Polymer physics is the field of physics that studies polymers, their fluctuations, mechanical properties, as well as the kinetics of reactions involving degradation of polymers and polymerisation of monomers. While it focuses on the perspective of condensed matter physics, polymer physics was originally a branch of statistical physics. Polymer physics and polymer chemistry are also related to the field of polymer science, which is considered to be the applicative part of polymers. Polymers are large molecules and thus are very complicated for solving using a deterministic method. Yet, statistical approaches can yield results and are often pertinent, since large polymers (i.e., polymers with many monomers) are describable efficiently in the thermodynamic limit of infinitely many monomers (although the actual size is clearly finite). Thermal fluctuations continuously affect the shape of polymers in liquid solutions, and modeling their effect requires the use of principles from statistical mechanics and dynamics. As a corollary, temperature strongly affects the physical behavior of polymers in solution, causing phase transitions, melts, and so on. The statistical approach to polymer physics is based on an analogy between polymer behavior and either Brownian motion or another type of a random walk, the self-avoiding walk. The simplest possible polymer model is presented by the ideal chain, corresponding to a simple random walk. Experimental approaches for characterizing polymers are also common, using polymer characterization methods, such as size exclusion chromatography, viscometry, dynamic light scattering, and Automatic Continuous Online Monitoring of Polymerization Reactions (ACOMP) for determining the chemical, physical, and material properties of polymers. These experimental methods help the mathematical modeling of polymers and give a better understanding of the properties of polymers.
Flory is considered the first scientist establishing the field of polymer physics. French scientists contributed since the 70s (e.g. Pierre-Gilles de Gennes, J. des Cloizeaux). Doi and Edwards wrote a famous book in polymer physics. Soviet/Russian school of physics (I. M. Lifshitz, A. Yu. Grosberg, A.R. Khokhlov, V.N. Pokrovskii) have been very active in the development of polymer physics.
Models Models of polymer chains are split into two types: "ideal" models, and "real" models. Ideal chain models assume that there are no interactions between chain monomers. This assumption is valid for certain polymeric systems, where the positive and negative interactions between the monomer effectively cancel out. Ideal chain models provide a good starting point for the investigation of more complex systems and are better suited for equations with more parameters.
Ideal chains
The freely-jointed chain is the simplest model of a polymer. In this model, fixed length polymer segments are linearly connected, and all bond and torsion angles are equiprobable. The polymer can therefore be described by a simple random walk and ideal chain. The model can be extended to include extensible segments in order to represent bond stretching. The freely-rotating chain improves the freely-jointed chain model by taking into account that polymer segments make a fixed bond angle to neighbouring units because of specific chemical bonding. Under this fixed angle, the segments are still free to rotate and all torsion angles are equally likely. The hindered rotation model assumes that the torsion angle is hindered by a potential energy. This makes the probability of each torsion angle proportional to a Boltzmann factor:
P ( θ ) ∝
exp ( − U ( θ ) / k T ) {\displaystyle P(\theta )\propto {}\exp \left(-U(\theta )/kT\right)} , where U ( θ ) {\displaystyle U(\theta )} is the potential determining the probability of each value of θ {\displaystyle \theta } . In the rotational isomeric state model, the allowed torsion angles are determined by the positions of the minima in the rotational potential energy. Bond lengths and bond angles are constant. The Worm-like chain is a more complex model. It takes the persistence length into account. Polymers are not completely flexible; bending them requires energy. At the length scale below persistence length, the polymer behaves more or less like a rigid rod. The finite extensible nonlinear elastic model takes into account non-linearity for finite chains. It is used for computational simulations.
Real chains Interactions between chain monomers can be modelled as excluded volume. This causes a reduction in the conformational possibilities of the chain, and leads to a self-avoiding random walk. Self-avoiding random walks have different statistics to simple random walks.
Solvent and temperature effect
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. 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:
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