Exact solutions of lattice polymer models
نویسندگان
چکیده
We consider directed path models of a selection of polymer and vesicle problems. Each model is used to illustrate an important method of solving lattice path enumeration problems. In particular, the Temperley method is used for the polymer collapse problem. The ZL method is used to solve the semi-continuous vesicle model. The Constant Term method is used to solve a set of partial difference equations for the polymer adsorption problem. The Kernel method is used to solve the functional equation that arises in the polymer force problem. Finally, the Transfer Matrix method is used to solve a problem in colloid dispersions. All these methods are combinatorially similar as they all construct equations by considering the action of adding an additional column to the set of objects.
منابع مشابه
Modeling the Transport and Volumetric Properties of Solutions Containing Polymer and Electrolyte with New Model
A new theoretical model based on the local composition concept (TNRF-mNRTL model) was proposed to express the short-range contribution of the excess Gibbs energy for the solutions containing polymer and electrolyte. This contribution of interaction along with the long-range contribution of interaction (Pitzer-Debye-Hückel equation), configurational entropy of mixing (Flory-Huggins relation)...
متن کاملSolvable Lattice Gas Models of Random Hetero - Polymers atFinite
We introduce 1-dimensional lattice gas versions of three common models of random hetero-polymers, in which both the polymer density and the density of the polymer-solvent mixture are nite. These solvable models give valuable insight into the problems related to the (quenched) average over the randomness in statistical mechanical models of proteins, without having to deal with the hard geometric...
متن کاملTwo-chamber lattice model for thermodiffusion in polymer solutions
When a temperature gradient is applied to a polymer solution, the polymer typically migrates to the colder regions of the fluid as a result of thermal diffusion ~Soret effect!. However, in recent thermodiffusion experiments on poly~ethylene-oxide! ~PEO! in a mixed ethanol/water solvent it is observed that for some solvent compositions the polymer migrates to the cold side, while for other compo...
متن کاملMapping of continuum and lattice models for describing the adsorption of an ideal chain anchored to a planar surface
An ideal polymer chain anchored to a planar surface is considered by using both lattice and continuum model approaches. A general equation relating the lattice and continuum model adsorption interaction parameters is derived in a consistent way by substituting the exact continuum solution for the free chain end distribution function into the lattice model boundary condition. This equation is no...
متن کامل2 6 M ay 1 99 8 Two exactly soluble lattice models in three dimensions
As a prelude to what might be expected as forthcoming breakthroughs in finding new approaches toward solving three-dimensional lattice models in the twenty-first century, we review the exact solutions of two lattice models in three dimensions obtained using the conventional combinatorial and transfer matrix approaches.
متن کامل