Michael Mullan, an independent food and beverages professional, discusses how to control the hardness of ice cream and gelato.
Frozen dairy desserts such as ice cream and gelato are consumed when the product is in the partly frozen state. They rely on a combination of mix composition, processing conditions and temperaturecontrol during freezing and final product storage to achieve a product of the required texture.
The manufacturing process for ice cream and gelato is similar and involves the preparation of a liquid mix; whipping and freezing this mix dynamically under high shear to a soft, semifrozen slurry; incorporation of favouring ingredients to this partially frozen mix; packaging the product; and further freezing (hardening) of the product under static, quiescent conditions.^{[1]}
Gelato while similar to ice cream has a lower overrun (reduced volume of air incorporated), reduced fat content, tends to be sweeter and softer and generally offers more intense fruit flavours.
In this article we will explore how food scientists and technologists can vary the mix composition and thus control the hardness or "scoopability" of ice cream, gelato and similar products. The volume of air added during freezing (overrun) and the type and concentration of emulsifier can also affect hardness but will not be considered further as these effects while important are generally less significant than the concentration of sweeteners used and the serving temperature. Because hardness and sweetness are related, and sweetness is only briefly discussed readers may wish to explore this area further.^{[2]}
There is an extensive range of flavoured ice creams (Plate 1) however there is frequently a marked difference in hardness between flavours in the UK, Ireland and the US compared with gelato in Italy e.g. the chocolate flavour is often harder, more difficult to scoop, than the vanilla or strawberry flavours.

Plate 1. Range of flavoured gelato in a retail display cabinet in Naples, Italy.

In recent years there has been a significant increase in the number of specialist ice cream shops / parlours or gelateria in the UK. Many of these gelateria owners require ice cream or gelato that is of consistent sweetness and hardness or resistance to scooping, also called dipping in the U.S. Consequently food technologists should have a good understanding of how to formulate an ice cream mix to control the hardness and sweetness of the ice cream.
Freezing point depression
Pure water at standard pressure (101.325 kPa) freezes at 0°C. Addition of sugar e.g. sucrose will lower the temperature at which the water freezes; the freezing point depression (FPD).
The FPD of an ice cream mix depends mainly on the number of sweetener molecules in the mix recipe and the number of milk salt ions. The number of molecules depends on the weight of the sweetener added and its molecular or formula weight. This effect can be illustrated using two common sugars, fructose and sucrose.
Fructose has a molecular weight of approximately 180 whereas sucrose has a molecular weight of about 342. The FPD of a 1% fructose solution is approximately twice that of a similar sucrose solution because there is almost twice as many molecules of fructose present in the fructose solution; fructose has about half the formula weight of sucrose.
The effect of a solute e.g. glucose on the freezing point depression of a solvent e.g. water can be calculated in dilute solutions using equation 1.
Equation 1. ΔTf = iK_{f}m
Where ΔTf is the freezing point depression, i is the van't Hoff Factor, K_{f} is the molal freezingpoint depression constant (this is solute specific) and m is the molar concentration of the solute. The units for K_{f} are °C m^{1}and the Kf value for water is 1.86 °C m1. The van't Hoff Factor is determined from the number of ions in the molecular formula of an ionic compound, e.g. 2 for NaCl, 3 for CaCl_{2}. Since carbohydratesweeteners are not ionic compounds the van't Hoff Factor will not be considered further and is removed from the equations in the examples below.
The use of equation 1 to calculate the theoretical freezing point depression of a 1% (w/w) solution of glucose in water is shown in Table 1.
Given: glucose has a molecular weight of 180.16 and water has a Kf of 1.86 °C m^{1}.
Calculate the moles of glucose present in 1 kg of water. Equation 1 is then used to calculate the freezing point depression.
Moles of glucose = 10 = 0.0555
180.16
ΔTf = 0.0555 x 1.86
Freezing point depression =  0.103°C.


Table 1. Calculate the FPD of a 1% w/w solution of glucose in water. 
Performing a similar calculation using sucrose, molecular weight 342.29, gives a FPD of only  0.054°C.
The calculations above provide the theoretical basis why monosaccharides such as glucose and fructose depress freezing point more than disaccharides such as lactose and sucrose. Pentose compounds such as xylitol, of even lower molecular weight, depress the freezing point even further.
This effect, the greater the number of molecules of sweetener then the lower the FPD, is known as a colligative effect.
The FPD of an ice cream mix, and the hardness of the final ice cream, can be controlled by varying the concentration of sweetener or sweeteners added. As the sucrose concentration is increased less water will be frozen at a given “frozen” storage temperature, say 18℃ and a softer ice cream will be produced.
Calculation of freezing point depression and freezing curves
Food scientists and technologists can calculate the theoretical freezing point depression or determine the actual freezing point of ice cream mixes and construct freezing curves. These can be used to calculate the concentration of ice and unfrozen water in ice cream at particular serving temperatures and to predict the relative hardness of the ice cream produced from particular mixes at designated temperatures. This information can also be used to calculate sensitivity to heat shock and resistance of product containers to deformation during distribution and storage.
Leighton^{[3]} devised a method for calculating FPD in ice cream and for calculating theoretical freezing point curves. The method involves calculating the sucrose equivalence of the sweeteners present and their FPD. This is combined with the FPD due to milk salts and using an iterative approach the % water frozen against the cumulative freezing point depression produced by sweeteners and salts is tabulated and used to construct freezing curves. Instructions on how to use the Leighton method have been published and computer programmes and spreadsheets are available.^{[4]}
A typical theoretical freezing curve is given in Figure 1. Note that around 80% of the water for the particular mix will be frozen at around 18℃. In practice, providing not more than 65% to 70% of the mix water is frozen at the serving temperature, the ice cream or gelato should be soft enough to serve. The mix shown would give a hard ice cream if served straight from the freezer at 18℃.
However, the ice cream may become too sweet prior to the desirable softness being obtained if sucrose is the only sweetener used. Alternatively, part of the sucrose can be replaced with a less sweet sugar e.g. dextrose, hydrolysed corn starch syrups known as glucose syrups or a polyol such as sorbitol.

Figure 1. A theoretical freezing point curve for a standard ice cream mix.
The mix contained 12 % sucrose, 1% dextrose and 12% skimmed milk powder. The curve was calculated using the Leighton method.^{[4}^{]}

Determination and practical use of the freezing point depression factor
Calculation of the actual freezing point and /or the determination of theoretical freezing curves of mixes while particularly useful in product development are usually not undertaken outside research institutes and the larger companies that employ graduate food scientists and technologists. Instead methods based on calculation of the freezing point depression factor (FPDF) of individual sweeteners in mixes are used to control hardness and to optimise the consumer eating experience.^{[4],[5]}
These calculations are based on summing the freezing point depression factor (FPDF) of each sweetener (lactose is not usually included outside continental Europe) used in the ice cream mix to give a total value that is used for control purposes. Lactose is included in the calculation of FPDF in continental Europe where the calculation is called Potere Anti congelante, PAC. FPDF is not the same as the FPD which was mentioned previously and is a dimensionless number.
Incidentally sweetness, while subjective to a large extent, can also be calculated using sucrose as a standard.^{[2] }Sucrose is allocated a value of 1 in both schemes.
The FPDF of sweeteners other than sucrose is obtained by dividing their formula weight into the formula weight of sucrose, [Table 2]. Sodium chloride and ethanol are included for comparative purposes. Note, manufacturers’ mean molecular weight data for syrups and maltodextrins should be used if available.
Sweetener 
Approximate molecular (or mean molecular) weight 
Freezing point depression factor^{[4]} 
Sucrose 
342 
1.0 
Sodium chloride 
58.4 
5.9 
Ethanol 
46 
7.4 
Dextrose 
180 
1.9 
Fructose 
180 
1.9 
Glucose Syrup 28 DE 
643 
0.5 
Glycerol 
92 
3.7 
Invert sugar 
190 
1.9 
Lactose 
342 
1.0 
Litesse® Polydextrose 
570 
0.6 
Maltodextrin 18 DE 
1000 
0.34 
Sorbitol 
182 
1.9 
Trehalose 
342 
1.0 
Xylitol 
152 
2.2 
Erythritol 
122.12 
2.8 
Table 2. The relative freezing point depression factor (FPDF) of selected sweeteners, sodium chloride and ethanol.
Calculation of the freezing point depression factor
Calculations illustrating how to determine the FPDF of sweeteners are shown for sorbitol [Table 3].
Sorbitol and sucrose have approximate formula weights of 182 and 342 respectively.
The FPDF of sorbitol is 342 = 1.9
182
This means that a solution of sorbitol depresses the freezing point by about twice as much as a similar solution of sucrose. Sorbitol is about 60% as sweet as sucrose.

Table 3. Determining the FPDF of sorbitol. 
Further examples are provided in a very useful book on glucose syrups by Hull.^{[5]}
Calculation of the FPDF of commercial ice cream mixes and its use in the control of hardness of ice cream (lactose not included)
Examples of FPDF calculations used to predict the hardness of ice cream are illustrated below. These calculations were performed by tabulating the sweeteners present in 100 g of mix, the weight of sweetener added, their FPDF from table 1 and the total FPDF of each sweetener (product of the FPDF of the sweetener and the weight added). The total FPDF of each sugar is summed to give a total FPDF value for the mix [Tables 4 and 5]. Lactose is supplied by the milk solids not fat (MSNF) component and is generally excluded from calculations outside mainland Europe. The justification for doing so is that the concentration of MSNF is generally constant between mixes (and is usually outside the manufacturer’s control). On the other hand the major variables affecting FPDF are the added sweeteners; these are controlled by the product developer and are included in the calculation. However, there are occasions when the lactose concentration must be considered and there is a case for routinely including it in FPDF calculations.
The mix in Table 4 has a FPDF of 15. Apart from sucrose no other sugars have been added. Note it is also advisable to calculate relative sweetness when undertaking these calculations.^{[2]}A mix with a FPDF of 15 will give a very hard ice cream. Note scooping hard ice cream can result in wrist and other injuries with the potential for industrial injury claims.^{[6]}
Sweetener 
Weight, g 
FPDF 
Total FPDF of sweetener 
Relative sweetness 
Sucrose 
15 
1 
15 
15 
Total FPDF or relative sweetness of mix 


15 
15 
Table 4. Determining the total FPDF of an ice cream mix containing added sucrose
The mix shown in table 5 has a FPDF of about 25 and a similar relative sweetness to the previous mix. A mix with this FPDF would be easy to scoop at 18°C.
Sweetener 
Weight, g 
FPDF 
Total FPDF of sweetener 
Relative sweetness 
Sucrose 
8 
1 
8 
8 
Dextrose 
8 
1.9 
15.2 
6.4 
Glucose Syrup 62 DE 
2 
0.8 
1.6 
1 
Total FPDF or relative sweetness of mix 


24.8 
15.4 
Table 5. Determining the total FPDF of an ice cream mix containing several added sweeteners.
Ice cream stored 18°C made with mixes with FPDFs ranging from around 20  25 will give easy to scoop ice cream. Similar ice cream stored at this temperature and made from mixes with FPDFs of <15 will be quite hard.
Application of the Potere Anti Congelante (PAC) method to control the hardness of ice cream
Lactose depresses the freezing point of water in a similar way to sucrose. An example of a PAC calculations is given in Table 6. In this example a multisweetener recipe for a typical Italian gelato recipe intended for serving at around 11°C is considered.
Given: a mix containing (w/w) 8% fat, 14% sucrose, 2% dextrose, 2% invert sugar, 10% skim milk powder (SMP), 0.3% emulsifier/stabiliser and 36.6 % total solids. Lactose constitutes 54.5% of MSNF.^{[7]} SMP contains 97% MSNF.
The fat and the emulsifier/stabiliser have minimal effect on the FPDF and are not considered.
The sugars present in 100 g of mix are calculated starting with the lactose present in the SMP*.
Lactose = 10 x 0.97 x 0.545
= 5.29g
Sucrose= 14g
Dextrose= 2g
Invert sugar= 2
The PAC of each sugar is calculated.
PAC from lactose= 5.29* x 1
= 5.29
The PAC from sucrose=14 x 1
= 14
The PAC from invert sugar=2 x 1.9
= 3.8
The PAC from dextrose=2 x 1.9
The PAC of the mix is 5.29 + 14 + 3.8 +3.8
=26.9

Table 6. How to calculate the PAC of an ice cream mix containing several added sweeteners 
With a PAC value of about 27 (FPDF of about 22, 275.3) this gelato has been designed to serve at around 11℃ where is should be acceptably soft. Examination of the theoretical freezing curve for this mix, Figure 2, shows that around 65% of the moisture in this mix would be frozen at 11℃.

Figure 2. A theoretical freezing curve for a typical gelato mix.
The mix contained 14% sucrose, 2% dextrose, 2% invert sugar and 10% skimmed milk powder. The curve was calculated using the Leighton method.^{[4]}

Are there advantages in using the Potere Anti Congelante method of calculating freezing point depression factor?
Yes, the PAC method should be used when batches of ice cream of significantly variable lactose concentration are being produced e.g. when ingredients containing high concentrations of lactose are used or mixes give softer than expected ice cream.
The effect of fat from nuts on hardness
Artisan gelato makers are particularly innovative and use a wide range of ingredients including nut pastes. Use of some nut pastes particularly those high in fat can result in harder than expected gelato requiring additional sweetener to further depress the FDP to compensate.
How to reformulate ice cream mixes to obtain desired hardness characteristics
It is usually straightforward to reformulate mixes to obtain ice cream of the required hardness using Excel spreadsheets or computer programmes. Replacing sucrose with a mixture of fructose or invert sugar and dextrose or high DE glucose syrups can easily be used to produce a range of mixes with defined hardness characteristics. The addition of relatively small quantities of salt, glycerol, sorbitol or ethanol (e.g. from whiskey, rum and various spirits) can also be used to significantly lower the FPD.
Conclusions
The hardness of ice cream or gelato can be manipulated by adjusting the initial FPD or FPDF of the mix used for product manufacture so that a target percentage of frozen water is achieved at the serving temperature. This is usually in the range 65% to 70%. The precise concentration will depend on overrun, the concentration of coalesced fat and other factors.
The major extrinsic factors contributing to FPD are added sugars, salt, polyols and ethanol. Lactose which is not usually included in FPDF calculations has a similar effect on FPD to sucrose and is included in PAC calculations.
The use of freezing curves that enable the percentage ice to be calculated is very useful for product development purposes but is used relatively little and generally only by larger companies. These curves are easily produced and the software to do this is inexpensive.
Adjustment of the FPD of mixes must also consider sweetness. As the sucrose concentration is increased ice cream becomes softer at a given frozen temperature. However, the sweetness may become excessive before the ideal texture is achieved. The use of less sweet sugars e.g. dextrose and /or glucose syrups that have greater FPD can be used to balance texture and sweetness. Sweeter hexoses such as fructose can also be used to obtain the ideal texture and to reduce the concentration of sucrose used.
Dr. W. Michael A. Mullan, FIFST
Email: michael.mullan@dairyscience.info
Web: www.dairyscience.info
References
1. Goff, H. D. and Hartel, R. W. (2013). Ice Cream. 7th Edn. Springer: New York.
2. Mullan, W.M.A. (2012). How do you get the sweetness of ice cream or gelato just right? Available from: https://www.dairyscience.info/index.php/icecream/220icecreamsweetnes.... Accessed: 3 December, 2017.
3. Leighton, A. (1927). On the calculation of the freezing point of ice cream mixes and of quantities of ice separated during the freezing process. J. Dairy. Sci., 10, 300308.
4. Mullan, W.M.A. (2013). Goldilock's ice cream. Using science to control hardness or "scoopability". Available from: https://www.dairyscience.info/index.php/icecream/228icecreamhardness.... Accessed: 3 December, 2017.
5. Hull, P. (2010). Glucose Syrups: Technology and Applications. WileyBlackwell: Chichester, U.K.
6. Dempsey, P. G., McGorry, R. R., Cotnam, J. and Braun, T. W. (2000). Ergonomics investigation of retail ice cream operations. Appl. Ergon., 31, 121—130.
7. Van Slyke, L. L. and A. W. Bosworth (1915). Condition of casein and salts in milk. J. Biol. Chem., 20, 435152.