Table 1. Open in new tab Symbols and...

Symbol

Units

Description

E

⁠,

F

⁠,

G

Internal energy, Helmholtz energy, Gibbs energy

^{3}

Total volume of system

σ

⁠,

σ_{i j}

Cauchy (“true”) stress. Negative under compression.

Pressure (-

δ_{k l} σ_{k l} / 3

⁠). Positive under compression.

τ

⁠,

τ_{i j}

Deviatoric stress (⁠

σ_{i j} + δ_{i j} P

⁠)

Temperature

J K⁻¹

Entropy

n^{ntwk}

mol

Molar amounts of network

n

⁠,

n_{i}

mol

Molar amounts of compositional/structural endmembers

s

⁠,

s_{i}

mol

How addition of one mole of

n_{i}

affects the amount of network

n^{ntwk}

p

⁠,

p_{i}

(unitless)

Molar proportions of endmembers

mol

Total number of moles of compositional/structural endmembers

x

Current material coordinates

ε^{ntwk}

⁠,

ε_{i j}^{ntwk}

(unitless)

Infinitesimal network strain tensor (eq. 3), negative under compression

ε

⁠,

ε_{i j}

(unitless)

Infinitesimal domain strain tensor (eq. 21)

ε^{chem}

⁠,

ε_{i j}^{chem}

(unitless)

Infinitesimal chemical strain tensor (eq. 25)

Ξ

⁠,

Ξ_{i j}

(unitless)

Chemical expansivity tensor (eq. 24)

{\bar{F}}_{k}

J mol⁻¹

Partial molar Helmholtz at fixed

ε^{ntwk}

and T (eq. 16)

{\bar{V}}_{k}

^{3}

mol⁻¹

Partial molar volume at fixed

ε^{ntwk}

and T (eq. 17)

μ

⁠,

μ_{i}

J mol⁻¹

Chemical potentials (non-specific)

μ_{i}^{Ξ}

⁠,

μ_{i}^{Ξ}

J mol⁻¹

Chemical potential at fixed

Ξ

(eq. 30)

μ^{I / 3}

⁠,

μ_{i}^{I / 3}

J mol⁻¹

Isotropic strain chemical potential (⁠

Ξ = I / 3

⁠, eq. 32)

μ^{\hat{n} \otimes \hat{n}}

⁠,

μ_{i}^{\hat{n} \otimes \hat{n}}

J mol⁻¹

Uniaxial chemical potential (⁠

Ξ = \hat{n} \otimes \hat{n}

⁠, eq. 36)

C_{T}

⁠,

C_{T i j k l}

Isothermal stiffness tensor

\dot{X}

Rate of change of a property X

^{ρ}

Indicates that a property is measured per unit volume

^{hyd}

⁠,

^{ntwk}

⁠,

_{0}

Hydrostatic, network or standard state property

^{liq}

⁠,

^{sol}

Property in a liquid or solid

I

⁠,

δ_{i j}

Identity matrix / Kronecker delta

Table 1.

Open in new tab

Symbols and subscripts used in this paper. Less familiar properties are listed with their defining equations.

Symbol	Units	Description
$E$ ⁠, $F$ ⁠, $G$	J	Internal energy, Helmholtz energy, Gibbs energy
V	m $^{3}$	Total volume of system
$σ$ ⁠, $σ_{i j}$	Pa	Cauchy (“true”) stress. Negative under compression.
P	Pa	Pressure (- $δ_{k l} σ_{k l} / 3$ ⁠). Positive under compression.
$τ$ ⁠, $τ_{i j}$	Pa	Deviatoric stress (⁠ $σ_{i j} + δ_{i j} P$ ⁠)
T	K	Temperature
S	J K⁻¹	Entropy
$n^{ntwk}$	mol	Molar amounts of network
$n$ ⁠, $n_{i}$	mol	Molar amounts of compositional/structural endmembers
$s$ ⁠, $s_{i}$	mol	How addition of one mole of $n_{i}$ affects the amount of network $n^{ntwk}$
$p$ ⁠, $p_{i}$	(unitless)	Molar proportions of endmembers
n	mol	Total number of moles of compositional/structural endmembers
$x$	m	Current material coordinates
$ε^{ntwk}$ ⁠, $ε_{i j}^{ntwk}$	(unitless)	Infinitesimal network strain tensor (eq. 3), negative under compression
$ε$ ⁠, $ε_{i j}$	(unitless)	Infinitesimal domain strain tensor (eq. 21)
$ε^{chem}$ ⁠, $ε_{i j}^{chem}$	(unitless)	Infinitesimal chemical strain tensor (eq. 25)
$Ξ$ ⁠, $Ξ_{i j}$	(unitless)	Chemical expansivity tensor (eq. 24)
${\bar{F}}_{k}$	J mol⁻¹	Partial molar Helmholtz at fixed $ε^{ntwk}$ and T (eq. 16)
${\bar{V}}_{k}$	m $^{3}$ mol⁻¹	Partial molar volume at fixed $ε^{ntwk}$ and T (eq. 17)
$μ$ ⁠, $μ_{i}$	J mol⁻¹	Chemical potentials (non-specific)
$μ_{i}^{Ξ}$ ⁠, $μ_{i}^{Ξ}$	J mol⁻¹	Chemical potential at fixed $Ξ$ (eq. 30)
$μ^{I / 3}$ ⁠, $μ_{i}^{I / 3}$	J mol⁻¹	Isotropic strain chemical potential (⁠ $Ξ = I / 3$ ⁠, eq. 32)
$μ^{\hat{n} \otimes \hat{n}}$ ⁠, $μ_{i}^{\hat{n} \otimes \hat{n}}$	J mol⁻¹	Uniaxial chemical potential (⁠ $Ξ = \hat{n} \otimes \hat{n}$ ⁠, eq. 36)
$C_{T}$ ⁠, $C_{T i j k l}$	Pa	Isothermal stiffness tensor
$\dot{X}$		Rate of change of a property X
$^{ρ}$		Indicates that a property is measured per unit volume
$^{hyd}$ ⁠, $^{ntwk}$ ⁠, $_{0}$		Hydrostatic, network or standard state property
$^{liq}$ ⁠, $^{sol}$		Property in a liquid or solid
$I$ ⁠, $δ_{i j}$		Identity matrix / Kronecker delta

Symbol	Units	Description
$E$ ⁠, $F$ ⁠, $G$	J	Internal energy, Helmholtz energy, Gibbs energy
V	m $^{3}$	Total volume of system
$σ$ ⁠, $σ_{i j}$	Pa	Cauchy (“true”) stress. Negative under compression.
P	Pa	Pressure (- $δ_{k l} σ_{k l} / 3$ ⁠). Positive under compression.
$τ$ ⁠, $τ_{i j}$	Pa	Deviatoric stress (⁠ $σ_{i j} + δ_{i j} P$ ⁠)
T	K	Temperature
S	J K⁻¹	Entropy
$n^{ntwk}$	mol	Molar amounts of network
$n$ ⁠, $n_{i}$	mol	Molar amounts of compositional/structural endmembers
$s$ ⁠, $s_{i}$	mol	How addition of one mole of $n_{i}$ affects the amount of network $n^{ntwk}$
$p$ ⁠, $p_{i}$	(unitless)	Molar proportions of endmembers
n	mol	Total number of moles of compositional/structural endmembers
$x$	m	Current material coordinates
$ε^{ntwk}$ ⁠, $ε_{i j}^{ntwk}$	(unitless)	Infinitesimal network strain tensor (eq. 3), negative under compression
$ε$ ⁠, $ε_{i j}$	(unitless)	Infinitesimal domain strain tensor (eq. 21)
$ε^{chem}$ ⁠, $ε_{i j}^{chem}$	(unitless)	Infinitesimal chemical strain tensor (eq. 25)
$Ξ$ ⁠, $Ξ_{i j}$	(unitless)	Chemical expansivity tensor (eq. 24)
${\bar{F}}_{k}$	J mol⁻¹	Partial molar Helmholtz at fixed $ε^{ntwk}$ and T (eq. 16)
${\bar{V}}_{k}$	m $^{3}$ mol⁻¹	Partial molar volume at fixed $ε^{ntwk}$ and T (eq. 17)
$μ$ ⁠, $μ_{i}$	J mol⁻¹	Chemical potentials (non-specific)
$μ_{i}^{Ξ}$ ⁠, $μ_{i}^{Ξ}$	J mol⁻¹	Chemical potential at fixed $Ξ$ (eq. 30)
$μ^{I / 3}$ ⁠, $μ_{i}^{I / 3}$	J mol⁻¹	Isotropic strain chemical potential (⁠ $Ξ = I / 3$ ⁠, eq. 32)
$μ^{\hat{n} \otimes \hat{n}}$ ⁠, $μ_{i}^{\hat{n} \otimes \hat{n}}$	J mol⁻¹	Uniaxial chemical potential (⁠ $Ξ = \hat{n} \otimes \hat{n}$ ⁠, eq. 36)
$C_{T}$ ⁠, $C_{T i j k l}$	Pa	Isothermal stiffness tensor
$\dot{X}$		Rate of change of a property X
$^{ρ}$		Indicates that a property is measured per unit volume
$^{hyd}$ ⁠, $^{ntwk}$ ⁠, $_{0}$		Hydrostatic, network or standard state property
$^{liq}$ ⁠, $^{sol}$		Property in a liquid or solid
$I$ ⁠, $δ_{i j}$		Identity matrix / Kronecker delta

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