Thermodynamics of Polymer Blends, Volume I

Anatoly E. Nesterov, Yuri S. Lipatov

• Publisher: CRC Press
• Year: 2020
• ISBN:
  9781000725483
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Thermodynamics is an indispensable tool for developing a large and growing fraction of new polymers and polymer blends.
These two volumes show the researcher how thermodynamics can be used to rank polymer pairs in order of immiscibility, including the search for suitable chemical structure of compatibilizers.
Because of the great current commercial interest in this most dynamic sector of the polymer industry, there is high interest in studying their physical and mechanical properties, their structures, and the processes of their formation and manufacture.
These Books are dedicated to Analysis of the Thermodynamics of Polymer Blends. Thermodynamic behavior of blends determines the compatibility of the components, their morphological features, rheological behavior, and microphase structures. As a result, the most important physical and mechanical characteristics of blends can be identified.
The information in these two volumes will be useful to all those involved in polymer research, development, analysis and advanced process engineering.

Chapter 1

BASIC PRINCIPLES OF THERMODYNAMICS OF POLYMER SOLUTIONS

1.1 THE MAIN THERMODYNAMIC CHARACTERISTICS OF SOLUTION

The main thermodynamic functions of any solution are the changes in enthalpy of its formation, ΔH, entropy changes, ΔS, and Gibbs free energy, $\Delta \text{G}=\Delta \text{H}-\text{T}\Delta \text{S}$. At constant temperature and pressure, the dissolution is a spontaneous process proceeding in the direction of diminishing Gibbs free energy of mixing. The solution has lower free energy as compared with the sum of free energies of solution components (polymer and solvent):

${\text{G}}_{\text{solution}}lt;{\displaystyle \sum _{\text{i}}{\text{n}}_{\text{i}}{\text{G}}_{\text{i}}^0}$

[1.1]

where G⁰ is the free energy of i-th component.

The excess free energy determined as

$\Delta \text{G}={\text{G}}_{\text{solution}}-{\displaystyle \sum _{\text{i}}{\text{n}}_{\text{i}}{\text{G}}_{\text{i}}^0}$

[1.2]

by spontaneous dissolution is negative. Correspondingly, the chemical potential of a component in solution, μ_i, should be lower than its value before dissolution, ${\text{μ}}_{\text{i}}<{\text{μ}}_{\text{i}}^0$ i.e., Δμ_i < 0. Values ΔG < 0, Δμ_i < 0 are the criteria of the affinity between components. Their values are determined by the absolute magnitude of the differences ΔG or Δμ_i.

The solution in which all molecules of components equally interact with each other are considered as ideal solutions. Their properties are the additive sum of the properties of components. Such solutions obey the Henry and Raul laws:

${\text{p}}_2=\text{Kx}$

[1.3]

${\text{p}}_1={\text{p}}_1^0(1-\text{x})$

[1.4]

where p₁ and p₂ are partial pressure of components, x is the molar fraction of component in solution. Because

$\Delta {\text{μ}}_{\text{i}}=\text{RT}\ln {\text{p}}_{\text{i}}/{\text{p}}_{\text{i}}^0$

[1.5]

we find that

$\Delta {\text{μ}}_{\text{i}}=\text{RT}\ln {\text{x}}_{\text{i}}$

[1.6]

It means that the chemical potential of any component is only determined by its molar fraction in solution. In the majority of cases, solutions do not obey Eqs 1.3 to 1.6. They are thus considered non-ideal. The deviations from the ideality (${\text{p}}_{\text{i}}/{\text{p}}_{\text{i}}^0={\text{x}}_{\text{i}}$) may be positive (${\text{p}}_{\text{i}}/{\text{p}}_{\text{i}}^0>{\text{x}}_{\text{i}}$) or negative (${\text{p}}_{\text{i}}/{\text{p}}_{\text{i}}^0<{\text{x}}_{\text{i}}$). To estimate the degree of deviation from the ideality, the concept of excess quantities is introduced as an excess of properties in comparison with the ideal magnitude. These are:

$\Delta {\text{μ}}_{\text{i}}^{\text{exc}}=\Delta {\text{μ}}_{\text{i}}-\Delta {\text{μ}}_{\text{i}}^{\text{id}}=\text{RT}\ln {\text{γ}}_{\text{i}}$

[1.7]

$\Delta {\overline{\text{S}}}_{\text{i}}^{\text{exc}}={\overline{\text{S}}}_{\text{i}}-{\text{S}}_{\text{i}}^{\text{id}}=-\text{RT}\ln {\text{γ}}_{\text{i}}-\text{RT}{\left(\frac{\delta \ln {\text{γ}}_{\text{i}}}{\text{γT}}\right)}_{\text{p}}$

[1.8]

$\Delta {\overline{\text{H}}}_{\text{i}}^{\text{exc}}=-{\text{RT}}^2{\left(\frac{\text{δ}\ln {\text{γ}}_{\text{i}}}{\text{δT}}\right)}_{\text{p}}$

[1.9]

$\Delta {\overline{\text{G}}}_{\text{i}}^{\text{exc}}=\text{R...}$

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• 1 Basic Principles of Thermodynamics of Polymer Solutions
• 2 Statistical Theories of Polymer Solutions
• 3 Thermodynamics of Polymer Mixing
• 4 Homopolymer-copolymer and Copolymer-copolymer Blends
• 5 Mechanism and Kinetics of Phase Separation in Polymer Solutions and Blends
• 6 Interface in Demixing Solutions and Polymer Mixtures
• Nomenclature
• Index