Thermodynamic phase diagram analysis of three binary systems shared by five neopentane derivatives

1994 Calphad Vol. 18, NO. 4, pp. 387-396, Copyright (0 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0364-5916194 $7.00 + 0.00 0364-5916(94)

THERMODYNAMIC

00022-o

PHASE DIAGRAM ANALYSIS

OF

THREE BINARY SYSTEMS SHARED BY FIVE NEOPENTANE DERIVATIVES

D.O.L6pez’;

J.Van

’ Departament

Braak’;

de Ffsica

J.LL.Tamarit’;

i Enginyeria

H.A.J.Oonk*

Nuclear, 08028

* Department

of Interfaces

Universitat

Politecnica

Barcelona,

and Thermodynamics, Utrecht,

Diagonal

647,

Spain.

Utrecht The

de Catalunya,

University,

Padualaan

8, NL-3584

CH

Netherlands.

A thermodynamic analysis was made of the solid-plastic and plastic-liquid equilibria of three binary systems in which the components are plastic crystals. These substances are neopentane derivatives: neopentylglycol (NPG), pentaglycerin (PGI, 2amino-2-methyl 1,3-propanediol (AMP), tris(hydroxymethyl)aminomethane (TRIS) and 2-methyl 2-nitro 1 -propanol (MNP). Each of the three systems, which are PGIMNP, NPGIMNP and TRWAMP, show a plastic-liquid loop and a solid-plastic phase

ABSTRACT

diagram example crossing

of the eutectoid type. One of them, i.e. PG/MNP, is an of crossed isodimorphism: two solid-plastic loops each other giving rise to a three-phase equilibrium. In the thermodynamic analysis the liquid mixtures were

taken as ideal mixtures and for the plastic crystalline mixtures the (A,B,O) model was used to express the excess thermodynamic functions. In this analysis, phase diagram data and experimental enthalpies of melting were used.

Introduction In this in which

paper

a thermodynamic

the components

are neopentane

phase

diagram

(C(CH,l,)

ordered solid form ( form II), a highly disordered to as the plastic crystalline

The three

systems

analysis

solid form

state or the ODIC (Orientationally

investigated

is presented

are PGIMNP,

of three

The substances

derivatives.

binary

Dlsordered

NPGIMNP

Crystalline)

and TRISIAMP

systems

apart from an

(form I). The latter is commonly

Original version received on 6 September 1993, Revised version on 14 April 1994 387

show,

referred

state.

and they

imply the

D. 0. LOPEZ et al.

388

following

five component

substances:

NPG, (CH,),C(CH,OH),, PG, (CH&(CH,OH),,

2,2-dimethyl-1,3-propanediol 2-hydroxymethyl-2

AMP, (NH2)(CH,)C(CH,0H),, TRIS, (NH,)C(CH,OH),,

2-amino-2-methyl

2-methyl-2-nitro

The crystallographic

,3 propanediol

(pentaglycerin)

1,3-propanediol

2-amino-hydroxymethyl-1,3

MNP, (N0,)(CH,),C(CH20H),

summarized

methyl-l

(neopentylglycol)

propanediol

(tris(hydroxymethylIaminomethane)

I-propanol.

and thermodynamic

transition

properties

of the

five

substances

are

in Table I.

TABLE I Thermal

and Crystallographic

2 is the number of molecules

NPG Monoclinic P2,In z=4

Properties

of the Pure Components.

per unit cell.

PG

AMP

Tetragonal

Monoclinic

I4 z=2

____ z=4

TRIS Orthorhombic

MNP Monoclinic

Pn2,a

P2,/c

z=4

z=12

-11 TRANSITION 314.6kl.O

357.5kl.O

352.6kl.O

406.8 f 1 .O

12.8kO.5

21.3kl.l

23.3 zt 1.2

34.0*

40.6 f 2.0

59.5*3.0

66.2k3.0

83.7 zt4.2

48.1 rt2.4

1.7

312.0*1.0 15.0*0.8

fee

fee

bee

bee

fee

z=4

z=4

z=2

z=2

z=4

401.3*1.0

471.7*1.0

4.4kO.2

5.1*0.3

2.8zt0.2

3.2kO.2

3.3kO.2

10.8kO.5

10.8iO.5

7.4rto.4

7.1 zto.4

9.0*0.4

For each of the three binary systems,

382.4 f 1 .O

the two components

442.7 f 1 .O

364.1 *I.0

have the same type of plastic

THERMODYNAMIC crystalline

PHASE DIAGRAM

state, with similar characteristics.

Figures 1-3, show a single-phase

As a result, the three liquid-plastic

field for the plastic state which extends

range. On the other hand, the ordered forms, rise to solid-plastic

phase diagrams

the ordered

state

is rather

immiscibility

in solid state can be considered.

isodimorphjsm: solid-plastic metastable

limited.

the solid-plastic

of the eutectoid

The other system,

phase diagram

we adopt,

function

can be considered

7’) =A (1-s)

is a measure 0 with

X(11-X) [1 +B(l-2X)

1

and X for mole fraction

of the magnitude the dimension

2’) =X”(X)

=AX(l-Xl

=SE(X)

=$X(1-X)

S”(X,T)

case (8=0)

In our analysis of melting

of two separate to the

mixed

states,

the following

excess

A with the dimension

of the function;

of temperature

(1 +Bfl-2X)

8 which

accounts

of energy per amount

is dimensionless

1

[1+/3(1-2X)1

is a measure

for the temperature

(lIEI and the excess entropy

dependence. (SE) which are

I21

[31

in earlier cases (7,2). A theoretical

foundation

of the

is found in a paper by Lupis and Elliot (3).

we use, apart from phase diagram

as a function

[ 11

of the second component.

parameters:

The (A, B, 0) model has proved to be successful symmetrical

total

of crossed

point of one of the components

of the binary

In this model 0 is also the ratio of the excess enthalpy

H=(X,

as a superposition

in

model and method

for the description

A, Band 0 are three system dependent

of the asymmetry;

miscibility

and TRWAMP,

PGIMNP, is an example

giving

(GE)

where T stands for temperature

of substance

mole fraction

The mutual

NPG/MNP

see

point of the other.

For our study

G”(X,

over the whole

type (see Figures l-3).

In the case of the systems

Thermodynamic

Gibbs energy

phase diagrams,

in each of the three cases, are not isomorphous,

loops. These loops run from the stable transition transition

389

ANALYSIS

of composition.

data, experimental

information

on the heats

D. 0. LOPEZ et al.

390

For the analysis

of the plastic-crystalline

which, in fact, averages GE independent ( G,, GJ, which

of temperature

and determine

mixture.

the EGC method

the values of the first two

Redlich-Kister

(4)

interval

coefficients

are

[51

is the mean temperature

T,

we adopt

the liquidus and solidus data. First of all, we assume in the transition

G2 =BG,

where

to liquid transition

of the data set. To do so, we take the liquid state as an ideal

Next, the phase diagram results are combined

with the data on the heats of melting to obtain

A. B and 0.

For the analysis excess enthalpy

solid state miscibility example

of the solid to plastic-crystalline

transition

the corresponding

( given by eqs. 2 and 3) for the plastic crystalline

and entropy cannot

be neglected,

of crossed isodimorphism.

i.e PG/MNP, we can consider

expressions

mixture

of

are used. If

the phase diagram

as an

In this case, in order to obtain the excess Gibbs energy function

of each ordered solid form, LIQFIT program (5,6) can be applied to the stable branches of the diagram, provided that the metastable In fact, the determination method,

transition

points and the corresponding

of metastable

points is an important

entropies

of transition

part of the analysis

are known.

(for details of the

see (7)).

The phase diagram program

calculations

for both equilibria

were

performed

by means of ProPhase

(8).

Experimental information The techniques: differential

experimental Differential

phase Scanning

form and by isothermal

diagram

data

Calorimetry equilibration

(9-12)

have

(DSC), scanning in an X-ray

been

obtained

by means

with heat flux calorimeters

camera.

All experimental

of various working

data are plotted

in Figures 1-3.

The experimental

excess enthalpy

differences

for the equimolar

mixture

in

in liquid-plastic

THERMODYNAMIC

equilibrium

PHASE DIAGRAM ANALYSlS

are given in Table II. The latter were derived,

versus composition,

for each system,

from a plot of heat of fusion

see Figure 4.

TABLE II The Experimental

Excess Enthalpy

Difference

between

the Liquid and the Plastic State for the Equimolar

Mixture,

Results The results obtained

for the three binary systems

the (A, B, 0) model, are shown

by means of thermodynamic

in Table III. The corresponding

calculated

analysis

phase diagrams

in Figures I-3.

TABLE Ill The A, B and 0 Parameters

of the Three Systems

refers to the solid mixed crystalline

/I

Analysed.

state of the tetragonal

The asterisk type.

Form

OKI

A(J,mol-‘1

B

Plastic (fee)

668

1769

-0.14

Solid (0)’

00

4628

2.84

Plastic (fee)

643

1060

-0.19

Plastic (bee)

450

-180

5.20

using

are drawn

D. 0. LOPEZ et a/.

392

In the case of the PG/MNP transition

points were obtained

system,

for the plastic-solid

equilibrium,

the two

as a result of a number of trial and error calculations.

value of 150 K for the metastable

transition

We prefer the

point of MNP (0 -- > fee) and 1 K for the metastable

transition

point of PG (M --> fee). As a rather arbitrary

transition

of the metastable

ordered

metastable

choice,

for each component,

form was set equal to the entropy

the entropy

of transition

of

of the stable

ordered form.

A comparison three systems,

between

the calculated

and experimental

values for the eutectoid

invariant

of the

is given in Table IV.

TABLE IV Comparison

between

the Experimental

and Calculated

System

Compositions

T(K)

i TRlSlAMP NPGlMNP PGlMNP

experimental calculated

Invariant

302.5 301.2 344.8 345.2 280.4 279.4

Equilibria.

(Xl

0.00 -- 0.20 0.01 0.18 -- 0.87 0.50 0.51 0.92 0.96 0.88 1 1.00 .oo

Discussion As shown in Figures l-3, there is quite satisfactory and the calculated

phase diagrams.

eutectoid

invariants

eutectoid

compositions

being about 0.02

are within

agreement

In spite of the approximations,

one degree from the experimental

are in good agreement

between

the experimental

the calculated

temperatures

data of the

values (see Table IV); the calculated

with the experimental

values, the maximum

difference

in molar fraction.

From Table III, we can observe the PGIMNP and NPGIMNP systems,

that the 0 values, for the plastic crystalline

state (fee form), of

are very close. Possibly,

both systems

we may consider

as

393

THERMODYNAMIC PHASE DIAGRAM ANALYSIS

members

of a family

of binary systems

common characteristic

temperature.

whose

disordered

A comparable

alkali halide systems

(3,131 and for the family

took for the ordered

form of tetragonal

form of the fee-type

situation

is characterized

by a

exists for the family of the common-anion

of p-dihalobenzene

systems

type of PGlMNP the 0 value

(2). For want of data we

infinite

(no excess entropy

of

mixing).

In Figure 4, the (A, B, 0) model-calculated systems

are shown

with the measured

values

of the enthalpy

of melting

for the three

values.

Acknowledgements The authors

would

like to express

information

about the compounds

de Recerca

i Innovacio

(fellowship

EE-92-2/387)

Interfaces project

and binary systems.

Tecnologica which

to M. Barrio for giving

(Utecht

government

D.O. L6pez to spend University)

where

by a DGYCIT grant (reference

some experimental

We also thank the Comissi6 lnterdepartamental

(CIRIT) of the Catalonia

allowed

and Thermodynamics

was supported

their gratitude

some

for the financial time

part of this work

number

support

in the Department was carried

of

out. This

PB-92-0800-CO3-02).

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D. 0. LOPEZ et al.

394

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Ekeren; Calphad,

19, 137 (1986).

(submitted),

THERMODYNAMIC PHASE DIAGRAM ANALYSIS

395

37l&=$iy

T(K)

*r

29lLL

c

I t

W+Ql

M+W

-J

2631 .6

.4

X

.6

PG

MNP

.6

.4

.2

FIG. 1

.L)

NPG

X

FIG. 2

FIGURES l-3 Calculated

phase diagrams

of the systems

and experimental

PG/MNP, NPGlMNP and

TRWAMP,

respectively.

M, M, and M, refer to monoclinic Q refers to tetragonal

states.

state.

0 refers to orthorhombic

state.

C, and C, refers to bee and fee forms,

3301 AMP

1 .2

I

1

I

I

.4

.6

.a X

FIG. 3

I

I TRIS

data

respectively.

D. 0. LOPEZ et

81.

I

&.i(kJ.rnOl”)

/ /

3.6

YNP

.2

.6

.4

X

.B

#

PO ‘

4.4 _

AMP

2

.4

.6

i(

.8

.6

x

.8

NPG

TRIS

FIG. 4 Calculated (-=I and experimental data of enthalpy of melting for each binary system