1. What components vary the freezing point of the ice cream mix?

The solutes (sugar and milk salts) in an ice cream mix depress its freezing point. As water progressively freezes out of an ice cream mix in the form of pure ice crystals, the concentration of solutes in the unfrozen water continues to go up and the freezing point continues to go down. Freezing point has a great influence in final product since unfrozen water is directly related to targeted firmness, smoothness and scoopability (Ice cream 7th edition, 2013).

Freezing point depression is the difference between 0°C and the temperature at which an ice cream mix first begins to freeze. In the ice cream mix, the sum of each of the components that impact freezing point is needed for calculation - the combination of mono- and disaccharides sweeteners such as glucose and sucrose and milk ingredients such as lactose and salt (sa). These two components leads to the specific freezing point depression curve upon any ice cream mix varieties whilst fat, protein and heavy molecular weight carbohydrates such as corn syrup, stabiliser and emulsifiers do not contribute to freezing point depression as fat being immiscible with the mix and protein; carbohydrates being huge in size. To calculate the freezing point of a given mix, first of all is to equalise the sugar contents of the mix as Sucrose Equivalent (SE) by either converting the sweetness of any non-sucrose and/or switching its molecular weight ratios to that of sucrose. There are different types of sugar in ice cream production such as mono- and disaccharides choices like glucose and sucrose. Sucrose, also known as table sugar, acts as the neutral, is of sweetness index 100 or 1.0; the one sweeter than sucrose will be of greater than 100 or 1.0; the one who is less will be of less than 100 or 1.0. Regarding to molecular weight of sweeteners, the lighter the stronger the freezing power. The equation for calculating the Freezing Point Depression temperature (FPDt) is as follows:

** FPDt = FPDse + FPDsa **

**FPDse** = ( Lactose from milk-solid-non-fat x 0.545)+(Sucrose x 1)+(Glucose x 1.9)+(Fructose x 1.9)+(WHEY SOLID x 0.765)

**FPDsa** = [(MSNF+WS) x 2.37]/W

Given the constant 2.37 is based on the average molecular weight and concentration of salts present in milk. W is the water content (100-total solids, shown as %)

*In artisan ice cream market, whey solid is seen as cheap solid option, so it is not necessarily utilised and is omitted in my ice cream compositions.*

Example 1: An ice cream mix containing 10.78% MSNF, 10.31% sucrose, 3.25% glucose and 54.86% water.

FPDse = 10.78 x 0.545+10.31 x 1+3.25 x 1.9

= 22.36

Now let y be the concentration of sucrose equivalent (se) in water:

54.86%y = 22.36

y = 22.36 x 100/54.86

y = 40.758

Now we can find the freezing point depression for this level of sucrose equivalent from this table created by Leighton (1927) as:

40.758/39

= 1.045

Aligning to the temperature, which is 2.40°C x 1.045

=2.51°C

FPDsa = [(MSNF+WS) x 2.37 ]/W

= [ (10.78 + 0) x 2.37 ]/54.86

= 0.47°C

FPDt = 2.51°C + 0.47°C

= 2.98°C

Thus, the initial freezing point temperature of this ice cream mix is -2.98°C.

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Another extreme example 2 to compare:

Ice cream mix containing glucose as the major sweetener with 10.77% MSNF, 10.67% glucose, 3.15% sucrose and 55.64% water.

FPDse = 10.77 x 0.545 + 3.15 x 10 + 10.67 × 1.9

=29.29

Now let y be the concentration of sucrose equivalent (se) in water:

55.64%y = 29.29

y = 29.29 x 100/55.64

y = 52.64

Now we can find the freezing point depression for this level of sucrose equivalent in the chart again :

52.64/51

=1.032

Aligning to the temperature, which is 3.20°C x 1.032

= 3.3°C

FPDsa = [(MSNF+WS) x 2.37]/W

= [(10.77 + 0) x 2.37] / 55.32

= 0.46

FPDt = 3.3°C + 0.46°C

= 3.76°C

Thus, the initial freezing point temperature of this ice cream mix is -3.76°C

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## 2. Freezing point control, the tendency and the curve.

An ice cream mix starting to freeze at -3.76°C is extremely late. In my experiences, I have found that my ice cream mix started to freeze at between -2.5°C to -3.0°C, between which I would say is normal and can predict that the ice cream will firm up to targeted extent upon withdrawal. Ice cream firmed up decently when withdrawn will have had around 60-70% solutes frozen and the remaining 30-40% will continue to harden in the freezer set at below -30°C in a static status. An unbalanced ice cream composition will fail to reach this level and suffer from massive amount of unfrozen water being recrystalised during the static status and thus ruin the texture through water migration.

Besides, in an ice cream shop there is always just one showcase freezer to sell over 15 flavours at one specific temperature. And since flavours themselves can vary within like alcoholic flavours with extremely low freezing point; chocolate who has high fat and fibre profile is prone to hardening or flavours that tend to go coarse easily like sorbet due to lack of fat and protein to stabilise the structure, ice cream makers must adjust the composition to reach an uniformed scoopability when all the products are stored in the same showcase at the same temperature, thus, the freezing point depression control becomes the key. With the aid of freezing point depression, it is able to plot a freezing curve in which we may see how the solute freezes in terms of tendency. Now take a look to **example 1**:

From above, we calculated that the initial freezing point (0% water frozen) was -2.98°C. When 20% of the water is frozen, 80% is still liquid, so W is now (54.86% x 0.8) = 43.89%. The g sucrose/100g water is now 22.36 x 100/43.89 or 50.945g/100g water. From Leighton's table, the FPDse corresponds to 3.19°C. For the milk salts, FPDsa = (10.78 + 0) x 2.37/43.89 = 0.58°C. Thus, FPDt = 3.19°C + 0.58°C = 3.77°C. Now it is concluded that at -3.77°C, 20% of the solute in this mix will be frozen. Similarly, we can calculate the 40%, 60% and so on until a curve forms.

Ice cream with a well-balanced composition will be withdrawn at around -5°C to -8°C with 60-70% frozen water in it whilst the extremely unbalanced one will fail to reach 60% but rather less at around 40-55% instead. Although both ice cream mix can reach 80% up frozen water after storage but the texture will end up being very different as the latter one has had that massive amount of unfrozen water to be undergoing recrystalisation, which integrates those unfrozen water to be frozen again, whose size is huge and detectable by our tongue.

**Conclusion:**

Freezing point depression (FPD) is about the difference between 0°C and the temperature at which the ice cream starts to freeze. Any substances like sugar and salt added in the water, the freezing tendency changes. It is crucial to control FPDt because it is thy key to directly affect the firmness, scoopability and most importantly, the texture of the final product. In calculation, we have equations and tables to get the answer mathematically, and through which ice cream makers can predict the result.

## Reference:

Ice cream science 7th edition (2013)

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