Clustering of Water in Polymers - ACS Symposium Series (ACS

26 Clustering of Water in Polymers GEORGE L. BROWN

Downloaded by UNIV OF MICHIGAN ANN ARBOR on October 15, 2014 | http://pubs.acs.org Publication Date: August 19, 1980 | doi: 10.1021/bk-1980-0127.ch026

Mobil Chemical Co., Edison, N J 08817

The perception that water sorbed in polymers can be clustered has a dual origin. The earliest inference of clustering was based on the development of opacity ("blushing") in films or coatings exposed to water. The occurrence of blushing is particularly prevalent in coatings or films, such as those produced from emulsion polymers, which contain water soluble impurities (emulsifiers and initiator residues). This form of clustering is not the same as that which can occur in homogeneous water swollen polymer films. It is, however, important to bear in mind because the presence of unrecognized traces of water soluble impurities may result in substantial errors in the interpretation of sorption measurements. In binary solutions - in the case under consideration, water sorbed in a polymer - non-random mixing is also described as clustering. For this case, the cluster size is rarely, if ever, sufficient to produce visual opacity, and the evidence for the phenomenon is found in peculiarities of the sorption isotherm. If the two cases cited - a polymer containing polymer insoluble, water soluble components, and a homogeneous polymer represent two ends of a spectrum, a variety of intermediate cases can be imagined which represent varying degrees of heterogeneity (graft or block copolymers, ionomers, non-random copolymers). Thus i t i s c l e a r that the term " c l u s t e r i n g " can be used i n a v a r i e t y o f s i t u a t i o n s , and i s not p r e c i s e l y d e f i n e d . In the present case, i t w i l l be used i n the context of the s t a t i s t i c a l thermodynamic treatment o f b i n a r y s o l u t i o n s developed by Zimm (1) and Zimm and Lundberg ( 2 ) , which provides a c a l c u l a t i o n o f a c l u s t e r i n t e g r a l , and which can be extended to s p e c i f y a c l u s t e r s i z e f o r each component. In d e s c r i b i n g the r o l e of the " c l u s t e r i n g " theory i n r e l a t i o n s h i p to p r e v i o u s l y developed s o l u t i o n t h e o r i e s , such as the widely used Flory-Huggins theory (3), Zimm and Lundberg p o i n t out that "Our c o n s i d e r a t i o n s a r e not intended as a replacement f o r the previous t h e o r i e s , but as 0-8412-0559-0/ 80/47-127-441 $05.00/0 © 1980 A m e r i c a n Chemical Society

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.


442

WATER IN P O L Y M E R S

an adjunct thereto, i n t e r p r e t i n g experimental data i n molecular terms." The a n a l y s i s which w i l l be described i s i n accord with the complementarity of the two approaches. Water s o r p t i o n of non-polar polymers ( p o l y o l e f i n s , polystyrene) i s very low, and i s probably adequately d e s c r i b e d by a p p l i c a t i o n of conventional s o l u t i o n thermodynamics, i . e . , The Flory-Huggins theory. For mixtures of water and p o l a r polymers, the i n c r e a s e i n water sorpt i o n with i n c r e a s i n g humidity i s much greater than that which would be p r e d i c t e d from t h i s theory. This i s not s u r p r i s i n g , because the theory i s based on an assumption of random mixing, and does not contemplate the s p e c i f i c a s s o c i a t i o n s p o s s i b l e between water and p o l a r groups i n the polymer and between water molecules which can l e a d to non-random mixing. A method w i l l be described which combines conventional s o l u t i o n theory and c l u s t e r theory and provides an i n t e r p r e t a t i o n f o r the s o r p t i o n of water by c e r t a i n p o l a r polymers. The t o t a l water sorbed by a polymer w i l l be viewed as a sum of an amount c o n t r i b u t e d by normal, random mixing, plus an increment due to a s s o c i a t i o n or c l u s t e r i n g of the water. Mathematically, the s o r p t i o n data f o r the amorphous a c r y l i c polymers which w i l l be considered here cannot be c o r r e l a t e d by a s i n g l e parameter s o r p t i o n isotherm. In the Flory-Huggins theory, the parameter i s the i n t e r a c t i o n parameter, which f o r the simplest p o s s i b l e case c h a r a c t e r i z e s the enthalpy of mixing which r e s u l t s from the i n t e r m o l e c u l a r bonding mismatch between polymer and water. A two parameter s o r p t i o n isotherm provides an e x c e l l e n t v e h i c l e f o r data treatment. The two parameters can be i d e n t i f i e d as the i n t e r a c t i o n parameter and a c l u s t e r i n g parameter. Methods f o r E v a l u a t i o n o f Experimental Data. A v a r i e t y of s o l u t i o n and s o r p t i o n isotherms have been developed to account f o r water-polymer mixtures, and t h i s has been e x t e n s i v e l y summarized by B a r r i e ( 4 ) . However, few s t u d i e s have been performed where simple, systematic changes i n polymer composition are i n v o l v e d . An examination o f published experimental data on amorphous a c r y l a t e polymers i n d i c a t e s that a r a t h e r simple, c o n s i s t e n t isotherm i s a p p l i c a b l e , which allows some i n t e r e s t ing conclusions as to the i n f l u e n c e of p o l a r content and g l a s s temperature on the c l u s t e r s i z e . Experimental data on water s o r p t i o n by polymers i s u s u a l l y presented based on some form of Henry's Law. That i s , a measure of the q u a n t i t y of water sorbed (weight, volume, moles) per u n i t q u a n t i t y of s u b s t r a t e o r s u b s t r a t e plus water i s p l o t t e d a g a i n s t the a c t i v i t y o f water i n the surrounding vapor. Since data f o r water r a r e l y d i s p l a y l i n e a r i t y over any a p p r e c i a b l e range of s o r p t i o n , a search was made f o r a f u n c t i o n which would provide b e t t e r l i n e a r i t y - p a r t i c u l a r l y f o r h i g h humidity s o r p t i o n measurements. From a p r a c t i c a l standpoint, accurate i n t e r p o l a t i o n and e x t r a p o l a t i o n f o r samples exposed to high humidity i s very important i n p r e d i c t i n g behavior o f coatings and b a r r i e r f i l m s .



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Water

443

For a l a r g e number of polymers, a p l o t of the r e c i p r o c a l of water s o r p t i o n against the r e c i p r o c a l of the p a r t i a l pressure of water e x h i b i t s n e a r - l i n e a r behavior. With the e x p e c t a t i o n that the volume f r a c t i o n of water w i l l be the expression of water concentration r e l e v a n t to b a s i c polymer s o l u t i o n thermodynamics, t h i s measure has been used. However, a v a r i e t y of other expres sions of c o n c e n t r a t i o n can be used (weight or volume per u n i t weight or volume of polymer, weight percent, etc.) and s u b s t i t u t i o n of these w i l l a l t e r the slope and i n t e r c e p t , but not the l i n e a r i t y of the p l o t . The use and i n t e r p r e t a t i o n of the technique are exempli f i e d i n Figures 1 and 2 f o r p o l y ( e t h y l methacrylate) s o r p t i o n data of W i l l i a m s , Hopfenberg, and Stannett C5). The upper curve i n F i g u r e 1 shows experimental data p l o t t e d i n the conventional manner. The lower curve i s the Henry s Law l i m i t i n g isotherm, tangent to the experimental curve at the o r i g i n . The lower l i n e i n F i g u r e 2 shows the p l o t of r e c i p r o c a l q u a n t i t i e s (l/φ vs 1/P). I t shows e x c e l l e n t agreement with the l i n e a r equation 1

with ki = 167.9, and k = 104.7 with a c o r r e l a t i o n c o e f f i c i e n t greater than 0.999. An i n t e r p r e t a t i o n of Equation (1) i s that i t represents Henry s Law s o r p t i o n f o r k = 0, a Langmuir or attentuated type of isotherm where k i s negative, and an en hanced or " c l u s t e r e d " isotherm where k i s p o s i t i v e . The l i m i t i n g , i n f i n i t e d i l u t i o n isotherm, as Ρ approaches zero, i s given by the i n v e r s e Henry's Law expression 2

1

2

2

2

Using the value of 168 f o r k j , t h i s equation i s p l o t t e d as the upper l i n e i n Figure 2. G r a p h i c a l l y , t h i s i s done by drawing a l i n e p a r a l l e l to the experimental data passing through the origin. The i n v e r s e of t h i s r e l a t i o n s h i p i s the Henry's Law isotherm shown i n F i g u r e 1. The p o s t u l a t e which w i l l be pursued i s that water s o r p t i o n at i n f i n i t e d i l u t i o n of the water i s normal i n behavior, r e p r e senting the true i n t e r a c t i o n of water and polymer molecules. That i s , i f water s o r p t i o n occurs on two types of s i t e s , a p o l y mer s i t e and a polymer-water s i t e , the i n f l u e n c e of the former w i l l predominate as Ρ and the amount of sorbed water s i m u l t a neously approach zero. A p l o t of φ vs Ρ with a slope of k j (the i n v e r s e of Equation 2), as shown i n F i g u r e 1, i s tangent to the experimental isotherm at the o r i g i n . The a n a l y s i s o u t l i n e d allows a unique s p e c i f i c a t i o n of χ, the i n t e r a c t i o n parameter, through use of the l i m i t i n g (Henry's Law) approximation of the Flory-Huggins theory ( 3 ) . That i s


WATER IN POLYMERS

444

1.2 EXPERIMENTAL DATA

l


1.0

0.6

0,4

Figure 1. Conventional plot of sorption of water by polyfethyl methacrylate): top curve, experimental data from Ref. 5. Bottom curve, calculated Henry's Law isotherm based on extension of low relative pressure sorption

-CALCULATED

0.2!

HENRY'S

LAW

-

(TANGENT TO EXPERIMENTAL CURVE AT O R I G I N )

I 0.2

0.4

0.6


I 1.0

26.

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Clustering

( 1

Ρ 2 Φβ

+

of

X )

445

Water

2 (3)


and χ = l n kx - 1 At any r e l a t i v e pressure, the experimental s o r p t i o n can be compared to that p r e d i c t e d f o r the Henry's Law isotherm to pro v i d e a r a t i o , Ν , which w i l l be termed the "enhancement number", c a l c u l a t e d from Equations (1) and (2) as f o l l o w s :

e

φ

Η

kx-k P

Ζ Ψ

2

The enhancement number i s a measure, then, of the extent to which the s o r p t i o n of water i s increased by the a b n o r m a l i t i e s of the process which r e s u l t from non-random mixing. Another index i s a v a i l a b l e from the c a l c u l a t i o n of the c l u s t e r s i z e , based on the Zimm-Lundberg concepts. In h i s i n i t i a l paper, Zimm CO provides f o r the c a l c u l a t i o n of a c l u s t e r i n t e g r a l from the s o l u t i o n isotherm. N e g l e c t i n g a small term i n v o l v i n g c o m p r e s s i b i l i t y , f o r component 1 i n a b i n a r y mixture, a c l u s t e r i n t e g r a l , G u , i s c a l c u l a t e d from:

where νχ i s the molecular volume, φχ the volume f r a c t i o n and ax the a c t i v i t y of component 1. For a random s o l u t i o n , the a c t i v i t y i s p r o p o r t i o n a l to the volume f r a c t i o n , and

The extent of c l u s t e r i n g i n s o l u t i o n s i s i n d i c a t e d by the extent to which βχχ/νχ exceeds minus one. A more u s e f u l index has been provided by Zimm and Lundberg (2), i n the q u a n t i t y φχΟχχ/νχ, which i s "the number of type 1 molecules i n excess of the mean c o n c e n t r a t i o n of type 1 molecules i n the neighborhood of a given type 1 molecule." From Equation (6), t h i s q u a n t i t y i s o b v i o u s l y -φ f o r a random s o l u t i o n . For many purposes, a c a l c u l a t i o n of the average number of solvent molecules i n a c l u s t e r i s u s e f u l . We s h a l l denote t h i s as Ν , the c l u s t e r number, and Starkweather (6) has suggested that t h i s i s provided by the e x p r e s s i o n : = 1I£LL+ ι

Ν C

(7)

νχ

For a random s o l u t i o n (an " i d e a l " s o l u t i o n i n t h i s context) the a c t i v i t y c o e f f i c i e n t , ax/φχ, i s i n v a r i a n t with c o n c e n t r a t i o n ,


W A T E R IN P O L Y M E R S

446

and from a combination of Equations f o r such a s o l u t i o n :


N

c

(7) and

- 1-φ

( 5 ) , t h i s would g i v e

(8)

However, there should be no c l u s t e r i n g f o r t h i s case, and the c l u s t e r number should be one. We b e l i e v e that the d i f f i c u l t y a r i s e s from the p e c u l i a r i t y of the d e f i n i t i o n of the q u a n t i t y Φι^ιχ/νι, which was provided above, which s p e c i f i e s the excess s o l v e n t molecules i n the neighborhood of (but not i n c l u d i n g ) the c e n t r a l s o l v e n t molecule. The c l u s t e r number should then be s p e c i f i e d as

N

c

= -Φΐ(ΐ-Φΐ)

0

3ax

+ 1

(9b)

Values of Ν c a l c u l a t e d from Equation (9a) or (9b) exceed those c a l c u l a t e d on the b a s i s of Equation (7) by the q u a n t i t y φχ. This d i f f e r e n c e i s n e g l i g i b l e f o r the cases which w i l l be t r e a t e d here, but could be a p p r e c i a b l e i f the method i s a p p l i e d to the determi n a t i o n of c l u s t e r number f o r d i l u t e aqueous polymer s o l u t i o n s , f o r example. These c o r r e c t e d equations provide a c l u s t e r number of one f o r an " i d e a l solution. Using the p a r t i a l pressure of water, P, as an adequate ap proximation to the a c t i v i t y , we see from Equation (1), that f o r the isotherm under c o n s i d e r a t i o n here, the d e r i v a t i v e w i t h i n the brackets i n Equation (9b) i s equal to - k . The c l u s t e r number i s , f o r t h i s case, given by: 1 1

2

Ν

- 1 + 1& φ - k 2 Φ 2

2

(10)

and comparing t h i s to the enhancement number from Equation (4): Ν

c

= Ν

e

-k^

Δ Ύ

2

(11)

E v a l u a t i o n and I n t e r p r e t a t i o n of Data. S o r p t i o n data on four polymers reported i n the l i t e r a t u r e have been examined. Data on p o l y ( e t h y l methacrylate) from Williams et a l (5) were s p e c i f i e d as volume f r a c t i o n of water sorbed as a f u n c t i o n of p a r t i a l pressure. In an e a r l i e r p u b l i c a t i o n of Stannett and W i l l i a m s (7) the g l a s s temperature of the polymer was given as 65°C. S o r p t i o n and d e s o r p t i o n measurements showed a very c l o s e concordance. Data on poly(methyl methacrylate) by Brauer and Sweeney (8) were transformed from g r a v i m e t r i c to volume f r a c t i o n using a d e n s i t y of 1.19. The g l a s s temperature of t h i s polymer i s 105°C. The authors r e p o r t that " t h i n specimens reach a steady s t a t e value w i t h i n a short time." Data f o r poly(methyl a c r y l a t e )



26.

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and a copolymer o f methyl a c r y l a t e and a c r y l i c a c i d , 89/11, are from Hughes and Fordyce Ç9). D e n s i t i e s used to convert g r a v i metric data to volume f r a c t i o n were 1.22 and 1.24, the l a t t e r based on the assumption o f volume a d d i t i v i t y using a d e n s i t y of 1.4 f o r p o l y a c r y l i c a c i d , k i n d l y furnished by D. B. Fordyce. The g l a s s temperature o f polymethyl a c r y l a t e i s 6°C. The s o r p t i o n r e s u l t s were reported to be e q u i l i b r i u m values. Measurements on p o l y ( e t h y l methacrylate) were made a t 25°C, and on the remaining three a t 30°C. Data on the four polymers, c a l c u l a t e d from the equations of the previous s e c t i o n , are presented i n Table I . In descending order, the s e r i e s represents i n c r e a s i n g h y d r o p h i l i c i t y , w i t h e s t e r groups per u n i t volume i n c r e a s i n g from e t h y l methacrylate to methyl a c r y l a t e , and w i t h carboxyl groups i n s e r t e d i n the f o u r t h polymer. This i s r e f l e c t e d i n terms of an o r d e r l y decrease i n χ and increase i n s a t u r a t i o n s o r p t i o n . However, no trend i n the c l u s t e r i n g can be discerned. Thus t h i s phenomenon appears to be r e l a t e d to the nature of the water molecule and q u i t e probably to the hydrogen bonding propensity o f the p o l a r groups on the polymer, but not to any appreciable extent to the concentration o f p o l a r groups. A number o f i n v e s t i g a t o r s have suggested that e f f e c t s of i n i t i a l water s o r p t i o n on polymer mechanical p r o p e r t i e s ( " p l a s t i c i z a t i o n " ) would f a c i l i t a t e f u r t h e r accommodation o f water. The f i r s t two polymers i n Table I are g l a s s y , and the t h i r d rubbery, and there i s no evidence o f any mechanistic d i f f e r e n c e i n sorp t i o n . Although r e l a x a t i o n e f f e c t s w i l l be expected to i n f l u e n c e r a t e o f s o r p t i o n f o r these amorphous polymers, i n f l u e n c e on e q u i l i b r i u m s o r p t i o n appears n e g l i g i b l e . Viewed i n another man ner, water i s c e r t a i n l y capable of p l a s t i c i z i n g polymers, but organic penetrants which sorb i n a normal f a s h i o n a l s o do so. I t i s t h e r e f o r e questionable to a s s i g n the unusual nature of water s o r p t i o n to p l a s t i c i z a t i o n . The a n a l y s i s produces a unique value f o r χ, which should r e l a t e to the fundamental i n t e r a c t i o n o f water and the polymer. An a l t e r n a t i v e view, which has been taken by many authors, i s to c a l c u l a t e χ f o r each experimental p o i n t . For p o l y ( e t h y l meth a c r y l a t e ) , f o r example, W i l l i a m s e t a l (5) show a decreasing χ with i n c r e a s i n g r e l a t i v e pressure. T h e i r values can be e x t r a polated to zero pressure, to give χ = 4.1, the value derived here. Two independent methods have been u t i l i z e d to examine the nature o f the s o r p t i o n isotherm. An a n a l y s i s of the experimental isotherm compared to an e x t r a p o l a t i o n o f the i n f i n i t e d i l u t i o n behavior allows c a l c u l a t i o n o f an enhancement number f o r any of the polymers a t any given p a r t i a l pressure. Calculation of a c l u s t e r number based on an independent method shows very c l o s e concordance w i t h the enhancement number, p r o v i d i n g strong sup port f o r the p o s t u l a t e that a s s o c i a t e d groups of water molecules sorb i n the polymer, and account f o r the anomolous s o r p t i o n .

American Chemical Society Library St. N. W. S.; In1155 Water in16th Polymers; Rowland, Washington, 0 . C. Society: 2 0 0 3 8Washington, DC, 1980. ACS Symposium Series; American Chemical

In Water in Polymers; Rowland, S.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980. 22

2.5

33

Methyl A c r y l a t e - A c r y l i c A c i d 89/11

0.091

3.0

2.8

2.5 2.6 0.030

3.5

53

86

Methyl A c r y l a t e

2.9 3.0 0.025

3.8

80

119

Methyl Methacrylate

c 2.6

Ν 2.7

0.016

4.1

Values a t Ρ = 1 Ν e

105

Φ

168

X

E t h y l Methacrylate

2

k

*1

Polymer o f

Table I


ζ

3

οο

26.

Clustering

BROWN

449

of Water


The s o r p t i o n isotherm u t i l i z e d :

can i n a sense be d e r i v e d analogously to the Langmuir isotherm, by p o s t u l a t i n g a forward r a t e i n which a d d i t i o n a l s o r p t i o n s i t e s are made a v a i l a b l e by sorbed water molecules, and a r a t e of de s o r p t i o n p r o p o r t i o n a l to t o t a l water content. A l t e r n a t i v e l y , a Henry's Law s o r p t i o n can be w r i t t e n f o r the polymer component and the water component, each term m u l t i p l i e d by the volume o f the component, and the c o n t r i b u t i o n s summed to give: φ = k'Pd-φ) + ^ Ρ φ (8) = k'P +

(k"-k'^

which i s s i m i l a r to Equation (1) when rearranged i n the form: φ - ^

+ ^Ρφ

(9)

At b e s t , the isotherm i s a l i m i t i n g form which could be true only f o r low s o r p t i o n . When r e w r i t t e n as p

- £ f e

10

We see that i t becomes Henry's Law f o r k 2 = 0 , and speculate that the s u b s t i t u t i o n o f the Flory-Huggins isotherm f o r to g i v e : 2

(1-φ)+(1-φ) χ

may provide more general a p p l i c a b i l i t y . Since the "base" isotherm used here u t i l i z e s the volume f r a c t i o n o f water as the measure of c o n c e n t r a t i o n , f o r conve nience the enhancement has been based on volume f r a c t i o n s . For h i g h l y h y d r o p h i l i c polymers, enhancements i n the range reported i n Table I would r e s u l t i n volume f r a c t i o n s of water greater than u n i t y . T h i s problem could be e l i m i n a t e d by t r e a t i n g the water s o r p t i o n i n the base isotherm on a volume f r a c t i o n b a s i s , as out l i n e d , but t r e a t i n g the c l u s t e r i n g on the b a s i s used f o r absorp t i o n processes, c o n s i d e r i n g the volume added by c l u s t e r i n g to a u n i t volume o f polymer c o n t a i n i n g u n c l u s t e r e d water. I n c o r p o r a t i o n of the two suggested improvements leads to a more complicated process f o r i d e n t i f y i n g the i n t e r a c t i o n parme t e r , the "base isotherm, and the extent o f enhancement, but we suggest that the simple, coherent p i c t u r e which emerges f o r the systems reported here j u s t i f i e s extension to develop the more general treatment. 11


450

WATER IN POLYMERS


The qualitative mechanism suggested by the data and i t s i n terpretation i s that at low relative pressures, water i s distributed throughout the polymer, but probably preferentially where hydrogen bonding i s possible. At higher pressures, chains of water on the hydrogen bonding sites predominate. The i n i t i a l process can be described i n terms of conventional solution theories and the enhancement process can be viewed as one of occupancy of sites - analogous to that found i n adsorption processes. REFERENCES (1)

Zimm, B.H. J. Chem. Phys., 1953, 21, 934-935

(2)

Zimm, B.H.; Lundberg, J.L. J. Phys. Chem., 1956, 60, 425-428

(3)

Flory, P.J. "Principles of Polymer Chemistry"; Cornell University Press, Ithaca, N.Y., 1953; p. 512-514

(4)

Barrie, J.A. In "Diffusion in Polymers", Crank, J.; Park, G.S., Ed.; Academic Press: London and New York, 1968; Chapter 8

(5)

Williams, J.L.; Hopfenberg, H.B.; Stannett, V.T. Preprints, 1968, 9(2), 1503-1510

(6)

Starkweather, H.W. Polymer Letters,

(7)

Stannett, V; Williams,

(8)

Brauer, G.M.; Sweeney, WT. 138

(9)

Thompson Hughes, L.J.; 22, 509-526

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