RDF & virial Expansion

Last time showedwe can obtain gel by measuring

SCH by scattering & farrier transform

Or predict sad by knowinggirlAlso Showed reversible work theorem

go ) = e- Bath, WG ) is

potential of mean forceIf short

¢or L '

range IIe V

A

& pair ) = 2M No fodrMuch gcr )

-

what about pressure?

D= KT Fu In QCNNII = ktff-logZCN.us)

2- C Niv ,t ) = Syd -

Ne

- P " "

, so where is volume

dependence

Imagine changing volume as moving everythingcloser together or father apart

→ →

Say S ;= Yu 's ri

⇒ ZCN , v. T , =vnfdsw e- Pulu "35'n' " si. . . ,

u"sin ,

DI =NUN

- ' fdsn - - - -

t UN Jds ,. - pddhz.lu"

- . I e- Put )

d=

Nj . Z

ok IT -

- I.If.si ,=-3.

Ki"

"il Fi= .IE

,

Tv - ri 87,

= - fu ?!,

ri.fi

- Buer )dfg = IZ t fdi . # Ea,

ri - Fi e

←urial

P =k.IQ#I--kostztdEu--NkgItztuL7?.riFi

)

Exi%m 7 = 42N last ⇒

D= IT ( ⇐,

tri . Fi ) f pressure estimatorIn MD

How does this correct to structure ?

Lastly , consider Upar =

IUcr in

Fi -

- Ji,

- off!' it '

= JI,

fig ,note fig = - fji

j

Tv TE! ri Fi ) -

- fu . ¥ fdrn,

ri fig e- Pur "

='tsu -

¥fdr N

Ig rijfij e- pupcir

each integral identical by swapping particles

=N -CN - l l 2-- IT - ¥fdridrzrizf " fan -

re- Pat )

=

. ¥ . fdr.dz rn If,

gunk )

= - Eufdrdr r II go ,Rs

= - 0% fdi'

i'

II got

isotropic- pyg . 4 te fdr r

'

II go

PAT =P -

2¥73,

fo%r3Cd£)gcr ) &

gcr ) depends on p IT

Imagine go ) can be written as

GG , = ZIP 'dg ,

Cr ) g ,somehow related to

*yldg 'd

Then PIKBT =p t&oBgtz is "

Bgtzltk-

Zig, Job is a

'

er )gjlri.tl

at small y , PPI ft us' Bz

Bz I -

Ifor f ! dr ? " " " 9 " )

Hu ? pub

one can show far long , go , nee- Pu " ) 4.5

her ) = - Kost logger )

Bz 21-213food . P .

dok- i I

a dud - § dS z- p duff girl

= Is Lissa. IF -

fingers.nd .DEI -

- TI '

= - 2n f ! r'

Cgm - Ddr = - 2h Jordi C e

- B " "-

1)

dogLoup , g G) = e

- Ruan

t÷Fmla run in

What is this correction to pressure?

we can try to solve by

pertwktimtheayth.ismeans usually ,

Ulrkaocntuccrl

where are can solve the problemfor how

For this potential ,whet happens to Z ?

Z = fdr e- P " "= fdre-pcuocritu.cn

]

= fdr e- Buon

ftp.rs.fdre-isaocrtenisuicrs→

Zo

= Zo . fdne- PUG [ e-Puz]←

Po "

= Zo Le- " "

So

(a)o

= fdr ache"

Zo

Suppose U,

is small compared to Uo

then Lets "%=I -p@is.tpzhhuisof .. .

=-3.tt?7ui2oto A- -

A =- kgTlogQ= - KBT log [Z÷,µn ] - kgtlogleis

" ' 7 o

log ( I -

X ) = - fx t x%tx% t - -A

So A,

2 BLU , > ot ETELUT> o

t ' Icu . 5.7 t . . .

I Lu , > o-

Plz[ Varo ( Ui ) ) t - -

-

^ C Curnutt expansion\ Cpg 1713

So what isTU

, > o?