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The viscosity anomaly of polymer mixture solution in extremely dilute concentration region
European Polymer Journal 38 (2002) 359±364
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The viscosity anomaly of polymer mixture solution in extremely dilute concentration region Yan Pan a,b,*, Weiwen Fu a, Feng Xue a, Yuanfang Luo a, Ju Gu a, Rongshi Cheng a a
College of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, China b The State Key Laboratory of Physics and Chemistry of Polymer, Beijing 100080, China Received 4 July 2000; received in revised form 22 February 2001; accepted 2 July 2001
Abstract The measured reduced viscosity±concentration gsp =C±C curves of compatible PPO/PS incompatible PMMA/PS mixtures with dierent composition in toluene all deviate linear and reveal downward turn in extremely dilute concentration region. Moreover, with the variation of composition, the gsp =C±C curve of PS/PMMA/m-xylene solution bends downwards sometimes and bends upwards sometimes in the extremely dilute concentration region. It indicates that such viscosity anomaly should not be attributed simply to incompatibility, but be related to solvent, composition and so on. It is further suggested that, like the single polymer solution, the viscosity anomaly of polymer mixture solution be resulted mainly from the interference of wall eects on viscosity measurement, which could be eliminated quantitatively with a proposed theoretical formula. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Polymer mixture solution; Viscosity anomaly; Wall eect
1. Introduction As early as 1950s it was found that solution viscosity of single polymer in extremely dilute concentration region usually reveals some abnormalities, i.e., the reduced viscosity±concentration gsp =C±C curve deviates from linear relationship and shows either an upward or a downward turn as concentration is very low. Over the last decades, much eorts have been made to investigate it [1±10]. However, the study on viscosity behavior of polymer mixture solution in extremely dilute concentration region is rather few. Dondos and coworkers [11, 12] once reported in 1980s that when measuring the dilute solution viscosity of PS/PMMA, PS/PEG and PS/
*
Corresponding author. Address: College of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, China. Tel.: +86-20-87114557; fax: +86-20-85511266. E-mail address: [email protected] (Y. Pan).
PVC mixture, they observed similar viscosity anomaly i.e. the gsp =C±C curves of these polymer mixtures show downward deviation from linear as concentration is very low (C < 0:3 g/dl). They attributed it to the incompatibility between dierent polymers, which acts strongly against overlapping and results in the decrease of hydrodynamic volume of the macromolecule as concentration reaches a de®nite point. Recently, Zhu and coworkers veri®ed it by the two ternary systems: incompatible PVC/PS mixture in THF solution and compatible PCL/PVC mixture in DMF solution [13±15]. The gsp =C±C curve of the former ternary system reveals a downward turn as concentration is below 0.7 g/dl, while the gsp =C±C curve of the latter system reveals an upward turn as concentration is very low. However, it is inconsistent that the gsp =C±C curve of incompatible PVC/PS mixture in DCE solution shows a sharply upward turn as concentration is below 0.6 g/dl. It showed that the eect of solvent is not negligible in interpreting such viscosity anomaly. Therefore, Dondos' explanation is actually questionable.
0014-3057/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 4 - 3 0 5 7 ( 0 1 ) 0 0 1 9 0 - 2
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Y. Pan et al. / European Polymer Journal 38 (2002) 359±364
Since considerable progress has been made [7±10] recently on the viscosity anomaly of single polymer solution in extremely dilute concentration region. It is plausible for us to revisit the problem of solution viscosity of polymer mixture on new basis. In the present work, we carefully measured the dilute solution viscosity of a typical compatible and a typical incompatible polymer mixture: PS/PPO and PS/PMMA. The eects of solvent, composition and surface structure of capillary wall of viscometer on the viscosity behavior of polymer mixture in extremely dilute concentration region were investigated. Finally, the observed viscosity anomaly was reinterpreted.
relative viscosity of the polymer solution was calculated simply as the ratio of the ¯ow time of solution to that of the pure solvent. Kinetic correction was neglected.
3. Results and discussion 3.1. Viscosity anomaly of PS/PPO, PS/PMMA mixture solution Figs. 1 and 2 show the variation of reduced viscosity gsp =C experimentally measured as a function of concentration C for PS/PPO and PS/PMMA mixture in toluene. Both the two ternary systems show obvious
2. Experimental 2.1. Materials The poly(2,6-dimethyl 1,4-phenylene oxide) (PPO) was purchased from Aldrich Chemical Co., the molecular weight was measured by GPC as Mw 67 500 and Mn 29 000. The polystyrene (PS) is a commercial sample with Mw 2:4 105 . The poly(methyl methacrylate) (PMMA) is a commercial sample with Mw 4:6 105 . Distilled analytical grade toluene was used as solvent. 2.2. Viscosity measurements A dilution type Ubbelohde viscometer was used. All the viscosity measurements were carried out at 25 °C. Stock solutions of polymer mixtures with known composition and known concentration were prepared by weighing the component polymers and solvent in a vessel. The ¯ow time of known weight of pure toluene in the clean viscometer was ®rst measured. Afterwards the stock solution with known weight was added successively into the viscometer by weighing for increasing the solution concentration in the viscometer. The ¯ow times of each solution with dierent concentration in the viscometer were measured. The procedure of siliconiting modi®cation of viscometer is keeping the viscometer in an oven at 200 °C for 8 h to activate the capillary surface, then adding trimethylchlorosilicone solution into the wide bore tube of the vertically held viscometer until the solution reach a position higher than the upper ori®ce of capillary and below the lower mark of measuring bulb, then sealing the viscometer and keeping it in an oven at 40 °C for three days. Finally, withdrawing the trimethylchlorosilicone from the wide bore tube of the viscometer and drying the viscometer under vacuum. The ¯ow times of pure toluene in original and coated viscometer are 165.46 and 165.38 s, respectively. The
Fig. 1. Variation of reduced viscosity gsp =C with concentration for PPO/PS mixture in toluene at 25 °C. The lines are calculated from Eq. (4) with the parameters listed in Table 1.
Fig. 2. Variation of reduced viscosity gsp =C with concentration for PMMA/PS mixture in toluene at 25 °C. The lines are calculated from Eq. (4) with the parameters listed in Table 1.
Y. Pan et al. / European Polymer Journal 38 (2002) 359±364
viscosity anomaly in extremely dilute concentration region. In the former system, the reduced viscosity±concentration gsp =C±C curve of single component (PS or PPO) solution bends upwards in extremely dilute concentration region. However, the gsp =C±C curves of their mixture solutions with dierent compositions all bend downwards in the extremely dilute concentration region. In the latter system, the gsp =C±C curve of PMMA solution bends downwards in the extremely dilute concentration region. But, like the formal ternary system, the gsp =C±C curves of PS/PMMA mixtures with dierent compositions all also show downward in¯ection in extremely dilute concentration region, which is similar to what Dondos et al. observed when measuring the dilute solution viscosity of PS/PMMA (50:50) in benzene. As is well known that PS and PPO are compatible. But, the gsp =C±C curve of their mixture solution also shows downward deviation from linear in extremely dilute concentration region. It demonstrates convincingly that it is unreliable to attribute simply the downward in¯ection of gsp =C±C curve of polymer mixture in extremely dilute concentration region to incompatibility. Besides the experimental facts [13,14] that the gsp = C±C curve of incompatible PVC/PS mixture solution in extremely dilute concentration region shows downward in¯ection in THF, but shows a sharply upward in¯ection in DCE, in order to illustrate the eects of solvent again, we measured the dilute solution viscosity of the PS/PMMA mixture in another solvent: m-xylene. The gsp =C±C curve of PS/PMMA mixture in m-xylene is showed in Fig. 3. It diers from that of PS/PMMA in toluene evidently. Firstly, the PS in m-xylene shows almost linear gsp =C±C curve even in extremely dilute concentration region. Secondly, with the variation of composition, the gsp =C±C curve of PS/PMMA/m-xylene
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solution in extremely dilute concentration region bends downwards sometimes, bends upwards sometimes and almost linear sometimes. It means composition also has some in¯uences on the viscosity anomaly of polymer mixture in extremely dilute concentration region. But, none of the past investigators noticed the eect of composition since they often investigated mixture solution with ®xed composition (50:50). These experimental facts indicate, at least, that the gsp =C±C curve of polymer mixture in extremely dilute concentration region deviates downwards or upwards from linear is not predominated mainly by compatibility, but is related to solvent and composition. 3.2. Reinterpretation of the viscosity anomaly Over the past decades, many eorts have been made to explain the viscosity anomaly of single polymer solution in extremely dilute solution. Some theories have been proposed. The most important include the theory of critical concentration [2,16,17], and the theory of solute adsorption [3,18±21]. But each of them has limitation. Recently, Cheng et al. showed [7±10] with abundant data that the interference of wall eect on viscosity measurement is the main reason for the viscosity anomaly of single polymer solution in extremely dilute concentration region, and the interference of wall eect could be eliminated in a quantitative way. It was shown that the measured relative viscosity gr could be related quantitatively to the true relative viscosity gr;true as [7] kC 1 gr gr;true 1 Ca C where k denotes the maximum fractional change of ¯ow time of pure solvent due to the variation of the surface property of viscometer wall during measuring solution viscosity. Solute adsorption leads to a reduction of capillary radius and hence results a positive k. Slippage due to surface property change will cause a negative k value. The parameter Ca is a characteristic concentration at which half of the available surface is ®lled with the polymer solute. For eliminating the interference of wall eect, the experimental relative viscosity could be corrected by gr;exp gr;true 2 1 CakCC The true relative viscosity gr;true is expressed in Huggins equation gr;true 1 gC kH g2 C 2
Fig. 3. Variation of reduced viscosity gsp =C with concentration C for PS/PMMA mixture in m-xylene at 25 °C. The lines are calculated from Eq. (4) with the parameters listed in Table 2.
3
kH is the Huggins coecient. Combining the Eqs. (1) and (3), the experimental reduced viscosity (gsp =C) should be
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Y. Pan et al. / European Polymer Journal 38 (2002) 359±364
Table 1 Viscosity parameters of PS/PPO, PS/PMMA mixtures in toluene solution k
Polymer mixture
[g] (ml/g)
kH
PPO PPO/PS (wPPO 0:682) PPO/PS (wPPO 0:50) PPO/PS (wPPO 0:354) PPO/PS (wPPO 0:116) PS PMMA/PS (wPMMA 0:25) PMMA/PS (wPMMA 0:50) PMMA/PS (wPMMA 0:667) PMMA
45.84 54.31 60.90 65.98 74.40 81.00 84.5 88.4 90.7 97.5
0.488 0.552 0.492 0.463 0.339 0.359 0.371 0.346 0.287 0.347
Ca (g/ml) 4.47E 3.13E 1.63E 2.88E 8.44E 1.81E 4.10E 3.42E 2.08E 1.07E
4 4 3 3 4 4 3 3 3 3
2.3E 9 5.41E 6 3.22E 4 2.40E 4 4.43E 7 3.1E 11 4.78E 5 4.11E 4 6.13E 4 0
Table 2 Viscosity parameters of PS/PMMA mixtures in m-xylene solution Polymer mixture
[g] (ml/g)
kH
PMMA PMMA/PS PMMA/PS PMMA/PS PMMA/PS PS
33.86 37.00 44.00 53.01 61.87 74.97
1.41 1.09 0.57 0.34 0.40 0.36
gsp =C
(wPMMA (wPMMA (wPMMA (wPMMA
0:875) 0:667) 0:50) 0:25)
k kC 1 g 6kH g2 C Ca C Ca C
4
and is no longer linear as concentration is very small. Much research has shown that Eq. (4) could agree well with experimental data. With Eq. (4), it is easy to deduce that the upward in¯ection of gsp =C±C curve of PS or PPO in toluene is originated from the reduction of eective capillary diameter due to solute adsorption onto the wall surface of capillary during measurement. In general, solute adsorption is universal for most polymer±solvent systems. The downwards in¯ection of gsp =C±C curve of PMMA in toluene indicates that it is not easy for the studied PMMA chains to be adsorbed onto the capillary surface, then the capillary ¯ow model transits from viscous ¯ow to slip ¯ow. Such slip ¯ow phenomenon is actually not unique. Similar phenomenon was also observed in measuring the dilute solution viscosity of PS-MEK system [10]. On the basis of the above theory, it seems possible for us to reinterpret the viscosity anomaly of polymer mixture. Since the wall eect is an unavoidable physical phenomena during measuring solution viscosity of polymer, the measurement procedure of solution viscosity of polymer mixture should be bound to suer the interference of wall eect too. Regarding the polymer mixture in solution as a single solute, Eq. (4) may also express the dilute solution viscosity of polymer mixture down to the extremely dilute concentration region. Then the measured viscosity data of PS/PPO, PS/PMMA
k
Ca (g/ml) 2.48E 1.61E 6.39E 3.34E 3.62E 3.76E
3 4 4 4 4 5
2.24E 5 1.28E 6 4.31E 4 0 0 0
mixtures were ®tted to Eq. (4) by iterative data ®tting procedure. The resulted viscometric parameters g, kH , k and Ca for all of the mixture solutions are listed in Tables 1 and 2. The solid lines in Figs. 1±3 are the calculated reduced viscosity±concentration curves with these parameters, which coincide the experimental points very well. It indicates that Eq. (4) could indeed be applied to polymer mixture solution. Having evaluated the parameters k and Ca , the original viscosity data could be corrected by Eq. (2) to eliminate the interference of wall eect. Figs. 4 and 5 are the plots of corrected gsp =C±C curves of PS/PPO, PS/PMMA mixtures in toluene, which exhibit good linearity as expected. The wall eect depends directly on the interaction between the inner surface of capillary wall and the ¯owing solution composed by solvent and polymer chains. Thus, the viscosity anomaly of polymer mixture solution should be related to the surface structure of capillary wall, solvent, polymer and composition. Then, the experimental facts in Section 3.1 become understandable. In order to investigate the eect of surface structure of capillary wall, we had the capillary surface coated by an even and thin trimethylchlorosilicane ®lm, hereafter, used it to measure again the viscosity of PS/PPO, PS/ PMMA mixture in toluene. In such way, the size parameters of the original and coated viscometer are alike. The mixtures measured with the original and coated viscometer are the same. The only change is surface structure of capillary. The results obtained by the original and coated viscometer are compared in Figs. 6 and 7.
Y. Pan et al. / European Polymer Journal 38 (2002) 359±364
Fig. 4. Corrected reduced viscosity±concentration curves of PS/PPO mixture in toluene.
363
Fig. 6. Comparison of the reduced viscosity of PS/PPO (50:50) in toluene measured with original viscometer with that measured with viscometer coated with trimethylchlorosilicane. The lines are calculated from Eq. (4) with parameters listed in Tables 1 and 3. The open symbol is due to original viscometer, solid symbol is due to coated viscometer.
Fig. 5. Corrected reduced viscosity±concentration curves of PS/PMMA mixture in toluene.
All the second measured viscosity data could also be represented satisfactorily by Eq. (4). The solid lines in Figs. 6 and 7 are calculated from Eq. (4) with the parameters listed in Table 3. The gsp =C±C curve of PS or PPO measured with siliconiting viscometer bends downwards in extremely dilute concentration region, while that measured with original viscometer bends upwards in extremely dilute concentration region. Almost none of the past theories could interpret such phenomena. According to the above theory of wall eect, however, it is easy to understand. That the Ca is zero for PS or PPO solution indicates the absence of solute adsorption onto the siliconiting capillary surface. The surface modi®cation leads to the conversion of capillary ¯ow from viscous model to wall slip model. It demonstrated the in¯uences of surface structure of capillary wall. But, the gsp =C±C curves of PMMA, PS/PPO or PS/PMMA mixtures do
Fig. 7. Comparison of the reduced viscosity of PS/PMMA (50:50) in toluene measured with original viscometer with that measured with viscometer coated with trimethylchlorosilicane. The lines are calculated from Eq. (4) with parameters listed in Tables 1 and 3. The open symbol is due to original viscometer, solid symbol is due to coated viscometer.
not change obviously with the variation of surface structure of capillary, still showing a downward deviation from linear as concentration is very small. On the other hand, for a given polymer±polymer± solvent system, its true viscosity behavior should be inherent properties of the system. So, its true gsp =C±C
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Y. Pan et al. / European Polymer Journal 38 (2002) 359±364
Table 3 Viscosity parameters of PS/PPO (50:50) and PS/PMMA (50:50) mixture in toluene measured with viscometer coated with trimethylchlorosilicane Polymer mixture
hgim (ml/g)
hKm im
PPO PPO/PS (50:50) PS PMMA/PS (50:50) PMMA
45.84 60.90
3.73 5.00
8.84E 5 5.20E 4
0 3.72E 5
81.00 88.40
4.85 5.10
4.70E 4 5.77E 3
0 7.81E 4
97.50
5.65
1.76E 3
1.30E 4
k
Ca (g/ml)
However, it is noticeable that the wall eect seems much more complicated for the mixture solution. At present, it is almost impossible to elaborate on its interference on viscosity measured experimentally. For example, since PS±toluene and PPO±toluene systems both reveal solute adsorption phenomenon, it is natural to expect that their mixture solution exhibit similar behavior. But, the experimental facts are beyond the anticipation. Since two kinds of polymer solutes coexist in the mixture solution, maybe more complex phenomena such as competitive or preferential adsorption, orientation change of the adsorbed layer and so on occur. In addition, it could not be well explained that the measured viscosity behavior of PS±PPO±toluene and PS±PMMA±toluene systems, whose gsp =C±C curves measured by original viscometer deviates downwards from linear in very low concentration region, do not change obviously with the variation of surface structure of capillary. More detailed investigation is continuing.
Acknowledgement The work was supported by National Nature Science Foundation of China.
References Fig. 8. Variation of corrected reduced viscosity with concentration for PS/PPO in toluene. Open symbol is due to original viscometer, solid symbol is due to coated viscometer.
curve obtained by dierent viscometers should be identical theoretically. Having evaluated the parameters k and Ca , the measured viscosity was corrected by Eq. (2). The plots of corrected gsp =C±C curve of PS/PPO in toluene are shown in Fig. 8. As anticipated, the corrected gsp =C±C curves derived from original and coated viscometer coincide very well, which represent the true viscosity behavior of the mixture solutions. It shows, to some extent, such correction is reasonable and reliable. Therefore, it was suggested that the viscosity anomaly of polymer mixture in extremely dilute concentration region should also arise materially from the interference of wall eect on viscosity measurement but not incompatibility or speci®c solution properties. Although the apparent viscosity of mixture solution in extremely dilute concentration region may show dierent abnormal behavior with the variation of solvent, composition, surface structure of capillary and so on. Eq. (4) could be applied to eliminate the interference of wall eect, then true reliable viscosity data could be obtained.
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21]
Cutler M, Kimball GE. J Polym Sci 1951;7:445. Streeter DJ, Boyer RF. J Polym Sci 1954;14:5. Ohrn OE. Arkiv Kemi 1958;12:397. Horth A, Rinfret M. J Am Chem Soc 1955;77:503. Dondos A, Tsitsilianis C, Staikos G. Polymer 1989; 30:1690. Dondos A, Papanagopoulos D. Makromol Chem, Rapid Commun 1993;14:7. Cheng R, Shao Y, Liu M, et al. Eur Polym J 1998; 34(11):1613. Yang Y, Yan X, Cheng R. J Macromol Sci Phys 1999;B38(3):237. Cheng R, Yang Y, Yan X. Polymer 1999;40:3773. Yang Y. The surface phenomena of polymer solution in viscosity measurement. Doctoral dissertation, Nanjing University, 1999. Dondos A, Skondras P, Pierri E. Makromol Chem 1983;184:2153. Pierri E, Dondos A. Eur Polym J 1987;23(5):347. Zhu P, Yang H, Wang S. Eur Polym J 1998;34(1):91. Zhu P, Yang H, Zeng Y. Eur Polym J 1999;35:915. Yang H, Zhu P, Wang S, et al. Eur Polym J 1998;34:463. Moore WR, Russell J. J Polym Sci 1952;9:472. Pepper DC, Rutherford PO. J Polym Sci 1959;35:299. Cutler M, Kimball GE. J Polym Sci 1951;7:445. Ohrn OE. J Polym Sci 1955;17:137±40. Ohrn OE. J Polym Sci 1956;19:199. Patat F, Elias HG. Makromol Chem 1954;14:40.
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The viscosity anomaly of polymer mixture solution in extremely dilute concentration region Yan Pan a,b,*, Weiwen Fu a, Feng Xue a, Yuanfang Luo a, Ju Gu a, Rongshi Cheng a a
College of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, China b The State Key Laboratory of Physics and Chemistry of Polymer, Beijing 100080, China Received 4 July 2000; received in revised form 22 February 2001; accepted 2 July 2001
Abstract The measured reduced viscosity±concentration gsp =C±C curves of compatible PPO/PS incompatible PMMA/PS mixtures with dierent composition in toluene all deviate linear and reveal downward turn in extremely dilute concentration region. Moreover, with the variation of composition, the gsp =C±C curve of PS/PMMA/m-xylene solution bends downwards sometimes and bends upwards sometimes in the extremely dilute concentration region. It indicates that such viscosity anomaly should not be attributed simply to incompatibility, but be related to solvent, composition and so on. It is further suggested that, like the single polymer solution, the viscosity anomaly of polymer mixture solution be resulted mainly from the interference of wall eects on viscosity measurement, which could be eliminated quantitatively with a proposed theoretical formula. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Polymer mixture solution; Viscosity anomaly; Wall eect
1. Introduction As early as 1950s it was found that solution viscosity of single polymer in extremely dilute concentration region usually reveals some abnormalities, i.e., the reduced viscosity±concentration gsp =C±C curve deviates from linear relationship and shows either an upward or a downward turn as concentration is very low. Over the last decades, much eorts have been made to investigate it [1±10]. However, the study on viscosity behavior of polymer mixture solution in extremely dilute concentration region is rather few. Dondos and coworkers [11, 12] once reported in 1980s that when measuring the dilute solution viscosity of PS/PMMA, PS/PEG and PS/
*
Corresponding author. Address: College of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, China. Tel.: +86-20-87114557; fax: +86-20-85511266. E-mail address: [email protected] (Y. Pan).
PVC mixture, they observed similar viscosity anomaly i.e. the gsp =C±C curves of these polymer mixtures show downward deviation from linear as concentration is very low (C < 0:3 g/dl). They attributed it to the incompatibility between dierent polymers, which acts strongly against overlapping and results in the decrease of hydrodynamic volume of the macromolecule as concentration reaches a de®nite point. Recently, Zhu and coworkers veri®ed it by the two ternary systems: incompatible PVC/PS mixture in THF solution and compatible PCL/PVC mixture in DMF solution [13±15]. The gsp =C±C curve of the former ternary system reveals a downward turn as concentration is below 0.7 g/dl, while the gsp =C±C curve of the latter system reveals an upward turn as concentration is very low. However, it is inconsistent that the gsp =C±C curve of incompatible PVC/PS mixture in DCE solution shows a sharply upward turn as concentration is below 0.6 g/dl. It showed that the eect of solvent is not negligible in interpreting such viscosity anomaly. Therefore, Dondos' explanation is actually questionable.
0014-3057/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 1 4 - 3 0 5 7 ( 0 1 ) 0 0 1 9 0 - 2
360
Y. Pan et al. / European Polymer Journal 38 (2002) 359±364
Since considerable progress has been made [7±10] recently on the viscosity anomaly of single polymer solution in extremely dilute concentration region. It is plausible for us to revisit the problem of solution viscosity of polymer mixture on new basis. In the present work, we carefully measured the dilute solution viscosity of a typical compatible and a typical incompatible polymer mixture: PS/PPO and PS/PMMA. The eects of solvent, composition and surface structure of capillary wall of viscometer on the viscosity behavior of polymer mixture in extremely dilute concentration region were investigated. Finally, the observed viscosity anomaly was reinterpreted.
relative viscosity of the polymer solution was calculated simply as the ratio of the ¯ow time of solution to that of the pure solvent. Kinetic correction was neglected.
3. Results and discussion 3.1. Viscosity anomaly of PS/PPO, PS/PMMA mixture solution Figs. 1 and 2 show the variation of reduced viscosity gsp =C experimentally measured as a function of concentration C for PS/PPO and PS/PMMA mixture in toluene. Both the two ternary systems show obvious
2. Experimental 2.1. Materials The poly(2,6-dimethyl 1,4-phenylene oxide) (PPO) was purchased from Aldrich Chemical Co., the molecular weight was measured by GPC as Mw 67 500 and Mn 29 000. The polystyrene (PS) is a commercial sample with Mw 2:4 105 . The poly(methyl methacrylate) (PMMA) is a commercial sample with Mw 4:6 105 . Distilled analytical grade toluene was used as solvent. 2.2. Viscosity measurements A dilution type Ubbelohde viscometer was used. All the viscosity measurements were carried out at 25 °C. Stock solutions of polymer mixtures with known composition and known concentration were prepared by weighing the component polymers and solvent in a vessel. The ¯ow time of known weight of pure toluene in the clean viscometer was ®rst measured. Afterwards the stock solution with known weight was added successively into the viscometer by weighing for increasing the solution concentration in the viscometer. The ¯ow times of each solution with dierent concentration in the viscometer were measured. The procedure of siliconiting modi®cation of viscometer is keeping the viscometer in an oven at 200 °C for 8 h to activate the capillary surface, then adding trimethylchlorosilicone solution into the wide bore tube of the vertically held viscometer until the solution reach a position higher than the upper ori®ce of capillary and below the lower mark of measuring bulb, then sealing the viscometer and keeping it in an oven at 40 °C for three days. Finally, withdrawing the trimethylchlorosilicone from the wide bore tube of the viscometer and drying the viscometer under vacuum. The ¯ow times of pure toluene in original and coated viscometer are 165.46 and 165.38 s, respectively. The
Fig. 1. Variation of reduced viscosity gsp =C with concentration for PPO/PS mixture in toluene at 25 °C. The lines are calculated from Eq. (4) with the parameters listed in Table 1.
Fig. 2. Variation of reduced viscosity gsp =C with concentration for PMMA/PS mixture in toluene at 25 °C. The lines are calculated from Eq. (4) with the parameters listed in Table 1.
Y. Pan et al. / European Polymer Journal 38 (2002) 359±364
viscosity anomaly in extremely dilute concentration region. In the former system, the reduced viscosity±concentration gsp =C±C curve of single component (PS or PPO) solution bends upwards in extremely dilute concentration region. However, the gsp =C±C curves of their mixture solutions with dierent compositions all bend downwards in the extremely dilute concentration region. In the latter system, the gsp =C±C curve of PMMA solution bends downwards in the extremely dilute concentration region. But, like the formal ternary system, the gsp =C±C curves of PS/PMMA mixtures with dierent compositions all also show downward in¯ection in extremely dilute concentration region, which is similar to what Dondos et al. observed when measuring the dilute solution viscosity of PS/PMMA (50:50) in benzene. As is well known that PS and PPO are compatible. But, the gsp =C±C curve of their mixture solution also shows downward deviation from linear in extremely dilute concentration region. It demonstrates convincingly that it is unreliable to attribute simply the downward in¯ection of gsp =C±C curve of polymer mixture in extremely dilute concentration region to incompatibility. Besides the experimental facts [13,14] that the gsp = C±C curve of incompatible PVC/PS mixture solution in extremely dilute concentration region shows downward in¯ection in THF, but shows a sharply upward in¯ection in DCE, in order to illustrate the eects of solvent again, we measured the dilute solution viscosity of the PS/PMMA mixture in another solvent: m-xylene. The gsp =C±C curve of PS/PMMA mixture in m-xylene is showed in Fig. 3. It diers from that of PS/PMMA in toluene evidently. Firstly, the PS in m-xylene shows almost linear gsp =C±C curve even in extremely dilute concentration region. Secondly, with the variation of composition, the gsp =C±C curve of PS/PMMA/m-xylene
361
solution in extremely dilute concentration region bends downwards sometimes, bends upwards sometimes and almost linear sometimes. It means composition also has some in¯uences on the viscosity anomaly of polymer mixture in extremely dilute concentration region. But, none of the past investigators noticed the eect of composition since they often investigated mixture solution with ®xed composition (50:50). These experimental facts indicate, at least, that the gsp =C±C curve of polymer mixture in extremely dilute concentration region deviates downwards or upwards from linear is not predominated mainly by compatibility, but is related to solvent and composition. 3.2. Reinterpretation of the viscosity anomaly Over the past decades, many eorts have been made to explain the viscosity anomaly of single polymer solution in extremely dilute solution. Some theories have been proposed. The most important include the theory of critical concentration [2,16,17], and the theory of solute adsorption [3,18±21]. But each of them has limitation. Recently, Cheng et al. showed [7±10] with abundant data that the interference of wall eect on viscosity measurement is the main reason for the viscosity anomaly of single polymer solution in extremely dilute concentration region, and the interference of wall eect could be eliminated in a quantitative way. It was shown that the measured relative viscosity gr could be related quantitatively to the true relative viscosity gr;true as [7] kC 1 gr gr;true 1 Ca C where k denotes the maximum fractional change of ¯ow time of pure solvent due to the variation of the surface property of viscometer wall during measuring solution viscosity. Solute adsorption leads to a reduction of capillary radius and hence results a positive k. Slippage due to surface property change will cause a negative k value. The parameter Ca is a characteristic concentration at which half of the available surface is ®lled with the polymer solute. For eliminating the interference of wall eect, the experimental relative viscosity could be corrected by gr;exp gr;true 2 1 CakCC The true relative viscosity gr;true is expressed in Huggins equation gr;true 1 gC kH g2 C 2
Fig. 3. Variation of reduced viscosity gsp =C with concentration C for PS/PMMA mixture in m-xylene at 25 °C. The lines are calculated from Eq. (4) with the parameters listed in Table 2.
3
kH is the Huggins coecient. Combining the Eqs. (1) and (3), the experimental reduced viscosity (gsp =C) should be
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Table 1 Viscosity parameters of PS/PPO, PS/PMMA mixtures in toluene solution k
Polymer mixture
[g] (ml/g)
kH
PPO PPO/PS (wPPO 0:682) PPO/PS (wPPO 0:50) PPO/PS (wPPO 0:354) PPO/PS (wPPO 0:116) PS PMMA/PS (wPMMA 0:25) PMMA/PS (wPMMA 0:50) PMMA/PS (wPMMA 0:667) PMMA
45.84 54.31 60.90 65.98 74.40 81.00 84.5 88.4 90.7 97.5
0.488 0.552 0.492 0.463 0.339 0.359 0.371 0.346 0.287 0.347
Ca (g/ml) 4.47E 3.13E 1.63E 2.88E 8.44E 1.81E 4.10E 3.42E 2.08E 1.07E
4 4 3 3 4 4 3 3 3 3
2.3E 9 5.41E 6 3.22E 4 2.40E 4 4.43E 7 3.1E 11 4.78E 5 4.11E 4 6.13E 4 0
Table 2 Viscosity parameters of PS/PMMA mixtures in m-xylene solution Polymer mixture
[g] (ml/g)
kH
PMMA PMMA/PS PMMA/PS PMMA/PS PMMA/PS PS
33.86 37.00 44.00 53.01 61.87 74.97
1.41 1.09 0.57 0.34 0.40 0.36
gsp =C
(wPMMA (wPMMA (wPMMA (wPMMA
0:875) 0:667) 0:50) 0:25)
k kC 1 g 6kH g2 C Ca C Ca C
4
and is no longer linear as concentration is very small. Much research has shown that Eq. (4) could agree well with experimental data. With Eq. (4), it is easy to deduce that the upward in¯ection of gsp =C±C curve of PS or PPO in toluene is originated from the reduction of eective capillary diameter due to solute adsorption onto the wall surface of capillary during measurement. In general, solute adsorption is universal for most polymer±solvent systems. The downwards in¯ection of gsp =C±C curve of PMMA in toluene indicates that it is not easy for the studied PMMA chains to be adsorbed onto the capillary surface, then the capillary ¯ow model transits from viscous ¯ow to slip ¯ow. Such slip ¯ow phenomenon is actually not unique. Similar phenomenon was also observed in measuring the dilute solution viscosity of PS-MEK system [10]. On the basis of the above theory, it seems possible for us to reinterpret the viscosity anomaly of polymer mixture. Since the wall eect is an unavoidable physical phenomena during measuring solution viscosity of polymer, the measurement procedure of solution viscosity of polymer mixture should be bound to suer the interference of wall eect too. Regarding the polymer mixture in solution as a single solute, Eq. (4) may also express the dilute solution viscosity of polymer mixture down to the extremely dilute concentration region. Then the measured viscosity data of PS/PPO, PS/PMMA
k
Ca (g/ml) 2.48E 1.61E 6.39E 3.34E 3.62E 3.76E
3 4 4 4 4 5
2.24E 5 1.28E 6 4.31E 4 0 0 0
mixtures were ®tted to Eq. (4) by iterative data ®tting procedure. The resulted viscometric parameters g, kH , k and Ca for all of the mixture solutions are listed in Tables 1 and 2. The solid lines in Figs. 1±3 are the calculated reduced viscosity±concentration curves with these parameters, which coincide the experimental points very well. It indicates that Eq. (4) could indeed be applied to polymer mixture solution. Having evaluated the parameters k and Ca , the original viscosity data could be corrected by Eq. (2) to eliminate the interference of wall eect. Figs. 4 and 5 are the plots of corrected gsp =C±C curves of PS/PPO, PS/PMMA mixtures in toluene, which exhibit good linearity as expected. The wall eect depends directly on the interaction between the inner surface of capillary wall and the ¯owing solution composed by solvent and polymer chains. Thus, the viscosity anomaly of polymer mixture solution should be related to the surface structure of capillary wall, solvent, polymer and composition. Then, the experimental facts in Section 3.1 become understandable. In order to investigate the eect of surface structure of capillary wall, we had the capillary surface coated by an even and thin trimethylchlorosilicane ®lm, hereafter, used it to measure again the viscosity of PS/PPO, PS/ PMMA mixture in toluene. In such way, the size parameters of the original and coated viscometer are alike. The mixtures measured with the original and coated viscometer are the same. The only change is surface structure of capillary. The results obtained by the original and coated viscometer are compared in Figs. 6 and 7.
Y. Pan et al. / European Polymer Journal 38 (2002) 359±364
Fig. 4. Corrected reduced viscosity±concentration curves of PS/PPO mixture in toluene.
363
Fig. 6. Comparison of the reduced viscosity of PS/PPO (50:50) in toluene measured with original viscometer with that measured with viscometer coated with trimethylchlorosilicane. The lines are calculated from Eq. (4) with parameters listed in Tables 1 and 3. The open symbol is due to original viscometer, solid symbol is due to coated viscometer.
Fig. 5. Corrected reduced viscosity±concentration curves of PS/PMMA mixture in toluene.
All the second measured viscosity data could also be represented satisfactorily by Eq. (4). The solid lines in Figs. 6 and 7 are calculated from Eq. (4) with the parameters listed in Table 3. The gsp =C±C curve of PS or PPO measured with siliconiting viscometer bends downwards in extremely dilute concentration region, while that measured with original viscometer bends upwards in extremely dilute concentration region. Almost none of the past theories could interpret such phenomena. According to the above theory of wall eect, however, it is easy to understand. That the Ca is zero for PS or PPO solution indicates the absence of solute adsorption onto the siliconiting capillary surface. The surface modi®cation leads to the conversion of capillary ¯ow from viscous model to wall slip model. It demonstrated the in¯uences of surface structure of capillary wall. But, the gsp =C±C curves of PMMA, PS/PPO or PS/PMMA mixtures do
Fig. 7. Comparison of the reduced viscosity of PS/PMMA (50:50) in toluene measured with original viscometer with that measured with viscometer coated with trimethylchlorosilicane. The lines are calculated from Eq. (4) with parameters listed in Tables 1 and 3. The open symbol is due to original viscometer, solid symbol is due to coated viscometer.
not change obviously with the variation of surface structure of capillary, still showing a downward deviation from linear as concentration is very small. On the other hand, for a given polymer±polymer± solvent system, its true viscosity behavior should be inherent properties of the system. So, its true gsp =C±C
364
Y. Pan et al. / European Polymer Journal 38 (2002) 359±364
Table 3 Viscosity parameters of PS/PPO (50:50) and PS/PMMA (50:50) mixture in toluene measured with viscometer coated with trimethylchlorosilicane Polymer mixture
hgim (ml/g)
hKm im
PPO PPO/PS (50:50) PS PMMA/PS (50:50) PMMA
45.84 60.90
3.73 5.00
8.84E 5 5.20E 4
0 3.72E 5
81.00 88.40
4.85 5.10
4.70E 4 5.77E 3
0 7.81E 4
97.50
5.65
1.76E 3
1.30E 4
k
Ca (g/ml)
However, it is noticeable that the wall eect seems much more complicated for the mixture solution. At present, it is almost impossible to elaborate on its interference on viscosity measured experimentally. For example, since PS±toluene and PPO±toluene systems both reveal solute adsorption phenomenon, it is natural to expect that their mixture solution exhibit similar behavior. But, the experimental facts are beyond the anticipation. Since two kinds of polymer solutes coexist in the mixture solution, maybe more complex phenomena such as competitive or preferential adsorption, orientation change of the adsorbed layer and so on occur. In addition, it could not be well explained that the measured viscosity behavior of PS±PPO±toluene and PS±PMMA±toluene systems, whose gsp =C±C curves measured by original viscometer deviates downwards from linear in very low concentration region, do not change obviously with the variation of surface structure of capillary. More detailed investigation is continuing.
Acknowledgement The work was supported by National Nature Science Foundation of China.
References Fig. 8. Variation of corrected reduced viscosity with concentration for PS/PPO in toluene. Open symbol is due to original viscometer, solid symbol is due to coated viscometer.
curve obtained by dierent viscometers should be identical theoretically. Having evaluated the parameters k and Ca , the measured viscosity was corrected by Eq. (2). The plots of corrected gsp =C±C curve of PS/PPO in toluene are shown in Fig. 8. As anticipated, the corrected gsp =C±C curves derived from original and coated viscometer coincide very well, which represent the true viscosity behavior of the mixture solutions. It shows, to some extent, such correction is reasonable and reliable. Therefore, it was suggested that the viscosity anomaly of polymer mixture in extremely dilute concentration region should also arise materially from the interference of wall eect on viscosity measurement but not incompatibility or speci®c solution properties. Although the apparent viscosity of mixture solution in extremely dilute concentration region may show dierent abnormal behavior with the variation of solvent, composition, surface structure of capillary and so on. Eq. (4) could be applied to eliminate the interference of wall eect, then true reliable viscosity data could be obtained.
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