Application of Statistical Experimental Design to Development of

Chapter 8 Application of Statistical Experimental Design to Development of Low-Density Polymer Foams Blanca L. Haendler, Lucy M . Hair, and Fung-Ming Kong

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 23, 2017 | http://pubs.acs.org Publication Date: August 29, 1989 | doi: 10.1021/bk-1989-0404.ch008

Lawrence Livermore National Laboratory, University of California, P.O. Box 5508 (L-482), Livermore, CA 94550

Statistical experimental designs have been used to improve the development of low-density poly mer foams for use as direct-drive targets for Laser Inertial Confinement Fusion (ICF). For polystyrene foams, which are made by polymeri zation of a high-internal-phase emulsion, a three-variable Box-Behnken response surface methodology experiment led to quick identifi cation of a reproducibility problem, which was resolved by moving to a different density regime. This experiment also confirmed the crucial role the surfactant (Span 80) plays in this system. For resorcinol-formaldehyde foams, which are made by a condensation poly merization in dilute solution, a fractional -factorial screening study identified key variables which were then investigated further. The striking result here was that testing ranges of variables outside what had previously been considered led to better quality samples with much lower densities. We a r e a p p l y i n g t h e p r i n c i p l e s o f s t a t i s t i c a l experimental d e s i g n t o t h e development o f l o w - d e n s i t y p o l y m e r foams f o r use a s d i r e c t - d r i v e h i g h - g a i n t a r g e t s f o r L a s e r I n e r t i a l C o n f i n e m e n t F u s i o n ( I C F ) . B o t h p o l y s t y r e n e (PS) a n d r e s o r c i n o l - f o r m a l d e h y d e (RF) foams a r e b e i n g d e v e l o p e d . F o r t h e PS c a s e , a t h r e e - v a r i a b l e Box-Behnken r e s p o n s e s u r f a c e methodology (RSM) d e s i g n u s i n g f o r m u l a t i o n v a r i a b l e s has been c a r r i e d o u t . F o r t h e RF system, an e i g h t - v a r i a b l e f r a c t i o n a l - f a c t o r i a l s c r e e n i n g s t u d y was done f i r s t t o s e l e c t s i g n i f i c a n t f a c t o r s , a n d t h i s was f o l l o w e d b y two RSM s w h i c h were s i m i l a r i n d e s i g n t o t h e one done f o r PS. The r e s u l t s have l e d d i r e c t l y t o s u b s t a n t i a l improvements i n b o t h m a t e r i a l s . 1

0097-6156/89/0404-0074$06.00/0 c 1989 American Chemical Society

Provder; Computer Applications in Applied Polymer Science II ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

8. HAENDLER ETAL.

Application of Statistical Experimental Design

75


Background The d e s i g n f o r a d i r e c t - d r i v e h i g h - g a i n ICF t a r g e t (1) r e q u i r e s a s p h e r i c a l s h e l l o f l o w - d e n s i t y p o l y m e r foam which would s t a b l y h o l d a m i x t u r e o f l i q u i d d e u t e r i u m and t r i t i u m (DT) and would be c o a t e d w i t h a DT-impermeable layer to prevent b o i l - o f f . The l i q u i d DT s e r v e s as b o t h f u e l and a b l a t o r and i s compressed t o h i g h d e n s i t y and i g n i t e d by t h e l a s e r e n e r g y . T h e r e a r e a number o f s p e c i f i c r e q u i r e m e n t s f o r foam p r o p e r t i e s w h i c h a r i s e f r o m t h e t a r g e t p h y s i c s and l i q u i d w e t t i n g s t a b i l i t y c o n straints. C u r r e n t l y , b o t h t h e PS and RF foams meet many o f t h e s e r e q u i r e m e n t s and a r e b e i n g a c t i v e l y p u r s u e d . The p r o c e s s we use f o r making t h e PS foams i s b a s e d on an i n v e r s e - e m u l s i o n system d e v e l o p e d by U n i l e v e r R e s e a r c h L a b o r a t o r y (2.) and a l s o r e p o r t e d by L i t t and c o w o r k e r s Q ) . S i g n i f i c a n t development work on t h e s e foams has a l s o been done by W i l l i a m s and coworkers a t t h e Los Alamos N a t i o n a l Laboratory(4,5). A water phase c o n t a i n i n g sodium p e r s u l f a t e as a p o l y m e r i z a t i o n i n i t i a t o r i s added t o an o i l phase which i s a m i x t u r e o f two monomers, s t y r e n e and d i v i n y l b e n z e n e , and an o i l - s o l u b l e s u r f a c t a n t . The s u r f a c t a n t i s s o r b i t a n monooleate m a n u f a c t u r e d by ICI A m e r i c a s I n c . under t h e tradename Span 80. The d i v i n y l b e n z e n e i s u s e d as a c r o s s l i n k i n g agent w h i c h s h o u l d i n c r e a s e t h e m e c h a n i c a l s t r e n g t h o f t h e foams. The water phase c o n s t i t u t e s from 92-95% o f t h e t o t a l m a t e r i a l , so t h a t upon a d d i t i o n t h e two phases form a h i g h - i n t e r n a l phase e m u l s i o n (HIPE), w i t h t h e water as t h e i n t e r n a l phase. T h i s e m u l s i o n i s mixed (a v a r i e t y o f d e v i c e s can be u s e d ) , and t h e n p o l y m e r i z e d a t 50°C i n a w a t e r b a t h o r oven, and t h e r e s u l t i n g foam d r i e d i n a vacuum oven a t room t e m p e r a t u r e t o 40°C u n t i l a l l t h e water i s removed. The r e s u l t i s a foam o f d e n s i t y 50-80 mg/cm d e p e n d i n g on t h e amount o f water phase u s e d . The d e t a i l s o f t h e p r o c e s s f o r making t h e foams a r e d e s c r i b e d i n R e f . £, and a d d i t i o n a l i n f o r m a t i o n about foam s t r u c t u r e and p r o p e r t i e s i s g i v e n i n R e f . 2 and £ . The c h e m i s t r y o f t h e r e a c t i o n between r e s o r c i n o l and f o r m a l d e h y d e has been known f o r some t i m e , and i t has r e c e n t l y been a d a p t e d t o make l o w - d e n s i t y o r g a n i c a e r o g e l s by P e k a l a , who g i v e s t h e d e t a i l s o f t h e development i n a p u b l i c a t i o n c o a u t h o r e d w i t h H a i r Q ) . R e s o r c i n o l and f o r m a l d e h y d e a r e mixed i n aqueous s o l u t i o n i n an a p p r o x i m a t e l y 1:2 m o l a r r a t i o i n t h e p r e s e n c e o f sodium c a r b o n a t e , which c o n t r o l s t h e pH o f t h e r e a c t i o n and hence the rate of p o l y m e r i z a t i o n . A f t e r s t i r r i n g , the s o l u t i o n i s s e a l e d i n g l a s s c o n t a i n e r s and h e a t e d a t 70-85°C f o r seven t o n i n e d a y s . D u r i n g t h i s t i m e t h e a e r o g e l forms, and a s u b s t a n t i a l amount o f c r o s s l i n k i n g o c c u r s . A f t e r the c u r i n g p r o c e s s i s complete, a s e r i e s o f s o l v e n t t r e a t m e n t s and exchanges l e a d i n g t o s u p e r c r i t i c a l d r y i n g f r o m l i q u i d C0 i s p e r f o r m e d . A f t e r t h e d r y i n g i s f i n i s h e d , a foam 3

2


76

COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE II 3

w i t h a d e n s i t y o f 70 mg/cm c a n be o b t a i n e d i f t h e o r i g i n a l s o l u t i o n c o n t a i n s 5 wt% r e a c t a n t s . R e c e n t l y , foams w i t h d e n s i t i e s o f 20 mg/cm have been made. 3


Experimental

Designs

and S t a t i s t i c a l A n a l y s i s

At t h e t i m e t h e d e c i s i o n was made t o a p p l y s t a t i s t i c a l e x p e r i m e n t a l d e s i g n t o foam development, an a s s e s s m e n t was made o f t h e s t a t u s o f e x p e r i m e n t a t i o n f o r e a c h foam i n o r d e r t o d e t e r m i n e which d e s i g n s were a p p r o p r i a t e . In t h e c a s e o f PS foams, t h e v a r i a b l e s f a l l f a i r l y n e a t l y i n t o f o r m u l a t i o n and p r o c e s s c a t e g o r i e s . P r e v i o u s c l a s s i c a l one-factor-at-a-time experimentation i n d i c a t e d that the r a t i o o f styrene t o divinylbenzene, the concentration o f i n i t i a t o r , and t h e c o n c e n t r a t i o n o f s u r f a c t a n t a l l have an e f f e c t on i m p o r t a n t foam p r o p e r t i e s . T h i s e x p e r i m e n t a t i o n a l s o s u g g e s t e d ranges t h a t would be a p p r o p r i a t e f o r e a c h o f these f a c t o r s . The p r o c e s s v a r i a b l e s i t u a t i o n was p o t e n t i a l l y more c o m p l i c a t e d , i n t h a t s e v e r a l d i f f e r e n t p r o c e s s e s were i n use, v a r y i n g c h i e f l y i n t h e t y p e o f mixing d e v i c e used. The d e v i c e t h a t a p p e a r e d t o g i v e t h e b e s t o v e r a l l r e s u l t s was a s y r i n g e pump, where t h e two p h a s e s a r e mixed by u s i n g an h y d r a u l i c d r i v e t o f o r c e t h e e m u l s i o n back and f o r t h between two g l a s s s y r i n g e s c o n n e c t e d by a s m a l l o r i f i c e . Accordingly, the decision was t o choose t h i s m i x i n g d e v i c e , s e t t h e p r o c e s s v a r i a b l e s at t h e b e s t h i s t o r i c a l v a l u e s , and c o n c e n t r a t e f i r s t on o p t i m i z i n g the formula. The p l a n was t o r e t u r n t o t h e problem o f o p t i m i z i n g t h e process a t a l a t e r time. On t h e b a s i s o f t h i s assessment, we d e s i g n e d a t h r e e v a r i a b l e , Box-Behnken r e s p o n s e s u r f a c e e x p e r i m e n t (ID.) . The d e t a i l s o f t h e d e s i g n and a l i s t o f t h e r e s p o n s e s c h o s e n a r e g i v e n i n T a b l e 1. S e v e r a l i m p o r t a n t d e c i s i o n s h a d t o be made about t h e f a c t o r s and t h e i r ranges a s w e l l a s c e r t a i n p a r a m e t e r s which h a d t o be f i x e d . The u n i t s a n d ranges f o r t h e f a c t o r s were chosen i n an e m p i r i c a l manner as weight p e r c e n t s b a s e d on t h e way t h e foams a r e a c t u a l l y formulated. Although, i t i s l i k e l y t h a t molar c o n c e n t r a t i o n s and more s t r i c t l y c h e m i c a l f a c t o r s may a c t u a l l y be c o n t r o l l i n g t h e system, o u r u n d e r s t a n d i n g o f t h e b a s i c c h e m i s t r y a t t h e time was n o t s u f f i c i e n t t o i d e n t i f y t h e s e . The p e r c e n t a g e s f o r e a c h f a c t o r a r e on t h r e e d i f f e r e n t bases. F o r t h e % s t y r e n e , t h e range i s 0 t o 100% o f t h e monomer used, which means t h a t we have foams w h i c h a r e made w i t h 100% d i v i n y l b e n z e n e , 100% s t y r e n e , and a 50:50 mixture. F o r t h e i n i t i a t o r , t h e p e r c e n t a g e i s b a s e d on t h e amount o f water phase, and t h e p e r c e n t a g e f o r t h e s u r f a c t a n t i s b a s e d on t h e amount o f o i l p h a s e . Hence, t h e p e r c e n t a g e s f o r t h e t h r e e f a c t o r s do n o t sum t o 100. The s i z e o f t h e b a t c h was f i x e d by t h e c a p a c i t y o f t h e s y r i n g e s , b u t i n t h e c a s e o f t h e d e n s i t y a c h o i c e h a d t o be made. We wanted t o keep a c o n s t a n t t a r g e t d e n s i t y , b u t , s i n c e t h e i n i t i a t o r and s u r f a c t a n t a r e n o t removed from t h e foams, t h e v a r i a t i o n i n t h e s e f a c t o r s would have t o be


HAENDLER ET AL.

Table 1. foams.


Three-variable Box-Behnken design f o r PS Fixed parameters: (1) batch s i z e : 25 g; (2) target density: 0.050 g/cm 3


Design run No.

xi

a

x

22.5

1

100

1,.5

100

0,.1

22.5

3

0

1,.5

22.5

4

0

0,.1

22.5

5

100

0,.8

35.0

6

100

0,.8

10.0

7

0

0..8

35.0

8

0

0,.8

10.0 35.0

9

50

1..5

10

50

1..5

10.0

11

50

0..1

35.0

12

50

0,.1

10.0

13

50

0,.8

22.5

14

50

0..8

22.5

15

50

0..8

22.5

*1 = =

2

3

2

Factor

x

x

2

*3 =

Range

% styrene % initiator % surfactant

d

b

0-100 \ of monomer 0.1-1 .5 wt% of water phase 10-35 wt% of o i l phase !

0

Response Yi

=

y

=

2

Y3

=

= a

b c d

emulsion droplet s i z e y = foam c e l l s i z e ye = foam pore s i z e Yi = density Yq = 5

density u n i f o r m i t y BET surface area hexane wetting rate compressive modulus

This sequence r e f e r s to the design only; experiments are performed i n random order. Remainder i s divinylbenzene. Sodium p e r s u l f a t e . Span 80 (sorbitan monooleate).



78

COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE II

compensated f o r , p a r t i c u l a r l y i n t h e c a s e o f t h e s u r f a c t a n t , which c o n s t i t u t e s as much as 35 wt% o f t h e o i l p h a s e . T h i s meant, however, t h a t t h e amount o f monomers a l s o v a r i e d i n o r d e r t o keep t h e t o t a l w e i g h t o f t h e o i l phase constant. No attempt was made t o d e a l w i t h t h i s v a r i a t i o n e x p l i c i t l y i n the a n a l y s i s of the experiment. In t h e c a s e o f t h e i n i t i a t o r , which amounts t o a maximum o f 1.5 wt% o f t h e water phase, t h e d e c i s i o n was made t o a c c e p t t h e r e l a t i v e l y s m a l l v a r i a t i o n i n i n i t i a t o r , because t h i s c o m p e n s a t i o n would have l e d t o a v a r i a t i o n i n t h e r a t i o o f water t o o i l phases. Since the s u r f a c e p r o p e r t i e s of the i n t e r f a c e a r e presumed t o be v e r y i m p o r t a n t i n t h e b e h a v i o r o f t h i s system, t h i s was j u d g e d t o be t h e g r e a t e r r i s k . The r e s p o n s e s chosen a l l r e l a t e t o i m p o r t a n t foam properties. We b e l i e v e d t h a t y the emulsion d r o p l e t s i z e , d e t e r m i n e s y , t h e c e l l s i z e i n t h e r e s u l t a n t foam, and we w i s h e d t o d e t e r m i n e whether t h i s i s t r u e o v e r t h i s range o f f o r m u l a t i o n s . The foam p o r e s i z e y3 s h o u l d d e t e r m i n e t h e w e t t i n g r a t e y , so t h e s e r e s p o n s e s c o u l d be c o r r e l a t e d , and y , t h e BET s u r f a c e a r e a , s h o u l d be r e l a t e d t o t h e s e as w e l l . The d e n s i t y y^ and d e n s i t y u n i f o r m i t y y a r e c r i t i c a l t o t a r g e t p e r f o r m a n c e as d e s c r i b e d above, and y , t h e c o m p r e s s i v e modulus, i s an i m p o r t a n t measure o f t h e m e c h a n i c a l p r o p e r t i e s o f t h e foam. i f

2

7

6

5

8

The e x p e r i m e n t s were c a r r i e d out i n random o r d e r and t h e r e s p o n s e s a n a l y z e d w i t h t h e program X-STAT ( H I which r u n s on an IBM PC computer. The model was t h e s t a n d a r d q u a d r a t i c p o l y n o m i a l , and t h e c o e f f i c i e n t s were d e t e r m i n e d by a linear least-squares regression. F o r t h e RF system, t h e development was n o t as f a r advanced. T h e r e were s t i l l d i f f i c u l t i e s i n making a c c e p t a b l e - q u a l i t y foams, and s i g n i f i c a n t f a c t o r s and r a n g e s had not been d e t e r m i n e d . T h e r e was a l s o no c l e a r i n d i c a t i o n o f t h e r e l a t i v e i m p o r t a n c e o f f o r m u l a t i o n and process v a r i a b l e s . F o r t h e s e r e a s o n s , i t was c o n s i d e r e d a p p r o p r i a t e t o execute a s c r e e n i n g experiment t o i d e n t i f y key v a r i a b l e s . The d e s i g n which we d e v e l o p e d , shown i n T a b l e 2, i s a r e s o l u t i o n IV f r a c t i o n a l - f a c t o r i a l t y p e t h a t u s e s e i g h t variables(12). The f i r s t t h r e e a r e f o r m u l a t i o n v a r i a b l e s r e l a t i n g t o t h e c h e m i s t r y o f t h e system, and t h e l a s t f i v e a r e c o n c e r n e d w i t h t h e p r o c e s s o f making t h e foams. Again, t h e r a n g e s were chosen b a s e d on h i s t o r i c a l i n f o r m a t i o n , b u t t h e y were b r o a d e n e d as much as we t h o u g h t f e a s i b l e i n o r d e r t o i n v e s t i g a t e as wide a range as p o s s i b l e . I t s h o u l d be noted t h a t the c o n t r o l l i n g v a r i a b l e f o r x i s almost c e r t a i n l y pH r a t h e r t h a n % c a t a l y s t (sodium c a r b o n a t e ) , b u t i t i s v e r y d i f f i c u l t t o c o n t r o l t h e pH i n t h i s s y s t e m i n t h e manner r e q u i r e d f o r an i n d e p e n d e n t v a r i a b l e , so t h e wt% c a t a l y s t was chosen f o r c o n v e n i e n c e . The a n a l y s i s o f t h e s c r e e n i n g s t u d y d a t a was c a r r i e d out i n t h e s t a n d a r d manner by hand s i n c e t h e computer program was not y e t a v a i l a b l e . The f i r s t t h r e e v a r i a b l e s were 1


HAENDLER ET AL.

Table

2.


F r a c t i o n a l - f a c t o r i a l screening design for RF foams x


0. 04 0. 7

*4

X

3

2

*6

*7

*8

3

1 :1

1

4

70

1

120

3

1 :1

0 .15

0.,5

70

7

120

0. 04

11

1 :1

0 .15

4

40

7

120

0. 7

11

1 :1

1

0.,5

40

1

120

0.,5

40

7

120

0. 04 0. 7

3

3 :1

1

3

3 :1

0 .15

4

40

1

120

0. 04

11

3 :1

0 .15

0.,5

70

1

120

0. 7

11

3 :1

1

4

70

7

120 60

0. 7

11

3 :1

0 .15

0. 5

40

7

0. 04

11

3 :1

1

4

40

1

60

0. 7

3

3 :1

1

0. 5

70

1

60

0. 04

3

3 :1

0 .15

4

70

7

60

0. 7

11

1 :1

0 .15

4

70

1

60

0. 04

11

1 :1

1

0. 5

70

7

60

0. 7

3

1 :1

1

4

40

7

60

0. 04

3

1.:1

0 .15

0. 5

40

1

60

Factor *1 = x = = 3 *4 = *5 = *6 = *7 = *8 2

X

X,

Low Value

wt% c a t a l y s t wt% reactants i n solvent molar r a t i o of F: R c o o l i n g rate (°C/min) s t i r r i n g time (h) s t i r r i n g temperature (°C) time i n oven (d) oven temperature (°C)

0 .05 5 .0 1 :1 0 .15 0 .5 40 1 60

High Value 1. 0 15 .0 3: 1 1 4 70 7 120

Response y y y y

x

2

3

4

= = = =

g e l formed or not g e l modulus density c e l l size


80


j u d g e d t o be t h e most s i g n i f i c a n t . Based on t h i s i n f o r m a t i o n , two RSM d e s i g n s s i m i l a r t o t h e one done f o r t h e PS s y s t e m were t h e n c a r r i e d o u t . The model and a n a l y s e s were a l s o t h e same.


R e s u l t s and D i s c u s s i o n In t h e PS c a s e , v e r y s t r i k i n g a n d u n e x p e c t e d i n f o r m a t i o n was o b t a i n e d by l o o k i n g a t t h e s t r u c t u r e s o f t h e t h r e e c e n t e r - p o i n t foams, a s d e t e r m i n e d by s c a n n i n g e l e c t r o n m i c r o s c o p y (SEM). F i g u r e 1 shows t h a t t h e y a r e w i d e l y different. One foam has t h e e x p e c t e d 2-3 ^im c e l l s i z e a n d i s r e a s o n a b l y u n i f o r m , one has c e l l s r a n g i n g up t o 10 \im, and t h e t h i r d has r e g i o n s o f a p p a r e n t c o a l e s c e n c e 100 \im a c r o s s and i s v e r y non-uniform. T h i s was t h e f i r s t t i m e t h a t t h e r e p r o d u c i b i l i t y o f t h e foam p r o c e s s h a d been c h e c k e d i n any s y s t e m a t i c way, a n d t h e r e s u l t s i n d i c a t e t h a t i t i s v e r y f a r from i d e a l . We u n d e r t o o k a s e r i e s o f experiments designed t o i d e n t i f y t h e source o f t h i s problem and d i s c o v e r e d t h a t u n i f o r m foams w i t h 2-3 \im c e l l s i z e cannot be made r e p r o d u c i b l y a t a d e n s i t y o f 50 mg/cm , b e c a u s e t h e r e i s s i m p l y n o t enough o i l t o c r e a t e s t a b l e interfaces. We have r a i s e d o u r d e n s i t y t o 85 mg/cm and now g e t c o n s i s t e n t l y good r e s u l t s . T h i s was a v e r y i m p o r t a n t d i s c o v e r y i n terms o f foam development, b u t u n f o r t u n a t e l y i t a l s o meant t h a t t h e s t a t i s t i c s o f t h e r e g r e s s i o n model f o r t h i s RSM were n o t p a r t i c u l a r l y good, so we were l i m i t e d t o d r a w i n g some q u a l i t a t i v e c o n c l u s i o n s . F i g u r e 2 shows t h a t t h e r e a p p e a r s t o be a good c o r r e l a t i o n between t h e e m u l s i o n and foam c e l l s i z e s and t h e amount o f s u r f a c t a n t used, as e x p e c t e d from t h e s u r f a c e c h e m i s t r y o f t h e system. The o t h e r two f a c t o r s do n o t seem t o have a significant effect. T h e r e a l s o a p p e a r s t o be a good c o r r e l a t i o n between c e l l s i z e (from SEM's) a n d d e n s i t y u n i f o r m i t y , w h i c h i s o b s e r v e d by x - r a y r a d i o g r a p h y . This r e s u l t i s i l l u s t r a t e d i n F i g u r e 3. The s t a t i s t i c s f o r t h e o t h e r r e s p o n s e s were n o t r e a l l y good enough t o draw f i r m conclusions. The r e s u l t s f o r t h e RF s c r e e n i n g s t u d y a r e shown i n T a b l e 3. The most s t r i k i n g r e s u l t t o come o u t o f t h i s e x p e r i m e n t was t h a t t h e r e a p p e a r s t o be a s t r o n g c o r r e l a t i o n between t h e low l e v e l o f c a t a l y s t c o n c e n t r a t i o n a n d gel formation. The low l e v e l was o u t s i d e t h e range o f what had p r e v i o u s l y been t r i e d . T h i s has been c o n f i r m e d i n many subsequent experiments. A n o t h e r i m p o r t a n t c o n c l u s i o n was t h a t t h e c h e m i s t r y appears t o dominate t h e p r o c e s s , so i t was r e a s o n a b l e t o p r o c e e d w i t h an RSM which d e a l t o n l y w i t h the f o r m u l a t i o n v a r i a b l e s . A l t h o u g h t h e oven t i m e was s i g n i f i c a n t a t t h e 90% c o n f i d e n c e l e v e l , i t was d e c i d e d t o o p t i m i z e t h e c h e m i s t r y f i r s t and d e a l w i t h t h i s a s p a r t o f the p r o c e s s i n g c o n d i t i o n s i n l a t e r experiments. 3

3

In f a c t , two RSM's were r u n , one w i t h r e s o r c i n o l a n d f o r m a l d e h y d e , and one w i t h t h e r e l a t e d compound p h l o r o g l u c i n o l and f o r m a l d e h y d e ( P F ) . In g e n e r a l , t h e s t a t i s t i c s



Figure

1.

Scanning e l e c t r o n micrographs of c e n t e r - p o i n t samples from PS foam RSM e x p e r i m e n t : (a) D e s i g n Run 13; (b) D e s i g n Run 14; (c) D e s i g n Run 15.



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2

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Application of Statistical Experimental Design to Development of

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