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Thermal Properties and Thermodynamics of Poly(l-lactic acid)

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Synthesis, Structure and Properties of Poly(lactic acid)

Part of the book series: Advances in Polymer Science ((POLYMER,volume 279))

Abstract

Thermal properties and thermodynamics of poly(l-lactic acid) PLLA at nonequilibrium and equilibrium states and during reversing and nonreversing processes are presented, based on the apparent heat-flow and heat capacity (C p ). The experimental, apparent heat capacity results from measurements by adiabatic calorimetry, standard differential scanning calorimetry, and temperature-modulated differential scanning calorimetry are interpreted in terms of microscopic molecular motion in the entire temperature range. The low-temperature, below the glass transition, experimental heat capacity of solid state is linked to the vibrational motion. The heat capacity of the liquid state of PLLA is linked additional to the vibrational, also to the conformational, and anharmonic motions or estimated from an empirical addition scheme based on contributions of the constituent chain-segments of polymers. Once calculated, solid C p (vibration) and liquid C p (liquid) heat capacities are established so they can serve as two reference baselines for the quantitative thermal analysis of nonequilibrium semicrystalline poly(lactic acid). Knowing heat capacities (C p (vibration), C p (liquid)) and transitions parameters, the integral functions such as the enthalpy (H), entropy (S) and free enthalpy (Gibbs function) (G) for equilibrium conditions are calculated and used as a reference for analysis. All recommended results for PLLA, are collected and organized as part of the ATHAS Data Bank. Examples of the qualitative and quantitative thermal analysis of amorphous and semicrystalline poly(lactic acid) are presented to characterize phases and phase transitions such as glass transition, enthalpy relaxation, cold crystallization/cystallization, reorganization and melting, as well as amount of phase: crystallinity, mobile and rigid amorphous fraction on the ATHAS scheme (Advanced Thermal Analysis System).

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Abbreviations

AFM:

Atomic force microscopy

A 0 :

Constant of Nernst–Lindemann equation

C p :

Heat capacity at constant pressure

C p (exp):

Experimental heat capacity at constant pressure

\( {C}_p^{\ast}\left(\exp \right) \) :

Apparent experimental heat capacity at constant pressure

C p (liquid):

Heat capacity at constant pressure of the liquid state

C p (semicrystal):

Heat capacity at constant pressure of the semicrystalline polymer

C p (solid):

Heat capacity at constant pressure of the solid state

C p (vibration):

Heat capacity at constant pressure due to vibrational motions

C v :

Heat capacity at constant volume

C v (box):

Heat capacity at constant volume due to frequencies box-like distribution

C V (conf):

Conformational contribution to heat capacity at constant volume

C v (Einstein):

Heat capacity at constant volume in Einstein equation

C v (exp):

Experimental heat capacity at constant volume

C v (group):

Heat capacity at constant volume due to group vibrations

C v (skeletal):

Heat capacity at constant volume due to skeletal vibrations

\( {C}_{v\left(\mathrm{sk}\right)}^{\mathrm{calc}} \) :

Calculated skeletal heat capacity at constant volume

\( {C}_{v\left(\mathrm{sk}\right)}^{\mathrm{exp}} \) :

Experimental skeletal heat capacity at constant volume

D 1 :

One-dimensional Debye function

D 2 :

Two-dimensional Debye function

D 3 :

Three-dimensional Debye function

DSC:

Differential scanning calorimetry

E I :

Total energy in Ising-like model

FSC:

Fast scanning chip calorimetry

G :

Free enthalpy (Gibbs function)

g 1 :

Degeneracy

H :

Enthalpy

h :

Plank’s constant

\( {H}_c^{{}^{\circ}} \) :

Reference enthalpy

k :

Boltzmann constant

L :

Lamellar thickness

m j :

Conformation number

N E :

Number of Einstein modes

N box :

Number of vibrational modes for the frequency box-like distribution

N gr :

Number of group vibrations

N sk :

Number of skeletal vibrations

P :

Pressure

P n :

Number of repeat units in the polymer chain

PDLA:

Poly(d-lactic acid)

PLDLA:

Poly(l,d-lactic acid)

PLLA:

Poly(l-lactic acid)

PPMS:

Physical property measurement system

Q :

Heat

R :

Universal gas constant

S :

Entropy

T :

Temperature

T a :

Annealing temperature (aging temperature)

t a :

Annealing time (aging time)

T c :

Crystallization temperature

T f :

Fictive temperature

T g :

Glass transition temperature

T m :

Melting temperature

\( {T}_m^{{}^{\circ}} \) :

Equilibrium melting temperature

TMDSC:

Temperature-modulated differential scanning calorimetry

T β :

β-transition temperature

V :

Volume

w a :

Mobile amorphous fraction

w c :

Crystal fraction

w RAF :

Rigid amorphous fraction

α :

Coefficient of thermal expansion

β :

Coefficient of compressibility

β KWW :

Stretching parameter

χ 2 :

Chi-square function (weighted sum of squares)

ΔC p :

Variation of heat capacity at T g (w)

Δh m :

Melting enthalpy (heat of fusion)

\( \Delta {h}_m^{{}^{\circ}} \) :

Equilibrium melting enthalpy

Δh r :

Enthalpy recovery

\( \Delta {s}_m^{{}^{\circ}} \) :

Equilibrium melting entropy

Φ :

Heat-flow rate

ϕ(t):

Time decay function

σ e :

Fold surface free energy

σ i :

Standard deviation

ρ :

Density of the crystal phase

τ :

Relaxation time

Γ :

Ratio of degeneracies of the conformational states

Θ Ei :

Einstein frequencies

Θ1, Θ2, Θ3 :

One-, two-, and three-dimensional Debye temperatures

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Authors and Affiliations

  1. Department of Chemistry, Rzeszow University of Technology, 35-959, Rzeszow, Poland

    Marek Pyda & Anna Czerniecka-Kubicka

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  1. Marek Pyda
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Correspondence to Marek Pyda .

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  1. Composites and Biomaterials, National Research Council, Institute of Polymers, Pozzuoli (NA), Italy

    Maria Laura Di Lorenzo

  2. Interdisciplinary Center for Transfer-Oriented Research in Natural Sciences, Martin Luther University Halle-Wittenberg, Halle/S., Germany

    René Androsch

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Pyda, M., Czerniecka-Kubicka, A. (2017). Thermal Properties and Thermodynamics of Poly(l-lactic acid). In: Di Lorenzo, M., Androsch, R. (eds) Synthesis, Structure and Properties of Poly(lactic acid). Advances in Polymer Science, vol 279. Springer, Cham. https://doi.org/10.1007/12_2017_19

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