Osmotic pressure(渗透压) As(@2, P+I1, T)=us(O, P, T) G(. n P +PV=G +P(nx+nv (,P,T)=。{G(n,P,7) Pn (△Gn +py IT, P,"p △F △G V kT △G RT|AF-中 a△Fn 2 (2,P,T)=+RT△Fm O△AF +py Polymer dO solution pure solvent H(n,P+∏,T)=(0.,P,T RT aAF V=nx+n △F
Osmotic pressure (⑇䘿): 3 Polymer solution pure solvent P P V nx n V m p ss 20 G n n P T G PV G P n x n V ps m m m p s s , ,, 2 , , ,, , ,, p s ps T Pn s PT G n n PT n P I w ª º ¬ ¼ w 0 2 2 2 , , m s sm s F PI P I P T RT F PV I § · w' ' ¨ ¸ w © ¹ 0 , , p m s s s T Pn G PV n P ª º w ' « » w ¬ ¼ 2 , , 2 p m m m s TPn G F RT F n I I ª º w ' § · w' « » ' ¨ ¸ w w ¬ ¼ © ¹ 2 , , 0, , 'PI P s s P T PT 3 2 2 m m s RT F F V I I § · w' ?3 ' ¨ ¸ w © ¹ s m m m V G F V kT ' ' 2 , , 0, , PI 3 P s s P T PT
Osmotic pressure(渗透压) n - RT OAF rT1 △F ap2 V x o 2 △G △F V kT dIn+21n的2+x(2 x 2 1 second Virial coefficent C M I=RTI-+A,cA p2 当<1x(0.5-)或x=12 RT 当吗>>1/x,即2>>
Osmotic pressure (⑇䘿): 21 2 2 m m s RT F F V I I § · w' 3 ' ¨ ¸ w © ¹ ᖃI2>>1/x, ণI2 2>> I2 /x ᖃI2<<1/x(0.5-F)ᡆF=1/2 2 1 s RT V x I ª º 3 « » ¬ ¼ 2 2 3 I ??? second Virial coefficent 2 1 2 s A V I F § · ¨ ¸ © ¹ 2 2 2 1 1 2 s RT V x I FI ª º § · « » ¨ ¸ ¬ ¼ © ¹ 2 1 1 2 12 ln ln s m m m V G F V kT x I I I I II F ' § · ' ¨ ¸ © ¹ ൌ െ ଵߤ߂ ܸത ௦ 2 2 , s c M xV I U U 2 c 2 RT c M 3 A ª º « » ¬ ¼ 2 2 2 1 1 2 A c V F U § · ¨ ¸ © ¹
Polymer Shapes in Dilute Solutions >Expanded, unperturbed, and I≈R collapsed chains 42 x|2 2 2000 A2>0,x<12 1500 ++" good solvent A2=0,x=12; Coil-globule 500 0 condtion transition A2<0,X>1/2; poor solvent The coil-globule transition in a solution of polystyrene in cyclohexane. The radius of concentration gyration R and the hydrodynamic radius x-1/!! Rh of the polymer show a dramatic change as temperature passes through the e temperature(Sun, S.T., etc. J. Chem. Phys. 1980,73,5971.)
Polymer Shapes in Dilute Solutions concentration 3/R Tc A2 < 0, F > 1/2; poor solvent A2 > 0, F < 1/2; good solvent A2 = 0, F = 1/2; 4 condition Coil-globule transition ¾Expanded, unperturbed, and collapsed chains The coil-globule transition in a solution of polystyrene in cyclohexane. The radius of gyration Rg and the hydrodynamic radius Rh of the polymer show a dramatic change as temperature passes through the 4 temperature. (Sun, S.T.; etc. J. Chem. Phys. 1980, 73, 5971.) F~1/kT !!! 2 2 2 1 1 1 2 RT V x I FI ª º § · 3 « » ¨ ¸ ¬ ¼ © ¹ 22
3.4 Chain Conformations in Dilute solutions (1)Flory-Krigbaum's Theory 有N2个体积为的“刚球” 两两刚球都不发生重叠的总概率 p≈(-U/)(-U/)(-U/)- N2(N2-1)/ N,-1 org≈ △F≈-TAS=- kTInQ2 In1 iU △1_O△F =-k7|N2n-20 C NU R ~R3~T? M12M4 g
3.4 Chain Conformations in Dilute Solutions (1) Flory-Krigbaum’s Theory ᴹN2њփ〟ѪUⲴĀࡊ“⨳ єєࡊ⨳䜭нਁ⭏䟽ਐⲴᙫᾲ⦷ 01 1 2 1 1 ... 1 // / N UV UV UV :| 2 22 2 1 /2 /2 1 1 NN N V V U U §· §· | | ¨¸ ¨¸ ©¹ ©¹ U V ' | ' : F T S kT ln ln 1 iU iU V V § · ¨ ¸ | © ¹ 1 1 2 2 2 F V V c N RT U c M M P 3 ' w' w ª º « » ¬ ¼ A2 23 3 ~ ~ ?? UR T g 2 1 0 1 N i iU V § · :| ¨ ¸ © ¹ or 2 2 2 ln 2 N kT N V V ª º U « » ¬ ¼
3. 4 Chain conformations in dilute solutions (2)Fory稀溶液理论 ideal chain 3h ((2x7 exp 4Th real chain in (、、$)2()ex/-2( kT solutions 体积排除修正 能量权重修正 体积排除修正:只统计单元间不发生重叠的构象状态,因为一旦发生了重叠,此构 象就不能存在。 能量权重修正:每种构象的实现概率还与实现此构象状态的能级有关,能级越高, 则实现的概率相应降低;能级越低,则反之
3.4 Chain Conformations in Dilute Solutions (2) Flory 〰ⓦ⏢⨶䇪 3/2 2 2 0 2 2 3 3 , exp 4 2 2 h W hx h xl xl S S § · § · ¨ ¸ ¨ ¸ © ¹ © ¹ ideal chain real chain in solutions 0 , , exp E h W hx W hx h kT : § · ¨ ¸ © ¹ փ〟ᧂ䲔؞ ↓㜭䟿ᵳ䟽؞↓ 24 փ〟ᧂ䲔؞˖↓ਚ㔏䇑অݳ䰤нਁ⭏䟽ਐⲴᶴ䊑⣦ᘱˈഐѪаᰖਁ⭏Ҷ䟽ਐˈ↔ᶴ 䊑ቡн㜭ᆈ൘DŽ 㜭䟿ᵳ䟽؞⿽⇿˖↓ᶴ䊑Ⲵᇎ⧠ᾲ⦷䘈оᇎ⧠↔ᶴ䊑⣦ᘱⲴ㜭㓗ᴹޣˈ㜭㓗䎺儈ˈ ࡉᇎ⧠Ⲵᾲ⦷ᓄ䱽վ˗㜭㓗䎺վˈࡉ৽ѻDŽ