Polymer mesoscopic approach

Entangled macromolecules, connected with weak van der Waals forces, make up a very concentrated polymer solution or a polymer melt. Mesoscopic approach considers the coarse-grained dynamics of a single macromolecule. The surrounding macromolecules are considered a reacting medium. 

Investigation of viscoelastic behaviour of linear polymer solutions and melts shows that there are universal laws for dependencies of the terminal characteristics on the length of macromolecules, which allows to interpret these phenomena on the base of behaviour of a single macromolecule in the system of entangled macromolecules (Ferry 1980, Doi and Edwards 1986). The validity of the mesoscopic approach itself rests essentially on the fundamental experimental fact that quantities that characterise the behaviour of a polymer system have a well-defined unambiguous dependence on the length of the macromolecule. 

The mesoscopic approach gives an amazingly consistent picture of the different relaxation phenomena in very concentrated solutions and melts of linear polymers. It is not surprising the developed theory is a sort of phenomenological (mesoscopic) description, which allows one to get a consistent interpretation of experimental data connected with dynamic behaviour of linear macromolecules in both weakly and strongly entangled polymer systems in terms of a few phenomenological (or better, mesoscopic) parameters it does not require any specific hypotheses. 

Although the microscopic theory remains to be the real foundation of the theory of relaxation phenomena in polymer systems, the mesoscopic approach has and will not lose its value. It will help to understand the laws of diffusion and relaxation of polymers of various architecture. The information about the microstructure and microdynamics of the material can be incorporated in the form of constitutive relation, thus, allowing to relate different linear and non-linear effects of viscoelasticity to the composition and chemical structure of polymer liquid. 

As mentioned, molecular and mesoscopic approaches will be needed. The first part of the book mainly considers molecules. We start with some basic thermodynamics, interaction forces, and chemical kinetics (Chapters 2-4). The next chapter is also concerned with kinetic aspects it covers various transport phenomena (which means that a few mesoscopic aspects are involved) and includes some basic fluid rheology. Chapters 6 and 7 treat macromolecules Chapter 6 gives general aspects of polymers and discusses food polysaccharides in particular, with a largish section on starch Chapter 7 separately discusses proteins, highly intricate food polymers with several specific properties. Chapter 8 treats the interactions between water and food components and the consequences for food properties and processes. 

As a preliminary step, we consider the dynamics of the macromolecular coil moving in the flow of a viscous liquid. The bead-spring model of a macromolecule is usually used to investigate large-scale or low-frequency dynamics of a macromolecular coil, while molecules of solvent are considered to constitute a continuum - viscous liquid. This is a mesoscopic approach to the dynamics of dilute solutions of polymers. There is no intention to collect all the available results and methods concerning the dynamics of a macromolecule in viscous liquid in this section. They can be found elsewhere [9,29]. We need to consider the results for dilute solutions mainly as a background to the discussion of the dynamics of a macromolecule in very concentrated solutions and melts of polymers. 

Due to the complexity of macromolecular materials computer simulations become increasingly important in polymer science or, better, in what is now called soft matter physics. There are several reviews available which deal with a great variety of problems and techniques [1-7]. It is the purpose of the present introduction to give a very brief overview of the different approaches, mainly for dense systems, and a few apphcations. To do so we will confine ourselves to techniques describing polymers on a molecular level. By molecular level we mean both the microscopic and the mesoscopic level of description. In the case of the microscopic description (all)... 

The problem of linking atomic scale descriptions to continuum descriptions is also a nontrivial one. We will emphasize here that the problem cannot be solved by heroic extensions of the size of molecular dynamics simulations to millions of particles and that this is actually unnecessary. Here we will describe the use of atomic scale calculations for fixing boundary conditions for continuum descriptions in the context of the modeling of static structure (capacitance) and outer shell electron transfer. Though we believe that more can be done with these approaches, several kinds of electrochemical problems—for example, those associated with corrosion phenomena and both inorganic and biological polymers—will require approaches that take into account further intermediate mesoscopic scales. There is less progress to report here, and our discussion will be brief. 

The second contribution spans an even larger range of length and times scales. Two benchmark examples illustrate the design approach polymer electrolyte fuel cells and hard disk drive (HDD) systems. In the current HDDs, the read/write head flies about 6.5 nm above the surface via the air bearing design. Multi-scale modeling tools include quantum mechanical (i.e., density functional theory (DFT)), atomistic (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational fluid mechanics, and system optimization) levels. 

Rubi and Perez-Madrid (2001) derived some kinetic equations of the Fokker-Planck type for polymer solutions. These equations are based on the fact that processes leading to variations in the conformation of the macromolecules can be described by nonequilibrium thermodynamics. The extension of this approach to the mesoscopic level is called the mesoscopic nonequilibrium thermodynamics, and applied to transport and relaxation phenomena and polymer solutions (Santamaria-Holek and Rubi, 2003). 

The Mesoscopic Non-Equilibrium Thermodynamics Approach to Polymer Crystallization... 

The use of a matrix to define the reaction space is an intrinsically attractive approach to the preparation of large amounts of material which could be deposited from solution or from the vapor phase. A number of matrices have been used including zeolites [80], layered solids [81], molecular sieves [82-84], micelles/ microemulsions [85-89], gels [90-92], polymers [93-97] and glasses [98]. The matrix provides a mesoscopic reaction chamber in which the crystal can only grow to a certain size. 

Quantum chemistry has estabhshed itself as a valuable tool in the studies of polymerization processes [25,26]. However, direct quantum chemical studies on the relationship between the catalyst structure and the topology of the resulting polymer, as well as on the influence of the reaction conditions, are not practical without the aid of statistical methods. We have to this end proposed a combined approach in which quantum chemical methods are used to provide information on the microscopic energetics of elementary reactions in the catalytic cycle, that is required for a mesoscopic stochastic simulations of polymer growth [25]. A stochastic approach makes it possible to discuss the effects of temperature and olefin pressure. 

There are three main modes of interaction between a polymer solution and a solid surface. The first interaction mode is depletion [2,3]. If the monomers are repelled by the surface (or in other words if the attractive interaction between the solvent molecules and the surface is larger than the interaction between the monomers and the surface), the polymer concentration in solution decreases as the surface is approached and a region depleted in polymer exists in the vicinity of the surface. The size of this region is the size of the polymer chain if the solution is dilute and the size of the correlation length of the solution if the solution is semidilute (if the polymer chains overlap). When two surfaces are brought in close contact, the density in the gap between the surfaces is smaller than the bulk concentration and the osmotic pressure in the gap is smaller than the bulk osmotic pressure. This osmotic pressure difference induces an attraction between the surfaces. The depletion interaction is not specific to polymers and exists with any particle with a size in the colloidal range [4]. It has sometimes been used to induce adhesion between particles of mesoscopic size such as red blood cells. The only limitation to this qualitative description of the depletion force is that at equilibrium the polymer chains (or any other particles) must leave the gap as the surfaces get closer. There is no attractive depletion force if they remain trapped in the gap. We will not consider further the depletion interaction. 

In order to expand the applicability of mesoscopic dot-, line- and honeycomb patterns in foe field of photonics and electronics, one promising approach is the incorporation of photofonctional low-molar-mass compoimds into the dewetted polymer patterns, or foe pattern formation of low molar rrtass compounds themselves. 

---