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\DOI{10.5802/crchim.280}
\datereceived{2023-09-12}
\daterevised{2023-11-25}
\dateaccepted{2023-12-08}
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\dateposted{2024-02-12}
\begin{document}

\begin{noXML}

%\makeatletter
%\makeatletter
%\def\TITREspecial{\relax}
%\def\cdr@specialtitle@english{Materials and Energy Valorization of Biomass and Waste : The Path for Sustainability and Circular Economy Promotion}
%%\def\cdr@specialtitle@french{Valorisation \'energ\'etique et mati\`ere de la biomasse et des d\'echets : la voie de la durabilit\'e et de la promotion de l'\'economie circulaire}
%\makeatother

\title{Recycled PVC content and particle size distribution effects on
morphological and mechanical properties of expanded PVC layer for
floorcoverings}

\alttitle{Effets de la teneur en PVC recycl\'{e} et de la distribution
granulom\'{e}trique des particules sur les propri\'{e}t\'{e}s
morphologiques et m\'{e}caniques de la couche de PVC expans\'{e} pour
rev\^{e}tements de sol}

\author{\firstname{Walid} \lastname{Chaouch}\CDRorcid{0000-0002-7441-0884}\IsCorresp}
\address{Textile Engineering Laboratory - LGTex, University of
Monastir, Monastir, Tunisia}
\email[W. Chaouch]{walid.chaouch@isetkh.rnu.tn}

\author{\firstname{Slah} \lastname{Msahli}}
\addressSameAs{1}{Textile Engineering Laboratory - LGTex, University of
Monastir, Monastir, Tunisia}

\keywords{\kwd{Recycled PVC powder}
\kwd{Floorcoverings}
\kwd{Expanded layer}
\kwd{Particle size distribution (PSD)}
\kwd{Desirability functions}
\kwd{Mechanical properties}}

\altkeywords{\kwd{Poudre de PVC recycl\'{e}}
\kwd{Rev\^{e}tements de sol}
\kwd{Couche expans\'{e}e}
\kwd{Distribution {granulom\'{e}trique}}
\kwd{Fonctions de d\'{e}sirabilit\'{e}}
\kwd{Propri\'{e}t\'{e}s m\'{e}caniques}}

\begin{abstract}
This work deals with circular economy and sustainability. It
investigates the use of recycled Polyvinyl chloride (PVC) powder as a
substitute for conventional PVC resin in the expanded layer of
floorcoverings without negative effects on their mechanical properties.

The first challenge is to transform PVC-coated fabric waste into PVC
powder completely separated from PET fibers, while simultaneously
ensuring the optimal recovery of small PVC particles. Then, a
comprehensive investigation focused on understanding the behavior and
characteristics of recycled PVC powders. Ultimately, this research
delves into the impact of varying PVC recycled content and particle
sizes on the mechanical characteristics ({Break Strength, Elongation at
Rupture, and Tear Resistance}) of the expanded PVC layer utilized in
floorcovering applications. The results showed that incorporating up to
25~g (33.34\% of the total PVC resin quantity) of recycled PVC
demonstrated favorable mechanical performance. However, higher
quantities lead to a substantial deterioration in the material's
mechanical properties, primarily due to the emergence of structural
defects. To refine the amount of recycled PVC used specifically for
this {floorcovering} application, an in-depth analysis was conducted by
meticulously adjusting the particle size distribution (PSD) through a
sequence of three distinct sieving processes. By achieving a PSD of
recycled PVC containing particles smaller than $200~\upmu \mathrm{m}$,
expanded layers of satisfactory quality can be produced using up to
86.67\% recycled PVC in relation to the total PVC resin quantity.
\end{abstract}

\begin{altabstract}
Ce travail se concentre sur les principes de l'\'{e}conomie circulaire
et de la durabilit\'{e} en explorant l'utilisation de poudre de
Polyvinyle Chlorure (PVC) recycl\'{e} comme alternative \`{a} la
r\'{e}sine de PVC classique dans la couche expans\'{e}e des
rev\^{e}tements de sol, tout en pr\'{e}servant leurs propri\'{e}t\'{e}s
m\'{e}caniques. Le premier d\'{e}fi consiste \`{a} convertir les
d\'{e}chets de tissu enduit de PVC en poudre, enti\`{e}rement
{s\'{e}par\'{e}e} des fibres de PET, tout en assurant la
r\'{e}cup\'{e}ration optimale des petites particules de PVC. Par la
suite, une analyse approfondie s'est concentr\'{e}e sur la
compr\'{e}hension du comportement et des caract\'{e}ristiques des
poudres de PVC recycl\'{e}.

Principalement, cette recherche explore l'impact des variations de la
teneur en PVC recycl\'{e} et des tailles de particules sur les
propri\'{e}t\'{e}s m\'{e}caniques (charge de rupture, r\'{e}sistance
\`{a} la d\'{e}chirure et allongement \`{a} la rupture) de la couche de
PVC expans\'{e} utilis\'{e}e dans les rev\^{e}tements de sol. Les
r\'{e}sultats ont montr\'{e} qu'une incorporation allant jusqu'\`{a} 25
g (33, 34 \% de la quantit\'{e} totale de r\'{e}sine de PVC) de PVC
recycl\'{e} pr\'{e}sente des performances m\'{e}caniques favorables.
Cependant, des quantit\'{e}s plus importantes entra\^{i}nent une
d\'{e}t\'{e}rioration significative des propri\'{e}t\'{e}s
m\'{e}caniques du mat\'{e}riau, principalement en raison de
l'apparition de d\'{e}fauts structuraux.

Pour affiner la quantit\'{e} de PVC recycl\'{e} utilis\'{e}e
sp\'{e}cifiquement pour ce rev\^{e}tement de sol, une analyse
minutieuse a \'{e}t\'{e} men\'{e}e en ajustant avec pr\'{e}cision la
r\'{e}partition des tailles de particules \`{a} travers une s\'{e}rie
de trois processus de tamisage distincts. En atteignant une
granulom\'{e}trie optimale des particules de PVC recycl\'{e},
inf\'{e}rieure \`{a} $200~\upmu \mathrm{m}$, il devient envisageable de
produire des couches expans\'{e}es de haute qualit\'{e} en utilisant
jusqu'\`{a} 86,67 \% de PVC recycl\'{e} par rapport \`{a} la
quantit\'{e} totale de r\'{e}sine de PVC.
\end{altabstract}

\maketitle

{\vspace*{.4pc}}

\twocolumngrid

\end{noXML}
\section{Introduction}\label{sec1}

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig01}
{\vspace*{2pt}}
\caption{\label{fig1}Different layers of PVC coated fabrics.}
{\vspace*{2pt}}
\end{figure*}


Coated textiles emerge through the application of a polymer coating
onto a textile substrate, resulting in a symbiotic fusion of 
materials.\pagebreak
The \mbox{different} components of a coated textile are important for the
overall properties of the final product~\cite{1,2,3,4,5,6,7}. The
choice of polymer exerts a direct impact on the textile's robustness,
longevity, and suppleness, shaping its fundamental properties.
Concurrently, the quantity of plasticizer integrated plays a pivotal
role in \mbox{determining} the textile's pliability. \mbox{Additionally,} the
selection of filler material wields authority over the textile's mass
and volume, contributing to its structural profile~\cite{4,5,6,7,8}.
The harmonious integration of these constituents culminates in the
creation of a plastisol, achieved through meticulous blending.
PVC-coated textiles are one of the most common types of coated
textiles. Renowned for their economical nature and adaptability,
PVC-coated textiles exhibit a remarkable resistance to moisture,
chemicals, and wear-induced abrasion. These textiles usually comprise a
tri-layered composition, as illustrated in Figure~\ref{fig1}:

\begin{itemize}
\item A thin PVC superficial layer, called the skin layer or
superficial layer, serves for aesthetic or technical enhancements.
\item A PVC expanded layer (foamed layer) that functions as a
sponge-like middle layer.
\item A textile substrate layer composed of PET fabric, which imparts
strength and durability to the material.
\end{itemize}

The different layers of a PVC-coated textile work together to provide
the material with its desired properties~\cite{4,5,6,7,8,9,10}. This
makes PVC-coated textiles a versatile material that can be used in a
variety of applications, such as footwear, automobiles, floorcovering
and wall coverings, upholstery, clothing, and many more. Tailoring the
manufacturing process to suit the requirements of the final product,
the polymeric layer is affixed directly (via direct coating) or
indirectly (via transfer coating) onto one or both surfaces of the
fabric~\cite{7,8}.

The polymer coating must adhere to the textile, and a doctor blade
controls the thickness of the viscous polymer. The coated fabric is
then heated and the polymer is cured (that is, polymerized). This is a
non-reversible process, which means that it is impossible to recover
plastisol from a PVC part after full fusion and complete curing has
taken place~\cite{11}.

The post-consumption disposal of PVC-coated fabrics as solid textile
waste is an environmental \mbox{pollution} source that is becoming a serious
problem recognized by society~\cite{11,12}. Manufacturers and consumers
of coated fabrics have suffered from the rise of this serious problem.
Recycling of PVC-coated fabrics is a solution that can help to reduce
the depletion of raw materials and energy, and eliminate or reduce
waste~\cite{11,12,13,14}.

Numerous studies~\cite{15,16,17} have underscored the preference for
mechanical recycling, particularly in managing identifiable PVC waste
since it ensures the consistent quality of reclaimed PVC and mitigates
the release of hazardous substances into the environment. However,
despite these inherent benefits, a noticeable gap in available
literature remains evident. Comprehensive data crucial for implementing
large-scale recycling strategies tailored to PVC-coated fabrics is
strikingly scarce, necessitating specialized approaches for recycling.

The challenges stem from the distinct properties of PET fabric and
plasticizer PVC, encompassing differences in melting temperatures,
densities, and hardness. As a result, conventional methods effective
for pure PVC cannot be seamlessly applied to PVC-coated fabric waste.
The amalgamation of PET fabric and plasticizer PVC during the recycling
process compromises their original properties and practical utility.
Consequently, the primary hurdle in recycling PVC-coated fabric waste
lies in efficiently separating the PET fibers from plasticizer
PVC~\cite{18}. By adopting circular principles, the conversion of
PVC-coated fabric waste into powder expands the possibilities for
recycling~\cite{19}. It can provide an alternative route to reutilize
the material by incorporating it into new products or processes,
thereby reducing the overall environmental impact of PVC waste.
Nevertheless, the handling of powders can be challenging, particularly
during processing, owing to the general presence of particles that are
frequently non-spherical and exhibit diverse shapes. To be able to
study the powder behavior properly, it is necessary to know the
characteristics of the particles, as well as the powder as a whole.

Understanding the particle size distribution (PSD) in powder systems
forms the bedrock of most manufacturing processes~\cite{20,21,22,23}.
Numerous studies~\cite{24,25,26,27} have emphasized the significance of
analyzing particle morphology to glean insights into powder behavior
across processing stages---compaction, flow, and dissolution. Edward
\etal~\cite{28} extensively investigated the impact of particle size
and distribution on viscosity, especially concerning shear rate and
time-dependent behavior. Their findings highlight that the presence of
coarse particles significantly alters paste flow, reducing viscosity at
low shear rates. Rasteiro \etal's study~\cite{29} conducted a
comparative analysis of various plastisol pastes, revealing higher
viscosities and modulus values with smaller PVC particles.
Additionally, Fischer \etal~\cite{30} emphasize the Gaussian
distribution of PVC powder size and stress the need to narrow this
distribution. Coarse fractions (${&gt;}$250~$\upmu \mathrm{m}$) led to
dispersion defects, while fines (${&lt;}$60~$\upmu\mathrm{m}$) caused powder
flow issues.

Rasteiro's research~\cite{31} underlines how particle characteristics,
particularly aggregate strength, significantly impact PVC plastisol
paste rheology. The type of aggregates in PVC powder determines the
particle size dynamics within the plastisol, directly influencing aging
behavior and viscoelastic properties. 

Similarly, Daniels~\cite{32} pointed out that optimizing the
rheological behavior of plastisol relies on meticulous selection of the
appropriate PVC distribution and shapes, as well as the type and
quantity of plasticizer, since this distribution is based on two
interactions. The first interaction occurs between the plasticizer and
PVC particles~\cite{20}. An effective plasticizer should adeptly forge
robust connections with the polymer. These connections wield influence
over various aspects of the plastisol formulation---such as size,
structure, distribution profile, and the agglomeration tendencies of
the PVC particles. The second interaction, known as the
inter-particulate PVC interaction, significantly impacts flow
characteristics~\cite{33,34}. Powders characterized by inadequate flow
often stem from heightened interparticle interactions~\cite{35},
originating from cohesive bonds between particles. Typically, elongated
shapes like rods or needles, deviating from spherical forms, tend to
exhibit inferior flow behavior~\cite{36}.

Mehdipour \etal~\cite{21} highlight that an increase in $K$-value
(indicative of molecular weight) correlates with heightened tensile
strength and elongation but also amplifies defect occurrence due to
reduced polymer chain mobility. Conversely, lower $K$-values lead to
better spreading and homogeneous plastisol with weaker mechanical
properties. Balancing defect mitigation and required mechanical
properties is crucial in tailored coating pastes~\cite{1}.

Marceneiro \etal~\cite{20} identified $K$-values ranging from 64 to 80 as
optimal for automotive interiors and floorcoverings. Moreover,
Pepperl~\cite{37} highlights how varying resin blends with diverse
$K$-values can effectively attain desired product properties,
particularly when the perfect resin is not accessible. This approach
proves successful, as long as the discrepancy between $K$-values remains
within a 10-unit range.

Other studies~\cite{3,4,5,38,39} have explored filler (calcium
carbonate CaCO$_3$) diameter and content impact on the mechanical
properties of PVC foam layers in coated textiles. Stambouli
\etal~\cite{5} observed negative structural impacts with excessive
CaCO$_{3}$ content (100 parts filler to 100 parts pure PVC resin) but
noted that smaller filler particle diameters improve mechanical
properties.

While prior research has delved into the rheological properties of
plastisol and its impact on the mechanical characteristics of
PVC-coated fabrics, the valorization of PVC-coated fabric waste through
incorporation into the plastisol formula, following its conversion into
powder and separation from the textile substrate, as a replacement for
PVC resin, has yet to be explored.

This study is dedicated to advancing current knowledge by pioneering a
specialized mechanical process tailored to convert PVC-coated fabric
waste into distinct PVC powder, effectively separated from PET fibers.
The primary goal is to not only develop this process but also delve
deeper into the characteristics of the derived PVC powders,
meticulously examining particle morphology and size distribution.

Within this research scope, our strategic direction was carefully
chosen following extensive consultations with the company's leadership.
Our focus lies within the domain of floorcoverings, aiming to integrate
this repurposed PVC material into the plastisol formula, replacing the
traditional PVC resin. This substitution aims to create a floorcovering
article that embodies sustainability without compromising quality. The
core of our endeavor revolves around investigating how the recycled PVC
content and particle size influence crucial mechanical properties such
as Break Strength (BS), Elongation at Rupture (ER), and Tear
Resistance (TR) of the expanded layer, essential in floorcovering
production.
\vspace*{-3pt}

\section{Materials and methods}\label{sec2}
\vspace*{-3pt}
\subsection{Raw materials}\label{sec21}

For articles intended for floorcovering, the formulations used to
produce PVC sheets (surface and expanded layers) are shown in
Table~\ref{tab1}. The different ingredients were kindly provided by the
PLASTISS company (Sayada, Monastir, Tunisia).

The plastisol formulation relies on ingredient proportions, measured in
parts per hundred of resin (phr). In the superficial layer, 100 parts
of PVC resin (with particles sized at 100~$\upmu \mathrm{m}$ and a
$K$-value of 66) are combined with 80 parts of plasticizer (DINP), 25
parts of filler (CaCO$_{3}$), and 1.5 parts of stabilizers (Ca/Zn).
Conversely, the expanded layer presents a distinct composition,
integrating a chemical \mbox{blowing} agent (azodicarbonamide) and a kicker
expansion accelerator (potassium--zinc K/Zn), both pivotal in shaping
the foam structure. These elements undergo meticulous blending using a
mechanical stirrer to ensure homogeneity, meeting the company's
specified viscosity standards. At PLASTISS, the targeted viscosity for
the surface layer stands at around 27,000 (${\pm}$900)
$\mathrm{Pa}{\cdot}\mathrm{s}$, while the expanded layer aims for
25,000 (${\pm}$500) $\mathrm{Pa}{\cdot}\mathrm{s}$. \vspace*{-5pt}

\subsection{Preparation of PVC-coated fabric}\label{sec22}
\vspace*{-3pt}

To prepare the samples, we used the lab-coaters method that operate
discontinuously. Samples with a maximum size of DIN A 4 can be produced
with this method because such a machine is only the size of a common
stove. But it enables us to get a first idea and to give a general
statement regarding the raw material and its temperature
reaction~\cite{4,5,6}.

We used the transfer coating technique for the production of PVC-coated
textiles. On the first coating head, the plastisol is spread on the
transfer paper using a blade while controlling the thickness
(Figure~\ref{fig2}a). The formed layer, superficial layer, is then
dried at 140~\textdegree C~for 20~s and cooled. On the second
coating head, the plastisol is spread on the first formed layer using a
blade at a given thickness. This second layer forms a foam after being
dried at 200~\textdegree C~for 80~s and is called the expanded
layer (Figure~\ref{fig2}b). Later, the textile substrate layer is
laminated to the resulting PVC layers (Figure~\ref{fig2}c), and the
complex thus formed is passed through the main furnace where gelling
and expansion of the cellular plastisol take place. After cooling, the
paper and the formed PVC-coated textile are detached and rolled up
separately (Figure~\ref{fig2}d). 

\begin{figure*}
\includegraphics{fig02}
\caption{\label{fig2}Depicts a typical coating process.\vspace*{-5pt}}
\end{figure*}

\subsection{SMF plastic pulverizer}\label{sec23}

Carthage Plastique company's pulverizer (Kaala Seghira, Soussa,
Tunisia) was used during this study. The plastic pulverizer machine is
chiefly designed to grind PVC and fibers in micronized form. This
pulverizer uses a high-speed rotor. This rotor, consisting of several
sections of discs and several blades, is responsible for grinding PVC
waste into a fine powder. Its output can reach 70--350~kg/h
(20--120~mesh). In this process, the utilization of a vibrating sieve
is crucial to ensure the desired output size. The vibrating sieve
comprises two outlets: the fine powder outlet ``7'' and the coarse
powder outlet ``6'' (Figure~\ref{fig3}). The fine particles that
successfully pass through the sieve mesh are collected at the fine
powder outlet ``7''. On the other hand, the coarse powders that are
retained by the sieve are directed to the milling chamber for further
grinding, utilizing the coarse powder outlet~``6''.

\begin{figure*}
\includegraphics{fig03}
\caption{\label{fig3}Plastic Pulverizer.}
\end{figure*}

\begin{table*} %tab1
\caption{\label{tab1}Superficial and expanded layer formulations}
\begin{tabular}{lcccccc}
\thead
Layer  &amp; \parbox[t]{1.7cm}{\centering PVC resin (g)} &amp;
\parbox[t]{1.5cm}{\centering Plasticizer (g)} &amp; 
\parbox[t]{1.5cm}{\centering Stabilizer (g)} &amp;
\parbox[t]{2cm}{\centering Calcium carbonate~(g)} &amp; 
\parbox[t]{1cm}{\centering Kicker (g)} &amp; 
\parbox[t]{2.8cm}{\centering Azodicarbonamide (g)}\vspace*{2pt}\\
\endthead
{Superficial}  &amp; 100 &amp; 80 &amp; 1.5 &amp; 25 &amp; - &amp; - \\
{Expanded}  &amp; \075 &amp; 50 &amp; - &amp; 50 &amp; 2 &amp; 4
\botline
\end{tabular}
\end{table*}

Regarding the PVC-coated fabric scraps, the fine powder particles are
directed through the vibrating sieve with the assistance of air flow
and collected in the product collector located at the fine powder
outlet  ``7'', designated as outlet P. However, the PET fibers, which
are retained by the sieve, are vacuumed and subsequently recovered in a
cloth bag connected to the coarse powder outlet  ``6'', identified as
outlet F (Figure~\ref{fig4}).

\begin{figure*}
\includegraphics{fig04}
\caption{\label{fig4}Pulverizer outlets: (a)~Recovered PVC powders
(outlet P).  (b)~Recovered fibers (outlet F).}
\end{figure*}

\subsection{Desirability function}\label{sec24}

The desirability function approach is one of the most widely used
methods in industry for the optimization of multiple-response
processes~\cite{40}. For each response $Y_i(x)$, a desirability
function $d_i(Y_i(x))$ assigns numbers between 0 and 1 to the
possible values of $Y_i$~\cite{40,41,42,43,44,45}.

Different functions may be built, depending on the optimization
criteria adopted, within an acceptable range of response values given
by ($U_i-L_i$), where $U_i$ is the upper acceptable value for the
response and $L_i$ is the lower. Thus, if the response has to be
maximized, $d_i(Y_i(x))$ is described by the following
equation~\cite{43,44,45}:
{\begin{equation}\label{eq1}
d_{i}\left(Y_{i}(x)\right)=\left\{\begin{array}{c@{\quad}l}
0 &amp; \mbox{ if } Y_{i}(x)&lt; L_{i}\\
\displaystyle\left(\frac{Y_{i}(x)-L_{i}}{U_{i}-L_{i}}\right)^{s} 
&amp;\mbox{ if }L_{i}\leq Y_{i}(x)\leq U_{i}\\
1 &amp;\mbox{ if }  Y_{i}(x)\geq U_{i}
\end{array}\right\}
\end{equation}}\noindent
where ${s}$ is a power value named weight, set by the analyst to
determine how important it is for $Y_i$ to be close to the maximum. 

When it has to be minimized, the equation for $d_i(Y_i)$
is~\cite{43,44,45}:
{\begin{equation}\label{eq2}
d_{i}\left(Y_{i}(x)\right)=\left\{\begin{array}{c@{\quad}l}
1 &amp;\mbox{ if }Y_{i}(x)&lt; L_{i}\\
\displaystyle\left(\frac{U_{i}-Y_{i}(x)}{U_{i}-L_{i}}\right)^{t}
&amp;\mbox{ if }L_{i}\leq Y_{i}(x)\leq U_{i}\\
0&amp; \mbox{ if }  Y_{i}(x)\geq U_{i}
\end{array}\right\}
\end{equation}}\noindent
where ${t}$ is the weight to determine how important it is for $Y_i$ to
be close to the minimum.

Finally, when a target value $T_i$ (with~$L_i\leq T_i \leq U_i$) is the
most desirable response, the function is given by~\cite{43,44,45}:
{\begin{equation}\label{eq3}
d_{i}\left(Y_{i}(x)\right)=\left\{\begin{array}{c@{\quad}l}
0 &amp;\mbox{ if }Y_{i}(x)&lt; L_{i}\\
\displaystyle\left(\frac{Y_{i}(x)-L_{i}}{T_{i}-L_{i}}\right)^{s}
&amp;\mbox{ if }L_{i}&lt; Y_{i}(x)&lt; T_{i}\\
1 &amp; \mbox{ if } Y_{i}(x)=T_{i}\\
\displaystyle\left(\frac{Y_{i}(x)-U_{i}}{T_{i}-U_{i}}\right)^{t}
&amp;\mbox{ if }T_{i}&lt; Y_{i}(x)&lt; U_{i}\\
0 &amp;\mbox{ if } Y_{i}(x)&gt; U_{i}
\end{array}\right\}
\end{equation}}\noindent
with the exponents~$\mathbi{s}$ and $\mathbi{t}$ determining how
important it is to hit the target value. 

The overall desirability function $D$ is defined as the geometric
average of the individual desirability functions of each
response~$d_i(Y_i)$: 
{\begin{equation}\label{eq4}
D={\left({d}_{1}^{r_{1}}\times {d}_{2}^{r_{2}}\times \cdots \cdots 
\cdot{d}_{n}^{r_{n}}\right)^{\sfrac{1}{n}}}=
\left(\prod_{i=1}^{n}\left({d}_{i}^{r_{i}}\right)\right)^{\sfrac{1}{n}}
\end{equation}}\noindent
where $n$ is the number of responses. 

The weighting coefficients ($r_i$) are used to emphasize certain
parameters over others, depending on their significance in determining
the overall quality~\cite{43,44,45}. 

\subsection{Test sieves shaker}\label{sec25}

Machine sieving is carried out by stacking the sieves in ascending
order of aperture size and placing the powder on the top sieve. 

Results are usually expressed in the form of a cumulative percentage of
the nominal sieve aperture. The sieves used for the analyses are RETSCH
standard sieves.                                                       


A sample (100~g) of the powder is placed on the top sieve. This sieve
set, containing openings of various sizes (1, 0.8, 0.6, 0.4, 0.3, 0.2,
0.09, 0.02~mm), is fixed to the mechanical shaker apparatus and shaken
(amplitude 1.2~mm) for 20~min. The powder retained on each sieve is
weighed. Then, the loss of mass was monitored every 1~min
by measuring the weight until no significant change was detected (less
than 0.1\% of the total feed) between two consecutives measurements.
After the sieving process, the data are evaluated, the sample material
is recovered and the sieves are thoroughly cleaned.

\subsection{Tensile and elongation tests}\label{sec26}

Tensile and elongation tests have been carried out according to NF EN
ISO 1421-2017 standards utilizing a testing machine (Zwich GmbH, Ulm,
Germany) with a crosshead speed of 100~mm/min. Test specimens had
dimensions of 50~mm ${\pm}$ 0.5 in width with a sufficient length to
obtain a distance of 200~mm ${\pm}$ 1 between the jaws of the testing
machine. For the reproducibility of the results, the test was
replicated three times.

\subsection{Tearing strength}\label{sec27}
Tearing strength test has been performed according to NF EN ISO
4674-1-2017 using an ELMENDORF dechirometer. Tests have been run in
triplicate to avoid experimental error.

\subsection{Optical microscopy}\label{sec28}

Morphology and structure of the expanded PVC layers have been observed
using Leica DM 500 optical microscope equipped with different
objectives connected to a camera and controlled by analysis software.
The materials have been observed in reflected light under different
magnifications of the objective. 

To ensure accurate characterization of the particle images, it was
necessary to utilize magnification and numerical aperture settings that
provided sufficient resolution. The magnification factors employed
ranged from 6.3$\times$ to 40$\times$, with the commonly used eyepieces
typically set at 10$\times$--40$\times$.


\section{Results and discussion}\label{sec3}

\subsection{Mechanical recycling process}\label{sec31}


\subsubsection{Grinding process of PVC-coated fabric scraps}\label{sec311}
The process of obtaining PVC powder from PVC-coated fabric scraps
involves several stages of cutting and grinding. Initially, the waste
PVC-coated PET fabric is cut into small pieces using a band saw,
ensuring that their dimensions are suitable for the subsequent steps
and equipment, with a maximum dimension of 1~m$^{2}$.

Subsequently, a first grinding process is conducted using a plastic
waste grinder machine to crush the PVC-coated fabric component and
generate a bulk mixture, typically ranging between 10 and 15~mm in
size. During this stage, the PVC remains combined with the PET knit,
and they are not yet separated from each other.

Next, a second grinding process is employed using a pulverizer. This
process further shreds the plasticized PVC component, resulting in the
production of fine PVC powders that are effectively separated from the
PET fabric. An additional advantage of this grinding process,
particularly with the involvement of a pulverizer, is its capability to
not only grind the coated fabric scraps into PVC powder but also to
separate them from PET fibers.

The following section presents a comprehensive quantitative analysis
conducted to investigate the effectiveness of separation between PET
fibers and PVC powder.

\subsubsection{Quantitative analyses using chemical\newline
\mbox{separation}}\label{sec312}

To determine the average weights of PET fibers and plasticized PVC in
each outlet (PVC powder outlet P and fiber outlet F) after
pulverization, the chemical separation method, which involves
solubilizing the PVC in Tetrahydrofuran (THF), was employed~\cite{46}.
To ensure accuracy, the experiments were conducted three times.

According to the chemical separation results (Table~\ref{tab2}), the
quantity recovered from outlet P primarily comprises PVC powder,
accounting for approximately 92\%. On the other hand, outlet F contains
a percentage of residual PVC, reaching 25.08\%, while the quantity of
PET fibers amounts to approximately 72\%. 

\begin{table*} %tab2
\caption{\label{tab2}Different amounts of PET fibers and PVC powder
after pulverizations}
\begin{tabular}{c}
\tbody
\inlinefig{fx01}
%\begin{tabular}{lcccc}
%\thead
%\multicolumn{2}{c}{Outlet}  &amp; Average (g)  &amp; Percent (\%)  &amp; CV (\%)\\
%\endthead
%\morerows{1}{\parbox[t]{2.5cm}{\raggedright PVC powder outlet (P) $=$ 50 g}}  &amp; Fibers  &amp; \03.07 &amp; \cellcolor[gray]{0.88} \06.15 &amp; 18.51 \\
% &amp; PVC  &amp; 46.19 &amp; \cellcolor[gray]{0.88}92.39 &amp; \02.62 \\
%\raisebox{1pc}{}
%\morerows{1}{\parbox[t]{2cm}{\raggedright Fiber outlet (F) $=$ 50 g}}  &amp; Fibers  &amp; 36.09 &amp; \cellcolor[gray]{0.88}72.17 &amp; \04.32 \\
% &amp; PVC  &amp; 12.54 &amp; \cellcolor[gray]{0.88}25.08 &amp; \05.80
%\botline
\end{tabular}
\tabnote{CV: Coefficient of variation.}
\end{table*}

Therefore, it can be concluded that the separation between PET fibers
and the PVC powder recovered from both pulverized outlets (outlet P and
outlet F) is not perfect, even though the PET fibers' percentage in the
powder does not exceed 6.15\% for outlet P. The presence of PVC
alongside PET fibers significantly compromises the quality of the
recycled material due to the distinct properties of these two
components. Consequently, the grinding process alone is insufficient
for reusing PVC-coated fabric scraps.

\subsubsection{Sieving separation}\label{sec313}

To achieve complete separation between PVC powder and PET fibers, a
supplementary \mbox{mechanical} sieving using a 1~mm aperture sieve was
implemented. This efficient separation was corroborated by the chemical
analysis, which demonstrated that approximately 90\% of the PVC powders
were successfully recovered through sieving, while all the PET fibers
were retained by the sieve. These results provide strong evidence of
achieving a complete separation of PVC powder (Figure~\ref{fig5}).

\begin{figure*}
\includegraphics{fig05}
\caption{\label{fig5}Process map of grinding supplemented by sieving.}
\end{figure*}

The combination of the mechanical process (cutting, grinding,
pulverization) along with sieving (Figure~\ref{fig5}) proves to be a
straightforward, cost-effective, environmentally friendly, and
potentially profitable approach. 

The results obtained compellingly substantiate mechanical recycling as
a practical methodology for safeguarding the intrinsic value of
PVC-coated fabric, while simultaneously upholding the material's
chemical structure and compositional integrity (especially the $K$-value
of PVC). 

\subsection{Particle morphology of recycled PVC
\newline\mbox{powders}}\label{sec32}

\subsubsection{Particle shape}\label{sec321}

Particle shape influences the bulk properties of powders, such as flow
behavior and the viscosity of suspensions~\cite{33,34,47}. Through
initial microscopic observations, a clear differentiation among various
non-spherical particle shapes was achieved, as depicted in
Figure~\ref{fig6}.

\begin{figure}
{\vspace*{-2pt}}
\includegraphics{fig06}
{\vspace*{-2pt}}
\caption{\label{fig6}Particle images acquired by optical microscopy
(magnification 10$\times$).}
{\vspace*{-2pt}}
\end{figure}


As stated by Hamilton~\cite{27}, powders comprising flat and elongated
particles frequently display elevated porosity and reduced flow
characteristics due to heightened inter-particle friction, leading to
the development of shear surfaces. Consequently, as highlighted in
previous studies~\cite{20,21,22,23,24,25}, powders exhibiting
inadequate flow properties are susceptible to cluster formation,
hindering the effective dispersion of these powders.


\subsubsection{Particle size distribution}\label{sec322}
Understanding the distribution of particle sizes across different
dimensions~\cite{24,26} is of crucial importance. Firstly, these
characteristics exert substantial influence over the physical behavior
of the powder, particularly affecting its flowability---a crucial
factor that signifies the powder's ability to move uniformly and
consistently. Simultaneously, the impact of PVC particle distribution
extends beyond the rheological properties of plastisols, playing a
pivotal role in establishing the necessary processing conditions to
achieve the desired characteristics in the final product~\cite{29}.
\looseness=-1

Sieve analysis stands as a traditional and extensively employed
technique for particle size determination. In this method, the sieves
are weighed empty and then with the oversize PVC particles after the
sieving process. The difference between these measurements represents
the weight of the individual fractions. The PSD was measured in
triplicate and is reported in Table~\ref{tab3}.

\begin{table*} %\tab3
\caption{\label{tab3}Summary for particle size distribution (PSD) study}
\begin{tabular}{ccccccccccc}
\thead
{Sieve size (mm)} &amp; \0\0{1} &amp; {0.8} &amp; {\00.6\0} &amp; {0.4} &amp;
{0.3} &amp; {0.2} &amp; {0.09} &amp; {0.02} &amp; {Pan} &amp; {Total} \\
\endthead
Average &amp; \0\00 &amp; 0.4 &amp; \03.2\0 &amp; 23.7\0 &amp; 32.8\0 &amp; 26.6\0 &amp; 12.65 &amp; 0.25 &amp; 0 &amp; 99.6 \\
{CV\%} &amp; \0\00 &amp; 10 &amp; \09.75 &amp; \01.98 &amp; \02.47 &amp; \02.85 &amp; \02.87 &amp; 14.42 &amp; 0 &amp;   \\
{Cum. Weight retained} &amp; \0\00 &amp; 0.4 &amp; \03.6\0 &amp; 27.3\0 &amp; 60.1\0 &amp; 86.7\0 &amp; 99.35 &amp; 99.6 &amp; 99.6 &amp;  \\
{\%Weight retained} &amp; \0\00 &amp; 0.40 &amp; \03.21 &amp; 23.80 &amp; 32.93 &amp; 26.71 &amp; 12.7\0 &amp; 0.25 &amp; 0 &amp;  \\
{\% Retained} &amp; \0\00 &amp; 0.40 &amp; \03.61 &amp; 27.41 &amp; 60.34 &amp; 87.05 &amp; 99.75 &amp; 100 &amp; 100 &amp;  \\
{\% Finer} &amp; 100 &amp; 99.6 &amp; 96.39 &amp; 72.59 &amp; 39.66 &amp; 12.95 &amp; \00.25 &amp; 0 &amp; 0.00 &amp; 
\botline
\end{tabular}
\xxtabnote{CV: Coefficient of variation.}
\end{table*}

Table~\ref{tab3} offers a comprehensive overview of a PSD analysis via
the sieving process. It encompasses multiple essential elements crucial
for characterizing the PSD, including individual and cumulative
percentages. By graphically depicting these two integral components, a
coherent and structured portrayal of the PSD study is achieved,
enhancing clarity and facilitating interpretation.

These graphs (see Figure~\ref{fig7}) offer a rapid and intuitive means
to comprehend the distribution of particle sizes within the sample.
They facilitate the discernment of underlying trends and the derivation
of overarching conclusions regarding the particle size characteristics
as a whole.

\begin{figure}
\includegraphics{fig07}
\caption{\label{fig7}Frequency distribution curve and Cumulative
distribution curve.}
\end{figure}

The individual percentages (weight retained) denote the proportion of
particles retained at each specific sieve aperture. By analyzing these
percentages, one can glean profound insights into the size distribution
across different sieve openings. As illustrated in Figure~\ref{fig7},
the preeminent percentages are evident for values such as 0.2, 0.3, and
0.4~mm. This observation signifies that the majority of particles
possess sizes falling between these values, with respective proportions
of 26.71\%, 32.93\%, and 23.80\%.

The cumulative distribution curve (percent of passing) is obtained by
adding up the individual fractions and interpolating between the points
of \mbox{measurement} (Figure~\ref{fig7}). The cumulative {percentages} provide a
broader perspective on the overall PSD within the sample. They indicate
the total percentage of particles retained up to a specific sieve
aperture, enabling a comprehensive assessment of the particle
distribution across various sizes within the entire sample.
Figure~\ref{fig7} shows that the majority of particles are smaller than
$600~\upmu \mathrm{m}$, representing 96.39\% of the total. The greatest
fraction (83.44\%) is in the size range between 200 and $600~\upmu
\mathrm{m}$.

{\vspace*{-2pt}}

\subsection{Quality characterization of the floorcovering product}\label{sec33}

{\vspace*{-2pt}}

\subsubsection{Parameter selection}\label{sec331}

{\vspace*{-2pt}}

In this study, we aim to comprehensively characterize the quality of
floorcovering products by assessing various properties that determine
their performance and user satisfaction. To achieve this, we have
gathered valuable information from client requirements and
specifications, and collaborated closely with PLASTISS company
executives. Through this collective effort, we have successfully
identified the essential properties that define the specific PVC-coated
fabric used for floorcoverings. Among these distinctive requirements,
the mechanical facets hold paramount significance, with a particular
focus on pivotal parameters like {BS, ER, and TR}. As we advance toward
the incorporation of recycled PVC powder as a sustainable alternative
to conventional PVC resin for the fabrication of floorcoverings, it is
imperative to maintain the same high-quality standards expected from
this finished product. Therefore, particular attention will initially
be devoted to preserving the quality of the expanded layer after
incorporating the recycled PVC powder. The surface layer, which is more
demanding in terms of mechanical properties, will retain the same
standard recipe.

{\vspace*{-1pt}}

\subsubsection{Upper and lower limits for each parameter}\label{sec332}

In order to convert product quality parameters to a common scale, the
upper and lower limits of each parameter must be identified. The lower
and upper limit useful for the product quality parameters are based on
the experimental results, the theoretical knowledge and the opinion of
the experts who participated in the survey. For the experimental study,
20 samples of the expanded layer were produced using the standard
PLASTISS formulation. Subsequently, various mechanical tests (BS, ER,
and TR) were conducted. Among the results obtained, the smallest value
was considered as the minimum threshold, while the average value was
considered as the target value. The results found are illustrated in\break
Table~\ref{tab4}. 

Upon reviewing Table~\ref{tab4}, it becomes evident that the expanded
layer's ER must fall within the range of 75\% to 150\% for optimal
performance. Striking a balance is crucial, as excessive flexibility
could undermine the quality of the final product. Our target values for
this parameter are set between 100 and 125\%. On the contrary, both BS
and TR are parameters that warrant maximization. We establish 15 N as
the minimum acceptable value for BS and 0.5 N as the minimum acceptable
value for TR. By adhering to these guidelines, we can ensure the
enhanced quality and durability of the end product.

{\vspace*{-2pt}}


\subsubsection{Desirability functions for individual\newline
\mbox{parameters}}\label{sec333}
Figure~\ref{fig8} visually illustrates the desirability functions for
each parameter, namely BS, TR, and ER. These functions provide a
comprehensive understanding of how each parameter performs in relation
to its ideal value. By incorporating the desirability function, we can
make informed decisions, striking an optimal balance between the
different parameters to achieve an overall high-quality product.

\begin{figure*}
\includegraphics{fig08}
\caption{\label{fig8}Graphical representation of Individual desirability
functions.}
\vspace*{6pt}
\end{figure*}

\begin{table*} %tab4
\caption{\label{tab4}Classification of expanded layer\vspace*{3pt}}
\begin{tabular}{cccc}
\thead
{Parameters} &amp; {Minimum value} &amp; {Target value} &amp; {Maximum value} \\
\endthead
{Break strength (N)}  &amp; 15 &amp; 20 &amp; - \\
{Elongation at rupture (\%)}  &amp; 75 &amp; 100--125 &amp; 150 \\
{Tear resistance (N)}  &amp; 0.5 &amp; 0.8 &amp; - 
\botline
\end{tabular}
\vspace*{6pt}
\end{table*}

{\vspace*{-1pt}}


\subsubsection{Weighting coefficients}\label{sec334}
In order to assess the importance of attaining the target value, a
comprehensive weighting scale should be implemented~\cite{44}.
According to Candioti~\cite{45}, the importance, established by the
analyst, may vary from 1 for the least important variable to 5 for the
most important one. 

This research, carried out at PLASTISS, greatly benefited from the
invaluable expertise of the company's specialists who meticulously
assigned these weightings. Notably, they placed particular emphasis on
two vital factors: BS and TR, ranking these aspects above ER.
Table~\ref{tab5} summarizes the weights assigned to the various
properties of the expanded layer.

\begin{table} %tab5
\caption{\label{tab5}Assignment of weights to the various properties
studied}
\begin{tabular}{cc}
\thead
{Properties}  &amp; {Weights ($r_{i}$)} \\
\endthead
{Break strength (N)} &amp; 5 \\
{Elongation at rupture (\%)} &amp; 3 \\
{Tear resistance (N)}  &amp; 5
\botline
\end{tabular}
\end{table}

{\vspace*{-1pt}}


\subsubsection{The overall desirability function $D$}\label{sec335}

In order to identify the most high-performing product, we have
established specific criteria, drawing on the valuable insights of
PLASTISS\break experts:
{\setlength{\fboxsep}{1.5pt}
\begin{itemize}
\item \raisebox{-.1pc}{\inlinefig{fx02}} denotes unacceptable
product quality (rejected product).
\item \raisebox{-.1pc}{\inlinefig{fx03}} indicates a considerable
deviation from the target value of 1, suggesting one or more properties
in need of improvement (can be accepted as Second-quality article).
\item \raisebox{-.1pc}{\inlinefig{fx04}} can be accepted as
First-quality article.
\item \raisebox{-.1pc}{\inlinefig{fx05}} signals Premium quality product.
\end{itemize}
}
The $D$ value closest to 1 reflects the utmost desirability in terms of
quality.

By adhering to these well-considered conditions, we can effectively
identify and promote the most desirable products in our evaluations.

\subsection{Reuse of recycled PVC to produce
\newline\mbox{floorcovering} products}\label{sec34}
The cumulative distribution curve shown in Figure~\ref{fig7} is used
for this initial study.

\subsubsection{Preparation of expanded layer formulations}\label{sec341}

In order to uphold the exacting standards requisite for the final
product's quality and achieve a consistent benchmark across all
floorcovering articles, it is imperative that we maintain specific
properties of the expanded layer. These properties, including viscosity
($25{,}000 \,{\pm}\, 500~\mathrm{Pa}{\cdot}\mathrm{s}$) and thickness (1.5~mm),
play a pivotal role in ensuring the desired performance and
characteristics of the end product.

The formulations used to produce the expanded layers are presented in
Table~\ref{tab1}. All ingredients were thoroughly blended using a
mechanical stirrer until achieving a homogeneous mixture with the
targeted viscosity of 25,000 (${\pm}$500) $\mathrm{Pa}{\cdot}\mathrm{s}$. 

The optimization process will focus on the formulation of the expanded
layer, involving variations in the quantity of recycled PVC particles
(5, 15, 25, 35 and 45~g).

However, incorporating recycled PVC particles into the expanded layer's
formulation results in a decrease in viscosity. The viscosity of the
plastisol is primarily influenced by the plasticizer content~\cite{24}.
Consequently, to attain the desired viscosity level of approximately
25,000 (${\pm}$500)~$\mathrm{Pa}{\cdot}\mathrm{s}$, which facilitates
effortless handling of the mixture, adjustments to the plasticizer
content ($z$) is necessary when increasing the proportion of recycled
PVC particles ($x$) in the expanded layer's composition. In fact, the
quantity of recycled PVC particles is directly correlated with the
quantity of plasticizer required to maintain the desired viscosity.
Table~\ref{tab6} summarizes the various tests carried out.

\begin{table*} %tab6
\caption{\label{tab6}Expanded layer formulations}
\begin{tabular}{ccccccc}
\thead
\xmorerows{1}{Test}&amp; \multicolumn{2}{c}{PVC (g)} &amp; 
\morerows{1}{\parbox[t]{2cm}{\centering Plasticizer ($z$) (g)}} &amp; 
\morerows{1}{\parbox[t]{2cm}{\centering Calcium carbonate (g)}} &amp; 
\morerows{1}{\parbox[t]{1cm}{\centering Kicker (g)}}&amp;
\morerows{1}{\parbox[t]{2.8cm}{\centering Azodicarbonamide (g)}}
\vspace*{2pt} \\\cline{2-3}
 &amp;Recycled PVC ($x$) &amp; PVC resin ($y$)  &amp; &amp; &amp;  &amp; \\
\endthead
{Test 1} &amp; \00 &amp; 75 &amp; 50  &amp; 50 &amp; 2 &amp; 4 \\
{Test 2} &amp; \05 &amp; 70 &amp; 50 &amp; 50 &amp; 2 &amp; 4 \\
{Test 3} &amp; 15 &amp; 60 &amp; 55  &amp; 50 &amp; 2 &amp; 4 \\
{Test 4} &amp; 25 &amp; 50 &amp; 60  &amp; 50 &amp; 2 &amp; 4 \\
{Test 5} &amp; 35 &amp; 40 &amp; 70 &amp; 50 &amp; 2 &amp; 4 \\
{Test 6} &amp; 45 &amp; 30 &amp; 80 &amp; 50 &amp; 2 &amp; 4
\botline
\end{tabular}
\end{table*}

When 5~g of recycled PVC (equivalent to 6,67\% of the total PVC added)
was added (Test 2), the amount of plasticizer needed to maintain a
viscosity of 25,000 (${\pm}$500)~$\mathrm{Pa}{\cdot}\mathrm{s}$ was the
same as Test 1 (50~g). However, upon introducing quantities exceeding
15~g of recycled PVC, a progressive augmentation of plasticizer amount
by 5~g was noted. This incremental rise escalated to 10~g as the
recycled PVC quantity reached 35~g (46.67\% of the total PVC).

The increase in the plasticizer quantity can be attributed to the
insufficient flowability of the recycled PVC powder, which emanates
from the distinctive shape and dimensions of its particles, hindering
smooth movement~\cite{20}. These findings are confirmed by
Daniels~\cite{32}, who proves that plastisols inadequately dispersed
often exhibit agglomerated resin particles, leading to
higher-than-anticipated viscosities due to robust interactions among
the PVC particles.

These interpretations align with microscopic observations
(Figure~\ref{fig6}) that unveiled the presence of flattened and
elongated particles within the powder, leading to pronounced porosity
and restricted flowability due to heightened inter-particle friction. 

The same phenomenon was observed by Stambouli \etal~\cite{5}, who
showed that an excessive \mbox{quantity} of CaCO$_{3}$ (100 parts filler to
100 parts pure PVC resin) led to insufficient dispersion within the
plastisol, thereby compromising the adhesion between the PVC matrix and
the filler.

\subsubsection{The effect of recycled PVC content}\label{sec342}

\paragraph{Using microscopic observation}\label{sec3421}
The microscopic images presented in Figure~\ref{fig9} offer valuable
insights into the impact of recycled PVC on the foam structure of the
expanded layer. 

\begin{figure*}
\vspace*{-3pt}
\includegraphics{fig09}
\vspace*{-3pt}
\caption{\label{fig9}Effect of recycled PVC content on the structural
properties of the expanded layer: (a)~without recycled PVC; 
(b)~with 5~g; (c)~with 15~g; (d)~with 25~g; (e)~with 35~g; (f)~with 45~g.
(Magnification $6.3\times$).}
\vspace*{-3pt}
\end{figure*}

Figure~\ref{fig9}a illustrates the cross-section of expanded layer
prepared at optimum conditions (without recycled PVC), displaying a
sponge-like micropore structure characterized by uniform bubbles. These
bubbles form through two key stages of the foaming process: bubble
nucleation and growth~\cite{8,9}.

As the quantity of recycled PVC increases, noteworthy changes occur
within the foam. The bubbles grow larger, and the structural integrity
begins to suffer. Notably, when the recycled PVC reaches 35~g, the foam
structure experiences significant degradation, which worsens with 45~g,
revealing the emergence of micro defects such as inclusions,
microcracks, macropores, etc~\cite{37}. This degradation can be
attributed to the inadequate dispersion of the recycled PVC within the
plastisol, which leads to poor adhesion. Moreover, excessive amounts of
recycled PVC tend to clump together to form clusters that prove
challenging to adequately incorporate into the plastisol. These
clusters induce heterogeneities and non-uniform stress transfer within
the plastisol, which lead to the formation of defects, notably
microvoids and cracks (Figure~\ref{fig9}e,f).


Interestingly, these findings corroborate the observations of various
independent studies~\cite{24,25,26,27,28,37,40}. As a result, it is
unfortunate that an excess of \mbox{recycled} PVC will not yield the desired
dispersion within the foam structure, despite employing a highly
effective mixing technique in PLASTISS.

\paragraph{Using mechanical properties}\label{sec3422}

Figure~\ref{fig10} illustrates the results of BS (N), TR (N) and ER
(\%) measurements for expanded layer samples at different amounts of
recycled PVC.

\begin{figure*}
\vspace*{-1pt}
\includegraphics{fig10}
\vspace*{-1pt}
\caption{\label{fig10}\fontsize{9.7}{12}\selectfont
Effect of Recycled PVC content on the mechanical
properties of PVC expanded layer (a)~Break Strength (N), (b)~Tear
Resistance (N), (c)~Elongation at Rupture (\%). Black scale bar:
without recycled PVC and representing the reference value (at 100\%) to
compare the evolution after incorporation of recycled PVC.}
\end{figure*}


Black scale bar: without recycled PVC and representing the reference
value (at 100\%) to compare the evolution after incorporation of
recycled\break PVC.


The mechanical results demonstrate that adding a quantity of recycled
PVC not exceeding 25~g (33.34\%) leads to a tolerable decrease in BS
(17.5 N, which represents 79.5\% of reference without recycled PVC) and
TR (0.69N, which represents 57.5\%) since these \mbox{values} remain within
acceptable ranges and exceed the minimum required values (15N for BS
and 0.5N for TR). However, a slight increase in ER was observed for the
samples with 15~g (20\%), and 25~g (33.34\%) of recycled PVC. This
slight increase could be attributed to the additional plasticizer
amount, which enhances flexibility and elasticity by affecting the
polymer's initial structure~\cite{26}. 

These mechanical properties, however, deteriorate rapidly as the added
quantity of recycled PVC exceeds 25~g (Figure~\ref{fig10}). More
critical, when the amount of recycled PVC reaches 45~g (60\%), all
three mechanical properties drop dramatically, recording very low
values of 6 N (27.3\%), 0.2 N (16.7\%) and 35\% (33.3\%), respectively,
for BS, TR and ER.

Saffert~\cite{11} proved the same point when he used PVC particles
inseparable from the textile \mbox{backing} after grinding the tarpaulins.
This ground material was used as a ``filler'' in plastisol. The results
revealed a rapid deterioration in the mechanical properties of the
resulting plastisolized PVC as the proportion of regrind increased.
Even with a ratio of 10 parts regrind to 100 parts virgin material,
tear strength decreased by around 10\%.

These results perfectly align with the microscopic observations
(Figure~\ref{fig9}), which clearly reveal the presence of microvoids
and cracks, particularly in the sample with 45~g of recycled PVC. These
defects weaken the material and make it more susceptible to failure.

\subsubsection{Overall desirability function $D$}\label{sec343}

In the context of this study, the overall desirability function was
used to determine the maximum amount of recycled PVC that could be used
in the plastisol formulation while still meeting the quality
requirements of the floorcovering application.

These requirements include the BS ($d_{\mathrm{BS}}$), TR
($d_{\mathrm{TR}}$) and ER  ($d_{\mathrm{ER}}$) of this floorcovering
application. The overall desirability for each sample is shown in
\mbox{Table~\ref{tab7}}.

\begin{table*} %tab7
\caption{\label{tab7}Overall desirability values for each expanded
layer sample}
\begin{tabular}{c}
\tbody
\inlinefig{fx06}
%\begin{tabular}{cccccc}
%\thead
%\xmorerows{1}{Test} &amp; \morerows{1}{\parbox[t]{2.8cm}{\centering  Product (Recycled PVC) (${x}$)}}
%&amp; \multicolumn{3}{c}{Individual desirabilities}  &amp; \xmorerows{1}{Function $D$} \\\cline{3-5}
%&amp;  &amp; \parbox[t]{2cm}{\centering  Break strength  ${d}_{\mathrm{BS}}$}
%&amp;\parbox[t]{2.5cm}{\centering  Tear resistance $d_{\mathrm{TR}}$} &amp;
%\parbox[t]{2cm}{\centering  Elongation at rupture  $d_{\mathrm{ER}}$}
%\vspace*{2pt} &amp;  \\
%\endthead
%{Test 1}  &amp; {P1}   (0 g) &amp; 1 &amp; 1 &amp; 1 &amp; \cellcolor{color-92D050}1 \\
%{Test 2}  &amp; {P2}   (5 g/6.67\%) &amp; 1 &amp; 1 &amp; 1 &amp; \cellcolor{color-92D050}1 \\
%{Test 3}  &amp; {P3}   (15 g/20\%) &amp; 0.8 &amp; 0.93 &amp; 1 &amp; \cellcolor{color-FFC000}0.61 \\
%{Test 4}  &amp; {P4} (25 g/33.34\%) &amp; 0.5 &amp; 0.63 &amp; 1 &amp; \cellcolor{red!80}0.15 \\
%{Test 5}  &amp; {P5} (35 g/46.67\%) &amp; 0 &amp; 0 &amp; 0 &amp; \cellcolor{black}\color{white}0 \\
%{Test 6}  &amp; {P6}   (45 g/60\%) &amp; 0 &amp; 0 &amp; 0 &amp; \cellcolor{black}\color{white}0 
%\botline
\end{tabular}
\vspace*{-3pt}
\end{table*}

Based on the findings presented in Table~\ref{tab7}, only expanded
layers P2 and P3 successfully adhere to the established criteria for
acceptable quality (with $D &gt;0.5$). Notably, the assessment of the P4
sample \mbox{reveals} its alignment with predetermined limit of acceptability
as a second-quality article. These deductions gain additional
validation through meticulous evaluation carried out by experts hailing
from the esteemed PLASTISS company, renowned for their profound
proficiency within the floorcovering industry. The study's outcomes
incontrovertibly demonstrate that the optimal quantity of recycled PVC
particles within a plastisol formulation, while upholding exacting
quality requisites, stands at 15~g (equivalent to 20\% of the total
PVC added). This determination arises from the intricate interplay
between the morphology of the recycled PVC particles, encompassing both
their configuration and size distribution, and the resulting quality of
the end product.

These mechanical results are in good agreement with previous work by
Syaban\i~\etal~\cite{22} who highlighted that internal defects,
such as micropores, can significantly compromise the product's
integrity, leading to damage, fractures, and failures. Therefore,
coating pastes necessitate specific rheological properties to ensure
optimal performance. This finding is confirmed by additional
studies~\cite{1,10,37,48,49}, which corroborate that the
enhancements in the mechanical properties of PVC-coated fabric stemmed
from the enhanced fluidity of PVC resin and the increased homogeneity
of plastisol during the mixing of PVC resin.
\vspace*{-3pt}

\subsection{Optimization}\label{sec35}
The results attained have already highlighted the substantial influence
of both the quantity and size distribution of recycled PVC particles on
the eventual product quality. To further investigate this relationship,
we performed a refined analysis by narrowing down the PSD of recycled
PVC through a series of three distinct sieving operations:
\begin{itemize}
\item In the first sieving operation, we used a $600~\upmu \mathrm{m}$
aperture sieve to exclude particles larger than $600~\upmu \mathrm{m}$
(distribution ``1''). 
\item In the second sieving operation, we used a $400~\upmu \mathrm{m}$
aperture sieve to exclude particles larger than $400~\upmu \mathrm{m}$
(distribution ``2'').
\item In the third sieving operation, we used a $200~\upmu \mathrm{m}$
aperture sieve to exclude particles larger than $200~\upmu \mathrm{m}$
(distribution ``3'').
\end{itemize}
This methodical approach allowed us to precisely control the PVC
particle sizes and better understand their impact on the final
product's properties and performance. 

The cumulative distribution function (CDF) illustrated in
Figure~\ref{fig11} underscores the retrieval percentages achieved during
sieving processes (distribution ``0''). Notably, when employing a
$600~\upmu \mathrm{m}$ aperture sieve (distribution ``1''), an
exceptional \mbox{recovery}
\mbox{percentage} of 96.44\% for recycled PVC particles
is evident. Similarly, the use of a $400~\upmu \mathrm{m}$ aperture
sieve (distribution ``2'') yields a remarkable recovery percentage of
73.01\%. However, only a recovery percentage of 12.81\% was obtained
when sieving using a $200~\upmu \mathrm{m}$ aperture sieve
(distribution ``3'').

\begin{figure}
\vspace*{-3pt}
\includegraphics{fig11}
\vspace*{-5pt}
\caption{\label{fig11}Cumulative distribution curve.}
\vspace*{-3pt}
\end{figure}

\subsubsection{Optimization according to the different
distributions}\label{sec351}

\paragraph{Preparation of expanded layer formulations}\label{sec3511}

Preliminary tests, coupled with microscopic examinations, enabled the
identification and exclusion of samples exhibiting cracks in the
expanded layer, akin to those portrayed in Figure~\ref{fig9}f.
Employing this methodology, we effectively streamlined the testing
protocol, thereby curtailing the requisite number of tests---each
mechanical evaluation necessitates three individual samples---conducted
for every distribution (``1'', ``2'' and ``3'').

The ensuing table succinctly encapsulates the exhaustive array of tests
undertaken for each distribution (``1'', ``2'' and ``3''), specifying
the plasticizer quantities incorporated within each respective
formulation. Table~\ref{tab8} summarizes all the tests to be
carried out.

\begin{table*} %tab8
\caption{\label{tab8}Correlating the plasticizer quantity in each
distribution with the amount of recycled PVC incorporated
\vspace*{-3pt}}
\tabcolsep=0pt
\begin{tabular}{c}
\tbody
\inlinefig{fx07}
%\begin{tabular}{cccccccc}
%\thead
%&amp; &amp; \multicolumn{6}{c}{$x$ (recycled PVC)} \\\cline{3-8}
%&amp;&amp;  \parbox[t]{1.5cm}{\centering 25~g\break (33.34\%)} &amp; 
%\parbox[t]{1.5cm}{\centering 35~g\break (46.67\%)} &amp; 
%\parbox[t]{1cm}{\centering 45~g\break (60\%)} &amp; 
%\parbox[t]{1.6cm}{\centering 55~g\break  (73.34\%)} &amp;
%\parbox[t]{1.5cm}{\centering 65~g\break (86.67\%)} &amp; 
%\parbox[t]{1.5cm}{\centering 75~g\break  (100\%)}\vspace*{2pt}\\
%\endthead
%\morerows{3}{\raisebox{-4pc}{\parbox[t]{2.5cm}{{${z}$ (Plasticizer) (g)}}}}
% &amp; \parbox[t]{3cm}{\centering {Distribution ``0''} Without sieving} 
% &amp; 60 &amp; 70 &amp; 80 &amp;\cellcolor{black}\hspace*{4em}  &amp;\cellcolor{black}\hspace*{4em}  &amp; \cellcolor{black}\hspace*{4em} \\
% \raisebox{1pc}{}
% &amp; \parbox[t]{3cm}{\centering {Distribution ``1''} Sieving ($600~\upmu \mathrm{m}$)}
% &amp; 55 &amp; 60 &amp; 75 &amp;\cellcolor{black}\hspace*{4em}  &amp;\cellcolor{black}\hspace*{4em}  &amp;\cellcolor{black}\hspace*{4em}  \\
% \raisebox{1pc}{}
% &amp; \parbox[t]{3cm}{\centering {Distribution ``2''} Sieving ($400~\upmu \mathrm{m}$)}
% &amp;  &amp;  &amp; 65 &amp; 80 &amp; \cellcolor{black}\hspace*{4em} &amp; \cellcolor{black}\hspace*{4em} \\
% \raisebox{1pc}{}
% &amp; \parbox[t]{3cm}{\centering {Distribution ``3''} Sieving ($200~\upmu \mathrm{m}$)}
% &amp;  &amp;  &amp;  &amp;  &amp; 80 &amp; 85 \vspace*{2pt}
%\botline
\end{tabular}
\end{table*}


Table~\ref{tab8}, shows that, for the same quantity of recycled PVC
added, the plasticizer amount required to achieve the targeted
viscosity of 25,000 (${\pm}$500)~$\mathrm{Pa}{\cdot}\mathrm{s}$
diminishes following each successive sieving stage. To illustrate, when
45~g of recycled PVC is employed, the plasticizer requirement drops from
80~g (distribution ``0'', no sieving) to 75~g (distribution ``1'', after
sieving 600~$\upmu \mathrm{m}$), and further decreases to 65~g
(distribution ``2'', sieving 400~$\upmu \mathrm{m}$). 

The incorporation of flattened and elongated recycled PVC particles,
ranging from 400 to $600~\upmu \mathrm{m}$ in size, into plastisol
formulations containing pure PVC resin particles (typically 100~$\upmu
\mathrm{m}$) hinders uniform particle dispersion. This issue can be
mitigated by increasing the plasticizer content to de-agglomerate the
PVC particles. Conversely, smaller recycled PVC particles ($200~\upmu
\mathrm{m}$), closer to the 100~$\upmu \mathrm{m}$ size of pure PVC
resin, promote the formation of a more uniform and compact coating,
leading to enhanced stress distribution, reduced deformation, and
consequently, a lower plasticizer requirement to achieve the desired
viscosity. \looseness=-1

Evidently, this phenomenon underscores that the best distributions stem
from the finest recycled PVC particles.

\paragraph{Mechanical properties}\label{sec3512}

Table~\ref{tab9} summarizes the results of the mechanical tests,
including BS, TR, and ER, corresponding to each distribution (``1'',
``2'' and ``3'') in relation to the incorporated quantities of recycled
PVC. Additionally, individual desirabilities ($d_{\mathrm{BS}}$,
$d_{\mathrm{TR}}$ and $d_{\mathrm{ER}}$) and overall functions ($D$) are
also presented.

\begin{table*} %tab9
\caption{\label{tab9}Impact of the quantity and size distribution of
recycled PVC particles on mechanical properties\vspace*{-3pt}}
\tabcolsep=0pt
\begin{tabular}{c}
\tbody
\inlinefig{fx08}
%\begin{tabular}{ccccccccc}
%\thead
%&amp;&amp; \multicolumn{3}{c}{\parbox[t]{3cm}{\cellcolor{color-767171}\centering Distribution ``1''\newline  Sieving ($600~\upmu \mathrm{m}$)}}
%&amp; \multicolumn{2}{c}{\parbox[t]{3cm}{\cellcolor{color-AEAAAA}\centering Distribution ``2''\newline Sieving ($400~\upmu \mathrm{m}$)}}
%&amp; \multicolumn{2}{c}{\parbox[t]{3cm}{\cellcolor{color-D0CECE}\centering Distribution ``3''\newline Sieving ($200~\upmu \mathrm{m}$)}} \\\cline{3-9}
%\endthead
%&amp;&amp; \multicolumn{7}{c}{X (recycled PVC)} \\
%&amp; &amp; \parbox[t]{1.5cm}{\cellcolor{color-767171}\centering 25~g (33.34\%)} &amp; \parbox[t]{1.5cm}{\cellcolor{color-767171}\centering 35 g  (46.67\%)} &amp;
%\parbox[t]{1.5cm}{\cellcolor{color-767171}\centering 45 g \break (60\%)} &amp; \parbox[t]{1.2cm}{\cellcolor{color-AEAAAA}\centering 45 g (60\%)} &amp;
%\parbox[t]{1.5cm}{\cellcolor{color-AEAAAA}\centering 55 g  (73.34\%)} &amp; 
%\parbox[t]{1.5cm}{\cellcolor{color-D0CECE}\centering 65 g (86.67\%)} &amp; 
%\parbox[t]{1.5cm}{\cellcolor{color-D0CECE}\centering 75 g  (100\%)} \\
%\raisebox{1pc}{}\morerows{1}{\parbox[t]{2.5cm}{\centering {Break strength (N)}}}  &amp; \parbox[t]{1cm}{Value} &amp; \cellcolor{color-767171}20.4 &amp; \cellcolor{color-767171}19.2 &amp; \cellcolor{color-767171}17.4 &amp; \cellcolor{color-AEAAAA}19.6 &amp; \cellcolor{color-AEAAAA}18.02 &amp; \cellcolor{color-D0CECE}19.1 &amp; \cellcolor{color-D0CECE}18 \\
% &amp; $d_{\mathrm{BS}}$ &amp; \cellcolor{color-767171}1 &amp; \cellcolor{color-767171}0.84 &amp; \cellcolor{color-767171}0.48 &amp; \cellcolor{color-AEAAAA}0.92 &amp; \cellcolor{color-AEAAAA}0.6 &amp; \cellcolor{color-D0CECE}0.82 &amp; \cellcolor{color-D0CECE}0.6 \\
%\raisebox{1pc}{} 
%\morerows{1}{\parbox[t]{2.5cm}{\centering {Tear resistance (N)}}}  &amp; Value &amp; \cellcolor{color-767171}0.85 &amp; \cellcolor{color-767171}0.76 &amp; \cellcolor{color-767171}0.62 &amp; \cellcolor{color-AEAAAA}0.78 &amp; \cellcolor{color-AEAAAA}0.69 &amp; \cellcolor{color-D0CECE}0.76 &amp; \cellcolor{color-D0CECE}0.65 \\
% &amp; $d_{\mathrm{TR}}$ &amp; \cellcolor{color-767171}1 &amp; \cellcolor{color-767171}0.87 &amp; \cellcolor{color-767171}0.4 &amp; \cellcolor{color-AEAAAA}0.93 &amp; \cellcolor{color-AEAAAA}0.63 &amp; \cellcolor{color-D0CECE}0.87 &amp; \cellcolor{color-D0CECE}0.5 \\
%\raisebox{1pc}{} 
%\morerows{1}{\parbox[t]{2.5cm}{\centering {Elongation at rupture (\%)}}}  &amp; Value &amp; \cellcolor{color-767171}108 &amp; \cellcolor{color-767171}101 &amp; \cellcolor{color-767171}92 &amp; \cellcolor{color-AEAAAA}102 &amp; \cellcolor{color-AEAAAA}93 &amp; \cellcolor{color-D0CECE}101 &amp; \cellcolor{color-D0CECE}98 \\
% &amp; $d_{\mathrm{ER}}$ &amp; \cellcolor{color-767171}1 &amp; \cellcolor{color-767171}1 &amp; \cellcolor{color-767171}0.68 &amp; \cellcolor{color-AEAAAA}1 &amp; \cellcolor{color-AEAAAA}0.72 &amp; \cellcolor{color-D0CECE}1 &amp; \cellcolor{color-D0CECE}0.92 \\ 
% \multicolumn{2}{c}{\raisebox{1pc}{}\centering {Function $D$}} &amp; \cellcolor{color-767171}\textbf{1} &amp; \cellcolor{color-767171}\textbf{0.59} &amp; \cellcolor{color-767171}\textbf{0.04} &amp; \cellcolor{color-AEAAAA}\textbf{0.78} &amp; \cellcolor{color-AEAAAA}\textbf{0.15} &amp; \cellcolor{color-D0CECE}\textbf{0.57} &amp; \cellcolor{color-D0CECE}\textbf{0.12}
%\botline
\end{tabular}
\vspace*{-8pt}
\end{table*}



The results shown in Figure~\ref{fig12} unequivocally establish a
discernible enhancement in mechanical properties subsequent to a
meticulous ``$600~\upmu \mathrm{m}$'' sieving process (distribution
``1''), when juxtaposed with distribution ``0'' that underwent no such
sieving. This improvement is particularly pronounced for the expanded
layers originating from 45~g of recycled PVC, as evidenced by
substantial increments in the ensuing parameters: a remarkable 190\%
surge in BS, an impressive 210\% surge in TR, and a striking 162.86\%
surge in ER. 

\begin{figure*}
\includegraphics{fig12}
\caption{\label{fig12}Effect of Recycled PVC content on the mechanical
properties of PVC expanded layer after sieving, (a)~Break Strength (N),
(b)~Tear Resistance (N), (c)~Elongation at Rupture (\%), 
{Black scale bar: without recycled PVC and representing the
reference value (at 100\%) for comparing the evolution after the
incorporation of recycled PVC}.}
\end{figure*}

These significant percentage increments can be traced back to the
notable degradation, vividly exemplified by the emergence of
discernible fissures, within the expanded layers obtained through
distribution ``0'' while utilizing a 45~g quantity of recycled PVC
(Figure~\ref{fig9}f).

Utilizing distribution ``2'' ($400~\upmu \mathrm{m}$ sieve aperture),
the expanded layers produced with 45~g of recycled PVC exhibited
notable enhancements compared to distribution ``1'' ($600~\upmu
\mathrm{m}$ sieve aperture). This translated to significant increments
of 12.6\% in BS, 25.8\% in TR, and 10.8\% in ER. However, when the same
distribution ``2'' was employed with a quantity of 55~g recycled PVC,
reductions were observed, with BS decreasing by 8\%, TR by 11.54\%, and
ER by 8.82\%.

It was only through distribution ``3'' ($200~\upmu \mathrm{m}$ sieve
aperture) that we achieved a successful formulation for expanded layers
utilizing quantities of recycled PVC up to 65~g (86.67\%) and 75~g
(100\%). With these two quantities (65~g and 75~g), we were able to
document the following respective values: BS of 19.1N and 18N, TR of
0.76N and 0.65N, and ER of 101\%\unskip\break and 98\%.

Finer recycled PVC particles yield a more consistent foam structure
with smaller pores compared to larger recycled PVC particles. This
occurs because finer particles boast a larger surface area, fostering
greater interaction and contact among the particles. Marceneiro et
al~\cite{20} validated these findings in their study, which encompassed
three distinct PVC powders distinguished by density, PSD, surface
charge, and microstructure. Their study elucidated the pivotal role of
interactions between PVC and plasticizer in characterizing the
mechanical properties of plastisols and the resulting PVC films.
Moreover, their findings highlighted the significant impact of
structural defects, emphasizing their role in hastening PVC
degradation, thus significantly impacting its long-term performance.
Stambouli \etal~\cite{4,5} also observed a similar phenomenon where the
incorporation of fine calcium carbonate particles resulted in
substantial improvements in mechanical properties. This enhancement was
attributed to the strengthened van der Waals interaction forces between
the plastisol and these particles.

\paragraph{Overall mechanical qualities}\label{sec3513}

The results of the overall functions, summarized in Table~\ref{tab10},
are critically important as they provide in-depth insight into
the acceptability of each expanded layer. These insights are contingent
upon the size distribution (distributions: ``0'', ``1'', ``2'', and
``3'') and the quantity of recycled PVC employed (5~g--75~g) in the
plastisol recipe formulations.

\begin{table*} %tab10
\caption{\label{tab10}Overall Desirability values for expanded layer
samples based on distribution and incorporated recycled PVC quantity}
\tabcolsep=0pt
\begin{tabular}{c}
\tbody
\inlinefig{fx09}
%\begin{tabular}{lcccccccc}
%\thead
% &amp; \parbox[t]{1cm}{\centering 5 g 6.67\%} &amp; \parbox[t]{1cm}{\centering 15 g  20\%} &amp; 
% \parbox[t]{1cm}{\centering 25 g 33.34\%} &amp; \parbox[t]{1cm}{\centering 35 g 46.67\%} &amp; 
%\parbox[t]{1cm}{\centering  45 g 60\%} &amp; \parbox[t]{1cm}{\centering  55 g 73.34\%}
% &amp; \parbox[t]{1cm}{\centering 65 g 86.67\%}  &amp; \parbox[t]{1cm}{\centering 75~g 100\%} \vspace*{2pt}\\
%\endthead
%\parbox[t]{2.4cm}{\centering {Distribution 0 Without Sieving}}  &amp; 
%\parbox[t]{2cm}{\cellcolor{color-92D050}\centering $D =1$ {Premium quality}} &amp; 
%\parbox[t]{1.5cm}{\cellcolor{color-FFC000}\centering $D = 0.61$\newline  First-quality} &amp; 
%\parbox[t]{1.7cm}{\cellcolor{red!80}\centering $D = 0.15$  Second-quality} &amp; 
%\multicolumn{5}{c}{\cellcolor{black}\color{white}Rejected} \\
%\parbox[t]{2.5cm}{\centering {Distribution 1 Sieving ($600~\upmu \mathrm{m}$)}}  &amp; 
%\multicolumn{3}{c}{\parbox[t]{2.5cm}{\cellcolor{color-92D050}\centering $D = 1$\newline  Premium quality}} &amp; 
%\parbox[t]{1.6cm}{\cellcolor{color-FFC000}\centering $D = 0.59$  First-quality} &amp; 
%\parbox[t]{1.7cm}{\cellcolor{red!80}\centering $D = 0.04$  Second-quality} &amp; \multicolumn{3}{c}{\cellcolor{black}\color{white}Rejected} \\
%\parbox[t]{2.5cm}{\centering {Distribution 2 Sieving ($400~\upmu \mathrm{m}$)}} &amp; \multicolumn{4}{c}{\parbox[t]{2.5cm}{\cellcolor{color-92D050}\centering $D = 1$\newline  Premium quality}} &amp; 
%\parbox[t]{1.5cm}{\cellcolor{color-FFC000}\centering $D = 0.78$  First-quality} &amp; 
%\parbox[t]{1.7cm}{\cellcolor{red!80}\centering $D = 0.15$  Second-quality} &amp; \multicolumn{2}{c}{\cellcolor{black}\color{white}Rejected} \\
%\parbox[t]{2.5cm}{\centering {Distribution 3 Sieving ($200~\upmu \mathrm{m}$)}}  &amp; \multicolumn{6}{c}{\cellcolor{color-92D050}\parbox[t]{2.5cm}{\centering $D = 1$\newline  Premium quality}} &amp; 
%\parbox[t]{1.5cm}{\cellcolor{color-FFC000}\centering $D = 0.57$  First-quality} &amp; 
%\parbox[t]{1.7cm}{\cellcolor{red!80}\centering $D = 0.12$  Second quality}\raisebox{1pc}{}
%\botline
\end{tabular}
\end{table*}

\begin{table*} %tab11
\caption{\label{tab11}Optimum conditions}
\tabcolsep=0pt
\begin{tabular}{c}
\tbody
\inlinefig{fx10}
%\begin{tabular}{cccccc}
%\thead
%{Conditions} &amp; {Distribution} &amp; 
%\parbox[t]{2.8cm}{\centering PVC recovery after sieving (\%)} &amp;
%\parbox[t]{2.3cm}{\centering $x$ (g, \%) recycled PVC} &amp; 
%\parbox[t]{2.2cm}{\centering $z$ (g) Plasticizer} &amp;
%\parbox[t]{2cm}{\centering Function $D$}\vspace*{2pt} \\
%\endthead
%{C1}  &amp; \parbox[t]{2.5cm}{\centering {Distribution 0} Without Sieving} &amp; 100\% &amp; \parbox[t]{1.3cm}{\centering 15\break  (25\%)} &amp; 55 &amp; 0.61\vspace*{2pt} \\
%\cellcolor{color-92D050}{C2}  &amp; \parbox[t]{2.5cm}{\cellcolor{color-92D050}\centering {Distribution 1}   Sieving ($600~\upmu \mathrm{m}$)} &amp; \cellcolor{color-92D050}96.44\% &amp; \parbox[t]{1.3cm}{\cellcolor{color-92D050}\centering 35  (46.67\%)} &amp; \cellcolor{color-92D050}60 &amp; \cellcolor{color-92D050}0.59\vspace*{2pt} \\
%{C3}  &amp; \parbox[t]{2.5cm}{\centering {Distribution 2}   Sieving ($400~\upmu \mathrm{m}$)} &amp; 73.01\% &amp; \parbox[t]{1.3cm}{\centering 45\break  (60\%)} &amp; 65 &amp; 0.78\vspace*{2pt} \\
%{C4}  &amp; \parbox[t]{2.5cm}{\centering {Distribution 3}   Sieving ($200~\upmu \mathrm{m}$)} &amp; 12.81\% &amp; \parbox[t]{1.3cm}{\centering 65  (86.67\%)} &amp; 80 &amp; 0.57\vspace*{2pt}  
%\botline
\end{tabular}
\end{table*}

Based on the outcomes highlighted in the aforementioned table,
satisfactory overall mechanical qualities are attained through varying
amounts of recycled PVC---15~g ({20\%), 35~g} (46.67\%), 45~g (60\%),
and 65~g (86.67\%)---corresponding to distribution 0 (No Sieving),
distribution 1 ($600~\upmu \mathrm{m}$ sieve aperture), distribution 2
($400~\upmu \mathrm{m}$ sieve aperture), and distribution 3 ($200~\upmu
\mathrm{m}$ sieve aperture), respectively. These conclusions are
robustly endorsed by PLASTISS \mbox{experts}. 

The results deduced from the overall functions facilitate the choice of
expanded layers that align with the necessary mechanical criteria. More
precisely, to decide and finalize the optimal plastisol recipe
formulation from these chosen expanded layers, additional factors must
be taken into account, notably including the percentage of particle
recovery for each distribution and the amount of plasticizer introduced
to attain the prescribed viscosity.

\subsubsection{Final decision}\label{sec352}

This finding has significant implications for ensuring a balance
between sustainability and achieving desired quality standards. On the
one hand, using large quantities of recycled PVC particles can help to
reduce the environmental impact of the floorcovering industry.
Conversely, an overreliance on plasticizers, which are known to be
deleterious substances with the ability to migrate to the surface of
floorcoverings, raises concerns about adverse health effects on
individuals exposed to them.

After extensive consultations among experts at PLASTISS company, the
decision was made to embrace the C2 conditions (Table~\ref{tab11}), as
the company prioritizes the maximization of PVC waste valorization. In
fact, this distribution C2, with particle sizes below 0.6~mm, yields an
acceptable quality (global function value of 0.59) for the expanded
layer while using less amount of plasticizer (60~g vs 65~g for C3) and
efficiently utilizing 96.44\% of the total recycled PVC, in contrast to
C3, which only recycles 73.01\% since only particles smaller than 0.4
mm are\break used.

However, an improved pulverization process favoring a distribution
primarily comprising PVC particles with sizes under 0.4~mm would make
C3 the preferred distribution.

By effectively managing the amount of both recycled PVC and
plasticizer, we can not only create a more sustainable floorcovering
but also ensure a safer environment for consumers and industry workers
alike.

\section{Conclusion}\label{sec4}

The findings from this research indicate the feasibility of utilizing a
significant amount of recycled PVC particles in plastisol formulations
to replace conventional PVC resin in the expanded layer of
floorcoverings. As an initial exploration, a meticulous analysis of the
quality standards expected from the final product, particularly the
expanded layer after integrating recycled PVC powder, proves
imperative. 

Simultaneously, a profound comprehension of morphology and PSD takes on
paramount significance in exploring the impacts of recycled PVC content
and particle dimensions on both the mechanical (including BS, ER, and
TR) and the morphological properties of the PVC expanded layer
intended for floorcoverings.

Morphology studies, using microscopic observation, allowed us to
distinguish the different flat and elongated shapes of particles making
up recycled PVC powder. These shapes of non-spherical particles
frequently display elevated porosity and reduced flow characteristics
which hinder the effective dispersion of the recycled PVC powder. This
behavior resulted in an augmentation of the plasticizer quantity, which
contributes to the flexibility and elasticity of the PVC material. As a
result, the amount of plasticizer required to produce an expanded layer
increases as the amount of recycled PVC powder increases. This
plasticizer quantity reaches 80~g for a 45~g quantity of recycled PVC.

As the proportion of recycled PVC increases, noticeable alterations
manifest within the foam structure. It is noteworthy that the
incorporation of 35~g of recycled PVC distinctly precipitates a
degradation of the foam structure, which becomes even more pronounced
at 45~g. This transition unveils the emergence of microvoids and
cracks, exacerbating the structural issues observed.

Mechanical outcomes, which align with microscopic observations,
validate that the mechanical properties deteriorated rapidly when the
amount of recycled PVC powder exceeded 25~g.

To further optimize the utilization of recycled PVC within this
specialized floorcovering application, a meticulous analysis was
conducted. This involved refining the PSD through a sequence of three
distinct sieving operations: distribution 1 (using a $600~\upmu
\mathrm{m}$ sieve aperture), distribution 2 (employing a $400~\upmu
\mathrm{m}$ sieve aperture), and distribution 3 (utilizing a $200~\upmu
\mathrm{m}$ sieve aperture). The outcomes present commendable overall
mechanical characteristics across various quantities of recycled
PVC---15~g (equivalent to 20\% of the total added PVC), 35~g (46.67\%),
45~g (60\%), and 65~g (86.67\%). These quantities correspond to
distribution 0 (No Sieving), distribution 1, distribution 2, and
distribution 3, respectively.

In our forward-looking approach, we remain dedicated to enhancing the
grinding process, aiming to attain an optimized PSD. Our goal is to
increase the proportion of fine particles, rendering them suitable for
utilization within both expanded and superficial layers. 

\section*{Declaration of interests}
The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations.

\section*{Acknowledgements}
The authors gratefully acknowledge the use of the services and
facilities at PLASTISS as the case study company.

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