Rheology and Printing Methods

In recent years, printing has emerged as an attractive option for printed electronics and energy storage devices. Different printing methods require the printing medium to fall within a specific viscosity window due to differing mechanisms of ink application and have their own benefits and drawbacks. Table 4.1 summarizes ink viscosity ranges for six common printing methods.

Table 4.1: Printing thicknesses and viscosities of various printing methods [46]

Printing Method Print Thickness [µm] Viscosity Range [cP]

Gravure 0.02-12 10-1100

Rheology is the study of the viscoelastic and flow properties of fluids and is an important characteristic in working with printed slurries. Rheological factors that dictate ink printing compatibility include the ink’s dynamic viscosity, shear response, and yield stress.

Typical fluids (e.g. water) are classified as Newtonian fluids, in which the fluid begins to flow immediately when a stress is applied and dynamic viscosity remains constant with changing stress. Therefore, for Newtonian fluids, the shear stress changes linearly when the applied shear rate is changed as well. This relationship is given by Newton’s law of viscosity (Eq. 4.1) , in which the viscosity, µ, is a constant of proportionality between the shear stress,

⌧, and the shear rate, ˙ .

⌧ = µ ˙ (4.1)

In contrast, many particle-laden fluids, such as inks used in this work, do not follow Newton’s law of viscosity and are thus labeled non-Newtonian fluids. Specifically, these are characterized by viscosity that can either increase or decrease when a stress is applied, called shear thickening and shear thinning fluids respectively. In addition, some non-Newtonian fluids require a threshold level of applied stress before they will begin to flow, called the yield stress, and are called Bingham plastics. The difference between all of these fluids is visualized on a plot of shear stress vs. shear rate in Figure 4.2.

For printing and other applications where fluid deposition is the desired outcome, the yield stress and viscosity play significant roles in determining the viability of a fluid. For printing specifically, the desired outcome is for the ink to flow during printing but not to flow afterward in order to retain ink in the exact quantity and shape as was dictated by the printing process. This calls for a shear-thinning ink with some requisite value of yield stress

Newtonian Shear Thinning

Shear Thickening Bingham Plastic

Bingham Pseudoplastic

Yield Stress

Figure 4.2: Shear stress responses of Newtonian and non-Newtonian fluids

to act as a threshold before flow occurs. The exact values for the viscosity during printing and the yield stress vary depending on the printing method.

For particle-laden inks such as the ones developed for this work, compositional factors that affect the rheology are the volume fraction of solvent relative to solid particles (active material and conductive additive) and the effective viscosity of the polymer binder and solvent mixture. Thus, the amount of solvent present effectively decides the rheology of the final ink. Conveniently, the solvent is driven off during the electrode drying process, so this provides a method to independently tune the ink viscosity for printing without significantly affecting the bulk electrode properties after drying.

For stencil printing with a doctor blade as done in this work, te printing process can be modeled as Couette flow in which a viscous fluid flows between two parallel plates, one moving (the doctor blade) and one stationary (the stencil). Couette flow can be described

by Equation 4.2, where ˙ is the shear rate, v is the velocity of the moving plate, and h is the separation distance between the two plates.

˙ = v

h (4.2)

The effective shear rate applied to the ink can therefore be determined with knowledge of the doctor blade spacing and velocity. In conjunction with empirical rheological charac-terization, the shear stress applied to the ink during printing can then be determined for any printing speed and doctor blade spacing for all effective shear rates within testing lim-its. This relationship between shear rate and velocity for various doctor blade spacings is presented in Figure 4.3.

Figure 4.3: Effective shear rates for blade coater and doctor blade.

4.2.3 Profilometry

The morphology of the electrode at the electrode-electrolyte interface affects the minimum thickness of the gel polymer electrolyte that must be printed. Because there is a range of particle sizes present in the electrode slurries, the resulting surface morphology is uneven and made up of peaks and valleys. This uneven surface dictates the minimum thickness of gel polymer electrolyte that must be printed in order to provide sufficient insulation against electronic conduction between the cathode and anode based on the relative heights

and depths of the peaks and valleys respectively. Since a thicker separator layer increases diffusion distances as well as ohmic losses (as well as requires the use of more ionic liquid), it is preferred to minimize the amount of gel polymer electrolyte needed, which means a smoother surface morphology is desired.

Traditional roll-to-roll battery manufacturing processes introduce a calendaring step af-ter slurry deposition, the goal of which is to decrease electrode porosity and flatten the surface to enable thinner overall layers prior to winding. For printed and flexible electronics applications, this may not be possible, particularly for cells that must be printed directly on substrates where other components are already present. Therefore, alternate methods for obtaining uniformly smooth electrode surfaces are desireable.

The approach taken in this work is to control the particle sizes and distributions of the solid particles in the electrode slurries themselves in order to minimize the variation in surface morphology. A Fourier transform was used to decompose a one-dimensional profile scan of the electrode surface into roughness and waviness values in order to quantify the morphology of each slurry composition.