Step 1: Understanding \( \mathrm{C_{sp^3}-OH} \) bond.
In most alcohols, the hydroxyl group is attached to an \( sp^3 \)-hybridised carbon atom.
Step 2: Analysing each option.
Phenylmethanol, 2-methylpropan-2-ol, and propan-2-ol all contain \( sp^3 \)-hybridised carbon atoms bonded to \(-\mathrm{OH}\).
Vinyl alcohol has the \(-\mathrm{OH}\) group attached to an \( sp^2 \)-hybridised carbon.
Step 3: Conclusion.
Therefore, vinyl alcohol does not have a \( \mathrm{C_{sp^3}-OH} \) bond.