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Your profile says you have a 105 f/2.8 VR which many people believe is an excellent portrait lens. With a DX camera you might find that a bit long, though folks shoot portraits with just about any lens. I have the 28-70 f/2.8 AF-s and it is a fine lens. It would work for portraits but since you love the 24-120 I'd suggest you stick with that. You'd likely find the 85mm focal length appealing for portraiture as well and from everything I've read I'm sure the Sigma would perform well. I have a couple of 85mm lenses on an FX camera and love it. Despite the fact these are faster lenses, the truth is most photographers will stop down simply because the focal plane is so narrow at f/1.4, meaning only part of the face is in focus. I can work with that but not everyone likes that kind of shot. Here's an image taken with an 85 f/1.4 AI-s wide open in low light.
Eyes are sharp... ears aren't. Stopping down would have been great but the ISO of this image was 4500. I didn't have much maneuvering room.