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Structure formation in solutions of polymer mixtures
Structm'e formation in solutions of polymer mixtures
1019
(2) From an anMysis of I R spectra it was established that dimethyl ether and tetrahydrofuran (3 : 1) additive reduce the association of PBL and the formation of a partially delocalized structure of terminal C : C bonds of "living polymers". Translated by E. SEM_EI~E REFERENCES 1. B. L. YERUSALIMSKII, Iomlaya polimerizatsiya polyarnykh monomerov (Ionic Polymerization of Polar Monomers). Izd. "Nauka", 1970 2. M. SZWARC, Carbanions, Living Polymers aild Electron Transfer Processes I~lterscience Publishers, 1969 3. tL MORITA a n d A. V. TOBOLSKY, J. Amer. Chem. Soc. 79: 5853, 1957 4. M. MORTON, L. J. FETTERS and E. E. BOSTICK, J. Polymer Sci. CI: 311, 1963 5. F. E. NAYLORp H. L. t t S I E I t and T. C. RANDAL, Macromolecules 3: 486, 1970 6. F. SCHUE, D. J. WORSFOLD and S. BYWATER, Polymer Letters 7: 821, 1969 7. M. MORTON, L. J. FETTERS, It. A. PETT and J. F. MEIER, Macromolecules 3: 377, 1970 8. I-I. L. LEWIS a n d T. L. BROWN, ft. Amer. Chem. Soc. 92: 4664, 1970 9. D. J. WORSFOLD a n d S. BY-WATER, J. Organomet. Chem. 9: 1, 1967 I0. W. H. GLAZE a n d P. S. JONES, Chem. Commtmic., 1434, 1969 11. P. WEST, J. I. PURMONT a n d S. V. MCKINLEY, ft. Amer. Chem. Soc. 90: 797, 1968
STRUCTURE FORMATION IN SOLUTIONS OF POLYMER MIXTURES* V. N. KVLEZl~EV and L. S. KROKI~I~i M. V. Lomonosov Institute of Fine Chemical Technology, Moscow
(Received 6 July 1971)
THE study of polymers is considerably hindered by the fact that their high viscosity does not enable complete equilibrium to be obtained in these systems over a short period of time. This fact does not enable an answer to be found to the simple question: can two polymers form a single-phase equilibrium system, i.e. are t h e y mutually soluble or insoluble. Considerable information concerning special features of structure formation in polymer mixtures is therefore given by a study of solutions of polymer mixtures. Here the study of interaction of polymers themselves is complicated by the presence of a solvent and at the same time is made easier owing to the relatively rapid attainment of equilibrium in the system. * Vysokomol. soyed. AI5: No. 4, 906-916, 1973.
1020
V. 1%7. KULEZNEV a n d L. S. KROKml~A
Processing of polymers is often effected in solution [1] and it was shown that solution structure may have a significant effect on the properties of the polymer obtained [2]. It is quite natural that the presence of a second polymer in the solution should have a specific effect on structure formation of the solution, mainly in macromolecular aggregation. The second polymer in the mixture may be regarded as a high molecular weight solvent in relation to the first polymer. Experimental data indicate that even in the presence of a two-phase structure, polymer mixtures influence the structure of each phase [3]. Therefore, the structure and behaviour of the polymer vary not only according to the type of solvent (if the polymer is formed in solution), but also according to the type of a second polymer in the mixture, if a polymer mixture is examined. The study of structure formation in the solution of a polymer mixture, apart from being of independent interest in the study of solutions, seeks to determine the main trends and the effect of a single polymer on the structure of the other both during mixing in solution and dining mixing in the absence of solvent. Based on these considerations we have examined structure formation in polymer mixtures in solution [4]. This paper describes the results of examining light scattering and viscosity of solutions of polystyrene (PS) and polyisobutylene (PIB) mixtures. A pair of apolar polymers was used in the study so that interaction according to polar groups did not eomplica¢e the patteru of structure formation of macromolecules due to high molecular weight a n d flexibility. Light scattering a n d viscosity of PS mixtures of different molecular weights were studied with the same unfractionated P I B of molecular weight M = 3.0 × 10 t. Molecular weights of PS fractions varied in the range of (0.65-8.3) × 105. The intensity of light scattering was measured using a photoelectric nephelometer a n d viscosity, b y a capillary viscometer with a suspended level. T A B L E 1. C O N C E N T R A T I O N AT T H E B E G I N N I N G OF ASSOCIATION ~1 AND T H E L I M I T OF S E P A R A T I O N Ca ( g / d ] ) FOR P S M I X T U R E S I N T O L U E N E AND
PS 5.50 3.7 2.2 1.2 __t-
0.65
/~/wX lOs PIB 3.0 3.0 3.0 3.0 3.0
AIqD P I B
CCl
Toluene Cl
0-09 0.20 0"24 0"41
SOLUTION
CCI4
Cl
0.9
0"25
1.1
0.36
1"3 1-7 2"4
0.42 0.65 0.79
~s
1.5
Solutions of polymer mixtures are thermodynamically stable a n d are single-phase only over a certain range of concentration. On achieving a certain concentration, which can conveniently he termed the !imit of stratification, the mixture becomes turbid a n d separates into two layers after a certain time. Solution concentration cs, which corresponds to the limit of separation, was determined from the optical density variation during the increase of solution concentration. A marked increase in optical density corresponded to the limit of separation [4, 5]. Table 1 gives results of determining the value of cs for PS and P I B mixtures in various solvents and according to the molecular weight of PS.
Structure formation in solutions of polymer mixtures
1021
I t can be seen that c~ depends on the polymer-solvent affinity [6] and increases noticeably with a reduction in the value of ~w of the polymer. As far as the affinity of solvents for polymers is concerned, according to literature results [7], both solvents are satisfactory in relation to PS. The quality of these solvents in relation to P I B was evaluated from the value of [t/]. For PIB in toluene the value of [t/] was 3.7 dl/g, whereas in CC14 it was 8.2 dl/g. According to these data CC14 can be regarded as a good solvent of PIB and toluene, as a poor one. The lower the affinity of the polymer and solvent (solvent being poorer) and the higher the molecular weight, the sooner will stratification take place. I t is well known that a deterioration in solvent quality and an increase in molecular weight of the polymer raise the degree of macromolecular association. Results of Table 1 indicate therefore that with an increase in the degree of macromoleeular association, the concentration of the solution of the polymer mixture at which separation occurs decreases. Subsequent investigations were carried out with solutions at a concentration lower than c2, i. e. in the region of single-phase solutions. I t is well k n o w n t h a t in fairly dilute p o l y m e r solutions a t a certain c o n c e n t r a tion, which is s o m e t i m e s t e r m e d critical c o n c e n t r a t i o n , m a c r o m o l e c u l a r i n t e r a c t i o n c o m m e n c e s w i t h t h e result t h a t m a n y p r o p e r t i e s of solutions b e g i n to dev i a t e f r o m t h e relations p r e d i c t e d b y t h e t h e o r y of dilute solutions. I t was s h o w n in p a r t i c u l a r [8] t h a t w i t h a certain c o n c e n t r a t i o n of P S in toluene a n inflexion is o b s e r v e d on t h e c u r v e (1/Rg0o)-C, where Rio° is t h e i n t e n s i t y of s c a t t e r i n g a t a n angle of 90 ° a n d c - - c o n c e n t r a t i o n . F o r P S w i t h M : 9 × l05 [8] inflexion corr e s p o n d e d to a 0.3~o c o n c e n t r a t i o n in toluene. This effect was essentially explained b y t h e f a c t t h a t a t t h e "critical c o n c e n t r a t i o n " i n d i c a t e d m a c r o m o l e c u l a r spheres begin to i n t e r a c t w i t h e a c h o t h e r a n d t h e solution ceases to be dilute. I t was interesting to establish t h e critical c o n c e n t r a t i o n for p o l y m e r m i x t u r e s . F i g u r e l a indicates t h a t w i t h low c o n c e n t r a t i o n s t h e curves coincide a n d a t a b o v e a certain c o n c e n t r a t i o n t h e y s e p a r a t e suddenly, light s c a t t e r i n g in m i x t u r e being c o n s i d e r a b l y higher t h a n in t h e solution of individual p o l y m e r s . Toluene was chosen as a s o l v e n t since its r e f r a c t i v e i n d e x is a l m o s t the s a m e as t h a t of P I B . Therefore, in a P S - P I B - t o l u e n e s y s t e m PS has t h e m a i n effect on scattering, since excess s c a t t e r i n g of P I B in toluene is close to zero. B e a r i n g in m i n d this f a c t w h e n a n a l y s i n g results in Fig. 1 it m a y be concluded t h a t s t a r t i n g f r o m a certain c o n c e n t r a t i o n P S m a c r o m o l e c u l e s in a m i x t u r e w i t h P I B begin to s c a t t e r light m u c h m o r e i n t e n s i v e l y t h a n in toluene. This can only be explained, in o u r view, b y the f a c t t h a t association of P S m a c r o m o l e c u l e s begins a t this c o n c e n t r a t i o n . W e therefore t e r m e d t h e c o n c e n t r a t i o n a t which curves begin to show incongruence for P S solution in toluene a n d in a solution of P I B in toluene, t h e c o n c e n t r a t i o n of initial association a n d d e n o t e d it as c~. I n Fig. lb t h e s a m e . e x p e r i m e n t a l d a t a are g i v e n in coordinates Kc/R~oo-C(where K is t h e c o n s t a n t in t h e e q u a t i o n of light scattering). I t is quite o b v i o u s t h a t t h e coordinates in Fig. lb are m o s t c o n v e n i e n t for d e t e r m i n i n g c o n c e n t r a t i o n c~. Values of c~ d e t e r m i n e d b y this m e t h o d are g i v e n in T a b l e 1. I t can be seen t h a t , as w i t h c2, the v a l u e of c~ increases w i t h a r e d u c t i o n o f t h e m o l e c u l a r weight of P S a n d decreases w i t h a red u c t i o n in affinity o f p o l y m e r a n d solvent, which is in a g r e e m e n t w i t h general views concerning t h e relations of association of p o l y m e r s in solution.
1022
V.N. KULEZNEVand L. S. KROKHINA
According to information previously obtained [8], the critical concentration of PS in toluene exceeds the value of c~ determined by the authors for a P S - P I B mixture. I t is impossible to make a quantitative comparison of these two values as in previous experiments [8] the solution only contained PS with M----9× 106 and in our experiments PS was mixed with P I B of high molecular weight (3 × ]0 s) which in itself could reduce the value of c1. At the same time, there is also another cause for the reduction of c1, compared with critical concentration.
~, I00
/
? '!
8g
fg I
s.2
I
I
o.~
i
aps,g/dt
( i I I I
Jl
cl
]
o.2
I
[
I
t
o.s' ~s,~/d/
FIO. 1. Relation between R~. (a) and Kc/R~. (b) of PS solutions (1) and a PS-PIB mixture (2) in toluene and the concentration of PS; MwPs~ 5"5 × 105. I n the presence of a second polymer, which has a low affinity for the first polymer, the number of segmental contacts of different macromolecules decreases thus, consequently, reducing the free volume in which molecules of each polymer can be located in solution. A reduction of free volume in a polymer mixture has the result t h a t the association of homogeneous macromolecules commences at a lower concentration t h a n in the solution of polymer alone, consequently, cl should normally be lower than the critical concentration determined for individual polymers. This fact ought to be emphasized specially since without giving sufficient attention to the specific properties of curves similar to curve 2 in Fig. la, the information concerning the molecular weight and dimension of molecules in the polymer mixture is inaccurate. The use of the theory of light scattering to block copolymer solutions, where association of units homogeneous in chemical composition should take place at very low concentrations, also requires special care from this point of view. I t should also be noted t h a t transition via cl with an increase in concentration
Structure formation in solutions of polymer mixtures
1023
causes a marked reduction in the second virial coefficient A~ [5]. Reduction of A~ is known to indicate a deterioration in the quality of solvent, which also confirms the assumption concerning a possible additional (excess) association of PS macromolecules in the presence of a. second polymer in the solution when c>cl. c, ~e/#t 2-4 2"0
~
/'6 /'2 0-8
"q
0.4 /
2
J 4 ~fw~ "fO -5
5
Fro. 2. Concentration limits of the existence of solutions of PS and P I B mixtures (7 : 3) in thr~e structural states according to Mwps: / - - i s o l a t e d macromolecules; / / - - a s s o c i a t e s in solution, I I I - - t w o - p h a s e solutions
Data obtained enable the entire range of concentrations, which contains solutions of polymer mixtures, to be separated into three ranges, according to polymer molecular weight. Figure 2 shows the dependence on the molecular weight of PS of cl and c2 of a P S - P I B - t o l u e n e system. When cc2 the solution consists of two phases. It was interesting to examine in more detail the structural variation of solutions.in the range of c
1024
V.N.
KULEZNEV and L. S. KROKHINA
of PS established by using the Zimm diagram. This can be done for different concentrations of the polymer solvent and the variation of molecular weight and dimensions ascertained of PS sphere according to P I B concentration in solution. We recall t h a t this experiment is possible when excess scattering of the polymer forming the polymer solvent (PIB), is practically zero.
The Zimm diagrams for a PS and P I B mixture were greatly distorted at lfigh concentrations. However, at low concentrations and small angles reliable extrapolation to zero angle and zero concentration could be made to determine sphere dimensions (~2)~ and the molecular weight of PS for different concentrations of polymer solvent (Table 2). TABLE 2. VALUES OF
.~1w,A~ AND
T H E D I M E N S I O N OF P S .-~IACROMOLECULES "[--~TOLUEI~E AND I N A P O L Y M E R SOLVENT
(PIB solution in toluene) Specimen, No.
Concen10 4 Radius tration A 2 × of inerPIB, tia, A
Specimen,
No.
g/d]
0 0.13 0.225
4"55 0"19 0"16
434 434 495
960
Concentration PIB, g/dl 0 0.1 0-2 0.3
A 2×
10 4 Radius of ineri tia, A
3"3 0-9 0.9 --0.3
620 620 720 848
(h~)l/2, h 1520
The molecular weight of specimen I is 6-45x105, specimen 2-9.55×105.
It can be seen that with an increase in the concentrations of the polymer solvent there is no association of PS macromolecules indicated b y constant molecular weight of PS. With low concentrations of P I B no changes are observed in sphere dimensions (radius of inertia). This is attributed to the view that with solution concentrations of less than cl molecules of PS and P I B are fairly distant from each other and have no mutual effect to the extent required for increasing the degree of association on changing sphere shape. I f the concentration of P I B in a polymer solvent becomes equal to or exceeds cl, the dimension of the PS sphere increases, molecular weight remaining constant. This takes place when the concentration of the initial solution of the polymer mixture before dilution with a polymer solvent becomes much higher than the concentration of initial association. B y diluting this solution with a polymer solvent we reduce the concentration of PS in the mixture. Dilution of PS with a polymer solvent results in the decomposition of PS associates to individual macromolecules (molecular weight of PS does not increase in the polymer solvent), however, a high concentration of P I B increases the dimensions of macromolecular spheres of PS. Results obtained m a y be explained as follows. With a solution concentration higher than c~ (but less than c2) molecular spheres of different polymers can pene-
Structure formation in solutions of polymer mixtures
1025
trate each other. This is quite possible since the solution in this range of concentration is single-phase and consequently, there is no physical interface between spheres of different polymers or polymer associates. It m a y thus be considered that in a single-phase solution of a polymer mixture inside a polymer sphere considerable segmental concentration is established of another polymer. Owing to preferential contacts between homogeneous segments, interaction of diffeIent segments will be equivalent to repulsion. Owing to the presence of P I B segments both outside and inside the PS spheres, the latter may either expand or be compressed according to whether the resulting effect of P I B segments is directed inside or outside the sphere. In our case the PS sphere expands increasing dimensions and thus this "expanded" macromolecule is prepared for association with similar ones, which takes place with a higher PS content in solution. In other cases [9] a reduction was observed in the polymer sphere on increasing the concentration of a "polymer" solvent. However, Kuhn established that there are more spheres in a "polymer 0 solvent than in a low molecular weight 0 solvent" [9].
,0~0
~d'Ob
PO,/.O
0"8
0"0
0"4
0"2
O PZB
FIG. 3. Relation between R"m. and the ratio of polymers for solutions and mixtures of P S - P I B (1--4) with a constant solution concentration of 0.5 (a) and 0.2 g]dl (b) with Mrs × l0 s = 5 . 5 (1), 2.2 (2), 1.2 (3) and 0-65 (4) and R"g0. for PS solutions in toluene (1'-4').
A s u b s e q u e n t s t a g e o f the s t u d y w a s t o e x a m i n e m a c r o m o l e c u l a r a s s o c i a t i o n o f P S in t h e c o n c e n t r a t i o n r a n g e cz--c2. All iso-refractive s o l v e n t w a s u s e d in this case. F i g u r e 3 s h o w s t h e relation b e t w e e n excess scattering a n d t h e P S : P I B
1026
V. ~'. KULEZNEVand L. S. Y~tOKHINA
ratio in solutions of different concentrations and different molecular weights of PIB. The excess scattering of P I B in toluene may therefore be ignored, the experimental scattering of PS and P I B mixtures should be compared with the scattering of PS in a toluene solution with a concentration equal to its partial concentration in a mixture with PIB. Broken lines in Fig. 3 represent experimental values of R~0o for PS in toluene with a concentration equal to its partial concentration in the mixture. The difference between scattering of PS in a mixture and scattering in toluene is due to excessive association of PS in the presence of PIB, compared with association of PS in toluene with the same concentrations of PS in both cases. The dimensions of associates cannot be theoretically determined in solution of finite concentration from data of light scattering, excessive scattering can therefore be compared only qualitatively with the dimensions of associates. I n our opinion, macromoleeular association of PS is the only cause of excessive scattering of PS in the presence of P I B in toluene solution. The more light scattering of PS in toluene in the presence of P I B exceeds the corresponding value of light scattering of PS in toluene with the same concentrations of PS, the higher the association of PS. We therefore used excess light scattering as a measure of excess association with a ratio of polymers in solution of PS : P I B ~- 7 : 3. The ratio of polymers was here selected to ensure a maximum excess of scattering for a given system. I t was interesting to determine the relation between AR~0o and the concentration of the solution of a polymer mixture with a given constant ratio in the mixture. Figure 4 shows t h a t excess light scattering increases with an increase in the concentration of the polymer mixture in solution and with an increase in molecular weight of PS. The relation between AR~0° and solution concentration is shown by a straight line which intersects the abscissa axis when c-~cl. This once more underlines the fact t h a t excess association of PS due to the presence of PIB, begins when c : c l and further increases with concentration up to c2, when PS associates reach this value and the density of the polymer material contained, so t h a t an interface is formed between heterogeneous associates and the solution is separated into two phases in micro-volumes. Association in a polymer mixture in solution, which begins with a concentration of initial association c~, takes place on increasing concentration and is completed by micro-stratification with a concentration corresponding to maximum stratification c2. Various polymers, according to chemical nature, molecular weight, type of solvent and other factors have very different c~ and c~ values and the smaller the c~-c~ concentration interval, the greater will be the increase in the apparent size and density of associates with an increase in concentration. All this suggests t h a t there are some relevant (equivalent) states of association in the polymer mixture in the range of single-phase solutions. I f the solution has a certain concentration, which is precisely in the middle of the c~-c~ range, the other pair of polymers in solution with a different concentration,
1027
Structtu'e formation in solutions of polymer mixture's
b u t also situated in the middle of the cl--c2 range, should be characterized by equivalent association. This assumption was not so far verified using completely different polymer pairs, since excess scattering in the various pairs depends on the increment of the refractive index of polymers and on the effect of each polymer on scattering. 40 > v
%
'Y~/
~2 o4
i 04
O'3 FxG.
4
o,u/d/
0.5
O.[
O.2
I-0 c a
FIG. 5
FIo. 4. Concentration dependence of excess scattering AR"~. of PS mixed with PIB (PS : :P~B=7:3), compared with an individual PS solution; MpsX105=5.5 (1, 5); 2.2 (2); 1.2 (3) and 0-65 (4); 1-4--solutions in toluene; 5--in CC1,. Fro. 5. Relation between excess scattering of PS in a mixture with PIB and the reduced concentration c*=(c--cl)/(cz--c,) when Mps×105=5-5 (1), 2.2 (2), 1.2 (3) and 0.65 (4). The accuracy of the assumption of the existence of corresponding states of association in solutions of polymer mixtures was demonstrated in this s t u d y with PS specimens of high molecular weight. Figure 5 plotted according to d a t a of Fig. 4 indicates the relation between excess light scattering AR'9'oo and concentration c*=(c--cl)/(c--c~). Reduced concentration is a measure of the corresponding state of association of the polymer mixture in solution. Solutions with different weight concentrations, but with the same reduced concentration should have a similar, or even identical excess association. The Figure illustrates this assumption: the dependence of excess scattering on reduced concentration is expressed by a single straight line, independent of the molecular weight of PS, i.e. independent of the values of cl and c~. I t may thus be assumed from results t h a t the same excess scattering near the point of stratification for all PS specimens corresponds to the same degree of association and density of polymer material in associates, which are required to form an interface between associates of different polymer molecules, i.e. to separate the solution into two phases. For comparison, Fig. 4 shows the relation between excess scattering and reduced concentration for a solution of a PS and P I B mixture in CC14. Excess scattering in this solvent is much higher than in toluene which is, apparently,
1028
V.N. K~zz~mv
and L. S. K R O X m ~ A
the consequence not only of a higher refractive index of PS in this solvent, but also a considerable excess light scattering due to PIB in this case. Data obtained by light scattering were confirmed viscometrically. Relative viscosity t/re,of solution mixtures with a different ratio of polymers was determined at constant concentration using a capillary viscometer. In studying the relation between any properties of the mixture and composition considerable difficultiesare involved in explaining the type of theoretical relation between property and composition, i.e. the relation which would be observed without a specific interaction between heterogeneous polymers. These difficultiesare also experienced in interpreting viscosity data. It is quite obvious that viscosity is not an additive property and the structural behaviour of a polymer mixture cannot therefore be evaluated from the deviation of experimental viscosities from additive values. W e have proposed two methods for deriving a theoretical relation between viscosity and composition. In the first ease [10] an equation was used tlsp=Lco~Nco1+P, where r&p is the specific viscosity of the solution of polymer mixture, Wl is the gravimetric proportion of one of the polymers in the mixture, L, N and P are coefficients dependent on polymer molecular weight, concentration in solution and the Huggins constant /c'in the equation showing the concentration dependence of viscosity. This equation is correct in a limited range of concentrations. Another equation was derived for a mixture of polymer melts [II] which can, in principle, be used for a solution mixture of any concentration. The equation takes the form
(1) where ~/ is the initial Newtonian viscosity of the melt of the polymer mixture; ~/1 and t/2 are the viscosities of components and ~-exponent in the equation ~I=KM". Equation (1) can be fairly accurately approximated by a straight line in logarithmic coordinates showing viscosity against composition (log ~/-w). This is in agreement with the N i n o m i y a - F e r m y equation [12] showing logarithmic additivity for a mixture of polymer fractions and with the empirical equation to calculate the viscosity of a plasticizer mixture [13]. The viscosity of the polymer-polymer-solvent system can also be calculated from the law of logarithmic additivity of viscosity as the viscosity of a mixture of two liquids, each of which is a polymer solution in a low molecular weight solvent. Figure 6a shows that the variations between experimental and calculated values, according to the rule of logarithmic additivity, increase with an increase in solution concentration. The variations in Fig. 6b are shown according to solution concentration. The straight line zt log ~rel-c intersects the abscissa at a point which corresponds to a solution concentration of 0-2 g/1. This point m a y be regarded as the concentration of initial association Cl obtained from viscosity data. In Table 1 the value of Cl for this system is 0.09, i.e. an increased concentration value of initial association is obtained from viscosity.
1029
S t r u c t u r e f o r m a t i o n in solutions of p o l y m e r m i x t u r e s
The relationship observed is quite natural bearing in mind that part of the associates may decompose in the process, particularly at low concentrations at which association only begins. This effect is similar to the influence of shear stress on maximum stratification of the solution of polymer mixture c2 [14], when shear deformation of the solution increases the concentration of stratification.
0-5 O.4 P~'I O
0.8
0.6" 0.4
Q'2
OPIB
c,s,/dl
O'8
FIG. 6. R e l a t i o n b e t w e e n log 1/re1 a n d the ratio of PS ( ~ w P s = 5.5 × 10 ~) a n d P I B in solution m i x t u r e s i n t o l u e n e a t P S c o n c e n t r a t i o n s of 0"8 (1), 0.6 (2), 0.4 (3}, 0.2 g/dl (4} {a) (the b r o k e n line shows the a d d i t i v e relations} a n d t h e relation b e t w e e n zllog/Trel a n d the solution conc e n t r a t i o n of PS a n d P I B m i x t u r e s (b).
Investigations of light scattering and solution viscosity of mixtures of two conventional apolar polymers of PS and PIB provide reliable proof of increased association in a solution of polymer mixture. There is no reason to believe that this effect is exceptional applying only to this particular pair of polymers. I t may be assumed that increased (excessive) association in a polymer mixture in solution characterizes most polymer mixtures, particularly those, which have similar properties to the PS-PIB pair examined. This effect can, at least, be regarded as an additional typical symptom of supermoleeular structures in solutions of apolar polymer mixtures, which have no polar functional groups ensuring strong interaction bet~'een heterogeneous macromolecules.
1030
V. N. K u ~ z N ~ . v and L. S. KROKm~A
When obtaining films of polymer mixtures from solution by gradually increasing concentration when the solvent is eliminated or when polymer melts are mixed and polymer relaxation times are rather short, in order to ensure structural change-over inside each polymer phase, increased association may be expected in each polymer and in the absence of solvent. Changes in the supermolecular structure of polymers during mixing were confirmed using a polyethylene and polypropylene mixture [3]. The interval between melting points and crystallization temperatures in the polyethylene and polypropylene phase in mixture became less compared with the appropriate intervals in polymers examined separately. A report has been made recently concerning the change in glass temperature in glassy polymer mixtures [15]. It may be assumed that a change in glass temperature is also the consequence of increased association (short-range order) in each polymer phase in the polymer mixture. We note the author's explanation [15], according to which displacement of the glass temperature of components in the mixture is attributed to the development of internal stress in a two-phase mixture on cooling. This is far from always being consistent with experimental facts. An increase in the degree of association in each polymer in the mixture, which was confirmed experimentally in our study, as previously, satisfactorily explains the results obtained by Flory [16], who pointed out that on mixing polymers (using polyethylene and P I B mixture), the entropy of the system does not increase but decreases. When large molecules are contained in the system, the effect of the combinatorial factor on entropy variation is low, as pointed out by Gee [17]. The presence of large flexible macromolecules results in association, i.e. an increase in the short-range order which, as pointed out by the authors, greatly increases in the presence of a second polymer. This fact should always be considered when analysing relations in the variation of the behaviour of polymers on adding a second polymer component, since a change in the supermolecular structure of the polymer on mixing may cause a marked change in the behaviour of each polymer phase in the polymer mixture. An increase in the short-range order in the system normally results in compression of the mixture and reduction in specific volume. However, in a twophase mixture, apart from compression of the polymer in each phase, the structure becomes looser as a result of segmental dissolving of polymers at the interface [18]. Breaking up the polymer (reduction of density) in the transitional layer at the interface and compressing the polymer in each phase by increasing the shortrange order--these are two processes which may as a result cause both an increase and a reduction in density on mixing polymers, compared with the additive value of density. This relation has previously been experimentally observed by the authors [19]. Finally, we note another conclusion which follows from this study. An increase in the degree of association of polymers in a mixture of polymer solutions
Structure formation in solutions of polymer mixtures
103I
on approaching maximum separation, is similar to association in individual polymer solutions when approaching critical temperature. The temperature dependence of several properties of polymer solutions separated is, in principle, similar to the concentration dependence of properties of the polymer mixture, as follows from a comparison of results of our studies and the studies carried o u t by Tager et al. [20]. CONCLUSIONS
(l) A study was made of light scattering and viscosity of polystyrene (PS) and polyisobutylene (PIB) mixtures in toluene, according to the molecular weight of PS and solution concentration. (2) In a mixture of PS and P I B an increase is observed in the dimensions of PS spheres on increasing the concentration of the polymer mixture provided t h a t the content of PS in the mixture is so low t h a t no molecular association takes place. (3) Single-phase solutions of polymer mixtures, according to concentration, are divided into two regions: a region characterized by the independent behaviour of different macromolecules (up to the concentration of initial association cl) and a region characterized by a high degree of association of homogeneous macromolecules (from c1 to m a x i m u m separation %). (4) A view is formulated concerning the interval of association cl--c2, in which processes of association develop resulting in stratification. The degree of association in this interval is determined by the reduced concentration, which functions as a parameter of corresponding states of association. By the moment of stratification the associates reach a certain size, independent of polymer molecular weight. (5) The concentration of initial macromolecular association cl, determined from solution viscosity exceeds the similar value determined from light scattering, which may be due to the effect of shear stress when determining viscosity, on the state of macromolecular aggregation in solution. (6) Increasing the short-range order in each polymer in the presence of a second polymer, m a y alter the properties of each polymer phase in the mixture in the absence of a solvent. Translated by E. SEVERE REFERENCES
1. S. P. PAPKOV, Fiziko-khimiohcskie osnovy pererabotki polimcrov (Physical and Chemical Principles of Processing Polymers). Izd. "Khimiya", 1971 2. T. V. DOROKHINA, A. S. NOIrIKOV and P. I. ZUBOV, Vysokomol. soyed. 1: 36, 1959 (Not translated in Polymer Sei. U.S.S.]~.); V. N. KULEZNEV, V. D. KLY]KOVAand B. A. DOGAI)KIN, Kolloidn. zh. 27: 139, 1965; M. KLrRBANALIEV, Dissertation, 1968; A. L. VOLYNSKII, Dissertation, 1971 3. G. V. VINOGRADOV, Yu. G. YANOVSKII, V. N. KULEZNEV a~ld T. A. IVANENKO, Kolloichl. zh. 28: 640, 1966 4. L. S. KROKItINA, Dissertation, 1971
1032
B. YA. TEITEL'BAUI~ and L. I. TUZOVA
5. V. N. KULEZNEV, L. S. KROKHINA, Yu. I. LYAKIN and B. A. DOGADKIN, Kolloidn. zh. 26: 475, 1964 4}. V. N. KULEZNEV, L. S. KROKHINA, Yu. G. OGANESOV aud L. M. ZLANTSEN, Kolloidu. zh. 33: 98, 1971 7. P. DOTY a n d R. STEINER, J. Polymer Sci. 5: 383, 1950 2. V. Ye. ESKIN a n d A. Yc. NESTEROV, Kolloidm zh. 28: 904, 1966; R. K U H N a n d H. J. CANTOW, Makromolek. Chem. 122: 65, 1969; H. I. HUDE aud A. G. TANNER, J. Colloid and Interface Sci. 28: 179, 1968 ~10. V. Ye. GUL', Ye. A. PENSKAYA a n d V. N. KULEZNEV, Kolloida. zh. 27: 341, 1965 11. V. N. KULEZI~EV, I. V. KONYUKH, G. V. VINOGRADOV a n d I. P. DMITRIEVA, Kolloidn. zh. 27: 540, 1965 12. K. NINOMIYA a n d J. FERRY, J. Colloid Sci. 18: 421, 1963 13. K. TINIUS, Plastifikatory (Plasticizers), Izd. " K h i m i y a " , 1964 14. V.N. KULEZNEV and L. B. KANDYRIN, Kolloidn. zh. 31: 245, 1969; V. N. KULEZNEV, L. B. KANDYRIN, L. S. KROKHINA and Ye. F. BUKANOVA, Kolloidm zh. 33: 589, 1971 15. R. MURAKAM], Kobunsi kagaku, Chem. High Polymer 27: 878, 1970 16. P. FLORY, B. E. EICHINGER a n d R. A. ORWOL, Maeromolecules 1: 287, 1968 17. G. GEE, Quart. Revs. London. Chem. Soc. 1: 265, 1947 18. V. N. KULEZNEV, V. D. KLYKOVA and B. A. DOGADK[N, Kolloidn. zh. 30: 255, 1968 19. V. N. KULEZNEV a n d K. M. IGOSHEVA, Vysokomol. soycd. 4: 1858, 1962 (Not translated in Polymer Sci. U.S.S.R.) 20. V. M. ANDREYEVA, A. A. ANtKEYEVA, S. A. VSHIVKOV and A. A. TAGER, Vysokomol. soyed. B12: 789, 1970 (Not translated in Polymer Sci. U.S.S.R.)
MULTIPLICITY OF DTA PEAKS AND CRYSTALLIZATION PHENOMENA DURING MELTING OF POLYMERS* B. YA. TEITEL'B~.U1K and L. I. TuzovA A. Ye. Arbuzov Institute of Organic a n d Physical Chemistry
(Received 6 July 1971) ~rHE problem of the causes of formation of multiple peaks of melting on thormograms of crystalline polymers is extensively discussed in the literature; there are dozens of differon~ explanations of this fact (Table). I t is quite evident t h a t there is no universal explanation since this phenomenon m a y in fact be the result of different causes in different cases. We would like to deal with one which is not always given sufficient a t t e n t i o n - - t h e problem of recrystaltization processes during partial melting [25, 26]. This factor is, in our opinion, of such general significance that in seeking to explain the existence of multiple DTA peaks, the effect of recrystallization processes should first be .excluded. I n m a n y cases rccrystallization and other factors accounting for multiplicity are m u t u a l l y superimposed. These processes in the purest form can be observed in the case ~ f homopolymcrs rendered amorphous, which crystallize while recording the thermograms. * Vysokomol. soyed. A15: :No. 4, 917-922, 1973.
1019
(2) From an anMysis of I R spectra it was established that dimethyl ether and tetrahydrofuran (3 : 1) additive reduce the association of PBL and the formation of a partially delocalized structure of terminal C : C bonds of "living polymers". Translated by E. SEM_EI~E REFERENCES 1. B. L. YERUSALIMSKII, Iomlaya polimerizatsiya polyarnykh monomerov (Ionic Polymerization of Polar Monomers). Izd. "Nauka", 1970 2. M. SZWARC, Carbanions, Living Polymers aild Electron Transfer Processes I~lterscience Publishers, 1969 3. tL MORITA a n d A. V. TOBOLSKY, J. Amer. Chem. Soc. 79: 5853, 1957 4. M. MORTON, L. J. FETTERS and E. E. BOSTICK, J. Polymer Sci. CI: 311, 1963 5. F. E. NAYLORp H. L. t t S I E I t and T. C. RANDAL, Macromolecules 3: 486, 1970 6. F. SCHUE, D. J. WORSFOLD and S. BYWATER, Polymer Letters 7: 821, 1969 7. M. MORTON, L. J. FETTERS, It. A. PETT and J. F. MEIER, Macromolecules 3: 377, 1970 8. I-I. L. LEWIS a n d T. L. BROWN, ft. Amer. Chem. Soc. 92: 4664, 1970 9. D. J. WORSFOLD a n d S. BY-WATER, J. Organomet. Chem. 9: 1, 1967 I0. W. H. GLAZE a n d P. S. JONES, Chem. Commtmic., 1434, 1969 11. P. WEST, J. I. PURMONT a n d S. V. MCKINLEY, ft. Amer. Chem. Soc. 90: 797, 1968
STRUCTURE FORMATION IN SOLUTIONS OF POLYMER MIXTURES* V. N. KVLEZl~EV and L. S. KROKI~I~i M. V. Lomonosov Institute of Fine Chemical Technology, Moscow
(Received 6 July 1971)
THE study of polymers is considerably hindered by the fact that their high viscosity does not enable complete equilibrium to be obtained in these systems over a short period of time. This fact does not enable an answer to be found to the simple question: can two polymers form a single-phase equilibrium system, i.e. are t h e y mutually soluble or insoluble. Considerable information concerning special features of structure formation in polymer mixtures is therefore given by a study of solutions of polymer mixtures. Here the study of interaction of polymers themselves is complicated by the presence of a solvent and at the same time is made easier owing to the relatively rapid attainment of equilibrium in the system. * Vysokomol. soyed. AI5: No. 4, 906-916, 1973.
1020
V. 1%7. KULEZNEV a n d L. S. KROKml~A
Processing of polymers is often effected in solution [1] and it was shown that solution structure may have a significant effect on the properties of the polymer obtained [2]. It is quite natural that the presence of a second polymer in the solution should have a specific effect on structure formation of the solution, mainly in macromolecular aggregation. The second polymer in the mixture may be regarded as a high molecular weight solvent in relation to the first polymer. Experimental data indicate that even in the presence of a two-phase structure, polymer mixtures influence the structure of each phase [3]. Therefore, the structure and behaviour of the polymer vary not only according to the type of solvent (if the polymer is formed in solution), but also according to the type of a second polymer in the mixture, if a polymer mixture is examined. The study of structure formation in the solution of a polymer mixture, apart from being of independent interest in the study of solutions, seeks to determine the main trends and the effect of a single polymer on the structure of the other both during mixing in solution and dining mixing in the absence of solvent. Based on these considerations we have examined structure formation in polymer mixtures in solution [4]. This paper describes the results of examining light scattering and viscosity of solutions of polystyrene (PS) and polyisobutylene (PIB) mixtures. A pair of apolar polymers was used in the study so that interaction according to polar groups did not eomplica¢e the patteru of structure formation of macromolecules due to high molecular weight a n d flexibility. Light scattering a n d viscosity of PS mixtures of different molecular weights were studied with the same unfractionated P I B of molecular weight M = 3.0 × 10 t. Molecular weights of PS fractions varied in the range of (0.65-8.3) × 105. The intensity of light scattering was measured using a photoelectric nephelometer a n d viscosity, b y a capillary viscometer with a suspended level. T A B L E 1. C O N C E N T R A T I O N AT T H E B E G I N N I N G OF ASSOCIATION ~1 AND T H E L I M I T OF S E P A R A T I O N Ca ( g / d ] ) FOR P S M I X T U R E S I N T O L U E N E AND
PS 5.50 3.7 2.2 1.2 __t-
0.65
/~/wX lOs PIB 3.0 3.0 3.0 3.0 3.0
AIqD P I B
CCl
Toluene Cl
0-09 0.20 0"24 0"41
SOLUTION
CCI4
Cl
0.9
0"25
1.1
0.36
1"3 1-7 2"4
0.42 0.65 0.79
~s
1.5
Solutions of polymer mixtures are thermodynamically stable a n d are single-phase only over a certain range of concentration. On achieving a certain concentration, which can conveniently he termed the !imit of stratification, the mixture becomes turbid a n d separates into two layers after a certain time. Solution concentration cs, which corresponds to the limit of separation, was determined from the optical density variation during the increase of solution concentration. A marked increase in optical density corresponded to the limit of separation [4, 5]. Table 1 gives results of determining the value of cs for PS and P I B mixtures in various solvents and according to the molecular weight of PS.
Structure formation in solutions of polymer mixtures
1021
I t can be seen that c~ depends on the polymer-solvent affinity [6] and increases noticeably with a reduction in the value of ~w of the polymer. As far as the affinity of solvents for polymers is concerned, according to literature results [7], both solvents are satisfactory in relation to PS. The quality of these solvents in relation to P I B was evaluated from the value of [t/]. For PIB in toluene the value of [t/] was 3.7 dl/g, whereas in CC14 it was 8.2 dl/g. According to these data CC14 can be regarded as a good solvent of PIB and toluene, as a poor one. The lower the affinity of the polymer and solvent (solvent being poorer) and the higher the molecular weight, the sooner will stratification take place. I t is well known that a deterioration in solvent quality and an increase in molecular weight of the polymer raise the degree of macromolecular association. Results of Table 1 indicate therefore that with an increase in the degree of macromoleeular association, the concentration of the solution of the polymer mixture at which separation occurs decreases. Subsequent investigations were carried out with solutions at a concentration lower than c2, i. e. in the region of single-phase solutions. I t is well k n o w n t h a t in fairly dilute p o l y m e r solutions a t a certain c o n c e n t r a tion, which is s o m e t i m e s t e r m e d critical c o n c e n t r a t i o n , m a c r o m o l e c u l a r i n t e r a c t i o n c o m m e n c e s w i t h t h e result t h a t m a n y p r o p e r t i e s of solutions b e g i n to dev i a t e f r o m t h e relations p r e d i c t e d b y t h e t h e o r y of dilute solutions. I t was s h o w n in p a r t i c u l a r [8] t h a t w i t h a certain c o n c e n t r a t i o n of P S in toluene a n inflexion is o b s e r v e d on t h e c u r v e (1/Rg0o)-C, where Rio° is t h e i n t e n s i t y of s c a t t e r i n g a t a n angle of 90 ° a n d c - - c o n c e n t r a t i o n . F o r P S w i t h M : 9 × l05 [8] inflexion corr e s p o n d e d to a 0.3~o c o n c e n t r a t i o n in toluene. This effect was essentially explained b y t h e f a c t t h a t a t t h e "critical c o n c e n t r a t i o n " i n d i c a t e d m a c r o m o l e c u l a r spheres begin to i n t e r a c t w i t h e a c h o t h e r a n d t h e solution ceases to be dilute. I t was interesting to establish t h e critical c o n c e n t r a t i o n for p o l y m e r m i x t u r e s . F i g u r e l a indicates t h a t w i t h low c o n c e n t r a t i o n s t h e curves coincide a n d a t a b o v e a certain c o n c e n t r a t i o n t h e y s e p a r a t e suddenly, light s c a t t e r i n g in m i x t u r e being c o n s i d e r a b l y higher t h a n in t h e solution of individual p o l y m e r s . Toluene was chosen as a s o l v e n t since its r e f r a c t i v e i n d e x is a l m o s t the s a m e as t h a t of P I B . Therefore, in a P S - P I B - t o l u e n e s y s t e m PS has t h e m a i n effect on scattering, since excess s c a t t e r i n g of P I B in toluene is close to zero. B e a r i n g in m i n d this f a c t w h e n a n a l y s i n g results in Fig. 1 it m a y be concluded t h a t s t a r t i n g f r o m a certain c o n c e n t r a t i o n P S m a c r o m o l e c u l e s in a m i x t u r e w i t h P I B begin to s c a t t e r light m u c h m o r e i n t e n s i v e l y t h a n in toluene. This can only be explained, in o u r view, b y the f a c t t h a t association of P S m a c r o m o l e c u l e s begins a t this c o n c e n t r a t i o n . W e therefore t e r m e d t h e c o n c e n t r a t i o n a t which curves begin to show incongruence for P S solution in toluene a n d in a solution of P I B in toluene, t h e c o n c e n t r a t i o n of initial association a n d d e n o t e d it as c~. I n Fig. lb t h e s a m e . e x p e r i m e n t a l d a t a are g i v e n in coordinates Kc/R~oo-C(where K is t h e c o n s t a n t in t h e e q u a t i o n of light scattering). I t is quite o b v i o u s t h a t t h e coordinates in Fig. lb are m o s t c o n v e n i e n t for d e t e r m i n i n g c o n c e n t r a t i o n c~. Values of c~ d e t e r m i n e d b y this m e t h o d are g i v e n in T a b l e 1. I t can be seen t h a t , as w i t h c2, the v a l u e of c~ increases w i t h a r e d u c t i o n o f t h e m o l e c u l a r weight of P S a n d decreases w i t h a red u c t i o n in affinity o f p o l y m e r a n d solvent, which is in a g r e e m e n t w i t h general views concerning t h e relations of association of p o l y m e r s in solution.
1022
V.N. KULEZNEVand L. S. KROKHINA
According to information previously obtained [8], the critical concentration of PS in toluene exceeds the value of c~ determined by the authors for a P S - P I B mixture. I t is impossible to make a quantitative comparison of these two values as in previous experiments [8] the solution only contained PS with M----9× 106 and in our experiments PS was mixed with P I B of high molecular weight (3 × ]0 s) which in itself could reduce the value of c1. At the same time, there is also another cause for the reduction of c1, compared with critical concentration.
~, I00
/
? '!
8g
fg I
s.2
I
I
o.~
i
aps,g/dt
( i I I I
Jl
cl
]
o.2
I
[
I
t
o.s' ~s,~/d/
FIO. 1. Relation between R~. (a) and Kc/R~. (b) of PS solutions (1) and a PS-PIB mixture (2) in toluene and the concentration of PS; MwPs~ 5"5 × 105. I n the presence of a second polymer, which has a low affinity for the first polymer, the number of segmental contacts of different macromolecules decreases thus, consequently, reducing the free volume in which molecules of each polymer can be located in solution. A reduction of free volume in a polymer mixture has the result t h a t the association of homogeneous macromolecules commences at a lower concentration t h a n in the solution of polymer alone, consequently, cl should normally be lower than the critical concentration determined for individual polymers. This fact ought to be emphasized specially since without giving sufficient attention to the specific properties of curves similar to curve 2 in Fig. la, the information concerning the molecular weight and dimension of molecules in the polymer mixture is inaccurate. The use of the theory of light scattering to block copolymer solutions, where association of units homogeneous in chemical composition should take place at very low concentrations, also requires special care from this point of view. I t should also be noted t h a t transition via cl with an increase in concentration
Structure formation in solutions of polymer mixtures
1023
causes a marked reduction in the second virial coefficient A~ [5]. Reduction of A~ is known to indicate a deterioration in the quality of solvent, which also confirms the assumption concerning a possible additional (excess) association of PS macromolecules in the presence of a. second polymer in the solution when c>cl. c, ~e/#t 2-4 2"0
~
/'6 /'2 0-8
"q
0.4 /
2
J 4 ~fw~ "fO -5
5
Fro. 2. Concentration limits of the existence of solutions of PS and P I B mixtures (7 : 3) in thr~e structural states according to Mwps: / - - i s o l a t e d macromolecules; / / - - a s s o c i a t e s in solution, I I I - - t w o - p h a s e solutions
Data obtained enable the entire range of concentrations, which contains solutions of polymer mixtures, to be separated into three ranges, according to polymer molecular weight. Figure 2 shows the dependence on the molecular weight of PS of cl and c2 of a P S - P I B - t o l u e n e system. When c
1024
V.N.
KULEZNEV and L. S. KROKHINA
of PS established by using the Zimm diagram. This can be done for different concentrations of the polymer solvent and the variation of molecular weight and dimensions ascertained of PS sphere according to P I B concentration in solution. We recall t h a t this experiment is possible when excess scattering of the polymer forming the polymer solvent (PIB), is practically zero.
The Zimm diagrams for a PS and P I B mixture were greatly distorted at lfigh concentrations. However, at low concentrations and small angles reliable extrapolation to zero angle and zero concentration could be made to determine sphere dimensions (~2)~ and the molecular weight of PS for different concentrations of polymer solvent (Table 2). TABLE 2. VALUES OF
.~1w,A~ AND
T H E D I M E N S I O N OF P S .-~IACROMOLECULES "[--~TOLUEI~E AND I N A P O L Y M E R SOLVENT
(PIB solution in toluene) Specimen, No.
Concen10 4 Radius tration A 2 × of inerPIB, tia, A
Specimen,
No.
g/d]
0 0.13 0.225
4"55 0"19 0"16
434 434 495
960
Concentration PIB, g/dl 0 0.1 0-2 0.3
A 2×
10 4 Radius of ineri tia, A
3"3 0-9 0.9 --0.3
620 620 720 848
(h~)l/2, h 1520
The molecular weight of specimen I is 6-45x105, specimen 2-9.55×105.
It can be seen that with an increase in the concentrations of the polymer solvent there is no association of PS macromolecules indicated b y constant molecular weight of PS. With low concentrations of P I B no changes are observed in sphere dimensions (radius of inertia). This is attributed to the view that with solution concentrations of less than cl molecules of PS and P I B are fairly distant from each other and have no mutual effect to the extent required for increasing the degree of association on changing sphere shape. I f the concentration of P I B in a polymer solvent becomes equal to or exceeds cl, the dimension of the PS sphere increases, molecular weight remaining constant. This takes place when the concentration of the initial solution of the polymer mixture before dilution with a polymer solvent becomes much higher than the concentration of initial association. B y diluting this solution with a polymer solvent we reduce the concentration of PS in the mixture. Dilution of PS with a polymer solvent results in the decomposition of PS associates to individual macromolecules (molecular weight of PS does not increase in the polymer solvent), however, a high concentration of P I B increases the dimensions of macromolecular spheres of PS. Results obtained m a y be explained as follows. With a solution concentration higher than c~ (but less than c2) molecular spheres of different polymers can pene-
Structure formation in solutions of polymer mixtures
1025
trate each other. This is quite possible since the solution in this range of concentration is single-phase and consequently, there is no physical interface between spheres of different polymers or polymer associates. It m a y thus be considered that in a single-phase solution of a polymer mixture inside a polymer sphere considerable segmental concentration is established of another polymer. Owing to preferential contacts between homogeneous segments, interaction of diffeIent segments will be equivalent to repulsion. Owing to the presence of P I B segments both outside and inside the PS spheres, the latter may either expand or be compressed according to whether the resulting effect of P I B segments is directed inside or outside the sphere. In our case the PS sphere expands increasing dimensions and thus this "expanded" macromolecule is prepared for association with similar ones, which takes place with a higher PS content in solution. In other cases [9] a reduction was observed in the polymer sphere on increasing the concentration of a "polymer" solvent. However, Kuhn established that there are more spheres in a "polymer 0 solvent than in a low molecular weight 0 solvent" [9].
,0~0
~d'Ob
PO,/.O
0"8
0"0
0"4
0"2
O PZB
FIG. 3. Relation between R"m. and the ratio of polymers for solutions and mixtures of P S - P I B (1--4) with a constant solution concentration of 0.5 (a) and 0.2 g]dl (b) with Mrs × l0 s = 5 . 5 (1), 2.2 (2), 1.2 (3) and 0-65 (4) and R"g0. for PS solutions in toluene (1'-4').
A s u b s e q u e n t s t a g e o f the s t u d y w a s t o e x a m i n e m a c r o m o l e c u l a r a s s o c i a t i o n o f P S in t h e c o n c e n t r a t i o n r a n g e cz--c2. All iso-refractive s o l v e n t w a s u s e d in this case. F i g u r e 3 s h o w s t h e relation b e t w e e n excess scattering a n d t h e P S : P I B
1026
V. ~'. KULEZNEVand L. S. Y~tOKHINA
ratio in solutions of different concentrations and different molecular weights of PIB. The excess scattering of P I B in toluene may therefore be ignored, the experimental scattering of PS and P I B mixtures should be compared with the scattering of PS in a toluene solution with a concentration equal to its partial concentration in a mixture with PIB. Broken lines in Fig. 3 represent experimental values of R~0o for PS in toluene with a concentration equal to its partial concentration in the mixture. The difference between scattering of PS in a mixture and scattering in toluene is due to excessive association of PS in the presence of PIB, compared with association of PS in toluene with the same concentrations of PS in both cases. The dimensions of associates cannot be theoretically determined in solution of finite concentration from data of light scattering, excessive scattering can therefore be compared only qualitatively with the dimensions of associates. I n our opinion, macromoleeular association of PS is the only cause of excessive scattering of PS in the presence of P I B in toluene solution. The more light scattering of PS in toluene in the presence of P I B exceeds the corresponding value of light scattering of PS in toluene with the same concentrations of PS, the higher the association of PS. We therefore used excess light scattering as a measure of excess association with a ratio of polymers in solution of PS : P I B ~- 7 : 3. The ratio of polymers was here selected to ensure a maximum excess of scattering for a given system. I t was interesting to determine the relation between AR~0o and the concentration of the solution of a polymer mixture with a given constant ratio in the mixture. Figure 4 shows t h a t excess light scattering increases with an increase in the concentration of the polymer mixture in solution and with an increase in molecular weight of PS. The relation between AR~0° and solution concentration is shown by a straight line which intersects the abscissa axis when c-~cl. This once more underlines the fact t h a t excess association of PS due to the presence of PIB, begins when c : c l and further increases with concentration up to c2, when PS associates reach this value and the density of the polymer material contained, so t h a t an interface is formed between heterogeneous associates and the solution is separated into two phases in micro-volumes. Association in a polymer mixture in solution, which begins with a concentration of initial association c~, takes place on increasing concentration and is completed by micro-stratification with a concentration corresponding to maximum stratification c2. Various polymers, according to chemical nature, molecular weight, type of solvent and other factors have very different c~ and c~ values and the smaller the c~-c~ concentration interval, the greater will be the increase in the apparent size and density of associates with an increase in concentration. All this suggests t h a t there are some relevant (equivalent) states of association in the polymer mixture in the range of single-phase solutions. I f the solution has a certain concentration, which is precisely in the middle of the c~-c~ range, the other pair of polymers in solution with a different concentration,
1027
Structtu'e formation in solutions of polymer mixture's
b u t also situated in the middle of the cl--c2 range, should be characterized by equivalent association. This assumption was not so far verified using completely different polymer pairs, since excess scattering in the various pairs depends on the increment of the refractive index of polymers and on the effect of each polymer on scattering. 40 > v
%
'Y~/
~2 o4
i 04
O'3 FxG.
4
o,u/d/
0.5
O.[
O.2
I-0 c a
FIG. 5
FIo. 4. Concentration dependence of excess scattering AR"~. of PS mixed with PIB (PS : :P~B=7:3), compared with an individual PS solution; MpsX105=5.5 (1, 5); 2.2 (2); 1.2 (3) and 0-65 (4); 1-4--solutions in toluene; 5--in CC1,. Fro. 5. Relation between excess scattering of PS in a mixture with PIB and the reduced concentration c*=(c--cl)/(cz--c,) when Mps×105=5-5 (1), 2.2 (2), 1.2 (3) and 0.65 (4). The accuracy of the assumption of the existence of corresponding states of association in solutions of polymer mixtures was demonstrated in this s t u d y with PS specimens of high molecular weight. Figure 5 plotted according to d a t a of Fig. 4 indicates the relation between excess light scattering AR'9'oo and concentration c*=(c--cl)/(c--c~). Reduced concentration is a measure of the corresponding state of association of the polymer mixture in solution. Solutions with different weight concentrations, but with the same reduced concentration should have a similar, or even identical excess association. The Figure illustrates this assumption: the dependence of excess scattering on reduced concentration is expressed by a single straight line, independent of the molecular weight of PS, i.e. independent of the values of cl and c~. I t may thus be assumed from results t h a t the same excess scattering near the point of stratification for all PS specimens corresponds to the same degree of association and density of polymer material in associates, which are required to form an interface between associates of different polymer molecules, i.e. to separate the solution into two phases. For comparison, Fig. 4 shows the relation between excess scattering and reduced concentration for a solution of a PS and P I B mixture in CC14. Excess scattering in this solvent is much higher than in toluene which is, apparently,
1028
V.N. K~zz~mv
and L. S. K R O X m ~ A
the consequence not only of a higher refractive index of PS in this solvent, but also a considerable excess light scattering due to PIB in this case. Data obtained by light scattering were confirmed viscometrically. Relative viscosity t/re,of solution mixtures with a different ratio of polymers was determined at constant concentration using a capillary viscometer. In studying the relation between any properties of the mixture and composition considerable difficultiesare involved in explaining the type of theoretical relation between property and composition, i.e. the relation which would be observed without a specific interaction between heterogeneous polymers. These difficultiesare also experienced in interpreting viscosity data. It is quite obvious that viscosity is not an additive property and the structural behaviour of a polymer mixture cannot therefore be evaluated from the deviation of experimental viscosities from additive values. W e have proposed two methods for deriving a theoretical relation between viscosity and composition. In the first ease [10] an equation was used tlsp=Lco~Nco1+P, where r&p is the specific viscosity of the solution of polymer mixture, Wl is the gravimetric proportion of one of the polymers in the mixture, L, N and P are coefficients dependent on polymer molecular weight, concentration in solution and the Huggins constant /c'in the equation showing the concentration dependence of viscosity. This equation is correct in a limited range of concentrations. Another equation was derived for a mixture of polymer melts [II] which can, in principle, be used for a solution mixture of any concentration. The equation takes the form
(1) where ~/ is the initial Newtonian viscosity of the melt of the polymer mixture; ~/1 and t/2 are the viscosities of components and ~-exponent in the equation ~I=KM". Equation (1) can be fairly accurately approximated by a straight line in logarithmic coordinates showing viscosity against composition (log ~/-w). This is in agreement with the N i n o m i y a - F e r m y equation [12] showing logarithmic additivity for a mixture of polymer fractions and with the empirical equation to calculate the viscosity of a plasticizer mixture [13]. The viscosity of the polymer-polymer-solvent system can also be calculated from the law of logarithmic additivity of viscosity as the viscosity of a mixture of two liquids, each of which is a polymer solution in a low molecular weight solvent. Figure 6a shows that the variations between experimental and calculated values, according to the rule of logarithmic additivity, increase with an increase in solution concentration. The variations in Fig. 6b are shown according to solution concentration. The straight line zt log ~rel-c intersects the abscissa at a point which corresponds to a solution concentration of 0-2 g/1. This point m a y be regarded as the concentration of initial association Cl obtained from viscosity data. In Table 1 the value of Cl for this system is 0.09, i.e. an increased concentration value of initial association is obtained from viscosity.
1029
S t r u c t u r e f o r m a t i o n in solutions of p o l y m e r m i x t u r e s
The relationship observed is quite natural bearing in mind that part of the associates may decompose in the process, particularly at low concentrations at which association only begins. This effect is similar to the influence of shear stress on maximum stratification of the solution of polymer mixture c2 [14], when shear deformation of the solution increases the concentration of stratification.
0-5 O.4 P~'I O
0.8
0.6" 0.4
Q'2
OPIB
c,s,/dl
O'8
FIG. 6. R e l a t i o n b e t w e e n log 1/re1 a n d the ratio of PS ( ~ w P s = 5.5 × 10 ~) a n d P I B in solution m i x t u r e s i n t o l u e n e a t P S c o n c e n t r a t i o n s of 0"8 (1), 0.6 (2), 0.4 (3}, 0.2 g/dl (4} {a) (the b r o k e n line shows the a d d i t i v e relations} a n d t h e relation b e t w e e n zllog/Trel a n d the solution conc e n t r a t i o n of PS a n d P I B m i x t u r e s (b).
Investigations of light scattering and solution viscosity of mixtures of two conventional apolar polymers of PS and PIB provide reliable proof of increased association in a solution of polymer mixture. There is no reason to believe that this effect is exceptional applying only to this particular pair of polymers. I t may be assumed that increased (excessive) association in a polymer mixture in solution characterizes most polymer mixtures, particularly those, which have similar properties to the PS-PIB pair examined. This effect can, at least, be regarded as an additional typical symptom of supermoleeular structures in solutions of apolar polymer mixtures, which have no polar functional groups ensuring strong interaction bet~'een heterogeneous macromolecules.
1030
V. N. K u ~ z N ~ . v and L. S. KROKm~A
When obtaining films of polymer mixtures from solution by gradually increasing concentration when the solvent is eliminated or when polymer melts are mixed and polymer relaxation times are rather short, in order to ensure structural change-over inside each polymer phase, increased association may be expected in each polymer and in the absence of solvent. Changes in the supermolecular structure of polymers during mixing were confirmed using a polyethylene and polypropylene mixture [3]. The interval between melting points and crystallization temperatures in the polyethylene and polypropylene phase in mixture became less compared with the appropriate intervals in polymers examined separately. A report has been made recently concerning the change in glass temperature in glassy polymer mixtures [15]. It may be assumed that a change in glass temperature is also the consequence of increased association (short-range order) in each polymer phase in the polymer mixture. We note the author's explanation [15], according to which displacement of the glass temperature of components in the mixture is attributed to the development of internal stress in a two-phase mixture on cooling. This is far from always being consistent with experimental facts. An increase in the degree of association in each polymer in the mixture, which was confirmed experimentally in our study, as previously, satisfactorily explains the results obtained by Flory [16], who pointed out that on mixing polymers (using polyethylene and P I B mixture), the entropy of the system does not increase but decreases. When large molecules are contained in the system, the effect of the combinatorial factor on entropy variation is low, as pointed out by Gee [17]. The presence of large flexible macromolecules results in association, i.e. an increase in the short-range order which, as pointed out by the authors, greatly increases in the presence of a second polymer. This fact should always be considered when analysing relations in the variation of the behaviour of polymers on adding a second polymer component, since a change in the supermolecular structure of the polymer on mixing may cause a marked change in the behaviour of each polymer phase in the polymer mixture. An increase in the short-range order in the system normally results in compression of the mixture and reduction in specific volume. However, in a twophase mixture, apart from compression of the polymer in each phase, the structure becomes looser as a result of segmental dissolving of polymers at the interface [18]. Breaking up the polymer (reduction of density) in the transitional layer at the interface and compressing the polymer in each phase by increasing the shortrange order--these are two processes which may as a result cause both an increase and a reduction in density on mixing polymers, compared with the additive value of density. This relation has previously been experimentally observed by the authors [19]. Finally, we note another conclusion which follows from this study. An increase in the degree of association of polymers in a mixture of polymer solutions
Structure formation in solutions of polymer mixtures
103I
on approaching maximum separation, is similar to association in individual polymer solutions when approaching critical temperature. The temperature dependence of several properties of polymer solutions separated is, in principle, similar to the concentration dependence of properties of the polymer mixture, as follows from a comparison of results of our studies and the studies carried o u t by Tager et al. [20]. CONCLUSIONS
(l) A study was made of light scattering and viscosity of polystyrene (PS) and polyisobutylene (PIB) mixtures in toluene, according to the molecular weight of PS and solution concentration. (2) In a mixture of PS and P I B an increase is observed in the dimensions of PS spheres on increasing the concentration of the polymer mixture provided t h a t the content of PS in the mixture is so low t h a t no molecular association takes place. (3) Single-phase solutions of polymer mixtures, according to concentration, are divided into two regions: a region characterized by the independent behaviour of different macromolecules (up to the concentration of initial association cl) and a region characterized by a high degree of association of homogeneous macromolecules (from c1 to m a x i m u m separation %). (4) A view is formulated concerning the interval of association cl--c2, in which processes of association develop resulting in stratification. The degree of association in this interval is determined by the reduced concentration, which functions as a parameter of corresponding states of association. By the moment of stratification the associates reach a certain size, independent of polymer molecular weight. (5) The concentration of initial macromolecular association cl, determined from solution viscosity exceeds the similar value determined from light scattering, which may be due to the effect of shear stress when determining viscosity, on the state of macromolecular aggregation in solution. (6) Increasing the short-range order in each polymer in the presence of a second polymer, m a y alter the properties of each polymer phase in the mixture in the absence of a solvent. Translated by E. SEVERE REFERENCES
1. S. P. PAPKOV, Fiziko-khimiohcskie osnovy pererabotki polimcrov (Physical and Chemical Principles of Processing Polymers). Izd. "Khimiya", 1971 2. T. V. DOROKHINA, A. S. NOIrIKOV and P. I. ZUBOV, Vysokomol. soyed. 1: 36, 1959 (Not translated in Polymer Sei. U.S.S.]~.); V. N. KULEZNEV, V. D. KLY]KOVAand B. A. DOGAI)KIN, Kolloidn. zh. 27: 139, 1965; M. KLrRBANALIEV, Dissertation, 1968; A. L. VOLYNSKII, Dissertation, 1971 3. G. V. VINOGRADOV, Yu. G. YANOVSKII, V. N. KULEZNEV a~ld T. A. IVANENKO, Kolloichl. zh. 28: 640, 1966 4. L. S. KROKItINA, Dissertation, 1971
1032
B. YA. TEITEL'BAUI~ and L. I. TUZOVA
5. V. N. KULEZNEV, L. S. KROKHINA, Yu. I. LYAKIN and B. A. DOGADKIN, Kolloidn. zh. 26: 475, 1964 4}. V. N. KULEZNEV, L. S. KROKHINA, Yu. G. OGANESOV aud L. M. ZLANTSEN, Kolloidu. zh. 33: 98, 1971 7. P. DOTY a n d R. STEINER, J. Polymer Sci. 5: 383, 1950 2. V. Ye. ESKIN a n d A. Yc. NESTEROV, Kolloidm zh. 28: 904, 1966; R. K U H N a n d H. J. CANTOW, Makromolek. Chem. 122: 65, 1969; H. I. HUDE aud A. G. TANNER, J. Colloid and Interface Sci. 28: 179, 1968 ~10. V. Ye. GUL', Ye. A. PENSKAYA a n d V. N. KULEZNEV, Kolloida. zh. 27: 341, 1965 11. V. N. KULEZI~EV, I. V. KONYUKH, G. V. VINOGRADOV a n d I. P. DMITRIEVA, Kolloidn. zh. 27: 540, 1965 12. K. NINOMIYA a n d J. FERRY, J. Colloid Sci. 18: 421, 1963 13. K. TINIUS, Plastifikatory (Plasticizers), Izd. " K h i m i y a " , 1964 14. V.N. KULEZNEV and L. B. KANDYRIN, Kolloidn. zh. 31: 245, 1969; V. N. KULEZNEV, L. B. KANDYRIN, L. S. KROKHINA and Ye. F. BUKANOVA, Kolloidm zh. 33: 589, 1971 15. R. MURAKAM], Kobunsi kagaku, Chem. High Polymer 27: 878, 1970 16. P. FLORY, B. E. EICHINGER a n d R. A. ORWOL, Maeromolecules 1: 287, 1968 17. G. GEE, Quart. Revs. London. Chem. Soc. 1: 265, 1947 18. V. N. KULEZNEV, V. D. KLYKOVA and B. A. DOGADK[N, Kolloidn. zh. 30: 255, 1968 19. V. N. KULEZNEV a n d K. M. IGOSHEVA, Vysokomol. soycd. 4: 1858, 1962 (Not translated in Polymer Sci. U.S.S.R.) 20. V. M. ANDREYEVA, A. A. ANtKEYEVA, S. A. VSHIVKOV and A. A. TAGER, Vysokomol. soyed. B12: 789, 1970 (Not translated in Polymer Sci. U.S.S.R.)
MULTIPLICITY OF DTA PEAKS AND CRYSTALLIZATION PHENOMENA DURING MELTING OF POLYMERS* B. YA. TEITEL'B~.U1K and L. I. TuzovA A. Ye. Arbuzov Institute of Organic a n d Physical Chemistry
(Received 6 July 1971) ~rHE problem of the causes of formation of multiple peaks of melting on thormograms of crystalline polymers is extensively discussed in the literature; there are dozens of differon~ explanations of this fact (Table). I t is quite evident t h a t there is no universal explanation since this phenomenon m a y in fact be the result of different causes in different cases. We would like to deal with one which is not always given sufficient a t t e n t i o n - - t h e problem of recrystaltization processes during partial melting [25, 26]. This factor is, in our opinion, of such general significance that in seeking to explain the existence of multiple DTA peaks, the effect of recrystallization processes should first be .excluded. I n m a n y cases rccrystallization and other factors accounting for multiplicity are m u t u a l l y superimposed. These processes in the purest form can be observed in the case ~ f homopolymcrs rendered amorphous, which crystallize while recording the thermograms. * Vysokomol. soyed. A15: :No. 4, 917-922, 1973.