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The actual solution of the beta form is given by Hudson as 45.14 parts to 100 parts of water at 0° and 94.75 at 100° C.

Hudson has also pointed out that there will be two cryohydrate temperatures when the ice line for lactose solutions is cut by the solubility curves representing the initial hydrate solubility and the final hydrate solubility. The first temperature is minus 0.281° and corresponds to an initial hydrate solubility of about 5 parts of lactose to 100 parts of water. The second temperature is minus 0.65°

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of water.

and corresponds to a lactose concentration of 11.9 parts to 100 parts

The ice line curve and the solubility curves of the initial and final hydrate equilibrium are given in the chart, Figure 1.

Since in this paper we shall confine ourselves to a rather general discussion of those factors which influence the crystallization of lactose from aqueous solution under ordinary conditions, we are not interested at this time in any further study of the physical-chemical relationships of the beta and alpha anhydrous milk sugar forms.

work on crystallization.

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Hallimond (3) has given a most excellent exposition of the theories of crystallization with especial reference to the supersaturation theories. He points out that there are three main principles which must be taken into account in a theory of crystallization:

The first concerns the existence, below the ordinary solubility curve for each constituent, of a range of temperature and concentration within which crys. tallization is only initiated upon the introduction of a suitable nucleus. The second is that the rate of growth of a crystal at first increases as the temperature falls below that of equilibrium (saturation) and then diminishes when a certain degree of supercooling is exceeded. The third is that the redistribution of heat and of dissolved matter, consequent on and essential to solidification at the surface of a growing crystal, is governed by gradients of temperature and concentration which depend in their turn upon the resnective coefficients of heat conductivity and of diffusion.

To discuss a little more in detail, still following Hallimond's paper: Miers (4) and Ostwald (5) have shown that when supercooling of a solution takes place, the tendency to crystallize first increas s with a drop in temperature and then diminishes again so that the material may be made to pass into an amorphous mass. They have also recognized that, with moderate supercooling, nuclei sometimes fail to appear even after many weeks' standing. Ostwald proposes the terms

metastable” for the condition wherein nuclei do not readily appear, and “labile” for that condition induced by a greater degree of supercooling wherein crystallization will, when once initiated, spread rapidly throughout the mass. It has been shown by Miers that under suitable conditions of experiment a very definite boundary line can be determined between the metastable and labile states. metastable state it is usually possible to induce crystallization only by a liberal seeding with the material itself or a substance which is isomorphous with it.

Experiments reported by Miers and Isaac (4) have shown that in this state it is also possible to have growing crystals which do not in turn cause a general separation. Another point of interest is that for each foreign substance there will be a characteristic temperature at which it is capable of initiating crystal growth. This means that if we plot a temperature concentration curve as showing the boundary between the metastable and labile states the actual position of this curve as compared with the normal solubility curve will vary definitely and characteristically with the addition of foreign substances to the system. This is an important point. Even in the labile state it must be pointed out that the time element is a factor. Crystallization may not take place even within this area. If crystallization does take place, time will often have to be allowed for it to proceed far enough to be observed, although frequently, when this state is encountered crystallization proceeds so rapidly that it has the appearance of being instantaneous. Hallimond emphasizes partiellarly that there is ground for regarding the true supersaturation or inoculation point as a definite limiting temperature, above, which crystallization will not occur even on indefinitely slow cooling.

The linear crystallization velocity at first increases with supercooling, then remains constant, and finally diminishes more or less sharply with falling temperature; probably owing, in the first place, to the usual increase in speed of a reaction with departure from equilibrium, and, in the second place, to the increase of viscosity and diminution of reaction velocity with falling temperature.

The continued growth of a crystal is conditional on the maintenance of a supply of material by diffusion, and on the dissipation of the latent heat developed in crystallization.

Jones (6) in a paper upon the spontaneous crystallization of the alkali nitrates shows not only the supersolubility curve of the nitrates but what he calls the supersolubility of ice. In other words, he gives a curve below the normal ice curve which shows the highest temperatures at which spontaneous separation of ice will occur. The intersection of this superfreezing point curve and the supersolubility curve give a supercryohydric point. This point does not of necessity lie directly under the true cryohydric point. The composition of the solution at the supercryohydric point is therefore not of necessity the same as that at the true cryohydric point.

We can now proceed to a discussion of all these relationships in their bearing on the crystallization of lactose.

Since it has been shown above that the equilibrium ratio between the alpha hydrate and the beta anhydride in solution is practically constant regardless of temperature or concentration, it follows that, once equilibrium has been established in solution, temperature changes occurring at temperatures beneath the transition point, 93°, and above the final solubility curve will not materially affect the solution. But, when a solution is cooled slowly until the saturation point is reached, and crystallization starts, the hydrate will separate out. If the temperature is then quickly lowered a few degrees, an amount of lactose will separate out equal to the supersaturation of the solution with the hydrate. Some of the beta form will then be transformed to the hydrate, and hydrate will be deposited further at the rate at which this reaction proceeds. If this deposition takes place at very low temperatures where the rate of transformation is slow (at 0° C., it is only about 3.4 per cent in one hour), it is very evident that the crystallization process will not proceed rapidly unless the speed of this transformation be hastened with acids or alkalis. Of course, this is true only if the velocity of crystallization exceeds the velocity of transformation. Hudson has shown that this is the case. The rate of the equilibrium transformation may therefore be a factor in the time required to completely crystallize lactose from a given solution.

It is at once apparent, then, that the rate of the establishment of the alpha-beta equilibrium—which is less, the lower the temperaturewill probably be a factor regulating the rate of separation whenever lactose crystallization occurs, be it from whey, from evaporated or condensed milk, or from ice cream. If it is desirable to eliminate this factor (which will be more important at lower temperatures), it can be accomplished by the introduction of the accelerating hydrogen or hydroxyl ions wherever possible. It seems as if the acidity would be an important factor in accelerating this equilibrium, particularly when we are dealing with the separation of lactose from whey.

Proceeding now to the laboratory work: In some preliminary experiments performed for the purpose of observing the actual crystallization of lactose, supersatured lactose solutions of varying concentration were rotated in closed bottles in a thermostat at about 20° C. These solutions were seeded with one crystal of lactose of moderate size. It immediately became evident that only the very highly supersaturated solutions crystallized, while those of moderate supersaturation could not be made to crystallize in this manner. For instance, at 20° C. crystallization could be induced only by heavy seeding in a solution containing 30 parts of lactose to 100 parts of water, which solution from the solubility curve is shown to be saturated at about

When seeded with one crystal and revolved in the thermostat for five days at 20° this solution showed no signs of crystallization, although the seeding crystal had grown slightly.

These experiments indicated that lactose solutions exhibit an extensive metastable area, and bearing in mind the crystallization theories of Hallimond quoted above, other experiments were conducted in the same thermostat wherein lactose solutions varying from one another by about 5 parts lactose to 100 parts water, were rotated in stoppered bottles as before. These bottles were seeded with bits of glass. The temperature of the bath was lowered a few degrees every 24 hours and note was made at that time of the bottles which had crystallized. In this way it was shown that the supersolubility curve of lactose lies in the neighborhood of 30° C. below the true solubility curve. The fact that these curves are separated to such an extent must be considered a very great factor in lactose crystallization, one which, so far as the authors know, has not been pointed out before. The position of the supersolubility curve of lactose is shown also in Figure 1.

These results have a practical bearing upon the separation of lactose from whey, evaporated and condensed milk, and ice cream. They show that the biggest factors controlling this separation are concentration, temperature, and seeding.

In the case of crystallization from wheys where the concentration is always very great, the lactose will always be in the labile state; any nucleus will induce crystallization and copious seeding should result in a rapid general crystallization.

With evaporated or condensed milks either condition may exist, but the milks will probably be in the labile state.

In this connection let us consider, for example, a condensed skim milk containing 48 parts of sugar, 26 parts milk solids not fat, and 26 parts water. The lactose is present in the ratio of 14.14 parts lactose to 28 parts water, or 50.5 parts lactose to 100 parts water. Barring the effect of the other constituents upon the solubility of lactose, this would be saturated with lactose at a temperature of 59° C. At room temperature it would be in the labile state, and with vigorous stirring and seeding, would give a rapid crystallization of fine crystals. If the milk were stirred but slowly at a temperature in the metastable area, large crystals would develop, the rate of growth depending upon the rate at which diffusion of the lactose can take place to the surface of the growing crystal. The above explains theoretically the commercial process wherein lactose is made to crystallize in a finely divided state in condensed milk in order to avoid a later development of large crystals.

We will discuss the application to ice cream later.

Since Hallimond has shown that the limits of the metastable area are affected by the presence of foreign substances, the next question is, What will be the effect of the foreign substances often present in milk and ice cream upon the relative positions of these curves? Lactic acid and sugar appear to force the two curves slightly farther apart. The milk salts in solution have apparently no effect. In the metastable area, however, any of the milk salts which may be precipitated by forewarming of milk apparently in. duce a slow crystallization which is appreciable at room temperature in about two days.

Since we know that forewarming of a milk may convert some of the milk salts to an insoluble form, it seems entirely probable that, aside from the effect on viscosity, forewarming may produce nuclei for the devlopment of lactose crystals. This possibly would then be a factor in milks stored for long periods or perhaps in the development of sand in ice cream.

Marc (7) has shown that many dyes inhibit crystal growth. The dyes do not inhibit the growth of crystals entirely but bring the crystallization to a standstill before normal equilibrium is reached. It is of course apparent that it would be impracticable to add dyestuffs to milk or ice cream to retard crystallization. It is known, however, that crystal growth may be retarded by materials which, adsorbed to the surfaces of the growing crystal, interfere with normal growth. Since dyes are by their very nature materials which are strongly adsorbed, it seemed worth while to investigate their effects upon lactose separation with the idea that if satisfactory results were obtained, some unobjectionable analogous substance might be used in milk. The effect of dy's on lactose crystallization was studied at room temperature with solutions containing 50 parts lactose to 100 parts water. Of 39 dyes investigated, only three had any apparent effect in retarding crystallization. Rosaniline hydrochloride, crystal violet, and rosaniline base did not exert a practical effect unless

а present in quantities which colored the solutions deeply. Experiments with the rosaniline showed that the supersolubility curve of lactose could be lowered about 5° by its use.

We may come now to a brief consideration of the sandy ice cream problem. It will not be necessary here to dwell at length upon the facts already known generally, namely, that if the lactose content is not too high, sand will not usually develop, that this defect can be avoided if products free from lactose crystals that may act as nuclei are used, and that trouble can be avoided by holding the ice cream at low temperatures.

But, before proceeding further, let us examine closely the solubility and freezing point curves of lactose-water solutions. We see, first, that if we freeze a lactose solution whose concentration is less than 11.9 parts of lactose to 100 parts of water, ice will separate before the solution becomes saturated with the sugar. This means that the unfrozen portion of the solution with lowering temperature then becomes more saturated with lactose. Theoretically, when the temperature of the cryohydric point is reached, ice and sugar should separate together; but we have shown that lactose is capable of forming highly supersaturated solutions, so in the absence of nuclei we might pass along the freezing point curve, with a further separation

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