Bjerrum length
Encyclopedia
The Bjerrum length
is the separation at which the electrostatic interaction between two
elementary charge
s is comparable in magnitude to the thermal energy scale,
, where 
is the Boltzmann constant and 
is the
absolute temperature in Kelvin
. This length scale arises naturally in discussions of electrostatic,
electrodynamic and electrokinetic phenomena in electrolytes, polyelectrolyte and colloidal dispersions.
In standard units, the Bjerrum length is given by
where
is the elementary charge
,
is the relative dielectric constant
of the medium
and
is the vacuum permittivity.
For water at
room temperature (
K), 
, so that
nm.
In Gaussian units
,
and the Bjerrum length has the simpler form
is the separation at which the electrostatic interaction between two
elementary charge
Elementary charge
The elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...
s is comparable in magnitude to the thermal energy scale,
, where is the Boltzmann constant and is theabsolute temperature in Kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
. This length scale arises naturally in discussions of electrostatic,
electrodynamic and electrokinetic phenomena in electrolytes, polyelectrolyte and colloidal dispersions.
In standard units, the Bjerrum length is given by
where
is the elementary chargeElementary charge
The elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...
,
is the relative dielectric constantDielectric constant
The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. In technical terms, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum...
of the medium
and
is the vacuum permittivity.For water at
room temperature (
K), , so that nm.In Gaussian units
Gaussian units
Gaussian units comprise a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs units. It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units...
,
and the Bjerrum length has the simpler form