Preface

In the late 1920s and early 1930s, Carothers's team of DuPont reported the synthesis of some aliphatic polyesters [63-65]. Unfortunately, the polyesters melted at too low temperatures to be commercialized. Meanwhile, Lemoigne extracted an aliphatic polyester, poly(()-3-hydroxybutyrate) (P3HB), from a bacterium, Bacillus megaterium [277, 278]. The equilibrium melting point of P3HB is as high as 203 °C. The asymmetric structure and steric hindrance of the methyl side chain restrict the degree of conformational freedom of the P3HB chain and, consequently, lead to the high melting point. Nowadays, P3HB attracts attention from polymer chemists and engineers because of its carbon neutrality, namely biosynthesis and biodegradability. The relationships between conformational characteristics and thermal properties of polymers are often discussed in this book.

In 1941, Whinfield and Dickson acquired a British patent on aromatic polyesters including poly(ethylene terephthalate) (PET), poly(trimethylene terephthalate) (PTT), and poly(butylene terephthalate) (PBT) [520]. The difference in structure among these polyesters is only the number of methylene units between the benzene rings. The high equilibrium melting point (262 °C) of PET is due partly to the intermolecular - interaction between the benzene rings. The aromatic polyesters are industrially manufactured all over the world. PET is molded to fibers, films, and bottles; PTT is so flexible as to be used for sports wears and carpets; and PBT is so superior in impact resistance as to be used in tooth and paint brushes, gears, and machine parts. The usages of the aromatic polyesters are mainly due to the mechanical properties. The crystalline Young's modulus in the chain-axis direction of PET is 182?GPa, that of PTT is as small as 7.1?GPa, and that of PBT ( form) is 20.8?GPa [266]. In the crystal, PET lies in a somewhat distorted all-trans structure, whereas PTT and PBT form bended tggt and distorted conformations, respectively. Here, t, , and represent trans, , and states, respectively. In this book, the mechanical properties of polymers are frequently interpreted in terms of chain conformations.

As described above and will be shown later, higher order structures and thermal and mechanical properties of polymers depend on conformational characteristics, more fundamentally, the primary structure?-?what the component atoms and chemical bonds are and how they are arranged. Furthermore, scientists have faced with the fact that proteins composed of only 20 amino acids form unique secondary, tertiary, and quaternary structures and exhibit specific functions. Consequently, polymer scientists have reached the concept of molecular design: we may predict the primary structure(s) from which the desired higher order structures, physical properties, and functions are realized.

In Japan, the idea of molecular design was advocated early on. In 1972, a book consisting of three volumes, titled "Molecular Design of Polymers," was published by The Society of Polymer Science, Japan [239]. In the book, Kawai defined the molecular design as follows: First, one must reveal the correlations between the chemical structures and physical properties. Next, one actually synthesizes the polymer with the structure that is expected to show the desired properties. On the other hand, Kambara's molecular design is different: when a new polymer is suggested, namely its constituent atoms and chemical bonds are specified, to predict the structures and morphology to be formed therefrom is the molecular design. Kambara's concept is to predict the higher order structures from the primary structure, whereas Kawai's idea is more idealistic; the molecular design should be to propose the primary structure that actualizes such higher order structures, physical properties, and functions as desired. In order to realize either molecular design, as both Kawai and Kambara suggested, it is requisite to establish relationships between the primary structure, higher order structures, and, furthermore, if possible, properties and functions.

For that purpose, it is essential to elucidate the structures and properties of a single polymeric chain. From an experimental viewpoint, it is significant to determine bond conformations of the skeletal bonds via, for example, NMR and reveal the conformational characteristics and, furthermore, to investigate the configurational properties of the polymeric chain in the Ø state free from the excluded-volume effect via, for example, scattering methods. From a theoretical viewpoint, the free energies and geometrical parameters of individual conformations of a polymeric chain are evaluated by quantum chemistry, and the Boltzmann factors are summed over all conformations to yield the partition function from which various thermodynamic functions can be derived according to statistical mechanical theorems.

However, a polymer chain forms an enormous (astronomical) number of conformations. For example, under the rotational isomeric state (RIS) approximation based on the three states (t, , and ), a single polyethylene chain of 100mer shows (approximately ) conformations. The average of a molecular parameter , depending on the conformations, may be calculated from

where is the energy of conformation , is the total number of conformations, is the gas constant, is the absolute temperature, and is the partition function defined as

To evaluate , one must solve the Schrödinger equation for each conformation, obtain its ground-state energy, and repeat this procedure times; however, such colossal computations are impossible for the time being at least, apart from the remote future. Fortunately, statistical mechanics of chain molecules, designated as the RIS scheme, has been developed and formulated as matrix operations. According to the RIS scheme, one can exactly calculate the bond conformations, various configurational properties, and thermodynamic functions of unperturbed polymeric chains (lying in the Ø state). The early studies of the RIS scheme were summarized in Flory's book [141], the ensuing studies can be found in Mattice and Suter's book [307], and Rehahn, Mattice, and Suter's book collected almost all RIS models reported until the end of 1994 [383].

It is known that the configurational properties of unperturbed polymeric chains depend only on short-range intramolecular interactions [141]; therefore, the conformational energies may also be evaluated from a small model compound with the same bond sequence as that of the polymer. In order to derive the conformational energies from quantum chemical calculations, therefore, one need not treat the polymer itself but the small model compound instead. The MO computations on the model are sufficiently practical even if a high-level MO theory including electronic correlations is employed, together with large basis sets.

The RIS scheme can exactly characterize unperturbed polymeric chains in dilute solutions, amorphous phases, and melts. However, polymer scientists have also been desiring to acquire precise theoretical information on the structures and properties of solid-state polymers. Fortunately, the density functional theory (DFT) under periodic boundary conditions has enabled us to calculate the electronic structures of crystals [120]. The methodology can also be applied to polymer crystals and yield the following information: optimized crystal structure (lattice constants and atomic positions); intermolecular interaction energy corrected for the basis set superposition error (BSSE); thermodynamic functions; and vibrational spectroscopic frequency and intensity. The DFT calculations have shown that the chain conformation is also the principal factor in the structures and properties of polymer crystals.

Part I of this book describes the fundamental physical chemistry that is necessary to understand the characteristics of polymers and study their conformations. The contents are stereochemistry, polymer models, and the lattice model (the Flory-Huggins theory); molecular characteristics; solution properties; and rubber elasticity. This part is written so as to be understood without difficulty by graduate and undergraduate students who have learned general chemistry. Derivations of some important equations, which are mostly omitted from textbooks and original papers, are given as problems, and the answers are presented in Appendix B.

Part II explains the quantum chemistry used in conformational analysis, together with a wealth of practical applications. The contents are the Schrödinger equation, the Hartree-Fock method, electron correlations, DFT, dispersion-force correction, solvent effect, general statistical mechanics, NMR parameters, and periodic DFT for crystals.

Part III explains the RIS scheme including mathematical expressions and their derivations. The contents are the conventional RIS scheme, the refined RIS scheme, the RIS scheme including middle-range interactions, inversional-rotational isomeric state (IRIS) scheme, the RIS scheme with stochastic processes, and the RIS scheme with internally rotatable side chains.

Part IV introduces typical experimental methods for conformational analysis of polymers. The contents are broadly divided into two portions: NMR spectroscopy and scattering techniques. The former deals with NMR vicinal coupling constants to evaluate bond...