- Email: [email protected]
Chapter 29 The analytical procedure
563
Chapter 29
THE ANALYTICAL PROCEDURE 29.1. THE BLACK BOX I n t h e p r e c e d i n g c h a p t e r , t h e b l a c k box was d e f i n e d as a system w i t h an unknown ( n t e r n a l ) s t r u c t u r e , b u t w i t h g i v e n magnitudes o f i n p u t and o u t p u t . R e f e r r i n g t o an a n a l y t i c a l procedure o r an a n a l y t i c a l i n s t r u m e n t as a b l a c k box means t h a
n o t h i n g i s known about t h e p h y s i c a l , chemical, mechanical o r e l e c t r o n i c
components o r processes t h a t c o n v e r t t h e sample w i t h an unknown c o m p o s i t i o n i n t o a sample w i t h a known composition.
A substantial p a r t o f the research e f f o r t i n
a n a l y t i c a l c h e m i s t r y has been and s t i l l i s devoted t o t h e e l u c i d a t i o n o f t h e unknown s t r u c t u r e o f b l a c k boxes o r , t o p u t i t d i f f e r e n t l y , t o t u r n b l a c k boxes i n t o w h i t e , o r a t l e a s t g r e y boxes.
Such an e l u c i d a t i o n s a t i s f i e s human c u r i o s i t y
and o f t e n l e a d s t o a procedure w i t h a s u p e r i o r performance.
However, f r o m an
a n a l y t i c a l p o i n t o f view, procedures can be, and o f t e n a c t u a l l y a r e , e q u a l l y u s e f u l when t h e i n t e r n a l s t r u c t u r e i s n o t ( f u l l y ) known t o t h e user.
Moreover,
f o r an a n a l y t i c a l chemist f a c e d w i t h w i d e l y d i f f e r e n t problems and procedures, i t i s v i r t u a l l y i m p o s s i b l e t o be ( e n t i r e l y ) f a m i l i a r w i t h t h e p h y s i c a l and
chemical p r i n c i p l e s t h a t u n d e r l i e t h e procedures and w i t h t h e d e t a i l s o f t h e design o f the instruments.
Even if procedures and equipment a r e w h i t e boxes t o
some s c i e n t i s t s t h e y may w e l l appear t o be b l a c k boxes t o o t h e r s .
A b l a c k box i s u s e f u l f o r t h e a n a l y s t i f , and o n l y i f , i t s o u t p u t can be used t o a r r i v e a t t h e ( a p p r o x i m a t e ) c o m p o s i t i o n o f t h e unknown sample.
To p u t i t
d i f f e r e n t l y , t h e i n p u t - o u t p u t r e l a t i o n o r t h e c a l i b r a t i o n f u n c t i o n has t o be known.
However, e v e r y a n a l y s t i s aware o f t h e i n f l u e n c e o f parameters ( a l s o
c a l l e d d e s c r i p t o r s ; K a i s e r , 1973) such as temperature, volume o f r e a g e n t and wavelength on t h e measurement.
C l e a r l y t h e b l a c k box i s n o t a d e q u a t e l y d e s c r i b e d
by t h e i n p u t - o u t p u t r e l a t i o n between, t h e c o m p o s i t i o n o f t h e sample and t h e measurement alone.
Parameters t h a t i n f l u e n c e t h i s r e l a t i o n s h o u l d be s p e c i f i e d ,
564
and o f t e n k e p t c o n s t a n t , i n o r d e r f o r u s e f u l a n a l y t i c a l r e s u l t s t o be o b t a i n e d . The a n a l y t i c a l procedure as a b l a c k box can be a d e s c r i p t i o n i n words o f what has t o be done i n o r d e r t o determine t h e c o m p o s i t i o n o f t h e sample ( t h e a n a l y t i c a l recipe).
Such a d e s c r i p t i o n can be supplemented o r r e p l a c e d w i t h a more
schematic model as p r e s e n t e d i n F i g . 29.1.
kz: "1
"
F i g . 29.1. The a n a l y t i c a l procedure as a b l a c k box E s s e n t i a l f o r t h i s model a r e t h e n a t u r e ( u n i t s ) o f t h e i n p u t v a r i a b l e s
. . ., x.,1 . . . , xn
x1
r e p r e s e n t i n g t h e c o m p o s i t i o n ( c o n c e n t r a t i o n s , amounts,
i d e n t i t i e s ) and o f t h e o u t p u t v a r i a b l e s yl, measurements ( v o l t a g e s , r e a d i n g s ) . (x
-
. . . , yjy . . . , y,
representing t h e
O f m a j o r importance a r e t h e i n p u t - o u t p u t
y ) relations t h a t are required i n order t o a r r i v e a t the analytical results
from t h e measurements.
The u v a r i a b l e s t h a t have t o be s p e c i f i e d a r e those which
i n f l u e n c e t h e measurements and consequently t h e x
-
y relations.
Because o f t h i s
i n f l u e n c e t h e y have t o be c o n t r o l l e d and a r e c a l l e d t h e c o n t r o l l a b l e v a r i a b l e s . I n p u t v a r i a b l e s t h a t cannot be k e p t c o n s t a n t a r e i n d i c a t e d by zl. o f these n o n - c o n t r o l l a b l e v a r i a b l e s i s o f t e n unknown.
The o r i g i n
They l e a d t o ( s t o c h a s t i c )
fluctuations i n the output variables. The g e n e r a l p i c t u r e o f F i g . 29.1 i s reduced t o a model w i t h one x and one y v a r i a b l e i n a one-dimensional a n a l y s i s . can be used f o r o n l y one t y p e of sample. c a l i b r a t i o n function.
U s u a l l y such one-dimensional analyses The t y p e o f sample i n f l u e n c e s t h e
I t can be c o n s i d e r e d as a c o n t r o l l a b l e v a r i a b l e .
565
A c l o s e r i n s p e c t i o n o f t h e a n a l y t i c a l procedure as a system, i . e . , a n a l y s i s , r e v e a l s s e v e r a l t y p e s o f i n p u t and o u t p u t .
a systems
We a r r i v e d a t s e t s o f i n p u t
and o u t p u t v a r i a b l e s t h a t a r e r e l e v a n t when l o o k i n g a t t h e c a l i b r a t i o n f u n c t i o n . However, o t h e r i n p u t s and o u t p u t s e x i s t .
F o r i n s t a n c e , m a t e r i a l s f l o w i n and
o u t o f t h e apparatus and energy and s k i l l s a r e r e q u i r e d t o produce r e s u l t s . These aspects w i l l n o t be d e a l t w i t h here, as t h e y a r e l e s s r e l e v a n t i n t h e c o n t e x t o f t h i s book, a l t h o u g h t h e y a r e e s s e n t i a l i n t h e d e s i g n o f i n s t r u m e n t s , the organization o f the laboratory, etc.
A few remarks must be made about a p a r t i c u l a r i n p u t and o u t p u t , namely t h a t Some o f t h e p r i n c i p l e s o f i n f o r m a t i o n t h e o r y have
connected w i t h i n f o r m a t i o n . been i n t r o d u c e d i n Chapter 8.
I n f o r m a t i o n o b t a i n e d from an a n a l y t i c a l procedure
has been d e f i n e d as t h e d i f f e r e n c e between t h e u n c e r t a i n t y p e r t a i n i n g t o t h e c o m p o s i t i o n b e f o r e and a f t e r a n a l y s i s .
The u n c e r t a i n t y b e f o r e a n a l y s i s
( p r e - i n f o r m a t i o n ) i s an i n p u t parameter and t h e u n c e r t a i n t y r e m a i n i n g a f t e r t h e a n a l y s i s i s an o u t p u t parameter.
These parameters do n o t r e f e r t o t h e c o m p o s i t i o n
o f t h e sample, b u t t o t h e (number o f ) p o s s i b l e compositions. i n p u t - o u t p u t r e l a t i o n , i.e.
, the
The c o r r e s p o n d i n g
d i f f e r e n c e between t h e u n c e r t a i n t i e s , cannot
be used f o r a r r i v i n g a t t h e c o m p o s i t i o n o f t h e sample.
I t merely r e f e r s ,
depending on t h e a n a l y t i c a l problem, t o t h e number o f d i f f e r e n t compositions t h a t can be d i s c r i m i n a t e d by t h e a p p l i c a t i o n o f t h e a n a l y t i c a l procedure. p a r a l l e l t o t h e a p p l i c a t i o n o f i n f o r m a t i o n t h e o r y i n communication
It runs
t h e o r y , i .e.
,
t h e d i s t i n c t i o n between s e v e r a l p o s s i b l e messages when these a r e t r a n s f e r r e d t h r o u g h a n o i s y channel ( t e l e p h o n e , e t c . ) .
R e p r e s e n t i n g t h e a n a l y t i c a l procedure
as a n o i s y channel, t h e process o f a n a l y s i s can be r e p r e s e n t e d by F i g . 29.2 ( f o r a comparison w i t h a communication diagram, see Shannon and Weaver, 1949). c o m p o s i t i o n i s coded as a ( p h y s i c a l ) p r o p e r t y . n o i s e i s added.
The
T h i s p r o p e r t y i s measured and
Decoding i s p o s s i b l e when t h e r e l a t i o n s h i p between x and y i s
known and when t h e r e l e v a n t s i g n a l i s n o t obscured by t h e n o i s e .
566
sample w i t h unknown composition
using physic a l o r chemical
compos it i on
function
F i g . 29.2. The a n a l y t i c a l procedure as a communication process.
2 9 . 2 . SOME INPUT AND OUTPUT VARIABLES AND THEIR RELATIONS L e t us r e t u r n t o t h e x and y v a r i a b l e s t h a t a r e r e l e v a n t f o r d e s c r i b i n g t h e r e l a t i o n s between t h e measurements and t h e c o m p o s i t i o n s .
The x v a r i a b l e s can, i n In a
q u a n t i t a t i v e a n a l y s i s , be expressed as e i t h e r c o n c e n t r a t i o n s o r amounts. number o f i n s t a n c e s we have r e p r e s e n t e d t h e v a r i a b l e s xl, +
...,
x
n
by t h e v e c t o r
x, d e f i n i n g t h e c o m p o s i t i o n i n t h e space o f compositions (Chapter 1 7 ) .
The
p r e s e n t a t i o n o f x v a r i a b l e s i n q u a l i t a t i v e a n a l y s i s i s more complicated.
In
c o n t r a s t t o t h e q u a n t i t a t i v e composition, t h e i d e n t i t y cannot be r e p r e s e n t e d by a s e t of continuous variables.
The n-dimensional space o f q u a n t i t a t i v e compositions
( w i t h t h e n c o n c e n t r a t i o n s as c o o r d i n a t e s ) as used i n t h i s book has t h e p r o p e r t y t h a t c l o s e l y r e l a t e d samples w i l l correspond w i t h a d j a c e n t p o i n t s i n t h a t space, whereas w i d e l y d i f f e r e n t samples a r e r e p r e s e n t e d by p o i n t s s e p a r a t e d by l a r g e distances.
T h i s p r o p e r t y o f t h e space o f compositions i s d e s i r a b l e when c o n s i d e r i n g
the c a l i b r a t i o n function. F o r q u a l i t a t i v e a n a l y s i s i t i s d e s i r a b l e t o d e f i n e a space o f compositions ( i d e n t i t i e s ) w i t h t h e same p r o p e r t y ( m i x t u r e s w i l l n o t be c o n s i d e r e d ) .
Depending
on t h e a n a l y t i c a l problem, each c o m p o s i t i o n s h o u l d be r e p r e s e n t e d by a d i s t i n c t p o i n t ( o r v e c t o r ) o r s h o u l d c l u s t e r w i t h p o i n t s r e p r e s e n t i n g s i m i l a r compositions ( f o r i n s t a n c e , a l l a l c o h o l s s h o u l d be r e p r e s e n t e d by a c l u s t e r o f p o i n t s ) .
For
s e v e r a l reasons such a space i s d i f f i c u l t t o d e f i n e , b u t o t h e r means o f a c h i e v i n g t h e same goal a r e a v a i l a b l e .
These means a r e t h e
s e v e r a l "codes" t h a t have
567
been invented t o represent the i d e n t i t y of a chemical compound. The most widely used codes a r e the name o r formula of the chemical compound. However, not a1 1 formulae and names i d e n t i f y chemical compounds unambiguously. The same molecular (elemental) formula, f o r instance, can represent d i f f e r e n t chemical compounds.
Use of the systematic IUPAC nomenclature o r the complete
s t r u c t u r a l formula can prevent ambiguities, b u t these names and formulae a r e not e a s i l y handled by computers.
Other codes t h a t a r e more s u i t a b l e f o r computer
handling, i . e . , f o r r e t r i e v a l o f , in p a r t i c u l a r , organic compounds, have been designed ( f o r reviews, see Lynch e t a l . , 1971 ; Ash and Hyde, 1975).
Three main
categories of s t r u c t u r a l representation can be distinguished.
The codes belonging t o the f i r s t category a r e t h e so-called fragmentation codes.
These codes do n o t describe the e n t i r e s t r u c t u r e of the molecule, b u t
r a t h e r i n d i c a t e the presence of c e r t a i n portions of the s t r u c t u r e , f o r instance functional groups.
Numbers o r l e t t e r s , o r t h e i r combinations, a r e used t o
encode the several possible s t r u c t u r a l elements. consists of a combination of such elements.
The code of a chemical compound
However, the r e l a t i v e position o f
the several s t r u c t u r a l elements i s not encoded.
Consequently, i t i s impossible
t o obtain t h e e n t i r e s t r u c t u r e from the code, b u t i t i s easy t o s e l e c t from a s e t of coded s t r u c t u r e s those which a r e s i m i l a r . The second category of codes c o n s i s t s o f connection (connectivity) t a b l e s . Every atom, a p a r t from hydrogen, i n t h e chemical s t r u c t u r e i s given an a r b i t r a r y number.
I n i t s simplest form, the s t r u c t u r e i s represented by a t a b l e with t h e
nature of each atom, the numbers of neighbouring atoms and t h e nature of t h e bonds ( s i n g l e , double, e t c . ) .
For computer use the connection t a b l e s can be
l i n e a r i z e d (sequence of symbols). equally important.
I n t h i s code a l l atoms a r e considered t o be
The code does not lead to a unique representation o f chemical
s t r u c t u r e s , although the introduction of a s e t of rules f o r numbering the atoms can convert t h e connection t a b l e i n t o a unique coding system.
Usually, s t r u c t u r a
elements cannot e a s i l y be recognized when inspecting a connection t a b l e .
However
computer programs have been developed f o r recognizing c e r t a i n s t r u c t u r a l elements ( t y p i c a l l y not functional groups, b u t r a t h e r p a r t s of the skeleton).
568
F r e q u e n t l y used a r e t h e s o - c a l l e d l i n e a r n o t a t i o n s , e s p e c i a l l y t h e Wiswesser l i n e n o t a t i o n and t h e IUPAC n o t a t i o n developed by Dyson.
Through t h e use o f
a d e t a i l e d s e t o f r u l e s a compact code, t h a t i s economical t o s t o r e , i s achieved. I n t h i s code some i m p o r t a n t chemical f e a t u r e s a r e h i g h l i g h t e d , e.g., structures.
ring
Every s t r u c t u r e i s r e p r e s e n t e d by o n l y one code and c o n s e q u e n t l y
e v e r y compound can be r e t r i e v e d by i t s code.
Some s t r u c t u r a l elements, e.g.,
those r e l a t e d t o t h e encoding r u l e s , a r e e a s i l y recognized.
I t can be concluded t h a t codes o t h e r t h a n t h e common s t r u c t u r a l formulae and names a r e a v a i l a b l e f o r u n i q u e l y r e p r e s e n t i n g m o l e c u l a r s t r u c t u r e s . them can be c o n v e r t e d i n t o each o t h e r .
Some o f
The codes t h a t have been developed f o r
computer h a n d l i n g o f i n f o r m a t i o n systems a l s o e n a b l e one t o search f o r s t r u c t u r e s w i t h common s t r u c t u r a l f e a t u r e s .
The c o d i n g systems have some p r o p e r t i e s t h a t
c a n be compared w i t h t h e space o f compositions as i n t r o d u c e d f o r q u a n t i t a t i v e a n a l y s i s , a l t h o u g h t h e y a r e n o t s t r i c t mathematical f o r m u l a t i o n s o f a "space o f iden t i ti es 'I
.
The o u t p u t v a r i a b l e s t h a t a r e o f p r i m a r y i n t e r e s t a r e t h e y v a r i a b l e s r e p r e s e n t i n g t h e r e s u l t s o f t h e measurements and t h a t can be used t o a r r i v e a t t h e c o m p o s i t i o n o f t h e sample.
These v a r i a b l e s can be r e p r e s e n t e d by v e c t o r s
o r p o i n t s i n a space o f measurements, i n b o t h q u a n t i t a t i v e a n a l y s i s (Chapter 1 7 ) and q u a l i t a t i v e a n a l y s i s . For q u a n t i t a t i v e analysis the p r i n c i p a l input-output (x-y) r e l a t i o n i s the c a l i b r a t i o n function.
To a l a r g e e x t e n t i t d e f i n e s t h e a p p l i c a b i l i t y o f t h e
a n a l y t i c a l procedure.
F o r a one-component q u a n t i t a t i v e a n a l y s i s t h i s i n p u t - o u t p u t
r e l a t i o n u s u a l l y i s g i v e n as S = y / x , t h e s e n s i t i v i t y o f t h e a n a l y t i c a l procedure (Chapter 6 ) .
I f t h e s e n s i t i v i t y i s zero, t h e a n a l y t i c a l procedure i s
useless, a l t h o u g h a v a l u e d i f f e r i n g f r o m zero does n o t always c o r r e s p o n d t o a u s e f u l procedure.
T h i s i s p a r t i c u l a r l y so i f t h e r e i s a l a r g e i n f l u e n c e o f t h e
z v a r i a b l e s upon t h e x v a r i a b l e ( n o i s e ) . The s e n s i t i v i t y o f a continuous procedure i s e q u a l l y d e f i n e d by y l x . t h e x - y r e l a t i o n i s t i m e dependent.
However,
F o r a f i r s t - o r d e r response, t h e i n f l u e n c e
569
o f x upon y i s governed by t h e s e n s i t i v i t y S and f i r s t - o r d e r t i m e c o n s t a n t T (Chapter 10). The concept o f t h e s e n s i t i v i t y r e p r e s e n t i n g t h e x-y r e l a t i o n s can a l s o be a p p l i e d t o multi-component analyses and l e a d s t o t h e general f o r m u l a i n m a t r i x n o t a t i o n ( f o r a more e l a b o r a t e d e s c r i p t i o n , see Chapter 17, eqn. 17.20) *
Is1
=
r
... . ... . . . . sji . . _ . . . .
SI1
*
1 2 (29.1)
. 'mn
where S . . a r e p a r t i a1 s e n s i t i v i t i e s and I S I i s t h e s e n s i t i v i t y o f t h e J1
multi-component procedure. method.
Again, a s e n s i t i v i t y o f z e r o corresponds t o a u s e l e s s
The " q u a l i t y " o f t h e procedure i n c r e a s e s w i t h i n c r e a s i n g s e n s i t i v i t y ,
p r o v i d e d t h a t t h e number o f dimensions (measurements) and t h e e r r o r s remain t h e same.
As has been shown i n Chapter 17, t h e s e n s i t i v i t y can be used as a c r i t e r i o n
f o r s e l e c t i n g t h e b e s t s e t o f wavelengths f o r a multi-component s p e c t r o p h o t o m e t r i c procedure.
I n p r i n c i p l e , t h i s method can be c o n s i d e r e d as a method o f f e a t u r e
selection. An e q u i v a l e n t o f t h e s e n s i t i v i t y as d e f i n e d by eqn. 29.1 f o r q u a l i t a t i v e a n a l y s i s does n o t e x i s t , owing t o t h e l a c k o f a s t r i c t mathematical f o r m u l a t i o n o f t h e space o f i d e n t i t i e s .
Consequently, t h e i n p u t - o u t p u t r e l a t i o n f o r a
q u a l i t a t i v e a n a l y s i s i s more c o m p l i c a t e d .
Usually i t consists o f a table o f
chemical compounds r e p r e s e n t e d by t h e i r names, formulae o r codes t o g e t h e r w i t h t h e c o r r e s p o n d i n g s p e c t r a o r p h y s i c a l o r chemical p r o p e r t i e s .
The q u a l i t y o f
t h e procedure i s determined e s s e n t i a l l y by t h e e x t e n t t o which s p e c t r a ( o r p h y s i c a l p r o p e r t i e s ) can be used t o i d e n t i f y chemical compounds. has a u n i q u e spectrum, an i d e n t i f i c a t i o n i s p o s s i b l e .
I f each compound
I n those i n s t a n c e s where
s i m i l a r compounds have s i m i l a r s p e c t r a , c e r t a i n s t r u c t u r a l f e a t u r e s can be d e r i v e d from t h e spectrum.
I f such s i m i l a r i t i e s e x i s t , i n t e r p r e t a t i o n r u l e s o r
570
s t r u c t u r e c o r r e l a t i o n t a b l e s can be used t o a r r i v e a t t h e i d e n t i t y o f chemical compounds from c e r t a i n s p e c t r a l f e a t u r e s .
The d e s i g n o f such r u l e s can be based
upon e i t h e r t h e o r e t i c a l c o n s i d e r a t i o n s o r e x p e r i e n c e .
Rules e x p r e s s i n g t h e
r e l a t i o n s h i p between s p e c t r a l f e a t u r e s and s t r u c t u r a l elements can a l s o be e s t a b l i s h e d by f o r m a l methods based upon t h e s t u d y o f c l u s t e r s [ p a t t e r n ( r e ) c o g n i t i o n , c l u s t e r a n a l y s i s ; see Chapters 16, 18 and 201
.
Although n o t
e s s e n t i a l , t h e use o f l i n e a r codes f o r r e p r e s e n t i n g t h e chemical s t r u c t u r e w i l l f a c i 1it a t e t h e s e s t u d i e s
, especial l y
when 1arge numbers o f s p e c t r a a r e used.
The u v a r i a b l e s were i n t r o d u c e d because o f t h e i r i n f l u e n c e upon t h e measurements I n f a c t , t h e u v a r i a b l e s correspond t o t h e
( f o r c o n s t a n t x, y v a r i e s w i t h u ) . knobs on t h e apparatus.
The apparatus i t s e l f a l s o can be a u v a r i a b l e , j u s t
l i k e t h e volume o f a p i p e t t e , t h e amount and s t r e n g t h s o f r e a g e n t s , e t c . obvious t h a t each procedure has i t s own s e t o f u v a r i a b l e s .
It i s
A l l o f these
c o n t r o l l a b l e v a r i a b l e s s p e c i f y t h e c o n d i t i o n s under which t h e procedure has t o be c a r r i e d o u t . procedure. exist.
I n fact, i t i s a description o r p a r t o f a description o f the
I f t h e box i s c o m p l e t e l y b l a c k , a l a r g e number o f p o s s i b l e u v a r i a b l e s
Some knowledge about t h e b l a c k box can be o f h e l p i n s e l e c t i n g t h e
v a r i a b l e s t h a t m i g h t i n f l u e n c e t h e measurements.
Even then t h e e x a c t i n f l u e n c e
may be unknown and c o n s e q u e n t l y t h e o p t i m a l s e t t i n g o f t h e knobs ( o p t i m a l conditions) i s d i f f i c u l t t o predict.
I n P a r t 11, on e x p e r i m e n t a l design, methods
were d i s c u s s e d t h a t can be used t o e s t a b l i s h t h e o p t i m a l c o n d i t i o n s . The e x a c t v a r i a t i o n s o f t h e z v a r i a b l e s i s u s u a l l y n o t known and consequently t h e z-y r e l a t i o n s remain undetermined.
Only t h e v a r i a t i o n s i n y a r e s t u d i e d
by u s i n g s t a t i s t i c a l methods.
2 9 . 3 . THE COMBINATION
OF BLACK BOXES
I n a number of i n s t a n c e s i t i s advantageous t o d i v i d e t h e b l a c k box i n t o a s e t o f b l a c k boxes (subsystems).
I n t h e schematic r e p r e s e n t a t i o n o f t h e
a n a l y t i c a l procedure as shown i n F i g . 28.1, f o u r b l a c k boxes can be d i s t i n g u i s h e d , viz.,
t h e sampling, t h e sample p r e p a r a t i o n , t h e rneasurement(s) and t h e d a t a
571 handling.
Each o f t h e s e subsystems has ( a n ) i n p u t ( s ) and (an) o u t p u t ( s ) and
consequently(a s e t o f ) i n p u t
-
output r e l a t i o n ( s ) .
box i s t h e i n p u t o f t h e n e x t .
The o u t p u t
o f a c e r t a i n black
Some i n p u t - o u t p u t r e l a t i o n s o f t h e whole system
can be c a l c u l a t e d f r o m t h e i n p u t - o u t p u t r e l a t i o n s o f t h e subsystems. T h i s i s e s p e c i a l l y h e l p f u l f o r t h e design o f a n a l y t i c a l procedures f r o m p a r t s w i t h known p r o p e r t i e s o r when l o o k i n g a t b o t t l e - n e c k s i n t h e c h a i n o f subsystems. The t o t a l s e n s i t i v i t y o f t h e procedure i s equal t o t h e p r o d u c t o f t h e s e n s i t i v i t i e s o f the parts, i.e.,
St =
S1.S2.S3...
Each s e n s i t i v i t y i s expressed
i n u n i t s c o r r e s p o n d i n g t o t h e u n i t s used f o r t h e r e l e v a n t i n p u t and o u t p u t . Thus t h e s e n s i t i v i t y o f a d i l u t i o n i s s i d p l y a c o n s t a n t (less
than u n i t y ) .
Whereas t h e t i m e l a g o r dead t i m e , t d yc l e a r l y has a d d i t i v e p r o p e r t i e s [thus td ( t o t a l ) = t d ( s a m p l i n g )
+
td (sample p r e p a r a t i o n )
+
...] , t h e
frequency
o f a n a l y s i s o r i t s r e c i p r o c a l , ta, i s n o t u n i q u e l y r e l a t e d t o , f o r i n s t a n c e , t h e sampling f r e q u e n c y o r , t h e measuring frequency.
However, t h e d e s i g n o f a
procedure ( o r o r g a n i z a t i o n o f a l a b o r a t o r y ) s h o u l d o b v i o u s l y always l e a d t o t h e same f r e q u e n c i e s o f sampling, sample p r e p a r a t i o n , e t c . f r e q u e n c i e s s h o u l d be t h e same.
A t l e a s t t h e average
I t o b v i o u s l y makes no sense t o g a t h e r samples
w i t h a 1a r g e r frequency than t h e measuring frequency
.
Time c o n s t a n t s o f c o n t i n u o u s subprocedures can be used t o p r e d i c t t h e t i m e c o n s t a n t ( s ) o f t h e whole procedure. be d e a l t w i t h h e r e .
The mathematics a r e c o m p l i c a t e d and cannot
However, i n many i n s t a n c e s i t i s s a f e t o s t a t e t h a t t h e
t i m e c o n s t a n t o f t h e whole procedure i s equal t o t h e l a r g e s t t i m e c o n s t a n t f o u n d i n t h e c h a i n o f subprocedures. A l t h o u g h t h e e x a c t z-y r e l a t i o n s a r e i n p r i n c i p l e unknown, and u s u a l l y need n o t be known, i t o f t e n i s d e s i r a b l e t o d e t e c t t h e sources o f t h e z f l u c t u a t i o n s . F o r t h i s d e t e c t i o n , use can be made o f t h e a d d i t i v e p r o p e r t y o f t h e v a r i a n c e , viz.,
u 2 ( t o t a l ) = u 2 ( s a m p l i n g ) + u 2 (sample i n t r o d u c t i o n ) +
...
Thus t h e
v a r i a n c e o f t h e o u t p u t y can be d i v i d e d i n t o p a r t s t h a t can be a s c r i b e d t o t h e s e v e r a l sources.
ANOVA (Chapter 4) can be used t o e s t i m a t e these c o n t r i b u t i o n s
as i t i s p o s s i b l e t o determine from a s e t o f experiments t h e v a r i a n c e c o n t r i b u t e d
572
by t h e measurement, t h e sum o f t h e v a r i a n c e s o f t h e measurement and t h e sample p r e p a r a t i o n and t h e t o t a l v a r i a n c e .
I t i s c l e a r l y i m p o s s i b l e , and n o t necessary,
t o e s t i m a t e t h e v a r i a n c e s o f t h e subsystems d i r e c t l y . I n t h e p r e c e d i n g p a r t s t h e t o t a l system has been regarded as a s e t o f subsystems t h a t a r e connected i n s e r i e s . boxes i n p a r a l l e l .
It i s a l s o possible t o connect black
F o r q u a n t i t a t i v e a n a l y s i s t h i s r e p r e s e n t s a multi-component
a n a l y s i s : a procedure f o r t h e d e t e r m i n a t i o n o f a c e r t a i n element i s combined w i t h a procedure s u i t a b l e f o r e s t i m a t i n g a n o t h e r .
Such combined systems, i n
f a c t , behave i n d e p e n d e n t l y (however, i n a l a b o r a t o r y o r g a n i s a t i o n t h e y cannot be c o n s i d e r e d as independent, see Chapter 3 0 ) . s i t u a t i o n arises.
For q u a l i t a t i v e analysis a d i f f e r e n t
The c o m b i n a t i o n o f , f o r i n s t a n c e , two procedures, each y i e l d i n g
a p a r t i a l i d e n t i f i c a t i o n , may be r e q u i r e d f o r a f u l l i d e n t i f i c a t i o n .
F o r such
combinations t h e c o r r e l a t i o n between t h e p h y s i c a l p r o p e r t i e s o r s p e c t r a o b t a i n e d f r o m t h e i n d i v i d u a l procedures has t o be t a k e n i n t o account.
Information
t h e o r e t i c a l s t u d i e s p e r m i t t h e e v a l u a t i o n o f t h e u s e f u l n e s s o f t h e combined system f o r i d e n t i f i c a t i o n purposes.
As has been shown i n Chapters 8 and 17,
t h e t o t a l amount o f i n f o r m a t i o n i s n o t equal t o t h e i n f o r m a t i o n o b t a i n e d f r o m t h e i n d i v i d u a l procedures. 29.4. AN EXAMPLE A1 though t h e use o f b l o c k diagrams t o r e p r e s e n t s c h e m a t i c a l l y s t r u c t u r e s t h a t a r e n o t e a s i l y d e s c r i b e d i n words i s widespread i n s c i e n c e and technology, a n a l y t i c a l r e c i p e s a r e u s u a l l y d e s c r i b e d i n words r a t h e r t h a n i n diagrams.
The
d e s c r i p t i o n of a n a l y t i c a l r e c i p e s u s i n g , o r supplementing them w i t h , such diagrams has c e r t a i n advantages.
L e t us c o n s i d e r t h e r e c i p e f o r t h e
complexometric d e t e r m i n a t i o n o f i r o n (111) as used by M a l i s s a and J e l l i n e k (1969) t o i l l u s t r a t e t h e use of a s y m b o l i c language (see t h e n e x t s e c t i o n ) .
The
procedure ( o f V o r l i l l e k and Vydra) i s d e s c r i b e d c o n c i s e l y as f o l l o w s : Remove m e t a l l i c i r o n by t r e a t i n g t h e powdered sample (Renn s l a g ) (1 g ) f o r 20 h w i t h FeC13 s o l u t i o n (6%) (50 m l ) .
F i l t e r t h e m i x t u r e , wash t h e r e s i d u e
573 w i t h h o t w a t e r (100 m l ) and h e a t i t i n a p l a t i n u m c r u c i b l e w i t h HC1-HF ( 1 : l ) f o r 1-2 h on a sand-bath ; r e p e a t t h e procedure, i f necessary.
D i l u t e the
r e s u l t i n g s o l u t i o n w i t h doubly d i s t i l l e d w a t e r (oxygen f r e e ) t o 150 m l , add H3B03 (2-3 g ) and a d j u s t t h e pH t o 1.5-2 by adding NaOH s o l u t i o n (10%). t h e s o l u t i o n a t 60-70" and t i t r a t e w i t h 0.05
Heat
M EDTA i n a n i t r o g e n atmosphere,
p o t e n t i o m e t r i c a l l y o r by t h e dead-stop method. T h i s d e s c r i p t i o n has a l a r g e number o f (apparently)
u variables, viz., variables t h a t
influence the c a l i b r a t i o n function.
These
u variables are the
n a t u r e and amount o f sample, t h e p r e - t r e a t m e n t o f t h e sample ( p o w d e r i n g ) , t h e amount and s t r e n g t h o f t h e FeC13 s o l u t i o r r , t h e t i m e r e q u i r e d f o r removal o f m e t a l l i c i r o n , t h e m a t e r i a l o f t h e c r u c i b l e , t h e amount and temperature o f t h e w a t e r t o be used f o r washing t h e r e s i d u e , e t c .
A l t o g e t h e r t h e r e a r e about 30
control lable variables. R e p l a c i n g t h e d e s c r i p t i o n i n words by a l i s t o f
u v a r i a b l e s p r o v i d e s a check
l i s t o f v a r i a b l e s t h a t i n f l u e n c e t h e performance c h a r a c t e r i s t i c s .
Information
w i t h r e s p e c t t o t h e course o f a n a l y s i s i s l o s t u n l e s s t h e a n a l y t i c a l procedure i s s p l i t i n t o p a r t s and f o r each p a r t t h e c o r r e s p o n d i n g u v a r i a b l e s a r e g i v e n (see t h e n e x t section). E s s e n t i a l l y t h i s d e s c r i p t i o n i s a b l a c k box, p r o v i d i n g i n f o r m a t i o n about t h e controllable factors.
A l t h o u g h i t m i g h t e a s i l y be i n c l u d e d , i t does n o t p r o v i d e
i n f o r m a t i o n on t h e performance c h a r a c t e r i s t i c s o f t h e procedure ( s e n s i t i v i t y , p r e c i s i o n , d e t e c t i o n l i m i t , t i m e parameters) and as such t h e d e s c r i p t i o n i s n o t complete.
A l t h o u g h t h i s b l a c k box can be c o n s i d e r e d t o be a d e q u a t e l y
d e s c r i b e d when a i m i n g a t t h e a p p l i c a t i o n o f t h e procedure, i t i s t o be c o n s i d e r e d as i n c o m p l e t e f o r t h e purpose o f comparison w i t h o t h e r procedures. F o r t h e a n a l y s t f a m i l i a r w i t h r e l a t e d procedures, t h e box p r o b a b l y i s n o t c o m p l e t e l y b l a c k and he may be a b l e t o e s t i m a t e t h e performance c h a r a c t e r i s t i c s from h i s e x p e r i e n c e w i t h r e l a t e d procedures.
Communicating an a n a l y t i c a l procedure t o
those who a r e n u t f a m i l i a r w i t h t h e p r i n c i p l e s o f t h e procedure i s p o s s i b l e w i t h a b l a c k box, p r o v i d e d t h a t a c a r e f u l d e s c r i p t i o n i s g i v e n .
574 29.5.
SOME OTHER WAYS OF DESCRIBING ANALYTICAL PROCEDURES
The course o f t h e a n a l y s i s i s obscure when t h e procedure i s r e p r e s e n t e d by t h e model i n F i g . 29.1.
More d e t a i l s a b o u t t h e course o f t h e procedure can be
i n c l u d e d when t h e system i s d i v i d e d i n t o subsystems.
A very rigorous d i v i s i o n
i n t o subsystems has been proposed by M a l i s s a and J e l l i n e k (1969) and by M a l i s s a and Simeonov (1978).
T h e i r symbolic language i s aimed a t r e t a i n i n g a l l
i n f o r m a t i o n r e q u i r e d f o r p e r f o r m i n g t h e procedure.
The symbolic r e p r e s e n t a t i o n
o f t h e procedure d e s c r i b e d i n t h e p r e v i o u s s e c t i o n i s shown i n F i g . 29.3.
resembles t h e r e p r e s e n t a t i o n o f a procedure by F i g . 28.1, sane i m p o r t a n t d i f f e r e n c e s .
It
although there are
The symbols i n F i g . 29.3 a r e b l a c k boxes t h a t y i e l d
i n f o r m a t i o n on t h e s e v e r a l u parameters and a r e i n f a c t r e p r e s e n t a t i o n s o f t h e u n i t operations t h a t a r e r e q u i r e d f o r performing t h e a n a l y s i s (heating, f i l t r a t i o n , etc.).
I n p u t and o u t p u t o f m a t e r i a l s a r e c l e a r l y i n d i c a t e d by arrows.
The whole scheme i s designed t o y i e l d t h e same i n f o r m a t i o n as t h e w r i t t e n t e x t .
RkI3 $0 F i g . 29.3.
Symbolic r e p r e s e n t a t i o n o f a complexometric t i t r a t i o n procedure.
I n o r d e r t o be a b l e t o d e s c r i b e a wide v a r i e t y o f procedures, a l a r g e number o f symbols unambiguously r e p r e s e n t i n g t h e v a r i o u s u n i t o p e r a t i o n s a r e r e q u i r e d ( t h e semantics o f t h e s y m b o l i c language).
I n a d d i t i o n , a s e t o f r u l e s has t o be
designed i n o r d e r t o connect t h e v a r i o u s u n i t o p e r a t i o n s ( t h e grammar).
I n our
o p i n i o n , f o r a f u l l d e s c r i p t i o n o f a n a l y t i c a l procedures a r a t h e r c o m p l i c a t e d language i s r e q u i r e d and f o r t h a t reason we d o u b t whether e v e n t u a l l y t h e goal o f more s i m p l y and c l e a r l y r e p r e s e n t i n g a n a l y t i c a l procedures w i 11 be reached.
575 Own e x p e r i e n c e i n d i c a t e s t h a t such a s y m b o l i c language i s u s e f u l f o r w e t chemical a n a l y s i s , b u t f a i 1s when i n s t r u m e n t a l and more dimensional procedures a r e considered.
Examples o f t h e comparison o f procedures u s i n g t h e s y m b o l i c language
has been g i v e n by G o t t s c h a l k (1972) and by O r t n e r and Scherer (1977). M a l i s s a and J e l l i n e k (1969) d i s c u s s e d a n o t h e r (computer) language, a i m i n g a t a f a c i l i t a t i o n o f t h e a u t o m a t i o n ( c o m p u t e r i z a t i o n ) o f a n a l y t i c a l procedures.
The
same r e c i p e f o r d e t e r m i n i n g i r o n (111) i r o n i n t h a t language i s shown i n Table 29.1.
I t i s easy, even w i t h o u t an e x p l a n a t i o n , t o r e a d Table 29.1.
Again, t h e
r e p r e s e n t a t i o n o f t h e procedure i s a b l a c k box.
Table 29.1. A n a l y t i c a l procedure i n computer language ( M a l i s s a and J e l l i n e k , 1969) Step 0 1 2 3 4 5 6 7 8 9 10 11 12 13
START SAMPL S 1 ADD L1 SOLV (1200) FILT WASH L2 ADD L3 HEAT (100;60) DILUT L4 (150) ADD S2 ADD L5 I F (PH.LT.2.0) GO TO 10 TITR L6 ( 7 0 ) END
L1 : FeC13 s o l u t i o n (6%) ; 50 m l
L2 L3 L4 L5 L6 S1 S2
: : : : : : :
Water ; 100°C ; 100 m l HCl/HF s o l u t i o n ( 1 : l ) Water ; doubly d i s t i l l e d NaOH (10%) EDTA (0.05 M) Sample ; 1 g H3B03 ; 3 g
Another computer language aimed a t l a b o r a t o r y a u t o m a t i o n has been d e s c r i b e d by Toren e t a l . (1972). uncertain.
However, t h e f u t u r e a p p l i c a t i o n o f . t h e s e languages i s
L a b o r a t o r y a u t o m a t i o n may w e l l develop a l o n g o t h e r l i n e s as a r e s u l t
o f the i n t r o d u c t i o n o f microprocessors.
29.6. QUALITY CONTROL
A n a l y s i n g i s a process, e i t h e r continuous o r d i s c o n t i n u o u s , t h a t has t o be k e p t under c o n t r o l .
The " q u a l i t y " o f t h e a n a l y t i c a l r e s u l t s produced by t h a t
516
process has t o be guaranteed. a c t i o n s have been i n c l u d e d .
T h e r e f o r e , i n t h e scheme i n F i g . 28.1 c o n t r o l Usually the u variables are kept constant o r varied For
i n a s p e c i f i e d way i n o r d e r t o p r e v e n t t h e p r o d u c t i o n o f i n c o r r e c t r e s u l t s . many a n a l y t i c a l procedures t h i s t y p e o f c o n t r o l i s n o t s u f f i c i e n t t o a v o i d (systematic) errors. specified.
A p p a r e n t l y i n such cases n o t a l l u v a r i a b l e s have been
I n such i n s t a n c e s a more o r l e s s f r e q u e n t c a l i b r a t i o n i s r e q u i r e d .
C o n s i d e r i n g t h e problem f r o m t h a t a n g l e , t h e process o f c a l i b r a t i o n i s a c o n t r o l action.
Several o t h e r methods have been developed t o keep t h e a n a l y s i n g process
under c o n t r o l , f o r i n s t a n c e , t h e use o f c o n t r o l c h a r t s (Chapter 5 ) .
29.7.
THE
ANALYTICAL PROCEDURE AS A SUBSYSTEM
A n a l y t i c a l procedures a r e used f o r s o l v i n g a n a l y t i c a l problems. ( g e n e r a l i z e d ) problems have been d i s c u s s e d i n P a r t I V .
I n general , a n a l y t i c a l
r e s u l t s a r e r e q u i r e d i n o r d e r t o be a b l e t o make d e c i s i o n s . h e l p s one t o decide whether a c t i o n s s h o u l d be taken.
Some o f these
A n a l y t i c a l chemistry
A n a l y t i c a l r e s u l t s from
t h e c l i n i c a l l a b o r a t o r y w i l l o r w i l l n o t be f o l l o w e d by t h e r a p y ; i n t h e r e s e a r c h l a b o r a t o r y , r e s u l t s w i l l be o f h e l p i n g u i d i n g t h e research, e t c . A l t h o u g h we have c o n s i d e r e d t h e a n a l y t i c a l procedure as a s e p a r a t e system, i t c l e a r l y shows i n t e r a c t i o n s w i t h t h e environment.
A g e n e r a l model f o r t h e s e
i n t e r a c t i o n s i s n o t available, although there are strong i n d i c a t i o n s t h a t every a n a l y t i c a l procedure i s p a r t of a c o n t r o l l o o p and t h u s h e l p s t o r e g u l a t e processes, whether t h e s e processes be t h e t h e r a p y o f p a t i e n t s o r r e s e a r c h a c t i v i t i e s .
The
g e n e r a l goal o f t h e a n a l y s i s w i l l be t o o p t i m i z e t h e s e processes. D e f i n i n g such o p t i m i z a t i o n problems r e q u i r e s conununication w i t h s c i e n t i s t s o f other disciplines. by b l a c k boxes.
I n t h a t c o n t e x t , a n a l y t i c a l procedures s h o u l d be r e p r e s e n t e d
F o r t h a t purpose, t h e f u n c t i o n and c h a r a c t e r i s t i c s as d e s c r i b e d
i n t h i s c h a p t e r a r e c e r t a i n l y more i m p o r t a n t t h a n t h e i n t e r n a l elements o f and r e l a t i o n s h i p s w i t h i n t h e b l a c k box.
Although the p i c t u r e o f the a n a l y t i c a l
procedure p r e s e n t e d i s f a r from complete, i t i s w o r t h s t i m u l a t i n g t h e development o f g e n e r a l ized p i c t u r e s
.
577
REFERENCES
J.E. Ash and E. Hyde, Chemical I n f o r m a t i o n Systems, Wiley, Mew York, 1975. G. G o t t s c h a l k , Z. a n a l , Chem., 258 (1972) 1. H. K a i s e r , i n Methodicum Chimicum, Band I : A n a l y t i k , T e i l I, p. 1 , G. Thieme, S t u t t g a r t and Academic Press, New York, 1973. M.F. Lynch, J.M. H a r r i s o n , W.G. Town and J.E. Ash, Computer H a n d l i n g o f Chemical S t r u c t u r e I n f o r m a t i o n , Macdonald, London and E l s e v i e r , New York, 1971. H . M a l i s s a and G. J e l l i n e k , Z. a n a l . Chem., 247 (19691 1. H. M a l i s s a and V. Simeonov, Z. a n a l . Chem., 289 (1978) 257. H.i+I. O r t n e r and V . Scherer, T a l a n t a , 24 (1977) 215. C.E. Shannon and W. Weaver, The Mathematical Theory of I n f o r m a t i o n , U n i v . I l l i n o i s Press, Urbana, I l l . , 1949. E.C. Toren, R.N. Carcy, A.E. S h e r r y and J.E. Davies, Anal. Chem., 44 (1972) 339.
Chapter 29
THE ANALYTICAL PROCEDURE 29.1. THE BLACK BOX I n t h e p r e c e d i n g c h a p t e r , t h e b l a c k box was d e f i n e d as a system w i t h an unknown ( n t e r n a l ) s t r u c t u r e , b u t w i t h g i v e n magnitudes o f i n p u t and o u t p u t . R e f e r r i n g t o an a n a l y t i c a l procedure o r an a n a l y t i c a l i n s t r u m e n t as a b l a c k box means t h a
n o t h i n g i s known about t h e p h y s i c a l , chemical, mechanical o r e l e c t r o n i c
components o r processes t h a t c o n v e r t t h e sample w i t h an unknown c o m p o s i t i o n i n t o a sample w i t h a known composition.
A substantial p a r t o f the research e f f o r t i n
a n a l y t i c a l c h e m i s t r y has been and s t i l l i s devoted t o t h e e l u c i d a t i o n o f t h e unknown s t r u c t u r e o f b l a c k boxes o r , t o p u t i t d i f f e r e n t l y , t o t u r n b l a c k boxes i n t o w h i t e , o r a t l e a s t g r e y boxes.
Such an e l u c i d a t i o n s a t i s f i e s human c u r i o s i t y
and o f t e n l e a d s t o a procedure w i t h a s u p e r i o r performance.
However, f r o m an
a n a l y t i c a l p o i n t o f view, procedures can be, and o f t e n a c t u a l l y a r e , e q u a l l y u s e f u l when t h e i n t e r n a l s t r u c t u r e i s n o t ( f u l l y ) known t o t h e user.
Moreover,
f o r an a n a l y t i c a l chemist f a c e d w i t h w i d e l y d i f f e r e n t problems and procedures, i t i s v i r t u a l l y i m p o s s i b l e t o be ( e n t i r e l y ) f a m i l i a r w i t h t h e p h y s i c a l and
chemical p r i n c i p l e s t h a t u n d e r l i e t h e procedures and w i t h t h e d e t a i l s o f t h e design o f the instruments.
Even if procedures and equipment a r e w h i t e boxes t o
some s c i e n t i s t s t h e y may w e l l appear t o be b l a c k boxes t o o t h e r s .
A b l a c k box i s u s e f u l f o r t h e a n a l y s t i f , and o n l y i f , i t s o u t p u t can be used t o a r r i v e a t t h e ( a p p r o x i m a t e ) c o m p o s i t i o n o f t h e unknown sample.
To p u t i t
d i f f e r e n t l y , t h e i n p u t - o u t p u t r e l a t i o n o r t h e c a l i b r a t i o n f u n c t i o n has t o be known.
However, e v e r y a n a l y s t i s aware o f t h e i n f l u e n c e o f parameters ( a l s o
c a l l e d d e s c r i p t o r s ; K a i s e r , 1973) such as temperature, volume o f r e a g e n t and wavelength on t h e measurement.
C l e a r l y t h e b l a c k box i s n o t a d e q u a t e l y d e s c r i b e d
by t h e i n p u t - o u t p u t r e l a t i o n between, t h e c o m p o s i t i o n o f t h e sample and t h e measurement alone.
Parameters t h a t i n f l u e n c e t h i s r e l a t i o n s h o u l d be s p e c i f i e d ,
564
and o f t e n k e p t c o n s t a n t , i n o r d e r f o r u s e f u l a n a l y t i c a l r e s u l t s t o be o b t a i n e d . The a n a l y t i c a l procedure as a b l a c k box can be a d e s c r i p t i o n i n words o f what has t o be done i n o r d e r t o determine t h e c o m p o s i t i o n o f t h e sample ( t h e a n a l y t i c a l recipe).
Such a d e s c r i p t i o n can be supplemented o r r e p l a c e d w i t h a more
schematic model as p r e s e n t e d i n F i g . 29.1.
kz: "1
"
F i g . 29.1. The a n a l y t i c a l procedure as a b l a c k box E s s e n t i a l f o r t h i s model a r e t h e n a t u r e ( u n i t s ) o f t h e i n p u t v a r i a b l e s
. . ., x.,1 . . . , xn
x1
r e p r e s e n t i n g t h e c o m p o s i t i o n ( c o n c e n t r a t i o n s , amounts,
i d e n t i t i e s ) and o f t h e o u t p u t v a r i a b l e s yl, measurements ( v o l t a g e s , r e a d i n g s ) . (x
-
. . . , yjy . . . , y,
representing t h e
O f m a j o r importance a r e t h e i n p u t - o u t p u t
y ) relations t h a t are required i n order t o a r r i v e a t the analytical results
from t h e measurements.
The u v a r i a b l e s t h a t have t o be s p e c i f i e d a r e those which
i n f l u e n c e t h e measurements and consequently t h e x
-
y relations.
Because o f t h i s
i n f l u e n c e t h e y have t o be c o n t r o l l e d and a r e c a l l e d t h e c o n t r o l l a b l e v a r i a b l e s . I n p u t v a r i a b l e s t h a t cannot be k e p t c o n s t a n t a r e i n d i c a t e d by zl. o f these n o n - c o n t r o l l a b l e v a r i a b l e s i s o f t e n unknown.
The o r i g i n
They l e a d t o ( s t o c h a s t i c )
fluctuations i n the output variables. The g e n e r a l p i c t u r e o f F i g . 29.1 i s reduced t o a model w i t h one x and one y v a r i a b l e i n a one-dimensional a n a l y s i s . can be used f o r o n l y one t y p e of sample. c a l i b r a t i o n function.
U s u a l l y such one-dimensional analyses The t y p e o f sample i n f l u e n c e s t h e
I t can be c o n s i d e r e d as a c o n t r o l l a b l e v a r i a b l e .
565
A c l o s e r i n s p e c t i o n o f t h e a n a l y t i c a l procedure as a system, i . e . , a n a l y s i s , r e v e a l s s e v e r a l t y p e s o f i n p u t and o u t p u t .
a systems
We a r r i v e d a t s e t s o f i n p u t
and o u t p u t v a r i a b l e s t h a t a r e r e l e v a n t when l o o k i n g a t t h e c a l i b r a t i o n f u n c t i o n . However, o t h e r i n p u t s and o u t p u t s e x i s t .
F o r i n s t a n c e , m a t e r i a l s f l o w i n and
o u t o f t h e apparatus and energy and s k i l l s a r e r e q u i r e d t o produce r e s u l t s . These aspects w i l l n o t be d e a l t w i t h here, as t h e y a r e l e s s r e l e v a n t i n t h e c o n t e x t o f t h i s book, a l t h o u g h t h e y a r e e s s e n t i a l i n t h e d e s i g n o f i n s t r u m e n t s , the organization o f the laboratory, etc.
A few remarks must be made about a p a r t i c u l a r i n p u t and o u t p u t , namely t h a t Some o f t h e p r i n c i p l e s o f i n f o r m a t i o n t h e o r y have
connected w i t h i n f o r m a t i o n . been i n t r o d u c e d i n Chapter 8.
I n f o r m a t i o n o b t a i n e d from an a n a l y t i c a l procedure
has been d e f i n e d as t h e d i f f e r e n c e between t h e u n c e r t a i n t y p e r t a i n i n g t o t h e c o m p o s i t i o n b e f o r e and a f t e r a n a l y s i s .
The u n c e r t a i n t y b e f o r e a n a l y s i s
( p r e - i n f o r m a t i o n ) i s an i n p u t parameter and t h e u n c e r t a i n t y r e m a i n i n g a f t e r t h e a n a l y s i s i s an o u t p u t parameter.
These parameters do n o t r e f e r t o t h e c o m p o s i t i o n
o f t h e sample, b u t t o t h e (number o f ) p o s s i b l e compositions. i n p u t - o u t p u t r e l a t i o n , i.e.
, the
The c o r r e s p o n d i n g
d i f f e r e n c e between t h e u n c e r t a i n t i e s , cannot
be used f o r a r r i v i n g a t t h e c o m p o s i t i o n o f t h e sample.
I t merely r e f e r s ,
depending on t h e a n a l y t i c a l problem, t o t h e number o f d i f f e r e n t compositions t h a t can be d i s c r i m i n a t e d by t h e a p p l i c a t i o n o f t h e a n a l y t i c a l procedure. p a r a l l e l t o t h e a p p l i c a t i o n o f i n f o r m a t i o n t h e o r y i n communication
It runs
t h e o r y , i .e.
,
t h e d i s t i n c t i o n between s e v e r a l p o s s i b l e messages when these a r e t r a n s f e r r e d t h r o u g h a n o i s y channel ( t e l e p h o n e , e t c . ) .
R e p r e s e n t i n g t h e a n a l y t i c a l procedure
as a n o i s y channel, t h e process o f a n a l y s i s can be r e p r e s e n t e d by F i g . 29.2 ( f o r a comparison w i t h a communication diagram, see Shannon and Weaver, 1949). c o m p o s i t i o n i s coded as a ( p h y s i c a l ) p r o p e r t y . n o i s e i s added.
The
T h i s p r o p e r t y i s measured and
Decoding i s p o s s i b l e when t h e r e l a t i o n s h i p between x and y i s
known and when t h e r e l e v a n t s i g n a l i s n o t obscured by t h e n o i s e .
566
sample w i t h unknown composition
using physic a l o r chemical
compos it i on
function
F i g . 29.2. The a n a l y t i c a l procedure as a communication process.
2 9 . 2 . SOME INPUT AND OUTPUT VARIABLES AND THEIR RELATIONS L e t us r e t u r n t o t h e x and y v a r i a b l e s t h a t a r e r e l e v a n t f o r d e s c r i b i n g t h e r e l a t i o n s between t h e measurements and t h e c o m p o s i t i o n s .
The x v a r i a b l e s can, i n In a
q u a n t i t a t i v e a n a l y s i s , be expressed as e i t h e r c o n c e n t r a t i o n s o r amounts. number o f i n s t a n c e s we have r e p r e s e n t e d t h e v a r i a b l e s xl, +
...,
x
n
by t h e v e c t o r
x, d e f i n i n g t h e c o m p o s i t i o n i n t h e space o f compositions (Chapter 1 7 ) .
The
p r e s e n t a t i o n o f x v a r i a b l e s i n q u a l i t a t i v e a n a l y s i s i s more complicated.
In
c o n t r a s t t o t h e q u a n t i t a t i v e composition, t h e i d e n t i t y cannot be r e p r e s e n t e d by a s e t of continuous variables.
The n-dimensional space o f q u a n t i t a t i v e compositions
( w i t h t h e n c o n c e n t r a t i o n s as c o o r d i n a t e s ) as used i n t h i s book has t h e p r o p e r t y t h a t c l o s e l y r e l a t e d samples w i l l correspond w i t h a d j a c e n t p o i n t s i n t h a t space, whereas w i d e l y d i f f e r e n t samples a r e r e p r e s e n t e d by p o i n t s s e p a r a t e d by l a r g e distances.
T h i s p r o p e r t y o f t h e space o f compositions i s d e s i r a b l e when c o n s i d e r i n g
the c a l i b r a t i o n function. F o r q u a l i t a t i v e a n a l y s i s i t i s d e s i r a b l e t o d e f i n e a space o f compositions ( i d e n t i t i e s ) w i t h t h e same p r o p e r t y ( m i x t u r e s w i l l n o t be c o n s i d e r e d ) .
Depending
on t h e a n a l y t i c a l problem, each c o m p o s i t i o n s h o u l d be r e p r e s e n t e d by a d i s t i n c t p o i n t ( o r v e c t o r ) o r s h o u l d c l u s t e r w i t h p o i n t s r e p r e s e n t i n g s i m i l a r compositions ( f o r i n s t a n c e , a l l a l c o h o l s s h o u l d be r e p r e s e n t e d by a c l u s t e r o f p o i n t s ) .
For
s e v e r a l reasons such a space i s d i f f i c u l t t o d e f i n e , b u t o t h e r means o f a c h i e v i n g t h e same goal a r e a v a i l a b l e .
These means a r e t h e
s e v e r a l "codes" t h a t have
567
been invented t o represent the i d e n t i t y of a chemical compound. The most widely used codes a r e the name o r formula of the chemical compound. However, not a1 1 formulae and names i d e n t i f y chemical compounds unambiguously. The same molecular (elemental) formula, f o r instance, can represent d i f f e r e n t chemical compounds.
Use of the systematic IUPAC nomenclature o r the complete
s t r u c t u r a l formula can prevent ambiguities, b u t these names and formulae a r e not e a s i l y handled by computers.
Other codes t h a t a r e more s u i t a b l e f o r computer
handling, i . e . , f o r r e t r i e v a l o f , in p a r t i c u l a r , organic compounds, have been designed ( f o r reviews, see Lynch e t a l . , 1971 ; Ash and Hyde, 1975).
Three main
categories of s t r u c t u r a l representation can be distinguished.
The codes belonging t o the f i r s t category a r e t h e so-called fragmentation codes.
These codes do n o t describe the e n t i r e s t r u c t u r e of the molecule, b u t
r a t h e r i n d i c a t e the presence of c e r t a i n portions of the s t r u c t u r e , f o r instance functional groups.
Numbers o r l e t t e r s , o r t h e i r combinations, a r e used t o
encode the several possible s t r u c t u r a l elements. consists of a combination of such elements.
The code of a chemical compound
However, the r e l a t i v e position o f
the several s t r u c t u r a l elements i s not encoded.
Consequently, i t i s impossible
t o obtain t h e e n t i r e s t r u c t u r e from the code, b u t i t i s easy t o s e l e c t from a s e t of coded s t r u c t u r e s those which a r e s i m i l a r . The second category of codes c o n s i s t s o f connection (connectivity) t a b l e s . Every atom, a p a r t from hydrogen, i n t h e chemical s t r u c t u r e i s given an a r b i t r a r y number.
I n i t s simplest form, the s t r u c t u r e i s represented by a t a b l e with t h e
nature of each atom, the numbers of neighbouring atoms and t h e nature of t h e bonds ( s i n g l e , double, e t c . ) .
For computer use the connection t a b l e s can be
l i n e a r i z e d (sequence of symbols). equally important.
I n t h i s code a l l atoms a r e considered t o be
The code does not lead to a unique representation o f chemical
s t r u c t u r e s , although the introduction of a s e t of rules f o r numbering the atoms can convert t h e connection t a b l e i n t o a unique coding system.
Usually, s t r u c t u r a
elements cannot e a s i l y be recognized when inspecting a connection t a b l e .
However
computer programs have been developed f o r recognizing c e r t a i n s t r u c t u r a l elements ( t y p i c a l l y not functional groups, b u t r a t h e r p a r t s of the skeleton).
568
F r e q u e n t l y used a r e t h e s o - c a l l e d l i n e a r n o t a t i o n s , e s p e c i a l l y t h e Wiswesser l i n e n o t a t i o n and t h e IUPAC n o t a t i o n developed by Dyson.
Through t h e use o f
a d e t a i l e d s e t o f r u l e s a compact code, t h a t i s economical t o s t o r e , i s achieved. I n t h i s code some i m p o r t a n t chemical f e a t u r e s a r e h i g h l i g h t e d , e.g., structures.
ring
Every s t r u c t u r e i s r e p r e s e n t e d by o n l y one code and c o n s e q u e n t l y
e v e r y compound can be r e t r i e v e d by i t s code.
Some s t r u c t u r a l elements, e.g.,
those r e l a t e d t o t h e encoding r u l e s , a r e e a s i l y recognized.
I t can be concluded t h a t codes o t h e r t h a n t h e common s t r u c t u r a l formulae and names a r e a v a i l a b l e f o r u n i q u e l y r e p r e s e n t i n g m o l e c u l a r s t r u c t u r e s . them can be c o n v e r t e d i n t o each o t h e r .
Some o f
The codes t h a t have been developed f o r
computer h a n d l i n g o f i n f o r m a t i o n systems a l s o e n a b l e one t o search f o r s t r u c t u r e s w i t h common s t r u c t u r a l f e a t u r e s .
The c o d i n g systems have some p r o p e r t i e s t h a t
c a n be compared w i t h t h e space o f compositions as i n t r o d u c e d f o r q u a n t i t a t i v e a n a l y s i s , a l t h o u g h t h e y a r e n o t s t r i c t mathematical f o r m u l a t i o n s o f a "space o f iden t i ti es 'I
.
The o u t p u t v a r i a b l e s t h a t a r e o f p r i m a r y i n t e r e s t a r e t h e y v a r i a b l e s r e p r e s e n t i n g t h e r e s u l t s o f t h e measurements and t h a t can be used t o a r r i v e a t t h e c o m p o s i t i o n o f t h e sample.
These v a r i a b l e s can be r e p r e s e n t e d by v e c t o r s
o r p o i n t s i n a space o f measurements, i n b o t h q u a n t i t a t i v e a n a l y s i s (Chapter 1 7 ) and q u a l i t a t i v e a n a l y s i s . For q u a n t i t a t i v e analysis the p r i n c i p a l input-output (x-y) r e l a t i o n i s the c a l i b r a t i o n function.
To a l a r g e e x t e n t i t d e f i n e s t h e a p p l i c a b i l i t y o f t h e
a n a l y t i c a l procedure.
F o r a one-component q u a n t i t a t i v e a n a l y s i s t h i s i n p u t - o u t p u t
r e l a t i o n u s u a l l y i s g i v e n as S = y / x , t h e s e n s i t i v i t y o f t h e a n a l y t i c a l procedure (Chapter 6 ) .
I f t h e s e n s i t i v i t y i s zero, t h e a n a l y t i c a l procedure i s
useless, a l t h o u g h a v a l u e d i f f e r i n g f r o m zero does n o t always c o r r e s p o n d t o a u s e f u l procedure.
T h i s i s p a r t i c u l a r l y so i f t h e r e i s a l a r g e i n f l u e n c e o f t h e
z v a r i a b l e s upon t h e x v a r i a b l e ( n o i s e ) . The s e n s i t i v i t y o f a continuous procedure i s e q u a l l y d e f i n e d by y l x . t h e x - y r e l a t i o n i s t i m e dependent.
However,
F o r a f i r s t - o r d e r response, t h e i n f l u e n c e
569
o f x upon y i s governed by t h e s e n s i t i v i t y S and f i r s t - o r d e r t i m e c o n s t a n t T (Chapter 10). The concept o f t h e s e n s i t i v i t y r e p r e s e n t i n g t h e x-y r e l a t i o n s can a l s o be a p p l i e d t o multi-component analyses and l e a d s t o t h e general f o r m u l a i n m a t r i x n o t a t i o n ( f o r a more e l a b o r a t e d e s c r i p t i o n , see Chapter 17, eqn. 17.20) *
Is1
=
r
... . ... . . . . sji . . _ . . . .
SI1
*
1 2 (29.1)
. 'mn
where S . . a r e p a r t i a1 s e n s i t i v i t i e s and I S I i s t h e s e n s i t i v i t y o f t h e J1
multi-component procedure. method.
Again, a s e n s i t i v i t y o f z e r o corresponds t o a u s e l e s s
The " q u a l i t y " o f t h e procedure i n c r e a s e s w i t h i n c r e a s i n g s e n s i t i v i t y ,
p r o v i d e d t h a t t h e number o f dimensions (measurements) and t h e e r r o r s remain t h e same.
As has been shown i n Chapter 17, t h e s e n s i t i v i t y can be used as a c r i t e r i o n
f o r s e l e c t i n g t h e b e s t s e t o f wavelengths f o r a multi-component s p e c t r o p h o t o m e t r i c procedure.
I n p r i n c i p l e , t h i s method can be c o n s i d e r e d as a method o f f e a t u r e
selection. An e q u i v a l e n t o f t h e s e n s i t i v i t y as d e f i n e d by eqn. 29.1 f o r q u a l i t a t i v e a n a l y s i s does n o t e x i s t , owing t o t h e l a c k o f a s t r i c t mathematical f o r m u l a t i o n o f t h e space o f i d e n t i t i e s .
Consequently, t h e i n p u t - o u t p u t r e l a t i o n f o r a
q u a l i t a t i v e a n a l y s i s i s more c o m p l i c a t e d .
Usually i t consists o f a table o f
chemical compounds r e p r e s e n t e d by t h e i r names, formulae o r codes t o g e t h e r w i t h t h e c o r r e s p o n d i n g s p e c t r a o r p h y s i c a l o r chemical p r o p e r t i e s .
The q u a l i t y o f
t h e procedure i s determined e s s e n t i a l l y by t h e e x t e n t t o which s p e c t r a ( o r p h y s i c a l p r o p e r t i e s ) can be used t o i d e n t i f y chemical compounds. has a u n i q u e spectrum, an i d e n t i f i c a t i o n i s p o s s i b l e .
I f each compound
I n those i n s t a n c e s where
s i m i l a r compounds have s i m i l a r s p e c t r a , c e r t a i n s t r u c t u r a l f e a t u r e s can be d e r i v e d from t h e spectrum.
I f such s i m i l a r i t i e s e x i s t , i n t e r p r e t a t i o n r u l e s o r
570
s t r u c t u r e c o r r e l a t i o n t a b l e s can be used t o a r r i v e a t t h e i d e n t i t y o f chemical compounds from c e r t a i n s p e c t r a l f e a t u r e s .
The d e s i g n o f such r u l e s can be based
upon e i t h e r t h e o r e t i c a l c o n s i d e r a t i o n s o r e x p e r i e n c e .
Rules e x p r e s s i n g t h e
r e l a t i o n s h i p between s p e c t r a l f e a t u r e s and s t r u c t u r a l elements can a l s o be e s t a b l i s h e d by f o r m a l methods based upon t h e s t u d y o f c l u s t e r s [ p a t t e r n ( r e ) c o g n i t i o n , c l u s t e r a n a l y s i s ; see Chapters 16, 18 and 201
.
Although n o t
e s s e n t i a l , t h e use o f l i n e a r codes f o r r e p r e s e n t i n g t h e chemical s t r u c t u r e w i l l f a c i 1it a t e t h e s e s t u d i e s
, especial l y
when 1arge numbers o f s p e c t r a a r e used.
The u v a r i a b l e s were i n t r o d u c e d because o f t h e i r i n f l u e n c e upon t h e measurements I n f a c t , t h e u v a r i a b l e s correspond t o t h e
( f o r c o n s t a n t x, y v a r i e s w i t h u ) . knobs on t h e apparatus.
The apparatus i t s e l f a l s o can be a u v a r i a b l e , j u s t
l i k e t h e volume o f a p i p e t t e , t h e amount and s t r e n g t h s o f r e a g e n t s , e t c . obvious t h a t each procedure has i t s own s e t o f u v a r i a b l e s .
It i s
A l l o f these
c o n t r o l l a b l e v a r i a b l e s s p e c i f y t h e c o n d i t i o n s under which t h e procedure has t o be c a r r i e d o u t . procedure. exist.
I n fact, i t i s a description o r p a r t o f a description o f the
I f t h e box i s c o m p l e t e l y b l a c k , a l a r g e number o f p o s s i b l e u v a r i a b l e s
Some knowledge about t h e b l a c k box can be o f h e l p i n s e l e c t i n g t h e
v a r i a b l e s t h a t m i g h t i n f l u e n c e t h e measurements.
Even then t h e e x a c t i n f l u e n c e
may be unknown and c o n s e q u e n t l y t h e o p t i m a l s e t t i n g o f t h e knobs ( o p t i m a l conditions) i s d i f f i c u l t t o predict.
I n P a r t 11, on e x p e r i m e n t a l design, methods
were d i s c u s s e d t h a t can be used t o e s t a b l i s h t h e o p t i m a l c o n d i t i o n s . The e x a c t v a r i a t i o n s o f t h e z v a r i a b l e s i s u s u a l l y n o t known and consequently t h e z-y r e l a t i o n s remain undetermined.
Only t h e v a r i a t i o n s i n y a r e s t u d i e d
by u s i n g s t a t i s t i c a l methods.
2 9 . 3 . THE COMBINATION
OF BLACK BOXES
I n a number of i n s t a n c e s i t i s advantageous t o d i v i d e t h e b l a c k box i n t o a s e t o f b l a c k boxes (subsystems).
I n t h e schematic r e p r e s e n t a t i o n o f t h e
a n a l y t i c a l procedure as shown i n F i g . 28.1, f o u r b l a c k boxes can be d i s t i n g u i s h e d , viz.,
t h e sampling, t h e sample p r e p a r a t i o n , t h e rneasurement(s) and t h e d a t a
571 handling.
Each o f t h e s e subsystems has ( a n ) i n p u t ( s ) and (an) o u t p u t ( s ) and
consequently(a s e t o f ) i n p u t
-
output r e l a t i o n ( s ) .
box i s t h e i n p u t o f t h e n e x t .
The o u t p u t
o f a c e r t a i n black
Some i n p u t - o u t p u t r e l a t i o n s o f t h e whole system
can be c a l c u l a t e d f r o m t h e i n p u t - o u t p u t r e l a t i o n s o f t h e subsystems. T h i s i s e s p e c i a l l y h e l p f u l f o r t h e design o f a n a l y t i c a l procedures f r o m p a r t s w i t h known p r o p e r t i e s o r when l o o k i n g a t b o t t l e - n e c k s i n t h e c h a i n o f subsystems. The t o t a l s e n s i t i v i t y o f t h e procedure i s equal t o t h e p r o d u c t o f t h e s e n s i t i v i t i e s o f the parts, i.e.,
St =
S1.S2.S3...
Each s e n s i t i v i t y i s expressed
i n u n i t s c o r r e s p o n d i n g t o t h e u n i t s used f o r t h e r e l e v a n t i n p u t and o u t p u t . Thus t h e s e n s i t i v i t y o f a d i l u t i o n i s s i d p l y a c o n s t a n t (less
than u n i t y ) .
Whereas t h e t i m e l a g o r dead t i m e , t d yc l e a r l y has a d d i t i v e p r o p e r t i e s [thus td ( t o t a l ) = t d ( s a m p l i n g )
+
td (sample p r e p a r a t i o n )
+
...] , t h e
frequency
o f a n a l y s i s o r i t s r e c i p r o c a l , ta, i s n o t u n i q u e l y r e l a t e d t o , f o r i n s t a n c e , t h e sampling f r e q u e n c y o r , t h e measuring frequency.
However, t h e d e s i g n o f a
procedure ( o r o r g a n i z a t i o n o f a l a b o r a t o r y ) s h o u l d o b v i o u s l y always l e a d t o t h e same f r e q u e n c i e s o f sampling, sample p r e p a r a t i o n , e t c . f r e q u e n c i e s s h o u l d be t h e same.
A t l e a s t t h e average
I t o b v i o u s l y makes no sense t o g a t h e r samples
w i t h a 1a r g e r frequency than t h e measuring frequency
.
Time c o n s t a n t s o f c o n t i n u o u s subprocedures can be used t o p r e d i c t t h e t i m e c o n s t a n t ( s ) o f t h e whole procedure. be d e a l t w i t h h e r e .
The mathematics a r e c o m p l i c a t e d and cannot
However, i n many i n s t a n c e s i t i s s a f e t o s t a t e t h a t t h e
t i m e c o n s t a n t o f t h e whole procedure i s equal t o t h e l a r g e s t t i m e c o n s t a n t f o u n d i n t h e c h a i n o f subprocedures. A l t h o u g h t h e e x a c t z-y r e l a t i o n s a r e i n p r i n c i p l e unknown, and u s u a l l y need n o t be known, i t o f t e n i s d e s i r a b l e t o d e t e c t t h e sources o f t h e z f l u c t u a t i o n s . F o r t h i s d e t e c t i o n , use can be made o f t h e a d d i t i v e p r o p e r t y o f t h e v a r i a n c e , viz.,
u 2 ( t o t a l ) = u 2 ( s a m p l i n g ) + u 2 (sample i n t r o d u c t i o n ) +
...
Thus t h e
v a r i a n c e o f t h e o u t p u t y can be d i v i d e d i n t o p a r t s t h a t can be a s c r i b e d t o t h e s e v e r a l sources.
ANOVA (Chapter 4) can be used t o e s t i m a t e these c o n t r i b u t i o n s
as i t i s p o s s i b l e t o determine from a s e t o f experiments t h e v a r i a n c e c o n t r i b u t e d
572
by t h e measurement, t h e sum o f t h e v a r i a n c e s o f t h e measurement and t h e sample p r e p a r a t i o n and t h e t o t a l v a r i a n c e .
I t i s c l e a r l y i m p o s s i b l e , and n o t necessary,
t o e s t i m a t e t h e v a r i a n c e s o f t h e subsystems d i r e c t l y . I n t h e p r e c e d i n g p a r t s t h e t o t a l system has been regarded as a s e t o f subsystems t h a t a r e connected i n s e r i e s . boxes i n p a r a l l e l .
It i s a l s o possible t o connect black
F o r q u a n t i t a t i v e a n a l y s i s t h i s r e p r e s e n t s a multi-component
a n a l y s i s : a procedure f o r t h e d e t e r m i n a t i o n o f a c e r t a i n element i s combined w i t h a procedure s u i t a b l e f o r e s t i m a t i n g a n o t h e r .
Such combined systems, i n
f a c t , behave i n d e p e n d e n t l y (however, i n a l a b o r a t o r y o r g a n i s a t i o n t h e y cannot be c o n s i d e r e d as independent, see Chapter 3 0 ) . s i t u a t i o n arises.
For q u a l i t a t i v e analysis a d i f f e r e n t
The c o m b i n a t i o n o f , f o r i n s t a n c e , two procedures, each y i e l d i n g
a p a r t i a l i d e n t i f i c a t i o n , may be r e q u i r e d f o r a f u l l i d e n t i f i c a t i o n .
F o r such
combinations t h e c o r r e l a t i o n between t h e p h y s i c a l p r o p e r t i e s o r s p e c t r a o b t a i n e d f r o m t h e i n d i v i d u a l procedures has t o be t a k e n i n t o account.
Information
t h e o r e t i c a l s t u d i e s p e r m i t t h e e v a l u a t i o n o f t h e u s e f u l n e s s o f t h e combined system f o r i d e n t i f i c a t i o n purposes.
As has been shown i n Chapters 8 and 17,
t h e t o t a l amount o f i n f o r m a t i o n i s n o t equal t o t h e i n f o r m a t i o n o b t a i n e d f r o m t h e i n d i v i d u a l procedures. 29.4. AN EXAMPLE A1 though t h e use o f b l o c k diagrams t o r e p r e s e n t s c h e m a t i c a l l y s t r u c t u r e s t h a t a r e n o t e a s i l y d e s c r i b e d i n words i s widespread i n s c i e n c e and technology, a n a l y t i c a l r e c i p e s a r e u s u a l l y d e s c r i b e d i n words r a t h e r t h a n i n diagrams.
The
d e s c r i p t i o n of a n a l y t i c a l r e c i p e s u s i n g , o r supplementing them w i t h , such diagrams has c e r t a i n advantages.
L e t us c o n s i d e r t h e r e c i p e f o r t h e
complexometric d e t e r m i n a t i o n o f i r o n (111) as used by M a l i s s a and J e l l i n e k (1969) t o i l l u s t r a t e t h e use of a s y m b o l i c language (see t h e n e x t s e c t i o n ) .
The
procedure ( o f V o r l i l l e k and Vydra) i s d e s c r i b e d c o n c i s e l y as f o l l o w s : Remove m e t a l l i c i r o n by t r e a t i n g t h e powdered sample (Renn s l a g ) (1 g ) f o r 20 h w i t h FeC13 s o l u t i o n (6%) (50 m l ) .
F i l t e r t h e m i x t u r e , wash t h e r e s i d u e
573 w i t h h o t w a t e r (100 m l ) and h e a t i t i n a p l a t i n u m c r u c i b l e w i t h HC1-HF ( 1 : l ) f o r 1-2 h on a sand-bath ; r e p e a t t h e procedure, i f necessary.
D i l u t e the
r e s u l t i n g s o l u t i o n w i t h doubly d i s t i l l e d w a t e r (oxygen f r e e ) t o 150 m l , add H3B03 (2-3 g ) and a d j u s t t h e pH t o 1.5-2 by adding NaOH s o l u t i o n (10%). t h e s o l u t i o n a t 60-70" and t i t r a t e w i t h 0.05
Heat
M EDTA i n a n i t r o g e n atmosphere,
p o t e n t i o m e t r i c a l l y o r by t h e dead-stop method. T h i s d e s c r i p t i o n has a l a r g e number o f (apparently)
u variables, viz., variables t h a t
influence the c a l i b r a t i o n function.
These
u variables are the
n a t u r e and amount o f sample, t h e p r e - t r e a t m e n t o f t h e sample ( p o w d e r i n g ) , t h e amount and s t r e n g t h o f t h e FeC13 s o l u t i o r r , t h e t i m e r e q u i r e d f o r removal o f m e t a l l i c i r o n , t h e m a t e r i a l o f t h e c r u c i b l e , t h e amount and temperature o f t h e w a t e r t o be used f o r washing t h e r e s i d u e , e t c .
A l t o g e t h e r t h e r e a r e about 30
control lable variables. R e p l a c i n g t h e d e s c r i p t i o n i n words by a l i s t o f
u v a r i a b l e s p r o v i d e s a check
l i s t o f v a r i a b l e s t h a t i n f l u e n c e t h e performance c h a r a c t e r i s t i c s .
Information
w i t h r e s p e c t t o t h e course o f a n a l y s i s i s l o s t u n l e s s t h e a n a l y t i c a l procedure i s s p l i t i n t o p a r t s and f o r each p a r t t h e c o r r e s p o n d i n g u v a r i a b l e s a r e g i v e n (see t h e n e x t section). E s s e n t i a l l y t h i s d e s c r i p t i o n i s a b l a c k box, p r o v i d i n g i n f o r m a t i o n about t h e controllable factors.
A l t h o u g h i t m i g h t e a s i l y be i n c l u d e d , i t does n o t p r o v i d e
i n f o r m a t i o n on t h e performance c h a r a c t e r i s t i c s o f t h e procedure ( s e n s i t i v i t y , p r e c i s i o n , d e t e c t i o n l i m i t , t i m e parameters) and as such t h e d e s c r i p t i o n i s n o t complete.
A l t h o u g h t h i s b l a c k box can be c o n s i d e r e d t o be a d e q u a t e l y
d e s c r i b e d when a i m i n g a t t h e a p p l i c a t i o n o f t h e procedure, i t i s t o be c o n s i d e r e d as i n c o m p l e t e f o r t h e purpose o f comparison w i t h o t h e r procedures. F o r t h e a n a l y s t f a m i l i a r w i t h r e l a t e d procedures, t h e box p r o b a b l y i s n o t c o m p l e t e l y b l a c k and he may be a b l e t o e s t i m a t e t h e performance c h a r a c t e r i s t i c s from h i s e x p e r i e n c e w i t h r e l a t e d procedures.
Communicating an a n a l y t i c a l procedure t o
those who a r e n u t f a m i l i a r w i t h t h e p r i n c i p l e s o f t h e procedure i s p o s s i b l e w i t h a b l a c k box, p r o v i d e d t h a t a c a r e f u l d e s c r i p t i o n i s g i v e n .
574 29.5.
SOME OTHER WAYS OF DESCRIBING ANALYTICAL PROCEDURES
The course o f t h e a n a l y s i s i s obscure when t h e procedure i s r e p r e s e n t e d by t h e model i n F i g . 29.1.
More d e t a i l s a b o u t t h e course o f t h e procedure can be
i n c l u d e d when t h e system i s d i v i d e d i n t o subsystems.
A very rigorous d i v i s i o n
i n t o subsystems has been proposed by M a l i s s a and J e l l i n e k (1969) and by M a l i s s a and Simeonov (1978).
T h e i r symbolic language i s aimed a t r e t a i n i n g a l l
i n f o r m a t i o n r e q u i r e d f o r p e r f o r m i n g t h e procedure.
The symbolic r e p r e s e n t a t i o n
o f t h e procedure d e s c r i b e d i n t h e p r e v i o u s s e c t i o n i s shown i n F i g . 29.3.
resembles t h e r e p r e s e n t a t i o n o f a procedure by F i g . 28.1, sane i m p o r t a n t d i f f e r e n c e s .
It
although there are
The symbols i n F i g . 29.3 a r e b l a c k boxes t h a t y i e l d
i n f o r m a t i o n on t h e s e v e r a l u parameters and a r e i n f a c t r e p r e s e n t a t i o n s o f t h e u n i t operations t h a t a r e r e q u i r e d f o r performing t h e a n a l y s i s (heating, f i l t r a t i o n , etc.).
I n p u t and o u t p u t o f m a t e r i a l s a r e c l e a r l y i n d i c a t e d by arrows.
The whole scheme i s designed t o y i e l d t h e same i n f o r m a t i o n as t h e w r i t t e n t e x t .
RkI3 $0 F i g . 29.3.
Symbolic r e p r e s e n t a t i o n o f a complexometric t i t r a t i o n procedure.
I n o r d e r t o be a b l e t o d e s c r i b e a wide v a r i e t y o f procedures, a l a r g e number o f symbols unambiguously r e p r e s e n t i n g t h e v a r i o u s u n i t o p e r a t i o n s a r e r e q u i r e d ( t h e semantics o f t h e s y m b o l i c language).
I n a d d i t i o n , a s e t o f r u l e s has t o be
designed i n o r d e r t o connect t h e v a r i o u s u n i t o p e r a t i o n s ( t h e grammar).
I n our
o p i n i o n , f o r a f u l l d e s c r i p t i o n o f a n a l y t i c a l procedures a r a t h e r c o m p l i c a t e d language i s r e q u i r e d and f o r t h a t reason we d o u b t whether e v e n t u a l l y t h e goal o f more s i m p l y and c l e a r l y r e p r e s e n t i n g a n a l y t i c a l procedures w i 11 be reached.
575 Own e x p e r i e n c e i n d i c a t e s t h a t such a s y m b o l i c language i s u s e f u l f o r w e t chemical a n a l y s i s , b u t f a i 1s when i n s t r u m e n t a l and more dimensional procedures a r e considered.
Examples o f t h e comparison o f procedures u s i n g t h e s y m b o l i c language
has been g i v e n by G o t t s c h a l k (1972) and by O r t n e r and Scherer (1977). M a l i s s a and J e l l i n e k (1969) d i s c u s s e d a n o t h e r (computer) language, a i m i n g a t a f a c i l i t a t i o n o f t h e a u t o m a t i o n ( c o m p u t e r i z a t i o n ) o f a n a l y t i c a l procedures.
The
same r e c i p e f o r d e t e r m i n i n g i r o n (111) i r o n i n t h a t language i s shown i n Table 29.1.
I t i s easy, even w i t h o u t an e x p l a n a t i o n , t o r e a d Table 29.1.
Again, t h e
r e p r e s e n t a t i o n o f t h e procedure i s a b l a c k box.
Table 29.1. A n a l y t i c a l procedure i n computer language ( M a l i s s a and J e l l i n e k , 1969) Step 0 1 2 3 4 5 6 7 8 9 10 11 12 13
START SAMPL S 1 ADD L1 SOLV (1200) FILT WASH L2 ADD L3 HEAT (100;60) DILUT L4 (150) ADD S2 ADD L5 I F (PH.LT.2.0) GO TO 10 TITR L6 ( 7 0 ) END
L1 : FeC13 s o l u t i o n (6%) ; 50 m l
L2 L3 L4 L5 L6 S1 S2
: : : : : : :
Water ; 100°C ; 100 m l HCl/HF s o l u t i o n ( 1 : l ) Water ; doubly d i s t i l l e d NaOH (10%) EDTA (0.05 M) Sample ; 1 g H3B03 ; 3 g
Another computer language aimed a t l a b o r a t o r y a u t o m a t i o n has been d e s c r i b e d by Toren e t a l . (1972). uncertain.
However, t h e f u t u r e a p p l i c a t i o n o f . t h e s e languages i s
L a b o r a t o r y a u t o m a t i o n may w e l l develop a l o n g o t h e r l i n e s as a r e s u l t
o f the i n t r o d u c t i o n o f microprocessors.
29.6. QUALITY CONTROL
A n a l y s i n g i s a process, e i t h e r continuous o r d i s c o n t i n u o u s , t h a t has t o be k e p t under c o n t r o l .
The " q u a l i t y " o f t h e a n a l y t i c a l r e s u l t s produced by t h a t
516
process has t o be guaranteed. a c t i o n s have been i n c l u d e d .
T h e r e f o r e , i n t h e scheme i n F i g . 28.1 c o n t r o l Usually the u variables are kept constant o r varied For
i n a s p e c i f i e d way i n o r d e r t o p r e v e n t t h e p r o d u c t i o n o f i n c o r r e c t r e s u l t s . many a n a l y t i c a l procedures t h i s t y p e o f c o n t r o l i s n o t s u f f i c i e n t t o a v o i d (systematic) errors. specified.
A p p a r e n t l y i n such cases n o t a l l u v a r i a b l e s have been
I n such i n s t a n c e s a more o r l e s s f r e q u e n t c a l i b r a t i o n i s r e q u i r e d .
C o n s i d e r i n g t h e problem f r o m t h a t a n g l e , t h e process o f c a l i b r a t i o n i s a c o n t r o l action.
Several o t h e r methods have been developed t o keep t h e a n a l y s i n g process
under c o n t r o l , f o r i n s t a n c e , t h e use o f c o n t r o l c h a r t s (Chapter 5 ) .
29.7.
THE
ANALYTICAL PROCEDURE AS A SUBSYSTEM
A n a l y t i c a l procedures a r e used f o r s o l v i n g a n a l y t i c a l problems. ( g e n e r a l i z e d ) problems have been d i s c u s s e d i n P a r t I V .
I n general , a n a l y t i c a l
r e s u l t s a r e r e q u i r e d i n o r d e r t o be a b l e t o make d e c i s i o n s . h e l p s one t o decide whether a c t i o n s s h o u l d be taken.
Some o f these
A n a l y t i c a l chemistry
A n a l y t i c a l r e s u l t s from
t h e c l i n i c a l l a b o r a t o r y w i l l o r w i l l n o t be f o l l o w e d by t h e r a p y ; i n t h e r e s e a r c h l a b o r a t o r y , r e s u l t s w i l l be o f h e l p i n g u i d i n g t h e research, e t c . A l t h o u g h we have c o n s i d e r e d t h e a n a l y t i c a l procedure as a s e p a r a t e system, i t c l e a r l y shows i n t e r a c t i o n s w i t h t h e environment.
A g e n e r a l model f o r t h e s e
i n t e r a c t i o n s i s n o t available, although there are strong i n d i c a t i o n s t h a t every a n a l y t i c a l procedure i s p a r t of a c o n t r o l l o o p and t h u s h e l p s t o r e g u l a t e processes, whether t h e s e processes be t h e t h e r a p y o f p a t i e n t s o r r e s e a r c h a c t i v i t i e s .
The
g e n e r a l goal o f t h e a n a l y s i s w i l l be t o o p t i m i z e t h e s e processes. D e f i n i n g such o p t i m i z a t i o n problems r e q u i r e s conununication w i t h s c i e n t i s t s o f other disciplines. by b l a c k boxes.
I n t h a t c o n t e x t , a n a l y t i c a l procedures s h o u l d be r e p r e s e n t e d
F o r t h a t purpose, t h e f u n c t i o n and c h a r a c t e r i s t i c s as d e s c r i b e d
i n t h i s c h a p t e r a r e c e r t a i n l y more i m p o r t a n t t h a n t h e i n t e r n a l elements o f and r e l a t i o n s h i p s w i t h i n t h e b l a c k box.
Although the p i c t u r e o f the a n a l y t i c a l
procedure p r e s e n t e d i s f a r from complete, i t i s w o r t h s t i m u l a t i n g t h e development o f g e n e r a l ized p i c t u r e s
.
577
REFERENCES
J.E. Ash and E. Hyde, Chemical I n f o r m a t i o n Systems, Wiley, Mew York, 1975. G. G o t t s c h a l k , Z. a n a l , Chem., 258 (1972) 1. H. K a i s e r , i n Methodicum Chimicum, Band I : A n a l y t i k , T e i l I, p. 1 , G. Thieme, S t u t t g a r t and Academic Press, New York, 1973. M.F. Lynch, J.M. H a r r i s o n , W.G. Town and J.E. Ash, Computer H a n d l i n g o f Chemical S t r u c t u r e I n f o r m a t i o n , Macdonald, London and E l s e v i e r , New York, 1971. H . M a l i s s a and G. J e l l i n e k , Z. a n a l . Chem., 247 (19691 1. H. M a l i s s a and V. Simeonov, Z. a n a l . Chem., 289 (1978) 257. H.i+I. O r t n e r and V . Scherer, T a l a n t a , 24 (1977) 215. C.E. Shannon and W. Weaver, The Mathematical Theory of I n f o r m a t i o n , U n i v . I l l i n o i s Press, Urbana, I l l . , 1949. E.C. Toren, R.N. Carcy, A.E. S h e r r y and J.E. Davies, Anal. Chem., 44 (1972) 339.