Huggins equation

The Huggins Equation is an empirical equation used to relate the reduced viscosity of a dilute polymer solution to the concentration of the polymer in solution. It is named after Maurice L. Huggins. The Huggins equation states:

$\backslash frac\{\backslash eta\_s\}\{c\}=\; [\backslash eta]\; +\; k\_H\; [\backslash eta]^2\; c$

Where $\{\backslash eta\_s\}$ is the specific viscosity of a solution at a given concentration of a polymer in solution, $[\backslash eta]$ is the intrinsic viscosity of the solution, $k\_H$ is the Huggins coefficient, and $c$ is the concentration of the polymer in solution.{{cite book|last1=Alger|first1=Mark|title=Polymer science dictionary|date=1996|publisher=Chapman & Hall|location=London|isbn=0412608707|page=249|edition=2nd}} In isolation, $n\_s$ is the specific viscosity of a solution at a given concentration.

The Huggins equation is valid when $[\backslash eta]c$ is much smaller than 1, indicating that it is a dilute solution.{{Citation|last1=Young|first1=Robert J.|title=Introduction|date=1991|work=Introduction to Polymers|pages=1–14|publisher=Springer US|isbn=9780412306402|last2=Lovell|first2=Peter A.|doi=10.1007/978-1-4899-3176-4_1|doi-broken-date=1 November 2024 }} The Huggins coefficient used in this equation is an indicator of the strength of a solvent. The coefficient typically ranges from $k\_H\; \backslash approx\; 0.3$ (for strong solvents) to $k\_H\; \backslash approx\; 0.5$ (for poor solvents).{{cite book|last1=Seidel|first1=Arza|title=Characterization analysis of polymers|date=2008|publisher=Wiley-Interscience|location=Hoboken, N.J.|isbn=978-0-470-23300-9|page=687}}

The Huggins equation is a useful tool because it can be used to determine the intrinsic viscosity, $[\backslash eta]$, from experimental data by plotting $\backslash frac\{\backslash eta\_s\}\{c\}$versus the concentration of the solution, $c$.{{Cite book|title=Polymers : chemistry and physics of modern materials|last=Cowie, John M. G.|date=2008|publisher=Taylor & Francis|isbn=978-0849398131|oclc=610115193}}{{cite web|last1=Pamies|first1=Ramón|last2=Ginés Hernández Cifre|first2=José|last3=López Martínez|first3=María del Carmen|last4=García de la Torre|first4=José|title=Determination of intrinsic viscosities of macromolecules and nanoparticles. Comparison of single-point and dilution procedures|url=http://leonardo.inf.um.es/macromol/publications/193CPS08.pdf|publisher=Colloid Polym Sci|accessdate=6 March 2017}}