The Scienomics’ Polymer Consistent Force Field (SciPCFF) is used in describing the interaction in all systems. SciPCFF is developed by Scienomics based on the polymer consistent force field (PCFF) with extended parameters from the condensed-phase optimized molecular potentials for atomistic simulation force field (COMPASS). Both PCFF and COMPASS force fields have been widely used in the simulation of polymeric and graphitic materials (Yang et al., 2013; Chawla and Sharma 2017). Lennard-Jones (9-6) potential is used in describing the van der Waals interaction.

The Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) program is used for MD simulations (Plimpton 1995). The atomic trajectory is integrated using the velocity Verlet algorithm. Timestep of 1 fs is used. All electrostatic interactions are calculated using the Coulombic terms with the reciprocal-space contribution calculated using the particle-particle-particle-mesh (pppm) method. A Nóse-Hoover thermostat and barostat are used in controlling the temperature and pressure, respectively. Periodic boundary conditions are applied in all directions. In simulations where no periodicity in the z-direction is wanted, the PBC in the z-direction is canceled and a large vacuum space is set in the z-direction.

One problem often encountered in inkjet printing is the adhesion strength of the ink/substrate interface. Stronger adhesion is favored for better electric performance as it helps improve the electric conduction of the circuits. Reduced-graphene oxide (rGO) inks are among the most commonly used graphitic inks. rGO is hydrophilic as normally no absolute reduction of GO can be achieved. However, as PI is a relatively hydrophobic material, usually its surface needs further modification to improve its adhesion with the rGO inks. Plasma treatment has been widely used as one of the most popular among many surface modification methods (Kondo et al., 2017; Rusu et al., 2020; Marques et al., 2019; Abdel–Fattah and Alshaer, 2020; Usami et al., 2012; Park et al., 2010; Chan et al., 1996; Least and Willis 2013; Ghosh et al., 1997; Huang et al., 2003; Shin and Kang, 2010) due to various advantages such as high efficiency, rapid and simple operation, no need for solvents, and the ability to introduce a wide range of functional groups onto the surface (Abdel–Fattah and Alshaer, 2020). Meanwhile, after plasma treatment, only the very surface of the polymer is etched without significantly changing the properties of the inner bulk (Abdel-Fattah 2019; Park et al., 2009; Xie et al., 2011). Based on previous research, the imide bond N-C in PI is proposed to be fairly weak and gets easily cleaved, forming amide and carboxylate groups under various conditions. This mechanism has been observed under the treatment of acid (Ghosh et al., 1997), base (Huang et al., 2003), UV irradiation (Rusu et al., 2020), and plasma (Zhou et al., 2019; Grandoni et al., 2017). Inagaki et al. investigated the modification of PI using seven different plasmas: Ar-, N₂-, O₂-, CO₂-, NO-, and NO₂-plasmas. The results show that these different types of plasma all lead to the cleavage of the N-C bond in the imide group as well as the following formation of secondary amide and carboxylate groups (Inagaki et al., 1992), as shown in Supplementary Figure S1. Therefore, we use the formula in Supplementary Figure S1 as the structure of modified PI (mPI).

However, the micro-scale mechanism of the improved adhesion after plasma treatment still needs a more thorough investigation for 2D materials. Here we use MD to explore the adhesion between two types of graphitic inks, PG and GO, with two substrates, the pristine PI and plasma-modified PI (mPI), in an attempt to explore the effects of graphitic inks and the surface-modification of PI on the adhesion strength. The detailed building process of models can be found in Section2.3. Here the adhesion under different temperatures is studied as the substrate’s temperature is a crucial parameter affecting the printing result of the inkjet printing process. The temperature control and related simulation details during calculation are described in Section 2.2. The adhesion strength is evaluated via the calculation of the interaction energy (E_in) between the polymer slab and the GO/PG ink, which is the reduced potential energy after the separated components combine with each other, as clarified as follow: E i n = E t o t − ( E i n k + E s u b s t r a t e ) (1)

E_tot, E_ink and E_substrate are the potential energies of the composite, ink and substrate, respectively. A lower E_in indicates stronger interfacial adhesion strength. The results are shown in Figure 1A.

First of all, one can observe in Figure 1A that under same temperatures the adhesion strength follows: PG-mPI< PG-PI< GO-PI< GO-mPI. The adhesion of polymeric substrates with GO is in general greater than that with PG. This is attributed to the fact that both the van der Waals (vdW) and the Coulomb electrostatic interactions exist between the polymers and GO, including the strong hydrogen bonding interactions, while with PG only the vdW interaction is present. The enhanced adhesion between mPI and GO is consistent with the experimental observation that PI surface turns more hydrophilic after plasma treatment, and the adhesion of rGO ink is much improved. This phenomenon is mainly attributed to the enhanced interfacial hydrogen bonding interactions. E.g., in mPI/GO, both COOH and NH, as well as OH groups on GO can donate their H in forming interfacial hydrogen bonds, while in GO/PI, only OH groups on GO can act as the hydrogen donors. The weakest adhesion is observed between PG and mPI, of which the difference in polarity is the greatest among all systems. The results indicate that though GO is more adhesive on mPI, if using PG as ink, unmodified PI will show better adhesion.

A lower temperature is found to help the improvement of adhesion strength for all systems, as reflected via the proportional relationship between E_in and temperature in the range investigated. This is mainly attributed to two reasons: first, the non-bonding interactions (vdW, hydrogen bonding, and other electrostatic interactions) are more unstable under higher temperatures. This can be viewed via the radial distribution functions (RDF). RDF describes the density of a specific particle B as a function of distance from a reference particle A, reflecting the possibility of finding B around A. r/σ is distance r divide the distance unit (Å in this case). g(r) represents the density of the specific particle in the micro-shell defined by r relative to the entire system. As aforementioned, the amide and carboxylate groups formed after cleavage of N-C bond as the result of plasma treatment is the main cause of the improved adhesion of mPI. Therefore, to explore the impact of temperature on the pair interaction between the amide hydrogens (NH) with the carbonyl oxygens (CO), the corresponding RDF under different temperatures is analyzed. Here the mPI/GO system is presented (RDF of mPI/PG is shown in Supplementary Figure S5) as illustrated in Figure 1B. Peaks 1, 2, and 3 correspond to the intra-molecular hydrogen bond between NH and the carboxylate oxygen (COO), the interaction between NH and the oxygen of the bonded carbonyl, and the inter-molecular NH-CO hydrogen bonds, respectively, as illustrated in Figure 1C. The magnified peak 3 is shown in the inset in Figure 1B, and peaks 1, 2 can be found in the Supplementary Figure S4. One can observe that all three peaks drop in intensity with increasing temperature, reflecting the instability of these interactions upon heating. A similar result is also observed for other non-bonding interactions, as reflected by the all-to-all RDF shown in Figure 1D (the all-to-all RDF of other systems is shown in Supplementary Figures S5D, S6). The first two peaks within 1.5 Å are considered to be the covalent bonds, while the peak at ca. 2.4 Å magnified in the inset is assigned to the overall non-bonding interactions, which drop in intensity with increasing temperature. Second, as higher temperature generally results in lower density of the system, the overall non-bonding interactions near the interface are also reduced.

As discussed before, the mPI/GO system shows the best adhesion performance due to enhanced hydrophilicity after plasma treatment. In fact, in real applications, mPI has already replaced PI as the substrates in flexible electronics. Therefore, we will focus the investigation on mPI systems. Apart from temperature, we are also interested in how the interface behaves under different inkjet velocities. Four velocities (1, 5, 10, and 20 Å/ps) are investigated. Nonetheless, it has to be pointed out that due to the consideration of computational cost, the simulated inkjet velocities are much higher in comparison to the ones used in real applications (ca. 5 × 10⁻⁴ Å/ps). The bottom part of the polymer substrate is set as rigid, while the ink (PG/GO) is given an initial velocity towards the substrate in the z-direction, as demonstrated in Figure 2A. It is found that the ink/substrate interface is affected by the inkjet velocity in two aspects. Faster printing velocity leads to a larger impact force of ink onto the substrate, and will also result in greater interfacial fluctuation. The impact force can be reflected via the amplitude of the stress fluctuation, as shown in Figure 2B; Supplementary Figure S7A. This can also be observed via the density profiles under different velocities (Figures 2C,D; Supplementary Figures S7B,C). As shown in Figure 2C; Supplementary Figure S7B, under slow velocities (1 Å/ps), the density near the interface (−90 to −80 Å) is relatively stable with the gap between the ink and the substrate clearly shown at −87.66 and −85.77 Å for systems mPI/GO and mPI/PG, respectively. While under higher velocities (Figure 2D; Supplementary Figure S7C, 10 Å/ps), the density fluctuates rather vigorously, especially near the interface, and the ink/substrate gap can no longer be observed. And the combined influence of impact force and interfacial fluctuation affects the interfacial adhesion, as reflected by E_in (Figure 2E; Supplementary Figure S7D). Higher inkjet velocity, in general, leads to greater fluctuation of E_in after hitting. Though higher inkjet velocity leads to a larger impact force, the greater interfacial fluctuation may also have a significant influence on the ink’s adhesion. And as observed in the inset in Figure 2E, after ca. 100 ps E_in is basically stabled. For mPI/GO, after 100 ps, E_in under higher inkjet velocities (10 and 20 Å/ps) is lower compared to lower velocities (1 and 5 Å/ps), indicating that the interfacial adhesion between mPI and GO is enhanced by higher inkjet velocity. While for mPI/PG, there is no significant difference between different velocities. Therefore, to achieve better adhesion via tuning inkjet velocities, both impact force, as well as interfacial fluctuation, should be considered.

Another issue often encountered in flexible electronics is that the flexible circuit is often under different types of loading during use, such as downward pressing, bending, stretching, detaching, etc. Therefore, understanding how the interface is affected under loading is critical in achieving better working performance. Here we have analyzed two types of loading, the downward pressing and the detachment under uniaxial tensile. In this section, the effects of downward pressing are firstly discussed. In many pressure-sensitive flexible electronics, the conduction and sensitivity of the circuits are highly related to the pressure applied. The pressure change in the electronics can be captured as electric signals. Therefore, it is crucial to understand how the interface is affected by pressures, which is the key to improving the sensitivity of the electronics. The results are shown in Figure 3. E_in of different systems under different pressures at 300 K are calculated (in each case forces 0, 0.35, 0.7, 1.05, 1.4, 1.75, 2.1, 2.45, and 2.8 pN are applied on each atom in the mPI slab downward, while PG/GO is fixed).

As the force applied on the atom increases from 0 to 1.75 pN, the adhesion is significantly improved as reflected by the drop of E_in (Figure 3A). However, the adhesion strength can only be improved through increasing the pressure to a limited extent, as it can be observed in Figure 3A that a further increment of force to 2.8 pN results in a much smaller change in E_in. The reason is mainly attributed to the interfacial density (ρ_in) change under different pressures, as demonstrated in the density profiles near the interface as illustrated in Figure 3B; Supplementary Figure S8. Higher density leads to a denser formation of non-bonding interactions and stronger adhesion strength in the interfacial regions. The changes in ρ_in are consistent with E_in. ρ_in gradually increases with compression at first, however with further pressure increases, the increase of ρ_in is relatively small, and significant enhancement in compaction can no longer be achieved. The results indicate that the interfacial adhesion can only be improved via increasing the pressure to a certain extent, which may help in the improvement of the electronics’ sensitivity.

As mentioned above, in flexible electronics, the ink/substrate interface is usually subjected to different types of external loading. In real applications, except the normal pressure or impact downwards, printed ink on flexible substrates may also suffer in the delamination off the interface. Here the investigation of the detachment process of the mPI systems has been conducted by applying uniaxial tensile loading.

The upper part of the polymer bulk is fixed, while the PG/GO layer is given a constant velocity downwards (1 Å/ps), as shown in the snapshot at time 0 ps in Figure 4A. The movable part of the polymer slab is kept at the thickness of 90 Å for both systems.

As shown in the snapshots in Figure 4A (The snapshots for mPI/PG are shown in Supplementary Figure S9), which can intuitively demonstrate the change during simulation, the downward movement of the ink is accompanied by the concurrent movement of the polymer chains attached to it due to interfacial adhesion. As reflected in the corresponding snapshots at different times for both systems, at the initial stage upon tensile (10 ps) the polymer slabs are stretched without apparent formation of micro-voids. Then along the process, the micro-voids within the polymer bulk witnesses a growth of size. The chains are separated from each other, and the ones near the surface are then detached. As shown in the last snapshots for both systems, the final detachment for mPI/GO occurs at a time of 140 ps with chain residues at the interface, while for mPI/PG, complete detachment occurs earlier, at 120 ps. The detachment can also be viewed via the E_in change as shown in Figure 4B. For both systems, E_in increases with the gradual interfacial detachment of chains. The most drastic increase of E_in is observed before ca. 30 ps, as in this stage, most chains are still attached to the interface. After this stage, as many chains are pulled away from the interface, the corresponding change of E_in also gets much slower, as more clearly illustrated in the snapshots at 50 and 80 ps. The complete detachment of mPI/PG is reflected by the E_in increase to 0 at the end, and for mPI/GO the chain residue on the interface is evaluated by the final E_in at ca. −337 kcal/mol. As shown in Figure 4B, though the final detachment for mPI/GO occurs at 140 ps, however after ca. 90 ps no apparent change of E_in is observed. This indicates that the chain residues are firmly attached to the interface, and the final fracture actually occurs between the chain residues on the interface and the ones in the polymer slab instead of exact failure at the surface. These results are ascribed to the stronger adhesion strength between mPI and GO. The results indicate that mPI/GO system shows better resistance against uniaxial detachment due to greater interfacial adhesion strength.