2 CUHK (Prof Wu) [Compatibility Mode]

8/3/2019 2 CUHK (Prof Wu) [Compatibility Mode]

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Introduction to MacromoleculesIntroduction to MacromoleculesCHM5080 (CUHK)CHM5080 (CUHK)CHEM588/324 (HKUST)CHEM588/324 (HKUST)CHEM6108 (HKU)CHEM6108 (HKU)

Lecturers: Chi WU (CUHK), E-mail: [email protected]

Ben Zhong TANG (HKUST), E-mail: [email protected]

Wai Kin CHAN (HKU), E-mail: [email protected]

Time/date: CUHK: L2 Science Centre Feb 18 &March 4;(10:30am-12:30pm, 2:00-4:00 pm)

HKUST: Rm 2306 (near lifts 17/18) March 18 &April 1;(10:00am-12:30pm, 2:00-5:00 pm)

HKU: Lecture Theatre P1 April 8 &April 22 ;LG1 Chemistry Building (10:30am-12:30pm, 2:00-4:00 pm)

Final Exam: CUHK/HKUST/HKU May 6(Saturday)

Textbooks:

Introduction to Polymers, 2nd edition

Introduction to Macromolecular ScienceBy Petr Munk, 1989, John Wiley & Sons, QD381.M85

y . . oung an . . ove , , apman a , .

2005/2006 Macromolecules


2/51

OutlinesCUHK

.2. Structures of macromolecules

.

HKUST4. Classification of polymerization reactions5. Step (or condensation) polymerization

. a n or a on po ymer za on7. Copolymerization

HKU

8. Ionic polymerization

9. Coordination polymerization10. Controlled radical polymerization

2005/2006 Macromolecules11. Synthesis of polymers with special properties


3/51

Detailed Outline-HKU

8. Ionic polymerizationAnionic polymerizations

Initiators, Choice of monomers, Synthesis of block

copolymers at on c o ymer zat on

Initiators, Monomers, Reaction mechanism and molecular

Ring opening polymerizations involving ionic intermediate

. oor na on po ymer za on

Ziegler-Natta Catalysts for the polymerization of olefins

properties

Other initiators for coordination ol merizations e. .


metallocene catalysts)


4/51

Detailed Outline-HKU Cont

10. Controlled radical polymerization

Overview of polymerization mechanism and kinetics

Nitroxide mediated polymerization (NMP)

Radical addition fragmentation Transfer (RAFT)

A lications of CRP in the s nthesis of functional block

copolymers

.Conjugated polymer

Ring Opening Metathesis Polymerizations

A lications of these ol mers



5/51

The Basics of Macromolecules

Natural Macromolecules Synthetic Macromolecules

Proteins, DNA, RNA

Polysaccharides cellulose: lants & animals

Polystyrene, polyethylene

Poly(vinyl chloride) Pol esters ol urethane ...

Sma mo ecu es

Macromo ecu es

The difference between small molecules and macromolecules

*Homogeneous

* No swellin in dissolution

* Inhomogeneous (size & mass)

* Swellin in dissolution* Purification methods

* Low viscosity

* Precipitation, GPC,

* High viscosity


mp e s ruc ures omp ca e s ruc ures.


6/51

Structures of macromolecules

*

Configuration:how they are connectedHomopolymer & heteropolymers:

block, seqential, graft, random, ... linear, branching, star, grafting, ladder, ...

* Secondary structures Comformation: folding, helix, sheet, ...

* Special arrangementsof larger segments(helix & sheet) to form a complicate structure

* Quaternary structures Spatial multi-chain aggregates, intra- andinter-chain interaction, e.g., triplethelix and enzyme



7/51

* Backbone contains only carbon atoms

- Polymeric hydrocarbons: PolyethylenePolypropylene isotactic, syndiotactic & atactic

Pol butadiene 1,2 addition and 1,4 addition cis & trans)

Low (H.P.) and high (L.P.) density PE

tures

Polyisoprene -(CH2C(CH3)=CHCH2)n-natural rubber

Polystyrene The most representative polymer

struc - Halogen-containing: Poly(vinyl chloride)

Polytetrafluoroethylene

-(CH2CCl)n- common polymer

Teflon, The king of plastic

Polytrifluorochloroethylene Tou h and inert

rima - With polar side groups: Poly(methyl methacrylate) Organic glass

Poly(hydroxyethyl methacrylate) Gel contains 35% water

Polyacrylamide Typical water soluble polymer

Polyacrylic acid Washing power, useful polymers

Pol vin l alcohol Pol vin l rrolidone .

- Polymers with heteroatoms in the backbone:

Polyether - PEO; Polyesters -(O-(CH ) -CO) -, PCL; Polycarbonates -(O-R-O-CO) -;


Polyamides -(NH-(CH2)a-CO)n-;Polyurethanes -(NH-R1-NH-CO-O-R2-O)n-;Polyureas; ...


8/51


*


block, seqential, graft, random, ... linear, branching, star, grafting, laddle, ...

* Secondary structures Conformation: folding, helix, sheet, ...

* Special arrangementsof larger segmentsto form a complicate structure, e.g., helix




9/51

Structure of a protein chain: Primary: Secondary and Tertiary Structures



10/51

*. Helical structure - Proteins am lose and nucleic acids

tion

Energy vs Entropy Random coil vs Ordered conformation

It re uires two h dro en bonds in the ormation o the helix not roline .

forma

It contains 3.6 amino acid residues per turn; subsequent residues are

rotated 100o

with a pitch of 5.4 A; and the translation is 1.5 A per residue.

s-Co *. Chain folding of some regulated heteropolymer chains

Stickers moverandomly like a

uctur

gas

Stickers move ina more correlatedfashion like a

liquid Stickers are

a

ryst

heat heat

res r c elike a

solid

Secon

Collapsedcore-shell


Random coil

nanoparticle


11/51

T < ~32 oCA single polymer chain

Tincreases

core-s e nanos ruc ure

dcreases

PNIPAM-g-PEO

, , ,

79, 620 (1998);Macromolecules, 30, 7921

1.8 80yrene: an imitated drug

Applications

1.4

1.6

40

60

1/I3

T

/o

ne o e env s one

applications is the smart

temperature-sensitive1.2

20

I C

. 010 20 30 40 50

t / min


Protein denaturation Heat denatured & chemical denatured


12/51


*




* Special arrangements of larger segmentsto form a complicate structure, e.g., helix




13/51

eat

Secondar structure - helix

em ca

Particular spatial arrangement

Specific & fast Energy - adenosine triphosphate (ATP)

Chymotrypsin - a hydrophobic pocket - aromatic amino acids

Tr sin - an ioni ed carbox l - interacted with the basic rou s



14/51



15/51



16/51

A zig-zag chain A thread chain A random coil

Let us start with a polymer chain in one dimensional space.

It hasN e ments and each se ment has a len th o b.o

b-b

After N steps and ifn steps are positive, R = bn + (-b)(N-n) = b(2n-N)2/Nn

NIf

The chance (probability) to findnpositive steps is a binomial

distribution because Pn is related to (p + q)Nwhen p = q = 1/2. !)(!

!

nNn

NP

N

n

=2

1

NN

nNn N! +The mean value ofncan be calculated as

22

2

1

1

1

2

1

2

1 1 NNnNn

NN

nNn

nNnPn

NN NNNNN

n =

=

=

=

= !! !)(!! !n

qp

nNn

qp

!)(!

+=0

= 0=

4

1

11

1

2

1

2

1

1 10

2

0

22 )(

!)(!)(

!

!)(!)(

!)(

!)(!

! +=

=

=

= =NN

nNn

N

nNn

Nn

nNn

NnPnn

N

n

N

n

NN

n

NN

n

n

4

2 Nn =

N

Step motion: Rn = b or -b nmmn bRR 2= 21

2

11

2NbRRRR

N

n

n

N

m

m

N

n

n = =11


( ) 20

222)]2([ NbPNnbRRR

n

n=

===22 NbR =bNRRRMS

222 =


17/51

N

!)(! nNn2

Pn = ?,

=nP



18/51



19/51

In a good solvent, a chain is in the random coil state.

Radius of gyrationHydrodynamicRadius (Rh)

End-to-End

Distant

R = rN - ro

R 121

21 N /rr 212005/2006 Macromolecules

.hR 0

NR

i

iRMS =

=

=r

6

= bRg


20/51

Radius of gyration (Rg) i i+1i+2

=

= Ni

i

N

i

ii mm11

/rrGrr

The gravity center:

1

Nri

r1rN

0

NmmRN

i

i

N

i

i

N

i

iig /)rr(/)rr( GG2

11

2

1

2 rrrr = 234

5

Thin rod: Rg2 = L2/12

S here: R 2 = 3/5 R2= ===

N

N

i

ii

N

N

i

jii

N

j

N

i

ii mmm

R 1

2

1

22

12

)rr()]rr()rr[()rr( GGGrrrrrrrr

Thin disk: Rg2 = (1/2)R2=i ii ii immm

111

22

For an idea chain ( ) jibjiij 222 rrR rrr2 NN NN

bNRRRMS21

212 /

/ =

)(

)(

16

2

22

211 112 ++==

==

==N

NNb

NNm

m

R ii j

N

i

i

i

g

4526 .RSM

R

R


=

( ) 66,2

12 bN

bRRNAs gg ===


21/51

bDimensions of chains with short-range interaction

The end-to-end distance: =

= Ni

i

1

bRrr

i-1 i

ri+1 b( ) 212 /NbRFJ =

( ) 2122111

21

1

1//

/

cos

cosbbRRR

+=

= bb

N

J

J

N

i

iFR NbR rrrrr

cos1

cos1

+

=b

b

FJ

FR

R

R

If the rotation is restricted,

2121

2

1

1

1

1//

cos

cos

+

+=

b

bRR NbR

b ~ 70 043.1

FJ

FR

R

R

In the state 7.0= FRR

R) 21276 NbR . )(6.27.6 PER

R

FJ

Statistical coil chain ( ) 212''bNRS = where b = mb, N = N/m and Nb = Nb = LSome defined parameters

M

RA =

2

2

2

2

Nb

R

R

RC

FJ

== 1

2=

b

LC

P

PP: 6 PEO: 4 PE: 7

LP: is the length

of persistence.


For linear chains:

5.053=

MNR PS: 10; PMMA: atactic: 7;

syndiotatic: ~7; isotatic: 4.


22/51

Worm-like polymer chain

cos1

cos1cos...coscos

12

=++++=

NN

bbbbbXx

dLd =rr

===

=

= cos1cos

1

11

1

bb

bL

i

i

i

iP rr ( ) ( )[ ]

===P

P

N

P

N

PL

LLLLX exp1)cos1(exp1cos1

The rigidity of a worm-like polymer chain depends on its chemical structure, the short and

long range interactions between chain segments, and ... e.g., PPTA and polyelectrolytes ...

2/1

=

=

PPLP

P

LL

Pe

L

LLLdLeLR 11212

0

2

dLXrd 22 = 2 311

2

+

+=

P

L

P

P

PG

L

Le

L

L

L

LLR P

For flexible chains 0/ >> PLL

PeLLQ LLLLLR PPP 222

22 =63

...1

3

R

L

RPPP

G=

+=

Short ran e 1) IR: vibration and rotation; 2) NMR: chemical shift;

Experimental Methods

Configuration 3) chemical analysis, GC, UV and MS; and .

1) viscometry: ~ Vhor Rh; 2) laser light scattering: Rg


Conformation

n h ; uorescence: ; x-ray an neu ron sca er ng

& diffraction; 5) relaxation: mechanical, electrial, optical, ...


23/51


*




* Special arrangementsof larger segmentsto form a complicate structure, e.g., helix

* Quaternary structures Spatial multi-chain aggregates, intra- andinter-chain interaction, e.g., triplethelix & enzyme



24/51

Small molecules Conventional colloidsassembly Physical methods

Chemical methods

Macromolecules Polymeric colloids (supramolecules)assembly

Poly(phenyl vinyl

sulfoxide)(PVSO)Polyacetylene (PA)Poly(p-methyl styrene)

n PhSOH



25/51

SelSel --assembl o rodassembl o rod--coil diblockcoil diblock

copolymers in dilute solutioncopolymers in dilute solution

Assembled

Rc

RR



26/51

Molar mass distributons Mn ,Mw ,Mz, M, ... fn(M); fw(M); fz(M)

Absolute methodsT e end-group, co igative properties

MS, light scattering, ultracentrifuge.

Relative methods viscosity, chromatography, FFF

f M Mf M w n( ) ( ) f Mf M M f M z w n=( ) ( )2 f MM

f Mwn

n ( )iii nMW =2

iiiii nMnWZ ==

The n-average molar mass M Mf M dM

f M dM n

no

no

=

( )

( )

M

M N

Nn

ii

i

ii

= =

=

1

1

The w-average molar mass M M f M dM

Mf M dM

Mf M dM

f M dM w

no

n

wo

w

= =

2 ( )

( )

( )

( )M

M W

W

M N

M Nw

ii

i

i

ii

i

i i

= =

=

1

2

1 = =The z-average molar mass M

M f M dM M f M dM

z

wo

no= =

2 3( ) ( )

M

M W M N

z

i

i

i i

i

i

= =

=

2

1

3

1

Mf M dM M f M dM wo

no( ) ( ) M W M N i ii i ii= 1 21

Schulz-Zimm Distribution+

Poisson Distribution Logarithmic normal distribution


f M

z

M ew z bM ( )

( )

=++

1f M

M

w

( ) ( ) exp[( )

]/= 22

1 2

2

f M A

z

nM

Pw

M

( ) exp[ ( ( )] 1 l


27/51

Review MacromoleculesNatural: DNA, protein,Polysaccharides...

Synthetic: i erent po ymers ...

Difference between small and macro-moleculesHigh-order structures

The statistic nature of chain conformations

R = 1/2 = N1/2b

Rg = 1/2 = (N/6)1/2b

Rh

~ Rhard

with the same D

- - -

31~Different scaling relationships between the

size and mass of linear flexible coiled chains

53g

[ ] 41 withM~



28/51

Experimental Methods

For polymer chains,molar mass distribution, conformation

chain size distribution are im ortant because M and R

are directly related to properties and performance.

Absolute methodsfor low molar mass chains :

end-group; vapor pressure osmometry; NMR;

which does not require at

least two or more narrowly

distributed standards with

co ga ve proper es; an - -

for high molar mass chains :

known molar masses

and static laser light scattering,

Relative methodsfractionation; translational diffusion;

viscocity; chromatographic methods;


which requires ca ibration dynamic laser light scattering; and


29/51

In solutionthermodynamics

hydrodynamics

In bulk (solid) amorphouscrystalline-

In solution:In solution: dissolution process G G n G mix i

N

i o

G

n i=

*The Flory-Huggins TheorySimple & Effective: ~1940s developed

G = H - TS when T = constant

G H T S mix mix mix )( pspsmix VH = solubility equationCondition : no volume change in the mixing

i iF=

= e1/2and e is the cohesive energy density,i.e., the vaporization energy of unit volume

F is the attraction

force per molar


m liquid under zero pressure.chemical groups.


30/51

The end-group analysis Mn < 10,000 g/mol

e.g., Nylon-6 H2N(CH2)5CO-(-NH(CH2)5CO-)n-NH(CH2)5COOH

We can titrate the number of ends H2N- and -COOH

For a monodisperse sample : M = W/n ;

For a polydispersed sample, W = niMi; n = ni, andMn = W/n

Colligative properties

The boiling or freezing point change

limC

b or f

v or f n

T

C

RT

H M=

0

2 1

why Mn ?

Membrane osmometry popo+

/C = RTMfor small molecules

solution solvent

/C = RT/Mfor macromolecules

CRT

MA C A C + + +( )1 2 3 2 L


MALDI-TOF-MS and NMR

Here we only ontline their basic principles.


31/51



32/51

Laser light scattering (LLS)

E = Eosin(2 vt - )Es = k (d

2P/dt2) = E = 4 P = p + H = ocE i = = oc

i

r

c E

r

Io

o o

o

o< > =16 164 2

4 2

2

4 2

4 2

' '

( )i ~ -4 i ~ r --2

i ~ 2 ~ V2For N particles

I = Ni

Rayleigh ratio : Rvv(q) =Ir2/Io = KCM K

ndn

dC

N

o

AV o

= 42 2 2

4

( )Rvv(q) =KCMw

For a large particle : Rqr

r

i jNN= 16 44 2

sin( ), KCA C+1 2 2

j

o vv w

qn

o

= 42

sin p q

R q q

R q

q Rvv

vv

g( )( )

( )

= == < > +0

11

3

2 2L

i KCR M

q R A C g Z( )+ < > +1 1 13 22 2 2

2005/2006 Macromoleculeswhy Z ? The z-average ?

400 pin holeCuvette


33/51

Focus Lens400 pin-hole

Position-sensitive

Spectra-Physics Helium Neon Laser632.8 nm WavelengthLaser

Monitor diode

o e aser umpe : aser532nm Wavelength

Cell housing and

Laser

Encoder Stepping motor

index matching vat

Photon

Static, Classic LLS(time average intensity)Rotating Arm

CounterDynamic, Modern LLS(digital time correlator)

Polymer : 5x103 - 107 g/mol

Particles : 2 - 2000 nm

Photomultiplier tube

Preamplifier/DiscriminatorDilute solution / suspension

C = 10-3 - 10-6 g/ml

2005/2006 MacromoleculesLaser Light Scattering Spectrometer incorporated with differential refractometer


34/51



35/51

Static LLS Angular and Concentration dependence of

CAqRKC g

22

211 + SII

MqR WVV 3)(+

222

)/(4 dCdnn= 4n=

)()()(

oo

rro

VVVV

n

n

I

IIqRqR =

4oAN o r

A plot ofR q

vs C AVV

q"[

( )] "

0 2

A plot ofKC

R qvs q R

VV

C g"[( )

] "

02 2

2

TheextroplationofKC

R qM

VV

C q W[( )

] ., 0 0

z1/21/Mw



36/51

Dynamic laser light scattering

* Intensity fluctuation :

I

slow fastDynamic LLS

I

t

The ast the movements,

the fast the fluctuation

* Doppler frequency shift :

+

0 0+0 ~ 1015Hz ; 10 510 7HzIt is rather difficult to detect . 202 )(

)( =

S

- 0 0+0

* Time correlation function: deSEE i )()()0( * deEES i= )()0(1)( * deGg )()(0)E(E)( *)1( 1=

),q()0,q(),q(

|)2( IIG =The Siegert relation


)0(0)E(E 0

c]|),q(|1[)0,q( gI


37/51

A typical time correlation function of the chains in solution

0.8012.00

0.604.00

8.00

G

(

)

0.40A]/A 0.00

-2

10-1

10 -1

2)

(t,q)

)1)(1( 222 qRfCkDq gd +0.20

[g Dq

Cq

=

00

2

0.0 20.0 40.0 60.0 80.0 100.00.00

2005/2006 Macromoleculest / ms


38/51

Size exclusion chromatorgraphy

V = V0 + Vifor small M : Ve = V0 + Vifor large M : Ve = V0

In general : Ve = V0 + ViV = A + B lo M V = A + B lo M standards e

In practice , one can obtain Veand calculate []M . If knowing [], one can findM.Detectors

* differential refractometer ; * viscometer ;

* UV ; and * small angle light scattering from Veto M

Field flow fractionation (FFF)wflow Tk

D

fuF

B

=

=

x = 0 exp -x w ere = u =

If d > l > 2 m, it will be a steric FFF - Larger ones come out first.


39/51

Viscoelastic Properties of Bulk Polymers Temperature

Small molecules (liquid) Crystals and glass

viscoelastic

Macromolecules (melts) Crystalline and amorphous

Stress : F/A = Shear stress

F

Strain : L/L = = L

L = = E E : the Youngs modulus Elasticity

The tensile strength : The elongation at break F

= omp ance

E = 2G (1 + )

Viscosity () LL

d =


= -( / ) / ( L/ )


40/51

The Maxwell Model The stress relaxation T = constantElastic

viselT + el = G vis = (d/dt)sinceViscous0

11=+=+=

dt

d

Gdtdtdt

dviselT

)exp(0

t=

where

=

CBBC +For a dynamic experiment

CBBC)sin()cos(assuming&)sin(If 0 tCtBtT +==

coss ncos0GG

22 G ("

0= GanG

++ )sin()1()cos()1()( 22220 ttt

G G

=m00 1)("G


Storage modulus Loss modulus )(' =G


41/51

The Voigt Model The creep experiment T = constant

viselT + el = G vis = (d/dt)since

dt

dGT

+

)exp(1)(

tG

t Twhere

=

astic

co

us

E Vi

+ CGB +0For a dynamic experiment )sin()cos(assuming&)cos(If

0tCtBt

T +==

0 BGC 0

=G )(" ++ )sin()1()cos()1()( 22220 ttt

G G

=00

=)("G2005/2006 Macromolecules

Storage modulus Loss modulus

=)('G

E l Polycarbonate with


42/51

Example Polycarbonate with

two molar masses.

The time domain can be divided intofour regions, I, II, III and IV.

I: t


43/51

logGThe Time-Temperature Equivalency

log a1

G(t, T) = G(t, T) G(t2, T1) = G(t1, T2)

G(t3, T1) = G(t2, T2)The Williams-Landel-

log a2

4, 1 = 2, 3

log t1 + log a = log t2

Ferry (WLF) equation

)(1 oTTC

aog

l log t1 log t3log t2 log t4

2 o t1 = t2 a

logGIf Tg is taken as T0 , VSP

The glass transition temperature (Tg)

log t2 - log a1log t3 - log a1

11

2

C

TT

C

C

aog

TT gg l

T

a

log t3 - log a2

The universal

values of C1and C2

C1 = 17.4

Tg,2

,

ec


log t1 log t2

4 - 2C2 = 51.6 T

g, true

T > T Plastic materials


44/51

The Glass Trenasition Temperature (Tg)Tg > Troom Plastic materials

or < T nd T , , , ,

3. The chain length Tg


4. The cross in ing o the chains. . e m x ng o erent po ymers.

m


45/51

The Avrami equation )exp(1m

Kt

Crystallization is the crystallized fraction and can be determined by any property,such as volume, diffraction intensity, . M depends on geometry,crystallization rate, & nucleation mode so that m is in the range 0.5-4.

P

PcP = Pa + (Pc - Pa) 0VVt =e.g.,

0 1Pa

0

In practice, plot ln [ ln [1/(1- )] ] versus ln t The glassy polymers

Non-equilibrium

The specific volume depends on how fast a sample was cooled

down and how long it remains at a particular temperature.

= 0 + free 0 : t e core an v rat on free : t e trans at onVfree ~ 2.5%V

S 22 vkB 1Tvke e as c ne wor sPTL ,

2 + 20 L1

TvkF

B dLTvk 2 2RT RT3 RT


2

VA LV

+2 2

+CM C

M

CM

H


46/51

The Crystalline Polymers fm

HT

=STHG f

Folding chains and Spherulites G is continuous at Tm, but not S or V.

G = H - ST; H = U + PV; U = Q - PdV;

Q = TdS dG = VdP - SdTS

T

G

P

V

P

G

T

=

dTT

dPP

dGPT

+

=

T

eT?

T

eT

,

T < Tg; Tg < T < Tm ; andT > Tm

Tg is related to the cooling rate, but not Tm.

In reality, the process of Crystal < > Melts is a kinetic process. For example,

Tmdecreases with Tcr; Tm is higher than Tcr, the crytal size decreases as thecooling rate increases; and Tm < Te (infinite size), .

Amorphous - it can be viewed as a supercooled liquid


assy s a eCrystalline (0-100%) - it can be viewed as crosslinking points

M h l f lli l


47/51

Morphology of crystalline polymers

The chain folding: 10-20 nm thicknessSpherulites in a concentrated solution.

Mechanical properties ofcrystalline polymers Drawn in fibers

0.5 < Tg/Tm < 0.8 Below Tg => Glassy and above Tm => Melts

If Tg < T < Tm,the crystalline regions act as crosslinking points, so that the


mater a s w e ar an toug . uc a structure can a so e ac eve y

copolymering some hard segments into flexible chain backbone.


48/51

Multicomponent and multiphase materials

Plasticization of polymers

nt sma mo ecu es to ecrease g.

Heterophase polymers

Blending of different polymers

Block and other structure copolymers

To obtain different Tg

and toughness.

2221 VnVnV

G mixmixV

mix +==

222,12

2

21

1

1 lnln BVV

RTGVmix + +


1

2,1

2,1V

B=where

MD2 MD3 MD4


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MD2 MD3 MD4

A ol mer el is a three-

dimensional networkswollen by a large amount

MD5 MD6 MD7p = . of solvent. It has some

properties betweensolutions and solids.

SEM micro ra h of H-

MD2 MD3 MD4

sensitive copolymer

P(DEAM-co-MAA)MD5 MD6 MD7

pH = 9.5

hydrogels obtained at

different pH values.



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25 oC 37 oC

mixingswelling state shrinking state



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2 CUHK (Prof Wu) [Compatibility Mode]

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