Glass Transitions of the Poly-(n-Alkyl Methacrylates)

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July, 1957

GLASS FORMATION IN POLYMERS

symbols, and estimated values quoted in parentheses. While no errors have been quoted for the tabulated values, a n indication of accuracy can be obtained from the number of significant figures given. It is also instructive to plot dissociation energies for the elements of a given column as a function of the period. This has been done in Fig. 2. It is apparent that in any one column energies decrease in a regular fashion with increasing atomic weight, except for the well-substantiated anomaly of Fs and the high value of Do(Auz).

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Acknowledgments.-The authors are greatly indebted to Professor P. Goldfinger for his helpful advice and unfailing encouragement. Mass spectrometer and auxiliary equipment were made available through financial aid from the ECA Administration, the “Institut pour 1’Encouragement de la Recherche Scientifique dans 1’Industrie et 1’Agriculture” (IRSIA) and the Fond National de la Recherche Scientifique” (FNRS). Thanks are due to theeLaboratoire de Calcul Numkrique at the University of Brussels for carrying out the least squares computations.

GLASS FORMATION IN POLYMERS. I. THE GLASS TRANSITIONS OF THE POLY-(n-ALKYL METHACRYLATES) ‘s2

BY SENTAS. ROGERSAND LEOMANDELKERN National Bureau of Standards, Polymer Structure Section, Washington, D. C. Received April 6 , 1967

The specific volume-temperature relations and glass temperatures, T,, have been determined for a series of poly-(n-alkyl methacrylates) ranging from poly-(methyl methacrylate) to poly-(n-dodecyl methacrylate). The glass temperatures of these polymers continuously decrease as the number of carbon atoms in the side chain is increased. Concomitant with the decrease in T , the specific volume a t a reference temperature in the liquid state continuously increases. The results are interpreted in terms of free volume concepts of the liquid state and the partitioning of the specific volume into its various components.

Introduction When a supercooled liquid does not crystallize, or when flexible chain molecules do not crystallize completely, vitrification will usually occur over a relatively narrow temperature range characteristic of the material. The temperature at which the transformation occurs is called the glass transformation temperature and is designated as Tg. Many of the physical properties of polymeric systems depend on whether the temperature of observation is above or below Tg. For example, a noncrystalline polymer will change from a highly viscous or a rubber-like material to an inelastic brittle substance as vitrification occurs. Those polymers which are capable of crystallizing rarely do so completely, so that the liquid-like portions of this type of polymer can also become a glass with the concomitant changes in physical properties. It is well recognized that glass formation occurs as a consequence of the fact that there are kinetic restrictions on the rate a t which molecules or segments of molecules of a liquid rearrange from one equilibrium configuration to another. Thus when an external parameter such as temperature or pressure is varied, time is required for the local liquid structure to regain its equilibrium configuration. When the temperature, for example, is lowered sufficiently so that the time necessary for this rearrangement t o occur is of the same order as the time scale of the experimental observation glass formation will O C C U T . ~ Therefore measurements of certain thermodynamic quantities as the specific (1) Presented in part before the 130th Meeting of the American Chemical Society, Atlantic City, N. J., Sept. 10, 1950. (2) The work reported here was aupported in part by the Navy Bureau of Aeronautics, Washington, D. C. (3) W. Kauemann, Chem. Revs., 43, 219 (1948).

heat, expansion coefficient, or compressibility will show abrupt changes at Tgsince the contributions of the changing liquid structure will be absent. Tg can therefore be detected by observation of changes in certain thermodynamic variables as well as by changes in the mechanical properties. Glass formation is not unique to polymeric systems since many low molecular weight materials also vitrify. However, the values of Tg for organic polymers vary over very wide extremes of temperature depending on the chemical nature of the chain repeating unit. This class of liquids, therefore, offers the unique opportunity of studying the effect of chemical structure on Tg. A great deal of success has been achieved in describing the variation of T , of a given homopolymer with variation in its structure and composition. By considering the changes in the specific volume, which serves as a convenient method of describing changes in local liquid configuration, the variation of Tg with molecular weight14 with cross-linking15 with copolymeri~ation~~~ and dilution6 has been quantitatively described and verified by experiment. On the other hand adequate methods have not as yet been developed by which to explain the wide variation observed in Tg for homopolymers of different type chain units. Hence predictions of the expected value of Tg for a homopolymer are difficult t o make and the solution of this problem is one of great importance. The dependence of glass formation on the local (4) T. G.Fox and P. J. Flory, J . Applied Phys., 21, 581 (1950). (5) S. Loshaek, J . Polurner Sci., 16, 391 (1955). ( 0 ) T.G.Fox, Bulletin of Am. Physical SOC.,Series 11, Vol. 1, No. 3, p. 123,March 15, 1950. (7) L. Mrtndelkern, G. M. Martin and F. A. Quinn, Jr., J . Research Natl. Bur. Standards, 58, 137 (1957).

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SENTA S. ROGERS AND LEOMANDELKERN

liquid structure would indicate that the configuration of the polymer chain and the forces of interaction between chain segments should be predominating factors in determining the location of Tg. Though glass formation in polymers has been discussed in terms of these properties8-11 quantitative relations between them and T , have not as yet been developed. Not only must the influence of these factors on the liquid structure be specified but reliable and systematic methods of describing these factors must also be developed. Polymers based on derivatives of acrylic and methacrylic acid offer the possibility, through the variation of the chemical nature of the side groups, of systematic and controlled variation of the chain configuration and interchain forces without, however, altering the backbone polymer structure. Consequently a series of polymers may be obtained which encompass a wide range in T g values. An accurate determination of the specific volumetemperature relations and Tg for these polymers if accompanied by a quantitative description of the chain configuration and interchain interactions would offer the opportunity to assess properly the role played by these quantities. Interchain interactions can be identified with the cohesive energy density12 or the solubility parameter 812 of the polymeric liquid and a reliable method of calculating these quantities for a majority of the polymers of interest is now a~ai1able.l~Methods have also been developed for deducing the over-all configuration in space of the unperturbed single polymer hai in'^,^^ from appropriate measurements of their dilute solution behavior. However, sufficient data describing chain configuration has not as yet been accumulated, nor is it clear just how the over-all extension in space of polymers of different types of repeating units should be compared in attempting to assess its influence on glass formation. I n the present paper we have determined the specific volume-temperature relations and Tg for a series of poly-(n-alkyl methacrylates) and interpret the change of T , with the number of carbon atoms in the side groups in terms of the freevolume concepts of the liquid state. This represents an effort in the direction of sorting out the factors influencing T,. Cohesive energy densities can be calculated for these polymers and limited data are available by which to describe the chain configuration of the first three members of the series. Polymers prepared from methyl methacrylate, ethyl methacrylate, n-propyl methacrylate, n-butyl methacrylate, n-hexyl methacrylate, noctyl methacrylat,e, n-dodecyl methacrylate and n-octadecyl methacrylate have been studied by dilatometric methods in this work. (8) E. Jenckel. Kolloid Z.,120, 160 (1950). (9) R. F. Boyer. Comptes Rendus de la Deuxieme Reunion Annuelle Soci6td de Chimie Physique, “Changements de Phases.” Presses Uni. versitaires de France, Paris, 1952, p. 384. (10) R . F. Boyer, J . Applied Phya., 2 5 , 825 (1954). ( 1 1 ) J. H. Gibbs. J . Chem. Phus.. 2 5 , 185 (1956). (12) J. H. Hildebrand and R. L. Scott, “The Solubility of NonElectrolytes,” Reinhold Publ. Corp., New York, N. Y., 1950, p. 123, 424. (13) P. A. Small, J . Applied Chen., 8 , 71 (1953). (14) P . J. Flory, “Principles of Polymer Chemistry,” Cornel1 University Press, Ithaca, N. Y., 1953, p. 595 ff. (15) T. A. Orofino and P. J. Flory, J . Chem. Phys., 26, 1067 (1957).

Vol. 61

Experimental Materials.-Except for n-dodecyl methacrylate and noctadecyl methacrylate all the monomers used in this work were obtained from 34onomer-Polymer Inc. The n-dodecyl and n-octadecyl methacrylates were prepared from methyl methacrylate by alcoholysis with the respective alkanols using p-toluenesulfonic acid as a catalyst with a small amount of p-hydroquinone added as an inhibitor. Prior to the initiation of the polymerization the inhibitor was removed from the monomers by washing several times with a 10% sodium hydroxide solution, rinsing with water and drying over calcium chloride. The monomer was then distilled under reduced pressure, in an oxygen-free atmosphere of prepurified nitrogen, into Pyrex olymerization tubes. The polymerization tubes were attacged to a closed vacuum line, the liquid monomer was frozen at liquid nitrogen temperatures and degassed under a vacuum of one micron. The solidification and degassing process were repeated twice more, and after the completion of the last degassing the tubes were sealed in uacuo. Some of the physical constants of the monomers employed are given in Table I.

TABLE I PHYSICAL CONSTANTS OF MONOMERS Methacrylate monoiner

Methyl Ethyl n-Propyl n-Butyl n-Hexyl n-Octyl n-Dodecyl n-Oc tadecyl

--------B.p.-OC.

Mm.

Refractive index, n at 25’

100.0-101 118.0-119 140-1 4 1 82-83 88-89 140- 142 142-143 195

760 760 760 50 14 30 2 6

1.4122 1.4130 1.4173 1.4212 1 ,4298 1.4374 1,4430 1,4500

The polymerization was then induced photochemically by means of sunlight,or a Hanovia arc lamp operating at a wave length of 3660 A. In order to remove residual monomer and any low molecular weight materials, the polymers thus prepared were precipitated by the slow addition of a dilute benzene solution to stirred methanol. The precipitated polymers were first air-dried and then dried i n vacuo at 60’ for 48 to 60 hours. After the initial drying the polymer was redissolved in benzene, and the precipitation and drying were repeated. Dilatometric Methods.-To prepare suitable specimens for use in the dilatometers the polymers were compressionmolded into rectangular strips. A vacuum mold similar to the one described by Wood, Bekkedahl and Roth16was used and molding accomplished by means of a WatsonStillman press operating between 10 and 20 tons on an 11inch ram a t temperatures ranging from 130 to‘ 165’. The temperature and pressure of molding were chosen to give optimum results for a given polymer. Some of the polymers were rubbery or tacky at room temperature and in order to remove them from the mold satisfactorily the complete mold assembly was placed in Dry Ice for a half hour after which time the polymer could be removed easily. The molded polymers were cut into narrow strips, weighed and placed in conventional type dilatometers which have been described previously in detail .17J8 Three different confining fluids were used in conjunction with the dilatometers depending on the temperature range being studied. Mercury was used in the range -30” to +150’, ethyl alcohol (95%) was used in the range -75” to O.O”, and a mercurythallium eutectic mixture (91.44% by weight of mercury and 8.56% by weight of thallium) was used over the range -55.0’ to f25.0’. The dilatometers were immersed in a suitable thermostat maintained constant to -f0.05’ and readings taken on both ascending and descending temperatures. For all the data reported here results reproducible to f0.0002cm.*/g. were obtained on both the heating and cooling cycles. (16) L. A. Wood, N. Bekkedahl and F. L. Roth, J . ReseaTch Natl. Bur. Standards, 29, 391 (1942). (17) P. J. Flory, L. Mandelkern and H. K. Hall, J . A m . Chem. Soe., 73, 2532 (1951). (18) L. Mandelkern and P. J. Flory, ibid., 73, 3206 (1951).

July, 1957

GLASSFORMATION IN POLYMERS

987

In order to convert the dilatometer scale reading to specific volume an independent measurement of the density of the polymer must be made a t some reference temperature. The method of hydrostatic weighingsle was used to determine the density of the molded specimens, and reproducible results were obtained when either distilled water, petroleum ether or methyl cellosolve was used as an immersion fluid. The specific volumes obtained in this manner at 25" are listed in the second column of Table I1 for the various polymers. They represent the limiting value obtained after successive moldings of the same specimen and hence the effect of entrapped air and microvoids on the density should be minimized.

Results Volume-Temperature Data.-The dependence of the specific volume on temperature for all of the polymers is illustrated in Fig. 1, where the size of the circles in the plot is representative of the experimental error. The curves pertinent to each of the polymers are designated by the symbol Ci where the subscript i represents the number of carbon atoms in the alkyl side group of the respective polymers. With the exception of the results for poly-(n-octadecyl methacrylate) the data are well represented, over a major portion of the temperature interval, by two intersecting straight lines. The glass temperahre Tg can then be taken in the conventional manner as the temperature of intersection of these two lines, since it represents the point where for the time scale of these experiments the liquid structure is no longer changing with a further decrease in temperature. For poly-(methyl methacrylate) and poly-(ethyl methacrylate), however, a linear volume-temperature relation is not maintained over the whole temperature range in the glassy state. The data in the glassy state for -80 -60 -40 -20 0 20 40 60 80 100 120 140 these two polyniers could be represented by several Temperature, "C. intersecting straight lines. The points of int,erFig. 1.-Specific volume-temperature relations for the section of these lines could be indicative of other poly-(n-alkyl methacrylates). CI designates the plot for poly-(methyl methacrylate), Cn the plot for poly-( ethyl transitions occurring below T,, a phenomenon which methacrylate), etc. has been reported for these ?polymers by other types of measurement^.'^-^^ On the other hand, case of a semi-crystalline polymer. I n the usual the volume-temperature data in the glassy state case partial melting and recrystallization invaricould be equally well represented by a gradual ably occurs below the melting temperature when curving line, as is illustrated. This would be due slow heating rates are employed, but in the case of to the fact that in the glassy state the volume- poly-(n-octadecyl methacrylate) this phenomenon temperature coefficient must approach zero as the is absent. Equilibrium volume is obtained conabsolute zero of temperature is appr0ached.~3dI,'?'. I current with temperature equilibrium and the The plot in Fig. 1 for poly-(n-octadecyl methac- melting is very sharp. This polymer can be superrylate) offers no evidence for glass transformation cooled only a very small amount in analogy with in the temperature range investigated. However, the observed crystallization of the low molecular a first-order transition evidenced by the large in- weight hydrocarbons. The specific volume-temcrease in specific volume over a small temperature perature relation in the liquid state below the meltinterval is indicated a t 37.5'. This transition has ing point for this polymer is given by the dashed been a t t r i b ~ t e d ~to~ the t ~ ~melting of crystallites line of Fig. 1 which represents a linear extrapolaformed by the long hydrocarbon side groups at- tion of the data obtained above the melting tached to the polymer. The backbone of the poly- temperature. Length-temperature measurements mer chain presumably does not participate in the were also made on this polymer from room temcrystallization. The melting behavior of this perature to -180' by means of an automatic repolymer contrasts rather markedly with the usual cording interfer0meter.~,~6The resulting plot of length against temperature was a gradual curving (19) K. Schmieder and K. Wolf, KoEloid Z . , 184, 149 (1953). (20) E. A. W. Hoff, J . Polymer Sci., 18, 1G1 (1955). one making it again impossible to determine Tg by (21) J. Heyboer, P. Dekking and A. J. Staverman, "Proo. 2nd this type of measurement. International Congress of Rheology," London, 1954, p. 123. Some of the pertinent data which are deduced (22) J. Heijboer, Kolloid Z.,148, 36 (1956). from the plot in Fig. 1 are given in Table TI. This (23) G. M . Martin, 6. 8. Rogers and L. Mandelkern, J . Polymer Sei., 20, 579 (1956). table contains the values of Tg that have been de(24) H. 8. Kaufman, A. Saoher, T. Alfrey and I. Fankuchen, J . Am. termined, the specific volume at 25", fits, the specific Chem. Soc., TO, 3147 (1948). ~

(25) S. Greenberg and T. Alfrey, ibid., '76, 6280 (1954).

(26) R. N. Work, J . Research Notl. Bur. Standards, 47, 80 (1951).

SENTAS. ROGERS AND LEOMANDELKERP~

988

Vol. 61

TABLE I1 SPECIFICVOLUMES,EXPANSION COEFFICIENTS AND GLASSTEMPERATURES FOR THE POLY-(~-ALRYL METHACYRLATES) &r. k, 3190, a b x 104 ag x lo', Aa X lo', Polymer

T,

cm.a/g.

Poly-( met'hyl methacrylate) 105 0.855 Poly-(ethyl methacrylate) 65 .889 Poly-(n-propyl methacrylate) 35 ,9285 Poly-(n-butyl methacrylate) 20 .050 Poly-(n-hexyl methacrylate) 5 ,9925 Poly-(n-oct,yl methacrylate) -20 1,030 Poly-(n-dodecyl methacrylate) -65 1.076 a Approximate value due to limited temperature range

-

cm.S/g.

0.870 ,900 .9315 .9475 .972 1.002 1.0155 studied in

volume a t T,, o, and the specific volume at 120°J All the polyniers are in the liquid state a t 120" and it will be taken as a reference temperature in the subsequent discussion. Also given in this table are the linear volume-temperature coefficients just above and below Tg, a~ and ag, respectively, and their difference designated as Aa. Glass Temperatures.-The temperature of glass formation for each of the polymers is indicated by the short vertical arrows in Fig. 1. Tg for poly(methyl methacrylate) is found to be at 105", which is in excellent agreement with the results previously reported by L ~ s h a e k . ~As the number of carbon atoms in the ester side chain is increased, Tg for the polymers continuously decreases 'reaching -65" for poly-(n-dodecyl methacrylate). Other investigators have reported that for this series of polymers,27for polymers derived from esters of poly-(acrylic and for fluorine substituted acrylate polymers,28 Tg goes through a minimum as the number of carbon atoms in the alkyl group is decreased. These discordant results may be a consequence of the methods used to determine Tg or perhaps the identification of the transition due to "side-chain crystallization" with glass formation by the previous investigators. The volume-temperature coefficients both above and below T , gradually increase as the number of carbon atoms in the side chain increase. Therefore, as the data in the last column of Table I1 indicates, the difference in these two coefficients remains essentially constant, within the experimental error, though the values of Act for the n-hexyl and n-octyl poIymers could be slightly below the average. If we select 120' as a reference temperature, which is in the liquid range for all the polymers under consideration, we observe that concomitant with the decrease in T,, as the length of the alkyl side group increases, the specific volume of the polymer a t this temperature is also increasing. This observation is reminiscent of the results obtained by Fox and Flory4 who studied the molecular weight dependence of T, for a series of fractionated polystyrenes. They observed that as the molecular !$eight decreased the specific volume at a reference temperature in the liquid state increased while Tg decreased. There is however a significant difference in the two situations. In the case of the polystyrenes the specific volume in the glassy state is essentially independent of molecular weight 8~10.

(27) R. H. Wiley and C. M. Brauer, J . Polymer Sci., 8 , 647 (1948). (28) F. A. Bovey, J. F. Abere, G. B. Rathman and C. L. Sandberg,

ibid., 16, 520 (1955).

crn.3/g.

crn.a/g./dei.

0.8775 4.60 ,928 5.40 ,9815 5.80 1.0075 6.10 1.055 6.60-7.00 1,089 5.80-6.20 1.141 6.80 glassy state.

cm.'/g./deg.

cin.a/g./deg.

2.15 2.75 3.15 3.80 4.20-4.60 3.90-4.40 3.80"

2.45 2.65 2.65 2.30 2.00-2.80 1.90-2.80

while the data in Fig. 1 for the poly-(n-alkyl methacrylates) clearly indicate that both the specific volume and the volume-temperature coefficient in the glassy state vary for the different polymers. These observations are illustrated in a more quantitative fashion in Fig. 2 where both 0 1 ~ 0and Tg are plotted against the number of carbon atoms in the polymer side chain. The systematic decrease in Tg as 0120 increases is clearly seen. The rate of change in both T, and ~ I Z Ois greater for the lower members of the series but there is no evidence for any asymptotic leveling off in either of these quantities for the polymers containing the larger number of alkyl groups. The close correspondence of these two curves and the inverse relation between T g and glzo suggests the plot made in Fig. 3. Thus when T , is plotted against ~ 1 2 a0 straight line is obtained which can be represented by the relation Tg 656 - 6.3 X 1020120 (1) where T , is expressed in degrees centigrade. The extrapolated value of glzo for poly-(n-octadecyl methacrylate) when used in conjunction with equation 1 suggests that Tg for this polymer should be in the vicinity of - 100. Discussion The problem of describing glass formation for all classes of liquids and quantitatively assessing the various molecular factors determining Tgmust ultimately depend on an adequate description of the liquid state. However, the more exact theories of the liquid state are of such form as to make practical application to problems of this type almost imp~ssible.~On the other hand, the freevolume concepts of the liquid state, though inadequate for many purposes, have been fruitful in quantitatively treating certain types of problems of glass formation which are unique to polymeric systems. The problems treated using this concept have been those where the free volume itself need not be specified but the changes in free volume, as manifested by the changes in specific volume of t'he system, are assessed. Then changes in Tgrelative t o a reference polymer can be calculated. This procedure is of course limited to situations where the changes that are occurring do not drastically alter the chemical or molecular structure of the system. This concept and procedure were first used by Fox and Flory4 in describing the molecular weight dependence of T , for fractions of poly(styrene), taking T , of the infinite molecular weight polymer as reference. This procedure has since been extended to describe the change in T , with

GLASSFORMATION IN POLYMERS

July, 1957 1.15

$110

1.10

+80

1.05

+SO

+80 +50

0.95

-10

- 10

0.90

- 40

-40

989

+I10

f 1.00

ia

- 70 6 7 8 9 1 0 1 1 1 2 #C atoms. Fig. 2.-Plots of specific volume at 120°, filzo, and ,Tg against the number of carbon atoms in the alkyl side group; iilzo represented by 0 , T , represented by 0 . 0.85

1

2

3

4

-70 0.86 0.90 0.94 0.98 1.02 1.06 1.10 1.14

5

cross-linking,6 dilution with low molecular weight materia1,e and c~polymerization.~~~ More recently Williams, Landel and Ferry29have been ab!e to describe the temperature dependence of the melt viscosity of polymeric systems in the vicinity of T , by describing the temperature dependence of the free volume. I n considering problems of this type the specific volume of the liquid is assumed to be composed of two parts. One portion, which represents a closepacked liquid structure, is termed the occupied volume gooc while the remaining volume is defined as the free volume 9. Both the free volume and the occupied volume are considered to be functions of temperature and composition. Thus as the specific volume is altered by changes in composition or polymer structure both uoco and 9 change. By an assessment of the relative changes in these two quantities together with an appropriate criterion for glass formation, the changes in T , with the induced changes can be p r e d i ~ t e d . ~ -This ~ general method is also suitable for analyzing the change in T , with the change in the length of the side group of the poly-(n-alkyl methacrylates). The free volume is assumed to vary linearly with temperature so that for a reference polymer designated by the superscript (1) at a reference temperature T

0120.

Fig. 3.-Plot

of T , against specific volume at 120". 8120.

mer in the liquid state, By rewriting equation 2 for polymer (n)we obtain the relation =4 p

+ A&(T - Tg(l))- acu(")(T- T g ( n ) ) + flOL("'(T)

- OL("(T)]

(4)

Since the data in the last column of Table I1 indicates, within the experimental uncertainty, that A a is a constant for this polymer series, equation 4 can be simplified to Tg(n)- Tg(l) = [&(n) - ,#,g(l)]/Aa ~ [ B J . , ( ~T) ()

- i i ~ ( l ) (T)]/ A a

(5)

Equation 5 can now be converted into a useful form by applying the appropriate criterion for glass formation. The simplest condition to take for glass formation is that a t their respective Tg's, 9, for each of the polymers is the same. This is the condition applied by Fox and Flory4 when they assumed that T , occurred a t a state of is0 free volume. When this condition is applied equation 5 reduces to the simple relation Tg(") = T,(') - ( f / A a ) T)T ) ] (6) If the same increment in free volrime is gained with each increase in specific volume irrespective of the number of carbon atoms in the side chain then f would be a constant for this series of polymers. If this condition is fulfilled and the underlying assumptions are valid a linear relation should be obtained between Tg and the specific volume at the + ( ' ) ( T )= +g(l) + A(u(l) ( T - T g ( ' ) ) (2) reference temperature. This is the situation acwhere c $ ~ is the free volume of the reference poly- tually observed as indicated by the plot of Fig. 3 mer a t its glass temperature Tg(l)and A a is the rate wherein 120' is taken as the reference temperature. a t which the free volume increases with tempera- A slope of 6.3 X lo2is observed in this plot, so that is taken as an average value of A a , ture. This latter quantity is usually identified if 2.45 X with the difference in the volume-temperature f is found to be 0.155 from equation 6. Though no coefficients above and below Tg. If we consider independent estimation off can be made at present another polymer in this series, designated by the the value that is deduced is not unreasonable. We superscript (n) and assume that the change in free can conclude therefore that as the length of the side volume in going from polymer (1) to polymer (n) chain increases, most of the increase in the specific is a fraction .f of the total specific volume change volume that is observed is attributable to an increase in the occupied volume. However, about that occurs, then a t the reference temperature 15% of the volume increase does become free vol+(")(T) = .$(')(T)+ f [ B L ( " ) ( T ) - iiL (1) (T)1 (3) ume, which is of sufficient magnitude to cause the where t~ designates the specific volume of the poly- systematic decrease that is observed in T g . If ,f mere zero then despite the increase in specific (29) M. L. Williams, R. F. Landel and J. TI. Ferry, J. A m . Chrm. volume Tg ~vould be expected to he invariant. S I J C . , 77, 3701 (1956).

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SENTA S. ROGERS AND

For all the systems studied to date,4-6 however, Tg decreases with increasing specific volume indicating a corresponding change of free volume. It has been s u g g e ~ t e drecently ~ ~ ? ~ ~ that a more satisfactory criterion for glass formation would be that the ratio dg/fig,the fractional free volume at Tg, is a universal constant. When this condition is imposed on equation 5 we obtain Tg@)

- Tg(')

= (k/Aa)(~~ -( ~~~ () 1 ) )

- ( . f / ~ a ) ( o ~ ( ~-) #( L T () ~ ) ( T )(7) )

where k the universal constant can be taken as 0.025.29830 Then Tg(') - Tg(') = [ ( k - f ) / A a ] [ i i ~ ( " ) ( T -) OL(*)(T)]

-

f (rk/Aa)(c~r,(~)(TTg(1))

- ~ L ( ~ )-( T

Tg(")))

(8)

For most cases of interest the second term on the right-hand side of equation 8 is negligibly small so that it reduces to Tg(")- Tg(') = [ ( I $ - f ) / A a ] [GL(')( T ) - OL(')( T)] (9) which is identical in form with the relation previously obtained. Equation 9 could also be developed in terms of the specific volume a t T, and the resulting equation predicts a linearity of T , with f i g . An analysis of the data in Table IJ indi* cates that this condition also is fulfilled. The above analysis indicates that the change in T, for this series of polymers can be explained by the variation in the specific volume of the polymers and the partitioning of the volume change between occupied volume and free volume. The fact that this simple consideration is valid for this polymeric series is probably due to the similarity of the chemical nature of the chain repeating unit in each case. This type of analysis has in fact only been successful when no major change is made in the nature of the polymer as in varying molecular weight4 or in cross-linking5 or when additivity laws are operative as in the case of copolymerization6and dilution.' When drastic alterations occur in n system, as changing the chemical nature of the chain repeating unit, the variation of the specific volume is not the sole consideration in determining the location of Tg. For example, though poly-(styrene) and poly- (methy1 methacrylate) have a1most identical values of T, their specific volumes in the liquid state are quite differente23 In this inst'ance, therefore, Tg does not vary with the liquid density. (30) F. Bueche, J . Chsm. Phy/a., 34, 418 (1956).

LEOM A N D E L K E R N

fiof. 61

Even when two polymers are identical chemically as for example poly-(n-butyl methacrylate) and poly-(t-butyl methacrylate) difficulties in interpretation arise. The specific volumes of the latter two polymers at a reference temperature are almost the same yet their glass temperatures differ by about 85°.31 I n this inst>ance differences in chain configuration may be playing a very important role. Though there are many other examples similar to the two just cited, they suffice to indicate the importance of assessing how such factors as configuration and cohesive energy density influence the partitioning of the specific volume of a given homopolymer into it,s two components. Despite the fact that this is a rather formidable task at present some limited conclusions can be made in regard to the poly-(n-alkyl methacrylates). The appropriate studies in dilute solutions have been made on molecular-weight fractions of poly(methyl methacrylate) ,323 poly-(ethyl methacrylate) 34 and poly-(n-butyl methacrylate) 35 from which to deduce the unperturbed dimensions of the polymer ~ 0 i l . l ~ A reanalysis of these data indicates that the, ratios of the root-mean-square end-to-end distance of the unperturbed chain t o the same quantity for the freely rotating chain are about the same. Thus the restrictions to free rotation are similar for these three polymers. The appropriate experimental data for the other members of the series have as yet not been published. For the lower members of the series, however, there is no significant change in the over-all configuration of the polymer as the number of carbon atoms in the side group is increased. The influence of chain configuration on Tg should be about the same for these polymers. On the other hand, calculation of the cohesive energy densities a t 25" for these polymers by the method described by SmallI3 shows that there is a systematic decrease in this quantity with increasing size of the alkyl group. It would thus appear that for this system a t least the increasing free volume and consequent decrease in T , can be ascribed to the decrease in the cohesive energy density. (31) S. 6 . Rogers and L. Mandelkern, unpublished results. (32) S. N . Chinai, J. D. Matlack, A. L. Resnick and R. J. Saniuels. J . Polymer Sci., 17, 391 (1955). (33) S. N. Chinai and C. W. Bondurant, Jr., Lbzd., 32, 552 (1956). (34) S. N. Chinai and R. J. Samuels, ibzd., 19, 463 (1956). (35) S. N. Chinai and R. A. Guszi, J . Polymer Sci., 21, 417 (1956).

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THERMAL DECOMPOSITION OF SODIUM TRIPHOSPHATE HEXAHYDRATE

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THE THERMAL DECOMPOSITION OF SODIUM TRIPHOSPHATE HEXAHYDRATE BY A. C. ZETTLEMOYER,C. H. SCHNEIDER,' H. V. ANDERSON AND R. J. FUCHS William H . Chandler Chenkislry Laboratory, Lehigh University, Bethlehena, P a . Weslvaco Mineral Products Division, Food Machinery and Chemical Corporatzon, Carteret, New Jersey Received April 10,106%

The products obtained by the thermal decompositions of sodium tripolyphosphate hexahydrate under various conditions have been examined by chemical analysis and X-ray diffraction methods. These methods show that a ratio of pyrophosphate to orthophosphate greater than 1:1 is found in the products. Rate studies of, the decomposition a t several temThe apparent heat of activation peratures show that a change in the mechanism of decomposition occurs a t about 110 is 41.5 kcal./mole a t lower temperatures and 18.4 kcal./mole at higher temperatures.

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Introduction Hydrolytic reversion of sodium triphosphate in aqueous solution has been studied under a wide variety of conditions to show the effects of temperature, concentrations, pH, added salts, etc.2-s The decomposition mechanism appears to be a simple hydrolysis of triphosphate into an equimolar mixture of ortho- and p y r o p h o ~ p h a t e . ~ ~ ~ * ~ On the other hand, the thermal decomposition of crystalline sodium triphosphate hexahydrate has not been investigated thoroughly and divergent views of the mechanisms involved have been published. Bonneman-Bemiag reported the formation of a mixture of tetrasodium pyrophosphate and sodium dimetaphosphate on the decomposition of the hexahydrate in the range 85-120". Thilo and Seemaii'oa and Raistrick1Obin independent studies over this temperature range claimed the formation of an equimolar mixture of tetrasodium pyrophosphate and monosodium dihydrogen orthophosphate which may react further to form trisodium monohydrogen pyrophosphate and disodium monohydrogen orthophosphate. Quimby11~'2has reported the decomposition of the hexahydrate to a mixture of pyrophosphate and Orthophosphate in the range of 95 t o 120" with preferential formation of the pyrophosphate. The work described below, conducted over a wider range than studied previously, reveals an abrupt change in decomposition rate a t 105-110", confirms the formation of a molar excess of pyrophosphate over orthophosphate, and gives evidence for both tetrasodium pyrophosphate and trisodium hydrogen pyrophosphate in the primary decomposition product. Since the decomposition was followed by X-ray analysis for the hexahydrate, any loss due to change from crystalline to amorphous phase was (1) This Baper is taken in part from a M.S. thesis a t Leliigh University by C. H. Sohneider, Westvaao Fellow, 1951-1955. (2) J. R. Van Wazer, E. J. Griffith and J. F. MoCullough, J . A m . Chem. Sac., 77, 287 (1955). (3) R . N. Bell, Ind. Eng. Chem., 39, 136 (1947). (4) G. Corsaro, A m . Per/umer Esaent Oil Rev., 64, Aug. (1946). ( 5 ) J. P. Crowther and A. E. R. Westman, Can. J . Chem., 3 2 , 42 (1954). ( G ) S. L. Fries, J . A m . Chem. Soc., 74,4027 (1952). (7) J. Green, Ind. Eng. Chem., 42, 1542 (1950). ( 8 ) R. Watrel, Die Chemie, 55, 356 (1942). (9) P.Bonneman-Bemia, Ann. chim., 16, 395 (1941). (10) (a) E. Thilo and H. Seeinan, 2. anorg. allgem. Chem., 267, 65 (1951); (b) B. Rsistriok, Rov. Coll. Sei., 19,9 (1949). (11) 0.T. Quiinby, Chem. Reus., 40, 141 (1947). (12) 0.T. Quimby, THISJOURNAL, 58, 603 (1954).

counted as reacted material. Because the rate data fitted a first-order expression very closely, this latter contribution appeared to be of minor importance. Products of the Thermal Decomposition Samples of hexahydrate were placed a t temperatures up to ca. 100" under a vacuum of 10" mm. of mercury. X-Ray diffraction patterns of the 25 and 50" samples showed only the lines of the hexahydrate, tvhich slowly became diffuse with time suggesting the presence of amorphous products. Analysis13 of the 50" products showed the orthophosphate content as Na2HP04 to be 3.3% after 16 hours and 5.8y0 after 112 hours. The X-ray diffraction patterns of the 85, 95 and 100" samples were essentially the same as those of the products of regular oven heating at 100"; that is, only the lines of Na4Pz07were produced. The estimated content of the oven-heated 100" product was 30y0. The X-ray pattern of the 100" oven-heated product after slurrying with water, air-drying and heating at 100-110' for an hour showed the lines of Na4Pz07, NazHP04 and Na3HPz07.\Hz0,with the Na4P207content about the same as in the original decomposition product. Here the appearance of trisodium hydrogen pyrophosphate did not necessarily indicate its presence in the original decomposition product, since both NaiHPz0, a.nd Na2HPO4may be formed by equilibration of Na4Pz07and NaH2P04in aqueous medium. Therefore, an attempt was made to form crystalline Na3HPz07 directly, without recrystallization from water, by tempering the original decomposition product for three days a t 110'. The X-ray pattern of this tempered product again showed the lines of Na4Pz07,Na2HP04and NagHPz07.HzO. In subsequent tests it was discovered that a t temperatures of 110, 115 and 120' crystalline Na3HPz07.Hz0 occurred in the decomposition product even after only soy0 decomposition of the original Na5P3Olo.6H20. The X-ray diffraction patterns of the 5070 decomposition products a t these temperatures contained the lines of both Na4Pz07 and Na3HPz07.Hz0. These results were additional evidence for the mechanism of the reaction suggested by Quimby.12 Chemical analysis showed 13y0 orthophosphate (as P z O ~ in ) the decomposition product tempered a t 110' and 12% orthophosphate in the recrystal(13) Jones, Ind. Eng. Chem., Anal. Ed., 14, 536 (1942).