[PPT] - MSE 590 tutorial on PS-b-PMMA copolymers 2011/10/28 Chemical PowerPoint Presentation

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MSE 590 tutorial on PS-b-PMMA copolymers

2011/10/28

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Chemical structure and physical properties of PS (Polystyrene)

An aromatic polymer made from the monomer styrene (C8H8)n Physical properties: Glass transition temperature: around 95 °C Dielectric constant: 2.4–2.7 Density: 1.05 g/cm3 Thermal conductivity: 0.08 W/(m·K) Sheet or molded polystyrene, polystyrene foam, copolymers… Chemical structure: Application:

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PS loss spectrum

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Frequency (Hz)

ε′′(ω)

PS 0 0C to 80 0C

Relatively small values, Dielectrically inactive

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Chemical structure and physical properties of PMMA (Poly(methyl methacrylate)

Chemically, it’s synthetic polymer of monomer methyl methacrylate (C5O2H8)n Physical properties: Glass transition temperature: around 105 °C (atactic) Refractive index: 1.4914 at 587.6 nm Density: 1.18 g/cm3 Melting point: around 160 °C Transparent glass substitute (fish tank), Medical technologies and implants, Artistic and aesthetic uses… Chemical structure: Application: Polymerization

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PMMA Loss Spectrum

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Frequency (Hz)

ε′′(ω)

PMMA 60 0C to 150 0C

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PS-b-PMMA and PS/PMMA samples

Sample preparation

PS-b-PMMA :

1. Heated to 180 °C for 10 minutes and pressed under 1000 lb load.
2. Decreased to room temperature by keeping 300 lb load.

Blends of PS /PMMA:

1. Heated to 180 °C for 30 minutes and pressed under 600 lb load test

for 5 minutes.

2. Decreased to room temperature by keeping 600 lb pressure.

After the hot pressing processes, samples were all polished and sputtered by Ag electrodes.

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PS-b-PMMA and PS/PMMA samples

Dielectric measurement

using Broad Band NOVOCONTROL spectroscopy with automatic temperature control from -40 °C to 150 °C and frequency range from 0.01 Hz to 1 MHz.

Samples Mw Diameter (mm) Thickness (mm) Volume fraction fPS PMMA 50 K 19.88±0.01 1.25±0.01 PS 50 K 19.865±0.005 0.94±0.01 PS-b-PMMA (Sample 1) 50K-50K 19.88±0.01 0.855±0.005 0.53±0.03 PS-b-PMMA (Sample 2) 50K-50K 19.82±0.01 0.575±0.005 0.53±0.03 PS-b-PMMA 50K-130K 19.82±0.01 0.575±0.005 0.53±0.03 PS/PMMA 50K/50K 19.90±0.01 0.905±0.005 0.53±0.03

Table 1. Molecular weight, diameter and thickness of the samples.

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2D imaginary permittivity plots of copolymer PS-b-PMMA

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0.5 1 1.5 2 log10(ω/Hz) log10ε′′ 60 oC to 150 oC DC Conductivity β Relaxation Process

α Relaxation Process

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Review on the Basic models

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Presentation of different Models on Complex Plane of Dielectric Constant

Cole-Cole Debye Davidson-Cole Havriliak-Negami Water Polymers Havriliak-Negami model Is most suitable for PS-b-PMMA

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2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 0.2 0.4

ε′(ω) ε′′(ω)

Complex plane of dielectric constant at T=40oC Experimental Data Cole-Cole Davidson-Cole Havriliak-Negami 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 0.2 0.4

ε′(ω) ε′′(ω)

Complex plane of dielectric constant at T=60oC 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 0.2 0.4

′( ) ε′′(ω)

Complex plane of dielectric constant at T=80oC

Comparison

1. Cole-Cole describes the

circular arc behavior at low frequencies.

2. Davidson-Cole

describes the skew line behavior at high frequencies.

3. Havriliak-Negami

combines the advantages of the above two models. Appearance of new relaxation process as T approaches Tg

Material of Sample: PMMA

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Physical Mechanisms

Conductivity term: The contribution of free charge carriers α-relaxation process: Attributed to long chain segmental motion within the main polymer chain β-relaxation process: Primary localized motion of side segments

frequency of occurrence increases

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Fitting Strategy: Least-Squares Fitting of HN parameters

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Modeling Example T < Tg

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0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Frequency (Hz) ε′′(ω) 90 oC experimental data relaxation conductivity term model superposition

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ε′′ (ω)

PS-b-PMMA 50K-50K T=105 0C Experimental data

α relaxation β relaxation

conductivity model superposition PS-b-PMMA 50K-130K T=105 0C

Modeling Example T > Tg

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Relaxation Map

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1 2 3 4 5 Temperature 1000/T (K-1) fmax (Hz) PMMA PS/PMMA blends PSbPMMA 50-50K PSbPMMA 50-130K (a)

2.4 2.45 2.5 2.55 2.6 2.65 2.7 2.75 3 3.5 4 4.5 5 5.5 Temperature 1000/T (K-1) fmax (Hz) PMMA PS/PMMA blends PSbPMMA 50-50K PSbPMMA 50-130K (b)

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Temperature-dependence Behavior

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αβ-type relaxation

For the region around glass transition temperature, the temperature dependence behavior can not be fitted well by both of Arrhenius Eqn. and Vogel-Fulcher Eqn., it is αβ-type complicated relaxation.

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Fitting parameters of α relaxation

α relaxation fmax D T0 (K) Tg (K) PMMA 3.97e8 2.50 337 95.4 PS/PMMA blends 1.68e7 1.80 342 96 PSbPMMA 50-50k 4.21e2 0.56 354 96.8 PSbPMMA 50-130k 2.65e2 0.44 358 97.6

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Fitting parameters of β relaxation

β relaxation EA (KJ, T >Tg) EA (KJ, T<Tg) PMMA 105.5 78.2 PS/PMMA blends 106.1 77.9 PS-b-PMMA 50-50K 88.6 75.4 PS-b-PMMA 50-130K 88.0 82.0

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Conductivity effects

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log10[Frequency (Hz)] log10[σ (S/m)] PMMA 135 0C PMMA 140 0C PMMA 150 0C PSbPMMA 50-50K 132 0C PSbPMMA 50-50K 140 0C PSbPMMA 50-50K 150 0C PSbPMMA 50-130K 132 0C PSbPMMA 50-130K 140 0C PSbPMMA 50-130K 150 0C

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Conductivity effects (Cont’d)

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Conductivity effects (Cont’d)

DC conductivity σ0 (S/m) A T0 (K) PMMA 5.39e-4 1985 283 PSbPMMA 50-50k 5.15e-6 1075 330 PSbPMMA 50-130k 1.99e-1 3584 257