Desmearing procedure

Small angle X-ray scattering (SAXS) was measured with a Kratky camera using nickel filtered CuKa radiation. The width of the entrance and detector slits were 20 and 50 pm, respectively. No desmearing procedure was applied to the scattering curves. Absolute measurements were carried out by using a Lupolen standard. 

Small angle X-ray scattering (SAXS) has been used by many authors to determine the interfacial thickness. An excellent review of this subject can be found in Perrin and Prud homme [1994]. Many methods of calculations can be used. One of these involves an analysis of the deviation from Porod s law, in which the desmearing procedure is avoided. This procedure was applied to blends of PS with PMMA added with a P(S-b-MMA) block copolymer. Upon addition of copolymer the interface thickness changed from A1 = 2 to 6 nm [Perrin and Prud homme, 1994]. 

The form of the measured function T(t) differs so much from the actual course of the real thermal event d>(t) in the system (upper Figure 6.13) that the desmearing procedure described in Section 6.3 provides the only way of reconstructing this true heat production fP(t) from the measured one. 

For the solution of measuring problems in optics and other fields of physics, there is a simple mathematical procedure (i.e., the theory of linear response) that makes use of the overall behavior of the apparatus in defined processes in order to calculate unknown complex processes from the measured function. Here we shall derive this relationship in order to define the conditions under which this desmearing procedure can be applied. We shall formulate the laws in a general manner using the variable x as in mathematics. Consider an abrupt (pulse-like) event taking place in the apparatus at x. Using the Dirac delta function d x),... 

Figure 6.23 Example of the desmearing procedure applied on the melting behavior of an octadecane sample measured by means of a differential scanning calorimeter.

In other words, the uncertainty (noise) of the desmeared function g(x) is much larger than the uncertainty of the measured function h x). Because of these reasons, the desmearing procedure should only be performed if really needed. 

The average density was determined by extrapolation to /i = 0 of the functions li h), li ih) and /h(fi). From Eq. (5), values of = 403.4 e.u./nm and y

= 427.9 e.u./nm were obtained, i.e. about 6% difference between the two measures of the average density. The smeared basis functions were calculated using Eq. (1). For each experimental point hi, a multi-variable linear regression procedure was employed, setting Apt and Apf as the independent parameters. Each basic function was then desmeared separately. 

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