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. ( ) ( ), (, , , ). (, -). . , - , . i j {u(ri,rj)}, , , , 6,03 , 100,2 2, 171 . / 8,314, / - 1.987. RT 592 /. : ri,j. ( ri rj , ri,j). , , , ( ). (3-, 4-) . .. . ( ) N(N-1)/ 2 » N2/ 2 ( N>> 1 2, ). Zv, . u ( ri, j ) - 1 Zv = ......... ( e kT d x1 d y1 d z1. ... d x N d y N d z N ) , , 3N h N! 3N u ( ri, j ) - Z v, N 1 Zv = ......... ( e kT d v1. ... d v N ) = N ! . , Z = N! N Z Z Zv. ( p 0) . . :

U (G + T S - p v = p p T, N T, N Cp G = v, = -T p T, N p T, N

F v v v , = - p = -T - p , T p, N p T , N p T, N p T, N 2 v . 2 T p, N

- . . . : r , ro - . u(r) = r < s, u(r) = - e s ( ) r ls, u(r) = 0 r > ls , l = 1,5. : U = B/ rn r > ro ( ) , (n 6). U = r ro. - : 1/ rn, - 1/ rm. n = 6 m = 12 ( 6 6 r 12 ro o - 2 . Do - ( 100 - 500 K) ro, s 12): U (r ) = D o

r

r

1


. .. U(r) = 0 r = , : ro =21/6 s 12 6 - . : 500. U (r ) = 4D o

r

r

, -: e AB = (e AA + e BB)1/2 sAB = (sAB + sAB) / 2. - : 3 r c c' o u (r ) = b exp ( -a r / ro ) - + exp -4 - 1 . 8 6 r

r

r





r ro 1. "4" , "6" -, "8" - . ro , e - , - (13,5), b = 0 - 0,2, b aro 6 6a b = - + (1 + )c ro e , c = , c' = ro 2c.

[

]

a (1 + ) - 6 - 8

, -, . r, 4 5 6 7 8 2000 U, K 0 - 1500 - -10 1000 -20 - 500 -30 r, 0 3.2 3.4 3.6 3.8 -40 U, K 2, = 13,5, b = 0,1. . . , , , . () . . ()

2


A A = A (T, p 2 , N ) - A (T, p1, N ) = p p
1

p2

dp. f
T, N

ln f = ln p -

1 RT

p RT

_ - v d p. 0 p

. , . (): f (i,j) = exp[ - u(rirj)/ kT] - 1. exp[-u(ri,j)/ kT] = 1+ f(i,j). -, 2 500 .

, , s, . s ( , ) ro ro= 2 s1/6, .. 6-12. , ( » 3ro ), . _ _ U = u (r i, j ) exp ( - U / k T ) = (1 + f ) . Zv,N
i< j , .

Z v, N = ......... ( (1 + f ij )dr1. ... dr N ). N(N-1)/2 » N2 / 2
Z v = .. .. [1 + (f12 + f13 +. .. ) + (f12 f13 + f12 f14 +.. . ) +...]d r1.. . d r N = ... dr1... dr N + . .. f ij d r1... d r N + ... f ijf k l d r1... d r N +. ..

i< j ik jl , ( ). . . () .

. . . f12 f 56 f 57 f 67 f 68 d r1... d r8 A

f12d r1d r2 d r3 d r4 f 56 f 58 f 67 f 68d r5d r6d r7d r8 .
bi. - (n) . , n - 1 .

3




1 1 f n (r1... r n )d r1. .. d r n . b1 = V.1! dr1 = 1 . Vn ! 1 1 b 2 = f12d r1d r2 = exp( - u / k T ) - 14 r 2d r . 20 V.2 ! bi =

[

]



exp -
exp -

FI GJ HK

1 (f12 f 23 +f12 f13 + f13 f 23 + f12 f13 f V.3 ! F 1 E = ZN = exp - dp 1 ... dp N dr1 . .. dr N kT kT N !h 3 N U exp - kT dr1... dr N F - F = V - N exp - = Zv = kT dr1... dr N b3 =

z

FI GJ HK

23

)d r1d r2 d r3 .

( E = E + U )
U kT dr1... dr N .

p = -

F ln Z = kT V T,N V

ln Z = kT V T,N

. T,N

. ln Z v Nk T N 1 - = . k - . bk : p = k T

v

v



+1

. b1 = 2b2, b2 = 3b3 - 6b .. :

2 2

v

B (T) C 3 (T) pV =1+ 2 + +... Nk T V V2


, - .. , : B2 = - (1/ 2) N b1, C3 = - (2/ 3) N2 b2 .. . k = 1 p = ). B2 ( 1 N 1 = B2 ) 1 = -4 e - u ( r ) / k T - 1 r 2d r. 2 0

Nk T 1 N 1- . .. ( v 2 v

(

)

: , ( ). , .. r , f 0. : , . , b1. n = 6. (). U/ k (100-200K) . , r , U(r) = f(r) = - 1, 6 6 Do r U (r ) = - D o f (r ) .

r

kT r

: 0 s s . 6 Do 2 8v D 4 3 4 D o 3 2 + = -8v o + o o . 1 = - 4 r d r + 4 r dr = - kT r 3 3kT kT 0 vo - ( s). : 4, 5, 7 ( , .. ), . : s
n



1 r
n -2

dr =

1 3- n r n -3

s 3 .

4


, b1,

4D o v pv N = 1 + 4v o - Nk T v kT

o

.

N 2a p + (v - N b ) = N k T - 2 v
: pv +

N 2a N 2a N b - Nb p - = Nk T . v v2

Nk T N 2a p= - Nk T , .. v >> Nb Na/ v2 << 1 (b 10-1 / , a - 1 .2 / ) .. 2 v - Nb v
(3- , a N 2a b pv N =1 + b - + . ). p NkT/ V , 2 Nk T v kT

kT v

4- : 3- - C3 =

N 2a b ( kT

, .. v2 >> ab). B2 = N b -

4D o v o = N 4v o - kT - b = 4v o , a = 4D o v o . , b a kT



. 2 , . B2 = 0. B2: 100 273 373 600 a{2./2} b {/} -2,5 13,7 16,6 0,2444 0,02661 -197,5 -22,0 -3,7 12,9 1,360 0,03183 -160 -10,5 6,2 21,7 1,390 0,03913 , ( () ). : , . . F :

exp( -F / kT) = ZN =

1 N! h3N

z

exp( -E / kT)dp1. . . dpN exp(- U / kT)dr1. . . drN.

Fp F : F p - F = - kT ln 1 + v

U

exp - (F - F ) / kT =

z

{

z

-N

[exp ( -U / kT) - 1] dr1... dr N .
= v- N exp( - U / kT)dr1. . drN

}

exp( - U / kT)dr1. . . drN

exp(-U/ kT) = 1 + [ exp(-U/ kT) - 1] , F - F = - kT ln 1 + v - N exp ( - U / kT) - 1 dr1... dr N . U = 0 F

z

dp1... dpN

z
}

{

[

]

- F = 0. . , - , Fp - F N2kTB2(T)/ V. : -

F + 3 Ib - 1g G 2 J3 = HK

8 , = V / V , = / , =/ .

5


. ( -).

Ur ) = f (r / ) U = (

: Zv =



Uri, j ) = (



f (rij / ).
dr1 3 ... dr1 kT V = 3N N , , 3 3



v

e

- / kT f ( ri j / )

d r1... d r N = 3N

v / 3


e

- / kT f ( ri j / )

N - .

p = kT

Fln Zv I G V J, HK TN

=

kT 3

F G( H

V / 3

ln N

I J, K TN

=

kT V N , . 3 3

F G H

I J K

yN - . p = p 3 / , T = T k / , V = V / 3 p = N (T , V ). .. . , --. -.

6