225 is the appropriate/optimal size for 18" wheels, the tyre shop will tell you. There might be a misconception that wider is better. While you wanna have as much tyre contact with the road as possible, there is an optimum limit to this. Having said that, 235 is not too excessive as well. Many brothers here run on 235 on 18".
Bear in mind that your car will already have some negative camber - means that the weight is already not evenly spread over the width of the tyre, and is only further shifted towards one edge (usually inside) of the tyre.
Wider tyres have other detrimental effects such as increased aquaplaning and friction (resistance) as well as increased steering feedback which may be good but up to a point.
In short, increasing the width of the tyre will not necessarily increase the contact patch as the weight of the car is the same. The shape of the contact patch will however change under these circumstances, hopefully to the benefit of lateral (cornering) grip but only if they are fitted to the correct rim size.