2.1 Chemicals and equipment

All chemicals were of analytical grade and used without further purification. Hydrazine hydrate (85%) was purchased from Shanghai Hushi Laboratorial Equipment Co. Ltd. (China). tert-Butylhydrazine (98%) and 2-hydroxyethylhydrazine (95%) were purchased from Shanghai Macklin Biochemical Co. Ltd. (China). Methylhydrazine, dimethylhydrazine, and p-dimethylaminobenzaldehyde were purchased from Sinopharm Chemical Reagent Co. Ltd. (China). Ethanol, nitric acid, and methane sulfonic acid (MSA) were purchased from Beijing Chemical Works (China). A beta particle accelerator (2 MeV), ion chromatograph (CIC-100), ultraviolet spectrophotomer (Perkin Elmer Lamda 45), and automatic potentiometric titrator (Mettler-Toledo G20 compact titrator) were used during the experiment. The beta particle accelerator was rented from the Department of Nuclear Technology Applications in China Institute of Atomic Energy, and the required safety protection was provided. The ion chromatograph was purchased from Qingdao Sheng Han Chromatography Technology Co. Ltd. (China); a CS12A column was used as the cation column, and the baseline noise was stabilized at around 20 mV before detection.

2.2 Experimental method

There are a few published research papers on the stability of hydrazine and its derivatives under radiation. For example, a group at the National Institute of Atomic Energy researched their stability under γ radiation. However, γ rays are difficult to use because of their high energy and radiation dose, which makes them unsuitable for large-scale industrial applications. There is no suitable kinetic data regarding the β radiation stability of hydrazine and its derivatives. Therefore, in this paper, source data were obtained using experimental and computational methods. The initial solutions of hydrazine and its derivatives were diluted to 0.05 mol/L; then, 250 mL aliquots of the solutions were prepared and irradiated using a pulsed electron beam from a beta particle accelerator. The accelerator used a 30 mA current, 50 Hz frequency, 4 μs pulse width, and 0.25 KGy/s dose. Then, 0.1 mL samples of the irradiated solutions were extracted using a syringe after the following irradiation durations: 0, 0.5, 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 18, and 21 min.

2.3 Analytic procedures

Using methane sulfonic acid as the eluent, the concentrations of the hydrazine, tert-butylhydrazine, 1,1-dimethylhydrazine, and 2-hydroxyethylhydrazine solutions were separately determined using ion chromatography. The concentration of methylhydrazine was determined using an ultraviolet visible spectrophotometer with the color rendering of p-dimethylaminobenzaldehyde. The concentrations of the irradiated solutions were determined after the following irradiation durations: 0, 0.5, 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 18, and 21 min. Then, the kinetic data for the decomposition of the hydrazine derivatives under beta radiation were obtained. The half-reaction times of hydrazine and its derivatives under β-radiation are expressed by τ₅₀, which is the time required for the compound to decompose to 50% of the original concentration: A smaller τ₅₀ value indicates a faster decomposition rate. The molecular formulas of various hydrazine derivatives and their τ₅₀ values are listed in Table 1.

4.1 3D stable molecular structures of the hydrazine compounds

Optimized geometric construction and frequency analysis of the hydrazine derivatives were conducted by adopting the density functional theory B3LYP method of the Gaussian 03 program package with the 6-311+(3d, 3p) basis set. No imaginary frequency occurred in the calculation results, indicating that they were reasonable and reliable. This also confirms that the most stable configuration was obtained. The optimized 3D structures are shown in Fig. 1.

Fig. 1Full-screen View

Optimized 3D structures of the hydrazine derivatives

4.2 Values of the quantum chemical parameters

The following parameter values were acquired from the quantum chemical calculations: E_LUMO, E_HOMO, ΔE (ΔE = E_LUMO − E_HOMO), μ, and E_total. In addition, the following parameters were obtained using the molecular simulation software, HyperChem: logP, R, V, molecular superficial area (A - approx, G - grid), M, P, and HE. The degradation rates of hydrazine and its derivatives under β irradiation are expressed by τ₅₀. The quantum parameter values are shown in Table 2.

4.3 Structure-performance equation for the hydrazine derivatives under β irradiation

Before a QSAR regression equation was established, the quantum chemical parameters adopted were applied for preprocessing. The Pearson correlation coefficient analysis parameters that were significantly related to the β irradiation half-reaction time were obtained to facilitate elucidation of the relationship between the parameters of each structure and the degradation rate of the target compound.

Statistical software, SPSS, was applied to conduct a correlation analysis on the QSAR parameters to obtain the Pearson correlation coefficient matrix (Table 3).

It is evident from the data in Table 3 that the correlations between τ₅₀ and E_total and M are significant. G, R, V, E_LUMO, HE, A, μ, P, ΔE, and logP also had strong correlations with τ₅₀. However, there was no significant correlation between E_HOMO and τ₅₀.

The Pearson correlation analysis shows that there is a close relationship between the total energy of the molecules and τ₅₀ of the hydrazine compounds radiolysis reaction under beta irradiation; their relationship diagram was established, as depicted in Fig. 2.

Fig. 2Full-screen View

Relationship between the molecular total energy and half-reaction time under β irradiation

In Fig. 2, a relationship between the E_total and τ₅₀ of the hydrazine derivatives hydrolysis reaction under beta irradiation is slightly evident. In general, τ₅₀ is positively correlated with E_total; however, the correlation cannot be defined using a mathematical relationship. Accordingly, we used a multiple linear stepwise regression method to analyze the data.

4.4 QSAR equation for the hydrazine derivatives under β irradiation

The QSAR equation for the hydrazine derivatives (i.e., hydrazine, methylhydrazine, 1,1-dimethylhydrazine, tert-butylhydrazine, and 2-hydroxyethylhydrazin) under β irradiation was established using a multiple linear stepwise regression method, and the results are shown in Tables 4, 5, 6 and 7.

The stepwise regression analysis results suggest the following: 1) Significant correlation exists between E_total and τ₅₀ as well as E_total and ΔE, as shown in Tables 4 and 5. The square root of the determination coefficient, determination coefficient, and adjusted determination coefficient were 0.995, 0.989, and 0.979, respectively; these values indicate that the equations could account for 97.9% of the change in the τ₅₀ and that the correlations between independent and dependent variable are evident. (2) The square of the equation, residual sum of the squares, total sum of the squares, F-statistics value, and significance were 5.858 × 10⁷, 0.955, 6.264 × 10⁵, 93.481, and 0.011< 0.05, respectively, indicating that a significant linear relationship exists between the dependent and independent variables. (3) From Table 7, it is evident that the QSAR equation for the hydrazine derivatives and τ₅₀ of the hydrazine derivatives hydrolysis reaction under beta radiation was Y = −7583.464 + 54.687X₁ + 94333.586X₂, where X₁ and X₂ represent E_total and ΔE, respectively. The significance levels of the regression coefficients are 0.006 and 0.031; these values are less than 0.05. This model fully represents the relationship between the hydrazine derivatives and β radiolysis stability.

4.5 The relationship between the hydrazine derivative structure and half-reaction time for β irradiation

In the structural activity equation, the τ₅₀ for hydrazine compound radiolysis relates closely with E_total and ΔE. A diagram of their relationship is shown in Fig. 3.

Fig. 3Full-screen View

Relationships between the half reaction time and molecular total energy and orbital transition energy of the hydrazine derivatives

The analysis results indicate the following: 1) The relationship between the structure of the hydrazine derivative and reaction time can be described quantitatively by the QSAR equation even for complex hydrazine derivative structures. 2) The decomposition rate under β irradiation and structure of the hydrazine derivatives are negatively correlated and can be described quantitatively by E_total and ΔE. 3) The relationship between the decomposition rate under β irradiation and structure of the hydrazine derivatives can be described quantitatively by the QSAR equation, which simplifies the complex problem and provides direction for the subsequent study of hydrazine and its derivatives.