Polymer Solutions

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Polymer Solutions ?????
2
??????????????????????? ???????
?????? Clt1-----???? 1ltClt5----??? Cgt5----???
??,????
??,????
5?????/????????????
3
9.1 ??????( Dissolution of polymers)
??????
1.???????????????????????
2.?????
(i)???????????????????,???????????,????????????
,???????????????????,?????,????,???????????????
(ii)?????????????,????????????,????????????????
???,???????????????,???????,???????????,??????????
????????,?????????
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3.????????
??????????????????,???????????? ??????????????
?????????? ??????PP????,????????gt140????
4?????????
5
???????
1.?????????????(Dissolution process is much
slower than low molecules),???????????
2?Crosslinkedpolymers can only swell (??),not
dissolve (??)
3.????????????????????
4.?????????????????????,??? ????,??????
The higher the molecular weight of the polymer,
the more difficult it is to select a good solvent
5.??????????????????
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???????
1.???????????
2.????????????????????????????????,?????
??????????????,???????(???),????????(???),????????
????
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???????? -SO3H, -COOH, -C6H4OH, CHCN, CHNO2,
-CHCl2, CHCl ???????? -CH2NH2, -C6H4NH2,
-CON(CH3)2, -CONH-, -CH2COCH2-,
-CH2OCOCH2-, -CH2-O-CH2-
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3. ??????????????
?(CED)1/2 Solubility rameter
CED??????????????
??????????????????????????????????????????????????
????????
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2)??????????? ????????,?????????????
???????????????GMlt0,?????????,?SMgt0,
?GM???????HM-??????????
???????????????????????? ??,?????? ?HMlt0,???????
?????????????????, ?HMgt0?T?SMgt
?HM,?GMlt0,??????,????????????????????HM,??????????
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????????????,??????????????????????,Hilde-brand???
?(non-polar system) 0lt?HMV?1?2(?1-?2)2-???
???
(??,????????????,???????????????)
??,????polymer, ?1-?2 ? 1.5,??????
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????????????,??????????????????????Solubility
parameterof mixed solvent
(f?????)
d2 - dm ? 2(1.72)??
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Solubility parameter of polymers
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Conclution?????????????????
????????polymer,??????? ???????polymer,?1?2???????
???
??????d119.8 ???d120.8 PVC
d219.2 ????????PVC??????????
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9.2 ?????????Thermodynamics of polymer solutions
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7.2.1 Types of Solution ????
Dilute solution Theoretical study Chain
conformation Molecular weight Radius of gyration
Semi-dilute solution2
Concentrated solution Application
Adhesives Coating
Plasticized plastics
Dilute Solution and Concentrated Solution
???????
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The Ideal Solution ????
In an ideal solution, the interaction between
solute and solvent are equivalent(??????????????)
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Free energy of mixing
Mole fraction
Entropy of mixing
Enthalpy of mixing
?????????
?????????
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7.2.2Thermodynamics of polymer solutions
?????????
??????????????? ????????????????
??????0?? ?????????
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Flory-Huggins??????? Quasilattice model
???????????????????,?????????????????????????????
???
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???? ??????????????????????,??
?????????,?????x???, x????
???????????????,????????? ????

?????????,????????????? ??
????????????
???????????
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Entropy ???
?????N1?????,?N2???x????????
Solvent
Polymer
Volume fraction
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Flory-Huggins values
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Free energy of mixing
Chemical potential
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??????????,?21? ln?1ln(1-?2)-?2-0.5?2..
?????????????????????, ???????????,????????
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????????????????????????????????,????10.5????
0,?????????????????,??1lt0.5?,
lt0,?????????????????????????????
gt0,??????????,????????????
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Undisturbed state ????
??????
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? ?????

• 1.?????????
• 2.?????????
• 3.????????

?????? ??A2? ?1?????
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• ???????
• (1)?H1,?S1???????????
• (2)?1????? ?1????????????????
  (?T????????)
• (3)Kuwahara????Mn1.33105?Tol ?
• ?????? ? ??,F-H??????
• ?2gt0.08 ???
• (REF J.Chem.Phys.
  1976,47,3357)
• ??
• F-H??????????????,?,???
  ??????????????????????,???,???????????????

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Flory-Krigbaum?????
???? (1)?????????????????????????????????,?????
????????????????,??????????,??????????????????????
???????,?????????,???????,???????????????????????

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(2)?????,????????????????????,????,??????????????
? ????????????????????????????????????????????????
???????????,???????????,??????????,
???????????????????????????????????????????,?????
???????????????,????,????????,??????????????
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????????,????????????????????????????,????????????
,?????????????,?????????????????????????(?H1),????
??????????????????(?S1)? ????????????,?????????
??K1??1?
???1???????????,?
?
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• ??????????????U
• ?? ??????????????????????????????,?????????
  ? ????

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??????????

• ????????????
• ?F-K??????,???????????G1E ???
• ?????? B ???????????????
• U (?????)
• M

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• ??????????????????(??)

?? ?? U B ?G1E ? X1 T Conformation
Good gt 0 gt 0 lt 0 gt1 lt0.5 gt? Expanding coil
Theta 0 0 0 1 0.5 ? Unperturbed coil
Poor lt 0 lt 0 gt 0 lt1 gt0.5 lt? Shrinkage coil
Non ltlt0 lt 0 gtgt0   gtgt0.5   Precipitation
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1. ?????(Ugt0)
(????? M ?????)

• ?F-K??

Uf (M, RG,T, ?, ?coil ) Excluded volume is
much important in polymer science ! For
instance DR, PPPD, Compatibility
??? U dependence of function of polymer or
system
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• ?????
• (1)

? ???????, ?5gtgt ?3, ?5-?3 ?5 ?5?M0.5
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• (2)

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• (3)

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• (4)

?KMa
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Summary 1 F-K??????????/????
2 A table of solvent effect on thermodynamic
parameters 3 Four exponential correlation in
good solvent systems
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2.Theta ????

• ????(Unperturbed dimension)??
  ?,(h?,R?,??
• ??? ??
• ?????????,??????????????????? or
  ??(Isolated chain)??? or ????????????
• ?G1E 0 (?,?????), T? Tb ( ?H1E? ?S1E
  ?0)
• ???????????????????? ?h/h? ,
  ?????????????????????,? A, ?, C8,

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A??M??,??????, ???A?

• ????(Flexibility parameter)
• 
  
• ??????(Steric factor)
• Flory ???(Florys characteristic ratio)

??????????????????
????????????????????,???????????
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???? (????) ?????? ???
Polymer ??? T/? A104n m ? C? K??? A3
PDMS ? 2-90 612 1.37 5.2 -
PMMA ? 25 640 2.08 - 0.059
PS CYH 34.5 655 2.17 10.3 0.0789
PAM H2O 30 1000 2.72 14.8 0.081
?????? AC 25 2410 4.7 - -
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???-?? () (Unperturbed dimension)

• ????(? LS ?? h? )
• ????(??????????,??????,????)
• ?gtgt?? (PVC/????155.4?, Syndo-PS???????????????)
• ???? ? ?? (????????)

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• (2) ????K? ???
• ??? ??
• (? ?2.84 1023/mol)
• K? ??????????,???????????
• K????????

P PMMA PS PB PVC PBD PET PVAl PC PA6 PAN
K? 0.059 0.079 0.125 0.149 0.166 0.178 0.205 0.215 0.226 0.258
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• ?K? ???
• ??????????? Mc
• (????????,? ????????,K? Mc1/213)
• ???? h? ,?? (Commonly)
• ????????,?????
• PS/CYH/61000
• ? K?
• 40 T/? 40
  T/?
• (REFA.Dondos, Makromol. Chem.Rapid
  Commun.1984,5,625)

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• ? K? ???
• ????? ()
• ??????,??????
• ????? (v)
• ??Theta??(?????)?K?
• A Viscosity
• B SEC(GPC)
• C Calculation

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??
???? ?10.5 0 ?? ??i
??????? (Gauss?,????-????????,?????? ??????????,??
??),??????????
????1lt0.5 lt 0 ?? lt0
???(????-???????????????????)
?????
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?-temperature
When the quantity u is zero, A2 is zero, and the
chains mix without recognizing each other's
presence. Also, since the forces are balanced
out, the chains cannot distinguish between
solvent molecules and segments of the other
polymer chains. Thus the simplified conditions of
mixing existing at the Flory ?-temperature become
apparent.
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7.3 ?????????
Phase separation in polymer solutions
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9.3.1Osmotic pressure ???
????
??????????????????????????,?????????????,?????,???
??????,???????,????
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????????????????????????,????????????????????????
?????
???????
Vant-Hoff ??
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????
g/ml
??????
molecular weight
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2)T???????????????????????????,??A2,?A2T??,????
,????????????????
3)?1?A2?????
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? ???????
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?????????????,????????????(?????), ???????,????,?
???,??????
??? ?????????? ???,??? ????????,???????????? ????
??????????????
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???????????????????????????-??????????????????
??????????,??????????,???????,????????,???????????
?????????????,????????
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9.3.2Phase separation in polymer
solutions ?????????
????????????????,????polymer?????,?????polymer??
????????????
??polymer and solution ?????,????????????
??????????????????????
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Phase diagram of polymer-solvent systems
UCST Upper Critical Soluble Temp.???????v LCST
Low Critical Soluble Temp.???????
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Critical point of phase separation ??????
?????????????????
???????
???????
??
????
????????????????
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?????????????,?
?????????
?temp. Critical soluble temperature when
molecular weight tends to infinite
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Precipitation fractionation????
?????????polymer solution????????????(???)??
???
??????????,???????????????polymer
solution?????????????????????,????????????????
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??????????????????????????,????????????polymer??
?? ?polymer ??????????????????????????
?,????????????,????,???????
?????.,????,,??????,????????????????
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????,???????,???????,??????,??????,????? ?????????
????,???????,????????,???????
??????????????????????
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9.5 Molecular weights and weight distribution
??????????
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Characteristics of polymer molecular weights
??????????
The molecular weights are very high, ranging from
about 25,000 to 1,000,000 g/mol or higher.?? The
molecular weight of ordinary size molecules is
fixed (e.g., benzene has a molecular weight of 78
g/mol regardless of its source). Most polymer
molecular weights, on the other hand, vary
greatly depending on the method of preparation.
In addition, most polymers are polydisperse that
is, the sample contains more than one species.
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Molecular weight averages?????
Number-average molecular weight
Weight-average molecular weight
Z-average molecular weight
Viscosity-average molecular weight
Schematic of a simple molecular weight
distribution, showing the various averages
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?????????
????????(polydispersity)????????
(1)?????(Heterodisperse Index,??HI)
(2)??????
???????,dgt1?sn gt0(swgt0)
???????,d1?snsw0
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???????????????
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1.???Viscosity-?????
??????? ?????(relative viscosity)?r?/?0,???????
???????? ?????(specific viscosity) ?sp?-?0/?0
?r-1, ?????(reduced viscosity)
?sp/c ?????(inherent viscosity)ln?r/c
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??????????????????????,??????????,????????????????
????????????????
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Intrinsic Viscosity Experiments
???????????? ???????????
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??????????(Ubbelohde)??????????,????????????t?t0,?
???(Poiseuille)????,????????
??????,?????????100s,??????B/t????,?????????C10-2
mol/l,??????
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???????????????????
Huggins???
??
Kraemer???
????
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??????????? ,?????????
(?????)
?? ????????????????????
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Mark-Houwink equation
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2.?????End-group analyses-?????
??????????????,???????????????????????????????-66?
????????????20
???????????,?????????
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?????????????,??????????????,??????????????????
??????
???????????????????,????,?????????
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Colligative methods?????
The colligative properties include boiling point
elevation, melting point depression, vapor
pressure lowering, and osmotic pressure.
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3.?????Ebulliometry --?????
4.?????Cryoscopicmethod --????? ?????????????
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5????? Film osmometry -?????
Schematic illustration of an osmometer
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6.??????Vapor-phase osmometry ( VPO )-?????
?????????????,??????????????,?????????????????,??
??????????????????????????????????????????????????
???????????????????????,?????????????????,???????,
???????????????????????????????
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7?????(Light Scattering)??????
Light scattering of polymer solution?????????
????????????????????????????????????
?????????????
??????? ???????(gt?/20)??????
?(lt?/20)????
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????(????)
RgS ?????? h???
?????????
Illustration of a light-scattering calculation
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??????
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Other methods to measure Mw????????????
????????????,????????,???????,????????????,???????
????,?????????????????Rayleigh??,????Mw?A2???,????
?????????,????????????????????(?????)?? ?????? ???
???
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???????????
?????????????????????????????
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1?????????????????
(1)??polymer??????????,?????????????,????????????
???????????????
(2)??????????????????????, eg?????????? (3)??????
?????????????, eg TEM, GPC
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??? ????????????????????????????????????????????
?????????,??????????????????????????,?????????????
??,??????????????? ???????,?????????,???????
,??????????????????????,????????????,?????????????
??
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Principle??
Gel permeation chromatography (GPC) makes use of
the size exclusion principle. The size of the
molecule, defined by its hydrodynamic radius, can
or cannot enter small pores in a bed of
cross-linked polymer. The smaller molecules can
diffuse into the pores and are delayed. The
larger molecules pass by and continue in the
solvent phase.
The size exclusion effect. The short chain can
enter the pore, whereas the long chain passes by.
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??,?????????????,?????????????????
????????
?????????,?????????????,????????,????,???????????
?????
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?????????????? ????????????,??????? ???,???????
????????,???? ??????,?????
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(3)GPC???????
GPC???(??a?????????b?????)
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Calibration??
Ve????????????????????????????????
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Calculation of molecular weight average ????????
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1???????????,??????????????????? 2?????????????
??????????????????,???????????.
3????????????????66???????????????
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4???????????????
?????????????????????????????????????????????,???
???
(1)????????????????MC?104???????,????????????
(2)?????????????MC,???????MC,????
(3)????,??????,???????
Mlt Mc?
M gt Mc?
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(4) ???????
(5)????????????? ??? ????????
(6) ???????
(7)  Tg?Tf???,Tg?MC(?????????????)?Tf??MC???????Tg
?Tf?Tb???(??)?
??????Tg?Tf?Tb???