Unless the smell is too strong, you could use styrene itself.

Why would you need a vacuum?

Nucleophilic attack of the dimsyl anion (deprotonated DMSO) on styrene at room temperature in DMSO, performed by slowly adding a solution of styrene to a solution of the dimsyl anion (the order of addition is important - adding base to styrene could cause polymerization), affords an addition product which, upon pyrolysis, decomposes to allylbenzene. According to the authors, this reaction "occurs rapidly below 200C." They then elaborate that the reaction begins at 145C with the neat substrate, proceeding smoothly at 165C - and at much lower temperatures (55C with one substrate in DMSO) with base, though they believe it may be cleaner when just thermally driven in the absence of base. It appears it would be possible to distill allylbenzene out of the crude reaction mixture if the chemist is sufficiently lazy, and owns a fractioning column.

With 0.22 eq. of dimsyl sodium, the yield is 71%, and with 2 eq. it is 88%. If 0.71 moles of allylbenzene can be had from 0.22 moles of base - that is, 3.2 moles of allylbenzene per mole of base - then lithium batteries could prove invaluable. 1 eq. of an  alkali metal will react with DMSO to produce 0.5 eq. of dimsyl anion and 0.5 eq. of methylsulfenate anion (CH3SO-). Li has an atomic mass of 6.95 so that means one measly gram is enough to make about 180-190 grams of allylbenzene (not a theoretical yield but based on the reported value of 71%). The methylsulfenate anion, though less nucleophilic, might react with styrene as well, though that should be of little concern as the amounts employed are catalytic, so little substrate would be lost, and the product would also be a sulfoxide, decomposed by pyrolysis back to styrene - nothing stinky or nasty. Given that the yield was improved not just by adding more base but also by slower addition of the styrene, it's probable that the yield with catalytic base could be improved by similarly minor modifications to the procedure. Also of interest is whether less than 0.22 eq. of base would be needed if the rate of addition of styrene was further reduced.

Separation of styrene from allylbenzene would be challenging, as the boiling points are only 11C apart (145C for styrene, 156C for allylbenzene), but this issue could perhaps be avoided by quenching the reaction and crystallizing the intermediate sulfoxide (m.p. 43-44C), which would at least remove any unreacted styrene. However, if any addition products from methylsulfenate are present - again, also sulfoxides, assuming they are even produced - and they do co-crystallize, then some styrene would inevitably be generated and distill over with the product. The remedy would be to use as little base as possible.

A vague outline for a procedure, suggested by Assyl: Lithium metal is added to DMSO, and allowed to dissolve. A solution of styrene in DMSO is added slowly at room temperature. When the reaction is complete, it is quenched, the intermediate sulfoxide crystallized, isolated, and heated to 165C with stirring at atmospheric pressure to produce allylbenzene, which is condensed and collected.

Allylbenzene from styrene (available by the gallon or from pyrolysis of styrofoam), DMSO, and lithium batteries, each containing enough to theoretically produce hundreds of grams of product - quite an exciting prospect.

Now THIS is very interesting!  Great find.

EDIT by fishinabottle
The following post of mine is obsolete as not true for me stupid interchange it with another post of Assyl where for a matter of fact the problem of unchristian amounts of solvents exists.
my apologies

...........

Allylbenzene from styrene (available by the gallon or from pyrolysis of styrofoam), DMSO, and lithium batteries, each containing enough to theoretically produce hundreds of grams of product - quite an exciting prospect.

Nobody does the maths - never. Why?

As if one did it came out that the reaction is volumetrically not so favorable. Hundreds of grams of product refer to hundreds of liters of solvent - quite an annoying prospect in my eyes.

Thats a pity as I am actually a big fan of "styrene to...." but a bathtub full of DMSO?

/ORG

The Dimethyl Sulfoxide (DMSO) Anion — Dimsyl Ion.  http://www.gaylordchemical.com/uploads/images/pdfs/literature/110B.pdf  Page 4 on Preparation.

Yeah, that or just burning lithium and pitching in the oxide. Or using the crude from those crazy thermochemical sodium rxns attempted at sciencemadness.org, allowed to run open to the air. Aluminum in the DMSO itself, or magnesium, in a process akin to the one found there, might work too, but that depends on whether the temperature required is too high, and whether the primary reaction will be production of NaH/Na or the reduction of DMSO by the Al/Mg. Also, surface passivation issues could be a concern.

Removing water from DMSO after throwing in NaOH or KOH may drive the equilibrium a little farther to the right, but the pKa issues are still going to be a problem, a difference of 10^4 in concentration, and the dimsyl anion decomposes fairly quickly at high temperatures, so there'd probably be a ceiling concentration (probably not a very high one) and buildup of methylsulfenate anions, thiolates, etc.

Methoxides, ethoxides, t-butoxides might work, references Assyl has found suggest this is more effective as the base itself is solvated (so the reaction isn't driven to the left by hydroxides wanting to drop out of solution).

Assyl is still skeptical about lithium being totally unreactive with DMSO. He's found several references that state that NaH reacts readily with DMSO near r.t., and others that call for heating to 70-80C for hours to get the reaction to go. There's similar variability with dissolving Na in DMSO, anything from a vigorous rxn at r.t. to a slow one at 60C is described. If you've ever worked with lithium wire you'll know the reason to be skeptical - it's a lot thicker than you'd think. Not a lot of surface area, and that's the point.

The problem that hasn't been discussed anywhere on the-collective.ws, or here, is that polymers are produced if the concentration of dimsyl anions is too low. Alkenes can be polymerized by strong bases, and hydroxide, being a naked nucleophile in DMSO, is - in this system - a very strong base. If you try throwing some allylbenzene etc. into DMSO with a bunch of NaOH you'll see near quantitative isomerization to the propenylbenzene, at r.t., very quickly (again, naked unsolvated hydroxide in solution - it can even drive the Wolff-Kishner at r.t.), but little if any of the desired product, and when crashed into water you're just going to see a nice cloudy precipitate of polymers that won't pull out with DCM or really anything.

Ultimately with regard to concentration of dimsyl anions it's like riding a bicycle, it's all about balancing rates. If you try to pedal too hard on the right side and steer violently like a convulsive epileptic on steroids, while your left side is fading out of a coma, you're going to careen over a bridge and punch through the windshield of a van full of reformed drug addicts on their way to church. The results might be awesome in retrospect but you won't be able to reach your intended destination after an incident like that.

To sum everything up: low temperatures are needed to avoid decomposition of dimsyl anions to methylsulfenate anions and thiolates, and to avoid base catalyzed decomposition of product sulfoxides -  which leads to all kinds of complex chemistry Assyl does not have the time to elaborate on at the moment (so short on time these days that, without the "other" Vitamin A Assyl would be whipping beer bottles at cars out the side hatch of a dive bombing Cessna in the death throes of a spastic psychotic fit).

As for the mechanism it looks like it's just a Michael addition. Using enones as suggested in that thread wouldn't lead to the desired product, the Michael addition is always a 1,4 conjugate addition so it would, for example, add alpha to the phenyl on cinnamaldehyde. The result is a very strong base derived from the product which then just deprotonates DMSO (or another product sulfoxide) regenerating the base - hence, catalytic in base.