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Comparison of some experimental methods of determining the molecular-weight distribution in polymers
Determining the molecular-weight distribution in polymers
2171
3. I. A. KRIVOSHEYEVA, A. I. RAZUMOV, B. Ya. TEITEL'BAUM and T. A. YAGFAROVA,
Vysokomol. soyed. 5: 160, 1963 (Not translated in Polymer Sci. U.S.S.R.) 4. A.N. PUDOVIK and R. G. KUZOVLEVA, Vysokomol. soyed. 6: 737, 1964 (Translated in Polymer Sci. U.S.S.R. 6: 4, 810, 1964) 5. C. L. ARKUS and R. J. S. MATTHEWS, J. Chem. See., 4607, 1956 6. B. Ya. TEITEL'BAUM, Peredovoi nauchno-tekhnicheskii i proizvodstvelmyi opyt. (Advanced Scientific and Commercial Experiment.) TslTEIN, Series 32, 1%o. 4, 2, 1961
COMPARISON OF SOME EXPERIMENTAL METHODS OF DETERMINING THE MOLECULAR-WEIGHT DISTRIBUTION IN POLYMERS* L. V. DUBROVIlVA, S. A. PAVLOVA a n d V. V. KORSHAK Institute of Elementary Organic Compounds, U.S.S.R. Academy of Sciences (Received 3 September 1965) MOLECULAR-WEIGHT distribution analysis is increasingly being used as a m e t h o d o f s t u d y i n g the f o r m a t i o n m e c h a n i s m o f a poIymer. T h e usual m e t h o d of determ i n a t i o n consists in p l o t t i n g integral a n d differential curves f r o m t h e results o f fractionation. Certain a s s u m p t i o n s are m a d e regarding t h e size o f t h e fractions. I t is a s s u m e d t h a t no f r a c t i o n contains molecules heavier or lighter t h a n t h e m e a n molecular weight o f t h e preceding or following one, i.e. t h a t t h e r e is some overlapping. As d e m o n s t r a t e d b y t h e e x p e r i m e n t s of [1], these assumptions r e d u c e the a c c u r a c y o f t h e results. A b e t t e r m e t h o d is t h a t of r a p i d s e d i m e n t a t i o n in an ultracentrifuge, which p r o d u c e s the molecular-weight value a n d molecular-weight distribution curve. W i t h a c o m b i n a t i o n o f f r a c t i o n a t i o n a n d s e d i m e n t a t i o n t h e molecular-weight d i s t r i b u t i o n can be more a c c u r a t e l y d e t e r m i n e d [2]. W e decided to c o m p a r e t h e molecular-weight distribution o f p o l y a r y l a t e s f r o m t h e results o f f r a c t i o n a t i o n a n d sedimentation, a n d also t h a t d e r i v e d f r o m the t o t a l distribution of the fractions with t h e distribution o f t h e initial, unfract i o n a t e d specimen. This paper gives the results of an investigation of polyarylates prepared by interfacial polycondensation of isophthalyl chloride and 2-phenyl-3,3-bis-(4-hydroxyphenyl)phthalimidine (polyarylate P-8) [3]. The fraetionation involved distribution between two liquid phases; the procedure and the optimum conditions for polyarylates have been described in [4]. This method is known to produce enough fractions for subsequent investigation, and still quite homogeneous. The fractions were studied by rapid sedimentation in an ultra* Vysokomol. soyed. 8: No. 11, 1965-1969, 1966.
2172
L. V. DUBROVINA eta/.
centrifuge and by intrinsic viscosity determination. The viscosity was measured in a viseometer with a "hanging,' level at 20±0.1 ° [5]. Tetrachloroethane and tetrahydrofuran were used as solvents. No independent molecular-weight measurements were made, a n d therefore the relation between a and the value of the side substituent at the central carbon atom of the bisphenol already found in [6] was used to find the parameters a and K~ in the Mark-ttouwinck equation. For the polyarylate produced b y interracial polyeondensation from the bisphenol and isophthalic acid this relation is given b y a~--0.77-0.86 log .M/Mo (M is the molecular weight of the unit with the substituent, M0 is t h a t of the u n i t without).
C
For a substituent molecular weight of 194 a was found to be 0.615 for polyarylate P-8. Then from the equation K = 0 . 2 6 8 (6"03X I0-5) a, suggested in [7], we were able to calculate the second parameter K~ of the Mark-Houwinek equation. The relation thus found is given by [t/]=6.82 x 104.M °'615 (tetrachloroethane as solvent). The molecular weight of the u n f r a c t i o n a t e d specimen calculated from this equation (M,~=17,600) is in good agreement with t h a t found by the light-scattering method (M w = 18,600), which proves the possibility of using the functions found for polyarylates. Knowing the parameters of the Mark-I-Iouwinck equation, M v of the fractions could then be calculated and the molecular-weight distribution curves plotted. The rapid sedimentation experiments were performed on an ultraeentrifuge type G-110 (Hungarian) (15,000 rpm, 20 °, tetra.hydrofuran as solvent). The variations in the solution concentration were recorded b y the optical system of the ultracentrifuge as differential curves of the refractive index, a n d from this we were able to calculate the sedimentation constant using the equation
where x~ a n d xl are the position of the boundary between solution and solvent at times tl a n d tl; W 2 is the angular velocity of the ultracentrifuge rotor. I n [7] it was found t h a t there was no concentration dependence for polyarylates, and therefore the value of S was taken as S0 (at c->0). The molecular weight was calculated from the sedimentation rate b y means of the Svedberg formula [8]:
M=
S RT D (1--~p)'
where R is the universal gas constant, T the absolute temperature, v the partial specific volume (0-760 for the system in question), p the density of the solvent (0.892 for tetrahydrofuran), D the diffusion coefficient which was calculated from the second moments (-~') of the experimental derivative curves from the graph [2] ~/2t vs. xm2.t (xm is the position of the peak on the derivative curves at time t). A c c o r d i n g t o t h e figures i n T a b l e 1, t h e d e r i v a t i v e - c u r v e m e t h o d o f f i n d i n g t h e d i f f u s i o n coefficient s e e m s t o g i v e e x a g g e r a t e d l y l o w v a l u e s , p a r t i c u l a r l y a t l o w m o l e c u l a r w e i g h t s . T h i s is b e c a u s e t h e d i f f u s i o n coefficient is u s u a l l y v e r y
Determining the molecular-weight distribution in polymers
2173
sensitive to the low molecular weight part, so that the beginning of diffusion is uncertain for low molecular weight fractions where the boundary is only slowly detached from the meniscus and the beginning of diffusion does not coincide with the moment when the derivative curve peak leaves the" meniscus. To calculate the diffusion coefficient we took the moment when the peak leaves the meniscus as the d a t u m time, using the graph In x ~t. The Gosting system [9] was used to plot the distribution curves, since the ambiguity in the starting time TABLE 1. M E A S U R E M E N T FOR P-8 S P E C I M E N
Frac- I tion ] No. l 1
2 3 4 5 6 7 8 9 10 11
[~/] TCE
[~] THF
0.135 0.156 0"160 0.165 0.225 0.294 0.337 0.345 0.373 0'482 0'502
0.130 0.146 0.148 0.152 0.193 0.225 0-254 0.257 0-275 0.329 0.338
Mv
S × 10 -13
5400 6900 7150 9100 12,400 19,400 24,000 25,000 28,300 42,900 47,600
2"089 2.426 2.190 2"392 2.78 3.00 3.605 3.841 3"960 4"953 5.30
Mww
a 2 × 10 ~
16,100 19,600 11,100 10,500 18,400 28,500 23,300 36,000 36,700 43,300 49,200
0.463 0.613 0'380 0.400 0.533 0.516 0.453 1.457 0.306 1.422 2.465
does not have such a big effect on the results. This method of converting sedimentation diagrams to differential distribution curves over sedimentation constants
~gs 08
0.4
i
~.o
l
~.s logM
FIG. 1. Sedimentation constants vs. molecular weight. is b a s e d o n t h e a s s u m p t i o n are independent:
that the shifts due to polydispersity and diffusion
~ = M4x~a2t~q- 2Dw t , the broadening of the curve due to diffusion being proportional to x/t-and that d u e t o d i s p e r s i t y p r o p o r t i o n a l t o t. A t t - > ~ t h e a p p a r e n t d i s t r i b u t i o n f u n c t i o n
2174
L . V . D~-~OVINA et
al.
q* (S)=(dc/dx) (Xmax !Xmen)~W2xt (1/%) is transformed to q (S) the true sedimentation constant distribution. Since the sedimentation constant is a function of the molecular weight, then according to the equations dc/dS-~(dc/dM) (dM/dS) and S-~KsM 1-b the distribution curves dc/ds~-f (S) are transformed to molecular-weight distribution curves
dc/dM----~ (M). The relation between S and M was established experimentally for polyarylate 1)-8 (Fig. 1) : S----6.55× 10-~.M 0"4. I t is interesting to compare Q~ (S) the distribution of the unfractionated specimen calculated b y the Gosting method, with the distribution obtained b y
/7'/ 2 \ /
,~~ ~ s
s 8 z i~
\
Z
3
~"
J
•
7 S
FIO. 2. Distribution curves of sedimentation constants of fractions of P-8. Fraction num. bers given on curves. the method of adding fractions [10], which consists in graphical summation of the partial distributions in order to get the total: n
Q~ (S)-~ ~ [q~ (S)]~. Figure 2 shows the S [qw(S)] distribution curves for 11 fractions of P-8, as calculated b y the Gosting method. The area below e a c h curve is equal to the weight fraction of the fraction in question. Then the ordinates of the curves qw (S) of individual fractions were summed for certain S values, to produce the Qw(S) curve of total distribution. Comparing the distributions shown: in Fig. 3, it can be seen that there is a difference between Qw(S) for the unfractionated specimen (curve 1) and that obtained b y adding together the fractions (curve 2). The first method gives quite a symmetrical curve and the second gives better resolution in the region of the high molecular weight peak (curve 2), making a difference in
Determining the molecular-weight distribution in polymers
2175
Q(s)
O2
2
4
6
S x IO -13
FIG. 3. Comparison of the differential curves Qw(S) (1) and Qw(S) ( 2 ) : / - f r o m sedimentation data for unfractionated specimen, 2 - - f r o m summation of fractions. T A B L E 2. R E S U L T S OF T H E ANALYSIS OF I~0LEOU-LAR-WEIGHT DISTRIBUTIOI"~" CURVES OF P - 8
Method
M~,
Fractionation Sedimentation of unfractionated specimen Summation of fractions
Mn
18,800 11,700 20,200
11,600 5000 8700
M w
Mn 1.62 2.34 2.32
the mean-molecular weights calculated from these curves. At the same time the values of the polydispersity coefficients were quite close together (Table 2). B u t in both cases the resolution is much better than for the fraetionation method of plotting the curves (Fig. 4).
l
w(M) /0
×..~--
×_x
0-6
04
02
I
5
/0
~/G ~
FIG. 4. Integral molecular-weight distribution curves of polyarylato P-8: / - - f r o m fraetionation c~ata, 2 - - s e d i m e n t a t i o n data, 3--fraction summation.
2176
Y~.. P. K~AS~OV et al.
CONCLUSIONS
A comparison has been made of molecular-weight distribution curves of polya r y ~ t e P-8 produced in three different ways: from fractionation data, the Gosting method which uses the sedimentation diagrams of an unfractionated specimen and by adding together all the fractions. The last method, which combines fractionation and sedimentation gives a coefficient very close to t h a t calculated from the figures for the high-speed sedimentation of an unfractionated specimen. Gosting's method of using data on the sedimentation of an unfraetionated specimen is quite suitable for finding the molecular-weight distribution of polyarylates.
Translated by V. ALFO~D
REFERENCES 1. E. W. CHANNEN, Rev. Pure Appl. Chem. 9: 225, 1959 2. S. Ya. FRENKEL', Uspekhi fiz. n a u k 53: 161, 1954 3. V. V. KORSHAK, S. V. VINOGRADOVA and S. N. SALAZKIN, Vysokomol. soyed. 4: 339, 1962 4. G.I. TIMOFEYEVA, L. V. DUBROVINA, V. V. KORSHAK and S. A. PAVLOVA, Vysokotool. soyed. 6: 2008, 1964 5. S. R. RAFIKOV, Vysokomol. soyed. 1: 1558, 1959 6. V. V. KORSHAK, S. A. PAVLOVA, G. I. TIMOFEYEVA, S. V. VINOGRADOVA and V. A. PANKRATOV, Dokl. Akad. Nauk SSSR 160: 119, 1965 7. G. I. TIMOFEYEVA, Dissertation, Moscow, 1965 8. T. SVEDBERG and K. O. PEDERSEN, The Ultracentrifuge, Oxford, 1940 9. L. J. GOSTING, J. Amer. Chem. Soe. 74: 1548, 1952 10. S. Ye. BRESLER, V. V. KORSHAK, S. A. PAVLOVA and P. A. FINOGENOV, Izv. Akad. Nauk SSSR, Otd. khim n a u k 344: 354, 1954
HYDROLYTIC PROCESSES OF THE THERMAL DEGRADATION OF ISOMERIC AROMATIC POLYAMIDES*t YE. :P. KRAS~OV, V. I. LOGV~OVA and L. B. SOKOLOV Vladimir Research I n s t i t u t e of Synthetic Resins
(Received 6 September 1965)
I~ A~ earlier work [1] it was suggested that hydrolytic processes were important in the general pattern of the degradation of isomeric aromatic polyamides at high temperatures. This was based on qualitative and quantitative analyses of * Vysokomol. soyed. 8: N o .
11, 1970-1975, 1966. ~f 4th Report of the series "Thermal degradation of polyamidds".
2171
3. I. A. KRIVOSHEYEVA, A. I. RAZUMOV, B. Ya. TEITEL'BAUM and T. A. YAGFAROVA,
Vysokomol. soyed. 5: 160, 1963 (Not translated in Polymer Sci. U.S.S.R.) 4. A.N. PUDOVIK and R. G. KUZOVLEVA, Vysokomol. soyed. 6: 737, 1964 (Translated in Polymer Sci. U.S.S.R. 6: 4, 810, 1964) 5. C. L. ARKUS and R. J. S. MATTHEWS, J. Chem. See., 4607, 1956 6. B. Ya. TEITEL'BAUM, Peredovoi nauchno-tekhnicheskii i proizvodstvelmyi opyt. (Advanced Scientific and Commercial Experiment.) TslTEIN, Series 32, 1%o. 4, 2, 1961
COMPARISON OF SOME EXPERIMENTAL METHODS OF DETERMINING THE MOLECULAR-WEIGHT DISTRIBUTION IN POLYMERS* L. V. DUBROVIlVA, S. A. PAVLOVA a n d V. V. KORSHAK Institute of Elementary Organic Compounds, U.S.S.R. Academy of Sciences (Received 3 September 1965) MOLECULAR-WEIGHT distribution analysis is increasingly being used as a m e t h o d o f s t u d y i n g the f o r m a t i o n m e c h a n i s m o f a poIymer. T h e usual m e t h o d of determ i n a t i o n consists in p l o t t i n g integral a n d differential curves f r o m t h e results o f fractionation. Certain a s s u m p t i o n s are m a d e regarding t h e size o f t h e fractions. I t is a s s u m e d t h a t no f r a c t i o n contains molecules heavier or lighter t h a n t h e m e a n molecular weight o f t h e preceding or following one, i.e. t h a t t h e r e is some overlapping. As d e m o n s t r a t e d b y t h e e x p e r i m e n t s of [1], these assumptions r e d u c e the a c c u r a c y o f t h e results. A b e t t e r m e t h o d is t h a t of r a p i d s e d i m e n t a t i o n in an ultracentrifuge, which p r o d u c e s the molecular-weight value a n d molecular-weight distribution curve. W i t h a c o m b i n a t i o n o f f r a c t i o n a t i o n a n d s e d i m e n t a t i o n t h e molecular-weight d i s t r i b u t i o n can be more a c c u r a t e l y d e t e r m i n e d [2]. W e decided to c o m p a r e t h e molecular-weight distribution o f p o l y a r y l a t e s f r o m t h e results o f f r a c t i o n a t i o n a n d sedimentation, a n d also t h a t d e r i v e d f r o m the t o t a l distribution of the fractions with t h e distribution o f t h e initial, unfract i o n a t e d specimen. This paper gives the results of an investigation of polyarylates prepared by interfacial polycondensation of isophthalyl chloride and 2-phenyl-3,3-bis-(4-hydroxyphenyl)phthalimidine (polyarylate P-8) [3]. The fraetionation involved distribution between two liquid phases; the procedure and the optimum conditions for polyarylates have been described in [4]. This method is known to produce enough fractions for subsequent investigation, and still quite homogeneous. The fractions were studied by rapid sedimentation in an ultra* Vysokomol. soyed. 8: No. 11, 1965-1969, 1966.
2172
L. V. DUBROVINA eta/.
centrifuge and by intrinsic viscosity determination. The viscosity was measured in a viseometer with a "hanging,' level at 20±0.1 ° [5]. Tetrachloroethane and tetrahydrofuran were used as solvents. No independent molecular-weight measurements were made, a n d therefore the relation between a and the value of the side substituent at the central carbon atom of the bisphenol already found in [6] was used to find the parameters a and K~ in the Mark-ttouwinck equation. For the polyarylate produced b y interracial polyeondensation from the bisphenol and isophthalic acid this relation is given b y a~--0.77-0.86 log .M/Mo (M is the molecular weight of the unit with the substituent, M0 is t h a t of the u n i t without).
C
For a substituent molecular weight of 194 a was found to be 0.615 for polyarylate P-8. Then from the equation K = 0 . 2 6 8 (6"03X I0-5) a, suggested in [7], we were able to calculate the second parameter K~ of the Mark-Houwinek equation. The relation thus found is given by [t/]=6.82 x 104.M °'615 (tetrachloroethane as solvent). The molecular weight of the u n f r a c t i o n a t e d specimen calculated from this equation (M,~=17,600) is in good agreement with t h a t found by the light-scattering method (M w = 18,600), which proves the possibility of using the functions found for polyarylates. Knowing the parameters of the Mark-I-Iouwinck equation, M v of the fractions could then be calculated and the molecular-weight distribution curves plotted. The rapid sedimentation experiments were performed on an ultraeentrifuge type G-110 (Hungarian) (15,000 rpm, 20 °, tetra.hydrofuran as solvent). The variations in the solution concentration were recorded b y the optical system of the ultracentrifuge as differential curves of the refractive index, a n d from this we were able to calculate the sedimentation constant using the equation
where x~ a n d xl are the position of the boundary between solution and solvent at times tl a n d tl; W 2 is the angular velocity of the ultracentrifuge rotor. I n [7] it was found t h a t there was no concentration dependence for polyarylates, and therefore the value of S was taken as S0 (at c->0). The molecular weight was calculated from the sedimentation rate b y means of the Svedberg formula [8]:
M=
S RT D (1--~p)'
where R is the universal gas constant, T the absolute temperature, v the partial specific volume (0-760 for the system in question), p the density of the solvent (0.892 for tetrahydrofuran), D the diffusion coefficient which was calculated from the second moments (-~') of the experimental derivative curves from the graph [2] ~/2t vs. xm2.t (xm is the position of the peak on the derivative curves at time t). A c c o r d i n g t o t h e figures i n T a b l e 1, t h e d e r i v a t i v e - c u r v e m e t h o d o f f i n d i n g t h e d i f f u s i o n coefficient s e e m s t o g i v e e x a g g e r a t e d l y l o w v a l u e s , p a r t i c u l a r l y a t l o w m o l e c u l a r w e i g h t s . T h i s is b e c a u s e t h e d i f f u s i o n coefficient is u s u a l l y v e r y
Determining the molecular-weight distribution in polymers
2173
sensitive to the low molecular weight part, so that the beginning of diffusion is uncertain for low molecular weight fractions where the boundary is only slowly detached from the meniscus and the beginning of diffusion does not coincide with the moment when the derivative curve peak leaves the" meniscus. To calculate the diffusion coefficient we took the moment when the peak leaves the meniscus as the d a t u m time, using the graph In x ~t. The Gosting system [9] was used to plot the distribution curves, since the ambiguity in the starting time TABLE 1. M E A S U R E M E N T FOR P-8 S P E C I M E N
Frac- I tion ] No. l 1
2 3 4 5 6 7 8 9 10 11
[~/] TCE
[~] THF
0.135 0.156 0"160 0.165 0.225 0.294 0.337 0.345 0.373 0'482 0'502
0.130 0.146 0.148 0.152 0.193 0.225 0-254 0.257 0-275 0.329 0.338
Mv
S × 10 -13
5400 6900 7150 9100 12,400 19,400 24,000 25,000 28,300 42,900 47,600
2"089 2.426 2.190 2"392 2.78 3.00 3.605 3.841 3"960 4"953 5.30
Mww
a 2 × 10 ~
16,100 19,600 11,100 10,500 18,400 28,500 23,300 36,000 36,700 43,300 49,200
0.463 0.613 0'380 0.400 0.533 0.516 0.453 1.457 0.306 1.422 2.465
does not have such a big effect on the results. This method of converting sedimentation diagrams to differential distribution curves over sedimentation constants
~gs 08
0.4
i
~.o
l
~.s logM
FIG. 1. Sedimentation constants vs. molecular weight. is b a s e d o n t h e a s s u m p t i o n are independent:
that the shifts due to polydispersity and diffusion
~ = M4x~a2t~q- 2Dw t , the broadening of the curve due to diffusion being proportional to x/t-and that d u e t o d i s p e r s i t y p r o p o r t i o n a l t o t. A t t - > ~ t h e a p p a r e n t d i s t r i b u t i o n f u n c t i o n
2174
L . V . D~-~OVINA et
al.
q* (S)=(dc/dx) (Xmax !Xmen)~W2xt (1/%) is transformed to q (S) the true sedimentation constant distribution. Since the sedimentation constant is a function of the molecular weight, then according to the equations dc/dS-~(dc/dM) (dM/dS) and S-~KsM 1-b the distribution curves dc/ds~-f (S) are transformed to molecular-weight distribution curves
dc/dM----~ (M). The relation between S and M was established experimentally for polyarylate 1)-8 (Fig. 1) : S----6.55× 10-~.M 0"4. I t is interesting to compare Q~ (S) the distribution of the unfractionated specimen calculated b y the Gosting method, with the distribution obtained b y
/7'/ 2 \ /
,~~ ~ s
s 8 z i~
\
Z
3
~"
J
•
7 S
FIO. 2. Distribution curves of sedimentation constants of fractions of P-8. Fraction num. bers given on curves. the method of adding fractions [10], which consists in graphical summation of the partial distributions in order to get the total: n
Q~ (S)-~ ~ [q~ (S)]~. Figure 2 shows the S [qw(S)] distribution curves for 11 fractions of P-8, as calculated b y the Gosting method. The area below e a c h curve is equal to the weight fraction of the fraction in question. Then the ordinates of the curves qw (S) of individual fractions were summed for certain S values, to produce the Qw(S) curve of total distribution. Comparing the distributions shown: in Fig. 3, it can be seen that there is a difference between Qw(S) for the unfractionated specimen (curve 1) and that obtained b y adding together the fractions (curve 2). The first method gives quite a symmetrical curve and the second gives better resolution in the region of the high molecular weight peak (curve 2), making a difference in
Determining the molecular-weight distribution in polymers
2175
Q(s)
O2
2
4
6
S x IO -13
FIG. 3. Comparison of the differential curves Qw(S) (1) and Qw(S) ( 2 ) : / - f r o m sedimentation data for unfractionated specimen, 2 - - f r o m summation of fractions. T A B L E 2. R E S U L T S OF T H E ANALYSIS OF I~0LEOU-LAR-WEIGHT DISTRIBUTIOI"~" CURVES OF P - 8
Method
M~,
Fractionation Sedimentation of unfractionated specimen Summation of fractions
Mn
18,800 11,700 20,200
11,600 5000 8700
M w
Mn 1.62 2.34 2.32
the mean-molecular weights calculated from these curves. At the same time the values of the polydispersity coefficients were quite close together (Table 2). B u t in both cases the resolution is much better than for the fraetionation method of plotting the curves (Fig. 4).
l
w(M) /0
×..~--
×_x
0-6
04
02
I
5
/0
~/G ~
FIG. 4. Integral molecular-weight distribution curves of polyarylato P-8: / - - f r o m fraetionation c~ata, 2 - - s e d i m e n t a t i o n data, 3--fraction summation.
2176
Y~.. P. K~AS~OV et al.
CONCLUSIONS
A comparison has been made of molecular-weight distribution curves of polya r y ~ t e P-8 produced in three different ways: from fractionation data, the Gosting method which uses the sedimentation diagrams of an unfractionated specimen and by adding together all the fractions. The last method, which combines fractionation and sedimentation gives a coefficient very close to t h a t calculated from the figures for the high-speed sedimentation of an unfractionated specimen. Gosting's method of using data on the sedimentation of an unfraetionated specimen is quite suitable for finding the molecular-weight distribution of polyarylates.
Translated by V. ALFO~D
REFERENCES 1. E. W. CHANNEN, Rev. Pure Appl. Chem. 9: 225, 1959 2. S. Ya. FRENKEL', Uspekhi fiz. n a u k 53: 161, 1954 3. V. V. KORSHAK, S. V. VINOGRADOVA and S. N. SALAZKIN, Vysokomol. soyed. 4: 339, 1962 4. G.I. TIMOFEYEVA, L. V. DUBROVINA, V. V. KORSHAK and S. A. PAVLOVA, Vysokotool. soyed. 6: 2008, 1964 5. S. R. RAFIKOV, Vysokomol. soyed. 1: 1558, 1959 6. V. V. KORSHAK, S. A. PAVLOVA, G. I. TIMOFEYEVA, S. V. VINOGRADOVA and V. A. PANKRATOV, Dokl. Akad. Nauk SSSR 160: 119, 1965 7. G. I. TIMOFEYEVA, Dissertation, Moscow, 1965 8. T. SVEDBERG and K. O. PEDERSEN, The Ultracentrifuge, Oxford, 1940 9. L. J. GOSTING, J. Amer. Chem. Soe. 74: 1548, 1952 10. S. Ye. BRESLER, V. V. KORSHAK, S. A. PAVLOVA and P. A. FINOGENOV, Izv. Akad. Nauk SSSR, Otd. khim n a u k 344: 354, 1954
HYDROLYTIC PROCESSES OF THE THERMAL DEGRADATION OF ISOMERIC AROMATIC POLYAMIDES*t YE. :P. KRAS~OV, V. I. LOGV~OVA and L. B. SOKOLOV Vladimir Research I n s t i t u t e of Synthetic Resins
(Received 6 September 1965)
I~ A~ earlier work [1] it was suggested that hydrolytic processes were important in the general pattern of the degradation of isomeric aromatic polyamides at high temperatures. This was based on qualitative and quantitative analyses of * Vysokomol. soyed. 8: N o .
11, 1970-1975, 1966. ~f 4th Report of the series "Thermal degradation of polyamidds".