磷酸二氢铵在水-乙二醇体系中的结晶动力学

doi:10.11949/0438-1157.20250647

摘要/Abstract

摘要：

对磷酸二氢铵（MAP）在水-乙二醇体系中的结晶动力学进行了实验探讨，利用经典成核理论研究了MAP结晶的成核机理，测定了在不同温度以及不同过饱和比条件下MAP的成核诱导时间，研究了温度及过饱和比对临界成核自由能（ΔG^* ）、晶体界面自由能（γ）、临界成核分子数（i^* ）、临界成核半径（r^* ）的影响规律，根据成核参数揭示其生长机理；此外，探讨了搅拌速率（N_P）、过饱和比（S）等因素对结晶过程的影响；在动力学数据的基础上，用最小二乘法拟合了MAP的成核及生长动力学方程，使用Canning-Randolph（C-R）及Abegg-Stevens-Larson（ASL）模型拟合线性相关生长动力学模型，揭示了溶剂组成对结晶动力学的协同调控机制。结果表明：温度和过饱和比增大时，i^* 、r^* 、ΔG^* 与诱导时间均减小，而初级成核速率增大；过饱和比在1.08及以上时均相成核成为主导机制，在1.06及以下时非均相成核为主要成核方式；表面熵因子值均小于1，该晶体的结晶机制为连续生长机制；在评估不同线性相关生长模型时发现ASL模型在描述晶体生长行为方面具有更高的准确性，从动力学模型阶数可以看出，过饱和比对成核生长速率的影响最大。本研究阐明了水-乙二醇体系中MAP结晶的响应规律，可为基于混合溶剂设计的晶体尺寸控制与工业化结晶工艺优化提供理论依据。

关键词: 磷酸二氢铵, 结晶动力学, 成核理论, 线性生长模型

Abstract:

In this paper, the crystallization kinetics of ammonium dihydrogen phosphate(MAP) in water-ethylene glycol system was experimentally discussed, the nucleation mechanism of MAP crystallization was studied by using classical nucleation theory, and the nucleation induction time of MAP at different temperatures and different supersaturation ratios was measured. The influence laws of temperature and supersaturation ratio on critical nucleation free energy (ΔG^* ), crystal interfacial free energy (γ), critical nucleation molecule number (i^* ), and critical nucleation radius (r^* ) were studied, and the growth mechanism was revealed according to nucleation parameters. In addition, the effects of stirring rate (N_P) and supersaturation ratio (S) on the crystallization process were explored. Based on the kinetic data, the nucleation and growth kinetics equations of MAP were fitted by least square method, and Canning-Randolph(C-R) and Abegg-Stevens-Larson(ASL) models fitted the linearly correlated growth kinetics model, revealing the synergistic regulation mechanism of solvent composition on crystallization kinetics. The results showed that when the temperature and supersaturation ratio increased, i^*, r^*, ΔG^* and induction time all decreased, while the primary nucleation rate increased. When the supersaturation ratio was 1.08 and above, homogeneous nucleation became the dominant mechanism, and when the supersaturation ratio was 1.06 and below, heterogeneous nucleation was the main nucleation mode. The surface entropy factor values were all less than 1, and the crystal crystallization mechanism was a continuous growth mechanism. When evaluating different linearly correlated growth models, it was found that the ASL model had higher accuracy in describing the crystal growth behavior. It can be seen from the order of the kinetic model that the supersaturation ratio has the greatest impact on the nucleation growth rate. This study elucidates the response law of MAP crystallization in water-ethylene glycol system, providing a theoretical basis for crystal size control based on mixed solvent design and industrial crystallization process optimization.

Key words: ammonium dihydrogen phosphate, crystallization kinetics, nucleation theory, linear growth model

中图分类号:

TQ 026.5

吕豪, 麦文浩, 郑雅元, 邢波, 杜怀明. 磷酸二氢铵在水-乙二醇体系中的结晶动力学[J]. 化工学报, 2025, 76(12): 6268-6276.

Hao LYU, Wenhao MAI, Yayuan ZHENG, Bo XING, Huaiming DU. Crystallization kinetics of ammonium dihydrogen phosphate in water-ethylene glycol systems[J]. CIESC Journal, 2025, 76(12): 6268-6276.

图/表 16

图1 诱导期实验装置1—激光接收仪;2—激光发射仪;3—温度监测系统;4—定制结晶器;5—循环水浴系统

Fig.1 Induction period experimental apparatus

表1 MAP在二元体系中的溶解度及实验参数

Table 1 Solubilities of MAP in binary systems and experimental parameters

T/K	MAP溶解度^[5]/(g/mol) (EG∶H₂O=2∶8)	搅拌速率/(r/min)	溶剂剂量/ml
313.2	2.328	200~400	诱导期实验：200 动力学实验：400
318.2	2.820
323.2	3.428
328.2	4.036
333.2	4.440

图2 动力学实验装置1—定制结晶器;2—循环水浴系统;3—搅拌电机;4—控制器;5—温度计;6—取样口;7—进液口;8—搅拌头

Fig.2 Kinetic experimental apparatus

图3 不同温度下的过饱和比与诱导时间的关系

Fig.3 Relationship between supersaturation ratio and induction time at various temperatures

图4 不同温度下lntind与1/(lnS)2的关系

Fig.4 Relationship between lntind and 1/(lnS)² at various temperatures

表2 温度、过饱和比与临界成核自由能的关系

Table 2 The relationship between temperature， supersaturation ratio， and critical nucleation free energy

T/K	ΔG^* ×10²¹/J
T/K	1.02	1.04	1.06	1.08	1.10	1.12	1.14
313.2	104.303	26.5896	12.0467	6.9056	4.5026	3.1847	2.3824
318.2	102.944	26.2431	11.8898	6.8156	4.4439	3.1432	2.3513
323.2	101.717	25.9304	11.7481	6.7344	4.391	3.1057	2.3233
328.2	92.1996	23.5041	10.6488	6.1043	3.9801	2.8151	2.1059
333.2	65.8046	16.7753	7.6003	4.3567	2.8407	2.0092	1.503

表3 温度、过饱和比与临界成核分子数的关系

Table 3 The relationship between temperature， supersaturation ratio， and critical nucleus size

T/K	i^*
T/K	1.02	1.04	1.06	1.08	1.10	1.12	1.14
313.2	2437.66	313.76	95.68	41.53	21.86	13.01	8.41
318.2	2368.08	304.8	92.95	40.34	21.24	12.63	8.17
323.2	2303.66	296.51	90.42	39.24	20.66	12.29	7.95
328.2	2056.29	264.67	80.71	35.03	18.44	10.97	7.1
333.2	1445.59	186.07	56.74	24.63	12.97	7.71	4.99

表4 温度、过饱和比与临界成核自由能的关系

Table 4 The relationship between temperature， supersaturation ratio， and critical nucleation free energy

T/K	r^/*Å
T/K	1.02	1.04	1.06	1.08	1.10	1.12	1.14
313.2	45.49	22.97	15.46	11.7	9.45	7.95	6.88
318.2	44.8	22.62	15.23	11.53	9.31	7.83	6.77
323.2	44.2	22.32	15.02	11.37	9.18	7.72	6.68
328.2	42.45	21.43	14.43	10.92	8.82	7.42	6.42
333.2	37.68	19.02	12.8	9.69	7.83	6.58	5.69

表5 均相成核过程中过饱和比与成核速率的关系

Table 5 Relationship between supersaturation ratio and nucleation rate in homogeneous nucleation

T/K	J×10^-27/(nuclei/(s·m³))
T/K	1.04	1.06	1.08	1.10	1.12	1.14
313.2	2.1273	61.566	202.3061	352.7781	478.5765	576.2051
318.2	2.5357	66.6645	211.7466	363.4264	488.7491	585.3431
323.2	2.9834	71.761	220.8801	373.5723	498.3608	593.9334
328.2	5.5704	95.224	259.7662	415.2352	537.0595	628.1081
333.2	26.0219	191.448	387.6566	539.0858	645.9572	721.1351

表6 成核参数

Table 6 Nucleation parameters

T/K	b	R²	γ/(J/m²)	f
313.2	0.00946	0.95675	1.2033×10^-3	0.3307
318.2	0.00919	0.97348	1.2243×10^-3	0.3275
323.2	0.00894	0.91457	1.2427×10^-3	0.3245
328.2	0.00798	0.95457	1.2216×10^-3	0.3124
333.2	0.00561	0.92757	1.1067×10^-3	0.2778

图5 MAP的粒数密度分布函数

Fig.5 Particle size distribution function of MAP

图6 不同因素对晶体成核生长速率的影响规律

Fig.6 Influence of different factors on crystal nucleation and growth rates

图7 成核速率模型与实验值的比较

Fig.7 Comparison between nucleation rate models and experimental data

图8 生长速率模型与实验值的比较

Fig.8 Comparison between growth rate models and experimental data

图9 两种线性相关生长速率模型对MAP粒数密度拟合

Fig.9 Fitting of MAP particle size distribution by two linear-correlated growth rate models

图10 两种线性相关生长速率模型的计算值与实验值的比较

Fig.10 Comparison between calculated and experimental values from two linear-correlated growth rate models

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