SOME THERMODYNAMIC AND KINETIC ASPECTS OF ADDITION POLYMERISATION By F. S. DAIKTON F.R.S. and K. J. IVIN PH.D. (DEPARTMENT OF PHYSICAL CHEMISTRY UNIVEHS~TY OF LEEIX) Introduction THE question is sometimes asked ‘ * Why does polyinerisation occur ’! ” The answer is divisible into two parts first that under the prevailing experimental conditions the free energy decreases during polymerisation the extent of reaction being determined by the magnitude of the decrease ; and secondly that a mechanism is available which perinits the reaction to proceed a t detectable speed. Much research in the high-polymer field has hitherto been devoted to the elucidation of the kinetics and mechanism of polymerisa- tions ; relatively little effort has been made towards the determination of free energies of polymerisation or towards the understanding of the factors which influence their magnitudes.I n this Review we shall summarise the existing thermodynamic data on the formation of addition polymers. Many of these data are derived from systems in which an effective equilibrium can be set up between the growth process and its reverse and we shall begin after a brief summary of addition polymerisation mechanisms by considering the effect of such reversal on the normal kinetic expressions. Theoretical outline Main Features of Addition Polymerisations.-The overall reaction of addition polymerisation can be represented by equation ( l ) in which n molecules of monomer M give a polymer niolecule M with an accompanying change of n.Axx in the thermodynamic function % e.g. H 8 or G the states of M and M being denoted by the subscript x (see p.67). I n eqn. (1) M has been used to denote the exact formula (MI), but i t will be more convenient to define M as any linear polymer molecule conhining 32 monomer units plus (or minus) two end-groups which are not closely related to the monomer. Thus M denotes the exact formula R(M,),R‘ where R and R‘ are end-groups not derived from MI and also denotes R(Ml),-lMl’ where M,’ is a group derived from MI e.g. by loss of a hydrogen atom. A given polymer sample always contains molecules of differing degrees of polymerisation 11 and the mean value is denoted by mp. The monomer either contains an unsaturated group e.y. C=C C=O or -P=N- or is a cyclic compound e.g. a cyclic ether imine ester anhydride Uurnett “ Mechanism of Yolymer Reactions ” Intersciencc New Y ork 19M.nM = M ; nAx (1) (u) Flory “ Principles of Polpier Clieniistry ” Cornell Univ. Press 19.53 ; 61 ( 6 ) 62 QUARTERLY REVIEWS sulphide or siloxane. I n both cases the reaction is usually a kinetically unbranched chain reaction in which the first step is the opening of the double bond or ring. This initiation step involves the conversion of a monomer molecule into an active centre represented by M1* which is capable of joining on to a second monomer molecule and of simultaneously transferring to it the capacity for further addition of monomer by the same type of reaction. This repetitive process is known as propagation and is represented by Mi* + MI+ Mi+1*. Again it should be noted that Mi* denotes a centre containingj monomer units plus (or minus) an end-group not re- lated to M,.The capacity for growth can be transmitted to another mole- cule X by the transfer of an electrically charged or neutral atom (or radical) in a process represented by Mi* + X+ MJ + X* (followed by X* + M + XM,*). X is called a chain-transfer agent and may be the monomer. The chain centres M3* are usually destroyed in terminatio?~ reactions which may involve two centres (mutual or quadratic termination) or one centre (linear termination). I n certain rare cases there may be no termination process e.g. (i) polymerisation of some cyclic monomers by a molecular mechanism,2 or (ii) anionic polymerisation in media of high polarity. Termination reactions not only control the concentration of chain centres and hence the rate of the propagation process but also together with transfer reactions are responsible for restricting the DP of the polymer.If the entities X are less than 100% efficient in starting new chains the transfer process will also function partly or wholly as a termination process and is then known as a degradative tramfer process is reasonably large (> loo) Axx in eqn. (1) is essentially the change in therniodynamic function for the propaga- tion process Axp. This point is amplified on pp. 67-68 Classification of Mechanisms.-Whilst the argument developed below is not contingent on the detailed polymerisation mechanism it will be con- venient to bear in mind the classification of mechanisms in terms of the chemical nature of the chain carriers. These may be free radicals cations anions or molecules according to the nature of the initiation step.Pree-radical centres can be generated by the action of heat light or ionising radiation on the monomer or by addition to the monomer of the free-radical products of a subsidiary reaction such as the decomposition of a peroxy- or azo-compound or an oxidation-reduction reaction. Mutual termination frequently predominates in radical polymerisation. Examples of linear termination are found in thc polymerisation of ally1 comp~unds,~ where termination is by degradative transfer to monomer and in systems to which terminating agents Y such as compounds of transition element^,^ have been added. Catalysts for catioizic polymerisation 6 are effective because either alone Fief. In p. 33G. Szwarc Ncifrtre 1956 178 1168 ; Szwaw Levy and Milkovich J . Anlei'. Chew.~ S O C . l93G 78 2666. Collinson Daintoii and NcKaughton. Z ' I ~ U ~ N . Famdny SOC. 19.57 53 489. Pepper Quad. Rev. 1954 8 88. We note here that provided '* Ref. lct p. 173. DAINTON AND IVIN THERMODYNAMICS OF ADDITION POLYMERISATION 63 or in association with a cocatalyst they can donate a cation to the monomer. For example initiation of the polymerisation of vinyl ethers by iodine,' and of styrene in 1 2-dichloroethane by stannic chloride in the presence of water as cocata,lyst are believed to involve the following processes OR 212 + 1+13- It-1,- + R-O-CH-SH2 + l-CH,-CH+I,- (M1*) CH3 I SnC1,,2H20 -1- C,H,-CH-CH -+ C,H -CH+,SnCl,OH-,H,O (M,*) Catalysts for anionic polymerisation are either bases such as sodium hydroxide or sodamide containing an anion capable of adding to the monomer or are entities of low ionisation potential such as dissolved sodium atoms or naphthalene anion^,^ which readily surrender an electron to the monomer to form a radical-ion such as C,H,-CH-CH,-.I n the latter case growth may occur simultaneously a t both radical and anionic ends. The mechanisms of ionic polymerisation are complex and difficult to unravel particularly when they involve the presence of solid catalysts such as those recently found to cause the formation of crystalline polymers from propene and ~ t y r e n e . ~ We simply note here that mutual termination is unlikely to be important because of the repulsion between two centres carrying a like charge. For example it is possible that under certain condit)ions the propagation step in the polymerisation of ethylene oxide may be written as .Some cyclic monomers may polyinerise by a moleculas. chain mechanism. R*[O*CH,*CH,].,,*OH + (CH2),0 -+ R*[O*CK2*CH2IrL+1*OH Equations for the Rate and Degree of Polymerisation and the Effect of Depropagation.-Addition polymerisation mechanisms can be summarised Rate Initiation RIP -+ M,* Ri Propagation Mj* + Ml + Mj+i* kp[M *][MI I Transfer (non-degradative) kfx 114 *I [XI Mj* -I- X+ Mj + X* Termination Mutual{ Linear (including degradative Combination Mj* + Mi* -+ Mi+j - d[M*]/dt = 21ctc[M*I2 isproportionation Mj* -+ Mi* + Mi -t Mj - d[M*]/dt = 2ktd[M*I2 chain transfer) Mj* -+ Y + Mj + Y' ~ t y r ~ * ~ [ y ~ oc) by the annexed scheme. [M*] = Z [Mi*] is t,he total concentration of chain centres and the velocity constants are assumed to be independent of j .When the degree of polymerisation is large the fraction of monomer removed by steps other than the propagqtion step is negligible so that the rate of polymerisation R, is given by j -1 12 - J q M 1 1 I ~ ~ " J ( 2 ) Eley mid Richards T r a m . Farnday Soc. 1949 45 425. 8 Colclough and Dainton Trans. Pa~aday SOC. in the press. Eirich and Mark J . Colloid Sci. 1956 11 748. 64 Q UARTEltLY REVlEtl'S and DP is given by the rate of reiuoval of niononier divided by the rate of formation of pairs of dead polymer molecule ends i.e. DP = R,,! (f([M*l) ) = k,lMlILM*l/ (f([M*I)) (3) where (it being assumed that initiation results in one dead end for each centre formed as in the benzoyl peroxide-initiated polymerisation of vinyl inonomers). I t should he noted that t#ermination by combination results in a polvmer molecule whose two dead ends have already been counted.Equations (2) and (3) have tieen widely and successfully used in the inter- pretation of the kinetics of inany systems under both steady- and non- steady-state c0nditions.l Thus many examples are known of the limiting cases of mutual (R cc A, ; DP cx Ri-l) and linear. termination (RIP cc Ri ; DP independent of Ri) in steady-state systems. However there are certain systems for which the above scheme is inadequate and in which the observed expressions for IZ, and DP can only be accounted for hy postulating the significant participation of the reverse of the propagation process The term depropagation lo appears to have found general acceptance. Equations (2) and (3) are now modified to 2f([M*]) =1 Xi + LM*](2kfJX] + kty[Y] + 2ktd[M*]) Depropagation Mi* -+ Mi-,* + M Rate = k,[M*] 3,) = (k,)lM,l - k,"*I (4) The variations of k and k with temperature will be given by Arrhenius expressions k, = A exp (-E,,/RT) k = A exp (-E,/RT).E, - Ed = A H - A H if DP is large. -AH is the enthalpy change for the overall reaction and is generally a positive quantity (polymerisation exothermic) several times larger than E so that Ed is usually much larger t,han E,. Thus although k may be negligible compared with kp[Ml] a t room temperature it will increase the more rapidly with increasing tempera- ture and we may predict that a teniperature will be reached when kJM,] will be equal to k, regardless of the variations of [M*] and f([M*]) with temperature. At this temperature which is called the ceiZing temperature T, the extrapolated R,-T and a - T curves will cut the temperature axis.Fig. 1 shows the relative values of k,,[M,] and Ed for pure styrene,ll calculated from known data and anassumed Ad of I O l 3 see.-'. It is clear that even in 0.01~1 solution k is not likely to be important for styrene below 150". vary with temperature will depend on the magnitude of the activation energy for the initiation process Ei. In Fig. 2 are show1 the variations which may be expected for the particular cases of catulysed (Ei finite) and rudiation-induced ( E - 0) reactions with and without chain transfer. The ceiling temperature can also be defined as the temperature above p The way in which R and 10Dainton and Ivin PTOC. Roy. SOC. 1952 A 212 207. Idem Nature 1948 162 705. DAINTON AND IVIN THERMODYNAMICS O F ADDITION POLYMERISATION 65 4 I- Tempera t w e (" K) FIG.1 Plots of kp[PYI1] and kd against temperature for styrene. A, = 100 1. mole-l sec.-l ; Ad = 1013 sec.-l (assumed) ; E = 6-5 kcal. mole- 1 ; Ed = 6.5 + 16.1 = 22.6 kcal. mole-l ; [MI] = 8 moles 1.-' (assumed constant). Curve I 10-4kd ; 11 10-4Ep[M1] ; 111 10 -P(kp[M1] - kd). [Modified with permission from nainton and Ivin Nature 1948 162 705.1 FIG. 2 Expected shapes of rate-temperature (full lines) and 1)P-temperature (broke?? lines) gi*aphs without ti>ansfer (upper three) and with transfer (lower two) to monomer. I n n c trnd e E is finite and in b and d Ei - 0. which the formation of Eong-chin polymer from monomer a t concentration [MI] is impossible. The fact that such a temperature exists is a direct result of the fact that polymerisation is a chemical aggregation process.A similar and more familiar situation exists for physical aggregation pro- cesses thus a solid cannot be obtained from a liquid unless the temperature is below the freezing point of the liquid. Solid liquid and freezing point E 66 QUARTERLY REVIEWS are physica,l analogues of polymer monomer and ceiling temperature respectively. Closer inspection of eqns. (4) and (5) shows that they cannot be expected to predict the variations of R and DP with temperature right up to T, because when k approaches k,[M,] becomes small and con- sumption of monomer in the initiation process is no longer negligible and k and kd may show a dependence on j. Nevertheless the limiting slope of dR,/dT as T approaches T may be numerically so large that such effects are of very minor importance and operate only over the last fraction of a degree below T,.A simple expression for the limiting slope is obtained by differentiating eqn. (4) with respect to temperature dR,/dT = [M*](kp[Ml]E,/RT2 - k,E,/RT2) -1 (kl)[JM1] - k d ) . d[M'k]/dT and substituting k,[M,] = E when T = T lim (dR,/dT) = k,[M,][M,*](E - Ed)/RTC2 T+T = k,[Ml][M*]AH,/RTC2 (6) k,~M,][&I*] is the rate which would have been observed at; T in the absence of depropagation. The curves in Fig. 2 have been drawn as though the effects of short-chain polymer formation were completely absent. Experimental curves may be expected to show some signs of turning to approach the temperature axis asymptotically in the temperature region where DP is less than 100.Provided such " tailing " is slight T as defined a t the beginning of the previous paragraph can be found by a short extrapolation of the approxi- mately linear portions of the rate or DP curves above the " tail ". In all cases the formation of very short-chain polymer is to be expected a t and above T because of the variation of AG with n when 72 is small. Again we have a physical analogy in the effect of crystal size on melting point ; l2 this effect is only detectable when the surface free energy contributes appreciably to the molar free energy of the solid i.e. for extremely small crystals. The predicted variation of T with [M,] can be found by equating k,[Ml] to k and inserting the Arrhenius expressions whence ( 7 ) An alternative approach to the problem is based on the recognition of T as the temperature a t which the free energy of polymerisation (for long- chain polymers) passes from a negative to a positive value as the temperature is raised (8) where AH and AS are the heat and entropy changes under the prevailing experimental conditions.Equation (8) emphasises the independence of T on Ri provided always that the polymer formed lias the same structure Tc = AH,/R In (Ap[M11/4 .'. T = A H,/aXP 12 See Partington " An Advanced Treatise on Physical Chemistry " Longmans London 1952 Vol. 111 pp. 246 466. DAINTON AND IVIN THERMODYNAMICS OF ADDITION POLYMERISATION 67 and hence the same thermodynamic properties. (S) we may write As = R In (APIAd) + R ln [M,] = ASI,' + R In [M,] where ASPo is the entropy change for [&I1] = 1 mole litre-1 Comparing eqns.( 7 ) and .'. T = AH,/(AS,O + R In [M,]) It would be better to choose unit activity instead of unit concentration for the standard state since ABPo may vary from one solvent to another because of variations in the activity coefficient of the monomer ; but lack of the necessary data usually renders this procedure impracticable. Instead of saying that a monomer a t concentration [MI] has a ceiling temperature T it will frequently be convenient to reverse the viewpoint and say that a t temperature T the monomer concentration in equilibrium with long-chain polymer is [MJ, where T = T and [MJe = [M1] = exp (AGpo/RT). Thermodynamic Defhitions and the Effect of Chain Length.-The thermo- dynamic quantities defined by eqn. (1) will depend on the states of the monomer and polymer and it is convenient to indicate these by means of the following subscripts Subscript x Monomer State Polymer State gg Gas Gas (usually hypothetical) gc Gas Condensed (liquid or amorphous solid) ls Liquid Solution in monomer ss Solution Solution sc Solution Condensed (liquid or amorphous solid) lc Liquid 9 9 9 9 $ 9 9 These are the symbols suggested earlier by us l3 (the m has been dropped from Ism).When the polymer is partially or wholly crystalline this may be denoted by appending a prime to the c of the above subscripts thus gc'. A superscript circle will be appended when the standard state is specified in terms of pressure or concentration e.g. ALY,," (standard state 1 mole 1.-l of monomer). This superscript is not necessary when the sub- script is lc and the 1 refers to the pure monomer which is taken as the standard state but must be retained when 1 refers to a mixture of two monomers when the standard state may be taken as unit concentration of each monomer.We have shown how the various quantities can be related to each other a t least in prin~ip1e.l~ Bywater l4 and Small l5 have also derived additional relations which allow correction for non-ideal polymer solution behaviour. The formation of a polymer molecule represented by M (see p. 61) may involve an initiation (or transfer) step n or n - 1 propagation steps depending on the nature of the initiation step and a termination (or transfer) step. When n is large enough the contributions to Axx from the steps other than propagation will be negligible and experimental values of Axx may be equated to that of the propagation step Axp.13Dainton and Ivh Trans. Paraday SOC. 1950 48 331. 1 4 Bywater ibid. 1955 51 1267. Small ibid. 1953 49 441. 68 QUARTERLY REVIEWS In two cases where the polymer can be represented exactly by (MJn the actual variations are known for ethylene l6 AHg,,' (kcsl. mole-l) = -22.348 + 19*592/n for n 3 a t 25" ; for cc-methylstyrene 1 7 AH, (kcal. mole-1) = 8-424 - 18-58/n for n = 11 to 46 a t 25" ; and for n > 120 the second terms in the equations are less than 2yo of the first terms. There are two factors determining the magnitude and sign of the second term (i) there are only n-1 additions required to form a polymer whose formula is ; this makes a positive coiitribution ; (ii) thc heat change may be abnormal for the first few additions of monomer ; this will be particularly marked in polymers whose main skeleton is under strain and will make a negative contribution as in cc-methylstyrene where (ii) evidently outweighs (i) Veriflcation and extensions of the theory General Conhnation.-For the common monomcrs such as styrene at concentrations of 0.1 - OM the values of AHx and ASx are such that T lies far beyond the range of the water thermostat and sometimes at tempera- tures where side reactions interfere.For these reasons few examples of ceiling temperatures and related phenomena are to be found in the literature hefore 1938. Indications of such effects occur in the observations that (1) gaseous formaldehyde at 300 mm. will not yolymerise at 100" in the presence of formic acid (Norrish and C,zrrutliers,18 1036) ; (2) isobutene and ol-methyl- styrene only yield high polymers when polymerised below room tempera- ture ; (3) the kinetics of polymerisation of rnethyl methacrylate show deviations from the Arrhenius law above 125" (Schulz [ y .n ' 0 ] and Blaschke,19 1942) ; (4) trimethylene disulphide is -c-c-s- stable in 0.05~1 solution but polymerises a t higher concentrations (Whitney and Calvin,20 1955) ; (5) the formation of allreiie polysulphones of general formula (I) from liquid mixtures of the alkene with sulphur dioxide only occurs below a certain temperature (Snow and Frey,21 1938). Snow and Frey were the first to notice the existence of a sharp temperature above which polymerisation would not occur and coined thc term '' ceiling temperature ". They later 22 obtained rate-temperature curves of the type shown in Pig.2 ( b ) and showed that T was independent of the catalyst (nitrates peroxides or ultraviolet light) used to initiate the reaction but were unable to offer a satisfactory explanation for their results. While all the observations listed above are consistent with the theory previously outlined a quantitative test of eqn. (9) is required to put i t on (1) l0 Jessup J . Chem. Phys. 1948 16 661. 1'Roberts and Jessup J . Res. Nat. Bur. Stand. 1951 46 11. l9 Schulz and Blaschke 2. phys. Chenr. 1942 51 B 75. ?O Whitney and Calvin J . Chcm. PIL~s. 1955 23 1750. Snow arid Frey I n d . Eng. Chem. 1938 30 176. 2 2 Idem J . Amer. Chem. SOC. 1943 65 2417. Norrish and Carruthers Trans. Faraday Soc. 1936 32 195. DATNTON AND IVIN THERMODYNAMICS OF ADDITION POLYMERISATION 69 a sound footing.This was first done by Dainton and Ivin lo who made a detailed investigation of the formation of but- 1 -em polysulphone and showed that contrary to Snow and Frey's earlier conclusions T did vary with composition in the rnanner required by eqn. (10) T = AHx,'(A&o + R In [MI 4- R In [S]) . . (10) This is eqn. (9) modified to allow for the fact that the overall repetitive process is represented by (MS)j* + M -t S -+ + (JlS).j+l" where M denotes the alkene and S the sulphur dioxide. A H and AsXo of In [M][S] against with rather greater can be obtained from the slope and intercept of a plot I/Tc. Calorimetric values of AH can be determined 20 30 40 50 60 Temperature ("c) F I G . 3 Rate of formcrtion of but- 1 -ene polysulphone f r o m monomer mixture containing 9.1 moles ?& of but-l-ene.A and R photochemical initiation a t two different intensities ; G and H initiation by silver nitrate a t two different concentrations ; J initiation by bonzoyl peroxide. [ Keproduced with permission from Dninton and Ivin Discuss. Paradrry Soc. 1953 14 199.1 precision and always come within the limits of error of those obtained by the application of eyn. (10) (see Table 1). Fig. 3 shows the rate-temperature curves obtained with a mixture containing 9.1 moles yo of but-l-ene (cf. Fig. 2) and demonstrates the independence of T of the niethod and rate of initia- tion.23 Fig. 4 shows that the same T, again independent of initiation conditions is obtttiiieti when the specific viscosity of the polymer (a measure 23 Daiiitoii and Ivin Discuss.Favaday Soc. 1953 14 199. 70 QUARTERLY REVIEWS TABLE I. Heats of formation of alkene pol.2/sulphones from monomers 1s 1s 1s ss (in CHCI, le lc 1s 1s Alkene a a a a b N a a Rut- 1 -eno cis-But -2-one trans-But-2-ene Hexadec- I - m e isoButene Propeiie Hex- 1 -ene cycZoPentene - AHx (kcal. base-mole-’)(l base-mole = M + S ) ~~ ~ From eqn. (10) 20.7 f 1.4 20.8 :k 0.7 19-3 f 0.5 19.2 f 1.2 20.0 -& 0.5 ~- ~ Calorimetric 21-2 3 0.1 20.15 & 0.1 19.9 & 0.1 20.2 f 0.1 18.7 & 0.1 20.7 -& 0.1 21.65 & 0.1 ~ I a Dainton Diaper ‘Ivin and Xheard Trans. Paraday SOC. 1957 53 1269 ; Cook Dainton and Ivin unpublished results. of m) formed a t a given percentage conversion is plotted against its temperature of preparation 10 [cf. eqn. (5)]. The striking nature of the ceiling-temperature effect is illustrated in 0 100 0.075 G * l- I 9 0.050 & 0.025 0 0 20 40 60 Tc Temperature o f preparation (“c 1 FIG.4 tempemture of pepwation with conditions as in Fig. 3. SpeciJic viscosily of but- 1 -ene polysulphone in acetone (c = 8 9. I. -1) plotted against IRcnrndnord. with nrrmfssinn frnm naintnn 2nd Tvin Pmr Rnii Sor 1052 A 919 2117 1 DATNTON AND IVIN THERMODYNAMICS OF ADDITION POLYMERISATION 'i 1 Fig. 5 which shows for a number of alkene-sulphur dioxide mixtures the rate of photochemical polymerisation determined in the same reaction tube nt successively lower t e i n p e r a t u r e ~ . ~ ~ Only in one or two cases are there FIG. 6 Contrccction rate plotted against temperature for the photochemical forniation of alkene polysulplzones.L Pent-2-ene ; M cyclohexene ; N trans-but-2-ene ; 0 equimoleculnr mixture of cis- and trans-but-2-ene ; P cis-but-2-cne ; Q pent-l-ene ; R hexadec-l-ene ; S propene ; T cyclopentene. [Reproduced with permission from Cook Dainton and Ivin .I. Polymer Sci. 1957 26 351 where full details can be found.] signs of " tailing " as T is approached. The magnitude of the viscosities in Fig. 4 indicates that DP > 100 a t least to within a few degrees of T for but-1 -ene polysulphone. The highest limiting slope is observed with cis-but-2-ene polysulphone formation the rate falls from about 0.4y0 per minute to zero in the 1 degree below T when reaction is induced by the unfiltered light from a 250-w compact-source mercury lamp. It is worth noting that in principle A H can be obtained from the limiting slope [see eqn.(G)] since kI,[M1][M*] at Tc can be found by extrapolation [point A in Fig. 2 ( e ) ] . It is interesting that a ceiling-temperature effect is also found in the reaction between sulphur dioxide and polyisoprene z5 which can be written [ =CHCH,*CH,*CMe-] +- SO + [-CH~CH,*C€€,-CMe -1 Depropagation a,lso plays a part in the reaction of sulphur dioxide with styrene but here the effect is somewhat different since styrene itself is readily polyinerised. 26 Monomer-Polymer Equilibria.-We have already drawn atkntion to the r-SO2-l 2 4 Cooli DtLinton and Ivin J . Polyvter Sci. 1057 26 351. 25 Van Amerongen ihid. 1951 6 633. 26 Barb ibid. 1953 10 4 0 ; Walling ibid. 1955 16 315. 72 QUARTERLY REVIEWS analogy which exists between physical aggregation and chemical aggregation processes.But whereas physical equilibria are mobile and rapidly established met'astable states being achieved only by cautious experimentation polymer- isation equilibria are generally immobile and metastability of both monomer and polymer is very common. The practical utility of this fact is obvious. To establish a reasonably mobile equilibrium between monomer and polymer it is necessary that a certain concentration of active centres be continually present. For systems in which there is no termination process every polymer molecule is an active centre whether molecular free-radical or ionic in nature and it is in these systems that equilibrium can be established rapidly and reversibly e.g. for or-methylstyrene catalysed 27 by sodium naphthalene in tetrahydrofuran (anionic centres) and also for gaseous formaldehyde in equilibrium with polyoxymethylene (unknown but presumably molecular centres) though no reliable equilibrium pressures are available.28 Further- more in such systems only long-chain polymer is present a t equilibrium and there is no danger of side reactions.I n the more usual case of systems where there is as loss of active centres in termination processes it is necessary 0. TO 1 - 0.08 R 2 4 6 8 70 12 Time ( h . 1 Ll I I ' 1 ' " 1 1 OO FIG. 6 Change of methyl methacrylate concentration with time ut 132.2" c. photoseiasitised by the solvent o -dichlorobenzene. [Reproduced with permission froin Bywater Trans. Paraday SOC. 1955 51 1267.1 if equilibrium is to be approached to balance this loss by continually supplying fresh active centres through a reaction of either monomer or polymer.Even then the approach to equilibrium is rather slow (for example see Pig. 6 for Bywater's results l4 on methyl methacrylate in o-dichlorobenzene solution with use of photochemical generation of centres) and in order to find the value of [MI] a t equilibrium it is politic to use extra- 2 7 McCormick J . Polymer Sci. 1957 25 488; Bywater and Worsfold ibid. 1957 26 299. 28 ( a ) Nielseii and Ebers J . Chem. Phys. 1937 5 824 ; ( b ) Nordgren Acta Path. Microbiol. Scand. (Stippl.) 1939 40 21. DATNTON AND IVIN THERMODYNAMICS OF ADDITION POLYMERISATION 73 0.2 r FIG. 7 Rate of fall of presswe (- d p / d t ) on irradiation of a mixture of gaseous methyl meth- acrylate with its solid polymer at A 107.0" ; B 118.0" ; C 128.3" ; D 138.5".The jleld above the pressure axis corresponds to polymarisation that below to depolymerisation. [Reproduced with permission from Ivin Trans. Faraday Soc. 1955 51 1273.3 polation or interpolation procedures [for example see Fig. 7 for Ivin's results 29 on the photochemically-induced equilibrium between gaseous methyl methacrylate a.nd its polymer from which it can be seen that for 34 2.1 n b F $2.1 7. ! 7.l 2-3 2.4 2-5 2 -6 2-7 FIG. 8 Equilibrium pressure of methyl methacrylate ( pe) as a function of temperature. [Reproduced with permission from Ivin Truns. Faruduy Soc. 1955 51 1273. ] zBIvin Trans. Faraduy SOC. 1955 51 1273. 74 QUARTERLY REVIEWS each temperature increase in applied pressure of monomer causes a tmnsition from net depolymerisation (dp/dt positive) t o net polymerisation (dpldt negative)].Extrapolation procedures are to be preferred because of the danger of side reactions and low polymer formation when the system is close to equilibrium. Fig. 8 shows the equilibrium pressures of met,hyl methacrylate over its polymer a t different temperatures plotted in the form of a Clapeyron-Clausius equation and emphasising the analogy with the vapour pressure of a liquid. 29 I n Table 2 are summarised the heat data obtained by the application of eqn. (9) and again there is good agreement with the calorimetric heats. Small discrepancies are readily accountable as (i) variations of AH with TABLE 2. Heats of polperisation from equilibrium monomer concentrations Monomer Methyl methacrylate Ethyl methacryla.te Me thacrylonitrile a-Methylstyrene 6-Hexanolactam 6-Hexanolactam Formaldehyde Formaldehyde Tetramethylem formal - AHx (ltcal.mole-') 13.4 0.5 (100-155") 12.9 14.4 f 0.6 (lOi'-138") 15.3 5 1 (110-144") 8.15 ( - 40" t o 0") 3.56 (220-280") 5-0 (7)" (65-120") (14)* (10-58") -3.5 (100-140") ss ( ? ) Calorimetric 13-9 f 0.3 14-1 (25") 8-42 3-8 (75") 3.25 (2 10- ~ 77") 230") 13 & 1 (20") 7.5 1 4.7 * Not reliable. X ~ lc Ic lc lc gc gc 1C 1C ss SS Ref. 3qn. (9 a b d f 9 i k m a 0 33 Cal. C e 7L j 1 n n Q a Bywater Trans. Faraday SOC. 1955 51 1267 ; b Ivin ibid. p. 1273 ; c Ekegren Ohm Granath and Kinell Acta Chem. Scand. 1950 4 126 ; d Cook and Ivin I'rans. Faraday SOC. 1957 53 1132 ; e Iwai J . SOC. Chem. Ind. Japan 1946 49 185 ; 1 By- water Canad. J. Chem. 1957 35 552 ; Bywater and Worsfold J. Polymer Scz. 1957 26 299; h Roberts and Jessup J .Res. Nut. Bur. Stand. 1961 46 11 ; i Meggy J. 1953 796 ; j Skuratov Strepikheev and Kanarsknya Kolloid. Zhur. 1952 14 185 ; k Hermans et al. Rec. Trav. chirn. 1955 74 1376 ; 1 Strepikheev et aE. Doklady Akad. Nauk S.S.f.R. 1966 102 105 ; m Nielsen and Ebers J . Chem. Phys. 1937 5 824 ; n Walker Formaldehyde " Reinhold New York 1953 ; 0 Nordgren Acta Patlz. Microbiol. Scand. (Suppl.) 1939 40 21 ; 9 Calc. from data given by Strepik- heev and Volokhina Doklady Akad. Nauk S.S.S.R. 1954 99 407 ; Q Strepikheev and Volokhina unpublished results reported at the Symposium on Macromolecular Chemistry Prague Sept. 1957. temperature (AC is commonly of the order -0.01 kcal. mole-1 deg.-l for polymerisation) and (ii) slight inaccuracy of eqn. (9) through use of concen- trations instead of activities (mriation of activity coefficients with tempera- ture will cause a systematic error in A H ) .Equilibrium concentrations of various monomers at 25" can be obtained by either interpolation or extrapolation of experimental values or when these are not available rough estimates can sometimes be made from kinetic data by assuming that A = 1013 sec.-l (see Table 3). Measure- DAINTON AND IVIN THERMODYNAMICS OF ADDITION POLYMERISATION 75 ments on the kinetics of degradation of poly(methy1 methacrylate) 30 have shown that A is of this order although of course the conditions are rather different (high temperature high viscosity) from those used to determine k,. TABLE 3. Equilibrium monomer concentrations at 25 O Monomcr Vinyl acetate Methyl acrylate Styreno Methyl methacryla!,e Methyl methacrylat,~ Methacrylonitrile a-Methylstyrene Trimethylene disulphide cycZoPenteno + SO But-l-ene + SO isoButene + SO 1 0 - 9 10-9 10-3 1.6 x 10-4 10-6 1.0 x 1 0 - 3 2.6 > 0.05 0.015 0.5 310 (AC,,' = RI' In 1hf,],) Method Est.imat,od from known values of k, E, AHp and an assumed Ad =1 1013 see.-'; -AHI values (Itcal.mole-') on right - 100-1 50" equilibrium data a t Extrapolated from Reported t o be stable in 0 . 0 5 ~ solution SO in excess ; obtained by extra- Value for isobutene unattainable polation from known values experimentally a Tong and Kenyon J . Amer. Chem. SOC. 1947,69 2245 ; Burnett " Mechanisms of Polymer Rea.ctions " Interscience New York 1954 ; c Roberts Walton and Jessup J . Polymer Sci. 1947 2 420 ; d Ebegren Ohm Granath and Kinell Acta Chem.Scand. 1850 4 126 ; c Bywater Trans. Faraday SOC. 1955 51 1267 ; f idem Canad. J . Chem. 1957 35 552; Bywater and Worsfold J . Polymer Sci. 1957 26 299; h Whitney and Calvin J . Chem. Phys. 1955 23 1750 ; i Cook Dainton and Ivin J . Polymer Sci. 1957 26 351 ; ridem unpublished results. Entropies of Polymerisation from Equations (9) and (lo).-Entropy changes as well as heat changes can be derived by the application of eqns. (9) and (10) and it would be interesting to know how these compare with those obtained from specific-heat measurements on the monomer and polymer by the application of the third law of thermodynamics. Unfortunately a t present there are no cases where both sets of measurements have been made although there are five systems in which specific-heat data are available.A minor difficulty arises in the application of the third law to polymers namely that polymers seldom approach perfect crystallinity a t the absolute zero and the degree of crystallinity may vary with the previous history of the specimen. Nevertheless the entropy differences between polymers subjected to various treatments such as quenching annealing and moulding are relatively small and the residual entropies a t the absolute zero will probably seldom exceed 1 cal. deg.-* inole-l (e.q. the value found for 30 Cowley and Melville Proc. Roy. SOC. 1949 A 199 1 14 24 39. 76 QUARTERLY REVIEWS TABLE 4. Experimental epztropies of polymerisation in cal. deg. - l bnse-mole-1 BIonoiiier From eqn. (10) Propene 4- SO But-l-ene + SO Hex-l-ene + SO Hexadec- l-ene + SO cis-But-2-ene + SO trans-But-2-ene + SO isoButene -$- SO cycZoPentene f SO From eqn.(9) Methyl methacrylate Ethyl methacrylate Met hacrylonitrile a-Meth y lstyreno 6 - Hexanolactain - ASx' 62.2 69.5 69- 1 66.3 69.7 66.7 78-5 64-2 28.0 & 1.5 29.5 29.7 f 1.5 34 & 2 26.3 2-85 X Ic 1s 1s 1s 1s lc 1s ss Ic lc lc lc ss ss Ref. a a a a a b a U c d f C C B h Kotes 1 base-mole = M + S For all except isobutene the calorimetric AHx has been eom- bined with the T values t o obtain ASXo by assuming both A H x and AS," to be independent of temperature. Standard state throughout 1 mole 1. for both M and S For temperature ranges see Table 2 Standard state 1 mole 1.-' Standard state 1 mole I.-' Doubtful value see Hermans et aZ. Rec. Trav. chim. 1955 74 1376 I Entropy (cal. deg.-lrnole-') Temp.(" C) I Monomer 1 Polymer From specific-heat measurements S tyrene isoButene Buta-1 3-diene Isoprene Tetrafluoroethylene 21.57 24.93 27.65 25.5 21.2 24-2 26.76 47.13 Ic lc lc lc lc lc lc' gc' - 23.16" 25.00 126-84 25.00 25.00 25.00 - 75.7 - 75.7 Other values I I l l Sulphur (S,) Ethylene Vinyl acetate Styrene Methyl methacrylate - 7.4 37.0 41.1 26 28 24-29 1s r S S S 49.75 57.16 70.84 51.7 47.6 54.8 44.00 64.37 28.18 32-23 43.1 9 22-9 26.4 30.6 17-24 17-24 159" ; from viscosity-temperature relation Entropy of polymer by extra- polation ofhomologous series; 25" From A values by taking Ad = 1013 see.-' at 25" ; stan- dard state 1 mole 1.-l a Cook Dainton and Ivin J. Polymer Sci. 1957 26 351 ; a idem unpublished results ; c Bywater Trans. Faraday Soc. 1955 51 1267 ; d Ivin ibid.p. 1273 ; C Cook and Ivin ibid. 1957 53 1132 ; f Bywater Canad. J. Chem. 1957 35 552 ; 0 Bywater and Worsfold J. Polymer Sci. 1957 26 299 ; h Meggy J. 1953 796 ; Boundy and Boyer " Styrene " Reinhold New York 1952 p. 67 ; j Dainton Devlin and Small Trans. Furaday SOC. 1955 51 1710; k Furukawa and Reilly J . Res. N a t . Bur. Stand. 1956 56 285 ; 1 Scott Meyers Rands Brickwedde and Bekkedahl ibid. 1945,35 39 ; 119 Furukawa and McCoskey ibid. 1953,51,321 ; fl Bekkedahl and Wood ibid. 1937 19 551 ; 0 Bekkedahl and Matheson ibid. 1935 15 503 ; * Furukawa McCoskey and Reilly ibid. 1953 51 69 ; Q Furukawa McCoskey and King ibid. 1952 49 273; r Fairbrother Gee a.nd Merrall J. Polymer Sci. 1955 16 45'5; 8 Burnett. '' Mechanism of Polymer Reactions " Interscience New York 1951. DAINTON AND IVIN THERMODYNAMICS OF ADDITION POLYMERISATION 77 TABLE 5 .Semi-empirim1 heats and entropies of polymerisation at 25" Heats and free energies in Itcal. entropies in cal. deg.-l mole-1 gg Values Ethylene Propene But- l-ene isoButene cin-But-2-ene t ~ m s - But - 2 -eno 2-Methylbut- l-ene &-Pent -2-ene 1 mns- Pent - 2-en0 2 3-l>imethylbut- 1-en( Hept- 1 -ene Styrene Butn-1 3-diem (1 2 polymn.) Buta-1 3-dienc (1 4 polymn.) Isoprene Ethylene CH :CHX( unconjug.) CH :CXY (unconjug.) Styrene 32.35 80.7 (20.91 18-4 (19.2) 18.1 (18.4) (18.7) (19.2) (18.1) ( 1 8-41 20.7 (20.5) 19.1 (194] 30.6 (20.51 (1 /-a; (l!) (18.7; ( I 6.9 23.1 22.9 25.0 17.8 lc Values alkenes Propene But- l-en? isol3u tene c i s - 13 u t - 2 -ene trccizs - B u t - 2 - ene Hex- 1 -en0 20.1 20.0 17.1 17.9 17-0 19.8 lc Values cycZoa.lkixne! [CH,] ; x = 3 -1 5 6 7 8 x = 3 4 C)H,*CH([CH,],-1 ; 27.0 25.1 5.2 - 0 - 7 5.1 8.3 25.1 23.9 4.1 - 2.2 23.3 22.3 3.2 - 1.8 34.0 39.9 39.8 41.0 39.1 38.0 40.1 34.4 39.8 40.7 35.6 Jossup a Dainton Diaper Ivin i ~ n d 8henrd.b Roberts's valuesf' given in paren- theses.Differenco in values for isobutene due to use by Dainton et u1.O of more recent value for its heat of form a t ion ' Dainton and Ivin,d by Anderson Beyer and Watson's generizlised I group method 26.95 (26-4 26.9 26-65 (27.3 24.85 23.95 26-85 12.1 12.0 9-2 10.5 9.9 11.8 16.5 13.2 10.2 2.5 0.7 - 8.9 20.2 17.2 15.3 7.6 22.3 18.0 15.7 8.5 22.1 21.2 2.2 - 1-4 4.9 11.0 19.1 18.8 - 0-5 - 4.5 16.6 16. 1 - 1-5 - 4.3 Dainton Diaper Ivin and Sheard.b Values in parentheses obtained by Dainton Devlin and Smalle with slightly different assumptions I in the coinnutation Dainton Dcvlin and Smal1.e Note correc- tions as below Sign of A S corrected A H and AG values cor- * rected for error.3 in ccjmputa tion a Jessup J .Chein. Phys. 1948 16 661 ; Dainton Diaper Ivin and SheiLrd Trans. Fai*aday SOC. 1957 53 1269 ; c Roberts J . Res. Eat. Bur. Stan . 1950 44 221 ; d Dainton and Ivin Trans. Faruday SOC. 1950 46 331 ; c Dainton Devlin m c l Small ibid. 1955 51 1710. 78 QUARTERLY REVIEWS amorphous rubber 31 is 0.28 cal. deg.-l mole-1). All available experimental entropies of polymerisation are listed in Table 4. The values for styrene give some idea of the extent to which AS," depends on temperature. The Semi-empirical Calculation of AH and AS,.-When experimental values of AH and AS are not available it is sometimes possible to make fairly reliable estimates by means of a semi-empirical group method such as that of Andersen Beyer and Watson.Such methods were reviewed recently by Janz 32 and depend upon the experimental fact that thermodynamic properties are approximately additive introduction of a given group into different compounds having the same effect so long as the substitution is made a t a structurally similar point. In a molecule such as polyisobutene the methods make no allowance for interaction between substituents on alternate carbon atoms. Any considerable difference between calculated and observed values may therefore be attributed to incomplete allowance for steric strain. Semi-empirical methods of this nature were first applied to the calculation of AHgg' for various alkenes by F1ory.l" Roberts 33 revised these values on the basis of improved thermochemical data and Dainton and Ivin l 3 extended the calculations to include both AHgg' and ASgg' for vinyl and vinylidene monomers over a range of temperature.While AHg,' and ASgg' are useful for indicating the magnitudes of structural and temperature effects AH, and AS, are more practical quantities ; but lack of information about the heat and entropy of vaporisation of the polymer is the usual obstacle to the calculation of AH, and AS,,. With hydrocarbons this information can be derived by extrapolation of data on homologous series and Dainton Devlin and Small 34 have estimated AH1 and AS, for the polymerisation of various substituted and unsubstituted cycloalkanes.The method can also be applied to the polymerisation of alkenes. I n Table 5 are summarised the more recent values derived by these methods. Structural Effects on Po1ymerisability.-Structural effects on polymerisa- bility in the thermodynamic sense can be studied by comparing either (i) free energies of polymerisation a t a given temperature or (ii) temperatures at which the free energy of polymerisation is zero i.e. ceiling temperatures. In either case a standard concentrat,ion condition must be specified e.g. the pure state 1 mole 1.-l or some other convenient concentration. -AH, values vary over a much wider range than -AS, values. Thus observed heats in kcal. mole-l range from about 8-4 (or-methylstyrene l7) to 21.3 (vinyl acet<ate 35) or 39 if the rather unreliable value for tetrufluoroethylene 36 37 is included ; Polymerisation of ethylene derivatives.31 Bekkedahl and Matheson J. Res. Nat. Bur. Stand. 1935 15 503. 32 Jam Quart. Rev. 1955 9 229. 33 Roberts J. Res. Nat. Bur. Stand. 1950 44 221. 34 Dainton Devlin and Small Trans. Faraday SOC. 1955 51 1710. 35Tong and Kenyon J. Amer. Chem. SOC. 1947 69 2245. 36 DUUS Ind. Eng. Chem. 1955 47 1445 ; Kirkbride and Davidson Natuye 1954 174 79 ; von Wartenberg and Schiefer 2. anorg. Chem. 1955 218 326 ; Scott, Good and Waddington J. Amer. Chem. SOC. 1955 77 245. 37 Furukawa McCoskey and King J. Res. Nat. Bur. Stand. 1952 49 273. DAINTON AND IVIN TIIERMODYNAMICS OF ADDITION POLYMERISATION 79 calculated values also lie within these limits. On the other hand observed entropies range only from 25 to 30 cal.deg.-l mole-l. (These limits are extended to 24 to 34 if the calculated value for truns-but-2-ene and the ss value for methacrylonitrile are included.) Thus the entropy contribution to the free-energy change a t 25" will usually lie between 7.4 and 9.0 kcal. mole-l. The effect of structure on AG, is therefore mainly through the heat term. Variations in AH arise mainly through (1) steric strain in the polymer as a result of bond stretching bond-angle deformation or interaction between non-bonded atoms ; (2) differences in stabilisatioii energy in the monomer and polymer as a result of conjugation or hyperconjugation. The variation in the semi-empirical AH values for simple alkenes (Table 5) must be due to hyperconjugation effects since (1) is not allowed for in the calculations and conjugation is absent.The difference between the observed l3 and calculated values of -AHl for isobutene (12.6 and 17-1 kcal. mole-' respec- tively) is accountable as (1). Steric hindrance also causes low heats of polymerisation of other 1 1 -disubstituted ethylenes such as vinylidene dichloride 35 ( - A H = 14.4 kcal. mole-1) and the methacrylate esters 38 39 ( -ANlc = 12-3-13.9 kcal. mole-l). The heat of hydrogenation of methyl methacrylate is the same as that of isobutene 40 so that conjugation in the methacrylates contributes very little towards stabilisation of the monomer. Conjugation to the ethylenic bond makes an appreciable contribution to the stabilisation of such monomers as styrene and its ring-substituted deriva- tives 41 (-AH, = 16.0-16.5 kcal. mole-l).In a-methylstyrene (1) and (2) combine to give an exceptionally low heat of 8.4 kcal. mole-l. The abnormal thermochemical properties of fluorine compounds are well known 4 2 and have been attributed to the effect of the antibonding electrons on the fluorine atom. It is therefore not surprising that -AH1 for tetrafluoro- ethylene is exceptionally high (39 & 4 kcal. mole-l) but in view of the experimental difficulties associated with the thermochemistry of fluorine compounds and the poor agreement between different investigators 36 it would be premature to discuss this value further until the limits of error have been confirmed. Structural modification of a monomer CH,:CHX or CH,:CXY by the introduction of a substituent on the group X has very little effect on AH so long as the substitution is made on an atom not adjacent to the double bond e.g.the methacrylates and the ring-substituted styrenes. But if the substitution is a t an atom adjacent to the double bond it substantial effect may result ; thus methyl 2-tert.-butylacrylate gives only a saturated dimer 43 in the presence of sodium and liquid ammonia at -80" whereas methyl methacrylate polymerises readily. Presumably the ceiling temperature of t'he former substance is below -80". 38 Ekegren Ohm Granath and Kinell Acta Chem. Scund. 1950 4 126. 39 Tong and Kenyon J . Amer. Chem. Xoc. 1946 68 1355. 40 Wheland " The Theory of Resonance " Wiley New York 1947 p. 61. 41Tong and Kenyon J . Amer. Chem. SOC. 1947 69 1402. 4 2 Sharpe Quart. Rev. 1957 11 49. 43 Crawford J. 1953 2658. 80 QUARTERLY REVIEWS We may now consider the relative constancy of -Ah', values.The calculated values for alkenes a t 25" range from 23-95 to 26.95 cal. deg.-l mole-1 (Table 5) but only in the case of isobutene is it possible to compare calculated (26.65) with the experimental value (28.S cal. deg. -l mole-l). The experimental value is thus 7% larger than that calculated (cf. -AH, where the experimental value is 26% less than that calculated). Thus steric hindrance in the polymer which markedly affects AH,, has comparatively little effect on AS1,. For example -4SlC for methyl methacrylate a t 25" can be estimated as about 26 cal. deg.-1 mole-I (from the value a t 120') while the value for cc-methyl- styrene a t -20" (26) is only a little higher than that for styrene (22). If anything it appears that steric hindranee raises -ASlc slightly i.e.causes the polymer to have a reduced entropy. This is understandable since the loss of internal rotational entropy in the polymer as a result of steric hindrance is likely to outweigh the gain of internal vibrational entropy. It is worth noting that A&', - ASggo a t 25" is approximately constant (10.5-14 cal. deg.-l mole-l) whether observed or calculated values of AS, are used. This difference is equal to the standard entropy of vaporisa- tion of the monomer less the standard entropy of vaporisation per unit of liquid or amorphous polymer. An approximate value for the latter may therefore be derived from the known values of As, and 8," (monomer) and a calculated value of Thus for styrene 8," (monomer) = 25.7 whence &','(polymer unit) = 15-1 cal.deg.-l mole-'. This may be com- pared with Svo(C,H unit) = 3.1G cal. deg.-l mole-l which can be obtained 34 by extrapolation of data on the ndkanes. It is of interest to analyse ASg," in terms of the component entropy changes translational AS, external rotational A& vibrational AS, and internal rotational AS,, in order to try to understand why it is that entropy is an approximately additive property so leading to approximately constant values of ASg,'. St S, and 8 for the monomer can be calculated from standard formula? its molecular weight moments of inertia and vibrational frequencies being known. Sir is found by difference between (St + LYr + 8,) and the experimental (third-law) value for Sgo(monomer). For the polymer it is readily shown from the standard formuh that Sv + Sir > St + S regardless of the molecular shape so that Xt + Xr may be neglected.Xv + Sir is thus the standard entropy of the gaseous polymer which must be found semi-empirically. The numerical values 44 for ethylene isobutene and styrene are summarised in Table 6. These values show that on polymerisation the loss of external rotational entropy nearly balances the gain in vibrational and internal rotational entropy so that -ASgg' has a value quite close to the monomer's translational entropy and this is fairly insensitive to the molecular weight of the monomer. Polysulphone formtion. Polysulphones are formed by the 1 1 copolymer- This conclusion appears to be a general one. * 4 Herzberg " Infra-red and Rrtrnan Spectra " Van Nostrand New York 1915 ; '' Tables of Thermodynamic Data " Amer.Petroleum Inst. New York 19 ; Kil- patriclr and Pitzer J . Res. Nut. Bur. Stand. 1946 37 163 ; Pitzer Guttman and Westrum J . Amer. Chern. SOC. 1946 68 2209. DAINTON AND TVIN THERMODYNAMICS O F ADDITION POLYMERISATION 81 TABLE 6. Analysis of A&,,,' into the contributions from various motions Ethylene isoBu tene Styrene ill 28-02 56.10 104.14 isation of sulDhur Mononier .~ cal. deg.-* irinlc-l 15.9 0.G 0 23- 1 !t. I 27.9 10.1 4 . 7 l'olyincr unit 52.4 1 S.4 70.2 29-2 82.5 47.0 cal. deg.-* mole-' 34.0 4 1.0 355 dioxide with a wide variety of ethylene derivatives. J. Heat and entropy data have been obtained for eight systems (see Tables 1 and 4) but a rather wider range of compounds can be compared if we confine our attention to ceiling temperatures determined at or corrected to a standard monomer concentration product of [M][S] = 27 mole2 (binary systems mole fraction of alkene about 0.09).I n Table 7 are summarised the values obtained by Cook Dainton and I ~ i n ~ ~ who also found that the following compounds would not copolymerise with sulphur TABLE 7 . Ceiling temperatures for polysulphone formation at [M][S] = 27 mole2 Stmiglit-chiiili alk-l-cnps Alk-2-enes and cyclic nllrenes Ethylene" > 135' isol3utene* 4.5' tmns-But-2-ene 33"(38")7 But- l-ene 64 3-Methylbut- I -cne* 36 But-2-ene(50yo cis 34.5 Pent-l-ene 63 4 4-Dirrieth),lj)ent- 14 Pent-2-eno 8 Propene* 90 2-Methylpent- 1 -ene - 34 cis-But-2-ene 36 (.iG)t 1 -ene* (-50% czs) Hex- 1 -ene 60 Hept-2-eno - 39 Hexadec- 1 -eneQ G9 cycloPen tene 108.5 (-88% cis) cycloHcxene 24 'The values for 5 allyl compounds range frvm 76" (alcohol*) t o 45' (forniate* and acetate).* Polymer insoluble in reaction mixture. t I'alues in parentheses corrected for isomerisation effect (see p. 89). dioxide a t any temperature down to - 80" 2-ethylbut-l-ene S-ethylhex- l-ene 2 4 4-trimethylpent-l-ene7 2-methylbut-2-ene 2 3-dimethylbut-2- ene 4-methylpent-2-ene allyl chloride and allyl bromide. The general pattern of behaviour is similar to that observed in the simple polymerisation of ethylene derivatives. Progressive substitution at the double bond lowers the ceiling temperature Tc. Substitution remote from the double bond produces a smaller but still quite large effect in alk-l-enes so long as sub- stitution leads to a branched alkene and in alk-2-enes regardless of the point of substitution.The series cis-but-%ene cyclopentene cyclohexene is rather remarkable. The high T for cyclopentene results from an abnormally high 82 QUARTERLY REVIEWS heat of reaction though the reason for the abnormality is uncertain. It may result from a reduction in interactions between non-bonded atoms in the polymer for example between a-methylene groups and the oxygen atoms as a result of the presence of t8he five-membered ring. Such an effect should lea,d to a more flexible polymer molecule and possibly t o a lower entropy of polymerisation. -Ah',," for the cyclopentene reaction is in fact the lowest for the five systems giving soluble polysulphones (see Table 4). However the standard entropies in these systems must be interpreted with caution because of the use of concentrations instead of activities in defining the standard state a.nd also because minor variations paralleling those calcu- lated for the simple polymerisation of alkenes (see Table 5) are to be 2 3 4 5 6 7 8 X F I G .0 Semi-empiricul free energy of polymerisation of cyclodkanes as a function of the number of atoms in the ring x. n Unsubstituted ; b methyl substituted ; c 1 1-dimethyl substituted. expected. The high -AS,,' for formation of isobutene polysulphone may result from stiffness in the polymer chain. The semi-empirical AH, and AS, values for the polymerisation of cyclonlkanes (Table 5) show that AH, makes the main contribution to AG', for 3- and 4-membered rings but that for 5- 6- and 7-membered rings the heat and entropy contributions are both important. I n Fig.9 are plotted the semi-empirical AGl values at 25" as a function of ring size. Two points stand out first the thermo- dynamic impossibility of polymerising the cydohexanes methylcyclopentane or 1 1-dimethylcyclopentsne at 25" ; secondly -AG, for a 3- or a 4-membered ring is greater than that for the corresponding 2-membered Polymerisation of ring compounds. DAINTON AND IVIN THERMODYNAMICS O F ADDITION POLYMERISATION 83 ring (alkene) mainly as a result of the higher value of -AH,,. However thermodynamic feasibility is no guarantee of practical realisation and there is no known way of polymerising cyclopropane or cyclobutane to high polymers. The only simple alkyl derivative of the cycloalkanes which forms high polymers is 1 :' l-dirnethylcyclopropane,45 which does so in the presence of aluminium tribromide.Some polymer is also formed with the 1 2- dimethyl ethyl and 12-propyl derivatives of cyclopropane and with the methyl and ethyl derivatives of cyclobutane but the reaction is not so fast or clean. isoPropylcyclobutane gives no polymer a t all.45 Compounds of formula cyclopropy1.R where R = CN CO*CH, or C6H are quite immune to the attack of free radicals which would cause rapid polymerisation of the compounds vinyl-R in similar circum~tances.~6 It appears that the best chance of opening a 3-membered carbon ring is by attack of an ionic reagent. It may be seen from Fig. 9 that it is not yet possible to estimate the free-energy changes for rings containing more than 8 atoms. However for much larger rings the values must approach zero and it is probable that AG, passes through a flat minimum in the region of x =9 or 10.Beyond this point crowding within the ring which is responsible for the curves' crossing AG, = 0 for a second time becomes less marked. Small 47 has considered the effect of ring size on AG, for heterocyclic compounds. The general shape of the relation between AG1 and x is expected to be similar to that calculated for the cycloalkanes particularly if the hetero-atom does not differ too much from carbon in size and bond angles (for example in oxygen and nitrogen compounds but not in sulphur compounds). Apart from a few heats of polymerisation there are very few quantitative thermodynamic data for the polymerisation of cyclic compounds. There is however a considerable body of information as to their polymerisability or otherwise and this is summarised in Table 8 together with the available heat data.The variations of AH of' the cyclic ethers with ring size and with substitution follow the pattern predicted for the cycloalkanes [cf. also formaldehyde -AH, approximately 7 kcal. mole-l (Table 2)]. In general mechanisms exist for the polymerisation of hetero- cyclic compounds when they are thermodynamically possible ; a negative sign in Table 8 can therefore be taken as very probably indicating a positive free-energy change for the hypothetical polymerisation. Unsubstituted rings containing less than 5 or more than 6 atoms are invariably polymerisable (cycloalkanes excluded). The signs of the free-energy changes for 5- and 6-membered rings are sometimes the same as for the cycloalkanes e.g.the cyclic ethers formals and amides sometimes reversed e.g. the cyclic esters sometimes both positive e.g. the cyclic anhydrides and amines and some- times both negative e.g. the polymethylene disulphides. The order of AG values for the 5- to %membered ring formals 48 is the same as that calculated for the cycloalkanes (8 7 5 6). Substitution in a heterocyclic 45Pines Huntsman and Ipatieff J. Amer. Chem. SOC. 1953 75 2315. 46Hammond and Todd ibid. 1954 76 4081. 47 Small Trans. Paraday SOC. 1955 51 1717. 48 Strepikheev and Volokhina Doklady Akad. Nauk S.S.S.R. 1954 99 407. F* I Ring atonis Sign of AC, tlkanes a t Alkanes calc. fo',,-c Ethers and formals Amides (lactams) Esters (lactones Anhydride Amines Sulphides TABLE 8. Polymerisability (+ or -) of some cyclic compounds as found by experiment with -AH (kcal.mole-1) in pareritheses Unsubstituted - cycZoPropane (27.0 Ic) + Ethylene oxide (22.6 Ic' ") Do not exist -+ Ethyleneimine 4 Negative - cycloButane (-25.1 Ic) + Trimethylene oxide (19-3 ss c ; + Propionolactone + Trimethylene sulphide d 5 Xegative - cycZoPentane (5.2 lc) + Tetrahydro- + Dimethylene furan" (3.6 lcf formal (6-2 lc e ) f Pyrrolidone (1.1 lcf) - y-Butyrolactonc - Ethylene carbonate - Succinic anhydride - Pyrrolidine f Trimethylene disulphideg. h 6 Positive - cycloHexane (-0.7 Ic) - Tetrahydro- pymn - Dioxan - Trimethylene (- 1.3 lcf) formal (0.0 lc e ) - 8-Valerolactam (2.2 lcf) + S-Valerol,zctono + Ethylene oxalate etc.i - Glutaric anhydride - Piporidins -+- Tetramethylene disulphide 7 Negative - cycloHeptane + Tetramethylene formal (4.7 lc 8) ? Oxacycloheptane (5.1 Ic) + 6-Hexanolactam (3-8 lcf) -t 6-Rexanolactonc -+- Adipic anhydride + Pentamethylene disulphide h + 1-Oxa-4 5- dithiacyclo- heptane (1.9 lc j 8 and higher Ncgat ive - cycZoOctane (8.3 lc) + Pentamethylene formal (12.8 lc e ) + 1 3 6 9-Tetra- oxacydoundec- ane 111 ring] -t- 7-Heptanolac- tam (5.3 lc f) $- 13 15 16 17 j- 18 26 dimeric ring carbona,tes ring carbonates + 8-19 ring a,nh ydrides + 11 18 26 ring cyclic dimers + Sulphur [S,] above 159" ( - 3.18 IS") + [CH?,lnS ; n = 6 - 10h Substituted Alkanes Ethers dmides Esters and siloxanes Amines + 1 1-Dimethyl- cyclopropane propane + n-Propylcyclo- propane 1 + Propylene + Ethylcyclo- oxide m + N-Substituted ethylene - imines p + Methylcyclo- butane + Ethylcyclo- butane - isoPropylcycZo- butane 1 + 3 3-Dimethyl- l-oxacyclo- butane ( 1 6-1 ss") + 3 3-Di(chloro- methyl)-1-oxa- cyclobutane [(CH,),NR,]+Br- ; + R = Me Et(?) - R = Prn Bun p - 2-Methyl- 2-chloromethyl- and 3-methyl- tetrahydro - furans - 4-Methyl-1 3- dioxano ? u-n-Propyl-8- - Lactone of valerolactone f u-2-hydroxy- ethoxybutyric acid i - 2-Phenyl-1 3- dioxac y clo hep - tane 0 - N-Substituted 6-hesanolac tam + 8 ring octa- met hylcyclo- tetrasiloxane r * T seems to be just above room temperature.t Estimated from heat of combustion of monomer given by Skuratov Kozina Shtekhsr and Varushyenko Sci. Trans. M.G.U. 1953 164 73 ; see Thermochemicnl Bulletin No. 3 (Internat. Union Pure Appl. Chem.). King J. 1949 1318; CRose J. 1956 546; d Bost md Conn Ind Eng. Chem. 1933 25 526 ; e Strepikheev and Volokhina unpublished results reported a t Symposium on Macromolecular Chemistry Prague Sept.1957 ; f Strepikheev et al. Doklady Akad. Nauk S.S.S.R. 1955 102 105 ; g Whitney and Calvin J . Chem. Phys. 1955 23 1750 ; Carothers Dorough and Van Natta J . Amer. Chern. SOC. 1932,54,561 ; j Dainton Davies Manning and Zahir Trans. Faraday SOC. 1957 53 813 ; k Fairbrother Gee and Merrall J . Polymer Sci. 1955 16 459 ; 1 Pines Huntsman and Ipatieff J . Amer. Chem. SOC. 1953 75 2315 ; Price and Osgan ibid. 1956 78 4787 ; n Farthing J . 1956 3648 ; O Strepikheev and Volokhina Doklady Akad. Nauk S.S.S.R. 1954 99 407 ; p Barb J . 1955 2577 ; Q Gibbs and Marvel J . Amer. Chem. SOC.. 1935. 57. 1137 r Scott. ibid.. 1946. 68. 2294. Where no reference is given. see Small. Trans. Faraduu SOC.. 1955.51. 1717. See Roberts J . Res. Nut. Bur. Stand. 1950 44 221 ; Affleck and Dougherty J . Org. Chem. 1950,15,865 ; 86 QUARTERLY REVIEWS compound invariably decreases its polymerisa.bility again as predicted for the cycloalkanes. ' The variation of AG with temperature is given by (d AG/dT) = -AX. When AS is small it is quite possible that its sign may change as the tempera- ture is changed. The cases in which AG is positive a t room temperature are the very ones in which AH and Ah' are small and in any given case it is impossible to predict without precise knowledge of the variation of AH and AX with temperature whether AG will become negative on raising or lowering the temperature or whether it will fall only to a positive minimum 960 - 840 - 720 - n 2 600 - -2 s 3 480 - .L * \ ?i 3 360 - 240 - 120 - I I I 750 200 250 300 FIG.10 Viscosity of liquid sulphur u,s a function of tentperntrrre. [Reproduced with perniission from Bacoii and It'anelli J. h w r . ('hem. Soc. 1943 G ( i U ! . ] Temperature ( O C 1 and then rise again. Because of the different possibilities it is desirable to vary the temperature over it wide range when testing a 5- to 8-membered ring compound for polymerisability. At present there appears to be only one case of a substance for which the free energy of polymerisation passes from a positive to a negative value as the temperature is raised and for which a polymerisation mechanism is available. This is the well-known case of sulphur where the change in sign occurs a t 159". The onset of polymerisation of S above this temperature accounts for the dramatic increase in viscosity 49 shown in Fig.10 the quantitative interpretation of 49 Bacon and Fanelli J . Amer. Chem. SOC. 1943 65 639. DAINTON AND WIN THERMODYNAMICS OF ADDITION POLYMERISATION 87 which by Fairbrother Gee and Merrall 50 has led to AH, = 3.18,kcal. mole-' and At?, = 7-4 cal. deg.-l mole-l for the addition of an S molecule t o the linear polymer. Above 159 O equilibrium is rapidly established between monomer (S,) and polymer (S8,J and it has been demonstrated by the measure- ment of paramagnetic resonance absorption that the polymer is free-radical in nature and not macr~cyclic.~~ It is well known that the equilibrium can be quenched giving " plastic " sulphur though this reverts to crystalline monomer fairly rapidly a t room temperature. By analogy with the com- moner ceiling-temperature phenomenon sulphur may be said to exhibit a " floor temperature " as a result of the positive heat and entropy of polymerisation.Many of the 5 6- and 7-membered ring compounds listed in Table 8 are readily interconvertible with polymer but to our knowledge only in the case of 6-hexanolactam have the equilibrium concentrations of monomer been derived. Several difficulties may arise in the determination of equili- brium concentrations or ceiling temperatures for these systems (1) the mobility of the equilibrium may make it difficult to quench; (2) the very influences which make AG small also make very small the changes in physical properties such as density and spectra which accompany polymerisation ; (3) the rate-temperature curves will be apt to have a low limiting slope because of the low heat change.However there is no reason why special methods should not be developed to deal with these cases and a rich harvest of results awaits the pat'ient investigator. Geometrical Isomerisation as Evidence of Depropagation Stereoisomeric Polymers.-For many polymerisations the average time interval betweeii successive propagation steps is about During this time the active centre will undergo many internal rotations about the skeletal bonds particularly about the terminal bond. Also if we are dealing with the polymerisation of an ethylenic compound the atoms attached to the terminal active carbon atom are likely to be coplanar with it or if not to be so nearly coplanar as to undergo many inversions during see. Hence we can expect that if cis- and trans-isomers can be polymerised separately or copolynierised with a third monomer t o yield 1 1 copolymers then (1) t,he polymers will be indistinguishable ; (2) if depropagation occurs there will be geometrical isornerisation with a t least one of the monomers and mually with both ; (3) if polymerisation is attempted above the ceiling temperature only isomerisation will result and the same equilibrium mixture will be reached whichever isomer is taken initially.The relevant propaga- tion and depropagation reactions may be represented thus see. H U R H H H These three expectations are borne out in the case of the forma.tion of 50 Fairbrother Gee and Merrall J. Polymer Sci. 1955 16 459. 5 1 Gardner and Fraenkel J. Amer. Ghem. SOC. 1956 78 3279. 88 QUARTERLY REVIEWS but-2-ene polysulphone from sulphur dioxide and cis- and rans-but-2-ene respectively.52 53 The difference in heat content of the two isomers in liquid sulphur dioxide derived from equilibrium measurements [ (3) above] is 1.4 kcal.mole-l which is slightly different from that of the pure gaseous isomers (1.04 kcal. mole-I) and when combined with the two heats of copolymerisation (Table 1) leads to the conclusion that the two polysulphones have heat contents which are identical within experimental error. The polymers also have identical infrared spectra 24 and further evidence for their identity has recently been obtained by Ske11.54 The relative rates of poly- merisation and isomerisation for the Irans- hut-2-ene system are shown in 0 Temperature (OC> F I G . 11 Sulphur dioxide-trans- but-2-ene system.A Photochemical polymerisation ; B isomerisation catalysed by benzoyl peroxide ; C polymerisation catalysed by benzoyl peroxide. The scales for polymer formation and isomerisation are multiplied by 108 and lo4 respectively. [Reproduced with permission from Bristow and Dainton Proc. Roy. Soc. 1955 A,’-229 525.1 Fig. 11. The polymerisation was followed dilatometrically so that the rate of polymerisation is the net rate of removal of alkene (the very small volume difference between the isomers being neglected). The various propagation and depropagation processes are represented by where M, M, and S denote cis-but-2-ene trans-but-2-ene and sulphur 5 2 Dainton Diaper Ivin and Sheard Trans. Faraday SOC. 1957 53 1269. 5 3 Bristow and Dainton Proc.Roy. SOC. 1955 A 229 500 525. 54 Skell Woodworth and McNamara J. Arner. Chem. SOC. 1957 79 1253. DAINTON AND IVIN TIIERMODYNAMICS OF ADDITION POLYMERISATION 89 dioxide and P and Q denote the two types of radical ends. The rate of alkene consumption falls to zero in the cis system when ([S][M,])o = ka8( kd + kdt)/kpckp8. Combining this with the corresponding expression for the trans system a t the same temperature we have ([S][M,])o/([S][M,])o = kpt/kpc. Thus the more reactive isomer (higher kp) gives the lower apparent equilibrium concentration product ([S][M]) a t a given temperature or conversely gives the higher apparent T a t a given concentration product. The qualification " apparent " must be used since a true equilibrium does not exist when the net rate of alkene consumption is zero rather a stationary state is attained in which one forward reaction is balanced by two back reactions.As might be expected from its higher free energy cis-but-2-ene is the more reactive isomer kpc/kpt having a constant value of 1.35 between 19.9" and 31.5". Combining this ratio with measurements on the cis-trans equilibrium in sulphur dioxide we obtain values of kdt/kd ranging from 1.87 a t 31.5" to 2.07 a t 19.9". The energy of activation difference Ed - Ed = 1.4 & 0.4 kcal. mole-l indicates that the separation of the energy levels in the transition states P..-M for the two isomers is about the same as that in the products P + M. The energies of activation for the isomerisation rates though less reliable fit into the same picture. These energy levels are clearly shown in Fig.4 of ref. 52. I n examining the effect of alkene structure on T for polysulphone formation it is desirable in the case of cis- and trans-but-2-ene to correct for the effect of isomerisation so as to obtain the T which would have been observed in its absence. This can be done and at [M][S] = 27 mole2 1.-2 raises T for cis-but-2-ene by 10" and for trans-but-2-ene by 5" (see Table 7). This effect must also be allowed for in deriving AH and A S from measure- ments of Tc in these systems (Table 1). There are a number of cases of induced cis-trans isomerisations where a similar mechanism involving the transitory opening of the double-bond pre~ails.5~ The theoretical possibility that because of a preferred mode of opening of the ethylenic bond and the subsequent retention of configuration of the active centres two geometric isomers might form stereoisomeric polymers was mentioned by Huggins 56 in 1944.Such stereoisomers might differ in physical properties. The original measurements 53 on the heats of copoly- inerisation of sulphur dioxide with cis- and trans-but-2-ene indicated that the two copolymers had heat contents differing by 2-3 & 0.6 kcal. base- mole-1. More recent and more accurate determinations 52 have shown the original results to be in error for reasons unknown and as mentioned above indicate identical heat contents for the two copolymers. Tong and Kenyon 5 7 concluded from measurements of the heat of 1 1 copolymerisa- t)ion of vinyl acetate with diethyl fumarate and with diethyl maleate that the copolymers differed in heat content by 0.7 0.5 kcal.monomer-unit-l and might be stereoisomers. However the slight difference may be account- able in terms of different heats of mixing of the monomers in the two systems. 5 5 Steinmetz and Noyes J . Arne?. Chem. SOC. 1952 74 4141. 6 6 Huggins ibid. 1944 66 1991. 6 7 Tong and Kenyon ibid. 1949 71 1925. 90 QUARTERLY REVIEWS For the polymerisation of a monomer such as styrene each monomer unit may be incorporated into the polymer chain in two ways D and L because of the presence of an asymmetric carbon atom. For the polymer- isation of dienes there are considerably more possibilities. In the past few years catalyst systems have been discovered which with appropriate monomers direct the propagation process in such a way as to produce polymer chains containing either identical or regularly alternating structural units.It has been possible to synthesise crystalline polystyrene and poly- propene as well as natural rubber and gutta-percha. These catalyst systems have been summarised and discussed recently by Eirich and Mark ; in all cases the propagation step appears to occur at a solid-liquid interface. A number of attempts have been made to induce optical activity in the main chain of a vinyl polymer by starting with a monomer containing an optically active side group. Only one of these has been suc~essfiil,~8 and then only when the monomer ( - )-a-methylbenzyl methacrylate was copolymerised witlh nialeic anhydride (azoisobutyronitrile being used as photosensitiser). Effect of Depropagation on Copolymer @omposition.-The copolymerisa- tion of two nionomers M and M generally involves four propagation steps addition of one or other monomer to one or other type of centre represented by MI* and M,*.M,* + M -+ M,* k, MI* + M -+ M,* kl M,* + M -+ M,* k2 Y l = wb2 r2 = W k 2 1 M,* -k RI -+ M,* k21 The copolymer composition d[M,]/d[M,] is given by and this equation has been found satisfactory for a wide variety of monomer pairs.l It is clear however that it will fail if one of the reverse reactions becomes important compared with its forward reaction provided of course that the latter is already important itself. Joshi 59 has suggested that this state of affairs may exist in systems such as styrene-fumaronitrile where eqn. (11) is unsatisfactory.60 It must be mentioned however that his detailed kinetic treatment is invalid because he has assumed that all M,” can break down to give M,* + M, wherea,s in fact only those with the terminal structure M,Ml* can do so.Further work is needed to test these ideas particularly in systems for which r2 w 0 where the theory can be considerably simplified. Thermal and Radiation Stability of Polymers.-The activation energy of the depropagation reaction is given by Ed = E - AH and since E is usually about 5 kcal. mole-1 the value of Ed is largely determined by that of AH,. k will be higher the lower Ed i.e. the lower -AH,. In fact 58 Beredjick and Schuerch J . Amer. Chem. SOC. 1956 78 2646. 69 Joshi J . Sci. I n d . Res. I n d i a 1956 15 B 553. 60Fordyce and Ham J . Amer. Chem. Xoc. 1951 73 1186. DAINTON AND IVIN THERMODYNAMICS OF ADDITION POLYMERISATION 91 those polymers which give high monomer yields on thermal degradation are the ones with low -AH, e.g.poly-formaldehyde -(methyl methacrylate) -or-methylstyrene and -methacrylonitrile.61 In many cases it has been shown that radicals are involved but the depropagation reaction may have to compete with abstraction and other reactions e.g. in polyisobutene and poly(viny1idene chloride) so that the number of successive depropagation steps is not always very large. These competing processes usually pre- dominate in polymers for which -AH is on the high side e.g. poly-ethylene -propene -acrylonitrile -(methyl acrylate) -(vinyl acetate). This is partly on account of the low kd but also because these polymers contain tertiary C-H bonds which are readily broken. A similar division of polymers is observed in the effect on polymers of ionising radiation which causes either cross-linking or degradation 62 (without production of monomer).Cross-linking is favoured when tertiary C-H bonds are present. When such bonds are absent the radicals produced by breakage of the main chain will tend to remain trapped within a cage of molecules and will either recombine to give the original molecule or dis- proportionate to give two smaller molecules so resulting in degradation. The latter will be favoured when the polymer molecule is under strain as in polymers of vinylidene-type monomers but several other factors enter into the interpretation of the results in these systems. Concluding remarks I n much of the early work on polymer chemistry the statement is fre- quently found that a particular compound will not polymerise even when heated for many hours a t high temperature.We can now be wise after the event and see that the simple Arrhenius formula relating rate and temperature does not always apply to a complex process such as poly- merisation. A rise in temperature is nearly always thermodynamically unfavourable towards polymerisation and if I - AGp I eventually falls to zero the rate of formation of high polymer is also bound to fall to zero whatever form the relation between rate and temperature may take a t lower temperatures. 61 Grassie " High Polymer Degradation Processes " Buttcrworths London 1956. 62 Wall J. Polymer Sci. 1955 17 141. 92 QUARTERLY REVIEWS Appendix Lists of heats of polymerisation not given elsewhere i n this Review X Rot,es - A H x Iron1 mnlo-l Monomer Ethylene Propene Acrylic acid Methacrylic acid Acrylonitrile Chloroprene Vinyl chloride Anethole Butyl vinyl ether Bu tadiene Isoprene 2 5 4 25" 2 r 0 gc 24.2 .) allowing 1.3 for heat of fusion lc 16.5 Room temp.lc 15.8 9 9 ? 1C' 17.3 76.8" lc 16.2 76.8" Ekegren et al.a lc 16-17 Estimated lc(?) 13.8 11( ?) 14.4 lc 17.4 lc 17.9 gc' Sc -16.5 - 78" Copolymerisat ion Monomer A Styrene Vinyl acetate isoPropeny1 Vinyl acetate Vinyl acetate Acry lonitrile Acrylonitrile acetate Monomer E Butadiene Maleic anhydride Maleic anhydride Diethyl maleate Diethyl fumarate Vinylidene dichloride Methyl methacrylate Moles o of A in polymer 4-30 50 50 60 50 0 -100 s lc lc lc lc lc sc - AZIx (Ircal. mole-') 17.1-17.7 Nelson et aLb 20.2 17.8 20.0 18.6 Nagao et ci1.c 13.0 -1 8.3 Baxendale et n2.d I For discussion of heat of copolymerisation as function of coinposit ion see Alfrey and Lewis J .Polymer Sci. 1949 4 221. For references see Dainton and Ivin (Trans. Famday SOC. 1950 46 331) or Roberts ( J . Res. Nut. Bur. Stand. 1950 44 221) except where otherwise stated a Ekegren ohm Granath and Kinell Actw Claem. Scand. 1950 4 126 ; b Nelson Jessup and Roberts J . Res. Nut. Bur. Stand. 1952 48 275 ; c Nagao and Yamaguchi J . Chem. Soc. Japan I n d . Chena. Sect. 1956 59 1363 ; 13axendale and Madaras J . Polymer Sci. 1956 19 171.