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Hydrogenated Polyisobutene is often used as a mineral oil replacement.

You'll likely see this in many BHA products because this is the go-to solvent for salicylic acid.

This ingredient is typically used at levels between 2-20%.

Regarding fungal acne:
In 2019, this ingredient was tested against multiple Malassezia species (the yeast that causes fungal acne) and showed no growth.

On a cellular level, it disrupts the cell membranes of microbes by poking holes that make the cell leak. This shuts down the chemical reactions the microbe needs to make energy so it can no longer survive.

Another perk of this ingredient is that it stays functional across a wide pH range (3-10).

You'll often see it paired with boosters like Ethylhexylglycerin; one study showed that a 1:9 ratio of Ethylhexylglycerin to Phenoxyethanol damages bacterial membranes as effectively as doubling the Phenoxyethanol concentration on its own.

Typical use concentrations range from 0.3-1% depending on the formula, and this ingredient is capped at 1% int the EU.

Safety-wise, the fear mongering does not hold up to the evidence. The EU's Scientific Committee on Consumer Safety and FDA consider it safe as a preservative at up to 1%, including for children of all ages.

Adverse systemic effects only showed up in animal studies at exposures roughly 200x higher than what people get from cosmetics. And despite its very widespread use, this ingredient is a rare sensitizer and allergic reactions are uncommon.