Andrzej Poniewierski

Determination of equilibrium and rate constants for complex formation by fluorescence correlation spectroscopy supplemented by dynamic light scattering and Taylor dispersion analysis

The equilibrium and rate constants of molecular complex formation are of great interest both in the field of chemistry and biology. Here, we use fluorescence correlation spectroscopy (FCS), supplemented by dynamic light scattering (DLS) and Taylor dispersion analysis (TDA), to study the complex formation in model systems of dye-micelle interactions. In our case, dyes rhodamine 110 and ATTO-488 interact with three differently charged surfactant micelles: octaethylene glycol monododecyl ether C12E8 (neutral), cetyltrimethylammonium chloride CTAC (positive) and sodium dodecyl sulfate SDS (negative). To determine the rate constants for the dye-micelle complex formation we fit the experimental data obtained by FCS with a new form of the autocorrelation function, derived in the accompanying paper. Our results show that the association rate constants for the model systems are roughly two orders of magnitude smaller than those in the case of the diffusion-controlled limit. Because the complex stability is determined by the dissociation rate constant, a two-step reaction mechanism, including the diffusion-controlled and reaction-controlled rates, is used to explain the dye-micelle interaction. In the limit of fast reaction, we apply FCS to determine the equilibrium constant from the effective diffusion coefficient of the fluorescent components. Depending on the value of the equilibrium constant, we distinguish three types of interaction in the studied systems: weak, intermediate and strong. The values of the equilibrium constant obtained from the FCS and TDA experiments are very close to each other, which supports the theoretical model used to interpret the FCS data.

Thermodynamics for chemists, physicists and engineers

Dedication.- Preface.- Part I: Foundations of thermodynamics.- 1 Historical introduction.- 2 Basic concepts and definitions.- 2.1 Concept of thermodynamic equilibrium.- 2.2 Extensive parameters of state.- 2.3 Intensive parameters of state.- 2.4 Equations of state.- Exercises.- 3 Internal energy, work and heat.- 3.1 First law of thermodynamics.- 3.2 Isochoric process.- 3.3 Isobaric process.- 3.4 Adiabatic process.- 3.5 Isothermal process.- 3.6 Evaporation of liquids.- 3.7 Chemical reaction.- Exercises.- 4 Entropy and irreversibility of thermodynamic processes.- 4.1 Second law of thermodynamics.- 4.2 Conditions of thermodynamic equilibrium.- 4.3 Entropy as a function of state parameters.- 4.4 Changes in entropy in reversible processes.- 4.5 Heat devices.- 4.6 Changes in entropy in irreversible processes.- 4.7 Third law of thermodynamics.- Exercises.- 5 Thermodynamic potentials.- 5.1 Legendre transformation of the internal energy and entropy.- 5.2 Natural variables.- 5.3 Free-energy minimum principle.- 5.4 Examples of application of thermodynamic potentials.- 5.5 Intrinsic stability of a system.- Exercises.- Part II: Phase transitions.- 6 Phase transitions in pure substances.- 6.1 Concept of phase.- 6.2 Classification of phase transitions.- 6.3 Conditions of phase coexistence.- 6.4 Phase diagrams.- 6.5 Two-phase coexistence lines.- 6.6 Liquid-vapour two-phase region.- 6.7 Van der Waals equation of state.- Exercises.- 7 Mixtures.- 7.1 Basic concepts and relations.- 7.2 Intrinsic stability of a mixture.- 7.3 Partial molar quantities and functions of mixing.- 7.4 Mixture of ideal gases.- 7.5 Ideal mixture.- 7.6 Real mixtures.- 7.7 Phase rule.- Exercises.- 8 Phase equilibrium in ideal mixtures.- 8.1 Liquid-gas equilibrium.- 8.2 Liquid-solid equilibrium.- 8.3 Osmotic equilibrium.- 8.4 Colligative properties.- Exercises.- 9 Phase equilibrium in real mixtures.- 9.1 Liquid-vapour equilibrium.- 9.2 Liquid solutions with miscibility gap.- 9.3 Liquid-vapour equilibrium in presence of miscibility gap.- 9.4 Liquid-solid equilibrium and solid solutions.- Exercises.- Part III: Chemical thermodynamics.- 10 Systems with chemical reactions.- 10.1 Condition of chemical equilibrium.- 10.2 Effect of external perturbation on chemical equilibrium.- 10.3 Law of mass action for ideal gases.- 10.4 Thermochemistry.- 10.5 Phase rule for chemical systems.- Exercises.- 11 Electrochemical systems.- 11.1 Electrolyte solutions.- 11.2 Aqueous solutions of acids and bases.- 11.3 Electrochemical cells.- 11.4 Reversible cell.- Exercises.- Solutions .- References.- Index.

Density functional theory of liquid crystal phases

Abstract A general discussion is given of the application of density functional theory of liquids to liquid crystal problems, with particular emphasis to the onset of smectic phases. Hard particle systems have long been used as useful paradigms of liquid crystal behaviour. In this paper we also present recent work on the phase diagram of hard spherocylinders, using a non-local density functional theory of a kind which has been successful in the study of hard sphere thermodynamics. We also discuss the effect of electric quadrupolar forces on the phase diagram of Onsager-like systems.

Entropy and Irreversibility of Thermodynamic Processes

This chapter is devoted to the concept of entropy and the second law of thermodynamics which for isolated systems can be expressed as the entropy maximum principle. The latter is used to derive the conditions of thermodynamic equilibrium between two subsystems of an isolated system: thermal, mechanical and with respect to the flow of matter. In particular, we obtain the relation between a reversible flow of heat and entropy, which leads to the fundamental relation between the internal energy, volume, amount of substance and entropy. As an example of the fundamental relation we derive the entropy of an ideal gas. We also give a few examples of how the entropy of a system changes in reversible and irreversible processes. Then heat devices: a heat engine, refrigerator and heat pump, are studied as examples of practical applications of the first and second laws of thermodynamics. In particular, we discuss the efficiency of the Carnot cycle and its relation to the thermodynamic temperature. We also discuss a few other thermodynamic cycles used in petrol, diesel and steam engines. Finally, we formulate and discuss briefly the third law of thermodynamics.

Phase Equilibrium in Ideal Mixtures

In this chapter, we use the ideal mixture model to phase transitions and related phenomena that occur in two-component systems. In the context of liquid–gas equilibrium, we discuss Raoult’s and Henry’s laws. According to Raoult’s law the partial vapour pressure of a component above an ideal solution is proportional to the molar fraction of that component in the solution. Henry’s law is similar to Raoult’s law but applies only to dilute solutions, for instance, to a small amount of a gaseous component dissolved in a liquid solvent, in equilibrium with the gaseous phase. Then we discuss the liquid–solid equilibrium, in particular, solubility of solids in liquids and the phase diagram of a system called the simple eutectic. We also discuss osmotic equilibrium which occurs between a pure solvent and the solvent in a solution in the presence of a membrane permeable only to solvent molecules. Finally, we summarize the properties of solutions which depend only on the amount of the solute but not on its characteristics, called colligative properties. Examples of colligative properties are the boiling point elevation, freezing point depression and osmotic pressure.

Phase Transitions in Pure Substances

In this chapter, we introduce the concept of phase and discuss various phase transitions in pure substances. Modern classification of phase transitions as well as the historical Ehrenfest classification are presented. We discuss mainly first order transitions but examples of continuous (second order) transitions are also given. First, we derive the conditions of twophase coexistence and then discuss also coexistence of three phases. The phase diagrams of a typical substance (e.g. carbon dioxide), water and helium 4He are discussed in more detail. Then the Clapeyron and Clausius–Clapeyron equations are derived to determine the solid–liquid, liquid–gas and solid–gas phase boundaries. Special attention is paid to the liquid–vapour coexistence and the critical point at which the difference between the two phases disappears. Next we discuss the liquid–vapour coexistence using the van der Waals equation of state and describe the Maxwell construction. Finally, the van der Waals equation of state is expressed in terms of the ratios of temperature, pressure and volume to their critical values (reduced variables). This form, independent of any characteristics of the substance, leads to the principle of corresponding states.

Basic Concepts and Definitions

In this chapter, we introduce basic concepts, such as thermodynamic equilibrium, the system and surroundings and different types of walls between them, state parameters and state functions, intensive and extensive parameters, and reversible and irreversible thermodynamic processes. The concept of the quasi-static process is an idealization of real processes and is very useful in practical applications of thermodynamics. Then we discuss in more detail a few examples of extensive parameters (volume, amount of substance, internal energy), as well as intensive parameters (pressure, temperature, chemical potential), in particular the methods of temperature measurement, different temperature scales and the special role of the Kelvin scale. We also explain in simple terms the concept of the chemical potential. The final section is devoted to relations between the state parameters of a thermodynamic system, called the equations of state. We describe three model systems for which the equations of state are known: the ideal gas, van der Waals gas and photon gas.

Internal Energy, Work and Heat

In this chapter, we formulate the first law of thermodynamics and study its implications on the example of reversible isochoric, isobaric, adiabatic and isothermal processes. The heat supplied to the system in isochoric and isobaric processes is expressed in terms of the heat capacity at constant volume and pressure, respectively. For processes at constant pressure, a new state function called the enthalpy is introduced, which plays a similar role as the internal energy for processes at constant volume. A reversible adiabatic process is studied for the ideal gas case. We also discuss irreversible adiabatic and isothermal processes at constant external pressure. In the latter case, we compare the work done by the system in the reversible and irreversible process between the same two states and conclude that the reversible process is always more efficient in changing heat into work. Then evaporation of a liquid is considered as an example of process at constant temperature and pressure. Finally, we apply the first law of thermodynamics to a simple chemical reaction.

Systems with Chemical Reactions

In this chapter, we apply thermodynamics to chemical systems. During a chemical reaction reactants change into products according to a certain equation. In some conditions, the reactants and products remain in equilibrium called the chemical equilibrium. First, we derive the condition of chemical equilibrium in terms of the Gibbs free energy. Then we consider the effect of temperature and pressure on the chemical equilibrium and formulate the Le Chatelier–Braun principle. Next we apply the general condition of chemical equilibrium to a mixture of ideal gases and introduce the concept of an equilibrium constant. This leads to the condition of chemical equilibrium in the form called the law of mass action. Then we discuss thermal effects of chemical reactions, which is the subject of thermochemistry. We formulate Hess’ law and give examples of calculation of the standard enthalpy of reaction. The latter can be expressed in terms of the standard enthalpy of formation of reactants and products from the elements. Finally, we extend the phase rule to systems with chemical reactions.

Orientation of Liquid-Crystal Molecules at the Nematic-Isotropic Interface and the Nematic Free Surface

Abstract Using the generalized Kirkwood-Buff formula for a surface tension we study the interfacial properties of liquid crystals. Surface tension, δ, is calculated for the dilute hard rod system in the sharp interface approximation as a function of a tilt angle, θt, measured from the normal to the flat interface. This function has a minimum at θeq t corresponding to the preferred orientation of liquid crystal molecule at the nematic-isotropic interface and in our case θeq t = 60°. We also argue that hard-core repulsion favours perpendicular alignment at the nematic free surface i.e θt=0°.