A polymer field theory is a
statistical field theory
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industr ...
describing the statistical behavior of a neutral or charged
polymer
A polymer (; Greek '' poly-'', "many" + ''-mer'', "part")
is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic and ...
system. It can be derived by transforming the
partition function from its standard many-dimensional integral representation over the particle degrees of freedom in a
functional integral representation over an
auxiliary field In physics, and especially quantum field theory, an auxiliary field is one whose equations of motion admit a single solution. Therefore, the Lagrangian describing such a field A contains an algebraic quadratic term and an arbitrary linear term, wh ...
function, using either the
Hubbard–Stratonovich transformation or the delta-functional transformation.
Computer simulation
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be deter ...
s based on polymer field theories have been shown to deliver useful results, for example to calculate the structures and properties of polymer solutions (Baeurle 2007, Schmid 1998), polymer melts (Schmid 1998, Matsen 2002, Fredrickson 2002) and thermoplastics (Baeurle 2006).
Canonical ensemble
Particle representation of the canonical partition function
The standard continuum model of flexible polymers, introduced by Edwards (Edwards 1965), treats a solution composed of
linear monodisperse homopolymers as a system of coarse-grained polymers, in which the statistical mechanics of the chains is described by the continuous Gaussian thread model (Baeurle 2007) and the solvent is taken into account implicitly. The Gaussian thread model can be viewed as the
continuum limit
In mathematical physics and mathematics, the continuum limit or scaling limit of a lattice model refers to its behaviour in the limit as the lattice spacing goes to zero. It is often useful to use lattice models to approximate real-world processe ...
of the discrete Gaussian chain model, in which the polymers are described as continuous, linearly elastic filaments. The canonical partition function of such a system, kept at an inverse temperature
and confined in a volume
, can be expressed as
:
where