- Email: [email protected]
Inverse gas chromatography for the study of one phase and two phase polymer mixtures
Eur. Polym. J. Vol. 19, No. 6. pp. 519-524, 1983 Printed in Great Britain. All rights reserved
0014-3057/83/060519-06503.00/0 Copyright © 1983 Pergamon Press Ltd
I N V E R S E GAS C H R O M A T O G R A P H Y F O R THE S T U D Y O F ONE PHASE AND TWO PHASE POLYMER MIXTURES CHAI ZHIKUAN
Institute of Chemistry, Academia Sinica, Beijing, China D. J. WALSH Department of Chemical Engineering and Chemical Technology, Imperial College of Science and Technology, London SW7, UK. (Received 26 August 1982)
Abstract--Experiment finds that, for a chlorinated polyethylene (chlorine content 62.1~o by weight)/ poly(ethyl methacrylate) blend, a negative value of Z~3 is obtained, which indicates compatibility. With increasing temperature, X~3 increases towards zero as required by the lower critical solution temperature behaviour of polymer blends. For chlorinated polyethylene/poly(butyl acrylate) blends however the specific retention volume is a linear function of composition and a positive Z~3 results if calculated by the conventional theory. The magnitude of Z~3 is determined by the difference between the retention volumes of the pure polymers and decreases with temperature. This effect is assumed to be a result of phase separation during coating the blend onto the support. A theoretical treatment is developed to explain this behaviour.
INTRODUCTION
Because of its convenience and versatility, inverse gas chromatography (IGC) has found wide application in polymer research. The technique has been applied to the determination of the first and second order transitions, degree of crystallility and related physical quantities [1], to the thermodynamics of polymer solutions [2] and to the study of polymer compatibility [3]. Recently it was extended to the study of microphase separation phenomenon and domain size in block copolymers [4]. For the study of polymer compatibility, one important problem is to measure the interaction parameter Z between polymer pairs. This can be done by measuring the heat of mixing of oligomers, but the Xu so obtained is only related to the interaction energy. For understanding phase boundaries, one needs to measure a 7~ which is related to the free energy of mixing. Vapour absorption [5] and IGC are the two methods for this measurement. Since vapour absorption is a static method which takes a long time to reach equilibrium, the difficulty of maintaining a constant high temperature limits the temperature range of measurements. Inverse gas chromatography is based on observations of the difference of the retention volumes of solvent probes between polymer blends and their pure components. Compatible polymer blends will have a smaller retention volume than the algebraic average of the homopolymers at the corresponding composition. If the blend is phase separated, the retention volume should be the same as the average value. The theory of IGC for the study of polymer compatibility is based on two assumptions: (1) The activity of the solvent probe at, at the limit of wt ~ 0, is related to the specific retention volume
V° as follows In(a,/w,)'-
=
/ 273.2R \ po "B ln~lov0-~l ) - ~( 11- V,)
(l)
where w~ is the weight fraction of solvent in the polymer (liquid phase), M1 is the molecular weight, p0 the saturated vapour pressure, V~ the molar volume, and B n the second virial coefficient of the solvent vapour. The first term on the right hand side of the equation is the definition of the activity of an ideal gas in equilibrium with the liquid phase in the gas chromatographic column. The second term is the correction for imperfect gas behaviour. Equation 1 is assumed to be true for both the homopolymer and blend coatings. (2) The activity of the solvent, at, can be related to the interaction parameter Z through conventional polymer solution theories, only if the limiting case of q5z ~ 1 is approached. Based on the framework of the Flory-Huggins theory, we have for a single polymer: l n ( a l / w O ~ = l n ( v l / v : ) + 1 + ~12
(2)
and for a blend: ln(al/wl)~3 = ln(vl/(w2v2 + W3U3)) + l
-~- (~2Z12 + (~3Z13 -- Z23~2~3
(3)
where vi and qSiare the specific volume and the volume fraction of component i, respectively. Z~3 = Z23/r2 and r 2 is the number of segments in the polymer molecule. Z23 is the usual parameter defined in Flory's terminology, (7.23 = z r 2 A w 2 3 / k T in which z is the lattice coordination number and Aw23 is the change in energy for the formation of an unlike contact pair.) 519
520
CHAI ZHIKUANand D. J. WALSH
Combining Eqns 1-3, we have
0 -Injection
3
I
V~3
In(
~__ ~b21n
\wzv2 + w3v3/
02
-~2
- ~b3 In (V°3 / = Z23@2~3 \ v3/
(4) m
where I/°23 is the specific retention volume of the homogeneous blend. This equation can also be rewritten in a logarithmic form as in the literature I-6].
F
ln/(w,v~ +
o
C
nr
w~v~)(voy~(vo),~j =
z134',~
(5) 50
In high polymer blends when the number of molecules is very small in the combinatorial entropy term, the free energy of mixing (AGm) is determined by the interaction between the polymers. = zi3n2r2~p 3 = 7 ~ 7 " . . Z i 3 4 ) 2 ~ b 3
lim r2,r3
~
(6)
Concentration
Fig. 1. A presentation of the profile of concentration of the solvent probe in the column and the configuration of the columns used: 1. packings coated with polyblend; 2. mixed packings; 3. packings in series.
~,
where n 2 is the number of moles of polymer 2 and m2 the molecular weight per segment. Therefore from Eqn 4, the algebraic difference of the logarithm of the retention volume per unit volume between the pure components and the blend depends on the free energy of mixing. Unlike most experiments, in I G C the systems are studied at very high concentration of polymers. An injection of solvent is only 0.1/zl in quantity. If, for example, a 2 m column is used, the peak retention volume is 50ml, and the half width of the peak is 10ml, then the solvent will spread over a zone of about 0.4m in length, as shown in Fig. 1. If, for example, the diameter of the column is 0.4 cm and 1 g of polymer is loaded on the support, the concentration of solvent in solution would be only about 0.1 pl/0.2g = 0.0005 volume fraction, or the concentration of polymer is around 0.9995 volume fraction. At high concentration of polymer the analysis of activity by the Flory-Huggins theory leads to al = q~l e l+x'
(7)
P, -~ e ° ~ l e 1+~'
(8)
or
Equations 7 and 8 are Henry's Law with e l+z' as the limiting constant, when the concentration of the diluent is expressed by its volume fraction [7]. Equation 7 was required to derive Eqn 2 and is also therefore the basis for any consideration of phase separated systems. In this work three compatible systems viz. poly(methyl methacrylate) (PMMA), poly(ethyl methacrylate) (PEMA) and poly(butyl acrylate) (PBA), each with chlorinated polyethylene (CPE, chlorine content 62.1% by weight) have been studied. Some of the results with P M M A / C P E were reported earlier [8]. The compatibility of P B A / C P E and P E M A / C P E will be discussed in greater detail in future publications. We used three different columns, as illustrated in Fig. 1: (1) with packings having polymer blend coatings; (2) packed with two mixed packings, each coated
with a single polymer; (3) packed in series with two single packings. The columns were run from below to above the phase separation temperatures. The differences of retention volumes between these columns were compared. The results are discussed in terms of I G C theory as described above and an analysis for phase separated blends which is given in this work. EXPERIMENTAL The apparatus consisted of a Pye GCD gas chromatograph. It contained a 2 m coiled pyrex column packed with a Teflon support (Phase Separation, 30/60 mesh) on which the polymer was deposited as a thin film. A uniform flow of N2 carrier gas was passed through the column which was kept at constant temperature in an air circulating oven. A pulse of solvent was injected at one end and detected at the exit by a flame ionization detector. The packing was prepared by coating from solution. The polymer (l.2g) was dissolved in MEK(A.R.) and the solution added to 15 g of the support which had been washed with MEK and dried in an oven at 100°C prior to use. The volatile solvent was evaporated slowly with heating and frequent stirring to prevent coagulation of the particles. The powder was then sieved (30/60 mesh) to remove any large particles (though none were found). The packing was packed into the glass column, applying a vacuum to end. The columns were packed in three ways as described in the previous section. The packed columns were loaded into the GLC oven and conditioned for 12hr at 100°C, while N2 was flushed through the column in order that it should come to equilibrium. The retention volumes were measured for several solvents (pentane, MEK, THF and chloroform). Samples of solvent (0.1 pl) were injected with a l pl Hamilton syringe. The retention time was recorded using a stopwatch or was calculated from the distance from injection on a well calibrated chart recorder. The dead volume was measured by injecting a sample of methane. The measurements were performed three times and an average was taken. The flow rates of carrier gas were taken rom 5-15 ml/min and the net retention volume extrapolated to zero flow rate. The specific retention volume is calculated by 273.2fp V° = (t, - tgas ) a
TW
(9)
The study of one phase and two phase polymer mixtures
521
Table 1. Physical properties of polymers*
Polymer PMMA PEMA PBA CPE 20+
M,, +
M,, +
T, (C)
72,800 235,000 119,000 242,000
29,000 70.700 33,000 25,800
15 65 -55 63
Density (d,g:cm "~) 25 25 25 70
C'. C, C, C,
1.201 1.12 1.0N 1.458
Thermal expansion coefficient :~ (K ~) 5.74 6.05 6.14 5.02
× × × ×
10 ~* 104 10 ** 10 "~
* Values of T,, d and :~ for P E M A and PBA are from the literature [9]. Others are experimental data. 1 Chlorine content 62.1 °, by weight. :~ Relative to polystyrene standards by GPC.
~q~ere V° is the retention volume at 0 C (cm'~). t, is the retention time of solvent (sect, t~,,, is the retention time for a non-interacting methane sample (sect, Q is the volume flow rate of carrier gas ( c m 3 s e c ) ) . Tis the operating temperature of the column (K), Wis the weight of stationary phase (g),jp is a correction for the pressure drop along the column and is given b_',, I; = 3[(p,//>f
-
IT2[(/'/p,,)-'
-
1]
(1o)
where I' i is the inlet pressure and Po is the outlet pressure. I~~ has a relative error of _+5% by repeat measurements on different columns. The polymers are P M M A , PEMA, PBA and CPE 20. The first three are commercial products. No further purification was carried out for P M M A and PEMA. PBA ~ a s supplied in toluene solution: it was evaporated to dryness in a large petri dish and then dried in a vacuum oven at I m m H g at 5 0 C for 2weeks. C P E 2 0 was prepared by solution chlorination to polyethylene as described in a previous paper [8]. Physical properties of these polymers arc listed in Table 1. For the measurements of interaction pararneter, it is recommended that the polymer should be in the molten state in order that diffusion control should not limit equilibrium adsorption. This temperature is usually taken as 77, + 50 C. For the P M M A : C P E system when the weight fraction of CPE is greater than 0.5, "~ + 5 0 C will be below 120C, the cxperimental temperature. For the PEMA,'CPE blends this requirement is fullilled at 12(') C, but the retention volumes of pure PEMA shows that this temperature could be lo~cr because the retention volume decreases at above 80 C. From the retention volume temperature relation, we can see that CPE 20 reaches the molten state at about 100 120 C. The choice of loading of polymer on the inert support is another problem for IGC. At low loadings the contribution of surface adsorption is relatively large, causing the specific retention volume 1/° to increase sharply. At high co',erage the coated film becomes so thick that solvent wtpour cannot reach equilibrium in a limited sweep time. For example, under the conditions discussed previously the sweep time would be about 120 sec for a 0.4 m zone to pass a section of packing if the flow rate is 5 ml:min. Nonequilibrium adsorption will cause V° to drop rapidly because all the stationary phase does not come into equilibrium with the solvent. Hence the suitable loading depends on the surface area of support, the density of polymer and the diffusion coefficient of the solvent in the stationary phase. Owing to the fact that solvents have quite different diffusion coefficients, it is difficult to find a common thickness for all solvents. If this work 8", w w coverage was used in accordance with previous usage [10]. l.P,r /9 fi
I
RESULTS AND I)ISCtSSION Cah'ulatio17 q / the retention eolume [or a phase sel)arated hfem[ If two p u r e p o l y m e r s are in e q u i l i b r i u m with a c o m m o n s o l v e n t v a p o u r in a small region, the activity of s o l v e n t c a n be e x p r e s s e d as: l n a ~ - ln4/t2) + 1 -- Xt2 = l n ~ ( 1 3 1 +
1 +/~3
(11)
w h e r e qS(F '~ a n d ~b((~i are the v o l u m e fractions of s o l v e n t in p o l y m e r s 2 a n d 3, respectively. T h i s is a logarithmic f o r m of E q n 7, H e n r y ' s Law. B a s e d on E q n 11, m u l t i p l y i n g the first e x p r e s s i o n for In at, by
--
(/)3/-13
(12)
If we i n t r o d u c e na~"L t h e weight fraction of s o l v e n t in the liquid p h a s e ( c o n s i s t i n g of two pure polymers).
w(~''I -- V1dl,'(l~d 2 +
I/3d3)
(I
3)
wlaere 1~I a n d d~ are t h e v o l u m e a n d d e n s i t y of c o m p o n e n t i. respectively. T h e n E q n 12 c a n be put in t h e form : In (at w(l"')) q52 In (qS~e):wIl'm) -h (/)3 ha 1(~(13)/'w(im) ) -- I +
(14)
u s i n g E q n 11 a n d n o t i n g t h a t : ,/5(i) = l<].),[
(I 5l
[ ' 1 - V1(2)-~ V(I3)
(16)
and
w h e r e l,'l(i) is the v o l u m e of s o l v e n t in p o l y m e r i. T h e limiting f o r m of E q n 14 b e c o m e s : In (a l, ~ (ira)) '
= ln(t'l,{)t,'2/! 2 + ~1,'3t'3}} -I- 1 + ~2Z12 + q53Z13 -- ln[(c/52 + ~3e/~2 + {ok3 + ~b2 e / ' ~ - z ~ : ) ' ~ ]
z~),l,: (17)
E q u a t i o n 17 gives t h e activity of s o l v e n t in e q u i l i b r i u m with t w o s e p a r a t e d p u r e p o l y m e r s at t h e limit w~") --, 0. I f E q n 2 is u s e d to e l i m i n a t e 7.~z a n d /~3 in E q n 17 a n d the l o g a r i t h m of t h e activity t e r m of E q n 2 is
522
CHAI ZHIKUAN a n d D. J. WALSH
substituted into Eqn l, the final equation becomes:
v.% WzU 2
-
-}- W3V3
vo2 +
vo 3
V2
V3
(is)
C hloroform 30
This is equivalent to: 20
v~°,., = w2 v°~ + w3 v°~
(19) tO
In Eqns 18 and 19, V° is the retention volume per unit weight of polymer and V°/v can be regarded as the retention volume per unit volume of polymer, hence dependence on weight fraction and volume fraction results, respectively. From the analysis of the activity of the solvent, it is shown that the retention volume of a phase separated blend is a linear function of composition if the blend is separated into two pure polymers. With mixed polystyrene and polybutadiene packings, Klein, Widdecke and Wolter verified Eqn 19 [11]. They further showed that if this incompatible polyblend was coated onto the support, V0° also obeyed the above equation. Dipaula-Baranyi and Degre [12] and Galin and Rupprecht [4] confirmed the last observation using high molecular weight polystyrene/poly(n-butyl methacrylate) and polystyrene/poly(dimethyl siloxane), respectively. Both are incompatible pairs. Thus the conclusion can be drawn that the retention volume of an immiscible polyblend is the same as that of mixed packings. In this work mixed packings are examined as a model of phase separated blends. As shown in Figs. 2-4, in all the cases the experimental V° values for
o
12 II I0 9
'v~
IO o
n-
Pentone A
L 0
o
I
0.5
CPE %
~
1.0 w/w
Fig. 2. Specific retention volumes of the PMMA/CPE system, (A) mixed packings; (©) packings coated with polyblends, for three solvents.
o
30
20
I0
1 05
CPE %
I 1.0
w/w
Fig. 3. Specific retention volumes of the PEMA/CPE system at 80°C (O), 100°C (E3)and 120°C (A) for mixed packings and (O, m, A) for polyblends with two solvents.
mixed packings are in agreement with Eqn 19. It was observed that for PBA and PEMA columns the retention volumes at low temperatures (30 or 100°C) are a little smaller than required by the linear relationship. The data are just beyond the experimental error. This may be due to the relatively larger thickness considering that the same weight percentage coverage were used for coating polymers in all experiments. As expected, the retention volume of the column with packings in series also obeys Eqn 19. The experimental values are purely due to the additivity of the columns.
Retention volumes of PBA/CPE and P M M A / C P E blends The retention volumes of these two systems are also found to be linear functions of composition as shown in Figs 2 and 4. This casts some doubts on the homogeneity of blend coatings. The conclusion can be drawn from Eqn 4 that V0°23must be smaller than the corresponding algebraic average even when the homogeneous polyblend reaches the phase separation temperature, i.e. Z~3 = 0. After phase separation the retention volume will follow Eqn 19. There is a gap between these two retention volumes and the magnitude of the gap depends on the difference between V~2 and V°o3,i.e. on the interactions of the pure polymers with the solvent. For example, for a homogeneous blend of w z = 0.5 in the PBA/CPE system at 80°C, the specific retention volume ought to be smaller than 35ml (where Z~3 = 0), while the additive value is 55 ml (after separating into two pure polymers). The gap is 20ml which is far beyond the experimental error.
The study of one phase and two phase polymer mixtures
able to a homogeneous ternary system. Instead, we need the analysis of phase separated blends as discussed above.
90
~o
80
Retention volumes and interaction parameters of PEMA/CPE blends As seen in Fig. 3, the retention volumes of the P E M A / C P E blends are below the linear relationship. The difference between them tends twoards zero as the temperature increases. Table 2 lists the interaction parameters calculated from Eqn 4 with an accuracy of _+ 0.20. This error in Z'23 results from an error of +_5'% in V0°. However, it can be seen that the system is more compatible at higher concentrations of CPE as a larger negative Z~3 is found. With increasing temperature Z~3 tends towards zero as would be expected.
70
c 6o 0e
o
b
~
4o
30
523
-
CONCLUSIONS
160°C
I 0
0.5
CPE %
I 1.0
w/w
Fig. 4. Specific retention volumes of the PBA/CPE system, (/M mixed packings; (©) packings coated with polyblend: (O) packings in series.
A calculation of the activity of a solvent in contact with phase separated blends shows that the specific retention volume is a linear function of composition if the blend is separated into two pure polymers. The measurements on mixed packings verified this analysis. It is further predicted that there is a gap between the retention volumes of homogeneous and phase separated polyblends. When phase separation takes place during heating, the retention volume will have a sudden change.
o
If the retention volume of the polyblend is linearly dependent on composition as in Eqn 18, a positive Z~3 will be calculated from Eqn 4, because
lnt<
4
+ 43
is no longer a linear function of q~. For PBA/CPE such a positive Z~3 is calculated. The value decreases with temperature, as shown in Fig. 5. We can see that both the sign and the trend of change with temperature of 7,~3 is contrary to the thermodynamics of polymer compatibility. Polymer compatibility needs Z'23 to have a negative or very small positive value. The lower critical solution temperature(LCST) behaviour suggests that Z'~3 should increase with temperature. The unusual Z'~3 is assumed to arise as a result of phase separation of the polyblend during casting onto the support or during heating. Experience on casting blend films shows that phase separation may take place during evaporating of a solvent. This will depend on the conditions under which the solvent is evaporated and the nature of the polymer/polymer/ solvent three component phase diagram. Incompatibility in the presence of a solvent is often observed for compatible polymers. For example if blends of PVC with various polyacrylates are cast from T H F , two phase systems result whereas if they are cast from butanone one phase systems result [13]. If phase separation does take place, then Eqn 4 cannot be used because the equation is strictly applic-
2
--
o
v
o o
I 0
0
5
I 1.0
CPE
Fig. 5. The apparent values of Z~3, as calculated from Eqn 5 and the data in Fig. 4, for the PBA/CpE system. The values for temperatures above 100'C are very small and the differences are lost within the errors. The symbols are as in Fig. 4.
524
CHAI ZHIKUAN and D. J. WALSH Table 2. Retention volumes and interaction parameters of P E M A / C P E blends
WceE
0
0.2547
0.5011
0.7451
1
V°
V°
Z23
V°
Z23
V°g
Z23
V°
Chloroform MEK
37.5 35.0
24.2 27.1
- 1.15 -0.64
14.9 20.5
-0.99 -0.88
8.5 14.5
- 1.58 - 1.65
6.9 16.5
100oc Chloroform MEK
28.8 20.3
23.2 19.2
-0.50 -0.24
15.9 17.4
-0.86 -0.53
12.0 16.8
- 1.00 -0.74
10.8 20.0
120oc Chloroform MEK
18.7 13.0
18.1 13.8
0.81 -0.31
12.0 12.0
-0.41 -0.49
10.0 11.4
-0.37 -0.41
8.5 11.6
80°C
T h e results on P B A / C P E and P M M A / C P E systems s h o w that phase s e p a r a t i o n may occur during c o a t i n g o n t o the s u p p o r t as the retention volumes follow the expression for a two p h a s e blend. T h e results on P E M A / C P E blends s h o w t h e m to be h o m o g e n e o u s as coated a n d the interaction para m e t e r tends t o w a r d s zero with increasing t e m p e r a ture as expected.
REFERENCES
l. O. Smidrod and J. E. Guillet, Macromolecule 2, 272 (1969). 2. D. Patterson, Y, B. Tewari, H. P, Schreiber and J. E. Guillet, ibid 4, 356 (1971). 3. D. D. Deshpande, D. Patterson, H. P. Schreiber and C. C. Su, ibid 7, 530 (1974).
4. M. Galin and M. C. Rupprecht, ibid 12, 506 (1979). 5. A. A. Tager, T. I. Scholokhovich and Yu S. Besseonov, Eur. Polym. J. I1,321 (1975). 6. T. C. Ward, D. P. Sheehy, J. S. Ripfle and J. g. McGrath, Macromoleeule 14, 1456 (1981 ). 7. P. J. Flory, Principles of Polymer Chemistry, p. 514. Cornell (1953). 8. D.J. Walsh, J. S. Higgins and Z. Chai Polymer 23, 336 (1982). 9. D. W. Van Krevlin, Correlation between Structure and Physical Properties of Polymers. Van Nostrand (1976). I0. D. J. Walsh and J. G. McKeown, Polymer 21, 1335 (1980). 11. J, Klein, H. Widdecke and G. Wolter, J. Polym. Sei., Polym. Syrup. 68, 221 (1980). 12. G. Dipaola-Baranyi and P. Degre, Macromolecule 14, 1456 (1981). 13. D. J. Walsh and J. G. McKeown, Polymer 21, 1330 (I 980).
0014-3057/83/060519-06503.00/0 Copyright © 1983 Pergamon Press Ltd
I N V E R S E GAS C H R O M A T O G R A P H Y F O R THE S T U D Y O F ONE PHASE AND TWO PHASE POLYMER MIXTURES CHAI ZHIKUAN
Institute of Chemistry, Academia Sinica, Beijing, China D. J. WALSH Department of Chemical Engineering and Chemical Technology, Imperial College of Science and Technology, London SW7, UK. (Received 26 August 1982)
Abstract--Experiment finds that, for a chlorinated polyethylene (chlorine content 62.1~o by weight)/ poly(ethyl methacrylate) blend, a negative value of Z~3 is obtained, which indicates compatibility. With increasing temperature, X~3 increases towards zero as required by the lower critical solution temperature behaviour of polymer blends. For chlorinated polyethylene/poly(butyl acrylate) blends however the specific retention volume is a linear function of composition and a positive Z~3 results if calculated by the conventional theory. The magnitude of Z~3 is determined by the difference between the retention volumes of the pure polymers and decreases with temperature. This effect is assumed to be a result of phase separation during coating the blend onto the support. A theoretical treatment is developed to explain this behaviour.
INTRODUCTION
Because of its convenience and versatility, inverse gas chromatography (IGC) has found wide application in polymer research. The technique has been applied to the determination of the first and second order transitions, degree of crystallility and related physical quantities [1], to the thermodynamics of polymer solutions [2] and to the study of polymer compatibility [3]. Recently it was extended to the study of microphase separation phenomenon and domain size in block copolymers [4]. For the study of polymer compatibility, one important problem is to measure the interaction parameter Z between polymer pairs. This can be done by measuring the heat of mixing of oligomers, but the Xu so obtained is only related to the interaction energy. For understanding phase boundaries, one needs to measure a 7~ which is related to the free energy of mixing. Vapour absorption [5] and IGC are the two methods for this measurement. Since vapour absorption is a static method which takes a long time to reach equilibrium, the difficulty of maintaining a constant high temperature limits the temperature range of measurements. Inverse gas chromatography is based on observations of the difference of the retention volumes of solvent probes between polymer blends and their pure components. Compatible polymer blends will have a smaller retention volume than the algebraic average of the homopolymers at the corresponding composition. If the blend is phase separated, the retention volume should be the same as the average value. The theory of IGC for the study of polymer compatibility is based on two assumptions: (1) The activity of the solvent probe at, at the limit of wt ~ 0, is related to the specific retention volume
V° as follows In(a,/w,)'-
=
/ 273.2R \ po "B ln~lov0-~l ) - ~( 11- V,)
(l)
where w~ is the weight fraction of solvent in the polymer (liquid phase), M1 is the molecular weight, p0 the saturated vapour pressure, V~ the molar volume, and B n the second virial coefficient of the solvent vapour. The first term on the right hand side of the equation is the definition of the activity of an ideal gas in equilibrium with the liquid phase in the gas chromatographic column. The second term is the correction for imperfect gas behaviour. Equation 1 is assumed to be true for both the homopolymer and blend coatings. (2) The activity of the solvent, at, can be related to the interaction parameter Z through conventional polymer solution theories, only if the limiting case of q5z ~ 1 is approached. Based on the framework of the Flory-Huggins theory, we have for a single polymer: l n ( a l / w O ~ = l n ( v l / v : ) + 1 + ~12
(2)
and for a blend: ln(al/wl)~3 = ln(vl/(w2v2 + W3U3)) + l
-~- (~2Z12 + (~3Z13 -- Z23~2~3
(3)
where vi and qSiare the specific volume and the volume fraction of component i, respectively. Z~3 = Z23/r2 and r 2 is the number of segments in the polymer molecule. Z23 is the usual parameter defined in Flory's terminology, (7.23 = z r 2 A w 2 3 / k T in which z is the lattice coordination number and Aw23 is the change in energy for the formation of an unlike contact pair.) 519
520
CHAI ZHIKUANand D. J. WALSH
Combining Eqns 1-3, we have
0 -Injection
3
I
V~3
In(
~__ ~b21n
\wzv2 + w3v3/
02
-~2
- ~b3 In (V°3 / = Z23@2~3 \ v3/
(4) m
where I/°23 is the specific retention volume of the homogeneous blend. This equation can also be rewritten in a logarithmic form as in the literature I-6].
F
ln/(w,v~ +
o
C
nr
w~v~)(voy~(vo),~j =
z134',~
(5) 50
In high polymer blends when the number of molecules is very small in the combinatorial entropy term, the free energy of mixing (AGm) is determined by the interaction between the polymers. = zi3n2r2~p 3 = 7 ~ 7 " . . Z i 3 4 ) 2 ~ b 3
lim r2,r3
~
(6)
Concentration
Fig. 1. A presentation of the profile of concentration of the solvent probe in the column and the configuration of the columns used: 1. packings coated with polyblend; 2. mixed packings; 3. packings in series.
~,
where n 2 is the number of moles of polymer 2 and m2 the molecular weight per segment. Therefore from Eqn 4, the algebraic difference of the logarithm of the retention volume per unit volume between the pure components and the blend depends on the free energy of mixing. Unlike most experiments, in I G C the systems are studied at very high concentration of polymers. An injection of solvent is only 0.1/zl in quantity. If, for example, a 2 m column is used, the peak retention volume is 50ml, and the half width of the peak is 10ml, then the solvent will spread over a zone of about 0.4m in length, as shown in Fig. 1. If, for example, the diameter of the column is 0.4 cm and 1 g of polymer is loaded on the support, the concentration of solvent in solution would be only about 0.1 pl/0.2g = 0.0005 volume fraction, or the concentration of polymer is around 0.9995 volume fraction. At high concentration of polymer the analysis of activity by the Flory-Huggins theory leads to al = q~l e l+x'
(7)
P, -~ e ° ~ l e 1+~'
(8)
or
Equations 7 and 8 are Henry's Law with e l+z' as the limiting constant, when the concentration of the diluent is expressed by its volume fraction [7]. Equation 7 was required to derive Eqn 2 and is also therefore the basis for any consideration of phase separated systems. In this work three compatible systems viz. poly(methyl methacrylate) (PMMA), poly(ethyl methacrylate) (PEMA) and poly(butyl acrylate) (PBA), each with chlorinated polyethylene (CPE, chlorine content 62.1% by weight) have been studied. Some of the results with P M M A / C P E were reported earlier [8]. The compatibility of P B A / C P E and P E M A / C P E will be discussed in greater detail in future publications. We used three different columns, as illustrated in Fig. 1: (1) with packings having polymer blend coatings; (2) packed with two mixed packings, each coated
with a single polymer; (3) packed in series with two single packings. The columns were run from below to above the phase separation temperatures. The differences of retention volumes between these columns were compared. The results are discussed in terms of I G C theory as described above and an analysis for phase separated blends which is given in this work. EXPERIMENTAL The apparatus consisted of a Pye GCD gas chromatograph. It contained a 2 m coiled pyrex column packed with a Teflon support (Phase Separation, 30/60 mesh) on which the polymer was deposited as a thin film. A uniform flow of N2 carrier gas was passed through the column which was kept at constant temperature in an air circulating oven. A pulse of solvent was injected at one end and detected at the exit by a flame ionization detector. The packing was prepared by coating from solution. The polymer (l.2g) was dissolved in MEK(A.R.) and the solution added to 15 g of the support which had been washed with MEK and dried in an oven at 100°C prior to use. The volatile solvent was evaporated slowly with heating and frequent stirring to prevent coagulation of the particles. The powder was then sieved (30/60 mesh) to remove any large particles (though none were found). The packing was packed into the glass column, applying a vacuum to end. The columns were packed in three ways as described in the previous section. The packed columns were loaded into the GLC oven and conditioned for 12hr at 100°C, while N2 was flushed through the column in order that it should come to equilibrium. The retention volumes were measured for several solvents (pentane, MEK, THF and chloroform). Samples of solvent (0.1 pl) were injected with a l pl Hamilton syringe. The retention time was recorded using a stopwatch or was calculated from the distance from injection on a well calibrated chart recorder. The dead volume was measured by injecting a sample of methane. The measurements were performed three times and an average was taken. The flow rates of carrier gas were taken rom 5-15 ml/min and the net retention volume extrapolated to zero flow rate. The specific retention volume is calculated by 273.2fp V° = (t, - tgas ) a
TW
(9)
The study of one phase and two phase polymer mixtures
521
Table 1. Physical properties of polymers*
Polymer PMMA PEMA PBA CPE 20+
M,, +
M,, +
T, (C)
72,800 235,000 119,000 242,000
29,000 70.700 33,000 25,800
15 65 -55 63
Density (d,g:cm "~) 25 25 25 70
C'. C, C, C,
1.201 1.12 1.0N 1.458
Thermal expansion coefficient :~ (K ~) 5.74 6.05 6.14 5.02
× × × ×
10 ~* 104 10 ** 10 "~
* Values of T,, d and :~ for P E M A and PBA are from the literature [9]. Others are experimental data. 1 Chlorine content 62.1 °, by weight. :~ Relative to polystyrene standards by GPC.
~q~ere V° is the retention volume at 0 C (cm'~). t, is the retention time of solvent (sect, t~,,, is the retention time for a non-interacting methane sample (sect, Q is the volume flow rate of carrier gas ( c m 3 s e c ) ) . Tis the operating temperature of the column (K), Wis the weight of stationary phase (g),jp is a correction for the pressure drop along the column and is given b_',, I; = 3[(p,//>f
-
IT2[(/'/p,,)-'
-
1]
(1o)
where I' i is the inlet pressure and Po is the outlet pressure. I~~ has a relative error of _+5% by repeat measurements on different columns. The polymers are P M M A , PEMA, PBA and CPE 20. The first three are commercial products. No further purification was carried out for P M M A and PEMA. PBA ~ a s supplied in toluene solution: it was evaporated to dryness in a large petri dish and then dried in a vacuum oven at I m m H g at 5 0 C for 2weeks. C P E 2 0 was prepared by solution chlorination to polyethylene as described in a previous paper [8]. Physical properties of these polymers arc listed in Table 1. For the measurements of interaction pararneter, it is recommended that the polymer should be in the molten state in order that diffusion control should not limit equilibrium adsorption. This temperature is usually taken as 77, + 50 C. For the P M M A : C P E system when the weight fraction of CPE is greater than 0.5, "~ + 5 0 C will be below 120C, the cxperimental temperature. For the PEMA,'CPE blends this requirement is fullilled at 12(') C, but the retention volumes of pure PEMA shows that this temperature could be lo~cr because the retention volume decreases at above 80 C. From the retention volume temperature relation, we can see that CPE 20 reaches the molten state at about 100 120 C. The choice of loading of polymer on the inert support is another problem for IGC. At low loadings the contribution of surface adsorption is relatively large, causing the specific retention volume 1/° to increase sharply. At high co',erage the coated film becomes so thick that solvent wtpour cannot reach equilibrium in a limited sweep time. For example, under the conditions discussed previously the sweep time would be about 120 sec for a 0.4 m zone to pass a section of packing if the flow rate is 5 ml:min. Nonequilibrium adsorption will cause V° to drop rapidly because all the stationary phase does not come into equilibrium with the solvent. Hence the suitable loading depends on the surface area of support, the density of polymer and the diffusion coefficient of the solvent in the stationary phase. Owing to the fact that solvents have quite different diffusion coefficients, it is difficult to find a common thickness for all solvents. If this work 8", w w coverage was used in accordance with previous usage [10]. l.P,r /9 fi
I
RESULTS AND I)ISCtSSION Cah'ulatio17 q / the retention eolume [or a phase sel)arated hfem[ If two p u r e p o l y m e r s are in e q u i l i b r i u m with a c o m m o n s o l v e n t v a p o u r in a small region, the activity of s o l v e n t c a n be e x p r e s s e d as: l n a ~ - ln4/t2) + 1 -- Xt2 = l n ~ ( 1 3 1 +
1 +/~3
(11)
w h e r e qS(F '~ a n d ~b((~i are the v o l u m e fractions of s o l v e n t in p o l y m e r s 2 a n d 3, respectively. T h i s is a logarithmic f o r m of E q n 7, H e n r y ' s Law. B a s e d on E q n 11, m u l t i p l y i n g the first e x p r e s s i o n for In at, by
--
(/)3/-13
(12)
If we i n t r o d u c e na~"L t h e weight fraction of s o l v e n t in the liquid p h a s e ( c o n s i s t i n g of two pure polymers).
w(~''I -- V1dl,'(l~d 2 +
I/3d3)
(I
3)
wlaere 1~I a n d d~ are t h e v o l u m e a n d d e n s i t y of c o m p o n e n t i. respectively. T h e n E q n 12 c a n be put in t h e form : In (at w(l"')) q52 In (qS~e):wIl'm) -h (/)3 ha 1(~(13)/'w(im) ) -- I +
(14)
u s i n g E q n 11 a n d n o t i n g t h a t : ,/5(i) = l<].),[
(I 5l
[ ' 1 - V1(2)-~ V(I3)
(16)
and
w h e r e l,'l(i) is the v o l u m e of s o l v e n t in p o l y m e r i. T h e limiting f o r m of E q n 14 b e c o m e s : In (a l, ~ (ira)) '
= ln(t'l,{)t,'2/! 2 + ~1,'3t'3}} -I- 1 + ~2Z12 + q53Z13 -- ln[(c/52 + ~3e/~2 + {ok3 + ~b2 e / ' ~ - z ~ : ) ' ~ ]
z~),l,: (17)
E q u a t i o n 17 gives t h e activity of s o l v e n t in e q u i l i b r i u m with t w o s e p a r a t e d p u r e p o l y m e r s at t h e limit w~") --, 0. I f E q n 2 is u s e d to e l i m i n a t e 7.~z a n d /~3 in E q n 17 a n d the l o g a r i t h m of t h e activity t e r m of E q n 2 is
522
CHAI ZHIKUAN a n d D. J. WALSH
substituted into Eqn l, the final equation becomes:
v.% WzU 2
-
-}- W3V3
vo2 +
vo 3
V2
V3
(is)
C hloroform 30
This is equivalent to: 20
v~°,., = w2 v°~ + w3 v°~
(19) tO
In Eqns 18 and 19, V° is the retention volume per unit weight of polymer and V°/v can be regarded as the retention volume per unit volume of polymer, hence dependence on weight fraction and volume fraction results, respectively. From the analysis of the activity of the solvent, it is shown that the retention volume of a phase separated blend is a linear function of composition if the blend is separated into two pure polymers. With mixed polystyrene and polybutadiene packings, Klein, Widdecke and Wolter verified Eqn 19 [11]. They further showed that if this incompatible polyblend was coated onto the support, V0° also obeyed the above equation. Dipaula-Baranyi and Degre [12] and Galin and Rupprecht [4] confirmed the last observation using high molecular weight polystyrene/poly(n-butyl methacrylate) and polystyrene/poly(dimethyl siloxane), respectively. Both are incompatible pairs. Thus the conclusion can be drawn that the retention volume of an immiscible polyblend is the same as that of mixed packings. In this work mixed packings are examined as a model of phase separated blends. As shown in Figs. 2-4, in all the cases the experimental V° values for
o
12 II I0 9
'v~
IO o
n-
Pentone A
L 0
o
I
0.5
CPE %
~
1.0 w/w
Fig. 2. Specific retention volumes of the PMMA/CPE system, (A) mixed packings; (©) packings coated with polyblends, for three solvents.
o
30
20
I0
1 05
CPE %
I 1.0
w/w
Fig. 3. Specific retention volumes of the PEMA/CPE system at 80°C (O), 100°C (E3)and 120°C (A) for mixed packings and (O, m, A) for polyblends with two solvents.
mixed packings are in agreement with Eqn 19. It was observed that for PBA and PEMA columns the retention volumes at low temperatures (30 or 100°C) are a little smaller than required by the linear relationship. The data are just beyond the experimental error. This may be due to the relatively larger thickness considering that the same weight percentage coverage were used for coating polymers in all experiments. As expected, the retention volume of the column with packings in series also obeys Eqn 19. The experimental values are purely due to the additivity of the columns.
Retention volumes of PBA/CPE and P M M A / C P E blends The retention volumes of these two systems are also found to be linear functions of composition as shown in Figs 2 and 4. This casts some doubts on the homogeneity of blend coatings. The conclusion can be drawn from Eqn 4 that V0°23must be smaller than the corresponding algebraic average even when the homogeneous polyblend reaches the phase separation temperature, i.e. Z~3 = 0. After phase separation the retention volume will follow Eqn 19. There is a gap between these two retention volumes and the magnitude of the gap depends on the difference between V~2 and V°o3,i.e. on the interactions of the pure polymers with the solvent. For example, for a homogeneous blend of w z = 0.5 in the PBA/CPE system at 80°C, the specific retention volume ought to be smaller than 35ml (where Z~3 = 0), while the additive value is 55 ml (after separating into two pure polymers). The gap is 20ml which is far beyond the experimental error.
The study of one phase and two phase polymer mixtures
able to a homogeneous ternary system. Instead, we need the analysis of phase separated blends as discussed above.
90
~o
80
Retention volumes and interaction parameters of PEMA/CPE blends As seen in Fig. 3, the retention volumes of the P E M A / C P E blends are below the linear relationship. The difference between them tends twoards zero as the temperature increases. Table 2 lists the interaction parameters calculated from Eqn 4 with an accuracy of _+ 0.20. This error in Z'23 results from an error of +_5'% in V0°. However, it can be seen that the system is more compatible at higher concentrations of CPE as a larger negative Z~3 is found. With increasing temperature Z~3 tends towards zero as would be expected.
70
c 6o 0e
o
b
~
4o
30
523
-
CONCLUSIONS
160°C
I 0
0.5
CPE %
I 1.0
w/w
Fig. 4. Specific retention volumes of the PBA/CPE system, (/M mixed packings; (©) packings coated with polyblend: (O) packings in series.
A calculation of the activity of a solvent in contact with phase separated blends shows that the specific retention volume is a linear function of composition if the blend is separated into two pure polymers. The measurements on mixed packings verified this analysis. It is further predicted that there is a gap between the retention volumes of homogeneous and phase separated polyblends. When phase separation takes place during heating, the retention volume will have a sudden change.
o
If the retention volume of the polyblend is linearly dependent on composition as in Eqn 18, a positive Z~3 will be calculated from Eqn 4, because
lnt<
4
+ 43
is no longer a linear function of q~. For PBA/CPE such a positive Z~3 is calculated. The value decreases with temperature, as shown in Fig. 5. We can see that both the sign and the trend of change with temperature of 7,~3 is contrary to the thermodynamics of polymer compatibility. Polymer compatibility needs Z'23 to have a negative or very small positive value. The lower critical solution temperature(LCST) behaviour suggests that Z'~3 should increase with temperature. The unusual Z'~3 is assumed to arise as a result of phase separation of the polyblend during casting onto the support or during heating. Experience on casting blend films shows that phase separation may take place during evaporating of a solvent. This will depend on the conditions under which the solvent is evaporated and the nature of the polymer/polymer/ solvent three component phase diagram. Incompatibility in the presence of a solvent is often observed for compatible polymers. For example if blends of PVC with various polyacrylates are cast from T H F , two phase systems result whereas if they are cast from butanone one phase systems result [13]. If phase separation does take place, then Eqn 4 cannot be used because the equation is strictly applic-
2
--
o
v
o o
I 0
0
5
I 1.0
CPE
Fig. 5. The apparent values of Z~3, as calculated from Eqn 5 and the data in Fig. 4, for the PBA/CpE system. The values for temperatures above 100'C are very small and the differences are lost within the errors. The symbols are as in Fig. 4.
524
CHAI ZHIKUAN and D. J. WALSH Table 2. Retention volumes and interaction parameters of P E M A / C P E blends
WceE
0
0.2547
0.5011
0.7451
1
V°
V°
Z23
V°
Z23
V°g
Z23
V°
Chloroform MEK
37.5 35.0
24.2 27.1
- 1.15 -0.64
14.9 20.5
-0.99 -0.88
8.5 14.5
- 1.58 - 1.65
6.9 16.5
100oc Chloroform MEK
28.8 20.3
23.2 19.2
-0.50 -0.24
15.9 17.4
-0.86 -0.53
12.0 16.8
- 1.00 -0.74
10.8 20.0
120oc Chloroform MEK
18.7 13.0
18.1 13.8
0.81 -0.31
12.0 12.0
-0.41 -0.49
10.0 11.4
-0.37 -0.41
8.5 11.6
80°C
T h e results on P B A / C P E and P M M A / C P E systems s h o w that phase s e p a r a t i o n may occur during c o a t i n g o n t o the s u p p o r t as the retention volumes follow the expression for a two p h a s e blend. T h e results on P E M A / C P E blends s h o w t h e m to be h o m o g e n e o u s as coated a n d the interaction para m e t e r tends t o w a r d s zero with increasing t e m p e r a ture as expected.
REFERENCES
l. O. Smidrod and J. E. Guillet, Macromolecule 2, 272 (1969). 2. D. Patterson, Y, B. Tewari, H. P, Schreiber and J. E. Guillet, ibid 4, 356 (1971). 3. D. D. Deshpande, D. Patterson, H. P. Schreiber and C. C. Su, ibid 7, 530 (1974).
4. M. Galin and M. C. Rupprecht, ibid 12, 506 (1979). 5. A. A. Tager, T. I. Scholokhovich and Yu S. Besseonov, Eur. Polym. J. I1,321 (1975). 6. T. C. Ward, D. P. Sheehy, J. S. Ripfle and J. g. McGrath, Macromoleeule 14, 1456 (1981 ). 7. P. J. Flory, Principles of Polymer Chemistry, p. 514. Cornell (1953). 8. D.J. Walsh, J. S. Higgins and Z. Chai Polymer 23, 336 (1982). 9. D. W. Van Krevlin, Correlation between Structure and Physical Properties of Polymers. Van Nostrand (1976). I0. D. J. Walsh and J. G. McKeown, Polymer 21, 1335 (1980). 11. J, Klein, H. Widdecke and G. Wolter, J. Polym. Sei., Polym. Syrup. 68, 221 (1980). 12. G. Dipaola-Baranyi and P. Degre, Macromolecule 14, 1456 (1981). 13. D. J. Walsh and J. G. McKeown, Polymer 21, 1330 (I 980).