6 = 2k z,F' d-F> +—— Im(nF' )^f' tan 0f' sin 0f' (17)
and Im(nF') is the imaginary component of the refractive index. The phase shifts yF>S and yF>F',c are expressed in terms of the associated reflection coefficients by y = arcsin[Im(r)/|r|].
In the absence of an F' layer, the above approach allows for the solution of the refractive index and thickness of the waveguiding film, nF and dF from the effective refractive indices of the transverse electric (NTE) and transverse magnetic (NTM) modes and from the known refractive indices of the support (nS) and cover (nC) solutions. Once known, these quantities maybeusedtocalculate nF' and dF' during an adsorption experiment. From these values, the mass density of an adsorbed layer is determined via de Feijter's formula (de Feijter et al. 1978):
dcb where the refractive index increase with bulk protein concentration, dnC/ dcb, has the nearly universal value of 0.182 cm3 /g. Alternatively, the mass density maybe determined via a single effective refractive index by:
ANte where the refractive index nF' and the term dNTE/ddF are determined by a separate double mode experiment. The angular scan required for a singlemode measurement is much narrower, so the rate at which measurements may be taken (approximately 3 s) greatly exceeds that of a double-mode experiment (approximately 20 s).
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