Chapter 1
Introductory Remarks

1. I. Strong Electrolytes
2. II. Polymer Science
   1. A. Light Scattering
      1. 1. Molecular Weights and the Second Virial Coefficient
      2. 2. Particle Scattering Factor ()
      3. 3. Light Scattering from Multicomponent Systems
3. III. Polyelectrolyte Solutions
   1. A. Models of Polyelectrolyte Molecules
4. IV. (Supplement) Preparation of Linear Polymers with Narrow Molecular Weight Distribution (NMWD)
5. References

A group of linear polymers that have many ionizable or ionized side groups are called polyelectrolytes. In 1929, Staudinger prepared the first synthetic polyelectrolyte, poly(acrylic acid) (PAA), by polymerizing an acrylic acid monomer. PAA has many ionizable groups (-COOH) on its backbone and is soluble in water. However, PAA has a limited amount of charges (fixed ions) because the degree of ionization of -COOH group is so low in aqueous solutions and, therefore, does not show any characteristic solution behavior as a polyelectrolyte. If PAA is neutralized with NaOH, the salt, poly(sodium acrylate) (PNaA), is fully dissociated into a poly(acrylate) ion with many fixed charges on its backbone and many sodium ions in aqueous solutions. PNaA shows various characteristic behaviors such as very high solution viscosity. Despite these differences, both PAA and PNaA are categorized as polyelectrolytes. Polyelectrolytes are also prepared by substitution reactions of functional reagents with nonionic polymers. For example, typical polyelectrolytes include carboxymethylcellulose (CMC) prepared by esterifying cellulose with monochloroacetic acid and poly(vinyl alcohol sulfate), which is prepared by esterifying poly(vinyl alcohol) with monochlorosulfonic acid. There are many biological polymers with electrolyte side groups such as alginic acid, sodium pectinate, chondroitin sulfuric acid. DNA also has many charged groups.

A polyelectrolyte molecule is dissociated into a macromolecule with many fixed charged groups and simple ions such as Na or K in solution. In this book, the macromolecular ion is often called "polyion" and simple ions are called "counter-ions". A simple electrolyte such as NaCl, which is chemically inert for polyelectrolytes, is often added to polyelectrolyte solutions. The electrolyte is called "added-salt" and the ion with the same electric charge as the polyion (for example, Cl to PNaA) is called a "by-ion." Unless noted otherwise, water is used as the solvent for dissolving polyelectrolytes. Most polyelectrolytes discussed in this book are linear polymers. Proteins are not included in the polyelectrolyte categories but are often discussed from the macroion perspective in this book.

A polyelectrolyte solution is a hybrid of electrolyte and polymer solutions. From the viewpoint of electrochemistry, most polyelectrolytes are a unique type of strong electrolytes. In addition, polyelectrolyte solutions have attracted the interest of many polymer scientists because of their characteristic solution behaviors such as high viscosity.

I. Strong Electrolytes

Many simple electrolytes are soluble in water with limited solubility and dissociated into cations and anions. In most electrolyte solutions, an ionization equilibrium holds between undissociated molecules and dissociated ions. For example, if acetic acid CHCOOH is dissolved in water, a part of the acetic acid molecules is dissociated as

but most of the molecules remain in the undissociated state. The equilibrium constant of the equilibrium can be related to the bond energy between constituting cation and anion.

In 1906, however, Bjerrum [1] pointed out that some electrolyte molecules are completely dissociated into ions in aqueous solutions, and undissociated molecules are not detected by optical or other physical methods even in concentrated solutions. The group of electrolytes is called "strong electrolytes". The idea of strong electrolytes is now well established. The reason for complete ionization is well explained by Fowler and Guggenheim [2] and others. In short, water is not merely a solvent for the molecule but participates in ionization by hydration. The ionization free energy of the molecule is substantially decreased because of the solvent's involvement in the ionization process.

Most strong electrolytes are salts of strong acids and strong bases such as NaCl and KSO. Strong acids, such as HCl and HSO, and strong bases, such as NaOH, themselves are strong electrolytes. Salts of strong acids with weak bases and salts of strong bases with weak acids, such as NHCl and CHCOONa, are also strong electrolytes. Sodium acrylate CH=CH(COONa), which is a monomer for PNaA, is a strong electrolyte. NaCl, a typical strong electrolyte, is frequently used as an inert added-salt in the study of polyelectrolyte solutions.

In spite of complete ionization of strong (simple) electrolytes, the colligative properties or electric conductivity of their aqueous solutions deviate, albeit small, from ideal solution behavior. It has been well confirmed that the source of this deviation is not the formation of undissociated molecules. In 1923, Debye and Hückel [3, 4] clarified the reason for the deviation by applying the Poisson-Boltzmann equation to solve the electrostatic interaction between ions. Their theory agrees with experimental data on colligative properties and electric conductivity of simple strong electrolytes quantitatively but only if the solution is dilute enough. The linearization approximation of the Poisson-Boltzmann equation, which Debye and Hückel used in solving the equation, is now called the Debye-Hückel approximation. The idea of ionic atmosphere around each ion, which they introduced to calculate the electrostatic interaction energy between ions, is now recognized as one of the most important ideas in electrochemistry.

The success of the D-H theory was limited to dilute solutions because of the failure of the D-H approximation in solutions of higher concentrations. Various attempts were presented to extend the D-H theory to more concentrated solutions. Among them, the ion-pair model by Bjerrum [5] may be most practical. Thus, the study of strong electrolyte solutions was one of the most active research fields in physical chemistry for decades.

PNaA is a salt of PAA with NaOH. Its monomer, sodium acrylate, as well as sodium salts of similar organic acids, such as sodium acetate, are surely strong electrolytes. Therefore, it was really amazing when Kern reported that the osmotic pressure of PNaA in aqueous solutions is much lower than the value expected from the complete ionization of PNaA [6]. Moreover, the deviation from complete ionization becomes clearer as the charge density (i.e., the degree of neutralization) of poly(acrylate) increases. Figure 1 shows a decrease in the osmotic coefficient of PNaA with an increasing degree of neutralization. Later studies showed that no optical or other physical observations revealed the formation of a nonelectrostatic bond between Na and -COO of PNaA [7].

Figure 1 Osmotic coefficient () versus degree of neutralization of PNaA () in pure aqueous solutions. Concn; 0.125 molar concentration of monomer. Degree of polymerization; 340. Temp. 20C. (Reproduced with permission from Ref. [6]. Copyright Wiley-VCH.)

The characteristic behavior of poly(strong electrolyte), first pointed out by Kern, attracted the interest of researchers. The interaction of counter-ions and polyion has been given various names, including ion-binding, ion-association, ion-fixation (ion-kotei) in Japanese) and ion-condensation. Kern expressed it as "elektrostatische Inaktivierung". Let us call it "ion-binding" in this book. The physical meanings of these terminologies were also numerous. Ion-binding sometimes refers to the "true" association which can occur in an undissociated simple acid or complex molecules due to the chemical bond though the nature of bond is unknown. The term is also used to describe the ionic association resulting from electrostatic force, such as the ion-pair in simple electrolyte solutions or counter-ions trapped within a polyion domain. All these terminologies seem to imply a similar image of the polyion-counter-ion interaction, which works to decrease the effective charge density of the polyion. All these ion-bindings successfully provided qualitative explanations for some thermodynamic properties of polyelectrolyte solutions [7]. The theories of Manning et al. [8] and Oosawa [9] are well known. However, the usefulness of the ion-binding ideas is limited to thermodynamic properties of polyelectrolyte solutions. There are various fields, such as transport behavior of polyions, in which the ion-binding model is not effective, as is discussed in Chapter "Transport Phenomena of Linear Polyelectrolytes".

II. Polymer Science

Although the presence of macromolecular compounds such as cellulose was already known in the 1930s, modern theories on (nonionic) linear polymers began to be actively developed after Flory and Huggins published their work on the thermodynamic properties of concentrated polymer solutions [10-12]. The remarkable progress of polymer science is partly due to the advancement of experimental instruments. In particular,...