**Abstract** Cure kinetics of epoxy resin E51/MP/methyltetrahydrophthalic anhydride (MeTHPA)/ 2-ethyl-4-methyl-imidazole (2,4-EMI) flame retardant composite were studied using the dynamical tortional vibration method. The influence of MP loadings on The cure showed has improved studied were well. The results showed that the rate of cure reactions depended distinctly on the cure temperature. At low MP loadings, the gelation time *t *_{g} for the systems did Not change obviously while at higher MP loading (higher than 20 phr) *t *_{g} had a remarkable increase. further, the Flory ‘s gelation theory and Avrami equation could be used to describe the cure behavior of epoxy composite system

**Curing kinetics of epoxy/MP/anhydride/accelerator composite flame retardant materials**

Cheng Yiyun Chen Dazhu He Pingyu** Wang Chunlei

( Department of Polymer and Science Engineering, University of Science and Technology of China, Hefei 230026, China)

**Summary **Study E51 epoxy resin / flame retardant MP / tetrahydrophthalic anhydride method using dynamic torsional vibration / 2–hexyl-4- methylimidazole curing kinetics of the system. The kinetic parameters such as apparent activation energy of the composite system were obtained. The results show that the cure rate has a significant temperature dependence. The effect of MP content on the curing reaction was studied. When the low MP content was less than 20 phr, the gelation time t _{g} value did not change much; but after the MP content exceeded 20 phr, the t _{g} value increased significantly. The Flory theory and the Avrami equation can better describe the curing behavior of the reaction system. **Key words** epoxy resin curing kinetics Flory theory Avrami equation

In today’s society, people’s requirements for flame retardant materials are getting higher and higher, but the traditional use of halogen-containing flame retardants generates smoke and poisonous gases when burned, causing serious secondary pollution, which has attracted close attention from people from all walks of life. Therefore, the development of non-toxic or low-toxic flame retardants is very urgent, and the market prospects are also very broad. The nitrogen and phosphorus flame retardant MP developed by Hefei Jinghui Chemical Research Institute is more eye-catching. The nitrogen-phosphorus element in MP has synergistic effect and synergistic effect, and the flame retardant effect is very good. In this experiment, the epoxy resin composite material with the flame retardant as the filler was used to study the influence of the flame retardant filler on the properties of the composite material, which is of great significance for the development of new flame retardant materials, selection of curing conditions and screening formulations.

Since the epoxy composite system is cured into a linear polymer cross-linking reaction, the process is complicated. Crosslinking leads to insoluble and infusible, and research into the curing process becomes difficult. In this experiment, the self-developed HLX-2 resin curing instrument was used to monitor the curing process of the resin composite system, and the whole forming process was simulated completely ^{[1, 2]} . The dynamic torsional vibration experiment reflects the change of mechanical properties, temperature and filler addition of the resin. Some important apparent kinetic parameters can be obtained from the experiment, and it is expected to analyze the comprehensive performance of the whole material.

**1 Experimental part ****1.1 Experimental material** epoxy resin E51, epoxy value 0.49–0.53, Shanghai Resin Factory; methyl tetrahydrophthalic anhydride (MeTHPA), chemically pure, Shanghai fine stone fine chemical plant; 2-ethyl- 4-methylimidazole (2,4-EMI), chemically pure, North China Special Chemical Reagent Development Center; flame retardant MP, white crystalline powder, particle size >300 mesh, phosphorus content >13%, nitrogen content >37%, Hefei Jinghui Chemical Research Institute. **1.2 Basic operation of the experiment** Weigh about 1.3g of epoxy resin E51 in the weighing mold of polytetrafluoroethylene (PTFE), and add 2,4-EMI, MP, MeTHPA according to the weight ratio of 100:2:n:80. In the experiment, the resin content was set to 100 parts, and the MP amount was n=5, 10, 20, 30, 40 phr), and the mixture was sufficiently stirred uniformly, and the entire reaction initial system was completed. The selected curing temperature is set in advance. After the temperature is kept stable, the mixture is added to the lower mold of the curing device, and the upper mold is closed, and the torsional vibration motor is turned on to start the constant temperature curing test. **1.3 Analysis** of the Curing Curve The horizontal axis of the experimental curve is the curing time, and the vertical axis corresponds to the torque *G* required for the composite resin system to be subjected to small-angle torsional vibration ^{[3, 4]} . The gelation time *T *_{G}before the resin system remains liquid, torque is zero. The reaction reaches a certain time, and the torque of the reaction system begins to appear due to the formation of the gel, which is the *t *_{g of the} resin system . *After t *_{g} , the degree of torque increase reflects the curing speed of the resin system. As the cure approaches completion, the increase in torque tends to be flat. The torque is no longer increased corresponding to the time is the full cure time. The outer envelope of the torque test line is the isothermal curing curve of the resin system.

**2Results and discussion ****2.1 Curing curve of epoxy resin composite flame retardant system** Figure 1 is the isothermal curing curve ( *G–t* relationship curve) of 110 °C epoxy composite system with different content of flame retardant MP . It can be seen from the figure that as the MP content increases, there is a critical point in the change of the gelation time *t *_{g} of the system . At low MP content ( < 20 phr), the *t *_{g} value hardly changed; however, after the MP content exceeded 20 phr, the *t *_{g} value increased significantly. A similar phenomenon has been reported in the literature [4]. This is because at higher filler contents, the concentration of reactants (such as curing agent and accelerator) in the mixed system is lowered, the reactive groups collide with each other, the probability of reaction decreases, and the *t *_{g}value increases; while the low filler content reacts to the reaction. The effect of the concentration of the substance is obviously small, and there is no significant change in the *t *_{g} value. **Figure ****1. **Isothermal cure curves for epoxy composite systems with different MP contents at 110 °C. **Figure 1** The isothermal cure curves of epoxy system with various MP loadings cured at 110 **Figure ****2** contains 20 phr MP

The isothermal curing curve of the epoxy composite system at different temperatures. **Figure 2** Isothermal cure curves of epoxy system with 20 phr MP filler at different temperatures.

2 is an isothermal cure curve of an epoxy composite system containing 20 phr MP at 90 ° C, 100 ° C, 110 ° C, and 120 ° C. The shape of the curing curve at different temperatures is similar, but the gelation time *t _{g}* and the curing reaction rate are different. It can be visually seen from the trend of the slope of the solidification curve that as the curing temperature increases, the gelation time is significantly shortened, and the curing reaction rate is gradually increased.

**2.2 Application of gelation theory Flory**

The gelled Flory theory

^{[6]}, the cured resin in the chemical conversion gel point is constant, independent of temperature and the experimental conditions of the reaction, it is possible according to the gelation time

*T*

_{G}to system for the estimation of the apparent activation energy

*E*, the relationship between

_{a}^{[7]}is:

㏑

*T*

_{G}=

*C*+

*E*/

_{a}*RT*(. 1)

to the MP 20phr ln at four different temperatures

*T*

_{G}-1

*/ T*plotted For example, as shown in Fig. 3 (in the following case, when the data is processed by the Avrami equation, the experimental data obtained under this condition is also taken as an example, and other MP contents also satisfy the obtained rule). As shown in Figure 3, the slope is the apparent activation energy

*E*

_{a}/

*R*. A good linear relationship indicates that Flory theory can be used to describe the gelation process of a curing system.

**FIG ****3 **containing 20 phr MP epoxy composite system LN *T *_{G} pair . 1 */ T* plot. **Figure 3** Plots of ln *t *_{g} versus 1 */T* for epoxy system with 20 phr MP filler.** **

**2.3 Apparent kinetic parameters of the curing system**

Generally, **the apparent kinetic parameters** of the curing reaction include the reaction rate constant *k *_{p} and the reaction degree P _{c of the} gel point . Let *G *_{∞} denote the torque of the system when fully cured, t is the relaxation time, and b is the relaxation time distribution width coefficient, then the modulus *G *_{t} and the time *t of* the system at any time satisfy the relation ^{[8]} :

*G *_{t }*= G _{∞{}* 1

*–*exp[-((

*tt*)

_{g}*/t*)b ]} ,

if the reaction is a first order reaction, then

ln(

*G*

_{∞}–

*G*

_{t})= –

*k*

_{p}Δ

*t*= –

*k*

_{p}(

*t*–

*t*) (2)

_{g}Taking the curing curve of an epoxy resin composite system with an MP content of 20 phr obtained at 100 ° C as an example, plotting ln(

*G*

_{∞}–

*G*

_{t}) versus (

*t – t*

_{g}) is shown in Fig. 4. The rate constant

*k*

_{p of}the curing reaction is obtained from the slope of the fitted straight line and is shown in Table 1.

Similarly, ㏑ (

*G*

_{∞}–

*G*

_{T}) and (

*T-T*

_{G}linear relationship between) has verified that the first-order reaction

^{[9]}, the reaction before and after the gel point is assumed instantaneous rate constant

*K*

_{P}unchanged According to the experimentally determined gelation time

*t*

_{g}, the degree of reaction at the gel point can be calculated according to the formula

P

_{c}= 1–

*exp*(–

*k*

_{p }

*t*

_{g}) (3)

.

**Figure 4** ln(G _{∞)} of the curing curve of an epoxy composite system containing 20 phr MP at 100 ° C–G _{t} ) plots (t–t _{g} ). **Figure 4** Plot of ln( G _{∞} – G _{t} ) versus ( t – t _{g} ) of the cure curve for epoxy system with 20phr of MP at 100 °C .

**2.4 The analysis of the curing reaction after the gel point using the Avrami equation **^{[10]}

^{ }defines the relative degree of solidification a at

any time *t* a = *G *_{t} / *G ¥ *(4)

If *α* is used instead of the relative crystallinity in the Avrami equation, then The curing kinetics can be described by the Avrami equation describing the crystallization of the polymer:

a = 1 – *exp* [– *k *_{p} ( *t–t *_{g} ) ^{n} ] (5)

where *n* is the Avrami index. A simple transformation from equation (5) yields:

1 – a = *exp* [– *k *_{p} ( *t–t *_{g} ) ^{n} ]

(6) takes two logarithms to equation (6) and obtains:

ln[ –ln( 1 – a)] =ln *k *_{p} + *n* ln( *t–t *_{g} ) (7)

It can be seen from equation (7) that ln[ –ln(1 – a )] is plotted against ln( *t–t *_{g} ). The obtained intercept and slope are ln *k *_{p} and exponent *n, respectively* .

**
Figure 5 is** an Avrami plot of ln[ –ln(1 – a )] versus ln(t–t

_{g}) for an epoxy composite system of 20 phr MP .

**. 5 figure**the Avrami Plots of ㏑ [ -㏑ ( . 1 – A ) ] versus ㏑ ( T – T

_{G}) of Epoxy System with the MP 20 is PHR Filler.

The Avrami curve of the epoxy composite system at four different temperatures is shown in Figure 5. It can be seen from the figure that the curve has a good linear relationship, indicating that the Avrami equation can be used to describe the curing process of the epoxy resin composite system after the gelation time. The curing reaction process is a thermal activation process, and the rate constant *k *_{p} increases with increasing temperature (Table 1). *k *_{p} and temperature satisfy ^{[11]} :

*k *_{p }^{1 / n}* *= *A **exp* ( *–E _{a}* *

*/ RT*) (8)

The logarithm of the equation can be obtained by the rate equation related to the Avrami exponent

*n*:

1

*/ n*ln

*k*ln

_{p}=*A – E**

_{a}*/RT*(9)

**contains 20 phr MP epoxy composite The system (1/n) lnk plots 1/T.**

Figure 6

Figure 6

**Figure 6**

Plots of (1/ n) lnk versus 1/T for epoxy system with 20 phr MP filler.

Figure 6 is a plot of 1 */ n* ln *k _{p}* versus 1

*/ T*, from the slope of the line in the figure to get the gel point The apparent activation energy of the system is

*E**. From the activation energies

_{a}*E*and

_{a}*E** obtained twice (see Table 1), it can be seen that the apparent activation energy of the reaction system before and after the gel point is not very different, and the results obtained by Dutta

_{a}^{[12]}are basically Consistent.

**Table 1** kinetic parameters of epoxy composite flame retardant system.

**Table 1** Kinetic parameters for the epoxy flame retardant composites.

T / °C |
t _{g }/min |
k _{p} |
n |
E /kJ/mol_{a} |
E * /kJ/mol_{a} |

90 | 61.37 | 6.87×10 ^{-3} |
1.78 |
93.0 |
75.3 |

100 | 28.50 | 3.08×10 ^{-2} |
1.47 | ||

110 | 15.38 | 4.94×10 ^{-2} |
1.76 | ||

120 | 6.39 | 3.68×10 ^{-1} |
1.46 |

**3 Conclusions **

1. Flame retardant MP can shorten the gelation time of epoxy resin E51 composite system, and promote synergistic effect on curing reaction, accelerate the curing reaction rate, but the relationship between the amount of addition and gelation time *t *_{g} More complicated, a turning point appeared near 20 phr.

2. Different curing temperatures have a significant effect on the curing curve. The gelation time *t *_{g is} approximately linear with the reciprocal 1 */ T of the* curing temperature . The temperature increases and the curing reaction rate increases geometrically.

3. Flory theory and Avrami equation can better describe the curing kinetics of the reaction system and can be used to predict the behavior of the curing system ^{[13]} .

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