Editing Polymer physics (section)

==Solvent and temperature effect==
{{Unreferenced section|date=November 2016}}
The statistics of a single polymer chain depends upon the solubility of the polymer in the solvent. For a solvent in which the polymer is very soluble (a "good" solvent), the chain is more expanded, while for a solvent in which the polymer is insoluble or barely soluble (a "bad" solvent), the chain segments stay close to each other.  In the limit of a very bad solvent the polymer chain merely collapses to form a hard sphere, while in a good solvent the chain swells in order to maximize the number of polymer-fluid contacts.<ref>{{cite web |last1=Gayvert |first1=James |last2=Chremos |first2=Alexandros |last3=Douglas |first3=Jack |title=Molecular Dynamics Study of the Conformational Properties of Polymers in an Explicit Solvent and the Identification of the θ-Temperature |url=https://www.nist.gov/system/files/documents/2020/03/03/Gayvert_Colloquium_Presentation.pdf |website=National Institute of Standards and Technology |publisher=Material Measurement Laboratory |access-date=1 February 2025 |pages=4-5 |url-status=live}}</ref>  For this case the [[radius of gyration]] is approximated using Flory's mean field approach which yields a scaling for the radius of gyration of:
::<math>R_g \sim N^\nu</math>,
where <math>R_g</math> is the [[radius of gyration]] of the polymer, <math>N</math> is the number of bond segments (equal to the degree of polymerization) of the chain and <math>\nu</math> is the [[Flory exponent]].

For good solvent, <math>\nu\approx3/5</math>; for poor solvent, <math>\nu=1/3</math>.  Therefore, polymer in good solvent has larger size and behaves like a [[fractal]] object.  In bad solvent it behaves like a solid sphere.

In the so-called <math>\theta</math> solvent, <math>\nu=1/2</math>, which is the result of simple random walk.  The chain behaves as if it were an ideal chain.

The quality of solvent depends also on temperature.  For a flexible polymer, low temperature may correspond to poor quality and high temperature makes the same solvent good.  At a particular temperature called theta (θ) temperature, the solvent behaves as an [[ideal chain]].