Characterization of Functionalized Side-Chain Liquid Crystal

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Characterisation of functionalized side-chain liquid crystal methacrylates containing non-mesogenic units by dielectric spectroscopy Alfonso Martinez-Felipe, Laura Santonja-Blasco, Jose David Badía, Corrie Thomas Imrie, and Amparo Ribes-Greus Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/ie3031339 • Publication Date (Web): 04 Jan 2013 Downloaded from http://pubs.acs.org on January 10, 2013

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Industrial & Engineering Chemistry Research

Characterisation of functionalized side-chain liquid crystal methacrylates containing non-mesogenic units by dielectric spectroscopy A. Martínez-Felipea, L. Santonja-Blascoa; J.D. Badíaa, C.T. Imrieb, and A. Ribes-Greusa* a

Instituto de Tecnología de los Materiales (ITM), Universitat Politècnica de València

Camino de Vera S/N, 46022 Valencia, Spain b

Department of Chemistry, School of Natural and Computing Sciences, University of Aberdeen, Meston

Walk, Aberdeen AB24 3UE, UK *Corresponding author: [email protected] Abstract The dielectric response of a series of side-chain liquid crystal copolymers, SCLCPs, the poly[6-(4’methoxyazobenzene-4’-oxy)hexyl

methacrylate]-co-poly[methyl -2

methacrylate]s,

MeOAzB/MMA

7

copolymers, is presented in the frequency range f = 10 to 10 Hz and over the temperature interval T = 150ºC to 120ºC. The relaxation spectra of these polymers have been studied in terms of the complex dielectric permittivity (ε’ and ε’’) and the dielectric loss tangent, tan(δ).The electric modulus, M* has been also calculated. It is possible to distinguish two relaxations zones, one at low temperatures (including γ and β relaxations) and another at higher temperatures (including the α and β1 relaxations), all of them reported for liquid crystalline poly(methacrylate)s. The individual relaxations have been analysed using Havriliak-Negami (HN) functions and the effect of conductivity at high temperatures is subtracted. The thermal activation of the relaxations at low temperatures is studied using the Arrhenius equations as a function of copolymer composition while the α and β1 relaxations are analysed using Vogel-TammannFulcher equations. The activation entropy has been also evaluated for all the relaxations through the Eyring equation. The temperature ranges, activation energies and entropies of the relaxations at low temperatures (γ and β) are similar in the homopolymer and copolymers. However, the introduction of MMA units promotes variations in all the parameters related to the relaxations associated to the motions of the ester groups adjoining the polymer backbone. Specifically, a decrease is observed in the activation entropy values of the β1 relaxation, which suggests that the activation of the local motions of the side groups involves smaller cooperative regions in the copolymers with respect to the homopolymer. This fact may account for the extinction of the smectic behaviour, together with the dilution of the anisotropic interactions between the mesogenic units on increasing MMA content. The study of this β1 relaxation can be then applied to anticipate the formation and stability of smectic phases in functionalised SCLCPs, by controlling the local mobility resulting in different mesogenic behaviour. Keywords: Side Chain Liquid Crystal Copolymers; complex dielectric spectra; poly(methyl methacrylate)

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1. Introduction Side chain liquid crystal polymers, SCLCPs, are of fundamental interest and have technological potential as self-assembling and externally controllable materials, due to the combination of mesomorphism and macromolecular properties, such as electro-optic response, glass behaviour and film formation1. SCLCPs consist of three basic units: a liquid crystal or mesogenic group, a polymer backbone and a flexible alkyl spacer connecting them. The liquid crystalline behaviour originates from the ability of the flexible spacer to decouple the anisotropic interactions between the mesogenic units from the tendency of the polymer backbone to form random-coil conformations1. In addition, the introduction of non-mesogenic units along the backbone by radical polymerisation permits the rational design of SCLCPs having different functionalities2-21. To realise this potential, the effect of the non-mesogenic units on the transitional properties of side-chain poly(methacrylate)s must be investigated as a function of the mesogenic group, the length of the flexible spacers or the nature of the end groups22-28. In general, the changes in phase behaviour on introducing non-mesogenic acrylates, methacrylates or ionogenic groups into a SCLCP may be explained by enthalpic and entropic effects2, 3, 22, 24, 26, 28. The potential to control the morphology of SCLCPs relies on the possibility of orienting the mesogenic groups. Therefore, molecular mobility is the root of their functionality, and indeed, of their final liquid crystal behaviour. The present work studies the molecular relaxations of a series of poly[6-(4’-methoxyazobenzene4’-oxy)hexyl methacrylate]-co-poly[methyl methacrylate]s, the MeOAzB/MMA copolymers, (Scheme 1), using dielectric spectroscopy (DS) over broad range of temperatures and frequencies below their clearing points, Tcl. The methyl methacrylate units, MMA, modify the temperature range of the smectic and nematic phases in these copolymers, and at sufficiently high concentrations the liquid crystalline behaviour is extinguished22. It is envisaged that the present study will provide new insights regarding molecular mobility and its effect on the formation of mesophases in comb-shape poly(methacrylate)s. Concretely, the motions of the ester bonds in the MMA and the mesogenic (MeOAzB) units will be examined with the aim to optimise the chemical architecture of new functional SCLCPs.


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O H3C

O

(CH 2)6

O

N

N

OCH 3

CH2 x O H3C

O

CH3

CH2 1-x

Scheme 1. MeOAzB/MMA copolymers



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2. Materials and experimental procedure The MeOAzB/MMA copolymers were obtained by radical polymerisation of the commercial monomer

methyl(methacrylate),

MMA,

and

6-(4-methoxy-4’-oxy-azobenzene)

methacrylate, MeOAzB, which was synthesised according to

decyl

22, 29-32

. The corresponding amounts

of the monomers were dissolved in dimethyl formamide (10%, weight %) using 1,1’azobis(cyclohexane carbonitrile) as the initiator (~3% molar). The reaction mixtures were flushed with nitrogen for 45 min and then heated at 80ºC in the absence of oxygen, to initiate the polymerisations, which were terminated after 24 h by precipitation into methanol. The polymers were then purified by several reprecipitations from dichloromethane into methanol. Copolymers are designated as XMeOAzB/MMA, in which X is the experimentally determined mole fraction of the MeOAzB (mesogenic) side chains. This was measured by means of 1HNMR spectroscopy and specifically using the relative ratios of the peaks at 7.9 ppm (aromatic protons, 4H) and 3.6 ppm (protons from the alpha CH3 group in the main chain, 3H)22. The thermal behaviour was analysed by differential scanning calorimetry, using a Mettler Toledo DSC 822e analyser (Columbus, OH, USA) on samples of around 5 mg. The thermal transitions were evaluated from thermograms obtained on heating scans at 10 K·min-1 under nitrogen atmosphere, after removal of the thermal history. The dielectric spectra (DS) of the MeOAzB homopolymer and the MeOAzB/MMA copolymers were obtained using an alpha mainframe frequency analyser in conjunction with an active cell (Concept 40, Novocontrol Technologies BmgH & Co. Kc, Hundsangen, Germany). The response was measured in the frequency range f = 10-2 - 107 Hz, at temperatures between T = 150ºC and 120ºC, controlled by the Quatro system (Novocontrol Technologies BmgH & Co. Kc, Hundsangen, Germany). The spectra were obtained under isothermal conditions, by increasing steps of 10ºC, starting from the lowest temperature (T=-150ºC). The sample electrode assembly (SEA) consisted of two stainless steel electrodes filled with the polymer at above the clearing temperature. The diameters of the electrodes were 20 mm and the thickness was kept around 300 µm. The SEA was placed in the cell and, prior to each experiment, heated to temperatures above their glass transition (T > 85ºC) to remove thermal history. Several variables were applied to study the dielectric behaviour of the MeOAzB/MMA copolymers. The analysis was conducted essentially through the complex dielectric permeability,

ε* (Eq. 1), taking into account the real and imaginary parts, as well as tan(δ) (Eq. 2): 4 ACS Paragon Plus Environment

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ε* = ε’-iε’’ (Eq. 1) tan(δ ) =

ε '' (Eq.2) ε'

where ε’ and ε’’ are the real and imaginary parts of the dielectric permittivity. At temperatures above the glass transition, Tg, ohmic conduction due to charge carriers, σ* (Eq. 3), frequently dominates the loss contribution (ε’’), potentially masking dielectric relaxations. In order to discriminate polarisation and conductive effects, the electric modulus, M* (Eq. 4), the logarithmic derivative of ε’, εder (Eq. 5), were also obtained33-37:

σ * = ε *·e0 ·ω = σ '+iσ ' ' (Eq. 3) M * = 1/ ε * =

1 ε' ε '' = 2 +i 2 = M '+iM ' ' 2 ε '−iε ' ' ε ' +ε ' ' ε ' +ε ' '2

ε der = −

π ∂ε ' 2 ∂ ln ω

(Eq. 4)

(Eq. 5)

where ε0 is the permittivity of free space (8.85·10-12 F·m-1) and ω the frequency in rad·s-1. The conduction-free dielectric loss, ε’’NC, was also determined by Eq. 6 38:

ε ' ' NC = ε ' '−

σ0 (Eq.6) ε 0 2πf S

with f the frequency in Hertz, σ0 a pre-exponential coefficient, and an exponent, S, normally close to 1. The data were deconvoluted considering the additive character of the dielectric response ( ε * = ε 1* + ε 2* + ε 3* + ... + ε k* ) and the ε* curves were fitted using several Havriliak-Negami (HN) functions (Eq. 7) 33, 39, 40:



ε * −ε ∞ = ∑  k

{

∆ε

 1 + (iwτ HNk )α k

}

βk

  

(Eq. 7)



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where αk and βk are parameters corresponding to the width and asymmetry of the relaxation time distributions, respectively; τHN is the Havriliak-Negami relaxation time and ∆ε = εS – ε∞ the dielectric strength (with εS and ε∞ are the real part of the permittivity when ω0 and ω∞, respectively). The sub index k represents the number of the individual HN contributions, which can vary from k =1 to 3, depending on the complexity of the ε’’ curve at any given temperature. The relaxation times and frequencies (fmax = 1/τmax) of the NH individual ε* curves were calculated according to Eq. 8 39:

τ max

  π (α NH ) β NH     sin  2( β NH + 1)     =τ HN   π (α NH )      sin   2( β NH + 1)   

1

α NH

(Eq.8)

The thermal activation of the dielectric phenomena was analysed in Arrhenius maps using the maxima temperature of the relaxations at each frequency, described by either linear (Eq. 9) or Vogel-Tammann-Fulcher (VTF, Eq. 10) behaviour 41-44:

 − Ea  f max = f0 exp   R·T 

 −B f max = f 0 exp  T − T∞

(Eq. 9)

  

(Eq. 10)

where Ea is the apparent activation energy, f0 is a pre-exponential term, B is related to the free volume and T∞ is the Vogel temperature below which polymeric segments become immobile

42-

44

.

Finally, the activation entropy contribution of the relaxations was also evaluated by the Eyring equation, Eq. 11 45-47:

f   k  ∆S ∆H 1 ln max  = ln B  + − · R T  2πh  R  T 

(Eq. 11)


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with h=6.63·10-34 J·s and kB=1.38·10-23 J·K-1 the Planck and Boltzmann constants, respectively, and ∆S, ∆H and ∆G the activation entropy, enthalpy and free energy of the relaxation, respectively.

3. Results and discussion 3.1 Calorimetric transitions The liquid crystalline homopolymer (MeOAzB) and 0.90MeOAzB/MMA show both smectic and nematic phases. Smectic behaviour is extinguished on further increasing the MMA content which also promotes reductions in both the clearing point, Tcl, and glass transition temperature, Tg. At sufficiently low concentrations of mesogenic units, 0.22MeOAzB/MMA, the copolymer is amorphous, with lower Tg than PMMA, due to the plasticising effect of the introduction of side chains, see Table 1 22.

Table 1. Composition and thermal properties of the polymers under study Sample

Tg/ºC

TSmA/ºC

TNI/ºC

MeOAzB

80

89

135

0.90MeOAzB/MMA

85

95

128

0.76MeOAzB/MMA

73

0.22MeOAzB/MMA

76

PMMA

123

110

3.2 Dielectric response of poly[6-(4’-methoxyazobenzene-4’-oxy)hexyl methacrylate] homopolymer, MeOAzB The

dielectric

spectrum

of

the

6-(4-methoxyazobenzene-4’-oxy)hexyl

methacrylate]

homopolymer, MeOAzB, contains the γ, β, β1 and α relaxations typical of comb-shaped poly(methacrylate)s 48-57, which have been schematically summarised in Figure 1.



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α δ

H3C

H3C CH2

CH2

1-x

O

O

O

O CH3

x

γ

β

β1(b)

β1(c)

O

N

N

O CH3

Figure 1. Relaxation modes for the MeOAzB/MMA copolymers. Figures 2 and 3 show the γ and β relaxations in the ε’, tan(δ) and ε’’ curves at low temperatures. These processes appear overlapped in the -150ºC ≤ T ≤ -20ºC temperature range within the experimental frequencies. The corresponding ε* curves were deconvoluted by using two Havriliak-Negami (HN) terms in Eq.7, and the individual relaxation times have been obtained using Eq. 8. The Arrhenius plots corresponding to the γ and β relaxations (see Figure 3b) are linear, according to the non-cooperative nature of the local motions involved58. The experimental results were fitted to Eq. 9 and the corresponding parameters calculated and listed in Table 2, being in excellent agreement with those reported previously for other comb-shaped poly(methacrylates)

48-57

. A value of Ea(γ) = 33.1 kJ·mol-1 was obtained, confirming the

assignment of this process to the motions of the six methylene spacer49. For the β relaxation, a value of Ea(β) = 60.5 kJ·mol-1 was obtained. This is in the typical range for molecular motions associated to the perpendicular component of the permanent dipole moment of the rigid rod-like (mesogenic) unit along its director axis, µ┴, in side-chain liquid crystal polymethacyrlates and polyacrylates, see Figure 1 48-50.


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log ε’

tan (δ)

a

0.6

b

-1.6

T=-20ºC T=-30ºC

-1.8

β

γ

T=-40ºC T=-50ºC

-2

0.55

T=-60ºC T=-70ºC T=-80ºC

-2.2

T=-90ºC T=-100ºC

-2.4

T=-110ºC

0.5

T=-120ºC

-2.6

T=-130ºC T=-140ºC T=-150ºC

-2.8

-3

0.45 -2 -1 0

1 2 3 4 log (f/Hz) log(f/Hz)

5

6

-2 -1 0

1

2

3

4

5

6

log(f/Hz)

Figure 2. Isotherms showing the frequency response of MeOAzB at low temperatures (-150ºC ≤ T ≤ -20ºC), in terms of: (a) real component of the dielectric permittivity, ε’, and (b) loss tangent, tan(δ). Red arrows indicate the relaxation frequency (log(fmax)) of the γ and β relaxations at T=90ºC.



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a

log ε’’

b ln (fmax/Hz)

-1.1

T=-20ºC T=-30ºC

-1.3

Page 10 of 40

β

γ

15 13

γ

T=-40ºC T=-50ºC T=-60ºC

-1.5

11 9

T=-70ºC T=-80ºC

-1.7

T=-90ºC

7 5

T=-100ºC

-1.9

T=-110ºC T=-120ºC

-2.1

3

β

1

T=-130ºC T=-140ºC

-2.3

T=-150ºC

-2.5 -2 -1 0

1

2

3

4

5

6

-1 -3 -5 0.003

0.005

0.007

1/T (K-1)

log(f/Hz)

Figure 3. (a) Isotherms showing the frequency response of MeOAzB at low temperatures (150ºC ≤ T ≤-20ºC), in terms of the dielectric loss factor, ε’’. Red arrows indicate the relaxation frequency (log(fmax)) of the γ and β relaxations at T=-90ºC; (b) Arrhenius maps of the γ and β relaxations at low temperatures.


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Figure 4 and 5 show the dielectric response of MeOAzB at high temperatures (-10ºC ≤ T ≤ 110ºC). At sufficiently high temperatures and low frequencies, the values of ε’’ rise exceeding the range typical of dielectric relaxations and suggesting the prevalence of conductivity in that region. Subtraction of the conductivity term by applying Eq. 6 revealed two processes overlapped, distinguishable at low frequencies in Figure 5b. These processes are assigned to β1 and α relaxations, in increasing temperature order. In order to discriminate polarisation and conductive effects, M’’ was calculated. The effect of conductivity at high temperatures and low frequencies is further illustrated in Figure 6, where M’’, ε’, εder, tan(δ) and σ’ have been plotted at T=110ºC. The appearance of a plateau in the σ’ plot at low frequencies confirms the occurrence of direct current conductivity (σdc), with the onset of σdc coinciding with a maximum in the M’’ peak59.The values of σdc were calculated then by extrapolating the σ’ plateaus to f 0, and all the values lie in the 10-13–10-11 S·cm-1 range. Such small values were expected considering the absence of easily ionisable groups in the chemical structure of the homopolymer. Similar behaviour has been previously reported for comb-shaped and amorphous polymethacrylates with different side chain lengths52-54, 60, 61. The εNC’’ curves were fitted to two HN functions (Eq. 6), and the corresponding Arrhenius maps are also shown in Figure 5c after calculating the respective relaxation times by Eq. 8. Despite the number of experimental points related to the α relaxation, it is possible to distinguish a certain deviation from linearity in the β1 and α relaxations. This is in coherence with the cooperativeness of the molecular motions involved, controlled by free volume effects. Thus, the curves were then fitted to VTF expressions, Eq. 10, and the results are summarised in Table 3. These results confirm that the β1 relaxation must be assigned to movements of the polarisable carboxyl group adjoining the main chain taking place in the glass state, while the α process represents segmental backbone rearrangements related to the glass transition61-64.



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log ε’

Page 12 of 40

tan (δ)

T=120ºC

1.5

T=110ºC 1.4

1

T=100ºC T=90ºC

0.5

1.2

T=80ºC 0

T=70ºC 1

-0.5

T=60ºC

-1

T=50ºC T=40ºC

0.8

-1.5

T=30ºC -2

T=20ºC

-2.5

T=10ºC

0.6

T=0ºC 0.4

-3

-2 -1 0

1

2

3

4

5

6

-2 -1 0

1

2

3

4

5

T=-10ºC

6

log(f/Hz)

log(f/Hz)

Figure 4. Isotherms showing the frequency response of MeOAzB at high temperatures (-10ºC ≤ T ≤ 110ºC), in terms of: (a) real component of the dielectric permittivity, ε’, and (b) loss tangent, tan(δ). log ε’’

log εNC’’

a

1

ln (fmax/Hz)

b

0

0.5

β1

α

-0.4

c

17

12

0

-0.5

-1

-0.8

7

-1.2

2

-1.6

-3

β1

α

-1.5

-2

-2.5

-2

-2 -1 0

1

2

3

log(f/Hz)

4

5

6

-2 -1 0

1

2

3

4

5

6

-8 0.0024

log(f/Hz)

0.0026

0.0028

0.003

1/T (K-1)

Figure 5. Isotherms showing the frequency response of MeOAzB at high temperatures (-10ºC ≤ T ≤110ºC) in terms of ε’’ (a) and εNC’’ (b). Arrows indicate the relaxation frequency (log(fmax)) of the β1 and α relaxations at T=80ºC; (c) Arrhenius maps of the β1 and α relaxations at high temperatures. 12 ACS Paragon Plus Environment

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2

-4

ε’ εder

σ’ (S/cm)

-5 1

-6

M’’

-7

tan(δ) 0

-8

δ

β1

α

-9

-1

-10 -11

-2

σdc

-12 -13

1/τσ -3

-14 -2

-1

0

1

2

3

4

5

6

7

log(f/Hz)

Figure 6. Dielectric response of MeOAzB. Isotherm plots at T=110ºC corresponding to: tan(δ), ε’, εder M’’ (left axis) and σ’ (right axis).

Also at low frequencies the maximum in the εder curve and the increase in the ε’ values reveal a dielectric process masked by the strong conductivity contribution, falling in the temperature range of the δ relaxation typical of SCLCPs48, 49, 52, 55. This transition becomes active above the Tg and is associated with the parallel component of the permanent dipole moment of the mesogenic units rotating around their short axes, µ║, see Figure 1. The vicinity of the M’’ and εder peaks in Figure 6 suggests that the onset of charge transport could be related to the δ relaxation, and particularly to the disruptions of the smectic phase by the translational movements of the mesogenic groups.



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3.3 Dielectric response of the 6-MeOAzB/MMA copolymers Figure 7 displays the frequency/temperature dependence of the dielectric loss factor, ε’’, of the MeOAzB/MMA copolymers. All the copolymers show the dielectric (γ, β, β1 and α) relaxations seen for the liquid crystalline homopolymer, MeOAzB together with the β1 and α relaxations arising from poly(methyl methacrylate), PMMA, see Figure 162-68. As expected, the γ and β relaxations, previously attributed to local modes of mobility of the side chains, have weaker intensities on decreasing the MeOAzB concentration, and are absent in the PMMA curve (Figure 7c). These processes appear in the same temperature/frequency ranges as for the homopolymer (-150º≤ T ≤ -20ºC), in all the copolymers, see Figure 7a-b.

The copolymers also display dc conductivity at high temperatures, see Figure 8, with slightly higher σdc values than those observed for the homopolymer. Such increase in the conductivity, together with the dilution of the mesogenic units, may account for the difficulty to characterise the εder maximum related to the δ transition in the copolymers. After subtracting the conductivity contribution, the β1 and α relaxations are also visible in the spectra of the copolymers, with the β1 relaxation being especially prominent for the case of PMMA (see Figure 7c).


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4

a

log (ε’’) 2

0

-2 -2 0 2

log(f/Hz)

4 6

-100

-150

100

50

0

-50

T (ºC) is Y Ax

4

b

δ, σ

α

2

log (ε’’)

β1

0

-2

β

-2

γ

0

log(f/Hz)

2 4 6

-150

-100

-50

50

0

100

T (ºC)

α

c

0

β1

log (ε’’) -2

-4 -2 0

log(f/Hz)

2

50

100

0

4

-50 6

-100 -150

T (ºC)

Figure 7. 3D plots of the imaginary component of the dielectric permittivity, ε’’, of: (a) 0.90MeOAzB/MMA; (b) 0.22MeOAzB/MMA and (c) PMMA.



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2

-4

Page 16 of 40

3

-2

σ’ (Scm-1)

-3

ε’

-5

2 -4

1

εder M’’

-6

1

-5

-7

0

-6

0

-7

-8

tan(δ)

-1 -1

-8

-9 -9

-2 -10

-10

-2 -3 -11

a -3

-12 -2

-1

0

1

2

3

4

5

6

7

-11

b -4

-12 -2

-1

0

log(f/Hz)

1

2

3

4

5

6

7

log(f/Hz) e1

3

ε’

-4

-5 2

εder

3

-6

2 -8

-6 1 1

-9 -7

M’’ tan(δ)

σ’ (Scm-1)

-7

0 0

-10

-8 -11

-1 -9 -1

-12 -2 -10

-2 -11

-13 -3

c -3

-12 -2

-1

0

1

2

3

4

log(f/Hz)

5

-14

d 6

7

-4

-15 -2

-1

0

1

2

3

4

5

6

7

log(f/Hz)

Figure 8. Dielectric variables of the MeOAzB/MMA copolymers at T=110ºC: (a) 0.90MeOAzB/MMA; (b) 0.76MeOAzB/MMA; (c) 0.22MeOAzB/MMA and (d) PMMA. Following the procedure described for the homopolymer, the relaxation times of the different molecular motions of the copolymers have been obtained. The corresponding Arrhenius map is shown in Figure 9 and the kinetic parameters were calculated and listed in Table 2. As


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expected, the two relaxations at low temperautres, γ and β, follow linear behaviour and the results were fitted to Eq. 9, see Figure 9a. The initial introduction of MMA units slightly increases the activation energies, followed by a subsequent decrease at higher MMA concentrations 0.22MeOAzB/MMA. These variations could indicate loss in the cooperativeness between neighbouring mesogenic units50, 57. As for the homopolymer, the relations between the relaxation times (τmax) and the temperature of the relaxations at higher temperatures, α and β1, have been fitted to VTF equations (Eq. 10), and the kinetic parameters are listed in Table 3. The Arrhenius maps corresponding to the α relaxation of the copolymers fall between the curves of the two homopolymers, see Figure 9b. These changes are accompanied with a decrease in the VTF parameters, log(f0) and B, and an increase in the T∞ values, as the MMA content increases, see Table 3. The isobaric expansion coefficient, was also calculated, αf = 1/B, and the values indicate an increase in the free volume on increasing the MMA content. This is in agreement with the reduction of the glass transition (see Table 1) exhibited by liquid crystalline copolymers on the addition of methyl methacrylate units22.



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ln (fmax/Hz) 16 14

γ

12 10 8

a

6 4

β

2 0 -2 -4 0.0035

0.0055

0.0075

0.0095

1/T (K-1) ln (fmax/Hz) 16 14 12 10

b

8

α

6 4

β1

2 0 -2 -4 0.002

0.0025

0.003

1/T

0.0035

0.004

(K-1)

Figure 9. Arrhenius maps of the relaxations corresponding to the MeOAzB/AMPS copolymers and the homopolymers: (a) Low temperatures (γ, β), (b) high temperatures (β1, α) ( MeOAzB ; 0.90MeOAzB/MMA;

0.76MeOAzB/MMA;

0.22MeOAzB/MMA; ,

PMMA)


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Figure 9b reveals strong variations in the β1 relaxation by the introduction of MMA groups. In order to analyse the cooperativeness of this and also the γ and β relaxations, the Eyring equation, Eq. 11, was applied. The calculated values of activation entropy, ∆S, and enthalpy, ∆H, are listed in Table 2. The most remarkable changes occur for β1, whose ∆S values show a large reduction on the introduction of MMA units. In addition, the zero-entropy principle was applied58. For a non-cooperative relaxation, the activation entropy, ∆S in Eq. 11, should be close to 0, due to the independent motion of kinetic units, leading to: Ea=RT’[1+ln(k/2πh)+lnT’]=RT’[22.92+lnT’]

(Eq. 12)

where T’ is the temperature at which the frequency of the corresponding relaxation is f=1 Hz. Eq. 12 represents a universal line in coordinates Ea vs. T’, where the relaxations with zero entropy should fall58. The experimental Ea vs. T’ values corresponding to the different relaxations (γ, β and β1) and Eq. 12 are shown in Figure 10. As expected, the values corresponding to the γ and β relaxations fall close to the ∆S=0 line, due to their non-cooperative nature. By contrast, most of the points corresponding to the β1 relaxation deviate from the straight line, indicating the role of intermolecular interactions. The largest deviation is seen for the β1 values of the liquid crystalline homopolymer, which decrease with increasing MMA concentration. These results confirm the combined origin of the β1 relaxation, and a lower cooperativeness on the molecular motions involved on increasing MMA content.



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Ea (kJmol-1) 250

MeOAzB 200

β1 150

∆S = 0 100

γ

50

β

PMMA

0 0

100

200

300

400

500

T’ (K) Figure 10. Zero entropy prediction (straight black line) and Ea vs T’ experimental data for the MeOAzB/MMA copolymers: Red –MeOAzB; Orange 0.90MeOAzB/MMA; Purple – 0.76MeOAzB/MMA; Green – 0.22MeOAzB/MMA;

– PMMA. Blue dotted arrow indicates

increasing MMA concentrations.

The previous results can now be interpreted from the point of view of how local and segmental mobility effects the formation of liquid crystal phases in SCLCPs. In the case of the MeOAzB/MMA copolymers, the changes in β1 indicate a more local character of the sub-glass motions of the methacrylate groups, which is translated to the mobility of the mesogenic units. The decrease in the entropy values by the introduction of MMA groups suggest that the local activation of side groups takes place more rapidly and probably involves smaller cooperative regions69-72. This may promote excessive decoupling between side and main groups motions, and ultimately inhibit microphase separation and the formation of smectic templates, see Figure 11. This effect may play a less important role in the suppression of the nematic phase of 0.22MeOAzB/MMA. In this case, the local/cooperative motions may not be so relevant, since no


Page 21 of 40

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microphase separation is expected. Instead, the suppression of nematic behaviour may be explained by the large distance between mesogenic units, which reduces the intermolecular interactions between them.

Cooperative regions

MeOAzB

Smectic

Mesogenic contents

Nematic

Isotropic

Temperature

Figure 11. Schematic representation of the formation of liquid crystal phases in the homopolymer and the MeOAzB/MMA copolymers.



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Page 22 of 40

4. Conclusions The poly[6-(4’-methoxyazobenzene-4’-oxy)hexyl methacrylate]-co-poly[methyl methacrylate]s, the MeOAzB/MMA copolymers, undergo dielectric relaxations characteristic of liquid crystalline poly(methacrylate)s: γ, β, β1, α and δ. The presence of non-mesogenic units slightly hinders the local mobility of the mesogens and the flexible spacers in the glass state. On the other hand, more pronounced changes with composition take place for the α and β1 processes. The methacrylate units favour the activation of local motions of the ester groups adjoining the main chain (β1 relaxation), decoupling the motions of the side groups and the polymer backbone, and may account for the extinction of smectic phase behaviour even at relatively low MMA contents. At sufficiently high MMA concentrations, the reorientation of the side-chains seems to be controlled by the mobility of the ester group in the vicinity of the glass transition, leading to the inhibition of liquid crystallinity as the interactions between the mesogens are now too diluted. The relationship between polymer architecture and the coexistence of mesogenic relaxations and sub-glass mobility is of significant interest in designing new SCLCPs with functionality in the glass state via the introduction of non-mesogenic units.

5. Acknowledgments This paper is meant to be a tribute and recognition to the research activity of professor Giulio Sarti. The authors would also like to thank Dr. Victor Saenz de Juano for his advice during the discussion of the results, and also the Spanish Ministry of Science and Innovation, through the Research Projects ENE2007-67584-C03, UPOVCE-3E-013, IT2009-0074, ENE2011-28735C02-01 and two FPI and FPU pre-doctoral grants, and the financial support of the Generalitat Valenciana, through the Grisolia and Forteza programs and the ACOMP/2011/189 program. UPV is also thanked for additional support through the PAID 05-09-4331 and PAID-06-11 program.


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Table 2. Results of the activation analysis of the different relaxations following Arrhenius model. Ea (kJ·mol-1)

log(f0/Hz)

R2

∆H (kJ/mol)

∆S (J/mol)

R2

γ relaxation MeOAzB

33.1

15.78

0.9604

32.4

68.9

0.9576

Cop(0.90)

38.1

17.27

0.9946

37.5

97.1

0.9941

Cop(0.76)

43.1

18.80

0.9854

42.7

126.7

0.9844

Cop(0.22)

34.7

16.72

0.9934

34.3

88.2

0.9931

-

-

-

-

-

-

0.9987

60.1

108.6

0.9987

PMMA

β relaxation MeOAzB

60.5

17.95

Cop(0.90)

60.9

17.82

0.997

60.5

106.1

0.9966

Cop(0.76)

61.5

18.31

0.9987

61.2

115.5

0.9987

Cop(0.22)

54.6 -

16.68 -

0.9964 -

54.1 -

84.7 -

0.9962 -

PMMA

β1(b) β1 relaxation MeOAzB

213.1

36.10

0.9914

214.9

451.6

0.9911

Cop(0.90)

145.7

25.83

0.9982

145.8

254.6

0.9981

Cop(0.76)

133.9

24.22

0.9938

133.7

223.6

0.9935

Cop(0.22)

115.3

21.67

0.9999

117.9

232.5

0.9999

PMMA

71.2

14.65

0.9953

70.2

41.91

0.9952

Table 3. Results of the activation analysis of the relaxations at high temperatures following a VFT model. f0 (Hz)

B (K)

T0 (K)

log(f0/Hz)

R2

αf (K-1·104)

α relaxation MeOAzB

41.06

5245.64

215

17.83

0.9988

1.9

Cop(0.90)

35.49

4212.56

229

15.41

0.9999

2.4

12.89

0.9941

3.9 11.5

Cop(0.76)

29.69

2574.38

231

Cop(0.22)

17.33

867.86

305

PMMA

7.85

527.00

349

7.53 3.41

0.9934 -

19.0

β1 relaxation MeOAzB

19.66

523.92

303

8.54

0.9980

19.1

Cop(0.90)

19.29

488.72

308

8.38

0.9838

20.5

0.9912

26.4

Cop(0.76)

-

-

-

-

Cop(0.22)

16.85

378.76

299

7.32

PMMA

174.5


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Scheme 1. MeOAzB/MMA copolymers 42x22mm (300 x 300 DPI)

ACS Paragon Plus Environment


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Figure 1. Relaxation modes for the MeOAzB/MMA copolymers. 44x23mm (300 x 300 DPI)


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Figure 2. Isotherms showing the frequency response of MeOAzB at low temperatures (-150ºC ≤ T ≤ -20ºC), in terms of: (a) real component of the dielectric permittivity, ε’, and (b) loss tangent, tan(δ). Red arrows indicate the relaxation frequency (log(fmax)) of the γ and β relaxations at T=-90ºC. 119x95mm (300 x 300 DPI)



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Figure 3. (a) Isotherms showing the frequency response of MeOAzB at low temperatures (-150ºC ≤ T ≤20ºC), in terms of the dielectric loss factor, ε’’. Red arrows indicate the relaxation frequency (log(fmax)) of the γ and β relaxations at T=-90ºC; (b) Arrhenius maps of the γ and β relaxations at low temperatures 120x97mm (300 x 300 DPI)


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Figure 4. Isotherms showing the frequency response of MeOAzB at high temperatures (-10ºC ≤ T ≤ 110ºC), in terms of: (a) real component of the dielectric permittivity, ε’, and (b) loss tangent, tan(δ) 111x82mm (300 x 300 DPI)



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Figure 5. Isotherms showing the frequency response of MeOAzB at high temperatures (-10ºC ≤ T ≤110ºC) in terms of ε’’ (a) and εNC’’ (b). Arrows indicate the relaxation frequency (log(fmax)) of the β1 and α relaxations at T=80ºC; (c) Arrhenius maps of the β1 and α relaxations at high temperatures. 100x67mm (300 x 300 DPI)


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Figure 6. Dielectric response of MeOAzB. Isotherm plots at T=110ºC corresponding to: tan(δ), ε’, εder, M’’ (left axis) and σ’ (right axis). 82x90mm (300 x 300 DPI)



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Figure 7. 3D plots of the imaginary component of the dielectric permittivity, ε’’, of: (a) 0.90MeOAzB/MMA; (b) 0.22MeOAzB/MMA and (c) PMMA. 163x354mm (300 x 300 DPI)


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Figure 8. Dielectric variables of the MeOAzB/MMA copolymers at T=110ºC: (a) 0.90MeOAzB/MMA; (b) 0.76MeOAzB/MMA; (c) 0.22MeOAzB/MMA and (d) PMMA 27x33mm (300 x 300 DPI)



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Figure 9. Arrhenius maps of the relaxations corresponding to the MeOAzB/AMPS copolymers and the homopolymers: (a) Low temperatures (γ, β), (b) high temperatures (β1, α) ( MeOAzB ; 0.90MeOAzB/MMA; 0.76MeOAzB/MMA; 0.22MeOAzB/MMA; , PMMA) 123x202mm (300 x 300 DPI)


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Figure 10. Zero entropy prediction (straight black line) and Ea vs T’ experimental data for the MeOAzB/MMA copolymers: Red –MeOAzB; Orange 0.90MeOAzB/MMA; Purple – 0.76MeOAzB/MMA; Green – 0.22MeOAzB/MMA; – PMMA. Blue dotted arrow indicates increasing MMA concentrations. 64x56mm (300 x 300 DPI)



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Figure 11. Schematic representation of the formation of liquid crystal phases in the homopolymer and the MeOAzB/MMA copolymers. 53x33mm (300 x 300 DPI)


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Characterization of Functionalized Side-Chain Liquid Crystal

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