Bjerrum length

The Bjerrum length (after Danish chemist Niels Bjerrum 1879–1958 )is the separation at which the electrostatic interaction between two elementary charges is comparable in magnitude to the thermal energy scale, k B T {displaystyle k_{B}T} , where k B {displaystyle k_{B}} is the Boltzmann constant and T {displaystyle T} is theabsolute temperature in kelvins. This length scale arises naturally in discussions of electrostatic,electrodynamic and electrokinetic phenomena in electrolytes, polyelectrolytes and colloidal dispersions. The Bjerrum length (after Danish chemist Niels Bjerrum 1879–1958 )is the separation at which the electrostatic interaction between two elementary charges is comparable in magnitude to the thermal energy scale, k B T {displaystyle k_{B}T} , where k B {displaystyle k_{B}} is the Boltzmann constant and T {displaystyle T} is theabsolute temperature in kelvins. This length scale arises naturally in discussions of electrostatic,electrodynamic and electrokinetic phenomena in electrolytes, polyelectrolytes and colloidal dispersions. In standard units, the Bjerrum length is given by λ B = e 2 4 π ε 0 ε r   k B T , {displaystyle lambda _{B}={frac {e^{2}}{4pi varepsilon _{0}varepsilon _{r} k_{B}T}},} where e {displaystyle e} is the elementary charge, ε r {displaystyle varepsilon _{r}} is the relative dielectric constant of the mediumand ε 0 {displaystyle varepsilon _{0}} is the vacuum permittivity.For water atroom temperature ( T = 300  K {displaystyle T=300{mbox{ K}}} ), ε r ≈ 80 {displaystyle varepsilon _{r}approx 80} , so that λ B ≈ 0.7 nm {displaystyle lambda _{B}approx 0.7{mbox{nm}}} . In Gaussian units, 4 π ε 0 = 1 {displaystyle 4pi varepsilon _{0}=1} and the Bjerrum length has the simpler form λ B = e 2 ε r k B T . {displaystyle lambda _{B}={frac {e^{2}}{varepsilon _{r}k_{B}T}}.}