Physics of Solid Polymers
Seoul National University 1
¾Up to C390H782
¾Strictly uniform in length
¾Models for understanding crystalline polymers, e.g. polyethylene
Physics of Solid Polymers
Part 4
Ultralong Monodisperse n-Alkanes
- First synthesised by Marc Whiting, Bristol, 1985.
- Most samples in this work by Gerald Brooke, Durham
- See reviews:
- G. Ungar et al., Adv. Polym. Sci., 2005 180 45-87.
- G. Ungar, X.B. Zeng, Chem. Rev., 2001 101 4157-4188
Paths to Integer Folding from Solution Solution
High Tg cc Low Tc
Extended (E)
Once-Folded (F2)
“Integer” folding
chain conform.
paraffin C H
E F2 F3 F4 F5
+ C102H206 C150H302 C198H398 C246H494 C294H590 C390H782
+ + + + +
+ + + + +
+ + +
+ +
+ +
+ +
Pathways of melt crystallization of pure linear alkanes
NIF E td F ld d
Melt
T <<TmNIF NIF = “Non-Integer Folding”
Transient, semicrystalline
crystalline amorphous
Extended Extd-Folded (Double Layer)
Extd-Folded (Triple Layer)
T T > mNIF T T=mNIF T T <mNIF time
Folded (Single layer)
microfibril
Initial form NIF
Final form Triple-layer folded + extd
Neutron
X-ray
Binary mixtures of long alkanes
¾Model polymer systems with controlled polydispersity.
C162H326+C246H4941:1 w:w C162H326(208Å):
C246H494(315Å):
Short alkanes (<50 C-atoms) do not co-crystallize.
Physics of Solid Polymers
Seoul National University 2
Stable mixed Semicrystalline Form in binary alkanes
300
lc
lc la
(a)
lc la lc
(b)
121 123 125 127 129
L Ext.+ L
Ext. + SF
0 50 100 150 200 250 300
La Lc
C246 90:10 75:25 60:40 50:50 35:65 25:75 12:88 C162
L/Å
Long/short weight ratio
115 117 119 121
0 0.1 0.20.3 0.4 0.5 0.6 0.70.8 0.91 SF
C246H494 C162H326
Overcrowding limit if Folding not allowed
Pathways of melt crystallization of pure linear alkanes
NIF E td F ld d
Melt
T <<TmNIF NIF = “Non-Integer Folding”
Transient, semicrystalline
crystalline amorphous
Extended Extd-Folded (Double Layer)
Extd-Folded (Triple Layer)
T T > mNIF T T=mNIF T T <mNIF time
Folded (Single layer)
microfibril
(ms)Gμ-1 0.6 0.8 1
4.75% in octacosane
Crystal growth rate of n-C246H494from solution – Growth rate minimum
(similar minimum in melt-crystallization)
Temperature ( C)o Growth rate,
G 110
G100
0 0.2 0.4
105 110 115 120
Macromolecules, 2003 36 5214
Dramatic changes in crystal habit
Also:
Minimum in concentration dependence of growth rate
G110
(ms-)Gμ1
C246 in octacosane 106.3oC
G100
Growth rate, G
Concentration (wt %)
Binary phase diagram C246 + octacosane
115 125
C)
G
slow ure fast
95 105 115
0 1 2 3 4 5 6
Concentration (wt%)
Temperature (Co G
extended
folded
concentration
temperatu
Physics of Solid Polymers
Seoul National University 3
Binary phase diagram C246 + octacosane
115 125
C)
G
slow ure fast
95 105 115
0 1 2 3 4 5 6
Concentration (wt%)
Temperature (Co G
extended
folded
concentration
temperatu
2-stage crystallization Æ“dilution wave”
Dilution wave - Folded
Dilution wave – Folded + Extended Dilution wave - Extended
Differential imaging: Plane wave Differential imaging: Circular wave
Physics of Solid Polymers
Seoul National University 4
Solutions of Fisher’s reaction-diffusion equation
(c-cE)/(cF-cE)
ÆCan find diffusion rate through solution
Higgs PG, Ungar G J Chem Phys 2001, 114, 6958
“Coarse-grain” model of competing processes
A B A B
E F
• competing processes added
• “Coarse-grain” with “pinning”
step up forbidden A
BF
GE= (1 - A/BF)(A - BE) , if BE< A < BF, GF= A - BF, if BF< A.
Theoretical Growth Rates for C198 at Two Different Concentrations
0.6 0.8
90 100
0.0 0.2 0.4
J. Chem. Phys.,1994 100 640
Measured rate vs. concentration for C246 in octacosane, 106.3oC
G110
(ms-)Gμ1
0.4 0.6 0.8
Rate vs. concentration for C198 (theoretical)
G100
Growth rate, G
Concentration (wt %)
0 1 2 3 4 5
0.0 0.2
C (Wt%)
Phys. Rev. Lett. 2000, 85, 4397
Monte Carlo simulation of Self- Poisoning Crystallization
C cycle)
Front thickness >=4 bonds
16-segment chains
Wenbing Hu, Nanjing
Y Ma, B Qi, W Hu, G Ungar, J Hobbs J.
Phys. Chem. B, in press 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0
1E-4 1E-3
Linear growth rate (units of sites/MC
Temperature (units of Ec/k) Front thickness >=10 bonds
higher barrier for sliding diffusion lower barrier for sliding diffusion
Monte Carlo simulation of Self- Poisoning Crystallization Average growth tip profile
8 10 12 14 16
em length
8 10 12 14 16
em length
8 10 12 14 16
em length
Folded chain has extended lifetime - “resting stage” in chain extension
Y Ma, B Qi, W Hu, G Ungar, J Hobbs submitted
0 2 4 6 8 101214161820
0 2 4 6
Mean ste
Distance from the growth front
0 2 4 6 8101214161820
0 2 4 6
Mean ste
Distance from the growth front
0 2 4 6 8 10 121416 1820
0 2 4 6
Mean ste
Distance to the growth front
Temperature
below TmF just above TmF well above TmF
