Ink-Jet Printing towards Ultra-High Resolution: A Review

Abstract

Ink-jet printing combines large-area film fabrication with low-cost solution processing. A high-resolution display calls for small-sized and closely arranged pixels, which can be realised using ink-jet printing. Here, we introduce the relevant steps of ink-jet printing, namely, droplet formation, falling, hitting the substrate, spreading, and the formation of a pixel. On the basis of a summarisation of factors that affect pixel formation, an approximation model is established to explore the minimum size of a pixel.

1. Introduction

Future display applications call for life-like colours and crystal-clear accuracy [1,2,3]. At the same time, the balance between high quality and low cost needs to be considered [4]. At present, producing pixel array mainly relies on photo-lithography printing, transfer printing, and ink-jet printing [5]. Among them, ink-jet printing is easier to operate, cheaper, and has a higher utilisation rate of raw materials [6,7,8,9,10,11,12], which is a promising strategy to produce small-sized and closely arranged pixels via low-cost solution processing [13]. Ink-jet printing, now, still has good prospects; in recent years, there are many relevant papers that have been published (Figure 1). Although laser printers currently have higher resolution and faster printing speed, ink-jet printing is cheaper and more mature, and it is still widely used in daily business and civilian use. Unlike other reviews, this paper focuses on the pixel formation process, and it is not directly linked to practical applications or techniques, nor does it discuss the case of pixel integration [14,15,16,17,18,19]. Resolution is an important indicator in ink-jet printing. The resolution size directly determines the refinement of the presentation pattern. This paper reviews the resolution of individual pixels [2].

The ink-jet printing process that transfers a flowing solution into ordered solids can be divided into five steps: droplet formation, droplet falling, droplet hitting the substrate, droplet spreading, and pixel formation. This process has nothing to do with the specific printing technology; To facilitate the description, we used the piezo-electric inkjet model as an example for the analysis (Figure 2a) [20,21]. In the first step, namely, droplet formation, the ink is ejected from the nozzle driven by pressure to form a liquid column, and then the liquid column transforms into a spherical droplet. The droplet radius determines the final pixel size. The droplet radius is a function of several independent variables, including the nozzle radius, liquid viscosity, liquid density, and pressure acting duration. The next step is droplet falling, where satellite droplets may form during this process, and the liquid viscosity plays an important role here. Then, when the droplet hits the substrate, it may splash if the momentum is too large or if the ink viscosity is too low. After that follows droplet spreading, which determines the pixel uniformity [22]. The spreading process is determined by the Weber number, contact angle, atmosphere, falling velocity, and surface tension. The last step is the formation of a pixel, which refers to the solvent evaporation and the solute condensation processes and is typically accompanied by the coffee ring effect, namely, solute accumulation at the edge of the droplet (Figure 2b). The formation of a coffee ring is mainly controlled by the following factors: substrate surface roughness, solution concentration, interparticle interaction, and temperature.

Here, an overview of the relevant steps of ink-jet printing, namely, droplet formation, falling, hitting the substrate, spreading, and the formation of a pixel are presented. We establish a simple model demonstrating that: the minimum pixel size can be achieved by decreasing the droplet diameter through reducing the nozzle radius, reducing the liquid viscosity, increasing the ink density, and shortening the actuation duration of the applied voltages and the nozzle radius is the determining factor in this process. Moreover, to some extent, reducing the ink density can make the droplet falling more stable; optimizing the momentum can prevent the droplets from impinging when hitting the substrate; increasing the distance between the nozzle and the substrate can reduce the pixel diameter; the nozzle applied pressure size will be the most important parameter in the whole process; creating an appropriate atmosphere, increasing the surface tension, increasing the Webber Count, and reducing the contact angle make the pixel more uniform—the contact angle is very important in this step; the pixel formation that accompanies the coffee ring can be influenced by the temperature, hydrophilicity of the droplet, droplet size, and atmosphere; and the appearance of a coffee ring can be suppressed by reducing the substrate surface roughness, controlling the solvent concentration, adjusting the interaction between particles, and choosing an appropriate temperature, among them, controlling the roughness size can make the three-phase line pinning, which is one of the decisive factors in inhibiting the coffee ring (Figure 3).

2. Discussion

2.1. Droplet Formation

We established a simple model based on the following approximations: (1) The solute (quantum dots, nanoclusters, polymers, small molecules, etc.) is uniformly dispersed in the solvent to form a uniform ink. (2) The applied pressure Ps produced by the piezoelectric transducer plays the dominant role rather than the viscous force F, the droplet gravity, or the surface tension. The F is linked to the Ps, where the stronger the Ps, the faster the liquid column falls, thus, the larger the F. Due to the fact that a liquid column rather than a droplet is typically formed at the beginning of the liquid ejection demonstrates that the influence of surface tension on droplet formation can be ignored. (3) The diameter of the liquid column is equal to the nozzle radius b. (4) The air resistance is ignored. (5) The viscosity of the liquid should be moderate during droplet falling. If the viscosity is too small, the ink is similar to a gas, which prevents the liquid from retaining its wholeness; if the viscosity is too large, droplet falling becomes quite difficult to happen. Only when the Reynolds number and Weber number (Reynolds number is a function of viscosity, and Weber number is a function of surface tension) are in a moderate range can thus enable the formation of a single droplet. The higher the viscosity, the smaller the Reynolds number; the higher the surface tension, the smaller the Weber number. A large Reynolds number with a small Weber number tends to lead to satellite droplets. When the Reynolds number and Weber number are both small, the ink will splash, which is not conducive to the formation of droplets (Figure 4) [24]. These assumptions are applicable to this whole work.

When the liquid column is generated, the sum of pressure and gravity in the droplet is greater than viscous at the beginning, and the liquid column begins to be elongated. When the sum of pressure and gravity in the droplet is equal to viscous, the length of the liquid column reaches its limit, and this point is analysed.

At first, the liquid is ejected from the nozzle in the form of a cylinder and disconnects from the droplet nozzle when the column is force-balanced, and then transforms into a spherical droplet. The liquid column is cut off for force analysis, where the bottom area is S, the height is z, and the side area is A. The equation is established at the force equilibrium point, and the momentum law is used to represent the velocity. Because P_s is the dominant force, only the velocity brought by P_s is calculated in momentum analysis.

$${\mathrm{P}}_{\mathrm{s}}\mathrm{S}+\mathrm{mg}=\mathrm{F}$$

(1)

$${\mathrm{P}}_{\mathrm{s}}\mathrm{S}+\mathsf{\rho }\mathrm{gSdz}=\mathsf{\mu }\mathrm{A}\frac{\mathrm{dv}}{\mathrm{dz}}$$

(2)

$$\mathrm{mdv}={\mathrm{P}}_{\mathrm{s}}\mathrm{Sdt}$$

(3)

Simultaneously,

$$\frac{\mathrm{m}}{\mathrm{A}}\mathrm{dz}=\mathsf{\mu }\mathrm{dt}$$

(4)

For the liquid column

$$\mathrm{m}=\mathsf{\rho }\mathrm{Sdz}={\mathsf{\rho }\mathsf{\pi }\mathrm{r}}^2\mathrm{dz}$$

(5)

$$\mathrm{A}=2\mathsf{\pi }\mathrm{rdz}$$

(6)

Obtaining

$$\mathrm{z}=\frac{2\mathsf{\mu }\mathrm{t}}{\mathsf{\rho }\mathrm{b}}$$

(7)

$$\mathrm{V}=\mathrm{zS}=\frac{2\mathsf{\pi }\mathrm{b}\mathsf{\mu }\mathrm{t}}{\mathsf{\rho }}$$

(8)

For the droplet

$$\mathrm{V}=\frac{4}{3}{\mathsf{\pi }\mathrm{r}}^3$$

(9)

$$\mathrm{r}={\left(\frac{3\mathrm{b}\mathsf{\mu }\mathrm{t}}{2\mathsf{\rho }}\right)}^{1/3}$$

(10)

On the basis of the above analysis, we came to the conclusion that the droplet radius can be decreased by reducing the nozzle radius, shortening the time of applied pressure (namely, the period of electrical signal), increasing the density, and increasing the liquid viscosity [25]. Experimentally, the liquid ejection from the nozzle to form liquid droplets has been observed (Figure 5a) [26,27]; the droplet’s size clearly shrinks when the tube diameter decreases (Figure 5b) [28]; as the applied pressure time becomes longer, the overall droplet size becomes larger; and the ink containing the dispersing agent (GNP2) has a lower activation energy (23.4 kJ/mol) than the ink without a dispersing agent (GNP1, 25.5 kJ/mol). Consequently, we can state that the cohesion of the ink GNP2 and the frequency of reactions between the ink molecules is lower than for ink GNP1. The ink with the lower value of activation energy should allow for easier drop formation without problems such as the detachment of droplets and the formation of satellite droplets (Figure 5c) [29]; as the solvent concentration increases, the density of the droplet also increases, and at the same time, the droplet size decreases. Specifically, the solute is a polystyrene/butyl acetate solution (PS/BuAc) (Figure 5d) [30]; to a certain extent, the droplet size increases as the viscosity increases, but when the viscosity increases further and when the viscosity occupies the main position, the droplet size decreases rapidly as the viscosity increases, which is caused because the liquid is too viscous to eject (Figure 5e) [31]. The liquid viscosity, droplet density, and applied pressure time are adjusted in the laboratory according to the specific situation; only the radius of the nozzle is restricted to a given number by the ink-jet printer itself. Most of the nozzle diameters used in ink-jet printers are 20 μm to 30 μm (https://www.epson.com.cn/Apps/PH/index.aspx, accessed on 20 November 2022).

2.2. Droplet Falling

During droplet falling, if the surface tension of the droplet is smaller than gravity, the droplet is not able to remain intact and will be destroyed and form satellite droplets (Figure 6a) [32,33]. Satellite droplets can make ink-jet printing uncontrollable, thereby losing the resolution and device performance [34]. We analyse the critical value when the surface tension of the liquid is equal to gravity (S₁ is the surface area of droplet; V is the droplet’s volume):

$$\mathrm{mg}=\frac{2\mathrm{r}}{\mathsf{\gamma }}{\mathrm{S}}_1$$

(11)

For a droplet

$${\mathrm{S}}_1=4{\mathsf{\pi }\mathrm{r}}^2$$

(12)

$$\mathrm{mg}=\mathsf{\rho }\mathrm{gV}=\frac{4}{3}{\mathsf{\rho }\mathrm{g}\mathsf{\pi }\mathrm{r}}^3$$

(13)

Simultaneously,

$$\mathsf{\rho }=\frac{6}{\mathsf{\gamma }\mathrm{g}}$$

(14)

Thus, the critical density of the droplet can be obtained. Once the density is too large, the droplet will be destroyed by gravity and form satellite droplets.

W_j is the coefficient related to the droplet, which is positively correlated with the density. It can be seen that the higher the density is, the higher the frequency and number of satellite droplets that are generated (Figure 6b).

2.3. Droplet Impinging

When a droplet impinges on the surface of a substrate, it receives impulse force from the substrate [37]. If the impulse force is greater than the surface tension of the droplet, the droplet will splash (Figure 7a) [38]. If the impulse force is less than the surface tension of the droplet, it will remain relatively intact (Figure 7b). We propose that the size P_s of the pressure applied by the nozzle will directly affect the initial velocity and, in turn, the momentum when the droplet impinges on the substrate. The droplet falls at an initial speed of v₀, and when it reaches the substrate, it is accelerated by gravity at a height of h, which is determined from the nozzle to the substrate, and it hits the surface at a speed of v and finishes the collision within t1 s.

$${\mathrm{v}}^2-{\mathrm{v}}_0^2=2\mathrm{gh}$$

(15)

$${\mathrm{v}}_0=\frac{{\mathrm{p}}_{\mathrm{s}}{\mathsf{\pi }\mathrm{b}}^2\mathrm{t}}{\mathrm{m}}$$

(16)

$$\mathrm{mv}={\mathrm{Ft}}_1$$

(17)

$$\mathrm{m}=\mathsf{\rho }\mathrm{V}=\frac{4}{3}{\mathsf{\rho }\mathsf{\pi }\mathrm{r}}^3$$

(18)

Compare the impulse force with the surface tension

$$\mathrm{F}=\frac{2\mathsf{\gamma }}{\mathrm{r}}\mathrm{S}=8\mathsf{\pi }\mathsf{\gamma }\mathrm{r}$$

(19)

This can obtain

$$\mathrm{h}=\frac{36{\mathsf{\gamma }}^2{\mathrm{t}}_1^2}{2{\mathrm{g}\mathsf{\rho }}^2{\mathrm{r}}^4}-\frac{{\mathrm{P}}_{\mathrm{s}}^2{\mathsf{\pi }}^2{\mathrm{b}}^4{\mathrm{t}}^2}{2{\mathrm{gm}}^2}$$

(20)

The only variable of the procedure is P_s. When P_s decreases, the critical height of the droplet splash h increases; the requirements for the machine itself decrease, and the adjustability increases. When the applied P_s gradually increases, kinetic energy and momentum will also become larger; the tolerable pressure of the droplet drops rapidly in the beginning stage and finally stabilises, indicating that reducing the applied momentum can improve the integrity of the droplet (Figure 7c) [39]. It is worth noting that P_s cannot be arbitrarily small and must have much larger than the surface tension of the droplet itself.

In some studies, it has also been found that increasing the height not only prevents the droplet from splashing but also reduces the drying area. This is because of the solvent, which evaporates when the droplets drop from a high place, making the droplets smaller and, thus, improving the resolution. This effect has been observed in the presence of polymers as solvents and becomes more pronounced as the concentration of polymers decreases; PS is polystyrene, and the effect of the polymer wt% on droplet diameter can be seen in Figure 5d (Figure 7d).

2.4. Droplet Spreading

The drive of the droplet spreading process is the difference between the surface energies of different interfaces and the resistance in the form of inertia force and viscous force. Theoretically, a droplet diffusion across a solid surface can be divided into two parts: an initial rapid phase where the duration depends on the inertial effect and a slow phase where the duration depends on the viscous effect (Figure 8a). In terms of droplet dynamics, there is also a theory that the driving force of droplet spreading is buoyancy and thermocapillary force, which will shape the droplet during spreading (Figure 8b). The spreading process is determined by many factors. For example, changes in the droplet surface tension due to the addition of the surfactant can increase the droplet’s maximum spreading radius, a rule independent of the droplet drop velocity. As the descent rate increases, the maximum spreading radius also increases (Figure 8c). Moreover, the droplet density, diameter, impact velocity, and other factors of the ink-jet printing process can also affect the spread of droplets, and some theories have pointed out that these variables are attributed to the Weber number and Reynolds number. A different Weber number and Reynolds number will bring different effects on the spread of droplets: with the same Reynolds number, the maximum diffusion factor becomes larger as the Weber number increases, while when the Weber number is constant, the maximum diffusion factor increases with the Reynolds number’s growth (Figure 8d).

There is an empirical theory regarding droplet spreading [47].

$${\mathrm{d}}_{\mathrm{eqm}}=\mathrm{rtan}\frac{\mathsf{\theta }}{2}[3+{(\tan \frac{\mathsf{\theta }}{2})}^2]$$

(21)

$$\mathsf{\theta }=\arccos \frac{{\mathsf{\gamma }}_{\mathrm{s}}-{\mathsf{\gamma }}_{\mathrm{sl}}}{{\mathsf{\gamma }}_{\mathrm{l}}}$$

(22)

where θ is the initial contact angle between the droplet and the substrate, r is the radius of the droplet, d_eqm is the theoretical spreading radius, and t_pinned is the theoretical spreading time. If the spread radius is to be as uniform as possible, the evaporation time should be as short as possible. According to the empirical formula [47]

$${\mathrm{t}}_{\mathrm{pinned}}=\frac{{\mathsf{\rho }}_{\mathrm{l}}{\mathrm{R}}_{\mathrm{b}}^2}{4{\mathrm{DC}}_{\mathrm{s}}\left(1-\mathrm{RH}\right)}{{\displaystyle \int }}_0^{\mathsf{\theta }}\frac{\mathsf{\beta }\left(\mathsf{\theta }\right)}{\left(2+\cos \mathsf{\theta }\right)\mathrm{F}\left(\mathsf{\theta }\right)}\mathrm{d}\mathsf{\theta }$$

(23)

On the basis of this theory, appropriately raising the atmosphere’s humidity is beneficial to droplet spreading; reducing the contact angle is also an important method to regulate.

2.5. Pixel Formation

Droplet evaporation is controlled by the relationship between heat conduction and temperature. The droplet has different evaporation phenomena on different substrates: the hydrophilicity of the droplet affects the contact angle; the smaller the contact angle, the faster the evaporation rate. For a hydrophilic droplet, the adsorbed film region forms due to the strong long-range inter-molecular forces between the solid and liquid phases. These forces result in a contact line region incorporating several length scales varying from nanometre in the adsorbed film (10–20 nm) to millimetre in the bulk droplet. The disjoining pressure in the adsorbed film prevents evaporation in this region (Figure 9a). The heating speed is mainly influenced by thermal radiation and convective: the higher the heating rate, the faster the solution evaporates (Figure 9b). Droplet size is also an important factor influencing the evaporation process. As the droplet diameter increases, the droplet evaporation rate decreases almost linearly. For a large droplet, because it takes some time to reach thermal equilibrium, the linear relationship broken (Figure 9c). Moreover, the external atmosphere also affects the evaporation rate. Humidity is one of the most important factors in atmospheric conditions on evaporation; the higher the external humidity, the lower the evaporation rate (Figure 9d).

In the actual evaporation process, the coffee ring effect has been widely considered. In the process of ink-jet printing, when the solute is not uniformly deposited on the contact surface but is concentrated on the droplet edge, this forms a ring stain similar to that left by coffee evaporation, namely, the coffee ring effect (Figure 10a) [52]. The coffee ring effect is lethal in ink-jet printing, and it leads to uneven electrical properties in the pixels, thereby preventing the construction of qualified electronic devices [53]. The formation of the coffee ring is mainly caused by the droplet shrinking at the receding angle due to the nailing action of the three-phase line and the capillary action caused by the different evaporation rates of the droplet at different positions (Figure 10b) [54]. The coffee ring phenomenon can be improved by optimizing the substrate’s surface roughness, solution concentration, interparticle interaction, and temperature.

Reducing the roughness of the substrate can suppress the three-phase line pinning so that the ring shrinks after reaching the receding angle. The pixel morphology is indeed improved by changing the species of substrates. The coffee ring is obvious on poly(9-vinlycarbazole) (PVK)-modified substrates (the right of Figure 10c) and disappears on poly-(9,9-dioctylfluorene-co-N-(4-(3-methylpropyl))dipheny-lamine) (TFB)-modified substrates (the middle of Figure 10c). The pixel on poly(N,N’-bis(4-butylphenyl)-N,N’-bis(phenyl)benzidine) (P-TPD)-modified substrates is broken into pieces (the left of Figure 10c).

The content of the solute and additive determines the ink concentration, and both of them are adjustable. The difference in additive concentration can directly affect the liquid surface tension gradient of the droplet, and a change in the surface tension gradient can enhance the Marangoni flow, namely, drive the liquid flow from the edge to the centre, which suppresses the coffee ring phenomenon. As shown in Figure 10d, ethylene glycol has been demonstrated as an efficient additive whereby the formation of the coffee ring was totally inhibited with the addition of 32 wt% ethylene glycol (pixels from left to right in Figure 10d, wherein totals of 0, 16, and 32 wt% ethylene glycol were added, respectively).

Moreover, we can also optimise the concentration of the solute to suppress the formation of coffee rings. As shown in Figure 11a, the uniformity of pixels gradually improves from left to right; the higher the image brightness, the greater the film thickness. Clearly, the coffee ring disappears as the solute concentration increases.

Interparticle interaction can also affect the formation of coffee rings. If solute particles are prone to cluster, they converge into a boundary line at the edge of the droplet during solvent evaporation, preventing rear solutes from continuously accumulating at the edge, thus, alleviating the coffee ring effect. By adjusting the morphology of solute particles, it can be seen that the uniformity of the formed pixel from the rod-like solute (the bottom of Figure 11b) is much better than that of the spherical-shaped solute (the top of Figure 11b); at the same time, the temperature can be controlled to adjust the evaporation rate to control pixel formation. When the temperature is low, the ink evaporates before the solute spreads, thereby forming raised pixels (the left of Figure 11c); when the temperature is high, it is easy to form a coffee ring (the right of Figure 11c); good-looking pixels can only be formed at an appropriate temperature (the middle of Figure 11c).

The fact that coffee rings are fatal in ink-jet printing has already been observed. However, in some special cases, we can also use coffee rings to form valuable print patterns. For example, silver particles are deposited using the coffee ring principle [62].

3. Conclusions

The above discussion mainly focused on droplet formation, falling, hitting the substrate, spreading, the formation of a pixel, and how internal factors (ink concentration, additive, solute morphology, and interparticle interaction) and external factors (atmosphere, temperature, heating rate, surface energy, and contact angle) determined pixel size, shape, and uniformity, without mentioning the period before droplet formation. The droplet size determines the pixel diameter, which is controlled by the diameter of the nozzle. At present, the diameter of a commercially available nozzle is around 25 μm. If one wants to further decrease the size of droplets, how to produce a narrower nozzle should be taken into consideration.

To explore the limits, carbon nanotubes, as one of the narrowest artificial tubes (Figure 11a), can be considered as a potential nozzle for producing the droplet. Carbon nanotubes can be either hydrophilic or hydrophobic, depending on their specific synthesis schemes and post-treatment strategies. Hydrophilic carbon nanotubes can be obtained by coating with chitosan (Figure 12a) [63], growing on MOF [64], doping with nitrogen and oxygen [65], and using glycolipid nanotubes as templates [66]. Hydrophobic carbon nanotubes can be obtained by fluoridation and oxidation post-treatments [67]. Moreover, silica nanotubes with a diameter about 200 nm can also be treated with hydrophobic groups [68]. A nanotube prepared by the pattern transfer method also has satisfactory diameters [69], and some of the tubes that have been used in supercapacitors also fulfil the requirements [70]. If carbon nanotubes with a diameter around 10 nm are used as a nozzle for ink-jet printers, and ideally, no satellite droplets form, no splash occurs, and the ink spreads well without forming a coffee ring, one can obtain pixels with much smaller diameters than that from present commercial nozzles (20 μm), which is about 8% of the existing limit value (about 80 μm).

For other manipulable parts, the waveform of the driving voltage that provides pressure in ink-jet printing is also an important variable. An appropriate adjustment of the waveform can make the droplet complete and affect droplet size (Figure 12b) [71].

In addition, some studies have pointed out that the formation of satellite droplets during the falling process is not only determined by density but also related to the surface tension between the nozzle and the droplet. This part of surface tension was neglected in our above theoretical analysis. During liquid column shedding, if the surface tension is appropriate, the liquid column will break at the nozzle, fall, and then form a droplet. If the surface tension is too high, satellite droplets will form due to the action of the reflected acoustic waves in the nozzle [72]. The applied force can also affect the formation of satellite droplets. If the applied force is too weak, the droplets cannot eject, and if the applied force is too strong, the liquid will be torn apart by the strong contractive force. Surface tension $\widetilde{Z_m }$ is proportional to the magnitude of the applied force, while nozzle Deborah number Den is the amount proportional to the viscosity. It can be clearly seen in Figure 12c that when the viscosity is large, the applied force must be large enough for the droplets to shoot out. However, when the viscosity is too small, if the force applied is too large, satellite droplets generate.

In summary, when using ink-jet printing to obtain small-sized and closely arranged pixels, several points should be taken into consideration. For the droplet, it is necessary to increase the ink viscosity and reduce the ink density to reduce the droplet size. For the printer, it is desirable to reduce the nozzle radius, to accelerate the frequency of electrical signals, to optimise the pressure, and to adjust the distance between the nozzle and substrate so that the droplet will not break during the falling and impinging processes. For film formation, the atmosphere, substrate roughness, droplet surface tension, solute concentration, interparticle interaction, heating temperature, and heating speed should be adjusted to reduce the coffee ring effect.

It is worth noting that ink-jet printing still has some demerit, and some researchers have made great efforts and proposed solutions. The clogging of nozzles can be solved by adjusting ink composition [75]; the traditional method of cleaning the nozzle uses high pressure water flushing, but the nozzle structure can be optimised to simplify the cleaning process [76]; and a slow printing speed is also a major problem of ink-jet printing technology, with studying showing ways to improve printing speed and accuracy by improving ink composition [77].

In this review, the related factors affecting pixel size in ink-jet printing were systematically analysed, and specific suggestions were given from three aspects, including ink, printing process, and equipment, which will provide a reference for future high-resolution patterning through ink-jet printing.