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Preface | |

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Acknowledgements | |

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Principles of Probability | |

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Principles of Probability Are the Foundations of Entropy | |

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What Is Probability? | |

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Rules of Probability | |

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Correlated Events/Conditional Probabilities | |

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Combinatorics | |

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Distribution Functions | |

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Averages, Standard Deviations | |

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Extremum Principles Predict Equilibria | |

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What Are Extremum Principles? | |

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What Is a State of Equilibrium? | |

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Maximizing Multiplicity | |

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Simple Models | |

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Heat, Work & Energy | |

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Heat Flows to Maximize Entropy | |

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Conservation Laws | |

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Heat Was Thought to Be a Fluid | |

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Atoms and Molecules Have Energies | |

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Why Does Heat Flow? | |

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Math Tools: Series and Approximations | |

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Physical Modelling Involves Series Expansions | |

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Making Approximations Involves Truncating Series' | |

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Gaussian Distribution/Random Walk | |

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Multivariate Calculus | |

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Functions of Multiple Variables | |

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Partial Derivatives | |

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Extrema of Multivariate Functions | |

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Integrating Multivariate Functions | |

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The Chain Rule | |

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Rearranging Dependent and Independent Variables | |

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Entropy & the Boltzmann Distribution Law | |

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What Is Entropy? | |

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Flat Distributions if there Are No Constraints | |

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Exponential Distributions if there Are Constraints | |

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Principle of Fair Apportionment | |

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Philosophical Foundations | |

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Thermodynamic Driving Forces | |

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Thermodynamics Is Two Laws | |

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The Fundamental Thermodynamic Equations | |

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Defining the Thermodynamic Driving Forces | |

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Homogeneous Functions | |

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Thermal, Mechanical, and Chemical Equilibria | |

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Thermodynamic Logic | |

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The First Law Interrelates Heat, Work, and Energy | |

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Why Is There an Absolute Temperature Scale? | |

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Other Statements of the Second Law | |

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Free Energies | |

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Switching from Entropy to Free Energy | |

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Free Energy Defines Another Extremum Principle | |

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Using the Heat Capacity | |

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Using Thermodynamic Cycles | |

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Maxwell's Relations & Mixtures | |

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Predicting Unmeasurable Quantities | |

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Maxwells Relations Interrelate Partial Derivatives | |

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Multicomponent Systems/Partial Molar quantities | |

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Linkage Relations | |

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Boltzmann Distribution Law | |

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Probability Distributions for Atoms and Molecules | |

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The Boltzmann Law Describes Equilibria | |

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What Does a Partition Function Tell You? | |

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Thermodynamic Properties from Partition Functions | |

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What Is an Ensemble? | |

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Statistical Mechanics of Simple Gases and Solids | |

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Macroscopic Properties from Atomic Structures | |

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Translational Motion | |

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Harmonic Oscillator Model | |

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Rigid Rotor Model | |

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Ideal Gas Properties | |

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The Equipartition Theorem | |

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Temperature, Heat Capacity | |

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A Microscopic Perspective | |

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A Graphical Procedure, from S to C[subscript v] | |

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What Drives Heat Exchange? | |

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The Heat Capacity Reflects Energy Fluctuations | |

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Chemical Equilibria | |

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Chemical Equilibria from Atomic Structures | |

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Le Chatelier's Principle | |

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Temperature Dependence of Equilibrium | |

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Equilibria Between Liquids, Solids, and Gases | |

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Phase Equilibria | |

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The Clapeyron Equation | |

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How Do Refrigerators and Heat Pumps Work? | |

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Surface Tension | |

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Solutions and Mixtures | |

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A Lattice Model Describes Mixtures | |

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Interfacial Tension | |

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What Have We Left Out? | |

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Solvation and Transfers of Molecules Between Phases | |

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The Chemical Potential | |

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Solvation | |

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Activity and Activity Coefficient | |

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Boiling Point Elevation | |

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Freezing Point Depression | |

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Osmotic Pressure | |

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Solutes Can Transfer and Partition | |

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Dimerization in Solution | |

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Vector Calculus | |

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Vectors Describe Forces and Flows | |

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Vectors Add and Subtract by Components | |

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The Dot Product | |

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Scalar and Vector Fields | |

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The Flux of a Vector Field | |

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Gauss's Theorem | |

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Physical Kinetics | |

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Forces Drive Molecules to Flow | |

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Linear Laws Relate Forces to Flows | |

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The Diffusion Equation | |

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Sources and Sinks: Examples from Population Biology | |

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Additional Forces | |

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The Einstein-Smoluchowski Equation | |

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Brownian Ratchets | |

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The Fluctuation-Dissipation Theorem | |

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Onsager Reciprocal Relations Describe Coupled Flows | |

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Chemical Kinetics & Transition States | |

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Rates Depend on Temperature | |

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Rates Are Proportional to Concentrations | |

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At Equilibrium, Rates Obey Detailed Balance | |

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Mass Action Laws Describe Mechanisms | |

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Reaction Rates Depend on Temperature | |

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Activated Processes and Transition State Theory | |

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Catalysts Speed Up Chemical Reactions | |

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The Bronsted Law | |

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Funnel Landscapes and Diffusional Processes | |

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Coulomb's Law | |

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Charges and Coulomb's Law | |

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Charge Interactions are Long-Ranged | |

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Charge Interactions Are Weaker in Media: Dielectric Constants | |

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Electrostatic Forces Add Like Vectors | |

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What Is an Electrostatic Field? | |

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Electric Fields Have Fluxes | |

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The Electrostatic Potential | |

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Electrostatic Potentials with Electrostatic Fields | |

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Dipoles Are Separated Charges | |

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The Poisson Equation | |

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Method of Image Charges | |

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Electrochemical Equilibria | |

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Electrochemical Potentials in Ionic Solutions | |

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The Nernst Equation | |

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Voltage-Gated Ion Channels | |

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Acid-Base Equilibria Are Shifted by Electrostatic Fields | |

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Electrostatic Gradients Cause Ion Flows | |

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Creating Charge Distribution Costs Free Energy | |

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Salt Ions Shield Charged Objects | |

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Salts Dissociate and Shield Other Charges | |

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Strong and Weak Electrolytes | |

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Intermolecular Interactions | |

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Short-ranged Repulsions and Long-ranged Attractions | |

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Short-ranged Attractions Are Electrostatic | |

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The van der Waals Gas Model | |

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The Lattice Model Contact Energy | |

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Phase Transitions | |

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Two States Can Be StabIe at the Same Time | |

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Liquids or Solids Mix at High Temperatures | |

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Phase Separations Are Driven to Lower the Free Energy | |

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The Spinodal Curve | |

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The Critical Point | |

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The Principles of Boiling | |

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Boiling a Liquid Mixture Involves Two Transitions | |

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Cooperativity | |

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Abrupt Transitions Occur in Many Different Systems | |

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Transitions and Critical Points Are Universal | |

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The Landau Model | |

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Helix-Coil Transitions | |

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The Ising Model Describes Magnetization | |

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The Kinetics of Phase Transitions and Nucleation | |

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Adsorption, Binding & Catalysis | |

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Binding and Adsorption Processes Are Saturable | |

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The Langmuir Model | |

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Binding and Saturation in Solution | |

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The Principle of Adsorption Chromatography | |

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Michaelis-Menten Model | |

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Sabatier's Principle for Stabilizing Transition States | |

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Multi-site Cooperative Ligand Binding | |

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Binding Polynomials | |

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The Two-site Model of Binding Cooperativity | |

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Binding Intermediate States | |

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Constructing Binding Polynomials from Rules of Probability | |

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Oxygen Binding to Hemoglobin | |

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Inhibitors | |

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Model of McGhee and von Hippel | |

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Rates Can Often Be Treated by Using Binding Polynomials | |

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Grand Canonical Ensemble | |

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Water | |

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Water Is an Unusual Liquid | |

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Water Has Hydrogen Bonded Structure | |

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Pure Water Has Anomalous Properties | |

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Water as a Solvent | |

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Oil and Water Don't Mix: The Hydrophobic Effect | |

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Signature of Hydrophobicity: Its Temperature Dependence | |

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Water Is Structured Near Cavities and Planar Surfaces | |

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Alcohols Constrict the Volumes of Aqueous Mixtures | |

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Ions Can Make or Break Water Structure | |

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Ion Pairing Preferences | |

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Polymer Solutions | |

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Polymers Are Governed by Statistics | |

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Polymers Have Distributions of Conformations | |

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Polymer Solutions Differ from Small Molecule Solutions | |

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The Flory-Huggins Model | |

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Nonideal Colligative Properties | |

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The Phase Behavior of Polymers | |

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Dilution Entropy Drives Solute Partitioning into Polymers | |

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The Flory Theorem | |

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Polymer Elasticity | |

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Polymeric Materials Are Elastic | |

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Random-flight Chains Are Gaussian | |

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Polymer Elasticity Follows Hooke's Law | |

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Elasticity of Rubbery Materials | |

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Polymer Collapse and Expansion | |

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Polymers Resist Confinement & Deformation | |

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Excluded Volume | |

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Chain Conformations Are Perturbed Near Surfaces | |

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Polymer Conformations by a Diffusion Equation Method | |

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Polymers Tend to Avoid Confined Spaces | |

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The Rouse-Zimm Model of Polymer Dynamics | |

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The Reptation Model | |

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Table of Constants | |

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Table of Units | |

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Useful Taylor Series Expansions | |

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Useful Integrals | |

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Multiples of Units, Their Names, and Symbols | |

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Index | |