Statistical thermodynamics overview

The development of solution chemistry in Japan is reviewed in connection with the history of solution chemistry in Europe and in the United States. Studies on solution chemistry from molecular aspects, as well as those by means of thermodynamics and statistical thermodynamics, are discussed from experimental and theoretical sides. Recent trends in solution chemistry, especially those in Japan, are overviewed from static and dynamic points of view. 

Abstract We present an overview of statistical thermodynamic theories that describe the self-assembly of amphiphilic ionic/hydrophobic diblock copolymers in dilute solution. Block copolymers with both strongly and weakly dissociating (pH-sensitive) ionic blocks are considered. We focus mostly on structural and morphological transitions that occur in self-assembled aggregates as a response to varied environmental conditions (ionic strength and pH in the solution). Analytical theory is complemented by a numerical self-consistent field approach. Theoretical predictions are compared to selected experimental data on micellization of ionic/hydrophobic diblock copolymers in aqueous solutions. 

We present an overview of the statistical thermodynamic theories of self-assembly in aqueous media for amphiphilic diblock copolymers that are composed of one PE block and one hydrophobic block. In all theoretical models, the hydrophobic block is assumed to be soft enough to ensure the equilibrium character of self-assembly. We outline here the arguments that were presented in more detail in the corresponding original papers [18-23]. 

Thus, the qualitative overview of energy forms given above is beyond the scope of classical thermodynamics. The detailed description of energy states and forms in the molecular structure of the substances is covered by the discipline of statistical thermodynamics. 

There is at least one major area of activity pertaining directly to the environment for which the reader will seek in vain. The complexity of environmental problems and the availability of personal computers have led to extensive studies on models of varying sophistication. A discussion and evaluation of these lie well beyond the competence of an old-fashioned experimentalist this gap is left for others to fill but attention is drawn to a review that covers recent developments in the application of models to the risk assessment of xenobiotics (Barnthouse 1992), a book (Mackay 1991) that is devoted to the problem of partition in terms of fugacity — a useful term taken over from classical thermodynamics — and a chapter in the book by Schwarzenbach et al. (1993). Some superficial comments are, however, presented in Section 3.5.5 in an attempt to provide an overview of the dissemination of xenobiotics in natural ecosystems. It should also be noted that pharmacokinetic models have a valuable place in assessing the dynamics of uptake and elimination of xenobiotics in biota, and a single example (Clark et al. 1987) is noted parenthetically in another context in Section 3.1.1. In similar vein, statistical procedures for assessing community effects are only superficially noted in Section 7.4. Examples of the application of cluster analysis to analyze bacterial populations of interest in the bioremediation of contaminated sites are given in Section 8.2.6.2. 

An overview of thermodynamics for elementary systems is presented. We describe the infrastructure for characterizing a system under the very special conditions of equilibrium. It is shown how a maximum entropy state connects with others via fluctuations. The information presented by a system hinges on the statistical structure of the fluctuations. 

Importance and General Overview.—The usefulness of thermodynamic information gleaned from studying polymer solutions has long been recognized. For the theoretician it is essential to his construction and assessment of statistical mechanical models of macromolecules. For the technologist, as is well illustrated... 

Chapter 1 introduces basic elements of polymer physics (interactions and force fields for describing polymer systems, conformational statistics of polymer chains, Flory mixing thermodynamics. Rouse, Zimm, and reptation dynamics, glass transition, and crystallization). It provides a brief overview of equilibrium and nonequilibrium statistical mechanics (quantum and classical descriptions of material systems, dynamics, ergodicity, Liouville equation, equilibrium statistical ensembles and connections between them, calculation of pressure and chemical potential, fluctuation... 

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