Recrystallization and Heat Shock

Approfondimento 2 followed the birth of countless tiny ice crystals in the mantecazione. But the story does not end there. Once the tub is in the freezer, the crystals go on growing, quietly. And nothing melts away: no water is lost. The total amount of ice hardly changes, and yet the crystals fall in number and gain in mean size. This coarsening during storage is recrystallization. Advanced Chapter 7 named variation in temperature as the thing to guard against most, and the reason lies here.

Small crystals lose out

What drives recrystallization is thermodynamics. The key is a single fact: small crystals dissolve more readily than large ones.

A crystal has a surface, and molecules at the surface sit less stable than those inside — surface free energy. The smaller the crystal, the greater the share of surface against volume, and the sharper the curvature. So a small crystal has a higher effective solubility against the unfrozen phase around it: the Gibbs–Thomson effect. For a particle of radius r, the relation can be written like this.

Inside the exponent, r sits in the denominator — and that is the whole of it. The smaller r is, the larger the exponent, and the solubility leaps. Where r is large the exponent goes toward zero, and the solubility settles at the value for a flat interface. At one and the same temperature, the water around a small crystal can still dissolve more. The water around a large one is already saturated. That is why.

Ostwald ripening — the large eat the small

This difference in solubility sets water molecules moving. Molecules dissolve off the surface of a small crystal, cross the unfrozen phase, and freeze onto the surface of a large one. The upshot: the small shrink and vanish, and the large grow larger still. This spontaneous process, lowering the surface energy of the whole system, is Ostwald ripening (maturazione di Ostwald).

The total ice is held, and only the count falls while the mean diameter rises. Crystals that were even at a few tens of micrometers or less when fresh grow, over storage, to a size the mouth reads as grit. This is what lies behind a texture that coarsens with time though the formulation has not changed.

This coarsening has a law of rate. Once a steady state is reached, the cube of the crystal radius rises in proportion to time.

Three things are written in this one line.

The first is that the coarsening slows down with time. The radius grows only as the cube root of time — to double in size takes eight times as long. Turn that around: the most dangerous period is the earliest. The rule of thumb that fresh is best (Foundations Chapter 5) has this non-linearity behind it.

The second is that the rate is set by a product of three quantities. α carries the interfacial tension, the same quantity that appeared in the exponent of the Gibbs–Thomson equation above. The interfacial tension between ice and the unfrozen phase is not something a figure in a formulation table can move. S(∞) is the solubility against a flat interface, that is, the size of the driving force itself. The one that remains is D — the diffusion coefficient of molecules crossing the unfrozen phase. This is the only one within reach.

The third is that temperature appears in this equation twice, and in opposite directions. T sits in the denominator of α, so the lower the temperature the larger α. On paper, cooling works to speed the coarsening as well. Even so, the measurements agree: the lower the temperature, the slower the recrystallization. As the glass transition temperature (Approfondimento 1) is approached, D falls by orders of magnitude and overwhelms the slight rise in α. Low temperature works not because the driving force vanishes, but because the molecules can no longer move.

There is one more road to coarsening. Accretion — where two neighboring crystals touch, the point of contact draws into a neck, and the neck fills until the two are one crystal. Where Ostwald ripening is a mechanism of molecules crossing between separated crystals, accretion is one of touching crystals fusing. Coarsening in storage runs both at once.

Heat shock — swings in temperature speed it up

Ostwald ripening is slow, but swings in temperature speed it up dramatically. On the floor, this destruction of texture by swinging temperature is called heat shock (shock termico).

The mechanism runs like this. When the product warms, part of the ice melts. The small crystals, with their high solubility, are the first to melt away. When the product cools again, the melted water freezes once more. And here is the point — as it refreezes, the water makes no new nucleus. It freezes onto the surfaces of the large crystals still there. A new crystal needs nucleation under supercooling; growth on an existing crystal surface does not (Approfondimento 2).

So with each cycle of temperature, small crystals vanish and large ones fatten. The more cycles are piled up, the faster the texture coarsens. Advanced Chapter 7 warned hard against the round trip — hardened at −22 °C, brought back to −16 °C, then down to −22 °C again. Each round trip advances this destruction for certain.

So: low, and steady

The remedy comes down to shutting both mechanisms.

One is to hold the temperature low. The lower it goes, the higher the viscosity of the unfrozen phase, and the slower the water molecules diffuse. In the terms of the equation above, that is a way of lowering D. Ostwald ripening, limited by diffusion, slows for certain in the cold (the viscosity of the unfrozen phase is Approfondimento 1 and 4). Below the glass transition temperature, where freeze concentration arrives (Approfondimento 1), diffusion effectively stops and recrystallization all but halts. The other is to hold the temperature steady. Take the swings away and the acceleration of heat shock disappears with them.

The formulation can lend support. Raising the viscosity of the unfrozen phase with stabilizers slows diffusion — this too is thought to be a way of lowering D (Approfondimento 4). That stabilizers slow recrystallization is settled; whether they do so through viscosity is not. Holding total solids high leaves more unfrozen water, and the crystals connect less. But what tells in the end is running the cold chain, from hardening to selling, low and steady. Whether the fineness made fresh (Approfondimento 2) can be kept hangs on that one point. Most of the defects of a coarse, icy texture (Advanced Chapter 13) come not from the formulation but from a failure of this temperature control.