Introducing interactions and bonds

We look first at deviations from the ideal-gas equation, caused by inter-particle interactions. Having described induced dipoles (and hydrogen bonds) the interaction strengths are quantified in terms of the van der Waals and virial equations of state. 

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Secondary Bonding. The atoms in a polymer molecule are held together by primary covalent bonds. Linear and branched chains are held together by secondary bonds hydrogen bonds, dipole interactions, and dispersion or van der Waal s forces. By copolymerization with minor amounts of acryhc (CH2=CHCOOH) or methacrylic acid followed by neutralization, ionic bonding can also be introduced between chains. Such polymers are known as ionomers (qv). 

In the absence of dyes, APA- and AdPA-grafted silica bind La(III) with, respectively, 0.20 and 0.27 mmol/g sorption capacity, resulting in formation of 1 2 (La L) complexes. 50% of introduced cation is bonded at pH=5 (APA), pH=6.1 (AdPA) and complete adsorption occurs at pH=6 (APA), pH=6.5 (AdPA). The grafted support in absence of La adsorbs the chosen dyes at pH<4 due to the electrostatic interaction with the -NH, groups on the surface, present as a result of grafting procedure. The adsorption of dyes at pH>4 is insignificant. 

According to Bartell (1961a), the relative motion of the interacting non-bonded atoms is described by means of a harmonic oscillator when the two atoms are bonded to the same atom, and by means of two superimposed harmonic oscillators when the atoms are linked to each other via more than one intervening atom. It is the second case which is of interest in connection with the biphenyl inversion transition state. The non-bonded interaction will of course introduce anharmonicity, but since a first-order perturbation calculation of the energy only implies an... 

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