Repositorio Institucional

Article

Understanding the Dynamic Loss Modulus of NR/SBR Blends in the Glassy–Rubbery Transition Zone

Angel J. Marzocca 1,* , Marcela A. Mansilla 2 , María Pía Beccar Varela 3 and María Cristina Mariani 3



1 Laboratorio de Polímeros y Materiales Compuestos, Departamento de Física, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires C1428EHA, Argentina

2 Dirección Técnica de Materiales Avanzados, INTI, CONICET, Av. General Paz 5445, San Martín B1650WAB, Argentina; mmansilla@inti.gob.ar

3 Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968, USA; mpvarela@utep.edu (M.P.B.V.); mcmariani@utep.edu (M.C.M.)

* Correspondence: marzo@df.uba.ar



Abstract: The motivation of this research was to analyze the dynamic properties, mainly the loss modulus, of vulcanized immiscible blends of natural rubber (NR) and styrenebutadiene rubber (SBR) in the glass transition zone, where the SBR phase is in a glassy state and the NR phase is in a rubbery state. The blends were cured at 433 and 443 K and studied around the glass transition using a dynamic mechanical analyzer. The dependence of the loss modulus on temperature was described by considering the phase separation, and the frequency dependence was also included to provide a deeper insight into the dynamic properties. This was achieved by integrating the mechanical model proposed by Zener, which considers a single relaxation time related to temperature using both the Arrhenius and Vogel–Fulcher–Tammann (VFT) relations. The best correlation with the data was obtained using the Arrhenius relationship. The activation energy of the NR phase increases with the NR content in the blend, while in the SBR phase, it varies slightly. The trends obtained are related to curative migration from the SBR to the NR phase, increasing the crosslink density at NR domain boundaries. These insights are valuable for optimizing the performance of these elastomeric blends in practical applications.



Academic Editor: Yutaka Oya

Received: 2 April 2025 Revised: 29 April 2025 Accepted: 9 May 2025 Published: 11 May 2025

Citation: Marzocca, A.J.; Mansilla, M.A.; Beccar Varela, M.P.; Mariani, M.C. Understanding the Dynamic Loss Modulus of NR/SBR Blends in the Glassy–Rubbery Transition Zone. Polymers 2025, 17, 1312. https:// doi.org/10.3390/polym17101312

Copyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).



Keywords: natural rubber; styrene-butadiene rubber; blends; vulcanization; dynamic mechanical properties; glass transition region

1. Introduction

Natural rubber (NR) and styrene-butadiene rubber (SBR) blends (NR/SBR) are employed in applications that require high technical performance, including tires and conveyor belts. NR exhibits low hysteresis, high elasticity, and a self-reinforcing characteristic resulting from strain-induced crystallization. On the other hand, SBR offers excellent abrasion resistance and reasonably good thermal properties.

NR is not miscible with synthetic rubbers such as SBR. Therefore, the components of the blend are arranged in different domain morphologies depending on many factors, such as the mixing ratio and variation in polymer type and microstructure, as well as polarity, viscosity, and mixing procedure [1–20]. Using atomic force microscopy, Klat et al. [11] observed that domain sizes increased from uncured to fully cured samples at the optimum cure time in a blend of 70 phr NR and 30 phr low-vinyl SBR. Their studies examined blends cured at 413 K and 433 K and found that phase separation was more pronounced at the lower cure temperature.



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https://doi.org/10.3390/polym17101312



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Having a good model to explain the dynamic mechanical properties of elastomers and elastomeric blends is very important for addressing technological applications. The studies of Klüppel et al. [14], Schuster et al. [15], Wunde and Klüppel [16], and Muller et al. [6] focused on the influence of the phase morphology on energy storage and dissipation during dynamic excitation in unfilled and filled NR/SBR and EPDM/BR blends. The observed, strongly nonlinear, dependence of the local loss modulus maxima on the blend ratio of unfilled blends was explained based on a percolation model that represents a useful framework for modeling the phase network.

Voges et al. [19] investigated NR/SBR blends considering heterogeneous morphologies that consist of regions with nearly pure phases and distinct interphases.

The dynamic mechanical behavior of rubber-like materials is both temperature- and time–frequency-dependent. Information on the changes in dynamic mechanical properties with time or frequency is required in products for engineering applications. Numerous viscoelastic models, namely Cole–Cole, Kohlrausch–Williams–Watts (KWW), Havriliak– Negami (HN), etc., have occasionally been used to describe dynamic mechanical properties. The HN model has a distinct advantage over the other viscoelastic models for its simplicity and ability to accurately predict results [21,22].

For several years, our research group has studied the NR/SBR system using different experimental attacks that include rheometric characterization, swelling, differential scanning calorimetry (DSC), microscopy, dynamic mechanical analysis (DMA), and positron annihilation lifetime spectroscopy (PALS), among others [7–9,13,23,24].

In a recent paper, we analyzed the local strains developed in vulcanized NR/SBR blends cured at 433 K and 443 K using sulfur and TBBS (n-t-butyl-2-benzothiazole sulfenamide) as a cure system [13]. The samples were characterized by dynamic mechanical properties between 193 K and 293 K, with interest in the glass transition region of the vulcanized immiscible blends, where the NR and SBR phases are rubbery and glassy, respectively. By studying the loss modulus, this research shows how the local strain in the NR phase varies depending on the amount of SBR in the blend.

This paper presents a new approach to analyzing the loss modulus (E) behavior with temperature, within the glass transition region, for cured NR/SBR blends. For a given temperature, the E of each elastomer is expressed by a law resulting from the contribution of its amorphous and rubbery structure according to its volume fraction of the glassy phase. Then, the influence of frequency is considered by applying Zener’s mechanical model [25], which assumes a single relaxation time. Finally, the E of the blend is presented taking into account the mixing law of the pure elastomers. It is assumed that the morphology and microstructure of each phase depend on the mix composition and curing conditions.

2. Materials and Methods

2.1. Materials

The compounds studied in this work are composed of NR (SMR-20 (Malaysia)) and SBR-1502 (Arpol (E-SBR) provided by Petrobras (Pto.Gral. San Martin, Argentina)). They were prepared at room temperature by solution blending with the formulation given in Table 1. Details of the sample preparation are given in ref [9]. In the formulation, sulfur (Sigma Aldrich, St. Louis, MO, USA) and TBBS (n-t-butyl-2-benzothiazole sulfenamide) (Vulkacit, NZ/EG-C, Lansexx, Germany) were used as the cure system. The accelerator/sulfur ratio, Λ, is 1; therefore, this cure system is semi-EV [26]. Stearic acid (Sigma Aldrich, St. Louis, MO, USA) and zinc oxide (Sigma Aldrich, St. Louis, MO, USA) are activators of the curing reaction. From the rheometer curves at 433 K and 443 K, the optimum cure time t100 (time to reach the maximum degree of cure) was obtained for each sample. The values are summarized in Table 2 for each compound and cure temperature. The onset



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NR (SMR20) SBR-1502

Stearic Acid Zinc Oxide

Sulfur TBBS



of cure, defined as the time of 5 percent conversion (t5), for each compound is also shown in Table 2.



Table 1. Blend formulations.



SBR NR10/SBR90 NR30/SBR70 NR50/SBR50 NR70/SBR30 NR90/SBR10



NR



0



10



30



50



70



90



100



100



90



70



50



30



10



0



2



5



1.5



1.5



Tv (K) 433 443



t (min)

t5

t100 t5 t100



Table 2. Cure times (t5 and t100) at 433 K and 443 K obtained from rheometer tests [13]. SBR NR10/SBR90 NR30/SBR70 NR50/SBR50 NR70/SBR30 NR90/SBR10



13.09



7.91



8.61



5.56



4.14



0.74



88.30 5.35 34.40



48.60 3.45 25.80



46.7 3.26 22.10



33.50 2.80 17.40



21.60 0.65 11.40



14.70 0.55 7.00



NR

0.57 0.5 0.57

13.70

0.40

7.70



All samples were cured at 433 K and 443 K at their respective t100 times, using a hydraulic press set at 5 MPa. The compounds were molded into sheets with dimensions of 50 × 40 × 2 mm3. After the curing process, the samples were immediately cooled in an

ice–water mixture.



2.2. Dynamic Mechanical Tests

Dynamic mechanical analysis (DMA) measurements were performed using a dynamic mechanical analyzer (Gabo Qualimeter (Hannover, Germany), model Eplexor 500N). Details of the measurements performed can be found in ref [13].



2.3. Methodology



In pure elastomeric compounds, for example, NR or SBR, there is a temperature range



(the glass transition region) where glassy and rubbery phases coexist. They have separate



contributions to the loss modulus, and the upper bound, known as the Reuss limit, is



reached in the limiting case of a homogenous distribution of the strain; this can be proposed



as [27]



E′′ = υgE′′ g + 1 − υg E′′ a



(1)



where E′′ a and E′′ g are the loss moduli of the rubbery and glassy phases, respectively, and υg is the volume fraction of the glassy phase.

A simple methodology is proposed in this paper to estimate υg from the loss modulus plot when it changes with temperature T in an isochronous state (at a fixed frequency).

Figure 1a shows a typical loss modulus of an elastomer as it changes from a rubbery to a glassy state with decreasing temperature. In this type of plot, a baseline Eb′′ase(T) is defined between the temperatures T0 and T1 (shown in Figure 1a). The resultant loss modulus can be introduced as



Er′′ (T) = E′′ (T) − Eb′′ase(T)



(2)



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   = 1    <   



glassy zone



By normalizing Equation (3), we can remove any scaling effects and focus purely on



the temperature-dependent behavior. The temperature dependence of   



4 of 16

is a key factor



in the behavior of elastomers, especially when it comes to how the proportions of the glass



phwahseicwhiitshsinhothwenminatFerigiaulrceh1abn.geT,haeffdeactsihnegditrseogvioenrailnl mFiegcuhraen1icbailsbtehheavinioterg. ral between T0 and T1.



Figure 1. (a) Loss modulus E as a function of temperature T. (b) Er′′ as a function of temperature T. Fig(cu)rυeg1a.s(aa)fLuonscstimonodouf ltuems Ep″eraastuarfeuTncotibotnaionfedtembypEerqautautrieonT.(3(b).) E″r as a function of temperature T. (c)    as a function of temperature T obtained by Equation (3).

In the next step, υg, the variation in the normalized integral of Er′′ (T) as a function of

the temperature is calculated as



υg(T) =



T To



Er′′



(T)dT



T1 T0



Er′′



(T)dT



(3)



This correlation is depicted in Figure 1c as a function of temperature. In this analysis,



υg = 0



T > To rubberyzone



υg



T1 < T < To glasstransitionzone



υg = 1



T < T1 glasszone



By normalizing Equation (3), we can remove any scaling effects and focus purely on the temperature-dependent behavior. The temperature dependence of υg is a key factor in the behavior of elastomers, especially when it comes to how the proportions of the glass phase within the material change, affecting its overall mechanical behavior.

The Boltzmann equation, often represented by a sigmoid curve, is commonly used to describe the transition of a dependent variable from one state to another, typically in relation to an independent variable. In this context, the Boltzmann sigmoidal equation can be used to model the transition of a property, such as the glassy volume fraction, υg, as a



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function of temperature. By fitting experimental data to this equation, we can gain insights



into the underlying physics driving the transition phenomena in the elastomers.



Due to the structural and morphological heterogeneity of semi-crystalline polymers



and their blends, simultaneous double crystallization processes are common [28].



In the case of an isochronous process in a DMA, performing tests at a constant fre-



quency while varying the temperature, an empirical double Boltzmann function can be



introduced as



υg =



∑2 i=1



1



−



fi exp((T −



Ti )/ki )



∑2 i=1



fi



=



1



(4)



If f = f 1, then f 2 = (1 − f 1), and by replacing it in Equation (4), the following relationship



is obtained:



υg =



f



+



(1 − f )



1 − exp((T − T1)/k1) 1 − exp((T − T2)/k2)



(5)



where k1 and k2 are the constant intervals that control the rise in phase 1 and phase 2 (also called slope factors).



It is known that temperature-induced crystallization (TIC) is a process that occurs



in NR [29]. The rate of crystallization depends on the temperature and duration of crys-



tallization. This factor can influence the size and number of crystallites with a random



orientation. For TIC samples, both amorphous chains and crystallites are present. The



process creates a wide distribution of crystallite sizes because the crystallization process



occurs under static conditions where random regions are crystallized [29]. Equation (5)



proposes that, in principle, two processes govern crystallization. This is a simplified way of



analyzing the problem, and the relationship is established empirically.



The dependence of the loss modulus E on the frequency, based on the mechanical



model proposed by Zener for a single relaxation time, has the relationship [25]



E′′



=



∆E ωτ 1 + ω2τ2



(6)



with the relaxation intensity



∆E = (Eu − Er)



(7)



where Eu is the unrelaxed modulus and Er is the relaxed modulus; ω is the angular frequency; and τ is the relaxation time of the process.

The α-relaxation in polymers associated with the glass transition has been analyzed using various models in the literature. Among these are the free volume theory [30], the Adams–Gibbs theory [31,32], the coupling mode theory [33], the coupling model [34,35], and atomistic simulations [36], among others. The Adam–Gibbs theory provides the theoretical foundation for the Vogel–Fulcher–Tammann (VFT) equation [37–39], which is widely regarded as an accurate representation of the temperature dependence of the relaxation time τ. It is expressed as



τ = Aexp



B T − Tv



(8)



where A is a hypothetical relaxation time at infinite temperature, B is a fitted parameter that is sometimes related to fragility, T is the absolute temperature, and TV is the Vogel temperature that is often considered the temperature that is reached upon quasi-static cooling, at which chain segments become immobile. TV is occasionally associated with an “ideal” glass transition, typically occurring 30–70 K below Tg [37–39].



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It is also quite common to find a dependence between τ and temperature that follows an Arrhenius relationship of the form [18,24,40–43]



τ = τoexp



Hac RT



(9)



where Hac is the activation energy of the single process, τo is a constant, and R is the gas constant (8.314 J/mol K).

Considering the contributions of Equations (1) and (6), the following relationship can be proposed for the loss modulus:



E′′ = E′′ gυg + E′′ a 1 − υg



+



1



∆Eωτ + ω2τ2



(10)



This equation assumes that the loss modulus behavior with frequency and temperature follows the Zener model (expressed by Equation (6)), but it adds a thermal background resulting from the structural change as the compound passes from the rubbery phase to the glassy phase as the temperature decreases (in the glass transition region).

In the context of immiscible blends of two components with loss moduli E′I′ and E′I′I, respectively, and volume fractions ϕI and ϕII, the loss modulus of the blend Eb′′lend can be analyzed by introducing a mixture law along with an additional term E′′ex [14]. This term accounts for the presence of an interface characterized by properties that differ from those of the individual components. Then,



Eb′′lend = ϕI E′I′ + ϕI I E′I′I + E′′ ex



(11)



In an immiscible blend where one domain is mainly in the rubbery state and the other one is changing from rubbery to glassy as the temperature decreases (this happens in NR/SBR blends in the glass transition region), we can analyze what happens when the interface term is small compared to the mixing law.

The interaction expressed by E′′ ex can be disregarded, and an attempt can be made to fit the experimental data using only the mixing law. It must be stressed that this solution is only an estimate and deviations may require the addition of this term.

Therefore, first-order analysis is conducted considering the following relationship:



Eb′′lend ≈ ϕI E′I′ + ϕI I E′I′I



(12)



Then, considering that Equation (10) represents the loss modulus of each component, a relationship to describe the case of blends is proposed as a mixture law:



Eb′′lend = ϕI



E′′ g,I υg,I + E′′ a,I 1 − υg,I



+



∆EI ωτI 1 + ω2τI2



+ ϕII



E′′ g,II υg, + E′′ a,II 1 − υg,II



+



∆EI I ωτI I 1 + ω2τI2I



(13)



The relaxation times τI and τII depend on whether the model used is VFT (Equation (8)) or Arrhenius (Equation (9)). In the first case, the parameters involved are AI, AII, BI, BII, TV,I, and TV,II, and in the second case, τo,I, τo,II, Hac,I, and Hac,II.



3. Results and Discussion

NR does not mix homogeneously with synthetic rubbers such as SBR, resulting in the formation of distinct domain morphologies within the blend. As an example, Figure 2 presents the microstructure of the 70NR/30SBR and NR50/SBR50 blends cured at 433 K used in this study, as observed through TEM (Philips CM200 (200 kV)). Heterogeneity is evident in the sample, with the NR and SBR phases distinctly visible.



Polymers 2025, 17, 1312



the NR matrix. The SBR domains are nearly spherical, with a most probable diameter of around 0.46 um.

Regarding the NR50/SBR50 blend (Figure 2b), which displays a nearly co-continuous shape, the percentage of NR was determined to be 48.1%, while the percentage of SBR7 owf 1a6s found to be 51.9%.



FFiigguurree22..TTEEMMmmiiccrrooggrraapphhooffNNRR7700//SBR30 ((aa)) aannddNNRR5500//SBR50 (b) blends. SBR is tthhee ddaarrkk pphhaassee aanndd NNRR iiss tthhee cclleeaarr pphhaassee..

TInhepNreRvioanuds sStBuRdiaerseoafs twheerNe Rca/lScBuRlabteldenidn ubosethd iimn athgeespuresisnegntImreasegaerJcsho,ftthweaNreR1.a5n3dt. FSoBrRthpehNasRes75w/eSrBeRo2b5sebrlevnedd (bFyigouprteic2aal)m, tihceropsecrocpeyntaangdesToEfMNR[8a,2n2d].STBhReswe efirned7i5n.g1%s aalingdn 2w4i.9th%o, trheesrpreecstuivlteslyr.epTohretebdleinndthseholiwtesraatusreea–[3is,1la0n–d12s]t.ructure with small SBR droplets in the NFRigmuraetr3ixa.,bTshheoSwBRthdeolomsasimnsoadruelunseaorflythsepchoemripcaolu, nwditshcuarmedosattp4r3o3bKabalneddi4a4m3 eKte. rTohfe avraoruiantdio0n.4i6nuEm″ .as a function of temperature can be used to make a first estimate of the glassRyevgaorludminge tfhraecNtioRn50c/hSaBnRge50obf ltehnedp(Fuirgeuerlea2stbo)m, wehr iccohmdpisopulanydssa(NneRaralnydcoS-BcoRn)tainsutohuesy sphaaspset,htrhoeupgehrcthenetgalgaessotfrNanRsiwtiaosndreegteiromn.inAeldthtooubgeh4s8o.1m%e,owf hthileestehme peaesrucernemtageentosfwSBerRe wreapsfloicuanteddt,onboes5ig1.n9i%fic. ant differences were found between them that would warrant placing errorInbaprrseivniothues fistguudrieess(othf ethinesNtrRu/mSeBnRtabl leernrodruwseads ainlsothveepryressmenatllr).esearch, the NR and SBR phases were observed by optical microscopy and TEM [8,22]. These findings align

with other results reported in the literature [3,10–12].

Figure 3a,b show the loss modulus of the compounds cured at 433 K and 443 K. The

variation in E as a function of temperature can be used to make a first estimate of the

glassy volume fraction change of the pure elastomer compounds (NR and SBR) as they pass

through the glass transition region. Although some of these measurements were replicated,

no significant differences were found between them that would warrant placing error bars

in the figures (the instrumental error was also very small).

Based on Figure 3a,b and using Equation (3), υg is calculated, and its temperature variation is presented in Figure 4a,b for NR and SBR vulcanized at 433 K and 443 K,

respectively.

The data from Figure 4a,b were then fitted using the double Boltzmann function

described in Equation (5), resulting in an excellent fit, as evidenced by the continuous line

shown in both figures. The optimal parameters obtained from the fitting are provided in Table 3, along with the R2 coefficient.

Figures 5 and 6 show the fitting of the experimental data of E as a function of the

temperature using Equation (10) in the glass transition region for the NR and SBR samples

cured at 433 K and 443 K, respectively. In the figures, both the VFT (Equation (8)) and

Arrhenius (Equation (9)) expressions have been used for the relaxation time in Equation (10). TFhigeuprear3a.mLoestesrms oudsuedlusfoEr″fiatstiangfutnhcetidonatoafatrheegtievstenteminpTearabtluer4e.fTorhepucroenctorimbuptoiuonndosfaEnqdubalteinodns (c1u)riesdaalst o(as)hTov w= 4n3i3nKthaendfi(gbu)rTevs.= 443 K. Data from ref [13].



Polymers 2025, 17, 1312



variation in E″ as a function of temperature can be used to make a first estimate of the glassy volume fraction change of the pure elastomer compounds (NR and SBR) as they pass through the glass transition region. Although some of these measurements were replicated, no significant differences were found between them that would warrant pla8coinf 1g6 error bars in the figures (the instrumental error was also very small).



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8 of 17

Based on Figure 3a,b and using Equation (3),    is calculated, and its temperature

variation is presented in Figure 4a,b for NR and SBR vulcanized at 433 K and 443 K, resFFpiigeguucrtreiev33e.. lLLyoo.ssss mmoodduulluussEEa″saas faunfuctnioctnioonf tohfettheesttetesmt tpeemrapteurraetuforrepfuorrepcuormepcooumnpdosuannddsbalennddbslceunrdesd

cautr(ead) Tatv (=a)4T3v3=K4a3n3dK(ban) dTv(b=) 4T4v3=K4.4D3 aKta. Dfraotma frreofm[1r3e]f. [13].



Figure 4. Volume fraction of the glassy phase as a function of the temperature of NR and SBR Fviuglucraeni4z.edVoatlu4m33eKfr(aa)catinodn4o4f3tKhe(bg)l.aSsoslyidplihnaesseaarestahefufinttcintigontooEfqtuhaetitoenm(5p)e. rature of NR and SBR vulcanized at 433 K (a) and 443 K (b). Solid lines are the fitting to Equation (5).

The data from Figure 4a,b were then fitted using the double Boltzmann function described in Equation (5), resulting in an excellent fit, as evidenced by the continuous line shown in both figures. The optimal parameters obtained from the fitting are provided in Table 3, along with the R2 coefficient.



Polymers 2025, 17, 1312 Polymers 2025, 17, 1312



9 of 16



Table 3. Fitting parameters of Equation (5) and R2 coefficient for data shown in Figure 4a,b, for NR and SBR vulcanized at 433 K and 443 K.



Tv (K) f

T1 (K) T2 (K) k1 (K) k2 (K)

R2



NR



433



443



0.28 ± 0.07



0.46 ± 0.05



212.62 ± 1.14



216.30 ± 0.20



218.65 ± 0.14



220.24 ± 0.17



3.17 ± 0.19



1.32 ± 0.06



2.06 ± 0.08



1.32 ± 0.05



0.99995



0.99992



SBR



433



443



0.32 ± 0.04



0.41 ± 0.12



223.62 ± 0.92



228.28 ± 1.13



233.27 ± 0.11



233.60 ± 0.28



4.36 ± 0.22



3.44 ± 0.11



2.39 ± 0.08



2.42 ± 0.14



0.9999



0.99997



Table 4. Fitting parameters of Equation (9) for data shown in Figures 5 and 6 using the VFT and the Arrhenius approaches for the relaxation time in Equation (10).



NR



SBR



Tv [K] Ea′′ [MPa] Eg′′ [MPa]

A [s]



433 0.056 133.9 3.9 × 10−16



443 0.076 160 4.0 × 10−16



433 0.281

98 1.0 × 10−13



443 0.35 50 0.8 × 10−13



VFT Equation (8)



B [K] Tv [K]

R2



3260 113.9 0.9493



3250 114.5 0.9153



2630 131.5 0.9367



2640

913o1f.017 0.9166



τo [s]



2.14 × 10−31 5.75 × 10−29 1.36 × 10−28 9.73 × 10−28



(E1q0u).atTEihoAqnerura(hp1teia)onrniiasum(sa9)lestoerssHhuoacws[ekRndJ2/ifnmootrhl]fietfitignugrte01h.s92e.504.d63ata



are



giv1e1n0.6in

0.9438



Table



4.1T16h.4e contributi1o1n2.2of



0.9568



0.9436



Figure 5. Loss modulus E for (a) NR and (b) SBR vulcanized at 433 K with fitting to Equation (10). Figure 5. Loss modulus E″ for (a) NR and (b) SBR vulcanized at 433 K with fitting to Equation (10).



Polymers 2025, 17, 1312



Figure 5. Loss modulus E″ for (a) NR and (b) SBR vulcanized at 433 K with fitting to Equation (101)0. of 16



Figure 6. Loss modulus E for (a) NR and (b) SBR vulcanized at 443 K with fitting to Equation (10). Figure 6. Loss modulus E″ for (a) NR and (b) SBR vulcanized at 443 K with fitting to Equation (10).

Table 4 shows the parameter R2 obtained by fitting the experimental data to ETqaubaleti4onsh(o1w0)s. tIhtecapnarbaemoebtesreRrv2eodbttahiantedwbhyenfitctoinngsitdheereinxgpetrhime AenrtrahlednaiutastroeElaqtuioantiofonr the (10).rIetlacxaantiboenotbimseervinecdlutdhaetdwinhEenqucaotniosind(e1r0in),gththeebeAsrtrRh2enwiuass arelwlaatiyosnofbotraitnheedr,erleagxaartidolness of timetihneclvuudlecadniinzaEtqiounattieomnp(1er0a),tuthree obfestht eR2sawmapslaelsw. Tayhseroebfotarien,ewde, rdeegcairddeldestsooufstehtehveuAlcrarhne- nius relationship instead of the VFT relationship in Equation (10) for the remaining fits of the experimental data of E of the vulcanized blends.

The mixing law proposed in Equation (13) can be used to represent the experimental loss modulus data obtained for the different NR/SBR blends prepared, where phase I = NR and phase II = SBR. Figures 7 and 8 show the plots of the data for the blends vulcanized at 433 K and 443 K, together with the fitted curves. The parameters of Equation (13) (considering Equation (9) as the relaxation time) that best fit the experimental data are shown in Figures 9–11 for the samples vulcanized at 433 K and 443 K. These figures show how these parameters change with the volume fraction, ϕ(NR), of NR in the vulcanized blends.

Figure 9 shows the relaxation intensity, ∆E, for the NR and SBR phases, as a function of the NR content in the blend ϕNR for the samples cured at 433 K and 443 K. In the case of the NR phase, ∆ENR tends to decrease as the blend is richer in NR. This behavior is observed for both curing temperatures, and it can be associated with the curative migration among phases.

In the present study, mapping of the distribution of curatives into the phases of the blends, as presented in the work of Cosa Fernandez et al. in NR/SBR mixtures [44], has not been carried out. The phenomenon of the migration of curatives (mainly sulfur and accelerators) has also been verified indirectly in NR/SBR blends [7,23,24,45,46]. Migration occurs from the BR or SBR phase toward the NR phase and results in a higher concentration of curatives in the NR phase, which leads to a change in the crosslinking density. As a result of this effect, there is a temperature shift in the glass transition temperature of each phase of the blend [46].



Polymers 2025, 17, 1312



at 433 K and 443 K, together with the fitted curves. The parameters of Equation (13) (con-

sidering Equation (9) as the relaxation time) that best fit the experimental data are shown

in Figures 9–11 for the samples vulcanized at 433 K and 443 K. These figures show11hoofw16 these parameters change with the volume fraction, ϕ(NR), of NR in the vulcanized blends.



Polymers 2025, 17, 1312



FFiigguurree77. .E″EfofrorNNR/RS/BSRBbRlebnldesndvus lvcaunlcizaendizaetd43a3t 4K3.3DKas.hDedaslhineedcloinrreescpoorrnedsspotontdhsetfiotttihneg ftio1tt1Einqoguf at1-o7 Equation (13). tion (13).



FFiigguurree 88.. EE″ ffoorrNNRR/S/BSRBRblebnlednsdvsuvlcualnciazneidzeadt 4a4t34K43. DKa.shDeadshliende clionrerecsoprornesdpsotnodths etofittthinegfittotiEnqgutaoEtiqouna(t1io3)n. (13).

FFiigguurree 99 ashlsoowshsothwesrtehlaexraetliaoxnatiinotneninsitteyn,si∆ty  f,ofor rththeeSNBRRpahnadseS,B∆REpShBaRs,eass, aasfuanfuctniocntioonf ϕofNtRhienNthRecbolnentedn.tAins tthhee ϕblNeRndinc  reasefos,rtthheerseadmucptlieosnciunrtehdearte4la3x3aKtioannidnt4e4n3siKty. Ionf tthhee cSaBsRe pohf athsee iNs mR oprheassieg,n∆if i cantt.eFnrdosmtothdeeocrbesaesrevaatsiotnheofbtl1e0n0dinisearcichhceorminpoNuRn.dT(hTiasbbleeh1a),viitocrains boebsceornvceldudfoedr bthoatht icnutrhinegmtoesmt pNeRra-rtiucrhesb,leannddsi,tthcaensebteimasessowcioauteldd bweitihnstuhfeficcuiernattitvoeamchiigervaetthioendaemveolnogpmpheansteos.f a complete crosslinked network in the SBR phase, and therefore this

phase is undervulcanized.



Polymers 2025, 17, 1312



of the NR content in the blend    for the samples cured at 433 K and 443 K. In the case



of the NR phase, ∆   tends to decrease as the blend is richer in NR. This behavior is



observed for both curing temperatures, and it can be associated with the curative migra-



tion among phases.



12 of 16



Polymers 2025, 17, 1312



13 of 17



Figure 9. ∆E for NR and SBR phases as a function of the NR content, ϕNR in the blends vulcanized at



433 K and 443 K. Figure 9. ΔE for NR



and



SBR



phases



as



a



function



of



the



NR



content,



  



, in the blends vulcanized



at 433 K and 443 K.



FigaFutirg4eu31r3e0K.1τ0ao.n,NτdRo(,4Na4)R3a(nKad.)



Daτnao,dSsBhRτe(odb,S)BlifRnoer(bsth)aerfoepriuntrhceelucpdoumerdpe tocouonsmhdposowaundnddaetsaaactnhednpdheeaancshecyop. fhtahseebolfenthdes



blends vulcanized vulcanized



at 433 K and 443 K. Dashed lines are included to show data tendency.



The trend with ϕNR is similar at both vulcanization temperatures used in this research for ∆ENR and ∆ESBR. In the case of the pure NR compound ( ϕNR = 1), ∆ENR is lower when the sample is cured at 443 K compared to 433 K. For the pure SBR compound



( ϕNR = 0), this situation is reversed. When the blends are analyzed, it is observed that the relaxation intensity of each



phase of the sample NR50/SBR50 presents a different tendency with the cure temperature compared to the other ones. For the other blends, ∆ENR is higher or equal for the samples cured at 433 K compared to those cured at 443 K, but the opposite situation is observed for ∆ESBR.



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Figure 10. τo,NR (a) and τo,SBR (b) for the pure compounds and each phase of the blends vulcanized

13 of 16

at 433 K and 443 K. Dashed lines are included to show data tendency.



Figure 11. Hac for NR and SBR phases as a function of the NR content, ϕNR, in the blends vulcanized Faitg4u3r3e K11a.n d  44f3oKr .NR and SBR phases as a function of the NR content,    , in the blends vulcan-

ized at 433 K and 443 K. Using the definition of the relaxation intensity in Equation (7), it is the difference

betwAeesnmtheenutinorneeldaxpedreavniodursellya,xethdemgordaduuli.alThinecurenarseelaixnedthmeoNdRulupsh,aEsue(iansstohceiaSteBdRwmitahtrthixe aglltaesrssythzeonvea)l,udeoseosfnto10t0cohbatnagineetdooinmtuhcehrwheiothmtehteernetetwsto(rTkafbolerm1e).dFdroumrintghethsee cvraolsuselsin, kitinisg epvriodceensst.thTahte, oabt sbeortvhedcusrtianbgilitteymcpanerbaetuartetrsibouf t4e3d3tKo tahnedfa4c4t3thKa,t,thweitahdinditthieongloafssjuyszto1n0e,pthhre omf aNteRrisailg’snisfiticfafnnetslys irsedpurecdeosmt10i0n.aInntltyhidsectaesrem, itnheedSbByRtphheainsetriisnlsiikceplyronpoetrtfiuelslyofctuhreedp,owlyhmileer tchheaNinRs pthheamsesieslvoevse,rrcautrheedr, tahsainndbiycattheedcbryosthsleinlokwdeernts1i0t0yv.aHluoews oefvtehr,etphuerreeNlaRxecdommpooduunluds., TEhre(apsrseosceinacteedofwmitohrethientreurbfabceersyinzoSnBeR),aiss m  oreisnecnresiatsivese, tcoomthbeintyepdewoifthnethtwe omrkigsrtartuiocntuorfe formed in both phases and it depends on the curing temperature.

The parameters τo,NR and τo,SBR were also estimated by fitting the data from Figures 7 and 8 to the proposed model described by Equation (13). Figure 10a,b show the dependence

of these parameters on ϕNR and the cure temperature in the studied compounds for the NR (a) and SBR (b) phases. It is observed that both parameters decrease when the blend

becomes richer in NR. However, it can also be observed that when a small amount of NR is

added to the pure SBR compound, τo,SBR increases initially but starts to decrease as the NR content ϕNR continues to rise.

Figure 11 shows the activation energy for the NR phase (Hac,NR) as a function of the NR content in the blend. The trend shows that Hac,NR increases as the NR content increases, regardless of the sample cure temperature. The monotonic increase in activation energy

with higher ϕNR for both cure temperatures indicates that the NR phase becomes more thermally stable or requires more energy to undergo molecular motion, implying that the

network structure in the NR phase becomes more constrained. The crosslink density in the

NR phase may increase with higher NR content, contributing to this effect. The migration

of curatives from the SBR to the NR phase during the vulcanization process can indeed

explain the observed trends in the activation energy for both phases due to the fact that

this migration increases the crosslink density in the NR phase [45,46].

As mentioned previously, the gradual increase in the NR phase in the SBR matrix

alters the values of t100 obtained in the rheometer test (Table 1). From these values, it is evident that, at both curing temperatures of 433 K and 443 K, the addition of just 10 phr of

NR significantly reduces t100. In this case, the SBR phase is likely not fully cured, while the



Polymers 2025, 17, 1312



14 of 16

NR phase is overcured, as indicated by the lower t100 values of the pure NR compound. The presence of more interfaces in SBR as ϕNR increases, combined with the migration of curatives into the NR phase, likely contributes to the rise in activation energy. Further investigation must be carried out to elucidate this point.

On the other hand, Figure 11 also presents the activation energy for the SBR phase (Hac,SBR) as a function of ϕNR in the blend. Initially, Hac,SBR is approximately 115 kJ/mol for the pure SBR compound ( ϕNR = 0), and decreases slightly with the addition of NR to the blend. However, for ϕNR > 0.3, this trend reverses and Hac,SBR begins to increase.

In previous research, our research group employed a sub-resonant forced pendulum to measure the loss tangent in the glass transition region, determining the activation energy for NR/SBR blends cured at 433 K [24]. The values were similar to those in the present study. Although these compounds were also prepared via solution casting, the curing system employed was the CV type with a Λ value of 0.31. In that study, Hac,NR and Hac,SBR exhibited the same trend, showing slightly higher values as ϕNR increased in the blend. This observation suggests that the curing system influences the activation energy, which is reasonable, as it likely results in a different type and distribution of crosslinks. Further investigation must be carried out to elucidate this point.

4. Conclusions

In this research, we have analyzed the variation in the loss modulus with temperature in unfilled NR/SBR composites cured at 433 K and 443 K. The studies focused on the glass transition region. The samples were prepared at their optimal curing conditions by vulcanizing them at time t100 obtained by means of rheometry.

As extensively reported in the literature, these types of blends are immiscible, and we have confirmed this through our TEM observations.

A new approach to fitting loss modulus data as a function of the temperature in the glass transition region, obtained by DMA, is introduced and validated. This methodology takes account of the coexistence of the rubbery and glassy phases of the pure elastomer as the temperature transitions between the rubbery and glassy states (and vice versa). In the analysis, the temperature and frequency dependence of the loss modulus is considered, based on Zener’s mechanical model for a single relaxation time.

This methodology was successfully applied to the case of an immiscible blend, namely cured unfilled NR/SBR, where a mixture law for both elastomers was considered.

This analysis yielded key model parameters—activation energy, intensity, and relaxation time—for each phase within the blends, highlighting how these parameters shift as the NR content increases in the blend. This reveals how the properties of each phase in the blend vary according to the blend composition.

Author Contributions: A.J.M. and M.A.M. conceived, designed, and performed the experiments. A.J.M., M.P.B.V. and M.C.M. analyzed the data. A.J.M. carried out the writing—review and editing. M.P.B.V. and M.C.M. reviewed the paper. All authors have read and agreed to the published version of the manuscript.

Funding: A.J.M and M.A.M. would like to acknowledge the University of Buenos Aires (Argentina) for the funding under Project UBACYT 20020120100051. M.P.B.V. and M.C.M. would like to acknowledge the Department of Mathematical Sciences at the University of Texas at El Paso, USA, and a project of the US Department of Education, P120A220040-FY 2022 MSEIP.

Institutional Review Board Statement: Not applicable.

Data Availability Statement: The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.



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Conflicts of Interest: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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