Computer Applications in the Polymer Laboratory - American

6 Silicone Acrylate Copolymers: Designed Experiment Success T. R. Williams and M . D. Nave

Downloaded by TUFTS UNIV on September 26, 2016 | http://pubs.acs.org Publication Date: June 27, 1986 | doi: 10.1021/bk-1986-0313.ch006

3M, St. Paul, M N 55144

Various statistically designed experiments and data analysis were used to investigate the properties of copolymers based on a new silicone acrylate oligomer (SiUMA). Both factorial and mixture designs were used, depending on the variables being investigated. Computers were used throughout the analysis of the data, and their use was essential to the timely investigation of many compositional variables. This paper presents the results and examples of output from computer software applied to this problem. It is shown that use of the principles of designed experiments and of the power of computers led to the successful identification of a material which satisfied many physical property targets simultaneously. Copolymers of s i l i c o n e a c r y l a t e s (SiAc) and various hydrocarbon (non-silicone) a c r y l a t e monomers have been i n use for some years (1) as materials f o r various diverse a p p l i c a t i o n s , i n c l u d i n g biomedical devices (2), release coatings (3), etching r e s i s t s (4), and adhes i v e s (5). A new SiAc oligomer has been developed at 3M with c e r t a i n advantages over competitive materials. We desired to develop an understanding of the behavior of t h i s new m a t e r i a l by i t s e l f and i n copolymers, but i t was not known how the new oligomer would best be combined with hydrocarbon monomers to give i n t e r e s t i n g and u s e f u l combinations of properties. This problem i s amenable to designed experimental techniques and response surface methodo1 ogy(11-13), and t h i s paper describes the successful a p p l i c a t i o n of these techniques to the problem's s o l u t i o n . The ready a v a i l a b i l i t y of both mainframe and personal computer programs, to handle the formidable mathematic a l manipulations i n v o l v e d i n a n a l y s i s and d i s p l a y of experimental r e s u l t s , was a key element i n the successful outcome of t h i s project. This paper does not aim at educating the reader i n how to use the concepts of s t a t i s t i c a l l y designed experiments, but rather at showing how computers can make the task r e l a t i v e l y rapid and convenient. I t i s assumed that the reader has at least a passing knowledge 0097-6156/86/0313-0039S06.00/0 © 1986 American Chemical Society

Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.

40

COMPUTER APPLICATIONS IN THE POLYMER LABORATORY

of the concepts and nomenclature of elementary s t a t i s t i c s and designed experiments.


Experimental The d e t a i l s of oligomer and polymer sample preparation w i l l be publ i s h e d separately(6). B r i e f l y , the synthetic scheme i s shown i n Figure 1. Tetramethyldisiloxane (TMDS, Petrarch Systems, Inc.), octamethylcyclotetrasiloxane (D^, Dow Corning), and isocyanatoethyl methacrylate (IEM, Dow Chemical) were used as received. The " d i hydride" was prepared with c o n t r o l l e d molecular weights by a known method(7). The h y d r o s i l y l a t i o n of protected a l l y l a l c o h o l was performed i n accordance with w e l l established practices(8). The f i n a l product oligomer i s a s i l i c o n e urethanemethacrylate. In t h i s paper the terminlogy "SiUMA-N" i s used to denote such an oligomer, i n which there are a number average of N s i l i c o n atoms per chain, where N = X+l i n F i g u r e 1. The cured polymer samples used f o r p h y s i c a l property t e s t i n g were prepared by photocuring 12 m i l thick sheets of degassed and photosensitized monomer mixtures, using a mold composed of g l a s s p l a t e s l i n e d with polyester f i l m and separated by a double thickness of v i n y l e l e c t r i c a l tape. A GE sunlamp was used f o r i l l u m i n a t i o n , and Darocure 1173 (E. Merck) was used as the p h o t o i n i t i a t o r . Hydrocarbon monomers were used as received from the manufacturers. A l l the v i n y l group-containing compounds were stored at -5°C u n t i l use. A l l numerical a n a l y s i s reported i n t h i s paper was done using computer software of the type widely a v a i l a b l e throughout the country. MINI TAB, licensed from Pennsylvania State U n i v e r s i t y , was convenient and e f f e c t i v e f o r entering data i n matrix form, performing Yates and various regression analyses, and some graphics. However, the contour p l o t s were done using a separate proprietary software package developed to a i d i n the creation, execution, and a n a l y s i s of "designed" experiments. The Figures i n t h i s paper were generated with a ma inframe-based graphics program using a personal computer as a smart terminal. F i n a l l y , t h i s manuscript was composed and printed with a word-processing program on the personal computer. Results and Discussion Table I i s a l i s t of p h y s i c a l properties of m a t e r i a l s which were of s p e c i a l concern, along with target values f e l t to indicate u s e f u l l e v e l s i n a p a r t i c u l a r a p p l i c a t i o n . From the beginning i t was predicted that one of the biggest problems would be to balance Propert i e s A and E, u s u a l l y considered mutually e x c l u s i v e . I t was a l s o assumed that Properties B and E were h i g h l y correlated. S t a t i s t i c a l l y designed experiments and data a n a l y s i s were chosen to determine most e f f i c i e n t l y the formulations which would give the best combination of a l l the target properties. The f i r s t design was intended as a "range-finding" experiment which would broadly i d e n t i f y promising ranges of the v a r i a b l e s , which could i n turn receive more d e t a i l e d i n v e s t i g a t i o n l a t e r . This design was a 2 f r a c t i o n a l f a c t o r i a l design with v a r i a b l e D assigned to the ABC three-factor i n t e r a c t i o n . This choice of design allowed the combination of three d i f f e r e n t v a r i a b l e types:


6.

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Silicone Acrylate Copolymers

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SiUMA chain length, component r a t i o s , and a component absolute percentage• Table I.

I n i t i a l Property Targets


PROPERTY Property A Property B Property C Property D Property E

TARGET >15 >80 30 , 18 . 55

THE ST. DEV OF Y ABOUT REGRESSION LINE IS S = 8.012 4 DEGREES OF FREEDOM WITH ( 12- 8) R-SQUARED R-SQUARED

98.0 PERCENT 94.6 PERCENT,

ANALYSIS OF

VARIANCE

DUE TO REGRESSION RESIDUAL TOTAL

DF 7 4 11

ADJUSTED

SS 12747.48 256.78 13004.26

FOR

D.F.

MS=*SS/DF 1821.07 64.20

FURTHER ANALYSIS OF VARIANCE SS EXPLAINED BY EACH VARIABLE WHEN ENTERED IN THE ORDER GIVEN DUE TO REGRESSION #SI/CHN SI/VAR I '/.POLAR VII/VIII AB AC BC

DF 7

SS 12747.48 4158.72 7762.58 16.82 0.98 699.38 89.78 19.22

DURBIN-WATSON STATISTIC *

1.18

Figure 4. Regression analysis f o r Property B from Design I .


46


Table I I I . C o r r e l a t i o n Table from MINITAB Property Property Property Property

D C B E

Property A 0.116 -0.694 -0.780 -0.342

Property D

Property C

-0.206 -0.250 0.393

0.361 -0.032

Property B

0.368

i t i s c l e a r that o n l y the #Si/chain, SiUMA/Variable I r a t i o , and t h e i r i n t e r a c t i o n are important v a r i a b l e s f o r t h i s response (critical 3*10.13). S i m i l a r a n a l y s i s of a l l the responses l e d t o Table IV, wh'ich l i s t s a l l the c o e f f i c i e n t s and adjusted R f o r these responses. Apparently, not a l l the data are adequately described by the mathematical models, as shown by the low R for some. This point w i l l be discussed below. One of the main reasons f o r d e r i v i n g models of the responses i s to use the models f o r p r e d i c t i n g the responses i n regions of the design space not a c t u a l l y covered by experiment. Such p r e d i c t i o n can be done mathematically, but i t i s u s u a l l y easier for the experimenter to look at graphical representations of the data. Again, computer software i s a v a i l a b l e to p l o t response models over various regions of the design space (i.e., various l e v e l s of the v a r i a b l e s ) . Figures 5 and 6 show the response surfaces p l o t t e d for Property A and Property B, r e s p e c t i v e l y . Note that two v a r i a b l e s are p l o t t e d at once, with the values of the other v a r i a b l e s fixed at l e v e l s chosen by the experimenter. The contours i n the graph represent constant l e v e l s of the response. Fortunately, the computer a l l o w s rapid r e p l o t t i n g f o r various l e v e l s of the f i x e d v a r i a b l e s , as w e l l as changing the i d e n t i t i e s of the fixed and f l o a t i n g v a r i a b l e s , so that the entire design space can be investigated. Inspection of Figure 5 shows that the desired l e v e l of Property A i s achieved above and to the r i g h t of the " I " contour. S i m i l a r inspection of Figure 6 shows that the Property B target i s below and to the l e f t of the "E" contour. Overlaying these two graphs a l l o w s the i d e n t i f i c a t i o n of a s m a l l region of o v e r l a p of the acceptable regions: a range of v a r i a b l e l e v e l s which gives materials which simultaneously s a t i s f y both property targets. S i m i l a r o v e r l a y i n g of other response surface p l o t s l e d to conc l u s i o n s regarding the formulation v a r i a b l e s and t h e i r e f f e c t s on the properties of the copolymers. In a d d i t i o n , another (proprietary) computer program was used, which allowed the combination of s e v e r a l regression equations (for the various responses) and the c a l c u l a t i o n of v a r i a b l e values needed to achieve any desired combination of response values ( i f the models permit). Note, however, there are two c r i t i c a l l i m i t a t i o n s to these "predicting" procedures. F i r s t , the mathematical models must adequately f i t the data. C o r r e l a t i o n c o e f f i c i e n t s (R ), adjusted f o r degrees of freedom, of 0.8 or better are considered necessary f o r r e l i a b l e p r e d i c t i o n when using f a c t o r i a l designs. Second, no predictions outside the design space can be made c o n f i d e n t l y , because no data are a v a i l a b l e to warn of unexpectedly abrupt changes i n d i r e c t i o n of the response surface. The areas covered by Figures 8 and 9 o f f i c i a l l y v i o l a t e t h i s l a t t e r l i m i t a t i o n , but because more d e t a i l e d


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American Chemical Society Library 1155 16th St.. N.W. Washington, O.C. 20036 Provder; Computer Applications in the Polymer Laboratory ACS Symposium Series; American Chemical Society: Washington, DC, 1986.

48

COMPUTER APPLICATIONS IN THE POLYMER LABORATORY DESIGN

I: 2 ( 4 X) FRACTIONAL. FACTORIAL.

RESPONSE SURFACE CONTOUR PLOT RESPONSE ~ PROPT A VERTICAL AXIS: SI/VAR I HORIZONTAL AXIS: #SI/CHN -2. ODD

-1.200

-0.400

0.400

1.200


+ . . . . + . . . . + . . . . -I- . . • • + , , . . + , , . . + . , . . + . . , . + . , . .

2.0000 1.8750 1.7500 1.6250 1.5000 1.3750 1.2500 1.1250 1.0000 0.8750 0.7500 0.6250 0.5000 0.3750 0.2500 0.1250 0.0000 -0.1250 -0.2500 -0.3750 -0.5000 -0.6250 -0.7500 -0.8750 -1.0000 -1.1250 -1.2500 -1.3750 -1.5000 -1.6250 -1.7500 -1.8750 -2.0000

2.000 +••••+

FF EE D CC BB AA FF E DD CC BB AA F EE DD CC BB A G FF EE DD C B AA GG FF EE D CC BB AA GG FF E DD CC BB AA H 6 F EE DD CC B A H GG FF EE DD C BB AA HH GG FF EE D CC BB AA HH GG F E DD CC BB AA II HH G FF EE DD CC B A II H GG FF EE DD C BB AA I HH GG FF EE D CC BB A J II HH GG F E DD CC BB JJ II HH G FF EE DD CC B JJ II H GG FF EE DD C BB J I HH GG FF EE D CC JJ II HH GG F E DD CC JJ II HH G FF EE DD CC JJ II H GG FF EE DD J I HH GG FF E D JJ II HH GG F EE DD JJ II HH G FF EE D JJ I H GG FF EE J II HH GG FF E JJ II HH GG F EE JJ II HH G FF JJ I H GG FF J II HH GG FF JJ II HH GG JJ II H G JJ I HH GG J I H G + . . . . + . . . + . . . . + . . . .4-. ••.+...,+....+....+. ...+

-2.000

-1.200

VALUES OF CONTOUR LINES: A 90.0000 B • E » 50.0000 F • I » 10.0000 J *

-0.400

80.0000 40.0000 0.0000

0.400

C • G •

1.200

70.0000 30.0000

D * H *

2.000

60.0000 20.0000

DESCRIPTION OF PLOT CONDITIONS: THE RESPONSE IS PROPT A HORIZONTAL AXIS IS #SI/CHN VERTICAL AXIS IS SI/VAR I LEVELS OF OTHER INDEPENDENT VARIABLES: "/.POLAR • 0.0000 V II/V I I I * 0.0000 AB * 0.0000 AC « 0.0000 BC a 0.0000

Figure 5 . Response surface contour plot f o r Property A from Design I.


WILLIAMS A N D NAVE DESIGN

49

Silicone Acrylate Copolymers la 2(4-1) FRACTIONAL

FACTORIAL

RESPONSE SURFACE CONTOUR PLOT RESPONSE « PROPT B VERTICAL AXIS: SI/VAR I HORIZONTAL AXIS: #SI/CHN


-2.000 -1.200 + . . . ....+... 2.0000 1.8730 1.7500 1.6250 1.5000 1.3750 1.2500 1.1250 1.0000 0.8750 0.7500 0.6250 0.5000 0.3750 0.2500 0.1250 0.0000 -0.1250 -0.2500 -0.3750 -0.5000 -0.6250 -0.7500 -0.8750 -1.0000 -1.1250 -1.2500 -1.3750 -1.5000 -1.6250 -1.7500 -1.8750 -2.0000

II

-0.400

0.400 •+••••+•••

2.000 1.200 ,..+... .+....+

JJ 11

JJ JJJ HH II JJ HH II JJ G HH II JJ GGG HH III JJ 66 HH II JJ FF GG HH II JJ FFF 66 HHH II JJ E FF GG HH II JJJ EE FF 66 HH II JJ EE FF GG HH II JJ DD EEE FF 666 HH III JJ DD EE FF GG HH II JJ C DD EE FF G6 HH II JJ CC DD EE FF 66 HH II JJ CC DDD EE FFF 66 HHH II JJJ BB CC DD EE FF 66 HH II JJ BB CC DD EE FF 66 HH II JJ A BB CCC DD EEE FF 6G HH 11 JJ AA BB CC DD EE FF G66 HH III J AA BB CC DD EE FF GG HH II AA BB CC DD EE FF 66 HH II AA BBB CC DDD EE FFF 66 HHH AA BB CC DD EE FF 66 HH AA BB CC DD EE FF 66 H AAA BB CC DD EE FF 66 AA BB CCC DD EEE FF 666 AA BB CC DD EE FF AA BB CC DD EE FF AA BBB CC DDD EE FF A B C D E H

II

+ . . . ,+....+... -2.000

-1.200

VALUES OF CONTOUR LINES: A « 120.0000 B « E = 80.0000 F = I « 40.0000 J =

...+...

...+...

-0.400

0. 400

110.0000 70.0000 30.0000

1. 200

100.0000 60.0000

D « H »

2.000

90.0000 50.0000

DESCRIPTION OF PLOT CONDITIONS: THE RESPONSE IS PROPT B HORIZONTAL AXIS IS #SI/CHN VERTICAL AXIS IS SI/VAR I LEVELS OF OTHER INDEPENDENT VARIABLES: '/.POLAR a 0.0000 V II/V III a 0.0000 AB = 0.0000 AC a o.0000 BC a o, 0000

Figure 6 .

Response surface contour plot for Property B from Design I.



50


experimentation was already planned, the r i s k of inaccurate predictions was considered acceptable. Note, a l s o , that because o f the uncertainty i n the models, the a c t u a l area of overlap could be larger or smaller than predicted from Figures 5 and 6. With these provisos, conclusions were derived from the r e s u l t s of t h i s f i r s t experimental design. There was no difference i n the e f f e c t s of V a r i a b l e I I vs. I l l for any of the properties measured. Because V a r i a b l e I I was judged easier to work with i n the lab and more s t a b l e than V a r i a b l e I I I , V a r i a b l e I I was chosen as the p o l a r monomer i n future work. Both the Property C and Property D targets appeared e a s i l y attainable. As had been foreseen, Property A was mutually e x c l u s i v e of both Properties B and E. However, note that adequate models were not obtained for Properties C, D, or E, so conclusions based on these models i n Table IV are questionable. In order to optimize the formulation, a d i f f e r e n t experimental design was used. Based on the r e s u l t s of the f i r s t design, the parti c u l a r molecular weight of SiUMA was chosen which seemed to have the best chance of g i v i n g the desired balance of properties. Further, i t had been established that V a r i a b l e I I (and not V a r i a b l e I I I ) was preferable for further work. With these v a r i a b l e types (i.e., not i n v o l v i n g a component amount) eliminated, the problem was reduced to a "constrained mixture design"(l2,13) i n v o l v i n g three components: SiUMA-18, V a r i a b l e I, and V a r i a b l e I I . The component amounts were r e s t r i c t e d to only c e r t a i n l e v e l s , based on the r e s u l t s of the f i r s t design. The l i m i t s of the components, and the responses measured for the polymers prepared, are shown i n Table V. This s i t u a t i o n i s n i c e l y depicted on t r i a n g u l a r Table V. Design I I : 3 Component Constrained Mixture Design Variables Studied SiUMA-18 Variable I Variable I I

Range 0.3-0.45 0.35-0.6 0.1-0.2

Responses Measured Property A Property B Property C Property D Property E

Range 5-19 40-115 40-51 1.4-3.8 2-4.5

graph paper, i n which each vertex represents 100% of one of the components. Figure 7a shows the f u l l factor space (each component from 0 t o 100%), with only the cross-hatched area being covered by the formulations. MINITAB standard regression a n a l y s i s does not perform very w e l l when the v a r i a b l e s do not change much, because MINITAB gives e r r o r messages that c e r t a i n v a r i a b l e s are h i g h l y c o r r e l a t e d and then refuses to include them i n the a n a l y s i s . In a d d i t i o n , when graphing response surfaces, i t i s d i f f i c u l t to see the contours w i t h i n a s m a l l design space. To avoid these problems the i n v e s t i g a t i o n a l area of Figure 7a was mathematically expanded i n t o Figure 7b. Each "pseudo" v a r i a b l e i s l i n e a r l y r e l a t e d t o i t s corresponding " r e a l " v a r i a b l e by the r e l a t i o n s h i p s :


6.

WILLIAMS AND

NAVE


51


P-SiUMA « 4 x SiUMA - 1.2 P-Var I « 4 x Var 1 - 1.4 P-Var I I « 4 x Var I I - 0.4 The t r i a n g l e i n 7b i s defined as the s m a l l e s t one which i n cludes a l l the v e r t i c e s of the hatched area i n 7a. The r e l a t i v e l y large change i n the pseudo-variables allowed MINITAB to perform the regression a n a l y s i s s u c c e s s f u l l y . The formulations chosen for t h i s design are shown i n Figure 7b as extreme v e r t i c e s , edge centroids, and an o v e r a l l centroid, f o r a t o t a l of 12 formulations, i n c l u d i n g four r e p l i c a t e s of the o v e r a l l centroid. This choice f u l l y and evenly covers the factor space. For the regression a n a l y s i s of a mixture design of t h i s type, the NOCONSTANT regression command i n MINITAB was used. Because of the constraint that the sum of a l l components must equal u n i t y , the r e s u l t a n t models are i n the form of Scheffe' p o l y n o m i a l s ^ ) , i n which the constant term i s included i n the other c o e f f i c i e n t s . However, the c a l c u l a t i o n of c o r r e l a t i o n c o e f f i c i e n t s and F values given by MINITAB are not correct for t h i s s i t u a t i o n . Therefore, these values had to be c a l c u l a t e d i n a separate program. Again, the comput e r made these r e p e t i t i v e and i n v o l v e d c a l c u l a t i o n s e a s i l y . The correct equations are shown below (13):

R

adjusted"

1

J

SSError/(N-p) " " " " " " SSTotal/(N-l) SSRegress/(p-l)

'regression "

- g ^ ; " ; ; ^ -

where N • number of observations, and p * number of c o e f f i c i e n t s i n the mixture regression model. Figure 8 shows a t y p i c a l printout of the regression a n a l y s i s for Property E. A f t e r t h i s numerical a n a l y s i s was done, another set of models was developed and conclusions were drawn from the data. These models are given i n Table VI. Note that e x c e l l e n t models were obtained f o r three of the f i v e responses, and that Properties A and E were again mutually e x c l u s i v e . Figure 9 and 10 show the response surfaces for Properties A and E. Overlaying these p l o t s shows that no combination of components was p o s s i b l e which allowed the simultaneous achievement of the target values of these two properties. At t h i s time i n the i n v e s t i g a t i o n , the discovery was made that incorporation of a d i f f e r e n t hydrocarbon monomer at modest l e v e l s improved Property E of these copolymers. Thus, another designed experiment was necessary to determine the optimal formulation. We decided to return to the f a c t o r i a l design because we wanted to reexamine the e f f e c t s of SiUMA chain length i n combination with V a r i a b l e IV. The design i s set out i n Table VII. Note that, again, three d i f f e r e n t types of v a r i a b l e s were combined: chain length, component r a t i o , and absolute component l e v e l . Thus, a "standard" constrained mixture design was not appropriate. In t h i s case a f u l l f a c t o r i a l , c e n t r a l composite design was used, with a t o t a l of 20 data points. The star points were



P-SUMA

SiUMA

VARI

P-VAKD

VARA


Figure 7. Constrained mixture design, showing relationship between real and pseudocomponents.

THE REGRESSION EQUATION IS Y = + 2.08 XI + 4.04 X2 + - 0.801 X4 - 4.61 X5 + + 14.4 X7

COLUMN NOCONSTANT XI PSIUMA X2 PVAR I X3 PVAR II X4 AB X5 AC X6 BC X7 ABC

COEFFICIENT 2.085 4.0401 1.933 -0.801 -4.61 6.611 14.42

1.93 X3 6.61 X6

ST. DEV. OF COEF.

T-RATIO * COEF/S.D. 1. 12 10. 11 0.40 -0. 19 -0.43 0.83 0.88

1.858 0.3997 4.780 4.304 10.69 7.970 16.40

THE ST. DEV. OF Y ABOUT REGRESSION LINE IS S = 0.4096 WITH ( 12- 7) * 5 DEGREES OF FREEDOM ANALYSIS OF VARIANCE DUE TO REGRESSION RESIDUAL TOTAL

DF 7 5 12

SS 152.1611 0.8389 153.0000

MS*SS/DF 21.7373 0.1678

FURTHER ANALYSIS OF VARIANCE SS EXPLAINED BY EACH VARIABLE WHEN ENTERED IN THE ORDER GI DUE TO REGRESSION PSIUMA PVAR I PVAR II AB AC BC ABC COLUMN COUNT ROW 1

DF 7 1 1 1 1 1 1 1 .

F REGR 1

SS 152.1611 62.3472 81.7921 5.4857 1.4884 0.4075 0.5104 0.1298 RSQR 1

MSTOTAL 1 1.17424

11.9970

COLUMN MS ERROR COUNT 1 ROW 1 0.0625000

RSQRADJ 1

MSREGR 1

MS RESID 1

2.01295

0.167788

F LK F I T 1

Figure 8. NOCONSTANT regression analysis for Property E from Design I I .


6. WILLIAMS AND NAVE

PLOT NUMBER

2 RESPONSE


53

1


PSIUMA + •+• +J + + J + + J •+• + J + + 1 J + + 1 J •+• + II J + + I J + + HHH I J + + HH I J + + HH I J+ + H I + + GGG H I + + GG H 1+ + G H + + G H + + FFF GG + + FF G + + FF + + FF + + EEEEE + + EE+ 4-

•+•

+ +DDDDDDDDD +

DDDDDD CC C CC

4-

+ + + CC + PVAR

B

C

B

C C

B B

CCCCC CCCCC

+ + B+ + + + +

A

I

•

PVAR I I

CONTOUR VALUES ARE8 A« F=

2.0000 B« 12.0000 G «

4.0000 C« 14.0000 H «

6.0000 D« 16.0000 I«

F i g u r e 9. Response s u r f a c e c o n t o u r p l o t Design I I .

8.0000 E« 18.0000 J *

10.0000 20.0000

f o r P r o p e r t y A from


54


PLOT NUMBER

3 RESPONSE

2


PSIUMA •f + + + + + B + + B • + + • B • + B • + + + B + + + +

B B B B

• + + + CC +C

CCCCCCC CC

+ A+ + + + B + B + +

c

+ +

+ + +

c c

+ +

C C

4-

+ + + + D + DD + D + D + D

B

DDDDDDDDDDDD DD

C DD

C DD D

C D

C D D

PVAR I

+ A+ + + + B + + + B + + *

PVAR II

CONTOUR VALUES AREI A«

1.0000 B«

2.0000 C*

3.0000 D*

4.0000 E»

S.0000

Figure 10. Response surface contour plot for Property E from Design I I .


6.

WILLIAMS A N D NAVE


55

Table VI. Models f o r Design I I Variables Property A A (P-SiUMA-18) 20748 B (P-Variable I ) 4.99 C (P-Variable I I ) -7.24 A x B -2.03 A x C 39.72 B x C 20.91 A x B x C -80.13


R squared, a d j . for degrees of freedom

0.975

Variables Property D A (P-SiUMA-18) 1.036 B (P-Variable I ) 2.617 C (P-Variable I I ) -0.003 A x B -0.951 A x C 13.35 B x C 6.8 A x B x C -7.05 R squared, a d j . for degrees of freedom

Property B 43.46 116.7 205.15 5.13 -271.55 -220.43 161.86

Property C 62.86 51.53 52.01 -39.53 -55.07 -32.21 44.87

0.885

0.393

Property E 2.085 4.04 1.933 -0.801 -4.61 6.611 14.42

0.435

0.857

J

Table VII. Design I I I : 2 FULL FACTORIAL CENTRAL COMPOSITE DESIGN VARIABLES STUDIED #Si/Chain SiUMA/Variable % Variable IV

I

RANGE 16-29 35/65 to 55/45 2-8

RESPONSES MEASURED Property A Property B Property C Property D

RANGE 1-34 40-115 50-57 2.4-3.3

necessary because we observed that second order terms i n the r e gression equations were required to f i t the data. The star points were measured i n a separate block, along with two center point r e p l i c a t e s . The "block e f f e c t " was not e x p l i c i t l y included i n the Yates a n a l y s i s , even though i t t h e o r e t i c a l l y should have been. The same a n a l y s i s techniques were used i n t h i s t h i r d design as were used i n the f i r s t design. The f i n a l models and R values are shown i n Table V I I I . Note that models f o r Properties C, D, and E are not given. Measurements f o r the f i r s t two responses were not taken on the star point formulations. Property E i s missing because of the i n a b i l i t y to develop a laboratory test to quantify the response adequately. This s i t u a t i o n i s an example of two things. F i r s t , there i s always a problem of


56


Table V I I I . Models from

Design I I I


Coefficients Variables Property A Property ] Constant 19.214 68.603 A (#Si/Chain) 2.7 -2.3 B (SiUMA/Variable I ) 9.724 -24.525 C (% Variable IV) 2.363 -1.815 A xB 1.125 -1.875 A xC 6.625 -4.125 B xC 0.375 -1.375 A x B xC 4.125 -3.875 ASQR 9.4 -3.119 BSQR 2.035 0.519 CSQR 2.212 -0.012 R squared, adjusted for degrees of freedom

0.922

0.883

d e v i s i n g laboratory tests which accurately predict r e a l i t y . Second, r e s u l t s of a n a l y s i s and computer printouts can look quite impress i v e ; but computers cannot think. The expertise of the experimenter i s a 1 way8 necessary to interpret these r e s u l t s properly. Although computers made the a n a l y s i s of the design data convenient, they could not t e l l that the test being used t o generate the Property E data was i t s e l f f a u l t y . Two s i g n i f i c a n t conclusions from t h i s l a s t design were: 1) the laboratory test f o r Property E was not a good predicter of a c t u a l performance, and 2) a s m a l l amount o f V a r i a b l e IV was important t o get a m a t e r i a l with good Property E. Based on the r e s u l t s o f t h i s l a s t design, a formulation was i d e n t i f i e d which was predicted t o meet a l l the c o n f l i c t i n g property goals. The properties of the f i n a l , optimized formulation are given i n Table IX. Comparison o f the measured properties with the targets shows that we were indeed able to reach those targets. Table IX. F i n a l Properties Property Property Property Property Property Property

A B C D E

Target >15 >80

Computer Applications in the Polymer Laboratory - American

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