硅酸盐学报

自修复水泥基材料微胶囊均匀分布设计策略及修复效率计算

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吕忠 ¹ , 宋向龙 ¹ , 梁可 ¹ , 袁静 ¹ , 史梦言 ¹ , 陈惠苏 ²

硅酸盐学报 | 研究论文 2025,53(11): 3114-3126

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硅酸盐学报 |研究论文 2025 , 53 (11) : 3114 -3126

自修复水泥基材料微胶囊均匀分布设计策略及修复效率计算

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吕忠¹, 宋向龙¹, 梁可¹, 袁静¹, 史梦言¹, 陈惠苏²

作者信息

^1．安徽工业大学建筑工程学院，安徽马鞍山 243032

^2．东南大学材料科学与工程学院，重大基础设施工程材料全国重点实验室，江苏省土木工程材料重点实验室，南京 211189

通讯作者:

陈惠苏（1973—），男，博士，教授。

作者简介:

吕忠（1982—），男，博士，教授。

A Design Strategy for Uniform Distribution of Microcapsules and Calculation of Healing Efficiency in Self-Healing Cementitious Materials

Zhong LYU¹, Xianglong SONG¹, Ke LIANG¹, Jing YUAN¹, Mengyan SHI¹, Huisu CHEN²

Affiliations

^1.College of Civil Engineering and Architecture, Anhui University of Technology, Ma'anshan 243032, Anhui, China

^2.School of Materials Science and Engineering, Southeast University, State Key Laboratory of Engineering Materials for Major Infrastructure, Jiangsu Key Laboratory of Construction Materials, Nanjing 211189, China

Corresponding Author:

CHEN Huisu (1973-), male, Ph.D., Professor. E-mail: chenhs@seu.edu.cn

LYU Zhong (1982-), male, Ph.D., Professor. E-mail: zhonglv1982@163.com

出版时间: 2025-11-20 doi: 10.14062/j.issn.0454-5648.20250361

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摘要

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微胶囊团聚和不均匀分布降低自修复作用的效率。受蜜蜂蜂巢结构形式的启发，设计一种微胶囊均匀分布的空间结构模型应用于胶囊法自修复水泥基材料。研究了基材内随机产生的裂纹与内置微胶囊相遇的概率关系，建立了相遇概率的表达式，分析了微胶囊尺寸、形态和掺量对相遇概率的影响，采用蒙特卡罗模拟验证了理论模型的准确性。结果表明：蜂巢式的设计策略能提高微胶囊的分布均匀性，增加胶囊的破裂概率，提升自修复效率；相较于球形胶囊，球柱形微胶囊具有更高的破裂概率和修复潜力。

关键词

自修复 / 微胶囊团聚 / 修复效率 / 水泥基材料 / 蒙特卡罗模拟

Abstract

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Introduction

The distribution characteristics of microcapsules incorporated into matrix can influence the quantity of microcapsules required for embedding in the cementitious matrix, thereby determining the self-healing efficiency. Self-healing systems are essentially passive systems that autonomously initiate the healing process when cracks occur. The efficacy of such systems necessitates both adequate distribution and sufficient bonding of the capsules with the matrix. The recent preparation of microcapsules in self-healing composites presents significant challenges in achieving optimal self-healing effects. One of the key obstacles is the aggregation and uneven distribution of capsules within the matrix, which can significantly impair the healing efficiency of microcapsule self-healing cementitious materials. This nonuniform distribution diminishes the effectiveness of the capsules and adversely affects properties like early mechanical strength. Furthermore, the uneven distribution of capsules in the matrix will lead to the reduction of the number of capsules encountered by cracks. It is therefore essential to ensure the uniform distribution of capsules within the matrix in order to maximise the probability of microcapsule rupture and self-healing capacity.

Methods

In order to avoid agglomeration of microcapsules, a uniformed distribution model for microcapsules inspired by the structural form of a honeybee's hive is designed in self-healing cementitious materials and some embedded microcapsules are dispersed within the honeycomb. This honeycomb model ensures the uniform distribution of microcapsules inside the matrix and prevent the aggregation of microcapsules, thereby achieving a design strategy for the uniform distribution of microcapsules in self-healing cementitious materials.

The probabilistic characteristics of a planar crack that appears inside a composite matrix and intersects with embedded microcapsules is investigated from the viewpoint of geometrical probability. The probability of a randomly occurring planar crack in the matrix when it encounters a spherical or spherocylindrical microcapsule is derived, and an intersection probability formula is obtained. Furthermore, the influences of capsule dimensions and quantities on the intersection probability is examined in capsule-based self-healing composites. In addition, comparative analysis is conducted on microencapsulated composite matrix models with varying shapes. Finally, the results of the theoretical model are validated using Monte Carlo simulation.

Results and discussion

The honeycomb-like composite structure is a three-dimensional structure composed of several small cubes (cells), with a certain number of spherical or spherocylindrical microcapsules randomly dispersed within the small cubes, ensuring the uniform distribution of the capsules and avoiding the aggregation of microcapsules. When a random planar crack appears within the composite, the crack will meet some microcapsules and causes the ones to rupture releasing a healing agent to heal the crack, which is necessary for self-healing to work. Three-dimensional probabilistic analytical models are developed for the spherical microcapsules and spherocylindrical microcapsules in order to represent the intersection of a planar crack with randomly dispersed microcapsules, respectively.

The findings indicate that uniformly dispersed microcapsules can increase the probability of capsule rupture and improve the self-healing efficiency. The developed three-dimensional geometric probability model of a planar crack intersecting with randomly distributed microcapsules in the matrix cells is close to a binomial probability distribution. The use of spherocylindrical microcapsules can increase the healing potential of the same volume fraction of spherical microcapsules if the microcapsules are correctly oriented. The theoretical probability values are verified by comparison with the results obtained independently by computer programming simulations.

Conclusions

The proposed theoretical formulas quantitatively express the effect of the size and dosage of different-shaped microcapsules within the matrix on the probability of a planar crack hitting microcapsules and to predict the number of microcapsules that are most likely to intersect. If the volume fraction (or size) of microcapsules is given and a planar crack requires a fixed number of microcapsules to heal, the maximum intersection probability can be calculated from the theoretical equation to determine the optimum size (or volume fraction) of microcapsules to be mixed within the model. The results of this research will help to provide a theoretical basis for the quantitative design of self-healing materials based on microcapsules of different shapes. Furthermore, employing 3D printing technology could be a feasible approach to realize the design strategy for the uniform distribution of microcapsules within self-healing cementitious materials.

Key words

self-healing / microcapsule aggregation / healing efficiency / cementitious material / Monte Carlo simulation

引用本文

吕忠, 宋向龙, 梁可, 袁静, 史梦言, 陈惠苏. 自修复水泥基材料微胶囊均匀分布设计策略及修复效率计算. 硅酸盐学报, 2025 , 53 (11) : 3114 -3126 . DOI: 10.14062/j.issn.0454-5648.20250361

Zhong LYU, Xianglong SONG, Ke LIANG, Jing YUAN, Mengyan SHI, Huisu CHEN. A Design Strategy for Uniform Distribution of Microcapsules and Calculation of Healing Efficiency in Self-Healing Cementitious Materials[J]. Journal of the Chinese Ceramic Society, 2025 , 53 (11) : 3114 -3126 . DOI: 10.14062/j.issn.0454-5648.20250361

基金

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安徽省高校科研项目(2024AH040029)
国家重点研发计划(2021YFB3802005)
高校优秀拔尖人才培育资助项目(gxyqZD2021106)
安徽省自然科学基金项目(2008085ME164)

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排序方式：

2025年第53卷第11期

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文章信息

doi: 10.14062/j.issn.0454-5648.20250361

接收时间：2025-05-06
首发时间：2026-10-21
出版时间：2025-11-20

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出版历史

收稿日期：2025-05-06
修回日期：2025-06-16

基金

安徽省高校科研项目(2024AH040029)

国家重点研发计划(2021YFB3802005)

高校优秀拔尖人才培育资助项目(gxyqZD2021106)

安徽省自然科学基金项目(2008085ME164)

作者信息

^1．安徽工业大学建筑工程学院，安徽马鞍山 243032

^2．东南大学材料科学与工程学院，重大基础设施工程材料全国重点实验室，江苏省土木工程材料重点实验室，南京 211189

通讯作者:

陈惠苏（1973—），男，博士，教授。

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https://castjournals.cast.org.cn/joweb/gsyxb/CN/10.14062/j.issn.0454-5648.20250361

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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