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Theoretical aspects of self-stratification
PROGRESS IN ORGAHIC COATINGS ELSEVIER
Progress in Organic Coatings 28 (1996) 161-171
Theoretical aspects of self-stratification Christopher Carr a, Eva WallstOm b a PRA, 8 Waldegrave Road, Teddington, Middx. TW118LD, UK b EnPro ApS, Lers¢ Parkall~ 42, DK-2100 Copenhagen, Denmark
Received 7 April 1995; accepted 13 April 1995
Abstract
In order to predict whether a system of two polymers or resins in a common solvent mixture will 'self-stratify', two predictive models, one based on UNIFAC and the other on surface tension relationships, have been developed. The UNIFAC model can predict phase behaviour, vapour pressure, evaporation rates and surface tensions for systems containing two polymers or resins in a solvent mixture. Comparisons between experimental and calculated data are made for acrylic/acrylic, epoxy/acrylic and alkyd/acrylic resin combinations. The prediction of phase separation during solvent evaporation from a thin film is satisfactory in most cases, especially when the difference in molecular weight between the two polymers is not too large. For epoxy/acrylic resin combinations, the calculated evaporation profiles are in reasonable agreement with observed values. The evaporation rate decreases with increasing epoxy molecular weight, but is almost independent of the acrylic resin and the resin ratio. The tendency of epoxy/acrylic resin combinations to undergo self stratification is predicted to increase as the molecular weight of the epoxy resin increases. The degree of phase separation is increased as the molecular weight of the acrylic resin is increased. These predictions agree with experimental observation but for acrylic/alkyd resin combinations, no phase separation is predicted which is not in agreement with experiment. This is probably because the model cannot allow for the broad molecular weight distribution of the alkyd resin. A second predictive model based on surface energy variation with concentration of two polymer solution phases in contact has been developed. This model can be used to predict which resin combinations will give rise to self-stratifiyng systems given the surface energy/concentration relationship of the pure resins in solution and assuming the systems have phase separated. For solutions of epoxy resins combined with a second resin the model correctly predicts the observed tendency for the resins to stratify provided the system phase separates at some point. Keywords: Self-stratification; Phase separation; Surface tension; Evaporationrate; UNIFAC
1. Introduction
The main aim of the ' B R I T E ' project studying self-stratifying coatings was to develop formulation guidelines for industry. The systems studied were combinations of two resins or polymers in a common solvent which should form different phases and separate into distinct layers during evaporation of solvent from a film. Evaporation rate, phase separation behaviour and surface energy relationships are important factors in deciding whether a resin pair in a common solvent will successfully form a self-stratifying coating. A full statistical treatment of the results is described by Joly [ 1 ] which allows stratification to be predicted from a knowledge of physical properties of the component materials based on the large amount of experimental data generated during the project. However, separate studies were undertaken to develop a model based on the UNIFAC method which can be used to predict phase behaviour and evaporation rates of solutions containing two polymers or oligomers. It 0300-9440/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSDI 0300-9440 ( 95 ) 00594-5
was hoped that this information could be used to select polymer pairs which show the desired phase behaviour, i.e. able to form homogeneous solutions up to 50 or 60% solids concentration but phase separating at higher concentrations as the solvent evaporated. The same model was used to predict the surface and interfacial surface tensions of the homogeneous or phase separated polymer solutions. Funke [ 2,3 ] has shown that a primary driving force for stratification is the surface energy difference between the two separating phases. Therefore, a second model was developed which can be used to predict whether a phase separated polymer or oligomer pair will stratify given the surface energy relationships of the two phases. Surface energies can be calculated from the UNIFAC model or measured directly. 2. U N I F A C model Calculation of the properties of a mixture requires a knowledge of the activity coefficients of the different components.
C Carr, E. WallstOm / Progress in Organic Coatings 28 (1996) 161-171
162
The UNIFAC model [4], which is based on the group contribution principle, uses a table of group interaction parameters estimated from experimental data, to calculate activity coefficients. According to the group contribution principle, properties of a molecule can be calculated by summing the properties of the functional groups constituting the molecule. Ethanol, for example, consists of three groups: --CH3, --CH2and -OH. UNIFAC can be used to estimate phase behaviour, vapour pressure, evaporation rate and surface tension. All these properties are of importance for a self-stratifying system as stratification is expected to occur after phase separation during the drying of the film. In addition, the surface tension of the phases and the interfacial tension between the two phases are important for successful stratification but difficult to measure directly. Activity coefficients of the components in a mixture, o3~,are a measure of how close the behaviour is to that of an ideal solution. The components in an ideal solution behave as if they were in their pure state, i.e. the activity coefficients are equal to 1. Activity coefficients significantly different from 1 indicate that the mixture is strongly non-ideal. The UNIFAC model calculates the activity coefficients according to Eq. (1) [4]: In o3i =
In
tt~ic°mbinat°rial"-[-In 0~iresidual
(1)
where 0~ic°mbinat°rial= the combinatorial activity coefficient accounting for contribution to the non-idealities from differences in size and shape of the molecules in solution. The combinatorial activity coefficient is dependent on the hardcore surface area and volume of the groups in solution and on the concentration of each component in mixture. o~iresidual= the residual activity coefficient accounting mainly for the energetic interaction between different groups. Parameters, characterising the interaction between groups in solution, are used in the calculation of the residual activity coefficients. It has been shown that UNIFAC can predict activity coefficients in solvent mixtures with good accuracy [4]. The restriction of the method is that not all interaction parameters of interest are available due to a lack of experimental data. In principle, it should also be possible to predict activity coefficients for polymer solutions. However, it has been shown that the solvent activity coefficients for the components in a polymer solution are, in general, underestimated by the UNIFAC model. The probable reason for this is that UNIFAC does not take into account that pure polymers are more closely packed than pure solvents. This was the background for the model developed by Elbro [ 5 ], where the combinatorial activity coefficients are calculated by a new method which accounts for the difference in polymer and solvent density. It has been shown that the revised model, using the original UNIFAC interaction parameter table, gives good agreement with experiment. However, the revised model is not used in this paper.
2.1. Phase separation Phase separation or liquid-liquid equilibrium (LLE) calculations are important applications of the UNIFAC model. The LLE calculations can be divided into two parts; detection of phase separation and calculation of the point of phase separation. Phase separation is detected by checking whether the matrix A, consisting of the second derivatives of the Gibbs free energy of mixing, A G~x, with respect to the mole fractions, is positive in a range of concentrations around the concentration of interest. The elements in the matrix A are given by: 02A Gmix A v - - i , j = l , 2 .... N C - 1
(2)
OXiOXj
where NC
A G ~ x = R T ~ x i In(a/)
(3)
i
NC= the number of different components in the system, ai = the activity of component i in the solution. It is calculated from: a i =xio_) i
(4)
where xi = the mole fraction of component i, o3i= the activity coefficient of i. The equilibrium condition of an LLE system can be expressed by the isofugacity criterion. ai I ----ai n
(5)
where aiI = the 'activity' of component i in phase I, aiH= the 'activity' of component i in phase II. This gives N non-linear equations (one for each component) with 2N unknowns, which must be solved by an iterative procedure. The isofugacity criterion, together with the mass balances, form the 2N necessary equations. A multivariable Newton-Raphson iteration procedure was used for the solution of the non-linear equations [ 6 ] and the necessary derivatives with respect to the unknowns were found numerically.
2.2. Evaporation rate The evaporation rate (ER) is a function of several factors, which can be divided into two categories; external and component. The external factors describe the environmental conditions: temperature, humidity, air velocity and surface geometry, which must be specified for each case. The component factors are: diffusion coefficient in air, vapour pressure, heat of vaporisation and activity coefficient in solution. The transfer of mass from the liquid to the surroundings is partly caused by the difference in equilibrium and bulk concentrations (the driving force) and partly caused by the phase displacement from liquid to vapour. The following expression is only valid if the vapour pressure of the solution is
C. Carr, E. WallstOm / Progress in Organic Coatings 28 (1996) 161-171
below the atmospheric pressure. The evaporation rate, Ri [ mass / ( area × time) ], for a component i, is described by: R i ~- ki(Yi eq - y i °) -t-yieqER i
y ieq --
(6)
x i ,~iP i TM
(7)
E Xjt~jpjsat
ki = 46MWiD i°'ss v ~r°6s
(8)
where yieq_ the equilibrium concentration of component i, y o = the bulk concentrations of component i in the vapour phase, k~= the mass-transfer coefficients of component i, p sat = the vapour pressure of pure component i at the system temperature, MWi = the molecular weight of component i, D~ = the diffusion coefficient in air of component i, v~r = the air velocity. The progress of evaporation from a film is described by the following differential mass balance:
dMi =ARi dt
(9)
where dM~ = the amount of component i evaporated in the time interval dt, A = the area of the film. The total amount evaporated in the time interval dt, dM, is thus: dMt=A dt )-'R~
2.3. Surface tension The surface tension of an 'ideal' mixture can be calculated according to: ideal_
liquid phase, X/surf = the mole fraction of component i in the surface layer, o3is ~ = the activity coefficient of component i in the surface layer, o3i = the activity coefficient of component i in the bulk liquid phase. Here it is assumed that: Ai =A~ = the molar surface area of pure component i The surface tension of a homogeneous mixture, Y~a~, (with NC different components) can thus be estimated from the above equation. Furthermore,
Ex-SUrf , 1
(13)
and the surface area, A~, is estimated from: A i = C V i 1/3
(14)
V~is the molar volume of component i at the system temperature, C is a constant, which equals 1 for all components but water. This gives N C + 1 equations, with unknowns Y~a~, Xls~f, x2SUrf...XNcs ~ which can be solved numerically using a Newton-Raphson iteration scheme with analytically derived derivatives.
2.4. Results
(10)
This equation is solved numerically by defining the total change of mass per step as 1.0% of the initial weight (Mo). Since A is known, Ri and dt can be calculated (by iteration). This means that dMi can be found and a new composition can be calculated. For mixtures containing polymers, the mass transfer will be limited by other factors when the remaining film contains less than around 10% solvents. The numerical integration is thus stopped at this point. Interpolation between the calculated points is performed by use of spline functions.
~Ynflx
163
v"~ X
(11)
- - 2,~ i ~/i
where Yi = the surface tension of component i. As most mixtures are non-ideal in their behaviour a model taking this into account has been used. A more sophisticated model for calculation of the surface tension of liquid mixtures is based on the assumption that the surface layer can be treated as a separate phase located between the vapour and the bulk liquid phases. From this assumption and from classical thermodynamics the following equation can be derived [7]: [
XiO) i
"Ai]/n~x=AiYi-RTln~xiS~)
i = I , 2,...NC
(12)
where Ai = the partial molar surface area of component i in the mixture, xi = the mole fraction of component i in the bulk
2.4.1. Phase separation In order to give an idea of the accuracy of the applied models some comparisons between the experimentally measured and the calculated results were made. The polymers included are listed in Table 1. Phase separation was experimentally measured [ 8] for the system Epikote 1001/Neocryl B700 with 4-methyl, 2-pentanone (MiBK)/xylene at 25 °C (Table 2). The polymer concentration was set at 30% (wt./wt.) and the ratio MiBK/ Xylene 7:13 as determined experimentally. The calculations predict: (i) no phase separation occurs for a ratio of Epikote 1001 :Neocryl B700 of 1:1; this is not in accordance with the experimental measurements; (ii) the calculated phase separation is not as sensitive to the polymer composition as experimentally observed; (iii) for ratios of Epikote 1001 to Neocryl B700 between 3:1 to 5:1 the calculated composition of the components in the two phases is an acceptable agreement with the observed behaviour; (iv) for a ratio of Epikote 1001 to Neocryl B700 of 9:1 it is seen that the composition of phase I is not in accordance with the observations. In order to study the influence of molecular weight of the polymers on phase separation behaviour further, the percent solids at phase separation for the system Neocryl B700 (Mw = 40 000) and PMMA (Mw varied between 10 000 and 65 000) dissolved in butyl ethanoate was experimentally measured at 25 °C [8]. Calculations are compared with experimental measurements in Table 3.
164
C. Carr, E. Wallst6m / Progress in Organic Coatings 28 (1996) 161-171
Table 1 Polymers used Epikote 828 Epikote 1 0 0 1 Epikote 1004 Epikote 1007 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B811 Neocryl B813 Crodac AC500 Crodac AC550 Lumiflon LF200 Lumiflon LF916 Alloprene R10 Synolac 6016 Synolac 9090 Plastokyd AC-4X Hythane 9 Plastokyd SC-7 Plastokyd SC-140 Plastokyd SC-400 Plastoprene 1S Hypalon 20 Uralac AD143
Uralac AD9
bispbenol-A epoxy bisphenoI-A epoxy bisphenol-A epoxy bisphenol-A epoxy thermoplastic acrylic (PiBMA) thermoplastic acrylic (PMMA) thermoplastic acrylic (PBMA) thermoplastic acrylic (PMMA) thermoplastic acrylic (PEMA) thermosetting acrylic thermosetting acrylic fluorinated polyether fluorinated polyether chlorinate rubber short oil alkyd short oil alkyd acrylic modified alkyd urethane alkyd siliconised polyester siliconised alkyd siliconised epoxy ester cyclised rubber chlorosulfonated polyethylene alkyd produced from phthalic anhydride, linseed oil and glycerol alkyd produced from phthalic anhydride, linseed oil and trimethylol propane
Shell UK Ltd. Shell UK Ltd. Shell UK Ltd. Shell UK Ltd. ICI Resins ICI Resins ICI Resins ICI Resins ICI Resins Croda Resins Ltd. Croda Resins Ltd. ICI Resins ICI Resins ICI Resins Cray Valley Products Cray Valley Products Croda Resins Ltd. Croda Resins Ltd. Croda Resins Ltd. Croda Resins Ltd. Croda Resins Ltd. Croda Resins Ltd. Dupont DSM Resins BV
DSM Resins BV
Table 2 Phase behaviour of Epikote 1001/Neocryl BT00 system: calculated and ( measured ) concentration of the component ( wt.% ) R~ioPhase Solids Epikom Neocryl MiBK Xy~ne 1:1 I -(29) -(10) -(19) -(26) -(45) 1I - (28) - (2) - (23) -(47) 3:1 1 27.8(30) 12.2(15) 15.6(15) 24.7(25) 47.6(45) II 32(36) 32.0(35) 0.0(1) 24.3(21) 43.7(43) 5:1 1 27.3(30) t2.4(16) 14.9(13) 24.8(25) 47.9(46) 1I 31.4(33) 31.4(33) 0.0(0) 24.4(22) 44.3(45) 9:1 1 26.9(30) 12.6(28) 14.3(2) 24.8(20) 48.3(50) 1I 30.8(32) 30.8(31) 0.0(1) 24.4(25) 44.8(43)
except with PMMA of 10 000 Mw where no phase separation is observed experimentally. Both calculation and experiment agree that the percent solids at phase separation decreases with increasing molecular weight of PMMA. However, according to calculation, the percent solids at phase separation has a minimum at a B700:PMMA ratio of 1:1 which is not observed experimentally. It can be concluded that the UNIFAC model is able to predict the phase behaviour of polymer-polymer-solvent systems reasonably well. The major problems occur when the difference between the molecular weight of the polymers involved is high. However, the calculation does not predict the dependency on the percent solids at phase separation on the ratio of the two polymers involved. 2.4.2. Evaporation rates
In order to illustrate the dependency of solvent evaporation rate on the different components present in the initial film, the evaporation profiles under different conditions were calculated for various epoxy/acrylic resin combinations (Figs. 1-4) The solvent mixtures used are given in Table 4. The environmental conditions were set at: temperature, 23 °C; humidity, 0%; air speed, 0.1 m/s; film thickness (initial), 100 g/m 2. The following conclusions can be made from the calculations of evaporation profile for the given polymers. (i) The drying time decreases slightly with increasing molecular weight of the Epikote, see Fig. 1. (ii) From Fig. 2 it is seen that the drying time is not very sensitive to the selected ratio of the two polymers involved. (iii) The drying time is very dependent on the chosen solvent mixture, see Fig. 3. The solvents with a low vapour pressure do not evaporate as fast as the solvents with a high vapour pressure, as expected. 100.0 90.0 tm
80.0
"t3 70.0
Table 3 Phase separation forB700and PMMA: calculated and experimental [8] (in parentheses) System
8 o
60.0
o. ¢2 > 50.0 t,l 40.0
Ratio between polymers 1:4
1:1
4:1
23(-) " 10(13) 8(10)
30(-) 9(11) 6(8)
91(-) 18(11) 12(7)
I
30.0
t
20.0
B700:PMMA 10 B700:PMMA 40 B700:PMMA 65
828 Epikote Epikote 1001 1007 • * - * * Epikote .....
lO.O
o.o
= No phase separation observed experimentally.
o.o
5.0
10;.0
15'.o
Neocryl 8700 3:1 Neocryl B700 3:1 Neocryl B800 3:1
2o'.o Time
The calculated and experimentally measured values for the percent solids at the point of phase separation agree very well
2~.o
30.0
(rain.)
Fig. 1. Different Epikote/Neocryl B700 in MiBK/xylene mixtures. Polymer ratio 3:1.
C. Carr, E. WallstiJm/ Progress in Organic Coatings 28 (1996) 161-171 100.0 90.0 80.0
¢)
P o
70.0
Q
60.0
t
o_ o> 50.0 Ld 40.0
Q
30.0 20.0
e
10.0
..... Epikote 828 - Neocryf B700 1:1 ,~.~.':,~ Epikote 828 - Neocryl 8700 3:1 Epikote 828 Neocryl B800 9:1
Q
0.0 0.0
s.b
lO;.O
lS'.o
20'.0
2s'.o
so o
Time (rain.) Fig. 2. Epikote 828/Neocryl B700 in MiBK/xylene. Different polymer ratios. 100.0 90.0
e
80.0 "0
e
70.0
1
60.0 0:> i,i
165
(iii) the interfacial tension between the two liquid phases should be large enough to stop the second phase being dispersed in the first phase; (iv) the interfacial tension between the bottom liquid phase and the substrate should be very low. This is obtained if: (a) the solvent mixture in the bottom phase has an affinity for the substrate; (b) the polymer in the bottom phase is partly compatible with the substrate. Evaporation rate, phase separation and surface tension calculations have been performed for a large number of systems. Each system consisted of an Epikote or an alkyd, a second polymer and a solvent mixture (S,, Sg or $3). The polymers were mixed at different ratios ( 1:1, 1:3 and 1:9). The initial concentrations in the calculations were set to 20 wt.% polymer and 80 wt.% solvent. Tables 5-7 summarise how the systems investigated behave with respect to the calculated self-stratifying behaviour. From the results it is predicted that stratification improves with increasing epoxy molecular weight. In order to obtain strong phase separation, where each phase contains predominantly one polymer, the molecular weight of the second polymer should be relatively high. Apparently the solvent mixture S 2 gives rise to the largest interfacial tension between the two liquid phases. This is because Dowanol PM concentrates in one of the liquid phases, whereas the other solvents are evenly distributed between the two phases. The investigated acrylic/alkyd sys-
@
50.0
t
100.0
40.0
90.0
30.0
80.0
20.0
t
70.0
..... Solvent mtxture I l ~ i l ..... Solvent mixture 2 * * * * * Solvent mixture 3
I0.0
0.0 0.0
5.b
lo:o
15'.0
20:0
251.0 30:0
35.0
Time (rain.) Fig. 3. Epikote 828/Neocryl B700 in different solvents (S,, $2, $3). Polymer ratio 3:1.
(~.
,,>,
60.0 50.0 40.0 30.0 20.0
(iv) The drying time, for the polymers investigated, is almost independent of the second polymer, see Fig. 4. The last conclusion is of course dependent on the chosen polymers.
10.0
0.0
,,
o.o
Ep|kote
828 828 828 828
Neocryt B700 Neocn/I B813 Neocryl B811 Alloprene RIO
lo'.o
15'.0
20'.0
iii:.i Eplkote •. •
s.~
Eplkote
3:1 3:1 3:1 3:1
25'.0
30.o
Time (rain.) Fig. 4. Epikote 828. Different polymers in MiBK/xylene. Polymer ratio 3:1.
2.4.3. Prediction of self-stratification of the mixtures In order to obtain a good self-stratifying system, containing two polymers and a solvent mixture, the following conditions need to be satisfied: (i) the system should separate into two phases during the drying process; (ii) one polymer should be concentrated in each of the phases;
Table 4 Solvent mixtures Solvent mixture
Composition (wt.%)
SI: MiBK-Xylene $2: MiBK-Xylene-Dowanol PM $3: Xylene
50:50 50:30:20 100
C. Carr, E. WaUst6m/ Progress in Organic Coatings 28 (1996) 161-171
166
Table 5 Self-stratification of different systems (solvent mixture 1 ( S~) ) Polymer 1
Polymer 2
Ratio 1:1 PS a
Epikote 828
Epikote 1001
Epikote 1007
Neocryl B700 Neocryl B813 Neocryl B811 Neocryl B700 Neocryl B813 Neocryl B811 Neocryl B700 Neocryl B 813 Neocryl B811
Ratio 3:1 PD b
X
u,"
'~t- -
'~II c
X
+
Ratio 9:1
PS
PD
Yl- Ya
PS
PD
Yl- "/ix
X
-
X
u,"
×
0.9
X
-
X
~
~
0.0
X
-
X
0.7
t,,"
-
0.2
0.3
~
+ + -
0.9 0.0 0.0 0.9
PS = phase separation. b PD = polymer distribution. ¢ Yt - Yn = the numerical difference between the surface tension of two formed liquid phases (at phase split). This can be taken as a relative measure of the interracial tension between the two phases. The system phase separates during drying process. + Each polymer is concentrated in a single phase. X The system does not phase separate. - The concentration of the polymers in each phase is significant. Table 6 Self-stratification of different systems (solvent mixture 2 ($2)) Polymer 1
Epikote 828
Epikote 100J
Epikote 1007
Polymer 2
Neocryl B700 Neocryl B813 Neocryl B811 Neocryl B700 Neocyl B813 Neocryl B811 Neocryl B700 Neocryl B813 Neocryl B811
Ratio 1:1
Ratio 3:1
Ratio 9:1
PS a
PD b
YI- Yll c
PS
PD
)5 - Yn
PS
×
-
X
(+ )
0.4
(+ )
X × × 1.3
tJ
tJ
X X × t,J
~
+
1.1
~ ~ tJ tJ
+ (+ ) -
0.4 1.1 0,7 0.4
t,~
PD
Yl - %1 0.9
+
1.2
a PS = phase separation. b PD = polymer distribution. c Yt- %1= the numerical difference between the surface tension of two formed liquid phases (at phase split). This can be taken as a relative measure of the interfacial tension between the two phases. u'r The system phase separates during drying process. + Each polymer is concentrated in a single phase. X The system does not phase separate. - The concentration of the polymers in each phase is significant. t e m s d o n o t r e s u l t in s t r a t i f i c a t i o n a c c o r d i n g to t h e s e c a l c u -
tions. T h e r e a s o n f o r d i s c r e p a n c y is p r o b a b l y t h a t t h e ' g r o u p '
lations.
d e f i n i t i o n s o f t h e a l k y d s a r e n o t a c c u r a t e e n o u g h but, as t h e a l k y d s are n o t w e l l - d e f i n e d s u b s t a n c e s , it is d i f f i c u l t to s o l v e the problem.
2.5. Conclusions It h a s b e e n s h o w n t h a t t h e U N I F A C m o d e l c a n b e u s e d to e s t i m a t e t h e p o i n t o f p h a s e s e p a r a t i o n in a t w o p o l y m e r s o l u tion system of the type epoxy/acrylic, but the phase separat i o n in a c r y l i c / a l k y d s y s t e m s w a s n o t p r e d i c t e d . Surface tension and interfacial tension were estimated using an ideal method which gave a relatively good calculated surface tension for these kinds of systems. The calculations do not predict that the acrylic/alkyd syst e m s will s t r a t i f y w h i c h is n o t in a c c o r d a n c e w i t h o b s e r v a -
3. Prediction of stratification based on surface energy T h e initial w o r k b y F u n k e [ 2,3 ], o n s e l f - s t r a t i f y i n g p o w d e r c o a t i n g s y s t e m s , s h o w e d that a p r i m a r y d r i v i n g f o r c e f o r s t r a t i f i c a t i o n is t h e s u r f a c e e n e r g y d i f f e r e n c e b e t w e e n t h e t w o r e s i n s . T h e r e f o r e , a n a t t e m p t w a s m a d e to d e v e l o p a m o d e l to p r e d i c t w h e t h e r a s y s t e m c o m p o s e d o f t w o p o l y m e r s o l u -
167
C. Carr, E. WallstOm / Progress in Organic Coatings 28 (1996) 161-171
tion phases will stratify based simply on surface energy relationships of the two phases. It is thermodynamically favourable for the disperse phase in a two-phase system to coalesce, unless the particles or droplets are stabilised somehow, as this leads to a lowering of interfacial area and hence surface energy of the system. Whether it is favourable for the two separating phases to form into distinct layers with the correct orientation can be predicted by analysing the interfaces produced in a two-component paint film (Fig. 5). Two simple conditions for stratification to occur in a thin film containing two phases can be stated: (A) the intended basecoat component must spontaneously wet the substrate; (B) the total surface and interfacial surface tension of the required layer sequence must be the lowest possible. Condition ( A ) is satisfied when the contact angle (0) between component 2 and the substrate is zero. Y o u n g ' s equation states that: 3'sl - - 3's2 - - 3"12 COS 0 = 0
Air
Component 1
'1
"/12 Ys2
Fig. 5. Interfaces in a two-componentpaint film. tension. For the sequence in Fig. 5 the total surface energy is given by: (18)
3's2 + 3"12 "F 3'1
For the alternative sequence, the total surface energy is: 3'sl + 3'12+ T2
(19)
Therefore, t h e r e q u i r e d l a y e r s e q u e n c e i s t h e m o s t f a v o u r a b l e when (19) > (18) or:
(15)
where 3',~ is the substrate/component 1 interfacial surface tension, 3",2is the substrate/phase 2 interfacial surface tension and 3'12 is the interfacial surface tension between components 1 and 2. The contact angle is zero when: (16)
3"sl - - 3"s2-- 712 > / 0
Also, the surface energy of the system should decrease for spontaneous wetting leading to the condition: 3's -- 3's2-- 3"12-- 3'1 > 0
(17)
where ys is the substrate surface energy with air. Condition (B) states that the most favourable layer sequence will be the one giving rise to the lowest total surface
(20)
3'sl - - 3'1 - - 3's2 -F 3'2 > 0
It is evident, therefore, that the prediction of stratification requires a knowledge of the surface energies of the two separating phases and their interfacial surface tensions plus their interfacial surface tensions with the substrate. In reality the surface tension of solution phases will be changing continuously as solvent evaporates. However, as a first approximation it was assumed that the surface energy of the pure solid resin which predominates in each phase could be used for predictions. The model was later refined to allow for the presence of solvent in each phase assuming that the concentration of the two phases remained equal and that each phase contained predominantly one of the resin components.
Table 7 Self-stratificationof different systems (solvent mixture 3 ($3) ) Polymer 1
Epikote 828
Epikote 1001
Epikote 1007
Polymer 2
Neocryl B700 Neocryl B813 Neocryl B811 Neocryl B700 Neocryl B813 Neocryl B811 Neocryl B700 Neocryl B813 Neocryl B811
Ratio 1:1
Ratio 3:1
Ratio 9:1
PS ~
PD b
T1- Tnc
PS
PD
3'1- Tn
~
-
+
tJ
-
0.6
~ tJ ~ j,1
_
0.2
tl
+
0.3
t,," ~ ~ ~
+ + -
0.2 0.3 0.2 0.6
PS
PD
TI- Tn
u,r
tJ
0.2
a PS = phase separation. b PD = polymerdistribution. c Yl- Tn= the numericaldifferencebetween the surface tensionof two formed liquid phases (at phase split). This can be taken as a relative measure of the interfacialtension betweenthe two phases. tJ The system phases separates duringdrying process. + Each polymeris concentratedin a single phase. × The systemdoes not phase separate. - The concentrationof the polymersin each phase is significant.
C. Carr, E. WallstOm/ Progress in Organic Coatings 28 (1996) 161-171
168 Table 8 Surface energies of various substrates
Substrate
Uncleaned steel Acetone cleaned Abraded steel Aluminium foil Polypropylene Polypropylene oxide Lexan TF 60
3.2. Prediction of stratification from solid resin surface energies
Td ( m N m -I )
"yP (mNm -l)
,,/total (mNm -1)
36.5 28.7 32 30.3 25.6 32.0
4.8 15.6 34 27.5 7.1 11.2
41.3 44.3 68 57.8 32.7 43.1
35.6 31.5
10.7 6.9
46.3 38.4
The values of polypropylene, polypropylene oxide Lexan and TF60 were kindly supplied by CoRI.
3.1. Results The disperse and polar contributions to the surface tension of a solid surface can be determined if the contact angle between the solid and two liquids with known disperse (3/) and polar ( T p) surface tension components is measured. The Harmonic Mean method of Wu [9] is the favoured technique. For an interface between two materials, 1 and 2, the interfacial surface tension is given by:
TI2 = T1 + T2
4TldT2 d
4TIPT2 p
Tld + T2 d
T1 p + T2 p
(21)
where Yl and T2 are the total surface energies of materials 1 and 2, respectively. Using Eq. (21) and Young's Law, the surface energy of any material can be calculated if the contact angles with two reference liquids are known. Table 8 shows the results obtained for various substrates. In the case of steel substrates a very high surface energy can only be achieved by cleaning the surface in a flame. Even so, absorption of material from the atmosphere reduces the energy to below that of water within two hours. An untreated steel surface has a surface energy of only 41.3 mN m - ~which is only marginally improved by degreasing with acetone. Degreasing with xylene had virtually no effect on the measured surface energy. Abrading the surface with 200 grade wet and dry paper caused a significant increase in the surface energy but subsequent cleaning with organic solvent reduced the surface energy. The surface energy of plastic substrates is normally much lower than metals. This is demonstrated in the surface energies in Table 8 which were measured by CoRI. All values are significantly lower than an abraded steel surface and aluminium foil. The method of Wu can also be applied to determine the surface energies of solid resins when cast as thin films. The results for some resins are presented in Table 9. It has been shown above that, for a two phase system to stratify, simple thermodynamic considerations give rise to three conditions which must be satisfied.
Using the nomenclature in Fig. 5 the conditions for stratification can be summarised as: Tsl - %2 - T12 >/0
(22)
~sl -- T1 -- ~s2 -'~-T2 > 0
(23)
T s - % 2 - T12- T1 > 0
(24)
Using the surface energies of the two pure resin components in place of the phase separated resin solutions, these conditions can be calculated for any combination of substrate and resins if the disperse and polar contributions to the surface energies of all components are known. The calculated and experimental behaviour observed at CoRI for six formulations on Lexan (a polycarbonate) are listed in Table 10. These suggest that the surface energies of the pure solid resins can be used to predict stratification with some accuracy in these six systems on Lexan. However, of the three systems experimentally observed to stratify on TF60 only one is predicted to stratify (Table 11). It could be argued that the condition which is not satisfied has an insignificant value. However, if the same principle is applied to the resins used at PRA the predictions are not as good (Table 12). In panicular, systems with Lumiflon are not predicted to stratify using this method, but they are observed to stratify strongly experimentally. The probable reason for this is that the effect of Table 9 Surface tensions ( m N m - i ) of solid resins Resin
Epikote 828 (amine cured) Epikote 1001 Epikote 1004 Epikote 1007 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B 811 Neocryl B 813 Crodac AC500 Crodac AC550 Lumiflon LF200 Lumiflon LF916 Plastokyd SC7 Plastokyd SC 140 Plastokyd SC400 Plastokyd AC4X Alkyd VAS 9223 Hythane 9 Synolac 6016 Synolac 9090 Plastoprene 1S Alloprene R 10 Hypalon 20
Harmonic mean Td
,yv
Ttotal
33.7 36.1 34.1 34.4 28.2 30.2 24.7 30.5 27.6 29.4 32.1 26.3 27.2 27.9 27.2 26.3 27.8 29.1 26.3 30.5 33.6 31.9 40.9 32.1
10.8 9.3 11.5 9.4 2.6 12.0 9.7 13.9 10.2 12.0 8.6 10.1 10.5 10.1 9.8 11.2 10.8 10.2 13.4 14.0 11.7 13.2 6.1 8.6
44.5 45.4 45.6 43.8 30.8 42.2 34.4 44.4 37.8 41.4 40.7 36.4 37.7 38.0 37.0 37.4 38.6 39.3 39.7 44.5 44.3 45.1 47.0 40.7
C. Carr, E. WallstOm/ Progress in Organic Coatings 28 (1996) 161-171
169
Table 10 Prediction o f stratification on L e x a n 7s - ~s2 - 712 - 71
Exp.
Resin 1
Resin 2
3',1 - "Ys2- 712
~sl - ~1 - 7 s 2 - 7 2
Theory
Lumiflon LF200 Lumiflon LF200 Lumiflon LF302 Lumiflon LF200 Desmophen 4125 Lumiflon LF200
Plexigum M890 Plexigum PM381 Plexigum M890 Desmolac 2770 Lumiflon LF200 Synthacryl VSC11
- 5.49
5.30
3.00
X
×
0.49
3.03
8.97
u,~
1, I
- 2.92
4.19
2.69
×
X
0.03
0.85
8.51
~
0.69
7.16
12.81
u,r
u~'
- 5.30
5.48
3.19
X
X
~s-- )'s2-- 712 -- 71
Theory
Exp.
x
X
Table 11 Prediction o f stratification on T F 6 0 Resin 1
Resin 2
%1 - - '~s2-- 712
'Ysl - -
Lumiflon LF200 Lumiflon LF200 Lumiflon LF302 Lumiflon LF200 Desmophen 4125 Lumiflon LF200
Plexigum M890 Plexigum PM381 Plexigum M890 Desmolac 2770 Lumiflon LF200 Synthacryl VSC11
- 8.12
2.67
- 7.19
0.46
3.01
1.39
- 4.55
2.55
- 7.50
X
- 0.26
0.56
0.67
X
- 1.34
5.14
5.25
×
u'r
- 8.00
2.78
- 7.07
×
X
Table 12 Prediction o f stratification on a l u m i n i u m foil Resin 2
Neocryi B700 Neocryl B 7 2 8 Neocryl B 8 0 4 N e o c r y l B811 Neocryl B813 Crodac AC500 Crodac AC550 Lumiflon LF200 Lumiflon L F 9 1 6 Plastokyd SC7 Plastokyd S C 1 4 0 Plastokyd SC400 Plstokyd A C 4 X Alkyd VAS 9226 Hythane 9 Synolac 6016 Synolac 9090 Plastoprene 1S Alloprene R 1 0 Hypalon 20
Resin
'~1 - - 7 s 2
"~" ' ~ 2
u," X
the solvent on surface energy has not been taken into account. Stratification occurs before all the solvent has evaporated, so it is the surface energies of the separating phases rather than the solid resins which are important.
1
E p i k o t e 828
Epikote 1001
Epikote 1007
Theory
Exp.
Theory
Exp.
Theory
Exp.
~ × ~ X X X ~ X × tJ ~ X X X
× × ~ X X ~ X X X × X X X ×
t,J × X X X × t,,," X × X X X × x
~ × X X × ~ x ~ u," x x X X u,r
tJ X × × X × ~ X X X X X X ×
t,~ × × X ×
x
x
X
x
X
X
X
X
x
X
X
x
3.3. Prediction of stratification from solution surface energies When a polymer is dissolved in a solvent or solvent mixture, the surface energy of the solution will be dominated by the solvent except at high polymer concentrations. This is illustrated in Fig. 6 which shows a plot of surface tension 45
t,," X X X X u,"
x
x
x
x
x
x
X
X
X
X
X
X
tJ I,,"
X
~
X
~
X
X
~
x
~
X
~
Calculated .O ~ 35
Experimental
+
+
/J j*
~'
.j~.J+
30
j-+ 2s
20
i
i
i
i
i
i
~
,
q
0.1
0.2
0.3
04
05
0.6
0.7
0.8
0.9
-~ !
Reshl Concentration
Fig. 6. Calculated a n d experimental surface tensions for Epikote 828 in methyl iso-butyl ketone ( M i B K ) .
C. Carr, E. WallstiSm/ Progress in Organic Coatings 28 (1996) 161-171
170 Table 13 Calculated coefficients in Eq. (25) Resin
Solvent
A
B
Epikote 828
xylene methyl iso-butyl ketone n-butyl acetate methoxy propanol methyl iso-butyl ketone n-butyl acetate methyl ethyl ketone n-butyl acetate methyl ethyl ketone n-butyl acetate xylene methyl iso-butyl ketone n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate
14.6 19.7 17.8 15.5 21.6 20.8 21.1 20.4 21.6 20.9 9.3 13.3 7.7 15.2 8.2 16. I 11.5
- 3.1 - 3.1 - 3.7 - 3.4 - 3.0 - 4.2 - 4.3 - 3.5 - 4.5 - 3.7 - 4.3 -4.7 - 3.4 - 2.2 -2.3 - 3.6 - 3.0
Epikote 1001 Epikote 1004 Epikote 1007 Lumiflon LF916 Lumiflon LF200 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B 811 Neocryl B 813
30
1
25 J I ~ - - A -
~',~ - 7,2 - 7.12
20 ~ _ _ ~
YYsl Yy~ - 7.s= +7.z 7' s
7'S2 - 7 1 2
- 7.1
15= 10 5
°
50
50
7o
8o
9o loo
Resin Concentration (%)
Fig. 7. Prediction of stratification for Epikote 1001/Neocryl BT00.
20
10
YYsl
7.1
~'s2 + 7.2
Ys
7's2
7"42 - 3"1
t : "-
0
,~
.
.
.
.
> ~
I
-5
I
0
la
20 a0 4a 55 aa 7b aa
ld0
Concentration (% resin) Fig. 8. Prediction of stratification for Epikote I 0 0 1 / L u m i f l o n LF 200.
versus concentration for Epikote 828 in MiBK. At high resin ~oncentrations, a small addition of solvent produces a large decrease in the solution surface tension. At 50% solids the surface tension is dominated by the solvent and further dilution has only a small effect on the solution surface tension. Surface tension/concentration relationships were either measured experimentally or calculated using the UNIFAC method described above. The traces all show the same general form described by: )'~x = %ol + A exp(Bf)
(25)
where 7~x = surface energy of the solution, %o~= surface energy of the solvent, f = weight fraction of the solvent, A, B = constants. The constant A can be calculated experimentally or from % - %ol f f = 0) where Tr is the surface energy of the pure resin. B can then be calculated from a surface energy/concentration plot. The calculated values of A and B for the systems studied are listed in Table 13. These data alone can be used to describe the total surface tension of the resin solutions at any concentration. However, in order to use the data to predict stratification, the disperse and polar components of the surface tension must be known. This cannot be measured directly but can be calculated if we assume they vary in a similar way to the total surface energy. We can calculate values for a polar and disperse contribution to the A coefficient of the solution, A p and A u respectively, from: Ap =
"yrp
Ad=
")/rd -
--
")/sol p
")/sold
(26)
Using the experimentally determined value for B, the variation in the polar and disperse components of the surface tension of the solution can be calculated at any concentration. Assuming that the concentration of the two phases is always the same, we can now predict whether stratification should occur during solvent evaporation. This is illustrated in Fig. 7 for the system Epikote 1001/Neocryl B700 in n-butyl acetate. The three conditions for stratification (Eqs. ( 2 2 ) - ( 2 4 ) ) are plotted against the resin concentration. Where all three conditions are positive we would predict that the system would stratify. As can be seen, this system is predicted to stratify at all concentrations (provided it is two phase) which is in agreement with experiment. For the system Epikote 1001/Lumiflon LF200 stratification is predicted for concentrations up to 80% when one of the conditions becomes negative (Fig. 8 ). This would explain why the system is not predicted to stratify using pure resin surface energies but is observed to stratify experimentally. Below 80% solids the two-phase system will form into two layers. At 80% solids the conditions for stratification are no longer satisfied but the viscosity is too high to allow much disruption of the layers. This is also consistent with optical examination of film formation from an unpigmented Epitoke/Lumiflon system where two layers appeared to form at low concentrations but some disruption was observed at high resin concentrations. The concentration ranges where stratification is predicted for the systems studied at PRA are listed in Table 14. The range quoted is the concentration range where all three conditions remain positive. The experiment column shows the degree of stratification measured by FTIR, where 4 represents complete separation into layers and 0 indicates no measurable separation of the polymers. For Epitoke 1001 and 1004, systems which are predicted to stratify at high concentrations appear to correiate well with systems observed to stratify in practice. For Epikote 828 the
C. Carr, E. Wallsti~m/ Progress in Organic Coatings 28 (1996) 161-171
171
Table 14 Predicted concentration ranges for stratification of systems used at PRA Resin 1
Resin 2
Solvent
Range
Exp.
Epikote 828
Lumiflon LF200 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B811 Neocryl B 813 Lumiflon LF200 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B811 Neocryl B813 Lumiflon LF200 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B 811 Neocryl B813
methyl iso-butyl ketone n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate methyl iso-butyl ketone n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate methyl iso-butyl ketone n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate
0-100 0-100 0--30 60-100 0 70-- 100 0-80 0-100 0 0 0 0 0-80 0-100 0 90-100 0 0
? 1 0 3 0 0 4 3 0 2 0 1 4 3 0 2 0 1
Epikote 1001
Epikote 1007
correlation is not so good, probably because some of these systems do not phase separate. For Epikote 828 and Neocryl 813, stratification is predicted when the concentration exceeds 70% solids. At this point the viscosity is probably too high to allow much movement and the system may become 'locked' in its non-stratified state as observed experimentally.
3.4. Conclusions
It can be concluded that the tendency to stratify can be predicted with some certainty given the concentration dependence of surface tension for the two resins in the correct solvent. The exception is where the particular resin combination is not observed to phase separate resulting in a film of uniform composition. The model could be refined by using the UNIFAC method to calculate the point of phase separation and the composition of phases at different concentrations. This would allow a more accurate calculation of the interfacial surface energies and tendency to stratify. However, the calculation would be very time consuming and the simple model used appears to give adequate predictions for all the systems used so far.
Acknowledgements The Self-Stratifying Coatings Project was supported by the Commission of the European Communities under a BRITE programme, Contract No RI 1B-246, Proposal No P2335-1. The research was conducted by eight partners: PRA (UK), CoRI (Belgium), NIF/EnPro (Denmark), DTI (Denmark), EOLAS (Ireland), FPL (Germany), TNO (Holland) and CERIPEC (France). The financial and technical support provided by the industrial members of the research institutes which participated in the project is also gratefully acknowledged.
References M. Joly, Prog. Org. Chem., 28 (1995). W. Funke, Prog. Org. Coat., 2 (1974) 289. W. Funke, J. Oil Colour Chem. Assoc., 59 (1976) 398. A. Fredeslund, J. Gmehling and P. Rasmussen, Vapour-Liquid Equilibria using UNIFAC, Elsevier, Amsterdam, 1977. [ 5 ] H. Elbro, Ph.D. Thesis, Technical University of Denmark, Instituttet for Kemiteknik, 1992. [6] W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes in PASCAL - - The Art of Scientific Computing, Cambridge University Press, UK, 1989, pp. 286-308. [7] F.B. Sprow and J.M. Prausnitz, Trans. Faraday Soc., 62 (1966) 1105. [ 8] S. Benjamin, PRA, personal communication. [9] S. Wu, J. Adhes., 5 (1973) 39. [ 1] [2] [3] [4]
Progress in Organic Coatings 28 (1996) 161-171
Theoretical aspects of self-stratification Christopher Carr a, Eva WallstOm b a PRA, 8 Waldegrave Road, Teddington, Middx. TW118LD, UK b EnPro ApS, Lers¢ Parkall~ 42, DK-2100 Copenhagen, Denmark
Received 7 April 1995; accepted 13 April 1995
Abstract
In order to predict whether a system of two polymers or resins in a common solvent mixture will 'self-stratify', two predictive models, one based on UNIFAC and the other on surface tension relationships, have been developed. The UNIFAC model can predict phase behaviour, vapour pressure, evaporation rates and surface tensions for systems containing two polymers or resins in a solvent mixture. Comparisons between experimental and calculated data are made for acrylic/acrylic, epoxy/acrylic and alkyd/acrylic resin combinations. The prediction of phase separation during solvent evaporation from a thin film is satisfactory in most cases, especially when the difference in molecular weight between the two polymers is not too large. For epoxy/acrylic resin combinations, the calculated evaporation profiles are in reasonable agreement with observed values. The evaporation rate decreases with increasing epoxy molecular weight, but is almost independent of the acrylic resin and the resin ratio. The tendency of epoxy/acrylic resin combinations to undergo self stratification is predicted to increase as the molecular weight of the epoxy resin increases. The degree of phase separation is increased as the molecular weight of the acrylic resin is increased. These predictions agree with experimental observation but for acrylic/alkyd resin combinations, no phase separation is predicted which is not in agreement with experiment. This is probably because the model cannot allow for the broad molecular weight distribution of the alkyd resin. A second predictive model based on surface energy variation with concentration of two polymer solution phases in contact has been developed. This model can be used to predict which resin combinations will give rise to self-stratifiyng systems given the surface energy/concentration relationship of the pure resins in solution and assuming the systems have phase separated. For solutions of epoxy resins combined with a second resin the model correctly predicts the observed tendency for the resins to stratify provided the system phase separates at some point. Keywords: Self-stratification; Phase separation; Surface tension; Evaporationrate; UNIFAC
1. Introduction
The main aim of the ' B R I T E ' project studying self-stratifying coatings was to develop formulation guidelines for industry. The systems studied were combinations of two resins or polymers in a common solvent which should form different phases and separate into distinct layers during evaporation of solvent from a film. Evaporation rate, phase separation behaviour and surface energy relationships are important factors in deciding whether a resin pair in a common solvent will successfully form a self-stratifying coating. A full statistical treatment of the results is described by Joly [ 1 ] which allows stratification to be predicted from a knowledge of physical properties of the component materials based on the large amount of experimental data generated during the project. However, separate studies were undertaken to develop a model based on the UNIFAC method which can be used to predict phase behaviour and evaporation rates of solutions containing two polymers or oligomers. It 0300-9440/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved SSDI 0300-9440 ( 95 ) 00594-5
was hoped that this information could be used to select polymer pairs which show the desired phase behaviour, i.e. able to form homogeneous solutions up to 50 or 60% solids concentration but phase separating at higher concentrations as the solvent evaporated. The same model was used to predict the surface and interfacial surface tensions of the homogeneous or phase separated polymer solutions. Funke [ 2,3 ] has shown that a primary driving force for stratification is the surface energy difference between the two separating phases. Therefore, a second model was developed which can be used to predict whether a phase separated polymer or oligomer pair will stratify given the surface energy relationships of the two phases. Surface energies can be calculated from the UNIFAC model or measured directly. 2. U N I F A C model Calculation of the properties of a mixture requires a knowledge of the activity coefficients of the different components.
C Carr, E. WallstOm / Progress in Organic Coatings 28 (1996) 161-171
162
The UNIFAC model [4], which is based on the group contribution principle, uses a table of group interaction parameters estimated from experimental data, to calculate activity coefficients. According to the group contribution principle, properties of a molecule can be calculated by summing the properties of the functional groups constituting the molecule. Ethanol, for example, consists of three groups: --CH3, --CH2and -OH. UNIFAC can be used to estimate phase behaviour, vapour pressure, evaporation rate and surface tension. All these properties are of importance for a self-stratifying system as stratification is expected to occur after phase separation during the drying of the film. In addition, the surface tension of the phases and the interfacial tension between the two phases are important for successful stratification but difficult to measure directly. Activity coefficients of the components in a mixture, o3~,are a measure of how close the behaviour is to that of an ideal solution. The components in an ideal solution behave as if they were in their pure state, i.e. the activity coefficients are equal to 1. Activity coefficients significantly different from 1 indicate that the mixture is strongly non-ideal. The UNIFAC model calculates the activity coefficients according to Eq. (1) [4]: In o3i =
In
tt~ic°mbinat°rial"-[-In 0~iresidual
(1)
where 0~ic°mbinat°rial= the combinatorial activity coefficient accounting for contribution to the non-idealities from differences in size and shape of the molecules in solution. The combinatorial activity coefficient is dependent on the hardcore surface area and volume of the groups in solution and on the concentration of each component in mixture. o~iresidual= the residual activity coefficient accounting mainly for the energetic interaction between different groups. Parameters, characterising the interaction between groups in solution, are used in the calculation of the residual activity coefficients. It has been shown that UNIFAC can predict activity coefficients in solvent mixtures with good accuracy [4]. The restriction of the method is that not all interaction parameters of interest are available due to a lack of experimental data. In principle, it should also be possible to predict activity coefficients for polymer solutions. However, it has been shown that the solvent activity coefficients for the components in a polymer solution are, in general, underestimated by the UNIFAC model. The probable reason for this is that UNIFAC does not take into account that pure polymers are more closely packed than pure solvents. This was the background for the model developed by Elbro [ 5 ], where the combinatorial activity coefficients are calculated by a new method which accounts for the difference in polymer and solvent density. It has been shown that the revised model, using the original UNIFAC interaction parameter table, gives good agreement with experiment. However, the revised model is not used in this paper.
2.1. Phase separation Phase separation or liquid-liquid equilibrium (LLE) calculations are important applications of the UNIFAC model. The LLE calculations can be divided into two parts; detection of phase separation and calculation of the point of phase separation. Phase separation is detected by checking whether the matrix A, consisting of the second derivatives of the Gibbs free energy of mixing, A G~x, with respect to the mole fractions, is positive in a range of concentrations around the concentration of interest. The elements in the matrix A are given by: 02A Gmix A v - - i , j = l , 2 .... N C - 1
(2)
OXiOXj
where NC
A G ~ x = R T ~ x i In(a/)
(3)
i
NC= the number of different components in the system, ai = the activity of component i in the solution. It is calculated from: a i =xio_) i
(4)
where xi = the mole fraction of component i, o3i= the activity coefficient of i. The equilibrium condition of an LLE system can be expressed by the isofugacity criterion. ai I ----ai n
(5)
where aiI = the 'activity' of component i in phase I, aiH= the 'activity' of component i in phase II. This gives N non-linear equations (one for each component) with 2N unknowns, which must be solved by an iterative procedure. The isofugacity criterion, together with the mass balances, form the 2N necessary equations. A multivariable Newton-Raphson iteration procedure was used for the solution of the non-linear equations [ 6 ] and the necessary derivatives with respect to the unknowns were found numerically.
2.2. Evaporation rate The evaporation rate (ER) is a function of several factors, which can be divided into two categories; external and component. The external factors describe the environmental conditions: temperature, humidity, air velocity and surface geometry, which must be specified for each case. The component factors are: diffusion coefficient in air, vapour pressure, heat of vaporisation and activity coefficient in solution. The transfer of mass from the liquid to the surroundings is partly caused by the difference in equilibrium and bulk concentrations (the driving force) and partly caused by the phase displacement from liquid to vapour. The following expression is only valid if the vapour pressure of the solution is
C. Carr, E. WallstOm / Progress in Organic Coatings 28 (1996) 161-171
below the atmospheric pressure. The evaporation rate, Ri [ mass / ( area × time) ], for a component i, is described by: R i ~- ki(Yi eq - y i °) -t-yieqER i
y ieq --
(6)
x i ,~iP i TM
(7)
E Xjt~jpjsat
ki = 46MWiD i°'ss v ~r°6s
(8)
where yieq_ the equilibrium concentration of component i, y o = the bulk concentrations of component i in the vapour phase, k~= the mass-transfer coefficients of component i, p sat = the vapour pressure of pure component i at the system temperature, MWi = the molecular weight of component i, D~ = the diffusion coefficient in air of component i, v~r = the air velocity. The progress of evaporation from a film is described by the following differential mass balance:
dMi =ARi dt
(9)
where dM~ = the amount of component i evaporated in the time interval dt, A = the area of the film. The total amount evaporated in the time interval dt, dM, is thus: dMt=A dt )-'R~
2.3. Surface tension The surface tension of an 'ideal' mixture can be calculated according to: ideal_
liquid phase, X/surf = the mole fraction of component i in the surface layer, o3is ~ = the activity coefficient of component i in the surface layer, o3i = the activity coefficient of component i in the bulk liquid phase. Here it is assumed that: Ai =A~ = the molar surface area of pure component i The surface tension of a homogeneous mixture, Y~a~, (with NC different components) can thus be estimated from the above equation. Furthermore,
Ex-SUrf , 1
(13)
and the surface area, A~, is estimated from: A i = C V i 1/3
(14)
V~is the molar volume of component i at the system temperature, C is a constant, which equals 1 for all components but water. This gives N C + 1 equations, with unknowns Y~a~, Xls~f, x2SUrf...XNcs ~ which can be solved numerically using a Newton-Raphson iteration scheme with analytically derived derivatives.
2.4. Results
(10)
This equation is solved numerically by defining the total change of mass per step as 1.0% of the initial weight (Mo). Since A is known, Ri and dt can be calculated (by iteration). This means that dMi can be found and a new composition can be calculated. For mixtures containing polymers, the mass transfer will be limited by other factors when the remaining film contains less than around 10% solvents. The numerical integration is thus stopped at this point. Interpolation between the calculated points is performed by use of spline functions.
~Ynflx
163
v"~ X
(11)
- - 2,~ i ~/i
where Yi = the surface tension of component i. As most mixtures are non-ideal in their behaviour a model taking this into account has been used. A more sophisticated model for calculation of the surface tension of liquid mixtures is based on the assumption that the surface layer can be treated as a separate phase located between the vapour and the bulk liquid phases. From this assumption and from classical thermodynamics the following equation can be derived [7]: [
XiO) i
"Ai]/n~x=AiYi-RTln~xiS~)
i = I , 2,...NC
(12)
where Ai = the partial molar surface area of component i in the mixture, xi = the mole fraction of component i in the bulk
2.4.1. Phase separation In order to give an idea of the accuracy of the applied models some comparisons between the experimentally measured and the calculated results were made. The polymers included are listed in Table 1. Phase separation was experimentally measured [ 8] for the system Epikote 1001/Neocryl B700 with 4-methyl, 2-pentanone (MiBK)/xylene at 25 °C (Table 2). The polymer concentration was set at 30% (wt./wt.) and the ratio MiBK/ Xylene 7:13 as determined experimentally. The calculations predict: (i) no phase separation occurs for a ratio of Epikote 1001 :Neocryl B700 of 1:1; this is not in accordance with the experimental measurements; (ii) the calculated phase separation is not as sensitive to the polymer composition as experimentally observed; (iii) for ratios of Epikote 1001 to Neocryl B700 between 3:1 to 5:1 the calculated composition of the components in the two phases is an acceptable agreement with the observed behaviour; (iv) for a ratio of Epikote 1001 to Neocryl B700 of 9:1 it is seen that the composition of phase I is not in accordance with the observations. In order to study the influence of molecular weight of the polymers on phase separation behaviour further, the percent solids at phase separation for the system Neocryl B700 (Mw = 40 000) and PMMA (Mw varied between 10 000 and 65 000) dissolved in butyl ethanoate was experimentally measured at 25 °C [8]. Calculations are compared with experimental measurements in Table 3.
164
C. Carr, E. Wallst6m / Progress in Organic Coatings 28 (1996) 161-171
Table 1 Polymers used Epikote 828 Epikote 1 0 0 1 Epikote 1004 Epikote 1007 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B811 Neocryl B813 Crodac AC500 Crodac AC550 Lumiflon LF200 Lumiflon LF916 Alloprene R10 Synolac 6016 Synolac 9090 Plastokyd AC-4X Hythane 9 Plastokyd SC-7 Plastokyd SC-140 Plastokyd SC-400 Plastoprene 1S Hypalon 20 Uralac AD143
Uralac AD9
bispbenol-A epoxy bisphenoI-A epoxy bisphenol-A epoxy bisphenol-A epoxy thermoplastic acrylic (PiBMA) thermoplastic acrylic (PMMA) thermoplastic acrylic (PBMA) thermoplastic acrylic (PMMA) thermoplastic acrylic (PEMA) thermosetting acrylic thermosetting acrylic fluorinated polyether fluorinated polyether chlorinate rubber short oil alkyd short oil alkyd acrylic modified alkyd urethane alkyd siliconised polyester siliconised alkyd siliconised epoxy ester cyclised rubber chlorosulfonated polyethylene alkyd produced from phthalic anhydride, linseed oil and glycerol alkyd produced from phthalic anhydride, linseed oil and trimethylol propane
Shell UK Ltd. Shell UK Ltd. Shell UK Ltd. Shell UK Ltd. ICI Resins ICI Resins ICI Resins ICI Resins ICI Resins Croda Resins Ltd. Croda Resins Ltd. ICI Resins ICI Resins ICI Resins Cray Valley Products Cray Valley Products Croda Resins Ltd. Croda Resins Ltd. Croda Resins Ltd. Croda Resins Ltd. Croda Resins Ltd. Croda Resins Ltd. Dupont DSM Resins BV
DSM Resins BV
Table 2 Phase behaviour of Epikote 1001/Neocryl BT00 system: calculated and ( measured ) concentration of the component ( wt.% ) R~ioPhase Solids Epikom Neocryl MiBK Xy~ne 1:1 I -(29) -(10) -(19) -(26) -(45) 1I - (28) - (2) - (23) -(47) 3:1 1 27.8(30) 12.2(15) 15.6(15) 24.7(25) 47.6(45) II 32(36) 32.0(35) 0.0(1) 24.3(21) 43.7(43) 5:1 1 27.3(30) t2.4(16) 14.9(13) 24.8(25) 47.9(46) 1I 31.4(33) 31.4(33) 0.0(0) 24.4(22) 44.3(45) 9:1 1 26.9(30) 12.6(28) 14.3(2) 24.8(20) 48.3(50) 1I 30.8(32) 30.8(31) 0.0(1) 24.4(25) 44.8(43)
except with PMMA of 10 000 Mw where no phase separation is observed experimentally. Both calculation and experiment agree that the percent solids at phase separation decreases with increasing molecular weight of PMMA. However, according to calculation, the percent solids at phase separation has a minimum at a B700:PMMA ratio of 1:1 which is not observed experimentally. It can be concluded that the UNIFAC model is able to predict the phase behaviour of polymer-polymer-solvent systems reasonably well. The major problems occur when the difference between the molecular weight of the polymers involved is high. However, the calculation does not predict the dependency on the percent solids at phase separation on the ratio of the two polymers involved. 2.4.2. Evaporation rates
In order to illustrate the dependency of solvent evaporation rate on the different components present in the initial film, the evaporation profiles under different conditions were calculated for various epoxy/acrylic resin combinations (Figs. 1-4) The solvent mixtures used are given in Table 4. The environmental conditions were set at: temperature, 23 °C; humidity, 0%; air speed, 0.1 m/s; film thickness (initial), 100 g/m 2. The following conclusions can be made from the calculations of evaporation profile for the given polymers. (i) The drying time decreases slightly with increasing molecular weight of the Epikote, see Fig. 1. (ii) From Fig. 2 it is seen that the drying time is not very sensitive to the selected ratio of the two polymers involved. (iii) The drying time is very dependent on the chosen solvent mixture, see Fig. 3. The solvents with a low vapour pressure do not evaporate as fast as the solvents with a high vapour pressure, as expected. 100.0 90.0 tm
80.0
"t3 70.0
Table 3 Phase separation forB700and PMMA: calculated and experimental [8] (in parentheses) System
8 o
60.0
o. ¢2 > 50.0 t,l 40.0
Ratio between polymers 1:4
1:1
4:1
23(-) " 10(13) 8(10)
30(-) 9(11) 6(8)
91(-) 18(11) 12(7)
I
30.0
t
20.0
B700:PMMA 10 B700:PMMA 40 B700:PMMA 65
828 Epikote Epikote 1001 1007 • * - * * Epikote .....
lO.O
o.o
= No phase separation observed experimentally.
o.o
5.0
10;.0
15'.o
Neocryl 8700 3:1 Neocryl B700 3:1 Neocryl B800 3:1
2o'.o Time
The calculated and experimentally measured values for the percent solids at the point of phase separation agree very well
2~.o
30.0
(rain.)
Fig. 1. Different Epikote/Neocryl B700 in MiBK/xylene mixtures. Polymer ratio 3:1.
C. Carr, E. WallstiJm/ Progress in Organic Coatings 28 (1996) 161-171 100.0 90.0 80.0
¢)
P o
70.0
Q
60.0
t
o_ o> 50.0 Ld 40.0
Q
30.0 20.0
e
10.0
..... Epikote 828 - Neocryf B700 1:1 ,~.~.':,~ Epikote 828 - Neocryl 8700 3:1 Epikote 828 Neocryl B800 9:1
Q
0.0 0.0
s.b
lO;.O
lS'.o
20'.0
2s'.o
so o
Time (rain.) Fig. 2. Epikote 828/Neocryl B700 in MiBK/xylene. Different polymer ratios. 100.0 90.0
e
80.0 "0
e
70.0
1
60.0 0:> i,i
165
(iii) the interfacial tension between the two liquid phases should be large enough to stop the second phase being dispersed in the first phase; (iv) the interfacial tension between the bottom liquid phase and the substrate should be very low. This is obtained if: (a) the solvent mixture in the bottom phase has an affinity for the substrate; (b) the polymer in the bottom phase is partly compatible with the substrate. Evaporation rate, phase separation and surface tension calculations have been performed for a large number of systems. Each system consisted of an Epikote or an alkyd, a second polymer and a solvent mixture (S,, Sg or $3). The polymers were mixed at different ratios ( 1:1, 1:3 and 1:9). The initial concentrations in the calculations were set to 20 wt.% polymer and 80 wt.% solvent. Tables 5-7 summarise how the systems investigated behave with respect to the calculated self-stratifying behaviour. From the results it is predicted that stratification improves with increasing epoxy molecular weight. In order to obtain strong phase separation, where each phase contains predominantly one polymer, the molecular weight of the second polymer should be relatively high. Apparently the solvent mixture S 2 gives rise to the largest interfacial tension between the two liquid phases. This is because Dowanol PM concentrates in one of the liquid phases, whereas the other solvents are evenly distributed between the two phases. The investigated acrylic/alkyd sys-
@
50.0
t
100.0
40.0
90.0
30.0
80.0
20.0
t
70.0
..... Solvent mtxture I l ~ i l ..... Solvent mixture 2 * * * * * Solvent mixture 3
I0.0
0.0 0.0
5.b
lo:o
15'.0
20:0
251.0 30:0
35.0
Time (rain.) Fig. 3. Epikote 828/Neocryl B700 in different solvents (S,, $2, $3). Polymer ratio 3:1.
(~.
,,>,
60.0 50.0 40.0 30.0 20.0
(iv) The drying time, for the polymers investigated, is almost independent of the second polymer, see Fig. 4. The last conclusion is of course dependent on the chosen polymers.
10.0
0.0
,,
o.o
Ep|kote
828 828 828 828
Neocryt B700 Neocn/I B813 Neocryl B811 Alloprene RIO
lo'.o
15'.0
20'.0
iii:.i Eplkote •. •
s.~
Eplkote
3:1 3:1 3:1 3:1
25'.0
30.o
Time (rain.) Fig. 4. Epikote 828. Different polymers in MiBK/xylene. Polymer ratio 3:1.
2.4.3. Prediction of self-stratification of the mixtures In order to obtain a good self-stratifying system, containing two polymers and a solvent mixture, the following conditions need to be satisfied: (i) the system should separate into two phases during the drying process; (ii) one polymer should be concentrated in each of the phases;
Table 4 Solvent mixtures Solvent mixture
Composition (wt.%)
SI: MiBK-Xylene $2: MiBK-Xylene-Dowanol PM $3: Xylene
50:50 50:30:20 100
C. Carr, E. WaUst6m/ Progress in Organic Coatings 28 (1996) 161-171
166
Table 5 Self-stratification of different systems (solvent mixture 1 ( S~) ) Polymer 1
Polymer 2
Ratio 1:1 PS a
Epikote 828
Epikote 1001
Epikote 1007
Neocryl B700 Neocryl B813 Neocryl B811 Neocryl B700 Neocryl B813 Neocryl B811 Neocryl B700 Neocryl B 813 Neocryl B811
Ratio 3:1 PD b
X
u,"
'~t- -
'~II c
X
+
Ratio 9:1
PS
PD
Yl- Ya
PS
PD
Yl- "/ix
X
-
X
u,"
×
0.9
X
-
X
~
~
0.0
X
-
X
0.7
t,,"
-
0.2
0.3
~
+ + -
0.9 0.0 0.0 0.9
PS = phase separation. b PD = polymer distribution. ¢ Yt - Yn = the numerical difference between the surface tension of two formed liquid phases (at phase split). This can be taken as a relative measure of the interracial tension between the two phases. The system phase separates during drying process. + Each polymer is concentrated in a single phase. X The system does not phase separate. - The concentration of the polymers in each phase is significant. Table 6 Self-stratification of different systems (solvent mixture 2 ($2)) Polymer 1
Epikote 828
Epikote 100J
Epikote 1007
Polymer 2
Neocryl B700 Neocryl B813 Neocryl B811 Neocryl B700 Neocyl B813 Neocryl B811 Neocryl B700 Neocryl B813 Neocryl B811
Ratio 1:1
Ratio 3:1
Ratio 9:1
PS a
PD b
YI- Yll c
PS
PD
)5 - Yn
PS
×
-
X
(+ )
0.4
(+ )
X × × 1.3
tJ
tJ
X X × t,J
~
+
1.1
~ ~ tJ tJ
+ (+ ) -
0.4 1.1 0,7 0.4
t,~
PD
Yl - %1 0.9
+
1.2
a PS = phase separation. b PD = polymer distribution. c Yt- %1= the numerical difference between the surface tension of two formed liquid phases (at phase split). This can be taken as a relative measure of the interfacial tension between the two phases. u'r The system phase separates during drying process. + Each polymer is concentrated in a single phase. X The system does not phase separate. - The concentration of the polymers in each phase is significant. t e m s d o n o t r e s u l t in s t r a t i f i c a t i o n a c c o r d i n g to t h e s e c a l c u -
tions. T h e r e a s o n f o r d i s c r e p a n c y is p r o b a b l y t h a t t h e ' g r o u p '
lations.
d e f i n i t i o n s o f t h e a l k y d s a r e n o t a c c u r a t e e n o u g h but, as t h e a l k y d s are n o t w e l l - d e f i n e d s u b s t a n c e s , it is d i f f i c u l t to s o l v e the problem.
2.5. Conclusions It h a s b e e n s h o w n t h a t t h e U N I F A C m o d e l c a n b e u s e d to e s t i m a t e t h e p o i n t o f p h a s e s e p a r a t i o n in a t w o p o l y m e r s o l u tion system of the type epoxy/acrylic, but the phase separat i o n in a c r y l i c / a l k y d s y s t e m s w a s n o t p r e d i c t e d . Surface tension and interfacial tension were estimated using an ideal method which gave a relatively good calculated surface tension for these kinds of systems. The calculations do not predict that the acrylic/alkyd syst e m s will s t r a t i f y w h i c h is n o t in a c c o r d a n c e w i t h o b s e r v a -
3. Prediction of stratification based on surface energy T h e initial w o r k b y F u n k e [ 2,3 ], o n s e l f - s t r a t i f y i n g p o w d e r c o a t i n g s y s t e m s , s h o w e d that a p r i m a r y d r i v i n g f o r c e f o r s t r a t i f i c a t i o n is t h e s u r f a c e e n e r g y d i f f e r e n c e b e t w e e n t h e t w o r e s i n s . T h e r e f o r e , a n a t t e m p t w a s m a d e to d e v e l o p a m o d e l to p r e d i c t w h e t h e r a s y s t e m c o m p o s e d o f t w o p o l y m e r s o l u -
167
C. Carr, E. WallstOm / Progress in Organic Coatings 28 (1996) 161-171
tion phases will stratify based simply on surface energy relationships of the two phases. It is thermodynamically favourable for the disperse phase in a two-phase system to coalesce, unless the particles or droplets are stabilised somehow, as this leads to a lowering of interfacial area and hence surface energy of the system. Whether it is favourable for the two separating phases to form into distinct layers with the correct orientation can be predicted by analysing the interfaces produced in a two-component paint film (Fig. 5). Two simple conditions for stratification to occur in a thin film containing two phases can be stated: (A) the intended basecoat component must spontaneously wet the substrate; (B) the total surface and interfacial surface tension of the required layer sequence must be the lowest possible. Condition ( A ) is satisfied when the contact angle (0) between component 2 and the substrate is zero. Y o u n g ' s equation states that: 3'sl - - 3's2 - - 3"12 COS 0 = 0
Air
Component 1
'1
"/12 Ys2
Fig. 5. Interfaces in a two-componentpaint film. tension. For the sequence in Fig. 5 the total surface energy is given by: (18)
3's2 + 3"12 "F 3'1
For the alternative sequence, the total surface energy is: 3'sl + 3'12+ T2
(19)
Therefore, t h e r e q u i r e d l a y e r s e q u e n c e i s t h e m o s t f a v o u r a b l e when (19) > (18) or:
(15)
where 3',~ is the substrate/component 1 interfacial surface tension, 3",2is the substrate/phase 2 interfacial surface tension and 3'12 is the interfacial surface tension between components 1 and 2. The contact angle is zero when: (16)
3"sl - - 3"s2-- 712 > / 0
Also, the surface energy of the system should decrease for spontaneous wetting leading to the condition: 3's -- 3's2-- 3"12-- 3'1 > 0
(17)
where ys is the substrate surface energy with air. Condition (B) states that the most favourable layer sequence will be the one giving rise to the lowest total surface
(20)
3'sl - - 3'1 - - 3's2 -F 3'2 > 0
It is evident, therefore, that the prediction of stratification requires a knowledge of the surface energies of the two separating phases and their interfacial surface tensions plus their interfacial surface tensions with the substrate. In reality the surface tension of solution phases will be changing continuously as solvent evaporates. However, as a first approximation it was assumed that the surface energy of the pure solid resin which predominates in each phase could be used for predictions. The model was later refined to allow for the presence of solvent in each phase assuming that the concentration of the two phases remained equal and that each phase contained predominantly one of the resin components.
Table 7 Self-stratificationof different systems (solvent mixture 3 ($3) ) Polymer 1
Epikote 828
Epikote 1001
Epikote 1007
Polymer 2
Neocryl B700 Neocryl B813 Neocryl B811 Neocryl B700 Neocryl B813 Neocryl B811 Neocryl B700 Neocryl B813 Neocryl B811
Ratio 1:1
Ratio 3:1
Ratio 9:1
PS ~
PD b
T1- Tnc
PS
PD
3'1- Tn
~
-
+
tJ
-
0.6
~ tJ ~ j,1
_
0.2
tl
+
0.3
t,," ~ ~ ~
+ + -
0.2 0.3 0.2 0.6
PS
PD
TI- Tn
u,r
tJ
0.2
a PS = phase separation. b PD = polymerdistribution. c Yl- Tn= the numericaldifferencebetween the surface tensionof two formed liquid phases (at phase split). This can be taken as a relative measure of the interfacialtension betweenthe two phases. tJ The system phases separates duringdrying process. + Each polymeris concentratedin a single phase. × The systemdoes not phase separate. - The concentrationof the polymersin each phase is significant.
C. Carr, E. WallstOm/ Progress in Organic Coatings 28 (1996) 161-171
168 Table 8 Surface energies of various substrates
Substrate
Uncleaned steel Acetone cleaned Abraded steel Aluminium foil Polypropylene Polypropylene oxide Lexan TF 60
3.2. Prediction of stratification from solid resin surface energies
Td ( m N m -I )
"yP (mNm -l)
,,/total (mNm -1)
36.5 28.7 32 30.3 25.6 32.0
4.8 15.6 34 27.5 7.1 11.2
41.3 44.3 68 57.8 32.7 43.1
35.6 31.5
10.7 6.9
46.3 38.4
The values of polypropylene, polypropylene oxide Lexan and TF60 were kindly supplied by CoRI.
3.1. Results The disperse and polar contributions to the surface tension of a solid surface can be determined if the contact angle between the solid and two liquids with known disperse (3/) and polar ( T p) surface tension components is measured. The Harmonic Mean method of Wu [9] is the favoured technique. For an interface between two materials, 1 and 2, the interfacial surface tension is given by:
TI2 = T1 + T2
4TldT2 d
4TIPT2 p
Tld + T2 d
T1 p + T2 p
(21)
where Yl and T2 are the total surface energies of materials 1 and 2, respectively. Using Eq. (21) and Young's Law, the surface energy of any material can be calculated if the contact angles with two reference liquids are known. Table 8 shows the results obtained for various substrates. In the case of steel substrates a very high surface energy can only be achieved by cleaning the surface in a flame. Even so, absorption of material from the atmosphere reduces the energy to below that of water within two hours. An untreated steel surface has a surface energy of only 41.3 mN m - ~which is only marginally improved by degreasing with acetone. Degreasing with xylene had virtually no effect on the measured surface energy. Abrading the surface with 200 grade wet and dry paper caused a significant increase in the surface energy but subsequent cleaning with organic solvent reduced the surface energy. The surface energy of plastic substrates is normally much lower than metals. This is demonstrated in the surface energies in Table 8 which were measured by CoRI. All values are significantly lower than an abraded steel surface and aluminium foil. The method of Wu can also be applied to determine the surface energies of solid resins when cast as thin films. The results for some resins are presented in Table 9. It has been shown above that, for a two phase system to stratify, simple thermodynamic considerations give rise to three conditions which must be satisfied.
Using the nomenclature in Fig. 5 the conditions for stratification can be summarised as: Tsl - %2 - T12 >/0
(22)
~sl -- T1 -- ~s2 -'~-T2 > 0
(23)
T s - % 2 - T12- T1 > 0
(24)
Using the surface energies of the two pure resin components in place of the phase separated resin solutions, these conditions can be calculated for any combination of substrate and resins if the disperse and polar contributions to the surface energies of all components are known. The calculated and experimental behaviour observed at CoRI for six formulations on Lexan (a polycarbonate) are listed in Table 10. These suggest that the surface energies of the pure solid resins can be used to predict stratification with some accuracy in these six systems on Lexan. However, of the three systems experimentally observed to stratify on TF60 only one is predicted to stratify (Table 11). It could be argued that the condition which is not satisfied has an insignificant value. However, if the same principle is applied to the resins used at PRA the predictions are not as good (Table 12). In panicular, systems with Lumiflon are not predicted to stratify using this method, but they are observed to stratify strongly experimentally. The probable reason for this is that the effect of Table 9 Surface tensions ( m N m - i ) of solid resins Resin
Epikote 828 (amine cured) Epikote 1001 Epikote 1004 Epikote 1007 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B 811 Neocryl B 813 Crodac AC500 Crodac AC550 Lumiflon LF200 Lumiflon LF916 Plastokyd SC7 Plastokyd SC 140 Plastokyd SC400 Plastokyd AC4X Alkyd VAS 9223 Hythane 9 Synolac 6016 Synolac 9090 Plastoprene 1S Alloprene R 10 Hypalon 20
Harmonic mean Td
,yv
Ttotal
33.7 36.1 34.1 34.4 28.2 30.2 24.7 30.5 27.6 29.4 32.1 26.3 27.2 27.9 27.2 26.3 27.8 29.1 26.3 30.5 33.6 31.9 40.9 32.1
10.8 9.3 11.5 9.4 2.6 12.0 9.7 13.9 10.2 12.0 8.6 10.1 10.5 10.1 9.8 11.2 10.8 10.2 13.4 14.0 11.7 13.2 6.1 8.6
44.5 45.4 45.6 43.8 30.8 42.2 34.4 44.4 37.8 41.4 40.7 36.4 37.7 38.0 37.0 37.4 38.6 39.3 39.7 44.5 44.3 45.1 47.0 40.7
C. Carr, E. WallstOm/ Progress in Organic Coatings 28 (1996) 161-171
169
Table 10 Prediction o f stratification on L e x a n 7s - ~s2 - 712 - 71
Exp.
Resin 1
Resin 2
3',1 - "Ys2- 712
~sl - ~1 - 7 s 2 - 7 2
Theory
Lumiflon LF200 Lumiflon LF200 Lumiflon LF302 Lumiflon LF200 Desmophen 4125 Lumiflon LF200
Plexigum M890 Plexigum PM381 Plexigum M890 Desmolac 2770 Lumiflon LF200 Synthacryl VSC11
- 5.49
5.30
3.00
X
×
0.49
3.03
8.97
u,~
1, I
- 2.92
4.19
2.69
×
X
0.03
0.85
8.51
~
0.69
7.16
12.81
u,r
u~'
- 5.30
5.48
3.19
X
X
~s-- )'s2-- 712 -- 71
Theory
Exp.
x
X
Table 11 Prediction o f stratification on T F 6 0 Resin 1
Resin 2
%1 - - '~s2-- 712
'Ysl - -
Lumiflon LF200 Lumiflon LF200 Lumiflon LF302 Lumiflon LF200 Desmophen 4125 Lumiflon LF200
Plexigum M890 Plexigum PM381 Plexigum M890 Desmolac 2770 Lumiflon LF200 Synthacryl VSC11
- 8.12
2.67
- 7.19
0.46
3.01
1.39
- 4.55
2.55
- 7.50
X
- 0.26
0.56
0.67
X
- 1.34
5.14
5.25
×
u'r
- 8.00
2.78
- 7.07
×
X
Table 12 Prediction o f stratification on a l u m i n i u m foil Resin 2
Neocryi B700 Neocryl B 7 2 8 Neocryl B 8 0 4 N e o c r y l B811 Neocryl B813 Crodac AC500 Crodac AC550 Lumiflon LF200 Lumiflon L F 9 1 6 Plastokyd SC7 Plastokyd S C 1 4 0 Plastokyd SC400 Plstokyd A C 4 X Alkyd VAS 9226 Hythane 9 Synolac 6016 Synolac 9090 Plastoprene 1S Alloprene R 1 0 Hypalon 20
Resin
'~1 - - 7 s 2
"~" ' ~ 2
u," X
the solvent on surface energy has not been taken into account. Stratification occurs before all the solvent has evaporated, so it is the surface energies of the separating phases rather than the solid resins which are important.
1
E p i k o t e 828
Epikote 1001
Epikote 1007
Theory
Exp.
Theory
Exp.
Theory
Exp.
~ × ~ X X X ~ X × tJ ~ X X X
× × ~ X X ~ X X X × X X X ×
t,J × X X X × t,,," X × X X X × x
~ × X X × ~ x ~ u," x x X X u,r
tJ X × × X × ~ X X X X X X ×
t,~ × × X ×
x
x
X
x
X
X
X
X
x
X
X
x
3.3. Prediction of stratification from solution surface energies When a polymer is dissolved in a solvent or solvent mixture, the surface energy of the solution will be dominated by the solvent except at high polymer concentrations. This is illustrated in Fig. 6 which shows a plot of surface tension 45
t,," X X X X u,"
x
x
x
x
x
x
X
X
X
X
X
X
tJ I,,"
X
~
X
~
X
X
~
x
~
X
~
Calculated .O ~ 35
Experimental
+
+
/J j*
~'
.j~.J+
30
j-+ 2s
20
i
i
i
i
i
i
~
,
q
0.1
0.2
0.3
04
05
0.6
0.7
0.8
0.9
-~ !
Reshl Concentration
Fig. 6. Calculated a n d experimental surface tensions for Epikote 828 in methyl iso-butyl ketone ( M i B K ) .
C. Carr, E. WallstiSm/ Progress in Organic Coatings 28 (1996) 161-171
170 Table 13 Calculated coefficients in Eq. (25) Resin
Solvent
A
B
Epikote 828
xylene methyl iso-butyl ketone n-butyl acetate methoxy propanol methyl iso-butyl ketone n-butyl acetate methyl ethyl ketone n-butyl acetate methyl ethyl ketone n-butyl acetate xylene methyl iso-butyl ketone n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate
14.6 19.7 17.8 15.5 21.6 20.8 21.1 20.4 21.6 20.9 9.3 13.3 7.7 15.2 8.2 16. I 11.5
- 3.1 - 3.1 - 3.7 - 3.4 - 3.0 - 4.2 - 4.3 - 3.5 - 4.5 - 3.7 - 4.3 -4.7 - 3.4 - 2.2 -2.3 - 3.6 - 3.0
Epikote 1001 Epikote 1004 Epikote 1007 Lumiflon LF916 Lumiflon LF200 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B 811 Neocryl B 813
30
1
25 J I ~ - - A -
~',~ - 7,2 - 7.12
20 ~ _ _ ~
YYsl Yy~ - 7.s= +7.z 7' s
7'S2 - 7 1 2
- 7.1
15= 10 5
°
50
50
7o
8o
9o loo
Resin Concentration (%)
Fig. 7. Prediction of stratification for Epikote 1001/Neocryl BT00.
20
10
YYsl
7.1
~'s2 + 7.2
Ys
7's2
7"42 - 3"1
t : "-
0
,~
.
.
.
.
> ~
I
-5
I
0
la
20 a0 4a 55 aa 7b aa
ld0
Concentration (% resin) Fig. 8. Prediction of stratification for Epikote I 0 0 1 / L u m i f l o n LF 200.
versus concentration for Epikote 828 in MiBK. At high resin ~oncentrations, a small addition of solvent produces a large decrease in the solution surface tension. At 50% solids the surface tension is dominated by the solvent and further dilution has only a small effect on the solution surface tension. Surface tension/concentration relationships were either measured experimentally or calculated using the UNIFAC method described above. The traces all show the same general form described by: )'~x = %ol + A exp(Bf)
(25)
where 7~x = surface energy of the solution, %o~= surface energy of the solvent, f = weight fraction of the solvent, A, B = constants. The constant A can be calculated experimentally or from % - %ol f f = 0) where Tr is the surface energy of the pure resin. B can then be calculated from a surface energy/concentration plot. The calculated values of A and B for the systems studied are listed in Table 13. These data alone can be used to describe the total surface tension of the resin solutions at any concentration. However, in order to use the data to predict stratification, the disperse and polar components of the surface tension must be known. This cannot be measured directly but can be calculated if we assume they vary in a similar way to the total surface energy. We can calculate values for a polar and disperse contribution to the A coefficient of the solution, A p and A u respectively, from: Ap =
"yrp
Ad=
")/rd -
--
")/sol p
")/sold
(26)
Using the experimentally determined value for B, the variation in the polar and disperse components of the surface tension of the solution can be calculated at any concentration. Assuming that the concentration of the two phases is always the same, we can now predict whether stratification should occur during solvent evaporation. This is illustrated in Fig. 7 for the system Epikote 1001/Neocryl B700 in n-butyl acetate. The three conditions for stratification (Eqs. ( 2 2 ) - ( 2 4 ) ) are plotted against the resin concentration. Where all three conditions are positive we would predict that the system would stratify. As can be seen, this system is predicted to stratify at all concentrations (provided it is two phase) which is in agreement with experiment. For the system Epikote 1001/Lumiflon LF200 stratification is predicted for concentrations up to 80% when one of the conditions becomes negative (Fig. 8 ). This would explain why the system is not predicted to stratify using pure resin surface energies but is observed to stratify experimentally. Below 80% solids the two-phase system will form into two layers. At 80% solids the conditions for stratification are no longer satisfied but the viscosity is too high to allow much disruption of the layers. This is also consistent with optical examination of film formation from an unpigmented Epitoke/Lumiflon system where two layers appeared to form at low concentrations but some disruption was observed at high resin concentrations. The concentration ranges where stratification is predicted for the systems studied at PRA are listed in Table 14. The range quoted is the concentration range where all three conditions remain positive. The experiment column shows the degree of stratification measured by FTIR, where 4 represents complete separation into layers and 0 indicates no measurable separation of the polymers. For Epitoke 1001 and 1004, systems which are predicted to stratify at high concentrations appear to correiate well with systems observed to stratify in practice. For Epikote 828 the
C. Carr, E. Wallsti~m/ Progress in Organic Coatings 28 (1996) 161-171
171
Table 14 Predicted concentration ranges for stratification of systems used at PRA Resin 1
Resin 2
Solvent
Range
Exp.
Epikote 828
Lumiflon LF200 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B811 Neocryl B 813 Lumiflon LF200 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B811 Neocryl B813 Lumiflon LF200 Neocryl B700 Neocryl B728 Neocryl B804 Neocryl B 811 Neocryl B813
methyl iso-butyl ketone n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate methyl iso-butyl ketone n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate methyl iso-butyl ketone n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate n-butyl acetate
0-100 0-100 0--30 60-100 0 70-- 100 0-80 0-100 0 0 0 0 0-80 0-100 0 90-100 0 0
? 1 0 3 0 0 4 3 0 2 0 1 4 3 0 2 0 1
Epikote 1001
Epikote 1007
correlation is not so good, probably because some of these systems do not phase separate. For Epikote 828 and Neocryl 813, stratification is predicted when the concentration exceeds 70% solids. At this point the viscosity is probably too high to allow much movement and the system may become 'locked' in its non-stratified state as observed experimentally.
3.4. Conclusions
It can be concluded that the tendency to stratify can be predicted with some certainty given the concentration dependence of surface tension for the two resins in the correct solvent. The exception is where the particular resin combination is not observed to phase separate resulting in a film of uniform composition. The model could be refined by using the UNIFAC method to calculate the point of phase separation and the composition of phases at different concentrations. This would allow a more accurate calculation of the interfacial surface energies and tendency to stratify. However, the calculation would be very time consuming and the simple model used appears to give adequate predictions for all the systems used so far.
Acknowledgements The Self-Stratifying Coatings Project was supported by the Commission of the European Communities under a BRITE programme, Contract No RI 1B-246, Proposal No P2335-1. The research was conducted by eight partners: PRA (UK), CoRI (Belgium), NIF/EnPro (Denmark), DTI (Denmark), EOLAS (Ireland), FPL (Germany), TNO (Holland) and CERIPEC (France). The financial and technical support provided by the industrial members of the research institutes which participated in the project is also gratefully acknowledged.
References M. Joly, Prog. Org. Chem., 28 (1995). W. Funke, Prog. Org. Coat., 2 (1974) 289. W. Funke, J. Oil Colour Chem. Assoc., 59 (1976) 398. A. Fredeslund, J. Gmehling and P. Rasmussen, Vapour-Liquid Equilibria using UNIFAC, Elsevier, Amsterdam, 1977. [ 5 ] H. Elbro, Ph.D. Thesis, Technical University of Denmark, Instituttet for Kemiteknik, 1992. [6] W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes in PASCAL - - The Art of Scientific Computing, Cambridge University Press, UK, 1989, pp. 286-308. [7] F.B. Sprow and J.M. Prausnitz, Trans. Faraday Soc., 62 (1966) 1105. [ 8] S. Benjamin, PRA, personal communication. [9] S. Wu, J. Adhes., 5 (1973) 39. [ 1] [2] [3] [4]