Molecular Driving Forces: Statistical Thermodynamics in Chemistry, Physics, Biology, and Nanoscience

by Dill, Ken A.; Bromberg, Sarina

• ISBN13: 9780815320517
• ISBN10: 0815320515
• Format: Paperback
• Copyright: 2002-09-13
• Publisher: Routledge

Summary

This text shows how many complex behaviors of molecules can result from a few simple physical processes. A central theme is the idea that simplistic models can give surprisingly accurate insights into the workings of the molecular world. Written in a clear and student-friendly style, the book gives an excellent introduction to the field for novices. It should also be useful to those who want to refresh their understanding of this important field, and those interested in seeing how physical principles can be applied to the study of problems in the chemical, biological, and material sciences. Furthermore,Molecular Driving Forcescontains a number of features including: *449 carefully produced figures illustrating the subject matter *178 worked examples in the chapters which explain the key concepts and show their practical applications *The text is mathematically self-contained, with 'mathematical toolkits' providing the required maths *Advanced material that might not be suitable for someelementary courses is clearly delineated in the text *End-of-chapter references and suggestions for further reading

Author Biography

Ken A. Dill is Professor of Pharmaceutical Chemistry and Biophysics at the University of California, San Francisco.

Table of Contents

Preface	xvii
Acknowledgements	xx
Principles of Probability	1	(26)
Principles of Probability Are the Foundations of Entropy	1	(1)
What is Probability?	2	(1)
Rules of Probability	3	(4)
Correlated Events/Conditional Probabilities	7	(2)
Combinatorics	9	(4)
Distribution Functions	13	(4)
Averages, Standard Deviations	17	(4)
Summary	21	(3)
Problems	24	(2)
Suggested Reading	26	(1)
Extremum Principles Predict Equilibria	27	(10)
What Are Extremum Principles?	27	(1)
What Is a State of Equilibrium?	28	(2)
Maximizing Multiplicity	30	(1)
Simple Models	31	(4)
Summary	35	(1)
Problems	36	(1)
Suggested Reading	36	(1)
Heat, Work & Energy	37	(12)
Heat Flows to Maximize Entropy	37	(1)
Conservation Laws	37	(3)
Heat Was Thought to Be a Fluid	40	(2)
Atoms and Molecules Have Energies	42	(2)
Why Does Heat Flow?	44	(2)
Summary	46	(2)
Problems	48	(1)
Suggested Reading	48	(1)
Math Tools: Series and Approximation	49	(12)
Physical Modelling Involves Series Expansions	49	(4)
Making Approximations Involves Truncating Series'	53	(4)
Gaussian Distribution/Random Walk	57	(2)
Summary	59	(1)
Problems	60	(1)
Suggested Reading	60	(1)
Multivariate Calculus	61	(20)
Functions of Multiple Variables	61	(1)
Partial Derivatives	62	(3)
Extrema of Multivariate Functions	65	(8)
Integrating Multivariate Functions	73	(4)
The Chain Rule	77	(1)
Rearranging Dependent and Independent Variables	78	(1)
Summary	79	(1)
Problems	80	(1)
Suggested Reading	80	(1)
Entropy & the Boltzmann Distribution Law	81	(24)
What Is Entropy?	81	(4)
Flat Distributions if there Are No Constraints	85	(1)
Exponential Distributions if there Are Constraints	86	(3)
Principle of Fair Apportionment	89	(10)
Philosophical Foundations	99	(2)
Summary	101	(1)
Problems	102	(1)
Suggested Reading	103	(2)
Thermodynamic Driving Forces	105	(26)
Thermodynamics Is Two Laws	105	(2)
The Fundamental Thermodynamic Equations	107	(1)
Defining the Thermodynamic Driving Forces	108	(3)
Homogeneous Functions	111	(1)
Thermal, Mechanical, and Chemical Equilibria	111	(8)
Thermodynamic Logic	119	(3)
The First Law Interrelates Heat, Work, and Energy	122	(4)
Why Is There an Absolute Temperature Scale?	126	(1)
Other Statements of the Second Law	127	(1)
Summary	127	(1)
Problems	128	(1)
Suggested Reading	128	(3)
Free Energies	131	(22)
Switching from Entropy to Free Energy	131	(1)
Free Energy Defines Another Extremum Principle	132	(10)
Using the Heat Capacity	142	(4)
Using Thermodynamic Cycles	146	(4)
Summary	150	(1)
Problems	151	(1)
Suggested Reading	152	(1)
Maxwell's Relations & Mixtures	153	(18)
Predicting Unmeasurable Quantities	153	(2)
Maxwells Relations Interrelate Partial Derivatives	155	(8)
Multicomponent Systems/Partial Molar Quantities	163	(3)
Linkage Relations	166	(2)
Summary	168	(1)
Problems	169	(1)
Suggested Reading	169	(2)
Boltzmann Distribution Law	171	(22)
Probability Distributions for Atoms and Molecules	171	(2)
The Boltzmann Law Describes Equilibria	173	(4)
What Does a Partition Function Tell You?	177	(6)
Thermodynamic Properties from Partition Functions	183	(5)
What Is an Ensemble?	188	(1)
Summary	189	(1)
Problems	190	(1)
Suggested Reading	191	(2)
Statistical Mechanics of Simple Gases and Solids	193	(28)
Macroscopic Properties from Atomic Structures	193	(2)
Translational Motion	195	(6)
Harmonic Oscillator Model	201	(2)
Rigid Rotor Model	203	(3)
Ideal Gas Properties	206	(6)
The Equipartition Theorem	212	(4)
Summary	216	(1)
Problems	217	(2)
Suggested Reading	219	(2)
Temperature, Heat Capacity	221	(14)
A Microscopic Perspective	221	(4)
A Graphical Procedure, from S to Cv	225	(2)
What Drives Heat Exchange?	227	(1)
The Heat Capacity Reflects Energy Fluctuations	228	(4)
Summary	232	(1)
Problems	233	(1)
Suggested Reading	234	(1)
Chemical Equilibria	235	(16)
Chemical Equilibria from Atomic Structures	235	(8)
Le Chatelier's Principle	243	(1)
Temperature Dependence of Equilibrium	244	(4)
Summary	248	(1)
Problems	249	(1)
Suggested Reading	249	(2)
Equilibria Between Liquids, Solids, and Gases	251	(16)
Phase Equilibria	251	(5)
The Clapeyron Equation	256	(3)
How Do Refrigerators and Heat Pumps Work?	259	(3)
Surface Tension	262	(2)
Summary	264	(1)
Problems	265	(1)
Suggested Reading	265	(2)
Solutions and Mixtures	267	(12)
A Lattice Model Describes Mixtures	267	(6)
Interfacial Tension	273	(2)
What Have We Left Out?	275	(1)
Summary	276	(1)
Problems	277	(1)
Suggested Reading	277	(2)
Solvation and Transfers of Molecules Between Phases	279	(22)
The Chemical Potential	279	(1)
Solvation	280	(2)
Activity and Activity Coefficient	282	(3)
Boiling Point Elevation	285	(3)
Freezing Point Depression	288	(1)
Osmotic Pressure	289	(2)
Solutes Can Transfer and Partition	291	(3)
Dimerization in Solution	294	(3)
Summary	297	(1)
Problems	298	(3)
Vector Calculus	301	(14)
Vectors Describe Forces and Flows	301	(1)
Vectors Add and Subtract by Components	301	(1)
The Dot Product	302	(1)
Scalar and Vector Fields	303	(5)
The Flux of a Vector Field	308	(2)
Gauss's Theorem	310	(1)
Summary	311	(3)
Problems	314	(1)
Physical Kinetics	315	(26)
Forces Drive Molecules to Flow	315	(1)
Linear Laws Relate Forces to Flows	316	(2)
The Diffusion Equation	318	(6)
Sources and Sinks: Examples from Population Biology	324	(2)
Additional Forces	326	(1)
The Einstein-Smoluchowski Equation	327	(3)
Brownian Ratchets	330	(3)
The Fluctuation-Dissipation Theorem	333	(2)
Onsager Reciprocal Relations Describe Coupled Flows	335	(2)
Summary	337	(1)
Problems	338	(1)
Suggested Reading	339	(2)
Chemical Kinetics & Transition States	341	(28)
Rates Depend on Temperature	341	(1)
Rates Are Proportional to Concentrations	341	(1)
At Equilibrium, Rates Obey Detailed Balance	342	(2)
Mass Action Laws Describe Mechanisms	344	(1)
Reaction Rates Depend on Temperature	345	(3)
Activated Processes and Transition State Theory	348	(8)
Catalysts Speed Up Chemical Reactions	356	(3)
The Bronsted Law	359	(4)
Funnel Landscapes and Diffusional Processes	363	(1)
Summary	364	(2)
Problems	366	(1)
Suggested Reading	367	(2)
Coulomb's Law	369	(18)
Charges and Coulomb's Law	369	(1)
Charge Interactions are Long-Ranged	370	(3)
Charge Interactions Are Weaker in Media: Dielectric Constants	373	(2)
Electrostatic Forces Add Like Vectors	375	(1)
What Is an Electrostatic Field?	376	(2)
Electric Fields Have Fluxes	378	(6)
Summary	384	(1)
Problems	385	(1)
Suggested Reading	385	(2)
The Electrostatic Potential	387	(22)
Electrostatic Potentials with Electrostatic Fields	387	(5)
Dipoles Are Separated Charges	392	(3)
The Poisson Equation	395	(4)
Method of Image Charges	399	(7)
Summary	406	(1)
Problems	407	(1)
Suggested Reading	407	(2)
Electrochemical Equilibria	409	(24)
Electrochemical Potentials in Ionic Solutions	409	(1)
The Nernst Equation	410	(7)
Voltage-Gated Ion Channels	417	(1)
Acid-Base Equilibria Are Shifted by Electrostatic Fields	418	(2)
Electrostatic Gradients Cause Ion Flows	420	(3)
Creating Charge Distribution Costs Free Energy	423	(7)
Summary	430	(1)
Problems	431	(1)
Suggested Reading	432	(1)
Salt Ions Shield Charged Objects	433	(16)
Salts Dissociate and Shield Other Charges	433	(7)
Strong and Weak Electrolytes	440	(4)
Summary	444	(2)
Problems	446	(1)
Suggested Reading	447	(2)
Intermolecular Interactions	449	(18)
Short-ranged Repulsions and Long-ranged Attractions	449	(1)
Short-ranged Attractions Are Electrostatic	450	(7)
The van der Waals Gas Model	457	(5)
The Lattice Model Contact Energy	462	(1)
Summary	463	(1)
Problems	464	(1)
Suggested Reading	465	(2)
Phase Transitions	467	(26)
Two States Can Be Stable at the Same Time	467	(1)
Liquids or Solids Mix at High Temperatures	468	(3)
Phase Separations Are Driven to Lower the Free Energy	471	(6)
The Spinodal Curve	477	(1)
The Critical Point	478	(1)
The Principles of Boiling	479	(6)
Boiling a Liquid Mixture Involves Two Transitions	485	(2)
Summary	487	(1)
Problems	488	(3)
Suggested Reading	491	(2)
Cooperativity	493	(22)
Abrupt Transitions Occur in Many Different Systems	493	(1)
Transitions and Critical Points Are Universal	493	(3)
The Landau Model	496	(3)
Helix-Coil Transitions	499	(9)
The Ising Model Describes Magnetization	508	(1)
The Kinetics of Phase Transitions and Nucleation	509	(2)
Summary	511	(1)
Problems	512	(3)
Adsorption, Binding & Catalysis	515	(18)
Binding and Adsorption Processes Are Saturable	515	(1)
The Langmuir Model	515	(4)
Binding and Saturation in Solution	519	(2)
The Principle of Adsorption Chromatography	521	(1)
Michaelis-Menten Model	522	(5)
Sabatier's Principle for Stabilizing Transition States	527	(2)
Summary	529	(1)
Problems	530	(1)
Suggested Reading	531	(2)
Multi-site Cooperative Ligand Binding	533	(30)
Binding Polynomials	534	(2)
The Two-site Model of Binding Cooperativity	536	(3)
Binding Intermediate States	539	(2)
Constructing Binding Polynomials from Rules of Probability	541	(5)
Oxygen Binding to Hemoglobin	546	(4)
Inhibitors	550	(2)
Model of McGhee and von Hippel	552	(4)
Rates Can Often Be Treated by Using Binding Polynomials	556	(1)
Grand Canonical Ensemble	556	(2)
Summary	558	(1)
Problems	559	(3)
Suggested Reading	562	(1)
Water	563	(14)
Water Is an Unusual Liquid	563	(1)
Water Has Hydrogen Bonded Structure	563	(5)
Pure Water Has Anomalous Properties	568	(7)
Summary	575	(1)
Problems	576	(1)
Suggested Reading	576	(1)
Water as a Solvent	577	(16)
Oil and Water Don't Mix: The Hydrophobic Effect	577	(1)
Signature of Hydrophobicity: Its Temperature Dependence	578	(4)
Water Is Structured Near Cavities and Planar Surfaces	582	(3)
Alcohols Constrict the Volumes of Aqueous Mixtures	585	(1)
Ions Can Make or Break Water Structure	586	(2)
Ion Pairing Preferences	588	(1)
Summary	589	(1)
Problems	590	(1)
Suggested Reading	591	(2)
Polymer Solutions	593	(16)
Polymers Are Governed by Statistics	593	(1)
Polymers Have Distributions of Conformations	593	(1)
Polymer Solutions Differ from Small Molecule Solutions	594	(2)
The Flory-Huggins Model	596	(5)
Nonideal Colligative Properties	601	(1)
The Phase Behavior of Polymers	601	(4)
Dilution Entropy Drives Solute Partitioning into Polymers	605	(1)
The Flory Theorem	606	(1)
Summary	607	(1)
Problems	608	(1)
Polymer Elasticity	609	(20)
Polymeric Materials Are Elastic	609	(4)
Random-flight Chains Are Gaussian	613	(1)
Polymer Elasticity Follows Hooke's Law	614	(5)
Elasticity of Rubbery Materials	619	(2)
Polymer Collapse and Expansion	621	(5)
Summary	626	(1)
Problems	627	(1)
Suggested Reading	627	(2)
Polymers Resist Confinement & Deformation	629	(16)
Excluded Volume	629	(2)
Chain Conformations Are Perturbed Near Surfaces	631	(3)
Polymer Conformations by a Diffusion Equation Method	634	(2)
Polymers Tend to Avoid Confined Spaces	636	(2)
The Rouse-Zimm Model of Polymer Dynamics	638	(2)
The Reptation Model	640	(2)
Summary	642	(1)
Problems	643	(1)
Suggested Reading	643	(2)
Appendix A Table of Constants	645	(1)
Appendix B Table of Units	646	(1)
Appendix C Useful Taylor Series Expansions	647	(1)
Appendix D Useful Integrals	648	(1)
Appendix E Multiples of Units, Their Names, and Symbols	649	(2)
Index	651