# Dynamic Rheological Investigation during Curing of a Thermoset Polythiourethane System

Authors: Weiping Du; Lianjiang Tan; Yang Zhang; Haipeng Yang; Huifang Chen
Journal: International Journal of Polymer Science
 (2019)

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## Abstract

A polythiourethane thermoset system based on a diisocyanate and a trithiol was investigated by dynamic rheological measurements. Strain sweep was performed to determine the linear elastic region of the thermosetting system. The changes of characteristic parameters including elastic modulus, viscous modulus, and complex viscosity were recorded in a heating ramp to trace the cross-linking and structural evolution during the curing process. Time sweep at constant temperatures was also performed to explore possible curing strategy at reduced temperatures. In addition, frequency sweep was conducted to confirm the temperature- and time-dependent viscoelastic properties of the thermoset system during the curing process. Both continuous heating and isothermal aging gave rise to solidification of the polythiourethane with similar critical structure, as evidenced by the critical values of relaxation exponent. A combination of isothermal aging and heating is expected to be a facile strategy for fabricating thermoset polythiourethane polymers at lower temperature or/and reduced curing time. A kinetic study was done to confirm the gelation characteristics of the polythiourethane system, and the activation energy was also calculated.


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## Body

## 1. Introduction

Transparent polymers have attracted great interest as alternative optical materials due to their excellent impact strength, lightness, good processability, and low cost. However, the frequently used optical polymeric materials such as polycarbonate (PC), polymethyl methacrylate (PMMA), and diethylene glycol bis(allyl carbonate) have a typical refractive index of 1.49-1.59 [1, 2], which is low compared with those of inorganic optical materials. Eyeglass lens made from these polymers thus suffer from the disadvantage of being thick at both center and edge, which limits the applications of these polymer materials. Optical polymers with enhanced refractive index and low chromatic dispersion are needed for producing lenses. A good way to increase the refractive index of optical polymers is to introduce sulfur atoms into polymer backbones. Polythiourethane is increasingly used as an optical material because of its high refractive index [3–6]. In fact, polythiourethane materials formed by the coupling reaction between thiols and isocyanate monomerare exhibit excellent optical, physical, and mechanical properties [7]. Polythiourethane is usually synthesized by polyaddition or chain polymerization. Thermoset cure has been a research focus of polythiourethane [8–10]. A complete understanding of the curing process is critical for the determination of optimal curing conditions and ultimately optimal properties of the final material. Rheological testing is a powerful tool for studying the research and development of thermoset polymers and is frequently used in combination with differential scan calorimetry (DSC) and chromatography [11].Thermoset structural development is usually accompanied by enormous rheological changes: the sample changes from a low-melting thermoplastic solid to a low-viscosity liquid, to a gel, and then to a stiff solid when cured with a gradual increase in temperature. Understanding this process has been advanced substantially by rheological measurements and analysis of viscosity, shear modulus, and damping. Dynamic oscillatory measurements of a thermoset sample’s viscoelasticity can be made as the reaction proceeds through the gel point until the sample becomes a stiff solid. In the present work, a thermoset polythiourethane from a trithiol/diisocyanate reaction system was examined by dynamic rheology. The structural evolution of the thermoset system during curing processes was investigated by tracing the typical rheological parameters such as elastic (storage) modulus, viscous (loss) modulus, loss tangent, and complex viscosity. Based on the rheological measurements in temperature sweep, time sweep, and frequency sweep modes, improved curing strategies with lower curing temperature or/and shortened solidification time can be expected. Furthermore, the kinetics of the polythiourethane system during the curing process were studied on the basis of the rheological results, and the gelation behavior of the polythiourethane was confirmed.


## 2. Materials and Methods

### 2.1. Materials

2,3-Bis((2-mercaptoethyl)thio)-1-propanethiol (BMPT, 99%) and m-xylylene diisocyanate (XDI, 98%) were provided by Mitsui Chemicals. Phosphate mold release agent was provided by Shanghai Longxu Chemicals. Dibutyltin dichloride (99%) was purchased from Macklin. All the chemicals were used without further purification.


### 2.2. Preparation of Polythiourethane System

The polythiourethane thermoset system was prepared from the reaction of BMPT and XDI. Specifically, 13 g of XDI, 0.08 mL of phosphate mold release agent, and 3.6 mg of dibutyltin dichloride were mixed under stirring for 10 min at room temperature. Then 12 g of BMPT was added, stirred for 5 min, degassed under vacuum for 20 min, and finally filtered by a 1μm filter. The polythiourethane reaction system was prepared freshly for rheological measurements. The glass transition temperature (Tg) of the polythiourethane reaction system and the cross-linked polythiourethane system was 16.5°C and 73.5°C, respectively, determined by differential scanning calorimetry (DSC).


### 2.3. Rheological Testing

Dynamic rheological experiments were performed using an advanced solution and melt rotation rheometer (ARES-RFS, TA) equipped with two parallel plates. The temperature control was done with a thermostatic bath within ±0.1°C of the preset value. The parallel plate on which samples were placed was 25 mm in diameter. The distance between the plates was 1 mm. A thin layer of low-viscosity silicone oil was applied to cover the exposed surface of the samples, protecting them from evaporation and thus minimizing the testing errors. The details of the rheological measurements were as follows: (1) strain sweep at a low temperature and a high temperature was conducted from 0.1 to 10% to observe the linear viscoelastic regime of the samples; (2) temperature sweep from room temperature to 130°C with a heating rate of 2°C/min at three constant frequencies (6.28, 39.4, and 100 rad/s) was aimed at tracing the storage modulusG′, the loss modulus G″, the complex viscosity η∗, and the loss tangent tanδ during the increase of temperature; (3) time sweep at different constant temperatures (55, 65, and 75°C) and a constant frequency of 6.28 rad/s was done to determine the influences of the gelation process on the dynamic viscoelastic parameters (G′, G″, and η∗); (4) frequency sweep at three constant temperatures (55, 65, and 75°C) was conducted to trace the changes of G′ and G″ with the oscillatory frequency; (5) frequency sweep at different time intervals during the isothermal aging process at 75°C was conducted to obtain the time dependence of G′ and G″ and thus the changes of relaxation exponents with the aging time.


## 2.1. Materials

2,3-Bis((2-mercaptoethyl)thio)-1-propanethiol (BMPT, 99%) and m-xylylene diisocyanate (XDI, 98%) were provided by Mitsui Chemicals. Phosphate mold release agent was provided by Shanghai Longxu Chemicals. Dibutyltin dichloride (99%) was purchased from Macklin. All the chemicals were used without further purification.


## 2.2. Preparation of Polythiourethane System

The polythiourethane thermoset system was prepared from the reaction of BMPT and XDI. Specifically, 13 g of XDI, 0.08 mL of phosphate mold release agent, and 3.6 mg of dibutyltin dichloride were mixed under stirring for 10 min at room temperature. Then 12 g of BMPT was added, stirred for 5 min, degassed under vacuum for 20 min, and finally filtered by a 1μm filter. The polythiourethane reaction system was prepared freshly for rheological measurements. The glass transition temperature (Tg) of the polythiourethane reaction system and the cross-linked polythiourethane system was 16.5°C and 73.5°C, respectively, determined by differential scanning calorimetry (DSC).


## 2.3. Rheological Testing

Dynamic rheological experiments were performed using an advanced solution and melt rotation rheometer (ARES-RFS, TA) equipped with two parallel plates. The temperature control was done with a thermostatic bath within ±0.1°C of the preset value. The parallel plate on which samples were placed was 25 mm in diameter. The distance between the plates was 1 mm. A thin layer of low-viscosity silicone oil was applied to cover the exposed surface of the samples, protecting them from evaporation and thus minimizing the testing errors. The details of the rheological measurements were as follows: (1) strain sweep at a low temperature and a high temperature was conducted from 0.1 to 10% to observe the linear viscoelastic regime of the samples; (2) temperature sweep from room temperature to 130°C with a heating rate of 2°C/min at three constant frequencies (6.28, 39.4, and 100 rad/s) was aimed at tracing the storage modulusG′, the loss modulus G″, the complex viscosity η∗, and the loss tangent tanδ during the increase of temperature; (3) time sweep at different constant temperatures (55, 65, and 75°C) and a constant frequency of 6.28 rad/s was done to determine the influences of the gelation process on the dynamic viscoelastic parameters (G′, G″, and η∗); (4) frequency sweep at three constant temperatures (55, 65, and 75°C) was conducted to trace the changes of G′ and G″ with the oscillatory frequency; (5) frequency sweep at different time intervals during the isothermal aging process at 75°C was conducted to obtain the time dependence of G′ and G″ and thus the changes of relaxation exponents with the aging time.


## 3. Results and Discussion

### 3.1. Linear Viscoelastic Region

Dynamic oscillatory rheology requires that the samples are in their linear viscoelastic region during the measurements. To determine the linear viscoelastic region of the polythiourethane thermoset system, a strain sweep from 0.1-10% at a frequency of 6.28 rad s-1 was performed at two typical temperatures. Prior to strain sweep, the samples were kept at that constant temperature for 3 min to equilibrate. The equilibrium time of 3 min was sufficient, confirmed by repeating the measurement for three times. The strain sweep results are shown in Figure 1. At a low temperature of 25°C, the reaction system showed a significant viscoelastic behavior, with close values of loss modulus G″ and storage modulus G′. At the temperature of 120°C, in contrast, the system was cross-linked and became more elastic. This is reflected by the fact that G′ was much larger than G″. Both G′ and G″ changed little in the data range, indicating that the polythiourethane system was in the linear viscoelastic region when the strain lay within 0.1-10%. 1% was chosen as the strain amplitude in the following dynamic rheological measurements.Figure 1
Strain sweep for the polythiourethane system at (a) 25°C and (b) 120°C. The frequencyω was set at 6.28 rad s-1.
(a)
(b)


### 3.2. Rheological Behavior in Temperature Sweep

Chambon and Winter proposed that the crossover point ofG′ and G″ could be considered as the inception of gelation process [12]. We performed temperature sweep at three selected frequencies for the polythiourethane reaction system from room temperature to 130°C at a heating rate of 2°C/min. G′, G″, and η∗ of the samples were recorded as shown in Figures 2(a)–2(c). It was found that all G′, G″, and η∗ are kept at low levels with fluctuation at the temperature below 100°C. As the temperature increased beyond 110°C, G′ and η∗ increased substantially within a narrow temperature range. The growing rate decreased when the temperature exceeded 120°C. G″ also increased greatly with the temperature, but at a smaller rate than G′ and η∗ and leveled off or even decreased beyond 120°C. This demonstrated that the cross-linking reaction occurred drastically in the system in the temperature range of 100-120°C. At the temperatures below 100°C, the samples had comparable solid-elastic and liquid-viscous components. In the range of 100-120°C, sol-gel transition led the samples to a more elastic state. G′ increased more rapidly than G″, and they crossed over at a certain point. With further increase of the temperature, the system became a viscoelastic solid, i.e., polythiourethane polymer. It is noted that, however, the crossover of G′ and G′′ depended to some extent on the testing frequency, which has been found in other viscoelastic systems [13, 14]. Considering the crossover of G′ and G″ is not a reliable criterion for the determination of gel point, another criterion based on the temperature dependence of tanδ at varied frequencies was used, where gel point is the temperature at which tanδ becomes frequency-independent. The curves at different frequencies cross over at a point, where G′ and G″ follow a power law [15–17]:
(1)tanδ=G″ωG′ω=tannπ2=constant,where n is the relaxation exponent. Therefore, the changes of tanδ with temperature at the three frequencies were plotted. As demonstrated in Figures 2(d)–2(f), tanδ did not show significant changes until the temperature increased to 110°C, beyond which tanδ dropped greatly. The tanδ curves at the three frequencies in the narrow temperature range were given in the same plot as shown in Figure 2(g). The curves crossed over at a point corresponding to 119.8°C, which can be regarded as the gel point of the polythiourethane system during the curing process. The tanδ value at this point was 0.0217, and the corresponding n value was 0.014. Beyond this point, the elastic polythiourethane polymers form, revealed by large G′ and η∗ and very small values of tanδ.Figure 2
Temperature sweep for the polythiourethane system at different frequencies. Changes ofG′, G″, and η∗ with temperature at (a) 6.28 rad s-1, (b) 39.4 rad s-1, and (c) 100 rad s-1. Changes of tanδ with temperature at (d) 6.28 rad s-1, (e) 39.4 rad s-1, and (f) 100 rad s-1. (g) Local region of the temperature sweep data showing the crossover of the tanδ curves at three frequencies.
(a)
(b)
(c)
(d)
(e)
(f)
(g)


### 3.3. Rheological Behavior in Time Sweep

In addition to heating, isothermal aging at appropriate temperatures also leads to curing of the polythiourethane system. Time sweep at three constant temperatures was conducted for the polythiourethane samples at a frequency of 6.28 rad s-1. The temperatures (55, 65, and 75°C) were selected as we intended to explore milder curing strategies in which moderate temperatures are applied. As shown in Figure 3, both G′ and G″ were small in the initial period in all the cases. G″ had larger values than G′, indicative of a viscous liquid. With the increase of aging time, both G′ and G″ gradually increased. Beyond a certain time point, the increase of G″ became more significant, since the viscosity grew greatly with intermolecular cross-linking. Similar phenomena were observed for G′ after a longer time. The samples underwent drastic structural changes and became solid-like viscoelastic polymers. This is evidenced by the more rapid growth of G′ and the crossover of G′ and G″. The time point at which G′ and G″ crossed over differed at varied temperatures. As indicated in Figure 3, the crossover point corresponded to 7801 s at 55°C, 5212 s at 65°C, and 2150 s at 75°C. These results showed that the curing proceeded more rapidly at a relatively high temperature. Moreover, the changes of tanδ during the aging process were analyzed. tanδ first increased with the aging time, signifying that cross-linking did not occur in the samples. On the contrary, the samples became even more liquid-like. Once the time increased beyond a point, tanδ decreased significantly to a low level and then kept almost unchanged with prolonged time. It was found that the turning point of the tanδ curves was close to the onset of rapid growth of G′. The intermolecular cross-linking reaction occurred drastically in the region where tanδ showed a burst decrease. Further aging resulted in crossover of G′ and G″, beyond which solid polythiourethane polymer formed. tanδ leveled off at long aging times.Figure 3
Time sweep for the polythiourethane system at (a) 55°C, (b) 65°C, and (c) 75°C. The frequencyω was set at 6.28 rad s-1 and the strain was 1%. The changes of G′, G″, and η∗ with time were recorded.
(a)
(b)
(c)


### 3.4. Frequency Dependence of Rheological Behavior

We further investigated the viscoelastic behavior of the polythiourethane system during frequency sweep in order to gain more information of the temperature effects on the curing of the polythiourethane systems. Once the sample was heated to the target temperature, the frequency sweep was started at the constant temperature. Figure4 shows G′ and G″ as a function of the angular frequency ω at three temperatures for the polythiourethane samples. In all the cases, G″ dominates the viscoelastic in the low frequency region, an indication of viscoelastic fluid before the gel point. With increasing frequency, both G′ and G″ increased, with G′ at a higher rate than G″. G′ and G″ crossed over at a certain frequency and then further increased, with the growth of G′ at a higher rate. At higher frequencies, the macromolecular chains did not have enough time to relax or realign [18] and thus behaved like an elastic solid with G′ dominating the viscoelastic properties. More importantly, the frequency at which G′ and G″ crossed over decreased with the increasing of the temperature, i.e., from 35 rad s-1 at 55°C to 12 rad s-1 at 75°C. These results agreed well with those of the time sweep. The intermolecular cross-linking reaction in the polythiourethane system was more favored at 75°C than at 55°C.Figure 4
Angular frequency sweep for the polythiourethane system at (a) 55°C, (b) 65°C, and (c) 75°C with the strain of 1%. The changes ofG′ and G″ with frequency were recorded.
(a)
(b)
(c)The rheological characteristics near the gel point can be described by power laws.G′ and G″ at the gel point can be expressed by the following power law [19–21]:
(2)G′ω~G″ω~ωn,where ω is the angular frequency. This power law relation has been widely used for a variety of polymeric gels. It is meaningful to investigate relationship between the dynamic moduli and the angular frequency during the isothermal aging process, from which the gel point of the system can be determined accurately.Figures5(a) and 5(b) show the changes of G′ and G″ against the angular frequency ω at different aging time intervals for the polythiourethane system at the aging temperature of 75°C. The frequency dependence of G′ and G″ followed the commonly observed relations of G′ω~ωn′ and G″ω~ωn″. It was found that G′ and G″ increased with both aging time and the frequency. At the same aging time, smaller G′ and G″ were observed at low frequencies, indicating that the polythiourethane system behaved more like liquids. As the frequency grew to larger values, the system was more solid-like since the time scale of oscillation became smaller than that of the molecular motion or rearrangement of the polythiourethane system. With the increase of aging time, both G′ and G″ showed reduced dependence on the aging time, indicative of gelation and solidification of the system. This was also reflected by the significantly larger G′ than G″ at long aging times.Figure 5
(a) Storage modulusG′ and (b) loss modulus G″ versus angular frequency ω at different aging time intervals for the polythiourethane system at 75°C. (c) Time dependence of the exponents n′ and n″ determined from linear fitting of G′ and G″ versus angular frequency data (log-log coordinates) in (a) and (b).
(a)
(b)
(c)The aging time dependence ofn′ (exponent of G′ versus ω) and n″ (exponent of G″ versus ω) for the polythiourethane system is shown in Figure 5(c). Both n′ and n″ decreased with increasing aging time, with n′ decreasing more rapidly than n″. n′ and n″ crossed over at an aging time of 2410 s. The critical gel time determined here was a little longer than that determined by the crossover of G′ than G″ aforementioned. The critical relaxation exponent n can be determined by the crossover point of the n′ and n″ curves, which was 0.022. The critical n value determined from the temperature sweep experiments was 0.014, close to 0.022. The n value reflects the unique nature of a critical gel. A stiff critical gel often has a small value (n<<0.5). The extremely small n of the polythiourethane system at the critical gel point indicated the stiff and highly elastic nature of the resultant thermoset polyurethane. More importantly, the similar critical n values of the thermoset polyurethane formed by continuous temperature increase and by isothermal aging demonstrate that either heating or aging can lead to gelation of the thermoset polythiourethane system, and a curing process of combined heating and isothermal aging may be preferable for fabricating thermoset polythiourethane polymers.


### 3.5. Rheokinetics Study

The viscosity of a curing polymeric system at a given time pointt can be related to the time via an exponential function as follows [22]:
(3)ηt=η0ekt,where η0 is the viscosity at t=0 and k is the rate constant for viscosity increase. The logarithmic form of equation (3) is as follows:
(4)lnηt=lnη0+kt.Thus, plottinglnηt against t would give a straight line, whose slope is the value of k. Herein, the complex viscosity of the polythiourethane system in the isothermal curing process was used to be plotted against the time in a double logarithmic form at the selected temperatures. As shown in Figures 6(a)–6(c), the double logarithmic plots show almost straight lines before a time point that differed at varied temperatures. Beyond this critical point, the data deviated from the straight line, indicating that the data no longer conformed to the first-order reaction kinetics [23]. The overall reaction rate of the bulk polymerization systems is usually determined by both reaction kinetics and diffusion rates of monomers [24]. These two factors are competitive and depend largely on the viscosity of the reaction system. For our polythiourethane system, the viscosity grows dramatically after gelation. It can be thus assumed that the diffusion becomes prominent after the gel point, which would lead to a deviation from the first-order kinetics. As denoted in Figures 6(a)–6(c), the point beyond which obvious nonlinear behavior is observed was regarded as the gel point. It was found that the gel points at the three temperatures determined by the rheokinetics analysis were in good accordance with those obtained by the dynamic rheological measurements.Figure 6
Plots oflnη∗ vs. time for the polythiourethane system at (a) 55°C, (b) 65°C, and (c) 70°C. (d) Arrhenius plot of gel times for the polythiourethane system.
(a)
(b)
(c)
(d)Furthermore, we calculated the activation energy of the cure reaction for the polythiourethane system. The Arrhenius plot of the gel times is shown in Figure6(d), which is on the basis of the following equation [25]:
(5)tgel=Ae−E/RT,where E is the activation energy; T is the absolute temperature of reaction; R is the universal gas constant. The activation energy of the cure reaction turned out to be 61.02 kJ mol-1.


## 3.1. Linear Viscoelastic Region

Dynamic oscillatory rheology requires that the samples are in their linear viscoelastic region during the measurements. To determine the linear viscoelastic region of the polythiourethane thermoset system, a strain sweep from 0.1-10% at a frequency of 6.28 rad s-1 was performed at two typical temperatures. Prior to strain sweep, the samples were kept at that constant temperature for 3 min to equilibrate. The equilibrium time of 3 min was sufficient, confirmed by repeating the measurement for three times. The strain sweep results are shown in Figure 1. At a low temperature of 25°C, the reaction system showed a significant viscoelastic behavior, with close values of loss modulus G″ and storage modulus G′. At the temperature of 120°C, in contrast, the system was cross-linked and became more elastic. This is reflected by the fact that G′ was much larger than G″. Both G′ and G″ changed little in the data range, indicating that the polythiourethane system was in the linear viscoelastic region when the strain lay within 0.1-10%. 1% was chosen as the strain amplitude in the following dynamic rheological measurements.Figure 1
Strain sweep for the polythiourethane system at (a) 25°C and (b) 120°C. The frequencyω was set at 6.28 rad s-1.
(a)
(b)


## 3.2. Rheological Behavior in Temperature Sweep

Chambon and Winter proposed that the crossover point ofG′ and G″ could be considered as the inception of gelation process [12]. We performed temperature sweep at three selected frequencies for the polythiourethane reaction system from room temperature to 130°C at a heating rate of 2°C/min. G′, G″, and η∗ of the samples were recorded as shown in Figures 2(a)–2(c). It was found that all G′, G″, and η∗ are kept at low levels with fluctuation at the temperature below 100°C. As the temperature increased beyond 110°C, G′ and η∗ increased substantially within a narrow temperature range. The growing rate decreased when the temperature exceeded 120°C. G″ also increased greatly with the temperature, but at a smaller rate than G′ and η∗ and leveled off or even decreased beyond 120°C. This demonstrated that the cross-linking reaction occurred drastically in the system in the temperature range of 100-120°C. At the temperatures below 100°C, the samples had comparable solid-elastic and liquid-viscous components. In the range of 100-120°C, sol-gel transition led the samples to a more elastic state. G′ increased more rapidly than G″, and they crossed over at a certain point. With further increase of the temperature, the system became a viscoelastic solid, i.e., polythiourethane polymer. It is noted that, however, the crossover of G′ and G′′ depended to some extent on the testing frequency, which has been found in other viscoelastic systems [13, 14]. Considering the crossover of G′ and G″ is not a reliable criterion for the determination of gel point, another criterion based on the temperature dependence of tanδ at varied frequencies was used, where gel point is the temperature at which tanδ becomes frequency-independent. The curves at different frequencies cross over at a point, where G′ and G″ follow a power law [15–17]:
(1)tanδ=G″ωG′ω=tannπ2=constant,where n is the relaxation exponent. Therefore, the changes of tanδ with temperature at the three frequencies were plotted. As demonstrated in Figures 2(d)–2(f), tanδ did not show significant changes until the temperature increased to 110°C, beyond which tanδ dropped greatly. The tanδ curves at the three frequencies in the narrow temperature range were given in the same plot as shown in Figure 2(g). The curves crossed over at a point corresponding to 119.8°C, which can be regarded as the gel point of the polythiourethane system during the curing process. The tanδ value at this point was 0.0217, and the corresponding n value was 0.014. Beyond this point, the elastic polythiourethane polymers form, revealed by large G′ and η∗ and very small values of tanδ.Figure 2
Temperature sweep for the polythiourethane system at different frequencies. Changes ofG′, G″, and η∗ with temperature at (a) 6.28 rad s-1, (b) 39.4 rad s-1, and (c) 100 rad s-1. Changes of tanδ with temperature at (d) 6.28 rad s-1, (e) 39.4 rad s-1, and (f) 100 rad s-1. (g) Local region of the temperature sweep data showing the crossover of the tanδ curves at three frequencies.
(a)
(b)
(c)
(d)
(e)
(f)
(g)


## 3.3. Rheological Behavior in Time Sweep

In addition to heating, isothermal aging at appropriate temperatures also leads to curing of the polythiourethane system. Time sweep at three constant temperatures was conducted for the polythiourethane samples at a frequency of 6.28 rad s-1. The temperatures (55, 65, and 75°C) were selected as we intended to explore milder curing strategies in which moderate temperatures are applied. As shown in Figure 3, both G′ and G″ were small in the initial period in all the cases. G″ had larger values than G′, indicative of a viscous liquid. With the increase of aging time, both G′ and G″ gradually increased. Beyond a certain time point, the increase of G″ became more significant, since the viscosity grew greatly with intermolecular cross-linking. Similar phenomena were observed for G′ after a longer time. The samples underwent drastic structural changes and became solid-like viscoelastic polymers. This is evidenced by the more rapid growth of G′ and the crossover of G′ and G″. The time point at which G′ and G″ crossed over differed at varied temperatures. As indicated in Figure 3, the crossover point corresponded to 7801 s at 55°C, 5212 s at 65°C, and 2150 s at 75°C. These results showed that the curing proceeded more rapidly at a relatively high temperature. Moreover, the changes of tanδ during the aging process were analyzed. tanδ first increased with the aging time, signifying that cross-linking did not occur in the samples. On the contrary, the samples became even more liquid-like. Once the time increased beyond a point, tanδ decreased significantly to a low level and then kept almost unchanged with prolonged time. It was found that the turning point of the tanδ curves was close to the onset of rapid growth of G′. The intermolecular cross-linking reaction occurred drastically in the region where tanδ showed a burst decrease. Further aging resulted in crossover of G′ and G″, beyond which solid polythiourethane polymer formed. tanδ leveled off at long aging times.Figure 3
Time sweep for the polythiourethane system at (a) 55°C, (b) 65°C, and (c) 75°C. The frequencyω was set at 6.28 rad s-1 and the strain was 1%. The changes of G′, G″, and η∗ with time were recorded.
(a)
(b)
(c)


## 3.4. Frequency Dependence of Rheological Behavior

We further investigated the viscoelastic behavior of the polythiourethane system during frequency sweep in order to gain more information of the temperature effects on the curing of the polythiourethane systems. Once the sample was heated to the target temperature, the frequency sweep was started at the constant temperature. Figure4 shows G′ and G″ as a function of the angular frequency ω at three temperatures for the polythiourethane samples. In all the cases, G″ dominates the viscoelastic in the low frequency region, an indication of viscoelastic fluid before the gel point. With increasing frequency, both G′ and G″ increased, with G′ at a higher rate than G″. G′ and G″ crossed over at a certain frequency and then further increased, with the growth of G′ at a higher rate. At higher frequencies, the macromolecular chains did not have enough time to relax or realign [18] and thus behaved like an elastic solid with G′ dominating the viscoelastic properties. More importantly, the frequency at which G′ and G″ crossed over decreased with the increasing of the temperature, i.e., from 35 rad s-1 at 55°C to 12 rad s-1 at 75°C. These results agreed well with those of the time sweep. The intermolecular cross-linking reaction in the polythiourethane system was more favored at 75°C than at 55°C.Figure 4
Angular frequency sweep for the polythiourethane system at (a) 55°C, (b) 65°C, and (c) 75°C with the strain of 1%. The changes ofG′ and G″ with frequency were recorded.
(a)
(b)
(c)The rheological characteristics near the gel point can be described by power laws.G′ and G″ at the gel point can be expressed by the following power law [19–21]:
(2)G′ω~G″ω~ωn,where ω is the angular frequency. This power law relation has been widely used for a variety of polymeric gels. It is meaningful to investigate relationship between the dynamic moduli and the angular frequency during the isothermal aging process, from which the gel point of the system can be determined accurately.Figures5(a) and 5(b) show the changes of G′ and G″ against the angular frequency ω at different aging time intervals for the polythiourethane system at the aging temperature of 75°C. The frequency dependence of G′ and G″ followed the commonly observed relations of G′ω~ωn′ and G″ω~ωn″. It was found that G′ and G″ increased with both aging time and the frequency. At the same aging time, smaller G′ and G″ were observed at low frequencies, indicating that the polythiourethane system behaved more like liquids. As the frequency grew to larger values, the system was more solid-like since the time scale of oscillation became smaller than that of the molecular motion or rearrangement of the polythiourethane system. With the increase of aging time, both G′ and G″ showed reduced dependence on the aging time, indicative of gelation and solidification of the system. This was also reflected by the significantly larger G′ than G″ at long aging times.Figure 5
(a) Storage modulusG′ and (b) loss modulus G″ versus angular frequency ω at different aging time intervals for the polythiourethane system at 75°C. (c) Time dependence of the exponents n′ and n″ determined from linear fitting of G′ and G″ versus angular frequency data (log-log coordinates) in (a) and (b).
(a)
(b)
(c)The aging time dependence ofn′ (exponent of G′ versus ω) and n″ (exponent of G″ versus ω) for the polythiourethane system is shown in Figure 5(c). Both n′ and n″ decreased with increasing aging time, with n′ decreasing more rapidly than n″. n′ and n″ crossed over at an aging time of 2410 s. The critical gel time determined here was a little longer than that determined by the crossover of G′ than G″ aforementioned. The critical relaxation exponent n can be determined by the crossover point of the n′ and n″ curves, which was 0.022. The critical n value determined from the temperature sweep experiments was 0.014, close to 0.022. The n value reflects the unique nature of a critical gel. A stiff critical gel often has a small value (n<<0.5). The extremely small n of the polythiourethane system at the critical gel point indicated the stiff and highly elastic nature of the resultant thermoset polyurethane. More importantly, the similar critical n values of the thermoset polyurethane formed by continuous temperature increase and by isothermal aging demonstrate that either heating or aging can lead to gelation of the thermoset polythiourethane system, and a curing process of combined heating and isothermal aging may be preferable for fabricating thermoset polythiourethane polymers.


## 3.5. Rheokinetics Study

The viscosity of a curing polymeric system at a given time pointt can be related to the time via an exponential function as follows [22]:
(3)ηt=η0ekt,where η0 is the viscosity at t=0 and k is the rate constant for viscosity increase. The logarithmic form of equation (3) is as follows:
(4)lnηt=lnη0+kt.Thus, plottinglnηt against t would give a straight line, whose slope is the value of k. Herein, the complex viscosity of the polythiourethane system in the isothermal curing process was used to be plotted against the time in a double logarithmic form at the selected temperatures. As shown in Figures 6(a)–6(c), the double logarithmic plots show almost straight lines before a time point that differed at varied temperatures. Beyond this critical point, the data deviated from the straight line, indicating that the data no longer conformed to the first-order reaction kinetics [23]. The overall reaction rate of the bulk polymerization systems is usually determined by both reaction kinetics and diffusion rates of monomers [24]. These two factors are competitive and depend largely on the viscosity of the reaction system. For our polythiourethane system, the viscosity grows dramatically after gelation. It can be thus assumed that the diffusion becomes prominent after the gel point, which would lead to a deviation from the first-order kinetics. As denoted in Figures 6(a)–6(c), the point beyond which obvious nonlinear behavior is observed was regarded as the gel point. It was found that the gel points at the three temperatures determined by the rheokinetics analysis were in good accordance with those obtained by the dynamic rheological measurements.Figure 6
Plots oflnη∗ vs. time for the polythiourethane system at (a) 55°C, (b) 65°C, and (c) 70°C. (d) Arrhenius plot of gel times for the polythiourethane system.
(a)
(b)
(c)
(d)Furthermore, we calculated the activation energy of the cure reaction for the polythiourethane system. The Arrhenius plot of the gel times is shown in Figure6(d), which is on the basis of the following equation [25]:
(5)tgel=Ae−E/RT,where E is the activation energy; T is the absolute temperature of reaction; R is the universal gas constant. The activation energy of the cure reaction turned out to be 61.02 kJ mol-1.


## 4. Conclusions

To sum up, the curing of a polythiourethane thermoset system has been studied by dynamic rheology. At a strain amplitude within their linear viscoelastic region, the polythiourethane reaction samples were tested by temperature sweep, isothermal time sweep, and frequency sweep. In a ramp of continuous temperature increase, the curing of the polythiourethane reaction system proceeds with a critical gel point at 119.8°C. The curing also occurred during an isothermal aging process. A higher curing rate is achieved at a higher aging temperature, which has been confirmed by the isothermal frequency sweep. The critical relaxation exponentn determined by frequency sweep at different time intervals during an isothermal aging was similar to that obtained from the continuous heating process, indicating the unique structure of the thermoset polythiourethane. In addition, the cure reaction kinetics of the polythiourethane system were investigated, and the critical gel points at varied temperatures were confirmed. In light of the finding that both heating and aging give rise to solidification of the thermoset polythiourethane system, curing strategies with combined heating and isothermal aging deserve further exploration for producing polythiourethane polymers. This work provides preliminary evidences of producing thermoset polythiourethane polymers by more facile and efficient procedures.



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*Source: 8452793-2019-03-31.xml*