## Introduction

^{1‐3}In addition, a corrosive reaction between the electrode slurry and aluminum current collector is a challenge during manufacturing of aqueous cathodes.

^{4‐6}Especially for thick, high-capacity electrodes and electrodes with low binder content, it is a major challenge to achieve sufficient adhesion of the active material to the current collector.

^{1,2,7‐12}Furthermore, there are materials that promise improved cell performance but have poor adhesion.

^{13,14}To improve adhesion of electrodes, multilayer configurations with different layer properties are promising.

^{10,15‐20}Kumberg et al. and Diehm et al. demonstrated concepts for two-layer electrodes with increased binder content in the lower layer and very low binder content in the upper layer of the two-layer electrodes in order to increase adhesion.

^{10,17}

^{4,21‐24}Furthermore, in production of aqueous cathodes, the coating of a primer layer as a blocking layer is an option to prevent corrosion reactions of the active material with the current collector aluminum foil.

^{4}

^{21,24}To inhibit corrosive reactions, the layer thickness of primer layers as blocking layers should be approx. 3–5 µm.

^{4}Different layer thicknesses result in different wet film thicknesses, which leads to different settings of the coating gap in production. Diehm et al. used a set-up with slot die and vacuum box, which prevents air-entrainment related defects, allowing to ramp up process speeds with the aim of an economically profitable production of thin aqueous primer layers for graphite anodes with low binder content.

^{21}Aqueous processing of primer layers or electrodes reduces production costs, since no solvent recovery has to be taken into account during drying.

^{25}It was also shown that the coated primer layers improve adhesion of the electrode to the current collector without deteriorating cell performance. In addition, process limits were investigated at a constant coating gap. It was shown that an extended coating window (ECW) exists at high coating speeds (approx. u

_{w}> 100 m min

^{−1}) for shear-thinning fluids with the known coating defect mechanism low-flow limit.

^{21}In general, the low-flow limit is a common coating defect, occurring as a result of an unstable downstream meniscus and typically visible as stripes in coating direction.

^{26‐30}For lower coating speeds (approx. u

_{w}< 100 m min

^{−1}), the minimum wet film thickness increases with coating speed, which is well known in the literature. In contrast, for higher coating speeds (approx. u

_{w}> 100 m min

^{−1}), the downstream meniscus is stabilized due to the increasing ratio of inertia to capillary forces and viscous forces. Consequently, the minimum wet film thickness h

_{wet}in the extended coating window is significantly lower than conventional predictions by calculations of the low-flow limit. As known from the literature, the low-flow limit is independent from material properties in the dimensionless representation of the coating window.

^{21,26}This behavior could not be shown for the extended coating window.

^{21,26}Diehm et al. were able to predict the minimum wet film thickness in the extended coating window for high-speed slot-die coating with vacuum box of shear-thinning primer fluids with a defined proportionality factor (h

_{min}= κ

_{ecw}u

_{w}

^{−1/}

^{2}) for a constant coating gap.

^{21}Carvalho and Kheshgi have also shown the reciprocal proportionality between wet film thickness and coating speed in the extended coating window for different Newtonian fluids (h

_{min}~ u

_{w}

^{−1/}

^{2}) for a constant coating gap.

^{26}In order to optimize formulations or solid content of primer slurries and to be able to adjust the thickness of primer layers and the coating gap as needed, it is important to generate an advanced understanding of high-speed slot-die coating with vacuum box. In the literature, no analytical predictive model for high-speed slot-die coating with vacuum box that includes shear-thinning viscosity and coating gap could be found. Therefore, the influence of different coating gap settings and different viscosities is investigated in this work. To predict the coating window of high-speed slot-die coating with vacuum box as a function of viscosity and coating gap, a combined analytical model, which includes the low-flow limit and the extended coating window, is presented.

## Methods

^{21,26}In order to predict the operating limits in slot-die coating, the models of the low-flow limit as well as the extended coating window must be combined to cover the entire range of coating speed.

^{26,28,29,31}

^{*}are included. In case of shear-thinning fluids and an approximated Couette flow, the capillary number is defined as [equation (2)]:

_{w}, coating gap h

_{G}, surface tension σ and the power-law parameters consistency index κ and flow index n. The dimensionless coating gap is the ratio of coating gap h

_{G}to wet film thickness h

_{wet}[equation (3)].

_{min, low flow}of shear-thinning fluids can be derived from equations (1)–(3).

^{30,32}

^{*}

_{max, low flow}can be calculated using equations (1) and (2).

^{33}In Fig. 2, the transfer of boundary-layer theory to slot-die coating is shown. p

_{vac}is the vacuum pressure adjustable by the vacuum box, p

_{atm}is the ambient pressure and Re is the Reynolds number.

_{w}[equation (6)].

^{33,34}In this case, inertia forces are low (low Reynolds numbers Re and low Weber numbers We).

^{34}

_{b}to wet film thickness h

_{wet}is a function of the ratio of inertia and viscous force [equation (8)].

^{27}Due to the conservation of mass, this must be also valid for the ratio of critical length of the boundary layer L

_{b}

^{*}to the minimum wet film thickness h

_{min}.

^{26}

^{27}

^{33}

_{wet}in pre-metered coating, with η being the viscosity of Newtonian fluids.

^{34}By rearranging equation (11), the length of the boundary layer L

_{b}can be described as follows [equation (12)]:

^{2}for pre-metered coating devices with sufficient accuracy for Newtonian fluids. Therefore, they observed the coating bead of a pre-metered coating device by using an argon laser beam and compared the observed length of the boundary layer to the calculated length of the boundary layer.

^{34}Arzate and Tanguy could also present an adequate accuracy comparing observed and calculated length of the boundary layer for high-speed jet-coating applications for Newtonian and shear-thinning fluids. They observed the impingement region between jet coater and substrate with a video camera. To calculate the viscosity of the shear-thinning fluid, they used a power-law approach and approximated the given viscosity for a corresponding shear rate, determined from the volumetric flow rate.

^{35}

_{min}of the extended coating window for high-speed slot-die coating with vacuum box of Newtonian fluids [equation (13)].

^{26}

^{26,34}Due to the complexity of the flow in the coating gap, it is impossible to analytically calculate the viscosity as a function of the shear rate for a given coating gap without numerical methods. Therefore, we neglect the pressure-driven flow component due to high coating speeds and assume a Couette flow in the coating gap at the inner edge of the downstream lip to calculate an effective viscosity as a function of the shear rate η

_{calc}. The effective viscosity of shear-thinning fluids in the coating gap is calculated with experimentally determined consistency factor κ and flow index n.

_{b,calc}

^{*}is the calculated critical length of the boundary layer.

_{b}

^{*}and the minimum wet film thickness h

_{min}are both unknown, an empirical equation of the form f(h

_{G}, η, u

_{w}, ρ) for L

_{b,calc}

^{*}is determined [equation (17)].

_{b,exp}

^{*}is calculated from the data of the minimum wet film thickness h

_{min,exp}determined in the experiments [equation (18)].

Parameter | Value/– |
---|---|

a | 0.018 |

b | 1.000 |

c | 0.553 |

d | 0.312 |

e | 1.565 |

^{2}for L

_{b,exp}

^{*}and L

_{b,calc}

^{*}is 0.939, which is sufficiently accurate (see Fig. 8). With equations (17) and (18) and the determined factors and exponents, the extended coating window of high-speed slot-die coating with vacuum box can be theoretically predicted for different coating gaps and different viscosities.

## Experimental methods and materials

### Slurry preparation

CMC-solution | CMC-content/wt% |
---|---|

CMC-A | 1.2 |

CMC-B | 0.5 |

CMC-C | 0.3 |

^{−1}.

### Experimental coating set-up and coating window characterization

_{G}via PET shims (105 µm, 180 µm and 250 µm) between slot die and steel roller. The slot width of the slot die was adjusted to l

_{S}= 200 µm, and the die outlet width was set to b

_{width}= 150 mm using a spacer shim. The dimensions of the slot die are shown in Fig. 4.

^{−1}were investigated. In all experiments, the vacuum pressure was adjusted until the mechanism of coating defects changed from air entrainment to low-flow limit. Then, the volume flow and, thus, the wet film thickness was adjusted using a pressure tank with a precision needle valve until the coating was stable. To make the defects clearly visible, the UV marker DSBB was used. This procedure was repeated for each coating speed. The pressure tank and the whole fluid handling system is designed for 6 bar maximum feed pressure. The wet film thickness was measured by using a chromatic confocal sensor with measuring range of 600 µm and a resolution of 20 nm in y-direction (CHRocodile SE, Precitec KG).

## Results and discussion

### Prediction of process stability

^{2}is above 0.999 for all calculations in the relevant range of shear rate.

CMC-solution | κ/Pa s ^{n} | n/– |
---|---|---|

CMC-A | 4.15 | 0.45 |

CMC-B | 0.44 | 0.59 |

CMC-C | 0.09 | 0.69 |

h _{G}/µm | \(\dot{\gamma }\) _{min}/s^{−1} | \(\dot{\gamma }\) _{max}/s^{−1} |
---|---|---|

105 | 7936.5 | 79365.1 |

180 | 4629.6 | 46296.3 |

250 | 3333.3 | 33333.3 |

^{−1}(standard deviation 0.73 mN m

^{−1}) and a density of approx. 1017 kg m

^{−3}.

^{26,28}The area for stable coatings in the extended coating window is above the calculated lines of the extended coating window in the dimensionless coating window. Below these calculated lines is the unstable area in the extended coating window. As known from literature, the dimensionless low-flow limit line is not affected by material properties. In contrast to the dimensionless low-flow limit, the influence of coating gap and material properties can be seen in the calculation of the dimensionless extended coating window. A decreasing coating gap results in smaller capillary numbers and smaller dimensionless coating gaps [equations (2) and (16)]. For shear-thinning fluids, the coating gap directly influences viscosity. A decreasing viscosity from material system CMC-A to CMC-C leads to a shift of the coating window towards smaller capillary numbers and higher dimensionless coating gaps [equations (2) and (16)]. In addition, a decreasing viscosity reduces the influence of the coating gap on the extended coating window. As a result, the calculated lines for different coating gaps converge with decreasing viscosity.

### Validation of the model

_{b,exp}

^{*}and calculated critical length of the boundary layer L

_{b,calc}

^{*}of all model systems and coating gap settings are plotted in Fig. 8.

_{b,calc}

^{*}compared with L

_{b,exp}

^{*}is sufficiently good. Deviations can be justified by errors in the experimental data (e.g., setting of the coating gap). The errors due to the maximum possible deviation of the set coating gap of Δh

_{G}= ± 10 µm are taken into account in the calculations of the low-flow-limit and the extended coating window and are represented by a shaded area around the calculated lines in the following graphs.

#### Influence of coating gap on process stability

_{G}= ± 10 µm show good agreement. Some of the experimental values are slightly below or above the calculation, but clearly follow the low-flow limit model.

^{−1}to 98 µm, for a coating gap of 180 µm until 70 m min

^{−1}to 53 µm, and for a coating gap of 105 µm until 100 m min

^{−1}to 30 µm. After reaching the described maximum of the low-flow limit, there is a transition point where the experimental values of the minimum wet film thickness decrease with increasing coating speed and follow the calculation of the extended coating window (intersections of the purple line with the interrupted dark green lines). For a coating gap of 250 µm, the experimental values of the wet film thickness decrease to 67 µm at 200 m min

^{−1}, for a coating gap of 180 µm to 38 µm at 300 m min

^{−1}and for a coating gap of 105 µm to 20 µm at 500 m min

^{−1}. For coating gap settings of 250 µm and 180 µm, the experimental values of the minimum wet film thickness would theoretically continue to decrease with increasing coating speed, but with the high viscosity of material system CMC-A it was impossible to experimentally determine stable values of wet film thickness at coating speeds above 200 and 300 m min

^{−1}, respectively. The volume flow in the experimental setup was limited due to the high pressure drop resulting from high viscosity at high coating speeds.

^{−1}.

_{G}= ± 10 µm show good agreement in both representations of the coating window. In case of the dimensionless coating window (Fig. 10, left), the critical capillary number of the low-flow limit increases with decreasing dimensionless coating gap for all investigated coating gaps. As previously explained, the dimensionless coating gaps reach a minimum in the dimensionless coating window and follow the calculation of the extended coating window after individual transition points (intersections of the purple line with the interrupted light red lines). Increasing coating gaps lead to higher capillary numbers and higher dimensionless coating gaps. As explained in Fig. 7, a decreasing viscosity leads to a decreasing influence of the coating gap on the coating window. In the case of a coating gap of 105 µm, the experimental values of the capillary number and the dimensionless coating gap deviate from the calculated low-flow limit and the extended coating window including the deviation from the coating gap setting. For very small coating gaps, the VCM may no longer be valid due to the high viscous pressure drop. The neglect of the pressure drop in the coating gap in the calculation of the extended coating window could cause the calculation to deviate from the experimental data.

^{−1}, for a coating gap of 180 µm to 34 µm at 150 m min

^{−1}, and for a coating gap of 105 µm to 24 µm at 250 m min

^{−1}. After reaching the described maximum of the low-flow limit, the experimental values of the minimum wet film thickness reach the individual transition point and decrease with increasing coating speed, following the calculation of the extended coating window (intersections of the purple line with the interrupted light red lines). For a coating gap of 250 µm, the experimental values of the wet film thickness decrease to 27 µm, for a coating gap of 180 µm to 23 µm and for a coating gap of 105 µm to 18 µm at a coating speed of 500 m min

^{−1}. In the case of a coating gap of 105 µm, the experimental values of the minimum wet film thickness of the extended coating window exceed the calculated ones, including the deviation from the coating gap setting on average by 19.0 % and 3.4 µm. For material system CMC-C, the required wet film thicknesses of typical primer coatings for adhesive layers of approx. 20–25 µm can be achieved with a coating gap of 180 µm at a coating speed of 500 m min

^{−1}.

#### Influence of viscosity on process stability

^{−1}to 98 µm, and for material system CMC-B until 100 m min

^{−1}to 62 µm, and for material system CMC-C until 150 m min

^{−1}to 42 µm. After reaching the individual transition point, the minimum wet film thicknesses decrease with increasing coating speed with the prediction of the extended coating window (intersections of the purple line with the interrupted dark green, medium blue and light red lines). For material system CMC-A, the experimental values of the wet film thickness decrease to 67 µm at 200 m min

^{−1}, for material system CMC-B to 42 µm at 400 m min

^{−1}and for material system CMC-C to 27 µm at 500 m min

^{−1}. For material systems CMC-A and CMC-B it was impossible to stabilize the coating at higher coating speeds. As explained earlier, the volume flow was limited due to increasing pressure drop with increasing viscosity.

## Conclusions

^{−1}). Decreasing viscosity leads to smaller values of the minimum wet film thickness, larger dimensionless coating gaps and smaller capillary numbers. In addition, a decreasing coating gap leads to smaller values of the minimum wet film thickness, larger dimensionless coating gaps and smaller capillary numbers. Consequently, the coating gap must be adjusted to achieve the target wet film thickness and, therefore, the target layer thickness for different material properties used for different coating applications. For the most viscous material system CMC-A, it is possible to reach typical wet film thicknesses of primer coatings for adhesive layers of 20–25 µm with a coating gap of 105 µm at a coating speed of 500 m min

^{−1}. The same target wet film thickness was reached for material system CMC-C with 2.5 times lower viscosity comparing the corresponding shear rates with a coating gap of 180 µm at a coating speed of 500 m min

^{−1}.