16 | 315 | 50
Cl-ada | 136 | 51 | 37 | 112 | 82
Br-ada | 104 | 76 | 73 | 62 | 60

Table 2: Entropy change across the disordered to ordered phase transition at
atmospheric pressure [$\Delta S_{d\rightarrow o}(p_{o})$]; and the volumetric
($\Delta S_{V}$) and configuration ($\Delta S_{C}$) entropy changes calculated
through equations 35 and 36, respectively. This table also presents the
corresponding fractions of each entropy change term.

####  V.1.4 Drawbacks

Aznar et al. [13] discussed the reversibility of the BC on the neopentane
plastic crystals. Two modified neopentane plastic crystals with the
substitution of the methyl groups were chosen for the study: amino (NH2) and
hydroxymethyl (CH2OH). The barocaloric evaluation revealed that the reversible
response is around 10-20 K lower than that for PG and NPA plastic crystals,
belonging to the hydroxymethyl group. The reversible entropy change ($\Delta
S_{rev}$) condition is given by overlapping the isothermal entropy change
curves, independently obtained on heating and on cooling.

In other words, the exothermic and endothermic transition temperatures should
be equal under an applied pressure - this is denoted as reversal pressure.
Consequently, due to hysteresis losses of the first-order phase transition,
$\Delta S_{irr}>\Delta S_{rev}$, as can be observed from Table 1 for NPA and
PG materials. In contrast, TRIS and AMP present a large hysteresis at low
pressures, turning the minimum pressure for the reversibility analysis
unfeasible [13]. Thus, for the mentioned plastic crystals, the BC is
irreversible. As can be seen from Table 1, the working temperature for the
barocaloric effect is also reduced for the reversible effect, being around 20
K lower for NPA plastic crystal.

###  V.2 Elastomers

####  V.2.1 Motivation

Elastomers is another family of materials presenting an extraordinary large
barocaloric response. Although a temperature change of $\sim$ 12 K was
observed in 1942 by stretching natural rubbers (NR) [31], only in recent years
the mechanocaloric effect of these materials have been explored systematically
for solid-state cooling application [2, 32]. The evaluations reported in the
literature revealed great barocaloric potentials for the elastomers, which are
interesting given the absence of structural transitions for most of these
materials. Such behavior has its origin at the molecular level; the
rearrangement of the polymeric chains during releasing/applying pressure is
the main mechanism for the barocaloric effect, as recently demonstrated by
Miliante et al. [2].

####  V.2.2 State of the art

Among the results reported in the literature, elastomers like acetoxy silicone
rubber (ASR) [19] and polydimethylsiloxane (PDMS) [26] present adiabatic
temperature changes comparable with the observed in plastic crystals, as can
be seen in Table 1. As can be noted, the barocaloric response of ASR occurs in
the vicinity of the PCs response, as can be seen in Figs. 6(a) and (b);
revealing its great potential for solid-state cooling technologies. The
supergiant BC of ASR is due to a crystalline-amorphous transition that occurs
around 250 K and, combined with the molecular rearrangement, leads to a
measured $\Delta T$ of 40 K for an applied pressure of 0.39 GPa. Above the
glass transition temperature, a $\Delta T$ of 30 K is observed, which is only
due to the amorphous phase contribution. For this reason, that compound is the
one presenting the best BC potentials compared with the other amorphous
materials, such as VNR and NBR. For the PDMS, as can be seen from Table 1, the
TG is far from room temperature, and $\Delta T$ of 28 K occurs for $\Delta P$
of 0.39 GPa. Although this value is below the observed for ASR, it is
comparable with those estimated for plastic crystals, such as neopentane PG
and AMP. More importantly, the BC for ASR is reversible at low applied
pressures ($\Delta P<0.2$ GPa), which is an important feature concerning
practical applications. Although these results seems promising, few reports
have been dedicated to these investigations.

Most of the barocaloric potentials for elastomers do not present a well-
defined peak. This is due to the high melting point of rubbers (well above 400
K) with the exception of PDMS. Given this, the $\Delta S$ and $\Delta T$
curves tend to present high values in a large temperature range. For instance,
the reversible entropy change of ASR has values above 150 J/kg.K in a
temperature range of $\sim$ 30 K for an applied pressure of 0.17 MPa. While
for NBR, a table-like behavior occurs between 255 K and 315 K for 0.086 MPa of
applied pressure. The temperature range of 40 K for an entropy change of -40
J/kg.K for ASR can be overestimated since the limit for the experimental setup
is 320 K. In this sense, it was not possible to obtain the temperature span
(TFWHM) for this class of materials, being the responsible for the absence of
these values on Table 1. For the reasons stated above the values depicted in
Fig. 6(a) are related to the global maximum of the curves available in
literature normalized for an applied pressure of $\sim$ 0.1 GPa. Although the
elastomers are in the lower region of the chart, the maximum adiabatic
temperature change for NBR, VNR and PDMS and polyurethane (PU) are in the same
range as TRIS and AMP. While ASR, as already mentioned, presents a larger
$|\Delta T^{max}/\Delta P|$ that is $\sim$ 10 K/GPa below NPG2, revealing its
great BC response among the evaluated elastomers.

A better approach to compare the barocaloric potential between plastic
crystals and elastomers is through the NRCmax versus $\Delta T_{h-c}$ curves,
shown in Figure 6(b). As previously mentioned, the plastic crystals tend to a
saturation above $\Delta T_{h-c}\approx 20$ K, whereas a linear increase of
NRCmax for the elastomers occurs, as seen for ASR, PDMS, VNR and NBR (for this
range of $\Delta T_{h-c}$). This behavior is an advantage for applications of
the elastomers, since it can be used in a wide range of temperatures and at
relatively low applied pressures (0.1 GPa). In addition, the reversibility of
the BC for the elastomers is appealing for solid-state cooling technology.

####  V.2.3 Microscopic scenario

From a fundamental point of view, the mechanism responsible for such a great
barocaloric effect is still under study. The best explanation so far is that
these outstanding results arise from a reduction of the free volume and number
of accessible vibrational/rotational states of the molecules due to the
applied pressure. In contrast to the plastic crystals, where only rotations of
the molecules are possible, polymers present intra/intermolecular interactions
with their rotational and vibrational modes available. For the elastomers, the
configurational contribution is associated to the volumetric change, since the
molecular interactions are pressure and volume dependent. In simple words, the
main contributions for the isothermal entropy change $\Delta S$ for this class
of materials are: (i) the potential energy contribution, comprising the inter-
and intra-molecular interactions; and, ii) volumetric change during
compression/decompression, $(\partial V/\partial P)_{T}$[2]. The
intramolecular contribution concerns the bond stretching and angle deformation
during compression, with the addition of a torsion from the C-C/C-H bonds in
the polymer, a dihedral energy; while the intermolecular interactions ($\Delta
S_{inter}$) comprises the Coulomb and van der Walls forces between a pair of
molecules. Note, that both terms in the potential energy are volume dependent.

Through molecular dynamics simulations, combined with thermodynamic analysis,
Miliante et al. [2] have elucidated that the origin of BC in non-vulcanized
natural rubbers (NR) relies on an unusual reduction of the intermolecular
potential energy [2]. Under an adiabatic process, the work performed on the
system by the compressing force must be equal to the variation of the internal
energy of the system. This last comprises kinetic energy (related to the
temperature) and potential energy (the sum of intramolecular and
intermolecular energies). Potential energy is governed by atomic interactions,
therefore atomic motion rules how much of the external energy, supplied as
work, can be converted into kinetic energy. From simulated atomic
trajectories, the contribution of each energy component was computed for the
natural rubber/cis-1,4-polyisopropene during compression and decompression
cycles: $U(T,V;P)=U_{pot}+U_{kin}$. Thus, using the simulation results under
isothermal conditions, the entropy change could be calculated through the
first law of thermodynamic $dU=dW=TdS-PdV$, as follows:

$\Delta S_{T}=\frac{1}{T}\left[\int\left(\frac{\partial U}{\partial
P}\right)_{T}dP+\int P\left(\frac{\partial V}{\partial
P}\right)_{T}dP\right].$ (37)

The result of these simulations are given in figure 7, showing a good
agreement with the experimental pressure dependence of the entropy change for
NR at 300 K. As can be noted, the potential contribution is the main term
contributing to the large BC observed in the elastomer. The main responsible
for this observation is the reduction of the energy related to the
intermolecular interactions, namely, van der Walls and Coulomb energies. As
pressure increases, intermolecular energy decreases, which enhances the gain
in kinetic energy perceived macroscopicaly, and temperature increases. When
submitted to higher pressures, the molecules approach each other, and at a
given point the intermolecular interaction become repulsive. Under these
conditions, the intermolecular energy increases, reducing the possible gain in
kinetic energy.

Figure 7: Simulated and experimental isothermal entropy change as a function
of the applied pressure for the natural rubber cis-1,4 polysoprene. The
potential energy and compressibility contribution, from equation 37, are given
separately where it is possible to observe that the inter/intramolecular
interactions are the main responsible for the BC in NR. Reprinted from
reference [2] with permission of American Chemical Society.

####  V.2.4 Drawbacks

Some of these elastomers crystallize under high stress values. For uniaxial
elongation, applied stress of the order of 200-400% of strain crystallizes the
NR, as shown by Toki et al. [33]. In the case of acetoxy silicone rubber
(ASR), a partial amorphous to crystalline transition at reduced temperatures
(ca. 200 K at atmospheric pressure), is responsible for a colossal BC response
[19]. For these cases, the rubber tends to maintain its configuration and may
not return to its initial condition in an irreversible process. In another
words, under this condition, the plastic behavior of the rubbers are
drastically reduced being one of the reasons for the appearance of mechanical
hysteresis [34]. For this reason, a throughout evaluation of materials
performances under a large range of mechanical stimuli is required to identify
the threshold for applied pressure, focusing on applications of these
materials [13].

##  VI Concluding Remarks

The colossal barocaloric effect in neopentylglycol (NPG), with a maximum
adiabatic temperature change of the order of 30 K and a maximum isothermal
entropy change of 550 J/kgK, for 0.57 GPa of applied pressure change, opened a
large avenue of research in caloric effects for plastic crystals. It is worth
saying that these astonishing values are very close to the isothermal entropy
change for R134a refrigerant, used nowadays in conventional gas-based
refrigerators. In addition to plastic crystals, we can also add to this
amazing family the elastomers (see Materials Survey section).

For a fair comparison of these materials, we have normalized both entropy
change and temperature change by the applied pressure: $|\Delta S_{max}/\Delta
P|$ and $|\Delta T_{max}/\Delta P|$. Materials with high values of $|\Delta
S_{max}/\Delta P|$, and, simultaneously, high values of $|\Delta
T_{max}/\Delta P|$, are better for barocaloric applications. Plastic crystals
present the largest normalized entropy changes in comparison to the
elastomers, being NPA and NPG2 the ones with better properties. For a further
analysis, we have also calculated the normalized maximum refrigerant capacity
NRCmax \- defined as in equation 34 and obtained from the entropy curves
around 0.1 GPa. Although plastic crystals present the higher NRCmax values
among all the presented materials, as the integration temperature width
$\Delta T_{h-c}$ increases, those curves tend to saturate. This fact reveals
the limitation on the barocaloric performance for plastic crystals. In
contrast, although presenting lower normalized entropy change, the NRCmax for
the elastomer Br-ada overcomes all the PCs at $\Delta T_{h-c}$ = 40 K,
revealing that it can be used in devices that require a large range of
temperature operations.

Thus, in this review, we have presented a brief survey about plastic crystals
and elastomers, as well as the thermodynamic for mechanocaloric effects. The
most important experimental techniques were also described, highlighting
possible divergences of analysis, such as the addition of an extra entropy
contribution obtained by X-ray diffraction. We also delivered a comprehensive
literature overview, for both families of compounds, plastic crystals and
elastomers. Along these discussions, we have presented the state of the art,
microscopic analysis for the entropy change and possible drawbacks for the
field.

## Acknowledgements

VMA thanks FCT/MCTES and IFIMUP for the portuguese funds in the framework of
the projects UIDB/50006/2020 and UIDP/50006/2020. MSR thanks the CNPq, FAPERJ,
INCT of Refrigeração e Termofísica. VF acknowledges the support of
US/JUNTA/FEDER-UE (grant US-1260179), Consejería de Economía, Conocimiento,
Empresas y Universidad de la Junta de Andalucía (grant P18-RT-746) and and
AEI/FEDER-UE (grant PID2019-105720RB-I00) .

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