Thermochimica

Acta

543 (2012) 88–

95

Contents

lists

available

at

SciVerse

ScienceDirect

Thermochimica

Acta

j o u r n a

l

h

o

m e

p a g e :

w w w . e l s e v i e r . c o m / l o c a t e / t c a

Determination

of

the

glass

transition

temperature

of

ionic

liquids:

A

molecular

approach

Seyyed

Alireza

Mirkhani

a

,

Farhad

Gharagheizi

a

,

∗

,

Poorandokht

Ilani-Kashkouli

a

,

Nasrin

Farahani

b

a

Department

of

Chemical

Engineering,

Buinzahra

Branch,

Islamic

Azad

University,

Buinzahra,

Iran

b

Department

of

Chemistry,

Buinzahra

Branch,

Islamic

Azad

University,

Buinzahra,

Iran

a

r

t

i

c

l

e

i

n

f

o

Article

history:

Received

27

October

2011

Received

in

revised

form

11

May

2012

Accepted

11

May

2012

Available online 22 May 2012

Keywords:
Glass

transition

temperature

Ionic

liquids

Quantitative

structure–property

relationship
Genetic

Function

Approximation

a

b

s

t

r

a

c

t

Following

our

recent

QSPR

models

for

the

glass

transition

temperatures

of

ammonium

[1]

and

1,3-dialkyl

imidazolium-based

ionic

liquids

[2,3]

,

a

similar

model

is

reported

in

this

work

for

remaining

classes

of

ionic

liquids.

The

roles

of

cations

and

anions

are

considered

separately.

The

Genetic

Function

Approxi-

mation

is

applied

to

select

suitable

variables

(molecular

descriptors)

and

to

develop

a

linear

QSPR

model.

Consequently,

a

simple

predictive

model

is

obtained.

Its

performance

is

quantified

by

the

following

sta-

tistical

parameters:

absolute

average

deviation

(AAD):

3.84%,

determination

coefficient:

0.8897,

and

root

mean

square

error

(RMSE):

10.594

K.

© 2012 Elsevier B.V. All rights reserved.

1.

Introduction

Historically,

the

luminous

age

of

ionic

liquids

(ILs)

has

begun

with

the

investigation

of

German

chemist

Paul

van

Walden

on

alkyl

ammonium

nitrates

for

their

low

melting

points

in

1914.

Today,

ionic

liquids

become

the

source

of

innovation

and

the

cornerstone

of

many

industrial

breakthroughs

for

their

unique

properties

such

as

high

thermal

stability,

large

liquidus

range,

high

ionic

conductivity,

high

solvating

capacity,

and

negligible

vapor

pressure.

Generally,

the

term

ionic

liquid

or

more

technically

Room

Temperature

Ionic

Liquids

(RTILs),

refers

to

the

class

of

salts

having

melting

points

close

or

below

100

◦

C

[4]

.

Ionic

liquids

also

possess

very

negligible

vapor

pressures

owing

to

their

ionic

natures

[5]

.

Besides

anions,

ionic

liquids

are

typically

made

of

cations

exhibiting

bulky

rings

containing

either

nitrogen

or

phosphorus

[6]

.

One

of

the

potential

application

of

ILs

is

to

employ

them

as

elec-

trolytes

in

electrochemical

applications

[7,8]

.

ILs

have

intrinsic

ion

conductivity

owing

to

their

ionic

nature.

In

addition,

thermal

stabil-

ity,

non-toxicity

and

non-volatility

of

ILs

are

requisite

features

for

their

future

application

as

electrolytes.

However,

ILs

possess

lower

ionic

conductivity

in

comparison

with

the

common

electrolytes

owing

to

their

higher

viscosity.

The

strong

electrostatic

interactions

of

ionic

counterparts

in

ILs

account

for

their

higher

viscosity.

∗ Corresponding

author.

Fax:

+98

21

88

48

10

87.

E-mail

addresses:

[e-mail]

,

[e-mail]

(F.

Gharagheizi).

One

of

the

important

features

of

electrolytes

is

to

possess

low

glass

transition

temperature.

The

glass

transition

temperature

refers

to

conspicuous

changes

of

thermodynamic

derivative

prop-

erties,

such

as

heat

capacity

and

thermal

expansivity

that

usually

accompany

the

solidification

of

a

viscous

liquid

during

cooling

(or

sometimes

compression)

[9]

.

Ionic

liquids

with

desired

glass

transition

temperature

could

be

tailored

by

selecting

the

proper

combination

of

anions

and

cations.

However,

selecting

right

combination

of

ionic

parts

of

ILs

from

experiment

is

a

challenging

task,

owing

to

enormous

numbers

of

possible

ionic

liquids

[10]

.

So,

predictive

models

are

essential

to

rationally

estimate

the

desired

property

before

the

synthesis

of

ionic

liquids.

In

this

com-

munication

a

model

based

on

Quantitative

Structure–Property

Relationship

(QSPR)

approach

[11–14]

was

developed

to

estimate

the

glass

transition

temperature

of

several

ionic

liquids.

2.

Methodology

2.1.

Data

preparation

The

experimental

data

for

glass

transition

temperature

of

139

diverse

ionic

liquids

were

collected

from

literatures

[15–53]

.

The

measurement

protocols

available

to

determine

the

glass

transition

temperature

are

Differential

Scanning

Calorimetry

(DSC),

cold-

stage

polarizing

microscopy,

NMR,

and

X-ray

scattering.

Since,

the

values

of

glass

transition

temperatures

strongly

depend

on

the

measurement

protocols,

it

is

essential

that

all

collected

data

0040-6031/$

–

see

front

matter ©

2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.tca.2012.05.009

S.A.

Mirkhani

et

al.

/

Thermochimica

Acta

543 (2012) 88–

95

89

Table

1

List

of

ionic

liquids

and

their

corresponding

frequency

in

this

study.

No.

Class

AARD%

T

exp

g

range

(K)

T

pred

g

range

(K)

N

1

1-Alkyl

imidazolium

7.5

174.15–211.15

189.92–213.85

6

2

Amino

acids

2.2

238.15–250.15

228.39–256.6

11

3

Guanidinium

2.6

192.49–215.45

181.73–214.91

12

4

Isoquinolinium

4.2

193.75–253.15

200.03–267.92

9

5

Morpholinium

5.0

195.15–285.15

200.98–250.11

15

6

Oxazolidinium

1.7

185.15–203.15

183.34–203.38

8

7

Phosphonium

2.9

197.66–433.15

195.13–409.44

15

8

Piperidinium

3.6

181.15–207.15

176.41–212.55

11

9

Pyrrolidinium

5.5

157.15–235.35

159.91–196.52

16

10

Tri-alkyl

imidazolium

3.9

191.15–215.15

201.26–210.65

8

11

Triazolium

3.8

203.15–261.15

198.93–253.59

28

for

model

development

are

measured

with

one

specific

protocol.

Our

database

includes

mostly

data

measured

using

DSC,

since

the

majority

of

data

reported

in

literature

was

obtained

by

this

tech-

nique.

The

investigated

ionic

liquids

and

their

corresponding

range

of

glass

transition

temperatures

of

each

group

are

presented

in

Table

1

.

37

anions

and

86

cations

are

present

in

the

in

the

structures

of

the

studied

ionic

liquids.

The

anion

and

cation

abbreviations

as

well

as

their

structures

are

enlisted

in

Tables

S1

and

S2,

respec-

tively,

as

supporting

information

.

2.2.

Calculation

of

descriptors

The

aim

of

this

study

is

to

correlate

ILs’

glass

transition

tem-

peratures

with

their

chemical

structures,

namely,

their

anion-

and

cation-based

descriptors.

For

this

purpose,

anion

and

cation

descriptors

are

separately

calculated

for

each

ionic

liquid.

This

approach

is

successful

to

correlate

the

studied

physical

property

with

the

structure

of

both

anion

and

cation.

However,

it

fails

to

account

for

anion–cation

interactions.

SMILES

(Simplified

Molecular

Input

Line

Entry

Specification)

structures

of

all

cations

and

anions

were

imported

to

Dragon

soft-

ware

for

the

sake

of

descriptor

calculation.

About

2000

descriptors

from

15

diverse

classes

of

descriptors

are

calculated

by

Dragon

soft-

ware.

These

15

classes

of

descriptors

are:

constitutional

descriptors,

topological

indices,

walk

and

path

counts,

connectivity

indices,

information

indices,

2D

autocorrelations,

Burden

Eigen

values,

edge-adjacency

indices,

functional

group

counts,

atom-centered

fragments,

molecular

properties,

topological

charge

indices,

Eigen

value-based

indices,

2D

binary

finger

print,

2D

frequency

finger

print.

After

the

completion

of

descriptors

calculation,

only

descrip-

tors

that

could

be

calculated

for

all

anions

or

cations

are

retained.

Next,

the

pair

correlations

for

each

binary

group

of

descriptors

(all

anions

and

cations

descriptors)

are

calculated.

For

binary

groups

with

the

pair

correlation

greater

than

0.9,

one

of

descriptors

is

omitted

randomly.

2.3.

Selection

of

training

and

test

sets

In

this

study,

k-mean

clustering

is

used

to

define

training

and

test

sets.

This

approach

is

based

on

performing

a

partition

of

col-

lected

ionic

liquids

in

four

statistically

representative

clusters

of

ionic

liquids,

in

which

each

ionic

liquid

belongs

to

the

one

with

the

nearest

mean.

This

procedure

ensures

that

any

ionic

liquid

classes

(as

determined

by

the

clusters

derived

from

k-mean

clustering)

will

be

represented

in

both

compounds

series

(training

and

test).

It

per-

mits

the

designing

of

both

training

and

predicting

series,

which

are

representative

of

the

entire

“experimental

universe”.

Selection

of

the

training

and

prediction

set

was

carried

out

by

taking,

in

a

ran-

dom

way,

compounds

belonging

to

any

IL

class.

112

ionic

liquids

are

selected

for

model

derivation

as

“training

set”.

The

ability

of

the

model

to

learn

from

“training

set”

and

reproduce

the

correct

prediction

is

tested

by

introducing

a

test

set

containing

27

ILs.

3.

Sub-set

variable

selection

In

this

study

Genetic

Function

Approximation

(GFA)

is

employed

for

sub

set

variable

selection.

GFA

as

a

genetic

based

variable

selec-

tion

approach-involves

the

combination

of

multivariate

adaptive

regression

splines

(MARS)

[54]

algorithm

with

genetic

algorithm

[55]

to

evolve

series

of

equations

instead

of

one

that

best

fit

the

training

set

data.

The

approach

was

originally

proposed

by

the

pioneering

work

of

Rogers

and

Hopfinger

[56]

.

In

most

cases,

QSPR

models

are

presented

as

a

sum

of

linear

terms:

F(X)

=

a

0

+

M



k

=1

a

k

X

k

(1)

where

a

0

is

the

intercept,

a

k

is

the

model

coefficient

and

X

k

s

are

molecular

descriptors.

The

initial

QSPR

models

are

constructed

by

random

selection

of

the

number

of

molecular

descriptors.

In

the

next

step,

the

qualities

of

the

derived

models

are

evaluated

by

Friedman’s

lack

of

fit

(LOF)

scoring

function,

which

is

a

penalized

least-squares

error

measures:

LOF

(model)

=

1

N

LSE(model)

(1

−

(c

+

1

+

(d

×

p))/N)

2

(2)

In

this

LOF

function,

c

is

the

number

of

non-constant

basis

func-

tions,

N

is

the

number

of

samples

in

the

data

set,

d

is

a

smoothing

factor

to

be

set

by

the

user,

and

p

is

the

total

number

of

parame-

ters

in

the

model

and

the

LSE

is

the

least

square

error

of

the

model.

Employment

of

LOF

leads

to

the

models

with

the

better

prediction

without

over

fitting.

At

this

point,

we

repeatedly

perform

the

genetic

recombination

or

crossover

operation:

• Two

good

models

in

terms

of

their

fitness

are

selected

as

‘parents’.

• Each

is

randomly

‘cut’

into

two

sections.

A

new

model

is

created

using

the

basis

functions

taken

from

a

section

of

each

parent.

• The

model

with

the

worst

fitness

is

replaced

by

this

new

model.

• The

overall

process

is

ended

when

the

average

fitness

of

the

mod-

els

in

the

population

stops

improving.

In

this

study,

population

and

the

number

of

maximum

genera-

tions

are

set

to

100

and

5000,

respectively.

The

value

of

Mutation

probability

is

considered

to

be

1.5

in

this

study.

4.

Results

and

discussion

The

procedure

of

model

development

with

optimal

number

of

descriptors

is

described

as

follows.

90

S.A.

Mirkhani

et

al.

/

Thermochimica

Acta

543 (2012) 88–

95

The

process

initiates

by

developing

the

model

with

one

descrip-

tor.

Then,

the

accuracy

of

model

is

calculated

in

terms

of

R

2

.The

process

continued

by

incremental

addition

of

descriptors

and

cal-

culation

related

R

2

values.

The

process

continued

until

the

addition

of

one

more

descriptor

does

not

improve

the

model

accuracy

sig-

nificantly.

In

our

study,

the

best

model

with

optimum

number

of

descriptors

contains

11

descriptors:

T

g

=

intercept

+

T

g,anion

+

T

g,cation

intercept

=

368.72472(

±35.00858)

T

g,anion

=

−Mor17p

anion

×

69.247(

±11.22717)

+

HATS2v

anion

×

45.39043(

±8.67212)+R1p

anion

×

16.76226(

±4.1989)

T

g,cation

=

−MWC05

cation

×48.48417(±7.56097)

+

ATS3m

cation

×41.25879(±4.89045)−Mor30v

cation

×

83.46733(

±18.02321)

+

G2m

cation

×

69.82063(

±34.33122)

+

G2p

cation

×

48.36684(

±36.46551)

−

nCrs

cation

×

7.06894(

±1.11807)

+

nCbH

cation

×

4.9144(

±0.73748)

−

F02[N–O]

cation

×

14.91919(

±4.21278)

(3)

R

2

=

0.8897;

n

Training

=

112;

n

Test

=

27;

AAD

=

3.84%,

RMSE

=

10.594

K

In

Eq.

(5)

:

• Mor17p

and

Mor30v

belong

to

MoRSE

[57]

(Molecule

Representa-

tion

of

Structures

based

on

Electron

diffraction)

descriptors.

They

are

derived

from

infra-red

spectra

simulation

using

a

generalized

scattering

function.

These

descriptors

are

defined

as

follows:

Mor(s,

w)

=

n



i

=2

i

−1



j

=1

w

i

w

j

sin(s

·

r

ij

)

(s

·

r

ij

)

(4)

where

w

and

r

ij

are

weight

(p

=

polarizability

and

v

=

Van

der

Waals

volume)

and

Euclidian

distance

between

i,

j

atoms,

respectively.

Morse

descriptors

also

referred

as

a

transformation

of

3D

struc-

tures,

in

which

atomic

3D

structures

could

be

transformed

into

the

molecular

descriptors.

• ATS3m

belongs

to

Broto-Moreau

Autocorrelation

Descriptors

[58]

.

It

reveals

the

distribution

of

the

relative

atomic

mass

along

the

topological

distance

of

3.

• G2m

and

G2p

are

2nd

component

of

symmetry

directional

WHIM

index

weighted

respectively

by

mass

and

polarizability

[59]

.

They

belong

to

WHIM

(weighted

holistic

invariant

molecular)

descrip-

tors

which

represent

holistic

view

of

the

molecule.

They

are

calculated

on

the

projection

of

atoms

along

principal

axes.

They

encode

information

about

shape,

molecular

size,

and

symmetry

and

atom

distribution

with

respect

to

invariant

frames.

• HATS2v

is

leverage-weighted

autocorrelation

of

lag

2/weighted

by

atomic

van

der

Waals

volumes

belong

to

HATS

descrip-

tors

which

itself

belong

to

the

larger

category

called

GETAWAY

(GEometry,

Topology

and

Atom-Weights

AssemblY)

descriptors

[60]

.

• R1p

is

R

autocorrelation

of

lag

1

weighted

by

atomic

polarizabil-

ities

[60]

.

• MWC05

is

a

molecular

walk

count

of

order

5

which

belongs

to

atomic

path/walk

topological

descriptors.

The

molecular

walk

count

is

related

to

the

molecular

branching

and

size

and

in

general

to

the

molecular

complexity

of

the

graph

[61]

.

• nCrs

refers

to

number

of

secondary

carbons

present

in

the

ring

structures.

• nCbH

refers

to

the

number

of

un-substituted

carbon

of

the

ben-

zene

ring.

• F02[N

O]

refers

to

frequency

of

N

O

at

the

topological

distance

of

2.

The

statistical

parameters

for

the

obtained

linear

model

are

pre-

sented

below

Eq.

(5)

.

where

n

trainiing

and

n

test

are

the

numbers

of

compounds

available

in

training

set

and

test

set,

respectively,

and

R

2

is

the

squared

correlation

coefficients

of

the

model.

SDE

is

stan-

dard

deviation

error

comparing

model

results

with

experimental

glass

transition

temperature

values.

One

of

the

important

outputs

of

the

derived

model

is

to

reveal

the

contribution

of

present

anions

and

cations

to

the

glass

tran-

sition

temperatures

in

terms

of

T

g,anion

and

T

g,cation

,

respectively.

All

T

g,cation

values

are

negative

and

vary

in

the

range

of

−221

to

−136

except

for

tetraphenylphosphonium

[P(ph)

4

]

+

which

has

the

positive

value

of

33.04.

It

is

not

surprising

that

the

ionic

liquid

associated

with

this

cation

has

highest

glass

transition

tempera-

ture

(T

g

=

433.15

K)

among

all

studied

ionic

liquids.

The

smallest

cation

contribution

belongs

to

pyrrolidinium-based

cations

with

the

average

value

of

−213.95.

It

is

not

surprising

that

all

pyrrolidinium-based

cations

have

the

lowest

negative

value

among

all

other

groups.

On

the

other

hand,

amino-acid

based

cations

with

the

average

of

−146.06

have

the

highest

negative

values

of

T

g,cation

.

Since,

ionic

liquids

with

low

glass

transition

temperature

is

highly

desirable,

the

Pyrrolidinium-

based

cations

would

be

preferred

to

the

others.

Unlike

T

g,cation

,

all

T

g,anion

values

are

positive.

(heptafluoro-n-propyl)

trifluorob-

orate

and

tetrakis

(3,5-bis(trifluoromethyl)phenyl)borate

anions

have

the

lowest

and

highest

values

of

T

g,anion

,

respectively.

To

tai-

lor

the

ionic

liquid

with

low

desired

glass

transition

temperature,

the

(heptafluoro-n-propyl)

trifluoroborate

([C

3

F

7

BF

3

]

−

)

anion

is

the

best

option

for

the

anion

part,

based

on

our

model.

Another

inter-

esting

output

of

our

model

is

to

determine

which

combination

of

cation

and

anion

present

in

our

study,

lead

to

the

ionic

liquid

with

lowest

glass

transition

temperature.

The

proposed

model

sug-

gests

that

the

combination

of

N-methylpyrrolidinium

([Hmpy]

+

)

cation

with

(heptafluoro-n-propyl)trifluoroborate

([C

3

F

7

BF

3

]

−

)

has

the

lowest

glass

transition

temperature

(T

g

=

156.2

K)

among

all

3182

possible

ionic

liquids

formed

by

the

combination

of

37

anions

and

86

cations

present

in

this

study.

5.

Validation

Validation

process

is

the

crucial

stage

for

the

assessment

of

the

model

stability

and

its

predictive

capability.

If

the

developed

model

stands

up

to

the

validation

scrutiny,

it

is

dubbed

as

“verified”

model

and

could

be

safely

employed

to

estimate

the

particular

properties.

The

various

validation

techniques

applied

in

this

study

described

as

follows:

5.1.

F-Test

F

is

the

F-ratio

which

is

defined

as

the

ratio

between

the

model

summation

of

squares

(MSS)

and

the

residual

summation

of

squares

(RSS)

[62]

:

F

=

MSS/df

M

RSS/df

E

(5)

where

df

M

and

df

E

denote

the

degree

of

freedom

of

the

obtained

model

and

the

overall

error

respectively.

It

is

a

comparison

between

the

model

explained

variance

and

the

residual

variance.

It

should

be

noted

that

high

values

of

the

F-ratio

test

indicate

the

reliability

of

models.

The

calculated

F-value

is

equal

to

73.31.

S.A.

Mirkhani

et

al.

/

Thermochimica

Acta

543 (2012) 88–

95

91

150

200

250

300

350

400

450

150

200

250

300

350

400

450

T

g

exp

(K)

T g

rep/pred

(K)

Training set
Test set

Fig.

1.

Experimental

glass

transition

values

versus

predicted

ones.

5.2.

LOO

(leave

one

out)

validation

technique

Leave-one-out

belong

the

most

common

and

extensively

used

validation

techniques

known

as

internal

validation.

Internal

or

cross-over

validation

techniques

based

on

partitioning

of

the

sam-

ple

data

into

two

different

subsets

one

serves

as

training

set

and

the

other

as

a

validation

set.

The

modified

training

set

was

generated

by

deleting

one

object

from

the

original

data

set.

For

each

reduced

data

set,

the

model

is

calculated

and

responses

for

the

deleted

object

were

calculated

from

the

model.

The

evaluated

leave-

one-out

cross

validation

parameter

of

the

obtained

linear

model

is

0.8559.

5.3.

Adjusted

R-squared

(R

2
adj

)

In

a

multiple

linear

regression

model,

adjusted

R

2

measures

the

proportion

of

the

variation

in

the

dependent

variable

accounted

for

by

the

explanatory

variables.

Unlike

R

2

,

adjusted

R

2

allows

for

the

degrees

of

freedom

associated

with

the

sums

of

the

squares.

Therefore,

even

though

the

residual

sum

of

squares

decreases

or

remains

the

same

as

new

explanatory

variables

are

added,

the

residual

variance

does

not.

For

this

reason,

adjusted

R

2

is

gen-

erally

considered

to

be

a

more

accurate

goodness-of-fit

measure

than

R

2

.

R

2
adj

=

1

−

(1

−

R

2

)



n

−

1

n

−

p





(6)

where

n

and

p



are

the

numbers

of

experimental

values

and

the

model

parameters,

respectively.

The

less

difference

between

this

value

and

the

R

2

parameter,

the

more

validity

of

the

model

would

be

expected.

The

evaluated

adjusted-R

2

parameter

of

the

obtained

linear

model

is

0.8775.

5.4.

RQK

validation

technique

In

lieu

of

avoiding

chance

correlations

in

the

model

and

improved

its

prediction,

Todeschini

et

al.

[63]

proposed

4

RQK

con-

straints

which

must

be

completely

satisfied

[12,64–72]

:

1.

K

=

K

XY

−

K

X

>

0

(quick

rule)

2.

Q

=

Q

2

LOO

−

Q

2

ASYM

>

0

(asymptotic

Q

2

rule)

150

200

250

300

350

400

450

−20

−15

−10

−5

0

5

10

15

T

g

exp

(K)

Relative Deviation %

Training set

Test set

Fig.

2.

Relative

deviation

of

the

model

prediction

versus

experimental

values

of

glass

transition

temperatures.

3.

R

P

>

0

(redundancy

RP

rule)

4.

R

N

>

0

(over-fitting

PN

rule)

The

calculated

values

of

RQK

test

are

presented

as

follows:

K

x

=

0.4264,

K

xy

=

0.4633,

K

=

0.037,

Q

=

0.006,

R

P

=

0.007

and

R

N

=

0.

These

values,

calculated

according

to

standard

procedures

[64]

,

are

non-negative,

which

supports

the

validity

of

the

model

and

the

lack

of

chance

correlation.

5.5.

Bootstrap

validation

technique

[73]

The

bootstrap

approach

was

applied

to

verify

robustness

and

internal

prediction

power

of

the

model.

In

this

method,

K

n-

dimensional

groups

are

generated

by

a

repeated

random

selection

of

n-chemicals

from

the

original

data

set

(K

=

300

and

n

=

139).

The

model

obtained

on

the

first

selected

chemicals

is

used

to

predict

the

values

for

the

excluded

compounds

and

then

Q

2

is

calculated

for

each

model.

The

bootstrapping

was

repeated

5000

times,

in

this

study.

Consequently,

the

value

Q

2

boot

parameter

of

the

obtained

model

has

been

evaluated

to

be

0.7992.

5.6.

y-Scrambling

validation

technique

[74]

The

objective

of

this

approach

is

to

assure

the

developed

model

is

not

to

be

a

chance

correlation.

For

this

purpose,

all

responses

variable

are

shuffled

randomly

without

any

changes

in

the

pre-

dictors

set.

If

the

prediction

power

of

the

model

in

terms

of

R

2

or

Q

2

does

not

change

significantly,

then

the

validity

of

the

model

is

disputable.

The

y-scrambling

parameter

is

the

intercept

of

the

following

equation:

Q

2

k

=

a

+

br

k

(y, ˜y

k

)

(7)

where

Q

2

k

k

is

the

explained

variance

of

the

model

obtained

using

the

same

predictors

but

the

kth

y-scrambled

vector;

r

k

is

the

cor-

relation

between

the

true

response

vector

and

the

kth

y-scrambled

vector.

The

numerical

value

of

the

intercept

a

is

a

criteria

for

assess-

ing

of

the

model

if

it

is

a

chance

correlation

or

not.

The

numerical

92

S.A.

Mirkhani

et

al.

/

Thermochimica

Acta

543 (2012) 88–

95

Table

2

Experimental

and

predicted

values

of

glass

transition

temperature

of

the

studied

ionic

liquids.

No.

Group

Abbreviation

Error,

T

g

(K)

T

g

T

pred

g

ARD%

Status

Reference

1

Phosphonium

[P666,2][Ace]

200.15

197.68

1.234074

Training

[17]

2

Phosphonium

[P666,3][Ace]

201.15

199.66

0.740741

Test

[17]

3

Tri-alkyl

imidazolium

[hmmim][TFSI]

199

208.06

4.552764

Training

[18]

4

Phosphonium

[P666,14][C(CN)3]

208.15

210.44

1.100168

Training

[19]

5

Phosphonium

[P444,14][TFSI]

213.15

203.75

4.41004

Test

[19]

6

Phosphonium

[P(ph)4][TFSI]

433.15

409.44

5.473854

Training

[19]

7

Pyrrolidinium

[P14][NfO]

194.15

185.96

4.218388

Test

[20]

8

Triazolium

[Bt14][dca]

208.15

218.38

4.914725

Training

[21]

9

Triazolium

[Bt14][mesy]

235.15

226.52

3.669998

Test

[21]

10

Triazolium

[Bt1Bn][TFSI]

246.15

253.59

3.022547

Training

[21]

11

Triazolium

[Bt1Bn][dca]

239.15

242.93

1.580598

Training

[21]

12

Triazolium

[Bt1Bn][mesy]

261.15

247.93

5.062225

Training

[21]

13

Tri-alkyl

imidazolium

[P1M2,3IM][TFSI]

191.15

208.86

9.264975

Training

[22]

14

Tri-alkyl

imidazolium

[BDMIM][BF4]

205.15

210.11

2.417743

Training

[22]

15

Tri-alkyl

imidazolium

[BDMIM][PF6]

215.15

210.65

2.091564

Training

[22]

16

Guanidinium

[(MeBu)N

(Me2Taz)][NO3]

204.15

210.39

3.056576

Test

[23]

17

Guanidinium

[(MeBu)N

(Me2Taz)][N(NO2)2]

207.15

211.83

2.259232

Test

[23]

18

Pyrrolidinium

[P12][mesy]

2

167.15

184.98

10.66707

Training

[24]

19

Pyrrolidinium

[P13][mesy]

2

201.15

183.77

8.640318

Training

[24]

20

Pyrrolidinium

[P14][mesy]

2

205.15

183.71

10.45089

Training

[24]

21

Morpholinium

[MO][(CF3CO)CH(COCH3)]

285.15

233.92

17.96598

Training

[25]

22

Morpholinium

[MO][(CF3CO)2CH]

211.15

240.02

13.67274

Test

[25]

23

Morpholinium

[MO][(Me3CCO)CH(CO(CF2)2CF3)]

235.15

250.11

6.361897

Training

[25]

24

Morpholinium

[MO][(CF3CO)CH(COfuran)]

225.15

247.4

9.882301

Test

[25]

25

Morpholinium

[MO1,2O2][NTf2]

220.15

216.18

1.803316

Training

[26]

26

Morpholinium

[MO1,2O5][NTf2]

219.15

217.36

0.816792

Training

[26]

27

Guanidinium

[C27guan][TFSI],

[((C6H13)2N)2C

NMe2][TFSI]

201.04

202.2

0.577

Test

[27]

28

Guanidinium

[((C6H13)2N)2C

NMe2][dca]

195.97

192.27

1.888044

Training

[27]

29

Guanidinium

[((C6H13)2N)2C

NMe2][TfO]

194.44

201.64

3.702942

Training

[27]

30

Guanidinium

[((C6H13)2N)2C

NMe2][Tos]

203.25

197.09

3.03075

Test

[27]

31

Guanidinium

[((C6H13)2N)2C

NMe2][CF3CO2]

192.49

196.68

2.176736

Training

[27]

32

Guanidinium

Dimethyl-ammonium

thiocyanate

200.72

181.73

9.460941

Training

[27]

33

Pyrrolidinium

[P14][dca]

2

167.15

176.49

5.587795

Training

[28]

34

Pyrrolidinium

[P16][dca]

2

173.15

174.39

0.716142

Training

[28]

35

Pyrrolidinium

[P13][TFSI]

2

183.15

185.85

1.474201

Training

[29,32]

36

Pyrrolidinium

[P12][TFSI]

171.15

185.87

8.600643

Training

[29]

37

1-Alkyl

imidazolium

[C1Im][OAc]

175.15

196.52

12.20097

Test

[30]

38

1-Alkyl

imidazolium

[C1Im][HCO2]

174.15

189.92

9.055412

Training

[30]

39

Pyrrolidinium

[Hmpy][OAc]

165.15

169.17

2.434151

Training

[30]

40

Pyrrolidinium

[Hmpy][HCO2]

157.15

159.91

1.756284

Training

[30]

41

Piperidinium

[PP13][TSAC]

190.15

195.57

2.850381

Training

[31]

42

Piperidinium

[PP1.1O1][TFSI]

188.15

185.61

1.349987

Training

[31]

43

Piperidinium

[PP1.1O2][TFSI]

182.15

197.15

8.234971

Training

[31]

44

Piperidinium

[PP1.1O2O2][TFSI]

191.15

212.55

11.1954

Training

[31]

45

Triazolium

1-Methyl-4-(3,3,3-trifluoropropyl)-

215.15

212.36

1.29677

Training

[33]

46

Triazolium

[C4(CH2)2CF3Taz][NTf2]

206.15

205.07

0.52389

Training

[33]

47

Triazolium

[C7(CH2)2CF3Taz][NTf2]

206.15

210.85

2.279893

Training

[33]

48

Triazolium

[C10(CH2)2CF3Taz][NTf2]

205.15

206.53

0.672679

Training

[33]

49

Triazolium

[C7C2FTaz][NTf2]

203.15

212.35

4.528673

Training

[33]

50

Triazolium

[C10C2FTaz][NTf2]

211.15

210.96

0.089983

Training

[33]

51

Triazolium

[C7CF3CH(OH)CH2Taz][NTf2]

221.45

211.49

4.497629

Training

[34]

52

Triazolium

[C10CF3CH(OH)CH2Taz][NTf2]

225.95

208.12

7.891126

Training

[34]

53

Triazolium

[C4(CH2)2CF

CF2Taz][NTf2]

250.75

219.99

12.2672

Test

[34]

54

Triazolium

[C7(CH2)2CF

CF2Taz][NTf2]

216.75

217.35

0.276817

Training

[34]

55

Triazolium

[C4CO(CF2)3COOH][TfO]

205.45

209.39

1.917742

Training

[34]

56

Tri-alkyl

imidazolium

[Em2Im][ba]

207.77

201.26

3.133272

Training

[35]

57

Tri-alkyl

imidazolium

[BM2Im][ba]

202.69

203.6

0.448961

Training

[35]

58

Tri-alkyl

imidazolium

[DMPIM][TFSI]

191.15

209.55

9.625948

Training

[36]

59

Isoquinolinium

[C12isoq][TFPB]

253.15

243.55

3.792218

Training

[37]

60

Isoquinolinium

[C18isoq][TFPB]

248.15

267.92

7.966955

Training

[37]

61

Tri-alkyl

imidazolium

[AcrylateC6MEIm][NTf2]

205.15

207.29

1.043139

Training

[38]

62

Pyrrolidinium

[PY2,AcrylateC6][TFSI]

196.15

190.66

2.798878

Training

[38]

63

Piperidinium

[AcylateC6MPiPer][NTf2]

207.15

194.94

5.89428

Training

[38]

64

1-Alkyl

imidazolium

[C2Im][ClO4]

192.15

213.85

11.29326

Test

[39]

65

1-Alkyl

imidazolium

[C2Im][BF4]

186.15

208.87

12.20521

Training

[39]

66

1-Alkyl

imidazolium

[C2Im][BETI]

187.15

194

3.660166

Training

[39]

67

1-Alkyl

imidazolium

[C2Im][PF6]

211.15

208.26

1.368695

Training

[39]

68

Phosphonium

[P666,4][Ace]

202.15

201.22

0.460054

Test

[40]

69

Phosphonium

[P6666][Ace]

207.15

203.4

1.810282

Training

[40]

70

Phosphonium

[P666,7][Ace]

204.15

201.12

1.484203

Training

[40]

71

Phosphonium

[P666,8][Ace]

203.15

205.17

0.994339

Training

[40]

72

Phosphonium

[P666,10][Ace]

203.15

199.91

1.594881

Test

[40]

73

Phosphonium

[P666,12][Ace]

201.15

197.99

1.570967

Training

[40]

74

Phosphonium

[P666,16][Ace]

203.15

195.13

3.947822

Training

[40]

S.A.

Mirkhani

et

al.

/

Thermochimica

Acta

543 (2012) 88–

95

93

Table

2

(Continued)

No.

Group

Abbreviation

Error,

T

g

(K)

T

g

T

pred

g

ARD%

Status

Reference

75

Pyrrolidinium

[P1,8][NTf2]

192.15

186.47

2.956024

Training

[41]

76

Piperidinium

[PP14][TFSI]

200.15

194.73

2.707969

Test

[41]

77

Piperidinium

[PP1,8][NTf2]

197.15

193.82

1.689069

Training

[41]

78

Triazolium

[EtOHNH2Taz][N3]

223.15

209.37

6.175218

Training

[42]

79

Triazolium

[AllylNH2Taz][N3]

216.15

211.75

2.035623

Training

[42]

80

Triazolium

[NH2AllylTaz][N3]

211.15

208.92

1.056121

Training

[42]

81

Pyrrolidinium

[P13][TFSI]

2

182.15

185.71

1.954433

Test

[43]

82

Amino

acids

[GlyC1][NO3]

247.15

249.12

0.797087

Test

[44]

83

Amino

acids

[AlaC1][NO3]

239.15

240.7

0.648129

Training

[44]

84

Amino

acids

[AlaC1][Ace]

250.15

248.13

0.807515

Test

[44]

85

Amino

acids

[AlaC1][PF6]

238.15

256.6

7.747218

Training

[44]

86

Amino

acids

[AlaC1][L-lactate]

249.15

247.06

0.838852

Training

[44]

87

Amino

acids

[AlaC1][SCN]

241.15

235.95

2.156334

Test

[44]

88

Amino

acids

[SerC1][NO3]

243.15

241.86

0.530537

Training

[44]

89

Amino

acids

[AlaC2][L-lactate]

244.15

240.85

1.351628

Training

[44]

90

Amino

acids

[ValC1][NO3]

240.15

233.11

2.931501

Training

[44]

91

Amino

acids

[Leu][NO3]

242.15

228.39

5.682428

Training

[44]

92

Amino

acids

[PheC1][NO3]

241.15

242.26

0.460294

Training

[44]

93

Isoquinolinium

[C8isoq][BETI]

193.75

204.85

5.729032

Training

[45]

94

Isoquinolinium

[C10isoq][BETI]

195.35

201.23

3.009982

Test

[45]

95

Isoquinolinium

[C12isoq][BETI]

197.15

200.03

1.460817

Training

[45]

96

Isoquinolinium

[C14isoq][BETI]

206.45

200.8

2.73674

Training

[45]

97

Isoquinolinium

[C16isoq][BETI]

211.35

202.56

4.158978

Test

[45]

98

Isoquinolinium

[C18isoq][BETI]

213.85

209.47

2.048165

Training

[45]

99

Isoquinolinium

[C8isoq][BETI]

218.15

202.87

7.004355

Training

[45]

100

Pyrrolidinium

[P14][BOB]

235.35

196.52

16.49883

Training

[46]

101

Triazolium

[MeNH2Taz][NO3]

213.15

198.93

6.671358

Training

[47,49]

102

Triazolium

[HN3Taz][Ntet]

238.15

234.05

1.721604

Training

[48]

103

Triazolium

[Me2Taz][ClO4]

239.15

209.9

12.23082

Training

[49]

104

Triazolium

[(CH2)2N3C1Taz][ClO4]

221.15

228.35

3.255709

Training

[50]

105

Triazolium

[(CH2)2N3C1Taz][NO3]

216.15

208.7

3.446681

Training

[50]

106

Triazolium

[N3(CH2)2Taz][ClO4]

217.15

226.78

4.434723

Training

[50]

107

Triazolium

[N3(CH2)2N3Taz][NO3]

219.15

210.44

3.974447

Training

[50]

108

Triazolium

[N3(CH2)2NH2Taz][ClO4]

227.15

228.16

0.44464

Training

[50]

109

Morpholinium

[HEMMor][BF4]

2

214.15

219.36

2.432874

Training

[51]

110

Morpholinium

[HEMMor][TFSI]

2

223.15

221.18

0.882814

Training

[51]

111

Phosphonium

[(C4H9)4P][Gly]

198.33

202.89

2.299198

Training

[52]

112

Phosphonium

[(C4H9)4P][Ala]

197.66

214.36

8.448852

Training

[52]

113

Phosphonium

[(C4H9)4P][Lys]

208.01

224.73

8.038075

Training

[52]

114

Triazolium

[Bt24][BF4]

218.15

221.69

1.622737

Training

[53]

115

Pyrrolidinium

[PY1,1O2][BF4]

180.15

184.85

2.608937

Test

[54]

116

Pyrrolidinium

[PY1,1O2][TFSI]

182.15

187.31

2.83283

Training

[54]

117

Piperidinium

[PP1.1O2][BF4]

196.15

193.21

1.498853

Training

[54]

118

Piperidinium

[PP1.1O2][TFSI]

191.15

196.25

2.668062

Training

[54]

119

Piperidinium

[PP1.1O2][C3F7BF3]

181.15

176.41

2.616616

Training

[54]

120

Piperidinium

[PP14][TFSI]

196.15

194.73

0.723936

Test

[54]

121

Morpholinium

[MO1,4][TFSI]

213.15

217.66

2.115881

Test

[54]

122

Morpholinium

[MO1,4][CF3BF3]

199.15

204.6

2.736631

Training

[54]

123

Morpholinium

[MO1,4][C2F5BF3]

200.15

204.41

2.128404

Test

[54]

124

Morpholinium

[MO1,1O2][BF4]

215.15

217.51

1.096909

Training

[54]

125

Morpholinium

bis((trifluoromethyl)sulfonyl)imide

207.15

220.18

6.290128

Training

[54]

126

Morpholinium

[MO1,1O2][C2F5BF3]

195.15

206.9

6.021009

Training

[54]

127

Morpholinium

[MO1,1O2][C3F7BF3]

198.15

200.98

1.428211

Training

[54]

128

Oxazolidinium

[OX14][BF4]

198.15

196.87

0.645975

Training

[54]

129

Oxazolidinium

[OX14][TFSI]

197.15

199.57

1.227492

Training

[54]

130

Oxazolidinium

[OX1,1O2][BF4]

203.15

200.36

1.373369

Training

[54]

131

Oxazolidinium

[OX1,1O2][TFSI]

200.15

203.38

1.61379

Training

[54]

132

Oxazolidinium

[OX1,1O2][CF3BF3]

187.15

189.67

1.346513

Test

[54]

133

Oxazolidinium

[OX1,1O2][C2F5BF3]

185.15

190.36

2.813935

Training

[54]

134

Oxazolidinium

[OX1,1O2][C3F7BF3]

189.15

183.34

3.071636

Training

[54]

135

Oxazolidinium

[OX1,1O2][C4F9BF3]

191.15

188.68

1.292179

Training

[54]

136

Guanidinium

[C19guan][BF4],

[((C4H9)2N)2C NMe2][BF4]

215.45

214.91

0.250638

Training

[55]

137

Guanidinium

[C27guan][BF4],

[((C6H13)2N)2C

NMe2][BF4]

197.55

200.21

1.346495

Training

[55]

138

Guanidinium

[C27guan][TFSI],

[((C6H13)2N)2C

NMe2][TFSI]

201.75

202.22

0.232962

Training

[55]

139

Guanidinium

[C35guan][BF4],

[((C8H17)2N)2C

NMe2][BF4]

197.85

192.12

2.896133

Training

[55]

values

close

to

zero

verify

that

the

model

is

not

a

chance

correla-

tion.

In

other

hand,

the

large

values

cast

doubt

on

the

validity

of

model

and

interpret

the

model

as

unstable,

chance

correlation.

The

y-scrambling

should

be

repeated

hundreds

of

times

(in

this

work

300

times).

The

value

of

intercept

a

has

been

calculated

as

0.061

for

the

developed

linear

model.

5.7.

External

validation

technique

External

validation

technique

is

conducted

by

testing

addi-

tional

compound

for

validation

set

in

order

to

assess

the

prediction

capability

of

the

model.

The

Q

2

ext

demonstrated

as

follows

[75]

:

94

S.A.

Mirkhani

et

al.

/

Thermochimica

Acta

543 (2012) 88–

95

Q

2

ext

=

1

−



n

test

i

=1

(



y

i/i

−

y

i

)

2



n

test

i

=1

(y

i

− ¯y

training

)

2

(8)

where ¯y

training

is

the

average

value

of

the

glass

transition

temper-

ature

of

the

compounds

present

in

training

set, ˆy

i/i

is

response

of

ith

object

predicted

by

the

obtained

model

ignoring

the

value

of

the

related

object

(ith

experimental

glass

transition

temperature).

The

less

difference

between

this

value

and

the

R

2

parameter,

the

more

validity

of

the

model

would

be

expected.

The

evaluated

Q

2

ext

parameter

of

the

obtained

linear

model

is

0.8449.

Ultimately,

all

the

validation

techniques

demonstrate

the

final

model

as

valid,

stable,

non-chance

correlation

with

high

predictive

power.

Fig.

1

depicts

the

predicted

glass

transition

temperature

val-

ues

versus

the

experimental

ones.

As

it

is

obvious

in

this

figure

the

majority

of

points

are

located

in

the

vicinity

of

bisection.

This

indicates

the

acceptable

accuracy

of

the

prediction.

Relative

errors

of

the

predicted

glass

transition

temperature

val-

ues

in

comparison

with

experimental

ones

are

portrayed

in

Fig.

2

.

As

it

is

shown

in

this

figure,

the

relative

errors

of

the

majority

of

points

lie

in

0–3%

interval

which

indicated

acceptable

prediction

error.

The

ionic

liquids

abbreviations,

predicted

glass

transition

values

and

the

prediction

are

tabulated

in

Table

2

.

More

complete

table

including

data

of

Table

2

and

the

calcu-

lated

model

descriptors

for

all

ionic

liquids

is

available

through

Supplementary

material

.

The

highest

error

of

prediction

belongs

to

morpholinium

1,1,1-trifluoro-2,4-pentanedionate

with

17.96%.

The

lowest

error

reported

in

our

study

is

0.089%

for

1-decyl-4-(1-fluoroethyl)-1,2,4-

triazolium

bis((trifluoromethyl)sulfonyl)imide.

The

groups

of

1-alkyl

imidazolium

and

oxazolidinium

ionic

liq-

uids

have

the

highest

and

lowest

prediction

error

with

8.29%

and

1.67%

respectively.

6.

Conclusion

In

this

study,

a

QSPR

model

was

presented

for

prediction

of

the

glass

transition

temperature

of

several

ionic

liquids.

The

pro-

posed

model

is

a

multivariate

linear

one

involving

eleven

variables

(molecular

descriptors),

which

has

been

developed

based

on

the

experimental

data

of

139

ionic

liquids.

The

molecular

descriptors

were

selected

using

GFA

technique

and

are

calculated

based

on

the

SMILE

structure

of

ionic

liquids.

The

obtained

results

show

that

the

presented

model

is

simple,

and

accurate.

Appendix

A.

Supplementary

data

Supplementary

data

associated

with

this

article

can

be

found,

in

the

online

version,

at

http://dx.doi.org/10.1016/j.tca.2012.05.009

.

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