Molecular structures and water diffusivity

As depicted in Fig. 1a, our model is composed of a lipid bilayer and a monolayer graphene or GO, which are separated by a certain distance of ∼1 nm. The composite structure is immersed in water. As reported in the previous studies, there is a thin layer of trapped water at its interface, which can be finely tuned by the humidity of experimental conditions18,19. Thus, we develop our computational model by filling the interfacial gap with water molecules. The molecular structures are equilibrated in our MD simulations at ambient condition. From the spatial density profiles of water molecules, we identify structured water layers adjacent to the graphene wall. For example, for the intercalated water layer with a thickness of t W =1.82 nm, the profile showed in Fig. 1b features two prominent peaks (peak 1 and 2), which demonstrate the layered structure. Here t W is defined as the span of region where the mass density of water is equal or higher than that in the bulk phase. The amplitudes of peak densities are higher than that of bulk water, which is a common feature of nanoconfined water and was reported for water trapped between graphene or GO layers at a similar length scale of spatial confinement20. From Fig. 1b, we also find that there are water molecules entering the lipid bilayer at a depth of ∼1 nm, with a smoothly decaying amplitude of density. From an application viewpoint, the presence of intercalated water layers not only modulates the mass and energy delivery between bio- and nanostructures but also could perturb the biological activity of cellular membranes due to its difference with the regular extracellular environment.

Figure 1: Graphene–water–lipid bilayer hybrid as a model system. (a) Illustration and a simulation snapshot of the model under exploration. (b) The mass density profile of water molecules plotted with that of bulk water, along the distance measured from graphene (top of panel). The simulation set-up to explore heat transfer across the interface (bottom of panel), which is aligned with the density profile plot. The thickness of intercalated water layer is t W =1.82 nm. Full size image

Recent experimental measurements suggest that at the graphene–lipid bilayer interface, the thickness of intercalated water layer between the lipid membrane and graphene is on the order of a few nanometres2. We thus explore a number of interfaces with t W ranging from 0 to 2 nm. Figure 2a shows that there is a notable difference between the density profiles of water at graphene and GO interfaces in both the amplitudes and positions of peaks, which is caused by the presence of charged functional groups in GO. From the correlation between t W and the mass of water under the first density peak, M 1 (Fig. 2b), we conclude that for both graphene and GO, water in the central region of interfacial gallery has a similar structure as bulk water with thickness t W above t Wc =1 nm, and the magnitude of the first peak becomes independent on the amount of trapped water.

Figure 2: Structural and dynamical properties of the intercalated water layers. (a) Mass density profiles of water molecules along the direction perpendicular to the interface, plotted for different numbers of intercalated water molecules. (b) The thickness of intercalated water layer t W and the water mass under the first peak (M 1 ) in the density profiles, plotted as a function of the number of intercalated water molecules. The latter one represents the number of water molecules in the first nearest neighbours. M 1 is calculated as M 1 = ∫ z 0 z 1 Aρ(z)dz, where ρ(z) is the mass density of water molecules, A is the area of interface, and z 0 and z 1 are the boundaries of the first peak in the density profiles. (c,d) The mean-square distance (MSD) and diffusion constant D measured for the intercalated water layer. D is compared with the diffusivity of bulk water calculated using the same water model58. Full size image

The presence of water in the nanogap between lipid bilayer and nanostructures allows the cell to exchange masses and energy with their surroundings through molecular diffusion, and thus are crucial for their survival. We further show that the molecular diffusivity of interfacial water is significantly lower than that in the bulk (Fig. 2c,d). The presence of bulk-like water at the bio-nano interface instead of structured water20 is important to maintain the biological activity of cell. Consequently, the value of t W should be assured to be larger than the critical value t Wc =1 nm, which could be controlled by, for example, tuning the humidity. On the other hand, one should also keep in mind that, to maintain active communication between lipid bilayer and nanostructures for effective electrical signal and energy exchange, the thickness of intercalated water layer has to be kept also below a critical length scale of ∼1 nm2,3.

Thermal dissipation at the bio–nano interface

We then explore the heat dissipation process based on the simulation set-up shown in Fig. 1b. We heat up the graphene or GO layer at a constant power density p. As shown in Fig. 3a, at a low heating power density, for example, p∼1 GW m−2, the heat generated can be efficiently dissipated across the interface, along the thermal gradient. No significant destruction of the bilayer structure at this rate of thermalization is observed in our MD simulations that reach steady states. Accordingly, temperature rise in the lipid bilayer is negligible and is almost power-density-independent. However, as the power density exceeds a critical value of p c , the temperature rise in lipid bilayer, ΔT, increases drastically and features an almost linear dependence on the power density (Fig. 3a; Supplementary Fig. 1a). The modest deviation from linearity may arise from the change in the structure and diffusivity of intercalated water at different heating power density, which is more significant for GO because of its stronger interaction with water. Specifically, at p=∼16.25 GW m−2, the temperature rise in lipid bilayer could reach ∼43 K within 400 ps before it reaches a plateau (Supplementary Fig. 2) that is significant enough to perturb the physiological behaviour of biological systems, while the temperature rise in graphene is ∼1,150 K that could break down the electronic device performance21.

Figure 3: Temperature rise in lipid bilayers on heat generation in graphene. (a) The rise in temperature, ΔT, in the lipid bilayer after heat flux with power density p is injected into graphene. A critical power density p c of ∼7.5 GW m−2 can be identified for a targeted threshold of temperature rise, ΔT c . Here we consider ΔT c =20 K as an example for illustration. (b) Temperature rise in the lipid bilayer as graphene is heated at a power density of p=∼9.35 GW m−2, plotted as a function of t W . Error bars are plotted based on results from five independent simulation runs. Full size image

One can then define the value of p c for a targeted threshold value, ΔT c . The calculated value of p c thus increases with t W . That is to say, the presence of intercalated water layer significantly enhances heat dissipation and maintains thermal stability of the bio–nano interface (Fig. 3b; Supplementary Fig. 1b). Without loss of the generality, we choose ΔT c =20 K according to the reported value of critical temperature rise for a cell to maintain its viability22,23. For the intercalated water layer with a thickness of ∼1 nm, which is an ideal value considering the competition between molecular diffusivity and cross-interface communication as we discussed earlier, we measure p c =∼7.5 GW m−2 for t W =1.03 nm (graphene) or ∼9.35 GW m−2 for t W =1.10 nm (GO).

Interfacial thermal coupling at the bio–nano interface

To quantify the role of intercalated water layers in enhancing the thermal dissipation and model the process of thermal energy transport across the graphene–lipid bilayer interface, we need to determine the key parameter for the interfacial thermal coupling, that is, the ITC or namely the Kapitza conductance, since the convection motion is negligible in this system. Here we consider the graphene–water–lipid hybrid as an integrated system in discussing the thermal coupling between graphene and lipids, where the interface is manifested by the presence of intercalated water layers. Our thermal relaxation simulation results show that the value of ITC increases with t W (Fig. 4a). To account for more realistic biological systems, we carried out additional MD simulations for a lipid bilayer membrane with potassium channel proteins (KcsA; Supplementary Fig. 3). The results show that the ITC of graphene–lipid contact ranges from 13.7 to 49.10 MW m−2 K−1, while that for graphene–lipid interface with proteins ranges from 15.8 to 41.1 MW m−2 K−1. This result suggests that the presence of proteins does not significantly change the value of ITC. Previous studies reported that hydrogen bonds between proteins and intercalated water molecules are responsible for a promotion of interfacial thermal transport, which explains the fact that the protein–water interface (with hydrogen bonds) has a higher ITC of 100–300 MW m−2 K−1 than that for the octane–water interface (without hydrogen bonds), that is, 65 MW m−2 K−1 (refs 24, 25, 26, 27, 28). In our model, however, this effect is negligible because of the limited contact between intercalated water layer and protein.

Figure 4: Interfacial thermal conductance (ITC) in typical systems. (a) The ITC plotted as a function of t W . The inset shows the exponential decay of temperature in the graphene layers after the heat pulse is removed, which is used to calculate the ITC in our thermal relaxation simulations. (b) A summary of ITC plotted as a function of the interfacial energy Γ at solid–solid, solid–polymer, liquid–polymer and solid–liquid interfaces. The data are collected from the literature26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43. Full size image

The thermal conductance of lipid–graphene interface calculated here is on the order of 10 MW m−2 K−1, which is compared with the ITC values reported for other nanoscale solid–solid, solid–polymer, liquid-polymer and solid–liquid interfaces as summarized as a function of the interfacial energy Γ in Fig. 4b. The ‘soft’ interface explored here between graphene/GO and lipid bilayer with intercalated water is in general at the lower bound of these interfaces with solids (Supplementary Note 1)26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43. This consistency arises because of the diffusive nature of interfacial thermal transport, and the similarity in the nature of interfacial intermolecular interactions (van der Waals forces, electrostatic interaction, hydrogen bonds and so on). Moreover, the quantitative difference in the ITCs measured for interfaces with graphene and GO suggests that by functionalizing the nanostructures, one could further tune the interfacial thermal coupling, by crosslinking the nanostructure with lipid bilayer for example44.

Predicting the thermal perturbation

Excess heat perturbs the physiological state of cells and tissues. For example, tumour cells are susceptible to heat treatment, resulting in cell death above 43 °C (ref. 45). Our results thus quantitatively predict the minimal power at which thermotherapic treatment could be efficiently achieved at the interface with graphene or GO. To obtain deeper insights into the heat transfer process at the bio–nano interface, we develop an analytical model for the thermal coupling of this bio–nano hybrid (Fig. 5a) based on the understandings and results obtained from our MD simulations. The model consists of two resistors connected in serial for the graphene/water/lipid interface and the lipid bilayer, respectively. We assume a diffusive heat transport regime due to the weak interaction across interfaces and strong scattering of heat carriers therein, which is similar as the interface between graphene and substrates we studied in earlier works46,47. Then the, interfacial heat transport can be described using the Fourier law, J=κAdT/dx, where J and T are the heat flux and temperature, respectively. κ is the thermal conductivity and A is the area of interface. The steady-state temperature profile then be calculated from

Figure 5: Model prediction of heat dissipation process across the bio–nano interface. (a) A resistor-network model for the heat transfer pathway across the graphene–lipid membrane interface, which consists of two resistors representing the graphene–water/lipid interface and the lipid bilayer, respectively. (b) Steady-state temperature profile across the interface and time-dependent temperature evolution in the graphene layer calculated from the model, which agree well with our MD simulation results summarized in c and d. Full size image

Here G C is the ITC we calculated from MD simulations for the graphene/water/lipid hybrid. T G , T L and T W are the temperature of graphene/GO, lipid and intercalated water layer, respectively. We consider T W as a constant because MD simulation results show that temperature distribution in the intercalated water layer is uniform because of its high thermal conductivity (∼0.61 W m−1 K−1) compared with the lipids (∼0.12 W m−1 K−1), and the convectional contribution can be neglected. z s is the position of surface in the lipid bilayer. δ and κ L are the thickness and thermal conductivity of the lipid bilayer, respectively. T e =300 K is the temperature of the water reservoir in contact with lipid bilayer on the other side, or the heat sink. By solving these set of Fourier’s equations with boundary and interface conditions, the temperature distribution across the whole hybrid, T(x), is plotted in Fig. 5b, which shows an abrupt drop at the graphene–water interface because of the high interfacial thermal resistance, followed by a plateau in water and a temperature gradient in the lipid bilayer. With fitted values of κ L =0.12 W m−1 K−1 and G C =12.60 MW m−2 K−1, we can predict the temperature profile that agrees well with our MD simulation results (Fig. 5c). The results for the lipid bilayer with embedded KcsA protein are similar as the pure lipid bilayer case, indicating the same mechanism of interfacial thermal coupling (Supplementary Fig. 3).

While the graphene or GO layer is heated at a specific power density p, our diffusive model can also make predictions for the temperature evolution, which approaches a plateau as the heating process proceeds to the steady state (Fig. 5b). The evolution of temperature T g (t) in graphene at time t follows the solution from the Fourier’s equation using the lumped-parameter method (see Supplementary Note 2 for details)