Statistical Mechanics of Simple Polar Fluids

The field of s tatis tic al mech anics h as received at le as t i ts f ai r sh are of attention from recent issues of the Annual Review of Physical Chemistry. For ex ample the p resent volume contains contribu tions from Alder on compu ter dynamics, Wheele r on cri tic al phenomena, and Egels taff on the li quid s tate. Wi th this excellent cover age in mind I h ave elec ted to p resent a c ri tic al review of a speci al topic in s tatis tic al mech anics of the li quid s tate. This topic, which h as been of interes t to me fo r m any ye ars, is the s truc tu re of simple pol ar fluids. In the l as t three ye ars there h as been a g re at de al of p rog ress in this area and i t seems approp ri ate to p resent a review for the nonspeci alis t. The topic deserves the attention of the nonspeci alis t prim arily bec ause w ate r and o ther pol ar fluids are of such g re at impor tance in nature, cer tainly more so th an the simple r are g as li quids which h ave received so much attention f rom theo ris ts. Of cou rse w ater is a more compl ic ated li quid th an a simple pol ar fluid bec ause of the p resence of hydrogen bonding. On the o ther h and i t seems unlikely th at a successful theo ry of w ate r c an be cons truc ted wi thou t taking into account the essenti al fe atures th at arise when the molecules inter ac t by d ipole-dipole forces. In a si mple li quid the p articles are cus tom arily assu med to inter ac t by p air­ wise addi tive inte rmolecul ar po tenti als u(i, j) [here the argument (i, j) deno tes the posi tion (ft, fj) and o rientation (wj, Wj) of two representative p articles i and j in the fluid]. For a si mple fl uid u(i, j) is assumed to h ave a h ard core fo r which u(i, j) = ex), rjj ::; a, and to be of sho rt range i.e. u(i, j) � 1 rtf 1n wi th n > d whe re d is the dimensionali ty of the sys tem. Mathem atic ally the sho rt r ange condi tion assu res th at the po tenti al is integr able over all sp ace ou tside the h ard co re. Physic ally the condi tion me ans th at the inter ac tion ene rgy of a one­ rep resentative p ar ticle wi th all i ts su rrounding neighbo rs will be fini te and th at 1 Work supported in part by the National Science Foundation and the Alfred P.