Why does DMSO help facilitate halohydrin reactions?

It would make sense, due to bond energy, that water molecules would have a hard time competing with $\ce{Br}$ in a bromonium ion intermediate. 


However, I was reading that by doing the reaction in DMSO, it encourages the protonation of the water molecules. How? What is the rational behind this?




Alkenes predominantly gives relevant 1,2-dihalo product when reacted with a halogen (*e.g.*, $\ce{Br2}$) in a organic solvent such as chloroform or dichliromethane. If the reaction is performed in water, the product is the corresponding 1,2-halohydrin due to restriction applied by polar water molecules caging $\ce{Br-}$ ion. Organic molecules are sparingly soluble in water as solvent. Thus, the halohydrin reaction is often done in a mixture of organic solvent and water. For example, bromohydrin can be achieved by using *N*-bromosuccinimide as the electrophilic bromine source in $\ce{DMSO/H2O}$.


Use of $\ce{DMSO/H2O}$ as a solvent has few advantages: 


1. The bromine source, *N*-bromosuccinimide (NBS) is readily soluble in this solvent system [Ref. 1]).
2. $\ce{DMSO}$ is also participated in reaction mechanism. Reference 1 has detailed labeling procedure using $\ce{DMSO^{18}}$ to show that isotopic $\ce{^{18}OH}$ was incorporated in $\ce{OH}$ group of bromohydrin [Ref. 1].
3. Evedence also suggest the participation of water in the medium, probably due to increasd basic nature of water in $\ce{DMSO}$ ($\mathrm{p}K\_\mathrm{a}$ of water in $\ce{DMSO}$ is $31.4$ at $\pu{25 ^\circ C}$ [Ref. 2]).


Suggested mechanism for involvement of $\ce{DMSO}$ as follows:


[![enter image description here](https://i.stack.imgur.com/LD3WL.jpg)](https://i.stack.imgur.com/LD3WL.jpg)


**References:**


1. Bromohydrin Formation in Dimethyl Sulfoxide: D. R. Dalton, V. P. Dutta, D. C. Jones , *J. Am. Chem. Soc.*, **1968**, *90(20)*, 5498–5501 (<https://pubs.acs.org/doi/abs/10.1021/ja01022a030>).
2. Acidities of water and simple alcohols in dimethyl sulfoxide solution: W. N. Olmstead, Z. Margolin, F. G. Bordwell, *J. Org. Chem.*, **1980**, *45(16)*, 3295–3299 (<https://pubs.acs.org/doi/abs/10.1021/jo01304a032>).


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