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Hydrodynamic devices use convection to enhance the rate of
mass transport to the electrode and can offer advantages over
techniques which operate in stagnant solution. The addition of convection
to the cell usually results in increased current and sensitivity in
comparison to voltammetric measurements performed in stagnant solution.
Also the introduction of convection (usually in a manner that
is predictable) helps to remove the small random contribution from natural
convection which can complicate measurements performed in stagnant
solution. Finally, it is possible to vary the rate of reaction at the electrode
surface by altering the convection rate in the solution and this can be
usefully exploited in mechanistic analysis and electroanalytical
applications. In the discussion below a range of traditional and recent
developments in the field of hydrodynamic techniques and their potential
applications are outlined.
Hydrodynamics
There are two main approaches of introducing convection into the
electrochemical cell. First the electrode can be held in a fixed position
and solution is flowed over the surface by an applied force (usually
a pressure). Second the electrode can be designed to move which acts to
mix
the solution via convection. The introduced (forced) convection
is generally made to be considerably stronger than any natural convection processes
and therefore the influence of natural convection becomes insignificant on the
electrolysis reaction. To allow quantitative analysis it is vital
that the forced convection introduced to the cell is predictable. The
cell and experimental conditions are therefore designed so that
the solution flow within the cell becomes laminar.
You will recall from the mass transport section (link) that in this
case solution flows in a well defined and non mixing way.
The the two figures below show the extremes of flow behaviour through a
pipe. First turbulent conditions where the flow is essentially random and
unpredictable and second the well defined Laminar flow conditions.
The transition between laminar and turbulent flow can be
predicted using the concept of the Reynolds number(link). When laminar flow
prevails the fluid dynamics within the cell can be predicted by the
Navier-Stokes equations (ref+link) and these allow the calculation of the
velocity throughout the device. Once these have been predicted the
concentration of the reagents and the relationship between
the current and the transport rate within the cell can then be
calculated.
Hydrodynamic techniques
In this section we take a historical look at the development of
hydrodynamic devices and the voltammetric behaviour of the different
techniques. The following techniques are covered:
The Dropping Mercury Electrode<
The Rotating Disc and Ring Disc Electrode
The Wall Jet Electrode
The Channel Electrode
The Confluence Reactor
Microelectrochemical reactors
The Dropping Mercury Electrode
The first of the hydrodynamic techniques developed was the Dropping
Mercury Electrode (DME). In this arrangement a fine capillary is connected to a
reservoir of mercury. The cell is designed so that mercury is allowed to
flow down the capillary at a controlled rate and out into the
solution.
Electrical contact to the mercury is made in the reservoir and a
reference and counter electrode are sited in the electrolyte solution.
Voltammetry can performed in an identical manner to that described
earlier, however, now the electrode is constantly changing area and so a
linear sweep voltammogram will exhibit significantly different
behaviour.
(Picture 1)
The current can be seen to go through a series of
peaks and troughs as the voltage is swept. The origin of these can be
seen by examining the animation below.
(animation 1)
As the mercury drop grows the surface area accessible to the
electrolyte also increases and consequently the current increases.
However, at some point the Mercury drops from the tip leaving a small new
area in contact with the electrolyte, consequently the current drops
rapidly at this point before gradually increasing as the drop grows again.
This behaviour is repeated throughout the scan. Clearly this process is
not something that is easily predicted and the fluid dynamics are still
not fully understood for this particular device. However, this technique
proved very popular due to the ability to continually refresh the
electrode surface during the experiment.
The Rotating Disc and Ring Disc Electrode
Due to the limitations of the DME a new device was developed called the
Rotating Disc Electrode (RDE). In this arrangement solution is brought to
the surface by a Teflon disc which rotates in solution.
A schematic of the cell including the working electrode is shown
below. The working electrode (typically Platinum or Gold) is embedded in
the top face of the Teflon shield.
When operated at rotation speeds of upto around 60 Hz (cycles per second) the flow
profile to the electrode is laminar and so can be predicted
mathematically. The figure below shows the type of flow profile that is
developed when a circular object is rotated in solution and how this
brings fresh reactant to the surface
The act of rotation drags material to the electrode surface where it can
react. Providing the rotation speed is kept within the limits that laminar
flow is maintained then the mass transport equation is given by
where the x dimension is the distance normal to the electrode surface.
It is apparent that the mass transport equation is now dominated by
both diffusion and convection and both these terms effect the
concentration of reagent close to the electrode surface. Therefore to
predict the current for this type of electrode we must solve this
subject to the reactions occurring at the electrode.
A typical voltammetric measurement used with the rotating disc
and other hydrodynamic systems detailed below
is linear sweep voltammetry. The figure below shows a set of current
voltage curves recorded for a reversible on electron transfer reaction and
different rotation speeds. The scan rate used was 1 mV/s (compared to
perhaps 20 mV s-1 for conventional cyclic voltammetry) and as
can be seen the total current flowing depends upon the
rotation speed used .
This can be understood by returning to the concept of the 'diffusion
layer' thickness controlling the flux of material to the
surface. As the rotation speed is increased the distance that material can
diffuse from the surface before being removed by convection is decreased.
This results in a higher flux of material to the surface at higher
rotation speeds. The mass transport limited current arises from the
fact that the system reaches a steady state and so the current reaches a plateau once
the equilibrium at the surface is driven to the products side.
We can analyse the variation of the mass transport limited current as a function of
the rotation speed. This was first solved mathematically by Levich who showed the
following relationship between the current and the rotation speed, for a reversible
electron transfer reaction.
Therefore by plotting iL vs the square root of the
rotation speed (w) for a set of experimental data a straight will
be observed if the reaction is reversible. Plots such as that shown
below can be employed to analyse whether reactions involve
adsorption/desorption steps chemical reactions or slow electron transfer
steps.
Hydrodynamic systems lend themselves particularly to the investigation of
mechanistic processes. This is because a steady supply of reactant is fed to the
electrode and the ability to vary the mass transport rate provide information regarding
the process under investigation. Let us use the ECE reaction as an example. In this
case it is easier to reduce the product (C) from the chemical reaction that the starting
material (A). A typical voltammogram for such reaction is shown below.
The current recorded in the experiment is shown as the solid line. The current that
would be recorded without chemical reaction is shown as a dashed line on the figure.
Analysis of this type of process is usually performed using the following
ratio
Neff can vary between 1 and 2. When no chemical reaction occurs the total current
flowing is the same as that for the (A) to (B) step so Neff is 1. When all of the product
from the reduction of (A) is converted to (C) then Neff becomes 2 since (C) is then
reduced at the electrode as well. The figure below shows how the
quantity Neff varies as a
function of rotation speed.
As can be seen Neff drops as the rotation speed increases. This occurs because as the
rotation speed increases the product (B) from electrolysis is removed from
the electrode more rapidly and therefore has less chance to react to form
(C). Consequently it is possible to outrun the reaction kinetics by
increasing the convection rate. Analysis of the shape of the curve in
the figure can reveal the rate constant for the chemical reaction.
The Rotating Ring Disc Electrode
Coming soon!
The Wall Jet Electrode
The Wall Jet Electrode (WJE) is an interesting alternative to the
RDE. The velocity profiles were first examined (under
laminar flow conditions) by Glauert who was working on the effects of jets
directed towards a flat plane (for applications in vertical take off
aircraft!). The basic arrangement is shown below, a fine nozel is
sited within a large container of electrolyte and positioned directly
above a disc working electrode.
Figure WJE1
Solution is pumped through the nozel
(under laminar flow conditions) and impinges on the surface containing
the electrode. The reagent then flows from the surface creating a complex
but predictable flow pattern.
Figure WJE2
Like the rotating disc it is possible to obtain an expression for the
transport of material to the electrode
WJE
and this can then be used to predict how the mass transport limited
current would vary as a function of the solution flow rate.
WJE Levich
The WJE has found many applications in the area of electroanalytical
Chemistry.
The Channel Electrode
Like the WJE above in this device the electrode is maintained in a
specific position and solution pumped through the cell. In the channel
electrode (ChE) the electrode is embedded into one wall of a
rectangular duct and solution pumped over the surface.
In this cell it is the volume flow rate (Vf) that controls the convection to the surface
and the corresponding Levich equation for a reversible electron transfer is predicted
by
h,d,w,and xe are constants for the cell size and Vf is the volume flow rate. It is
possible to obtain such an expression because when the solution flow rate is
controlled appropriately it is possible for a parabolic laminar profile to
develop
This is mathematically well defined and consequently allows quantitative
analysis.
The Confluence Reactor
The above devices have allowed a range of (electro)chemical process to be
examined, however, they each have limitations when reactions of interest
involve bringing together different starting materials which are highly
reactive. Consequently more recently new devices have been developed
which permit the introduction of two or more species into a cell at a
predetermined point and under well defined transport conditions. The
confluence reactor (CR) shown below is constructed of two separate
rectangular ducts which are independently supplied with different
reagents.
CR fig1
A some point the separation between the two ducts finishes and the
separate streams can then mix. The cell is designed so that laminar flow
conditions prevail and so the concentration of reagents can be computed
CR Fig2
A detector electrode is sited in one wall and is used to sense the
products as they are generated.
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