DSC法与流变学法在测定HTPB基PBX代料固化动力学参数中的应用对比

doi:10.12382/bgxb.2023.0786

摘要/Abstract

摘要：

为优化高聚物黏结炸药(Polymer Bonded Explosive,PBX)制备工艺并深入理解其性能,探寻适用于研究PBX炸药固化动力学的最佳方法,分别采用非等温差示扫描量热(Differential Scanning Calorimetry,DSC)法、流变学等温法及流变学非等温法对HTPB/TDI/Na₂SO₄/Al体系的固化反应动力学进行深入研究,得到在这3种测试条件下的固化反应动力学方程。同时,针对目前广泛使用的流变学非等温法进行合理优化。实验结果表明: HTPB与TDI间的固化反应遵循自催化模型;使用Kissinger法和Ozawa法获得的固化反应活化能相近,二者相差不超过3%;PBX代料体系的恒温固化表现为起始温度423.29K,峰值温度440.23K,终止温度444.49K;流变学研究固化动力学过程中,需考虑温度对储能模量的影响,不能仅用测量值表征固化度,需要对数据进行修正;DSC法与流变学法各有优劣,若仅需获得固化动力学参数,DSC法是一个更好的选择,但欲了解固化过程中药浆内部结构变化,必须借助流变学法。

关键词: 高聚物黏结炸药, 非等温差示扫描量热法, 流变学法, 固化反应动力学

Abstract:

In order to optimize the preparation process of polymer bonded explosive (PBX) and deeply understand its performance, and explore the best method suitable for studying the curing kinetics of PBX, the curing reaction kinetics of HTPB/TDI/Na₂SO₄/Al system are thoroughly investigated using non-isothermal differential scanning calorimetry (DSC) method, rheological isothermal method, and rheological non-isothermal method. The curing reaction kinetic equations are obtained under these three test conditions, and the widely used non-isothermal rheological method is optimized. The results show that The curing reaction between HTPB and TDI follows an autocatalytic model, and the activation energies of curing reaction obtained using Kissinger and Ozawa methods are similar, with a difference of no more than 3% between the two. The thermostatic curing of PBX surrogate system exhibits an onset temperature of 423.29K, a peak temperature of 440.23K, and a final temperature of 444.49K. The effect of temperature on the energy storage modulus needs to be considered in the rheological study of curing kinetics. The measured values cannot be used solely to characterize the degree of curing, and the data need to be corrected. DSC method and rheological method have their own advantages and disadvantages: if the objective is to obtain only the parameters of curing kinetics, the DSC method is a better choice. However, the rheological method must be used to understand the internal structure of slurry in the curing process.

Key words: polymer bonded explosive, differential scanning calorimetry method, rheology method, curing reaction kinetics

中图分类号:

TJ55
TQ560.1

王泓, 王天翔, 尹艳华. DSC法与流变学法在测定HTPB基PBX代料固化动力学参数中的应用对比[J]. 兵工学报, 2024, 45(10): 3596-3607.

WANG Hong, WANG Tianxiang, YIN Yanhua. Comparison of the Applications of DSC and Rheology Methods in Determining the Curing Kinetics Parameters of HTPB-Based PBX Simulants[J]. Acta Armamentarii, 2024, 45(10): 3596-3607.

图/表 30

表1 固化反应配方(质量分数)

Table 1 Curing reaction formulations (mass fraction)

材料	无水硫酸钠	金属+黏结剂(3∶1)	TDI
质量比例/%	23	76	1

表2 试剂规格

Table 2 Reagent specification

药品	规格与性质	生产厂家
HTPB	Ⅲ型	天元军融化工有限公司
铝粉	工业级	鞍钢实业微细铝粉有限公司
无水硫酸钠(Na₂SO₄)	工业级	四川同庆南风责任有限公司
TDI	化学纯	太仓沪试试剂有限公司

图1 固体颗粒粒径分布

Fig.1 Solid particle size distribution

表3 主要测试设备

Table 3 Major test equipment

设备名称	生产厂家
电子天平	上海卓精电子科技有限公司
HAAKE RS300旋转流变仪	赛默飞世尔科技公司
DSC-60差示扫描量热仪	岛津企业管理(中国)有限公司

表4 测试参数设置

Table 4 Test parameter setting

测试方法	药品质量/mg	升温速率/ (℃·min^-1)	温度范围/℃	平板直径/mm	板间隙/ mm	测试频率/rad	测试条件
DSC法	6	3,5,7,9	30~300				铝制坩埚,氮气氛围
流变学等温法			60,70,80,90	25	1.5	20
流变学非等温法		3,5,7,9	30~300	25	1.5

图2 不同升温速率热流量变化

Fig.2 Heat flux variation curves with different heating rates

表5 DSC非等温动力学特征参数

Table 5 Characteristic parameters of DSC non-isothermal dynamics

β/ (K·min^-1)	T_i/ K	T_p/ K	T_f/ K	ΔH_t/ mJ	ΔH_t 平均值/mJ
3	430.9	447.6	463.1	69.13
5	434.7	456.8	469.2	64.07	70.11
7	441.7	462.2	478.6	77.29
9	445.0	465.6	495.7	69.93

图3 T-β外推法固化工艺

Fig.3 T-β xtrapolation cure process

表6 固化线性拟合情况表

Table 6 Linear fit for curing

特征参数	线性方程	拟合度
T_f	T_f=5.36β+444.49	0.9485
T_p	T_p=2.97β+440.23	0.9537
T_i	T_i=2.47β+423.29	0.9803

图4 Kissinger法求解动力学参数

Fig.4 Kinetic parameters solved by Kissinger method

图5 固化度变化

Fig.5 Variation curve of curing degree

图6 Ozawa法求解动力学参数

Fig.6 Kinetic parameters solved by Ozawa method

表7 不同方法求解动力学参数对比统计表

Table 7 Comparison statistics of different methods for solving kinetic parameters

求解方法	ΔE/(kJ·mol^-1)	n	拟合度
Kissinger法	96.86	0.9268	0.9948
Ozawa法	99.31	0.9503	0.9954

图7 y(α)和z(α)随固化度的变化

Fig.7 Variation curves of y(α) and z(α) with curing degree

图8 自催化模型线性拟合情况

Fig.8 Linear fit of autocatalytic model

表8 自催化模型线性关系统计表

Table 8 Statistical table of linear relationships for autocatalytic models

升温速率/ (K·min^-1)	斜率k	截距b	拟合度
3	0.06421	20.39	0.9929
5	0.1926	19.93	0.9937
7	0.08475	19.47	0.9576
9	0.03312	20.87	0.9961

图9 60℃恒温动态时间扫描

Fig.9 Dynamic time scanning at 60℃ constant temperature

图10 90℃恒温动态时间扫描

Fig.10 Dynamic time scanning at 90℃ constant temperature

表9 不同时刻储能模量数值

Table 9 Values of energy storage modulus at different moments Pa

温度/℃	G'₀	G'_∞
60	2558.790	3127870.000
90	6282.860	3127870.000

表10 等温过程不同固化度表观活化能

Table 10 Apparent activation energy of isothermal process at different curing degrees

α	E/(kJ·mol^-1)	α	E/(kJ·mol^-1)
0.01	86.31	0.4	87.39
0.02	102.12	0.5	86.14
0.05	116.37	0.6	84.97
0.1	119.69	0.7	87.88
0.2	93.06	0.8	90.46
0.3	89.00	0.9	92.10

图11 恒温固化活化能随时间变化

Fig.11 Variation of activation energy with time for thermostatic curing

表11 等温条件动力学参数

Table 11 Kinetic parameters for isothermal conditions

动力学参数	温度/℃
动力学参数	60	70	80	90	平均值
m	0.312	0.261	0.281	0.273	0.282
n	2.39	2.37	2.22	2.45	2.36
ln A	20.7	20.7	20.6	20.6	20.7

图12 升温速率3℃/min温度扫描实验

Fig.12 Rising temperature rate of 3℃/min in scanning test

图13 储能模量随温度变化

Fig.13 Variation of energy storage modulus with temperature

表12 直线方程参数统计表

Table 12 Statistics of the parameters of linear equation

k	A	直线方程	拟合度
-0.0584	12.183	y=-0.0584T+12.183	0.9006

图14 储能模量随温度变化

Fig.14 Energy storage modulus versus temperature

图15 固化度随温度变化

Fig.15 Temperature dependence of curing degree

图16 表观活化能求解

Fig.16 Solution plot of apparent activation energy

图17 表观活化能

Fig.17 Apparent activation energy

表13 不同测试方法动力学参数比较统计

Table 13 Comparison statistics of kinetic parameters of different testing methods

方法	lnA	m	n
DSC法	20.1599	0.3761	0.09937
流变学法	17.2026	0.2542	0.05291

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