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Viscosity study of oligomer-induced shrinking of polystyrene chains in benzene
Eur. Polym.J. Vol. 31, No. 7. pp. 659-663, 1995
Pergamon
0014-3057(95)00002-X
Copyright 0 1995Elsevierscieace Ltd
Printedin Great
Britain. All rightr raemed oow3onps $9.50 + 0.00
VISCOSITY STUDY OF OLIGOMER-INDUCED SHRINKING OF POLYSTYRENE CHAINS IN BENZENE PENG
WE1 ZHU
School of Chemistry, The University of Sydney, NSW 2006, Australia (Received 19 April 1994; accepted in final form 28 June 1994)
Abstract-The
paraffin-induced
dimension
shrinking of polystyrene
chains in paraffin/polystyrene/
benzene mixtures is reported in terms of the variation of the reduced viscosity 9 /c as a function of the concentration of polystyrene. The critical concentration c ** in which a strong repu‘p. sron between molecules of polystyrene and of paraffin occurs is determined. This critical concentration is found to be dependent on the weight ratio of two components and molecular weight of polystyrene. Plots of the normalized reduced viscosity the normalized concentration are found to be scaled to a single master curve.
INTRODUCTION
As is well known, the monomer pair interaction of a polymer is repulsive and tends to swell the coil in a good solvent. However, the mean force acting between segments of a polymer chain becomes attractive when this polymer is in a poor solvent below the 8 temperature. The attraction will lead to a shrinkage of a single polymer coil below its size under 8 conditions. Generally speaking, the degree of shrinkage and therefore the segment density change with varying temperature. A single polymer chain can change its state from an open coil to a globular particle if the temperature is lowered (or increased) to the 6 temperature. This is usually called the coil-globule transition or chain collapsed transition. Theories for the coil-globule transition have been proposed [l-3]. The coil-globule transition of a polymer can also be induced by another polymer in a dilute solution at a fixed temperature. For example, DNA of high molecular weight was observed to be collapsed into a very compact particle in a salt solution in the presence of a second neutral polymer, polyethylene oxide with lower molecular weight, above a certain critical concentration [4, 51. The coil-globule transition of high molecular weight poly(styrene-maleicanhydride) was found by the addition of oligomer polyethylene oxide in toluene [6]. The concentration dependent shrinking of a polymer gel in solutions of incompatible polymers was reported by Momii and Nose [7]. Tanaka [8] has discussed a polymer-induced coil-globule transition of another polymer by using the self-consistent field approach. Nose [9] has presented a theory to describe a coil-globule transition on the basis of the thermal- and concentration-bob [lo] models. Accordingly, a polymer induced coil-globule transition of another polymer chain is expected under the following conditions: (1) the intermolecular interaction is repulsive and sufficiently strong compared with the intramolecular repulsive interaction between segments in a large polymer; and (2) the difference
of polymerization degree between two species is very large. The coil shrinking of polymer chains in ternary mixtures has also been studied [l l-l 51. Some studies have established that viscosity methods can be used for determining the dimension shrinking of polymer chains in two-polymer mixtures [l l-141. The principle of using dilute solution viscosity to measure the compatibility characterization is based on the fact that molecules of both components may exist in a molecularly dispersed state and undergo a mutual attraction or repulsion in dilute solutions, which will influence the viscosity. The variation of reduced viscosity in a ternary system with concentration of a component can be schematically displayed in Fig. 1 [12-141. As can be seen, there are two regimes divided by critical concentrations, c*+ and c* (c** < c*). The concentration c** here is a very low critical concentration which was first observed by Dondos and Benoit [l 11. The concentration c** is defined as the concentration corresponding to the incipient overlap of spherical coils. At c**, the distance between centres of macromolecular chains is of the order of their diameters and contacts between molecules (like or unlike) are avoided. The chains do not tend to overlap and therefore shrink in their sizes. If the concentration is higher than c**, an incompatibility between two components appears and the hydrodynamics volume of chains is lower. The reduction of hydrodynamic volume will result in a decrease in the reduced viscosity of solutions, e.g. the slope of the plot of reduced viscosity against concentration may suddenly decline [l l-141. The critical concentration c* was first introduced by de Gennes [16]. When the concentration is lower than c*, there is no complete interpenetration of individuality of molecules. When the concentration is higher than c*, the coils overlap and the individuality of the molecules disappears. In this paper, the paraffin-induced dimension shrinking of polystyrene in benzene is studied. The concentrations c** are carefully determined. It has 659
Peng Wei Zhu
660
r
Fig. I. The variation of reduced viscosity with concentration is schematically shown.
were obtained from Pressure Chemicals. The polydispersity indexes of PS samples are less than 1.2. Viscometric measurements were carried out using a dilution modified Ubbelohde viscometer which was immersed in a constant temperature bath. The temperature was measured close to the capillary by a thermometer with an accuracy of 0.03”C. The precision of viscosity measurements depends on the concentration since the specific viscosity measures differences in the viscosity between the solution and solvent. As the concentration is lowered, the determination of the viscosity becomes more and more inaccurate. In this case, viscosity measurements were carried out with two viscometers immersed in the same temperature bath in order to check the accuracy of data. Solutions were filtered by a 0.45 pm Millipore filter before viscosity measurements. RESULTS
been known that paraffins, as an oligomer version of polyethylene, are not miscible with polystyrene. The interaction between polystyrene and polyethylene segments is very large. Because the molecular weights of paraffins used in experiments are very much smaller than those of the polystyrene, the contributions of changes in hydrodynamic volume of polystyrene are dominant. EXPERIMENTAL All paraffins were obtained from the Aldrich Chemical Co. They are of high purity (99%). Polystyrene (PS) samples
160
0.0020
Figure 2 shows the variation of the reduced viscosity qrp/c against the concentration of polystyrene (molecular weight of 2.33 x 10’) in the PS/C,,H,,/benzene system at 25°C. The weight ratios of C6HJ4 to polystyrene are 4.03, 7.14, 13.44 and 20.1. As can be seen, when the weight ratio of C,,H,, to PS is 4.03, no crossover is observed in the reduced viscosity concentration plot, which implies that &H,, and polystyrene are potentially compatible in benzene and the interaction between two kinds of molecules is expected to be avoided. No phase separation occurs at such high weight ratio because of the shorter chain
150
(a)
0.0065
0.0155
0.01 IO
r
0.000
(b)
0.015
0.010
0.005
C (g/ml)
0.020
C (g/ml)
160
0.000
AND DISCUSSION
Cd)
I
I
0.005
0.010
C (g/ml)
I 0.015
I
I 0.020
0.001
0.003
I 0.005
I 0.007
C (g/ml)
Fig. 2. The variation of the reduced viscosity as a function of concentration of polystyrene in the C,,H,/PS/benzene mixtures at 25°C. The molecular weight of the polystyrene is 2.33 x 105.The weight ratios of C,,H, to PS are: (a) 4.03; (b) 7.14; (c) 13.44 and (d) 20.1.
Oligomer-induced shrinking of polystyrene chains in benzene 9c-3 MW of PS = 2.3385 ?e-3 2 E r * c,
5c-3
3e-3 2
1 lc-3
p 3
10
17
C 16IPS
24
(w/w)
Fig. 3. Plot of the critical concentration c** as a function of the weight ratio of C,,H, to PS at 25°C. The molecular weight of polystyrene is 2.33 x 10’.
185 2e-3
4e-3
r (b)
310
6e-3
ae-3
le-2
C (idmU
661
of C,,H, compared to the polystyrene sample. As the weight ratio increases, the crossovers in the reduced viscosity-composition plots appear. This evidence suggests that C,,H, and polystyrene are strongly incompatible at higher weight ratios of C,,HJPS, but dissimilar molecules refuse. to overlap and therefore polystyrene molecules shrink in size, which leads to a decrease in the hydrodynamic volumes and then causes the reduction of the reduced viscosity. The critical concentrations c** (indicated by concentration of polystyrene) at which the dissimilar molecules begin to repel each other are determined from Fig. 2. This concentration is found to be dependent on the weight ratio of C,6HM/PS. The higher the weight ratio, the smaller is the critical concentation c**. The critical concentration c** as a function of the weight ratio of C,6H34/PS is shown in Fig. 3. As is already known, the compatibility between different polymers is a function of their molecular weight. An increase of the molecular weight causes a decrease in the compatibility of two components. Consequently, it can be expected that an increase in the molecular weight of polystyrene will cause a decrease in the compatibility between paraffins and PS. The decrease in the compatibility should result in a decrease in the critical concentration c**, as reported by Pierri and Dondos [13]. Figure 4 shows plots of the reduced viscosity vs the concentration of polystyrene at a fixed weight ratio of ClzHZ6/PS at 25°C. The molecular weights of polystyrene are 5.75 x lo’, 9.0 x IO5 and 1.6 x 106. Indeed in this figure, a decrease in the critical concentration c** of polystyrene with increasing the molecular weight of polystyrene is observed. In Figs 5 and 6, log-log plots of the critical concentration c** as a function of the molecular weight of polystyrene for C,,H,,/PS/benzene and C,,H,,/PS/benzene mixtures are shown, respectively. The plots give good straight lines with slopes of -0.5. From these figures, we have the following relations for the C,,H,,/PS/PS/benzene with the weight ratio of C,*HZ6/PS = 20.1 $+
C Wml)
-2.0
=
3.g56,+f,0,5 f 0.02
r
I \ 450 -
-2.2 t
2 g
430 -
:c,
0 ‘.a F”
410 -
0” -1
-2.6
390 370
.
le-3
-2.4
t
I 2c-3
3e-3
4e-3
5e-3
6e-3
C Wml) Fig. 4. The variation of the reduced viscosity as a function of concentration of polystyrene in C,,H,/PS/benzene mixtures at 25°C. The weight ratio of C12Hz6to P!S is 20.1. The molecular_. weights (a) 5.75 x 10’; __ .__of polystyrene: . . _ __I (b) Y.0 x IO’; and (c) 1.6 x ICY.
t
-2.8
4.5
I
I
5.0
5.5
6.0
Log MW
Fig. 5. Log-log plot of the critical concentration c** as a function of the molecular weight of polystyrene in the C,,H,,/PS/henzene mixture at 25°C. The weight ratio of C,,H,, to PS is 20.1.
Peng Wei Zhu
662
A .
2.0 -2.2 :
:P F P
-2.3
c,
a2
-2.4
F
.U
1.5
&T
I .o
s*”
-2.5 0.5
-2.6 -2.1
4.00E5 5.7585 6.5985 9.00E5 1.60E6
If+@ 1 5.5
I
I
I
I
5.1
5.9
6.1
6.3
0.0
Log MW Fig. 6. Log-log plot of the function of the molecular C,,H,/PS/benzene mixture C,,H,, to
with the weight ratio
The relation between the critical concentration c** and the molecular weight has been discussed by Benoit et al. [l 1, 121, and Pierri and Dondos [I 31. If it is assumed that at the critical concentration, the total volume V of the solution is equal to the volume of polymers plus the excluded volume V, between these polymers, one has $r xn,R;,
+ V, = V
(I)
where R, is the radius of gyration and n, is number of macromolecules with molecular weight equal to M, . Polymer solution theory [lo] gives the following relation between the radius of gyration and molecular weight R;, a M;’
(2)
and therefore one has V rc Cn,M:‘.
(3)
For the concentration or the segment density p, of one component, one has p,~n, M,J V, and for the critical concentration c**, one has
CniM
x-x-
V
(
0
1
2
3
4
(c/c**)*
critical concentration c** as a weight of polystyrene in the at 25°C. The weight ratio of PS is 13.44.
and for the C,,H,,/PS/benzene of C,,H3.,/PS = 13.4, at 25°C
+
MW 0 . 0 . A
Fig. 7. Plots of the normalized reduced viscosity vs the normalized concentration of polystyrene for C,,H,,/PS/ benzene mixtures at 25°C. The weight ratio of C,,H, to PS is 20.1.
styrene for C,,/H,,/PS/benzene mixtures. A similar result is also obtained for C,,H,,/PS/benzene mixtures. It is interesting to note that all the data, after normalization by their critical data, can be superimposed to a single master curve, independent of the molecular weight of polystyrene. The viscometric results obtained have demonstrated that an oligomer can induce the dimension shrinking of a polymer molecule. By changing the weight ratio of polystyrene to paraffin, polystyrene molecules can be brought to a stage between regions of a good solvent and of a poor solvent. When the weight ratio of polystyrene to paraffin is higher than a value, a strong repulsion between molecules of polystyrene and of paraffin leads to a shrinkage of a single polystyrene molecule. These repulsions are found to occur in the region of dilute solutions. In the present mixtures, the critical concentration c** is in essence considered to be equivalent to the 0 concentration. It should be pointed out that the coil-globule transition is conceptually different from the shrinkage of a polymer chain. For a coil-globule transition, the concentration of a single polymer should be much more dilute [10~5-10~6(g/ml)] [17-191 in order that inter-polymer entanglements are expected to be totally avoided.
Cn,M c n, M:’
If it is assumed that two components density, one has
REFERENCES
have the same
The v is equal to 0.5 [IO]. For a system composed of a polymer and an oligomer, M, % M2, like the present case, equation (5) can approach c** cc A4;o5.
(6) The experiments are in good agreement with above relation. Figure 7 shows plots of the normalized reduced viscosity vs the normalized concentration of poly-
I. P.-G. de Gennes. J. Ph~‘s. (Paris) 36, 55 (1975). 1. I. Lifshitz, A. Grosberg and A. Knokholov. Rer. Mod. Phys. SO, 683 (1978). 3. P.-G. de Gennes. J. Phys. (Paris) 39, 299 (1978). 4. L. Lerman. Proc. natn. Arad. Sci. U.S.A. 68, 1886 (1971). 5. L. Lerman. Proc. natn. Acud. Sci. U.S.A. 72, 4288 (1975). 6. H. Ushiki and F. Tanaka. Eur. Polym. J. 21,701 (1985). 7. T. Momii and T. Nose. Macromolecules 22, 1384 (1989). 8. F. Tanaka. J. them. Phys. 78, 2788 (1983). F. Tanaka. J. them. Phys. 82, 2466 (19SSj. 9. T. Nose. J. Phvs. fPuris1 47. 517 11986). 10. H. Fujita. Pdrym& SoUdns. EBevidr, Amsterdam (1990). 11. A. Dondos and H. Benoit. Makromol. Chem. 176.3441 (1975).
Oligomer-induced shrinking of polystyrene chains in benzene 12. A. Dondos,
P. Skondras, E. Pierri and H. Benoit.
Makromol. Chem. 184,2153 (1983). 13. E. Pierri and A. Dondos. Eur. Polym. J. 23, 347 (1987). 14. D. Papanagopoulos. Makromol. Chem. lM, 439
(1994). 15. K. Huber. J. Phys. Chem. 97, 9825 (1993).
663
16. P.-G. De Gennes. Scaling Concepts in Polymer Physics. Cornell University Press, New York (1979). 17. S. Sun, I. Nishio, G. Swislow and T. Tanaka. J. them. Phys. 73, 5971 (1980). 18. P. Perzynski, M. Delsanti and M. Adam. J. Phys. (Paris) 45, 1765 (1984). 19. B. Chu and 2. Wang. Macromolecules 22, 380 (1989).
Pergamon
0014-3057(95)00002-X
Copyright 0 1995Elsevierscieace Ltd
Printedin Great
Britain. All rightr raemed oow3onps $9.50 + 0.00
VISCOSITY STUDY OF OLIGOMER-INDUCED SHRINKING OF POLYSTYRENE CHAINS IN BENZENE PENG
WE1 ZHU
School of Chemistry, The University of Sydney, NSW 2006, Australia (Received 19 April 1994; accepted in final form 28 June 1994)
Abstract-The
paraffin-induced
dimension
shrinking of polystyrene
chains in paraffin/polystyrene/
benzene mixtures is reported in terms of the variation of the reduced viscosity 9 /c as a function of the concentration of polystyrene. The critical concentration c ** in which a strong repu‘p. sron between molecules of polystyrene and of paraffin occurs is determined. This critical concentration is found to be dependent on the weight ratio of two components and molecular weight of polystyrene. Plots of the normalized reduced viscosity the normalized concentration are found to be scaled to a single master curve.
INTRODUCTION
As is well known, the monomer pair interaction of a polymer is repulsive and tends to swell the coil in a good solvent. However, the mean force acting between segments of a polymer chain becomes attractive when this polymer is in a poor solvent below the 8 temperature. The attraction will lead to a shrinkage of a single polymer coil below its size under 8 conditions. Generally speaking, the degree of shrinkage and therefore the segment density change with varying temperature. A single polymer chain can change its state from an open coil to a globular particle if the temperature is lowered (or increased) to the 6 temperature. This is usually called the coil-globule transition or chain collapsed transition. Theories for the coil-globule transition have been proposed [l-3]. The coil-globule transition of a polymer can also be induced by another polymer in a dilute solution at a fixed temperature. For example, DNA of high molecular weight was observed to be collapsed into a very compact particle in a salt solution in the presence of a second neutral polymer, polyethylene oxide with lower molecular weight, above a certain critical concentration [4, 51. The coil-globule transition of high molecular weight poly(styrene-maleicanhydride) was found by the addition of oligomer polyethylene oxide in toluene [6]. The concentration dependent shrinking of a polymer gel in solutions of incompatible polymers was reported by Momii and Nose [7]. Tanaka [8] has discussed a polymer-induced coil-globule transition of another polymer by using the self-consistent field approach. Nose [9] has presented a theory to describe a coil-globule transition on the basis of the thermal- and concentration-bob [lo] models. Accordingly, a polymer induced coil-globule transition of another polymer chain is expected under the following conditions: (1) the intermolecular interaction is repulsive and sufficiently strong compared with the intramolecular repulsive interaction between segments in a large polymer; and (2) the difference
of polymerization degree between two species is very large. The coil shrinking of polymer chains in ternary mixtures has also been studied [l l-l 51. Some studies have established that viscosity methods can be used for determining the dimension shrinking of polymer chains in two-polymer mixtures [l l-141. The principle of using dilute solution viscosity to measure the compatibility characterization is based on the fact that molecules of both components may exist in a molecularly dispersed state and undergo a mutual attraction or repulsion in dilute solutions, which will influence the viscosity. The variation of reduced viscosity in a ternary system with concentration of a component can be schematically displayed in Fig. 1 [12-141. As can be seen, there are two regimes divided by critical concentrations, c*+ and c* (c** < c*). The concentration c** here is a very low critical concentration which was first observed by Dondos and Benoit [l 11. The concentration c** is defined as the concentration corresponding to the incipient overlap of spherical coils. At c**, the distance between centres of macromolecular chains is of the order of their diameters and contacts between molecules (like or unlike) are avoided. The chains do not tend to overlap and therefore shrink in their sizes. If the concentration is higher than c**, an incompatibility between two components appears and the hydrodynamics volume of chains is lower. The reduction of hydrodynamic volume will result in a decrease in the reduced viscosity of solutions, e.g. the slope of the plot of reduced viscosity against concentration may suddenly decline [l l-141. The critical concentration c* was first introduced by de Gennes [16]. When the concentration is lower than c*, there is no complete interpenetration of individuality of molecules. When the concentration is higher than c*, the coils overlap and the individuality of the molecules disappears. In this paper, the paraffin-induced dimension shrinking of polystyrene in benzene is studied. The concentrations c** are carefully determined. It has 659
Peng Wei Zhu
660
r
Fig. I. The variation of reduced viscosity with concentration is schematically shown.
were obtained from Pressure Chemicals. The polydispersity indexes of PS samples are less than 1.2. Viscometric measurements were carried out using a dilution modified Ubbelohde viscometer which was immersed in a constant temperature bath. The temperature was measured close to the capillary by a thermometer with an accuracy of 0.03”C. The precision of viscosity measurements depends on the concentration since the specific viscosity measures differences in the viscosity between the solution and solvent. As the concentration is lowered, the determination of the viscosity becomes more and more inaccurate. In this case, viscosity measurements were carried out with two viscometers immersed in the same temperature bath in order to check the accuracy of data. Solutions were filtered by a 0.45 pm Millipore filter before viscosity measurements. RESULTS
been known that paraffins, as an oligomer version of polyethylene, are not miscible with polystyrene. The interaction between polystyrene and polyethylene segments is very large. Because the molecular weights of paraffins used in experiments are very much smaller than those of the polystyrene, the contributions of changes in hydrodynamic volume of polystyrene are dominant. EXPERIMENTAL All paraffins were obtained from the Aldrich Chemical Co. They are of high purity (99%). Polystyrene (PS) samples
160
0.0020
Figure 2 shows the variation of the reduced viscosity qrp/c against the concentration of polystyrene (molecular weight of 2.33 x 10’) in the PS/C,,H,,/benzene system at 25°C. The weight ratios of C6HJ4 to polystyrene are 4.03, 7.14, 13.44 and 20.1. As can be seen, when the weight ratio of C,,H,, to PS is 4.03, no crossover is observed in the reduced viscosity concentration plot, which implies that &H,, and polystyrene are potentially compatible in benzene and the interaction between two kinds of molecules is expected to be avoided. No phase separation occurs at such high weight ratio because of the shorter chain
150
(a)
0.0065
0.0155
0.01 IO
r
0.000
(b)
0.015
0.010
0.005
C (g/ml)
0.020
C (g/ml)
160
0.000
AND DISCUSSION
Cd)
I
I
0.005
0.010
C (g/ml)
I 0.015
I
I 0.020
0.001
0.003
I 0.005
I 0.007
C (g/ml)
Fig. 2. The variation of the reduced viscosity as a function of concentration of polystyrene in the C,,H,/PS/benzene mixtures at 25°C. The molecular weight of the polystyrene is 2.33 x 105.The weight ratios of C,,H, to PS are: (a) 4.03; (b) 7.14; (c) 13.44 and (d) 20.1.
Oligomer-induced shrinking of polystyrene chains in benzene 9c-3 MW of PS = 2.3385 ?e-3 2 E r * c,
5c-3
3e-3 2
1 lc-3
p 3
10
17
C 16IPS
24
(w/w)
Fig. 3. Plot of the critical concentration c** as a function of the weight ratio of C,,H, to PS at 25°C. The molecular weight of polystyrene is 2.33 x 10’.
185 2e-3
4e-3
r (b)
310
6e-3
ae-3
le-2
C (idmU
661
of C,,H, compared to the polystyrene sample. As the weight ratio increases, the crossovers in the reduced viscosity-composition plots appear. This evidence suggests that C,,H, and polystyrene are strongly incompatible at higher weight ratios of C,,HJPS, but dissimilar molecules refuse. to overlap and therefore polystyrene molecules shrink in size, which leads to a decrease in the hydrodynamic volumes and then causes the reduction of the reduced viscosity. The critical concentrations c** (indicated by concentration of polystyrene) at which the dissimilar molecules begin to repel each other are determined from Fig. 2. This concentration is found to be dependent on the weight ratio of C,6HM/PS. The higher the weight ratio, the smaller is the critical concentation c**. The critical concentration c** as a function of the weight ratio of C,6H34/PS is shown in Fig. 3. As is already known, the compatibility between different polymers is a function of their molecular weight. An increase of the molecular weight causes a decrease in the compatibility of two components. Consequently, it can be expected that an increase in the molecular weight of polystyrene will cause a decrease in the compatibility between paraffins and PS. The decrease in the compatibility should result in a decrease in the critical concentration c**, as reported by Pierri and Dondos [13]. Figure 4 shows plots of the reduced viscosity vs the concentration of polystyrene at a fixed weight ratio of ClzHZ6/PS at 25°C. The molecular weights of polystyrene are 5.75 x lo’, 9.0 x IO5 and 1.6 x 106. Indeed in this figure, a decrease in the critical concentration c** of polystyrene with increasing the molecular weight of polystyrene is observed. In Figs 5 and 6, log-log plots of the critical concentration c** as a function of the molecular weight of polystyrene for C,,H,,/PS/benzene and C,,H,,/PS/benzene mixtures are shown, respectively. The plots give good straight lines with slopes of -0.5. From these figures, we have the following relations for the C,,H,,/PS/PS/benzene with the weight ratio of C,*HZ6/PS = 20.1 $+
C Wml)
-2.0
=
3.g56,+f,0,5 f 0.02
r
I \ 450 -
-2.2 t
2 g
430 -
:c,
0 ‘.a F”
410 -
0” -1
-2.6
390 370
.
le-3
-2.4
t
I 2c-3
3e-3
4e-3
5e-3
6e-3
C Wml) Fig. 4. The variation of the reduced viscosity as a function of concentration of polystyrene in C,,H,/PS/benzene mixtures at 25°C. The weight ratio of C12Hz6to P!S is 20.1. The molecular_. weights (a) 5.75 x 10’; __ .__of polystyrene: . . _ __I (b) Y.0 x IO’; and (c) 1.6 x ICY.
t
-2.8
4.5
I
I
5.0
5.5
6.0
Log MW
Fig. 5. Log-log plot of the critical concentration c** as a function of the molecular weight of polystyrene in the C,,H,,/PS/henzene mixture at 25°C. The weight ratio of C,,H,, to PS is 20.1.
Peng Wei Zhu
662
A .
2.0 -2.2 :
:P F P
-2.3
c,
a2
-2.4
F
.U
1.5
&T
I .o
s*”
-2.5 0.5
-2.6 -2.1
4.00E5 5.7585 6.5985 9.00E5 1.60E6
If+@ 1 5.5
I
I
I
I
5.1
5.9
6.1
6.3
0.0
Log MW Fig. 6. Log-log plot of the function of the molecular C,,H,/PS/benzene mixture C,,H,, to
with the weight ratio
The relation between the critical concentration c** and the molecular weight has been discussed by Benoit et al. [l 1, 121, and Pierri and Dondos [I 31. If it is assumed that at the critical concentration, the total volume V of the solution is equal to the volume of polymers plus the excluded volume V, between these polymers, one has $r xn,R;,
+ V, = V
(I)
where R, is the radius of gyration and n, is number of macromolecules with molecular weight equal to M, . Polymer solution theory [lo] gives the following relation between the radius of gyration and molecular weight R;, a M;’
(2)
and therefore one has V rc Cn,M:‘.
(3)
For the concentration or the segment density p, of one component, one has p,~n, M,J V, and for the critical concentration c**, one has
CniM
x-x-
V
(
0
1
2
3
4
(c/c**)*
critical concentration c** as a weight of polystyrene in the at 25°C. The weight ratio of PS is 13.44.
and for the C,,H,,/PS/benzene of C,,H3.,/PS = 13.4, at 25°C
+
MW 0 . 0 . A
Fig. 7. Plots of the normalized reduced viscosity vs the normalized concentration of polystyrene for C,,H,,/PS/ benzene mixtures at 25°C. The weight ratio of C,,H, to PS is 20.1.
styrene for C,,/H,,/PS/benzene mixtures. A similar result is also obtained for C,,H,,/PS/benzene mixtures. It is interesting to note that all the data, after normalization by their critical data, can be superimposed to a single master curve, independent of the molecular weight of polystyrene. The viscometric results obtained have demonstrated that an oligomer can induce the dimension shrinking of a polymer molecule. By changing the weight ratio of polystyrene to paraffin, polystyrene molecules can be brought to a stage between regions of a good solvent and of a poor solvent. When the weight ratio of polystyrene to paraffin is higher than a value, a strong repulsion between molecules of polystyrene and of paraffin leads to a shrinkage of a single polystyrene molecule. These repulsions are found to occur in the region of dilute solutions. In the present mixtures, the critical concentration c** is in essence considered to be equivalent to the 0 concentration. It should be pointed out that the coil-globule transition is conceptually different from the shrinkage of a polymer chain. For a coil-globule transition, the concentration of a single polymer should be much more dilute [10~5-10~6(g/ml)] [17-191 in order that inter-polymer entanglements are expected to be totally avoided.
Cn,M c n, M:’
If it is assumed that two components density, one has
REFERENCES
have the same
The v is equal to 0.5 [IO]. For a system composed of a polymer and an oligomer, M, % M2, like the present case, equation (5) can approach c** cc A4;o5.
(6) The experiments are in good agreement with above relation. Figure 7 shows plots of the normalized reduced viscosity vs the normalized concentration of poly-
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