Influence of Grubbs Catalyst Concentration on the Rheokinetics, Mechanical, and Thermomechanical Properties of Dicyclopentadiene-Based Networks

Abstract

Dicyclopentadiene (DCPD) undergoes rapid ring-opening metathesis polymerization (ROMP) in the presence of Grubbs catalyst (GC), yielding a highly cross-linked thermoset polymer known for its exceptional mechanical strength, chemical resistance; high glass transition temperature (T _g); low dielectric constant; and superior thermal, hydrolytic, and radiation stability. This study systematically examines the effect of varying GC concentrations from 0.04 to 0.3 wt % on the curing kinetics, thermomechanical behavior, and mechanical performance of poly-DCPD networks. Rheological analysis demonstrates that increasing GC concentration significantly accelerates polymerization and gelation, effectively reducing pot life and presenting challenges for controlled processing. However, despite the variations in curing rate, the activation energy of the polymerization reaction remains essentially constant across all catalyst concentrations, indicating that GC influences the reaction kinetics by increasing the number of active catalytic sites rather than altering the intrinsic energy barrier. The curing behavior is well described by the Winter–Chambon criteria, with both storage modulus (G′) and loss modulus (G″) exhibiting power-law dependence on frequency, and their respective exponents intersecting precisely at the gel point. Dynamic mechanical analysis reveals a clear trend of increasing storage modulus and T _g with higher GC levels, signifying enhanced cross-link density and a more rigid polymer network. Mechanical characterization shows a near-linear increase in tensile strength as GC content rises, while elongation at break improves up to an optimal catalyst concentration (∼0.2 wt %), after which it slightly decreases due to increased network stiffness and reduced chain mobility. These results demonstrate that precise tuning of GC concentration offers a robust strategy to modulate curing kinetics and achieve an optimal balance between strength and toughness in poly-DCPD thermosets. Such control is critical for scaling up processing and improving fracture resistance in large-area coatings and composite applications where controlled cure profiles and mechanical reliability are paramount.

Introduction

Dicyclopentadiene (DCPD) is a unique bicyclic olefin that has garnered significant attention in polymer science due to its rich chemical reactivity, low cost, and favorable balance between rigidity and processability. − Derived from the dimerization of cyclopentadiene, DCPD contains two distinct reactive sites: a highly strained norbornene ring and a less reactive cyclopentene moiety. This structural asymmetry plays a critical role in its polymerization behavior, particularly in ring-opening metathesis polymerization (ROMP), which preferentially opens the norbornene ring, leaving the cyclopentene largely unreacted under typical conditions. As a result, ROMP of DCPD produces networks with highly tunable properties depending on the polymerization pathway, network architecture, and catalyst system employed. −

Polydicyclopentadiene (pDCPD) is known for its outstanding toughness, thermal stability, and chemical resistance, making it a candidate material for applications that span automotive components, protective coatings, high-impact structural parts, and dielectric encapsulants in harsh environments. − Furthermore, the low viscosity of DCPD monomer facilitates rapid infusion into complex molds or fiber preforms, which is advantageous for high-throughput manufacturing processes such as reaction injection molding (RIM) and vacuum-assisted resin transfer molding (VARTM). Recent interest in sustainable polymers has also catalyzed the exploration of DCPD-based networks as potentially recyclable thermosets when designed with cleavable cross-links or degradable moieties, opening new directions in circular economy approaches for advanced materials. −

Several studies have investigated the thermal and polymerization kinetics of DCPD and related ROMP systems, providing mechanistic insights that complement the understanding of catalyst effects. The cure kinetics of endo-DCPD using different generations of GC has been investigated, reporting activation energies and thermal conversion profiles, but without addressing rheological or mechanical behavior. Biorenewable ROMP copolymers cross-linked with DCPD derivatives have been examined, focusing on T _g and thermal behavior rather than catalyst-dependent rheokinetics, highlighting the influence of monomer composition on network formation. The ROMP of acetoxy-substituted DCPD has been studied, emphasizing monomer modification and linear polymer structure rather than cross-linked networks, demonstrating how subtle changes in monomer chemistry can affect polymer properties. Cross-linked ROMP polymers from odorless DCPD derivatives have been characterized for thermal properties but not for rheokinetics or mechanical outcomes, underlining the need for systematic exploration of structure–property relationships in standard DCPD systems. Finally, a tandem ROMP/hydrogenation approach to cross-linked DCPD-containing polyolefins has been explored, highlighting posthydrogenation crystallinity and oxidative stability rather than catalyst-dependent network formation, and suggesting potential strategies for tuning postpolymerization properties. Collectively, these studies establish a foundation for understanding DCPD polymerization but also reveal a gap in knowledge regarding the combined effects of catalyst concentration, curing kinetics, and the resulting mechanical and thermomechanical behavior, which remains critical for designing high-performance pDCPD materials.

Central to the successful formation of high-performance pDCPD is the use of efficient ROMP catalysts. Among these, Grubbs-type catalystsespecially second-generation variants based on ruthenium-alkylidene complexeshave proven exceptionally effective. − These catalysts offer several advantages, including high functional group tolerance, ambient processing capability, and the ability to catalyze polymerizations in the presence of air and moisture, which is not common for many transition-metal systems. Mechanistically, Grubbs catalysts initiate ROMP by forming a metal-carbene complex that engages in a [2 + 2] cycloaddition with strained cyclic olefins, followed by rapid ring opening and propagation. − The high ring strain of the norbornene group in DCPD (∼26 kcal/mol) provides a strong thermodynamic driving force for polymerization, while the robustness of the catalyst system ensures consistent conversion even under less-than-ideal industrial conditions. −

The concentration of GC a pivotal role in determining the kinetics and outcome of the ROMP reaction. − At low concentrations, the initiation and propagation steps occur slowly, which may result in long gelation times and incomplete conversion, especially in the case of thick or thermally insulated parts. Conversely, high catalyst concentrations can drastically reduce gel time, sometimes leading to runaway exotherms, uneven cross-linking, and mechanical anisotropy due to poor control over the network formation. Therefore, optimizing catalyst loading is essential for tailoring the curing profile, cross-link density, and final thermomechanical behavior of pDCPD-based materials.

Beyond kinetics, catalyst concentration has a profound influence on the final network architecture. At higher loadings, the faster gelation and increased initiation density can lead to higher cross-link densities and shorter polymer chains between junctions. − This is often manifested as increased stiffness and modulus, as measured by dynamic mechanical analysis (DMA), and elevated glass transition temperature (T _g) due to restricted segmental mobility. However, excessive cross-linking can compromise toughness and elongation at break, as observed in tensile stress–strain measurements. At lower catalyst loadings, the resulting networks may display improved ductility but reduced modulus and thermal performance, suggesting that there is a delicate balance between mechanical integrity and flexibility that must be controlled through catalyst selection and concentration.

Thermal analysis and rheological measurements provide further insight into the effects of catalyst concentration. The evolution of the storage modulus (G′) and loss modulus (G″) as a function of time and temperature reveals critical information about the gelation process and viscoelastic transitions. The crossover point between G′ and G″ often used to determine the gel point shifts with catalyst loading, reflecting changes in the onset of network formation. − When analyzed using the Chambon–Winter criterion, which describes the scaling behavior of moduli near the gel point, deviations from ideal gelation behavior can signal phase separation, heterogeneous cross-linking, or vitrification effects. − Moreover, analysis of the temperature dependence of cure kinetics using Arrhenius models enables the extraction of activation energies associated with network formation, providing mechanistic insights into how different catalyst levels influence energy barriers for initiation and propagation. −

In addition to processing and mechanical concerns, the environmental and economic aspects of Grubbs catalysts cannot be ignored. These catalysts are based on precious metals and represent a significant portion of the cost in DCPD formulations. Thus, achieving optimal performance at minimal catalyst loadings is not only technically desirable but also critical for scalability and commercialization. Several approaches have been proposed to lower catalyst use, including the incorporation of cocatalysts, latent formulations, or encapsulated catalyst systems that enable spatiotemporal control over the curing process. Nonetheless, a fundamental understanding of how catalyst concentration alone affects curing behavior and final properties remains essential for rational formulation design.

Despite the extensive use of GC in ROMP systems, systematic studies on the influence of catalyst concentration on both cure kinetics and final thermomechanical properties remain limited, especially in industrially relevant DCPD formulations. Existing reports often focus either on the mechanical outcomes or on kinetic modeling in isolation, without establishing clear correlations between curing behavior and performance metrics such as tensile strength, T _g, and cross-link density. A comprehensive analysis combining rheology, mechanical testing, and thermal characterization is necessary to elucidate the role of catalyst concentration in determining structure–property relationships. This work will be focused on studying the influence of GC on curing kinetics, activation energy, and the Chambon–Winter criterion. The effect of Grubbs catalyst on the mechanical and thermomechanical properties will be also investigated by stress–strain tensile and DMA measurements, respectively.

Experimental Section

Materials and Sample Preparation

The DCPD and second-generation GC were obtained from Sigma-Aldrich and used as received without further purification. DCPD is a colorless liquid with a boiling point of 170 °C, a specific gravity of 0.97 g/cm³ at 25 °C, a viscosity of 1.0 mPa·s (1.0 cP) at 20 °C, a melting point of – 20 °C, and a vapor pressure of 0.3 kPa at 20 °C.

Samples were prepared by mixing DCPD with varying concentrations of GC, which is fully soluble in DCPD. The curing kinetics were investigated rheologically as described below. For DMA and mechanical property testing, samples with different GC concentrations were cured at room temperature for 24 h, followed by a postcuring step at 100 °C for 2 h in aluminum Petri dishes. The cured sheets were subsequently machined into standard dog-bone specimens and rectangular specimens for mechanical and DMA testing, respectively, using a Wazer waterjet cutter to ensure dimensional accuracy and reproducibility.

Rheological Measurements

The curing kinetics of DCPD were systematically investigated by varying the GC concentration (0.04, 0.12, 0.20, and 0.30 wt %). All rheological experiments were conducted using a TA Instruments AR2000EX rheometer equipped with 25 mm parallel plate geometry. The sample mixtures were loaded between the plates with a fixed initial gap, and the instrument was purged with nitrogen to minimize any oxidative interference during the curing process. Temperature control was achieved using a Peltier system, with a precision of ± 0.1 K.

To determine the appropriate linear viscoelastic regime for each formulation, strain sweep tests were initially performed at a constant angular frequency. Based on these results, time sweep experiments were then carried out at various constant isothermal temperatures to monitor the evolution of the viscoelastic properties during the ring-opening metathesis polymerization of DCPD. The G′, G″, η*, and tan δ were recorded as functions of time to characterize the curing behavior.

The gelation point was identified from the crossover of G′ and G″, and the gelation time was used to study the temperature-dependent curing behavior of each formulation. The influence of GC concentration on gel time (t _gel ) and network development was also evaluated. The activation energy of curing for each GC concentration was calculated from the temperature dependence of the gel point using the Arrhenius equation. Furthermore, the critical gel state was characterized according to the Chambon–Winter criterion by analyzing the frequency dependence of the moduli at various curing times.

Dynamic Mechanical Analysis (DMA)

The thermomechanical behavior of fully cured DCPD-based materials was characterized using a TA Instruments Q800 dynamic mechanical analyzer operated in dual cantilever bending mode. Rectangular specimens approximately 3.0 mm thick, 12 mm wide, and 60 mm long were machined from each cured formulation using a Wazer waterjet cutter to ensure precise dimensions and smooth edges, minimizing geometric variability and potential edge defects. Testing was performed under a nitrogen atmosphere to prevent oxidative degradation during heating.

Temperature sweeps were conducted from 20 to 220 °C at a controlled heating rate of 3 °C/min, with a fixed oscillation frequency of 1 Hz. In dual cantilever mode, samples are clamped at both ends and subjected to bending deformation at the center, enabling sensitive measurement of viscoelastic transitions across the temperature range.

The T _g was identified as the temperature corresponding to the peak of the tan δ curve. The value of E′ was analyzed in both the glassy region (below T _g) and the rubbery plateau (approximately 45 °C above T _g) to evaluate stiffness, elastic energy storage, and network integrity. Variations in the rubbery plateau modulus were further interpreted in terms of cross-link density differences between formulations, calculated based on rubber elasticity theory. The influence of GC concentration on T _g, E′, and cross-link density was systematically assessed, facilitating correlation between catalyst loading, network architecture, and final thermomechanical performance.

Mechanical Testing

The mechanical performance of the fully cured DCPD with different GC was evaluated through uniaxial tensile testing using an Instron 5582 universal testing machine. The tensile testing was conducted in accordance with ASTM D638–22 using a constant strain rate of 5 mm/min. Appropriate mechanical grips were used to avoid slippage or premature failure at the clamping area. A high-resolution noncontact laser extensometer was used to accurately monitor strain and determine the elongation at break. For each formulation, a minimum of five specimens were tested, and the average values of tensile strength, elastic modulus, and strain at break were reported with standard deviations.

Dynamic mechanical and tensile testing provided complementary insights into the stiffness, ductility, and cross-link density of the polymer networks formed under various curing conditions, enabling a comprehensive evaluation of the role of GC concentration in the final material properties.

Results and Discussion

Real-Time Curing Kinetics of DCPD

Dynamic rheology is an exceptionally powerful technique for studying and quantifying the curing kinetics of thermosetting polymers such as dicyclopentadiene (DCPD). − Unlike conventional analytical methods, rheology captures real-time changes in viscoelastic properties that directly reflect the evolving molecular architecture of the material during polymerization. − DCPD, which undergoes ROMP in the presence of GC, transforms from a low-viscosity liquid into a rigid cross-linked network. In the early stages of curing, the system is dominated by low molecular weight species, leading to low G′, G″, and η*, all of which reflect a fluid-like behavior. As the ROMP reaction proceeds, chain propagation and the onset of cross-linking cause a rapid increase in molecular weight and chain entanglement. These changes are captured sensitively by dynamic rheology.

This transformation is clearly observed in Figure , which shows the evolution of G′, G″, and η* over time during isothermal curing of DCPD at 55 °C with 0.04 wt % GC. A distinct t _gel is identified at approximately 19.7 min, marked by the crossover of G′ and G″. At this point, a three-dimensional network starts to span the system, and the material transitions from a viscous liquid to an elastic solid. Molecularly, this corresponds to the formation of a percolating network structure, where the longest relaxation time diverges and molecular motion becomes significantly restricted. Beyond the t _gel , G′ increases more rapidly than G″, indicating the rapid growth of elastic network domains and confirming the dominance of cross-linking reactions. At extended curing times, G′ becomes a few orders of magnitude greater than G″, reflecting the development of a highly elastic and tightly cross-linked structure. This behavior provides direct evidence of the mechanical stiffening that accompanies network formation and polymer vitrification. The steady increase in η* throughout the process further supports the conclusion that molecular mobility decreases substantially as the curing proceeds. Taken together, these observations validate the use of dynamic rheology as a highly sensitive and accurate method for evaluating the gelation behavior and overall curing kinetics of DCPD-based systems.

1.

Evolution of storage G′, G″, and η* of DCPD containing 0.04 wt % GC during curing at 55 °C and 1 rad/s angular frequency as a function of curing time. The arrow indicates the gel time (t _gel ) at 19.7 min.

The curing kinetics of DCPD were strongly dependent on GC concentration, as illustrated in Figure . At 50 °C and an angular frequency of 1 rad/s, the complex viscosity (η*) increased sharply with curing time for all catalyst loadings, reflecting the progressive formation of the polymer network. The onset of η* growth occurred noticeably earlier at higher GC concentrations, indicating that elevated catalyst levels accelerate the initiation of polymerization and cross-linking reactions, leading to faster gelation and network development. For example, at 0.3 wt % GC, η* rose by nearly 5 orders of magnitude, whereas at 0.04 wt % GC, the increase was about 4 orders of magnitude over the same curing period. At higher GC loadings, this rapid viscosity buildup was followed by an earlier leveling-off around 170 min signifying a reduced overall magnitude of η* growth and a quicker approach to the final cured state. The plateau suggests that network growth or cross-link density reaches a limit, potentially due to rapid consumption of reactive sites or steric hindrance effects at high GC levels. Together, these trends imply that cross-link density in the cured polymer increases with GC concentration. This is further supported by the inset schematic in Figure , which depicts a progressively denser cross-linked network with increasing catalyst loading. The resulting higher cross-link density likely enhances mechanical properties while reducing molecular mobility within the cured material.

2.

η* evolution during the curing of DCPD at 50 °C and 1 rad/s for varying concentrations of GC. Increasing GC concentration results in an earlier onset of viscosity rise, indicating accelerated polymerization and cross-linking. Higher catalyst loadings also lead to a reduced magnitude of η* increase and earlier plateauing around 170 min, suggesting a limit in network growth or cross-link density. The inset schematics illustrate the corresponding increase in cross-link density and network structure with higher GC concentrations.

The t _gel of DCPD formulations with varying GC concentrations was accurately determined using the crossover point of G′ and G″ a well-established and reliable method for assessing gelation in thermosetting systems. , During curing, the material transitions from a predominantly viscous (liquid-like) behavior, where G″ > G′, to a predominantly elastic (solid-like) behavior where G′ > G″. The point at which G′ and G″ intersect marks the t _gel , indicating the formation of an infinite network and the onset of the material’s solid-like behavior. This crossover-based approach is highly sensitive and provides reproducible t _{ge l} values, making it especially suitable for comparing different catalyst concentrations and curing conditions. As shown in Figure , t _gel decreases significantly with increasing curing temperature and GC concentration. For instance, at a fixed GC concentration (0.12 wt % GC), t _gel decreased from about 50 to 5 min as the curing temperature increased from 40 to 60 °C. Similarly, at a constant curing temperature of 50 °C, increasing the GC content from 0.04 wt % to 0.12 wt % reduced t _gel from 70 to 10 min. These trends clearly demonstrate the acceleration of curing kinetics with both higher temperature and catalyst loading ad demonstrated in Figure .

3.

t _gel determined from the crossover of G′ and G″, decreases substantially with increasing curing temperature and GC concentration. Gelation time dropped from 50 to 5 min as temperature rose from 40 to 60 °C, and from 70 to 10 min as GC content increased from 0.04 to 0.12 wt %, demonstrating the strong acceleration of curing kinetics under higher thermal and catalyst conditions.

Effect of GC on the Activation Energy of Curing

The curing kinetics of DCPD were analyzed using the Arrhenius approach to evaluate the effect of GC concentration on the activation energy (E _a ) of the polymerization reaction. The Arrhenius equation, expressed as

$$t_{gel}(T)=A{\exp }^{(E_{\mathrm{a}}/RT)}$$ 1

$$\ln (t_{gel})=\ln (A)+\frac{E_{\mathrm{a}}}{R}\frac{1}{T}$$ 2

where A is the pre-exponential factor, R is the universal gas constant, and T is the absolute temperature. By evaluating the curing times at different temperatures and plotting ln­(t _gel ) against 1/T, a linear relationship is obtained, where the slope corresponds to -E _a /R. As shown in Figure , the curing reaction closely followed the Arrhenius behavior, confirming that the polymerization of DCPD is a thermally activated process. The activation energy calculated from the linear fits remained approximately constant across different GC concentrations. This observation indicates that while the GC content significantly accelerates the reaction rate, it does not substantially alter the intrinsic energy barrier of the reaction pathway. The calculated activation energy was found to be 79.3 ± 1.0 kJ/mol, regardless of the GC concentration. This result suggests that the role of GC is to increase the frequency of effective collisions or to lower the pre-exponential factor threshold needed for initiation, rather than modifying the energetic profile of the curing process. Based on the data, the Arrhenius analysis confirms that the curing of DCPD follows a temperature-dependent mechanism with a consistent activation energy, regardless of GC concentration. This supports the conclusion that the catalyst primarily enhances the reaction kinetics without significantly affecting the fundamental thermodynamic energy barrier of the curing process.

4.

Arrhenius analysis shows a linear relationship between ln(t _gel ) and 1/T, confirming thermally activated curing. The activation energy (∼79 kJ/mol) remains constant across GC concentrations, indicating that GC accelerates the curing rate without altering the energy barrier, thus enhancing kinetics while leaving the fundamental thermodynamics unchanged.

Winter–Chambon Criterion

The t _gel can be determined with high precision using the Winter–Chambon criterion, a rigorously validated and widely adopted framework for identifying the gel point in thermosetting systems. − This criterion is grounded in the fundamental rheological scaling behavior exhibited by viscoelastic materials during the sol–gel transition. At the gel point, the evolving polymer network reaches a state in which the G′ and G″ no longer display distinct frequency dependencies but instead follow an identical power-law dependence on ω, expressed as

$$G^{\prime }\sim G^{″}\sim {\omega }^n$$ 3

A direct consequence of this condition is that the ratio G″/G′ defined as the loss tangent, tan δ becomes independent of frequency. This invariance is captured mathematically as

$$\tan \delta =\tan \left(\frac{n\pi }{2}\right)$$ 4

This frequency independence of tan δ is one of the most definitive and model-independent rheological signatures of gelation, providing a precise and unambiguous marker for the transition from a predominantly viscous (liquid-like) to a predominantly elastic (solid-like) state. The robustness of this criterion has been verified for a broad spectrum of systems, encompassing both chemically cross-linked thermosets and physically gelled networks, and is especially valuable because it does not depend on prior assumptions about reaction kinetics or network topology. − As illustrated in Figure , application of the Winter–Chambon analysis to the DCPD formulations investigated here yielded a highly accurate determination of t _gel . This approach not only complements other gelation time evaluation methods, such as modulus crossover analysis, but also offers deeper mechanistic insight into the curing processcapturing the universal scaling behavior that underpins network formation and solidification.

5.

Frequency-independent tan δ observed at the gel point, providing a precise and model-independent criterion for identifying the transition from a liquid-like to a solid-like state. The arrow indicates the t _gel determined from the frequency independence of tan δ.

Figure a,b demonstrate this behavior over a broad frequency spectrum. During curing at elevated temperature (55 °C) for DCPD containing 0.04 wt % GC, both the G′ and G″ evolve and exhibit converging power-law trends. The convergence of the exponents derived from log–log plots of G′ and G″ versus angular frequency signals the approach to the critical t _gel . At t _gel both moduli scale identically with frequency, rendering the relaxation exponent n invariant to frequency variations.

6.

(a) Log–log plots of G′ versus angular frequency during curing at 55 °C for DCPD containing 0.04 wt % GC, illustrating the development of power-law behavior. (b) Log–log plots of G″ versus angular frequency under the same conditions, also showing evolving power-law behavior.

This gelation process is further substantiated by monitoring the frequency dependence of the loss tangent, tan δ, which remains constant at the t _gel before declining as cross-linking intensifies. The postgelation decrease in tan δ arises from the more rapid growth of G′ relative to G″, indicative of the formation of a progressively elastic and percolated network structure. The observed frequency-independence of tan δ (Figure ) at a well-defined time confirms the applicability of the Winter–Chambon model to this system and suggests that the evolving microstructure attains self-similarity at the gel threshold.

The power-law exponents for G′ and G″ ″, designated as n′ and n″ respectively, were extracted as functions of curing time. Initially, both exponents were high, consistent with a predominantly viscous, liquid-like state and minimal network formation. As curing progressed, n′ and n″ decreased exponentially and converged at a distinct point corresponding to t _gel . This intersection represents the hallmark of critical gelation, where viscoelastic behavior is governed by a delicate balance between energy storage and dissipation mechanisms. Beyond gelation, the continued reduction in n′ and n″ reflects the transition to a rigid, highly elastic network (Figure a), signifying diminished frequency dependence of the moduli and the dominance of solid-like properties in the evolving gel. This analysis provides compelling evidence of gelation dynamics within this thermosetting system. The application of the Winter–Chambon criterion, validated through both modulus scaling and exponent convergence, offers a robust, quantitative framework for defining t _gel . Furthermore, the rheological signatures identified including the frequency-independent tan δ at gelation, the evolution of η* and the synchronized decline of n′ and n″ underscore the formation of a percolated, fractal-like network transitioning from a viscoelastic liquid to an elastic solid over the curing duration.

7.

(a) Curing time dependence of the frequency exponents n′ and n″, derived from the power-law relationship between G′ and G″ with angular frequency, capturing the transition toward gelation. (b) Angular frequency dependence of η* at various curing times for the 0.04 wt % GC formulation, illustrating the evolution of viscoelastic behavior during curing.

Consistent with the behavior of G′ and G″, the viscoelastic transformation and evolution of η* as a function of curing time for DCPD with 0.04 wt % GC are depicted in Figure b. At early reaction stages, the system exhibited weak shear-thinning behavior, with η* remaining nearly constant at low frequencies and increasing slightly at higher frequencies. This response is typical of systems dominated by viscous flow with minimal network connectivity. As curing advanced, η* increased dramatically by over 4 orders of magnitude, particularly at low frequencies. This sharp rise in complex viscosity, coupled with enhanced frequency dependence, signifies the onset of an interconnected cross-linked network and highlights η*’s sensitivity to microstructural evolution during gelation.

Effect of GC on the Thermomechanical Properties

Dynamic Mechanical Analysis (DMA) in dual cantilever mode is a highly sensitive and precise technique for evaluating the T _g and cross-link density of DCPD as a function of GC concentration. DMA probes the viscoelastic properties of polymer systems across a range of temperatures, yielding critical thermomechanical parameters such as storage modulus (E′), loss modulus (E″), and tan δ. These parameters collectively provide profound insight into the polymer’s molecular mobility, network architecture, and degree of cross-linking key factors dictating its thermal stability and mechanical integrity. In this study, the addition of GC to DCPD formulations significantly altered their thermomechanical behavior. As depicted in Figure a, the T _g, identified from the peak maximum of tan δ, exhibited a systematic increase with rising GC content. This shift toward higher T _g values reflects a pronounced restriction of polymer chain mobility, which can be attributed to enhanced effective cross-link density and/or stronger intermolecular interactions catalyzed by GC. Increased cross-linking restricts segmental motions within polymer chains, thereby elevating the thermal energy threshold required for the transition from the glassy to the rubbery state.

8.

(a) T _g determined from the peak of tan δ as a function of GC in DCPD formulations, showing a systematic increase in T _g with higher GC loading, indicating reduced polymer chain mobility and enhanced cross-link density. (b) Effective υ _e calculated from the value of E′ measured at 45 °C above T _g, based on rubber elasticity theory, demonstrating a nearly linear increase with GC concentration. These results confirm that the increase of GC promotes a more uniform and tightly cross-linked polymer network, improving thermal stability and mechanical integrity in the rubbery state.

Below T _g, the E′ reflects the rigidity of the polymer network in its glassy state. For DCPD cured with a low GC content (0.04 wt % GC), E′ was relatively low, suggesting a less densely cross-linked or more compliant structure. In contrast, samples with higher GC concentrations (up to 0.3 wt % GC) exhibited a nearly constant and higher E′ below T _g, implying that GC promotes a stiffer glassy network. This could be attributed to its role in modifying cure kinetics or promoting a more uniform and interconnected network structure. At elevated temperatures well above T _g (e.g., 210 °C, at least 45 °C above the T _g of all samples), the storage modulus is primarily governed by the network integrity and resistance to thermal softening. The observed increase in E′ at 210 °C with higher GC concentrations further supports the conclusion that GC enhances thermal stability and maintains load-bearing capacity under high-temperature conditions. This is consistent with a higher cross-link density, which limits viscous flow and prevents rapid modulus decay in the rubbery plateau region. Overall, the DMA results reveal that GC acts as a network modifier in DCPD, improving both low- and high-temperature mechanical properties through increased T _g and modulus. These improvements are directly related to changes in polymer microstructure, most notably an enhancement in cross-link density and reduced chain mobility, which are critical for applications demanding long-term thermal and mechanical stability.

At temperatures well above the tan δ peak, the plateau of E′ showed a clear increasing trend with rising GC content, indicating an increase in cross-link density. The cross-link density (υ _e ) was quantified from the storage modulus measured at 45 °C above T _g, using the principles of rubber elasticity theory: ,

$$E^{’}=3{\upsilon }_{e}RT$$ 5

where υ _e is the effective cross-link density, E′ is the plateau storage modulus at the specified temperature, R is the universal gas constant, and T is the absolute temperature. As shown in Figure b, the analysis revealed that a linear increase in both T _g and υ _e with rising GC concentration suggests that higher GC loadings promote the formation of a more uniform and tightly interconnected polymer network. This structural refinement is consistent with a progressive restriction in chain mobility, as a denser cross-linked architecture limits segmental motion and reduces free volume. The more efficient curing associated with elevated GC levels produces a network that maintains higher stiffness in the glassy state and exhibits enhanced elasticity in the rubbery regime. Consequently, the material demonstrates greater resistance to thermal softening, which supports superior dimensional stability and sustained mechanical integrity under demanding service conditions. These findings highlight the critical role of GC concentration in tailoring the thermomechanical behavior of DCPD-based systems.

Effect of GC on Mechanical Properties of DCPD Thermoset

A typical tensile strength measurement was performed to evaluate the mechanical behavior of the DCPD formulations. The effect of GC concentration on their mechanical performance was examined in detail, revealing pronounced improvements in key tensile properties. As shown in Figure a, which presents the stress–strain curves for fully cured samples, elongation at break increased markedly with rising GC content up to an optimal range. Specifically, formulations containing 0.12 and 0.20 wt % GC exhibited substantially higher elongation compared to lower concentrations, indicating enhanced ductility and toughness. This enhancement is attributed to the development of a network architecture that achieves a balance between adequate cross-link density and retained chain mobility, facilitating more effective energy dissipation under tensile loading. Conversely, at 0.30 wt % GC, a modest decrease in elongation was observed relative to the intermediate concentrations. This nonlinear behavior suggests that excessive catalyst levels may promote the formation of an overly dense or structurally heterogeneous network, which restricts segmental motion and slightly reduces ductility.

9.

Influence of GC concentration on the mechanical properties of DCPD samples. (a) Stress–strain curves showing increased ductility up to 0.2 wt % GC, with a slight decline at 0.3 wt %. (b) Tensile strength (MPa) displaying a near-linear rise with higher GC content, reflecting improved cross-link density and network strength. (c) Elongation (%) illustrating a nonlinear response to GC concentration, indicating an optimal level for balancing toughness and strength.

Figure b,c detail the mechanical properties as they vary with GC concentration, with Figure b showing tensile strength and Figure c illustrating elongation percentage. Tensile strength increased in a clear, nearly linear fashion as GC concentration rose, underscoring the catalyst’s role in enhancing cross-link density and reinforcing the polymer network. This improvement reflects more efficient load transfer within the matrix, where stronger intermolecular interactions and improved network connectivity contribute to greater resistance against mechanical failure. Notably, this upward trend continues even at the highest GC concentration tested (0.3 wt %), demonstrating the material’s increasing capacity to endure higher stress with greater catalyst content.

In contrast, Figure c highlights the nonlinear behavior of elongation with respect to GC concentration. Elongation rises significantly up to 0.2 wt % GC but declines slightly at 0.3 wt %, supporting the existence of an optimal catalyst range that balances ductility and strength. Together, these results reveal a complex interplay between GC concentration, network architecture, and mechanical performance. Up to an optimal range (between 0.12 and 0.2 wt %), GC simultaneously enhances strength and ductility by fostering a network that is both well-cross-linked and sufficiently flexible. Beyond this point, further increases in GC continue to boost tensile strength through network densification but cause a modest reduction in elongation due to restricted chain mobility. These insights are vital for optimizing DCPD formulations aimed at achieving a precise balance of toughness and mechanical integrity, especially for demanding structural applications.

Conclusion

The increase in GC concentration significantly affects the curing behavior, viscoelastic properties, and mechanical performance of DCPD-based thermoset formulations. Rheological measurements demonstrate that higher GC levels accelerate curing kinetics, as shown by a rapid increase in η* and a reduced onset time for gelation, confirming faster network formation via the ROMP reaction. Despite this acceleration, the activation energy of the curing reaction remains essentially unchanged across GC concentrations, indicating that catalyst concentration increases the reaction rate by providing more active sites without altering the fundamental energy barrier. The curing kinetics align well with Winter–Chambon criteria, where both G′ and G″ follow power-law dependencies on frequency, intersecting at the t _gel . The DMA shows that the E′ above the T _g systematically increases with GC concentration, reflecting enhanced cross-link density and network stiffness. Correspondingly, the tan δ peak systematically shifted to higher temperature, suggesting altered molecular mobility and improved network homogeneity consistent with the observed curing behavior. Mechanically, increasing GC concentration leads to a nearly linear rise in tensile strength, indicating a stronger polymer network with better load-bearing capacity. Elongation at break improves significantly up to an optimal GC concentration (∼0.2 wt %), reflecting increased toughness and flexibility. Beyond this concentration, elongation decreases slightly due to excessive cross-link density restricting chain mobility and reducing extensibility. This balance highlights the importance of optimizing GC content to achieve the desired combination of strength and ductility for targeted applications. In summary, increasing GC concentration effectively modulates curing kinetics, cross-link density, T _g, and mechanical properties in DCPD thermosets. While higher GC accelerates polymerization and gelation by enhancing catalytic activity, it does not change the intrinsic activation energy of the reaction. These kinetic improvements correspond with increased cross-link density, improved viscoelastic behavior, and enhanced mechanical strength. However, careful control of catalyst levels is critical to maintain a balance between rigidity and toughness, enabling tailored performance for structural and functional uses. These findings provide a foundation for designing advanced DCPD formulations with optimized cure profiles and mechanical characteristics for composites and coatings.

The authors declare no competing financial interest.