A Processing Model toward Printing High-Flatness Layers for Direct-Ink-Writing Printed Self-Leveling Inks

Abstract

The direct-ink-writing (DIW) has been widely used to print various functional devices using different self-leveling inks. Due to the complicated rheological behavior and multiple processing parameters, how to rapidly determine the crucial parameter for high-precision printing is still challenging. Here we adapt a widely used commercial silver paste and identify the critical parameter for dominating the flatness through observation of the microstructure evolution for the line-to-layer forming process. An analytical model for flatness with printing parameters was established. Using the proposed model, the printing process parameters for achieving high flatness can be directly determined, avoiding the high cost of extensive experimental exploration.

1. Introduction

Direct-ink-writing (DIW) is an additive manufacturing technology that is widely employed in diverse fields, ranging from sensors [1,2,3,4,5], soft robotics [6,7,8], wearable electronics [9,10], tissue engineering [11,12,13], stretchable electronics [14,15,16], to microfluidics [17,18]. This technology offers the possibility of rapid printing of complex 3D structures using various inks, including conductive pastes [14,16], elastomers [8,19,20,21], and hydrogels [22,23,24,25,26]. In the realm of rheological materials, inks that possess self-leveling properties, such as conductive inks, hydrogels, and PDMS, are highly printable and versatile, which demonstrate immense potential for a wide range of electronic applications [15,16].

Compared to traditional manufacturing methods, DIW is constrained by the shaping process from lines to layer. Additionally, the printing process involves a complex array of parameters, making it difficult to rapidly optimize these parameters to achieve controlled layer thickness, high flatness, and precision printing. Regarding this particular issue, Yuk and Zhao [27] built a phase diagram of printing parameters, which can guide the printing of viscoelastic ink fibers of different shapes, and break through the limitation of line resolution to print fibers finer than the diameter of the nozzle. Their main contribution inspired this paper on how to construct a geometric model describing the layer surface and control key parameters to achieve high-precision printing of ink layers.

At present, there are few studies on the flatness of the DIW printing surface. Felden et al. [28] used different nozzle diameters to print ceramic materials and found that large nozzle diameters lead to a lower dimensional accuracy. Buj-Corral et al. [29] studied the effect of printing parameters on the dimensional error and the surface roughness of the ceramic part. In our previous study [3], we provided an optimized set of process parameters for achieving high surface smoothness in self-leveling ink printing based on the observed effects of changes in needle inner diameter and line spacing. However, experimental observations and measurements typically only yield descriptive and phenomenological laws, whose applicability is usually limited to the same type of material.

In addition, there are many studies on optimizing surface flatness for fused deposition modeling (FDM) [30,31,32]. Although the line-to-plane forming process of DIW is similar to FDM, the surface morphology of DIW is significantly different from that of FDM, especially the self-leveling inks is used for DIW. For the FDM materials, the section of the printed line almost keeps a circle shape after welding. The roughness of the FDM printed surface is mainly determined by the rising height (related to line width) [30]. For the DIW-printed self-leveling inks studied in this work, the extrusion-formed surface before curing tends to reach high flatness but finally forms a rippling morphology induced by the evaporation speed gradient. The different mechanisms of material forming behaviors between the FDM and DIW lead to different mathematical models. Therefore, the generality of the proposed model is not expected to be compatible with the FDM surface flatness optimization.

To investigate the influence mechanism of crucial parameters on the flatness of printing layers, we carefully observed the microstructure evolution process from line to plane of the self-leveling printing ink and identified the critical parameters that effect the flatness. A quantitative parameter for flatness characterization was proposedly based on the microstructure geometric features. On this basis, a mathematical model for flatness with printing parameters was established. Using the proposed model, the printing process parameters for achieving high flatness can be directly determined, avoiding the high cost of extensive experimental exploration.

2. Materials and Methods

Printing of ink surface: A three-axis robot (SHOT, mini 200SX, MUSASHI) was used to control the nozzle to move in an S-shaped path, with the path programmed using the software (MUCADV). A dispensing machine (ML-5000XII, MUSASHI) was used to control the extrusion of ink from the nozzle. During the printing process, only nozzles with an inner diameter of 410 μm (RUIWING) were used, and the nozzle height h_n was kept greater than or equal to the nozzle inner diameter d_n to avoid the nozzle scraping the ink. Glass slides were used as substrates. After printing, the ink was cured for 24 h in the atmosphere. The air pressure of the dispensing machine could not be too low to ensure continuous extrusion of ink from the nozzle in a cylindrical shape (as shown in Figure 1). It was found through experimentation that the silver paste could be extruded in a cylindrical shape from the nozzle with an inner diameter of 410 μm when the air pressure of the dispensing machine was 400 KPa.

Measurement of ink surface flatness: A white light interferometer (FMD-D) was used to obtain surface information of the ink layers. The surface profile data of the ink surface were obtained and processed using software (gwyddion).

Rheological properties of the silver paste: Figure 2a shows that the silver paste used has a low zero-shear rate viscosity and shear-thinning characteristics. Figure 2b,c show that the silver paste has no significant yield stress and tends to remain in a liquid state. When measuring viscosity and shear stress, the parameters are set as follows: Mod is CR, distribution is line, type is stepwise, Duration is 120 s and Temperature is 25°. When measuring storage modulus G′ and loss modulus G″, the parameters are set as follows: Mode is CS, Shear stress τ₀ is 1.00 Pa, Distribution is Log, Freq/Decade is 6 based on ω and Temperature is 25°. For the measurement of rheological properties of carbon paste (CH-8, JELCON), please see Supplementary Materials.

Measurement of the contact angle: The contact angle between the ink and the substrate is a parameter related to the surface tension. The width of the single printed ink line is affected by the contact angle. When printing the ink layer, the contact angle affects the slope of the border between stacked ink lines. The measuring instrument (XG-CAM, XYCXIE) is used to measure the contact angle at different contact diameters. Figure 3 shows the measured contact angle data. For the detailed process of measuring contact angle, please see Supplementary Materials.

3. Results

3.1. Analytical Modelling

Figure 4 illustrates the typical steps and parameters of printing a layer using self-leveling ink through DIW technology. During the printing process, the nozzle moves laterally at a speed of v_n at a height h_n from the substrate, while the ink is extruded from the nozzle by air pressure to print an ink line with a width l on the substrate. Surface tension causes a contact angle θ to form between the ink line and the substrate. Multiple ink lines with a spacing of l_s (l_s < l) can be printed side by side to create an ink layer. The crucial parameter controlling the layer thickness is the line width l, which depends mainly on process parameters such as the nozzle inner diameter d_n, nozzle moving speed v_n, and ink extrusion speed v_e. Previous work has shown that printing thinner layers is critical for improving the interface strength of multi-layer sensor composite structures [3]. Among the related printing parameters, the line spacing ls is the crucial parameter controlling the flatness of the ink layers. When the line spacing is too small, the overlap between adjacent ink lines increases the overall layer thickness (higher than the height of a single line), making it difficult to obtain the desired thin layer. Increasing the line spacing leads to the formation of ripples on the surface of the layer during the process of forming lines into a surface due to surface tension, which affects the flatness of the layer. In addition, if the spacing between adjacent ink lines exceeds the maximum gap that can be covered by self-leveling fusion, it is unable to print a complete flat surface. To achieve controllable printing of layer thickness and surface ripple, a large number of expensive process optimization experiments are necessary, and usually only empirical rules can be summarized, making it difficult to obtain a universal theoretical model.

To address the aforementioned issues, we first observed and summarized the microstructural evolution of the ink during the forming process of lines-to-layer using DIW printing, and then identified the key governing parameters. Subsequently, a processing model was established to control the surface morphology with high precision. Based on this model, high-precision printing of layers with controllable thickness and high flatness can be achieved. The work presented in this paper offers a low-cost and rational solution for achieving high-precision, controllable direct writing printing.

A widely used silver ink (CD-03, Conduction) is used to print multiple ink lines, with the spacing between lines controlled to be less than the line width, so that multiple lines can merge to form a plane. However, the uncured layer with planar surface (Figure 5a–c) becomes rippled after curing (Figure 5d–f). Figure 5a shows the optical image of the ink surface before solidification, where the color at the intersection of the ink lines is darker than at other locations. Figure 5b shows the white light interference image of the ink surface before curing, indicating high flatness. Figure 5c shows the cross-sectional profile corresponding to Figure 5b. Figure 5d,e show the optical and white light interference images of the ink surface after curing, respectively, revealing that the wave-like ripples on the layer surface are formed. Figure 5f shows the cross-sectional profile corresponding to Figure 5e. It is indicated that this is caused by differences in density at the intersection of the ink lines compared to other locations, which will be discussed later. Figure 6a shows the general process of lines to layer. The extruded ink lines merge to form a layer with relatively high flatness due to the self-leveling of the ink. The contact angle affects the slope of the border between stacked ink lines (Figure 6a), which may affect the flatness of the ink layer before leveling to a plane. However, the printed ink layer only keeps ripple morphology as a processing intermediated state and will tend to flat-plane induced by the leveling. The final flatness after curing is mainly dominated by the evaporation gradient from the interfaces among the adjacent lines into the inner of the lines. In order to reduce the ripples to improve the flatness, we established a model to quantify the relationship for the ripple height with the crucial parameter of line spacing. Using this model, the optimization processing parameters for high flatness printing can be directly determined. In order to simplify the model, some assumptions are put forward according to the observation based on tests: (i) the ink layer is fully leveled before curing; (ii) the lateral dimension of the ink layer will not change after curing; (iii) the angle α between the circular arc and the vertical line passing through the highest point of the stripe is a constant value; (iv) the solid loading of the ink is not taken into account.

Experimental results have shown that the geometric shape of the stripes formed after ink curing varies slightly with the spacing l_s between ink lines on the printing plane. As shown in Figure 6b, when l_s is less than or equal to a certain value l_s0, the vertical cross-sectional profile of the ink-cured surface can be approximated by multiple circular arcs. Assuming that the angle α between the circular arc and the vertical line passing through the highest point of the stripe is a constant value, we can establish a model to describe the profile of the ink-cured surface:

$$y=r_c-\sqrt{r_c^2-{\left(x-k{l}_s\right)}^2},-\frac{l_s}{2}+k{l}_s<x<\frac{l_s}{2}+k{l}_s,k=0,\pm 1,\pm 2,\dots ,$$

(1)

where (x, y) are the cartesian coordinate points, representing the cross-sectional profile of the ink layer. The symbol k represents the number for kth strip; r_c = l_s/2cosα is the radius of the arc. As shown in Figure 6c, when the distance between ink lines on the printing surface l_s is greater than a certain value l_s0, the height of the striped protrusions no longer changes, and the radius of the arc r_c also remains unchanged. There is a relatively flat contour between the striped protrusions. Therefore, we can represent the contour model as:

$$y=\{\begin{array}{c}{r}_{c0}-\sqrt{r_{c0}-{\left(x-k{l}_s\right)}^2},-\frac{l_{s0}}{2}+k{l}_s\le x<k{l}_s\\ 0\\ r_{c0}-\sqrt{r_{c0}^2-{\left(x-\left(l_s-l_{s0}\right)-k{l}_s\right)}^2},l_s-l_{s0}+k{l}_s\le x<l_s-l_{s0}+\frac{1}{2}{l}_{s0}+k{l}_s\end{array},k=0,\pm 1,\pm 2,\dots ,$$

(2)

where, r_c0 = l_s0/2cosα is the constant radius of the arc when the line spacing l_s is greater than l_s0. For detailed derivation of the geometric model, please see Supplementary Materials.

If the maximum height difference ΔH of the cross-sectional profile is used to describe the flatness of the ink surface, theoretical calculations can be performed to obtain:

$$\mathsf{\Delta }H=\{\begin{array}{c}{r}_c-r_{c}sin\alpha ,l_s\le l_{s0}\\ r_{c0}-r_{c0}sin\alpha ,l_s>l_{s0}\end{array}$$

(3)

3.2. Model Verification

For the silver paste, α of 81° and a nominal line spacing l_s0 of 409 μm are determined by testing. Figure 7 shows the white light interference images of the ink surface obtained at different line spacings, as well as a comparison of the experimental and theoretical cross-sectional profiles. Figure 8 shows a comparison between the maximum height difference of the ink surface obtained experimentally and that predicted by the theoretical model for different line spacings. The average value of height measured for each peak of the ripple are calculated as the ΔH. It is shown that the experimental results agree well with the theoretical model. Furthermore, it is suggested from the model that the smaller the line spacing l_s, the smaller the height difference ΔH. However, in practical experiments, there is a lower limit for the line spacing l_sm, below which the flatness of the ink surface cannot be further improved. In this case, the surface roughness is dominated by the inclusion particle sizes, which are greater than the height of ripples. Moreover, the critical line spacing l_sm for the silver paste is experimentally calibrated around 204 μm.

The layer thickness can be adjusted by controlling the extrusion volume per unit length. As shown in Figure 6a, based on the volume conservation for the printing ink, the layer thickness is determined by:

$$h_l=\frac{a{S}_p}{l_{sm}},$$

(4)

where S_p is the cross-sectional area of a single printed ink line. As shown in Figure 4, if S_p is calculated using the ink line width l, then S_p = bl²/4, where b is a fixed value determined by the contact angle θ and is given by b = θ/sin²θ − cosθ/sinθ. The symbol h_l is the overall thickness of the cured ink surface, and a is the solid content. If the layer thickness is estimated based on the width of a single ink line, then:

$$h_l=\frac{ab{l}^2}{4l_{sm}}.$$

(5)

For detailed derivation of the equation for calculating layer thickness, please see Supplementary Materials.

4. Discussion

One of the novelties revealed in this work is the transition status with a highly flat surface before the curing. How the ripples emerge from a flat uncured layer is curious. For the silver paste with high viscosity, the boundary of the extruded line cannot be completely eliminated after the adjacent lines merge. Therefore, in the optical image in Figure 5a, there are visually dark stripes even if the layer surface is quite flat (Figure 5b,c). After curing, the ripples form at the periodic dark-stripe locations, affecting the flatness. The residual boundary between the overlapped lines accelerates the curing process. The adjacent ink is driven by surface tension to gather at the boundary location. Consequently, the gathered ink forms the ripple after curing is completed. This phenomenon may be similar to the coffee ring effect. The ink at the boundary evaporates and solidifies faster, so that the ink at other positions flows to this place, resulting in more solidified ink at the boundary than other positions. A carbon paste similar to the silver paste is used to print the ink layer (see Figure S5 in the Supplementary Materials). Ripples were also observed on the surface of the carbon paste layer. The in-depth mechanism for this phenomenon will be explored in the future studies.

When the spacing is small (204–307 μm), as shown in Figure 7, the proposed theoretical model predicts ΔH is slightly higher than the experimental value. It is concluded that the α becomes slightly larger than the constant value for small l_s (204–307 μm). α slightly decreases with l_s and tends to a stable value until l_s > l_s0. It is believed that α can be generally treated as material constant. The slight increment of α for l_s around 204–307 μm may be attributed to the enhanced interaction between excessively overlapped lines.

5. Conclusions

In this study, we systematically analyzed the microscope morphology evolution during the forming process from lines to layer, in order to precisely control the thickness and flatness for DIW printing. We identified the key parameters and developed a mechanical model for optimizing the processing parameters of self-leveling. The proposed model provides new insights into the analytical-model-based processing parameter optimization for extrusion-type DIW 3D printing technology.