- Email: [email protected]
Abnormal scattering of polymer in binary solvent
Physica A 254 (1998) 292–299
Abnormal scattering of polymer in binary solvent a
b
Kiwing To a; ∗ , Chul A. Kim b , Hyoung J. Choi b
Institute of Physics, Academia Sinica Nankang, Taipei, Taiwan 11529, ROC Department of Polymer Science and Engineering, Inha University, Inchon, 402–751, South Korea
Abstract The behavior of a high molecular weight polymer (polyethylene-oxide, PEO) in a binary liquid mixture (nitroethane=3-methyl-pentane, NE=MP) is studied at the one-phase temperature of NE=MP by static and dynamic light scattering methods. We found that the scattering intensity increased abruptly near the critical composition of NE=MP although the sample was very far from the critical temperature of NE=MP. Explanations in terms of critical opalescence and wetting layer c 1998 Elsevier Science B.V. All rights reserved inversion are discussed. PACS: 78.35.+c; 61.25.Hq; 36.20.Ey Keywords: Light scattering; Polymer solution; Polymer conformation
1. Introduction The behavior of a polymer in solutions has been studied for a long time. When the solvent is a simple liquid consisting of one single component, the dimension and conformation of the solute can be understood satisfactorily using the two-parameter theory and the renormalization group theory [1]. However, when the solvent is composed of more than one component, the situation becomes more complicated. In the simple case when the solvent is a binary liquid mixture, a mean- eld-type theory had been proposed by Scott [2] who approximated the mixture as a single liquid with an e ective interaction parameter. The picture in which the binary solvent is treated as an e ective liquid is inadequate when one of the components is preferentially or even totally adsorbed by the polymer. Intuitively, one expects the better solvent to be adsorbed. Nevertheless, there have been reports that the poor solvent may be preferentially adsorbed in some situation [3]. In a more re ned theory which allows di erent solvent compositions inside and outside the polymer coils, Shultz and Flory [4] derived an expression of the e ective interaction parameter which agrees well with the intrinsic viscosity data of polystyrene in mixtures of benzene and cyclohexane which ∗
Corresponding author. E-mail: [email protected].
c 1998 Elsevier Science B.V. All rights reserved 0378-4371/98/$19.00 Copyright PII S 0 3 7 8 - 4 3 7 1 ( 9 8 ) 0 0 0 2 6 - 0
K. To et al. / Physica A 254 (1998) 292–299
293
does not have a critical consolubility point. However, the mean- eld-type theory of Shultz and Flory may not apply to polymer in a near critical binary solvent when critical composition uctuation may be highly susceptible to the presence of the polymer. Brochard and deGennes [5] predicted that composition uctuation of the binary solvent may contribute an extra attractive potential to the monomers which causes the polymer to collapse near the critical point of the binary solvent. Nevertheless, no experimental con rmation of such polymer collapsing has been reported. It was our original goal to look for such interesting phenomenon near the solvent critical point. However, it turns out that even far away from the solvent critical point, one cannot fully understand the physical processes involved when the composition of the binary solvent is varied. The light scattering results of this study suggest that the polymer molecules may be decorated by a wetting layer of solvent of critical composition. It is also possible that a wetting inversion has occurred near the critical composition of the solvent. In this paper, we present light scattering data from polyethylene oxide (PEO) in nitroethane+3-methyl-pentane (PEO=NE=MP). It has been shown that the scattering of the ternary system consisting of a polymer in a binary solvent is the same as that for polymer in a single-component solvent if the components of the binary solvent have equal refractive index [6]. Since the refractive indices of nitroethane and 3-methylpentane are 1.39 and 1.38, respectively, one can interpret the light scattering data of PEO=NE=MP using the expression for polymer solution of single-component solvent. Although scattering by composition uctuation of a binary mixture can be signi cant near the critical point, it can be neglected for NE=MP due to the near iso-refractive nature of this binary mixture. Nevertheless, when we vary the solvent composition at 15◦ C away from the critical temperature we observe abrupt increases in the scattering in this ternary system near the critical composition of NE=MP. We propose several possible explanations in terms of critical opalescence and the wetting inversion.
2. Experimental Nitroethene (NE) of 99.5% purity and 3-methyl-pentane (MP) of 99.6% were purchased from Aldrich and they were ltered by 0.47 m disposable lter (Millipore, LCR) before use. PEO of molecular weight MW = 9 × 105 was dissolved in NE. Then the NE solution of PEO was added to binary mixtures of NE=MP at 23◦ C in 12 mm diameter threaded test tubes so that the resultant PEO concentration in the nal samples was 0.075 mg=cc with known MP volume fraction . The samples were then sealed by plastic screw caps with Te on liners. Note that the binary mixture NE=MP has an upper critical temperature at 26:5◦ C and the critical composition is c = 65% MP by volume [7]. So we put the samples in a temperature regulated air bath at 35◦ C overnight for them to reach equilibrium while in one single homogeneous phase. To measure the scattering intensity, we put the sample in a goniometer whose temperature was kept at 42 ± 0:1◦ C. The light source of the goniometer was a vertically polarized 150 mW
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argon ion laser and a phototube with a 488 nm interference lter was installed such that the scattering plane was horizontal. After the sample was put in the goniometer, we waited for at least 30 min until the scattering intensity became constant before the measurement was taken. The signal from the phototube was fed to a digital correlator (BI-9000AT from Brookhaven Instrument Corporation) for measuring the scattering intensity as well as the intensity auto-correlation function.
3. Results Fig. 1 shows how the scattering intensity I of a sample with 0.075 mg=cc PEO at = 90◦ scattering angle varies with the solvent composition . For ¡0:58, the scattering by the sample is very weak. In fact, the scattering with PEO is the same as that without PEO within experimental uncertainty. When increases from 0.58 to 0.7, the sample scatters very strongly. One observes more than two orders of magnitude increase in the scattering intensity within this narrow composition range. We checked that this abnormal scattering is not due to phase separation of the PEO from the solvent because the scattering persists for 3 days and no precipitation is observed in the sample. On the other hand, at higher MP composition, i.e. ¿0:7, the scattering intensity reduces by a factor of 10 within 1 day and one can observe precipitation of PEO at the bottom of the sample cell. It should be pointed out that the abnormal light scattering in the composition ranges from 0:58¡ ¡0:70 persists for PEO of other molecular weights (MW = 4 × 106 and 5 × 106 ) and other PEO concentrations (0.01
Fig. 1. The scattering intensity I at 90◦ scattering angle for PEO (MW = 9 × 105 ) in NE=MP with concentration 0.075 mg=cc at 42◦ C.
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Fig. 2. Variation of the scattering intensity I with scattering vector q for PEO in NE=MP at 42◦ C for di erent NE=MP composition = 0:55 ( ), 0.63 ( ) and 0.70 (4).
Fig. 3. Variations of the inverse scattering intensity I −1 with q2 for = 0:63 (), 0.65 ( ), 0.68 ( ) and 0.70 (4), respectively.
and 0.1 mg=cc). More surprisingly, although the scattering intensity increases with both molecular weight and the PEO concentration, the abnormal scattering always takes place when the solvent composition is higher than 0.58 for PEO of di erent molecular weights and polymer concentrations. If the abnormal scattering was the result of phase
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Fig. 4. Variations of the decay rate
with q2 for (a) = 0:63; (b) = 0:65; (c) = 0:68 and (d) = 0:70:
separation due to reducing solvent quality by the addition of MP, one would expect to observe the abnormal scattering at smaller at higher molecular weight and higher PEO concentration. To investigate the source of the abnormal scattering in the PEO=NE=MP sample, we examine how the scattering intensity vary with the scattering vector q ≡ (4n=) sin =2 where n = 1:385 is the refractive index of the solvent and = 488 nm is the wavelength of the incident light. Fig. 2 shows the angular variation of the scattering intensity at solvent composition = 0:55; 0:63 and 0.70. One can see that the scattering at = 0:55 is weak and isotropic, while those at = 0:63 and 0.70 are stronger in the forward direction. Since the inverse scattering I −1 of a dilute polymer solution is proportional to (1 + 13 R2g q2 ) where Rg is the radius of gyration of the polymer molecule, we attempt to extract Rg by plotting I −1 with respect to q2 . Fig. 3 shows the results for 2 = 0:63; 0:65; 0:68 and 0.70. Clearly, for = 0:63; I −1 varies q linearly with q when the x-intercept equals q02 = −3:2 × 10−4 nm−2 . Then Rg =
3=|q02 | = 96 nm. However,
for other solvent composition, I −1 bends toward the origin at small q2 and one cannot extract a meaningful Rg by extrapolating to zero I −1 . Nevertheless, the linear behavior
K. To et al. / Physica A 254 (1998) 292–299
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of I −1 at large scattering angles suggests the existence of mono-disperse scatterers and one may extract their size by just examining the scattering data at large scattering angles. One can estimate the size of the scatterers from the temporal behavior of the scattering intensity, if the scatterers undergo Brownian motion in the solution [8]. Using a digital correlator, we extract the intensity auto-correlation function, g2 (t) ≡ hI (t 0 )I (t 0 + t)i of the abnormal scattering. Within the composition range 0:6¡ ¡0:7; g2 (t) can be tted to a single exponential decay function: hI i2 (1 + e− t ). Here hI i is the average intensity, is an optical constant that depends on the experimental setup and is the decay rate. For polymer solution, = 2Dq2 where D is the di usion constant of the polymer molecule. Using the Stokes–Einstein equation D = kT=(6Rh ) with k; T; and = 0:26 cp being, respectively, the Boltzman’s factor, the temperature and the viscosity of NE=MP, we can obtain the hydrodynamic radius Rh of the polymer. Fig. 4 shows the variation of the measured decay rates for 0:6¡ ¡0:7 with respect to q2 . Note that except at small scattering angles, increases linearly with q2 . Deviation from the q2 -dependence of is the result of the very strong scattering at small scattering angles. Using the values of at 60◦ ; 75◦ ; 90◦ ; 105◦ ; 120◦ and 135◦ scattering angles, we calculate the slope of vs. q2 and obtain the hydrodynamic radius Rh = 56:5; 45:7; 47:6 and 40.9 nm for = 0:63; 0:65; 0:68 and 0.7, respectively. One can see that the Rh does not change appreciably within this composition range.
4. Discussions The experimental results described above indicate that the abnormal scattering in the composition range 0:58¡ ¡0:70 consists of big scatterers together with fairly mono-disperse scatterers of radius of gyration Rg ∼ 100 nm and hydrodynamic radius Rh ∼ 50 nm. One possible source of the strong scattering may be the critical composition
uctuation of the solvent because the critical composition of NE=MP is c = 0:65 which is within the composition range of the abnormal scattering. However, we are 15◦ C away from the critical temperature and the correlation length of the composition uctuation is less than 2 nm at this temperature [9]. Thus, the correlation length is too small to produce a hundredfold increase in the scattering intensity. In fact, the scattering by pure solvent NE=MP without PEO changes less than 40% thorough the whole composition range. Therefore, we rule out the possibility that the abnormal scattering is the critical opalescence from NE=MP at the critical composition. Nevertheless, the abnormal scattering may be the result of a wetting layer that exists around the PEO molecules. Assume that the molecules of the good solvent (NE in this case) wet the PEO. Then the solvent composition inside the PEO molecules may be di erent from that outside. In other words, the solvent composition should be a function (r) of distance r from a PEO molecule. As r increases one would expect (r) to monotonically approach the composition of the mixed solvent when the ternary system is prepared i.e. (∞) = . Fig. 5 shows several possible (r) with di erent
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Fig. 5. Schematic diagrams showing the possible composition pro le (r) of the solvent near a polymer molecule for the situations when the solvent composition (0) at the polymer molecule is less than the critical composition c of the solvent. The solvent composition far away from the polymer molecule is (∞) which is the same as .
(0). Since the refractive index n of a binary mixture depends on composition, the spatial variation of (r) will not contribute to I if dn=d = 0 and the binary solvent can be treated as a single solvent in the light scattering experiment. However, in general, dn=d may not vanish and complicated expression for the excess scattering from the ternary system has been derived by Yamakawa [6] in 1967. The e ect of the spatial variation of (r) on the excess scattering may be subtle when the binary solvent has a critical point. Let (0) be less than the critical composition c of the binary solvent as depicted in Fig. 5. If ¡ c , nowhere in the solution such that (r) = c . On the other hand, if ¿ c , there always exists a layer where (r) = c . Note that the characteristic size of this critical layer should be larger than the size of the polymer and the scattering from this region of critical composition will be signi cant even far away from the critical temperature of the binary solvent. Since the radius of gyration and the hydrodynamic radius of the abnormal scattering are ∼100 and ∼50 nm, respectively, which are larger than those (Rg = 70 nm and Rh = 38 nm) obtained for PEO (MW = 106 ) in water at 30◦ C [10], it is reasonable to identify the abnormal scattering as the PEO macromolecules decorated by a layer of solvent of critical composition. Another possible cause of the abnormal scattering is the occurrence of a wetting layer inversion at = 0:58. When the solvent contains less than 58% MP, the PEO molecule may be wetted by NE which is a good solvent of PEO. When more and more MP is added to the solvent, MP may become preferentially adsorbed to PEO and cause an abrupt change in the refractive index close to the PEO molecules. Since the macromolecules are now surrounded by the poor solvent MP, PEO molecules should aggregate when they touch in order to avoid contact with MP. Such aggregation of PEO for ¿0:58 may be the source of the big scatterers that were observed in the light scattering experiment. The above scenario is consistent with the fact that as even more MP is added ( ¿0:70), PEO becomes insoluble in the mixture and precipitation takes place. However, more experimental studies are needed to con rm such a conjecture. We are planning to estimate the preferential sorption, which is de ned as the total
K. To et al. / Physica A 254 (1998) 292–299
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di erence in the contents of components between the domain of the macromolecules and the same volume of the bulk solvent, by measuring the refractive index increments with respect to the solvent composition and the polymer concentration [3]. Such results will enable us to determine if wetting inversion does occur at = 0:58. Acknowledgements The author would like to thank Dr. C.K. Chan and Prof. Philip Pincus for their valuable discussions and suggestions. This work was supported by a grant (NSC-852112-M001-033) from the National Science Council of the Republic of China. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
H. Fujita, Polymer Solution, Elsevier, Amsterdam, 1990. R.J. Scott, J. Chem. Phys. 17 (1949) 269. C.I. Simionecus, S. Ioan, M. Bercea, N. Mitu, B.C. Simionecus, European Polym. J. 29 (1993) 183. A. Shultz, P.J. Flory, J. Polym. Sci. 15 (1976) 231. F. Brochard, P.G. de Gennes, Ferroelectrics 30 (1980) 33. H. Yamakawa, J. Chem. Phys. 46 (1967) 973. A.M. Wims, D. McIntyre, F. Hynne, J. Chem. Phys. 50 (1969) 616. B. Berne, R. Pecora, Dynamic Light Scattering, Wiley, New York, 1976. R.F. Chang, P.H. Keyes, J.V. Sengers, C.O. Alley, Phys. Rev. Lett. 27 (1971) 1706. K. Devanand, J.C. Selser, Macromolecules 24 (1991) 5943.
Abnormal scattering of polymer in binary solvent a
b
Kiwing To a; ∗ , Chul A. Kim b , Hyoung J. Choi b
Institute of Physics, Academia Sinica Nankang, Taipei, Taiwan 11529, ROC Department of Polymer Science and Engineering, Inha University, Inchon, 402–751, South Korea
Abstract The behavior of a high molecular weight polymer (polyethylene-oxide, PEO) in a binary liquid mixture (nitroethane=3-methyl-pentane, NE=MP) is studied at the one-phase temperature of NE=MP by static and dynamic light scattering methods. We found that the scattering intensity increased abruptly near the critical composition of NE=MP although the sample was very far from the critical temperature of NE=MP. Explanations in terms of critical opalescence and wetting layer c 1998 Elsevier Science B.V. All rights reserved inversion are discussed. PACS: 78.35.+c; 61.25.Hq; 36.20.Ey Keywords: Light scattering; Polymer solution; Polymer conformation
1. Introduction The behavior of a polymer in solutions has been studied for a long time. When the solvent is a simple liquid consisting of one single component, the dimension and conformation of the solute can be understood satisfactorily using the two-parameter theory and the renormalization group theory [1]. However, when the solvent is composed of more than one component, the situation becomes more complicated. In the simple case when the solvent is a binary liquid mixture, a mean- eld-type theory had been proposed by Scott [2] who approximated the mixture as a single liquid with an e ective interaction parameter. The picture in which the binary solvent is treated as an e ective liquid is inadequate when one of the components is preferentially or even totally adsorbed by the polymer. Intuitively, one expects the better solvent to be adsorbed. Nevertheless, there have been reports that the poor solvent may be preferentially adsorbed in some situation [3]. In a more re ned theory which allows di erent solvent compositions inside and outside the polymer coils, Shultz and Flory [4] derived an expression of the e ective interaction parameter which agrees well with the intrinsic viscosity data of polystyrene in mixtures of benzene and cyclohexane which ∗
Corresponding author. E-mail: [email protected].
c 1998 Elsevier Science B.V. All rights reserved 0378-4371/98/$19.00 Copyright PII S 0 3 7 8 - 4 3 7 1 ( 9 8 ) 0 0 0 2 6 - 0
K. To et al. / Physica A 254 (1998) 292–299
293
does not have a critical consolubility point. However, the mean- eld-type theory of Shultz and Flory may not apply to polymer in a near critical binary solvent when critical composition uctuation may be highly susceptible to the presence of the polymer. Brochard and deGennes [5] predicted that composition uctuation of the binary solvent may contribute an extra attractive potential to the monomers which causes the polymer to collapse near the critical point of the binary solvent. Nevertheless, no experimental con rmation of such polymer collapsing has been reported. It was our original goal to look for such interesting phenomenon near the solvent critical point. However, it turns out that even far away from the solvent critical point, one cannot fully understand the physical processes involved when the composition of the binary solvent is varied. The light scattering results of this study suggest that the polymer molecules may be decorated by a wetting layer of solvent of critical composition. It is also possible that a wetting inversion has occurred near the critical composition of the solvent. In this paper, we present light scattering data from polyethylene oxide (PEO) in nitroethane+3-methyl-pentane (PEO=NE=MP). It has been shown that the scattering of the ternary system consisting of a polymer in a binary solvent is the same as that for polymer in a single-component solvent if the components of the binary solvent have equal refractive index [6]. Since the refractive indices of nitroethane and 3-methylpentane are 1.39 and 1.38, respectively, one can interpret the light scattering data of PEO=NE=MP using the expression for polymer solution of single-component solvent. Although scattering by composition uctuation of a binary mixture can be signi cant near the critical point, it can be neglected for NE=MP due to the near iso-refractive nature of this binary mixture. Nevertheless, when we vary the solvent composition at 15◦ C away from the critical temperature we observe abrupt increases in the scattering in this ternary system near the critical composition of NE=MP. We propose several possible explanations in terms of critical opalescence and the wetting inversion.
2. Experimental Nitroethene (NE) of 99.5% purity and 3-methyl-pentane (MP) of 99.6% were purchased from Aldrich and they were ltered by 0.47 m disposable lter (Millipore, LCR) before use. PEO of molecular weight MW = 9 × 105 was dissolved in NE. Then the NE solution of PEO was added to binary mixtures of NE=MP at 23◦ C in 12 mm diameter threaded test tubes so that the resultant PEO concentration in the nal samples was 0.075 mg=cc with known MP volume fraction . The samples were then sealed by plastic screw caps with Te on liners. Note that the binary mixture NE=MP has an upper critical temperature at 26:5◦ C and the critical composition is c = 65% MP by volume [7]. So we put the samples in a temperature regulated air bath at 35◦ C overnight for them to reach equilibrium while in one single homogeneous phase. To measure the scattering intensity, we put the sample in a goniometer whose temperature was kept at 42 ± 0:1◦ C. The light source of the goniometer was a vertically polarized 150 mW
294
K. To et al. / Physica A 254 (1998) 292–299
argon ion laser and a phototube with a 488 nm interference lter was installed such that the scattering plane was horizontal. After the sample was put in the goniometer, we waited for at least 30 min until the scattering intensity became constant before the measurement was taken. The signal from the phototube was fed to a digital correlator (BI-9000AT from Brookhaven Instrument Corporation) for measuring the scattering intensity as well as the intensity auto-correlation function.
3. Results Fig. 1 shows how the scattering intensity I of a sample with 0.075 mg=cc PEO at = 90◦ scattering angle varies with the solvent composition . For ¡0:58, the scattering by the sample is very weak. In fact, the scattering with PEO is the same as that without PEO within experimental uncertainty. When increases from 0.58 to 0.7, the sample scatters very strongly. One observes more than two orders of magnitude increase in the scattering intensity within this narrow composition range. We checked that this abnormal scattering is not due to phase separation of the PEO from the solvent because the scattering persists for 3 days and no precipitation is observed in the sample. On the other hand, at higher MP composition, i.e. ¿0:7, the scattering intensity reduces by a factor of 10 within 1 day and one can observe precipitation of PEO at the bottom of the sample cell. It should be pointed out that the abnormal light scattering in the composition ranges from 0:58¡ ¡0:70 persists for PEO of other molecular weights (MW = 4 × 106 and 5 × 106 ) and other PEO concentrations (0.01
Fig. 1. The scattering intensity I at 90◦ scattering angle for PEO (MW = 9 × 105 ) in NE=MP with concentration 0.075 mg=cc at 42◦ C.
K. To et al. / Physica A 254 (1998) 292–299
295
Fig. 2. Variation of the scattering intensity I with scattering vector q for PEO in NE=MP at 42◦ C for di erent NE=MP composition = 0:55 ( ), 0.63 ( ) and 0.70 (4).
Fig. 3. Variations of the inverse scattering intensity I −1 with q2 for = 0:63 (), 0.65 ( ), 0.68 ( ) and 0.70 (4), respectively.
and 0.1 mg=cc). More surprisingly, although the scattering intensity increases with both molecular weight and the PEO concentration, the abnormal scattering always takes place when the solvent composition is higher than 0.58 for PEO of di erent molecular weights and polymer concentrations. If the abnormal scattering was the result of phase
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Fig. 4. Variations of the decay rate
with q2 for (a) = 0:63; (b) = 0:65; (c) = 0:68 and (d) = 0:70:
separation due to reducing solvent quality by the addition of MP, one would expect to observe the abnormal scattering at smaller at higher molecular weight and higher PEO concentration. To investigate the source of the abnormal scattering in the PEO=NE=MP sample, we examine how the scattering intensity vary with the scattering vector q ≡ (4n=) sin =2 where n = 1:385 is the refractive index of the solvent and = 488 nm is the wavelength of the incident light. Fig. 2 shows the angular variation of the scattering intensity at solvent composition = 0:55; 0:63 and 0.70. One can see that the scattering at = 0:55 is weak and isotropic, while those at = 0:63 and 0.70 are stronger in the forward direction. Since the inverse scattering I −1 of a dilute polymer solution is proportional to (1 + 13 R2g q2 ) where Rg is the radius of gyration of the polymer molecule, we attempt to extract Rg by plotting I −1 with respect to q2 . Fig. 3 shows the results for 2 = 0:63; 0:65; 0:68 and 0.70. Clearly, for = 0:63; I −1 varies q linearly with q when the x-intercept equals q02 = −3:2 × 10−4 nm−2 . Then Rg =
3=|q02 | = 96 nm. However,
for other solvent composition, I −1 bends toward the origin at small q2 and one cannot extract a meaningful Rg by extrapolating to zero I −1 . Nevertheless, the linear behavior
K. To et al. / Physica A 254 (1998) 292–299
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of I −1 at large scattering angles suggests the existence of mono-disperse scatterers and one may extract their size by just examining the scattering data at large scattering angles. One can estimate the size of the scatterers from the temporal behavior of the scattering intensity, if the scatterers undergo Brownian motion in the solution [8]. Using a digital correlator, we extract the intensity auto-correlation function, g2 (t) ≡ hI (t 0 )I (t 0 + t)i of the abnormal scattering. Within the composition range 0:6¡ ¡0:7; g2 (t) can be tted to a single exponential decay function: hI i2 (1 + e− t ). Here hI i is the average intensity, is an optical constant that depends on the experimental setup and is the decay rate. For polymer solution, = 2Dq2 where D is the di usion constant of the polymer molecule. Using the Stokes–Einstein equation D = kT=(6Rh ) with k; T; and = 0:26 cp being, respectively, the Boltzman’s factor, the temperature and the viscosity of NE=MP, we can obtain the hydrodynamic radius Rh of the polymer. Fig. 4 shows the variation of the measured decay rates for 0:6¡ ¡0:7 with respect to q2 . Note that except at small scattering angles, increases linearly with q2 . Deviation from the q2 -dependence of is the result of the very strong scattering at small scattering angles. Using the values of at 60◦ ; 75◦ ; 90◦ ; 105◦ ; 120◦ and 135◦ scattering angles, we calculate the slope of vs. q2 and obtain the hydrodynamic radius Rh = 56:5; 45:7; 47:6 and 40.9 nm for = 0:63; 0:65; 0:68 and 0.7, respectively. One can see that the Rh does not change appreciably within this composition range.
4. Discussions The experimental results described above indicate that the abnormal scattering in the composition range 0:58¡ ¡0:70 consists of big scatterers together with fairly mono-disperse scatterers of radius of gyration Rg ∼ 100 nm and hydrodynamic radius Rh ∼ 50 nm. One possible source of the strong scattering may be the critical composition
uctuation of the solvent because the critical composition of NE=MP is c = 0:65 which is within the composition range of the abnormal scattering. However, we are 15◦ C away from the critical temperature and the correlation length of the composition uctuation is less than 2 nm at this temperature [9]. Thus, the correlation length is too small to produce a hundredfold increase in the scattering intensity. In fact, the scattering by pure solvent NE=MP without PEO changes less than 40% thorough the whole composition range. Therefore, we rule out the possibility that the abnormal scattering is the critical opalescence from NE=MP at the critical composition. Nevertheless, the abnormal scattering may be the result of a wetting layer that exists around the PEO molecules. Assume that the molecules of the good solvent (NE in this case) wet the PEO. Then the solvent composition inside the PEO molecules may be di erent from that outside. In other words, the solvent composition should be a function (r) of distance r from a PEO molecule. As r increases one would expect (r) to monotonically approach the composition of the mixed solvent when the ternary system is prepared i.e. (∞) = . Fig. 5 shows several possible (r) with di erent
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Fig. 5. Schematic diagrams showing the possible composition pro le (r) of the solvent near a polymer molecule for the situations when the solvent composition (0) at the polymer molecule is less than the critical composition c of the solvent. The solvent composition far away from the polymer molecule is (∞) which is the same as .
(0). Since the refractive index n of a binary mixture depends on composition, the spatial variation of (r) will not contribute to I if dn=d = 0 and the binary solvent can be treated as a single solvent in the light scattering experiment. However, in general, dn=d may not vanish and complicated expression for the excess scattering from the ternary system has been derived by Yamakawa [6] in 1967. The e ect of the spatial variation of (r) on the excess scattering may be subtle when the binary solvent has a critical point. Let (0) be less than the critical composition c of the binary solvent as depicted in Fig. 5. If ¡ c , nowhere in the solution such that (r) = c . On the other hand, if ¿ c , there always exists a layer where (r) = c . Note that the characteristic size of this critical layer should be larger than the size of the polymer and the scattering from this region of critical composition will be signi cant even far away from the critical temperature of the binary solvent. Since the radius of gyration and the hydrodynamic radius of the abnormal scattering are ∼100 and ∼50 nm, respectively, which are larger than those (Rg = 70 nm and Rh = 38 nm) obtained for PEO (MW = 106 ) in water at 30◦ C [10], it is reasonable to identify the abnormal scattering as the PEO macromolecules decorated by a layer of solvent of critical composition. Another possible cause of the abnormal scattering is the occurrence of a wetting layer inversion at = 0:58. When the solvent contains less than 58% MP, the PEO molecule may be wetted by NE which is a good solvent of PEO. When more and more MP is added to the solvent, MP may become preferentially adsorbed to PEO and cause an abrupt change in the refractive index close to the PEO molecules. Since the macromolecules are now surrounded by the poor solvent MP, PEO molecules should aggregate when they touch in order to avoid contact with MP. Such aggregation of PEO for ¿0:58 may be the source of the big scatterers that were observed in the light scattering experiment. The above scenario is consistent with the fact that as even more MP is added ( ¿0:70), PEO becomes insoluble in the mixture and precipitation takes place. However, more experimental studies are needed to con rm such a conjecture. We are planning to estimate the preferential sorption, which is de ned as the total
K. To et al. / Physica A 254 (1998) 292–299
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di erence in the contents of components between the domain of the macromolecules and the same volume of the bulk solvent, by measuring the refractive index increments with respect to the solvent composition and the polymer concentration [3]. Such results will enable us to determine if wetting inversion does occur at = 0:58. Acknowledgements The author would like to thank Dr. C.K. Chan and Prof. Philip Pincus for their valuable discussions and suggestions. This work was supported by a grant (NSC-852112-M001-033) from the National Science Council of the Republic of China. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
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