Free Energy Of Material Research Articles

Free energies for materials with memory in terms of state functionals

The aim of this work is to determine what free energy functionals are expressible as quadratic forms of the state functional \(I^t\) which is discussed in earlier papers. The single integral form is shown to include the functional \(\psi _F\) proposed a few years ago, and also a further category of functionals which are easily described but more complicated to construct. These latter examples exist only for certain types of materials. The double integral case is examined in detail, against the background of a new systematic approach developed recently for double integral quadratic forms in terms of strain history, which was used to uncover new free energy functionals. However, while, in principle, the same method should apply to free energies which can be given by quadratic forms in terms of \(I^t\), it emerges that this requirement is very restrictive; indeed, only the minimum free energy can be expressed in such a manner.

Constructing free energies for materials with memory

The free energy for most materials with memory is not unique. There is a convex set of free energy functionals with a minimum and a maximum element. Various functionals have been shown to have the properties of a free energy for materials with particular types of relaxation behaviour. Also, over the last decade or more, forms have been given for the minimum and related free energies. These are all quadratic functionals which yield linear memory terms in the constitutive equations for the stress. &nbsp A difficulty in constructing free energy functionals arises in making choices that ensure a non-negative quadratic form both for the free energy and for the rate of dissipation. We propose a technique which renders this task more straightforward. Instead of constructing the free energy and determining from this the rate of dissipation, which may not have the required non-negativity, the procedure is reversed, which guarantees a satisfactory free energy functional. &nbsp Certain results for quadratic functionals in the time and frequency domains are derived, providing a platform for this alternative approach, which produces new free energies, including a family of functionals that are generalizations of the minimum and related free energies.

How Substrate Properties Control Cell Adhesion. A Physical–Chemical Approach

Most living cells derived from solid tissues require an adhering surface to live in vitro conditions. A good understanding of the relationships between the behavior of cells and the physicochemical properties of substrates such as the surface free energy, the surface polarity, the presence of functional groups and surface charges is of prime importance for the optimization of adhesion, spreading and proliferation of cells. Polystyrene and treated polystyrene surfaces were characterized by determining their surface free energies using wettability measurements. The knowledge of the surface properties of the culture substrates provides a good view of the influence of the substrate properties on cell adhesion. However, this study shows that it is not directly the surface free energy of materials that controls cell adhesion but rather the interfacial free energy between the culture medium and the substrate. The interfacial free energy between the culture medium and the solid surface controls the adsorption of serum components that may inhibit or promote cell adhesion. One of the components inhibiting cell adhesion is serum albumin. The results indicate that the adsorption of serum albumin is related to the interfacial free energy between the culture medium and the substrate. Hydrophilic substrates, such as plasma treated polystyrene substrates, have a lower interfacial free energy with water than hydrophobic polystyrene leading to a lower adsorption of proteins inhibiting cell adhesion. In addition, it is observed that there is a competition between proteins inhibiting (serum albumin) and proteins promoting cell adhesion (such as fibronectin).

Free energies of materials with memory

For many materials with memory (mechanical, electromagnetic, etc.) the free energy is not uniquely determined. There is a convex set of free energies, with a maximum and a minimum. This property is discussed in broad terms in the present article and, for the case of a linear viscoelastic material, an expression is presented for the minimum free energy, which applies to a wide range of relaxation functions. Finally, the interpretation of the energy dissipation related to the minimum free energy is discussed briefly.

Nonisothermal free energies for linear theories with memory

Explicit expressions for minimum, maximum, and intermediate free energies have recently been given for isothermal linear theories. In this paper, these results are generalized to a nonisothermal, linear model. Certain results about free energies of materials with memory are proved, using the abstract formulation of thermodynamics, both in the general case and as applied within a linear theory. In particular, an integral equation for the continuation associated with the maximum recoverable work from a given state is shown to have a unique solution and is solved directly, using the Wiener-Hopf technique. This leads to an expression for the minimum free energy, generalizing a result previously derived in the isothermal case. A new variational method developed for the isothermal case is extended to nonisothermal conditions. In the time domain, this approach yields integral equations for both the minimum and maximum free energies associated with a given state. In the frequency domain, explicit forms of a family of free energies, associated with a given state of a discrete spectrum material, are derived. This includes both maximum and minimum free energies. These latter developments, given previously for the isothermal scalar case, are generalized (with some restrictions) in this work to the tensor case. The physical relevance of various results are discussed.

Maximum and minimum free energies for a linear viscoelastic material

Certain results about free energies of materials with memory are proved, using the abstract formulation of thermodynamics, both in the general case and as applied within the theory of linear viscoelasticity. In particular, an integral equation for the strain continuation associated with the maximum recoverable work from a given linear viscoelastic state is shown to have a unique solution and is solved directly, using the Wiener-Hopf technique. This leads to an expression for the minimum free energy, previously derived by means of a variational technique in the frequency domain. A new variational method is developed in both the time and frequency domains. In the former case, this approach yields integral equations for both the minimum and maximum free energies associated with a given viscoelastic state. In the latter case, explicit forms of a family of free energies, associated with a given state of a discrete spectrum viscoelastic material, are derived. This includes both maximum and minimum free energies.

Consequences of non-uniqueness in the free energy of materials with memory

It is well known that for many materials with memory, the free energy and entropy are not uniquely defined. Such arbitrariness cannot extend to directly measurable quantities. The consequences of this requirement are explored in the work reported here both in a general framework and within the context of a quadratic model of free energy. In the latter case, it is shown that a quantity, which reduces in the linear isothermal case to the time-dependent part of the relaxation function, must be proportional to the absolute temperature.

The structural-energetic concept in the theory of friction and wear (synergism and self-organization)

The absence of a fundamental approach to friction and wear does not allow for well-founded solutions to the problems of machine service life and reliability control; interdisciplinary nature of tribology is a typical example of this. To find solutions to tribology problems one needs a synthesis of knowledge of mechanics, thermodynamics, material science, physico-chemistry, technology and operation. The fundamentals of tribology lie in the structural-energetic principle (based on the theoretical physics findings on the nature of self-organization and the formation of new phases, i.e. ordered and stable dissipative structures). Dissipative structures form by kinetic phase transition occurring under the cooperative (synergetic) actions of strain, mass transfer and heating. Tribosystems are considered to be open thermodynamic systems that exchange energy and matter with the environment. In the case of friction, all of the processes result from two fundamental phenomena: activation (an increase in the free energy of materials in the tribosystems) and passivation (a decrease). A comprehensive approach is developed that allows us to use a good store of experimental and technical data (graphs, diagrams and tables) as a vast and ever-replenishing bank of tribotechnical characteristics. Possibilities are opened up for an optimal choice of materials, strengthening methods, coatings, lubricants and additives to fit the loading conditions of tribosystems for machines used for various purposes. A systematized physical methodology is presented that allows us to control friction, lubrication and wear through regulation of the activation and passivation processes in tribomaterials by design, technological and operational means. Integral self-organization indexes of tribosystem materials and invariant criteria for the evaluation of the tribosystem state are proposed.