Water-Soluble Polymers - ACS Publications - American Chemical

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Downloaded by UNIV OF MICHIGAN ANN ARBOR on May 23, 2016 | http://pubs.acs.org Publication Date: May 5, 1986 | doi: 10.1021/ba-1986-0213.ch016

Surface Viscoelasticity and Foam Stability of Waterborne Polymers and Coatings Richard R. Eley, Richard A. Zander, and Mark E. Koehler Glidden Coatings and Resins Division, Division of S C M Corporation, Strongsville, OH 44136

The dilational surface rheology of two series of waterborne, acid-functional, amine-neutralized, model polymer systems and commercial coatings of similar composition was studied. Within each series, the real part of the complex surface dilational modulus (derived from a dynamic surface tension experiment) was found to correlate better to foam stability than the complex modulus itself, the imaginary part (surface dilational viscosity), the bulk fluid shear viscosity, or the equilibrium surface tension. A novel instrument for measuring the dilational surface viscoelastic properties of aqueous polymer systems is also described. Fast Fourier transform analysis was used to remove noise from the data and obtain the amplitude and phase relationships of stress and strain signals.

THE PROPERTIES OF SURFACE VISCOELASTICITY

and foam stability o f w a t e r b o r n e p o l y m e r systems a n d c o m m e r c i a l c o a t i n g s w e r e s t u d i e d , a n d t h e c o r r e l a t i o n b e t w e e n t h e m w a s d e t e r m i n e d . T h i s c h a p t e r also d e s c r i b e s a n o v e l i n s t r u m e n t that measures t h e d i l a t i o n a l s u r f a c e v i s c o elastic p r o p e r t i e s o f a q u e o u s p o l y m e r systems ( J ) a n d uses fast F o u r i e r t r a n s f o r m analysis t o o b t a i n r e l a t i o n s h i p s o f stress a n d s t r a i n .

Static and Dynamic Surface Tension I n a n y l i q u i d o f at least t w o c o m p o n e n t s , t h e c o m p o s i t i o n o f t h e l i q u i d - a i r interface m a y b e different f r o m the bulk, or subphase, c o m p o s i t i o n . T h a t i s , a p a r t i t i o n i n g o f t h e c o m p o n e n t s m a y o c c u r s u c h that the s u r f a c e l a y e r is e n r i c h e d i n t h e m i n o r c o m p o n e n t f o r t h e r m o d y n a m i c reasons; n a m e l y , t h e free e n e r g y o f t h e s y s t e m is m i n i m i z e d b y t h e p a r t i t i o n i n g . I f t h e c o n c e n t r a t i o n o f a c o m p o n e n t is greater at t h e i n t e r f a c e t h a n i n t h e b u l k s o l u t i o n , t h e c o m p o n e n t has a p o s i t i v e " s u r f a c e excess" 0065-2393/86/0213-0315$06.00/0 ® 1986 American C h e m i c a l Society

Glass; Water-Soluble Polymers Advances in Chemistry; American Chemical Society: Washington, DC, 1986.

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a n d is s a i d to b e s u r f a c e a c t i v e . T h e s u r f a c e t e n s i o n ( i d e n t i c a l w i t h the s u r f a c e f r e e e n e r g y p e r u n i t a r e a f o r a l i q u i d i n e q u i l i b r i u m w i t h its v a p o r ) o f the m i x t u r e w i l l b e l o w e r e d , r e l a t i v e to that o f the p u r e m a j o r c o m p o n e n t , b y the p r e s e n c e o f the s u r f a c e - a c t i v e c o m p o n e n t . W h e n the s u b p h a s e a n d i n t e r p h a s e c o n c e n t r a t i o n s o f a l l c o m p o n e n t s are at e q u i l i b r i u m , the static, o r e q u i l i b r i u m , s u r f a c e t e n s i o n w i l l b e m e a s u r e d . A n i n c r e a s e i n the s u r f a c e a r e a o f a l i q u i d w i l l c r e a t e n e w s u r f a c e f r o m b u l k l i q u i d . T h e e q u i l i b r i u m concentration of surface-active c o m p o n e n t s (surfactant) is l o w e r i n the s u b p h a s e l i q u i d t h a n i n the s u r f a c e l a y e r , b y d e f i n i t i o n . T h e r e f o r e , the c o n v e r s i o n o f b u l k l i q u i d to s u r f a c e w i l l r e d u c e the s u r f a c e c o n c e n t r a t i o n o f the s u r f a c t a n t ; this r e d u c t i o n raises the s u r f a c e t e n s i o n . I f the s u r f a c e is c o m p r e s s e d f r o m e q u i l i b r i u m , the s u r f a c e excess o f s u r f a c t a n t w i l l b e i n c r e a s e d , a n d the s u r f a c e t e n s i o n w i l l d r o p . T h e s y s t e m , d i s p l a c e d f r o m e q u i l i b r i u m , t h e n relaxes at a rate d e p e n d e n t o n the r e l a x a t i o n p r o c e s s e s a v a i l a b l e to the s y s t e m . M e c h a n i s m s o f r e l a x a t i o n i n c l u d e a d s o r p t i o n - d e s o r p t i o n i n t e r c h a n g e w i t h the s u b p h a s e a n d m o l e c u l a r r e l a x a t i o n w i t h i n the s u r f a c e l a y e r . T h e d e p e n d e n c e o f s u r f a c e t e n s i o n o n f l u c t u a t i o n s i n s u r f a c e a r e a is c a l l e d the d y n a m i c surface tension.

Dynamic Surface Tension and Coatings S u r f a c e t e n s i o n is q u i t e u n i v e r s a l i n its i n f l u e n c e o n c o a t i n g s , p a r t i c u l a r l y f o r w a t e r - b a s e d s y s t e m s , a n d c a n e i t h e r d r i v e o r i n h i b i t coatings p r o cesses. T h e r e f o r e , w h e t h e r a n d to w h a t d e g r e e s u r f a c e t e n s i o n m a y v a r y d u r i n g a g i v e n p r o c e s s are i m p o r t a n t to k n o w . A l t h o u g h this c h a p t e r w i l l b e c o n c e r n e d o n l y w i t h d y n a m i c surface tension, coatings p e r f o r m a n c e m a y also b e a f f e c t e d b y s u r f a c e t e n s i o n g r a d i e n t s that arise f r o m causes o t h e r t h a n s u r f a c e a r e a v a r i a t i o n , s u c h as s o l v e n t e v a p o r a t i o n (2) a n d s u r f a c e c o n t a m i n a t i o n o r i n h o m o g e n e i t i e s (3). B i e r w a g e n (3) a n d also K o r n u m a n d R a a s c h o u - N i e l s e n (4) r e v i e w e d the r o l e o f b o t h static a n d d y n a m i c s u r f a c e t e n s i o n i n c o n t r o l l i n g c o a t ings d e f e c t s . S m i t h (5) r e c e n t l y d e s c r i b e d the g e n e r a l r e l a t i o n s h i p of d y n a m i c s u r f a c e t e n s i o n to c o a t i n g s a p p l i c a t i o n p r o p e r t i e s a n d r e p o r t e d o n e x p e r i m e n t a l m e a s u r e m e n t s o f the d y n a m i c s u r f a c e t e n s i o n o f c o a t i n g s - l i k e s y s t e m s . S u r f a c e o r i n t e r f a c i a l t e n s i o n is a f a c t o r i n the d i s p e r s i o n o f p i g m e n t s a n d the a t o m i z a t i o n o f l i q u i d s a n d a d r i v i n g f o r c e f o r d r o p l e t c o a l e s c e n c e a n d l e v e l i n g . C r a t e r i n g , f o a m s t a b i l i t y , substrate w e t t i n g , a n d c u r t a i n s t a b i l i t y l i k e w i s e are p h e n o m e n a that are d e p e n d e n t o n static o r d y n a m i c s u r f a c e t e n s i o n ( 2 - 9 ) . A n applied coating w i l l definition. A coating must be l i q u i d f i l m , b y m e a n s of s o m e surface area w i l l increase b y

have a high surface-to-volume ratio, b y c o n v e r t e d f r o m a l i q u i d i n b u l k to a t h i n a p p l i c a t i o n p r o c e s s . U p o n a p p l i c a t i o n , the a v e r y l a r g e f a c t o r , at a h i g h rate. ( T h e



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s u r f a c e a r e a o f a c u b i c d e c i m e t e r o f b u l k l i q u i d increases b y a f a c t o r o f a b o u t 3,000,000 w h e n c o n v e r t e d to 20- jum l i q u i d d r o p s a n d t h e n d e c r e a s e s b y a f a c t o r o f 750 w h e n d e p o s i t e d as a 1 - m i l f i l m . ) A s a c o n s e q u e n c e , the s u r f a c e t e n s i o n m a y v a r y d r a m a t i c a l l y , as a f u n c t i o n of b o t h the rate a n d d e g r e e o f s u r f a c e e x p a n s i o n . T h e p r o p e r t i e s o f the c o a t i n g w i l l b e g o v e r n e d n o t b y the e q u i l i b r i u m s u r f a c e t e n s i o n , b u t b y the d e p e n d e n c e o f the s u r f a c e t e n s i o n o n the c h a n g e o f s u r f a c e a r e a o f the material. T h e effectiveness of a surfactant i n a coating m a y not necessarily b e i n its a b i l i t y to l o w e r s u r f a c e t e n s i o n f r o m the p u r e - l i q u i d v a l u e ( e q u i l i b r i u m effects) b u t r a t h e r m a y b e i n the d e g r e e to w h i c h the s u r f a c e t e n s i o n d e v i a t e s f r o m its e q u i l i b r i u m v a l u e u p o n s u r f a c e d e f o r m a t i o n ( d y n a m i c effects) a n d its rate o f r e c o v e r y . T h e r e f o r e , u n d e r s t a n d i n g a n d c o n t r o l o f c o a t i n g s a p p l i c a t i o n m a y r e q u i r e a k n o w l e d g e o f the d y n a m i c e f f e c t s o f a p p l i c a t i o n p r o c e s s e s o n the s u r f a c e o r i n t e r f a c i a l t e n s i o n . S u r f a c t a n t s that p r o d u c e s t r o n g d e p e n d e n c e o f s u r f a c e t e n s i o n o n s u r f a c e a r e a s h o u l d g e n e r a l l y b e a v o i d e d (5).

Foam Stability F o a m is t h e r m o d y n a m i e a l l y u n s t a b l e b u t c a n b e s t a b i l i z e d i n a k i n e t i c sense b y the o p e r a t i o n o f t w o f a c t o r s : (a) h y d r o d y n a m i c f a c t o r a n d (b) f i l m s t r e n g t h f a c t o r (JO, I I ) . T h e h y d r o d y n a m i c f a c t o r i n f l u e n c e s the rate o f d r a i n a g e o f l i q u i d o u t o f the f o a m - f i l m l a m e l l a e f r o m the d u a l causes o f g r a v i t y a n d the c a p i l l a r y s u c t i o n of f l u i d i n t o the P l a t e a u b o r d e r s ( F i g u r e 1). T h e h y d r o d y n a m i c f l o w w i t h i n the l a m e l l a e is c o n t r o l l e d b y the r h e o l o g y o f the b u l k f l u i d a n d the g e o m e t r y o f the f o a m a n d also has c o n s e q u e n c e s f o r the f l o w p r o p e r t i e s o f f o a m i n a b u l k sense (12), as w e l l as f o r the m i c r o s c o p i c f l o w i n v o l v e d i n f i l m d r a i n a g e . T h e f i l m s t r e n g t h f a c t o r is d e t e r m i n e d b y the i n t e r f a c i a l v i s c o e l a s t i c p r o p e r t i e s i n d i l a t i o n a n d i m p a r t s to the f o a m l a m e l l a a s e l f - h e a l i n g a b i l i t y ; this a b i l i t y m a k e s the f o a m l a m e l l a r o b u s t w i t h r e s p e c t to disturbances. F i l m r u p t u r e o c c u r s v i a d r a i n a g e o f i n t r a l a m e l l a r l i q u i d so that t h i n n i n g o f t h e l a m e l l a e p r o c e e d s to a c r i t i c a l t h i c k n e s s (less t h a n 1000 A ) , w h e r e u p o n s u r f a c e i n s t a b i l i t i e s ( w a v e s d u e to t h e r m a l m o t i o n ) , e n h a n c e d b y v a n d e r W a a l s f o r c e s , cause f i n a l r u p t u r e (13, 14). H i g h v i s c o s i t y o r r i g i d i t y o f the s u r f a c e f i l m o f the f o a m l a m e l l a s i g n i f i c a n t l y r e t a r d s f i l m d r a i n a g e a n d thus i n f l u e n c e s f o a m s t a b i l i t y v i a the h y d r o d y n a m i c f a c t o r (14). T h e p r e s e n c e o f a r i g i d s u r f a c e f i l m o r g e l results i n v e r y s t a b l e f o a m s . A n e x a m p l e o f f o a m o f this t y p e is b e e r f o a m , w h e r e a s u r f a c e g e l l a y e r o f d e n a t u r e d p r o t e i n is i n v o l v e d (7,15). I n the c o n c e p t o f i n t e r f a c i a l d i l a t i o n a l e l a s t i c i t y ( P l a t e a u - M a r a n g o n i G i b b s e f f e c t ) (16), the s u r f a c e f i l m e l a s t i c i t y does n o t arise f r o m a n y consideration of m i c r o s c o p i c n e t w o r k structure or m o l e c u l a r entanglem e n t (i.e., r u b b e r l i k e e l a s t i c i t y ) . E l a s t i c i t y refers i n s t e a d to a r e s t o r a t i v e


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Plateaus Border

- 3

Figure 1. Schematic diagram of the intersection of foam lamellae to form a Plateau border. The fluid flow is indicated by arrows. CF is capillarydriven flow.

flow i n d u c e d b y s u r f a c e t e n s i o n g r a d i e n t s a r i s i n g o u t o f l o c a l d e f o r m a t i o n o f f i l m s d u e t o s p o n t a n e o u s t h i n n i n g (6). I n f a c t , a r e d u n d a n c y o f effects c o u l d o c c u r , b e c a u s e f i l m h e a l i n g c o u l d b e a c h i e v e d b y the a c t i o n o f c a p i l l a r y f o r c e s a l o n e . L o c a l t h i n n i n g o f a p l a n e f i l m necess a r i l y i n v o l v e s a b e n d i n g o f the s u r f a c e , a n d the r e s u l t i n g c a p i l l a r y f o r c e s w o u l d t e n d to restore the u n i f o r m i t y o f the f i l m (13). A n u n e q u i v o c a l dilational elasticity effect m a y be described, h o w e v e r ( t h o u g h s u r f a c e shear v i s c o s i t y o r p l a s t i c i t y m a y p l a y a d o m i n a n t r o l e , i f p r e s e n t ) . A m e c h a n i s m o f s e l f - h e a l i n g is i l l u s t r a t e d i n F i g u r e s 1 a n d 2 (14, 17). F o a m l a m e l l a e i n t e r s e c t at angles ( G i b b s angle) o f 120° at m e c h a n i c a l e q u i l i b r i u m (15). T h e i n t e r s e c t i o n s o f f o a m l a m e l l a e a r e k n o w n as P l a t e a u b o r d e r s ( F i g u r e 1). I n i t i a l l y , the f o a m f i l m is t h i n n e d b y d r a i n a g e o f l i q u i d i n t o the P l a t e a u b o r d e r s . T h i s d r a i n a g e o c c u r s b e c a u s e the p r e s s u r e w i t h i n t h e P l a t e a u b o r d e r s w i l l b e less t h a n i n t h e l a m e l l a e d u e to the c u r v a t u r e o f t h e b o u n d i n g l i q u i d s u r f a c e . T h e s u m o f surface tension vectors i n the c u r v e d r e g i o n produces a net o u t w a r d thrust o r c a p i l l a r y f o r c e ; this thrust causes the s u r f a c e to b e h a v e as a s t r e t c h e d m e m b r a n e . L i q u i d is d r a w n i n t o the P l a t e a u b o r d e r s v i a t h e r e s u l t i n g p r e s s u r e g r a d i e n t . T h e flow o f l i q u i d i n t o the P l a t e a u



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Figure 2. Figure 1 after sweeping of surfactant into Plateau borders by capillary flow. MCF is the surface-tension gradient-driven Marangoni counterflow.

b o r d e r s also s w e e p s a l o n g s u r f a c t a n t m o l e c u l e s , h o w e v e r . A s u r f a c e t e n s i o n g r a d i e n t is c r e a t e d so that the f o a m f i l m n o w acts as a s t r e t c h e d m e m b r a n e , a n d a M a r a n g o n i c o u n t e r f l o w occurs i n the surface layer; this c o u n t e r f l o w d r a g s s u b s u r f a c e l i q u i d w i t h i t a n d thus restores t h e t h i c k n e s s o f the f o a m l a m e l l a (17) ( F i g u r e 2). T h u s , h i g h d i l a t i o n a l elast i c i t y s h o u l d c o r r e s p o n d to m o r e stable f o a m s .

Experimental Section Materials. This study consisted of two sample sets representing coatings systems, based on two generically different resin types. Both sets were dispersions of amine-neutralized, acid-functional, polymer resins in a water-glycol ether-alcohol cosolvent blend. Set 1 contained an epoxy-acrylic graft copolymer, and set 2 was based on a commercial acrylic resin having an acid number of 90. Antifoam additives were present in some samples. Set 1 was a visually incompatible but stable dispersion, and set 2 was relatively homogeneous. Composition variations within the sample sets were reasonably broad; these variations roughly approximated the span of practical coatings formulations. Wilhelmy Plate M e t h o d . The surface tension of liquids is ordinarily measured by equilibrium methods, such as the du Nouy ring, capillary rise, or drop volume methods. These methods are generally unsatisfactory for polymer solu-



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tions or where surface aging effects m a y occur (18). T h e Wilhelmy plate method, however, provides an accurate a n d convenient method of surface tension measurement for such materials (19). In the W i l h e l m y plate method, a platinum plate or glass slide (roughened to minimize the contact angle) is suspended in a liquid, minimally immersed. C a p i l lary forces due to the curvature of the meniscus act on the plate to produce a net d o w n w a r d force, or apparent increase in weight, proportional to surface tension. T h e surface tension a n d weight increase (expressed as a force, F ) are related b y


F = py cos 0

(1)

where p is the length of the perimeter of the plate in contact with the liquid a n d 0 is the angle m a d e b y the l i q u i d in contact with the plate. Assuming the contact angle is zero, the surface tension, y , is given b y 7 = F/p

(2)

Instrument Design and Data Analysis. T h e apparatus most often used for d y n a m i c surface tension measurements b y the Wilhelmy plate method is the L a n g m u i r trough (20), in w h i c h vertical plane barriers are positioned in the l i q uid surface a n d m o v e d in opposition to each other to create the d i l a t i o n - c o m pression cycle. This design has acknowledged drawbacks primarily leakage of surface around the barriers a n d surface wave effects. A novel design was selected f r o m the recent literature (I) that circumvents these problems, while allowing higher frequencies and strain rates to b e achieved. Instead of the m o v i n g barriers, a porous cylinder (of stainless steel mesh) is used that oscillates vertically through the liquid surface, entraining liquid as it does so and thereby creating new surface. Simulation of coatings processes requires large, high-frequency deformations. In this respect, the instrument chosen for this work represents an improvement over the L a n g m u i r trough method; both strain a n d strain-rate capabilities exceed those of the L a n g m u i r trough method. T h e schematic design of the instrument is shown in Figure 3. A variablespeed gear motor drives a c a m wheel. T h e rotating c a m drives a crank shaft, w h i c h is translated to vertical motion b y a slider, to w h i c h is attached the 150mesh stainless steel cylindrical screen. T h e vertical travel of the cylinder is measured b y a "string-pot" position-sensing transducer. T h e platinum plate is susp e n d e d from a microforce transducer. T h e outputs of both transducers are r e c o r d e d on a strip-chart recorder and b y a microprocessor interfaced with the instrument. T h e data are later analyzed b y a Fortran program. Operating frequencies for our experiments ranged f r o m 0.15 to 2.2 r a d / s . Surface dilation ratios were f r o m 97% to 190$. Stress-strain Lissajous loops generated f r o m the force-displacement outputs were generally quite symmetrical; this result indicates linear viscoelastic behavior, even for these relatively large strains. Strain rates were computed as a two-dimensional average H e n c k y strain rate, H (equation 3), a n d varied from 0.018 to 0.38 s . - 1

H = a>/2n In (1 + A A / A )

(3)

0

In equation 3, co is the angular frequency, AQ is the initial surface area, and A A is the area increment. T h e data were taken at a strain rate of 0.25 s . T h e data analysis incorporated a fast Fourier transform algorithm (Scientific Subroutine Program Package for the Digital E q u i p m e n t Corporation P D P _ 1



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T E S T FLUID JACKETED BEAKER

Figure 3. Oscillating cylinder instrument for dynamic surface tension measurement. 11/44). The raw force and displacement data are transformed from the time domain to the frequency domain by the Fourier transform operator. The fundamental (experimental) frequency is then easily chosen by examination of the power spectrum (Figure 4). Noise is edited out by zero-filling all frequencies except the fundamental in both the real and imaginary frequency-domain spectra for the force and displacement. An inverse Fourier transformation is then performed, to recover the noisefree force and displacement data curves in the time domain. Figure 5 shows a raw force data curve superimposed on noise-free data obtained by Fourier treatment. Figure 6 shows the same for the relatively noiseless displacement data. Amplitude and phase-shift information are simultaneously obtained for both force and displacement data, by Fourier analysis. The modulus and relative phase shift are calculated, as well as the viscoelastic parameters, from equations 6-10.



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Measurement of F o a m Stability. Foam stability was evaluated by beating air into a standard volume of liquid with a Brookfield counterrotating mixer. Foam height was followed as a function of time. The area under the foam height-time curve was obtained by numerical integration and was then normalized to the initial foam height, to give an average foam lifetime, according to Bikerman (15). An advantage of this method of treatment is that the entire defoaming curve is taken into account, while the normalization to initial foam volume allows us to take account of foam stability, independent of foaming ability. In the case of set 1, the foams were so unstable that the average foam lifetime could not be computed, so the foam height at 3.5 min was used to correlate the data. Surface Viscoelasticity. The three-dimensional analogue of the surface dilational modulus is the bulk modulus, K, which describes the change in pres-

20 30 40 Frequency Index (*10 ) _1

Figure 4. Power spectrum in the frequency domain from forward Fourier transformation.


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0.08—


0.04-

X

0.00

-0.04

-0.08-1 0

25

1

50 Time (sec)

75

100

Figure 5. Superimposed raw and noise-free force vs. time data. Key: •, force vs. time (fast Fourier transformation); O , raw data.

sure, P, for a relative change in volume, V, upon isotropic compression of a fluid. K is defined as K = dP/d(ln V)

(4)

Polymers often display a time-dependent response to compression; this response indicates that K is a complex modulus, describing a viscoelastic response to isotropic compression-dilation (21) K* =K' + * "

(5)

where K' and K " are the compressional storage and loss moduli, respectively (21). In most dynamic surface tension experiments, variation in surface area is caused mechanically by some means, and the resulting variation in surface tension is measured. The principal quantity derived from the experiment is the surface dilational modulus, €, given by e = A y / ( A A / A ) « d / d ( l n A) 7


(6)



324

The analogy to equation 4 (in two dimensions) is obvious. As stated above, dilation or compression of a surface results in a displacement of surface tension from its equilibrium value, followed by a time-dependent relaxation toward equilibrium. Any relaxation process occurring during surface deformation will result in a phase difference between the strain (area change) and the resulting stress (surface tension change). The dilational modulus (equation 6) is actually a complex modulus, therefore, containing both real (energy storage) and imaginary (energy loss) components. Complex moduli are most conveniently defined in the frequency domain, because the magnitude of the measured stress is dependent on both the deformation rate and history (22). Hence, by analogy to equation 5 and linear viscoelasticity (21) e*(ito) = € ' ( « ) + fc"(

Water-Soluble Polymers - ACS Publications - American Chemical

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