Introduction

Carbon fiber-reinforced polymer (CFRP) has seen extensive development and widespread utilization in bridge reinforcement projects, owing to its advantages such as high strength, excellent reinforcement performance, and fast construction [1,2,3]. Epoxy resin adhesive, known for its strong bonding strength and low shrinkage, can establish a stable composite interface system during repair and reinforcement processes [4]. In CFRP reinforcement projects, the bonding performance between CFRP and the existing concrete interface is a crucial factor in forming a sound and durable reinforcement structure. According to previous experience and research [5,6,7,8], epoxy resin plays a vital role in the organic–inorganic interface bonding and is widely applied in CFRP reinforcement projects. The bonded interface strength significantly determines the mechanical properties of CFRP-concrete composite structures [9], under normal temperature conditions, previous researchers have conducted in-depth studies on the bonding issues of the CFRP-concrete interface [10,11,12]. However, the CFRP/concrete interface faces challenges under harsh environmental conditions such as high temperature, high humidity, and freeze–thaw cycles in different regions. The interface strength tends to decrease significantly under such conditions [13], leading to the deterioration of the entire system, causing incalculable economic losses, and posing a severe threat to structure safety. Therefore, it is necessary to investigate the interface performance between CFRP and concrete structures under different conditions.

Researchers have conducted significant study on the durability performance of the CFRP/concrete interface [14,15,16,17]. In their study, Au et al. [18] examined the efficacy of interface bonding and failure patterns of FRP-concrete beams under high temperature and high humidity conditions using shear fracture and peel-off tests. Their findings demonstrated a shift from concrete fracture to debonding at the interface between concrete and epoxy. A shear test was conducted by Sharma et al. [19] to evaluate the bond strength and determine the effective bond length of the FRP/concrete interface. Ali et al. [20] employed a shear test combined with digital image correlation technology to measure the strain distribution in concrete and FRP fabric. Another study [21] investigated the mechanical properties of the FRP/concrete interface through double shear tests, providing formulas and laws for calculating interface shear stress, average shear stress, and stress distribution. The bond-slip constitutive relationship of the CFRP/concrete interface serves as the theoretical basis for studying other interface behaviors and is primarily studied through numerical analysis and fitting of experimental data. Currently, there are six main types of bond-slip constitutive relationships for the CFRP/concrete interface [18, 21]: truncated model, elastoplastic model, bilinear model, stress softening model, bilinear stress softening model, and trilinear model. The truncated model was commonly used in the early stages but failed to consider interface softening behavior, leading to inconsistency with actual conditions [22]. The latter two models, especially the bilinear model, are simple to derive, easy to use, and more consistent with actual conditions, making them widely applied in engineering [23]. Lee [24] defined the constitutive relationship as the bilinear stress softening model, while Yuan [25] simplified the model to a trilinear model, when the stress reaches the limit of interface strength, softening initiates, and the subsequent decline is approximated as a linear segment.

However, most of these studies were based on macroscopic experiments or finite element simulations, and the experimental methods and models were influenced by scale and precision, resulting in more general regularities or mathematical models specific to certain experimental conditions. Further research is needed to explore the interface evolution and principles of the CFRP/concrete interface under different environmental factors from a deeper level at nanoscale.

Many researchers have utilized molecular dynamics simulation (MDS) to study concrete reinforcement interfaces and pores at the nanoscale level [4, 9, 26, 27]. From a molecular standpoint, Hou et al. [28] provided an explanation for the robust adhesion between epoxy resin coatings and cementitious materials. They highlighted that the presence of epoxy molecules results in a reduction of the gel pore entrance and enhances the hydrophobic nature of the inner surface, effectively impeding the movement of water within the C–S–H gel channels. Molecular dynamics simulations (MDS) were utilized by Yu et al. [29] to investigate the local structure, dynamic properties, and water transport mechanism of composite coatings consisting of graphene oxide and epoxy resin. Wang et al. [30, 31] investigated the bonding mechanism at the epoxy/calcium silicate hydrate (C–S–H) interface under erosive environments. Thermodynamic analysis revealed that in the presence of water and salt, the epoxy resin gradually detached from the C–S–H surface, indicating a deterioration in the bonding between the epoxy resin and the C–S–H matrix. The simulation results highlighted the crucial role of calcium ions in bridging between the oxygen atoms on the C–S–H surface and the epoxy resin, which is essential for achieving strong adhesion in the epoxy resin/C–S–H interface.

From a nanoscale perspective, the epoxy resin is first crosslinked with the curing agent before being applied as an adhesive to the concrete surface, and then water molecules gradually participate in the interaction of the crosslinked epoxy/C–S–H interface. The water molecules and other ions are transported through the nanopores, that is of fundamental importance in determining the mechanical strength and durability performance of concrete materials. The infiltration of water molecules weakens bonding strength of the epoxy-modified C–S–H, causing the debonding and degradation over time. This capillary transport behavior varies under different temperature conditions is also very important. However, a comprehensive understanding of the physical and chemical processes of water molecules within nanoscale pores cannot be achieved solely through macroscopic experiments. Therefore, molecular simulation methods have provided significant assistance in unraveling the transport mechanisms of water molecules within epoxy-modified C–S–H nanoscale pores. In this study, a molecular dynamics model of crosslinked epoxy resin covering the C–S–H nanopore was proposed. After that, the influence of temperature on the transportation of water molecules in this model was investigated through equilibrium configurations, dynamic properties, and chemical bond connections. This research offers atomistic insights to enhance the durability of the CFRP/concrete interface and gain a better understanding of the water molecule transport mechanism in epoxy-modified C–S–H nanopores.

Simulation method

Model construction

The entire model consists of three components: C–S–H pore, crosslinked epoxy resin layer, and solution, as shown in Fig. 1a. The simulation box size is 79.12 Å × 22.56 Å × 225.29 Å. Two C–S–H substrates are derived from the structure obtained by slicing Tobermorite 11 Å crystals along the [0 0 1] plane, as proposed by Hamid [32]. Layered Tobermorite 11 Å crystals have been used as C–S–H models due to their structural similarity observed in experimental data [32,33,34]. After supercell expansion, the size of a single C–S–H is 16.52 Å × 21.23 Å × 80.37 Å, and the pore width is set to 4.5 nm, inside the usual range of C–S–H nanopores widths [35]. On the surface of C–S–H, hydroxyl groups are added to non-bridging oxygen atoms to decrease their hydrophobicity and regulate the number of calcium ions on the surface to maintain charge equilibrium in the system. The solution part contains 4800 water molecules with a density of 1 g/cm3, and its dimensions are 22.00 Å × 78.20 Å × 83.68 Å. Figure 1b and c illustrate the details of epoxy resin crosslinking and modeling. The crosslinked epoxy resin layer is formed by crosslinking reaction of 14 bisphenol-A diglycidyl ether (DGEBA) epoxy monomers and 7 4′4-sulfonyldianiline curing agents. The crosslinking process follows the method proposed by Du [36], where the C–O–C bonds in the epoxy groups of the resin and the N–H bonds in the curing agents are initially broken, followed by crosslinking of the epoxy monomers and curing agents through C–N bonds. Unreacted atoms are modified with hydrogen atoms. The resulting crosslinked molecular structure is energy-minimized and arranged into a crosslinked epoxy resin layer with dimensions of 20.89 Å × 78.55 Å × 5.23 Å, which is then superimposed on the surface of C–S–H. Afterwards, an energy minimization process is conducted to find the low-energy configuration of the epoxy/C–S–H interface. Throughout the simulation, the two C–S–H sheets were fixed within a distance of 14 Å from the x-boundary of the simulation box, while the rest of the components are allowed to relax. This approach ensures interactions between water molecules/epoxy and the C–S–H surface, while maintaining the positions of the pores.

Figure 1
figure 1

Illustration of water molecules transport in epoxy-modified C–S–H model. a Three-component transport model: solution, epoxy resin, and C–S–H pore; b Crosslinked epoxy layer representation in YZ plane; c Schematic illustration of the crosslinking process; d Atomic color legend and detailed view of the C–S–H substrate.

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Force field and molecular dynamic procedure

During the entire simulation, the Clayff force field and its corresponding parameters were utilized to simulate the atomic interactions within the C–S–H gel. This force field has gained significant recognition for its ability to accurately describe the energy, configuration, and various properties of different calcium silicate phases. As a result, it has been widely employed in simulations of C–S–H gel systems [37,38,39,40]. The parameters for van der Waals and chemical bond interactions in the Clayff force field can be found in the reference [40]. The epoxy component was described using the consistent-valence force field (cvff), which is widely employed in the modeling of atomic interactions in organic compounds and epoxy-based systems [41]. The literature sources [41, 42] provide the necessary parameters for the cvff force field. Previous studies [25, 28] have demonstrated the successful application of the combined Clayff and Cvff force fields in accurately representing the interactions within inorganic–organic hybrid systems. In all simulations, a cutoff distance of 12 Å was used for non-bonded interactions.

The modeling and simulation were performed using the Lammps software package [43, 44]. The calculations were divided into two separate parts. Firstly, a reflective region was placed in the water molecule region (z: 35–133 Å) to prevent premature infiltration of water molecules into the nanopores. Molecular dynamics relaxation simulations were subsequently conducted in the NVT ensemble for a duration of 500 ps at temperatures of 253 K, 273 K, 293 K, and 313 K. These simulations aimed to achieve the equilibrium state of the epoxy/C–S–H interface inside the channels under dry conditions at each temperature. Following that, the obstructive region that prevented the entry of water molecules was eliminated, enabling unrestricted ingress of water molecules into the nanochannels. The four models underwent transport simulations in the NVT ensemble under their respective temperatures for a duration of 2000 ps. The time step for the entire simulation stage was set to 1 fs, and the trajectories of all atoms were output every 1000 steps to obtain the trajectories for subsequent thermodynamic analysis.

Results and discussion

Transport of water solution in epoxy-modified C–S–H nanopores

Figure 2 demonstrates the progressive infiltration of water molecules into the gel pores during a time span of 2000 ps. The snapshots at 0 ps exhibit noticeable differences in the epoxy/C–S–H configuration after relaxation for 500 ps at different temperatures. At 253 K, 273 K, and 293 K, the epoxy is laid flat above the C–S–H. However, at 313 K, clustering phenomena occur in the epoxy during relaxation. Indicating that rising temperature can change the equilibrium configuration of epoxy. When the solution passes through the region without epoxy coverage, such as the 60 ps snapshot in Fig. 2d, The contact angle between the water solution and C–S–H substrate is less than 90°, indicating the hydrophilic nature of the C–S–H surface. However, when passing through the epoxy-covered C–S–H region, this characteristic is absent, indicating that the presence of epoxy has altered the original interface properties and has an inhibitory effect on the immersion process. As the solution immersion depth increases, the epoxy resin transitions from uniformly covering the C–S–H walls to forming compacted, clustered clusters with varying shapes and densities. These clusters, which cover the C–S–H substrate, can persist for a longer time under low-temperature conditions (Fig. 2a, 253 K) during the course of the simulation. Meanwhile, with increasing temperature, the epoxy clusters gradually detach from the C–S–H substrate and disperse within the pore space, as depicted in Fig. 2c, or even become free-floating, as shown in Fig. 2d. Furthermore, when comparing the snapshots of the transportation process between 600 and 2000 ps, it becomes apparent that water molecules face difficulties in passing through the “barrier” formed by epoxy clusters within the channels of C–S–H. This “barrier” phenomenon is closely linked to the size and atomic density of the clusters. Based on the snapshots in Fig. 2, it is clear that with increasing temperature, the effective bonding area of the epoxy/C–S–H interface decreases, while the immersion depth increases. During the immersion process, the real-time pore size undergoes continuous changes due to epoxy clustering or detachment, resulting in three different scenarios: narrowing of the epoxy/C–S–H channels (253 K, 273 K), block the channel (293 K), and complete detachment (313 K).

Figure 2
figure 2

Snapshots of water molecules transport at different temperature: a 253 K, b 273 K, c 293 K, d 313 K.

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To further understand the dynamic immersion process, all water molecules were grouped together, and the center of mass of this group of atoms was identified using the “compute com” command. The depth-time curve was plotted by tracking the movement of the water molecules' center of mass, as shown in Fig. 3. In this part, Figs. 2 and 3 were combined to explain the water immersion process in these four models. At the beginning of water immersion (0–30 ps), the solution progresses from the initial liquid state to transport in the epoxy/C–S–H channel. All of the solution molecules are densely arranged in the negative direction of the z-axis. The solution molecules at the top of the liquid are only influenced by the van der Waals and electrostatic forces from the solution molecules below, forcing them to migrate toward the positive direction of the z-axis. During this process, there is no change in the inner diameter of the pore, which can be attributed to the significant concentration gradient between the liquid surface and the pore. This phenomenon is observed in all four models, leading to an equal infiltration depth within 0–30 ps. From 30 to 600 ps, water immersion occurs in the front half of the pore. During this stage, the transport phenomenon is characterized by the continuous contraction of the epoxy-modified C–S–H interface due to inter-molecular interactions between water and epoxy molecules. As water molecules penetrate, epoxy molecules become entangled and stacked, resulting in a reduction of the epoxy/C–S–H interface area. However, the accumulation of epoxy on the surface of C–S–H forms large molecular clusters that hinder the further movement of water molecules. The presence of these large molecular clusters leads to a decrease in the C–S–H pore size, which is one of the reasons why water molecules in the models at 253 K, 273 K, and 293 K exhibit slow migration within the subsequent 1400 ps. Within this time range, the four curves maintain their respective slopes and continue to evolve along the timeline, exhibiting distinct developmental patterns at different temperatures. In the subsequent 1400 ps, two main scenarios occur in the pores: Firstly, at lower temperatures (253 K and 273 K), epoxy tends to form and maintain large molecular clusters on the C–S–H surface due to more stable interfacial interactions. This is the primary reason for inhibiting further erosion of water under these temperature conditions, resulting in a decrease in the pore diameter. Secondly, as the temperature increases (293 K and 313 K), molecular activity intensifies, facilitating the penetration of water molecules into the epoxy/C–S–H channel. As shown in Fig. 4, water molecules engage in a competitive process for atomic coordination, thereby weakening the effective bonding between atoms at the epoxy/C–S–H interface, which will be further discussed in the coordination number analysis). The Casur (The first layer of calcium atoms near the pore) and Oe (The oxygen atoms in the epoxy resin) atoms of the C–S–H surface, along with epoxy molecules, detach from the hydration layer due to the higher atomic velocity. Consequently, under these two temperature conditions, epoxy tends to detach from the C–S–H surface, forming overall clusters that obstruct the pore and impede further water transport (in the case of 293 K). Alternatively, at 313 K, epoxy molecules exist as freely moving large or small clusters alongside water molecules, resulting in the complete degradation of the epoxy/C–S–H interface functionality.

Figure 3
figure 3

Variation curve of immersion depth with time at different temperatures.

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Figure 4
figure 4

Epoxy/C–S–H interface before and after immersion a before; b after. The red line in the graph represents water molecules.

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Atomic intensity of epoxy-modified C–S–H

The intensity dispersion of the atoms for the immersion models under four different temperatures are shown in Fig. 5. The Oe and Ne (The oxygen atoms in the epoxy resin) atoms exhibit almost identical intensity peaks and valleys in all four models, indicating good crosslinking and high degree of motion coordination between these epoxy and curing agent molecules at the molecular simulation scale. As the temperature increases, the relative concentration peak of the Carsur decreases, and more peak points appear, concentrated within the interior of the C–S–H gel pore. This implies that the diffusion range within the C–S–H has increased, but the Carsur is restricted by the existence of epoxy resin molecules on the nanopore walls, preventing them from achieving free mobility. In all four models, the distribution range of Casur remains limited to the epoxy/C–S–H interface, within x-axis values ranging from 20 to 60 Å. As the temperature increases, the distribution range of epoxy gradually expands. Specifically, at temperatures of 253 K, 273 K, 293 K, and 313 K, the distribution ranges of epoxy on the X-axis measure 39.5 Å, 45.03 Å, 51.35 Å, and 54.51 Å, respectively. The concentration peak of Ow is observed at the center of the pore in Fig. 5a and b. The presence of epoxy resin clusters near the wall restricts water molecule transport, leading to lower relative concentration values. In Fig. 5c and d, the relative concentration peak of Ow is located near the wall. This is due to a greater degradation/detach of the epoxy/C–S–H interface within these models, resulting in increased attraction of the hydroxyl groups on the C–S–H substrates to water molecules.

Figure 5
figure 5

Strength distribution of each atom in C–S–H gel pore a 253 K; b 273 K; c 293 K; d 313 K.

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The radial distribution function (RDF) quantifies the probability of locating other particles at a given distance r from a central particle. It characterizes the spatial correlation between two types of particles and is commonly used to study the microstructure of system. The calculation formula for RDF is as follows:

$$g\left(r\right)=\frac{dN}{\rho 4\pi {r}^{2}dr}$$
(1)

In the given formula, ρ represents the density of the system, and N represents the entire number of particles in the system. The mathematical interpretation of the formula is the ratio of the local density in the system region to the average density. Figure 6 shows the RDF of epoxy/C–S–H interface. In Fig. 6a, the radial distribution function curve of Casur–Oe exhibits a prominent peak at 0.285 nm, indicating that 0.285 nm is the equilibrium distance for the Casur–Oe ion pair. This suggests the presence of a strong ionic bonding interaction between epoxy and C–S–H. With increasing temperature, the peak of the radial distribution function curve for Casur–Oe drops significantly, indicating a decrease in the orderliness and a weakening of the ionic bonding interaction between Casur–Oe ion pairs. In Fig. 6b, the radial distribution function (RDF) values of Casur–Ow (The oxygen atoms in water) ion pairs show an increasing trend with temperature, indicating that as the temperature rises, the tendency of Casur to coordinate with oxygen atoms in water becomes stronger. This affects the original coordination of Oe atoms with Casur, as shown in the coordination number (CN) analysis in Table 1. The reciprocal changes in the coordination of Oe and OW atoms provide further explanation for the previously mentioned phenomenon. It illustrates the detachment of epoxy from the C–S–H surface, resulting in pore blockage or the formation of freely mobile large molecular clusters at elevated temperatures. Figure 6c and d highlight the pairing of hydrogen and oxygen atoms at the epoxy/C–S–H interface, playing a critical role in the hydrogen bonding network. The RDF for OS (The oxygen atoms on the surface of C–S–H) –He (The hydrogen atoms in epoxy resin) and Oe–HS (The hydrogen atoms on the C–S–H surface) exhibit peaks at 0.321 nm and 0.228 nm, respectively. Considering the distance threshold (0.245 nm) required for hydrogen bonding formation, it can be concluded that the hydrogen bonding interactions at the epoxy/C–S–H interface primarily involve oxygen atoms on the epoxy as donors and hydroxyl hydrogen atoms on the C–S–H surface as acceptors. Furthermore, the RDF curves for Hs-Oe and Os-He show a decreasing trend in peak intensity in the higher temperature models, indicating a weakening of the hydrogen bonding interactions between epoxy and the C–S–H matrix with increasing temperature.

Figure 6
figure 6

Radial Distribution Function (RDF) of atoms near the epoxy/C–S–H interface. a RDF of Casur–OW; b Casur–Oe; c Os–He; d Oe–Hs.

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Table 1 Coordination number of Casur atom
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The mean squared displacement (MSD) is the average of the square of particle displacements and is an important parameter in dynamic analysis. It is used to evaluate the motion characteristics of atoms. The calculation formula for MSD is as follows [45]:

$$\mathrm{MSD}=\;<|{r}_{i}\left(t\right)-{r}_{i}\left(0\right){|}^{2}>$$
(2)

In Eq. (2), ri(0) and ri(t) represent the positions of atom i at the initial time and time t, respectively, where <  > denotes an average over all atoms in the ensemble. At the same time, a larger value of MSD for an atom indicates faster motion. Figure 7 shows the MSD values of calcium atoms on the C–S–H surface (Casur) and oxygen atoms in water molecules (OW) within the nanopores in different temperatures. This analysis aims to explore the influence of crosslinked epoxy resin modification on the dynamic performance of water at the C–S–H interface. In Fig. 7a, it is evident that the MSD value of Casur at 313 K is 5 times larger than that value at 253 K. Additionally, at 313 K, there is a more pronounced increase in the MSD value of Casur during the later stage of the transport process. This can be attributed to the extensive delamination of the epoxy resin at this temperature (see Sect. "The evolution process of the epoxy/C–S–H interface."), leading to the loss of protection at the epoxy resin interface and a greater tendency for Casur to become free to move. From Fig. 7b, it can be observed that the MSD values of OW exhibit a uniform gradient difference within the range of 0–2000Ps, regardless of the different evolution of the epoxy/C–S–H interface. This presents that the motion state of water molecules is hardly affected and that the MSD values exhibit a characteristic that is solely controlled by the temperature factor. From the observations in Fig. 7, it is clear that the diffusion of Casur and Ow shows a positive correlation with temperature. However, it is important to note that the MSD curve of Casur exhibits less smoothness compared to that of water molecules within the pore, and its magnitude is significantly smaller by an order of magnitude. This can be attributed to the complex structure of the epoxy/C–S–H interface. The cross-linked epoxy resin serves as a barrier, limiting the infiltration of most water molecules, but it also hinders the movement of Casur ions. As a result, Casur faces difficulty in penetrating this "barrier" and experiences constrained spatial mobility. By fitting the slopes of the curve in Fig. 7, Table 2 presents the diffusion coefficients of OW and Casur at different temperatures. This provides a more visual representation of the differences in diffusion performance between OW and Casur, as well as the observed phenomenon of enhanced atomic diffusion with increasing temperatures.

Figure 7
figure 7

MSD of a Casur; and b OW.

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Table 2 Diffusion coefficients of Casur and OW at different temperatures
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The evolution process of the epoxy/C–S–H interface.

The investigation of the coordination within the epoxy molecules aims to understand the clustering mechanism. The RDF curves in Fig. 8a and b exhibit multiple peaks, which can be attributed partly to the presence of numerous covalent bonds within the epoxy, resulting in a stable structure. However, it also indicates the tendency of the epoxy to form clusters to some extent. Similarly, the inherent covalent bond structure of the molecules leads to minimal differences in RDF peak positions at different temperatures. However, it cannot be ruled out that temperature factors may influence the clustering within the epoxy. Therefore, based on the analysis of the transport phenomena discussed in Sect. "Transport of water solution in epoxy-modified C–S–H nanopores", it can be concluded that the epoxy is more prone to form cluster at lower temperatures, whereas the probability of cluster formation decreases in environments above 293 K. Figure 9 illustrates the MSD curves of oxygen atoms in the epoxy. An interesting phenomenon can be observed: the first 600 ps of transport, the MSD curve of Oe at 313K is actually the lowest among the four temperature conditions, and the diffusion coefficient (slope) follows the same trend. Meanwhile, the depth of water infiltration is the highest at this temperature. It can be speculated that 313 K represents a temperature threshold at which water molecules no longer drive the clustering of the epoxy (clustering leads to higher MSD values for epoxy in 253K, 273K, and 293K). Instead, due to their higher velocity, water molecules directly penetrate through the epoxy and move deeper into the pore.

Figure 8
figure 8

Coordination of main atoms in epoxy molecules at different temperatures a RDF of Oe–He; b RDF of Oe-Oe.

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Figure 9
figure 9

MSD curve of oxygen atom Oe in epoxy resin.

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To quantify the degradation of the epoxy/C–S–H interface, the number of epoxy atoms lost near the C–S–H interface at different time steps was collected. By calculating the ratio of this number to the initial number of epoxy atoms near the C–S–H interface, a discrete data model of epoxy detachment rate over time was created, as shown in Fig. 10a. After fitting the data, it was observed that the epoxy detachment rate follows a linear relationship with simulation time. Furthermore, as the temperature increases, the slope of the linear function also increases. This indicates a stronger correlation between water infiltration time and epoxy detachment rate, which is detrimental to the stability of the epoxy/C–S–H interface.

Figure 10
figure 10

Quantitative characterization of epoxy resin viscosity a debonding rate-time fitting; b debonding rate-immersion depth discrete point model.

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Figure 10b presents a discrete data model showing the epoxy detachment rate as a function of immersion depth into the C–S–H gel pores. It is evident that as the water infiltration into the C–S–H gel becomes more severe, the epoxy detachment rate increases. However, there is an interesting observation to explore further. All the data points in the plot are divided into two parts precisely at the coordinate point (55Å, 55%). In the four temperature models, when the immersion depth is less than 55Å, the data points are located below the proportional function. This indicates that during the early stages of water infiltration, the rate of epoxy detachment relative to the immersion depth greater than 55Å appears to be slower. In other words, as the depth of pore infiltration increases, the epoxy/C–S–H interface is more affected by water erosion, increasing the likelihood of epoxy detachment from the C–S–H surface. The influence of temperature on this phenomenon is relatively small, as the same pattern is observed across the four temperature models. However, this observation is closely related to the time duration of water immersion on the epoxy/C–S–H interface under the same immersion depth.

Table 3 provides a numerical summary of the influence of temperature on capillary transport of water molecules in epoxy-modified calcium silicate hydrate nanopores.

Table 3 Summary of the influence of temperature on capillary transport of water molecules in epoxy-modified calcium silicate hydrate nanopores
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Conclusions

In this study, MD simulation was employed to investigate the effect of temperature on capillary transport of water molecules in epoxy-modified calcium silicate hydrate nanopore. Temperature changes lead to epoxy resin clustering or debonding at the C–S–H interface, affecting pore size and water transport efficiency. In brief, higher temperatures worsen damage to the epoxy-modified C–S–H interface, while enhancing water movement in gel pores. The main findings are as follows:

  1. (1)

    At 253 K and 273 K, the epoxy-modified C–S–H interface performs well. The epoxy resin reduces the surface’s hydrophilicity, aggregating at the interface, which narrows transport openings and hinders capillary action in gel pores. At 293 K, epoxy exists in a state between clustering and debonding, causing pore blockage. Despite deeper water penetration, the ratio of capillary transport slows. At 313 K, the epoxy-modified C–S–H interface completely degrades, eliminating transport inhibition by the epoxy coating.

  2. (2)

    An increase in temperature enhances the activity of various atoms, which is detrimental to the formation of stable coordination between atoms. Simultaneously, water molecules will invade the epoxy-modified interface, displacing the coordination points of Oe near Ca. This further accelerates the degradation of the epoxy-modified C–S–H interface.

  3. (3)

    Under the coupling effect of temperature and water erosion, the proportion of epoxy detachment from the C–S–H interface exhibits a linear relationship with time. In addition, the increased penetration depth of water molecules leads to a significant increase in the detachment rate of epoxy.

In summary, the behavior of capillary transport for water molecules within epoxy-modified calcium silicate hydrate (C–S–H) nanopores exhibits responsiveness to temperature fluctuations. Varied temperature settings distinctly influence both the activities of water molecules and the internal morphologies of these nanopores. This finding provides valuable insights for the development and durability design of cementitious materials. Further research is needed to elucidate the effects of different transporting liquids (carrying harmful ions in solutions), calcium-to-silicon ratios, and modified materials on capillary transport behavior. A holistic understanding of these factors promises to illuminate the nuanced mechanisms governing capillary transport within C–S–H nanopores. Such comprehensive insights bear significant implications for the evolution of advanced cement-based materials and their applications in engineering.