## 2 Simulation Methods
### Epoxy Resin-Sand Surface Interactions  
Apart from physical interactions, molecular systems may also involve weak chemical interactions induced by electron transfer [49]. One prominent example of such weak chemical interaction is hydrogen bonding [50]. Hydrogen bonding, being an exceptional type of intermolecular force, exerts a pivotal role in surface adsorption phenomena. In this study, the combination models were examined using Materials Studio to calculate the hydrogen bonds. The hydrogen bonds in the resin and sand models were also analyzed. Subsequently, the number of the interface hydrogen bonds after the adsorption was determined according to Equation (1):  
\[N_{surface}=N_{total}-N_{resin}-N_{sand} \tag{1}\]  
where \(N_{surface}\) denotes the count of the interface hydrogen bonds after the adsorption, \(N_{total}\) signifies the total number of hydrogen bonds encompassing all atoms within the comprehensive system, \(N_{resin}\) corresponds to the intrinsic count of hydrogen bonds associated with the resin, and \(N_{sand}\) represents the inherent count of hydrogen bonds pertaining to the sand.  
To eliminate the influence of molecular weight differences and better highlight the contribution of hydrogen bonding in adsorption, the number of hydrogen bonds per unit molecular weight (\(N_{unit}\)) was introduced to compare the adsorption performance of the three resins on the sand surface. Equation (2) was employed for calculation purposes [33]:  
\[N_{unit}=N_{surface}/M_{resin} \tag{2}\]  
where \(N_{surface}\) denotes the count of the interface hydrogen bonds generated at the interfacial region, while \(M_{resin}\) represents the molecular weight of the epoxy resin.  
The adsorption energy represents the capacity of a material to adhere to other substances, and its magnitude plays a crucial role in determining the speed and efficiency of material adsorption. Therefore, understanding the adsorption energy is vital for investigating the curing process of sand with curing agents [34]. Under vacuum conditions, the adsorption energy of a material can be calculated using Equation (3) [51]:  
\[E_{ads}=E_{total}-E_{polymer}-E_{quartz} \tag{3}\]  
where \(E_{total}\) corresponds to the configurational energy of the overall system comprising all constituent atoms in kcal \(\cdot\) mol\({}^{-1}\), \(E_{polymer}\) relates to the configurational energy specific to the polymer in kcal \(\cdot\) mol\({}^{-1}\), \(E_{quartz}\) represents the configurational energy associated with the sand, specifically quartz in kcal \(\cdot\) mol\({}^{-1}\), while \(E_{ads}\) signifies the adsorption energy at the interface of adsorption in kcal \(\cdot\) mol\({}^{-1}\). \(E_{ads}\) governs the intermolecular interaction energy necessary for the polymer to disrupt the surface of the sand, concurrently serving as a measure of the adhesive strength at the interface.  
The radius of gyration is a critical parameter in molecular dynamics simulations, providing valuable insights into both the structural arrangement and dynamic behavior of epoxy resin-sand systems. This property can be leveraged to predict the mechanical properties of these composites, optimize their design for enhanced performance, and gain a deeper understanding of the interfacial interactions occurring at the epoxy resin-sand surface. The radius of gyration, which quantifies a molecule's spatial extension, can be calculated as follows:  
\[Rg^{2}=(\sum_{i}\left\|r_{i}\right\|^{2}m_{i})/\sum_{i}m_{i} \tag{4}\]  
where \(m_{i}\) is the mass of atom \(i\), and \(r_{i}\) is the distance of the atom \(i\) in the molecule from their common center of mass.