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:

 

fghara@gmail.com

,

 

fghara@ut.ac.ir

 

(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]

: