Rheology of Film-Forming Liquids - ACS Symposium Series (ACS

31 Rheology of Film-Forming Liquids RAYMOND R. MYERS and CARL J. KNAUSS

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 26, 2017 | http://pubs.acs.org Publication Date: September 25, 1985 | doi: 10.1021/bk-1985-0285.ch031

Chemistry Department, Kent State University, Kent, OH 44242

Tests and Evaluation Drying Tests Evaluation of Mechanical Properties Viscosity of Shear-Sensitive Materials Dispersed Systems Polymer Solutions Viscoelasticity Viscous and Elastic Systems Time Dependence Rigidity Modulus Trends Morphological Changes during Drying Physical Chemistry of Film Formation Drying from Solution High Solids Coatings Latex Drying Population Dynamics Future Possibilities Latexes and Other Polymer Dispersions High Solids Conclusions

Tests and Evaluation Numerous methods are a v a i l a b l e for the conversion of l i q u i d s to s o l i d s , ranging from freezing to chemical reactions leading to cross-linking. Over 15,000 years ago paintings were dried i n caves on both sides of the Pyrenees mountains by evaporating an aqueous matrix made from egg white or blood. M i l l e n i a l a t e r , oxidative polymerization of naturally occurring unsaturated o i l s allowed the Chinese to coat objects that were designed to be handled, and this technique i s the one that carried us through the I n d u s t r i a l Revolution. Synthetic resin systems added a dimension to these ancient formulations: they were solutions that i n many cases dried by 0097^6156/85/0285-O749$07.00/0 © 1985 American Chemical Society

Tess and Poehlein; Applied Polymer Science ACS Symposium Series; American Chemical Society: Washington, DC, 1985.


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APPLIED POLYMER SCIENCE

evaporation and then cured. Whether or not they needed to be baked, they were c a l l e d thermoset systems. Then, l a r g e l y because of r h e o l o g i c a l reasons, a high molecular weight r e s i n dispersed i n water came on the market for trade sales coatings. Under the name of latex, these coatings actually paced the ecology movement for about half of the coatings market. The other half, industrial coatings, had to wait a few decades for the development of aqueous systems. Modern coatings continue to be developed i n response to both economical and ecological pressures. Two promising routes are via aqueous solution/dispersion systems using polymers with carboxyl functionality temporarily neutralized by amines and via high-solids systems where small r e a c t i v e molecules are applied i n high concentrations. Because the success of any of these systems depends on t h e i r a b i l i t y to form hard, n e a r l y impermeable, adherent f i l m s , the methods a v a i l a b l e to monitor and characterize t h i s t r a n s i t i o n are important to the manufacture or a p p l i c a t i o n of c o a t i n g s . One i s dealing with high technology i n the sense that the approaches used i n c o l l o i d , s o l u t i o n , and polymer chemistry converge i n the development of "compliance coatings." D r y i n g T e s t s . Measurements of the r h e o l o g i c a l changes t h a t take p l a c e on d r y i n g and subsequent c u r i n g are q u i t e numerous and have undergone a s i m i l a r s h i f t to h i g h t e c h n o l o g y . U n t i l recent years more r e l i a n c e was p l a c e d on the "educated f i n g e r " of the p a i n t t e c h n i c i a n than on any i n s t r u m e n t a l d e v i c e . As l o n g as the d e p o s i t e d f i l m possessed the q u a l i t i e s of a l i q u i d , i t remained tacky. Thereafter, i t was considered to be a s o l i d . The f i r s t i n s t r u m e n t s were based on r h e o l o g y but d i d not make f u l l use of i t . The Gardner d r y i n g time r e c o r d e r Q_, 2) measured the time when a s t y l u s r i d i n g on the f i l m detected v i s c o s i t y i n c r e a s e s as the c o a t i n g passed through the tacky stage i n d r y i n g and f i n a l l y encountered a surface dry to the touch. No measurement of the hardness of the f i l m was made i n t h i s attempt to r e c o r d l i t t l e more than the time required to achieve a given state. Only a f t e r r h e o l o g i s t s entered the f i e l d w i t h d e t e r m i n a t i o n s of the mechanical properties of the f i l m s was progress made on r e v e a l i n g the mechanisms of the various drying processes. E a r l y drying t e s t s only monitored the gel-forming tendencies of l i q u i d c o a t i n g s . I f the l i q u i d i n c r e a s e s i n v i s c o s i t y w i t h o u t reaching the g e l state, i t s surface w i l l be tacky. A piece of f e l t weighted by a s m a l l b l o c k w i l l d e p o s i t s t r a n d s on the f i l m . No i n d i c a t i o n of the degree of r i g i d i t y of the f i l m i s g i v e n , and so t h i s p r i m i t i v e test must be considered nonrheological i n the sense t h a t the o n l y r e a d i n g t h a t makes sense i s the time to a c h i e v e the f e l t - f r e e state. Drying t e s t s t h a t have been d e v e l o p e d by r h e o l o g i s t s are designed to characterize coatings at p r o g r e s s i v e stages of d r y i n g and c u r i n g r a t h e r than s i m p l y to monitor these changes. Two techniques t h a t have been used f o r over a decade to gather d r y i n g data d e s c r i p t i v e of the s t a t e of the f i l m are d e s c r i b e d l a t e r i n t h i s chapter. They opened a new s u b d i s c i p l i n e that l a t e l y has been referred to as chemorheology.



31.

MYERS AND KNAUSS

Rheology of Film-Forming Liquids

751

Evaluation of Mechanical Properties. An applied coating must form a tough and f a i r l y impregnable f i l m i n order to be p r o t e c t i v e . Film formation always r e s u l t s i n s h r i n k a g e , so t h a t a d h e s i v e and/or c o h e s i v e l o s s often accompanies d r y i n g . Measurements must be capable of i s o l a t i n g these catastrophic effects from the r h e o l o g i c a l changes that one seeks to measure. E v a l u a t i o n of p a i n t s and p a i n t i n g r e d i e n t s can be done w i t h conventional viscometers, i n which the material i s sheared between two mating surfaces. Constant shear rates or known frequencies of o s c i l l a t i o n may be u s e d . Raw m a t e r i a l s a r e e v a l u a t e d and f o r m u l a t i o n changes are monitored by c o n v e n t i o n a l v i s c o m e t r i c methods. Two problems complicate the s e l e c t i o n and use of rheometers i n the study of supported f i l m s : (1) the f i l m s t a r t s o f f the d r y i n g c y c l e with l e s s pronounced mechanical properties than the substrate and (2) one free surface must be maintained i n order for the coating to dry i n the manner intended f o r s u r f a c e c o a t i n g s . The f i r s t of these problems renders i t d i f f i c u l t to detect the onset of r i g i d i t y i n a f i l m r e s i d i n g on a r i g i d s u b s t r a t e , and the second problem r u l e s out the s e l e c t i o n of viscometers of standard design wherein a s t r e s s i s a p p l i e d at one s u r f a c e and the s t r a i n r a t e response i s read at the o t h e r . The c o a t i n g s s c i e n t i s t c a n n o t use t h e conventional gap-loading type of viscometer, for he must work with systems that have one free surface. The f i r s t step i n the s o l u t i o n of both of these problems r e q u i r e s the use of a c y c l i c s h e a r i n g s t r e s s i n measuring the two major components of a m a t e r i a l i n t r a n s i t i o n : v i s c o s i t y and e l a s t i c i t y . These parameters measure the resistance of the material to flow and deformation, r e s p e c t i v e l y . Most a r t i c l e s of commerce d i s p l a y both components s i m u l t a n e o u s l y ; they are s a i d to be viscoelastic. Because t h i s chapter c o v e r s l i q u i d s , the f i r s t p r o p e r t y discussed i s the u n i v e r s a l c h a r a c t e r i s t i c of a l l l i q u i d s , namely, viscosity. V i s c o s i t y of Shear-Sensitive Materials Dispersed Systems. Newtonian Behavior. Most film-forming l i q u i d s are dispersions. The rheology of these systems i s simpler than the rheology of polymers and i s treated f i r s t . Primers on rheology a l l portray v i s c o s i t y as resistance to flow. P r a c t i c a l l y every t e x t (.3, 4_) shows t h a t the s t r e s s Ο needed to effect a given shear rate γ obeys the r e l a t i o n σ = ηγ

(1)

where η i s the v i s c o s i t y . Dimensions of σ are pascals (Pa), where 1 Pa e q u a l s 1 (N/m >t The c g s e q u i v a l e n t i s dynes per s q u a r e c e n t i m e t e r . Shear r a t e , γ , i s i n s ; t h e r e f o r e , η i s i n p a s c a l seconds or newton seconds per square meter. Substances obeying t h i s r e l a t i o n over wide ranges of shear rates are of l i t t l e i n t e r e s t , at l e a s t to r h e o l o g i s t s . D i l u t e dispersions tend to obey t h i s law of Newton, i n which case the v i s c o s i t y i s found from the v i s c o s i t y of the medium T\Q by (5)


752


Π = η ο ( 1 + 2.5φ)

(2a)

where φ i s the d i m e n s i o n l e s s volume f r a c t i o n of the pigment or dispersed r e s i n . Equation 2a can be w r i t t e n i n the form

n

s p

- (n/no) - ι - 2.5Φ

(2b)

where η ρ , the s p e c i f i c v i s c o s i t y , i s seen to bear a l i n e a r r e l a t i o n to φ. This equation i s v a l i d only at φ below 0.1 or even l e s s . Newtonian f l o w may be observed i n suspensions of h i g h e r concentrations than those obeying Equation 2a. Higher-order powers of φ are needed, for which there are over 100 proposed v a r i a t i o n s of equations and c o e f f i c i e n t s . One i s advised to s t a r t with the e a r l y work of Vand (j>, 7) and Robinson (8-10) and then r e f e r to the studies by Krieger (11, 12).


3

S h e a r - S e n s i t i v e Systems. In a d d i t i o n to hydrodynamic effects and simple viscous behavior, the act of pigmentation creates a c e r t a i n amount of complex b e h a v i o r (13). I f the p a r t i c l e s are f i n e , Brownian movement (14-17) and r o t a t i o n a l diffusion (14, 18, 19) are among the phenomena that cause dispersed systems to d i s p l a y complex rheology. The r o l e o f v a n der W a a l s f o r c e s i n i n d u c i n g f l o c c u l a t i o n (20) and the c o u n t e r v a i l i n g r o l e of two e l e c t r o v i s c o u s effects (17, 21, 22) i n imparting s t a b i l i t y , p a r t i c u l a r l y i n aqueous systems, have been noted. S t e r i c r e p u l s i o n s appear to be the r e s p o n s i b l e f a c t o r i n nonaqueous systems (23, 24). The adsorbed l a y e r can be q u i t e l a r g e (25-28), as detected by d i f f u s i o n and density measurements of f i l l e d systems or by viscometry and normal s t r e s s differences (29). One e m p i r i c a l advance t h a t h o l d s promise i s the f i n d i n g by Casson (30) that 1

1 - 5φ (3)

η = no

(1 - 1.755Φ)

2

where b_is unity for spheres and independent of φ. I t i s a material parameter that converts φ to a larger value r e f l e c t i v e of the amount of s o l v e n t immobilized (i.e., 5φ i s the sediment volume). For p a r t i c l e s i n o i l , b decreases w i t h σ and a l s o w i t h φ. In f a c t , the c o n t r o l l i n g parameter i s σφ. G e n e r a l l y , a p l o t of 1/5 versus σφ w i l l produce a s i n g l e curve i n which b may drop from 5 at low s t r e s s to 2 at h i g h s t r e s s where the i m m o b i l i z e d l a y e r i s l a r g e l y sloughed off. As the pigment c o n c e n t r a t i o n i s i n c r e a s e d toward p r a c t i c a l l e v e l s , p r a c t i c a l l y no d i s p e r s i o n obeys Newton's law. V i s c o s i t y becomes a v a r i a b l e q u a n t i t y i n t h a t i t becomes dependent on the shear r a t e . G e n e r a l l y , t h i s dependency i s i n the d i r e c t i o n of a decrease i n η w i t h γ . Flow c u r v e s of σ v e r s u s γ become concave toward the γ a x i s (31). When the pigment i s a c i c u l a r , w i t h a length-to-diameter r a t i o greater than unity, shear s e n s i t i v i t y can be imparted at e x c e e d i n g l y low c o n c e n t r a t i o n due to the e f f e c t of o r i e n t a t i o n of the p a r t i c l e s on the r e s i s t a n c e to f l o w (32, 33).



31. MYERS AND KNAUSS


753

Transient effects lead to v i s c o s i t y increases that depend c y c l i c a l l y on the r a t e of shear. The degree of c o n c a v i t y i s a measure of the s h o r t n e s s , or b u t t e r l i k e q u a l i t y , of the dispersion. The system i s known as shear t h i n n i n g (34). N a t u r a l l y , a system d i s p l a y i n g opposite concavity would be c a l l e d shear t h i c k e n i n g . Such terms as t h i x o t r o p i c and pseudoplastic are to be avoided, even though they appear frequently i n the l i t e r a t u r e . Viscometers designed to measure s h e a r - s e n s i t i v e systems have p a r a l l e l shearing surfaces, as i n r o t a t i o n a l viscometers, or e l s e they have s u r f a c e s t h a t d i f f e r i n a n g u l a r v e l o c i t y by an amount equal to the difference i n clearance, as i n cone-plate viscometers. These different gap-loading types are designed to assure a constant shear rate. Flow through a c a p i l l a r y r e s u l t s i n a shear rate that v a r i e s from the c e n t e r of the c a p i l l a r y to the w a l l (35) and i s to be avoided i n measuring shear-sensitive materials. Both σ and γ can be determined at the w a l l , but the material being measured w i l l be subjected to γ values f a l l i n g off to 0. Polymer Solutions. A l l film-forming l i q u i d s are polymers or polymer s o l u t i o n s . The v i s c o s i t y of these systems i s constant o n l y at extremely high d i l u t i o n where the measurements leading to knowledge of m o l e c u l a r dimensions are made. At p r a c t i c a l c o n c e n t r a t i o n s polymer s o l u t i o n s i n v a r i a b l y become shear s e n s i t i v e . In the Newtonian range the v i s c o s i t y of a polymer s o l u t i o n can be measured by p a s s i n g the s o l u t i o n through a c a p i l l a r y and measuring the e f f l u x time at a g i v e n temperature. At h i g h e r concentrations the p a r a l l e l p l a t e or cone/plate designs are used. In contrast with Equation 2a, showing that dispersion v i s c o s i t y i s independent of m o l e c u l a r weight M, the v i s c o s i t y of a polymer s o l u t i o n depends strongly on molecular weight. As M increases, the swept-out volume of the d i s t e n d e d polymer m o l e c u l e i n c r e a s e s , so t h a t φ of E q u a t i o n 2b mounts r a p i d l y . Instead of d e a l i n g w i t h an unknown volume f r a c t i o n , one uses c o n c e n t r a t i o n , c, i n g/dL and evaluates the quantity, r] p/c. For good measure, the value of t h i s f r a c t i o n i s determined at various concentrations and extrapolated to zero c, g i v i n g the i n t r i n s i c v i s c o s i t y [η] i n dL/g. The molecular weight dependence of the polymer's i n t r i n s i c v i s c o s i t y therefore i s r e l a t e d to i t s swept-out volume by (36). S

[η] = KM

a

(4)

where Κ (the Staudinger constant) runs around 10~^ and a i s a f r a c t i o n a l exponent e x p r e s s i n g the extent of p o l y m e r - s o l v e n t i n t e r a c t i o n . Because of the v a r i a t i o n and f r a c t i o n a l value of a, Κ cannot be assigned u n i t s . As the s o l v e n t a t t r a c t i o n decreases, the polymer m o l e c u l e b a l l s up; a approaches z e r o , and the v i s c o s i t y approaches that of a dispersion. A l i m i t e d amount of s t r u c t u r a l information can be obtained v i a viscometry of polymer s o l u t i o n s . M o l e c u l a r dimensions have been mentioned as the p r o v i n c e of d i l u t e s o l u t i o n v i s c o s i t y . Flow p r o p e r t i e s of more concentrated s o l u t i o n s p r o v i d e i n f o r m a t i o n on whether s o l v e n t d r a i n s f r e e l y from the polymer c o i l s and on how s o l v e n t a t t r a c t i o n s compete w i t h the i n t e r a c t i o n s among macromolecules that are bound to occur (37, 38).



754


Proper treatment of polymer s o l u t i o n s requires one to s t a r t with equations of change (continuity, motion, and energy) and expressions for the heat f l u x vector and the stress tensor. Such treatments are beyond the scope of t h i s c h a p t e r , but an e x c e l l e n t r e v i e w a r t i c l e has appeared (39) that points out the importance of e v a l u a t i n g the s t r e s s tensor i n p l a c e of s i m p l y f i n d i n g a shear v i s c o s i t y and observing i t s dependence on shear r a t e . R h e o l o g i c a l equations of state, or " c o n s t i t u t i v e equations," can be derived from rheometric measurements i n simple modes of flow, from continuum mechanics, and from molecular theory. Models are selected to describe a polymer m o l e c u l e ' s o r i e n t a b i l i t y , e x t e n s i b i l i t y , and i n t e r n a l modes of motion (40). Using a simple model c o n s i s t i n g of beads connected by Hookean springs, one can write a c o n s t i t u t i v e equation with a time constant that characterizes the v i s c o e l a s t i c response of the polymer s o l u t i o n (41). U n f o r t u n a t e l y , the a b i l i t y of t h i s e q u a t i o n to account for shear thinning requires further assumptions. Pigmented polymer s o l u t i o n s that are the basis of conventional coatings d i s p l a y t r u l y complex v i s c o s i t y phenomena. I f the pigment possesses a s u r f a c e of h i g h energy, i t w i l l i m m o b i l i z e s o l v e n t ( g i v i n g φ c o e f f i c i e n t s greater than 2.5 i n Equation 2a) or polymer ( d r a s t i c a l l y e x t e n d i n g the volume f r a c t i o n ) . I n t e r a c t i o n s now become subject to s t e r i c and entropie factors (42); these factors, being of thermodynamic nature (43, 44), cause v a r i o u s temperature dependencies t h a t are i n e x t r i c a b l y c o u p l e d w i t h the shear r a t e dependencies described above. Viscometric determinations of these phenomena a l l i n v o l v e the destruction of the very structures that one sets out to measure and therefore are not emphasized i n t h i s chapter. I t i s more important to recognize the p a r t i a l s o l i d l i k e character of f i l m formers at the outset and to treat them i n a manner that e l u c i d a t e s both the s o l i d and t h e l i q u i d c h a r a c t e r i s t i c s i n t h e same n o n d e s t r u c t i v e measurement. That i s , one should measure v i s c o s i t y and e l a s t i c i t y simultaneously. Viscoelasticity A limpid f l u i d such as water or paint thinner has been characterized adequately by i t s shear v i s c o s i t y , η , i n Equation 1. On the other extreme, the dried coating i s a s o l i d of e l a s t i c i t y modulus, G. I f the coating i s not deformed e x t e n s i v e l y by the shear stress, i t w i l l obey a r e l a t i o n i n v o l v i n g the deformation, γ (4): σ = Gy

(5a)

Deformation i s expressed as a f r a c t i o n such as d i s p l a c e m e n t d i v i d e d by the thickness of the specimen; i t i s dimensionless. Both σ and G have the dimensions of dynes per square c e n t i m e t e r or newtons per square meter. Viscous and E l a s t i c Systems. When both v i s c o s i t y and e l a s t i c i t y are present i n the m a t e r i a l , an a d d i t i v e combination of the two responses i s needed. In the case of a drying f i l m , the stresses are added, g i v i n g the r e s u l t for a v i s c o e l a s t i c body: σ = ηγ + Gy


(5b)


755


I f the mass of the f i l m i s taken i n t o account, p a r t of the s t r e s s w i l l be used to a c c e l e r a t e i t (F = ma), so t h a t an i n e r t i a l term i s added i n v o l v i n g the a r e a , A, o v e r which the s t r e s s i s applied:


σ = (m/A)y + ηγ + Gy

(6)

Here γ i s the second time d e r i v a t i v e of displacement, i n r e c i p r o c a l squared seconds. E q u a t i o n 6 d e s c r i b e s a damped harmonic o s c i l l a t o r , suggesting that the coatings be studied i n o s c i l l a t i o n . In fact, t h i s decision i s f o r c e d on the experimenter by the inadequacy of g a p - l o a d i n g i n s t r u m e n t s . When a p p l i e d to the s i t u a t i o n represented by a free o s c i l l a t i o n , Equation 6 i s solved with σ = 0. I f forced o s c i l l a t i o n provides the stress, the left-hand side i s represented by OQ s i n u)t, where ω i s the c i r c u l a r frequency. Examples are given l a t e r of both types. Because η i s time dependent and G i s not, i t behooves one to s o l v e the second-order d i f f e r e n t i a l equation e i t h e r i n terms of a c o e f f i c i e n t (η) or a modulus (G). E i t h e r r o u t e may be chosen, but one u s u a l l y s e l e c t s the modulus. In t h i s case the response to the a p p l i e d s t r e s s i s measured as the s t r a i n r a t h e r than the s t r a i n rate. D e v i c e s f o r making the o s c i l l a t o r y measurement are c a l l e d rheometers r a t h e r than v i s c o m e t e r s . The r e s u l t i s the complex modulus of r i g i d i t y G*, which c o n t a i n s the i n - p h a s e response, G , and the out-of-phase response, G \ That i s f

f

f

G* = G + i G

, f

(7)

Two unknowns r e q u i r e two measurements. For a f r e e o s c i l l a t o r these measurements are the resonant frequency and the damping. For a forced o s c i l l a t o r the favored combination i s the amplitude r a t i o and phase a n g l e o v e r a range of a p p l i e d f r e q u e n c i e s . This combination i s not a v a i l a b l e for the e v a l u a t i o n of coatings because of the requirement that one surface be free. The two measurements described i n the example below are damping and phase angle. Time Dependence. When drying k i n e t i c s are studied and rheology i s used as a monitor of the p r o c e s s , i t i s d i f f i c u l t to measure phase angles; as a r e s u l t , one monitors drying by a s i n g l e measurement of G and makes approximations of the out-of-phase component, G . Time dependence e n t e r s the d a t a - g a t h e r i n g process i n another way. The e s s e n t i a l nature of k i n e t i c studies i s that they use time as the main v a r i a b l e , and the data are p l o t t e d a g a i n s t t i m e . In v i s c o e l a s t i c s t u d i e s time e n t e r s the e q u a t i o n by v i r t u e of the dependence of the mechanical properties on the time of measurement. This problem i s resolved by expressing a l l measurements i n terms of the frequency, ω. A material on the borderline between l i q u i d and s o l i d behaves more l i q u i d l i k e when the time of observation l / ω i s i n c r e a s e d , and more s o l i d l i k e when l / ω i s decreased. (See F i g u r e f

t f

1.)

R h e o l o g i s t s make use of a d i m e n s i o n l e s s q u a n t i t y known as the Deborah number (45, 46), D:


756


(8)

D = τ/t

where τ i s the r e l a x a t i o n time of the specimen. Expressed i n terms of ω, D becomes the f a m i l i a r D = ωτ. E l a s t i c i t y p r e v a i l s when D exceeds unity, for the time required for r e l a x a t i o n of the applied stress i s not exceeded. Of course, G i s a f u n c t i o n of time when measured s t a t i c a l l y . Under dynamic c o n d i t i o n s Ο'(ω) takes i t s p l a c e , r e p r e s e n t i n g energy s t o r e d per c y c l e . There i s a l s o a G ((ja) c o r r e s p o n d i n g to energy l o s t per c y c l e , and i n many quarters one evaluates the dimensionless r a t i o G ' V G , or tan δ, as a measure of the l o s s c h a r a c t e r i s t i c s of a film. When D f a l l s below unity, viscous responses p r e v a i l (47). Both G and G" f a l l to low values under conditions of s m a l l τ or large t , but under these c i r c u m s t a n c e s the c o n t r i b u t i o n from G can be amplified by converting i t i n t o a c o e f f i c i e n t rather than a modulus by the r e l a t i o n


tf

1

f

ff

η' = G'Vu)

(9)

Long times of observation correspond to s m a l l ω and, an i n c r e a s e i n η f o r a g i v e n l e v e l of G . 1

therefore,

f f

R i g i d i t y Modulus Trends. I f one now superimposes the c u r i n g time dependency on the measuring time dependency, the r e s u l t can be expressed by Figure 2 (48). The abscissa represents measuring time, and the various curves represent different times of drying. M e c h a n i c a l measurements do not range over many decades of frequency, so t h a t the w e l l - e s t a b l i s h e d p r i n c i p l e of t i m e temperature e q u i v a l e n c y (49) i s used to f i l l i n the gaps. The continuous p l o t of l o g modulus v e r s u s l o g frequency obeys a d i s t i n c t i v e p r o f i l e f o r a l i q u i d (Systems 1 and 2), f o r l i g h t l y g e l l e d s o l i d (Systems 3 and 4), and f o r the hardened f i l m (System 5). The v e r t i c a l l i n e on the l e f t of Figure 2 at a frequency of 1 Hz i s best viewed as an i n d i c a t i o n of d r a s t i c a l l y increasing modulus l e v e l s at v a r i o u s degrees of c u r e ; the l e v e l s range from f l o w i n g l i q u i d G that disappears from the s c a l e (and would drop to zero i f a l o g p l o t would permit) to hard s o l i d s whose dependence of modulus on frequency i s v i r t u a l l y n o n e x i s t e n t . In between, the p r o f i l e s have s l o p e s r a n g i n g from z e r o at the p l a t e a u s to u n i t y i n the transition region. By c o n t r a s t , the v e r t i c a l l i n e on the r i g h t of F i g u r e 2 at 10? Hz indicates hardly any change from polymer s o l u t i o n to dried f i l m . What t h i s region l a c k s i n spread of G* values i t gains i n two ways: the measuring time i s short enough to monitor even the most rapid of polymerizations and the wavelength of the c y c l i c stress i s s m a l l e r than the t h i c k n e s s of the f i l m . Both of these v i r t u e s are of s u f f i c i e n t importance to warrant the use of u l t r a s o n i c frequencies i n characterizing f i l m s . We have devised instruments to conduct measurements at both ends of the spectrum. They are described i n various places (50-56) and t h e r e f o r e are r e f e r r e d to i n o n l y the b r i e f e s t of terms i n the following section. One i s known as TBA, f o r t o r s i o n a l b r a i d 1




2

Figure 1.

Rheology

i

757

Liquids

—

LOG FREQUENCY, ω

1

Change from l i q u i d to s o l i d b e h a v i o r as measurement frequency i s i n c r e a s e d . The dashed l i n e p o r t r a y s a c r o s s - l i n k e d system.

-2

0

2 L O G

Figure 2.

of Film-Forming

4

6

F R E Q U E N C Y ,

8

10

12

ω

R i g i d i t y modulus trends for f i v e types of coatings. The modulus depends on frequency of the measurement or i n v e r s e l y on t h e t i m e o f a p p l i c a t i o n o f s t r e s s . Differences between e s s e n t i a l l y l i q u i d f i l m s and those possessing varying amounts of structure can be observed at f r e q u e n c i e s at which the r e l a x a t i o n time of the c o a t i n g approximates the time r e q u i r e d f o r the measurement. At a frequency of 1 Hz, shown by the s l e n d e r v e r t i c a l l i n e at l o g ω = 0, v a r i a t i o n s of 10*0 are displayed by G \


758



a n a l y z e r (54), and the other i s r e f e r r e d to as ARP, f o r attenuated r e f l e c t i o n of pulses (55). M o r p h o l o g i c a l Changes d u r i n g D r y i n g . A r e c e n t development i n understanding how the ambient c o n d i t i o n s d u r i n g cure a f f e c t the morphology of coatings was provided by G i l l h a m (57-59). Borrowing from the teachings of metallurgy, he constructed a time-temperaturet r a n s i t i o n (TIT) diagram for each film-forming m a t e r i a l , the general features of which appear i n Figure 3. Construction of the diagram was aided by exhaustive measurements using the low-frequency TBA device, where the l o c a t i o n s and s h i f t s of r e l a x a t i o n peaks were used as e v i d e n c e of v i t r i f i c a t i o n and g e l a t i o n , complemented by the d e t e c t i o n of p o s t c u r e . In t h i s diagram there are three c h a r a c t e r i s t i c temperatures: (1) r e s i n Tg, the g l a s s t r a n s i t i o n temperature of the s t a r t i n g m a t e r i a l ; (2) g e l Tg, the temperature at which g e l a t i o n and v i t r i f i c a t i o n occur s i m u l t a n e o u s l y ; (3) Tgoo, the g l a s s t r a n s i t i o n temperature of the f u l l y cured polymer of e s s e n t i a l l y i n f i n i t e molecular weight. C u r i n g below Τ poo i s u n a b l e to produce a t h e r m a l l y s t a b l e coating. Baking w i l l r e s u l t i n further reaction and a merging of Tg and Tgcc, Gelation before v i t r i f i c a t i o n should be minimized i n order to reduce the r e s i d u a l stresses present i n the f i l m . C u r i n g below the g e l Tg w i l l a v o i d the n e g a t i v e a s p e c t s of premature extensive g e l a t i o n but w i l l produce a "green" f i l m whose p r o p e r t i e s d e v i a t e w i d e l y from those t h a t are a t t a i n a b l e by the polymer. C u r i n g below the r e s i n T w i l l be no cure at a l l . The g l a s s y condition of the reactants w i l l prevent reaction. This condition, n a t u r a l l y , does not p r e v a i l when one deals with l i q u i d f i l m formers, which are the subject of t h i s chapter. Bauer and D i c k i e (60) d e v i s e d the concept of a cure window to e x p l a i n i n p r a c t i c a l terms how to c o n t r o l f i l m morphology. The cure window i s the range of temperatures and cure times over which a c c e p t a b l e p r o p e r t i e s are o b t a i n e d . Too low a temperature w i l l produce green p r o p e r t i e s , and too h i g h a temperature l e a d s to decomposition. The u l t i m a t e s t a t e of a c o a t i n g i s t h a t of a hard s o l i d . T h i s state of matter f a l l s i n the province of t h i s chapter and i s covered here i n a manner that completes the l i f e h i s t o r y of a film-forming liquid. &

Physical Chemistry of Film Formation During the l a t t e r stages of drying, depending on whether the polymer i s thermosetting or thermoplastic, c r o s s - l i n k i n g must be established so t h a t the c o a t i n g i s not o n l y r i g i d but a l s o i s c o n v e r t e d i n t o a composition that r e s i s t s water. The s t a t i c modulus of r i g i d i t y , G, depends on the molecular weight between c r o s s - l i n k s more or l e s s as f o l l o w s (61): f

G = K /M

c

(10)

where M i s the molecular weight between c r o s s - l i n k s . The constant K has a magnitude of about 25,000 g atm so t h a t d i v i s i o n by M i n c

?

c


31.

MYERS AND KNAUSS

Rheology

of Film-Forming

Liquids

759

grams per mole produces G v a l u e s of the order of hundreds of atmospheres (i.e., 10^ dyn/cm or 10? N/m ). When the degree of c r o s s - l i n k i n g i s low ( H i s large), the g l a s s t r a n s i t i o n temperature increases s l i g h t l y as c r o s s - l i n k i n g proceeds. As E approaches v a l u e s i n the hundreds, Τ becomes a s e n s i t i v e measure of cure. E q u a t i o n 10 can be derived i n i t s e s s e n t i a l features from the k i n e t i c theory of rubber e l a s t i c i t y (62), g i v i n g 2

2

c

Q


(11)

where FT i s the number-average m o l e c u l a r weight of the s t a r t i n g polymer, F / F Q i s the r a t i o of the mean square d i s t a n c e between network junctures to the corresponding distance of network chains i n free space (generally assumed to be 1.0), ρ i s polymer density, and RT i s the thermal k i n e t i c energy (62). G c a l c u l a t e s out to be of the order of magnitude of R [8.314 χ 10 ergs/(deg mol)]. The stress that leads to coating f a i l u r e depends on the product of G and the extent of shrinkage. But coatings u s u a l l y are a p p l i e d to substrates that do not shrink, so that considerable ingenuity i s needed to e v a l u a t e the e f f e c t p l a y e d by d i m e n s i o n a l changes t h a t occur when a f i l m d r i e s . A c a n t i l e v e r d e v i c e d e s c r i b e d by Gusman (63) and e l a b o r a t e d on by Corcoran (64), F i g u r e 4, u t i l i z e s the d e f l e c t i o n of a t h i n metal shim by the s h r i n k a g e of a c o a t i n g applied to one side. Corcoran used a more general theory based on the d e f l e c t i o n of a p l a t e r a t h e r than a beam and a r r i v e d at the relation n

2

2

7

2

σ = dEh3/3cl (h + c ) ( l - v)

(12)

where the l a t e r a l stress σ depends d i r e c t l y on the d e f l e c t i o n , d, per u n i t l e n g t h , 1. Young's modulus Ε (where Ε - 3G) i s used i n place of G. The stress a l s o depends on the thickness h of the p l a t e and i n v e r s e l y on the coating thickness c. C a l c u l a t i o n of Ο requires a knowledge of Poisson's r a t i o ν of the p l a t e , which can be assumed to be l e s s than 0.5 but which must be gotten from handbooks. Internal stresses develop e a r l y i n the drying of c r o s s - l i n k a b l e c o a t i n g s , and at a time t h a t i s c r i t i c a l to the subsequent development i n f i l m morphology and o r i e n t a t i o n ( 6 5 ) . A c a n t i l e v e r device cannot detect e a r l y and subtle evidences of stress because the weight of the shim and i t s c o a t i n g produces a d e f l e c t i o n from the s t a r t . C r o l l solved t h i s problem by devising a version with two suspension p o i n t s l o c a t e d at d i s t a n c e 1 from each other and an overhang of distance 1Q at either end. (See Figure 5 ) . C a l c u l a t i o n s of the proportions of Irj to 1 that would o b l i t e r a t e the effect of f i l m weight on the h o r i z o n t a l bar revealed that lrj = 0 . 4 5 6 4 I f or proper b a l a n c e w i t h the c a n t i l e v e r p o r t i o n of the bar rather than 1Q = 0 . 5 1 as l e s s rigorous analyses l e d one to b e l i e v e . C r o l l ' s design gave s t r a i n v a l u e s (which c o n v e r t to s t r e s s ) t h a t were independent of the f i l m t h i c k n e s s . T h i s independence i s important not only i n r a t i n g the effects of dry f i l m thickness but a l s o i n a l l o w i n g the e n t i r e drying process to be monitored without interference from the weight changes taking place i n the coating.



760


Figure 3.

Time-temperature transformation diagram for the curing of coatings, from G i l l h a m (59).

CLAMP

COATED SD IE

ι MEASURN IG SCALE Figure 4.

C a n t i l e v e r device for measuring i n t e r n a l stresses during cure (top view). The coating thickness i s not indicated.





761

In effect, the p h y s i c a l chemistry of drying from s o l u t i o n i s a problem i n mechanics. In p r a c t i c e , i n s t e a d of warping the substrate, a t y p i c a l lacquer develops stresses ( i n excess of Ο as c a l c u l a t e d by E q u a t i o n 12, because some s t r e s s r e l i e f i s brought about by bending) that may exceed a threshold v a l u e , whereupon the system ruptures. Inasmuch as the system for a l l p r a c t i c a l purposes i s a two-dimensional laminated structure, rupture w i l l occur at or near the interface. Laminar f a i l u r e does not n e c e s s a r i l y s i g n i f y poor adhesion, for the f a i l u r e may be cohesive as indicated by ESCA and SEM d e t e c t i o n of r e s i d u a l polymer on separated s u r f a c e s (66). In some cases, f a i l u r e i s , indeed, a d h e s i v e as r e v e a l e d by the absence of radioactive-tagged molecules (67). In order to measure r e s i d u a l s t r a i n i n d e p e n d e n t l y of the r e s t r a i n t of the substrate, one must separate the dried coating from the s u b s t r a t e and measure i t s d i m e n s i o n a l changes. C r o l l (65) showed that epoxy coatings dried from s o l u t i o n shrank a p p r e c i a b l y when they were released from t i n - p l a t e d substrates by amalgamation. The shrinkage ranged from 1.4% to 1.8% when the epoxy content i n m e t h y l c e l l u l o s e was decreased from 70% to 30% i n the applied f i l m , i n d i c a t i n g that the lengthened time for drying allowed g e l a t i o n to occur w h i l e c o n s i d e r a b l e r e s i d u a l s o l v e n t remained i n the f i l m . This conclusion was v e r i f i e d by the discovery that s t r a i n s as high as 9% resulted from the use of a s l o w l y evaporating s o l v e n t such as one of the higher g l y c o l ethers. Of f u r t h e r i n t e r e s t was the f i n d i n g t h a t r e s i d u a l s t r a i n was independent of applied coating thickness i n the case of three lowb o i l i n g s o l v e n t s but i n c r e a s e d w i t h t h i c k n e s s w i t h h i g h - b o i l i n g s o l v e n t s (68). Pigmented systems a l s o show a dependency on loading (69, 70). Apart from oleoresinous systems that form f i l m s by c r o s s - l i n k i n g the neat polymer, a major p o r t i o n of today's t r a d e s a l e s market i s served by aqueous dispersions. Aqueous s o l u t i o n r e s i n systems are being developed for i n d u s t r i a l coatings. Aqueous r e s i n dispersions made t h e i r e n t r y v i a a l k y d e m u l s i o n s , f o l l o w e d a decade l a t e r by s t y r e n e - b u t a d i e n e r e s i n s as an outgrowth of the s y n t h e t i c rubber program. Later came p o l y ( v i n y l acetate) and a c r y l i c latexes, long before s o c i a l pressures were applied to reduce the v o l a t i l e organic constituents from coatings as an ecology measure. Drying from S o l u t i o n . The simplest coatings are those that contain a polymer i n a s o l v e n t . Organic s o l v e n t systems are hardy perennials destined to l a s t for s e v e r a l more decades, u n t i l t h e i r i n s u l t to the environment requires the development of one or more of the new t e c h n o l o g i e s d e s c r i b e d above. The p h y s i c a l c h e m i s t r y of drying from s o l u t i o n therefore becomes one's f i r s t concern. Wetting, of course, i s a prime requirement; but since a coating f o r m u l a t o r who has not a c h i e v e d i n i t i a l w e t t i n g of the s u b s t r a t e w i l l not remain i n b u s i n e s s , d r y i n g poses a more fundamental r h e o l o g i c a l problem than an i n t e r f a c i a l one, even though the interface i s i n v o l v e d . During the e a r l y stage the mechanical p r o p e r t i e s of polymer s o l u t i o n s are governed by t h e i r v i s c o s i t y . For l i n e a r polymers the c o n t r i b u t i o n of the f i l m - f o r m i n g i n g r e d i e n t to v i s c o s i t y i s expressed by the Staudinger r e l a t i o n , Equation 4, where a g e n e r a l l y



762


l i e s between 0.6 and 0.8. From the i n t r i n s i c v i s c o s i t y [ η ] (which i n r e a l i t y expresses the s i z e of the swollen polymer molecule), one could work backward and compute the v i s c o s i t y of the coating at any g i v e n c o n c e n t r a t i o n , but t h i s e x e r c i s e would be both f u t i l e and inaccurate. No c o a t i n g d r i e s at i n f i n i t e d i l u t i o n . I t i s of g r e a t e r s i g n i f i c a n c e to q u a n t i f y the s t r e s s e s t h a t occur v i a the development of r i g i d i t y i n the f i l m as the s o l v e n t evaporates, the s w o l l e n m o l e c u l e s take o v e r the e n t i r e volume, and s h r i n k a g e p e r s i s t s after that point. Two examples of d r y i n g of polymer from aqueous s o l u t i o n were p u b l i s h e d by Myers and coworkers. S e l e c t i n g a polymer t h a t had w e l l - c h a r a c t e r i z e d m o l e c u l a r s t r u c t u r e and f a i r l y w e l l - k n o w n morphology, T s u t s u i and Myers (71) a l l o w e d 7% s o l u t i o n s of p o l y ( a c r y l i c acid) to dry on the ARP device with varying degrees of n e u t r a l i z a t i o n α and learned that retention of water by the dried f i l m depended on a. As l o n g as l e s s than h a l f of the c a r b o x y l groups were n e u t r a l i z e d , the r e s i d u a l water content was determined by the primary hydration number of carboxyl groups and carboxylate ions. The gently s l o p i n g portion of the water retention curves (71) of Figure 6 shows t h i s phenomenon. I n c r e a s i n g the degree of n e u t r a l i z a t i o n beyond α = 0.5 w i t h a l k a l i introduced secondary hydration, as evidenced by the steeply r i s i n g p o r t i o n s of the c u r v e s . A c o n s i d e r a b l y reduced tendency toward secondary hydration was observed with amines. Because water r e t e n t i o n and water s e n s i t i v i t y are p o s s i b l e sources of poor wet adhesion, these findings have p r a c t i c a l s i g n i f i c a n c e . Water retention determines the mechanical properties of f i l m s i n general and of water-dispersible coatings i n p a r t i c u l a r . Coincident w i t h the i n c r e a s e d water r e t e n t i o n of p o l y ( a c r y l i c a c i d ) , the r i g i d i t y modulus of p a r t i a l l y amine-neutralized s o l u t i o n s (0 < α < 1.0) of the polymer was h i g h e r than t h a t of the zero or f u l l y n e u t r a l i z e d polymer, as shown by the ARP d r y i n g c u r v e s (72) of Figure 7. R i g i d i t y i s measured i n terms of the attenuation Δ of the shear p u l s e . I n i t i a l l y , water i s t i g h t l y bound i n the polymer c o i l s , which are spread somewhat by charges on the carboxylate i o n ; l a t e r the spreading i s more l i k e l y to produce water c l u s t e r s that p l a s t i c i z e the f i l m . The r e s u l t i s a peak i n m o d u l u s a t intermediate a. N e u t r a l i z a t i o n w i t h the branched amine homologues 2 - a m i n o - l p r o p a n o l and 2-amino-2-methy1-1-propanol r e q u i r e d h i g h e r α to a c h i e v e peak r i g i d i t y . The e f f e c t was not s t e r i c (72) and so decreased h y d r o p h i l i c i t y was suspected. A copolymer of b u t y l a c r y l a t e and a c r y l i c acid was synthesized so as to approximate f o r m u l a t i o n s used i n waterborne f o r m u l a t i o n p r a c t i c e w i t h o u t d e p a r t i n g d r a s t i c a l l y from the a c r y l i c a c i d homopolymer. When 2-methyl-2-propanol s o l u t i o n s of these polymers were d i l u t e d with water and then dried, the r i g i d i t y trends followed the p a t t e r n (72) shown i n F i g u r e 8 and no e v i d e n c e of secondary h y d r a t i o n was p r e s e n t . Reference to the o r i g i n a l a r t i c l e s w i l l r e v e a l that the number of carboxylate t r i a d s should be minimized i n the c o p o l y m e r i z a t i o n i f one wishes to ensure t h a t the marketed product w i l l be water i n s e n s i t i v e . Considerable a c t i v i t y has been reported i n the development of water-reducible coatings (73-76).



Figure 6.

Water r e t e n t i o n by p o l y ( a c r y l i c a c i d ) f i l m s at v a r i o u s degrees of n e u t r a l i z a t i o n and three r e l a t i v e humidities. Temperature: 40 °C. NaOH used as the n e u t r a l i z e r .


764


CO Û

o

=

0.50

Ζ Ο

< Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 26, 2017 | http://pubs.acs.org Publication Date: September 25, 1985 | doi: 10.1021/bk-1985-0285.ch031

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Rheology of Film-Forming Liquids - ACS Symposium Series (ACS

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