The Relations Between Yolk and White in the Hen’s Egg: VI. The Equilibrium Between Ice and Egg-Yolk, and the Freezing-Point Difference Between Yolk and White

In previous papers it has been shown that the disequilibrium is not maintained, as Straub (1929) suggested, by the expenditure of energy derived from the oxidation of glucose, since it persisted in hydrogen (Hill, 1930), and since the intact egg did not show a measurable consumption of oxygen (Smith, 1931 a) ; and, more-over, biochemical data gave no definite support to the existence of an anaerobic energy-supplying metabolism of sufficient magnitude (Needham, Stephenson and Needham, 1931). On the other hand there was considerable experimental evidence in favour of the view that equilibration of the freezing-points was merely retarded by the slowness of diffusion through the membrane and through the substance of the white and yolk, which have complicated physical structures (Smith and Shepherd, 1931 ; Needham and Smith, 1931).

More recently, however, the actual existence of the difference in freezing-points has been denied. Grollman (1931), using a thermo-electric technique due originally to Meyerhof, found it impossible to obtain consistent values for the freezing-point of egg-yolk, Instead of a definite plateau he obtained variable maxima of temperature according to the degree of overcooling. By dialysis against water or against a salt solution he found that both yolk and white eventually came into equilibrium with solutions having a freezing-point of approximately −0·45° C. Meyerhof (1931) a little later showed that some of his results were vitiated by the absence of a correction for the water initially held in the collodion dialysis membranes.

Howard (1932) reinvestigated the question, concluded that with suitable precautions the ordinary Beckmann technique could be used, and obtained with it identical values, within a few thousandths of a degree, for the freezing-points of white and yolk. Confirmation of this result was forthcoming from dialysis experiments, and from vapour-pressure measurements in which a modification of the method of Berkeley and Hartley was employed. In other words, previous workers had, according to this observer, been studying a phenomenon which had no real existence.

So much uncertainty with regard to so simple a measurement is disconcerting. If the freezing-point difference does not exist the classic Beckmann technique must be liable to grave and unexplained errors : if it does exist the problem retains a greater interest to biologists from the standpoint of the osmotic relations of cells and tissues. A critical re-examination of the technique is described in the first part of this paper. The results have completely confirmed the reality of the difference in freezing-points between white and yolk which was previously reported¹.

The difficulties in the way of an accurate measurement of the freezing-point of egg-yolk are real, but not insuperable, if certain simple precautions are taken; these precautions are necessitated by the special physical properties of the material. Some of the possible sources of error are of general interest in the technique of freezing-point measurements in numerous biological materials, and may be briefly mentioned : they are connected primarily with the transfer of heat, the transfer of dissolved substances, and the transfer of momentum, inside the fluid.

Owing to the high viscosity of egg-yolk the thermal equivalent of the work done in stirring it becomes an important factor in the heat balance, of which the plateau of temperature in a freezing-point determination is a measure. According to Gane (1933) the viscosity of egg-yolk at high rates of shear is about 7000 times that of water. The frictional resistance (R) to the movement of a stirrer at a given rate will not be a linear function of the viscosity unless the fluid’s motion is stream-line; but using the relation R ∝ pv^0·36 (where p is the density and v the kinematic viscosity) deduced by Lees (1914) from the results of numerous observers on the turbulent flow of fluids in pipes, it follows that stirring at a given rate will contribute nearly 2000 times as much heat to egg-yolk as to water under otherwise similar circumstances.

In freezing-point measurements with egg-yolk it can easily happen that a plateau of temperature is obtained without the presence of ice in the mixture, through a balance between the heat gained by stirring and lost to the cooling bath. This seems to have happened in Howard’s (1932) experiments, where the temporary fall in temperature (of about 0·03° C.) consistently recorded on the graphs whenever the mixture was re-seeded, is not accounted for by the mere introduction of a cold nichrome ring with its negligibly small heat capacity, but is presumably the result of temporarily interrupting the vigorous stirring, in a mixture which actually contained no ice. Renewed stirring will then restore the fictitious plateau.

The rate of formation, and apparently also the rate of disappearance, of ice is much slower, under similar conditions, in egg-yolk than in aqueous solutions. A temporary co-existence of ice and egg-yolk at temperatures other than the true freezing-point is thus much more apt to occur ; in other words, the mere fact that ice is temporarily present in the mixture is no guarantee that the thermometer is reading the true temperature of equilibrium between the two phases. Even if equilibrium can be assumed at the actual ice interface, it must, when ice is appearing or disappearing, be equilibrium at a different temperature, and with a solution of different composition, from that in the body of the fluid. This fact applies to a simple aqueous solution, but applies with much greater force when, as with egg-yolk, the diffusion film at the interface is thicker on account of the greater viscosity of the fluid, or has smaller coefficients for the transfer of heat or of dissolved substances ; increased rapidity of stirring can diminish these difficulties only at the cost of introducing the source of error previously mentioned.

For similar reasons the growth of crystal nuclei is more difficult in egg-yolk than in aqueous solutions. Intact eggs have been kept at − 11° C. for seven days without freezing (Moran, 1925). In measurements of the freezing-point it is usually impossible, in a reasonably short time, to induce the formation of ice by seeding the yolk, unless it is overcooled by at least 0·25° C. Incidentally there is a rather sharp transition between consistent failure, at an overcooling of about 0·2° C., and consistent success, at about 0·3° C.

A correction for the effect of overcooling on the observed temperature of equilibrium is of course applied to all the results. It is greater than the correction for aqueous solutions, owing to the low water content of egg-yolk, the effect of which is only partly counterbalanced by its low specific heat. The magnitude of the correction is referred to in a later section.

The apparatus employed for measurements of the freezing-point of egg-yolk was designed to overcome or to minimise these various difficulties.

The fluid was mechanically stirred at a known and controllable rate, and the work of stirring was approximately measurable. Under the usual working conditions, it was of the order of 1 gm. cal. per 150 –200 revolutions, so that about 15 revolutions (of the stirrer) would melt a milligram of ice in the egg-yolk.

Double-jacketed tubes with known heat-loss constants were used to hold the fluid. Under normal working conditions the rate of loss of heat to the cooling bath was of the order of 1 gm. cal. per minute per degree Centigrade difference in temperature, and with the cooling bath at − 0·9° C. and a rate of stirring of 60 r.p.m., heat loss and heat gain were approximately balanced. This is the most favourable condition for a long maintenance of the freezing-point plateau.

Heat could be supplied to the fluid or withdrawn from it, while it remained in the constant-temperature bath, by circulating air at an appropriate temperature between the walls of the jacket. The effect on the temperature of the fluid of supplying or withdrawing heat in this way served as a criterion of the presence or absence of ice, since to cool the mixture by a small amount δ θ while in equilibrium with ice required about 90 times as much heat, as to cool or undercool the same mixture through δ θ when ice was absent.

Overcooling was carried out very slowly by circulating cold air through the jacket. The final rate of cooling was no more than about 0·02° C. per minute. The fluid was stirred uniformly the whole time. Seeding was effected at the minimal overcooling of about 0·25° C. by the method of Johlin (1931), using small rings of nichrome wire, frosted by preliminary immersion in solid carbon dioxide, and then momentarily exposed to the air of the room.

The cooling bath was a vacuum flask of 500 c.c. capacity filled with a solution of glucose freezing at − 0·9° C. All the observations were made in a room at 0° C. The cooling bath is normally kept in a room at − 1 ° C.

The Beckmann thermometers were permanently kept at o° C. ; they were standardised against distilled water before each set of observations, and the readings were corrected, when necessary, for the effects of hydrostatic pressure on the bulb at varying degrees of immersion.

In the course of various studies on the changes which occur in the freezing-points of yolks and whites of eggs stored at different temperatures and in atmospheres of different composition, it has been necessary to make some three or four hundred observations of the freezing-point of egg-yolk in this or a closely similar form of apparatus.

The freezing-point, apart from a correction for overcooling, was taken as that temperature to which the fluid rapidly rose after being undercooled by not more than 0·3° C. and seeded, and at which it remained constant to ±0·001° C. for at least i o min. This criterion excludes all the plateaus figured in Howard’s paper (1932). On several occasions the thermal history of the mixture was followed for periods of 6 − 7 hours in order to investigate the possible occurrence of “pseudoplateaus” (Howard, 1932). These experiments need not be described in detail, since their only result was to show that such temporary equilibria as might occur—and they were never well defined as was the initial thermal arrest—were due to changes in the extraneous heat quantities, and did not measure a physical constant of the experimental material.

Efforts were made to disturb the results by modifying in turn each of the following factors : the amount of fluid used, the type of containing vessel, the temperature of the cooling bath, the rate of overcooling, the rate of stirring during overcooling, the degree of overcooling, the rate of stirring during the thermal arrest, and the duration of stirring. Apart from the avoidable difficulties already discussed, there was no evidence of an inherent fault in the method.

The degree of consistency attainable can be sufficiently illustrated by a single example (Table I), showing the results of thirteen determinations on separate samples from a single batch of mixed egg-yolks. The observations were made with different amounts of overcooling, as indicated in the second column, but otherwise followed standard conditions. Fig. 1 illustrates some of the results. The remaining figures in the table refer to samples of a solution of sodium chloride approximately isotonic with the egg-yolk.

When the depression of freezing-point is plotted as a function of the degree of overcooling the best straight line through the points for egg-yolk has a slope corresponding to 0·0017° C. per 0·1° C-overcooling. The calculated value is 0·0011° C., but this ignores the by no means negligible heat capacity of the containing tube and thermometer. The average deviation of individual values from the straight line is 0·0015° C. With the same degree of overcooling readings can usually be checked, with the same or with duplicate samples, to within ±0·000° C., which is the limit of accuracy in reading the thermometer. Extrapolated to zero overcooling the above results give a value of −0·55° C. for the true freezing-point. The average of all determinations on the yolks of fresh eggs is approximately −0·57° C., and the maximal variations approximately + 0·02° C.

Since the freezing-point of egg-white at approximately − 0·45° C. is not in dispute, the results completely substantiate the reality of the difference of about 0·12° C. in the newly laid egg. As a more crucial test, however, the experiment described in the next section was devised.

Theoretically the freezing-point method has the inherent disadvantage that it measures a steady state and not an equilibrium. The one condition under which the plateau of temperature has strict validity as a temperature of phase equilibrium— namely, when ice is neither forming nor melting—is also the point at which, unless the presence of ice can be visually recognised, it has no critical significance, since it then represents merely a balance in extraneous sources of heat and cold which could equally well occur in the absence of the solid phase.

The presence or absence of ice can, however, be tested by cooling the mixture when steady conditions have been reached. If ice is not present the mixture can be overcooled to a considerable extent until finally spontaneous crystallisation occurs. If ice is present the rate of cooling will be of a different order, since for every small decrement of temperature more ice must be frozen out to maintain equilibrium.

The freezing-points of two samples of the same egg-yolk (10 gm.) were separately measured, as described above, in double-walled test-tubes with similar constants of heat loss, which had been previously determined. The rapid rise to a plateau of temperature after seeding (at − 0·8° C.) was conclusive evidence of the formation of ice in the mixture ; the value arrived at was the same for the two samples within 0·002° C.

The tubes were immediately transferred to two separate constant-temperature baths and stored for 7 days. The temperatures were as follows:

(The apparent freezing-points of the two samples of yolk were :

If egg-yolk has the freezing-point of egg-white (− 0·45° C.) ice should remain in both samples; if the value given above is correct it should disappear from A but persist in B. If insufficient time has been allowed for equilibrium the error will lie in a direction to support the first assumption. The cooling curves (Fig. 2, A and B) obtained when the tubes were eventually placed together in a bath at − 5° C., show emphatically that it is the second which is correct.

The experiment was repeated at temperatures approximately 0·02° C. on either side of the apparent freezing-point, as follows :

(The apparent freezing-point of the two samples of yolk were :

A period of 6 days was allowed for equilibrium : the final cooling bath was held at − 4·3° C. The cooling curves (Fig. 2, C and D) show that ice had disappeared at −0·53° C., but persisted at −0·58° C.

Anomalies in the process of separation of ice from egg-yolk, which are apt to cause errors in determining the point of equilibrium, have been reported both by Grollman (1931) and by Howard (1932). The latter found a difference of about 25 per cent, between the linear velocities of ice formation in the dialysate of egg-yolk and in an isotonic solution of sodium chloride in long tubes seeded at one end, and concluded that egg-yolk contains a dialysable substance which retards crystallisation.

Incidentally this difference is no greater than exists, for example, according to Walton,Brann and co-workers (1914, 1916, 1918) between tenth molar solutions of sodium chloride and lithium chloride, or between half molar solutions of potassium nitrate and potassium sulphate. An alternative explanation for these results will be suggested below.

That the separation of ice from egg-yolk is much slower than from aqueous solutions under similar conditions, is quite evident when the usual measurement of the freezing-point is being carried out. If the overcooling is not too great the rate of increase of temperature after seeding can in fact be followed by the Beckmann thermometer, and the rate of formation of ice calculated from it. The results of a series of observations carried out in this way are summarised in Fig. 3.

The fluid, cooled to the required extent, was seeded in the usual way with a frosted nichrome ring. The thermometer was read at intervals of 20 sec. and the readings were corrected for thermometric lag. The maximum rate of increase of temperature was computed from the temperature-time curves, and the maximum rate of ice formation was calculated from it, using known values for the heat capacity of the fluid. With solutions of sodium chloride (isotonic with egg-yolk) the rate becomes too rapid for convenient measurement when the overcooling is greater than 0·4° C. ; with egg-yolk crystallisation cannot readily be induced with an overcooling of less than 0·2° C. In the intermediate range the rate of formation of ice was from 3 to 4·5 times as great in isotonic sodium chloride as in egg-yolk.

The velocity of ice formation in a mixture such as egg-yolk, is presumably a function of at least four terms :

• the effective area of the interface, which may be reduced by the adsorption of foreign substances ;

• the speed at which water molecules can orientate themselves in the crystal lattice ;

• the rate of transfer of heat from the interface to the body of the fluid ;

• the rate of diffusion of water towards and of solutes away from, the interface.

By analogy with other examples of reaction velocity in heterogeneous systems it might be supposed that the film effects (c) and (d) would preponderate, but in the crystallisation of salts from supersaturated solutions, according to Marc (1908-1912), the limiting rate is the rate of the process corresponding to (b), when the stirring is rapid. However this may be, it is fairly certain that film effects predominate in all experiments in which the linear velocity of crystallisation is measured in a tube, and that Howard’s (loc. cit.) results should be interpreted in this sense. Moreover, it seems improbable that film effects have been eliminated in the experiments summarised by Fig. 3, although the fluid was actively stirred, and the simplest view is to look to them for an explanation.

Diffusion through the superficial film of fluid (stagnant or in stream-line motion, parallel to the interface) will be a function of the thickness of the film, and of the diffusion constants. The thickness of the film at a given rate of stirring depends on the viscosity, and is presumably much greater with egg-yolk than with aqueous solutions. It is not so certain that an increase of viscosity will proportionately lower the diffusion constants for dissolved substances, since the Einstein-Schmolukovski relation does not hold in many such cases, notably for the diffusion of salts through gelatin and agar gels; but the emulsoid structure of egg-yolk may be expected to retard the diffusion of solutes, and there is already evidence (Smith and Shepherd, 1931) that the diffusion of water through yolk is considerably impeded.

The rate of transfer of latent heat away from the interface is similarly a function of the thickness of the film and its thermal conductivity. In gm. cal./cm./sec./° C. the thermal conductivity of olive oil at 4 ° C. is 0·00042, of water 0·00138. The conductivity of a mixture, and presumably of an emulsion, is less than the value calculated from a linear law of conductivity, more than that calculated from a linear law of resistivity (Lees, 1898), but approaches the latter more nearly than the former. Egg-yolk, treated as a mixture of fat and water in approximately equal proportions, should therefore have a thermal conductivity about half that of pure water, even without taking into account the possibility of a further accumulation of fat in the interfacial film. Increased thickness due to the greater viscosity is probably, however, a much more important factor than decreased thermal conductivity.

The importance of heat transfer in governing the velocity of crystallisation of pure substances from their melts has been stressed by Tammann (1926), Nacken (1917), and others, and has been analysed mathematically by Wilson (1898) ; but the importance of diffusion effects, when a system of more than one component is being dealt with, has not been emphasised by the majority of observers, although Hardy (1926) mentions it in connection with the freezing of gelatin gel. Possibly this factor alone will serve to explain the results of some previous workers, for example of Walton and Brann (loc. cit.) who tried to correlate the observed differences in the linear velocity of crystallisation of ice from various aqueous solutions, with the supposed degree of hydration of the solute, on the assumption that hydration reduced the effective concentration of free water at the interface. The earlier data of von Pickardt (1902) and others, on the retardation of the velocity of solidification of benzophenone by various dissolved organic compounds, results for which Freundlich (1910) has suggested an explanation based on adsorption at the solid interface, are also of interest in this connection. The kinetics of ice formation, and particularly of crystal-nucleus formation, in complex mixtures such as egg-yolk, has a wide biological interest in connection with the frost resistance of plant tissues and their frequent ability to be undercooled without the formation of ice. The winter storage of food reserves in the form of oil in many plants at once suggests itself for consideration.

There is some evidence that the rate of disappearance of ice is also retarded in egg-yolk. The curves of Fig. 2 show that although the samples A (stored at −0·50° C.) and C (stored at − 0·53° C.) contained no macroscopic ice, since they could be overcooled, yet the formation of ice commenced in them spontaneously at temperatures distinctly higher than are normal for overcooled yolk, and higher for sample C, stored at -0-53° C. than for sample B, stored at −0·50° C. This is consistent with the supposition that crystal nuclei may persist in egg-yolk for several days at temperatures a few hundredths of a degree above the freezing-point, their size or frequency, or both, being a function of the temperature within this narrow range. The method of these experiments could perhaps be adapted to a study of the rate of decay of crystal nuclei in such mixtures at temperatures just above the temperature of phase equilibrium.

All observers seem to have ignored the fact that the freezing-points of yolk and white in newly laid eggs are considerably affected by the escape of carbon dioxide in the first few hours of the egg’s existence outside the hen. The importance of this factor is evident from data already published on the output of carbon dioxide from infertile eggs (Smith, 1931 a). Account must be taken not only of the additional freezing-point depression due to dissolved (ionised and unionised) carbon dioxide, but of its effects on various ionic equilibria in the mixture, particularly those involving phosphate and protein ions ; and in considering the effects of the escape of carbon dioxide during the first few hours, it must be remembered that this will occur first from the white and only secondarily from the yolk, and that the transfer of carbon dioxide across the vitelline membrane will tend to alter the distribution of the other ions as between the two sides.

In our own experiments eggs have been accepted as “fresh” if laid within the preceding 12 hours, and most other observers have adopted a similar criterion. The subsequent changes in the freezing-points of white and yolk, analysed in a previous paper (Smith and Shepherd, 1931) are relatively slow. In the first few minutes after the egg is laid they are rapid, as is shown by Table II :

Neglecting the small ionisation of carbonic acid, the freezing-point depression of a solution of carbon dioxide in water, in equilibrium with an atmosphere of the gas (less the partial pressure of water), would be approximately 0·14° C. A few measurements have been made on the freezing-point of egg-yolk and egg-white when saturated with carbon dioxide, as follows :

Saturation with carbon dioxide was effected by slowly rotating a tube containing about 50 c.c. of the yolk or white in the form of a moderately thin layer on the walls, while a current of pure carbon dioxide, previously saturated with water vapour, was passed through the tube. The whole apparatus was at 0° C. The first freezing-point determination was made after 5 hours’ saturation, the second after 24 hours. The fluid was rapidly transferred to the freezing-point apparatus, and a stream of pure wet carbon dioxide was passed over it during the whole period of the determination.

The effect of saturating with carbon dioxide is greater than would be estimated on the basis of a simple solution of the gas in the water contained in the yolk or white. This is hardly surprising, but the data for a closer quantitative analysis are lacking.

The immediate point of interest is that although the escape of carbon dioxide in the very early phase of the egg’s existence has a considerable effect on the freezing-points of both yolk and white, it does not at any stage bring them into even approximate equality. If, for example, it were postulated that equality existed at the tension of carbon dioxide in the hen’s blood, then the difference should be reversed when the fluids are saturated with the gas at the pressure of an atmosphere ; but nothing of the sort occurs.

A final possibility to be considered is that the difference in freezing-points although real in the fluids dealt with in an experimental determination, does not exist in the intact egg, but is produced in some way by wrecking the structure of the yolk when a sample is being taken. It is of interest therefore to investigate the activity of water in the intact yolk, by measuring the changes in weight, and the changes in freezing-point, which yolks undergo when immersed in various aqueous solutions which are unlikely to exert injurious effects.

In solutions of glucose the behaviour, in so far as changes in weight are concerned, is normal. Water passes into the yolk from weak solutions, out of the yolk into concentrated solutions. The amount of water transferred in 6 days (measured by the change in weight) is approximately a linear function of the freezing-point depression of the solution of glucose, and the straight line expressing the relationship intersects the zero axis at Δ = 0·55−60° C. (Fig. 4).

Changes in the freezing-points of the yolks (Fig. 4) give a parallel set of results; at Δ = 0·55−60° C. there is no appreciable change.

In other words the measured freezing-point of the yolk fluid is the same as the freezing-point of that glucose solution with which the intact yolk is in osmotic equilibrium, and presumably therefore is the same as the freezing-point of the intact yolk itself.

The parallel data for yolks immersed in Ringer solutions (NaCl 60, KC1 1·5, CaCI₂ 1·5, NaHCO₂ 1) are shown for comparison on the same diagram. The results are similar in so far as changes in freezing-point are concerned, but differ as regards the changes in weight. The latter will clearly not be a reliable criterion of equilibrium if the membrane is freely permeable to all or some of the ions of the solution.

The “dilution” of egg-yolk by the addition of isotonic solutions was adopted as a method of testing how far the difficulties associated with a high fat content had been overcome in freezing-point measurements. Moderate dilution with an isotonic Ringer solution (75 yolk : 25 Ringer) merely confirmed the accuracy of the freezing-point technique (Smith, 1931 b) : further addition of the aqueous solution produced an anomaly although not the evidence of a technical error. In general the freezing-point depression of mixtures of yolk and approximately isotonic Ringer solution was greater than the calculated value, and rose to a rather sharp maximum corresponding to the mixture yolk 60 : Ringer 40 (Fig. 5).

With isotonic solutions of glucose the result was even more striking : through a broad zone of mixtures (between yolk 25 : glucose 75, and yolk 60 : glucose 40) the freezing-point depression was about 0·05° C. greater than that of either constituent (Fig. 5).

A decrease in the activity of the water when two isotonic solutions are mixed is not in itself surprising, in view of Abegg’s (1894) results, cited by Briggs (1931) ; but the magnitude of the effect in this case is of interest. For example in a case like this, estimations of “bound” water by the method of Newton and Gortner (1922) would clearly be liable to error. Anomalies in the vapour pressures of mixtures of egg-white and egg-yolk (Bateman, 1932) and in the relative freezing-point changes of white and yolk in stored eggs (Smith and Shepherd, 1931) have probably a related basis.

In the case of glucose the visible changes in colour and in opacity as the egg-yolk is “diluted” suggest a change in the aggregation of the emulsion. Increased dissociation of phosphates is also probable.

It was found, however, that the relation between freezing-point and water content in diluted or concentrated egg-yolk (or egg-white) is linear (Fig. 6). This is of interest as tending to confirm the validity of the dilution technique used by Bialascewicz (1929), in his investigation of the composition of the intermicellar fluid in the egg cells of various birds and fishes.

The ultra-filtrates of white and yolk, obtained with a filtration pressure of 60-70 cm. of mercury, still show the difference in freezing-point characteristic of the original fluids (Smith, 1931 b), which supports the conclusion that difficulties due to the high fat-content of egg-yolk have been overcome by the freezing-point technique described above.

Egg-yolk from newly laid infertile hen’s eggs is in equilibrium with ice at approximately −0·57° C., and the difference between the freezing-points of egg-white and egg-yolk is a real phenomenon.

The osmotic behaviour of intact egg-yolks confirms this value for the freezing-point and indicates that the difference still exists in the intact egg.

At the moment of leaving the hen the freezing-point depression of both white and yolk is considerably greater owing to the presence of carbon dioxide which sub-sequently escapes.

Ice forms much more slowly in egg-yolk than in aqueous solutions under similar conditions, probably because of the retardation of diffusion and heat transfer in a viscous medium of high fat content.

The author’s acknowledgments are due to Mr H. J. Shepherd, who carried out the whole of the experimental work described in the paper.