\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[ngerman,greek,english]{babel}



\usepackage{float}








\begin{document}

\title{Toward understanding the cross-linking from molecular chains to
aggregates by engineering terminals of supramolecular hyperbranched
polysiloxane}



\author[1]{zhang yuanbo}%
\author[1]{Junshan Yuan}%
\author[1]{Jingzhi Hu}%
\author[1]{Zhixuan Tian}%
\author[1]{Weixu Feng}%
\author[1]{Hongxia Yan}%
\affil[1]{Northwestern Polytechnical University}%


\vspace{-1em}



  
  \date{May 27, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Crosslinking thermosets with hyperbranched polymers confers them
superior comprehensive performance. However, it still remains a further
understanding of polymer crosslinking from the molecular chains to the
role of aggregates. In this study, three hyperbranched polysiloxane
structures (HBPSi-R) are synthesized as model macromolecules, each
featuring distinct terminal groups (R denotes amino, epoxy, and vinyl
groups) while similar molecular backbone (Si-O-C). These structures were
subsequently copolymerized with epoxy monomers to construct
interpenetrating HBPSi-R/epoxy/anhydride co-polymer systems. The spatial
molecular configuration and flexible Si-O-C branches of HBPSi-R endow
them with remarkable reinforcement and toughening effects. Notably, an
optimum impact strength of 28.9 kJ mol-1 is achieved with a mere 3\%
loading of HBPSi-V, nearly three times that of the native epoxy (12.9 kJ
mol-1). By contrasting the terminal effects, the aggregation states and
crosslinking modes were proposed, thus clarifying the
supramolecular-dominant aggregation mechanism and covalent-dominant
dispersion mechanism, which influences the resulting material
properties. This work underscores the significance of aggregate science
in comprehending polymer crosslinking and provides theoretical insights
for tailoring material properties at a refined molecular level in the
field of polymer science.%
\end{abstract}%



\sloppy


Toward understanding the cross-linking from molecular chains to
aggregates by engineering terminals of supramolecular hyperbranched
polysiloxane

Yuanbo Zhang, Junshan Yuan, Jingzhi Hu, Zhixuan Tian, Weixu Feng,
Hongxia Yan*

Y. Zhang, J. Yuan, J Hu, Z. Tian, Prof. W. Feng, Prof. H. Yan

Shaanxi Key Laboratory of Macromolecular Science and Technology, Xi'an
Key Laboratory of Hybrid Lumines-cent Materials and Photonic Device,
School of Chemistry and Chemical engineering, Northwestern Polytechnical
University, Xi'an 710129, China

E-mail: \emph{hongxiayan@nwpu.edu.cn}

Keywords: hyperbranched polymers, aggregates, crosslinking

\textbf{Abstract:}Crosslinking thermosets with hyperbranched polymers
confers them superior comprehensive performance. However, it still
remains a further understanding of polymer crosslinking from the
molecular chains to the role of aggregates. In this study, three
hyperbranched polysiloxane structures (HBPSi-R) are synthesized as model
macromolecules, each featuring distinct terminal groups (R denotes
amino, epoxy, and vinyl groups) while similar molecular backbone
(Si-O-C). These structures were subsequently copolymerized with epoxy
monomers to construct interpenetrating HBPSi-R/epoxy/anhydride
co-polymer systems. The spatial molecular configuration and flexible
Si-O-C branches of HBPSi-R endow them with remarkable reinforcement and
toughening effects. Notably, an optimum impact strength of 28.9 kJ
mol\textsuperscript{-1} is achieved with a mere 3\% loading of HBPSi-V,
nearly three times that of the native epoxy (12.9 kJ
mol\textsuperscript{-1}). By contrasting the terminal effects, the
aggregation states and crosslinking modes were proposed, thus clarifying
the supramolecular-dominant aggregation mechanism and covalent-dominant
dispersion mechanism, which influences the resulting material
properties. This work underscores the significance of aggregate science
in comprehending polymer crosslinking and provides theoretical insights
for tailoring material properties at a refined molecular level in the
field of polymer science.

1. Introduction

Aggregation and dispersion have long been regarded as mutually exclusive
concepts, but this dichotomy is in fact a fundamental feature of the
natural world. From the gravitational coalescence of dispersed celestial
bodies in the universe, to the islands in the ocean, and even to the
intricate network-formation of polymer cross-linking, this trend seems
like ubiquitous across all scales of the natural world. This universal
significance underscores the importance of understanding the mechanisms
that govern aggregation and dispersion phenomena in diverse fields of
science.\textsuperscript{{[}1\emph{-} 5{]}}

Conventionally, the cross-linking of polymer is known as a
network-formation process from linear monomer to three-dimensional
structures, namely the crosslinked network.\textsuperscript{{[}6\emph{-}
8{]}} But if substitute the linear monomer with a spatial topological
macromolecule, such as dendrimer,\textsuperscript{{[}9{]}}star
polymer,\textsuperscript{{[}10{]}}hyperbranched
polymer.\textsuperscript{{[}11{]}} These topological macromonomers will
occupy all or part of the cross-linking site to form a
topologically-extended network with respect to their three-dimensional
one, we coined it topological crosslinking networks (TCNs) that link
through all or part of topological units. In such system, it could be
recognized that the macromonomers should undergo both aggregation and
dispersion behaviors during polymer crosslinking, which relies on their
interface nature (for example, functional groups, surface energy, system
temperature).\textsuperscript{{[}12\emph{-} 14{]}} Therefore, the
aggregate state and nano-interface control over the cross-linked
structure, and attributes the final properties of the resulting
polymer.\textsuperscript{{[}15\emph{-} 19{]}}

Aggregate science contributes a fresh enlightenment to incline the view
of the polymer crosslinking into a more refined and precise
direction.\textsuperscript{{[}15\emph{-} 19{]}} People customarily
consider the crosslinking of chemical bonds at the molecular level,
however, in case of a multi-components
system,\textsuperscript{{[}23{]}}although many efforts have been made
toward concepting supramolecular interpenetration or other related ideas
among hydrogels and elastomers,\textsuperscript{{[}24\emph{-} 28{]}} The
crosslinking modes should be included but not limited in covalent-bonds
and weakly supramolecular interactions. Especially, in case of a
thermoset polymer system, over-agglomeration of additives has always
been regarded as an undesired matter that dampens material
properties,\textsuperscript{{[}29\emph{,} 30{]}} but the aggregates at
nano- or micro- scales could be the positive one reasoned from their
nano-phase separation and forming a strong interface between
double-phase polymer.\textsuperscript{{[}31{]}}

As a representative crosslinked example, epoxy resins (EPs) feature
excellent thermal and mechanical properties due to their
highly-crosslinked network-forming
architecture,\textsuperscript{{[}32\emph{-} 34{]}} which are widely
involved in human society for aerospace, navigation, wind power. To meet
the ever-growing demands for advanced application, the integrals on
realizing high-performance and multi-function purposes still require an
incisive understanding from structure-to-property relations toward
in-principle building and tailoring polymers. The state-of-the-art work
focuses their insights overlapping supramolecular
chemistry,\textsuperscript{{[}35\emph{-} 38{]}}dynamic covalent and/or
no-covalent chemistry\textsuperscript{{[}39\emph{-} 42{]}} to engineer
the polymer network and to regulate the chemical crosslinks and physical
entanglement, which inspires us insightful viewpoints to further
understand the cross-linking, and the real formation of
polymer.\textsuperscript{{[}43{]}}

In this study, three kinds of hyperbranched polysiloxane (HBPSi-R) were
designed and synthesized, respectively, each featuring with different
terminals but similar molecular backbone (Si-O-C), and they were
copolymerized with epoxy resin/anhydride system to construct
supramolecular HBPSi-R/epoxy interpenetrating polymer networks. The
thermal performance, curing behaviors and mechanical properties of
resulting materials were studied in a fresh viewpoint of aggregation and
dispersion to co-polymer crosslinking. To contrast the terminal effects,
the aggregation states and nano-interface were revealed, as the
double-crosslinking modes and their aggregate mechanism were proposed in
combining their mechanical properties and different terminal groups.
Highlighting the importance for understanding the polymer crosslinking
from the concept of aggregate science, this work provides theoretical
guidance toward in-principle tailoring material properties from a more
refined molecular structure in polymeric science.

\section*{2. Results and discussions}

{\label{results-and-discussions}}

\textbf{2.1. Reagent materials and Methods}

The reagent materials and method information are supplied in\textbf{S1}
.

\textbf{2.2. Synthesis and structural investigation of HBPSi-R}

The synthesis of hyperbranched polysiloxane (HBPSi-R) bearing Si-O-C
molecular backbone is straightforward using
A\textsubscript{2}+B\textsubscript{3} ester-exchange polycondensation,
where R represent their terminal groups of amino
(HBPSi-NH\textsubscript{2}), epoxy (HBPSi-EP) and vinyl group (HBPSi-V).
Synthetic details are described in\textbf{S1.} \textbf{2} . Briefly, a
simple diol (1,3-propanediol, PDO) was employed as
A\textsubscript{2}monomer to react with (3-aminopropyl) triethoxysilane,
(3-glycidyloxypropyl) triethoxysilane and triethoxyvinylsilane,
respectively, yielding liquid products (\textbf{Figure 1} ). The
concentration of hydroxyl group (-OH) was quantified by titration
experiments, with details given in \textbf{S2.3} , yielding approximate
-OH concentration of 1.69 \selectlanguage{ngerman}× 10\textsuperscript{-2} mol
g\textsuperscript{-1}, 1.33 × 10\textsuperscript{-2} mol
g\textsuperscript{-1} and 1.45 × 10\textsuperscript{-2} mol
g\textsuperscript{-1} for HBPSi-NH\textsubscript{2}, HBPSi-EP and
HBPSi-V, respectively. Since the -OH concentration of HBPSi-R is much
lower than that of epoxy resin, thus the incorporation of HBPSi-R does
not change the equivalence dosage of epoxy formulation.

The chemical structure of HBPSi-NH\textsubscript{2}, HBPSi-EP and
HBPSi-V are evidenced by fourier transform infrared
(FT-IR),\textsuperscript{1}H nuclear magnetic resonance
(\textsuperscript{1}H-NMR), respectively. To prove the proceeded
polycondensation, the distillates from reaction systems were collected
for IR detection, showing the same IR profiles compared with that of
standard ethanol (See \textbf{Figure S1a} ), demonstrating the
as-expected polycondensation.\textsuperscript{1}H-NMR was performed to
assign the chemical shifts of protons in spectra of HBPSi-R
(\textbf{Figure 1b} ) and their monomers (\textbf{Figure S2} ). It's
noted that the protons from H1 and H2 in PDO are separated into three
different modes in each spectrum of HBPSi-R, which is attributed to
various linked modes of protons in dendritic, linear and terminal sites
upon hyperbranched structure.\textsuperscript{{[}44{]}} Besides, the
protons from amino, epoxy and vinyl groups can be recognized as marking
a-e involving in the synthetic polymers (\textbf{Figure 1b} ),
indicating their characteristic groups. The FT-IR information of HBPSi-R
and their monomers are presented in \textbf{Figure 1c} and \textbf{S2.1}
, respectively. In the spectrum of HBPSi-NH\textsubscript{2}, two peaks
around 3300 cm\textsuperscript{-1} are attributed to the stretching
vibration of primary amine group, which can also be founded in the
spectrum of its monomers (\textbf{Figure S1b} ). In the spectrum of
HBPSi-EP, the peak at 880 cm\textsuperscript{-1} corresponds to the
C-O-C absorption in epoxy group. In the spectrum of HBPSi-V, the peak at
1600 cm\textsuperscript{-1} is attributed to the stretching vibration of
carbon-carbon double bond.\textsuperscript{{[}45{]}} These results prove
the hyperbranched structure information with the presence of
characteristic terminals.

\textbf{2.3. Fabrication ofHBPSi-R/EP co-polymer system}

The HBPSi-R/EP co-polymer system was fabricated using a thermoset
workflow (\textbf{S1.3} ). The resin matrix consisted of an epoxy resin
(DGEBA, E51) and an anhydride curing agent (methyl tetrahydrophthalic
anhydride, MTHPA). The fabrication of xHBPSi-R/EP composites involved a
thermocuring process by casting method, where 'x' represents the mass
fraction of HBPSi-R in the whole resin matrix. In brief, different mass
fractions (3\%, 6\%, 9\%) of HBPSi-R were mixed with 70 g of DGEBA epoxy
resin and stirred at 80 °C for 15 minuntil a clear yellowish solution
was obtained. Subsequently, 56 g of MTHPA and two drops of
tris(dimethylaminomethyl)phenol (DMP-30, curing accelerator) were added
and stirred for another 15 min. The mixture was then poured into a
preheated mold, and then follows thoroughly degassing in an 80 °C vacuum
for 30 min. The curing process involved a heating procedure of 120 °C
for 2 h, followed by 150 °C for 3 h and 180 °C for 2 hours. After
curing, the samples were demolded and prepared for testing.

\textbf{Figure 2} illustrates a schematic model describing the distinct
reaction modes of HBPSi-R with epoxy substrates. These HBPSi-R
structures possess unique terminals and abundant -OH groups upon their
molecular backbone (\textbf{Figure 2a} ). The -OH groups can react with
both DGEBA epoxy resin and anhydride curing agent, resulting in clear
and uniform resin solutions after brief pre-polymerization. The
characteristic terminal groups of HBPSi-R control over their
crosslinking behavior and aggregate state of HBPSi-R. Specifically, the
amino group in HBPSi-NH\textsubscript{2} react with both epoxy group and
anhydride group, while the epoxy group in HBPSi-EP participates in the
curing reaction likewise another epoxy component, and the carbon-carbon
double bond (vinyl) in HBPSi-V does not react with epoxy resin and
anhydride-type curing agent, which plays a supportable role in
interpenetrating thermoset network with hyperbranched structure.

\textbf{2.4. Curing and thermal performance of HBPSi-R/EP}

To investigate the influence of HBPSi-R with varying terminal groups on
the curing performance of epoxy resin, the pre-polymer resin compounds
were initially characterized using isothermal differential scanning
calorimetry (DSC, See\textbf{Figure 2b} ). Upon the incorporation of
HBPSi-R, the DSC thermograms exhibited a single exothermic peak
resembling that of the native EP, indicating excellent compatibility of
the three types of HBPSi-R with the epoxy/anhydride matrix. It is
noteworthy that the peak temperature slightly decreased from 165°C to
155°C, suggesting that the inclusion of HBPSi-R does not compromise the
processability of the epoxy resin. To determine the real chemical
bonding of HBPSi-R within epoxy resin, Fourier-transform infrared
(FT-IR) spectra of the cured resin samples were performed
(\textbf{Figure 2d} ). Obviously, a wider stretching vibration of Si-O
at 1080 cm\textsuperscript{-1} is recognized in spectra of
HBPSi-NH\textsubscript{2}/EP, HBPSi-EP/EP and HBPSi-V/EP, meanwhile, the
peak intensity of hydroxyl group is significantly lower than that of the
native EP, indicating the consummation of residual hydroxyl groups and
confirming the participation of HBPSi-R in the copolymerization and
crosslinking with the epoxy network. X-ray diffraction (XRD,
\textbf{Figure S3} ) profiles revealed that the branching structures did
not influence the molecular arrangement, thereby maintaining the
amorphous crosslinked structure of the epoxy resin.

Thermogravimetric analysis (TGA) was conducted to assess the impact of
HBPSi-R on the thermal properties of materials. Given in \textbf{Figure
2c} , overall, the addition of hyperbranched polysiloxanes primarily
enhanced the residual char of the materials while exerting minimal
influence on the initial decomposition and main decomposition behavior
(as indicated by the derivative thermogravimetry, DTG, shown
in\textbf{Figure S7} ). This improvement can be attributed to the
introduction of the inert silicon-containing component. Notably,
compared to neat EP, HBPSi-EP/EP exhibited the most substantial increase
in char residue, rising from 6.0\% to 11.7\%, whereas the amino and
vinyl variants showed a char residue of 9.5\%. This can be attributed to
the superior uniform dispersion of HBPSi-EP within the resin matrix
compared to the other variants. The detailed curing and thermal
parameters are supplied in \textbf{Table S3} .

\textbf{2.5. Aggregation mechanism and crosslinking modes of HBPSi-R/EP}

Based on the aforementioned discussion, hyperbranched polysiloxanes with
similar molecular backbone (Si-O-C) but varying terminals could serve as
nice model to explore the terminal effects on polymer crosslinking. The
aggregate behaviors and crosslinking modes are proposed and described
in\textbf{Figure 3} . It is important to note that HBPSi-R not only
possesses abundant -OH groups for reactiveness but also characteristic
terminals (-NH\textsubscript{2}, -EP, vinyl groups) for adjusting its
overall interface features with epoxy resin. The -OH groups can react
simultaneously with the DGEBA monomer (ring-opening) and the anhydride
monomer (forming ester bonds), thus covalently crosslinking with epoxy
network. In addition, it will also supramolecularly crosslinks within
the network through hydrogen bond interactions. Therefore, the three
systems should exhibit a consistent double-crosslinking behavior
involving both covalent and supramolecular modes regardless of their end
groups.

To elucidate the characteristic terminal effects, the distribution
states of HBPSi-R were visually observed using transmission electron
microscopy (TEM) and scanning transmission electron microscopy tools
(STEM, the magnification images in Figure 3). A staining method was
adopted to enhance the imaging clarity since HBPSi-R is embedded in the
cured resin (\textbf{S1.4} ).\textsuperscript{{[}5{]}} It can be founded
that the hyperbranched components are uniformly dispersed with varying
aggregation degrees at the nanoscale. This fact indicates that HBPSi-R
forms a series of supramolecular hyperbranched polysiloxane aggregates
during polymer crosslinking, driven by their low surface
energy\textsuperscript{{[}46{]}} and intermolecular hydrogen
bonds\textsuperscript{{[}47{]}}.

Specifically, HBPSi-NH\textsubscript{2} shows typical sea-island
characteristic, where the HBPSi-NH\textsubscript{2} acts as the
dispersed phase and the resin matrix serves as the continuous phase,
featuring the tightest aggregation behavior with size of
\textasciitilde{} 90 nm than HBPSi-V and HBPSi-EP as seen in Figure 3,
coined as aggregately crosslinking whose supramolecular behavior
dominates during polymer crosslinking, where the strong intermolecular
hydrogen bonds between -NH\textsubscript{2} and -OH terminals drive the
assembly of HBPSi-NH\textsubscript{2}, as clearly defined by the
silicon-rich scanning surface in element mapping. In contrast, HBPSi-EP
shows dominant uniform dispersion behavior in its TEM image, without
apparent nano-phase separation. This is referred to as evenly
crosslinking, wherein HBPSi-EP behaves likewise to another epoxy
component to covalently bond in such system (covalent-dominance in
crosslinking). Between the two structure, HBPSi-V demonstrates uniform
dispersion with also stable nano-sized aggregates, whose particle sizes
is more regular than that of HBPSi-NH\textsubscript{2}. This behavior,
termed bulky crosslinking, arises from the moderate interface in which
the non-reactive vinyl groups of HBPSi-V play a supportive role to make
sure a balance between covalent and non-covalent supramolecular forms.
These finds provide deeper insights from the holism of aggregate science
into the terminal-dependent crosslinking of HBPSi-R within epoxy
network, consequently influencing the overall material properties.

\textbf{2.6. Mechanical performance of HBPSi-R/EP}

The mechanical strength of HBPSi-R/EP was tested to contrast the
terminal effects among the three hyperbranched structures modifying
epoxy resin (\textbf{Figure 4a-c} ), following the test results in
\textbf{Table S4} . The impact fracture microsurfaces are presented in
\textbf{Figure 4d-g} . Generally, the impact failure of thermosets often
owns to their high crosslinking density and rigid polymer chains that
are difficult to dissipate the impact energy.\textsuperscript{{[}48{]}}
As the natural EP displayed typical brittleness ``river-like'' fracture
covering a large microscopic area (\textbf{Figure 4d} ), with impact
toughness of only 12.9 kJ/m\textsuperscript{2}. In contrast, the
incorporation of the hyperbranched structures, benefiting the merit of
hyperbranched architecture and flexible Si-O-C chains, all demonstrate
excellent strengthening and toughening effects, with a gradual decrease
as the content is further increased. As shown in Figure 4a-c, HBPSi-V
performs superior reinforcement effects regarding toughness, strength
and modulus with respect to the other two hyperbranched structures, with
an increasingly tough feature from native EP to
HBPSi-NH\textsubscript{2}, HBPSi-EP and HBPSi-V in SEM photographs
(Figure 4d-g\textbf{)} . The optimal impact strength of 28.9 kJ/m² was
achieved with 3\% incorporation of HBPSi-V, nearly three times higher
than that of the pristine EP. Based on the aforementioned analyses,
these hyperbranched structures possess similar molecular backbones with
approximate hydroxyl concentration, as their terminals give rise to such
significant differences in mechanical properties, which might be closely
related to their unique crosslinking and aggregate
behavior.\textsuperscript{{[}49\emph{,} 50{]}}

Among the three structures, HBPSi-V bears a moderate aggregation and
dispersion behavior due to its non-reactive vinyl group, which could
forms an appropriate nano-silicone aggregates to toughen the polymer
network in case of elastomer mechanism being
dominant.\textsuperscript{{[}51\emph{,} 52{]}} Meanwhile, their abundant
-OH terminals can interact covalently and/or non-covalently within the
epoxy network, acting as a supramolecular ``nano-rivets'' that tightly
entangle within the network for strengthening
effort.\textsuperscript{{[}53{]}} However, it should be note that
excessive aggregation of HBPSi-R does a negative effect on mechanical
performance, where the bulk agglomeration of excessive hyperbranched
polymer becomes a stress concentration area, leading to the
deterioration in impact strength. It is worth mentioning that the
deterioration in impact strength is less significant in HBPSi-V/EP
compared to HBPSi-NH\textsubscript{2}/EP at the same filler load.
Furthermore, the impact toughness of HBPSi-NH\textsubscript{2}/EP is
even lower than that of the pristine EP, indicating that
HBPSi-NH\textsubscript{2} has a lower tendency to form bulk
agglomerations than HBPSi-V at high filler additions. Regarding strength
and modulus (\textbf{Figure 4b, c)} , the flexural strength increases by
36.4\% from 106.1 MPa to 144.7 MPa with the incorporation of 3\%
HBPSi-EP. Both HBPSi-V and HBPSi-EP exhibit better strengthening effects
compared to HBPSi-NH\textsubscript{2}, and HBPSi-V performs better at
high filler loads (9\%). Therefore, it is evident that the
nano-reinforced and supramolecular ''nano-rivets'' mechanisms both
depend on appropriate aggregate and uniform dispersion of supramolecular
HBPSi-V.

The thermomechanical behaviors were evaluated using dynamic
thermomechanical analysis (DMA), as shown in\textbf{Figure 5} . Overall,
the temperature-dependent storage modulus (E') curves in \textbf{Figure
5d-f} exhibit a consistent trend in all the three systems with
increasing addition of hyperbranched polysiloxane. The co-crosslinking
of HBPSi-R significantly improves the E' value from the room temperature
region to the glass transition of the materials (\textbf{Figure 5a} ),
indicating the excellent reinforcement effect of HBPSi-R. The overall
decreasing in crosslink density (\emph{d\textsubscript{crosslink}} ) is
presented in \textbf{Figure 5b}according to the rubber elasticity theory
(\textbf{S3.1} ).\textsuperscript{{[}54\emph{,} 55{]}} As a results, the
decrease in \emph{d\textsubscript{crosslink}} is lower for
HBPSi-NH\textsubscript{2} compared to HBPSi-EP and HBPSi-V, which
further confirms the tightly aggregated nature of
HBPSi-NH\textsubscript{2} that is unfavorable for forming the free
volume in crosslinking network. As a whole, these hyperbranched
structures can reduce the crosslinking density of thermoset but do not
deteriorate their mechanical strength, which is attributed to their
highly branched chains and abundant reactive
terminals.\textsuperscript{{[}44\emph{,} 56{]}} The glass transition
temperatures (\emph{T\textsubscript{g}} ) of EP,
6HBPSi-NH\textsubscript{2}/EP, 6HBPSi-EP/EP, 6HBPSi-V/EP are
131\textsuperscript{o}C, 118 \textsuperscript{o}C, 111
\textsuperscript{o}C and 110 \textsuperscript{o}C, respectively,
indicating they are glassy polymer at room
temperature.\textsuperscript{{[}57{]}} The decrease
in\emph{T\textsubscript{g}} is foreseeable due to the amorphous
structure, as well as the flexible molecular chains of HBPSi-R.
Therefore, the co-crosslinking of HBPSi-R encourages a
weakly-crosslinked but high-strength thermoset network, and its terminal
nature comprehensively affects the aggregation, dispersion, even to
crosslinking and the final material properties.

\textbf{Conclusion}

In summary, we successfully synthesized three hyperbranched structures
with a common Si-O-C molecular backbone but differing terminal groups.
These structures were co-crosslinked with thermoset epoxy to explore
their terminal effects on affecting the overall material performance.
The special molecular characteristics of HBPSi-R involves abundant -OH
groups for their reactiveness, as well as distinctive terminals
(-NH\textsubscript{2}, -EP, vinyl groups) that impart characteristic
interface features. All three variants of HBPSi-R exhibit well
compatibility within the epoxy matrix, showcasing diverse nano-interface
and aggregation behavior. Benefiting their spatial molecular
configuration and flexible Si-O-C branches, HBPSi-R manifests
exceptional strengthening and toughening effects regardless of their
terminal groups. Among them, HBPSi-NH\textsubscript{2} predominantly
exhibits the aggregation behavior from supramolecular interaction, while
HBPSi-EP show predominantly exhibits dispersion behavior from covalent
effect. HBPSi-V achieves a balance of the both, surpassing the other two
structures in terms of optimal impact toughness (28.9 kJ
mol\textsuperscript{-1}) and better mechanical performance under high
dosage, where the non-reactive vinyl group acts as a supportable role
during polymer crosslinking. These findings not only emphasize the
pronounced reinforcement effects of HBPSi-R but also provide a fresh
perspective from aggregate science in the context of polymer
crosslinking.

\textbf{Acknowledgments}

This work was sponsored by National Natural Science Foundation of China
(22175143), Key Research and Development Project of Shaanxi
(2022GY-353), Science Center for Gas Turbine Project
(P2022-DB-V-001-001), and Fundamental Research Funds for the Central
Universities (D5000230086). Many thanks Analytical \& Testing Center of
Northwestern Polytechnical University for test assistance

\textbf{Conflict of Interests}

The authors declare no conflict of interests.

\textbf{Supporting Information}

Supporting Information is available from the Wiley Online Library or
from the author.

Received: ((will be filled in by the editorial staff)) Revised: ((will
be filled in by the editorial staff)) Published online: ((will be filled
in by the editorial staff))

\textbf{References}

1. H. Zhang, Z. Zhao, A. T. Turley, L. Wang, P. R. McGonigal, Y. Tu, Y.
Li, Z. Wang, R. T. K. Kwok, J. W. Y. Lam, B. Z. Tang, Adv.
Mater.\textbf{2020} , 32, 2001457.

2. T. Han, D. Yan, Q. Wu, N. Song, H. Zhang, D. Wang, Chinese J.
Chem.\textbf{2021} , 39, 677.

3. J. Mei, Y. Hong, J. W. Y. Lam, A. Qin, Y. Tang, B. Z. Tang, Adv.
Mater.\textbf{2014} , 26, 5429.

4. Z. Zhao, H. Zhang, J. W. Y. Lam, B. Z. Tang, Angew. Chem. Int.
Edit.\textbf{2020} , 59, 9888.

5. L. Albertazzi, D. van der Zwaag, C. M. A. Leenders, R. Fitzner, R. W.
van der Hofstad, E. W. Meijer, Science \textbf{2014} , 344, 491.

6. N. Zheng, Y. Xu, Q. Zhao, T. Xie, Chem. Rev. \textbf{2021} , 121,
1716.

7. G. Li, J. Zhao, Z. Zhang, X. Zhao, L. Cheng, Y. Liu, Z. Guo, W. Yu,
X. Yan, Angew. Chem. Int. Edit. \textbf{2022} , 61, e202210078.

8. H. Chen, J. Zhang, W. Yu, Y. Cao, Z. Cao, Y. Tan, Angew. Chem. Int.
Edit. \textbf{2021} , 60, 22332.

9. D. A. Tomalia, Prog. Polym. Sci. \textbf{2005} , 30, 294.

10. D. Döhler, H. Peterlik, W. H. Binder, Polymer \textbf{2015} , 69,
264.

11. S. Chen, Z. Xu, D. Zhang, Chem. Eng. J. \textbf{2018} , 343, 283.

12. M. A. Ashraf, W. Peng, Y. Zare, K. Y. Rhee, Nanoscale Res.
Lett.\textbf{2018} , 13, 214.

13. C. Cui, C. Fan, Y. Wu, M. Xiao, T. Wu, D. Zhang, X. Chen, B. Liu, Z.
Xu, B. Qu, W. Liu, Adv. Mater. \textbf{2019} , 31, 1905761.

14. N. Jouault, P. Vallat, F. Dalmas, S. Said, J. Jestin, F. Boué,
Macromolecules \textbf{2009} , 42, 2031.

15. F. S. Kim, G. Ren, S. A. Jenekhe, Chem. Mater. \textbf{2011} , 23,
682.

16. B. Huang, W. Chen, Z. Li, J. Zhang, W. Zhao, Y. Feng, B. Z. Tang, C.
Lee, Angew. Chem. Int. Edit. \textbf{2018} , 57, 12473.

17. Y. Zare, Compos. Part A-Appl. S. \textbf{2016} , 84, 158.

18. D. Astruc, E. Boisselier, C. Ornelas, Chem. Rev. \textbf{2010} ,
110, 1857.

19. R. Yu, M. Li, Z. Li, G. Pan, Y. Liang, B. Guo, Adv. Healthc.
Mater.\textbf{2022} , 11, 2102749.

20. M. Kang, Z. Zhang, N. Song, M. Li, P. Sun, X. Chen, D. Wang, B. Z.
Tang, Aggregate \textbf{2020} , 1, 80.

21. J. Li, J. Wang, H. Li, N. Song, D. Wang, B. Z. Tang, Chem. Soc.
Rev.\textbf{2020} , 49, 1144.

22. S. Tao, S. Zhu, T. Feng, C. Zheng, B. Yang, Angew. Chem. Int.
Edit.\textbf{2020} , 59, 9826.

23. T. Yamakado, S. Saito, J. Am. Chem. Soc. \textbf{2022} , 144, 2804.

24. J. Liu, C. S. Y. Tan, Z. Yu, N. Li, C. Abell, O. A. Scherman, Adv.
Mater. \textbf{2017} , 29, 1605325.

25. Y. Liu, J. Wan, X. Zhao, J. Zhao, Y. Guo, R. Bai, Z. Zhang, W. Yu,
H. W. Gibson, X. Yan, Angew. Chem. Int. Edit. \textbf{2023} , n/a,
e202302370.

26. Y. Gao, K. Peng, S. Mitragotri, Adv. Mater. \textbf{2021} , 33,
2006362.

27. E. A. Appel, J. Del Barrio, X. J. Loh, O. A. Scherman, Chem. Soc.
Rev.\textbf{2012} , 41, 6195.

28. Y. Zheng, H. Zhu, Y. Tan, F. Liu, Y. Wu, Chinese J. Polym.
Sci.\textbf{2023} , 41, 84.

29. Y. Zhang, K. Yang, R. Liu, J. Yao, H. Yan, Chem. Eng. J.
\textbf{2023} , 460, 141773.

30. Z. Chen, M. Zhang, P. Ren, Z. Lan, Z. Guo, H. Yan, Y. Jin, F. Ren,
Chem. Eng. J. \textbf{2023} , 466, 143086.

31. Y. Zheng, R. Kiyama, T. Matsuda, K. Cui, X. Li, W. Cui, Y. Guo, T.
Nakajima, T. Kurokawa, J. P. Gong, Chem. Mater. \textbf{2021} , 33,
3321.

32. J. Liu, S. Wang, Y. Peng, J. Zhu, W. Zhao, X. Liu, Prog. Polym.
Sci.\textbf{2021} , 113, 101353.

33. S. Huo, P. Song, B. Yu, S. Ran, V. S. Chevali, L. Liu, Z. Fang, H.
Wang, Prog. Polym. Sci. \textbf{2021} , 114, 101366.

34. T. Kaiser, Prog. Polym. Sci. \textbf{1989} , 14, 373.

35. L. Yang, X. Tan, Z. Wang, X. Zhang, Chem. Rev. \textbf{2015} , 115,
7196.

36. T. Aida, E. W. Meijer, S. I. Stupp, Science \textbf{2012} , 335,
813.

37. Y. Liu, Z. Wang, X. Zhang, Chem. Soc. Rev. \textbf{2012} , 41, 5922.

38. S. J. D. Lugger, S. J. A. Houben, Y. Foelen, M. G. Debije, A. P. H.
J. Schenning, D. J. Mulder, Chem. Rev. \textbf{2022} , 122, 4946.

39. S. J. Rowan, S. J. Cantrill, G. R. L. Cousins, J. K. M. Sanders, J.
F. Stoddart, Angew. Chem. Int. Edit. \textbf{2002} , 41, 898.

40. M. J. Webber, M. W. Tibbitt, Nat. Rev. Mater. \textbf{2022} , 7,
541.

41. P. Song, H. Wang, Adv. Mater. \textbf{2020} , 32, 1901244.

42. Y. Yang, Y. Xu, Y. Ji, Y. Wei, Prog. Mater. Sci. \textbf{2021} ,
120, 100710.

43. X. Huang, D. Lv, L. Ai, S. H. Cheng, X. Yao, Chinese J. Polym.
Sci.\textbf{2021} , 39, 1310.

44. Y. Zhang, H. Yan, G. Feng, R. Liu, K. Yang, W. Feng, S. Zhang, C.
He, Compos. Part. B-Eng. \textbf{2021} , 222, 109043.

45. T. Bai, Y. Zhang, L. Wang, H. Yan, W. Zhou, Aggregate \textbf{2023}
, 4, e267.

46. K. Chen, H. Li, S. Huang, W. Chen, K. Sun, F. Chang, Polym.
Int.\textbf{2011} , 60, 1089.

47. Y. Luan, X. Zhang, S. Jiang, J. Chen, Y. Lyu, Chinese J. Polym.
Sci.\textbf{2018} , 36, 584.

48. S. Huo, Z. Zhou, J. Jiang, T. Sai, S. Ran, Z. Fang, P. Song, H.
Wang, Chem. Eng. J. \textbf{2022} , 427, 131578.

49. L. Boogh, B. Pettersson, J. E. Månson, Polymer \textbf{1999} , 40,
2249.

50. G. Ye, S. Huo, C. Wang, Q. Shi, L. Yu, Z. Liu, Z. Fang, H. Wang,
Compos. Part. B-Eng. \textbf{2021} , 227, 109395.

51. S. Chen, Z. Xu, D. Zhang, Chem. Eng. J. \textbf{2018} , 343, 283.

52. W. Huang, D. Restrepo, J. Jung, F. Y. Su, Z. Liu, R. O. Ritchie, J.
McKittrick, P. Zavattieri, D. Kisailus, Adv. Mater. \textbf{2019} , 31,
1901561.

53. R. Liu, H. Yan, Y. Zhang, K. Yang, S. Du, Chem. Eng. J. 2022, 433,
133827.

54. Y. Wang, K. Kou, G. Wu, L. Zhuo, J. Li, Y. Zhang, Polymer
\textbf{2015} , 77, 354.

55. L. Tang, J. Zhang, Y. Tang, Y. Zhou, Y. Lin, Z. Liu, J. Kong, T.
Liu, J. Gu, Compos. Part. B-Eng. \textbf{2020} , 186, 107827.

56. Y. Zhang, R. Liu, R. Yu, K. Yang, L. Guo, H. Yan, Compos. Part.
B-Eng.\textbf{2022} , 242, 110101.

57. H. Wang, H. Liu, Z. Cao, W. Li, X. Huang, Y. Zhu, F. Ling, H. Xu, Q.
Wu, Y. Peng, B. Yang, R. Zhang, O. Kessler, G. Huang, J. Wu, Proc. Natl.
Acad. Sci. U.S.A. \textbf{2020} , 117, 11299.

\textbf{Figure 1}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1.} a) The synthesis route of HBPSi-R featuring with
varying terminals, b) \textsuperscript{1}H-NMR spectra and c) FT-IR
information of the synthetic polymers

\textbf{Figure 2}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2.} a) The schematic illustration for HBPSi-R/EP
co-polymer systems with their unique reactive modes, b) DSC thermograms
for pre-polymer mixtures at heating rate of
15\textsuperscript{o}C\selectlanguage{ngerman}·min\textsuperscript{-1}, c) weight loss curves
under nitrogen atmosphere, d) FT-IR spectra of the cured samples,
samples are 6HBPSi-NH\textsubscript{2}/EP, 6HBPSi-EP/EP, and
6HBPSi-V/EP, respectively.

\textbf{Figure 3}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3.} The schematic model and TEM morphologies describing
the terminals effect and nano-crosslinking modes of
HBPSi-NH\textsubscript{2}, HBPSi-EP and HBPSi-V within the thermoset
matrix

\textbf{Figure 4}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 4.} The mechanical performance test of a) impact
strength, b) flexural strength, and c) modulus at 25
\textsuperscript{o}C; d-e) SEM photographs indicates the impact tough
facture from native EP to HBPSi-NH\textsubscript{2}/EP, HBPSi-EP/EP,
HBPSi-V/EP

\textbf{Figure 5}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 5.} a) The temperature-dependent storage modulus of
6HBPSi-R/EP with distinct terminals, b) network crosslinking density, c)
Tan \selectlanguage{greek}δ \selectlanguage{english}curves; d-f) storage modulus curves with different content of
HBPSi-R

\textbf{The table of contents entry}

This study presents a novel perspective towards the understanding of
polymer crosslinking from individual molecular chains to the role of
aggregates. The aggregate states and crosslinking modes are proposed by
engineering amino, epoxy and vinyl terminals upon hyperbranched
structures. Benefiting spatial molecular configuration and flexible
Si-O-C branches, these hyperbranched structures demonstrate exceptional
enhancements in both strength and toughness, and among other superior
features, striking a delicate balance between dispersion and
aggregation, as well as forming robust nano-interfaces. This research
emphasizes the significance of aggregate science in comprehending the
intricacies of polymer crosslinking and offers valuable theoretical
insights for tailoring material properties at a refined molecular level.

Yuanbo Zhang, Junshan Yuan, Jingzhi Hu, Zhixuan Tian, Weixu Feng,
Hongxia Yan*

\textbf{Toward understanding the cross-linking from molecular chains to
aggregates by engineering terminals of supramolecular hyperbranched
polysiloxane}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

Supporting Information

Toward understanding the cross-linking from molecular chains to
aggregates by engineering terminals of supramolecular hyperbranched
polysiloxane

Yuanbo Zhang, Junshan Yuan, Jingzhi Hu, Zhixuan Tian, Weixu Feng,
Hongxia Yan*,

\textbf{S1. Materials and Methods}

\textbf{S1.1. Materials}

Siloxane monomers including a (3-aminopropyl)triethoxysilane (KH-550), a
(3-Glycidyloxypropyl)triethoxysilane (A-1871) and a triethoxyvinylsilane
(A-151) were purchased from Hubei Jianghan New Materials Co.,Ltd, Both
1,3-Propanediol (PDO, AR) and Tris(dimethylaminomethyl)phenol (DMP-30)
were obtained from Macklin Biochemical Co., Ltd. Methyl
Tetrahydrophthalic Anhydride (MTHPA, mixture of isomers) were purchased
from Qihua Chemical Co., Ltd. Epoxy resin, based on a bisphenol A
diglycidyl ether (DGEBA, E51, epoxy value: 0.48 \textasciitilde{} 0.54)
was purchased from Guangzhou Suixin Fine Chemical Co., Ltd. Solvents
such as ethanol and acetone are provided by Guanghua Sci-Tech Co., Ltd.
All chemicals were used as received without a further purification.

\textbf{S1.2. Synthesis details of HBPSi-R}

The synthesis of hyperbranched polysiloxanes (HBPSi-R) is
straightforward using
A\textsubscript{2}+B\textsubscript{3}transesterification
co-polymerization,\textsuperscript{{[}1-5{]}} where R represents their
terminal groups of amino (HBPSi-NH\textsubscript{2}), epoxy (HBPSi-EP),
vinyl group (HBPSi-V). Siloxane monomers including KH-550, A-1871 and
A-151 were used as the B3 monomers with similar molecular structure but
different functional groups, and a simple diol (PDO) was used as the
B\textsubscript{2} reactant. The feed ratio follows in accordance from
the Florey-Carothers law to avoid over-crosslinking. Briefly, 0.16 mol
of siloxanes and 0.35 mol of PDO were put into a three-necked flask
equipped with a mechanical stirrer, a N\textsubscript{2} inlet and a
thermometer. The mixtures were heated from 120 \selectlanguage{ngerman}°C to 180 °C at a heating
rate of 5 °C h\textsuperscript{-1}, then maintain stirring until no more
distillate generated. Theoretically, the distillates from all three
reactions should be the same ethanol with low-boiling point, which could
be consistently separated from the reaction system by a condenser to
drive the polymerization proceeded. The distillates were collected for
IR detection. Taking a rough purification by pressure-reduce drying to
remove the small molecules from reaction, the liquid products can be
final obtained (\textbf{Figure 1} ).

\textbf{S1.3. Fabrication of HBPSi-R/EP co-polymer systems}

The fabrication of HBPSi-R/EP co-polymer systems employed a facile
thermosetting workflow via casting methods. The resin matrix included a
bisphenol-A diglycidyl ether epoxy resin (DGEBA, E51) and an
anhydride-type curing agent (Methyl tetrahydrophthalic anhydride,
MTHPA). A drop of tertiary amine (Tris(dimethylaminomethyl)phenol,
DMP-30) was used as the curing accelerator. Firstly, 70 g of DGEBA with
different mass fraction of HBPSi-R (3\%, 6\%, 9\%) was pre-polymerized
at 80 °C for 15 min. Since a uniform resin solution of xHBPSi-R/EP was
obtained, where x is the mass fraction of HBPSi-R. 56 g of MTHPA and a
drop of DMP-30 were added and stirred for another 15 min. The
pre-polymer mixture was fully degassed in an 80 \textsuperscript{o}C
vacuum for 30 min and then poured into a pre-heated mold. The curing
process underwent a heating procedure of 120 °C × 2h, 150 °C × 3h and
180 °C × 2h, and then demolding and tailoring for test.

\textbf{S1.4. General characterizations}

The fourier transform infrared spectra (FT-IR) were recorded on a
Nicolet Is50 spectrometer (U.S.A) equipped with an attenuated total
reflectance (ATR) model. The nuclear magnetic resonance spectroscopy of
\textsuperscript{1}H,\textsuperscript{13}C and \textsuperscript{31}P
(\textsuperscript{1}H-NMR,
\textsuperscript{13}C-NMR,\textsuperscript{31}P-NMR) was performed using
a Bruker Avance 400 MHz spectrometer. The concentration of hydroxyl
groups was determined by a titration experiment in accordance with GB/T
7383-2007 (Chinese standard). XRD patterns of the cured thermoset
samples was acquired on a Bruker XRD machine (D8 DISCOVER A25). The
transmission electron microscope (TEM, FEI Talos F200X) equipped with an
energy dispersive spectrometer (EDS, Thermo NS7) microanalyzer was used
to observe the distribution and aggregate state of HBPSi-R within the
resin, with the cured sample cut by LEICA UC7 freezing microtome at room
temperature first, then staining by a phosphotungstic acid (1 wt.\%
aqueous solution, 2 h).

The mechanical properties were performed on an electro-mechanical tester
(CMT 6303) in accordance with GB/T 2567-2008 (Chinese standard), with
the sample dimension of 80 mm × 15 mm × 4 mm for flexural test and 80 mm
× 10 mm × 4 mm for impact test. Dynamic thermomechanical analysis (DMA)
was conducted using a three-point bending model on a NETZSCH DMA 242E
machine at the frequency of 1 Hz. Differential scanning calorimetry was
performed under nitrogen (N\textsubscript{2}) atmosphere using a
Mettler-Toledo DSC3 at a heating rate of 15 K·min\textsuperscript{-1}.
Thermogravimetric analysis (TGA) was performed under
N\textsubscript{2}atmosphere using a STA 449F3 thermal analyzer with a
heating rate of 15 °C·min\textsuperscript{-1}. The morphology of impact
fracture surface was observed by a Scanning Electron Microscope equipped
with a tungsten filament gun (TESCAN VEGA 3 LMH).

\textbf{S2. Structural Investigations Supplements}

\textbf{S2.1. FT-IR information of HBPSi-NH\textsubscript{2}, HBPSi-EP,
HBPSi-V and their monomers}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

\textbf{Figure S1} a) IR spectra of the reaction distillates from three
systems show same IR profiles with that of the standard ethanol. IR
spectra of b) HBPSi-NH\textsubscript{2}, c) HBPSi-EP and d) HBPSi-V show
significant -OH absorption compared with PDO (B2 monomer) and specific
characteristic peaks compared with their B3 monomers, respectively.

\textbf{S2.2. \textsuperscript{1}H-NMR assignments of
HBPSi-NH\textsubscript{2}, HBPSi-EP, HBPSi-V and their monomers}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

\textbf{Figure S2} The \textsuperscript{1}H-NMR assignments of a)
HBPSi-NH\textsubscript{2}, b) HBPSi-EP and c) HBPSi-V with
their\textsuperscript{1}H-NMR information compared with monomers,
respectively.

As given in \textbf{Figure S2} , \textsuperscript{1}H-NMR spectra of
HBPSi-NH\textsubscript{2}, HBPSi-EP and HBPSi-V were assigned on by one
in accordance with their hyperbranched structures. Due to the different
solubility in deuterated reagents, DMSO-d6 was selected for HBPSi-V, and
CDCl\textsubscript{3} were chosen for HBPSi-NH\textsubscript{2} and
HBPSi-EP. It is noted that some small offsets as well as emerging new
peaks can be recognized in comparison with their reaction monomers,
indicating the proceed polymerization. Besides, it could be recognized
that the H2 from PDO are separated into three link modes in the
resulting hyperbranched polymers, corresponding to H5, H7, H9 in
HBPSi-NH\textsubscript{2}, H7, H9, H11 in HBPSi-EP, and H3, H5, H7 in
HBPSi-V. These separated protons in NMR spectra after polymerization are
attributed to the various linked modes of dendritic (D), linear (L) and
terminal (L) units upon the hyperbranched backbone. Moreover, the
protons from amino, epoxy and vinyl groups can be assigned in each
HBPSi-R, indicating their characteristic functional groups within the
synthetic polymers,

\textbf{S2.3. Hydroxyl titration record of HBPSi-R}

The concentration of hydroxyl group (-OH) was obtained according to a
titrimetric method (GB/T 7383-2007, Chinese standard). Firstly,
\textasciitilde{}1.00 g of HBPSi-R was mixed with 25 ml phthalic
anhydride pyridine solution (140.00 g to 1 L pyridine). The mixture was
heating upon 115 \textsuperscript{o}C for 60 min in a flask with
condensing reflux. Then adding 4 \textasciitilde{} 5 drops of
phenolphthalein indicator, the solution was titrated by 0.5 M sodium
hydroxide solution (repeating 3 times) until the pink color maintaining
more than 15 s. The control test was carried out for also 3 times
without adding HBPSi-R. The \emph{Q\textsubscript{(OH)}} can be
calculated using \emph{Eqn} (1).\textsuperscript{{[}6{]}}

\begin{equation}
Q_{(OH)}=\frac{c\times\left(V_{0}-V_{1}\right)}{m_{0}}\mathrm{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)}\nonumber \\
 \end{equation}

Where \emph{c} is the concentration of sodium hydroxide solution (0.50
mol\selectlanguage{ngerman}·L\textsuperscript{-1}); \emph{V\textsubscript{0}}
and\emph{V\textsubscript{1}} are consumed volume of sodium hydroxide
solution, respectively; \emph{m\textsubscript{0}} is the mass of
HBPSi-R.

\textbf{Table. S1} Titration experimental records for
HBPSi-NH\textsubscript{2}, HBPSi-EP, HBPSi-V\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
Run & Run & \emph{c} (mol\selectlanguage{ngerman}·L\textsuperscript{-1}) &
\emph{V\textsubscript{0}} (ml) & \emph{V\textsubscript{1}} (ml) &
\emph{m\textsubscript{0}} (g) & \emph{Q\textsubscript{(OH)}} (mol
g\textsuperscript{-1})\tabularnewline
\midrule
\endhead
Control & Test 1 & 0.50 & 82.00 & --- & --- & ---\tabularnewline
& Test 2 & 0.50 & 83.50 & --- & --- & ---\tabularnewline
& Test 3 & 0.50 & 84.50 & --- & --- & ---\tabularnewline
& Average & 0.50 & 83.33 & --- & --- & ---\tabularnewline
HBPSi-NH\textsubscript{2} & Test 1 & 0.50 & 83.33 & 50.00 & 1.025 &
1.62\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
& Test 2 & 0.50 & 83.33 & 47.00 & 1.069 &
1.69\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
& Test 3 & 0.50 & 83.33 & 46.00 & 1.052 &
1.77\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
& Average & --- & --- & 47.67 & 1.049 &
1.69\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
HBPSi-EP & Test 1 & 0.50 & 83.33 & 54.50 & 1.008 &
1.43\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
& Test 2 & 0.50 & 83.33 & 58.50 & 1.022 &
1.21\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
& Test 3 & 0.50 & 83.33 & 56.00 & 1.015 &
1.35\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
& Average & --- & --- & 56.33 & 1.015 &
1.33\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
HBPSi-V & Test 1 & 0.50 & 83.33 & 55.00 & 1.021 &
1.44\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
& Test 2 & 0.50 & 83.33 & 54.50 & 1.017 &
1.42\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
& Test 3 & 0.50 & 83.33 & 52.50 & 1.033 &
1.49\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
& Average & --- & --- & 54.00 & 1.024 &
1.45\selectlanguage{ngerman}×10\textsuperscript{-2}\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{ngerman}

\textbf{S3. Material Performance Supplements}

\textbf{S3.1. Calculation of network crosslinking density}

Based on the rubber elasticity theory, the crosslinking density can be
calculated using the equation (2), with the results listed
in\textbf{Table S2} and \textbf{Figure 5b} .

\begin{equation}
d_{\text{crosslink}}=\frac{E^{\prime}}{[2(1+\gamma)RT]}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)\ \nonumber \\
 \end{equation}

Where \emph{E'} is the rubbery plateau storage modulus
at\emph{T\textsubscript{g}} + 40 \textsuperscript{o}C; \selectlanguage{greek}γ \selectlanguage{english}represents the
Poisson's ratio that is assumed to be 0.5 when the crosslinked network
is incompressible for thermoset; \emph{R} and \emph{T} represent the gas
constant and the Kelvin temperature, respectively. Note that the
equation is applicable for lightly crosslinked materials and therefore
is used only to qualitatively compare the crosslinking level in the
casting resins.\textsuperscript{{[}7\emph{,} 8{]}}

\textbf{Table S2} Some parameters obtained from DMA results\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
Run & \emph{T\textsubscript{g}} / \textsuperscript{o}C & \emph{E'} at
\emph{T\textsubscript{g}} + 40 \textsuperscript{o}C / MPa & \emph{E'} at
\emph{T\textsubscript{g}} + 40 \textsuperscript{o}C / MPa &
\emph{d\textsubscript{crosslink}} / mol
m\textsuperscript{-3}\tabularnewline
\midrule
\endhead
EP & 131 & 39.1 & 3.53 & 3.53\tabularnewline
3HBPSi-NH2/EP & 131 & 38.1 & 3.44 & 3.44\tabularnewline
6HBPSi-NH2/EP & 118 & 37.4 & 3.48 & 3.48\tabularnewline
9HBPSi-NH2/EP & 109 & 31.1 & 2.95 & 2.95\tabularnewline
3HBPSi-EP/EP & 127 & 39.5 & 3.60 & 3.60\tabularnewline
6HBPSi-EP/EP & 111 & 33.6 & 3.18 & 3.18\tabularnewline
9HBPSi-EP/EP & 97 & 25.8 & 2.52 & 2.52\tabularnewline
3HBPSi-V/EP & 121 & 37.1 & 3.43 & 3.43\tabularnewline
6HBPSi-V/EP & 110 & 27.9 & 3.08 & 3.08\tabularnewline
9HBPSi-V/EP & 94 & 32.5 & 2.75 & 2.75\tabularnewline
\bottomrule
\end{longtable}

\textbf{S3.2. Thermal and thermomechanical test}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

\textbf{Figure S3} a) XRD profiles and b) derivation weight curves (DTG)
of EP and its blend with HBPSi-NH\textsubscript{2}, HBPSi-EP and HBPSi-V

\textbf{Table S} \textbf{3}Curing and thermal parameters of EP and its
blends with HBPSi-R\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
Samples & DSC & DSC & DSC & TGA & TGA & TGA\tabularnewline
\midrule
\endhead
& \emph{T\textsubscript{i}} (\textsuperscript{o}C) &
\emph{T\textsubscript{Ex}} (\textsuperscript{o}C) &
\emph{T\textsubscript{f}} (\textsuperscript{o}C) &
\emph{T\textsubscript{5\%}} (\textsuperscript{o}C) &
\emph{T\textsubscript{max}} (\textsuperscript{o}C) & Char yield
(\%)\tabularnewline
EP & 101 & 163 & 199 & 362 & 401 & 6.0\tabularnewline
6HBPSi-NH2/EP & 99 & 157 & 194 & 344 & 392 & 10.1\tabularnewline
6HBPSi-EP/EP & 99 & 155 & 194 & 358 & 401 & 11.7\tabularnewline
6HBPSi-V/EP & 98 & 152 & 191 & 361 & 398 & 10.0\tabularnewline
\bottomrule
\end{longtable}

\emph{\textsuperscript{a}T\textsubscript{i}} : The initial peak
temperature; \emph{T\textsubscript{EX}} : The peak temperature;
\emph{T\textsubscript{f}} : The end of peak temperature.

\textsuperscript{c}\emph{T\textsubscript{5\%}} : The temperature at 5\%
weight loss; \emph{T\textsubscript{max}} : The temperature at maximum
decomposition.

\textbf{S3.2.} \textbf{Mechanical performance test}

\textbf{Table S4} Mechanical test results of EP and its blends with
HBPSi-R\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Run & Impact strength / kJ\selectlanguage{ngerman}·mol-1 & Flexrual strength /
MPa\tabularnewline
\midrule
\endhead
EP & 12.94 \selectlanguage{ngerman}± 1.37 & 106.09 \selectlanguage{ngerman}± 5.53\tabularnewline
3\% HBPSi-NH2/EP & 15.45 \selectlanguage{ngerman}± 2.12 & 124.02 \selectlanguage{ngerman}± 1.18\tabularnewline
6\% HBPSi-NH2/EP & 10.13 \selectlanguage{ngerman}± 1.60 & 119.95 \selectlanguage{ngerman}± 1.89\tabularnewline
9\% HBPSi-NH2/EP & 8.32 \selectlanguage{ngerman}± 1.78 & 123.37 \selectlanguage{ngerman}± 1.36\tabularnewline
3\% HBPSi-EP/EP & 20.65 \selectlanguage{ngerman}± 3.69 & 144.73 \selectlanguage{ngerman}± 0.72\tabularnewline
6\% HBPSi-EP/EP & 17.03 \selectlanguage{ngerman}± 3.39 & 138.75 \selectlanguage{ngerman}± 1.93\tabularnewline
9\% HBPSi-EP/EP & 11.20 \selectlanguage{ngerman}± 1.46 & 121.45 \selectlanguage{ngerman}± 13.81\tabularnewline
3\% HBPSi-V/EP & 28.88 \selectlanguage{ngerman}± 1.75 & 137.85 \selectlanguage{ngerman}± 1.16\tabularnewline
6\% HBPSi-V/EP & 23.10 \selectlanguage{ngerman}± 6.03 & 141.01 \selectlanguage{ngerman}± 5.61\tabularnewline
9\% HBPSi-V/EP & 18.77 \selectlanguage{ngerman}± 4.51 & 131.69 \selectlanguage{ngerman}± 1.28\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{ngerman}

\textbf{References}

1. Y. Zhang, K. Yang, R. Liu, J. Yao, H. Yan, Chem. Eng. J.\textbf{2023}
, 460, 141773.

2. Y. Zhang, R. Liu, R. Yu, K. Yang, L. Guo, H. Yan, Compos. Part.
B-Eng. \textbf{2022} , 242, 110101.

3. Y. Zhang, H. Yan, G. Feng, R. Liu, K. Yang, W. Feng, S. Zhang, C. He,
Compos. Part. B-Eng. \textbf{2021} , 222, 109043.

4. L. Guo, L. Yan, Y. He, W. Feng, Y. Zhao, B. Z. Tang, H. Yan, Angew.
Chem. Int. Edit. 2022, 61, e202204383.

5. R. Liu, H. Yan, Y. Zhang, K. Yang, S. Du, Chem. Eng. J. 2022, 433,
133827.

6. T. Cai, L. Yuan, G. Liang, H. Wang, A. Gu, Mater. Chem.
Phys.\textbf{2019} , 234, 67.

7. Y. Wang, K. Kou, G. Wu, L. Zhuo, J. Li, Y. Zhang, Polymer
\textbf{2015} , 77, 354.

8. L. Tang, J. Zhang, Y. Tang, Y. Zhou, Y. Lin, Z. Liu, J. Kong, T. Liu,
J. Gu, Compos. Part. B-Eng. \textbf{2020} , 186, 107827.

\selectlanguage{english}
\FloatBarrier
\end{document}

