Why should potassium serve to stabilize a welding arc? Of the many types of electric arc welding electrodes, there are two that consist of a steel core surrounded by a coating of “High cellulose sodium” and “High cellulose potassium.”  The web sites (for example AWS Classifications Explained) say that the sodium based electrodes should be used with DC with the electrode connected to positive (DC+) whereas the potassium based rods can be used for all of DC+, DC- and AC current.  
Since sodium and potassium are so chemically similar, I have been wondering why there should be any difference.
One explanation that I got was that “potassium stabilizes the arc.” It makes sense that some sort of ions would be required to allow the arc to be reestablished after a zero crossing of the current but why should potassium work better than sodium? Potassium has an atomic mass 1.7 times that of sodium.  That would mean it diffuses (I think I have this right) $\sqrt{1/1.7}=0.767$, about 77 percent as fast.  I would not think that would make that much of a difference.
 A: 
Since sodium and potassium are so chemically similar, I have been wondering why there should be any difference.

WeldGuru - "Guide to Welding Electrodes"
Coating, Current and Polarity Types Designated By the Fourth Digit in the Electrode Classification Number
$$\begin{array}{l}
\text{Digit} & \text{Coating} & \text{Weld Current} \\
\text{...} & \text{...} & \text{...} \\
\text{2} & \text{Titania sodium} & \text{ac, dcsp} \\
\text{3} & \text{Titania potassium} & \text{ac, dcsp, dcrp} \\
\text{...} & \text{...} & \text{...} \\
\end{array}$$
...
The principal types of welding electrode coatings for mild steel and are described below.


*

*Cellulose-sodium (EXX10): Electrodes of this type cellulosic material in the form of wood flour or reprocessed low alloy electrodes have up to 30 percent paper. The gas shield contains carbon dioxide and hydrogen, which are reducing agents. These gases tend to produce a digging arc that provides deep penetration. The weld deposit is somewhat rough, and the spatter is at a higher level than other electrodes. It does provide extremely good mechanical properties, particularly after aging. This is one of the earliest types of electrodes developed, and is widely used for cross country pipe lines using the downhill welding technique. It is normally used with direct current with the electrode positive (reverse polarity).

*Cellulose-potassium (EXX11): This electrode is very similar to the cellulose-sodium electrode, except more potassium is used than sodium. This provides ionization of the arc and makes the electrode suitable for welding with alternating current. The arc action, the penetration, and the weld results are very similar. In both E6010 and E6011 electrodes, small amounts of iron powder may be added. This assists in arc stabilization and will slightly increase the deposition rate. 

*...

"The Study of Complex (Ti, Zr, Cs) Nanopowder Influencing the Effective Ionization Potential of Arc Discharge When Mma [Commonly referred to as SMAW] Welding", by S B Sapozhkov and E M Burakova, on page 2:

"Air like all gases has quite a weak electroconductivity in normal conditions due to low concentration of free electrons and ions. That is why, air gap (or other gaseous medium) between electrodes is to be ionized to generate a high electric current, i.e. an electric arc. Ionization can result from applying a rather high voltage to electrodes; electric filed accelerates a few free electrons or ions of the gas; as the result of acquiring a high energy they can break neutral atoms or molecules into ions. 
High voltages are not allowed by safety engineering regulations of welding. Therefore, thermal electron and field electron emissions are preferred to carry out research into this process. A lot of free electrons, occurring in metal and having a high kinetic energy, pass to the gaseous medium of the interelectrode space, causing its ionization. 
Thermal electron emission involves “vaporization” of free electrons from the surface of metal due to high temperatures. The number of free electrons, acquiring energy sufficient for passing through the energy barrier in the surface layer and leaving the metal is dependent directly on the temperature. The point of field electron (cold) emission is that an outer electric field is developed, which transforms the energy barrier near the surface of metal and supports liberation of electrons with energy sufficient for passing through this barrier.
Gaseous medium ionization is characterized by the degree of ionization, i.e. relation of charged particles in the certain volume to the primary number of particles (before ionization) $^{[3]}$. Welding is more stable and easier if the ionization potential is low.".

Bottom of page 3:

"This paper presents theoretical research into the effect, which complex (Ti, Zr, Cs) nanopowder has on the efficient ionization potential (Ueff) of welding arc discharge. 
The energy of atom ionization characterizes the particle and it is independent on the method of ionization, whereas ionization potential characterizes the first historical method of ionization. 
The energy of atom ionization, measured in eV (electron-volts) is similar numerically to atom ionization potential, measured in V (volts). 
The energy of ionization is an important atom characteristic and influences on the nature and bound strength of chemical compounds made by the atom. The energy of atom ionization has a strong effect on deoxidizing properties of the corresponding elementary substance. 
Ionization potential is a relation of electron work function of the substance atom to the electron charge:

$$\qquad\qquad\qquad\qquad\qquad\qquad\qquad U = \frac{W}{e_,} \qquad\qquad\qquad\qquad\qquad\qquad\qquad(1)$$

where $U$ — ionization potential, V; $W$ — electron work function, J; $е$ — electron charge, C.
Complex atoms, consisting of a lot of electrons, have several ionization potentials. The first ionization potential meets electron removal from the shell of the atom, having the weakest bonds with it. The removal of other electrons, which are closer to the atomic nucleus and have stronger bonds, 
  requires more work. Therefore, the second and further ionization potentials, corresponding to removal of the second and further electrons are higher $^{[3]}$.

Table. First ionization potentials (U) of elements 
$$\begin{array}{c}
\text{Elements} & \text{Cs} & \text{K} & \text{Na} & \text{Ca} & \text{Zr} & \text{Ti} & \text{Mg} & \text{C} & \text{H} & \text{O} \\
U & 3.88 & \text{4.30} & \text{5.11} & 6.11 & 6.63 & 6.8 & 7.64 & 11.22 & 13.53 & 13.56
\end{array}$$

It is seen from the Table above that cesium, potassium, sodium, calcium, zirconium, titanium etc. have the lowest ionization potentials. Therefore, these substances are added to electrode coatings or fluxes to support stability of welding arc burning. 
We should know how elements affect the weldability of a product to avoid difficulties and eliminate problems when welding.

[Please continue reading the document for further information and the mathematics behind this.]
References: [3] Electric welding arc [Electronic resource] Mode of access: http://soedenimetall.ru/e-lektricheskaya-svarochnaya-duga/#ixzz3r9JfpMQ3 (date of application: 24.11.15) - Google Translate: Russian -> English
From the translated webpage:

"When an alternating current is used, the anode and cathode spots change places with a frequency equal to the current frequency. Over time, the voltage $U_d$ and current $I$ periodically vary from zero to the largest, as shown in Fig. 4 ($U_{x • x}$ - arc ignition voltage).



When the current passes through zero and the polarity changes at the beginning and at the end of each half-cycle, the arc goes out, the temperature of the active spots and the arc gap decreases. As a result, deionization of gases and a reduction in the electrical conductivity of the arc column occur. The temperature of the active spot located on the surface of the weld pool in connection with the removal of heat to the bulk of the base metal falls more intensively. Reignition of the arc at the beginning of a small half-period is possible only at an increased voltage, called the peak of ignition. It was found that the peak of the ignition is somewhat higher when the cathode spot is on the base metal. To reduce the peak of the ignition, facilitate the reignition of the arc and increase the stability of its combustion, measures that reduce the effective ionization potential of gases in the arc are used. In this case, the electrical conductivity of the arc after its extinction lasts longer, the peak of the ignition decreases, the arc is more easily excited and burns more steadily.
These measures include the use of various stabilizing elements (potassium, sodium, calcium, etc.) introduced into the arc zone in the form of electrode coatings or in the form of fluxes.
It is important to shift the phases between voltage and current: it is necessary that when the current passes through a zero value, the voltage is sufficient to excite the arc.".

