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Finding a theoretical formula for the persistence length of polyelectrolytes
for the whole experimental range of salt concentration is a long standing
challenge. Using the Tethered Particle Motion technique, the double-stranded
DNA persistence length is measured for four monovalent and divalent salts on a
three-decade concentration range. The formula proposed by Trizac and Shen [EPL,
116 18007 (2016)] and extended to divalent ions fits the data. This formula
mixes the high salt limit solution of the Poisson-Boltzmann equation together
with the DNA charge renormalisation. Magnesium ions induce a fitted DNA radius
smaller than the geometrical one, consistent with a site-specific binding.
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