Mechanical behavior thermodynamics

The linkage of microscopic and macroscopic properties is not without challenges, both theoretical and experimental. Statistical mechanics and thermodynamics provide the connection between molecular properties and the behavior of macroscopic matter. Coupled with statistical mechanics, computer simulation of the structure, properties, and dynamics of mesoscale models is now feasible and can handle the increase in length and time scales. 

There is a need to better understand the physical, chemical, and mechanical behaviors when modeling HE materials from fundamental theoretical principles. Among the quantities of interest in PBXs, for example, are thermodynamic stabilities, reaction kinetics, equilibrium transport coefficients, mechanical moduli, and interfacial properties between HE materials and the... 

The point of view adopted toward thermodynamics in this book is the classic or phenomenological one. This approach is the most general but also the least illuminating in molecular insight. The three basic principles of phenomenological thermodynamics are extracted as postulates from general experience, and no attempt is made to deduce them from equations describing the mechanical behavior of material... 

Fortunately, most cryogens, with the exception of helium II, behave as classical fluids. As a result, it has been possible to predict their behavior by using well-established principles of mechanics and thermodynamics applicable to many room-temperature fluids. In addition, this has permitted the formulation of convective heat transfer correlations for low-temperature designs of simple heat exchangers that are similar to those used at ambient conditions and utilize such well-known dimensionless quantities as the Nusselt, Reynolds, Prandtl, and Grashof numbers. 

The viewpoint sketched above has been so far developed and applied mainly in the context of mechanics and thermodynamics of complex fluids (Grmela, 2009 and references cited therein, also Section 3.1.6 of this review). The coupling between macroscopic (hydrodynamic) flow behavior and the behavior of a microstructure (e.g., macromolecules in polymeric fluids or suspended particles or membranes in various types in suspensions) is naturally expressed in the multiscale setting. In this review we shall include in illustrations also... 

This somewhat critical situation may be resolved by the determination of specific and general physical and chemical regularities governing the formation and behavior of polymeric foams, which requires the use of a wide range of ideas and techniques developed in other sciences physical and colloidal chemistry, physicochemical mechanics, rheology, thermodynamics, physics of polymers, physics and mechanics of non-continuous media, physics of surface and transfer phenomena, chemical physics of oxidation and degradation processes, etc. 

Although the emphasis here will, by necessity, be placed on more recent data, several key reviews of transport in nanocrystalline ionic materials have been presented, the details of which will be outlined first. An international workshop on interfacially controlled functional materials was conducted in 2000, the proceedings of which were published in the journal Solid State Ionics (Volume 131), focusing on the topic of atomic transport. In this issue, Maier [29] considered point defect thermodynamics and particle size, and Tuller [239] critically reviewed the available transport data for three oxides, namely cubic zirconia, ceria, and titania. Subsequently, in 2003, Heitjans and Indris [210] reviewed the diffusion and ionic conductivity data in nanoionics, and included some useful tabulations of data. A review of nanocrystalline ceria and zirconia electrolytes was recently published [240], as have extensive reviews of the mechanical behavior (hardness and plasticity) of both metals and ceramics [13, 234]. 

The dynamic mechanical behavior of block copolymers depends on the mechanical and morphological nature of each block. If polymer block A is thermodynamically incompatible with polymer block B, microphase domains form (J-5). The concentration and chemical structure of these domains can be controlled to produce desired mechanical and thermal properties. 

In describing thermodynamic and equilibrium statistical-mechanical behaviors of a classical fluid, we often make use of a radial distribution function g r). The latter for a fluid of N particles in volume V expresses a local number density of particles situated at distance r from a fixed particle divided by an average number density p = NjV), when the order of IjN is negligible in comparison with 1. Various thermodynamic quantities are related to g(r). For a single-component monatomic system of particles interacting with a pairwise additive potential 0(r), the relationship connecting the pressure P to g(r) is the virial theorem, ... 

An important feature of idealized elastic behavior is its complete mechanical and thermodynamic reversibility as the load is taken off, the object restores its initial shape, and there is no dissipation of energy taking place upon applying and removing the load. The energy stored in a unit volume of elastically strained object is given by... 

Newton s equation can be represented graphically in a y -t coordinates as a straight line passing through the origin (Fig. IX-4). Inverse slope of this line yields the viscosity, r. This idealized viscous behavior is completely irreversible, both mechanically and thermodynamically, meaning that the original shape of the object is not restored after one stops to apply stress. 

The last two theories described (chemical and thermodynamic) are intimately linked together because both of them induce a modification of the chemical composition at the surface. On the one hand, this modification can change the thermodynamic parameters (wettability) of the surface. On the other, changes in chemical composition influence the chemical adhesion established between the adherend and the adhesive layer. Numerous treatments are available for surface modification with coronas [8], plasmas [9, 10], lasers [11, 12], ion-assisted reactions [13], or coupling agents [14, 15]. All these treatments do not only change the chemical composition they can also affect the roughness, the orientation of macromolecular chains, and the mechanical behavior. 

The study of biomechanics, or biological mechanics, employs the principles of mechanics, which is a branch of the physical sciences that investigates the effects of energy and forces on matter or material systems. Biomechanics often embraces a broad range of subject matter that may include aspects of classical mechanics, material science, fluid mechanics, heat transfer, and thermodynamics, in an attempt to model and predict the mechanical behaviors of living systems. As such, it may be called the liberal arts of the biomedical engineering sciences. 

Since nanoparticles in PNC are orders of magnitude smaller than conventional reinforcements, the models developed for composites are not applicable to nanocomposites. However, development of a universal model for PNC is challenging since the shape, size, and dispersion of the nanoparticles vary widely from one system to another. On the one hand, exfoliated clay provides vast surface areas of solid particles (ca. 800 m /g) with a large aspect ratio that adsorb and solidify a substantial amount of the matrix polymer, but on the other hand, the mesoscale intercalated clay stacks have a much smaller specific surface area and small aspect ratio. However, in both these cases the particle-particle and particle-matrix interactions are much more important than in conventional composites, affecting the rheological and mechanical behavior. Thus, the PNC models must include the thermodynamic interactions, often neglected for standard composites. 

Determination of the properties of the system components and their interactions that affect the mechanical behavior of ERC is at present quite a complicated problem. In this connection it is assumed that the most convenient method of analyzing processes that occur during ERC formation is the thermodynamic method [141—149], At the same time, the thermodynamic approach is the most rigorous because it allows one to evaluate completely all kinds of interactions in the system. However, this approach has not so far acquired wide application because of difficulties related to the nonequUihrimn nature of the process of ERC formation, which is determined not only hy thermodynamics hut also hy kinetic considerations. As the conversion level of the system increases, its viscosity increases, which prevents the reaching of thermodynamic equUihrimn. 

Block polymers and polymer blends deserve now a great intere because of their multiphase character and their related properties. The thermodynamic immiscibility of the polymeric partners gives rise indeed to a phase separation, the extent of which controls the detailed morphology of the solid and ultimately its mechanical behavior. The advent of thermoplastic elastomers and high impact resins (HIPS or ABS type) illustrates the importance of the industrial developments that this type of materials can provide. In selective solvents, and depending on molecular structure, concentration and temperature, block polymers form micelles which influence the rheological behavior and control the morphology of the material. 

Section 2.2 described the thermodynamic reasons causing combinations of two structurally different polymers to phase separate. The actual extent of phase separation (and inversely, the extent of actual inter-molecular solution), phase continuity, phase size, and shape all contribute to the mechanical behavior patterns actually observed. 

---