Hydrodynamic radius
Encyclopedia
The hydrodynamic radius of a macromolecule
or colloid
particle has two meanings. Some books use it as a synonym for the Stokes radius
.
Section 6.4 page 290.
Others books define a theoretical hydrodynamic radius
. They consider the macromolecule or colloid particle to be a collection of 
subparticles. This is done most commonly for polymer
s; the subparticles would then be the units of the polymer.
is defined by
where
is the distance between subparticles 
and 
, and where the angular brackets 
represent an ensemble average
.
Chapter 10, Section 7.4, pages 415-417. The theoretical hydrodynamic radius
was originally an estimate by John Gamble Kirkwood
of the Stokes radius
of a polymer.
The theoretical hydrodynamic radius
arises in the study of the dynamic properties of polymers moving in a solvent
. It is often similar in magnitude to the radius of gyration
.
Macromolecule
A macromolecule is a very large molecule commonly created by some form of polymerization. In biochemistry, the term is applied to the four conventional biopolymers , as well as non-polymeric molecules with large molecular mass such as macrocycles...
or colloid
Colloid
A colloid is a substance microscopically dispersed evenly throughout another substance.A colloidal system consists of two separate phases: a dispersed phase and a continuous phase . A colloidal system may be solid, liquid, or gaseous.Many familiar substances are colloids, as shown in the chart below...
particle has two meanings. Some books use it as a synonym for the Stokes radius
Stokes radius
The Stokes radius, Stokes-Einstein radius, or hydrodynamic radius RH, named after George Gabriel Stokes, is not the effective radius of a hydrated molecule in solution as often mentioned. Rather it is the radius of a hard sphere that diffuses at the same rate as the molecule. The behavior of this...
.
Section 6.4 page 290.
Others books define a theoretical hydrodynamic radius
. They consider the macromolecule or colloid particle to be a collection of subparticles. This is done most commonly for polymerPolymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
s; the subparticles would then be the units of the polymer.
is defined bywhere
is the distance between subparticles and , and where the angular brackets represent an ensemble averageEnsemble average
In statistical mechanics, the ensemble average is defined as the mean of a quantity that is a function of the micro-state of a system , according to the distribution of the system on its micro-states in this ensemble....
.
Chapter 10, Section 7.4, pages 415-417. The theoretical hydrodynamic radius
was originally an estimate by John Gamble KirkwoodJohn Gamble Kirkwood
John "Jack" Gamble Kirkwood was a noted chemist and physicist, holding faculty positions at Cornell University, the University of Chicago, California Institute of Technology, and Yale University.-Early life and background:Kirkwood was born in Gotebo, Oklahoma, the oldest child of John Millard and...
of the Stokes radius
Stokes radius
The Stokes radius, Stokes-Einstein radius, or hydrodynamic radius RH, named after George Gabriel Stokes, is not the effective radius of a hydrated molecule in solution as often mentioned. Rather it is the radius of a hard sphere that diffuses at the same rate as the molecule. The behavior of this...
of a polymer.
The theoretical hydrodynamic radius
arises in the study of the dynamic properties of polymers moving in a solventSolvent
A solvent is a liquid, solid, or gas that dissolves another solid, liquid, or gaseous solute, resulting in a solution that is soluble in a certain volume of solvent at a specified temperature...
. It is often similar in magnitude to the radius of gyration
Radius of gyration
Radius of gyration or gyradius is the name of several related measures of the size of an object, a surface, or an ensemble of points. It is calculated as the root mean square distance of the objects' parts from either its center of gravity or an axis....
.