Impact of different sugar types (and substitutes) on ice cream

Question

I am really interested in theoretical fundamentals of ice cream making. Everyone who is a little sophisticated whith homemade ice cream knows, that the are certain ingredients and ratios that have to be satisfied to make good ice cream.

In fact understanding the theoretics of ice cream making and knowing how to calculate the ratios of ingredients helped me getting my ice cream perfect every time.

A big influence on texture and storability (in terms of hardness when storing the ice cream in the freezer) has sugar.

Sucrose is the most common used sugar, but other types used are lactose (from milk products), dried glucose syrup, dextrose and inverted sugar syrup

They all have influence on the freezing point of the mixture. The lower the freezing point of the ice cream mass, the softer it is when it comes out of the freezer. The sugars also differ in sweetness, which is measured relative to sucrose (1.0). Lactose (0.3), Dried Glucose Syrup (0.5), Dextrose (0,75), Inverted sugar syrup (1.25)

For this reasons a part of the sucrose is often substituted by dextrose, since you can use more of it (to have the same sweetness) and increase dry mass and lower the freezing point.

My chemistry skills are nearly non existent, so my question is how can I quantify the influence of different sugar types on the freezing point of my mixture? I want to determine how much Xylitol I must use to get the same results (in terms of freezing point) as when I used sucrose. To get to the meta level: How can those figures be calculated (I guess it involves molar masses, oh boy!)

Some figures for the sugars above and also Xylitol and Erythritol would be appreciated.

Criteria for an accepted answer:

• Must name a measure for influence of sugar on freenzing point on a mixture
• Must give figures for all mentioned sugar (alcohol) types.
• Nice to have: A way to calculate the figures
• Can use basic math and chemisty

OR: Explain why this isn't achievable (for a non chemistry expert)

Answer 1

As already mentioned in comments above, this is quite a complex mixture with equally complex set of properties to balance. However, if you are just looking at it as a simple binary system with water as the solvent and various sugars as solutes, one at a time, then there is a very simple answer (not necessarily useful alone).

For dilute solutions, freezing point depression is primarily driven by the solvent and not so much the solute, and the relationship is linear. For sugars,

Freezing Point Depression (°C) = 1.86 * M

M is mass/molecular-mass of whichever sugar you use in 1000ml of water. For your example of 10g of sucrose in 100ml water, M is 0.29 and your freezing point is minus 0.5C.

For disaccharides like sucrose and lactose, they have identical molecular mass of 342. For simple sugars like glucose and fructose (dextrose is just d-glucose), it is 180. For inverted syrup, you have a mixture. For polyalcohols, you can look up their masses easily.

I would still advise against using this sort of tool alone for icecream making.

Separately, sweetness is less about just dry mass but molar concentration, which is why inverted syrup is sweeter than sucrose, 1 unit of sucrose in the same amount of water is less sweet than if it was broken into their constituent mono-saccharide glucose and fructose; instead of 1 unit of sucrose, you have 1 unit of glucose and 1 unit of fructose, double the concentration.

Answer 2

People who formulate ice cream professionally have a relatively simple method for handling the math. It codifies the more advanced math in user 110084's excellent post.

Basically every ingredient is assigned a sweetness value (called POD) and freezing point depression value (called PAC). These values are relative to sucrose. A gram of sucrose in a 1000g batch of ice cream has a POD and PAC value of 1. 100 grams of sucrose has a value of 100. And so on.

Every water-soluble ingredient has a PAC value, based on its molecular mass. Every ingredient with a perceptible sweetness has a POD value. Relationships are linear, so you can just create a simple spreadsheet using basic arithmetic.

The system is imperfect, but good enough. It doesn't not account for increased hardness you get from ingredients that increase the water-to-solids ratio. And it does not account for added hardness you get from some non-water-based ingredients. Like cocoa butter and nut oils that can be hard as a rock at freezer temperatures. I've compensated for this by assigning (estimated) negative PAC values to these ingredients. But this isn't really precise.

Nevertheless, the goal here isn't to do analytical chemistry or to make ice cream that's perfectly consistent in the eyes of lab instruments. We just want a simple, predictable method for getting ice cream qualities into whatever range that we prefer. This system is effective for this purpose.

I've posted some related information here: https://underbelly-nyc.blogspot.com/2016/05/sugars-in-ice-cream.html and here: https://underbelly-nyc.blogspot.com/2017/03/ice-cream-solids-water-ice.html

Soon I plan to post some updated information, including possibly putting a spreadsheet online.