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Viscosity studies of filled oligo-ester melts
VISCOSITY STUDIES OF FILLED OLIGO-ESTER MELTS* YU. S. LIPATOV, V. P. PRIVALKO a n d V. F . SHUMSKII High Polymer Chemistry Institute, Ukr.S.S.R. Academy of Sciences
(Received 3 January 1972) The viscosities of the oligo-ester (OE) melts containing various amounts of aerosfl were studied over a wide range of temperatures. The thickness of the boundary layer of the oligomer was evaluated on the solid particles. The analysis of the temperature dependence of viscosity forms the basis of the assumption that glass formation and an "iso-entropic" transition applies to the filled polymers.
THE viscosity of filled polymer melts has been studied before [1-5]. The behaviour of the filled polymer compositions was found to differ substantially from that predicted on the basis of existing hydrodynamic theories for the viscosities of solid particle suspensions [6] as a result of the adsorption of polymer on the surface of the filler particles [3-5], although the activation energy of viscous flow of filled and unfilled systems remained almost the same [1-3]. It should
FIG. 1. Electron-photomicrograph of an EA-2770 sample filled with 10% aerosil (Magn. x 10,000).
be noted, however, that these results had been obtained by measurements within a narrow range of temperatures on polymers with molecular weights (mol.wt.) well above those critical for "contact" formation [6]. We therefore wished to find out how filled systems would behave in the mol.wt, range below the critical (using oligomers). * Vysokomol. soyed. AIS: No. 9, 2106-2109, 1973. 2386
Viscosity studies of filled oligo-ester melts
2387
EXPERIMENTAL The study objects were the oligo-ethylene glycol adipate (EA-2770) with a mol.wt. M ~ 2 7 7 0 , a n d the oligotetramethylene glycol (TMG-3700) with M = 3 7 0 0 , containing 1.5 a n d 10yo w/w aerosil. The viscosities of these oligomers were described elsewhere [7]. The aerosil type A-175 had a specific surface of 175 m2/g a n d was added to the oligomer melt by stirring it in at 80°C/1 hr. The electron-microscope studies of the filled samples were carried out after etching in a gas discharge. (The authors t h a n k L. I. Bezruk for the electronmicroscope studies of the filled oligomcrs). These showed the solid-phase particles, created b y these conditions a n d b y the aerosil concentrations used, to be 200-500/tl, which was evidence of good dispersion without a n y aggregation occurring (Fig. 1). The melt viscosities of the filled systems were determined in the range 20-160°C by varying the shear rate from 10 -3 to 101 see -1 on the apparatus described before [7]. The filled oligomers b e h a v e d like Newtonian liquids in this range of shear rates, as no structure formation took place with the aerosil at these ~ contents, as mentioned earlier.
RESULTS
The viscosity as a function of filler content. The temperature dependence of the viscosity of filled oligo-esters (OE) shows a steady increase in viscosity with aerosil content (Fig. 2). The dependence of ~ of the liquid on the solid phase LZ
b /
2
74
0 2.2
I
J-O
J.,~
Z.S
3"0 /0 ~/'~°R-~
Fro. 2. The temperature dependence of the melt viscosity of: a--EA-2770; b--TMG-3700 with aerosil contents (~oW/W) of: 1--0; 2--1; 3--5; 4--10.
content by volume ~ is normally described by the Einstein equation ~~-~o(1 -]- 2-5 ~), or that of Simha-Gut y----y0(l~2.5~-14.1@~), or of Mooney ~-~/0exp [(2.5~/ /(1--]¢~)] and others [1] (70 is here the viscosity of the pure liquid, k a constant ----1.35-1.9). One can show that the experimentally determined ~/~o values increase much more rapidly with increasing q than is predicted by the abovementioned equations. This behaviour, observed earlier on high polymers of different chemical composition [3-6], is evidence for an apparent increase of the
Yu. S. LIPATOVet al.
'2388
disperse phase q u a n t i t y as a result o f the adsorbed oligomer layer f o r m a t i o n ~)n t h e surface o f the aerosil particles. The a m o u n t o f oligomer present as a b o u n d a r y layer, d ~, can be assessed f r o m the e x p e r i m e n t a l results b y regarding in t h e theoretical equations as the t r u e (total) a m o u n t o f solid phase containing b'K
To,°K
180
o
I
0.75
I
I
f'O
I
O.75
f'O Pz
Fro. 3. Parameters To and B as functions of ~2 for: I--EA-2770; 2--TMG-3700.
t h e adsorbed oligomer layer, i.e. that ~----{ao+Aia, in which 9o is the "true" aerosil quantity of the system. The q- and d c-values calculated from the experiments! results in accordance with the Mooney equation (for k~=l.5) are listed in the Table. THE
P A R A M E T E R S OF T H E ~ O 0 1 ~ E Y AND OF T H E V O G E L - - T A M M A N E Q U A T I O N S AS A F U N C T I O N OF A E R O S I L CONTENT
Aerosfl Oligo-ester
content,
A9
To p OK
0 0.005 0.155 0.30 0 0.005 0.18 0.30
175 175 165 155 150 150 130 120
B, °K
A
~2
--4.76 --4.80 --4.11 --2.87 --4.46 --4-54 -- 3.50 --2.27
1.0 0.995 0.845 0.70 1.0 0.995 0.82 0.70
% w/w EA-2770
TMG-3700
0 1 5 10 0 1 5 10
i
0 0.01 0.18 0.355 0 0.01 0.20 0"345
1260 1280 1330 1420 1380 1400 1490 1510
0.032 0.031 0.033 0.043 0.025 0.025 0.037 0.043
Our findings show t h a t EA-2770 and TMG-3700 are subject to a p p r o x i m a t e l y t h e same changes in d ~ w h e n the aerosfl c o n t e n t is increased; this is due to the similar mol.wt, o f these oligomers. T h e thickness o f the adsorbed (boundary) l a y e r Ar o f macromolecules can be d e t e r m i n e d from: q~/9o-~V/Vo=(r+Ar)3/r3, in which V0 a n d r - - v o l u m e a n d d i a m e t e r of the particles respectively. As Fig. 1 shows, the average d i a m e t e r 2r o f the aerosil particles is a b o u t 250 A in our case. B y using the t a b u l a t e d values o f ~ and qo we get dr----120-140 A for b o t h t h e s y s t e m s (at 120°C).
Viscosity studies of filled oligo-ester melts
2389
The comparison of the Ar with those determined by an independent method was of interest. A calorimetric evaluation of A~ according to A q ~ 1--ACACo, in which AC, AC0--heat content differential at the glass temperature Tg of two amorphized EA-2770 samples, one unfilled, the other containing 10 parts of aerosil, had been suggested in earlier work [8, 9]. (Additional crystallization of the filled sample was avoided during cooling [10] by precooling the calorimeter to below the Tg of the polymer). The experimental calorimetry showed the Tg of the filled and unfilled samples to be practically the same (--56 and --55°C respectively), which is typical for polymers with flexible chains [9]. The ACo- and AC-values were 0.138 and 0.098cal/g.°C respectively. The insertion of these values in the earlier given equation yielded A~a:0.29, which agrees with the viscometric A~a of 0.30 (see Table). The temperature-viscosity func,tion of filled systems. Figure 2 shows the log g1/T functioh to be non-linear for the unfilled as well as filled oligomers [7]. The Vogel-Tamman equation: In g~A-kB/(T--To) is widely used [11] to describe .the non-Arrhenian behaviour of the viscosity. The processing of our experimental results by using this equation led to the empirical parameters A, B and To listed in the Table. Figure 3 shows the dependence of parameters B and T o on the amount of polymer not bound to the filler surface, i.e. q ~ 1--A ~. The data given in the Table and in Fig. 3 make it clear that this dependence is linear in the studied range of filler contents, which is expressed by the equations To~--x-~-yq~2, and B :x'-ky'q~, for which the numerical values of the coefficients are (°K): x~175, y------ 67, x ' : 1260, y'~-515 (for systems based on EA-2770), and x ~ 150, y = -- 101, x'----1380, y'~490 (for systems based on TMG-3700). This means that a ~-decrease will produce a linear decrease of T o, and increases of B and A for both the systems. As the apparent activation energy of viscous flow (temperaturedependent) Ea is linked with parameters B and T o by the function Ea-~RB[T/ ](T--To)] ~ [11, 12], it follows from our results that the B-increase due to the filler addition will be almost compensated at sufficiently high temperatures (T>>To) by the To in the numerator of the above equation for Ea, so that this value will be similar for filled and unfilled systems. This conclusion agrees with the findings of others [1-3]. One can expect at the same time that a temperature reduction will produce a noticeable decrease of Ea due to a (T--To) increase, when the filler is added; this can be physically explained by the greater ease of molecular movement as a result of the free volume increase in the filled system. This conclusion is formally confirmed by the calculations of the "apparent" free volume present at the Tg, i.e. in fg~(Tg--To)/B [12], which is also given in the Table. Please note that the fg increases parallel with A~, which means that the packing density of the macromolecules in the boundary layer is less than in the rest of the polymer bulk. Similar results were got in other studies
[9, 13]. Attention is drawn to the earlier mentioned fact of the agreement between the
2390
"Yu. S. LIPATOVet al.
Tg-values of filled und unfilled EA-2770, in which the filled system contained 10% aerosil. As only insignificant Tg changes occurred in a number of polymer systems on adding the filler [9], disregarding its loosening effect on packing density in the boundary layer and the consequent increase of the free volume at T~ (see [9] and also the tabulated values), one can assume that the macromolecules present in the boundary layers do not participate in the glassification [8, 9]. This means t h a t the criterion for the constancy of the free volume at T~ is not valid in the case of filled polymers [14]. The thermodynamic approach is preferable, i.e. t h a t glassification will occur when the system reaches some minimal configurational entropy AS~ [15]. This value can be calculated at T~ from ASg=AC.ln Tg/To [15]. Insertion of the numerical values of the parameter into this formula for the unfilled EA-2770 and for one filled with 10% aerosil showed that ASg was about the same in both cases, i.e. 5.1 and 5.5 cal/mole. °C respectively. The theories about glass formation as well as of an "iso-entropie" transition are thus probably valid for both, unfilled and filled polymer systems. Translated by K . A. A L I E ~
REFERENCES 1. (L KRAUS (Ed.), Sb.: Usilenie elastomerov (The Reinforcement of Elastomers.) Izd. "Khimiya", 1968 2. (L V. VINOGRADOV, A. Ya. MALKIN, Ye. P. PLOTNIKOVA, O. Yu. SABSAI and N. Ye. NIKOLAYEYA, Sb.: Problema teplo- i massoperenosa (In: Problems of Heat- and Mass-transfer). p. 222, Izd. "Energiya", 1970 3. G. M. BARTENEV and N. V. ZAKHARENKO, Kolloid. zh. 24: 121, 1962 4. P. P. A. SMIT, Reol. Acta 8: 277, 1969 5. V. V. GUZEYEV, Yu. M. MALINSKII, M. N. RAFIKOV, G. P. MALYSHEVA and V. S. KOVAL'CHIIK, Plast. massy, No. 2, 60, 1969 6. G. KRAUS, Rubber Chem. and Technol. 38: 1070, 1965 7. Yu. S. LIPATOV, V. P. PRIVALKO and V. F. SHUMSKII, Vysokomol. soyed. AI4: 764, 1972 (Translated in Polymer Sci. U.S.S.R. 14: 4, 848, 1972) 8. V. P. PRIVALKO, Yu. S. LIPATOV, Yu. Yu. KERCHA and L. V. MOZZHUKHINA, Vysokomol. soyed. A13: 103, 1971 (Translated in Polymer Sci. U.S.S.R. 13: 1, 119, 1971) 9. Yu. S. LIPATOV and V. P. PRIVALKO, Vysokomo]. soyed. A14: 1643, 1972 (Translated in Polymer Sci. U.S.S.R. 14: 7, 1843, 1972) 10. V. P. PRIVALKO, Yu. S. LIPATOV and Yu. Yu. KERCHA, Vysokomol. soyed. A l l : 237, 1969 (Translated in Polymer Scl. U.S.S.R. 11: 1, 266, 1969) 11. G. S. BERRY and T. G. FOX, Advances Polymer Sei. 5: 261, 1968 12. A. A. MILLER, J. Polymer Sei. A2: 1095, 1964 13. Yu. S. LIPATOV, Fiziko-khimiya napolnennykh polimerov (The Physical Chemistry of Filled Polymers). Izd. "Naukova dumka", 1967 14. R. F. BOYER, Rubber Chem. and Technol. 36: 1303, 1963 15. G. ADAM and J. H. GIBBS, J. Chem. Phys. 43: 189, 1965
(Received 3 January 1972) The viscosities of the oligo-ester (OE) melts containing various amounts of aerosfl were studied over a wide range of temperatures. The thickness of the boundary layer of the oligomer was evaluated on the solid particles. The analysis of the temperature dependence of viscosity forms the basis of the assumption that glass formation and an "iso-entropic" transition applies to the filled polymers.
THE viscosity of filled polymer melts has been studied before [1-5]. The behaviour of the filled polymer compositions was found to differ substantially from that predicted on the basis of existing hydrodynamic theories for the viscosities of solid particle suspensions [6] as a result of the adsorption of polymer on the surface of the filler particles [3-5], although the activation energy of viscous flow of filled and unfilled systems remained almost the same [1-3]. It should
FIG. 1. Electron-photomicrograph of an EA-2770 sample filled with 10% aerosil (Magn. x 10,000).
be noted, however, that these results had been obtained by measurements within a narrow range of temperatures on polymers with molecular weights (mol.wt.) well above those critical for "contact" formation [6]. We therefore wished to find out how filled systems would behave in the mol.wt, range below the critical (using oligomers). * Vysokomol. soyed. AIS: No. 9, 2106-2109, 1973. 2386
Viscosity studies of filled oligo-ester melts
2387
EXPERIMENTAL The study objects were the oligo-ethylene glycol adipate (EA-2770) with a mol.wt. M ~ 2 7 7 0 , a n d the oligotetramethylene glycol (TMG-3700) with M = 3 7 0 0 , containing 1.5 a n d 10yo w/w aerosil. The viscosities of these oligomers were described elsewhere [7]. The aerosil type A-175 had a specific surface of 175 m2/g a n d was added to the oligomer melt by stirring it in at 80°C/1 hr. The electron-microscope studies of the filled samples were carried out after etching in a gas discharge. (The authors t h a n k L. I. Bezruk for the electronmicroscope studies of the filled oligomcrs). These showed the solid-phase particles, created b y these conditions a n d b y the aerosil concentrations used, to be 200-500/tl, which was evidence of good dispersion without a n y aggregation occurring (Fig. 1). The melt viscosities of the filled systems were determined in the range 20-160°C by varying the shear rate from 10 -3 to 101 see -1 on the apparatus described before [7]. The filled oligomers b e h a v e d like Newtonian liquids in this range of shear rates, as no structure formation took place with the aerosil at these ~ contents, as mentioned earlier.
RESULTS
The viscosity as a function of filler content. The temperature dependence of the viscosity of filled oligo-esters (OE) shows a steady increase in viscosity with aerosil content (Fig. 2). The dependence of ~ of the liquid on the solid phase LZ
b /
2
74
0 2.2
I
J-O
J.,~
Z.S
3"0 /0 ~/'~°R-~
Fro. 2. The temperature dependence of the melt viscosity of: a--EA-2770; b--TMG-3700 with aerosil contents (~oW/W) of: 1--0; 2--1; 3--5; 4--10.
content by volume ~ is normally described by the Einstein equation ~~-~o(1 -]- 2-5 ~), or that of Simha-Gut y----y0(l~2.5~-14.1@~), or of Mooney ~-~/0exp [(2.5~/ /(1--]¢~)] and others [1] (70 is here the viscosity of the pure liquid, k a constant ----1.35-1.9). One can show that the experimentally determined ~/~o values increase much more rapidly with increasing q than is predicted by the abovementioned equations. This behaviour, observed earlier on high polymers of different chemical composition [3-6], is evidence for an apparent increase of the
Yu. S. LIPATOVet al.
'2388
disperse phase q u a n t i t y as a result o f the adsorbed oligomer layer f o r m a t i o n ~)n t h e surface o f the aerosil particles. The a m o u n t o f oligomer present as a b o u n d a r y layer, d ~, can be assessed f r o m the e x p e r i m e n t a l results b y regarding in t h e theoretical equations as the t r u e (total) a m o u n t o f solid phase containing b'K
To,°K
180
o
I
0.75
I
I
f'O
I
O.75
f'O Pz
Fro. 3. Parameters To and B as functions of ~2 for: I--EA-2770; 2--TMG-3700.
t h e adsorbed oligomer layer, i.e. that ~----{ao+Aia, in which 9o is the "true" aerosil quantity of the system. The q- and d c-values calculated from the experiments! results in accordance with the Mooney equation (for k~=l.5) are listed in the Table. THE
P A R A M E T E R S OF T H E ~ O 0 1 ~ E Y AND OF T H E V O G E L - - T A M M A N E Q U A T I O N S AS A F U N C T I O N OF A E R O S I L CONTENT
Aerosfl Oligo-ester
content,
A9
To p OK
0 0.005 0.155 0.30 0 0.005 0.18 0.30
175 175 165 155 150 150 130 120
B, °K
A
~2
--4.76 --4.80 --4.11 --2.87 --4.46 --4-54 -- 3.50 --2.27
1.0 0.995 0.845 0.70 1.0 0.995 0.82 0.70
% w/w EA-2770
TMG-3700
0 1 5 10 0 1 5 10
i
0 0.01 0.18 0.355 0 0.01 0.20 0"345
1260 1280 1330 1420 1380 1400 1490 1510
0.032 0.031 0.033 0.043 0.025 0.025 0.037 0.043
Our findings show t h a t EA-2770 and TMG-3700 are subject to a p p r o x i m a t e l y t h e same changes in d ~ w h e n the aerosfl c o n t e n t is increased; this is due to the similar mol.wt, o f these oligomers. T h e thickness o f the adsorbed (boundary) l a y e r Ar o f macromolecules can be d e t e r m i n e d from: q~/9o-~V/Vo=(r+Ar)3/r3, in which V0 a n d r - - v o l u m e a n d d i a m e t e r of the particles respectively. As Fig. 1 shows, the average d i a m e t e r 2r o f the aerosil particles is a b o u t 250 A in our case. B y using the t a b u l a t e d values o f ~ and qo we get dr----120-140 A for b o t h t h e s y s t e m s (at 120°C).
Viscosity studies of filled oligo-ester melts
2389
The comparison of the Ar with those determined by an independent method was of interest. A calorimetric evaluation of A~ according to A q ~ 1--ACACo, in which AC, AC0--heat content differential at the glass temperature Tg of two amorphized EA-2770 samples, one unfilled, the other containing 10 parts of aerosil, had been suggested in earlier work [8, 9]. (Additional crystallization of the filled sample was avoided during cooling [10] by precooling the calorimeter to below the Tg of the polymer). The experimental calorimetry showed the Tg of the filled and unfilled samples to be practically the same (--56 and --55°C respectively), which is typical for polymers with flexible chains [9]. The ACo- and AC-values were 0.138 and 0.098cal/g.°C respectively. The insertion of these values in the earlier given equation yielded A~a:0.29, which agrees with the viscometric A~a of 0.30 (see Table). The temperature-viscosity func,tion of filled systems. Figure 2 shows the log g1/T functioh to be non-linear for the unfilled as well as filled oligomers [7]. The Vogel-Tamman equation: In g~A-kB/(T--To) is widely used [11] to describe .the non-Arrhenian behaviour of the viscosity. The processing of our experimental results by using this equation led to the empirical parameters A, B and To listed in the Table. Figure 3 shows the dependence of parameters B and T o on the amount of polymer not bound to the filler surface, i.e. q ~ 1--A ~. The data given in the Table and in Fig. 3 make it clear that this dependence is linear in the studied range of filler contents, which is expressed by the equations To~--x-~-yq~2, and B :x'-ky'q~, for which the numerical values of the coefficients are (°K): x~175, y------ 67, x ' : 1260, y'~-515 (for systems based on EA-2770), and x ~ 150, y = -- 101, x'----1380, y'~490 (for systems based on TMG-3700). This means that a ~-decrease will produce a linear decrease of T o, and increases of B and A for both the systems. As the apparent activation energy of viscous flow (temperaturedependent) Ea is linked with parameters B and T o by the function Ea-~RB[T/ ](T--To)] ~ [11, 12], it follows from our results that the B-increase due to the filler addition will be almost compensated at sufficiently high temperatures (T>>To) by the To in the numerator of the above equation for Ea, so that this value will be similar for filled and unfilled systems. This conclusion agrees with the findings of others [1-3]. One can expect at the same time that a temperature reduction will produce a noticeable decrease of Ea due to a (T--To) increase, when the filler is added; this can be physically explained by the greater ease of molecular movement as a result of the free volume increase in the filled system. This conclusion is formally confirmed by the calculations of the "apparent" free volume present at the Tg, i.e. in fg~(Tg--To)/B [12], which is also given in the Table. Please note that the fg increases parallel with A~, which means that the packing density of the macromolecules in the boundary layer is less than in the rest of the polymer bulk. Similar results were got in other studies
[9, 13]. Attention is drawn to the earlier mentioned fact of the agreement between the
2390
"Yu. S. LIPATOVet al.
Tg-values of filled und unfilled EA-2770, in which the filled system contained 10% aerosil. As only insignificant Tg changes occurred in a number of polymer systems on adding the filler [9], disregarding its loosening effect on packing density in the boundary layer and the consequent increase of the free volume at T~ (see [9] and also the tabulated values), one can assume that the macromolecules present in the boundary layers do not participate in the glassification [8, 9]. This means t h a t the criterion for the constancy of the free volume at T~ is not valid in the case of filled polymers [14]. The thermodynamic approach is preferable, i.e. t h a t glassification will occur when the system reaches some minimal configurational entropy AS~ [15]. This value can be calculated at T~ from ASg=AC.ln Tg/To [15]. Insertion of the numerical values of the parameter into this formula for the unfilled EA-2770 and for one filled with 10% aerosil showed that ASg was about the same in both cases, i.e. 5.1 and 5.5 cal/mole. °C respectively. The theories about glass formation as well as of an "iso-entropie" transition are thus probably valid for both, unfilled and filled polymer systems. Translated by K . A. A L I E ~
REFERENCES 1. (L KRAUS (Ed.), Sb.: Usilenie elastomerov (The Reinforcement of Elastomers.) Izd. "Khimiya", 1968 2. (L V. VINOGRADOV, A. Ya. MALKIN, Ye. P. PLOTNIKOVA, O. Yu. SABSAI and N. Ye. NIKOLAYEYA, Sb.: Problema teplo- i massoperenosa (In: Problems of Heat- and Mass-transfer). p. 222, Izd. "Energiya", 1970 3. G. M. BARTENEV and N. V. ZAKHARENKO, Kolloid. zh. 24: 121, 1962 4. P. P. A. SMIT, Reol. Acta 8: 277, 1969 5. V. V. GUZEYEV, Yu. M. MALINSKII, M. N. RAFIKOV, G. P. MALYSHEVA and V. S. KOVAL'CHIIK, Plast. massy, No. 2, 60, 1969 6. G. KRAUS, Rubber Chem. and Technol. 38: 1070, 1965 7. Yu. S. LIPATOV, V. P. PRIVALKO and V. F. SHUMSKII, Vysokomol. soyed. AI4: 764, 1972 (Translated in Polymer Sci. U.S.S.R. 14: 4, 848, 1972) 8. V. P. PRIVALKO, Yu. S. LIPATOV, Yu. Yu. KERCHA and L. V. MOZZHUKHINA, Vysokomol. soyed. A13: 103, 1971 (Translated in Polymer Sci. U.S.S.R. 13: 1, 119, 1971) 9. Yu. S. LIPATOV and V. P. PRIVALKO, Vysokomo]. soyed. A14: 1643, 1972 (Translated in Polymer Sci. U.S.S.R. 14: 7, 1843, 1972) 10. V. P. PRIVALKO, Yu. S. LIPATOV and Yu. Yu. KERCHA, Vysokomol. soyed. A l l : 237, 1969 (Translated in Polymer Scl. U.S.S.R. 11: 1, 266, 1969) 11. G. S. BERRY and T. G. FOX, Advances Polymer Sei. 5: 261, 1968 12. A. A. MILLER, J. Polymer Sei. A2: 1095, 1964 13. Yu. S. LIPATOV, Fiziko-khimiya napolnennykh polimerov (The Physical Chemistry of Filled Polymers). Izd. "Naukova dumka", 1967 14. R. F. BOYER, Rubber Chem. and Technol. 36: 1303, 1963 15. G. ADAM and J. H. GIBBS, J. Chem. Phys. 43: 189, 1965