Molecular Dynamics Study of a Superabsorbent Polymer (SAP)-Modified Calcium Silicate Hydrate (C-S-H) Gel’s Mechanical Properties
Abstract
1. Introduction
2. Materials and Methods
2.1. Model Construction of C-S-H Gel
2.1.1. Selection of Initial C-S-H Structure Model
2.1.2. Molecular Dynamics Simulation Protocol
2.2. SAP-Induced Pore Generation Criteria
2.2.1. Effect of Pores on Concrete Strength
2.2.2. Pore-Refining Effect of SAPs on Concrete
2.2.3. Pore Diameter Definition Method Post-SAP Water Release
2.3. C-S-H Gel Model Construction with SAP-Induced Pores
3. Results
3.1. C-S-H Weak Region Bulk Modulus Evolution
- The bulk modulus of the three C-S-H gel groups exhibits an initial increase followed by a decrease as the pore size reduces within the 0.3–1.5 nm range. The maximum bulk modulus occurs at 0.2% SAP content, indicating optimal mechanical performance. Controlling the SAP content to 0.2% ensures that pore sizes within 0.3–1.5 nm exert the most favorable influence on concrete mechanics;
- For group H1, the bulk modulus of the C-S-H system with 0.37 nm pores is 9.214 GPa. Increasing the pore size to 0.74 nm elevates the modulus to 10.606 GPa. This trend may arise from the minimal impact of pore size variation on K within the H1-H2 range (ultra-small pores), coupled with heightened system energy and water molecule mobility due to increased hydration, which collectively enhance K;
- In contrast, at 0.3% SAP content (H3 group, 1.12 nm pores), K drops sharply to 7.343 GPa. This decline suggests that pore expansion-induced weakening of compressibility resistance outweighs any modulus enhancement from additional water molecules, resulting in a net reduction in the mechanical stability.
3.2. C-S-H Weak Region Shear Modulus Evolution
- The shear modulus of the three C-S-H gel groups exhibits a non-monotonic relationship with pore size within the 0.3–1.5 nm range: it initially increases and then decreases as pore size reduces.
- Specifically, for the H2 group (pore size reduced from 1.12 nm to 0.74 nm), G rises to 5.315 GPa. For the H1 group (pore size further reduced to 0.37 nm), G declines to 4.877 GPa.
- This trend may arise from two competing mechanisms:
- (1)
- Enhanced interlayer contact: Smaller pores increase the contact area between C-S-H gel layers, restricting relative sliding and thereby improving shear resistance.
- (2)
- Reduced viscous resistance: At a fixed water density (1 g/cm3), fewer water molecules occupy smaller pores, lowering viscous damping between layers. These opposing effects lead to an initial increase in G followed by a decrease.
- The highest shear modulus (5.315 GPa) occurs at 0.2% SAP content, corresponding to an optimal pore size of 0.74 nm within the 0.3–1.5 nm range.
3.3. C-S-H Weak Region Young Modulus Evolution
- E initially increases from 12.437 GPa to 13.663 GPa but subsequently decreases to 9.657 GPa as pore size expands within the 0.3–1.5 nm range.
- This non-monotonic trend stems from two competing mechanisms:
- (1)
- Enhanced energy from hydration: Increased water molecule density at smaller pores elevates system energy, improving deformation resistance.
- (2)
- Structural weakening: Larger pores reduce structural integrity, facilitating compressive strain.
- When the pore size grows from 0.37 nm to 0.74 nm (H1 to H2 groups), the hydration effect dominates, increasing E. The further expansion to 1.12 nm (H3 group) shifts the balance toward pore-induced structural weakening, causing E to decline.
4. Nanomechanical Behavior of SAP-Modified C-S-H: Verification and Discussion
4.1. Verification
4.2. Discussion
4.2.1. Fundamental Insights into SAP-Modified C-S-H Mechanics
4.2.2. Engineering Implications for Concrete Design
- (1)
- SAP particle size control: Smaller SAP particles (<50 μm) generate sub ~0.74 nm pores during swelling, minimizing mechanical degradation while sustaining internal curing efficiency [116]. The smaller SAP-induced pores (0.37–1.12 nm) promote distributed microcracking at the nanoscale [117]. This aligns with experimental observations of increased fracture energy (25–40%) in SAP-modified concrete proposed by Mechtcherine et al. [114], where 40 μm SAPs improved pavement durability by 35% without compromising the 28-day strength.
- (2)
- Dosage optimization: Nonlinear mechanical degradation (e.g., 41% G, 44% K, 41% E reduction at 0.3% SAP vs. 0.2% SAP) suggests an optimal SAP dosage of 0.1–0.2 wt% cement, balancing pore refinement (desirable for curing) and strength retention (critical for load-bearing structures).
- (3)
- Material–structure synergy: The observed nanoscale mechanical degradation and pore refinement induced by SAPs have profound implications for macroscale concrete performance. In cast-in-place concrete structures (e.g., high-performance concrete bridge deck presented in Appendix C (Figure A1a,b)), the targeted SAPs used in low-stress zones could enhance crack resistance, whereas SAP exclusion from high-stress regions (e.g., beam tension faces) preserves structural integrity.
4.2.3. Limitations and Future Directions
- (1)
- Simplified pore morphology: Spherical pores in simulations neglect real SAP-induced pore anisotropy observed via TEM. Future work should incorporate irregular pore geometries.
- (2)
- Multi-ion effects: Simulations assumed pure pore water, whereas real cement pore solutions contain Ca2+, K+, Na+, and SO42−, which may alter the interfacial water structure.
- (3)
- Scale integration: The current MD-to-macro correlation relies on phenomenological models. Multiscale frameworks (e.g., FE-MD coupling) are needed to predict component-level performance.
5. Conclusions and Prospects
5.1. Key Findings
- (1)
- Pore classification and SAP refinement mechanism: SAP addition refines transition/capillary pores into gel pores (0.6–3.2 nm), with a distinct 0.74 nm peak in pore size distribution. Pores < 0.74 nm dominate interfacial energy dissipation, whereas larger pores (>0.74 nm) trigger localized stress concentrations.
- (2)
- Molecular dynamics framework: We established a validated MD workflow for C-S-H gel with SAP-induced pores (0.37–1.12 nm), enabling the atomic-scale analysis of pore–property relationships.
- (3)
- Optimal SAP content: A 0.2% SAP dosage generates ~0.74 nm pores, maximizing interfacial bulk (10.61 GPa), shear (5.31 GPa), and Young’s modulus (13.66 GPa) values.
5.2. Scientific Prospects
- (1)
- Pore morphology realism: Replace idealized spherical pores with TEM-informed irregular geometries to capture anisotropic stress distributions.
- (2)
- Multiscale bridging: Integrate MD-predicted nanomechanics into phase-field or FEM frameworks to predict macroscale crack propagation in SAP-modified concrete.
5.3. Applied Engineering Prospects
- (1)
- SAP material design: Prioritize SAPs with crosslinked networks (e.g., acrylic acid-co-acrylamide) to limit swelling and stabilize pore sizes <0.74 nm.
- (2)
- Optimize particle size distribution (e.g., 20–50 μm) to enhance pore refinement efficiency.
- (3)
- Concrete mix optimization: Apply 0.1–0.2% SAPs in high-stress zones (e.g., bridge decks) for crack suppression, while minimizing SAPs in compression-critical regions (e.g., columns). Combine SAPs with nano-silica to offset strength loss via pozzolanic reactivity.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Items | H1 Group | H2 Group | H3 Group | |||
---|---|---|---|---|---|---|
Initial | Final | Initial | Final | Initial | Final | |
Tot. energy (kcal/mol) | −21,346.382 | −20,712.823 | −21,346.382 | −20,712.823 | −21,814.6649 | −21,216.576 |
Pot. energy (kcal/mol) | −22,763.189 | −22,091.413 | −22,763.189 | −22,091.413 | −23,364.698 | −22,830.948 |
Kin. energy (kcal/mol) | 1416.807 | 1378.590 | 1416.807 | 1378.590 | 1550.049 | 1614.372 |
Tot. enthalpy (kcal/mol) | −24,500.171 | −23,483.741 | −24,500.171 | −23,483.741 | −24,595.401 | −23,306.257 |
Temperature (K) | 298.000 | 289.962 | 298.000 | 289.962 | 298.000 | 310.366 |
Pressure (GPa) | −0.980 | −0.861 | −0.980 | −0.861 | −0.810 | −0.609 |
Volume (Å3) | 22,361.199 | 22,361.199 | 22,361.199 | 22,361.199 | 23,838.302 | 23,838.302 |
Density (g/cm3) | 1.756 | 1.756 | 1.756 | 1.756 | 1.710 | 1.710 |
Appendix B
(a) Stiffness Matrix of H1 | (b) Flexibility Matrix of H1 |
(c) Stiffness Matrix of H2 | (d) Flexibility Matrix of H2 |
(e) Stiffness Matrix of H3 | (f) Flexibility Matrix of H3 |
Appendix C
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Items | Algorithm | Energy (kcal·mol−1) | Force (kcal·mol−1·A−1) | Maximum Number of Iterations | External Pressure (GPa) | Motion Groups Rigid | Optimize Cell |
---|---|---|---|---|---|---|---|
Parameters | Smart | 0.001 | 0.5 | 500 | 0.001 | No | No |
Items | Atomic Number | Tools | Force Field | MD Ensemble | Temperature (K) |
---|---|---|---|---|---|
Parameters | 100 | Discover | COMPASS | NPT | 300 |
Items | Pressure (Gpa) | Temperature Control | Pressure Control | Time Step (fs) | Relaxation Time (ps) |
Parameters | 0.01 | Nose-Hoover | Parrinello | 1 | 20 |
Tot. Energy | Pot. Energy | Kin. Energy | Tot. Enthalpy | Temperature | Pressure | Bulk | Density | |
---|---|---|---|---|---|---|---|---|
(kcal·mol−1) | (K) | (GPa) | (A3) | (g·cm−3) | ||||
Initial | −1135.969 | −1199.461 | 63.491 | −1216.436 | 300.000 | −0.595 | 938.837 | 2.146 |
Final | −1073.531 | −1151.184 | 77.653 | −1279.237 | 366.916 | −1.522 | 938.837 | 2.146 |
Std.Dev. | 22.225 | 12.678 | 12.758 | 101.724 | 60.284 | 0.705 | 0.000 | 0.000 |
Pore Parameters | Authors | Models | Authors | Models |
---|---|---|---|---|
Void | Feret [82] | F = K [C/(C + W + A) | Abrams [82] | F = K1/K2W/C |
Powers [83] | F = fXn | / | / | |
Porosity | Balshin [84] | F = F0(1 − P)k | Ryshewitch [85] | E = E0e−BP |
Schiller [42] | F = kln(P0/P) | Hasselman [43] | F = F0(1 − kP) | |
Jambor [41] | Diamond [86] | |||
Pore Size Distribution | Older [39] | F = 12 − 0.1P<10nm − 3.7P10–100nm − 3P>100nm | Atzeni [40] | F = F0 − a·P<10.6nm − b·P10.6–53nm − c·P53–106nm − d·P>106nm |
Ma [87] | F = F0 − a·P<50nm − b·P50–100nm − c·P>100nm | / | / |
Pore Types in Concrete Structures | Pore Classification (IUPAC) | Location in Structure | Pore Size Range (nm) | Pore Scales |
---|---|---|---|---|
Micro-crystalline Pores | Supermicropores | Inner Gel Microcrystal | <0.6 | Nanoscales |
Gel Pores | Ultramicropore–Nanopores | Within C-S-H Matrix | 0.6–3.2 | Nanoscales |
Capillary Pores | Mesopores | Outer Gel–Inner Cement Particle | 3.2–50 | Mesoscales |
Corse Pores | Macropores | Outer Cement Particle | >50 | Macroscales |
Literatures | Samples | Porosity (%) | Critical Aperture (nm) | Pore Volume Distribution (mL·g−1) | |||
---|---|---|---|---|---|---|---|
<10 nm | 10–100 nm | 100–1000 nm | >1000 nm | ||||
Kong [94] | Control group | 22.7 | 90 | 0.023 | 0.080 | 0.018 | 0.004 |
85.25 kg of SAP per cubic meter of concrete | 28.7 | 86 | 0.031 | 0.115 | 0.005 | 0.018 | |
85.25 kg of SAP and 170.5 kg of Water per cubic meter of concrete | 30.8 | 79 | 0.028 | 0.136 | 0.007 | 0.024 | |
Shen [95] | Control group | 5.0337 | 40.32 | 15.49 | 81.27 | 2.97 | 0.27 |
Concrete containing 0.18% SAP (by weight) and 0.056 times the standard water content | 9.8190 | 28.64 | 39.81 | 57.50 | 2.54 | 0.15 |
Pore Size | Author | SAP Mass Content (%) | SAP Fineness | Year of Publication |
---|---|---|---|---|
<2 nm | Fazhou Wang [105] | 0.3, 0.5, 0.7 | SAP: 500 μm | 2009 |
<10 nm | Klemm [106] | 0.1–1 | / | 2013 |
<10 nm | Xianwei Ma [36] | 0.3, 0.6, 0.9 | SAPH100: 20–250 μm SAPH30: 250–1400 μm | 2017 |
<10 nm | Sung-Hoon Kang [104] | 0.3, 0.4 | SAP-AA: 100–700 μm SAP-AM: 100–700 μm | 2018 |
<10 nm | Yanwei Tong [107] | 0.3 | SAP-A: 30–50 mesh SAP-B: 50–70 mesh; SAP-C:100 mesh | 2019 |
1.5–2 nm | Snoeck [108] | 0.22, 0.45 | SAPA: 79–121 μm SAPB: 424–530 μm | 2019 |
<10 nm | Yan Lu [109] | 0.1, 0.2, 0.3 | SAP: 200 mesh | 2022 |
Sample Code | Pore Size (nm) | SAP Mass Content (%) |
---|---|---|
H1 | 0.37 | 0.1 |
H2 | 0.74 | 0.2 |
H3 | 1.12 | 0.3 |
This Study Tobermorite 4a × 6b × 2c | LI Zongli [63] Jennite Unit Cell | Shahsavari [113] | Hajilar [111] Jennite | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Jennite Tobermorite Unit Cell | ||||||||||
1a × 1b × 1c | 2a × 2b × 2c | |||||||||
Pores (nm) | 0.37 | 0.74 | 1.12 | 1.0 | 1.5 | 2.0 | No | No | ||
K (GPa) | 9.21 | 10.61 | 7.34 | 50.5 | 52.5 | 48.0 | 31.83 | 58.00 | 64.8 | 65.0 |
G (GPa) | 4.87 | 5.31 | 3.77 | 25.0 | 23.5 | 22.0 | 21.96 | 32.56 | 34.6 | 34.1 |
E (GPa) | 12.44 | 13.66 | 9.66 | 62.5 | 61.0 | 60.0 | 53.55 | 82.29 | 88.2 | 87.1 |
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Zhou, S.; Cai, J.; Lai, K.; Li, G.; Liu, S.; Wang, J.; Sun, X. Molecular Dynamics Study of a Superabsorbent Polymer (SAP)-Modified Calcium Silicate Hydrate (C-S-H) Gel’s Mechanical Properties. Buildings 2025, 15, 1752. https://doi.org/10.3390/buildings15101752
Zhou S, Cai J, Lai K, Li G, Liu S, Wang J, Sun X. Molecular Dynamics Study of a Superabsorbent Polymer (SAP)-Modified Calcium Silicate Hydrate (C-S-H) Gel’s Mechanical Properties. Buildings. 2025; 15(10):1752. https://doi.org/10.3390/buildings15101752
Chicago/Turabian StyleZhou, Shengbo, Jinlin Cai, Ke Lai, Gengfei Li, Shengjie Liu, Jian Wang, and Xiaohu Sun. 2025. "Molecular Dynamics Study of a Superabsorbent Polymer (SAP)-Modified Calcium Silicate Hydrate (C-S-H) Gel’s Mechanical Properties" Buildings 15, no. 10: 1752. https://doi.org/10.3390/buildings15101752
APA StyleZhou, S., Cai, J., Lai, K., Li, G., Liu, S., Wang, J., & Sun, X. (2025). Molecular Dynamics Study of a Superabsorbent Polymer (SAP)-Modified Calcium Silicate Hydrate (C-S-H) Gel’s Mechanical Properties. Buildings, 15(10), 1752. https://doi.org/10.3390/buildings15101752