Lattice statistics polymer adsorption

Statistical-mechanical treatments of polymer adsorption at a planar surface have been pursued extensively using both analytical and Monte Carlo techniques. These procedures place polymer chain configurations in a one-to-one correspondence with random walk configurations on a lattice. While the analytical methods are limited to massless segments, and the Monte Carlo techniques are restricted to relatively short chains because of computational limitations, both provide results capable of experimental verification. The restriction to dilute solutions and non-interacting adsorbed molecules has been circumvented in recent theoretical treatments of concentrated pol3nner solutions. 

Several theories exist that describe the process of polymer adsorption, which have been developed either using a statistical mechanical approach or quasi-lattice models. In the statistical mechanical approach, the polymer is considered to consist of three... 

In this review, we introduce another approach to study the multiscale structures of polymer materials based on a lattice model. We first show the development of a Helmholtz energy model of mixing for polymers based on close-packed lattice model by combining molecular simulation with statistical mechanics. Then, holes are introduced to account for the effect of pressure. Combined with WDA, this model of Helmholtz energy is further applied to develop a new lattice DFT to calculate the adsorption of polymers at solid-liquid interface. Finally, we develop a framework based on the strong segregation limit (SSL) theory to predict the morphologies of micro-phase separation of diblock copolymers confined in curved surfaces. 

Lattice models play a central role in the description of polymer solutions as well as adsorbed polymer layers. All of the adsorption models reviewed so far assume a one-to-one correspondence between lattice random-walks and polymer configurations. In particular, the general scheme was to postulate the train-loop or train-loop—tail architecture, formulate the partition function, and then calculate the equilibrium statistics, e.g., bound fraction, average loop... 

Other lattice polymer efforts have been based on the self-consistent fleld theory of Scheutjens and Fleer (150,151). This approach differs from previously posed statistical theories for chain molecules in that the partition function is expressed in terms of the distribution of chain conformations rather than the distribution of segment densities. The equilibrium distribution of chain (ie model protein) conformations is thus calculable. Quantities predicted using this approach include the force between parallel plates coated with protein (152,153), the adsorption isotherm (154,155), and the segmental density distribution (154-157). 

The SCLF method was developed by Koopal and coworkers [46-50] to describe adsorption of surfactant molecules at the solution-solid interface. The method derives from two earlier statistical thermodynamic lattice theories (1) the Flory and Fluggins [51 ] model describing properties of polymers in solution, and (2) the methods of Scheutjens and coworkers [52-55] developed to describe the properties of polymer molecules adsorbed at the solution-solid interface and in associated mesomorphic solution structures such as micelles and vesicles. 

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