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It is known that (chloromethoxy)ethane forms stable carbonium ions based on Nobel prize Chemist George Olah research Olah's method. This would indicate that (chloromethoxy)ethane reacts through $\mathrm{S_N1}$ mechanism. However, $\mathrm{S_N2}$ mechanism is also very feasible for highly electrophile carbon.

Which one of the mechanisms is dominant?

Organic chemistry books in this case are not very clear. For example Clayden speaks about Olah's method and neighbouring group participation (pp. 419, 970 1st ed) but also gives relative rate for $\mathrm{S_N2}$ mechanism (pp. 425 1st ed)

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Probably both mechanisms can happen and it would require experimental data from reaction kinetics and computational calculations to determine which one of the mechanism is domintant.

One example of determined mechanism about neighboring group effect, also called anchimeric assistance is mustard gas (chloromethine) alkylation reaction with DNA.

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Effect of chloromethine is based on its ability to block DNA replication by alkylating guanine, and after the war it has been also used as cancer drug.

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