# Embedding Intelligence in Materials for Responsive Built Environment using
Liquid Crystal Elastomer Actuators and Sensors

Mathew Schwartz
New Jersey Institute of Technology
College of Architecture and Design
University Heights
Newark, NJ, USA
<EMAIL_ADDRESS>
Jan P.F. Lagerwall
University of Luxembourg
Department of Physics & Materials Science
162a, avenue de la faiencerie
1511 Luxembourg city, Luxembourg
<EMAIL_ADDRESS>
http://smart-art.org)www.lcsoftmatter.com)

###### Abstract

Liquid Crystal Elastomers (LCEs) are an exciting category of material that has
tremendous application potential across a variety of fields, owing to their
unique properties that enable both sensing and actuation. To some, LCEs are
simply another type of Shape Memory Polymer, while to others they are an
interesting on-going scientific experiment. In this visionary article, we
bring an interdisciplinary discussion around creative and impactful ways that
LCEs can be applied in the Built Environment to support kinematic and kinetic
buildings and situational awareness. We focus particularly on the autonomy
made possible by using LCEs, potentially removing needs for motors, wiring and
tubing, and even enabling fully independent operation in response to natural
environment variations, requiring no power sources. To illustrate the
potential, we propose a number of concrete application scenarios where LCEs
could offer innovative solutions to problems of great societal importance,
such as autonomous active ventilation, heliotropic solar panels systems which
can also remove snow or sand autonomously, and invisible coatings with strain
mapping functionality, alerting residents in case of dangerous (static or
dynamic) loads on roofs or windows, as well as assisting building safety
inspection teams after earthquakes.

_K_ eywords Liquid Crystal Elastomers $\cdot$ Cholesteric Structural Color
$\cdot$ Situational Awareness $\cdot$ Embedded Control $\cdot$ Soft Actuation
$\cdot$ Responsive Materials $\cdot$ Shape Memory Polymers $\cdot$ Kinetic
Buildings

##  1 Introduction

A lively development in today’s materials science research is the creation of
new ’smart’ or ’intelligent’ materials. This should not be confused with the
quest for true artificial intelligence, but it generally refers to materials
that respond to specific stimuli, such as mechanical strain or changes in
temperature, humidity, lighting conditions etc. in such a way that their own
appearance or shape changes. If the response has a beneficial impact, e.g.,
changing color, texture or shape to blend in with a new environment or prevent
an undesired outcome, we can describe the material as adaptive. When we use
adaptive materials to drive a change that is foundational to the performance
or function of a technology or device– in response to relevant stimuli– we may
say that the system has embedded intelligence. One of the most impactful areas
that such materials can be applied in is the Built Environment, enabling
’smart cities’ with minimum impact on communication bandwitdh and energy
consumption [1].

An important characteristic of embedded intelligence, defined in this way, is
that the adaptive nature is inherent to the material, rather than arising from
the interaction of multiple components with specific function, each made of
passive and static materials like standard metals, plastics, wood or glass. In
other words, while the same functionality may be realized by engineering
traditional machines of varying complexity, we here mean with embedded
intelligence that the responsiveness is provided by the material itself. This
allows single elements in a construction to be their own actuator or sensor,
while at the same time filling the basic passive function that they were
designed for. A simple example is a hinge with embedded intelligence; while a
classic hinge is passive, allowing motion but requiring an external engine for
the motion to take place, the hinges we deal with in this paper move on their
own, indeed driving the motion of components attached to them. We thus
consider not simply embedding intelligent machines in a system, but rather
embedding intelligence of a system via a material.

Among the most impactful consequences is the independence that arises, as
fully implemented embedded intelligence requires no energy source—like a
battery, solar cell or fuel tank—nor engines for doing mechanical work—like
pumps or motors—nor wiring or tubing connecting components. As the
actuation/sensing function is inherent to the material, relying on no other
input than the stimulus triggering the response and the thermal energy driving
it, adaptive materials enable unprecedented autonomy as well as ease in
design. At the same time, however, the responsiveness cannot be turned off:
with fully embedded intelligence, the material adapts to its environment
whether we want it or not. For this reason, and for situations where we want
to turn the response on at any time, it is sometimes motivated to develop the
concept only partially, sacrificing complete autonomy for active control.

In the architecture, construction and design fields, adaptive materials
capable of motion are often collectively known as Shape Memory Materials, with
Shape Memory Alloys perhaps being the most well known class[2, 3]. However,
there are many types of material that classify as adaptive, with strongly
varying characteristics, challenges and opportunities. In the materials
science community, several visionary papers have recently appeared,[4, 5, 6,
7, 8, 9, 10, 11] presenting the potential of new and old adaptive materials as
actuators and sensors, often focusing on applications in robotics. While they
paint a bright and exciting picture, they also highlight the need for research
to present adaptive materials solutions that compete favorably with
established solutions, in particular those based on electronics and
pneumatics. This can be challenging in state-of-the-art robotics, where rapid
and high-powered actuation is often required.

We believe that more prolific targets for nearby applications of adaptive
materials may be those where there is no competition, because the new
materials fill functions currently not existing–solving problems that
presently have no satisfactory solution. A simple yet representative example
is in architecture, where embedded intelligence through materials has been
discussed through concepts such as incorporating Shape Memory Alloys into
facades for opening walls when temperatures rise [12]. Incorporation of
embedded intelligence in the built environment offers many such targets, and
these opportunities are the topic of this forward-looking article, aimed to
stimulate creativity and discussion. We consider several application
scenarios, some of which may end up more challenging to realize than others,
but all of them present highly stimulating opportunities for research and
innovation. Our focus is particularly on truly autonomous applications, i.e.,
where the trigger for actuation appears naturally, e.g. through light
variations across the day, humidity rising in the environment, or the
mechanical strain on a window during a storm.

We limit the discussion to one prolific class of adaptive material, namely
Liquid Crystal Elastomers (LCEs). LCEs are Shape Memory Elastomers and, as
such, a subset of Shape Memory Polymers. They are highly responsive materials
that can be designed to change shape, stiffness or color—often several of
these characteristics together—in response to stimuli such as heat, light,
exposure to water or mechanical strain. After introducing the working
principle of LCEs and briefly surveying the different actuation modes they
offer—all very attractive from an architecture, design and construction point
of view—we provide a number of concrete examples of how appropriately designed
and applied LCEs could embed intelligence into the built environment. Our
examples illustrate how LCEs could support a transition towards more organic
design solutions, where manmade artifacts work with, rather than against,
daily and seasonal variations, giving them a lower energy consumption
footprint. In addition, we show how LCEs might introduce highly valuable
safety features into buildings occupied by people, potentially saving many
lives in case of accidents or natural disasters.

As we present LCEs in the context of innovation for the Built Environment, a
brief discussion on contextualizing the materials may be beneficial to readers
in that community. Our goal is to connect our own two disciplines—Design of
the Built Environment and Materials Physics—to introduce to designers how LCEs
work, and show to physicists what LCE functionality is the most useful in the
Built Environment. We hope that our article can help to speed up the much
anticipated transition from today’s situation, with a plethora of fascinating
LCE actuators and sensors that are custom-made in limited numbers in research
labs, to a situation where LCEs can be practically applied to solve real-life
problems, thanks to LCE components being mass produced and readily available
for purchase from standard retailers.

##  2 Principles of LCEs as actuators and sensors

A simple way of illustrating the operation of LCE actuators is to consider
them as pieces of rubber that stretch and relax on their own, driven by
temperature changes or different light exposures. Indeed, the Elastomer in LCE
is another word for rubber, and on a fundamental structural level, LCEs and
ordinary rubbers share three key components:[13] (1) both are polymers, i.e.,
they are made up of very large molecules that can be described as chains of
repeating units (monomers); (2) at operating temperature these molecules are
in a highly mobile state which would normally correspond to the macroscopic
state of a liquid, were it not for the significant fact that (3) these
molecules are loosely connected into a volume-spanning network that prevents
the system from flowing. In other words, elastomers can be considered liquids
that are prevented from flowing by a 3D network connectivity of their
molecules. The bonds that connect the molecular chains into the 3D network are
called crosslinks and their density is a key parameter for determining the
mechanical properties of elastomers: high crosslink density gives a tough,
stiff rubber, as in car tires, whereas low crosslink density gives a soft,
extremely stretchable rubber, as in a rubber band.

The crosslinked network has genuinely fascinating consequences, because it
provides a direct link between the nanometer scale molecular conformation with
the macroscopic scale shape of the entire object. In fact, when you pull at a
rubber band, you are changing the shape of its molecules:[13] you are forcing
the molecular chains to stretch out along the direction you are pulling. In
doing so, the molecules occupy less space in the plane perpendicular to the
pulling direction, which is why the rubber band gets thinner perpendicular to
the pulling direction. As soon as you stop pulling, however, the molecule
chains are freed from their restraints and thermal energy (heat) will reorder
them more or less randomly such that the macroscopic material shortens along
the stretching direction and thickens in the perpendicular plane, thus
reverting the rubber to its original state.

The key difference between a regular rubber and an LCE is that the process
just described can take place fully autonomously, within the LCE. The reason
is that the molecules of an LCE tend to align along a specific direction at
room temperature, as illustrated in Figure 1a. We call this direction, which
can be defined macroscopically at the stage of crosslinking, the director
(abbreviated n). The liquid-like mobility combined with the orientational
order makes the phase a Liquid Crystal (LC) phase.[14] The orientational order
means that the molecular chains of an LCE, in contrast to an ordinary rubber,
are stretched out along n without any external force applied.[15, 16] However,
if we heat beyond a critical temperature $T_{c}$, this spontaneous ordering is
lost and the LCE switches to the behavior of an ordinary rubber that is
spontaneously disordered. Because of the link between molecular order and
macroscopic shape afforded by the 3D network of crosslinks, the consequence is
that an LCE is elongated along n (and compact perpendicular to n) in the
ground state, but it contracts along n (and expands perpendicular to n) if
heated above $T_{c}$, see Figure 1b. Not only does the LCE change its shape in
response to the temperature change, but it can even exert a force when doing
so, pulling or pushing at objects attached to the LCE. This is what makes it
possible for LCEs to be actuators, or artificial muscles.

Figure 1: 2D illustration of the working principle of an ordinary nematic LCE
operated as actuator, triggered by heat and light, respectively. The ovals
represent "mesogenic" segments, LC-promoting sections that prefer parallel
alignment below $T_{c}$, in the ordered nematic phase. The green kinked shapes
represent the order-disrupting illuminated state of light-responsive molecules
such as azo-dyes, which reduce $T_{c}$ to below room temperature ($T_{r}$) and
thus trigger actuation without heating. Whether triggered by light or heat,
the actuated state is a disordered (isotropic) state, in which the elongation
along the director (n) present in the nematic phase disappears. Because the
system is crosslinked (pink bonds) into a 3D network, the molecular shape
change induces a corresponding shape change of the macroscopic object,
shortening along n and thicknening perpendicular to it.

Heating and cooling is the most basic way of triggering actuation, but
regardless of how it is initiated, the heart of the process is the transition
from the LC phase ground state to a disordered phase at temperatures above
$T_{c}$. Importantly, we can achieve this phase change also without heating or
cooling, by changing $T_{c}$ instead (Figure 1c). By incorporating light-
responsive molecules which change their shape between rod-shaped and kinked
when exposed to light of different wavelengths, we can tune $T_{c}$ back and
forth below and above room temperature, by exposing with ultraviolet (UV) and
visible light, respectively. The LCE can now be actuated by light at constant
temperature. We can also combine light- and temperature-driven actuation by
incorporating dyes in the LCE,[17] which absorb light but immediately release
the energy as heat: the LCE itself heats up internally due to the light
exposure, yet the surrounding does not need to be heated. Finally, recent
advances in the chemistry of LCEs has also allowed humidity [18] and electric
field-driven [19] actuation.

While the first LCEs were limited in the freedom to choose the ground state
shape and actuation mode, where actuation modes were defined by a uniform
orientation of n throughout the sample that was obtained by stretching it
unidirectionally during production[20], a major breakthrough were the
demonstrations of controlled bending, allowing the LCE to function as an
active hinge. This was first realized by irradiating light-responsive LCEs
with collimated light [21, 22], later by deforming the ground state director
field, n(r) (where r is the space coordinate), into a bend.[23] This last step
was seminal, as it inspired a creative explosion of innovative approaches to
pattern complex n(r) into LCEs over the last decade [24, 25, 26, 27, 28].
These references are far from exhaustive, but they contain some of the most
striking examples.

Moreover, also the ground state shape is no longer restricted to the flat
monolithic sheet of the original unidirectional stretching approach, but now
LCEs can be realized as self-closing ribbons,[29, 30] spheroids,[31, 32],
Janus particles,[33] shells,[34, 35, 36] fibers,[37] tubes,[38]–indeed in any
conceivable shape. When actuated; ribbons can function as motors that drive
axle rotation[29, 30], shells can function as micropumps [34] and tubes, if
they are fully developed with the right n(r), should function as a peristaltic
pump.[39] Among the most inspiring demonstrations is that of the Verduzco
group, which defined complex 3D ground state shapes such as doll’s faces and
flowers by spanning the LCE precursor over the corresponding 3D molds,
obtaining reversible actuation from the arbitrary shape into a flat sheet by
heating above $T_{c}$.[40] As the procedure is simple and the LCEs are quite
large, this truly holds promise for applications. Combining the freedom of
determining the ground state shape with the freedom of tailoring n(r) into
complex patterns, highly complex actuation modes can be programmed into LCEs.
Adding the different options for triggering the shape change, LCEs arise as
incredibly versatile and advanced actuators. By realizing components in LCEs
or LCE composites, we can thus truly speak of embedded intelligence for these
components.

Like many actuators, LCEs can also be operated in reverse, giving a signal in
response to mechanical strain– a sensor. The ideal solution for this is the
cholesteric LCE (CLCE), which exhibits a helical modulation of n with period
(called pitch, p) on the scale of light wavelengths, giving rise to so-called
selective reflection of light with wavelength $\lambda\approx p$.[14] By
varying the chemical composition, $p$, and thus $\lambda$ can be varied at
will, allowing us to tune this "structural color" from the infrared (IR),
across the full visible band, and into the UV.

As the helix is linked to the macroscopic object shape via the 3D network of
crosslinks, an extension of a CLCE sheet with the original helix perpendicular
to the sheet will lead to a compression of the helix, thus a reduction of $p$
and $\lambda$, with a consequent blue-shift of the reflection color.[41, 42,
43] This means that an originally red-reflecting CLCE sheet can give us
continuous mechanical strain sensing (it works equally well for tensile and
compressive strain [43]) with immediate read-out visible to the naked eye, in
form of a color change from red to orange, yellow, green, blue and finally
violet. The response is also highly localized, i.e., if the strain varies
across the CLCE, it shows different color in different points, enabling strain
mapping with very high resolution.[43, 44]

An interesting possibility is to prepare the CLCE sheet with $p$ long enough
to reflect IR, but not visible, light. The CLCE thus looks colorless
transparent in the ground state. But if it is stretched perpendicular to the
helix, $p$ and $\lambda$ reduce, and if the original helix is properly tuned,
a red color appears. De Haan and co-workers patterned such a CLCE within a
passive transparent rubber sheet such that a red warning sign became visible
beyond a critical strain threshold.[45] Clearly, such CLCE strain sensors can
be enormously useful tools in the built environment, as we will exemplify
below.

##  3 Examples of opportunities of LCE actuators and sensors embedding
intellingence into the built environment

In the Architecture and Design fields, leveraging materials for use in
building function and even user interaction is of great interest. While so
many modern construction materials are created around standards to reduce both
risk (standardized constraints) and cost (standardized shape in
manufacturing), a desire for customization continues to drive innovation.
While mass customization has gained traction in architecture research, this
area is dominated by CNC (Computer Numerical Control) and robotic
manufacturing techniques. Still, there has been an area, which continues to
grow, of both industrial and academic works where customization and
environment-specific interactive buildings are enabled through materials
themselves. Most recently, Persiani published a detailed book discussing
numerous actuating materials in the context of kinetic building design,
referring to materials that enable kinetic responses to stimuli as
Autoreaction [2]. This follows on the book by Bengisu and Ferrara, published
only two years earlier, detailing multiple case-studies and uses of Materials
That Move [3].

In the vain of these books, we here give a few concrete application examples
of embedded intelligence in the built environment, with the specific focus on
the opportunities offered by LCEs (Figure 2). We first consider them operating
in tandem with additional devices that allow a user to freely choose when the
actuation should take place, continuing with some scenarios where we can
safely do without such devices, thereby reaching full embedded intelligence
and truly autonomous operation. Finally, we go beyond the core concept of
’materials that move’ and discuss the valuable potential of CLCE sensors
triggered by motion, delivering a color response that can be life saving for
people inhabiting a building.

Figure 2: Topology of the three themes of LCE interactions we discuss. The
arrows connecting the themes illustrate the relationship between the types of
inputs and outputs, from simple sensing, to sensing leading to actuation, to
actuation arising from sensing an artificially created stimulus.

###  3.1 Actuation on Demand

In this theme, we consider the situation where a user should be able to turn
on or off actuation at will. From a materials design perspective, it is then
an inherent requirement that the LCE does not respond to the natural changes
in environment, in terms of temperature, light, humidity or other factors. The
chemistry must be tailored for a $T_{NI}$ much higher than any expected
ambient temperature, and if light-responsive molecules are incorporated, these
should not be sensitive to sunlight or normal artificial lighting, but rather
respond to UV light of rather low wavelength. The LCE must be complemented by
artificial sources of actuation stimulus, e.g., a heater or light source which
the user controls to actuate or relax the LCE. Of course, this solution
consumes energy and will require some kind of power/energy supply, hence we
have—by definition—sacrificed autonomy for control. We refer to this way of
using LCEs in a controlled way entirely independent of the environment as
Actuation on Demand.

We suspect that the most common application scenarios considered by the LCE
research community belong to the Actuation on Demand category, often in the
context of soft robotics. While the term robotics is broad, work relating to
actuating LCEs often revolves around some sort of exo-skeleton or locomotive
device. Importantly, many of the design paradigms used for mobile robotics can
be translated to the situation of immobile built environment, solving
important problems that have not been so much in focus for the LCE community.
We see buildings not as monolithic static structures, but instead as objects
that should—but are not always able to—conform to the occupants within them.
Our static environments are not always the result of intention, but rather a
limitation of the materials and technologies available to designers. There
have been various projects from architects and designers that explore
actuation on demand for replacing static with kinetic components. Here we will
look at two specific illustrative examples, one initiated in the architect and
design community, the other in the LCE community.

####  3.1.1 Modulating acoustics

Sound is an integral part of how many people experience an environment, from
hearing someone speaking during a lecture, to enjoying the art of musicians
performing in a concert hall, to reducing noise in a crowded station. The two
most common ways designers modify the sound of a space are (1) the absorption
of materials used, (2) the geometry to guide and scatter. In the approach of
[46], a ceiling-type system of panels containing perforations are aggregated
in an origami-like structure that is actuated through a mechanical system to
open and close, thereby changing the acoustics. The system relies on
electrical stepper motors, hence also continuous wiring from the power source
to each individual element.

An extension of this concept using LCEs, replacing the stepper motors with
(perfectly silent) light-reactive LCE hinges, might allow an elimination of
the wiring, as the light signal for triggering actuation (which can be
invisible) can be sent through the air. A significant challenge is that the
panels may be of significant size and weight, and many LCE hinges would need
to be applied in tandem to deliver sufficient force. Significant gains can be
achieved by layering LCE sheets,[47] but more important may be to design the
overall structure with counterbalances, such that the force needed from each
LCE is minimized. Lifting large heavy plates against gravity with LCE hinges
is most likely unrealistic.

This application opportunity also puts the spotlight on an area of LCE
research that is yet under-explored: bistability. Normally, LCEs relax as soon
as the stimulus is removed, which means that the switch to a different type of
acoustics would require continuous irradiation of the LCE hinges. It would
obviously be highly desirable to be able to lock the new shape into place,
allowing the light source to be turned off. Some success in promoting
bistability was demonstrated using LCE-wire composites [48] but more research
is required. In fact, this type of application would benefit the most from
multistable actuators, which could be locked into a multitude of different
shapes. This might be achievable by using LCEs that are in a glassy, stiff
state at room temperature, and combine actuation via light-responsive tuning
of $T_{NI}$ with heating or cooling above or below the glass transition
$T_{g}$. An ideal solution might be the recent demonstration of actuation by
light-induced heating via carbon nanotube sheets in composites with LCEs [49].
By tuning $T_{g}$ to well above room temperature, the LCE could be switched
between stiff and responsive by turning on or off IR radiation. Using UV
light, $T_{NI}$ could then be switched between temperatures below and above
the IR-induced temperature, in order to control whether the hinge actuates or
relaxes while in the soft state above $T_{g}$.

Figure 3:  A wall is composed of LCE coatings that change form at a smaller
scale to modify acoustics. The arrows represent sound scattering from an
exterior source due to the geometric changes of the wall surface. The inset on
the left shows an LCE shell exhibiting reversible buckling upon heating and
cooling (from Jampani et al. [35] CC BY-NC-ND 4.0 license), as an example of
how a ’bubbly’ texture could be modulated on demand using LCEs for tunable
acoustics.

In a different approach, Decker uses the concept of soft robotics in
architecture to modulate the walls of a chamber by expanding a rubber sheet
into a pre-molded bubble-like topography using pneumatics.[50] Again, LCEs
might elevate this solution for controlling acoustic properties by removing
the need for connectivity—in this case via tubing rather than electrical
wiring—as an LCE can be actuated on demand through heat (Figure 3) and light.
Following the approach of Barnes and Verduzco,[40] the bubble-like topography
could be imprinted as the ground state, actuation yielding an increasingly
flat surface. Another interesting approach would be to decorate a surface with
LCE shells, spheres of diameter 0.1–1 mm which can be reversibly switched
between taught, smooth and irregularly buckled, soft states.[36, 35] The
actuation/relaxation may affect both the absorption and scattering of sound
waves, the effect depending on the scale of the buckles as well as of the
overall spheres. To control such LCE-based sound modulation, light panels
could back-illuminate the LCE surface, or ceiling track-lighting could
illuminate the LCE-covered surfaces in different
patterns/intensities/configurations to provide unique acoustic modifications
to the environment. Depending on the chemical design of the LCE, the light
could be visible, for effect, or invisible, for discreteness.

####  3.1.2 Modulating adhesion

Photovoltaics (PV) technology, or solar energy, has enormous potential to
solve our future energy needs, but before it can reach that goal, further
advances are required both in terms of the basic PV performance and in terms
of the practical reliability of PV installations. In this article, we consider
two examples of how LCEs can help in the second respect–starting with the
importance of keeping solar panels clean. If a solar panel is covered by
debris, it will not deliver much electrical energy no matter how performing
the actual PV module is.[51] Unfortunately, some of the sunniest areas in the
world, thus where PV is the most useful, are also regions where sand and dust
are ubiquitous, hence efficient PV installations must be able to remove layers
of dry particles covering the solar panel. Also in colder regions of the
world, PV is considered a viable energy alternative, and here the
corresponding challenge is to remove snow from the solar panels, which
prevents the sunlight from reaching the active PV elements to generate
electricity.

Liu and co-workers have taken on this challenge in their research, developing
films of liquid crystal networks (LCNs), which can be viewed as very densely
crosslinked LCEs, in which the surface naturally develops a fingerprint-like
or randomly varied topography. When these films are actuated, the troughs and
valleys exchange location, and the amplitude of the topographic modulation can
be increased. Importantly, the team recently reached a significant break-
through in the LCN chemistry, allowing the actuation to be directly
electrically triggered,[19, 52] without intermediate light or heat stimuli. As
a result, they could demonstrate release-on-demand of sand covering an
inclined glass surface. [53] By applying a voltage over the film, the dynamic
modulation of its surface reduced the adhesion of the sand to such an extent
that gravity pulled the sand grains down, leaving a surface free of debris.
While much research still remains to be done, this is a highly inspiring
concept, not least as the reliance on electrical power is a minor issue when
dealing with PV cells, which deliver orders of magnitude greater electrical
power than needed to activate the LCN. Different types of sand and dust may
adhere to different extents, hence the concept may need to be boosted by
varying the periodicity and amplitude of the topography modulation and also
introduce specific chemical functionality in the coating.

An alternative procedure for dynamic adhesion modulation with LCEs, inspired
by the gecko’s ability to switch between adhesion and release via the hairy
surface topography of its attachment pads, is to realize an LCE film in the
form of arrays of pillars with switchable height [54, 55, 56]. Combining with
rigid rails that align with the pillar array in its relaxed state but protrude
above the pillars when they are actuated, thus terminating contact between
pillars and external objects, Cui et al. could switch between adhesive and
non-adhesive states of their substrates. Of particular interest for snow
removal may be the dynamic tuning of wettability achieved by Wu et al.[55,
56]. Here no rigid array was needed but the effect was realized by tuning the
aspect ratio of the pillars, thereby switching from Cassie to Wenzel style
wetting. Such a surface may be able to act on a liquid water layer between the
solar panel and the snow, promoting the snow to slide down.

Of course, the best way to deal with debris covering on solar panels is if the
source of the debris can be avoided in the first place. In the next section we
will see how LCEs, in conjunction with a new type of miniaturized PV elements,
may also be useful in this way.

###  3.2 Actuation by Sensing

In many areas of the world, buildings are a major contributor to greenhouse
gases through their massive energy requirements. While the structural aspect
of a building is typically a one-time cost (i.e., concrete is poured once),
the ongoing regulation that balances the variation of nature with the human
expectation of consistency is a major challenge. Simply put, we spend an
incredible amount of energy making buildings warm when nature is cold, light
when it is dark, and dark when it is too light.

Here we consider application scenarios for LCEs where they assist buildings to
provide a consistent environment for the occupants, with minimum energy
requirements–by actuating fully autonomously in response to the natural
environmental variations. This means that we often need to work with a rather
low $T_{c}$ in order to reach actuation without artificial heating. A weakness
of LCEs operating at low $T_{c}$ is the slow relaxation, arising from the time
needed to cool down below $T_{c}$ if this is near room temperature.
Fortunately, compared to applications in robotics, the low speeds of change in
the scenarios considered here are more forgiving in this respect, rendering
this weakness acceptable.

####  3.2.1 Regulating facades and roofs in response to periodic temperature
and light variations

Consider the basic scenario of balancing natural light and heat radiation
input with the active temperature control of an air conditioning system,
consuming energy for heating in winter and for cooling in summer. While in
warmer months we could rely on coated glass that blocks infrared light from
the outside, we would hope to increase the infrared light input from the
outside during colder months. On a shorter time scale, such dynamic facade
modulation would be valuable even as it is cooler in the mornings and
evenings. An exciting solution to this challenge is in phase-change materials,
as simple as wax, that absorb heat above a threshold, and release heat below
it. The phase change in question is also coupled to a very significant
specific volume change, standard paraffin wax expanding on the order of 20% in
volume upon melting. By preparing spherical shells of cholesteric liquid
crystal with a paraffin wax core, and polymerizing the shell into a CLCE, the
volume expansion would lead to a shell thinning with consequent reduction of
$p$ and a consequent blue-shift of the retroreflection color,[43] which is
omnidirectional in the shell.[57]. By tuning the initial pitch to values long
enough that the most important heat radiation is let through in the cold
state, moving into the heat blocking part of the spectrum upon compression,
wax-filled CLCE shells might thus be able to couple the classic latent heat-
based temperature regulation well known from phase-change materials with
variations in IR transmission.

While the realization of wax-filled shells with perfectly tuned CLCE is a
challenge to be met, light-driven autonomous irises have already been realized
from LCEs.[58] Here a circular LCE sheet is prepared with n(r) patterned into
a bend from top to bottom, and radial cuts are made towards the center. The
result is that the LCE sections curl upwards under low illumination intensity,
exposing a central hole through which light can enter. When irradiated with
sufficient UV light, however, the sections flatten out towards the center,
thereby blocking the light path. While this iris thus expands in the third
dimension during actuation, a strictly 2D actuation-on-demand version of an
LCE iris was demonstrated by the Zentel group.[59] Here a radial array of
electrical heaters integrated within the LCE sheat increased the size of the
central hole in the iris without any bending.

An even more accessible means of achieving autonomous modulation of light and
heat input for a building facade may be to combine light- or heat-driven LCE
hinges with passive facade elements. Schwartz and co-workers demonstrated a
concept for glare management based on vertical louvers organized into pairs,
where the blades are split in two, with one half offset along the normal of
the blade face [60]. By rotating the pair such that the normal to the louver
surface always points to the sun, direct sunlight is fully blocked, while
indirect sunlight and good visibility can be ensured as the parallel rays of
the sun align only with the rotated louver, and indirect light is reflected
inside (Figure 4(a)). The glare reduction is beneficial not only in reducing
IR light and thus counteracting heat gain, but also through human comfort in
visual glare. Unfortunately this type of heliotropic (sun-following) rotation
mechanism is uncommon, most likely because of the expense and difficulty in
manufacturing mechanical systems that are either preprogrammed, or equipped
with sensors – both of which require electrical power and wired
electromechanical solutions. Designing an LCE actuator-based system that
responds to the highest intensity light direction could be a way forward.

(a)

(b)

Figure 4: (Fig4(a)) Sun-tracking louver in plan (top view), where the rotating
blades block direct sunlight but allow indirect light and a view to the
exterior. (Fig4(b)) Concept drawings of how the heliotropic function could be
realized using LCE sheets that protrude as pillars when actuated. As an
example of LCEs with significant lifting power we show the patterned and
layered LCE sheets realized by the White team [47] (CC BY 4.0 license). If the
louver surfaces are covered with micro-PV panels, the system will
automatically direct them towards the sun throughout the day. If each PV panel
is attached via a light-activated LCE hinge, it will show its active face only
during the light part of the day, while it is folded inwards against the
louver, protected agains sand, snow and dust, during the night.

A simple solution might be to use an active LCE hinge that bends in response
to sun irradiation, counterbalanced by a passive spring that pulls back under
low light conditions. More elegant may be to place the louvers between two
horizontal platforms, suspending the entire system around an axle using a
ballbearing, such that it can easily rotate in response to subtle mechanical
stimuli. We visualize this concept in Figure 4(b). The top platform could be
of glass, and below it we could pattern a circular array of LCE actuators,
capable of protruding upwards under light illumination or local heating. To
ensure sufficient stimulus, convex lenses may be used to concentrate the solar
radiation onto each LCE. By adding small radially aligned opaque walls between
each LCE actuator, only those that are facing the sun get irradiated and thus
actuated. The top of the louver system would have a disc almost in contact
with the platform, with a soft notch in one point. This notch would be locked
in place by that particular LCE that protrudes the furthest into the notch. By
the design, this happens to be the LCE pointing towards the sun, thereby
providing the heliotropic rotation. An appropriately balanced spiral spring
could act as a reset system each day. A suitable solution for the circular LCE
actuator array would be stacks of LCE sheets with n(r) patterned into
concentric rings, which can displace loads greater than 2500 times their own
weight a distance of 0.5 mm.[47] To make the system less sensitive to gusts of
wind, it may be of interest to suspend the axles in a strongly shear
thickening liquid, such as the colloidal suspensions used for ’liquid armor’
[61], which would counteract rapid motion due to wind but allow the slow
motion driven by the LCE.

With louvers orienting autonomously to follow the sun, a natural further
extension is to cover them with PV cells to also use the facade for generating
electricity. Rather than today’s large and heavy PV panels that typically
cover roof tops, a more useful option would be the miniaturized micro-PV cells
used in arrays, often in combination with optical elements to concentrate the
sunlight (Concentrator Photovoltaics, or CPV), which are a hot current area of
research.[62] These can have a lateral extension as small as 0.2 mm [63] and
be very thin and light-weight, making it easy to pattern louvers with such PV
cells. Most importantly, considering the scope of this article, each micro-PV
cell could be attached to the louver via an LCE hinge that lifts the cell with
its active side out during the day, while illuminated by light, but folds it
down during night, when it cannot generate electricity anyway. The active side
is then protected from snowfall, sand or dust, and should such debris have
accumulated on the active side during the day, it may fall off by gravity as a
result of the bending. This concept for autonomous regular PV cell cleaning
could of course be extended to other contexts, like replacing roof-top solar
panels with LCE-driven selfcleaning CPV systems, largely eliminating the need
for the very dangerous action of cleaning solar panels on the roof of a home.
It may also be desirable to realize it in an Actuation-on-Demand version, as
the need for electrical power is not an issue here. In particular in large
solar parks in desert areas it could be very powerful to fold all PV panels
away ahead of an incoming sand storm. In this context, it is worthwhile
mentioning that LCE-driven heliotropic solar cells of rather large scale have
already been realized [64].

####  3.2.2 Regulating ventilation in response to heat and humidity variations

Of similar importance to occupants of a building, and to their comfort, is the
role of wind and air circulation. Tuning LCEs to actuate at a temperature
above or below common room temperatures could facilitate dynamic facades that
prioritize natural air and ventilation when possible (a particularly
attractive feature for hygiene), while minimizing the energy usage of HVAC
(Heating, Ventilation and Air Conditioning) systems. While it would be
valuable to be able to construct entire exterior walls with this
functionality, also more modular or localized components could have
significant impact. Kinetic buildings could be pushed to a new standard that
further breaks down the relationships between inside and outside through
building skins that actuate when sensing humidity. Smaller applications such
as awnings or coverings at bus stations could provide airflow and semi-open
ceilings, and then close to provide coverage when humidity reaches a point of
rain.

Figure 5:  Concept of a facade opening as humidity increases. The envelop of a
building is shown as a concept covered in LCEs that actuate as humidity
increases, allowing air to circulate throughout. The photos of a humidity-
sensitive LCE strip bending away from a vial filled with water when
approaching the water surface (adapted with permission from [28], copyright
(2014) American Chemical Society) show an example of the technical
implementation of the concept.

In parts of the world where concrete and stone housing is common, even more
interesting than responding to outdoor high humidity during rain may be to
activate ventilation in response to indoor high humidity, e.g. in kitchens and
bathrooms. Mold formation inside living spaces is an enormous problem in many
non-wooden houses during the cold part of the year. Insulated walls keeping
the home warm also block the path for removing excess humidity, with the
consequence that liquid water condenses from the air on cold surfaces, e.g. at
corners of rooms with exterior walls. This forms an ideal environment for mold
growth, with devastating health consequences, often related to allergies. In
kitchens, the humid air arising during cooking fills fridges and freezers
every time they are opened, their low temperature leading to significant water
condensation or ice formation on the surfaces of the items in the fridge,
which may become inedible as a consequence. Such food spoilage could be
avoided by dynamic ventilation, in the kitchen walls and possibly even in the
concerned household appliances.

Humidity-responsive LCEs might offer a way of realizing such dynamic
ventilation (Figure 5). The Schenning and Broer groups demonstrated LCE sheets
that bend towards or away from humid air, depending on orientation.[18] Many
such LCE patches could be placed on a grid such that they form a closed wall
when the air is dry, maximizing insulation and thus keeping heating/cooling
costs low. However, if the internal humidity rises, the LCE sheets bend away
from the humid air, opening channels for air exchange with the environment.
While this obviously also reduces the thermal insulation efficiency, it is a
temporary measure that stops as soon as the humidity has been reduced to
acceptable levels. The channels opened during LCE actuation can be kept very
small, hence air flow is enabled without allowing insects to enter. As neither
energy nor user intervention is required to run the process, it is fully
autonomous.

A particularly interesting example of water-responsive LCE is the humid air-
driven cellulose-based motor developed by Geng et al.[30] The team prepared a
ribbon of hydroxypropylcellulose (HPC) that bends away from humidity, and
closed it into a loop. When one side of the loop is exposed to humid air, the
local bending in conjunction with the topological constraints of the self-
closing loop leads to a continuous motion of the ribbon. When suspended on two
wheels, the ribbon rotates around the wheels as long as there is a gradient in
humidity in the surrounding air. Not only can the humidity gradient thus, in
principle, be used to do work but, perhaps more importantly, the HPC ribbon
should be an ideal transporter of humidity out of a humid environment, as it
autonomously moves humid HPC out to dry air and moves dry HPC into the humid
environment, until the humidity gradient has been evened out. If such a ribbon
in a ventilation shaft would be combined with the equally autonomous humidity-
driven shutters describe above, a very efficient way of improving indoor air
quality and saving energy overall might be realized.

###  3.3 Sensing by Actuation

We end this section by discussing some very beneficial uses of LCEs ’operated
in reverse’, in the sense that an externally imposed mechanical strain changes
the properties of the LCE, giving it the properties of a strain sensor. To
this end we focus on CLCEs, the color of which can be tuned by strain. A
compression along the helix, or an extension perpendicular to it, reduces $p$,
thus blueshifting the color. This includes a blueshift from the IR region,
i.e. the strain leads to the appearance of color in a CLCE that was colorless
transparent in the relaxed state. Significantly, the response is local with
negligible granularity, hence it can be used for strain mapping with very high
resolution.[44, 43] To illustrate the usefulness of CLCE-based strain mapping,
we consider applications in safety, the existence of which could save many
lives in accidents or natural disasters. We see potential in this area for the
incorporation of CLCEs that change color under strain. They could be used as
an autonomous system giving a clearly visible warning at critical areas,
directly alerting the occupants of an impending danger.

####  3.3.1 CLCE coatings alerting building occupants of a pending collapse of
a roof, false floor or window

The weight of snow on a roof can be very significant in cold parts of the
world and sadly, accidents where roofs cave in, sometimes killing people
underneath, are not as uncommon as one would wish. A notorious examples is the
Katowice Trade Hall roof collapse in 2006,[65] leaving 65 people dead and more
than 170 injured. Although there are many building standards that exist, they
are largely a means to defining a minimal risk threshold and are by no means
all encompassing. For example the northeastern United States had numerous
building failures during a snow storm in 2011, and a lack of national safety
guidelines encouraged a report on snow loads by FEMA [66].

At least in case of glass roofs, it would be relatively easy to coat the glass
plates with a CLCE film tuned for infrared selective reflection in the relaxed
state, leaving it transparent in the absence of mechanical strain. In
contrast, with the weight of snow on the film, $p$ would be compressed and the
reflection blue-shifted. With properly tailored CLCE properties, the glass
roof would start reflect red when the weight on the roof is at the limit of
what it can safely withstand, alerting occupants of an unexpectedly heavy
load. The CLCE would provide crucial information during a time-sensitive
situation, making the occupants aware that they must evacuate the building.
While this approach could be applied to any similar roof styles such as
concrete slabs, the ability of CLCEs to present as a transparent material
until actuated, provides unique opportunities, combining aesthetics with
potentially life-saving functionality.

Figure 6:  Concept of a CLCE coated window that flashes a warning when strong
winds deform it to a critical level. The ability to show a pattern or image
during strain is demonstrated in the two photos, reprinted with permission
from [45], copyright (2019) Wiley-VCH.

Along these same lines, CLCE coatings could be applied to all types of glass
panels. In areas of the world where hurricanes or tornados are a risk, having
CLCE-coated storm windows would give visual indications of how much force was
being applied (Figure 6). They could possibly be tuned to provide a threshold
in which there is danger of the window breaking, or even a warning threshold
for when to seek underground shelter.

Even more informative than a general color change would be to pattern warning
signs into the film, as demonstrated by de Hahn et al.,[45] reproduced in
Figure 6. Here a CLCE film with its helix axis perpendicular to the film plane
was designed to be featureless in the relaxed state, but upon stretching
perpendicular to the helix near to its limiting extensability, making rupture
a risk, a red warning triangle appeared, alerting the user that the tensile
strain is now on a dangerous level. As demonstrated by Kizhakidathazhath et
al.[43], tensile strain perpendicular to the helix elicits the same
mechanochromic response from CLCEs as compressive strain along the helix,
hence the same patterning principle could be used for glass roofs. At the same
time, there are many situations where rupture of an elastic component under
tensile strain can have catastrophic consequences, and where human observers
would notice a color change, hence this functionality could be applied in many
contexts.

In the same way the strain in construction materials themselves could be
indicated by means of CLCE films coating critical elements. Again, they could
be designed for colorless transparency under normal conditions, but in case of
excessive strain, a color would appear. Since the color response is nearly
immediate and fully reversible [43], the CLCE film would be well adapted to
visualize dangerous dynamic loads. The CLCE could, for instance, be applied to
supporting elements of false-floors, which are typically used as stages or
audience platforms in concert halls or convention centers, the users often
unaware of the designated maximum capacity. Again such instances can lead to
tragic accidents, an example being the 2012 collapse of an audience platform
in the Stockholm Globe Arena in Sweden, not withstanding the synchronized
jumping during a concert by the artist Avicii. If the platform would have been
coated with CLCE sheets generating reflections of different colors, security
staff would have been able to see that the load was reaching dangerous levels
before the accident occurred, allowing them to take evasive action.

####  3.3.2 CLCE coatings mapping out the deformation of buildings during and
after an earthquake

In many parts of the world, seismic activity has proven to cause catastrophic
building failures, resulting in numerous lost lives. During this activity,
extreme deformations of the building could cause CLCE-coated elements to flash
in a specific color, or even with a predetermined message. This type of user-
environment interaction, through embedded intelligence of materials responding
through the building’s actuation, could aid in emergency route planning as
signage dynamically appears based on the specific conditions of that
emergency, guiding occupants to the safest places or, if possible, the exits.

Perhaps even more valuable would be the post-earthquake situation, where CLCE
coatings would greatly facilitate the evaluation of the building integrity.
The common visual inspection done by inspectors and engineers could be greatly
sped-up and improved by clear indicators that are now displaying warning
colors/signs that show—even to a high degree of accuracy—remaining
deformations and changes of the building compared to the original state.
Significantly, for such an application the films could also be mounted in
areas like service shafts, where also the regular pre-earthquake state does
not need to be transparent. This maximizes the flexibility in tuning the color
gamut of the response as well as the relaxed characteristics. Indeed, having
the films colored from the beginning would facilitate the work of the
inspection teams, as they will easily find them, whether the building has been
deformed or not.

##  4 Outlook

We present a few of the many ways LCEs can be used in substantive and creative
applications for improving the environments we live and work. Along with these
various applications come the challenges and research needed to fully explore
the potential. From a building perspective; cost of materials, both in the
sourcing but also in the integration and installation, is critically
important. There is also a need for Architects and Designers to better
understand how materials perform and the bounds of this performance.
Currently, licensed Architects and Structural Engineers learn about the
properties of typical building materials such as concrete, wood, and steel,
but from a safety and reliability standpoint, LCEs (and for that matter, most
shape memory polymers) are currently out of sight.

The size and longevity of buildings is also an issue not often discussed in
the LCE community, given the focus primarily on robotics, with much shorter
life cycle. Considering that many of these applications assume permanent or at
least semi-permanent installations over decades, we must understand how the
very same natural elements that we here consider the actuation triggers for
LCEs might also cause failures or erode the polymers’ ability to actuate and
sense. Strategically, some implementations, such as coating windows for storm
sensing, might be applied on the interior of buildings. However this is not
always possible, for instance, on building envelopes that are dynamically
adjusting to exterior humidity and temperature variations for modulating air
flow. Long-term exposure to sunlight, large variations in temperature, strong
winds, rain, snow and even hail are conditions that the LCEs, at least up to a
point, must sustain when applied on a building exterior. From this point of
view, as well as from the point of view of minimizing the financial and
ecological costs of massive scale-up of LCE production, it is noteworthy that
bioderived LCEs have started appearing on the research arena. The humidity-
driven motor ribbon of Geng et al.[30] was made of HPC, the same cellulose
derivative that is commonly used as excipient in the pharmaceutical industry.
Very recently, MacLachlan and co-workers succeeded in making the first
mechanochromic CLCE based on cellulose nanocrystals.[67] Although this was
still a hybrid of oil-based and cellulose-derived components, such
developments hint at future LCEs which can be sustainably produced and which
are less sensitive to weather, given that cellulose is the main component of
all plants on Earth.

Before LCEs can be realistically considered for many of the scenarios sketched
in this article, several of these practical issues must be addressed by LCE
materials scientists and engineers. While many recent developments are still
far from mature, basic functionalities such as linearly contracting/expanding
LCE strips capable of lifting loads and sheets bending as active hinges have
now been around for about two decades. We believe the time is ripe for an
active effort to bring these types of LCE devices to market, thus taking on
the chemistry and engineering hurdles on the way to mass production at low
cost and with high reliability. While the solutions of these problems may not
involve the fundamental research challenges that typically lead to high-
profile scientific publications, they are absolutely essential for the
successful practical implementation of LCEs in the built environment, or
elsewhere for that matter. We also hope that industry will engage, leveraging
the highly mature state of the most basic, and very useful, LCE actuators and
sensors in order to add LCE hinges and pullers/pushers to their product
catalogs. When architects can design with LCE devices in mind and engineers
can build with them, their true potential can be unveiled.

With the numerous research papers and experiments elaborating on the ways of
developing LCEs, mass adoption can now be the next immediate focus. Part of
this process includes a standardized description of material characteristics
and performance: an MSDS for LCEs. How long does a certain LCE last in the
sun, at different temperatures, with certain binders, connected to metal or
plastic or wood? Creating a catalog with systematic expression of material
characteristics—how much does it deform in response to what stimulus? how soft
is it in each state? etc.—would allow architects, designers, and general
populace to easily connect the material itself to the creative and unique
applications that propel society into the future.

If the technical challenges and expected costs seem prohibitive at present, we
should remember how an earlier liquid crystal-based technology, that of
displays (LCDs), developed. In the early 1990s few people thought LCDs would
ever compete realistically with cathode ray tube displays and when large-area
color LCDs eventually appeared, they had costs relegating them to the realm of
luxury goods. But as technical challenges initially deemed insurmountable were
solved, and chemistry was tailored for high-speed, high-contrast operation
across an enormous temperature range, LCDs became the all-dominating display
technology, with prices coming down to the lowest grade of consumer
technology. It is thanks to this development that the IT revolution became
possible, as LCDs enabled small, high-resolution information output devices
anywhere and everywhere. What future revolutions will LCEs enable, when the
key actors have joint forces and brought LCEs to a standard, reliable and
readily available technology?

Acknowledgements

JPFL gratefully acknowledges financial support from the European Research
Council under the European Union Seventh Framework Programme
(FP/2007-2013)/ERC Grant Agreement no. 648763 (consolidator project INTERACT).

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Towards a New nCTEQ global nPDF release

P. Rissea,† , N. Derakhshaniane , P. Duwentästerb,c , T. Ježoa , C. Keppeld ,
M. Klasena , K. Kovaříka , A. Kusinae , C. Légerf , J.G. Morfíng , F.I.
Olnessh , R. Ruize , I. Schienbeinf , J.Y. Yuf

aInstitut für Theoretische Physik, Westfälische Wilhelms-Universität Münster,
Wilhelm-Klemm-Straße 9, D-48149 Münster, Germany
bUniversity of Jyväskylä, Department of Physics, P.O. Box 35, FI-40014
University of Jyväskylä, Finland
cHelsinki Institute of Physics, P.O. Box 64, FI-00014 University of Helsinki,
Finland
dJefferson Lab, Newport News, VA 23606, U.S.A.
eInstitute of Nuclear Physics Polish Academy of Sciences, PL-31342 Krakow,
Poland
fLaboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes,
CNRS/IN2P3, 53 avenue des Martyrs, 38026 Grenoble, France
gFermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
hDepartment of Physics, Southern Methodist University, Dallas, TX 75275-0175,
U.S.A.

> We discuss the foundation for a new global nCTEQ nuclear PDF analysis,
> combining a number of our previous analyses into one consistent framework
> with updates to the underlying theoretical treatment as well as the addition
> of new available data. In particular, the new global release will be the
> first nCTEQ release containing neutrino DIS scattering data in a consistent
> manner together with JLab high-$x$ DIS data and new LHC p-Pb data. These
> additions will improve the data-driven description of nuclear PDFs in new
> regions, especially the strange quark and the gluon PDF at low-$x$.

> PRESENTED AT
>
>
>
>
> DIS2023: XXX International Workshop on Deep-Inelastic Scattering and Related
> Subjects,
> Michigan State University, USA, 27-31 March 2023
>

††footnotetext<EMAIL_ADDRESS>
##  1 Motivation

Parton Distribution Functions (PDFs) describe the structure of hadrons as
composed of quarks and gluons. They are one of the key elements in making
predictions for collider experiments in the theoretical framework of
perturbative quantum chromodynamics (QCD). So far, PDFs cannot be reliably
computed from first principles. Only the evolution with the energy scale $Q$
is calculable through the DGLAP evolution equations. Thanks to the QCD
factorization theorem, it is possible to use their universality and determine
the $x$-dependence at some initial scale $Q_{0}$ by comparing PDF-dependent
predictions with experimental measurements. This is a process called ‘global
QCD analysis’ [1]. In the nuclear case additional effects such as shadowing,
antishadowing, the EMC effect and Fermi motion need to be parameterized as
well.

Several collaborations perform global analyses of nuclear PDFs (e.g. [2, 3,
4]). In the nCTEQ framework the parametrisation of nuclear PDFs is done in two
steps. First, at the initial scale $Q_{0}=1.3$ GeV, the so-called bound proton
PDF, $f^{p/A}$, is parametrized as

$\displaystyle xf^{p/A}_{i}(x,Q_{0})\,\,$
$\displaystyle=\,\,c_{0}x^{c_{1}}(1-x)^{c_{2}}e^{c_{3}x}(1+e^{c_{4}}x)^{c_{5}},$
(1) $\displaystyle c_{k}\,\,$
$\displaystyle\rightarrow\,\,p_{k}+a_{k}\left(1-A^{-b_{k}}\right)$ (2)

and depends explicitly on the nuclear mass number $A$. The bound neutron PDFs
$f^{n/A}$ are obtained by making use of isospin symmetry and the full nucleus
is constructed via

$f^{(A,Z)}_{i}(x,Q)=\frac{Z}{A}f^{p/A}_{i}(x,Q)+\frac{A-Z}{A}f^{n/A}_{i}(x,Q).$
(3)

The nCTEQ15 fit, the latest global release from the nCTEQ collaboration, used
data from deep-inelastic scattering (DIS) and Drell-Yan (DY) to constrain the
quark and anti-quark nPDFs as well as data from RHIC neutral pion production
for the gluon. From today’s perspective the fit had a number of limitations
including the precision in the high-$x$ region, the gluon and the strange PDF.
Lowering the energy cuts in the data opens up new constraints on the high-$x$
region for the up and down quarks. LHC data and a reanalysis of neutrino DIS
and charm dimuon data allows us to improve this fit in the gluon and strange
directions. We design a new global fit built upon these results.

##  2 New proton Baseline and nuclear parametrization

The new release will use an improved proton baseline from the “CTEQ-Jefferson
Lab” (CJ) proton release [5]. This will update the current CTEQ6 baseline. The
parametrization

$xf^{p/A}_{i}(x,Q_{0})\,\,=\,\,c_{0}x^{c_{1}}(1-x)^{c_{2}}(1+c_{3}\sqrt{x}+c_{4}x)$
(4)

itself is simpler than eq. 1, leading to less correlated parameters in the
fit. Furthermore, CJ made use of constraints from newer data and includes a
careful treatment of deuterium corrections and high-$x$ effects, making it
especially suited for an extension to the nuclear dimension.

The second parametric update is a new $A$-dependence of the parameters:

$c_{k}\,\,\rightarrow\,\,p_{k}+a_{k}\ln(A)+b_{k}\ln^{2}(A).$ (5)

Compared to eq. 2 the correlations are limited between the parameters yielding
a more accessible $\chi^{2}$-function and a more truthful representation of
uncertainties.

##  3 Relaxed kinematical cuts

Figure 1: Coverage of the kinematic $(x,Q^{2})$-plane of the experimental data
sets. The nCTEQ15 $Q$\- and $W$-cut (black dashed line) removed most of the
HERMES DIS data and all of the data from JLAB. The improved cut is shown as
the red dashed line.

The nCTEQ15 fit used restrictive cuts for the DIS data with $Q=2$ GeV and
$W=3.5$ GeV. Whilst this allows for a simplified theoretical prediction, it
removes a significant amount of data points: a large fraction of the data from
HERMES and all of the JLAB data. The cut is depicted by the black dashed line
in fig. 1. Relaxed cuts within the nCTEQ15HIX analysis [6], shown as the red
dashed line, allowed us to include these data and therefore improve the
constraints on the high-$x$ region. In total, about 850 new data points were
added. The most notable improvement is the reduction in uncertainties in the
up- and down-sector for $x$-values between $10^{-2}$ and 0.7.

The new cuts of $Q=1.3$ GeV and $W=1.7$ GeV are possible due to a careful
treatment of target mass corrections, the inclusion of higher twist effects
and an improved description of Deuterium. The details of the target mass
corrections have been worked out for different nuclei in Ref. [7] and lead to
corrections of up to 15% in the $F_{2}$ structure function at $Q=1.3$ GeV. At
this energy the span between different nuclei is at about 2% from the lightest
to the heaviest nuclei. The effects decrease quickly with higher energies.

A parametrization of the higher twist effects has been worked out in the CJ
proton release. It leads to a reduction in the intermediate-$x$ region ($x\sim
0.3$) and becomes large and positive at large $x$. A possible nuclear
dependence of these corrections has been tested but had very limited impact.

A large fraction of the nuclear DIS data are expressed as a
$F^{A}_{2}/F^{D}_{2}$ ratio of structure functions on a heavy nuclear target
and on a deuteron target. The deuteron structure is more complex than a
isoscalar combination of proton and neutron PDFs. Although a sizable part of
the deuteron system can be captured by these charge factors weighting the
quark PDFs, the residual dynamical nuclear effects are not negligible.
Particularly at large-$x$ values deviations of up to 7% exist.

##  4 Heavy-quark and quarkonium data

The experiments at the LHC have provided data on $W/Z$ boson and single
inclusive hadron production in $pA$ scattering. This improved the
determination of the gluon PDF within the nCTEQ15WZ [8] and nCTEQ15WZSIH [9]
global fits. The uncertainty was reduced in both fits by a factor of two in
the low-$x$ region: $x\sim 10^{-3}-10^{-2}$. Also, the central value of the
strange PDF was affected but the uncertainty remained substantial.

Heavy quarkonium and open heavy-flavor meson production data can constrain the
nuclear gluon further. The gluon contribution dominates the overall cross
section of these processes and a naive leading order estimation of

$x\approx\frac{2p_{T}}{\sqrt{s}}\exp(-|y|)$ (6)

shows that the data is sensitive to $x$ values below $10^{-5}$. A fast
evaluation of the cross section is possible by the data driven approach of the
Crystal Ball function [10, 11]. The ansatz assumes that the cross section is
dominated by the gluon and its parameters are inferred via the well measured
proton-proton cross sections. The prediction has been verified by the next-to-
leading order calculations in QCD [12] and NRQCD [13].

Figure 2: Ratio lead to proton PDFs from the nCTEQ15 fit (black), the
nCTEQ15WZ fit (blue) and the nCTEQ15WZSIH (red). The new nCTEQ15HQ fit is
shown in green.

In fig. 2 the resulting nCTEQ15HQ fit, shown in green, is compared to the
nCTEQ15 in black, the nCTEQ15WZ in blue and the nCTEQ15WZSIH in red. Clearly,
the central value in the up- and down-sector is not affected whereas the
uncertainty is reduced. The gluon is impacted the most. Its fit results in a
shifted central value compatible with the former results whilst yielding a
significantly reduced uncertainty.

##  5 Neutrino DIS and dimuon data

As the uncertainty of the strange PDF remains large, other additional data
needs to be utilized. Charged Current neutrino DIS and charm dimuon production
data have long been known to be sensitive to the strange PDF. However, the
compatibility of the corresponding measurements from CDHSW, CCFR, NuTeV and
Chorus and also with neutral current DIS measurements exhibits tensions.

In a global fit in Ref. [14] an extensive compatibility study was carried out
both within the charged current data sets and those used in nCTEQ15WZSIH. Even
with an improved calculation of the deuteron structure and a larger
$\Delta\chi^{2}$ tolerance of 45 instead of 35 the tension persists. One way
of removing the tension is to use a kinematical cut of $x>0.1$ but a better
result was obtained by using only Chorus and dimuon data.

Overall the central value of the PDFs from the best neutrino fit
(BaseDimuChorus) is only affected in the case of the strange quarks whilst all
uncertainties are decreased. At the same time the data has an impact on the
uncertainty of the valence PDFs but they are dominantly constrained by the
neural current DIS experiments.

##  6 Conclusion

In conclusion, the next nCTEQ global fit will extend the nCTEQ15 results in
several directions. An update in the proton baseline, i.e. the CJ PDFs, will
provide improved proton boundary conditions. The parametrization update on the
level of nuclear modifications (obtained by the new $A$-dependence) provides a
better disentanglement between individual parameters which simplifies the
fitting procedure and results in a more truthful representation of PDF
uncertainties.

Relaxed kinematical cuts in the DIS data with a careful treatment of target
mass corrections, higher twist effects and improved prediction for the
deuterium kinematics yield stronger constrains in the high-$x$ region
throughout all flavors. Additionally it opens up the possibility of including
new data from HERMES and JLAB increasing the coverage of the data sets
overall.

The LHC has produced precise data on $W/Z$, heavy quark and quarkonium
production in $pA$ collisions. We will include the new data sets, where the
heavy quark and quarkonium production provides access to very low values of
$x$ in heavy nuclei and is accurately described by a data-driven approach. In
consequence the new fit will include refined constraints on the gluon PDF even
down to $10^{-5}$ in the momentum fraction.

Finally, improved flavor separation is gained by incorporating fixed-target
neutrino DIS and charm dimuon production data with high statistics. By
concentrating only on the CHORUS and dimuon data the compatibility with
neutral current DIS is obtained. It yields better constraints on the strange
quark and also reduces uncertainties on the up- and down-quarks.

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