Jozef Hodyl PhD Thesis - Theses - Flinders University

Rearranging equation 1.4 gives equation 1.5:KG 2 + G(KH T - KG T + 1) – G T = 0 (1.5),which can be solved to give the concentration of G by using equation 1.6:G = -b + -b2 - 4ac2a(1.6),wherea = Kb = KH T – KG T + 1c = -G TEquation 1.5 can be related to the observed 1 H NMR guest chemical shifts throughthe use of equation 1.7:where: χ G = G/G T , mole fraction of unbound guestχ HG = mole fraction of bound guest = 1 - χ Gδ G = chemical shift of unbound guestδ HG = chemical shift of bound guestδ calc = δ G χ G +δ HG χ HG (1.7),An estimate of G at each H T value is obtained by the computer subjecting a trialvalue of K and known values of H T and G T to equation 1.6. Equation 1.7 then allowsthe determination of preliminary values for δ calc , at each H T , for a trial value of δ HG .The computer program then iteratively varies K and δ HG , until the best match of δ calcat each H T with δ obs at that H T is obtained.Several sample titration curves are shown in Figure A.1. These simulationsshow the variation in guest chemical shift (δ obs ) for illustrative values of the bindingconstant (logK), and indicate the difference in the shape of these curves as thebinding constant varies. A chemical shift difference of 1.0 ppm between bound andcomplexed guest is assumed, and the guest concentration is set at 1 x 10 -3 mol dm -3 ,which was the concentration used in the experimental work described in this thesis.155