Velocity of sound and the compressibility of copolymers of methyl methacrylate and methacrylic acid

Velocity of sound and compressibility of copolymers of MMA and MAA

1471

CONCLUSIONS (1) The heat capacities of two samples of SKD butadiene rubber of different degrees of stereoregularity, crystallized under different thermal routines, have been measured by quantitative thermographic analysis, using the principle of the differential heat bridge. (2) The degree of crystallinity of the samples, the dependence of the phase composition on the experimental conditions and the heats of crystallization and melting were determined. (3) It is shown that when the sample is previously crystallized a higher degree of crystallinity is obtained than in a thermographic experiment in which a chilled sample is heated. The additional crystalline formations produced in this way break down easily. (4) When heated at a rate of 2.4 deg/min most of the crystals of the highly stereoregular rubber melt between --37 and --8 °. The heat of melting, measured in this temperature interval, is almost the same for all the thermal routines of crystallization. Translated by E. O. PHILLIPS

REFERENCES 1. W. COOPER and R. K. SMITH, J. Polymer Sci. AI: 159, 1963 2. M. L. DANNIS, J. Appl. Polymer Sci. 7: 231, 1963 3. B. Ya. TEITEL'BAUM and N. P. ANOSHINA, Vysokomol. soyed. 7: 1188, 1965 (Translated in Polymer Sci. U.S.S.R. 7: 7, 1315, 1965) 4. M. Sh. YAGFAROV, Tez. dokl. 2-i mezbvuzovskoi konferentsii po metodam i priboram dlya teploizolyatsionnkh ispitanii (Report Summaries of the Second Inter-Institutional Conference on Methods and Apparatus for Heat Insulation Tests). p. 28, Leningrad, 1960 5. K. EIERMAN and K. HELLWEGE, Kolloid-Z. 174: 134, 1961 6. M. DOLE, Khimiya i tekhnol, polimerov, No. 1, 62, 1967

VELOCITY OF SOUND AND THE COMPRESSIBILITY OF COPOLYMERS OF METHYL METHACRYLATE AND METHACRYLIC ACID* I. I. PAVLII~OV, I. B. RABII~OVICH, V. Z. POGORELKO a n d A. V. RYABOV Research Institute of Chemistry

(Received 19 May 1968)

THE velocity of sound in a polymer and its compressibility are very sensitive to the rigidity of its structural framework. Consequently the curves of the temperature dependence of these properties should clearly indicate structural transi* Vysokomol. soyed. A10: No. 6, 1270--1276, 1968.

1472

I . I . PAVLI~OV et a/.

tions in polymers. In addition these properties must be very sensitive to "crosslinking" of the chains by hydrogen bonding. Up to the present time however the velocity of sound and compressibility have been studied in only a few polymers [1-9]. I n this c o n t e x t we h a v e m e a s u r e d t h e v a r i a t i o n w i t h c o m p o s i t i o n a n d t e m p e r a t u r e o f t h e v e l o c i t y of s o u n d in, a n d t h e d e n s i t y of, a n u m b e r o f c o p o l y m e r s o f m e t h y l m e t h a c r y l a t e (MMA) a n d m e t h a c r y l i c acid (MAA), a n d c a l c u l a t e d t h e a d i a b a t i c a n d i s o t h e r m a l compressibility a n d t h e h e a t c a p a c i t y a t c o n s t a n t v o l u m e o f t h e c o p o l y m e r s . F o r calculation o f t h e i s o t h e r m a l c o m p r e s s i b i l i t y a n d t h e h e a t c a p a c i t y a t c o n s t a n t v o l u m e we m a d e use o f o u r earlier results on t h e h e a t c a p a c i t y a t consta~lt pressure of t h e s a m e c o p o l y m e r s [10]. Since n o r m a l p o l y m e r i z a t i o n of m i x t u r e s o f MMA a n d M A A c o n t a i n i n g m o r e t h a n 2 5 ~ o f t h e l a t t e r gives c o p o l y m e r s of insufficient h o m o g e n e i t y , in t h e p r e s e n t w o r k we used c o p o l y m e r s m a d e b y p o l y m e r i z a t i o n u n d e r pressure.

EXPERIMENTAL The monomers were purified by drying first over calcium chloride, then over calcium hydride, followed by repeated vacuum distillation. The refractive indices of the purified monomers were n~ 1.4317 (MAA) and n~ 1.4146 (MMA). The MMA-MA_A_copolymers were prepared by polymerizing mixtures of the monomers in flexible aluminium tubes at 50± 1% The tubes were placed in thermostatically controlled autoclaves, pressurized by a liquid. Polymerization was initiated by 0.1% by weight of benzoyl peroxide. Copolymers containing 40, 50, 60 and 80 mole % of MAA were polymerized at pressures of 1 arm and 100 arm. Various samples of poly(methacrylio acid) (PMAA) were prepared by polymerization at pressures from 1 to 150 arm. Polymethylmethacryiate (PMMA) and copolymers of other compositions were prepared at 1 arm. The molecular weights of the polymers, determined viscometricaUy, ranged from 1.8× l0 t (PMMA) to 6.2 × 105 (PMA_A_). For measurement of the velocity of ultrasonic sound and density, specimens in the form of cylinders of height 40 mm and diameter 20 m m were used. The velocity of sound at 20 °, Co, in these samples was measured at a frequency of 1 Mc/s by the ordinary impulse method [11] with a precision of about 1~/o. At all other temperatures the relative change in the velocity of sound, AC, due to change in temperature was measured at the same frequency by the phase method, using an ultrasonic delay line as a phase-meter. The ultrasonic vibrations passing through the specimen and the reference liquid (castor off) in the delay line were converted to electrical signals, which were passed through an amplifier to an oscillograph. The phase difference between these vibrations, due to change in the temperature of the test specimen, is compensated by change in the distance between the receiver and the sound generator, situated in the reference liquid. The change in the velocity of the ultrasonic sound in the specimen is then given by

~ o = --O~zh/O~ho

(1)

where C1 is the velocity of sound in the reference liquid at 20 °, zth the change in distance between the receiver and generator in the delay line, and h0 the height of the specimen. By this method the precision of measurement of zig is ~0.2%. The density of the copolymers was measured by the hydrostatic weighing method, with a precision of N0-1~/o [12]. Doubly distilled water was used as the hydrostatic liquid for measurements between 20 and 80 °, and glycerol for measurements between 80 and 160°. Before the measurement the copolymer specimens were coated with a protective lacquer

Velocity of sound and compressibility of copolymers of MMA and MAA

1478

film and dried to constant weight at 80% Control weighing showed that the increase in weight after coating was about 0.002 g, which introduces a slight error (about 0-01%) in the density results. For measurements between 80 and 160° the specimens were loaded with a piece of lead weighing 1 g. All specimens were held at the chosen temperature for 2 hr. The density was calculated from the formula:

P~

a m x "Pgl a gl a eI (ml,t--/?tl,2)( m 2 - - ~'/?,,~ )

~*

where m~ is the weight of the specimen in air at 20°, m~ and m]* the weights of the lead in air at 20 ° and in glycerol at the temperature of measurement, m~.2 and m~ s the total weights of the specimen plus lead in air at 20 ° and in glycol at the temperature of measurement, and p,z the density of glycerol. RESULTS AND DISCUSSION

Velocity of ultrasonic sound. F i g u r e 1 shows t h e v a r i a t i o n in t h e v e l o c i t y o f s o u n d in P M A A w i t h p o l y m e r i z a t i o n pressure. I t is seen t h a t t h e v e l o c i t y increases b y a b o u t 150 m / s e c w i t h a n increase in pressure f r o m 1 to 75 a r m . ,), m/sec 3200

C,m/~eL"

o

2800 50

FIG. 1

100

150 P, arm

I

20

I

60 M AA . mole %

I

100

FrG. 2

FIG. 1. Dependence of ultrasonic velocity in samples of PMAA (20°) on polymerization pressure. FxG. 2. Dependence of ultrasonic velocity on MAA content of MMA-MAA copolymers prepared by polymerization: 1 - - a t 1 arm, 2 - - a t 100 arm. F u r t h e r increase in p o l y m e r i z a t i o n pressure has p r a c t i c a l l y no effect on t h e v e l o c i t y o f sound. F i g u r e 2 shows c o m p a r a t i v e curves of t h e d e p e n d e n c e of the v e l o c i t y o f ultrasonic s o u n d on t h e MAA c o n t e n t of M M A - M A A c o p o l y m e r s p r e p a r e d a t 1 a r m (curve 1) a n d 100 a t m (curve 2). I t is seen t h a t t h e v e l o c i t y o f s o u n d increases considerably as t h e mole fraction of MAA in t h e c o p o l y m e r is. increased. H o w e v e r t h e velocity, c o m p o s i t i o n c u r v e for t h e c o p o l y m e r s p o l y m e r i z e d a t 100 a r m , lies c o n s i d e r a b l y a b o v e the c u r v e for t h e c o p o l y m e r s prep a r e d a t n o r m a l pressure. T h e s e p a r a t i o n o f t h e curves is already" noticeable w h e n t h e c o p o l y m e r contains a b o u t 30 moles ~/o of MAA a n d t h e effect increases a s t h e M A A c o n t e n t increases.

I. I. PAVI.U~OV et aZ.

1474

The combination of results presented in Figs. 1 and 2 suggests t h a t increase in the polymerization pressure causes increase in the packing density of the chains in the polymeric mass being formed, as a result of decrease in the interglobular volume, which not only increases the inter-chain Van der Waals interaction but also possibly increases the number of hydrogen bond crosslinkages, both of which would increase the rigidity of the chain framework. I t is also interesting to note t h a t the experimental velocity figures for all of the copolymers are higher than those calculated on the additivity principle in relation to the composition of the copolymers.

C, rn/sec ~00

3200

3000

2600

2600

/40

60

12_0

T.°C

160

FiG. 3. Temperature dependence of ultrasonic velocity in MMA-MAA copolymers containing: •--0; 2--5"8; 3--11.4; 4--17.0, 5--22.5; 6--33"3 mole% of MAA (polymerization at 1 atm); 7--40; 8--60; 9--80; 10--100 mole% of MAA (polymerization at 100 atm). Figure 3 shows the temperature dependence of the velocity of ultrasonic sound in PMMA, PMAA and a number of MMA-MAA copolymers. Our results for PMMA (curve 1) in the 20-80 ° region are in agreement with those of reference [1] to within 2-3°/o, but differ by 7-8°/o from those of reference [2]. It is seen from the graphs t h a t in all the copolymers the decrease in the velocity of sound with increase in temperature is not uniform. Two inflexions, at about 40 ° and between 100 and 140 °, are seen in each of the curves 1-7. In curve 8

Velocity of sound and compressibility of copolymers of MMA and MAA

1475

the second inflexion is scarcely discernible and in curves 9 and 10 it evidently occurs above 160 °, which is the limit of the measurements. Curves 1-7 are similar to those obtained for PMMA in references [3] and [4]. The inflexion in the velocity-temperature curves at about 40 ° is probably due to the onset of motion of certain groups in the polymer (for example --CH a , ester groups, ete). The mobility of groups in glassy polymers has been demonstrated in a study of molecular motion in polymers by the NMR method [13] and from data on the frequency dependence of the dielectric constant [14]. The second inflexion in the velocity-temperature curves, which is more sensitive to the MAA content of the copolymer, is probably brought about by transition of the polymer from the glassy to the high-elastic state. The temperature corresponding to this inflexion increases as the mole fraction of MAA in the copolymer increases and is in the glass transitioD regions as found for these copolymers from the temperature dependence of the heat capacity [10] and from their themomechanical curves [15]. The Table shows a comparison of the glass temperatures of MMA-MAA copolymers, found by different methods. The small differences in the corresponding values is explained by difference in the sensitivity of the different methods in determination of the glass transition point, and also by different thermal prehistories of the copolymer specimens. Density o f M M A - M A A copolymer8. Figure 4 shows curves of the temperature dependence of the density of MMA-MAA copolymers. The densities found by us for PMMA over the entire range of temperatures studied agree within 1% with the results of dilatometric measurements [16]. It is seen from the graph

?,jIcm,~

~'<~-o, 7

~..o-..~.~>_.~,_ .

/ L

~,m,.~ L _ _ ±

:~9

__1__ - 80

....

i_ _"< ~"'_ Z: t'

_

,::>J il %~

FxG. 4. Temperature dependence of the density of MMA-MAA copolymers: •--0; 2--5.8; 3--11.4; 4--17.0; 6--22-5; 6--33.3 mole~o of MAA (polymerization at 1 atm); 7--40; 8--50; 9--60; •0--80; 1 1 - - 100 mole~o of MAA (polymerization at 100 arm).

that the curves contain two linear sections joined by a well defined inflexion. The temperatures at which the inflexions occur correspond to the glass temperatures found for the copolymers by other methods (Table). The composition

I . I . PAvia~ov e¢ a/.

1476

dependence of the glass temperature (Tg) of the copolymers, found from the position of the inflexions in the density-temperature curves, can be expressed with an accuracy of about 1% by the linear equation:

T

=100+0.83xx

(a)

where X is the weight percent of MAA. It is seen from Fig. 4 that the density of the copolymers increases regularly with increase in the mole fraction of MAA. We present below the coefficients of thermal expansion (~X 104 degree-z), eMculated from the density, for the MMA-MAA copolymers. They decrease as the MAA content increases at temperatures both below and above the glass transition region: MAA, mole% 0 5.8 11.4 17 22.5 33.3 40 60 80 100 TT~ 5.30 4.75 4.30 3.87 3.66 3.17 3.05 2.45 2-00 It is important to note also that the additivity principle with respect to composition does not apply to the density of the copolymers (Fig. 5). This is seen most clearly in the case of the copolymer containing 50 moles% of MAA. p,g/cma

1"2,9

121

1"13

\

I 20

I

i I 60 - M A A , mole %

100

Fxo. 5. Composition dependence of the density of MMA-MAA copolymers: 1--20°; 2--100°; 3-- 1 6 0 ° .

For this composition the deviations of the density from the value calculated on the additivity principle are from 1 to 2%. These results show that in copolymerization of MMA and MAA the volume of the copolymer is less than the volume calculated on the basis of additivity of the volumes of the homopolymers, i.e. the copolymer chains are more densely packed than the additivity principle requires. This is probably due to partial crosslinking by hydrogen bonding. Relationship between ultrasoni~ velocity and the density of the copolymer& I t was shown in reference [4] that the velocity of sound in polymers is closely associated with the intermolecular free volume, the generalized Rao rule being applicable. The results for our homopolymer and eopolymers samples over the temperature range of 20-160 ° are also in accord with the generalized Rao rule: R-----CTM X V

(4)

Velocity of sound and compressibility of copolymers of MMA and MAA

1477

where R is the Rao constant, C - - t h e velocity of sound (m/sec), V the assumed molar volume of the copolymer, corresponding to the arbitrarily assumed repeating unit* [10], and n a constant dependent on the type of intermolecular interaction. I f for all the MMA-MAA copolymers we take the value/~----489 found from formula (4) for PMMA, then n varies between 4.50 and 4.07 with change in MAA content from 0 to 100 mole °/o. The decrease in n reflects the increase in intermolecular interaction as the MAA content increases. DETERMINATION OF T g OF M ~ z ~ k - M . A ~ COPOLYMERS BY DIFFERENT METHODS

Glass temperature, °C MAA content, mole %

from velocity of sound

from density

present paper 0 5.8 11.4 17.0 22.5

100 103 107 111 116 124 132

33.3

40.0* 60.0* 80.0*

100 104 108 112 119 122 134 147 165

from heat capacity [10]

thermomechanieal data [15]

105 110 117 120 126 138

104 111 119 131 140

* Copolymers prepared at 100 atm.

Adiabatic and isothermal compressibility of MMA-MAA copolymers.

When ultrasonic vibrations pass through a polymer adiabatically, i.e. when the rate of change of pressure in the sound wave is so high t h a t heat exchange between contiguous sections of the medium can be neglected, the rate of propagation of the ultrasonic wave, C, in a sample of density p is given by:

-

\pB

o/

where p~ is the adiabatic compressibility, fl~o the isothermal compressibility, and C~ and C V are the specific heats at constant pressure and constant volume respectively.

~-~Ptuo/Baa~C~/Cv, 100

1

*V---X/Mx+(IOO,X)/M n. _~' where X

is the weight% of the component of molecular

weight M, and p the density of the eopolymer.

I. I. PAVLINOV e~ a~.

1478

Figure 6 shows curves of the temperature dependence of the adiabatic compressibility of MMA-MAA copolymers calculated from the experimental values of ultrasonic velocity and density, by means of formula (5). The precision of the calculated values of adiabatic compressibility is about 1~ . It is seen from the graph that as the MAA content of the copolymer increases the compressibilitytemperature curves shift to lower values of ]~ad, corresponding to increase in the rigidity of the polymeric framework. The curves of the temperature dependence of ~ad, like the C = f ( T ) curves, contain two inflexions, which become less well defined as the MAA content of the copolymer increases. The second infiexion in the 100-140 ° region corresponds to the glass transition. The composition dependence of ]~ad of the copolymers deviates markedly from linear additivity. At 20 ° Pad for the copolymer containing 50 mole ~ of MAA is lower than the additive value by approximately 10~. Figure 7 shows the results of calculation of the isothermal compressibility of copolymers containing from 0 to 30 mole ~/o of 1KAA. The calculations, with a precision of 1-1.5~, were made by means of the formula:

(6)

#,,o = A , , + e- x

P ieo" lorZ, crn ~dune

/,

p=,lO~ cmt/dyne 12

I5

15

"/

8

I

10

80

Fio. 6

r, oc

170

I

80

I

180 7-,°O

FzG. 7

Fio. 6. Temperature dependence of the adiabatic coml~esaibility of M M A - M A ~ copolymers: 1--0; 2--5.8; 3--11.4; 4--17.0; 5--22.5; 6 ~ 3 3 . 3 mole~o of MAA (polymerization at I arm); 7-- 40; 8-- 60; 9-- 80; 10-- 100 mole% of MAA (polymerization a t 100 arm). Fio. 7. Temperature dependence of the isothermal compressibility of MMA-MAA copolymers: •--0; 2~5"8; 3~11.4; 4--22-5; 5--88.3 mole% ~ M A A .

Velocity of sound and compressibility of copolymers of MMA and M_hA

1479

where ~ is the average coefficient of thermal expansion and M the weight of the assumed repeating unit. * In these calculations we used the data given above for p, ~ and flad, and the value of C~ was taken from reference [10]. It is seen from Fig. 7 that the isothermal compressibility-temperature curves are similar on the whole to the corresponding adiabatic curves. In the region of Ta, however, the isothermal compressibility curves show a sharp change in direction. The values of fluo found for PMMA by the static method [8] in the temperature region below Tg correspond to within about 2% with our values. There is a large divergence in the glass temperature region and above. This is quite understandable because at these temperatures fl~o found by the static method is dependent to a considerable extent on the experimental conditions [8, 9]. Heat capacity at cOnstant volume. In view of the considerable interest in specific heat at constant volume for the solid state, especially for chain structures such as the MMA-MAA copolymers, we calculated this quantity for a number of the copolymers. The calculations, with a precision of about 1.5%, were made by means of the formula: Cv=C,P,

/P

o

.

(7)

Below Ta the specific heat (Cv) of the MMA-MAA copolymers decreases as the MAA content increases, i.e. it behaves in the same way as C~ [10]. Above the glass transition region C v increases with increase in temperature, this increase being greater in copolymers with higher MAA contents. This is evidently explained by partial breakdown of hydrogen bonds at temperatures above the glass temperature. ' CONCLUSIONS

(I) A study has been made of ultrasonic velocity in, and t h e density, adiabatic and isothermal compressibility and the specific heat at constant volume of eopolymers of methyl methacrylate and methacrylic acid, in relation to composition, temperature and polymerization pressure. (2) Increase in the proportion of MAA in the copolymer and also increase in the polymerization pressure give rise to increase in the velocity of sound and a decrease in compressibility, corresponding to the increase in the rigidity of the chain framework of the copolymer. This is explained by the fact that both conditions cause strengthening of the inter-chain hydrogen bonding, and increase in polymerization pressure in addition causes increase in the Van der Waals interaction in the polymer. A valuable indication of the occurrence of increase in the rigidity of the copolymer chain structure by hydrogen bonding is given by the fact that the adiabatic compressibility of a copolymer containing 50 moles°//o of MAA is 10% lower than the average of the compressibility of polymethylmethacrylate and poly(methacrylic acid). (3) The temperature dependence curves of density, ultrasonic velocity and • M~s.unlt

~--~

100 X (M~)+ (100--X)/M,"

1480

S . V . Roaozm~ e¢ a/.

adiabatic compressibility clearly show the glass temperatures of the copolymers. The change in the isothermal compressibility is particularly rapid in the glass temperature region. (4) The Rao rule with the same constant, R-~489, is applicable to the system studied, and tl~e constant n varies between 4.50 and 4.07 with change in the methacrylic acid content from 0 to 100 m o l e s t . ~ r e r ~ t ~ , d b~ E. O. pHTT,T,TPS

REFERENCES 1. T. F. PROTZMAN, J. AppL Phys. 20: 627, 1949 2. M. KRISHNAMURTHI and G. SASTRY, Nature 174:' 132, 1954 3. Y. WADA, J. Appl. Phys. Japan 24: 159, 1955 4. Y. WADA and K. YAMAMOTO, J. Phys. Soc. Japan U: 887, 1956 5. J. L. MELCHOR and A. A. PETRAUSKAS, Ind. Engng. Chem. 44: 716, 1952 6. S. V. SUBRAHMANYAM, J, Chem. Phys. 22: 1562, 1954 7. W. BRANDT, J. Chem. Phys. 26: 262, 1957 8. M. M. MARTYNYUK and V. K. SEMENCHENKO, Kolloid. zh. 26: 83, 1964 9. H. TAUTZ and L. STROBEL, Kolloid.Z.~nd Z. f(ir Polymere 202: 33, 1965 10. L. I. PA.VLINOV, I. B. RABINOVICH, N. A. OKLADNOV and S. A. ARZHAKOV, Vysokomol. soyed. AP: 483, 1967 (Translated in Polymer Sci. U.S.S.R. 9: 3, 539, 1967) 11. L. BERGMAN, Ul'trazvuk (Ultrasonics). p. 216, Foreign Literature Publishing House, 1957 12. H. J. KOLB and E. F. IZARD, J. Appl. Phys. 20: 564, 1949 13. W. SLICHTER, Sb. Fizika polimerov (Collected papers. Polymer Physics). p. 171, Foreign Literature Publishing House, 1960 14. K. W. WOLF, Z. Elektrochem. 65: 604, 1961 15. V. A. MYAGCHENKOV and L A. GIBADUT.LTI~T,Tr. Kazanskogo khim..tekh, ins-ta, No. 33, 259, 1964 16. G. MARTIN, S. S. ROGERS and L. MANDEL]gEltN, J. Polymer SoL 20: 579, 1956

SYNTHESIS AND PROPERTIES OF ION-EXCHANGE RESINS BASED ON ~-AMINO ACIDS AND HALOMETHYLATED STYRENE-DIVINYL BENZENE COPOLYMERS* S. V. ROGOZHr~,V. A. Dxv~Kov, S. G. VYBRA_N'OVand V. V. KORSHAK Institute of Hereto-organic Compounds, U.S.S.R. Academy of Sciences

(Received 23 May 1967) THE r e a c t i o n of ~-amino acids w i t h h a l o m e t h y l a t e d c o p o l y m e r s of s t y r e n e a n d d i v i n y l b e n z e n e (DVB) is o f und~)ubted interest because b y this m e a n s it is possible t o o b t a i n a n u m b e r of a m p h o t e r i c , c o m p l e x - f o r m i n g a n d a s y m m e t r i c ion* VysokomoL soyed. A10: No. 6, 1277-1282, 1968.