Can DNA be denatured at acidic pH?
Alkaline denaturation neutralize the charge of acids but also cause hydrolysis of bases upon prolonged treatment. Strong bases will raise pH until the H+ shared between the N-base electronegative centers (N-H and O=) is stripped from the H-bond, effectively breaking them.

Organic solvents such as dimethyl sulfoxide and formamide, or high pH, could break the hydrogen bonding between DNA strands too. Low salt concentration could also denature DNA double-strands by removing ions that stabilize the negative charges on the two strands from each other.

Low pH (less than pH 1): both RNA and DNA hydrolyze (phosphodiester bonds break and the bases break off).

High pH (greater than pH 11): RNA hydrolyzes, DNA will denature but the phosphodieser backbone remains intact.

[salt]
Tm is sensitive to Na+ concentration.
Na+ acts to shield the negative charges of the sugar-phosophate backbone from interacting with one another. The repulsion between the negatively charged phosphate backbones is the major force destabilizing the double helix, therefore increasing Na+ concentration increases helix stability and decreasing Na+ concentration decreases helix stability.

References:

http://faculty.tru.ca/dnelson/courses/biol335/335notes/3recdna/4-hybrization/recDNA3a.html

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1367631/pdf/biophysj00681-0002.pdf