Directing lateral growth of lithium dendrites in micro-compartmented anode arrays for safe lithium metal batteries

Uncontrolled growth of lithium dendrites during cycling has remained a challenging issue for lithium metal batteries. Thus far, various approaches have been proposed to delay or suppress dendrite growth, yet little attention has been paid to the solutions that can make batteries keep working when lithium dendrites are already extensively present. Here we develop an industry-adoptable technology to laterally direct the growth of lithium dendrites, where all dendrites are retained inside the compartmented copper current collector in a given limited cycling capacity. This featured electrode layout renders superior cycling stability (e.g., smoothly running for over 150 cycles at 0.5 mA cm−2). Numerical simulations indicate that reduced dendritic stress and damage to the separator are achieved when the battery is abusively running over the ceiling capacity to generate protrusions. This study may contribute to a deeper comprehension of metal dendrites and provide a significant step towards ultimate safe batteries.

to normalize the values of corresponding E field results as discussed below.

Revised text 1:
Simulation setup: A finite element analysis (FEA) method simulation was performed to predict the compartment effects on the distribution of electric field (E field) as well as the growth of lithium dendrites inside the compartments of E-Cu. The ANSYS models used are electrical conduction model 1,2 and structural stress analysis model 3,4 (based on the Hook's law). In this work, all numerical simulation analysis about E-Cu is conducted on one compartment (Fig. 3, top and side views), which is a typical unit of E-Cu and thus is expected to reflect the average phenomena occurred in all other compartments.
As for bare E-Cu model (see Supplementary Fig. 3b), the compartment has a cylindrical structure with the diameter (D) of 150 μm and height (H) of 45 μm, and the thickness of the upper PI film is 25 μm. The height of the bulk electrolyte in the domain is assumed to be 100 μm.
Typical conductivity and mechanical strength are assumed for Li metal, PI film, Cu, electrolyte, and separator, as shown in Supplementary Table 2. The conductivity of the Li dendrites is considered to be half of normal Li metal due to the existence of crystal boundaries in the dendrites; even so, it is still much better than that of the PI membrane and electrolyte.
Then, we built the E-Cu@Li structure model based on one compartment with randomly distributed cylindrical lithium dendrites via Monte Carlos method with random generator (see Fig.   3a), where each of these dendrites randomly starts from the Cu scaffold and extents into the compartment. The diameter and length of each cylindrical dendrite are generated as a white noise distribution with the following ranges: according to the SEM observations (Fig. 4), the diameter distribution of the dendrites is estimated to range from 3 to 10 μm, while the length distribution is from 0 to 120 μm. The total number of dendrites depends on the volume of plated lithium in the compartments, which varies from 0% to 60% in the present simulated cases. When a potential difference of V 0 (V) is applied across the top and bottom electrodes, we can obtain the electric field intensity of E 0 = V0/100 (V μm-1) generated across these two electrodes. Then, we use this E 0 to normalize the values of corresponding E field results as discussed below (Supplementary Fig.   3

and 4).
It is noted that the electrolyte was assumed as a statically distributed medium instead of a dynamic one when calculating the electric field distribution for all cases. During the simulation of von Mises stress distributions on the dendrite protrusions (Fig. 3), the diameter of the simulated protrusion is assumed to be 5 μm, which is positioned at the center of the pinhole. Revised text 2:

Supplementary
According to the above theory, when the practical D value in our experimental condition is larger than the order of magnitude of 10 -7 (cm 2 s -1 ), the electric field in the electrodeposition system would become a significant factor toward dendritic lithium growth. From literature 8, 9, 10 , the Li + diffusion constant of 1 M LiTFSI in 1:1 (v/v) DOL:DME was at the order of 10 -5 (cm 2 s -1 ).
Even considering the dimensional condition that the pinhole area is about 1/10 of the compartment area, the diffusion constant of lithium ion in the pinhole shall be at the order of magnitude of 10 -6 (cm 2 s -1 ), which is still larger than the calculated one from Chazaviel's model (10 -7 ). This indicates that the diffusion of electrolyte is at a fast-enough time scale to provide an electrochemically active surface inside the compartment at the range of current densities employed in the experiment (0.25 to 1.0 mA cm -2 ), thus can maintain a stable electric current. Therefore, electric field becomes the dominant factor which determines the growth of lithium dendrite inside the compartments, according to the space-charge model in Chazaviel's theory 1 . Consequently, the influence of potential gradient generated from the uneven anion depletion during a dynamic charging/discharge process is less significant, so that the electrolyte can be assumed to be a static medium (charge carrier) to simplify the simulation.  to improve the quality of this paper. We have added the following discussions in the revised manuscript to reinforce the connection between the modeling and experiments, as depicted below.

Simulation on electric field distribution and lithium plating/stripping behaviors in E-Cu
The distribution of electric field generated in P-Cu and E-Cu is schematically depicted in Fig. 2a.
On the planar P-Cu, the direction of electric field exhibits a simple vertical pattern (perpendicular to the separator). Whereas, the distribution of electric field generated inside E-Cu presents a unique lateral pattern, confirmed by numerical simulation using electrical conduction model as exhibited in Fig. 2b; in this pattern, the electric field propagates from the counter electrode, through the pinhole, and extends laterally to the Cu scaffold surface. This unique distribution pattern derives from the distortion effect of the top insulative PI layer on the electric field. Here, the electric field distribution is considered as one of the dominant factors (see supplementary information), which could modulate the growth behavior of lithium dendrite 35 , as discussed below.
Along the distribution of electric field, plated Li metal primarily forms into small and mossy Li dendrites on the smooth surface of P-Cu due to limited electroactive sites. During the charging process, the subsequent dissolution of Li will result in many sharp ends and dead Li on the surface of P-Cu. Since Li metal is preferentially deposited along the sharp ends where local current density is dramatically increased 5 , larger Li dendrites and more dead Li will be evolved after repeated cycles (Fig. 2c). In contrast, owing to the existence of insulative PI film on E-Cu, Li metal is limited to deposit laterally inside the Cu scaffold and grows into Li dendrites. Even after cycling for a long time, Li dendrites will always be confined inside these hollow compartments as long as the cycling capacity is not exceeded (Fig. 2c). Here, the upper PI film in E-Cu can act as a physical barrier that shields the Li dendrites from protruding out of the pinholes in upper PI film.
Despite some distortion effect on the electric field distribution within the compartment with the presence of this PI layer, electrochemical plating/stripping behavior of Li metal in E-Cu can still be observed, since the electric field can propagate into the compartment (see Supplementary Fig. 3 and 4 for discussion).
Once the cycling capacity approaches the limit capacity of E-Cu for effective Li storage, vertical Li dendrites will protrude out of the pinholes of upper PI film (extreme case). Even so, these protrusions are often long and curvy compared with short and sharp ones on P-Cu, meaning that they are mechanically much weaker than that on P-Cu, and therefore producing lower stress and being less probable to impale the separator. Accordingly, we simulated using structural stress analysis model, and observed an approximately 60% reduction of stress from protruded Li dendrites in E-Cu over P-Cu (Fig. 3). In these simulation cases, a vertical dendritic protrusion is positioned against the separator under different deposition capacities (Fig. 3a). When the compartment is filled up to the top PI film with Li dendrites (Fig. 3c-e), the stress on the separator is still significantly less than that of the control case (planar configuration, Fig. 3b). In another word, the predicted reduction of protrusion stress would further alleviate the safety problem of the lithium anodes based on E-Cu and enhance the structural integrity. It's worth mentioning that broken Li strips will stay inside the compartment, and thus Li metal can only grow along these broken strips until they are reconnected with newly formed lateral Li dendrite, which is quite different to the situation for P-Cu; in this case, the stress distribution in reconnected dendrites would be similar to the case without remnants.

Original text 2:
Numerical Simulation: A finite element analysis (FEA) simulation was performed on E-Cu@Li model with randomly generated cylindrical dendrite from the Cu scaffold in single compartment.
The FEA package from ANSYS Inc. was used for simulation and post-processing.

Revised text 2:
Herein, we develop a scalable technology with photolithographic-level conformity for the fabrication of polyimide (PI)-clad copper grid current collectors (E-Cu) for Li metal anodes, where the electric field presents a lateral pattern inside E-Cu and thus guides the Li dendrites to grow laterally within the interior Cu scaffold. Instead of suppressing/delaying the dendritic growth, this technology is dedicated to regulate the dendrite growth direction parallel to the separator so that the batteries can still work safely even when dendrites are already massively existed. All the processes involved, including hot lamination, laser ablation and alkaline etching (as schematically illustrated in Fig. 1a), have been widely used in the fields of electronic and semiconductor industry for more than half a century 32, 33, 34 , which can ensure the highest conformity level.

Revised text 3:
In summary, this manuscript demonstrates that guiding Li dendrites to grow laterally in compartmented micro-electrodes is an effective way to manage the safety issue of Li anodes, which is different to the widely adopted strategies in suppressing/delaying the dendritic growth.
The model structure can effectively change the electric field distribution and make accommodation to the plated Li metal.

Revised text 4
Besides, the excellent compatibility between this compartmented electrode structure with industrially-available fabrication techniques, including hot lamination, laser ablation and alkaline etching, also renders this technology with unprecedented conformity and reliability. Therefore, it would be a critical step towards large scale manufacturing of Li metal anode based batteries. This unique strategy is a first attempt to deal with the extreme situation when lithium dendrites have massively presented via manipulating the electric field distribution and growth dynamics of Li dendrites, which provides new insights into the unwelcomed dendrite-growth issue, and will inspire technological development of other metal anodes in rechargeable systems. It is noted that the electrolyte was assumed as a statically distributed medium instead of a dynamic one when calculating the electric field for all cases. During the simulation of von Mises stress distributions on the dendrite protrusions (Fig. 3), the diameter of the simulated protrusion is assumed to be 5 μm, which is positioned at the center of the pinhole.

Revised text 2:
This indicates that the diffusion of electrolyte is at a fast-enough time scale to provide an electrochemically active surface inside the compartment at the range of current densities employed in the experiment (0.25 to 1.0 mA cm -2 ), thus sustaining the electric current. Therefore, electric field becomes the dominant factor which can determine the growth of lithium dendrite inside the compartments, according to the space-charge model in Chazaviel's theory. Consequently, the influence of potential gradient generated from the uneven anion depletion during a dynamic charge/discharge process is less significant, so that the electrolyte can be assumed to be a static medium (charge carrier) to simplify the simulation.  (Fig. 1e), porosity analysis result for E-Cu with mercury porosimetry (Fig. 1f), and the simulation of von Mises stress distributions on the dendrite protrusions (Fig. 3), in the revised manuscript. In addition, the corresponding description are also updated in the revised manuscript.
Original Figures: Figure 1 Revised Figures: weight of E-Cu tested here was 0.3141 g and the total surface area for all compartments was 9 cm 2 ; thus, the effective pore volume of E-Cu is 1.88×10 -3 cm 3 cm -2 .

Revised text 1:
Whereas, the extreme situation when controlled dendrite suppression/delay is lost in these strategies has been rarely discussed because the emergence of Li dendrites cannot be completely avoided during prolonged cycling 3 , especially when batteries are operated at high current densities, in overcharge ultimate, or at low operation temperatures 26, 27 .

Original text 2:
On the other hand, the electro-deposition/dissolution behaviors of Li metal and corresponding influence factors are intrinsically complicated, rendering it hardly predictable and extremely difficult to be managed with available technologies.

Revised text 2:
On the other hand, the electrodeposition/dissolution behaviours of Li metal and the corresponding influencing factors are intrinsically complicated, rendering the control over these behaviours hardly predictable and extremely difficult to be managed with available technologies.

Original text 3:
Accordingly, we simulated using structural stress analysis model, and observed an approximately 60% reduction of stress from protruded Li dendrites in E-Cu over P-Cu (Fig. 3).

Revised text 3:
Accordingly, we simulated this stress using a structural stress analysis model and observed an approximately 60% reduced stress from the protruded Li dendrites in E-Cu as compared to that in P-Cu (Fig. 3).

Original text 4:
In addition, several dendrites-induced short circuits occurred in P-Cu based Li anode during cycling, which can be observed from the voltage profile where voltage abruptly swooped from high potentials to lower ones as indicated in Fig. 6c.

Revised text 4:
In addition, several dendrites-induced short circuits occurred in the P-Cu based Li anode during cycling, which can be observed from abrupt voltage drops from high potentials to lower potentials in the voltage profile, as indicated in Fig. 6c.

Original text 5:
In a sandwich cell structure, the distribution of electric field predominately presents a vertical pattern; thus once Li dendrite forms, it will grow vertically towards separator and cathode 3,4,29,30 , and eventually could impale the separator and cause internal short circuit of the battery 3 .

Revised text 5:
In a sandwich cell structure, the electric field is predominately distributed in a vertical pattern; thus, upon Li dendrite formation, the dendrite will grow vertically towards the separator and cathode 3,4,29,30 , and eventually could impale the separator and cause an internal short circuit in the battery 3 .