Epoxy resins are composed of a three-dimensional network formed by chemical reactions between epoxy and amino compounds, which plays an important role in the mechanical properties. Thus, to use epoxy resins in various applications, it is necessary to gain a better understanding of their network structure. Here, we study the structural heterogeneity evolved in an epoxy−amine mixture during the curing process on the basis of a particle tracking technique, in which the thermal motion of probe particles in the mixture was tracked, small-angle X-ray scattering measurements in conjunction with coarse-grained molecular dynamics simulation. The heterogeneous environment was generated even at the initial stage of the curing process. Notably, the characteristic length scale was on the order of several hundreds of nanometers down to several tens of nanometers, depending on the extent of curing. Once a reaction occurs between a pair of epoxy and amino groups, the temperature at the site is locally elevated due to the heat of formation, accelerating a subsequent reaction nearby. Repeating such a situation, actively and scarcely reacted domains are formed. This is the main origin of the structural heterogeneity in epoxy resins.

Epoxy is a class of thermosetting resins and has been widely used as a representative example of structural adhesives. Nevertheless, it remains unclear how the epoxy resin and curing agent are present on the adherend surface and how they move around dynamically and react with each other to form a three-dimensional network. We here adopt a fully atomistic molecular dynamics (MD) simulation to study molecular events of an epoxy resin composed of hydrogenated bisphenol A diglycidyl ether and 1,4-cyclohexane­bis­(methylamine) at the interface using a narrow gap, which was sandwiched between copper surfaces. The depth profiles of the density, molecular orientation, and concentration in addition to molecular diffusivity at the interface are addressed. These are finally combined with the kinetics for the curing reactions at the interface. Although some of the information here obtained is accessible by experimentation, most is not. We believe that the findings of this study will lead to a better understanding of the adhesion phenomenon.

Schematic diagram of diffusion of water molecules. They are clustered at a preferred site where hydrogen bonds can be formed with hydroxyl, ether and amino groups of the network in the free space, and heterogeneously moved from there to other sites.

The self-consistent GWΓ method satisfies the Ward-Takahashi identity (i.e., the gauge invariance or the local charge continuity) for arbitrary energy (ω) and momentum (q) transfers. Its self-consistent firstprinciples treatment of the vertex Γ = Γ v or Γ W is possible to first order in the bare (v) or dynamicallyscreened (W) Coulomb interaction. It is developed within a linearized scheme and combined with the Bethe-Salpeter equation (BSE) to accurately calculate photoabsorption spectra (PAS) and photoemission (or inverse photoemission) spectra (PES) simultaneously. The method greatly improves the PAS of Na, Na 3 , B 2 , and C 2 H 2 calculated using the standard one-shot G 0 W 0 + BSE method that results in significantly redshifted PAS by 0.8-3.1 eV, although the PES are well reproduced already in G 0 W 0 . 1The quasiparticle (QP) equation method in many-body perturbation theory [1] is powerful for simultaneously determining the photoemission (or inverse photoemission) spectra (PES), i.e., QP energy spectra, and QP wave functions of target materials from first-principles. In this method, we expand the skeleton diagrams, i.e., the diagrams drawn with the full Green's function lines, for the self-energy in terms of the electron-electron Coulomb interaction v, and solve the QP equation, which is equivalent to the Dyson equation, as a self-consistent (SC) eigenvalue problem. The Hartree-Fock (HF) approach provides the first-order approximation. In Hedin's set of equations[1] known as the GWΓ approach, the exchange-correlation part of the self-energy is expressed aswhere G σ and Γ σ are the one-particle Green's function and the vertex function (σ is the spin index), respectively, and W = (1 − vP) −1 v represents the dynamically screened Coulomb interaction (P = −i σ G σ G σ Γ σ is the polarization function). The simplest approximation is to assume Γ σ = 1, which is called the GW approximation.It is well known that the SC GW method usually overestimates the energy gap [2, 3], while the one-shot GW approach (G 0 W 0 ) using the Kohn-Sham (KS) wave functions and eigenvalues[4] results in a better energy gap. However, quite recently, it has been pointed out that the photoabsorption spectra (PAS) for small molecules obtained by solving the Bethe-Salpeter equation (BSE) [5, 6] using G 0 W 0 are often significantly redshifted by about 1 eV [7,8]. The use of the Heyd-Scuseria-Ernzerhof (HSE) functional or the SC GW calculation (hereafter referred to as GW) improves the results, but they are not perfect [8,9]. For a spin-polarized sodium atom (Na) and trimer (Na 3 ), G 0 W 0 + BSE is extremely bad, although the G 0 W 0 QP energies are reasonably good [10]. The calculated and experimental [11] optical gaps for Na are 1.32 eV and 2.10 eV, respectively, and the calculated and experimental [12] PAS for Na 3 are shown in Fig. 1. These calculated results are far off from the experimental data [13].Here, we develop a GWΓ method, which involves a SC treatment of the vertex Γ = Γ v or Γ W and satisfies the Ward-Takahashi identity [14][...