Advances in the Application of Optimization Methodology in Chemistry

1 Advances in the Application of Optimization Methodology in Chemistry STANLEY N. DEMING

Downloaded by 182.73.201.170 on August 31, 2015 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0052.ch001

Department of Chemistry, University of Houston, Houston, TX 77004 STEPHEN L. MORGAN Department of Chemistry, University of South Carolina, Columbia, SC 29208 Many chemical measurement processes can be viewed as systems (1) c o n s i s t i n g of inputs, transforms, and outputs (see Figure 1). The primary input to a chemic a l measurement process i s a sample, some property of which i s to be assigned a numerical value (2). Examples of s p e c i f i c properties that might be measured are the percentage of i r o n i n an ore, the concentration of calcium i n a patient's blood serum, and the parts per m i l l i o n of hydrocarbons i n urban air. In addition to the primary input, many secondary inputs (or factors) can have an e f f e c t upon the numerical value that i s eventually assigned to the property of i n t e r e s t . These a d d i t i o n a l factors include temperature, reagent amount, wavelength, time, homogeneity, and the presence of i n t e r f e r i n g substances. I f the numerical r e s u l t of the measurement process is to be a precise representation of the property of i n t e r e s t , it is c l e a r l y important that the more s i g n i f i c a n t of these factors must be c o n t r o l l e d . As Mandel has stated. "The development of a method of measurement i s to a large extent the discovery of the most important environmental factors and the s e t t i n g of tolerances for the v a r i a t i o n of each one of them" (3,4). Ideally, the method should be "rugged" against uncont r o l l e d changes i n the environmental factors so that the tolerances can be broad. I t i s often convenient to c l a s s i f y factors as known or unknown, and c o n t r o l l e d or uncontrolled. A further c l a s s i f i c a t i o n r e s u l t s if it is noted at what point a factor enters the measurement scheme (see Figure 2); s p e c i f i c a l l y , i s the factor associated with the measurement process itself (e.g., temperature, reagent amount) or i s i t instead associated with the sample (e.g., homogeneity, presence of i n t e r f e r i n g substances)? 1 In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

CHEMOMETRICS: THEORY AND APPLICATION


INPUTS ·

TRANSFORMS

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Figure 1. Systems view of the measurement process

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Figure 2. Expanded view of the measurement process

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.


1.

DEMiNG AND MORGAN

Optimization Methodology

3

This l a t t e r d i s t i n c t i o n i s often important i n the development of a n a l y t i c a l methods. I f a known e n v i r onmental f a c t o r i s associated with the measurement process i t s e l f , then i t i s usually possible to control that factor during both the development and implement a t i o n of the method; thus, by s u f f i c i e n t l y close cont r o l , the factor's influence, on the numerical r e s u l t can be minimized. I f a known environmental factor i s associated with the sample, i t might not be possible to control that factor when the method i s a c t u a l l y implemented. I t i s , however, usually possible to cont r o l the factor during the development of the method in such a way that the range of values normally encountered f o r that f a c t o r can be simulated. By t h i s mechanism, the e f f e c t of a factor associated with the sample can be assessed, and the method can be developed so as to minimize the e f f e c t of t h i s normally uncontrolled factor. The primary output from a chemical measurement process i s the numerical value of the property of i n t e r e s t i n the sample. But many other, secondary outputs (or responses) might also be important: examples include cost per measurement, s e n s i t i v i t y to i n t e r f e r i n g substances, and l i n e a r i t y of the assigned numerical value vs. the property being measured. Thus, the development of a method of measurement can be more than the discovery of the most important environmental factors and the s e t t i n g of tolerances f o r the v a r i a t i o n of each one of them; i t can also be the adjustment or optimization of the most important cont r o l l a b l e environmental factors so as to achieve the best possible compromise among the many d i f f e r e n t r e sponses (5) . The "advances" reported here i l l u s t r a t e the use of c l a s s i c a l experimental designs i n conjunction with optimization techniques to automatically produce a chemical measurement process possessing desirable performance c h a r a c t e r i s t i c s (6). Automated Continuous Flow System Automated continuous flow methods of chemical analysis (7) have become widely accepted as r e l i a b l e means of carrying out a large number of determinations i n a short period of time with minimal analyst i n t e r action. In the future, many e x i s t i n g continuous flow methods w i l l need to be improved and many new continuous flow methods w i l l need to be developed both to meet the more exacting requirements of established d i s c i p l i n e s , as w e l l as to f u l f i l l the growing demands


CHEMOMETRICS: THEORY AND APPLICATION


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of r e l a t i v e l y new areas such as environmental and c l i n i c a l chemistries (8) . The instrument used i n t h i s work i s b u i l t around standard Technicon AutoAnalyzer-II continuous flow components and a Hewlett-Packard 9830A computer. Many of the operations normally c a r r i e d out by the analyst are under d i r e c t computer c o n t r o l . These operations include s t a r t i n g and stopping a tray of samples, acq u i r i n g d i g i t i z e d absorbance values from the c o l o r i meter, and c o n t r o l l i n g the flow rate of i n d i v i d u a l reagents. This l a t t e r operation i s accomplished by using i n d i v i d u a l p e r i s t a l t i c pumps f o r each reagent l i n e ; each p e r i s t a l t i c pump i s driven by a stepping motor which can be made to turn at a rate that w i l l d e l i v e r the desired flow. Computer options include: 16K bytes of read/write memory; thermal page p r i n t e r ; p l o t t e r ; d u a l - p l a t t e r d i s c ; and read-only-memories f o r input/output, matrix, and s t r i n g operations, and f o r advanced programming c a p a b i l i t y . A 32-bit s e r i a l , b i d i r e c t i o n a l , time multiplexed i n t e r f a c e i s used to communicate information between the instrument and computer. Chemical System The concentration of calcium i n blood serum can be determined by d i a l y s i s of calcium ion i n t o a rec i p i e n t stream followed by reaction with the complexing agent cresolphthalein complexone i n b a s i c s o l u t i o n (9^) . Figure 3 i s a diagram of the flow scheme used i n t h i s work. Before d i a l y s i s , the serum sample i s mixed with a s o l u t i o n containing hydrochloric acid (HCL-B), 8hydroxyquinoline (8HQ-B), and water (used as a d i l u e n t to make up a f i x e d t o t a l flow). During d i a l y s i s , the calcium i s t r a n s f e r r e d to a r e c i p i e n t stream containing hydrochloric acid (HCL-A), 8-hydroxyquinoline (8HQ-A), cresolphthalein complexone (CPC), and water. Diethylamine (DEA) i s added to make the s o l u t i o n basic and the absorbance of the colored product i s measured at 570 nm. Figure 4 i s a systems view of the continuous flow method f o r calcium. Six c o n t r o l l a b l e f a c t o r s a s s o c i ated with the measurement process have an influence e i t h e r upon the number that i s assigned to the calcium concentration, or upon some of the secondary outputs, or both. These factors are HCL-B, 8HQ-B, HCL-A, 8HQ-A, CPC, and DEA. Two uncontrollable factors that are associated with the sample are the concentrations of magnesium and protein i n the serum. Magnesium i s


DEMINC AND MORGAN

Optimization Methodology

SAMPLE HCL-B -«

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Advances in the Application of Optimization Methodology in Chemistry

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