Concept of Orthogonality

How can one be assured that all the samples components are resolved This is particularly important in critical assays such as pharmaceutical impurity testing to ensure that no impurity peaks are co-eluting with other components or hidden under the active ingredient peak. The standard practice is the use of an orthogonal separation technique or method to demonstrate that all impurities are accounted for. An orthogonal method is one based on different separation mechanism from the primary method. 

Variants of RPLC RPLC RPLC with ion pairing 

CE = capillary electrophoresis, SFC = supercritical fluid chromatography, HILIC = hydrophilic interaction chromatography. 

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We may use the concept of orthogonal functions to identify components. In the present case, our component functions are sinusoids, and we find that the Fourier transform of the sum is the sum of the Fourier transforms ... 

Since many of the basic arguments in Section 4.3 will lean heavily on the concept of orthogonal vectors in generalized, multidimensional space, a brief summary of the essentials will be included here. 

Next, it is necessary to define the concept of orthogonality of sign vectors. Two sign vectors a and b are said to be orthogonal (a T b) if either (1) the supports of a and b have no indices in common, or (2) there is an index i for which a, and bi have the same signs and there is another index j (j i) for which aj and bj have opposite signs. Given these definitions, the thermodynamic constraint may be stated as ... 

Rucker, C. and Rucker, G. (1992) Understanding the properties of isospectral points and pairs in graphs the concept of orthogonal relation. J. Math. Chem., 9, 207-238. 

Figure 2.24. The concept of orthogonality as shown by retention plots of two sets of columns for a variety of different analytes. (A) Since the log k data of the two columns (C8 and C18) are well correlated for most analytes, these two columns are expected to yield similar elution profiles. (B) The selectivity differences of a C18 and a polar-embedded phase (amide) column lead to very scattered correlation of their respective retention data. Methods using a C18 and a polar-embedded column are therefore termed orthogonal and expected to yield very dissimilar profiles. Diagram courtesy of Supelco, Inc.

This concept of orthogonality can be obtained by extension from the concept of orthogonality of two ordinary vectors in three-dimensional space. If the x, y, and z components are a, Uy, for the first vector and b, by, b for the second vector, then the condition for orthogonality is... 

An extension to this protocol is the concept of orthogonality allowing for the selective removal of one PG in the presence of another PG. For example, in the synthesis of oligo(para-phenyleneethynylene) rods by Godt et al. [128], the hydroxymethyl (HOM) and TIPS moieties in 35 were independently removed by treatment either with MnOj and KOH to give 36 in 86% yield or with TBAF to afford 37 in 96% yield, respectively (Scheme 9.12). 

The concept of orthogonal collocation for ordinary differential equations can be easily extended to solve parabolic partial differential equations. The difference is that the application of orthogonal collocation method on the two-point boundary-value differential equation discussed earlier results in a set of algebraic equations, whereas application of orthogonal collocation method on parabolic partial differential equations results in a set of ordinary differential equations. 

FIGURE 23 SIMCA graphical illustration of the concepts of orthogonal and score distances. 

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