Section 6.2. Electrospray throughput
6.2.1. Experimental details
Simulations were done to gain insight on the electrospray system. COMSOL is a multi-physics simulation package used to calculate the trajectory and magnitude of the electric field lines emitted from a capillary. COMSOL simulations give insight to the behavior of the electric field with differing geometries. This is important because the electric field lines predict the particle flight path. This is because electrostatic forces on the charged particles are dominant, in comparison to drag force as a result of the sheath gas, and the gravitational pull on the charged particles. The electric field can be derived from the negative gradient of the scalar potential as shown in Equation 6.2.1. Taking the divergence of the electrostatic field we obtain Poissonβs equation in Equation 6.2.2:
πΈ = ββΟ, (6.2.1) β2π = β π
π0 , (6.2.2)
where Ο is the space charge density and Ξ΅0 is the permittivity of free space. In the electrospray model the space charge density is a function of distance and time. The charged droplets after emission from the Taylor cone experience a changing charge density as they move towards the substrate. This makes solving the Poissonβs equation almost impossible. Some groups have developed models with intensive computing methods to simulate the electrospray space charge cloud184 185. The COMSOL package can model the Laplace equation (β2π = 0). Therefore, in these simulations it is assumed that the space charge density is zero. This is an assumption that the electric field information calculated by COMSOL represents the initial behavior of the droplet right after emission from the Taylor cone.
The electric field required to overcome the surface tension of a liquid and establish a Taylor cone is given as 71
πΈπ = (2πΎπππ π
π0ππ )
1
2, (6.2.3)
where rc is the capillary radius, Ξ³ is the gas-liquid surface tension, ΞΈ is the cone semi vertex angle, and Ξ΅0 is the permittivity of free space. The equilibrium cone semi-vertex is 49.30, ignoring space charge effects 71. The onset capillary voltage required to establish this electric field at the capillary tip is
ππ = 0.667 (2πΎπππππ π
π0 )
1 2ln (4β
ππ) , (6.2.4)
where h is the distance between the capillary tip and the grounded substrate. The greater the distance between the capillary tip and substrate, the higher the voltage required to establish a Taylor cone.
From the calculated electric field at the capillary tip, it can determine if a Taylor cone will form on a capillary in a defined setup, and a specified set of parameters, with Equation 6.2.3.
Figure 6.2.1 is a map of the electric field at the tip of a capillary.
Figure 6.2.1. Electric field map showing top view and side view, to the right is the scale bar depicting red as the highest electric field value. A schematic of Taylor cone formation shown at bottom left. (a) Flat capillary (b) Frustum shaped capillary.
The side view shows that the electric field is highest at the sharp edges of the capillary. In addition, bottom left schematic shows where Taylor cones will form according to Equation 6.2.3 (electric field > 106 V/m). This agrees with literature findings that the capillary tips must be sharpened to anchor the Taylor cone 64, 71, 194, 195. The angle at which the authors in the literature sharpened the tip is never really specified. Therefore, simulations were made to calculate the electric field above the tip of the capillary and at the corner of the capillaries to see if the tip angle has an effect on the electric field. Figure 6.2.2 shows that the tip angle does not really affect the electric field above the capillary but the electric field at the sharp edges of the capillary increases with an increase in tip angle. A tip angle of zero corresponds to the flat capillary. On the other hand, there is a limit on the angle of a frustum for a given height. Hence, getting as close to this limit when sharpening the capillary tip is paramount. With this insight from COMSOL, an electrospray setup was constructed for testing.
(a) (b)
0 10 20 30 40 50 2E6
4E6 6E6 8E6 1E7 1.2E7
|E| at the top of the capillary tip
|E| at the corner of the capillary
Electric field (V/m)
Tip angle (degree)
Figure 6.2.2. Plot of electric field versus the capillary tip angle
The aqueous solution electrosprayed was 10g/L of CsH2PO4 and 20g/L polyvinylpyrrolidone (PVP) dissolved in a 1 : 1 molar ratio of methanol : water mixture. This gives the optimized balance between conductivity and surface tension of the solution to maintain a steady cone-jet and deposit porous, fractal nanostructures 7. The PVP serves as a surfactant that keeps the solute in solution and also prevents the nanostructures deposited from agglomerating. CsH2PO4 was prepared by precipitation from an aqueous solution of Cs2CO3 and H3PO4. The solution enters the deposition chamber at a controlled flow rate by a syringe pump via a stainless steel capillary (ID 127ΞΌm, OD 1.6mm, L 50mm) that has been sharpened to a frustum shape. The capillary tip is opposite an aluminum substrate holder. The spray geometry is upwards in order to avoid instabilities that can arise from dripping of excess droplets. A positive bias in the 4.5 kV β 8 kV range is applied to the capillary and the substrate is grounded. The chamber is an aluminum casing with insulating caps to electrically isolate the capillary from the substrate holder. The chamber walls are heated independently of the substrate. Two inlets on the side of the wall allow preheated N2 gas to flow towards the outlets on the substrate holder. The N2 gas serves as a drying gas for the charged wet particles moving towards the substrate. The current carried by the flux of charged particles to the substrate was measured using a Keithley 40 Digital 3.5 digit Bench Picoammeter connected in series between the ground wire and the substrate holder. Monitoring the current is an easier and
safer way to monitor the stability of the Taylor cone versus looking through the chamber windows at high proximity to high voltage wires. The parameters leading to the porous fractal structure ideal for an SAFC are summarized in Table 6.2.1.