ET&I | 中国农业科学院杨相东：控释肥料养分通过膜孔扩散释放

在一次性施肥情况下，控释肥料的养分供给能够与植物养分吸收同步，从而达到保障作物产量、减少氮素损失、优化农田氮素管理的目标，实现环境效益与经济效益的统一。现有控释肥料基本上是储库型的包膜尿素，释放期在1~6个月左右。控释养分通过什么途径跨膜释放？膜层微观结构特征是怎样的？膜层结构参数与释放速率之间存在什么数学关系？这些是包膜控释技术研究领域的基础理论问题。近20年来所建立的控释肥料养分渗透释放模型，把影响养分释放的膜层结构因素归结到渗透系数中，没有阐明膜层结构与养分释放的内在关系，属于黑箱模型。随着对控释膜层结构研究的逐步深入，越来越多的证据表明控释肥料膜层上存在微纳米大小的孔隙，且养分释放速率与大孔尺寸具有一定的相关关系。因此，本文基于Fick定律，建立了养分释放与膜层孔径大小之间的数理关系，将控释膜层渗透释放模型发展为膜孔扩散释放模型，进一步明确了养分释放与膜层微观结构的内在联系，这不但推动了控释肥料养分释放机理的发展，还为控释肥料养分精准调控提供了思路和发展方向。

A single application of the controlled release fertilizer (CRF) can match the nutrient supply with uptake by plants and achieve the goal of enhancing crop yield, reducing nitrogen loss, optimizing farmland nitrogen management, and realize both the environmental benefits and economic benefits at the same time. The existing CRF are basically “reservoir system” with the release period of 1~6 months. However, the nutrient release pathways, microstructure characteristics of the membrane layer, and the mathematical relationship between the membrane structure parameters and the release rate of nutrients were still the basic theoretical problems of limiting the development of coating technology in the production of CRF. The nutrient permeation release model of CRF established in recent 20 years belongs to a black box model. It attributed the membrane structure which influencing nutrient release to the Ps(permeability coefficient),. and not clarify the relationship between the membrane structure parameters and the nutrients release rate. With the gradual deepening of the research on the structure of controlled release membrane, more and more researches point that there are micro-nano pores in the membrane of CRF, and the nutrient release rate has some correlation with the size of large pore. Thus, on the basis of Fick’s diffuse law, a mathematical relationship between the nutrients diffusion rate and the membrane pore size was established in this study. This study develops the permeation release model into the diffusion release model, shed light on the relationship between nutrient diffusion rate and membrane structure parameters in CRF, not only promotes the development of nutrient release theory of CRF, but also provides ideas and development direction for the precise regulation of nutrients in CRF.

一、膜孔释放模型的理论推导 | 

Establishment and theoretical calculation of the model

控释膜层上的最大孔为养分扩散释放的主要通道。为此，假设：（1）致密的聚合物膜层上分布有孔径大小不一的微孔，微孔是水分与养分溶液跨膜的通道；（2）膜层上的微孔为圆形或等效的圆形孔；（3）在养分释放期内，膜层的微孔结构稳定；（4）膜内养分通过孔道向膜外扩散释放，遵守Fick定律。当可进行扩散释放的微孔被合并看作一个微孔时，最简单的膜孔释放原理如图1-E所示。本模型也将膜孔扩散释放过程分为滞后期、稳定期和衰退期三个阶段。滞后期为从水气的进入，到水分占满孔隙，溶解尿素形成尿素饱和溶液，并将要释放的阶段。稳定期为膜内尿素从固体到完全溶解的阶段，该阶段膜内尿素溶液一直处于饱和状态。衰退期为膜内由饱和尿素溶液到尿素浓度逐步变为零的阶段。扩散推动力为膜层内外的养分浓度差，推导出的养分扩散释放的分段函数表达式如下：

Since the maximum pore on the controlled release membrane layer is the main channel for nutrient diffusion release, when developing a mathematical model for the nutrients release, the following assumption was considered:(1) micro pores with different sizes distribute on the dense polymer membrane layer, which are the channels for water and nutrient transporting through the membrane; (2) the micro pores on the membrane layer are circular or equivalent circular; (3) the structure of the membrane is stable during the nutrient release period; (4) nutrients inside diffuse through the micro pores in the membrane based on the Fick’s law. And when the micro pores for diffusion release are considered to merge into one pore, the simplest principle of nutrient diffusion release is as shown in Figure 1-E. This model also divides the process of urea diffusion release into three stages: the lag period, the constant release period, and the decay phase. The lag period is the period from the entry of water vapor to the water filling the pore, and then dissolving a small fraction of solid urea to form a urea saturated solution and to be released. The constant release period is the period in which the core is from solid to fully dissolved, and the intramembrane urea solution still remains saturated. The decay phase is the period in which the concentration of the internal solution decreases from saturated to zero. The driving force of diffuse is the difference between the urea solution concentration inside and outside the membrane.The expression for the urea diffusion release, for the three release stages:

图1 模拟扩散释放装置及模型的示意图

Fig.1 A schematic diagram of the simulative diffusion release device and model

二、模型验证（一）

|Experimental verification of model by using the device

钨针在PE膜上所开孔如图2所示，所开孔规则圆润，孔径分别为454，450，449μm。用上述规格的具孔膜制作的膜孔控释装置，进行尿素养分释放率的测定，其释放行为为零级释放，即尿素扩散速率与时间无关。根据膜孔扩散释放模型的释放量方程，达到与上述装置相同的释放量的理论孔径值为467、504、459μm，膜孔实测值与模型理论计算值非常接近。

The pore of the PE membrane is shown in Figure 2 and the shape of pore is circular. The average dimeter of the three pores was 454, 450 and 449 μm respectively. We determined the cumulative percentage of urea release from the simulative diffusion release device with these three PE membranes respectively. The result indicating that the release of this device is zero-order release, the diffusion rate of urea is independent of time. The theoretical dimeter of pore in the coating of CRF which can make the cumulative release of urea achieving the same amount as that in the above device is 467, 504 and 459 μm. It showed that this calculated value of the mathematical model agreed well with the experimental data.

图2 具孔PE膜的SEM图片

Fig. 2 The SEM picture of the pore of PE membrane

三、模型验证（二）

|Experimental verification of model by using CRF

从约40个用钨钢探针开孔的包膜肥料颗粒中优选了11个用于研究分析，膜孔径如图4-1~11所示。利用水浸泡法测定的11个大颗粒尿素的累积释放百分率符合零级动力学方程，释放速率恒定，释放量只随时间的变化而变化，即释放快慢只由膜孔大小决定。

11 CRF particles were selected for this study analysis, and the diameter of pore in the coating is as shown in Figure 4-1~11. The cumulative release percentage of 11 urea particles confirms that the release of those single-pore CRF is zero-order release, the release rate is constant and the cumulative release percentage of urea is increased with the increasing of time. That is to say, the speed of urea release is only determined by the size of membrane pore.

图3 膜孔及膜层截面的扫描电镜图片

注：图3-11为控释肥料颗粒外表面孔径SEM图片，图3-12膜层截面

Fig.3 The SEM picture of pore and sectional appearance of the membrane layer

Note: Figure 3-1~11 is the SEM picture of the outer surface diameter of the CRF particles, and Figure 3-12 is the sectional appearance of the membrane layer.

总结 | Conclusions

基于物质扩散的Fick定律，建立了膜孔径与养分释放百分率之间数理关系的膜孔扩散释放模型。模型表明：包膜控释肥料养分释放率与膜孔面积A（或孔径的平方）、释放时间t成正比，与膜层厚度l、颗粒质量M成反比。膜孔扩散释放模拟装置与单孔控释肥料的验证结果可以很好地阐明膜孔径与尿素累积释放的关系。该模型很好地再现了尿素溶液在整个释放周期内通过膜孔的扩散过程。当膜孔扩散模型中的孔面积被看作控释肥料中的有效孔面积时，该模型能预测养分的释放。该模型可为今后包膜材料的选择和控释肥料的制备指明方向。

On the basis of Fick’s diffuse law, a new diffusion model of nutrient release from membrane pore, about the mathematical relationship between the percentage of nutrient release and the membrane pore area, was established in this study. The mathematical model shows that the percentage of urea release has positive correlation with the membrane pore area (A, or the square of the pore radius r) and the release time (t), however, was negatively correlated with the membrane thickness (l) and particle mass (M). The verified results of the experiment conducted by using the simulative diffusion release device and the diffusion model of nutrient release can well clarify the relationship between the membrane pore size and the cumulative release of urea. This model gives excellent reproduction of the urea solution diffusion through membrane pores within the whole release period. And the pore area in the model can be used to predict the nutrient release when it is regarded as the effective pore area of CRF. This model can be applied into the selection of coating material and preparation of CRF in the future.

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https://www./science/article/

pii/S2352186421008178?via%3Dihub

本文内容来自ELSEVIER旗舰期刊Environ Technol Innov第21卷发表的论文：

Wang Y. J., Li J., Yang X. D., 2022. The diffusion model of nutrient release from membrane pore of controlled release fertilizer. Environ Technol Innov 25, 102256.

DOI: https:///10.1016/j.eti.2021.102256

第一作者：王亚静 硕士

中国农业科学院农业资源与农业区划研究所

在中国农业科学院获得硕士学位，主要研究方向为控释肥料。以第一作者在Environmental Technology & Innovation、Polymers等国际期刊发表论文2篇。

共同作者：李娟 副研究员

中国农业科学院农业资源与农业区划研究所

中国农业科学院农业资源与农业区划研究所副研究员，农业农村部新型肥料创新团队核心骨干，中国植物营养与肥料学会施肥技术专委会/肥料产业发展工作委员会副主任委员。围绕绿色可控、环境响应、生物降解、成本降低等控释技术研发目标，在新型绿色控释肥料的控释材料研发、养分释放机制、成膜工艺技术、应用效果评价等方面进行了全链条的研究工作。主持国家自然基金等国家和省部级项目5项，发表SCI论文30余篇，获得省部级奖励2项。

通讯作者：杨相东 研究员