Chemical potential and free energy

Plants and animals require a continual input of free energy. If we were to remove the sources of free energy, organisms would drift toward equilibrium with the consequent cessation of life. The ultimate source of free energy is the sun. Photosynthesis converts its plentiful radiant energy into free energy, which is stored first in intermediate energy currencies like ATP and then 

To every chemical component in a system we can assign a free energy per mole of that species. This quantity is called the chemical potential of species) and is given the symbol p,j. We can view p,j as a property of species), indicating how that species will react to a given change, for example, a 

The condition for a spontaneous change — a decrease in chemical potential — has important implications for discussing fluxes from one region to another. In particular, we can use the chemical potential difference between 

Darcy s law (Chapter 9, Section 9.3), Poiseuille s law (Chapter 9, Section 9.4) 

Because electrical potential also affects the chemical potential of charged particles, it must be considered when predicting the direction of 

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Just as one may wish to specify the temperature in a molecular dynamics simulation, so may be desired to maintain the system at a constant pressure. This enables the behavior of the system to be explored as a function of the pressure, enabling one to study phenomer such as the onset of pressure-induced phase transitions. Many experimental measuremen are made under conditions of constant temperature and pressure, and so simulations in tl isothermal-isobaric ensemble are most directly relevant to experimental data. Certai structural rearrangements may be achieved more easily in an isobaric simulation than i a simulation at constant volume. Constant pressure conditions may also be importai when the number of particles in the system changes (as in some of the test particle methoc for calculating free energies and chemical potentials see Section 8.9). 

Ion-Dipole Forces. Ion-dipole forces bring about solubihty resulting from the interaction of the dye ion with polar water molecules. The ions, in both dye and fiber, are therefore surrounded by bound water molecules that behave differently from the rest of the water molecules. If when the dye and fiber come together some of these bound water molecules are released, there is an increase in the entropy of the system. This lowers the free energy and chemical potential and thus acts as a driving force to dye absorption. 

OSMOTIC PRESSURE THERMODYNAMIC FOUNDATIONS 3.2a Gibbs Free Energy and Chemical Potential... 

The ideas underlying elemental structures models are to establish microstructures experimentally, to compute free energies and chemical potentials from models based on these structures, and to use the chemical potentials to construct phase diagrams. Jonsson and Wennerstrom have used this approach to predict the phase diagrams of water, hydrocarbon, and ionic surfactant mixtures [18]. In their model, they assume the surfactant resides in sheetlike structures with heads on one side and tails on the other side of the sheet. They consider five structures spheres, inverted (reversed) spheres, cylinders, inverted cylinders, and layers (lamellar). These structures are indicated in Fig. 12. Nonpolar regions (tails and oil) are cross-hatched. For these elemental structures, Jonsson and Wennerstrom include in the free energy contributions from the electrical double layer on the water... 

Of the three quantities (temperature, energy, and entropy) that appear in the laws of thermodynamics, it seems on the surface that only energy has a clear definition, which arises from mechanics. In our study of thermodynamics a number of additional quantities will be introduced. Some of these quantities (for example, pressure, volume, and mass) may be defined from anon-statistical (non-thermodynamic) perspective. Others (for example Gibbs free energy and chemical potential) will require invoking a statistical view of matter, in terms of atoms and molecules, to define them. Our goals here are to see clearly how all of these quantities are defined thermodynamically and to make use of relationships between these quantities in understanding how biochemical systems behave. 

To apply the preceding concepts of chemical thermodynamics to chemical reaction systems (and to understand how thermodynamic variables such as free energy vary with concentrations of species), we have to develop a formalism for the dependence of free energies and chemical potential on the number of particles in a system. We develop expressions for the change in Helmholtz and Gibbs free energies in chemical reactions based on the definition of A and G in terms of Q and Z. The quantities Q and Z are called the partition functions for the NVT and NPT systems, respectively. 

Melting and sublimation temperatures, internal energy (i.e., structural energy), enthalpy (i.e., heat content), heat capacity, entropy, free energy and chemical potential, thermodynamic activity, vapor pressure, solubility... 

The free-energy and chemical potentials of the solvent is slightly altered from the case of small solute molecules (Flory, 1970) ... 

Free energy and chemical potential Thermodynamic activity Vapor pressure Solubility... 

TABLE 5.4 Free Energy and Chemical Potential for Surfactant Adsorption Layers ... 

Osmotic equilibrium, free energy, and chemical potential... 

In this question we use absolute free energies. Their relative magnitudes are more or less reasonable, but of course in real life you never get to deal with quantities like these. The exercise is useful, however, because you should get used to the idea that free energies and chemical potentials are finite, absolute quantities, even if unknown. 

If one employs the partition function Z for an ideal gas, as given by equations (28-59) and (28-87), then the Helmholtz free energy and chemical potential are calculated by combining classical and statistical thermodynamics ... 

Stress Relaxation Free energy and chemical potential considerations, reptation [55]... 

Herman and Edwards [55] extended the Brochard and de Gennes approach [53] by considering in detail the stress accompanying the swelling of the polymer within the reptation model. They evaluated the contributions to the free energy and chemical potentials due to the deformation of the polymer due to swelling. The chemical potential of the solvent, pi, was obtained by taking two contributions into account. The first was the classical osmotic pressure... 

F. Free Energy and Chemical Potential the Stumbling Block of Conventional Canonical Ensemble Calculations... 

The Relationship Between Free Energies and Chemical Potentials... 

Fig. 15.2 The molar free energy and chemical potential of Ga at each site as a function of Ga occupancy (a) in the D site of LGS (langasite) and (b) B site of LTG (langatate).

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