Physical models and numerical methods, from molecular dynamics and chain statistics to coarse-graining, continuum mechanics and parameter transfer across scales.
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Why does the same long molecule expand in one liquid, contract in another, or make a solution turn cloudy? Starting with the space occupied by a flexible chain, this chapter connects molecular contacts to coil size, mixing, osmotic pressure and concentration.
Choose bead mappings and effective interactions for biomolecular networks, then plan equilibration and independent validation. Worked diagrams connect atomic groups, reference distributions and the mechanical quantities a coarse-grained model should preserve.
How does a chain acquire structure, a collection of molecules form a droplet, or a local reaction grow into stripes and waves? Folding experiments and material balances lead into free energy, kinetics, diffusion and the energy supplies that organize living materials.
Why can a liquid become a connected load-bearing material? How does a sparse set of conducting fillers span a specimen? Begin with shapes that remain irregular under magnification, then follow connection, mechanical support and solvent uptake to distinguish gel formation from gel-volume transitions.
Knowing where a chain or particle is does not fully determine its next motion, and one observation need not give a stable material property. Begin with position and momentum, build state space and probability averages, and distinguish ensembles through energy, thermal contact and particle exchange. A slow-jump model then connects equilibrium probabilities with finite observation times.
A polymer pellet that looks dry may still hold water or solvent inside. Follow a small molecule's route out to understand diffusion, humidity, heat, thin films, and bubbles, then explore how thickness, air conditions, and melt viscosity change the rate of removal.
Build a lysozyme-in-water simulation from coordinates and topology through minimization, equilibration and production. Track the files exchanged by grompp and mdrun, then distinguish what RMSD, RMSF, radius of gyration and hydrogen-bond analysis measure.
The same soft material can flow under slow loading and recoil under rapid deformation. Follow loading, waiting and release to understand stress relaxation, then connect it to segment motion, fluid coupling and entanglement. An adjustable oscillatory experiment makes storage and loss directly visible.
During fibre drawing or coating of a liquid-crystal polymer, molecules change orientation as well as position. They may settle at a steady angle or keep tumbling, while elasticity, boundaries and fields organize their collective texture. Begin with a rotating rod and connect these motions to rheology, optics and the structure retained after processing.
Rubber recovers, polymer melts flow slowly, and proteins change shape to perform specific functions. These behaviors involve many possible states of long-chain molecules. Begin with connectivity and countable conformations, then connect probability, entropy, thermal motion and observation time to mechanics, mixing and biological function.
Ice absorbs heat as it melts, some blends turn cloudy near demixing, and magnets lose spontaneous magnetization on heating. How do collective changes emerge from molecular motion? Starting with phase equilibrium and order parameters, connect free energy, fluctuations, correlation length and scaling, and compare continuous and discontinuous transitions through an interactive free-energy model.
Contour length, end-to-end distance and overall molecular size measure different things. Random steps lead to the radius of gyration, Kuhn length, probability distributions and entropic elasticity, followed by semiflexible chains, rings and branches.
A uniform polymer solution can develop connected domains, a flat film can open holes, and two blocks of one chain can organize into nanoscale stripes. Follow the amplification of small fluctuations, competition between length scales and eventual retention of structure to understand why patterns emerge and how processing changes them.
Forming a protein helix balances molecular contacts against conformational choices. Why does initiation differ from propagation, and how do many arrangements become an experimental curve? Move from a three-position counting example to finite chains, and distinguish cooperativity, mean helicity and folding times.
Why can the same formulation produce a different material in different equipment? Follow the reactants through vessels, tubes, films and screws, then explore how flow, heat transfer and mechanical action change during scale-up.
A strictly deterministic rule can produce motion that does not repeat over long times and is highly sensitive to its starting state. Begin with a rule that can be calculated by hand, follow fixed points, period doubling and chaos, then connect these ideas to structural feedback, measurement and prediction in flowing materials.
Why does rubber recover, plastic creep, and a water-rich gel hold its shape? Begin with atoms, molecules and long chains, distinguish connectivity from conformation, then connect condensed states, thermal motion and mechanical response through an interactive relaxation experiment.
Long molecules can flow while retaining collective alignment, combining mobility with direction-dependent optical and mechanical properties. Starting with order inside a fluid, use orientation probability, excluded volume and mean fields to explain liquid-crystal formation, then connect molecular models to flexible chains, local textures and processed materials.
Two polymers can form a uniform material or separate into domains. Connecting unlike blocks within each molecule can instead produce organized layers and cylinders. Follow these phenomena from the free energy of mixing to microphase separation and folded-chain crystals, and see how connectivity, interfaces and conformation organize a material.
Read the structure of a LAMMPS input, set up a first molecular dynamics calculation and inspect basic trajectory outputs. Periodic-distance and Lennard-Jones diagrams explain boundary conditions and interactions before force-field and timestep choices.
Choose molecular, mesoscopic and continuum representations for biomaterial questions. Follow the transfer of conformational statistics and effective stiffness between models, using representative-volume averaging and Python examples to connect scales.
Start with a cup of curing resin and follow heat generation, transfer and reactant consumption. Historical insights, heat-flow diagrams and adjustable reactor models explain temperature recovery, state changes, polymerization autoacceleration and the consequences of scale-up.
Whether a drop spreads, colloids aggregate or a coating adheres can depend on a very thin boundary region. Follow a chain as it approaches a wall, adsorbs or becomes tethered at one end. Connect conformation, osmotic pressure and interfacial free energy, then apply the ideas to polymer brushes, blend interfaces and transport through pores.
Tea cools, dye spreads, and a flowing polymer converts mechanical work into heat. Energy conservation alone does not prohibit the reverse processes, so where does their direction come from? Connect particle counting and random motion to entropy, diffusion, heat flow and viscous dissipation, distinguishing equilibrium from continuously driven materials.
A batch vessel, a continuously stirred tank and a flowing tube expose molecules to different concentrations and reaction histories. Starting with a material balance, this chapter develops reaction rates, three ideal reactor models, product selectivity and reactor combinations, showing when a larger vessel helps and when a different operating strategy matters more.