Molecular Driving Forces

Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience

Ken Dill, Sarina Bromberg

• Publisher: Garland Science
• Year: 2010
• ISBN:
  9781136672989
• Edition: 2
• Topic: Biological Sciences
• Subtopic: Cell Biology
• Index: Biological Sciences

Molecular Driving Forces, Second Edition E-book is an introductory statistical thermodynamics text that describes the principles and forces that drive chemical and biological processes. It demonstrates how the complex behaviors of molecules can result from a few simple physical processes, and how simple models provide surprisingly accurate insights into the workings of the molecular world.

Widely adopted in its First Edition, Molecular Driving Forces is regarded by teachers and students as an accessible textbook that illuminates underlying principles and concepts. The Second Edition includes two brand new chapters: (1) "Microscopic Dynamics" introduces single molecule experiments; and (2) "Molecular Machines" considers how nanoscale machines and engines work. "The Logic of Thermodynamics" has been expanded to its own chapter and now covers heat, work, processes, pathways, and cycles. New practical applications, examples, and end-of-chapter questions are integrated throughout the revised and updated text, exploring topics in biology, environmental and energy science, and nanotechnology. Written in a clear and reader-friendly style, the book provides an excellent introduction to the subject for novices while remaining a valuable resource for experts.

1	Principles of Probability

The Principles of Probability Are the Foundations of Entropy

Fluids flow, boil, freeze, and evaporate. Solids melt and deform. Oil and water don’t mix. Metals and semiconductors conduct electricity. Crystals grow. Chemicals react and rearrange, take up heat, and give it off. Rubber stretches and retracts. Proteins catalyze biological reactions. What forces drive these processes? This question is addressed by statistical thermodynamics, a set of tools for modeling molecular forces and behavior, and a language for interpreting experiments.

The challenge in understanding these behaviors is that the properties that can be measured and controlled, such as density, temperature, pressure, heat capacity, molecular radius, or equilibrium constants, do not predict the tendencies and equilibria of systems in a simple and direct way. To predict equilibria, we must step into a different world, where we use the language of energy, entropy, enthalpy, and free energy. Measuring the density of liquid water just below its boiling temperature does not hint at the surprise that, just a few degrees higher, above the boiling temperature, the density suddenly drops more than a thousandfold. To predict density changes and other measurable properties, you need to know about the driving forces, the entropies and energies. We begin with entropy.

Entropy is one of the most fundamental concepts in statistical thermodynamics. It describes the tendency of matter toward disorder. Entropy explains how expanding gases drive car engines, liquids mix, rubber bands retract, heat flows from hot objects to cold objects, and protein molecules tangle together in some disease states. The concepts that we introduce in this chapter, probability, multiplicity, combinatorics, averages, and distribution functions, provide a foundation for describing entropy.

What Is Probability?

Here are two statements of probability. In 1990, the probability that a person in the United States was a scientist or an engineer was 1/250. That is, there were about a million scientists and engineers out of a total of about 250 million people. In 1992, the probability that a child under 13 years old in the United States ate a fast-food hamburger on any given day was 1/30 [1].

Let’s generalize. Suppose that the possible outcomes fall into categories A, B, or C. ‘Event’ and ‘outcome’ are generic terms. An event might be the flipping o...