Molecular dynamics and experimental study on the adhesion mechanism of polyvinyl alcohol (PVA) fiber in alkali-activated slag/fly ash

Abstract This paper aims to study the adhesion mechanism of polyvinyl alcohol (PVA) fiber within alkali-activated slag/fly ash (AASF) matrix using molecular dynamics (MD) simulation in combination with systematic experimental characterization. The adhesion of PVA to C-(N-)A-S-H gel with different Ca/(Si+Al) and Al/Si ratios was modeled using MD simulation, with the related adsorption enthalpy calculated and the adhesion mechanism explored. The experimentally attained chemical bonding energy of PVA fiber in AASF coincides well with the simulation results. In both cases, the adhesion enhances primarily with increasing Ca/(Si+Al) ratio of C-(N-)A-S-H gel. Additionally, MD simulation indicates preferential element distributions of Ca around PVA molecule, which was confirmed experimentally by the detection of the Ca-rich C-(N-)A-S-H gel in the interfacial transition zone (ITZ). This study provides further insights into the adhesion mechanism of PVA fiber to C-(N-)A-S-H gel formed in AASF, which is particularly valuable for the future development of PVA-based high-performance alkali-activated composites.


Introduction
Alkali-activation technology has been considered as a promising approach to transforms different wastes and industrial by-products into cement-free building materials. Alkali-activated materials (AAMs) including those geopolymers are derived by the reaction of an alkali metal source (solid or dissolved) with a solid alumino-silicate powder [1,2]. Compared with conventional cementitious binders, AAMs are environmental-friendly with a considerable reduction of global warming potential and embodied energy [3][4][5]. Meanwhile, AAMs as binder material for concrete could maintain comparable mechanical properties and even better durability under different exposure conditions [6][7][8][9]. Therefore, AAMs serve as a promising alternative binder material for sustainable construction and perfectly meet the Sustainable Development Goals (SDGs) by the United Nations. Among all AAMs, the ones based on blast furnace slag, class F fly ash, and their blends are most intensively studied due to the large quantity of annual production as well as the relatively stable chemical compositions of these two solid precursors [1,2,10,11]. Previous studies on the slag/fly ash-based AAMs system, or namely alkali-activated slag/fly ash (AASF), have focused on microstructure development, nature of reaction products as well as mechanical properties [12][13][14][15][16]. The application of AASF for engineering practices has been also greatly promoted.
However, AAMs as binder materials are found to be also inherently (quasi-)brittle like conventional cementitious binder [17][18][19][20] and thereby susceptible to cracking. Both alkali-activated fly ash-based concrete [17,18] and alkali-activated slag concrete [19,20] exhibited a higher brittleness than its OPC concrete counterpart with similar compressive strength. Previous studies reported that the brittleness of AASF-based concrete is at least comparable to that of OPC concrete with similar compressive strength [21,22]. As one of the classic approaches in controlling the brittleness of cementitious materials, fiber reinforcement has been researched in AAMs systems and was found to hold promises in achieving advanced fracture and tensile performances [23][24][25][26].
For the development of PVA fiber reinforced cementitious and/or alkali-activated composites such as SHCC and SHGC, the fiber/matrix interface properties are crucial. Many previous studies thereby focused on the characterization and modification of PVA fiber/matrix interface properties and single-fiber pullout tests have been widely used to determine the interface properties [28][29][30]. Among the interface properties, the chemical bonding energy (G d ) due to adhesion between the PVA fiber and the reaction products plays an essential role. However, the available studies concerning the adhesion of PVA fiber within AAMs are still rare. Only a few experimental studies on the interface bonding properties of PVA fiber in alkali-activated matrices could be found. For instance, Ohno and Li studied the interface properties [23] of PVA fiber in a fly ash-based geopolymer matrix after strength optimization. They found that, in comparison to those in conventional SHCC materials, the value of G d is almost 5 times higher while the frictional bond and tendency for slip-hardening behavior is considerably lower. Nematollahi et al. tested the interface properties of PVA fiber/matrix properties in alkali-activated fly ash mixtures. The influence of using both sodium and potassium silicate-based activators and the surface oiling treatment on the interface properties were addressed [24]. Besides, the correlations of G d with frictional bond and slip-hardening behavior were suggested. Additionally, Nematollahi et al. concluded that strong chemical bonding of PVA fiber within a one-part AASF matrix could effectively enhance the fiber-bridging strength of the composite [26]. Zhang et al. investigated the interface properties of PVA fiber within AASF matrices and reported that G d is predominantly related to microstructure and reaction product chemistry, which could be effectively modified by changing the silicate modulus of alkaline activator [25]. However, the scope of most of these studies is limited to the mesoscale experimental determination of interface properties and their impact on the composite behavior. In all these works, the main purpose of interface characterization relates to the development of SHGC. The adhesion mechanism of PVA fiber within AAMs, however, has seldom been discussed.
Due to the limitations of current experimental techniques at the necessary length-scale, speculation into the interaction between an organic matter (PVA fiber) and an inorganic matrix (AAMs) is not straightforward. As a result, many researchers used molecular dynamics (MD) simulation to provide a complementary understanding of the experimental findings concerning the adhesion at micro/meso scales, which was achieved by looking into the interface interaction to provide insights on the adhesion-related mechanical properties [31]. Most of the times, the adhesion properties were studied by the implementation of molecular dynamics (MD) to calculate critical values of the interaction energy (including adsorption enthalpies). Besides, the interfacial connection mechanism could be also unraveled by investigation of the interaction between organic matter and inorganic matrix using different force fields. Several studies could be found concerning the adhesion properties between the cementitious matrix and different organic matter, which includes polymer fiber [32], polymer additives [33,34], and epoxy resin [35,36]. However, the studies on adhesion between PVA fiber and alkali-activated matrix are still rare. Since the main reaction product in the cementitious matrix and the alkali-activated matrix is not the same, the knowledge on the influence of reaction product chemistry on the adhesion properties of PVA fiber as well as its interaction mechanism with the AAMs system such as AASF is still largely unknown.
This study aims to provide better understanding on the PVA fiber/ AASF matrix adhesion mechanism. Through MD simulation, the influence of reaction product chemistry on the PVA fiber adhesion within AASF matrices is modeled and the preferential element distribution around PVA fiber is determined. Furthermore, the corresponding microscale characteristics of adhesion influenced by reaction product chemistry were also studied experimentally through single-fiber pullout tests. Besides, the influence of PVA fiber on the spatial element distribution of reaction products was experimentally confirmed. This study offers new insights into the adhesion properties and adhesion mechanism of PVA fiber within C-(N-)A-S-H type reaction products within AASF and thereby also contributes to the fundamental design basis for the development and tailoring of PVA-SHGC based on alkali-activated matrices.

The starting point for MD simulation
Many studies have reported the chemical composition and phases within the reaction products of sodium silicate-based AASF. When the slag content is dominant (≥50 wt%), the AASF is considered to be a high or intermediate calcium AAMs system with typical main reaction products of C-(N-)A-S-H gel along with minor phases like hydrotalcite and possible coexistence of (N,C)-A-S-H gel [3,12,[37][38][39]. The traces of calcium-free N-A-S-H type gel is rarely reported in AASF. This is because N-A-S-H is only stable at low pH values (<12) in a Ca-rich alkali-activated system [40]. The system with high pH favors the formation of C-A-S-H type gel to the detriment of N-A-S-H type gel, with the experimental evidence showing the coexistence of C-A-S-H and N-A-S-H leads to degradation of N-A-S-H and its transformation to C-A-S-H until equilibrium conditions are reached [41]. In fact, it has been confirmed by our previous study that the C-(N-)A-S-H gel is the predominant binding phase in sodium silicate-based AASF [39,42]. Consequently, this study focuses on the adhesion between PVA fiber and the C-(N-)A-S-H gel as the main binding phase in AASF.
For the MD simulation, the chemical composition of C-(N-)A-S-H gel by EDX spot analysis in AASF matrices is selected as the starting point for the construction of the C-(N-)A-S-H models. Notably, these AASF matrices share similar mixture designs for experimental testing in the current study [39]. Based on this, five C-(N-)A-S-H models were considered covering various Ca/(Si+Al) and Al/Si ratios, from 0.5 to 1.3 and from 0.25 to 0.5 respectively. Further discussion concerning the correlation between the chemical composition of the C-(N-)A-S-H models and the AASF matrices will be provided in Section 3.4.1.

Construction of the C-(N-)A-S-H model
The C-(N-)A-S-H models were created following the procedure described by Pellenq [43] and refined by Qomi [44], based on the modification of the structure of tobermorite 14 Å minerals. In the construction of the C-(N-)A-S-H model, the restrictions imposed by Kovačević [45] and Kumar [46] in their procedures were also considered to avoid the presence of monomeric species. The construction procedure is shown schematically in Fig. 1.
In the first step, the structure of the tobermorite 14 Å described by Bonaccorsi et al. [47] is taken as the starting point for building the C-(N-)A-S-H model. The unit cell of this mineral is replicated to obtain a simulation box with dimensions in the x, y, and z directions of 5.2 nm × 6.2 nm × 3.3 nm, respectively, and periodic boundary conditions (PBC) were applied to approximate to an infinite system. The chemistry of the tobermorite mineral was modified in a second step to reach the desired composition of the C-(N-)A-S-H gel. To this effect, all water molecules were removed from the interlaminar spaces and some bridging silicate groups were deleted randomly. The remaining bridging silicates are partially substituted by aluminates to adjust the Al/Si ratio to values between 0.25 and 0.5. The negative charge generated by the replacement of Si 4+ by Al 3+ is compensated by inserting one Na ion per Al. Additionally, Ca is added to match the Ca/(Si+Al) ratio, increasing it from 0.83 (the typical value of tobermorite 14 Å minerals) up to 1.3, while no silicate monomers are generated [45,46]. To reach values below 0.83, the interlaminar Ca is replaced by Na ions.
Once the Ca/(Si+Al) and Al/Si ratios are adjusted, water is reintroduced in the pore space using a geometry-based algorithm [48] up to a density of 1 g/cm 3 and the structure was equilibrated in the following step. The LAMMPS code [49] and the force field ReaxFF [50] were used to perform an energy minimization and MD simulations in the isobaricisothermal ensemble (NPT) at room conditions (300 K and 1 atm) for 5 ns with barostat and thermostat coupling constants of 0.2 and 1 ps, respectively. ReaxFF is a reactive force field that allows the structural and chemical relaxation of the C-(N-)A-S-H gel. Thus, water molecules can dissociate into hydroxyl groups in the new Q 1 sites formed after the bridging silicate deletion [51].
The last step comprises the expansion of the pore space (1.5 nm) to accommodate the PVA molecules. Then, the pore is filled with water and the PVA/C-(N-)A-S-H composite is equilibrated using a combination of CSHFF [52] and CHARMM [53] force fields to describe the C-(N-)A-S-H gel and the PVA fiber. An initial relaxation was conducted in the canonical ensemble (NVT) for 0.5 ns at 300 K with the thermostat coupling constant of 0.1 ps, followed by further equilibration in the isobaricisothermal ensemble (NPT) at room conditions (300 K and 1 atm) with barostat and thermostat coupling constants of 0.2 and 1 ps, respectively. A final MD simulation, long enough to capture all the properties properly, was carried out in the canonical ensemble for 0.1 μs at 300 K. The lattice parameters and densities of the different PVA/C-(N-)A-S-H composite after equilibration are shown in Table 1.

Construction of the PVA molecules
The Avogadro Builder [54] was employed to create the PVA molecules formed by 100 monomeric units of vinyl alcohol as shown in Fig. 2. The structure of the PVA molecules was equilibrated by performing MD simulations using the LAMMPS simulation package [49]. CHARMM force field [53] was used to describe the bonding and non-bonding interactions in the PVA molecules, while the atomic charges were derived by electrostatic potential (ESP) analysis of DFT results, using the ChelpG scheme [55].
First, energy minimization was performed, relaxing the atomic positions of the molecule and its simulation box. Then, the structure of the PVA molecules was equilibrated in the canonical ensemble (NVT) at 300 K during 2.5 ns, with a time step of 0.5 fs and a thermostat coupling constant of 0.1 ps. Finally, the atomic positions and the volume of the simulation box were further relaxed in the isobaric-isothermal ensemble (NPT) at 300 K and 1 atm for another 2.5 ns with a thermostat and barostat coupling constants of 0.1 ps.

In situ polymerization
The in situ polymerization of the C-(N-)A-S-H gel was performed using monomeric species including Ca(OH) 2 , Si(OH) 4, and Al(OH) 4 Na. The complicated polymerization process from these monomers to C-(N-) A-S-H gel and the interfacial potential reactions between PVA and the monomers are crucial factors to reveal the microstructures of the matrix and the interfacial transition zone (ITZ). GULP was used to perform this in situ polymerization, which consists basically placing a PVA fiber and the precursors Ca(OH) 2 , Si(OH) 4, and Al(OH) 4 Na into a simulation box with dimensions 4 nm × 4 nm × 4 nm in the x, y and z directions, allowing the formation of C-(N-)A-S-H gel under the influence of PVA fiber. To this effect, a combination of the reactive Garofalini potential [56] for the polymerization of the C-(N-)A-S-H gel and CHARMM force field [53] for the PVA molecules was employed. The polymerization requires high temperatures and long simulation times, so the samples were equilibrated in the canonical ensemble (NVT) at 1500 K for 5 ns, with a time step of 0.5 fs and a thermostat coupling constant of 0.5 ps.

Interaction between the PVA fiber and the C-(N-)A-S-H gel
In the MD simulations, the PVA/C-(N-)A-S-H composites are built placing the PVA fiber in the center of the expanded pore at about 0.7 nm from the C-(N-)A-S-H surface. During the relaxation of the system, it is observed that the PVA fiber approaches the C-(N-)A-S-H surface, with the hydroxyl groups pointing towards C-(N-)A-S-H surface. Accordingly, the structural and compositional differences of the C-(N-)A-S-H models with different Ca/Si and Al/Si ratios should influence the interaction with the PVA molecules. Thus, the radial distribution function (RDF) and the coordination number (CN) can provide useful information about the interactions in the PVA/C-(N-)A-S-H composites. The RDF gives the probability of finding an observed particle as a function of a distance, between r and r+dr, from a reference particle, in this way describing the density variation as a function of the distance. It is calculated using the following equation [57]:  Table 1 Lattice parameters and densities for the PVA/C-(N-)A-S-H composites after MD equilibration at the studied Ca/(Si+Al) ratio with Al/Si ratio of 0.5.
where r i and r j define the position vectors of the particle i and j. The parameter δ takes the value 1 in the interval [− w, w) (with w being the bin width), otherwise 0. This function can be used to link the microscopic details to macroscopic properties since the computed RDFs can be compared with experimental RDFs obtained from neutron and X-ray diffraction, allowing the validation of the atomic structure of the simulated composites [58]. In this case, the RDFs were computed to study the microscopic adhesion mechanism of the PVA fiber to C-(N-)A-S-H gel and its association with experimental proofs were later discussed in Section 3.4.2.
The integration of the RDF gives the CN, which can be defined as the total number of particles that a reference particle holds as neighbors within a shell between r and r+dr. The CN of a certain atom is given by the following Eq. (2): where ρ the atomic density.
In particular, the RDFs and CNs of the hydroxyl groups of the PVA fibers were calculated with the cations and with the oxygen atoms from the C-(N-)A-S-H surfaces to analyze the evolution of the interaction with various Ca/(Si+Al) and Al/Si ratios.

Experimental testing 2.2.1. Materials and mixture design
The solid precursors were ground granulated blast furnace slag and Class F fly ash according to ASTM 618. Material density for slag is 2890 kg/m 3 and 2440 kg/m 3 for fly ash. The d50 particle size is 17.88 μm for slag and 33.19 μm for fly ash. The chemical compositions deduced from X-ray Fluorescence along with other properties of precursors (including the loss on ignition (LOI) at 950 • C and the fineness passing 45 μm) are shown in Table 2. As reported in our previous studies [16,25], the main crystalline phases determined by powder X-ray diffraction (XRD) in fly ash are quartz, mullite, and hematite, while the blast furnace slag contains mainly amorphous phases (>95%). The reactivity of fly ash is reflected by its reactive silica content (43.04%) and reactive alumina content (14.51%) as determined by selective chemical dissolution [16]. A polyvinyl alcohol (PVA) fiber with 1.2% oiling on the surface was used, and the mechanical and physical properties of which are presented in Table 3. The alkaline activator was a sodium-based silicate solution prepared by dissolving NaOH pellets (analytical grade, purity ≥98%) and sodium silicate (Na 2 O: 8.25 wt%, SiO 2 : 27.50 wt%) in distilled water.
Five levels of silicate moduli (ratio of SiO 2 wt% to Na 2 O wt%) of alkaline activator were considered for preparation of AASF matrices with a fixed binder combination of 50 wt% blast furnace slag and 50 wt % class F fly ash. The detailed mixture designs are shown in Table 4. In all mixtures, the w/b ratio and Na 2 O content (in alkali activator with respect to total binder mass) were kept constant to be 0.32 and 4%, respectively. This w/b ratio was chosen to maintain adequate workability for all the paste mixtures. The mixtures were named M0.5, M0.8, M1.0, M1.2, and M1.5 accordingly, with the number representing the silicate modulus.
For sample preparation, the solid precursors were firstly dry mixed for 5 min using a HOBART® mixer at a low speed. Alkaline activator solution was then added gradually, and the batches were mixed for an additional 5 min at a medium speed. The fresh pastes mixtures were cast in a specially made mould for fiber pullout tests and small polyethylene vessels for ESEM/EDX analysis. The cast samples were further compacted with a vibration table before finally sealed with a plastic foil. After 1 day, the samples were demolded and were cured in a climate room (20 • C and ≥98% RH) until 28 days before testing.

ESEM/EDX characterization
Chemical compositions of reaction products in AASF matrices and within the fiber/matrix interfacial transition zone (ITZ) were characterized by environmental scanning electron microscopy (ESEM) and energy dispersive X-ray (EDX) analysis, using a Philips-XL30-ESEM equipped with Thermofisher UltraDry EDX detector. All    characterizations on the matrix and ITZ were conducted using paste samples at 28 days. Mixtures including M0.5-M1.5 were used for the characterization of reaction product composition in AASF matrices. For the interface characterization on element distribution within ITZ around PVA fiber, only the M1.0 specimen was used as a representative example. The samples were prepared following the method for single fiber pullout tests as described in Section 2.2.2, It is important to note that PVA fiber with a diameter of 300 μm was used for better clarification of fiber/matrix interface as well as ITZ. EDX analysis of flat-polished samples is used to determine the phase assemblage in AASF matrices [59,60]. The reaction of investigated samples was stopped by solvent exchange using isopropanol followed by low vacuum drying. Before ESEM analysis, the samples were then impregnated using low viscosity epoxy resin and polished down to 0.25 um. The polished samples were examined for the observations of microstructure and backscattered electron (BSE) images were taken at an accelerating voltage of 15 kV. Additionally, the polished samples were carbon-coated before EDX measurement under high vacuum mode. The analysis was performed on the chemical compositions of the reaction products in AASF matrices and those around PVA fiber. Both spot analysis and line analysis were carried out. It should be noted that the atomic number, absorption, and fluorescence (ZAF) corrections were made in each EDX measurement, which is an implemented function in the Pathfinder software. ZAF corrections could convert apparent concentrations (raw intensities) into corrected concentrations to eliminate inter-element matrix effects, which makes it possible for semiquantitative comparisons of element ratios.

Single-fiber pullout test
The adhesion properties of PVA fiber in M0.5-M1.5 AASF matrices were experimentally tested by single-fiber pullout tests following Redon et al. [28]. A mould with two-layer polyethylene bricks developed by Katz and Li [61] was used for casting as shown in Fig. 3 (a). A filamenttype PVA fiber with a diameter of 40 μm was first cut, aligned, and fixed onto the bottom layer block using double-sided tape. Afterwards, the fibers were allowed for embedment into the matrices during the casting of fresh mixtures. The samples were put on a vibration table to remove entrapped air before sealing with plastic wrap. After 24 h, the samples were demolded and transferred to a climate room (20 • C and 95% RH) until 28 days. At 28 days, the hardened samples were cut into very thin specimens using a low-speed saw (Minitom, Struers) with fiber extruded out from one side (see Fig. 3 (b)). The embedded length (L e ) of PVA fiber was controlled to be around 1 mm to avoid fiber rupture while providing enough information for the bonding behavior during the pullout.
A micro tension-compression testing device (Kammrath & Weiss) shown in Fig. 4 (a) was used for single-fiber pullout tests. Both the surface of the thin specimen and the free end of the PVA fibers were glued to two small metal blocks. Afterwards, they were mounted on the testing device using two metal blocks, which were fixed to an actuator and a load cell. A 10 lb. (44.48 N) load cell was included in the system for pullout load testing with an accuracy of 0.1%. Displacement controlled pullout was used with a constant displacement rate of 0.01 mm/s. At least 20 tests were conducted for each matrix.

Coordination of PVA to Ca and Na
The radial distribution functions (RDFs) of Ca and Na ions with the oxygen atoms from PVA molecules and their respective CNs for the composites with the considered Ca/(Si+Al) and Al/Si ratios are shown in Fig. 5. The coordination to the cations from the C-(N-)A-S-H surface can be related to the formation of electrostatic forces between the PVA molecules and the C-(N-)A-S-H gel.
As shown in Fig. 5, these plots show sharp peaks at distances around 2.0 Å and 2.2 Å for the RDFs of Na-O PVA and Ca-O PVA , respectively. These peaks correspond to the first coordination shell of the oxygen atoms of the PVA to the cations from C-(N-)A-S-H gel and consequently to the Ca-O PVA and Na-O PVA distances. It must be noted that neither the Ca/(Si+Al) ratio nor the Al/Si ratio affects Na-O PVA and Ca-O PVA distances. Nevertheless, as the Ca/(Si+Al) ratio increases from 0.75 to 1.2, the coordination of the PVA molecules to Ca ions grows progressively from 0.03 to 0.43 Ca ions per oxygen atom as a consequence of the higher Ca content. The increasing coordination to Ca ions provokes a slight decrease in the coordination of the oxygen atoms to the Na ions as the Ca/(Si+Al) ratio rises. This is because Ca is a divalent cation that can establish stronger electrostatic interactions with the negative charged functional groups of the PVA fiber and can displace the Na ions. It should be noted that the Ca/(Si+Al) ratio of 0.5 relates to the complete replacement of the interlaminar Ca by Na. This replacement (1 Ca 2+ by 2 Na + ) results in much higher Na content than in the other systems, explaining the high Na-O PVA coordination for that system. Regarding the effect of the Al/Si ratio, the CNs reveals that the coordination of PVA to Na is increased significantly due to the larger amount of Na at high Al/Si ratios. This can be better visualized in Fig. 6, which compares the values of the CNs for Ca and Na to the oxygen atoms of the PVA molecules at the studied Ca/(Si+Al) and Al/Si ratios.
The large capacity of the PVA fiber to coordinate with cationic species suggests that the incorporation of these polymers to the C-(N-)A-S-H gel may help to increase the Ca and Na content during the reaction. This behavior was analyzed by performing an in situ polymerization of the C-(N-)A-S-H gel in presence of a PVA fiber as shown in Fig. 7 (a). It should be noted that the precursors are present in the appropriate proportion to reach the average Ca/(Si+Al) ratio of 1.3 and the Al/Si ratio of 0.5. The Ca/(Si+Al) ratio is monitored as a function of the distance to the PVA fibers (see Fig. 7 (b)), computing the pair distribution function of those ratios around the oxygen atoms from PVA molecules. Here, the Ca/ (Si+Al) ratio is significantly higher around the PVA fibers than the average (1.3), suggesting that the incorporation of PVA during the synthesis of the C-(N-)A-S-H gel may result in higher Ca/(Si+Al) ratios.

Coordination of PVA to the C-(N-)A-S-H surface
Besides the interaction of the PVA fibers with the C-(N-)A-S-H gel through the Ca and Na cations from the surface, the formation of hydrogen bonds is also possible between the hydroxyl groups of the PVA molecules and the oxygen atoms from the surface. The RDFs and CNs of H atoms of the hydroxyl groups in PVA fibers to the oxygen atoms of the C-(N-)A-S-H surface are plotted in Fig. 8, which can be used to investigate the formation of hydrogen bonds between the polymer and the matrix [33].
It is observed that the main peak of the RDFs is around 1.8 Å, which matches the characteristic distance between the donor H atoms and the acceptor O atoms in hydrogen bonds [62,63]. As shown in Fig. 9, the CNs reveal that the coordination between the donor H from the PVA fibers and the acceptor O atoms from the surface decreases as the Ca/ (Si+Al) ratio increases and the Al/Si ratio decreases, suggesting that there is a higher number of hydrogen bonds between the PVA molecules and the C-(N-)A-S-H gel at low Ca/(Si+Al) ratios and high Al/Si ratios. The reduction at higher Ca/(Si+Al) ratios is attributed to the greater Ca content, which can prevent the formation of hydrogen bonds by coordinating to the hydroxyl groups, while the presence of Na ions does not hinder the formation of the hydrogen bonds between the PVA and the C-(N-)A-S-H surface, probably due to the smaller size and charge than those of Ca ions.
It is also essential to determine the angle of the hydrogen bonds between the hydroxyl groups of the PVA fibers and the oxygen atoms from the C-(N-)A-S-H surface since the strength of these bonds is strongly dependent on the bonding angle. The maximum strength is achieved when the three atoms involved in the hydrogen bond are aligned so that the donor H points directly to the acceptor electron pair [64].

To analyze the most probable distances and angles for hydrogen bonding in the PVA/C-(N-)A-S-H composites, a combined distribution function (CDF) of H PVA ⋯O C-(N-)A-S-H distances and O PVA -H PVA ⋯O C-(N-)A-
S-H angles was calculated and was illustrated in Fig. 10.
The CDF shown in Fig. 10 indicates that the most probable distance between donor hydrogen atoms and acceptor oxygen atoms from the C-(N-)A-S-H surface is around 1.8 Å, as seen in the RDFs, while the most probable angle defined by those atoms and the donor oxygen atom from PVA is between 145 • and 165 • , which indicate that they are not fully aligned. It is remarkable that despite the structural and chemical differences, the most probable distances and angles for the hydrogen bonds are in the same range for all the composites analyzed in this study.

Adhesion mechanism of PVA in C-(N-)A-S-H gel
The functional form of the potential energy in the force fields (CSHFF [52] and CHARMM [53] force fields) employed in the MD simulations in this study includes bond terms to describe the interactions of the atoms       linked by covalent bonds and non-bonded terms that describe the electrostatic interactions and the van der Waals forces between particles. Since the PVA molecules are not covalently linked to the C-(N-)A-S-H surface, the interaction between them is due to electrostatic and van der Waals interactions. The adsorption enthalpy of PVA fibers in C-(N-)A-S-H gel for the different Ca/(Si+Al) and Al/Si ratios can be determined as indicated in Eq. (3), which serves as an indicator for the adhesion property.
where  Fig. 11, is more favorable as the Ca/(Si+Al) ratio rises regardless of the Al/Si ratio. This can be attributed to the higher Ca content as the Ca/(Si+Al) ratio increases, allowing the development of more electrostatic interactions between those cations and the PVA fibers, as illustrated in Fig. 6. Additionally, the stronger adsorption is observed with a lower Al/Si ratio, particularly when Ca/(Si+Al) is high (>1.0). The higher coordination of the PVA molecules to the Na cations at high Al/Si ratios may be responsible for the decrease in the adsorption strength, since the electrostatic interactions with Ca, a divalent cation, are much stronger than with Na, a monovalent cation.
In addition to the coordination of the PVA to the cations, there are also hydrogen bonds between the oxygen atoms from the C-(N-)A-S-H surface and the hydroxyl groups of the PVA fibers. Despite the lack of clear consensus on the nature of the hydrogen bonds, this study describes the hydrogen bonds as a sort of Van der Waals interactions and their contribution to the adsorption enthalpy could be estimated. To this effect, the enthalpy of a single hydrogen bond for the most probable H PVA ⋯O C-(N-)-A-S-H distance of 1.8 Å and O PVA -H PVA ⋯O C-(N-)-A-S-H angle of 160 • according to Fig. 10, and the value has been estimated to be − 4.84 kcal mol − 1 . Considering the number of H atoms from PVA coordinated to oxygen atoms from the C-(N-)A-S-H surface, the adsorption enthalpy due to the hydrogen bond network between the PVA and C-(N-) A-S-H gel can be estimated. As can be seen in Fig. 12, the values of these adsorption enthalpies in both unit (kJ/m 2 and kJ/g) are one order of magnitude smaller in absolute terms and its contribution to the total adsorption enthalpy ranges from nearly 15% in the composite with Al/Si and Ca/(Si+Al) ratios of 0.5 and 0.5 to 1.3% at high Ca/(Si+Al) ratios. It is found that the contribution to adhesion of the hydrogen bond network decreases as the Ca/(Si+Al) ratio rises and the Al/Si ratio declines, in agreement with the number of hydrogen bonds estimated in the previous section. Therefore, the contribution to the adhesion of the hydrogen bonds is only significant at low Ca/(Si+Al) ratios when the ionic concentration in the interlaminar space is low. At high Ca/(Si+Al) ratios, the adsorption mechanism of the PVA fibers in the C-(N-)A-S-H gel is almost exclusively electrostatic.

Experimental evidence
Experimental characterization was performed to provide further evidence of the adhesion properties and adhesion mechanism between PVA fiber and AASF matrix in addition to the MD simulations.

Chemical composition of AASF matrices
As indicated by the MD simulation, the chemical composition of C-(N-)A-S-H gel has a predominant influence on the adhesion properties between PVA fiber and AASF matrices. Hence, EDX point analysis was carried out on M0.5-M1.5 at 28 days to confirm the chemical nature of the main reaction product in AASF matrices. These points were selected carefully within the binder region, keeping sufficient distance from the unreacted particles [65]. A total of 80 to 90 measurements have been conducted for each AASF matrix. The microstructure of all AASF by BSE imaging tends to be quite similar and only one representative BSE image of the M1.0 matrix is shown in Fig. 13 (a). The binder region in darker grey color has a grey level between that of slag and fly ash and demonstrates a quite homogenous formation of reaction products and a dense microstructure with very limited capillary pores in black color. Additionally, the CaO-SiO 2 -Al 2 O 3 ternary diagram is plotted in Fig. 13 (b), in which Ca, Al, and Si are normalized to 100% on an oxide basis. Similar to [39], the experimental EDX data of all AASF matrices fall well in the region of AAS [66][67][68] as well as AASF [12][13][14][69][70][71][72], which again confirms the formation of C-(N-)A-S-H gel as the main reaction product in AASF paste. Also, the chemical compositions of the five C-(N-)A-S-H models for MD simulation are illustrated in the ternary diagram. It could be observed that the selected Ca/(Si+Al) and Al/Si ratios for C-(N-)A-S-H models provide a good estimation of the experimental data of all AASF matrices, particularly under low Ca/(Si+Al) ratios.
To further evaluate the consistency between the chemical  Fig. 14 (c) and (d) is also fitted with the simple Gaussian curve with the minimization of the least-squares using Origin Software. The characteristics of the fitted Gaussian distribution are thus characterized by its mean of the distribution (μ) and its standard deviations (STDs, or σ). According to the central limit theorem in statistics, the well-fitted Ca/(Si+Al) and Al/Si ratios indicate that the results are influenced by a large number of independent random variables. In this case, they could be different experimental errors induced by either the random error of the equipment and procedures, or the intermixing of multiple phases within reaction products. Most likely, the influence is due to the acquisition of information from an "interaction volume" within an EDX spot analysis. Under the acceleration voltage of 15 kV, the interaction volume has a radius of approximately 1.0-2.5 μm into the sample surface when this major reaction product is C-(N-)A-S-H gel [73], which causes intermixed analysis of phases. Although the mean of the distribution (μ) in each of the ratios could reasonably reflect the chemical composition of the intermixed phases, it cannot properly describe the true chemical composition of "pure" C-(N-) A-S-H gel. Considering the presence of remnant fly ash particles and unreacted silicate-based activator within the matrix, the intermixing is often towards Si-rich phases, which could lead to underestimation of the true Ca/(Si+Al) ratio. In contrast, the true Al/Si is possibly overestimated considering the higher Al/Si ratio (0.60) of fly ash. As a result, the higher end value of Ca/(Si+Al) ratio (μ+2σ) and the lower end value of Al/Si ratio (μ− 2σ) are selected to reflect the chemical composition following previous studies on C-A-S-H gel [59]. Notably, they correspond to the value at 95% level and 5% level of the Ca/(Si+Al) ratio and Al/Si ratio in its Gaussian distribution, respectively. These proposed chemical compositions of "pure" C-(N-)A-S-H gel determined experimentally along with the five C-(N-)A-S-H models for MD simulation are again plotted in the CaO-SiO 2 -Al 2 O 3 ternary diagram in Fig. 15. The grey-colored area constructed by the tie lines corresponds to the chemical compositions of the C-(N-)A-S-H gel covered by the MD simulation. It is evident that the proposed chemical composition of "pure" C-(N-)A-S-H gel with Ca/(Si+Al) ratio of 0.50-0.69 and Al/Si ratio of 0.30-0.36 fall well into the grey areas, which confirms the consistency between the C-(N-)A-S-H gel formed in M0.5-M1.5 AASF matrices. Consequently, the C-(N-)A-S-H model (Section 2.1.2) can reasonably represent the realistic C-(N-)A-S-H gel as the main reaction product in AASF matrices. Besides, the reliability of using these models as the basis for MD simulation is further substantiated.

Element distribution around PVA fiber
The influence of PVA fiber on the reaction products and the spatial  distribution of elements in the ITZ were studied by EDX element mapping and spot analysis on the reaction products in ITZ formed around PVA fiber. Fig. 16 illustrates EDX element mapping (Na, Mg, Al, Si, and Ca in atomic %) of the reaction products around PVA fiber. The higher brightness in the map represents the atomic concentration of certain elements regardless of different colors. As shown in Fig. 16, the correlation between Al and Si could be observed in fly ash particles. Slag particles, rich in Ca and Mg content, show a more homogenous Ca and Mg distribution. More significantly, the Ca map depicts a rim of reaction products with high brightness around PVA fiber, which distinguished itself from the dominant C-(N-)A-S-H gel in median brightness within the AASF matrix. This indicates the formation of a Ca-rich reaction product near the fiber/matrix interface in comparison to the reaction products away from PVA fiber. Notably, other elements including Na, Mg, Al, and Si, on the other hand, do not show preferential space distribution due to the presence of PVA fiber. The EDX spot analysis in the ITZ between fiber and matrix was conducted to further determine the detailed chemical nature of the reaction products and the results are presented in a CaO-SiO 2 -Al 2 O 3 ternary diagram in Fig. 17 (a). Except for the evident increase of Ca, the reaction product in the ITZ has at least a similar Al/Si ratio in comparison with the one in the matrix. On the contrary, the related Ca/ (Si+Al) ratio (1.44) is considerably higher than that in the matrix (0.53). Fig. 17 (b) gives the representative EDX spectra for both reaction products. Considering the similarity between the two EDX patterns, the reaction product formed within ITZ near the PVA fiber is believed to be a kind of Ca-rich C-(N-)A-S-H gel to be distinguished from the C-(N-)A-S-H gel formed in AASF matrix. Another possibility relates to the formation of a portlandite (CH) layer at the PVA fiber surface, which was reported in previous studies concerning PVA fiber reinforced cementitious composite. The adhesion properties of PVA fiber in the cementitious matrix are also believed to be closely related to the CH layer in the ITZ [30,74]. The formation of CH in the AASF system is highly unlikely at ambient  temperature since the solubility product K sp of CH is much higher than of C-(N-)A-S-H gel [75]. In this case, the preferential formation of the amorphous C-(N-)A-S-H gel will be dominating the reaction process over the formation of crystalline phases as predicted by thermodynamics modeling [42,76]. This evidence also effectively precludes the possibility of the intermixing of C-(N-)A-S-H gel with CH. In fact, the main reaction products of sodium silicate-based AASF is reported to be amorphous [12,71,77] and seldom has new crystalline phases except for hydrotalcite has been reported.
Additionally, to reveal the influence of PVA fiber on the elemental space distribution and element ratios of reaction products within ITZ, carefully selected EDX Line scans from an AASF matrix to the PVA fiber were performed to avoid visible unreacted slag and fly ash. The chemical compositions in terms of atomic percentage of Na, Mg, Al, Si, and Ca are plotted representatively in Fig. 18. As demonstrated, the concentration of elements including Na, Mg, Al, Si decrease progressively from the ITZ to the PVA fiber region. Some fluctuations of element concentrations are detected within the ITZ, which is due to the heterogeneous characteristics of the AASF matrix. Particularly, a substantial decline of Si along the line into the PVA fiber region is observed, indicating the reaction products within ITZ is also dominated by Si content along with Ca. On the other hand, the concentration of Ca experiences a marked increase within ITZ before its continuous decrease into the fiber region. Furthermore, the corresponding atomic ratio of Ca/Si and Ca/(Si+Al) are also plotted in Fig. 18. Both element ratios significantly increase within the ITZ and reach maximum precisely at the fiber/matrix interface. All these above-mentioned findings are well in line with the EDX spot analysis indicating Ca-rich reaction products at the ITZ. Additionally, the relatively stable Mg concentration within ITZ precludes the contribution of extra Ca by the unreacted slag in the EDX analysis. Notably, it also indicates the presence of PVA fiber has no significant influence on the Mg distribution or the related formation of hydrotalcite, which was detected to be strongly intermixed with the C-(N-)A-S-H gel [78]. Thus, the hypothesis of Ca-rich C-(N-)A-S-H gel formation at the fiber/matrix interface is further justified.
These results from EDX coincide well with the MD simulation results of RDF and CNs of Ca, Si, Al to O PVA as well as the in situ polymerization results (Section 3.1), which all indicate a strong affinity of Ca 2+ cation and weak interaction of Si and Al to PVA fiber. This is significant since it serves as experimental evidence that the inclusion of PVA fiber into the AASF matrix could have a non-negligible impact on the formation of reaction products at least in the ITZ. This could be the reason for the differences found between G d of PVA fiber in AAMs systems and cementitious systems [23][24][25]. Furthermore, this effect leading to the formation of Ca-rich C-(N-)A-S-H gel in the ITZ will have considerable influence on the adhesion properties and is thereby essential for interface modification for high-performance alkali-activated composite based on AASF. Finally, unlike those of Ca, the RDF and CN of Na to O PVA shows no strong affinity around PVA fiber, which could be due to the very abundant concentration of Na in the pore solution throughout the

Chemical bonding energy between PVA fiber and AASF matrix
The single-fiber pullout load-displacement curves of PVA fibers embedded in the M1.0 AASF matrix are shown in Fig. 19 (a). The general profile of a single-fiber pullout curve can be decomposed into three main regimes [28]. Initially, a stable fiber debonding process occurs along the fiber/matrix interface. The load resisted by the fiber is increasing up to P a when the debonded length L d equals the fiber embedded length L e . The fiber was then fully debonded but the embedded fiber end was not yet moving. At this point, the displacements were only contributed by the elastic stretching of the debonded fiber segment and the free length. The sudden load decrease from P a to P b corresponds to the chemical bonding energy (G d ). Finally, the fiber starts to slip in the slippage phase, in which the pullout is resisted by frictional forces. The fiber undergoes sliding with an evident slip-hardening effect, characterized by the coefficient β (β>0) [80]. Slip-hardening occurs due to their lower rigidness in comparison to the surrounding matrix. The accumulated damages on the fiber surface could induce a so-called 'jamming' effect, which leads to an increasing fiber pullout resistance.
The adhesion between PVA fiber and the AASF matrix was quantified based on single-fiber pullout tests. The debonding process during the fiber pullout is assumed to be a tunnel crack propagation along the fiber/matrix interface, which is resisted by the debonding fracture energy [81]. This assumed fracture energy is also widely known as the chemical bonding energy G d between PVA fiber and matrix and could be calculated using Eq. (4) [28].
where E f , d f, and L e are the elastic modulus, diameter, and embedded length of the PVA fiber, respectively. P a is the load up to full debonded length (debonded length L d =embedded length L e ) and P b is the load when the fiber begins to slip. The G d of PVA in M0.5-M1.5 AASF matrices in box plots are summarized in Fig. 19 (b). Each of the box plots is derived from at least 16 individual pullout tests. It is worth noting that relatively large standard deviations (STD) have been observed for G d , which can be the result of an inhomogeneous distribution of reaction products around PVA fibers. Previous studies on interface properties using single-fiber pullout tests also present quite large STDs [23][24][25]. Therefore, the data is considered reliable as long as the trend of influencing factors could be revealed. A clear trend of the average value of G d could be found in Fig. 19 (b), which decreases from 6.2 to 2.9 J/m 2 with increasing activator silicate modulus from 0.5 to 1.5. By increasing the silicate modulus, more available silica species were introduced into the matrix and consequently changed the global reaction and chemical nature of the reaction products [66,82,83], which is reflected by the decreasing Ca/(Si+Al) ratio. Therefore, G d is positively correlated with the Ca/(Si+Al) ratio of the C-(N-)A-S-H gel in matrices. This trend is compared with the MD simulation results and is depicted in Fig. 20. It is clearly shown that experimentally attained G d as a function of Ca/ (Si+Al) is well in line with the MD simulation results on the adsorption enthalpy, which also rises primarily with increasing Ca/(Si+Al) ratio of the C-(N-)A-S-H model. Compared with Al/Si ratio, the Ca/(Si+Al) ratio plays a more dominant role in determining the adhesion properties, which also agrees well with the MD simulation results suggesting that the favored absorption at a lower Al/Si ratio is only significant at high Ca/(Si+Al) ratio. Notably, the simulated adhesion enthalpy and the G d as adhesion property also present a certain gap with a difference in magnitude of 100 times regardless of the Al/Si ratio of C-(N-)A-S-H gel used for MD simulation. Since the G d acquired experimentally relates to an effective bonding energy per m 2 , the difference between G d and the one given by the MD simulation could be related to the effective surface coverage of C-(N-)A-S-H gel over the PVA fiber. It is important to note that the MD simulation considers saturation electrostatic interaction between Ca 2+ to O PVA , which despite the contribution of hydrogen bonding, has the main contribution to adhesion. However, the PVA fiber surface in reality is not fully occupied by C-(N-)A-S-H gel. The reason could be the heterogeneous distribution of reaction products. Specifically, a more porous ITZ on the fiber surface despite the minimized "wall effect" due to the small magnitude of fiber diameter [84,85] could decrease the effective coverage rate of reaction products on the fiber surface. Besides, the oiling treatment on the fiber surface hinders the coverage as well. All these factors contributed to a low rate of effective coverage of C-(N-)A-S-H gel over the PVA fiber, and thereby a lower experimental value of G d in comparison to simulated ones. Furthermore, it seems that the difference between MD simulations and the experimental results could be also attributed to the disparities of length scale involved, similar to the size effect found in brittle materials like concrete [86]. Thus, the direct linking of adhesion properties in MD simulation to the mesoscale bonding G d is only possible with essential upscaling processes.
Despite the difference in the magnitude of the adhesion properties, the consistency between experiment and MD simulation suggests that the reaction products chemistry of C-(N-)A-S-H gel predominantly affects the PVA/C-(N-)A-S-H adhesion properties. It is also confirmed that the interface property tailoring could be achieved by the proper mixture design of AASF. Particularly, this information is highly valuable for the development of future PVA-based SHGC, the performance of which is largely governed by the adhesion properties.

Conclusions
This work presents a combined approach using both molecular dynamics (MD) simulation and experimental characterization to investigate the adhesion mechanism, the interface nanostructure, and the  related adhesion properties of PVA fiber to C-(N-)A-S-H gel as the main reaction product in alkali-activated slag/fly ash (AASF) matrix. Various Ca/(Si+Al) and Al/Si ratios of C-(N-)A-S-H gel were considered and their impacts on the adhesion energy and element space distribution within reaction products to PVA were simulated and experimentally verified. Based on the results and discussions of this study, the following conclusions can be drawn: • The MD simulations indicate that the origin of adhesion between PVA and C-(N-)A-S-H gel at high Ca/(Si+Al) ratios (>1) is almost entirely due to the electrostatic interactions between the hydroxyl group in PVA and the Ca 2+ and Na + ions within C-(N-)A-S-H gel, whereas the contribution to the adhesion due to the hydrogen bonding between PVA molecule and C-(N-)A-S-H gel is only considered significant at low Ca/(Si+Al) ratios (<1). • The study provides further insights into the adhesion mechanism of PVA fiber to C-(N-)A-S-H gel formed in the AASF system and contributes to the tailoring strategies for composite performance enhancement through proper mixture design. These findings are particularly valuable for the development of future PVA-based strain-hardening geopolymer composite.