响应面法优化D-甘露糖醇改性磷酸镁水泥性能研究

doi:10.16552/j.cnki.issn1001-1625.2026.0255

摘要/Abstract

摘要：

针对磷酸镁水泥（MPC）因传统缓凝剂硼砂掺入后导致早期强度损失的问题，采用响应面法研究D-甘露糖醇与硼砂复配体系对MPC性能的影响及协同调控机理。结果表明：D-甘露糖醇的缓凝效应在低硼砂掺量（2.50%~3.50%，质量分数）时更为显著；高硼砂掺量（4.50%~5.01%）下强度随D-甘露糖醇掺量增加呈先升高后降低趋势，而低硼砂掺量下则呈现单调下降规律。通过模型优化获得最佳配合比，即硼砂掺量为2.50%（质量分数），D-甘露糖醇掺量为4.78%（质量分数），在该配合比下，凝结时间为29.0 min，1 d抗折强度、抗压强度分别为8.6和48.1 MPa。优化后的复配体系通过分散-成膜效应调控pH值演变特征，降低MPC早期水化速率；该体系可在水化特定阶段加速保护膜的解离，释放氧化镁颗粒表面的活性位点，提高水化产物的生成量，改善基体密实度，促进早期强度发展。

关键词: 磷酸镁水泥, 缓凝剂, 响应面法, 性能优化, 机理分析, 凝结时间

Abstract:

Magnesium phosphate cement （MPC） is formed by magnesium-based raw materials （whose main components include magnesium oxide or magnesium hydroxide）， phosphates， and retarders. MPC exhibits excellent performances such as rapid setting and hardening， high early strength， superior bonding capability and good volume stability， and it has been widely applied in road rapid repair， airport runway maintenance and special structural rehabilitation. Nevertheless， the traditional retarder borax causes obvious early strength deterioration of MPC when it is incorporated， and it fails to achieve a good balance between working performance and mechanical strength. Moreover， most new retarders still exert adverse impacts on the early mechanical properties of MPC， so their retarding effect and strength development could not be coordinated well. To address the above deficiency， this study adopted response surface methodology to explore the synergistic influence and regulation mechanism of D-mannitol and borax compound system on MPC performances.

Borax and D-mannitol content were selected as experimental variables， both ranging in mass fraction from 2.50% to 5.01%. A two-factor， five-level central composite design was adopted， and quadratic polynomial regression models were established to correlate borax content and D-mannitol content with setting time， 1 d flexural strength， and 1 d compressive strength. Variance analysis results indicate that all regression models were highly significant， with high coefficients of determination and low coefficients of variation， demonstrating satisfactory fitting accuracy and predictive reliability of the models. Experimental results show that the retarding effect of D-mannitol is more pronounced at a low borax content of 2.50%~3.50% by mass. At a high borax content of 4.50%~5.01% by mass， the early strength initially increases and then decreases with rising D-mannitol content. By contrast， strength declines monotonically as D-mannitol content increases at low borax content. The optimal mix proportion is obtained by model optimization： borax content is 2.50% and D-mannitol content is 4.78%. Under this optimal proportion， the measured setting time is 29.0 min， the 1 d flexural strength is 8.6 MPa， and the 1 d compressive strength is 48.1 MPa. Multiple characterization analyses show that in the optimized composite system， D-mannitol reduces the agglomeration of magnesium oxide particles through its dispersion effect， whereas borax acts as a retarder by forming a protective film on the surfaces of magnesium oxide particles. This dispersion-film formation effect regulates pH evolution， thereby reducing the early hydration rate of MPC. Meanwhile， the optimized composite system accelerates the dissociation of the protective film at specific hydration stages， exposes active sites on magnesium oxide particle surfaces， enhances the generation of hydration products， improves the density of the matrix， and effectively promotes the early strength development of MPC.

This study clarifies the synergistic mechanism of D-mannitol and borax， and provides theoretical support and technical reference for the application of D-mannitol-modified MPC.

Key words: magnesium phosphate cement, retarder, response surface methodology, property optimization, mechanism analysis, setting time

中图分类号:

TQ172

王秋澳, 陈烽, 彭荩影, 李悦, 钱珊珊. 响应面法优化D-甘露糖醇改性磷酸镁水泥性能研究[J]. 硅酸盐通报, 2026, 45(8): 2612-2623.

WANG Qiuao, CHEN Feng, PENG Jinying, LI Yue, QIAN Shanshan. Optimization of D-Mannitol-Modified Magnesium Phosphate Cement Properties Using Response Surface Methodology[J]. BULLETIN OF THE CHINESE CERAMIC SOCIETY, 2026, 45(8): 2612-2623.

图/表 18

图1 氧化镁的XRD谱

Fig.1 XRD pattern of MgO

表1 氧化镁的化学组成

Table 1 Composition of MgO

Composition	MgO	SiO₂	Al₂O₃	Fe₂O₃	CaO	Other
Mass fraction/%	86.17	5.02	0.64	0.46	1.90	5.81

表2 试验因素编码及水平

Table 2 Test factor codes and levels

Design variable	Level
Design variable	-1.414	-1	0	1	1.414
B content （X₁）/%	2.50	2.87	3.76	4.64	5.01
DM content （X₂）/%	2.50	2.87	3.76	4.64	5.01

表3 试验配合比

Table 3 Mix proportion of test

Sample No.	Design variable
Sample No.	B content （X₁）/%	DM content （X₂）/%
1	3.76	2.50
2	4.64	2.87
3	3.76	5.01
4	3.76	3.76
5	2.50	3.76
6	4.64	4.64
7	3.76	3.76
8	3.76	3.76
9	2.87	4.64
10	3.76	3.76
11	3.76	3.76
12	5.01	3.76
13	2.87	2.87

表4 各组试件的凝结时间与力学性能

Table 4 Setting time and mechanical properties of each group of specimens

Sample No.	Setting time （Y₁）/min	1 d flexural strength （Y₂）/MPa	1 d compressive strength （Y₃）/MPa
1	16.0	8.9	51.9
2	16.5	8.2	45.6
3	32.5	8.1	43.3
4	18.0	8.7	49.3
5	17.0	9.2	52.8
6	27.0	8.2	44.0
7	17.5	8.7	48.5
8	18.0	8.8	48.8
9	28.0	8.5	47.8
10	18.5	8.6	49.2
11	17.5	8.8	48.6
12	18.5	8.1	43.8
13	13.0	9.3	54.9

表5 试验结果的方差分析

Table 5 Analysis of variance for test results

Source of variance	Setting time			1 d flexural strength			1 d compressive strength
Source of variance	Mean square	F-value	P-value	Mean square	F-value	P-value	Mean square	F-value	P-value
Model	75.77	397.20	<0.000 1	0.360	55.30	<0.000 1	29.63	100.94	<0.000 1
X₁	2.67	13.99	0.007 3	1.090	166.16	<0.000 1	83.39	284.05	<0.000 1
X₂	298.10	1 562.69	<0.000 1	0.470	70.95	<0.000 1	54.40	185.32	<0.000 1
X₁X₂	5.06	26.54	0.001 3	0.160	24.35	0.001 7	7.56	25.76	0.001 4
X₁²	0.01	0.07	0.799 2	0.012	1.80	0.221 5	0.47	1.59	0.248 2
X₂²	71.51	374.88	<0.000 1	0.094	14.30	0.006 9	2.58	8.78	0.021 0
	R²=0.997， $R A d j 2$ =0.994 CV=2.20%			R²=0.975， $R A d j 2$ =0.958 CV=0.94%			R²=0.986， $R A d j 2$ =0.977 CV=1.12%

表5 试验结果的方差分析

Table 5 Analysis of variance for test results

Source of variance	Setting time			1 d flexural strength			1 d compressive strength
Source of variance	Mean square	F-value	P-value	Mean square	F-value	P-value	Mean square	F-value	P-value
Model	75.77	397.20	<0.000 1	0.360	55.30	<0.000 1	29.63	100.94	<0.000 1
X₁	2.67	13.99	0.007 3	1.090	166.16	<0.000 1	83.39	284.05	<0.000 1
X₂	298.10	1 562.69	<0.000 1	0.470	70.95	<0.000 1	54.40	185.32	<0.000 1
X₁X₂	5.06	26.54	0.001 3	0.160	24.35	0.001 7	7.56	25.76	0.001 4
X₁²	0.01	0.07	0.799 2	0.012	1.80	0.221 5	0.47	1.59	0.248 2
X₂²	71.51	374.88	<0.000 1	0.094	14.30	0.006 9	2.58	8.78	0.021 0
	R²=0.997， $R A d j 2$ =0.994 CV=2.20%			R²=0.975， $R A d j 2$ =0.958 CV=0.94%			R²=0.986， $R A d j 2$ =0.977 CV=1.12%

图2 凝结时间、1 d抗折强度和1 d抗压强度实测值与预测值

Fig.2 Measured and predicted values of setting time， 1 d flexural strength， and 1 d compressive strength

图3 B掺量与DM掺量交互作用对凝结时间的影响

Fig.3 Interaction effect of B content and DM content on setting time

图4 B掺量与DM掺量交互作用对1 d抗折强度的影响

Fig.4 Interaction effect of B content and DM content on 1 d flexural strength

图5 B掺量与DM掺量交互作用对1 d抗压强度的影响

Fig.5 Interaction effect of B content and DM content on 1 d compressive strength

表6 MPC配合比及性能预测值

Table 6 Mix proportion and predicted performance values of MPC

Group	B content/%	DM content/%	Setting time/min	1 d flexural strength/MPa	1 d compressive strength/MPa
BD	2.50	4.78	30.3	8.4	46.8

表7 预测值与实测值的对比

Table 7 Comparison of predicted values and measured values

Item	Setting time/min	1 d flexural strength/MPa	1 d compressive strength/MPa
Predicted value	30.3	8.4	46.8
Measured value	29.0	8.6	48.1
Relative error/%	4.5	2.3	2.7

表8 BD与B1配合比及性能测试结果

Table 8 Mix proportion and performance test results for BD and B1

Group	M/P	W/C	B content/%	DM content/%	Setting time/min	1 d flexural strength/MPa	1 d compressive strength/MPa	28 d flexural strength/MPa	28 d compressive strength/MPa
BD	2	0.18	2.50	4.78	29.0	8.6	48.1	9.5	60.7
B1	2	0.18	7.28	0	10.5	7.5	41.8	8.6	52.6

图6 BD和B1液相pH值随时间的变化

Fig.6 Evolution of liquid phase pH value over time of BD and B1

图7 BD和B1水化1 d的XRD谱

Fig.7 XRD patterns of BD and B1 hydrated for 1 d

图8 BD和B1水化1 d的TG-DTG曲线

Fig.8 TG-DTG curves of BD and B1 hydrated for 1 d

图9 BD和B1水化1 d的SEM照片

Fig.9 SEM images of BD and B1 hydrated for 1 d

图10 DM与B复配影响MPC反应的机理示意图

Fig.10 Schematic diagram of mechanism by which compound of DM and B affects MPC reaction

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