Colloidal Soft Matter Physics

Colloidal soft matter is a class of materials that exhibit rich equilibrium and non-equilibrium 0thermodynamic properties, it self-assembles (spontaneously or driven externally) to form a large diversity of structures, and its constituents display an interesting and complex transport behavior. In this contribution, we review the essential aspects and the modern challenges of Colloidal SoftMatter Physics. Our main goal is to provide a balanced discussion of the various facets of this highly multidisciplinary field, including experiments, theoretical approximations and models for molecular simulations, so that readers with various backgrounds could get both the basics and a broader, more detailed physical picture of the field. To this end, we first put emphasis on the colloidal physics, which allows us to understand the main driving (molecular and thermodynamic) forces between colloids that give rise to a wide range of physical phenomena. We also draw attention to some particular problems and areas of opportunity in Colloidal Soft Matter Physics that represent promising perspectives for future investigations.

Thermodynamics and Gradient Manipulation Mechanism in Entrepreneurial Actions

Entrepreneurship researches started to have traction at the start of 1980 and underwent paradigmatic shift. However despite the varied veins of exploration from opportunities to innate traits, entrepreneurship literatures have yet developed a unifying conceptualization and theory with key concepts that can clearly explain why entrepreneurs act the way they do? What inspires them to action? What seduce them to move at all? This paper intends to relate the study of entrepreneurship, entrepreneurial actions and activities with references to thermodynamic and energy gradient manipulation mechanism. Studying business ventures from a process view in an attempt to reconstruct the entrepreneurial process by illustrating a range of relevant perspectives from energy gradients in naturally occurring chemicals and suspension coils, this paper hopes to pull together a unifying theory on entrepreneurship basing on the forces at work with thermodynamic concepts and expressions with gradient-manipulation mechanism to explain the entrepreneurial action-motion phenomena. The gradient-manipulating mechanism and thermodynamic expressions thus become the “nature” invisible hand that operates the motion of actions. Kirzner’s theory of entrepreneurship explains the coordination of markets and of knowledge. It is that knowledge, the recognition of the opportunities in the actual imperfect markets that triggers the gradient-manipulation mechanism. The findings of this paper suggest that entrepreneurial actions are force-driven by the lure of profits to select of best pathways and means to achieve the ends. The idea that entrepreneurial actions are the results of the play of forces with thermodynamic forces at work is a powerful suggestion in the finding of this paper.

Onsager relationships

This chapter discusses Onsager relationships. These relationships result from the linear response at the macroscale off-equilibrium from the reversibility of the microscale and represent an example of cause and chance at work. Flux-flow formalism—flux densities tied to thermodynamic forces—is developed to build the generalized linear relationships for heat, electric, chemical composition and free energy. The relationships are then applied to examples from previous chapters—thermoelectric and others—to show how results of interest can be derived more easily through exploiting Onsager relationships’ linearity and reciprocity relationships. The chapter discusses Onsager relationships with respect to Ohm’s law, Fourier’s law, Fick’s law, Darcy’s law, Gibbs free energy, thermoelectric effects and fluctuation-dissipation.

Supercritical behavior of magnetic and liquid model systems

The supercritical transitions are widely occurring. They include the supercritical transitions in the liquid-vapor system, ferromagnetic transitions, transitions in polymers, many transitions in liquid crystals, and some structural transitions. In the paper it is emphasized that the nature of the critical and supercritical transitions is the same – these are continuous fluctuation transitions. Above the critical temperature the system passes through a region of lowered stability, which leads to increase of fluctuations of energy and external parameters of the system. From the point of view of thermodynamic stability this indicates the existence of a continuous supercritical transition between supercritical mesophases. Knowing the basic stability characteristics of a system, we derive the equation of these mesophase transitions. Depending on a thermal equation type, we can get one or several such equations, which may not coincide. This approves the fact that a supercritical transition occurs in a certain interval of thermodynamic forces. In the paper the relations between the critical exponents of thermodynamic parameters of the system are obtained and the conditions of continuous conjugation of the lowered stability line to subcritical coexistence line are investigated. The results are applied to the Curie–Weiss and van der Waals models: we obtain the quasi-spinodal equation for these systems and analyze the critical and supercritical behavior of the stability characteristics.

Supercritical behavior of thermodynamic systems

It is known that basic stability characteristics of a system are inversely proportional to fluctuations of external parameters. Above the critical point there is a region remaining homogeneous macroscopically, but becoming microheterogeneous within an interval of thermodynamic forces. Within this interval thermodynamic coefficients of stability pass finite non-zero minima. This corresponds to the considerable growth of fluctuations and indicates the occurrence of supercritical transition of continuous kind. The limit case of such continuous phase transitions is the critical state, which is also the limit point of some first-kind transitions (the limit point of phase equilibrium curve).In this paper we consider the relation between thermodynamic stability conditions and fluctuations of external parameters of the system. We study the behavior of a simple one-component thermodynamic system (liquid, magnet, and ferroelectric) in the supercritical region and derive the equation of the line of supercritical transition for this system.

Coupled constitutive relations: a second law based higher-order closure for hydrodynamics

In the classical framework, the Navier–Stokes–Fourier equations are obtained through the linear uncoupled thermodynamic force-flux relations which guarantee the non-negativity of the entropy production. However, the conventional thermodynamic descrip- tion is only valid when the Knudsen number is sufficiently small. Here, it is shown that the range of validity of the Navier–Stokes–Fourier equations can be extended by incorporating the nonlinear coupling among the thermodynamic forces and fluxes. The resulting system of conservation laws closed with the coupled constitutive relations is able to describe many interesting rarefaction effects, such as Knudsen paradox, transpiration flows, thermal stress, heat flux without temperature gradients, etc., which cannot be predicted by the classical Navier–Stokes–Fourier equations. For this system of equations, a set of phenomenological boundary conditions, which respect the second law of thermodynamics, is also derived. Some of the benchmark problems in fluid mechanics are studied to show the applicability of the derived equations and boundary conditions.

Mechanical approach to chemical transport

Nonequilibrium thermodynamics describes the rates of transport phenomena with the aid of various thermodynamic forces, but often the phenomenological transport coefficients are not known, and the description is not easily connected with equilibrium relations. We present a simple and intuitive model to address these issues. Our model is based on Lagrangian dynamics for chemical systems with dissipation, so one may think of the model as physicochemical mechanics. Using one main equation, the model allows a systematic derivation of all transport and equilibrium equations, subject to the limitation that heat generated or absorbed in the system must be small for the model to be valid. A table with all major examples of transport and equilibrium processes described using physicochemical mechanics is given. In equilibrium, physicochemical mechanics reduces to standard thermodynamics and the Gibbs–Duhem relation, and we show that the First and Second Laws of thermodynamics are satisfied for our system plus bath model. Out of equilibrium, our model provides relationships between transport coefficients and describes system evolution in the presence of several simultaneous external fields. The model also leads to an extension of the Onsager–Casimir reciprocal relations for properties simultaneously transported by many components.