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\begin{document}

\title{Leveraging Data-Driven strategy for Accelerating the Discovery of
Polyesters with Targeted Glass Transition Temperatures}



\author[1]{Xiaoying He}%
\author[1]{Mengxian Yu}%
\author[2]{Jian-Peng Han}%
\author[3]{Jie Jiang}%
\author[1]{Qingzhu Jia}%
\author[1]{Qiang Wang}%
\author[2]{Zheng-Hong Luo}%
\author[1]{Fangyou Yan}%
\author[2]{Yin-Ning Zhou}%
\affil[1]{Tianjin University of Science and Technology}%
\affil[2]{Shanghai Jiao Tong University}%
\affil[3]{East China University of Science and Technology}%


\vspace{-1em}



  
  \date{June 18, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
To overcome the limitations of empirical synthesis and expedite the
discovery of new polymers, this work aims to develop a data-driven
strategy for profoundly aiding in the design and screening of novel
polyester materials. Initially, we collected 695 polyesters with their
associated glass transition temperatures (Tgs) to develop a quantitative
structure-property relationship (QSPR) model. The model underwent
rigorous validation (external validation, internal validation, Y-random
and application domain analysis) to demonstrate its robust predictive
capabilities and high stability. Subsequently, by employing an in-silico
retrosynthesis strategy, over 95000 virtual polyesters were designed,
largely expanding the available space for polyester materials. External
assessments highlight the good extrapolation ability of the QSPR model.
Furthermore, we experimentally synthesized diverse virtual polyesters
with Tgs covering a sufficient large temperature range. It is believed
that this data-driven approach can drive future product development of
polymer industry.%
\end{abstract}%



\sloppy


\textbf{Introduction}

Synthetic polymers are indispensable in our daily
life.\textsuperscript{1, 2} Polyesters, in particular biodegradable
polyesters, are widely used in automotive parts, medical apparatus,
packaging products, electronic devices, and other fields owing to their
good thermomechanical properties and
biocompatibility.\textsuperscript{3-5} Polyesters are generally
consisting of ester containing repeating units produced by
esterification reaction between diacids and diols.\textsuperscript{6,
7}Thus, combination of different functional diacids with various diols
can yield an enormous space of polyester materials. As a result, it
becomes a non-trivial task to design and synthesize polyesters with
targeted properties.

Glass transition temperature (\emph{T} \textsubscript{g}) of polymer
governs the dynamic state of polymer chains, and further affects the
performance and application domains. For example, the high-\emph{T}
\textsubscript{g} polyester with a rigid ring structure improves the
thermal stability of polyester materials, aiming to provide bio-based
polymers for the plastic consumer market.\textsuperscript{8-10} In
addition, aliphatic polyesters with low\emph{T} \textsubscript{g} have
been studied as environmentally friendly pressure-sensitive adhesives
because of their low cost and potential
biodegradability.\textsuperscript{11, 12} \emph{T} \textsubscript{g} is
therefore an essential indicator for determining the properties of
polymers.

Given the large polymer design space, it is difficult, time-consuming,
and ineffective to screen polymers with targeted properties (e.g.,
specific \emph{T} \textsubscript{g}) through experimental
procedures.\textsuperscript{13-15} To enable rapid polymer molecular
design and high-throughput screening of ideal products prior to
laboratory synthesis and analysis, data-driven
alternatives,\textsuperscript{16-23} such as the quantitative
structure-property relationship (QSPR)
modeling\textsuperscript{24-28}and machine learning (ML)
approaches\textsuperscript{29-33} have been successfully used to predict
the properties for diverse polymers.

In this regard, Wang et al. used successfully trained machine learning
to predict the gas permeability of more than 11,000 homopolymers and
found that the upper bound of
CO\textsubscript{2}/CH\textsubscript{4}separation was exceeded by
synthesizing two promising polymeric membranes.\textsuperscript{34}
Recently, Tao et al. first studied the performance of 79 different
models by combining polymer representation, feature engineering and ML
algorithms.\textsuperscript{35, 36} They then designed millions of
hypothetical polyimides by polycondensation of existing dianhydrides and
diamines or diisocyanates, and built an ML model to predict a diversity
of their properties and verified the predictive ability of the ML
through molecular dynamics simulations. Finally, a new polyimide with
excellent thermal stability was successfully synthesized experimentally.
By trained machine learning models, Wang and Jiang have screened nearly
30,000 hypothetical polymers with fractional free volume (FFV)
\textgreater{} 0.2, enabling the design of high FFV polymers.
\textsuperscript{37} Wang et al. present a method for designing
high-temperature polymer dielectrics by combining tailored structural
units, and the design method is justified by analyzing ML predictions
and experimental results.\textsuperscript{38}Chen et al. developed an ML
model that accurately predicts different frequency-dependent dielectric
constants(\selectlanguage{greek}ϵ\selectlanguage{english}), and subsequently utilized the model to successfully design
ten polymers with the desired \selectlanguage{greek}ϵ \selectlanguage{english}and\emph{T} \textsubscript{g} for
application in the capacitor and microelectronics
fields.\textsuperscript{39} Meanwhile, Lin et al. proposed using a
material genome approach design and screening of new heat-resistant
resin materials by define gene and extracting key features of
properties.\textsuperscript{40-42} This strategy was subsequently used
in the design of various high-performance polymers. These advances
highlight the innovative potential of data-driven approaches in the
design of polymers. However, rational design of polyester materials is
still less explored. Therefore, it is promising to use data-driven
methods to predict the target properties of polyesters and to design new
polyesters to complement the existing library.

Herein, we report a data-driven strategy to enable the evaluation of the
relationship between molecular structure and \emph{T}
\textsubscript{g}of polyesters and further guide the design of novel
polyesters with specific \emph{T} \textsubscript{g}s. The workflow is
illustrated in\textbf{Figure 1} . First, an multiple linear regression
(MLR)-based QSPR model is developed by employing ring repeating unit
(RRU)\textsuperscript{43, 44} to uniquely represent polyesters and norm
descriptors for feature engineering. The predictability, robustness, and
chance correlation of the model are evaluated by internal validation,
external validation, and\emph{Y} -randomized analysis, respectively. We
then construct a virtual library by designing over 95000 hypothetical
polyesters by in-silico retrosynthesis. Later on, the\emph{T}
\textsubscript{g} prediction is performed by using the well-trained QSPR
model. Ultimately, several polyesters with specific\emph{T}
\textsubscript{g} are synthesized and characterized to validate the
data-driven polymer design strategy. This work puts the QSPR modeling
approach a further step forward by expanding the application scope from
properties prediction to model-based design of polymers.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1.} The workflow of this work

\textbf{Methods}

\textbf{2.1 Data Collection and Pretreatment}

An available dataset, Dataset A, is established by collecting
experimental \emph{T} \textsubscript{g} values of polyesters from the
polymer database,\emph{PolyInfo} \textsuperscript{45}. The data
selection criteria include: number average molar mass
(\emph{M\textsubscript{n}} ) \textgreater{} 6000 g
mol\textsuperscript{-1}, weight average molar mass
(\emph{M\textsubscript{w}} ) \textgreater{} 10000 g
mol\textsuperscript{-1}, and \emph{T} \textsubscript{g} measured by
differential scanning calorimetry (DSC). For polyesters with
multiple\emph{T} \textsubscript{g} values from different sources, a
median is chosen. The final dataset includes 695 polyesters with\emph{T}
\textsubscript{g} values ranging from -78 to 345  (Figure S1). The
dataset is randomly divided into a training set and a testing set by the
ratio of 4:1.

\textbf{2.2 Modeling process}

The diagram of modeling process shown in \textbf{Figure 2} includes 4
steps.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2} The pipeline of QSPR model construction

(i) The first step is unique representation of the molecular structure,
which is vital for reliable property prediction.\textsuperscript{43,
44}Here, the structures of polyesters are approximated by RRU.

(ii) Subsequently, norm descriptors are adopted to characterize the
RRU-based polymer structures, which contain details about the properties
and topological connections of each atom. Among them, the topological
connection relation is represented by step matrix (\emph{MS} ), showing
the position relationship of each atom in a molecule. In this work, 10
basic step matrices (i.e., \emph{MS} \textsubscript{F}\emph{, MS}
\textsubscript{A}\emph{, MS} \textsubscript{B}\emph{, MS}
\textsubscript{C}\emph{, MS} \textsubscript{AB}\emph{, MS}
\textsubscript{ABC}\emph{, MS} \textsubscript{bon},\emph{MS}
\textsubscript{ABC\_aro}, \emph{MS} \textsubscript{ABC\_cyc}, and
\emph{MS} \textsubscript{bon\_cyc}) are derived according to the
definitions by Eqs (S1)-(S10) in Supporting Information.

The property information of an atom refers to some basic properties of
the atom (e.g. ionization energy, and number of outermost electrons),
which are expressed in the form of a property matrix (\emph{P} ), as
shown in Table S1. As such, the atomic distribution matrix (\emph{M} )
is generated by combining \emph{MS} and \emph{P} according to Eq. (1).
Finally, the normal descriptors are obtained by using 7 norm indexes,
whose formulas are expressed by Eqs. (S11)-(S17) in Supporting
Information.

(iii) The dimensionality of the norm descriptors is then reduced by
using bidirectional stepwise regression. Ultimately, 29 norm descriptors
are screened out. Lastly, the QSPR model between chemical structures and
targeted properties is developed through MLR.

\textbf{2.3 Model validation and evaluation}

The statistical parameters, including squared correlation coefficient
(\emph{R\textsuperscript{2}} ), average absolute error (AAE), and
correlation coefficient for leave-one-out cross validation (\emph{Q}
\textsuperscript{2}\textsubscript{LOO-CV}) are employed to evaluate the
goodness-of-fit of the model. The definitions of these statistical
parameters are given in Eqs (2)-(4). Additionally, the testing set is
used in the external validation to assess the external predictive
abilities of the model. To evaluate the model's robustness, the internal
validation results are offered. Application domain analysis and
Y-randomized analysis are performed to confirm the reliability of the
model and to exclude chance-related aspects from the modeling process.

Note: \emph{T} \textsubscript{g i,exp} and \emph{T} \textsubscript{g
i,cal} represent experimental and calculated values of the polyesters,
respectively. \emph{n} is the number of data points.\emph{n}
\textsubscript{train} is the number of data points in the training set.

\textbf{2.4 Chemical space under exploration}

In order to explore the chemical structure space and broaden the
existing library of polyester at this stage, a larger polyester library
is built by retrosynthesis. \textbf{Figure 3a-3c} illustrates the
process of building the virtual polyester library. By assuming that the
polyesters are formed by the polycondensation of a diol and a diacid,
the collected polyesters are split into secondary building blocks,
namely, diols and diacids. Subsequently by de-duplicating the same
structure, we obtain a total of 267 diacids and 358 diols, which are
listed in Sheet S2 in the Supporting Information (data.xlsx).
Ultimately, 95586 hypothetical polyesters are generated and their
\emph{T} \textsubscript{g}s are predicted by the as-developed QSPR model
(\textbf{Figure 3d} ), which are described as dataset B and given in
Sheet S3 in the Supporting Information(data.xlsx). \textbf{Figure 3e}
lists the structures of some hypothetical polyesters.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

\textbf{Figure 3.} Design process of virtual polymers. Colors of
R\textsubscript{i} represent different substructures. a. Splitting
polyesters into diacids and diols, where D\textsubscript{i} and
A\textsubscript{i} represent the diol and the diacid, respectively. b.
De-duplicating the molecules with same structure that are generated
during splitting. c. Exhaustive combination of diol and diacid into
hypothetical polyesters. d. Prediction of \emph{T} \textsubscript{g} for
virtual polyesters by using the as-developed QSPR model. e. Examples of
hypothetical polyesters.

\textbf{2.5 Synthesis and characterization of polyesters}

Synthesis of 10 selected polyesters from dataset B with diverse\emph{T}
\textsubscript{g}s is carried out via a successive esterification and
condensation two-stage polymerization process in a 250 mL three-neck
flask equipped with mechanical overhead stirrer, vacuum-tight stirrer
bearings and distillation columns. Detailed synthesis procedure for each
polyester is shown in supporting information.

The \emph{T} \textsubscript{g} values of final products are measured by
differential scanning calorimetry (DSC) analysis. DSC was carried out on
a Q2000 (TA Instruments, USA) with a temperature range of -70 to 200 .
The data are collected from the second heating thermogram and the
heating curves are presented in supporting information.

\textbf{3.Results and Discussion}

\textbf{3.1 QSPR model and validation}

A QSPR model was developed with 29 NI descriptors to quantify the
relationship between the molecular structure characteristics and\emph{T}
\textsubscript{g}s of 695 polyesters, as shown in Eq. (4). The norm
descriptors (\emph{I} ) and the corresponding coefficients (\emph{b} )
in the model are listed in Table S2 of the Supplementary Information.

\textbf{Figure 4} shows the predictability of the QSPR model. With 556
data points used as the training set and 139 data points used as the
testing set, the scatter plot of predicted and experimental\emph{T}
\textsubscript{g} values is shown in \textbf{Figure 4a} . It is obvious
that the majority of the data points are distributed close to the
diagonal line, which indicates that the model provides good prediction
accuracy, with AAE \textless{} 20  and\emph{R} \textsuperscript{2}
\textgreater{} 0.90. The calculated and experimental \emph{T}
\textsubscript{g}s for the 695 polyesters are shown in the Sheet S1 of
the Supporting Information(data.xlsx). Moreover,\emph{R}
\textsuperscript{2}\textsubscript{training} = 0.9054 and\emph{R}
\textsuperscript{2}\textsubscript{testing} = 0.9077 are significantly
greater than 0.6, proving the good predictive performance of the model.
Meanwhile, the two \emph{R} \textsuperscript{2} are very close, implying
that the model has strong generalizability and is capable of well
learning the relationship between the chemical structure of polyesters
and their associated \emph{T} \textsubscript{g}.

n = 695; \emph{R} \textsuperscript{2} = 0.9060;\emph{Q}
\textsuperscript{2}\textsubscript{LOO-CV}= 0.8889; AAE = 17.7197 

where \emph{n\textsubscript{A}} is number of
atoms,\emph{n\textsubscript{nH}} is number of non-hydrogen
atoms;\emph{MS\textsubscript{F}} are calculated with the polyester
structures (H-suppressed); \emph{b\textsubscript{i}} is the parameters
and\emph{I\textsubscript{i}} is the norm descriptors.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

\textbf{Figure 4.} Results of the QSPR model. (a) plot of
calculated\emph{vs.} experimental \emph{T} \textsubscript{g} of training
set and testing set, (b) plot of internal validation via LOO-CV, (c)
distribution of errors of the QSPR model and LOO-CV, (d) result of the
10,000\emph{Y} -randomization tests and (e) William plot.

To further confirm the robustness of the developed model, the scatter
plots of the experimental and LOO-CV estimated values, as well as the
error distributions for the LOO-CV and the QSPR model, are shown
in\textbf{Figure 4b} and \textbf{Figure 4c} , respectively.
Specifically,\emph{Q} \textsuperscript{2}\textsubscript{LOO-CV} is
0.8889 and greater than 0.5, showing that the model is robust and
stable. Further, the absolute error (AE) distribution of LOO-CV is
generally in good agreement with that of the QSPR model, with most
polyesters having an error of\emph{T} \textsubscript{g} within 20 .

\textbf{Table 1.} Statistical parameters of the QSPR model\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Methods & Variables & Samples & Values\tabularnewline
\midrule
\endhead
LOO-CV & \emph{Q}\textsuperscript{2}\textsubscript{LOO-CV} & 695 &
0.8889\tabularnewline
& AAE\textsubscript{LOO-CV} & 695 & 18.9256\tabularnewline
External validation &
\emph{R}\textsuperscript{2}\textsubscript{training} & 556 &
0.9054\tabularnewline
& \emph{R}\textsuperscript{2}\textsubscript{testing} & 139 &
0.9077\tabularnewline
& AAE\textsubscript{training} & 556 & 17.6530\tabularnewline
& AAE\textsubscript{testing} & 139 & 17.9863\tabularnewline
Overall data set & \emph{R}\textsuperscript{2} & 695 &
0.9060\tabularnewline
& AAE & 695 & 17.7197\tabularnewline
\emph{Y}-random validation & & 695 & 0.0521\tabularnewline
& & 695 & 0.0038\tabularnewline
\bottomrule
\end{longtable}

Subsequently, 10,000 times of \emph{Y} -random validation was performed
to assess the chance correlation. Plot of\emph{R}
\textsubscript{Y}\textsuperscript{2} versus\emph{Q}
\textsubscript{Y}\textsuperscript{2} is shown in Figure 3d. The average
values of \emph{R} \textsubscript{Y}\textsuperscript{2} and\emph{Q}
\textsubscript{Y}\textsuperscript{2} for the 10,000\emph{Y} -random
validation are 0.0521 and 0.0038, respectively, which are much lower
than the \emph{R} \textsuperscript{2} and\emph{Q}
\textsuperscript{2}\textsubscript{LOO-CV} of the developed model.
Therefore, the influence of randomness of the dataset itself on the
instability of the QSPR model can be ruled out. William plot was used to
visualize the developed model's application domain. Almost all the
plots, as depicted in \textbf{Figure 4e} , are within the tolerance of
three standard deviations of {[}-3, 3{]} and critical leverage level
(\emph{h} \textsuperscript{*}=0.1619). It therefore can be concluded
that the QSPR model is reliable to predict \emph{T} \textsubscript{g}.
The values of relevant statistical parameters of QSPR model are shown
in\textbf{Table 1} .

\textbf{3.2 Virtual Library of Designed Polyesters}

Traditional polyesters are mainly made by the condensation of diacids
and diols. In silico retrosynthesis route enables the generation of a
virtual library of 95,586 polyesters, i.e., dataset B, based on 695
original polyesters. From the computer-aided design point of view, we
assumed that once the ester group is correctly present the corresponding
polyester is yielded. To illustrate the relationship between datasets A
and B more clearly, we then visualized the two datasets separately in
two-dimensional chemical space, as shown in \textbf{Figure 5a} . It
shows that the chemical diversity of the two datasets is quite similar,
while compared to dataset A (blue points), dataset B (pink points)
clearly covers more possible chemical structures of polyesters. This
result implies these virtual polyesters significantly expand the
chemical space of the existing polyesters and effectively overcomes the
issue of data scarcity. In silico design of these virtual polyesters
helps us to explore new polyesters with desired properties from a wider
region of chemical space.

However, it is unrealistic to obtain over 95000 polyesters by
experimental synthesis. By using the as-developed QSPR model,\emph{T}
\textsubscript{g}s of the hypothetical polyesters in dataset B were
predicted. \textbf{Figure 5b} depicts the distributions of\emph{T}
\textsubscript{g}s in datasets A and B. Similar trend in both datasets
demonstrates that the hypothetical polyesters are almost consistent with
the polyesters already presented in the database A. Therefore, a
trustworthy virtual library for polyester has been successfully
established, expanding the existing space for polyester materials and
providing certain data support for the synthesis analysis of polyester
materials.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}

\end{center}
\end{figure}

\textbf{Figure 5} . (a) Chemical space visualization of the dataset A
(blue points) and the dataset B (pink points). (b)\emph{T}
\textsubscript{g} distribution of datasets A and B in red and blue,
respectively. There are 269 and 47708 polyesters with\emph{T}
\textsubscript{g} higher than 100  in datasets A and B, respectively.
Samples of polyesters in dataset B with different\emph{T}
\textsubscript{g} range show in (c) \emph{T}
\textsubscript{g}\textgreater{} 100 , (d) 0  \textless{} \emph{T}
\textsubscript{g}\textless{} 100  and (e) \emph{T} \textsubscript{g}
\textless{} 0 .

Polyesters with high \emph{T} \textsubscript{g} have good heat
resistance and thermal stability, thereby offering great potential in
high temperature and harsh environments. Typically, we describe
polyester materials as high-\emph{T} \textsubscript{g} polyester if
the\emph{T} \textsubscript{g} \textgreater{} 100 . As shown
in\textbf{Figure 5b} , in dataset A, there are only 269 polyesters
with\emph{T} \textsubscript{g} higher than 100 , which may also include
some polyesters that are not easy to synthesize experimentally. By
comparison, there are 47708 virtual polyesters with \emph{T}
\textsubscript{g} higher than 100  in dataset B, which means that more
than 170 times of potential candidates for high-\emph{T}
\textsubscript{g} polyester materials are explored. These screened
high-\emph{T} \textsubscript{g} polyesters provide a sound support for
further synthesis of high-temperature resistant polyester materials. It
can be found that the screened high-\emph{T} \textsubscript{g}
candidates all have ring groups, as shown in \textbf{Figure 5c} , such
as benzene and alicyclic rings, and the presence of these ring groups
increases the rigidity of the polyester chains, which leads to high
\emph{T} \textsubscript{g} values. Additionally, by screening the
candidate polyesters with 0 \textless{}\emph{T} \textsubscript{g}
\textless{} 100  (\textbf{Figure 5d} ), compared with the candiates
with\emph{T} \textsubscript{g}\textgreater{}100,these have more
aliphatic carbon chain and fewer rigid structures. And for\emph{T}
\textsubscript{g} \textless{} 0  (\textbf{Figure 5e} ), almost all the
candidates have longer aliphatic carbon chain structures. Lower\emph{T}
\textsubscript{g} is ascribed to the longer chains polyester molecules
more flexible and facilitating an easier inter-chain segment movement.
As shown in \textbf{Figure 5e} , the \emph{T} \textsubscript{g}of M7 is
lower than that of M95760, which is attributed to all aliphatic chain
structure of M7, while the rigid hexatomic ring in M95760 trade-offs the
chain flexibility.

\textbf{3.3 Experimental validation}

Lastly, 10 polyesters with different predicted\emph{T}
\textsubscript{g}s were selected from the dataset B for experimental
synthesis and characterization to verify the design rationality and
further validate the predictability of the model. The DSC curves for
determining \emph{T} \textsubscript{g}s are provided in the supporting
information (Figure S2 with data summarized in Table S4).\textbf{Figure
6} visualizes that the experimentally determined\emph{T}
\textsubscript{g}s are in good agreement with those predicted ones. The
AAE of these screened polyesters is 17.4045 , which is smaller than the
model's AAE of 17.7197 . Also, the effect of various groups on \emph{T}
\textsubscript{g} were then compared. For instance, cyclic alkanes in
diols contribute more to \emph{T} \textsubscript{g}than linear alkanes
do for M4584, M4594, and M4642. For long chain acids, the \emph{T}
\textsubscript{g}s of the polyesters decrease as the length of the chain
increases (M1413, M1612 and M20). This is mostly caused by the increased
chain flexibility by contrast to that of the cycloalkanes, which gives
the polyesters lower\emph{T} \textsubscript{g}s. Additionally, it is
found that para-phthalic acids (e.g., M436 and M26484) are more
beneficial for improving\emph{T} \textsubscript{g} when compared to
ortho-phthalic acids.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}

\end{center}
\end{figure}

\textbf{Figure 6} . Comparison of \emph{T} \textsubscript{g} of the
selected 10 polymers between the experimental method and the theoretical
calculation method.

\textbf{Conclusions}

In this contribution, we have successfully developed the QSPR model for
evaluating the chemical structure of 695 polyesters with respect to
their \emph{T} \textsubscript{g} through a series of rigorous
validations. Specifically, \emph{R} \textsuperscript{2} \textgreater{}
0.90 and \emph{Q} \textsuperscript{2}\textsubscript{LOO-CV} = 0.88.
Following this, a virtual library of nearly 100,000 polyesters has been
built by in silico retrosynthesis, which greatly expands the available
space for polyester materials. Their associated\emph{T}
\textsubscript{g}s were predicted by the developed model as well. t-SNE
shows significant chemical overlap with the known polyester database,
i.e., dataset A, and the virtual library, i.e., dataset B, which
demonstrates the rationality and feasibility of the design process.

Subsequently, 10 designed polyesters with different\emph{T}
\textsubscript{g}s located in different temperature ranges were screened
out for experimental synthesis. Good agreement between the experimental
and predicted \emph{T} \textsubscript{g}s not only demonstrates the
accurate prediction performance of the QSPR model, but also verifies the
efficiency of the design method. The rationality of the relationship
between chemical structures and\emph{T} \textsubscript{g}s was analyzed
accordingly.

The methodology presented and the results gained in this work offer the
potential to accelerate the design of high-performance polyesters, and
may drive future product development of polymer industry.

\textbf{Acknowledgments}

This work was financially supported by the National Natural Science
Foundation of China (22222807 and 22278319).

\textbf{Supporting Information}

Additional results can be found online in the Supporting Information
section.

\textbf{Data Availability and Reproducibility Statement}

The numerical data from Figures 3, 4, and 5 are tabulated in the
Supplementary Material(data.xlsx) Sheet S2, Sheet S1 and Sheet S3. The
code for the proposed model is available from the corresponding author
upon reasonable request.

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