SMALL-SOLUBILITY OF POLYMERS 71

SOME FACTORS AFFECTING THE SOLUBILITY OF POLYMERS By P. A. SMALL

The solubility of a polymer in a non-polymeric liquid depends mainly on the heat of mixing. When no polar forces are concerned, the cohesive energy densities of polymer and solvent must be close; a method is given for estimating the cohesive energy densities of polymers from a set of additive constants, and it is shown that good agreement is found between values so calculated and values obtained by swelling measurements. The effects of dipole interactions and hydrogen bonding are also discussed. The solubility of polyvinyl chloride in a number of solvents is considered, and correlated with both the cohesive energy density of the solvent and its ability to form hydrogen bonds.

Introduction This paper discusses some of the factors which control the solubility of polymers in non-

polymeric liquids. Only those factors which can, at least in principle, be determined from the properties of the bulk materials are considered. Thus the specific effects of molecular size, shape and flexibility are not considered, though they may in some exceptional cases have a large effect.

The subject is of technical importance in the fields of paints, spinning fibres and casting films, and the plasticization of polymers; the last perhaps is the most important. The principles governing the solubility of polymers are not very different from those governing the solubility of non-polymeric solutes, and the main differences are those arising from the low entropy of mixing, in concentrated solutions at least, of polymers as compared with more usual substances.

Thermodynamics of solutions Two substances mix when the free energy of mixing is negative. This quantity should

strictly be calculated from the partition function of the mixture, but this is impracticable, and approximate methods must be used.

Hugginsl has given an equation for the free energy of mixing a linear, liquid, homogeneous polymer and a solvent, equivalent to

(1) RT VS AG,, = - (+,In 4, + $ + p4s4p) ......................

where AG,, is the free energy/c.c. of mixture, 4 is the volume fraction (subscripts s and p refer to solvent and polymer respectively) and V, is the molar volume of solvent; m is the ratio of molar volumes of polymer and solvent, so that mV, is the molar volume of the polymer. The constant p is the sum of two parts,

where pz is a small constant (empirically 0.2-0.3) depending upon the co-ordination number of the quasi-lattice assumed in the entropy calculation, and K is a heat of mixing constant for the system concerned defined by

where AH,, is the heat of mixing/c.c. of mixture. Amorphous polymers above their second-order

transition points may be considered to be liquids ; 2.0 other polymers will be discussed later. Equation (I) is probably also valid for a branched polymer of low degree of branching. For a heterogeneous polymer, the number-average value of m may be used.

From equation (3), the conditions for the equilib- rium of two phases can be found by a numerical calculation; the phase-equilibrium diagram is given for selected values of m in Fig. I, in which the ordinate has been taken as ~ / p ; when: k is positive (heat of mixing unfavourable to solution) this increases with increasing temperature.

A mixture which is thermodynamically a single phase is regarded as a solution, irrespective of its mechanical properties.

The asymmetry of the curves of Fig. I is striking. The critical composition is given by q& = 2/m/(I + dm); when m is large the critical composition is nearly all solvent. Just below the critical temperature the systems

............................. p = pz + V,k/RT * (2)

AHcc = K$s+p ............................... .(3)

1.5

1

p,,o

FIG. I. phase equilibn.um in polymer-solvent

J. appl. Chem., 3, February, 1953

72 SMALL-SOLUBILITY OF POLYMERS

two phases are a highly swollen polymer-gel in equilibrium with substantially pure solvent; this is qualitatively in accord with experiment. 2J

The critical value of p is &(I + r / d m ) z ; when m is very large this is about 0.5; if for any solvent-polymer system p is less than 0.5, the components will be miscible over the entire composition range. Since the value of p depends largely on the value of k, i.e. on the heat of mixing, the factors affecting this are the main topic of this paper. Intermolecular forces

mentioned briefly. For un-ionized molecules these are as follows. Dispersion forces

Before heats of mixing are discussed the various types of intermolecular force must be

An approximate equation for the energy of a pair of molecules at a distance r is:

E = _ _ _ _ . 3 alaz ____ 41, ............................ 2 r6 Il + I , (4)

where a, I are the polarizabilities and ionization potentials respectively? This is temperature-independent ; and since the polarizabilities of organic groups differ

more than their ionization energies, polarizability largely determines the magnitude of the interaction.

Dipole orientation.-Two dipoles of moment pl, p,, oriented in the most favourable position, have an energy

Thermal motions tend to destroy the orientation, which will, however, be fairly complete when plpz/r3 b kT. When p1p2/r3 << kT, the molecules rotate, but still have an attractive energy; according to Keesom5 for a pair

.............................. E = - 2 plpZ/+. * ( 5 )

. . . . . . . (6)

DipoZe-induction effect.-For a pair of polarizable, polar molecules,

......................... . (7) (Q& + QZP3 E = -

r6 Repulsion energy.-This arises from resonance between the orbitals of molecules which are

close enough for appreciable overlap. When the molecular orbitals are already fully occupied (as in saturated molecules) the net effect is repulsive. The main effect of the repulsive forces is to determine the volume occupied by a liquid, in conjunction with the attractive forces and the disordering effects of thermal motions.

Hydrogen bonding A special case of an interaction which is mainly electrostatic in nature6 is the hydrogen bond:

X-H, . .Y. When the X-H bond has enough ionic character, the bonding electrons are partly withdrawn from the neighbourhood of the hydrogen: because of its small size this can closely approach ' lone pair ' electrons of Y. When X-H and Y are organic molecules, the usual inductive effects of attached groups will alter the electron distribution in the X-H bond, and the negative charge density near Y, and so affect the strength of the- interaction.

Dispersion forces and repulsion forces are always present, and, being non-directional in character, are additive over all pairs of molecules in a liquid and do not depend much on the rotational states of the molecules. A strong interaction involves permanent orientation of the molecules ; a molecule favourably oriented with respect to a second may be unfavourably oriented with respect to a third. It is therefore only when there is a regular long-range orientation of molecules, as in some crystals or pseudo- crystalline liquids, that the contribution from dipole orientation can be large. If this orientation were present in a liquid, its entropy of vaporization would be abnormally high (as in hydrogen- bonded liquids). Ordinary polar organic liquids such as halides, ethers, ketones and esters have entropies of vaporization very little, if at all, higher than for non-polar liquids of similar boiling points: this is even true of aliphatic nitriles, despite the large dipole moment. This indicates that dipole orientation can make little contribution to the total cohesive energy, no doubt because the dipoles are buried deeply in the molecule. Weak dipole interactions not associated with permanent orientation may, however, account for a small part of the cohesive energy.

For a close-packed liquid of molar volume IOO C.C. consisting of spherical molecules with point dipoles of I D. at their centres, the interaction energy, 2p2/r3, is about 120 cal./mole. As this is much less than kT at normal temperatures (some 600 cal.) orientation will be slight.

J. appl. Chem., 3, February, 1953

Dipole orientation is usually much less important.

SMALL-SOLUBILITY OF POLYMERS 73

Using equation (6) , the molar cohesive energy at 25' is about 24 cal./mole. Since for liquids boiling at or above room temperature the total molar cohesive energy is at least 5 kcal. at 25" (e.g. for n-pentane 5 77 kcal.) this is negligible.

The cohesive energy due to these weak dipole-interactions cannot be correlated directly with the dipole moment; it depends upon the detailed charge distribution in the molecules and the way in which other molecules are distributed and oriented round a central molecule, factors impossible to evaluate in a general way; there is thus no simple way of calculating it, but it will be generally assumed in the rest of this paper that dipole-orientation energy is negligible in comparison with the dispersion energy even for polar organic molecules, unless hydrogen bonding occurs. Heat of mixing

The molar cohesive energy of a liquid is defined as the energy necessary to break all the intermolecular contacts in a mole of the liquid; it is thus equal to the internal energy of vaporization to a perfect gas, provided that the intramolecular contacts are similar in the gas state and the liquid states; this proviso may fail for long flexible organic molecules which can coil up in the gas phase.

Since perfect gases mix without heat change, if the cohesive energy of a liquid mixture is greater than the sum of the cohesive energies of the component liquids, heat is liberated and AH is negative; since the entropy is always positive mixing will then occur. In the opposite case, AH may be so positive as to outweigh the mixing entropy, so that the free energy is positive. Such a solution, if formed, will unmix. In the polymer field, such unstable sqlutions do actually occur; an example is a polymer containing an excess of an incompletely compatible plasticizer (which has been rolled in hot); the plasticizer often exudes. Because of the slowness of diffusion through polymers, the unmixing process may be quite slow, and observable.

The heat of mixing thus depends upon the difference of cohesive energies of solution and unmixed components. When the cohesion is due to dispersion forces, the energy of a pair of dissimilar molecules is approximately the geometric mean of the energies of the corresponding pairs of similar molecules.

where E and V are the molar cohesive energies and molar volumes; this gives for the K of equation (3)

where S = d E / V . The quantities EIV and 6 are called respectively the ' cohesive energy density' (c.e.d.)

and the ' solubility parameter '. Equation (8) does not give the heat of mixing very accurately. Nevertheless Hildebrand

and his co-workers have shown that the solubility of many non-polar solutes in non-polar solvents can be accounted for satisfactorily, from this equation for the heat of mixing and an expression for the entropy of mixing based upon the assumptions of randomness and no volume change.8 There are probably three reasons for this apparent discrepancy. First, volume changes do in fact occur; a change of volume on mixing will change both the AH and AS terms, but will have only a second-order effect on the free energy of mixing. In solubility problems it is the free energy of mixing that is important, and failure of equation (8) does not matter if the free energy of mixing is given correctly by combining equation (8) with a suitable expression for the entropy of mixing; the empirical fact is that this procedure does give reasonable results for the solubility for non-polymeric solutes. Secondly, the postulate of the geometric mean for the interaction of a pair of dissimilar molecules is an approximation which may break down when the size and shape of the molecules are very different. Thirdly, when the solubility parameters of the two components are close, so that the calculated heat of mixing is very small, other effects (e.g. those of quadrupole moments) may outweigh the dispersion-energy effect ; here however the entropy of mixing determines the free energy. When the solubility parameters are widely different, the assumption of random mixing upon which equation (8) is based will break down.

Since this approach has given reasonably good results for non-polymeric solutes, it is reasonable to attempt to extend it to polymers. Gee9 showed that the swelling of vulcanized rubbers in different liquids could be correlated with the c.e.d. of the liquids; and it is now widely recognized that the c.e.d. of the polymer is an important factor in determining polymer solubility. When equation (9) holds, we have

The dipole induction effect is probably negligible in all ordinary cases.

Scatchard' proposed a semi-empirical relation for this case ..................... AHcC = (bldz[(EJL'$ - (E,/VZ)+]'

K = [(Es/Vs)I - (Ep/L'p)~]' == (8s - 6,)'

- (8)

(9) . . . . . . . . . . . . . . . . . __

I.

vs ........................... p = pz + RT ~. - ( a s - 6 , ) 2 . . . (10) Since the maximum value of p for complete miscibility is about o * 5, and since F~ is of the order 0.3, if we take V, = IOO C.C. and T = 300' K., we have (as - aP)' < I * 2 as a condition for the

J. appl. Chem., 3, February, 1953

74 SMALL-SOLUBILITY OF POLYMERS

solubility of the polymer in the solvent, when dispersion forces are the only interaction, i.e. the c.e.d.s of polymer and solvent must be close.

When weak dipole-interactions occur, the energy of a dissimilar pair is again approximately the geometric mean of the energies of the corresponding pairs of similar molecules; it may be possible to take this into account by means of a second parameter,1° e.g. by writing:

K = (61 - 62)2 + ; 42] ........................... . (II) [ Here E is a parameter for the dipole interaction analogous to the parameter for dispersion energies; the denominator T is suggested for the term involving E, for then both 6 and E will probably vary only slowly with temperature, since the dipole-interaction energy of a pair varies as I/T [equation (6)].

We then have, for a single substance,

so that 6 and E cannot be estimated from a knowledge of E and V alone. For athermal mixing, the conditions now are 6, = 6, and E, = E ~ ; this implies EJV, = E,/V2,

but is a more stringent condition. If S2 > E2/T it will be possible to estimate 6, without serious error, by neglecting E . But

if, say, in equation (11) 6, = 10, a2 = 9, c l / f T = r, E~ = 0, the weak dipole interactions will make as large a contribution to the heat of mlxing as the dispersion energy, though their' contri- bution to the cohesive energy is negligible. Thus for polymers, it is a necessary condition, but not sufficient, that the c.e.d. of solvent and polymer should be close.

Calculation of cohesive energy densities

important. Since c.e.d.s. are important in controlling solubility, methods of estimating them are

For non-polymeric liquids, this is comparatively easy. The molar cohesive energy is given by V= a0

0 3 ) bU

v = Vvap

where U is the internal energy. The integral is the correction for the imperfection of the vapour ; this is small when the vapour pressure is low (of the order 2% at I atm.) and thus Eis approximately the internal energy of vaporization. This may be calculated from calorimetric or vapour-pressure data; when these are lacking, various empirical correlations are available.8

This method can obviously not be applied to polymers. The c.e.d. of a polymer can be estimated by determining the equilibrium swelling of a slightly cross-linked analogue in various solvents and correlating with the c.e.d. of the solvent; the swelling is a maximum in solvents of the same ~ . e . d . ~ Another method would be to determine p from a plot of reduced osmotic pressure versus concentration in various solvents, and plot p against the c.e.d. of the solvent; it would be a minimum in solvents of the same c.e.d. Both these methods are laborious and time-consuming.

The Scatchard equation (8) is equivalent to the statement that the cohesive energy E of a mixture of n, moles of a liquid I with cohesive energy El and molar volume V, with n2 moles of liquid 2, is given by

That is, (EV)t is an additive property. The author considered it reasonable that it might add, in compounds, on an atomic and constitutive basis. Scatchardll has shown that in several homologous series (EV)t is linear with the number of carbon atoms.

It proved possible to find a set of additive constants for the commoner groups in organic molecules, which allow the calculation of (EV)t. These are called molar-attraction constants, and are denoted by the symbol F.

Then C F summed over the groups present gives the value of (EV)& for one mole of the substance concerned; the molar cohesive energy E, c.e.d. and solubility parameter are then given by

E = AU,~, + J ( n ) d V = AH,, - RT .................. T

E+(n,V, + nzV2)a = n,(E,V,)t + n,(E,V,)a.. .................. (14)

EF X F V V * . (15)

(W2 E = ~- ;c.e.d.= (7) ; F = - ... . . . . . . . . . . . . . These values, given in Table I, have been estimated from the available vapour-pressure and

heat of vaporization data in the literature; all compounds such as hydroxyl compounds, amines,

J. appl. Chem., 3, February, 1.953

SMALL-SOLUBILITY OF POLYMERS 75

amides, and carboxylic acids, in which hydrogen bonding occurs, have been excluded. It has been assumed that for the classes of compounds considered the dipole-interaction energy is negligible; the only compounds for which this seems to be possibly in error are the lower esters and ketones, and in these cases data for the higher members of the series have been used where possible.

Table I Molar-attracriotz constaiits, 25 '

All the values given refer to 25O.

Group F, ca1.t c.c.4 Group F, cal.4 c.c.4 214 H (variable) 80-100 I33 0 ethers 70

CH, cH2 1 -4H [ single-bonded

1 CH, = -CH = double-bonded ,> c =- CH=C- -c=c- Phenyl Phenylene (0, m, p ) Naphthyl Ring, 5-membered I

Conjugation ,, 6-membered

28 CO ketones

93 COO esters

CN Igo I 1 1 ~1 (mean) 19 ~1 Single '

C1 twinned as in CCl? C1 triple as in -CC1,

222 285 Br sinele 735 I sing6 658

- . 425

95-105 0 . NO, nitrates -440 20-30 NO, (aliphatic nitro-compounds) "440

PO, (organic phosphates) -500

The additivity of (EV)t is well established for hydrocarbons. Thus the value of (EL')$ calculated for 72 hydrocarbons (paraffins and olefins) from the additive constants given was compared with values derived from the National Bureau of Standards data12; the root mean square deviation was only 0-8q i , of the mean for the set. For other classes of organic compound there is no comparable set of data, and the evidence for additivity is not so strong. In particular, packing several large groups round a central atom results in a real lowering of the F constant; this effect is taken into account in the values for the hydrocarbon groups, but it is impracticable to give a complete analysis for all substituents. For instance, calculating (El')* for carbon tetra- chloride from F(-C-) + 4F (single Cl) 987 ca1.k.c.t is obtained, whereas the observed value is

835. This effect is always in the same direction and is to be expected for steric reasons. There are other effects such as conjugation, as in styrene or butadiene, and ring-closure, which result in a change of F, in these cases an increase: analogous effects are found in molecular refraction and the parachor. The ring increment varies with ring size, and increases somewhat with degree of substitution on the ring.

Table I1 gives some values of the solubility parameter calculated from the constants of Table I, and experimental values from the literature, mostly obtained by swelling experiments; the agreement is quite satisfactory. In calculating the values for cellulose diacetate and dinitrate a value of 170 was assigned to the OH group, the sum of IOO for the hydrogen and 70 for ether oxygen. This is rather arbitrary, but the contribution of the OH group to C F for the molecule is only some IO%, so that small errors in the value used will not be serious.

Frequently the main source of uncertainty in the calculated value of 6 is the polymer density; unfortunately there are rather few reliable values of density for well-characterized polymers in the literature.

There is, unfortunately, no simple means available for estimating the dipole-interaction parameter E for weakly polar liquids, although, as pointed out above, its contribution to the heat of mixing may not always be negligible. A possible method would be to determine the heat of mixing of a weakly polar liquid and a non-polar liquid, either directly or by measuring the solubility of, e.g. naphthalene; if we assume zZ = o for the non-polar liquid, the heat of mixing becomes

AHcc = $1q$,[(81 - a2)' + E ? / T ] . ........................ .(16)

when AH,,, EJV,, and 6, are known, there are two equations available to determine the two parameters a1 and q.

I

............................. Since, also, E1/Vl = 8; f E ? / T . . .(17)

J. appl. Chem., 3, February, 1953

76

Polymer Polytetrafluoroethylene Polyisobutylene Polythene Natural rubber

Polybutadiene Butadiene/styrene

85: 15 75: 15

60: 40 Polystyrene

SMALL-SOLUBILITY OF POLYMERS

Table I1 Calculated and observed solubility parameters of polymers

6 in cal.*/c.c.+

Polystyrene/divinylbenzene Buna N (butadiene 75) 9-25 9’38(7)

(acrylonitrile 25) 9.5(4) ( I ) Assumed liquid (CF,),, (2) Assumed liquid (CH,),I (3) Amorphous form (4) Scott & Magat13 (5) Richards14 (6) Magat15

Polymer 6 (calc.) Polymethyl methacrylate 9’25 Neoprene G N 9‘38

Polyvinyl acetate 9’4 Polyvinyl chloride 9’55

Polyvinyl bromide 9.6 Polymethyl chloroacrylate 10‘1 Cellulose dinitrate 10.48 Polyglycol terephthalate I0.7(3) Polyme thacrylonitrile 10.7 Cellulose diacetate 11.35 Polyacrylonitrile 12‘75

(7) Gee1e (8) Boyer & Spencer” (9) Alfrey, Goldberg & PricelS (10) Doty & Zablelg (I I) Edelson & FuossZ0

For example, from the data of Scatchard’ and International Critical Tables on the solubility of naphthalene, the value of s2 /T for acetone has been computed as 4 cal.1c.c. at 20’; for ethyl acetate it is about I cal./c.c. For several other polar compounds-chlorobenzene, ethylene dichloride, ethylene dibromide, chloroform, nitrobenzene, pyridine-it is too low to estimate. In this calculation allowance has been made for the difference of molar volumes of solute and solvent, in the expression for the mixing entropy. Since the total cohesive energy of acetone is about 97 cal./c.c., the fraction due to dipole interactions is a small one, even in this liquid which is certainly one of the most polar of ordinary organic solvents. Crystalline and vitreous polymers

So far, the discussion has been limited to liquid polymers, i.e. amorphous polymers above their second-order transition points. A polymer below its transition point is in a thermo- dynamically unstable state, like a glass or supercooled liquid. When a solvent is absorbed, the transition temperature is lowered, which liberates the excess free energy of the unstable state. Polymers below their transition points should be more readily soluble than their c.e.d.s would indicate; the thermodynamic equilibria will not be changed, but the release of this excess free energy during the solution process should increase the rate of solution or rate of swelling.

Partially crystalline polymers have a lower free energy than the corresponding liquid polymers (which are sometimes obtainable by quenching the melt). In order to dissolve them, the free energy necessary to melt the crystals must be supplied. If the polymer is much below its melting point, this free energy will be considerable and the entropy of mixing will not suffice; crystalline polymers are thus, as a rule, appreciably soluble (much below their melting points) only in solvents that have some specific interaction with them, other than dispersion forces, which can only give a positive AH of mixing. Thus polythene and polytetrafluoroethylene are insoluble in any solvent at room temperature; having no hydrogen- bonding groups they cannot show such specific interactions. But nylon is soluble in some solvents in the cold, e.g. formic acid and phenols, with which it can form hydrogen bonds. Another interesting case is ‘ Terylene’ (polyglycol terephthalate), which is soluble in phenols and also in tetrachloroethane. Direct calorimetric measurements have shown that even highly crystalline ‘Terylene’ dissolves in phenol with the evolution of heat, more than I cal./g., whereas amorphous quenched (Terylene’ evolves about 7 cal./g. The heat of solution of ‘Terylene’ in tetrachloroethane has not been measured, but both dimethyl phthalate and dibutyl terephthalate mix with tetrachloroethane with evolution of heat; this is probably due to hydrogen bonding between the ester grouping of the terephthalate and the CH groups of the tetrachloroethane, analogous to that between chloroform and acetone. Evolution of heat on mixing is always evidence of specific interactions. Hydrogen bonding

Such interactions are usually hydrogen bonding.

It is believed that although in most cases weak dipole-interactions have only slight effects

J. appl. Chem., 3, February, 1953

SMALL-SOLUBILITY OF POLYMERS 77

on solubility, hydrogen bonding usually controls the solubility of polymers containing functional groups such as hydroxyl, carboxide or amide, either in the main chain or as pendant groups. Polyvinyl alcohol and polymethacrylic acid are thus water-soluble; if cellulose is etherified (as in methyl cellulose) enough to break up its crystal structure, it also becomes soluble in cold water, though the polymer is precipitated upon warming. Lower critical solution temperatures with water are frequently shown by liquids which are likely to form hydrogen bonds, e.g. nicotine, tetrahydrofurane and triethylamine.

The energy of a hydrogen bond cannot be calculated in any but the simplest cases, and there is not any established equation for the heat of mixing of two hydrogen-bonded liquids. Since hydrogen-bond formation depends upon two factors, one relating to the X-H bond and one to the group Y in a bond X-H, . . Y, at least two parameters will be required to express the properties of a hydrogen-bonded liquid. (Probably more than two parameters will be needed, since the concentration of groups/c.c. and their specific nature come into consideration for both X-H and Y; it is not obvious that both these factors can be combined into one parameter for each type of property.) If the proton-donating and proton-attracting powers of a liquid are expressed by two parameters o and T respectively, the cohesive energy per C.C. of liquid due to hydrogen-bond formation will be some function of o and T which is zero when either o or t is zero; the product ~7 is the simplest such function. If in a liquid mixture, o and t should be added on a volume- fraction basis, we find for the contribution to the heat of mixing due to hydrogen-bonding effects,

AH,, = C$lC$a(ol - a2)(t1 - r2) = 41C$L(oltl + 02t2 - o1r, - 02t1). . . . . . . . . . . . ( IS)

Since hydrogen-bond formation is a localized, specific and saturable type of interaction analogous to valence-bond formation, mole fractions may be more appropriate than volume fractions when the interactions are strong. However, this equation seems to give some qualitative indication of the effect to be expected.

When both liquids are hydrogen-bonded, all four of a,, c2, T ~ , and 7% are non-zero and the sign of AH can be either positive or negative, and the net effect is not easily predictable.

When only one substance can form hydrogen bonds, so that c, and t2 are both zero, AH,, is necessarily positive. Substances possessing neither proton-donor nor proton-acceptor powers are commonly insoluble in water; thus carbon disulphide, despite its high c.e.d. (8 = 10) is incompletely miscible at room temperature with water, methanol or ethanol, though it will mix with the propanols and higher alcohols, for which the hydrogen-bonding energy per C.C. is no doubt lower. But if the second component has strong proton-attracting properties, even if it is without proton-donor properties, i.e. if o2 = o but t2 > q, A H can be zero or negative; thus strong proton-attractors such as acetone (8 = 9-7), triethyl phosphate (8 zz 9.2) and pyridine (8 = 10.7) are not only completely miscible with water, but actually evolve heat on mixing, though 6 for water is considerably higher, perhaps about 16.

If the equation suggested has the correct form, it is a sufficient condition for the contribution to AHcc from hydrogen-bonding effects to be zero if either o, = c2 or T~ = T~ (contributions due to differences in 8 or E may still be large enough to prevent miscibility).

No scheme of o and T values has yet been formulated, however, so that no quantitative test of the equation suggested can be made. It seems, qualitatively, that o tends to increase with increasing acidity of X-H, and t to increase with the basicity of Y.

A simpler case arises when the X-H and Y components are located in different molecules, i.e. when T~ and o2 are zero. Then the contribution to AH,, is always a negative one. Such cases occur when the active hydrogen atom is that of a C-H bond which is polarized by negative substituents (e.g. in chloroform, tetrachloroethane, methylene chloride, the bromine analogues and acetylenes; these substances usually evolve heat on mixing with ethers, ketones, esters, phosphates and tertiary amines). The strong deviations from ideality in chloroform-acetone and chloroform-ether systems have been ascribed to hydrogen bonding by various authors, and Copley, Zellhoefer & Marvel2' have provided much fresh evidence of hydrogen-bond formation involving C-H bonds.

Compounds of this type are good solvents for polymeric esters, if the c.e.d. is in the right range; thus chloroform is an excellent solvent for polymethyl methacrylate and polyvinyl acetate, and tetrachloroethane dissolves cellulose triacetate and polyglycol terephthalate; hept- I-yne dissolves polyvinyl acetate,22 although its c.e.d. is considerably lower than that of the polymer (6, 7.8; for polyvinyl acetate 8 = 9.4). In these cases the ester groups of the polymer show proton-attracting power for the active hydrogen of the solvent.

The author considers that, as first suggested by Marvel, Dietz & CopleyYz3 polyvinyl chloride possesses a C-W bond sufficiently negative to form weak hydrogen bonds, and that its solubility in various solvents is best accounted for when both the c.e.d. and the proton-attracting power of the solvent are considered together. Since a consideration of polyvinyl chloride solvents

J. appl. Chem., 3, February, 1953

78 SMALL-SOL UBILIT Y OF POL YMERS

illustrates in an interesting way how two properties (namely the c.e.d. and the hydrogen-bonding power of the solvent) together control the solubility, it will be discussed in some detail. Solubility of polyvinyl chloride

Polyvinyl chloride is rather unusually insoluble in the cold even in the best solvents. This is very probably due to partial crystallinity of the polymer, since Alfrey, Wiederhorn, Stein & Tob01sky~~ have shown that plasticized polyvinyl chloride when stretched shows an X-ray- diffraction pattern characteristic of crystalline polymers.

In order to test the hypothesis of association between solvents and polyvinyl chloride, the infra-red absorptions of two typical plasticizers (dibutyl phthalate and tricresyl phosphate) were examined at 5% concentration in solution in carbon tetrachloride, chloroform and polyvinyl chloride. The absorption maxima due to the ester carbonyl and the phosphate P=O groups were found to shift considerably in chloroform, and significantly, though less, in polyvinyl chloride. The shift to longer wavelengths indicates a weakening of the oxygen bond, as is to be expected if association of the types C - 0 . . . H-C or P=O. . . H-C occurs. The results are shown in Table 111.

Table I11 Absorption inaxinla of dibutyl phthalate and tricresyl phosphate solutioti

an.-’ cm.? Solvent Solute Band position, Band shift,

- None Dibutyl phthalate 173.5 Carbon tetrachloride ,, >, 173s 0 Chloroform ” 9, 172s I 0 Polyvinyl chloride 2 1 Y, 1731 4 None Tricresyl phosphate 1307 Carbon tetrachloride ’Y 9 1 I 306 I ? Chloroform , J ,1 I297 I 0 Polyvinyl chloride ,, > > 1302 5

-

The experimental error is about I or 2 per cm. It is thus clear that polyvinyl chloride can behave like chloroform, as the differences, though small, are significant.

Further evidence for association between this polymer and solvents is provided by the value of the coefficient cc of the Houwink equation: it has the unusually high value of I ’22 for both cyczohexanone and tetrahydrofuran. This indicates that the polymer chain is more extended than a random coil in both these solvents, which possess considerable proton-attracting powers because of the presence of ketonic and etherial oxygen. Doty & ZablelB determined p values for polyvinyl chloride in various solvents by a swelling method; some values were so low-even negative-as to indicate association between polymer and solvent.

T o interpret solubility data some way of assessing the proton-attracting power of a solvent was sought. Gordy & Stanford25 determined the shifts of the absorption frequency of the OD band at 3 . 7 3 t ~ . in CH, . OD dissolved in a variety of organic liquids (as a measure of this property), and found that the shift correlated well with the basicity in water of several of these liquids; they found that the shift increased in the order esters, aldehydes, ketones, ethers, amines. How- ever, their results omit many compounds which are of interest as possible solvents, and the shifts observed do not seem to run proportionally to the property of the solvent relevant to its solvent power.

Another method of assessing this property was therefore tried, depending upon the colour change of iodine in association with some solvents. In aliphatic hydrocarbons, chlorinated hydrocarbons, carbon disulphide and similar inert solvents, iodine has the same violet colour as in the vapour, with an absorption maximum at about 5400 A., but in alcohols, ethers, esters, ketones and amines it has a brown colour, with an absorption maximum at about 4650 A. In the substituted benzenes the colour changes from almost violet to brownish as the degree of substitution increases ; dielectric-polarization measurements by Fairbrother26 in such solutions show that there is transfer of electrical charge in this complex-formation. This association is at least superficially similar to hydrogen-bond formation (though possibly different in its mechanism) and it has therefore been used to compare different compounds.

The method used was the following: For each compound investigated a series of solutions were made up in 6 in. x I in. test-tubes, each containing 4.66 mg. of iodine (0.14 g./l.) and variable amounts of the test substance, being made up to 30 ml. with carbon tetrachloride. The colours of the set were compared by eye with a standard consisting of 4 ml. of trioctyl phosphate (purified by molecular distillation) and 26 ml. of carbon tetrachloride containing the same amount of iodine; this standard is arbitrary but gives a solution of suitable intensity for visual comparison and about mid-way in shade between the violet solution of iodine in carbon tetrachloride alone and the yellow-brown solution of iodine in trioctyl phosphate. The reciprocal of the concentration of the substance needed to give a match with the standard is termed the ‘iodine-bonding number ’,

J. appl. Chem., 3, February, 1953

SMALL-SOLUBILITY OF POLYMERS 77

which is greater the more effective the substance concerned in forming the iodine complex. For polyfunctional compounds (e.g. phthalates, sebacates, diketones) the concentration of the grouping believed responsible for the bonding (ester, carbonyl groups) was used rather than the molar concentration. It was found in preliminary tests that visual comparison is more sensitive in this part of the spectrum than such instruments as the Hilger Spekker absoptiometer and Lovibond tintometer.

Reaction with the iodine was a cause of error with some compounds (aldehydes, morpholine), and no satisfactory values were obtained for these.

The values of the iodine-bonding number found for different classes of organic liquid bore some relation to the shifts in the 0-D bond positions found by GordyZ5; thus the genera€ order was esters < ethers < ketones < tertiary amines < phosphates. In the esters, ethers, and ketones it was evident that the presence of rings in the molecules increased the iodine-bonding number : thus phthalates > adipates; cydohexanone > acetone and butanone; tetrahydrofuran >> aliphatic ethers. Most of the liquids tested had c.e.d. values in the range 80-100 cal./c.c.

The liquids tested were divided into three classes: (i) “on-solvents’, in which a 1% solution of ‘ Corvic DR ’ could not be made by heating at IOO’, or those which formed a solution in the hot but gave a precipitate on cooling to room temperature; (ii) ‘poor solvents’, those in which a 1% solution stable on cooling could be prepared, but which precipitated polymer on the addition of less than half a volume of cydohexane at room temperature; (iii) ‘solvents’, which tolerated dilution by more than half a volume of cyclohexane.

The solubility parameters, and ‘ iodine-bonding members ’ of some 50 liquids of these classes are shown in Fig. 2. Those liquids are generally good solvents whose solubility parameters are near 9 . 7 and whose ‘ iodine-bonding members ’ are high, and the general effects of c.e.d. and proton-attracting power are shown (the parabola has no theoretical significance).

There are some anomalies : thus acetone (represented by the non-solvent point inside the parabola drawn) is much worse as a solvent than its properties indicate. However, it has been shown27 that a one-to-one volume mixture with carbon disulphide is a very good solvent. The acetone-carbon disulphide system shows strong deviations from ideality and AH is very positive. When allowance is made for the heat of mixing and volume change the c.e.d. of the mixture works out at about 92 cal./c.c., very close to that of the polymer itself; it is thus not surprising that the mixture is a good solvent. The anomalously poor solvent power of acetone is probably due to the high value of E ~ / T , i.e. its highly polar nature; the value of E ~ / T for the mixture would be approximately I cal./c.c., which is not excessive.

The anomalously good solvent power

I I

Poor Solvents e

Non- Solvents

I 2 IODINE BONDING No., 1. /mole

FIG. 3. FIG. 2 . Solvents and non-solvents for polyvinyl

chloride

J. appl. Chem., 3, February, 1953

80 FARRER et n1.-PRESERVATION OF ANCIENT BURIED IRON OBJECTS

of methylene chloride and ethylene dichloride (the two points on the axis of ordinates in Fig. 2) cannot, however, be explained. Cohesive energy densities of polymers and solvents

T o give a general survey of polymers and solvents, Fig. 3 has been prepared in the form of a spectrum, on which the values of S and c.e.d. are shown for a selection of substances, both polymers and non-polymeric liquids. Acknowledgments

My thanks are due to my colleagues, Mr. I. Marshali, Mr. H. A. Willis and Dr. I. Harris, for permission to quote their results on the heat of solution of (Terylene', the infra-red spectrum of polyvinyl chloride, and the molecular weight/solution-viscosity relation for polyvinyl chloride, respectively.

Research Department Imperial Chemical Industries Ltd. (Plastics Division)

Welwyn Garden City, Herts. Received I September, 1952

References Huggins, M. L., 3. Amer. chem. SOC., 1942, 64, 1712 l7 Boyer, R. F. & Spencer, R. S.J . PolJm. Sci., 1948,

Alfrey, T., Goldberg, A. I. & Price, J. A.,J. Colloid Bronsted, J . N. & Volqvartz, K., Trans. Faraday Sci., 1950, 5, 251

l D Doty, P. M. & Zable, H. S., 3. Polym. Sci., 1946,

Keesom, W. H., Phyrys. Z., 1922, 23, 225 Edelson, D. & FUOSS, R. M.,J. Amer. chem. SOC.,

Scatchard, G., Chem. Rev., 1931, 8, 321 21 Copley, M. J., Zellhoefer, G. F. & Marvel, C. S., Hildebrand, J. H. & S,Cott, R. L., ' The Solubility J . Anier. chem. SOC., 1938, 60, 2666, 2714

of Non-electrolytes , 1950, 3rd ed. (New York: 2 2 Marvel, C. S., Jones, G. D., Maston, T. W. & Reinhold Publishing Corpn.) Schertz, G. L.,3. Amer. chem. SOC., 1942,64,2358

Gee, G., Z.R.I. Trans., 1943, 18, 266 53 Marvel, C. S., Dietz, F. C . & Copley, M. J., J. Amer. chem. SOC., 1940, 62, 2273

24 Alfrey, T., Wiederhorn, N., Stein, R. S. & Tobolsky, A., J . Colloid Sci., 1949, 4, 211

8 5 Gordy, W. & Stanford, S. C.,3. chem. Phys., I940,8,

3 6 Fairbrother, F.9 Nature, Lond.9 1947, 16% 87 37 SociCtC Rhodiaceta, 1942, Belg. Pat. 433,870; B.P.

Bronsted, J. N. & Volqvartz, K., Trans. Faraday 3, 97 sot., 19399 35, 576

SOC., 1940, 36, 617 London, F., Trans. Faraday SOC., 1937, 33, 8 I, 90

Davies, M., Rep. Progr. Chem., 1946, 43, 5 1949,7I> 3548

1" van Arkel, A. E., Trans. Faraday SOC., 1946,42B, 81 l1 Scatchard, G., Chem. Rev., 1949, 44, 7 l 3 National Bureau of Standards, 1947, Circular C 461,

13 Scott, R. L. & Magat, M., 3. Polym. Sci., 1949, 4,

1 4 Richards, R. B., Trans. Faraday &c., 1946, 42, 10 l5 Magat, M., 3. Chini. phys., 1949, 46, 344 l 6 Gee, G., Trans. Faraday SOC., 1942, 38, 418

Washington

555 170; 1941, 9, 204

626,988

THE ROLE OF TANNATES AND PHOSPHATES IN THE PRESERVATION OF ANCIENT BtJRIED IRON OBJECTS

By T. W. FARRER,* L. BZEKt and F. WORMWELL*

Archaeological specimens of iron are occasionally found to be well preserved under conditions that would normally be regarded as highly aggressive. A striking example arose during excavations at Hungate, York, where iron articles were found in an excellent state of preservation after a period of about 2000 years. Investigation revealed that the lack of corrosion was attributable mainly to inhibition of the activity of sulphate-reducing bacteria by tannates present in the :oil. Phosphates likewise present probably assisted by reason of their known corrosion-inhibitive properties.

Investigations of the corrosion of buried iron and steel pipelines have shown that most of the cases of rapid corrosion in this country can be ascribed to the activity of sulphate-reducing bacteria in waterlogged clay soils? Examples are known, however, of non-aggressive clays and it is considered important to study these in the hope of elucidating the mechanism of microbiological corrosion and of establishing a sound and effective method of prevention. Much useful informa- tion has come to light from the study of ancient iron articles. Examination of iron articles and soil samples

Articles of iron and other materials have been found in an excellent state of preservation on a site at Hungate, York, excavated under the supervision of the Inspectorate of Ancienr Monuments, Ministry of Works. The general archaeological aspects of the site will be dealt

* Chemical Research Laboratory, D.S.I.R., Teddington t Ancient Monuments Laboratory, Ministry of Works, Lambeth Bridge House, London, S.E.1

J. appl. Chem., 3, February, 1953

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