An interesting application of our mean field MPCD-MD Debye-Hückel algorithm is the determination of the electrophoretic mobility of net neutral polyampholytes.
One might think that since the chains have a net neutral charge that an electric field can’t induce them to electrophorese but this isn’t true. We investigated net neutral diblock ring polymers cut to create a net neutral linear triblock polyampholyte with a negatively charged centre. The ends were both positively charged but had different lengths.
If the cut makes a diblock polyampholyte then the mobility is indeed zero. But if the cut is at any other position they have a non-zero mobility. The mobility is largest for symmetric triblock polyampholyte (one little detail here – non-monoticity can occur if the field is large enough to fold the chain over and polarize).
Why is there a non-zero electrophoretic mobility? The monomers at the ends matter more than those in the centre. Less counterion condensation occurs at the ends and their effective charge is significantly higher. For this difference to be apparent, the Debye screening length must be significantly smaller than the length scale of the charge heterogeneity of the polyampholyte. This means that the electrophoretic mobility is large for thin Debye layers and disappears as the Debye layer thickens.
Find more details or the citation for this in our article in the PRL.