Macromolecular materials:

Organic and inorganic chemicals can form large bonded molecules with molar mass greater than 10,000 Daltons (gram per mole).  By strict definition we could term any of these molecules a macro-molecule.  These materials would include metallically bonded iron, ionically bonded sodium chloride crystals, ceramic aggregates of silica and titania, folded proteins, denatured proteins, DNA, RNA, an automotive tire, polyethylene in a plastic bag, a micelle bonded by static charge, van der Waals interactions and hydrogen bonding.  From a molecular weight perspective a definition of a polymer or plastics is less than sufficient. 

Generally we will consider covalently bonded molecules with molecular weights greater than 10 kg/mole although this is by no means a definition of polymer since it does not include all polymers and does not exclude non-polymers.  For example, a folded protein is an essentially linear, covalently bonded chain with molecular weight between 500 kDa and 50,000 kDa.  A folded protein has virtually no configurational entropy, that is it can assume essentially only one molecular shape and size.  This is in contrast to a denatured protein with no biological function which can have some variability in shape and size and some configurational entropy.  Biomolecules such as DNA and RNA, on the other hand, display molecular flexibility that is inherent to their function during transcription for instance.  These molecules display some of the largest persistence lengths of macromolecules which is also related to their biological function.  Further, biomolecules are generally on the order of 1 micron in size which is far beyond the limits of thermodynamic equilibrium, that is, while a DNA molecule can assume variable configurations it can not fully reach thermodynamic equilibrium in terms of these configurations due to the mass of a persistence unit of DNA.  We can think of a long piece of thread lying on the table.  Although the thread can access an infinite number of configurations, the string can not reach an equilibrium state with respect to these (http://  www.eng.uc.edu  /~gbeaucag/PDFPapers/  PolymerAnalogues.pdf) configurations, that is, the chain can not move by thermal molecular motion since its mass it too large.  Nonetheless, structures such as strings and DNA can mimic structures at thermal equilibrium, i.e. real polymers and plastics.  At times this can lead to a misunderstanding of the nature of the observed disordered morphology.

Thermal access to configurational entropy defines polymer and plastic materials.  For instance, a polymer chain, when stretched from the ends will have a reduction in the number of configurations that are possible.  In order to increase the number of configurations, and the entropy, the chain will shorten with respect to the chain ends and will display a retracting force associated with entropy.  This entropic shrinking associated with thermal motion is the hallmark of rubber elasticity.  Materials that display rubber-like elasticity show thermal contraction under stress indicating that the behavior is governed by entropy.

It is possible to build chain structures from ceramic nano-particles that are bonded by ionic bonds and much weaker van der Waals interactions.  Such aggregates are not polymers because, despite being on a size scale small enough to display thermal equilibration, have bonds that are inherently inflexible.  The common mechanism for polymers and plastics to display equilibration of configurational states is through bond rotation.  Paul Flory recognized this in the 1960's and it is for this subject that he developed in the US that he was given the Nobel Prize in Chemistry.  We can consider a polymer chain as a collection of covalent bonds that display some degree of rotational freedom depending on the substituent groups along the polymer chain.  The configuration of one pair of bonds, that is the rotational angle, will effect the energetic state of the next bond in what is called a Markovian (random with energetics) process.  The thermally equilibrated state for a polymer chain can be calculated using the Metropolis Method describe in IsingModel.html.  In this class we will write a computer program to do a simple iteration to minimize the energy of a polymer chain using the Metropolis Method.  The iteration is based on a chain bond having 3 states, trans, gauche + and gauche -.  Here we are not particularly interested in the specific chemistry of the chain but rather in the bond length, bond angles and the energetics associated with each of these three states. 

For this purpose we will consider a polymer chain composed of tetrahedral carbon-carbon bonds.  Each Carbon has a coordination number of 4 and for single bonds we assume rotational freedom for these bonds.  Steric interference to rotation leads to inequality in the bond energies.  We can consider the trans state as the absolute minimum but that there is some probability depending on the temperature, that the chain can rotate a given bond.  The randomness of these bond rotations increases exponentially with temperature.  This will effectively lead to a higher configurational entropy for the chain.  The chain size in terms of the end-to-end-distance will show a characteristic behavior in temperature with at first a gradual and well behaved thermal contraction followed by chain collapse at the theta temperature which can be determined from the Metropolis calculation. 

It should be clear from this discussion that polymer/plastic materials are drastically different than other materials commonly studied by Materials and Chemical Engineers.  Of the three major types of materials, polymers are the only group not defined by their bond type, they are the only materials where dynamic features and entropy dominant behavior and the only class of materials where the purely crystalline state is not the dominant form of interest.