Acknowledgments
3.2 Mechanism of the Preparation Method
X-ray Spectrometry (SEM-EDX) observation, and by nuclear magnetic resonance (NMR), or Gel Permeated Chromatography (GPC) measurement. Furthermore, several types of functional properties are discussed especially for smart performance, which were caused by the graded structure. Finally, the prospects of functionally graded polymer blends and their applications are discussed.
3.2 Mechanism of the Preparation Method
3.2.1 Diffusion–Dissolution Method
Th e mechanism of formation of a graded structure by the diff u- sion–dissolution method is considered to be the following [27].
Aft er a polymer B solution is poured onto a polymer A fi lm in a glass petri dish, polymer A begins to dissolve and diff use in the solution on the air side (Figure 3.2), but the diff usion is inter- rupted when all the solvent evaporates. Th us, a blend fi lm is pro- duced, which consists of a concentration of gradient of polymer A/polymer B in the thickness direction.
100
Position of measuring point Polymer A Polymer B
Content of polymer A (%)
Laminate Functionally graded blend
Homogeneous blend 0
100
0 100
0
FIGURE 3.1 Schematic model of functionally graded blend.
TABLE 3.1 Various Types of Functionally Graded Polymeric Materials
Types of Used Materials Structure Preparation Method Size of Dispersion Phase
Metal (or ceramic)/polymer Composites • Laminate method Big
• Electric fi eld method
• Centrifugation method
• Flame spraying method Polymer–polymer Immiscible polymer blend • Surface inclination in melt state
method
• Surface inclination in solution method
• Dissolution–diff usion method
Miscible polymer blend • Diff usion in melt method Molecular order
• Dissolution–diff usion method Atom–atom (intramolecules) Copolymer (random) • Diff usion method of monomer
in polymer gel
Atom order Copolymer (tapered) • Living anion or radical
polymerization method Density of cross-linking • Changing method of
cross-linking concentration High-order structure (same
polymer)
• Changing method of cross-linking temperature
Same atoms and molecules Crystal structure • Injection mold method
Following the steps of dissolution and diff usion of polymer A, the graded structures should be classifi ed into three types (Figure 3.3).
First type: Polymer A begins to dissolve and then diff uses, but does not yet reach the air side surface of polymer B solution. Th e blend has three phases (polymer A, poly- mer B, and a thin graded structure).
Second type: Just when all of polymer A has dissolved, the diff usion frontier reaches up to the air side surface of polymer B solution. Th e blend has one graded phase from the surface to the other one, while the surfaces are composed of polymer A only or polymer B only.
Th ird type: Aft er the dissolution and diff usion of polymer A reached up to the air side surface of polymer B solu- tion, polymer A and polymer B molecules began to mix with each other and became miscibilized. Th e concen- tration gradient then began to disappear.
Th e formation of a concentration gradient should depend on (a) dissolution rate of polymer A in polymer B solution, (b) diff usion
rate of polymer A in polymer B solution, and (c) interruption time for the diff usion due to the completion of solvent evapora- tion. Factors for controlling the above phenomena are (1) the type of solvent, (2) the casting temperature, (3) the molecular weight of polymer A, and (4) the amount of polymer B solution.
Until polymer A completely dissolves or reaches the surface of polymer B solution, i.e., in the formation of the fi rst and second types of structure, the diff usion of polymer A in the polymer B solution is considered to obey Fick’s second law (Equation 3.1) by the assumption of neglecting the evaporation of the solvent in polymer B solution during the diff usion:
⎛ ⎞
∂∂ = ⎜⎝∂∂ ⎟⎠
2
A A
AB 2
C D C
t x (3.1)
where
CA is the concentration of polymer A t is the passed time
x is the distance from the surface of polymer A sheet DAB is an apparent diff usion coeffi cient
Th e point where CA approaches 1 and shift s to the petri glass side, thus carrying forward the dissolution of polymer A. Th us, by considering this eff ect and rearranging mathematically Equation 3.2 is obtained from Equation 3.1:
∞
( )
⎛ − ⎞
= ⎜⎝ ⎟⎠
⎛ ⎞
=⎜⎝ ⎟⎠
∫
−A
AB
2
( )
erfc 2
erfc( ) 2 exp d
x
C x b
D t
x x x
p
(3.2)
where b is the distance between the petri glass side surface and the other side of remainder of polymer A, which has not dis- solved yet. Th erefore, the gradient profi le in the blend at t can be estimated by Equation 3.2.
Adaptability of Equation 3.2 to the experimental data was examined in the PVC/PMMA graded blend, which is given a detailed explanation in Section 3.3.1. Th e experimental data agreed approximately with the ones predicted by Equation 3.2, as shown in Figure 3.7. DAB and b were obtained as 6.38 mm2/s and 57 mm, respectively. Th e DAB value was much larger than the value obtained by diff usion in melt state method, which implies that the dissolution–diff usion method is very useful.
Further, a thicker and a more excellent graded blend fi lm was pre- pared by the multiple-step method, as illustrated in Figure 3.4. In this case, the graded blend was obtained by repeatedly preparing and changing the composition of the blend in the pouring solution.
3.2.2 Polymerization–Diffusion Method The mechanism of formation of a graded structure by polym- erization during the diff usion method is as follows [30]. Aft er the polymer A fi lm containing a macroazoinitiator, i.e., a radical type ini- tiator, with oligomeric polymer A segment is cast on a fi lter, the FIGURE 3.2 Schematic model of dissolution–diff usion method.
Polymer A film Polymer B solution
Dissolution and diffusion Evaporation
FIGURE 3.3 Schematic models of various types of graded structures.
Polymer B
Polymer A
Wide graded blend
Gentle graded blend Graded structure 1
Graded structure2
Graded structure3
Narrow graded phase
resulting laminate is put on a monomer B solution in a aluminum petri dish kept at a constant temperature (Figure 3.5). Th e monomer B begins to diff use into polymer A fi lm to the air side with polymer- ization. When the process is interrupted on the way by enough diff u- sion of the monomer B, a blend fi lm is produced, which consists of a concentration gradient of polymer A/polymer B in the thickness direction.
Th e graded structures could be determined by the balance of polymerization and diff usion of monomer B. Th e temperature content of a macroazoinitiator, time, i.e., largely eff ected the balance. Th e temperature and the time enhanced both the poly- merization and the diff usion, and the content of the macroazoini- tiator enhanced only the polymerization. Ease of evaporation of monomer B enhanced only the diff usion.
Dissolution–diffusion Polymer B solution
Polymer B solution
One-step method Two-step method Four-step method
Polymer A film
Polymer A/Polymer B (5/5) solution
Polymer A/Polymer B (5/5) solution Polymer A/Polymer B
(7/3) solution Evaporation of solvent
Dissolution–diffusion Evaporation of solvent
Dissolution–diffusion Evaporation of solvent
Dissolution–diffusion Evaporation of solvent
Dissolution–diffusion Evaporation of solvent
Evaporation of solvent
Dissolution–diffusion
Dissolution–diffusion Evaporation of solvent First
step
Second step
Third step
Fourth step
Polymer A film
Film formed in the first step Film formed in the first step
Film formed in the second step
Film formed in the third step Polymer A film
Polymer A/Polymer B (3/7) solution
Polymer B solution
FIGURE 3.4 Schematic models of multiple steps method.
Monomer B Polymer A film Diffusion of Monomer B
Filter Polymerization
Heating
Evaporation of Monomer B
FIGURE 3.5 Schematic model of polymerization–diff usion method.