The implications of various molecular interactions on the dielectric behavior of cimetidine and cimetidine hydrochloride

Abstract

Herein, we employed broadband dielectric spectroscopy to characterize the molecular dynamics of the two related materials, cimetidine base and cimetidine hydrochloride, with similar structural skeletons but involving different molecular interactions (ionic vs. non-ionic). BDS experiments performed at ambient and elevated pressures, combined with rheology and temperature-modulated calorimetry studies, revealed significant discrepancies in the supercooled dynamics of both samples. The strong electrostatic interactions resulted in slower dynamics of the ionic counterparts, manifested by a higher T_g value. However, the samples exhibited some similarities in the glassy dynamics. The dielectric response of cimetidine hydrochloride revealed features similar to those previously observed for the other molten hydrochloride salts, wherein decoupling between the timescales of the structural and ionic displacements affirms the universal character of the behavior presented herein.

---

Introduction

Molecular dynamics studies have attracted significant attention of the scientific community since they can provide answers to the questions that have long been unresolved. Experimental and theoretical efforts were addressed to investigate the various glass-forming materials (i.e. van der Waals liquids, polymers, metallic glasses, and ionic liquids) with diverse dynamic behavior patterns. It is believed that the systematic search for the common features will help to elucidate the nature of glass transitions and even to reach a definitive theory of this fascinating phenomenon. However, only a deep understanding of the fundamental problems may result in significant advancement in the use of glass-forming materials in various industrial areas in the future.

It is widely known that the dynamics of glass-forming liquids do not depend only on the chemical structure, but are also governed by the interplay of the intermolecular attractions involved. Hence, finding a quantitative correlation between the relaxation properties and existing interactions remains the prime goal of the ongoing research activity. The most universal way to describe the potential between the two interacting neutral particles relies on the application of an empirical Lennard-Jones (LJ) equation:¹

where r describes the distance between both particles, whereas ε and σ denote the depth of the potential well and the distance at which the potential is equal to zero, respectively. For the majority of glass formers, considered as van der Waals liquids, the molecular dynamics can be satisfactorily described by the abovementioned relationship. The ultimate value of the intramolecular potential is governed by the balance between the long-range attractive forces (including dipole–dipole, dipole–induced dipole, and London interactions) and short-range contributions originating from Pauli repulsion. However, for materials that are entirely composed of ions, the electrostatic long-range forces are regarded as the dominant factor that determines their unique dynamic behavior.² For simple salts, the long-range Coulomb forces between the charges of the constituent ions will have a crucial role; however, for ionic samples with bulky molecular cations, the effective intramolecular potential may have a much more complex form with respect to their advanced ionic and molecular nature.³

In the past two decades, ionic liquids (ILs) have attracted growing interest, and nowadays, they find outstanding roles in applied science. This is due to the fact that these liquid-state salts may cover a wide range of properties that are attractive with regard to a multitude of daily and industrial applications. Among ILs, protic ionic liquids (PILs), obtained by the proton transfer from a Brønsted acid to Brønsted base, create a distinctive group with unique features arising from their ability to enhance the proton transfer through a hydrogen-bonded network.⁴ Due to the increasing interest in the properties of PILs, the amount of research dedicated to a better understanding of their proton transport behavior has systematically grown. At the same time, significant progress has been made with respect to the theoretical and computational approaches, shedding more light on the crucial structure–property relationships.⁵ Investigations dealing with ionic materials in relation to their non-ionic counterparts have been particularly insightful, providing an excellent survey of the interplay of various molecular factors governing their unique features. However, a limited number of analogous experimental investigations have been reported. This may be due to the specificity of each class of such systems, which may cause their shared experimental characteristics to be challenging at times. However, this may be overcome by using broadband dielectric spectroscopy (BDS), a method being designed to explore the dynamic processes with a distinct molecular origin.

Herein, we present dielectric relaxation studies on cimetidine (CIM) base and cimetidine hydrochloride (CIM HCl). Both materials are pharmaceutically relevant since they are histamine H2-receptor antagonists that inhibit the production of acid in the stomach. Although the structural cores of both materials are similar (see Fig. 1), the course and character of the molecular attractions involved are totally different. CIM HCl belongs to the PILs class, whereas CIM base can be considered as a van der Waals liquid. In the present study, we use the BDS method to get an insight into their dynamics over a broad range of frequencies, temperatures, and pressures. Since the selected materials are characterized by the opposite, neutral, and ionic natures, it is obvious that each of them will possess unique dynamic features. Herein, we focus on verifying how the variations in the intramolecular potentials will be reflected in the parameters describing (i) the many-body cooperative dynamics in a supercooled liquid regime, (ii) faster local dynamics observed below T_g, and (iii) the sensitivity of the dynamics to the applied pressure. To achieve a complete insight into the issues raised, the dielectric investigations were supported by rheological and temperature-modulated differential scanning calorimetry experiments.

Fig. 1 Chemical structure of cimetidine base.

Materials and methods

Investigated materials

Crystalline cimetidine base (CIM) and cimetidine hydrochloride (CIM HCl) were purchased from Sigma-Aldrich as crystalline powders. Both materials were characterized with purity greater than 98%. The amorphous forms of both the samples were prepared by quench cooling of the melt. The crystalline powder was placed on a heating block until complete melting was achieved. After that, the sample was quickly transferred to a very cold metal plate. The melting temperatures, determined by means of DSC, were T_m = 414 K and T_m = 461 K for CIM base and CIM HCl, respectively. Since it is well known that glasses have history-dependent properties, therefore, considering this, we precisely controlled the conditions for the sample preparation and performed the analogous preparation routes for both materials.

Dielectric measurements at ambient and elevated pressures

Dielectric measurements were performed under atmospheric pressure using a Novocontrol GMBH Alfa analyzer with frequency values limited to 10⁶ Hz. The temperature was precisely controlled with a Quatro temperature controller using a nitrogen gas cryostat (accuracy better than 0.1 K). During the measurements, the tested samples were placed between the steel electrodes of a capacitor (15 mm diameter), with a fixed distance between the electrodes (0.1 mm) provided by fused silica spacer fibers. The same experimental setup was used in time-dependent dielectric measurements.

The pressure-dependent dielectric measurements were performed using an automatic high-pressure system developed by Unipress. As above mentioned, the investigated sample was placed between the steel electrodes of the capacitor (diameter 15 mm; gap 0.1 mm; Teflon spacer). Then, the capacitor was placed inside a Teflon ring and sealed. The tested sample, which was not in contact with the compression medium, was fixed to a pressure chamber filled with silicon oil.

Temperature-modulated differential scanning calorimetry (TMDSC)

Stochastic temperature-modulated differential scanning calorimetry (Mettler-Toledo) was used to determine the structural relaxation times. The quenched samples were analyzed at a heating rate of 0.5 K min⁻¹. In the experiment, a temperature amplitude of 0.5 K for the pulses was selected at a switching time range with minimum and maximum values of 15 and 30 s, respectively. The relaxation times, τ_α = 1/2πf, were determined from the temperature dependences of the real part of the complex heat capacity c′_p(T), obtained at different frequencies in the glass transition region.

Rheological (RH) measurements

The rheological measurements were carried out using an ARES-G2 rheometer (TA Instruments), in which the sample was placed between two 8 mm diameter parallel circular plates with a controlled gap distance. During the experiments, we measured the dynamic shear modulus G*(f) by applying an oscillatory strain and measuring the resultant stress. The strain was produced by rotating the bottom plate, whereas the stress was determined from the torque, required to hold the top plate in its position. The frequency dependences of G′ and G′′ were measured for various temperatures in the frequency range 0.1–100 rad s⁻¹.

Results and discussion

Many-body cooperative dynamics in the supercooled liquid regime

The application of the BDS spectroscopy offers tremendous opportunities to get an insight into the molecular dynamics of the various types of glass formers. Moreover, its advantage over other techniques arises from the possibility to characterize the materials over a wide range of frequencies, temperatures, and what seems the most beneficial, pressures. Another convenience results from the free choice of representation, which can be applied during data analysis. Although all attainable formalisms are related to each other, the proper conversion between one representation to another may give a valuable insight into the different features of the analyzed experimental data. Thus, using the BDS technique, one can easily study the processes of distinct origin, such as those resulting from ion diffusion or local molecular motions. In general, the dielectric data can be presented by means of three different formalisms: the complex permittivity ε*(f) = ε′(f) − iε′′(f), the complex conductivity σ*(f) = σ′(f) + iσ′′(f), and the complex electric modulus M*(f) = M′(f) + iM′′(f). The susceptibility formalism is favored in the case of non-conductive samples, wherein reorientations of the permanent dipoles give rise to distinctive frequency-dependent features of the permittivity dielectric loss spectra. The other representations assume greater importance in the studies of ion-containing systems, such as CIM HCl, investigated in this work.

The dielectric spectra of CIM base, covering seven decades in frequencies (10⁻¹ to 10⁶ Hz), are presented in Fig. 2 in the permittivity representation. The well-resolved maximum in the frequency dependence of the imaginary part of the dielectric permittivity ε′′(f) corresponds to the characteristic time required for the reorientation of molecular dipoles, i.e. the α-relaxation time. When the system cools down, this maximum shifts toward the lower frequencies, indicating an increase in the time scale of such cooperative motions. Finally, when the structural relaxation time exceeds τ_α = 1000 s, the global mobility becomes frozen in the glassy state and the dielectric spectra become dominated by the secondary modes.

Fig. 2 Dielectric spectra of the CIM base measured at an ambient pressure above and below the glass transition temperature.

Since the intramolecular potential inherently determines the dynamics of the investigated materials, the main dielectric characteristics, such as the shape of the dielectric curves or dielectric strength, should clearly reflect their properties. Recently, Paluch et al. instigated a universality in the dielectric behavior of the various glass-formers, expressed as a correlation between the dielectric strength (Δε = ε₀ − ε_∞ ≈ Nμ², where ε₀ denotes the dielectric permittivity of vacuum and N is the number of relaxing dipoles, whereas μ corresponds to the value of the permanent dipole moment) and the broadening of the dielectric response.⁶ The higher the dipole moment of the investigated system, the larger the observed β_KWW value (or equivalently narrower α-relaxation peak). The value of the β_KWW parameter, an exponent in the Kohlrausch–Williams–Watts function:⁷

φ(t) = exp[−(t/τ_α)^β_KWW] (2)

describes the frequency dispersion of the relaxation times, being an inherent hallmark of the many-body and heterogeneous nature of the supercooled dynamics. As shown in the inset of Fig. 3, CIM base is characterized by a high value of dielectric strength, Δε ≈ 69. This indicates that the dipole–dipole energy term will have a significant contribution to the total value of the intramolecular potential. According to a reported correlation, such a high Δε value should correspond to a high β_KWW. From a mastercurve constructed for CIM base, we found that β_KWW = 0.76. Such a high value of Δε was also observed for other polar glass formers, e.g. propylene carbonate,⁸ bicalutamide, or ROY.⁹ Among these, bicalutamide was characterized by a narrower dispersion of α-relaxation times, with β_KWW = 0.85.

Fig. 3 Masterplot constructed for CIM base by imposing the dielectric spectra, obtained for various temperatures, on a spectrum registered at T = 325 K. The inset shows an exemplary dielectric loss (ε′′) and dielectric dispersion (ε′) spectra obtained at T = 333 K. The solid grey line indicates the HN fit function obtained after subtraction of the dc-conductivity term. The arrow indicates the position of the primitive frequency f₀, calculated according to a coupling model (CM).

To thoroughly analyze the temperature dependence of the relaxation times, we applied the Havriliak–Negami (HN) function, which is widely used to parametrize the relaxation behaviour of various glass formers:¹⁰

where ω = 2πf is the angular frequency, ε_∞ denotes the high frequency limit permittivity, Δε is the dielectric strength, and τ_HN is a parameter connected to a characteristic relaxation time. The exponents α and β describe the shapes of the dielectric loss curves. This numerical analysis enabled us to precisely determine the relaxation time corresponding to the maximal dielectric loss frequency (τ = 1/2πf_max). Moreover, the τ value is related to τ_HN in the following manner:¹¹

The logarithm of the determined relaxation times as a function of inverted temperature is depicted in a so-called relaxation map (Fig. 4, right panel) illustrating all the key dynamic features of the material under study. Using the map, one can easily find the relaxation time corresponding to log₁₀(τ_α) = 3, indicating the glass transition temperature, which for CIM base was equal to T_g = 312 K. At this point, it should be clarified that the same strategy was also applied to characterize the secondary relaxations. In this case, the parameter β in eqn (4) was equal to one that was equivalent to the transformation of the HN equation into the Cole–Cole function. In addition, the following peculiarity, τ = τ_HN, is, therefore, true. As observed in Fig. 2, two secondary modes (assigned as β and γ) were found for CIM base; however, their plausible nature has been discussed later. Now, we would focus on the character of their temperature dependencies. The secondary relaxation modes observed in the glassy state usually obey the Arrhenius law. However, when the material is heated above the glass transition temperature (defined by η = 10¹² Pa s and τ_α = 1000 s) its properties, such as viscosity, diffusion coefficients, relaxation times, begin to change suddenly in a way characteristic for particular substance. The rapidity of the change in τ_α near the glass transition defines the material ‘fragility’.¹² In most cases, the cooperative dynamics of the supercooled liquid state have been well parametrized by the empirical Vogel–Fulcher–Tammann (VFT) equation:^13–15

where τ_∞, D, and T₀ are the fitting parameters (for CIM base: log τ_∞ = −14.9s ± 0.1, D = 11.8 ± 0.2, and T₀ = 242 ± 1 K). The D value, known as the strength parameter, is helpful in classifying the glass formers as so-called strong (with large D-values) or fragile (with small D, typically D < 10), as was reported by Angell.¹⁶ According to this nomenclature, CIM base should be categorized as an intermediate glass-former since its calculated D value is within the range 10 < D < 100. An alternative way of estimating the ‘fragility’ involves the determination of steepness index m, being defined as follows:¹⁷

Fig. 4 Relaxation map obtained for CIM base. Relaxation times assessed from BDS – τ_α–M′′ and τ_α (circles), TMDSC – τ_TOPEM (asterisks), RH – τ_η (pentagons), and τ_G′′max (tringles) techniques are depicted. To properly compare the BDS and RH data, τ_α−M′′ values were determined from M′′ data. Open stars denote the aging relaxation times obtained from eqn (12). The secondary relaxation times – τ_β and τ_γ are shown together with the calculated values of activation energies. Solid and dashed lines denote VFT and Arrhenius fit functions, respectively.

For various glass formers, the value of m may change within a broad range, from about 17 (strong glass formers) to about 200 (fragile one).¹⁸ The value obtained for CIM base, m = 80 (for τ_α = 1000 s), falls roughly in the middle of this range. Moreover, the m value is also governed by the intramolecular potential. The results of a simulation performed by Bordat et al. clearly show that by adjusting the properties of the theoretical potential, in particular by increasing its value and anharmonicity, an increase in the fragility is observed. This is an effect of density growth resulting in stronger intramolecular coupling.¹⁸

The dielectric spectra of the ionic CIM HCl sample are shown in Fig. 5 in all the aforementioned formalisms. It can be observed that the loss peak in the ε′′(f) spectra is almost completely covered by the conductivity contribution originating from the translational motions of the cations and anions in the investigated sample. The only recognizable features appear below T_g as secondary modes. Thus, a detailed analysis of CIM HCl behavior in the supercooled regime was performed for data in the electric modulus and conductivity representation. From the imaginary part of the complex modulus function M′′(f), the conductivity relaxation time was calculated as τ_σ = 1/2πf_max with f_max corresponding to the maximum of the M′′ peak. It was observed that upon cooling, this maximum is shifted to a low frequency due to a decrease in the ion mobility. Simultaneously, the downturn of the ion displacement was disclosed as a decrease in the value of dc-conductivity (σ_dc), assigned from the frequency-independent plateau-like region of the real part of the complex conductivity σ′ (see Fig. 5).

Fig. 5 Representative dielectric spectra for CIM HCl at an ambient pressure above and below the glass transition temperature presented in various representations.

After thorough observation of the registered spectra M′′(f), an interesting feature can be observed: above a certain temperature, the interval between the succeeding spectra is decreasing, although the same temperature step is maintained. Such behavior, known as ‘decoupling’ in the field of ionic liquids, denotes separation between the time-scales of ion diffusion and structural dynamics.¹⁹ Moreover, this phenomenon has been reflected in the temperature characteristics of the conductivity relaxation times, as depicted in Fig. 6. One can easily see that for log τ_σ = 0.74, a crossover in the dynamic behavior of CIM HCl occurs. Then, the temperature dependence of the conductivity relaxation times shows a visible departure from the VFT-like into the Arrhenius-like behavior. Usually, for conventional glass-formers, such crossovers can be observed for much longer relaxation times, i.e. as large as hundreds or thousands of seconds. To compare the timescales of the conductivity and structural relaxation times, we assessed structural relaxation times using temperature-modulated differential scanning calorimetry (TMDSC). Although these measurements were performed for both CIM base and CIM HCl, only in the former, the agreement between the τ values determined from both the methods was observed.

Fig. 6 The temperature dependence of the relaxation times for CIM HCl. From BDS studies, conductivity relaxation times τ_σ (circles), β'- and γ'-relaxation times (squares), and aging relaxation times (open stars) were determined. Additionally, structural relaxation times measured by TMDSC are shown. From rheological measurements, τ_η (from Maxwell equation) and τ_G′′max were determined. Solid and dashed lines denote VFT and Arrhenius fit functions, respectively. Inset shows the relation of log τ_σ to log η, together with the assessed value of the decoupling index s.

As obvious from the relaxation map, at the crossover temperature, the structural relaxation time for CIM HCl reached approximately 1000 s. However, the corresponding conductivity relaxation time was much shorter, corresponding to the decoupling index,²⁰ R_τ(T_g) = log[τ_α(T_g)/τ_σ(T_g)], being equal to 3. For comparison, the R_τ(T_g) values found for other protic ionic conductors were equal to 3 for procaine HCl, procainamide HCl,²¹ and sumatriptan succinate,²² 3.5 for phosphoric acid, and 7 for lidocaine di-(dihydrogen phosphate).²³

Another approach shedding more light on the decoupling phenomenon is the application of the rheological measurements to probe the mechanical relaxation in the tested materials. In this study, we investigated the dynamic shear modulus by applying an oscillatory strain and measuring the resultant stress. The determined viscosity values (η) were then converted into the relaxation times (τ_η) according to the Maxwell relation,²⁴ i.e. η = G_∞τ_η. The infinite frequency shear modulus (G_∞), determined as the high-frequency asymptote of G′(f), was found to be G_∞ = 2.3 × 10⁸ Pa for CIM base and G_∞ = 2.7 × 10⁸ Pa for CIM HCl. The real G′(f) and imaginary G′′(f) parts of the shear modulus spectra for both materials are presented in Fig. 7. One can see that the frequency dependence of the G′′ is characterized by a single peak, which moves to the higher frequency on heating. From the maximum of the G′′(f) peak, we determined the mechanical relaxation times, defined as τ_G′′max = 1/2πf_max. These relaxation times, together with the dielectric data, are depicted in the left panel of Fig. 4 for CIM base and Fig. 6 for CIM HCl. To properly compare the relaxation data obtained from the different spectroscopic methods, it is necessary to analyze the data in the analogous representations. We can decide whether we choose the dynamic susceptibilities (i.e. dielectric ε* or mechanical compliance J*) or the dynamic modulus (M* or G*). Note that, because the former refers to a retardation process and the latter to relaxation, the resultant characteristic relaxation time may be different. In our study, we applied modulus representation and thus we had to convert the dielectric data for CIM base from dielectric susceptibility to modulus representation according to the following relation: ε* = 1/M*. At this point, it should be noted that this conversion can affect the shape of the relaxation peak. This is particularly important for the molecules with high conformational freedom and a diverse pattern of secondary processes. Then, changes in the magnitude of particular modes associated with the data transformation may artificially broaden the relaxation peak.

Fig. 7 The frequency dependence of the real G′ and imaginary part G′′ of the shear modulus measured for CIM base (upper panels) and CIM HCl (bottom panels). The rightmost panels show the masterplots obtained by the horizontal shifting of the normalized G′′(f) spectra, registered at different temperatures, together with the value of the β_KWW parameter (from eqn (2)).

The τ_η(T) and τ_G′′max(T) relationships (see Fig. 4 and 6) have non-Arrhenius characteristics over the whole investigated range of temperatures. In the case of CIM base, the temperature dependences of the mechanical and dielectric relaxation times have parallel courses and significantly overlap with each other. However, a different behavior was observed for CIM HCl, where mechanical data were significantly shifted, indicating the existence of decoupling between the viscosity and conductivity relaxation.

To quantify the extent of decoupling, the Stokes–Einstein relation can be applied, where τ_ση^−s = const. Then, the slope assigned from log(τ_σ) vs. log(η) corresponds to the decoupling parameter, s.²⁵ The values obtained here were 0.79 and 0.98 for CIM HCl and CIM base, respectively. The degree of decoupling is related to the efficiency of proton hopping, which seems to increase when the Grotthuss mechanism is involved.²⁶ In CIM HCl, decoupling can be further enhanced by tautomerization. However, the privileged mechanism of proton transfer will be dependent on the PIL chemical structure and, essentially, on the number of proton-donor and proton-acceptor sites that may be used to create a hydrogen-bonded network. Hence, the outstanding properties of the PILs will be conditioned by the balance between the columbic forces and dispersion forces, such as the abovementioned hydrogen bonds.²⁷ It is experimentally proven that the overall potential of the ionic conductors can be reinforced by the proper selection of its constituent anions and cations. As reported in an insightful FTIR and DFT study by Ludwig, depending on the composition, the contribution of hydrogen bonding to the intramolecular potential may vary from a small fraction to more than 50%, for aprotic [C₄C₁mim][BF₄] and protic ionic liquid [PrAm][NO₃], respectively.²⁸

Since the dielectric response of an ionic sample is dominated by the conductivity contribution, a comparison of the structural relaxation data for CIM base and CIM HCl was not possible. However, we analyzed the τ_η values determined from the mechanical response of both samples. To quantify τ_η(T) dependencies, we used the VFT equation. We obtained the following fitting parameters: log τ_∞ = −15.7s ± 0.2, D = 11.7 ± 0.4, and T₀ = 243 ± 1 K for CIM base and log τ_∞ = −16.7s ± 0.1, D = 21 ± 0.4, and T₀ = 233 ± 1 K for CIM HCl. This parameterization leads to the glass transition temperatures (determined for τ_η = 1000 s) being equal to T_g,η = 309 K for CIM base and T_g,η = 340 K for its ionic counterpart. Moreover, the corresponding fragility values were m = 80 and m = 64 for the non-ionic and ionic forms, subsequently. Regardless of the assessment method, the T_g value found for CIM HCl was higher in comparison to that for CIM base, indicating slower dynamics of the ionic sample. In recent years, the development of powerful computational approaches, in particular, finding a proper force field that will appropriately describe the interactions between atoms in ILs, has led to an improvement in the understanding of the basic phenomena governing ILs dynamics.²⁹ The excellent comparison reported by Shirota and Castner revealed that the stronger ion–ion interactions lead to higher densities of the ionic samples in relation to their neutral counterparts.³⁰ However, a theoretical study reported by Roy for the idealized ionic liquids modeled on [Im₄₁][PF₆] showed that the IL behavior is mainly driven by the structural rigidity of the electrostatic coupling, leading to high viscosities and consequently, inhibited the dynamics observed in ILs.³¹ A comparison of the mechanical data revealed another interesting fact, i.e. lower fragility and lower β_KWW values for the ionic sample. This result may be discussed in terms of differences in dynamic heterogeneities in both materials. The breakthrough in quantifying the dynamic heterogeneities occurred when Berthier et al. proposed an approach that enabled an easy calculation of the number of dynamically correlated molecules, N_c, directly from the accessible experimental parameters, i.e.:^32,33

where Δc_P denotes the change in the heat capacity between the liquid and glassy states, and k_B is the Boltzmann constant. The last factor in the bracket is proportional to the material fragility m. According to this concept, we can infer that CIM HCl, with smaller fragility and β_KWW values, should have a lower N_c in comparison to CIM base. Moreover, this was confirmed by Grzybowska and co-workers, who investigated the difference between the characteristic number of dynamically correlated molecules for different ionic and non-ionic samples. CIM base and CIM HCl were among the materials selected for their study. The authors reported that the number of correlated molecules was remarkably smaller for the ionic materials in comparison to their neutral counterparts. The smaller length scale of the heterogeneous dynamics was explained by the stronger long-range electrostatic interactions in ILs. Moreover, a plausible correlation between the size of the dynamic heterogeneity and the cation complexity was indicated.³⁴ Theses attempts to correlate the material properties with the structural features are also valid in terms of the fragility behaviour. Recently, Ueno and co-workers investigated the relation between fragility and ionicity in decahydroisoquinoline (DHiQ)-based PILs. The authors found that the fragile character of pure DHiQ with m = 128 may be entirely inverted after its conversion to the ionic form. They observed a decrease in m with increasing ionicity of the investigated material. Indeed, an extremely low fragility value (m = 45) was reported for DHiQ with the hydrogen sulfate anion. The abovementioned drastic change in the properties was attributed to an extended hydrogen bond network formed by the HSO₄ anion, which was also responsible for the high viscosity and efficient proton conductivity via the Grotthuss mechanism.³⁵

Dynamic sensitivity to increasing pressure

To gain a deeper insight into the impact of the molecular attractions on the dynamics of both systems, i.e. CIM base and CIM HCl, we performed molecular dynamics studies at various pressures. It is well known that the application of pressure through altering interatomic distances will reinforce the molecular interactions, as it was observed for some H-bonded systems.³⁶ In the case of materials consisting of ions, such pressure-induced changes in the distances between an equally and oppositely charged particles will modify the nature of the repulsive and attractive forces in the system under study.³⁷ The question is how the effect of compression will be reflected in the dielectric properties of the materials selected to study, which are entirely different from the viewpoint of the interactions determining their overall properties. Fig. 8a shows the dielectric spectra registered during the compression of CIM base at T = 333 K. By isothermal squeezing, we obtained an effect analogous to that obtained during isobaric cooling, i.e. slowing down of the sample dynamics being reflected in the shifting of the maxima of the dielectric loss spectra towards the low frequencies. The spectra registered for several different temperatures (from T = 333 K to T = 373 K) and pressures up to p = 410 MPa were analyzed, and the α-relaxation times were calculated. These values of τ_α as a function of pressure are presented in Fig. 8b. Basically, there are several models that may be used to describe the pressure dependence of τ_α. We chose the pressure version of the VFT equation, which provided an excellent description of the obtained experimental data. The obtained pVFT parameterization was then used to find out the pressure value, P_g, corresponding to τ_α = 100 s, being an indicator of the glass transition. We chose such a relaxation time, instead of the previously adopted τ_α = 1000 s, to avoid an excessive data extrapolation. The pressure dependence of T_g is presented in the inset to Fig. 8b. One can see that the T_g(P_g) dependence reveals a nonlinear character that can be well described by the empirical relation proposed by Andersson and Andersson:³⁸

Fig. 8 (A) The dielectric isothermal spectra registered during the compression of CIM base at T = 333 K. (B) Pressure dependence of the structural relaxation times τ_α. Solid lines denote the VFT pressure counterpart fit function. The inset shows T_g(P_g) dependence parametrized by the Andersson–Andersson equation (solid line).

The fitting parameters k₁, k₂, and k₃ were found to be equal to k₁ = 315.6 ± 0.2, k₂ = 5.5 ± 0.1, and k₃ = 2188.5 ± 31. At first glance, one can see that after the compression, T_g value increases; as the higher pressure is applied, the gradient dT_g/dP is decreasing, indicating dwindling T_g(P) dependency. The effect of pressure on the glass transition temperature has been investigated for miscellaneous classes of glass-forming materials covering various molecular architectures and a wide spectrum of the physical properties. These valuable findings clearly show that the manner in which the T_g value varies with the pressure is characteristic for a given material and essentially reflects the nature of the molecular attractions involved. In general, van der Waals liquids are characterized by the significant sensitivity to the applied pressure.³⁹ Systems with extended hydrogen-bonded structures behave in the opposite way. In the latter, the reinforcing of the supramolecular network under pressure may give rise to deviations from the commonly observed behavior.⁴⁰ When we look at the chemical structure of CIM base, we will notice the presence of NH groups that can act as hydrogen bond donors. Moreover, nitrogen atoms can potentially accept a hydrogen atom, leading to intra- or intermolecular N⋯HN attractions. However, according to reports, CIM base is not an example of a strongly associated liquid.^41,42 On the other site, its remarkable ability for an intramolecular proton transfer, i.e. tautomerization, is repeatedly stressed.⁴³ A diverse form of cimetidine tautomers, formed by the conversion within the imidazole ring or guanidine moiety, has been anticipated in several theoretical studies.^44,45 However, only the form corresponding to the structure presented in Fig. 1 was found in the crystalline cimetidine.

To quantify the pressure sensitivity of T_g, we determined the pressure coefficient of the glass transition temperature, dT_g/dP, taken in a limit of low pressure according to the following relationship:³⁶

The calculated value, equal to 0.149 K MPa⁻¹, indicates a rather moderate sensitivity to pressure, comparable to those reported for diisobutyl phthalate (0.15 K MPa⁻¹).⁴⁶ This is lower than that observed for van der Waals liquids (usually more than 0.20 K MPa⁻¹), but at the same time is higher than those observed for strongly hydrogen-bonded systems, such as glycerol (0.04 K MPa⁻¹) or m-fluoroaniline (0.081 K MPa⁻¹).³⁶

At this point, the following question naturally arises: how will change the pressure sensitivity of the material in which coulombic interactions between the constituted charged particles govern intramolecular potential? To investigate this issue, we performed isothermal measurements for the CIM HCl sample at elevated pressures. The M′′(f) dielectric spectra of CIM HCl registered at T = 352 K for pressures varying from 10 MPA to 410 MPa are presented in Fig. 9a. The logarithms of conductivity relaxation times as a function of pressure are presented in Fig. 9b. It is easy to recognize, starting from a certain pressure, that the character of the pressure dependence of the conductivity relaxation times changes apparently indicating decoupling phenomenon. Moreover, one can see that the relaxation time corresponding to this dynamic crossover is reduced after compression, indicating that decoupling, i.e. separation between the timescales of the structural and ionic motions, is enhanced with the increase in pressure. To express the sensitivity of decoupling to pressure, a parameter that is a derivative of the decoupling index (R_τ), has been calculated using the following formula:⁴⁷

Fig. 9 (A) The dielectric isothermal spectra registered during the compression of CIM HCl at T = 352 K by means of the imaginary part of electric modulus M′′. (B) Pressure dependence of the conductivity relaxation times τ_σ. Solid and dashed lines denote the Arrhenius fit functions. The black dashed line is just a guide for the eye. (C) T_g(P_g) dependence parametrized by the Andersson–Andersson equation (solid line). (D) The values of relaxation times at glass transition pressures (τ_cross) determined for various temperatures. Solid line denotes linear fit to these data.

The obtained value dlog R_τ/dp = 0.00268 MPa⁻¹ is similar to that obtained for carvedilol HCl (0.0029 MPa⁻¹) or lidocaine hemisuccinate (0.0029 MPa⁻¹).¹⁹

Returning to the question concerning the sensitivity of the glass transition temperature to the pressure, let us look again at the data shown in Fig. 9b. As reported for many ionic glass-formers, the data points, for which the crossover is observed, correspond to the iso-viscosity line (for η = 10¹² Pa s) and can be satisfactorily applied to determine the T_g(P_g) values.²⁶ Therefore, we used these values to designate the pressure coefficient of the glass transition temperature, as was previously done for CIM base. The calculated value of 0.139 K MPa⁻¹ (see Fig. 9c) was only slightly lower than those obtained for the non-ionic counterpart. A very similar value was reported for lidocaine hemisuccinate (0.127 K MPa⁻¹) and lidocaine docusate (0.132 K MPa⁻¹).²³ The dT_g/dp values mentioned in the reports for other ionic glass formers were usually slightly higher i.e. carvedilol dihydrogen phosphate (0.170 K MPa⁻¹), carvedilol hydrochloride (0.152 K MPa⁻¹),⁴⁸ verapamil hydrochloride (0.208 K MPa⁻¹),⁴⁹ lidocaine hydrochloride (0.170 K MPa⁻¹),⁵⁰ procainamide hydrochloride (0.150 K MPa⁻¹).⁵¹ An insufficient number of reports, especially those regarding comparative analysis of ionic samples and their neutral counterparts, does not allow the formulation of general rules regarding the high pressure behavior of the ionic liquid in relation to the corresponding non-charged form. In the case of the carvedilol salts both abovementioned ionic materials possessed a higher pressure coefficient of the glass transition temperature when compared to their non-ionic analogue (0.137 K MPa⁻¹).⁴⁸ In the case of CIM base and HCl, the values determined for the pressure coefficients were roughly similar and indicated rather moderate T_g susceptibility to the applied pressure.

Glassy dynamics

When we look closer at the dielectric spectra of CIM base and CIM HCl, we will see similarities in the patterns of their secondary relaxation behavior. Also, according to reports, the secondary relaxations, being a fingerprint of glassy dynamics, in ionic glasses share features common to those observed in the molecular glasses. However, it is hard to find reports comparing the glassy dynamics of ionic conductors and their non-ionic counterparts. Nonetheless, recently, several papers on the glassy dynamics of various PILs have been published, shedding more light on their complex dynamics below the T_g.^52,53 Basically, in molecular glasses, the origin of secondary processes may be twofold: one can reflect the local internal rearrangements, whereas another may involve the motions of all the atoms in a molecule.^54,55 The latter, due to its intramolecular cooperative nature and contribution to the glass transition, gained recognition as being particularly important. From their discovery by Johari and Goldstein, the so-called JG relaxations determined the course of the discussion on the glassy dynamics for the next few decades. Note that both types of motions were found for various PILs. However, according to previous reports, being rather rare, they may have either a bipolar or ionic origin. Moreover, in some cases, an extra feature can be observed, such as nearly constant loss (NCL) regions reflecting ionic motions restricted by cages formed by the surrounding molecules.^56–58

Returning to our results, the dielectric spectra of CIM base revealed two easily distinguishable secondary modes, assigned as β and γ, both showing the Arrhenius behavior with activation energies E_β = 56 ± 2 kJ mol⁻¹ and E_γ = 30 ± 1 kJ mol⁻¹. To decide whether the observed processes have an intrinsic nature or rather a JG character, we performed detailed investigations using pressure as a variable. This is a widespread approach to use pressure sensitivity as a reliable factor to directly determine whether the analyzed process has an intramolecular nature.^59,60 According to a classification proposed by Ngai and Paluch, depending on the response to increasing compression, secondary modes can be categorized as strongly sensitive (true-JG) or indifferent to densification by pressure (non-JG). The third group includes processes weakly sensitive to pressure, sometimes described as pseudo-JG.⁵⁹ In such cases, it is necessary to perform additional tests to reliably verify the origin of the analyzed process. The dielectric spectra of CIM base at T = 333 K registered for increasing pressures are presented in Fig. 8. Also, in ambient pressure experiments, two secondary modes were found, although under the applied thermodynamic conditions, the γ-process was only partially visible in the experimental window. However, this does not preclude the assessment of its pressure sensitivity. The presented results indicate that the γ-process was totally insensitive to compression, whereas for the β-process, pressure sensitivity, with ΔV = 11.61 cm³ mol⁻¹ (see Fig. 10), was observed. To remove the resulting uncertainty and determine the origin of the slightly pressure-sensitive β-process, we calculated the primitive relaxation time (τ₀), which, based on the assumptions of the Coupling Model (CM), can rationally predict the position of true JG-relaxation. We use the well-known relationship to calculate τ₀:^61,62

τ₀ = (τ_c)^1−β_KWW(τ_α)^β_KWW (11)

where τ_c ≈ 2 ps for most glass-formers and describes the characteristic time required for an intermolecular cooperativity, whereas β_KWW = 0.76. As shown in Fig. 3 there is no agreement between the position of primitive frequency f₀ = 1/2πτ₀ and the frequency value corresponding to the β-process maximum. In view of the foregoing, we assumed that both secondary modes in CIM base possess an intramolecular origin.

Fig. 10 The comparison of the ambient pressure dielectric loss spectra for CIM base and CIM HCl at T = 313 K. The inset shows the pressure sensitivity of the β-relaxation times for both samples. ΔV denotes an activation volume obtained as a fit parameter of the pressure counterpart of the Arrhenius relation to the presented data.

As mentioned in the beginning of this section, the comparison of the dielectric spectra registered for CIM base and CIM HCl revealed many similarities (see Fig. 10). As in the non-ionic sample, two secondary modes were found for CIM HCl. We assigned these as β′ and γ′, with activation energies E_β′ = 48 ± 1 kJ mol⁻¹ and E_γ′ = 35 ± 1 kJ mol⁻¹, respectively. These secondary modes were visible in both ε′′(f) and M′′(f) spectra and thus we assumed their bipolar nature. The previously reported results for other PILs with the analogous Cl⁻ anion but different cations, i.e. lidocaine,⁵³ procaine, and procainamide hydrochlorides,²¹ revealed the presence of secondary processes of ionic nature, which were described as β-conductivity relaxations. However, in CIM HCl as well as in the previously investigated chlorpromazine hydrochloride, both the secondary modes were due to dipolar cation relaxations.⁵² The questions concerning their JG or non-JG nature remains open. The performed experiments verifying the CIM HCl response to compression did not bring decisive results. Within these measurements the γ′-process was out of the accessible frequency range, whereas the β′-process seems to be pressure-sensitive with ΔV = 10.95 cm³ mol⁻¹. Almost the same effect was observed for CIM base. Contrary to the non-conductive sample, decision-making calculations based on CM were not possible in this case since the structural relaxations were completely covered by the conductivity contribution, making it impossible to assess the width of the structural relaxation peak. On the other hand, in the discussion on the origin of secondary processes in CIM HCl, we can appeal to undeniable similarities in the chemical structure of CIM base and its cation. In fact, they only differ in the presence of one proton, which may be irrelevant with respect to the dipole moment of a material. Since both processes found in CIM base reflect the local internal rearrangements, due to their similar structural skeleton, they should also appear in CIM base. To determine which part of a molecule is responsible for a particular mode, theoretical calculations in the framework of density functional theory (DFT) must be performed. Such results will also be helpful in determining whether the β′-process in CIM HCl is true-JG or not. It interesting is that the results presented herein clearly show that intramolecular forces govern the dynamics of the investigated samples to a greater extent in the supercooled liquid state. This is directly related to its cooperative and many-body character.

It is well known that when the liquid is quenched below the glass transition temperature, it deviates from the equilibrium and starts to relax towards more energy-favorable states.⁶³ The deeper the material kept in the glassy state, the longer the time required for the structural rearrangement into the equilibrium configuration. This time evolution of glass properties is called physical aging and can be investigated by monitoring the dielectric, mechanical, or thermal responses of the materials. This is possible because aging affects the various features of glassy materials, i.e. density, rate of stress, strain, enthalpy, and volume.⁶⁴ Aging is a general phenomenon, observed for all glasses regardless of their ionic or non-ionic nature. The undeniable fundamental and practical importance of history-dependent and time-evolving properties of glassy materials stimulated experimental and theoretical efforts to improve the understanding of their non-equilibrium behavior.^65,66 To shed more light on this problem, we performed time-dependent dielectric experiments and investigated the effects associated with the isothermal aging of CIM base and CIM HCl. The representative dielectric spectra registered in a time-dependent manner and analyzed in the framework of permittivity formalism are presented in Fig. 11. With time, the right slope of the α-process moves to lower frequencies, reducing its contribution to the β-process. These data clearly show that the gradual decline in the amplitude of β-relaxation peak is the most prominent hallmark of the ongoing aging process. The dielectric loss ε′′ values at fixed frequency plotted as a function of aging time are presented in Fig. 11. To their quantification, we applied the equation proposed by Lunkenheimer et al.⁶⁷

ε′′(t) = A exp(−[t/τ_age]^β) + ε′′_∞ (12)

where ε′′_∞ corresponds to ε′′ in the limit of infinite times, A expresses the difference in ε′′ for t → 0 and t → ∞, β is a stretching parameter, and τ_age denotes the aging relaxation-time. The τ_age values determined for each aging temperature were subsequently added to the relaxation maps for CIM base and CIM HCl (see Fig. 4 and 6, respectively). It can be observed that aging relaxation times obtained from the analysis of β-relaxation adeptly mimic the structural relaxation times corresponding to the glassy states of the investigated materials. For ionic materials, such information can also be obtained from the analysis of changes in the conductivity relaxation times during physical aging. The validity of such an approach was discussed for several ILs, e.g. CKN,⁶⁸ carvedilol phosphate, and procaine hydrochloride.⁶⁹

Fig. 11 Shift of dielectric loss peak during physical aging of CIM base at T = 298 K and CIM HCl at T = 308 K. The inset panels present the normalized dielectric loss ε′′ values at fixed frequency plotted as a function of aging time for indicating temperatures (open circles), as well as the fits of eqn (12) to the experimental data (solid lines).

Conclusions

The aim of our study assumed the comparison of the dielectric responses of two systems with a similar chemical backbone but totally distinct molecular interactions involved. As an object of our research, we chose CIM base and CIM HCl. The CIM base represents a van der Waals liquid, whereas CIM HCl belongs to the class of protic ionic conductors. While the dynamic properties of the former can be well described by the Lennard-Jones potential, in the latter, the long-range electrostatic interactions between the positively and negatively charged ions dominate over the short-range components. In our study, we address the vital problem related to the search for a relationship between the relaxation characteristics and the pattern of attractions involved. We confirmed that strong electrostatic interactions between the ions affect the material fluidity and leads to slowing of molecular dynamics, indicated by a higher T_g obtained for the conductive counterpart. Besides T_g, there are other characteristics attainable from dielectric loss spectra that can reflect the properties of the intramolecular potential. As shown for CIM base, its polar nature was indicated by a high Δε value and a narrow α-relaxation peak. This is related to the large value of the attractive part of the overall intramolecular force. This additional contribution originates from the interactions among the permanent dipoles in cimetidine base and is proportional to μ⁴/kT. We show that the careful analysis of the dielectric spectra above T_g can depict much valuable information about the nature of the molecular interactions governing the properties of the materials under study. On the contrary, below T_g, some similarities were found in the dynamic behavior of both samples. A comparison of the effects observed after the sample compression revealed another similarities, such as moderate pressure sensitivities of both materials. We showed that the BDS spectroscopy is a convenient method of choice for the comparative analysis of samples with distinct dynamic behavior, together with the TMDSC technique and rheology, enabling a detailed comparison of the relaxation features of ionic and non-ionic materials.

CIM HCl, investigated here, is an another representative of a protic ionic liquid explored by our group. It is a succeeding example of a molecule in which decoupling is accelerated due to compression, which confirms the assumption that fast proton hopping is probably involved in its conductivity mechanism. Previously, we investigated PILs with the same monoatomic Cl⁻ anion and various molecular cations, i.e. lidocaine, procaine and procainamide, chlorpromazine, and carvedilol. These results, together with the outcome of the present study, make a huge contribution to the study on establishing a universal pattern of PIL behavior, also including the interplay between the intramolecular factors affecting their behavior. This is necessary for a further successful implementation of PILs in various industrial areas.

Acknowledgements

The authors highly acknowledge the financial support received from the National Science Centre within the framework of the Opus8 project (Grant DEC-2014/15/B/ST3/04246).

Notes and references

1. D. Chandler, J. D. Weeks and H. C. Andersen, Science, 1983, 220(4599), 787–794.
2. K. Dong and S. Zhang, Chem.–Eur. J., 2012, 18, 2748–2761.
3. H. Weingrtner, Angew. Chem., Int. Ed., 2008, 47, 654–670.
4. L. T. Greaves and C. J. Drummond, Chem. Rev., 2015, 115, 11379–11448.
5. E. J. Maginn, J. Phys.: Condens. Matter, 2009, 21, 373101.
6. M. Paluch, J. Knapik, Z. Wojnarowska, A. Grzybowski and K. L. Ngai, Phys. Rev. Lett., 2016, 116(2), 025702.
7. G. Williams and D. C. Watts, Trans. Faraday Soc., 1970, 66, 80–85.
8. P. Lunkenheimer, in Habilitation, Augsburg, 1999.
9. Y. Sun, H. Xi, M. D. Ediger, R. Richert and L. Yu, J. Chem. Phys., 2009, 131, 074506.
10. S. Havriliak and S. Negami, Polymer, 1967, 8, 161–210.
11. F. Kremer and A. Schönhals, Broadband Dielectric Spectroscopy, Springer Verlag, Berlin, 2003.
12. D. Saha, Y. M. Joshib and R. Bandyopadhyay, Soft Matter, 2014, 10, 3292.
13. H. Vogel, Phys. Z., 1921, 22, 645–646.
14. G. S. Fulcher, J. Am. Ceram. Soc., 1925, 8, 339–355.
15. G. Tammann and W. Hesse, Z. Anorg. Allg. Chem., 1926, 156, 245–257.
16. C. A. Angell, in Relaxations in complex systems, ed. K. L. Ngai and G. B. Wright, NRL, Washington, DC, 1985, pp. 3–11.
17. R. Bohmer, K. L. Ngai, C. A. Angell and D. J. Plazek, J. Chem. Phys., 1993, 99, 4201.
18. P. Bordat, F. Affouard, M. Descamps and K. L. Ngai, Phys. Rev. Lett., 2004, 93(10), 105502.
19. Z. Wojnarowska and M. Paluch, J. Phys.: Condens. Matter, 2015, 27(7), 073202.
20. F. S. Howell, R. A. Bose, P. B. Macedo and C. T. Moynihan, J. Phys. Chem., 1974, 78, 639–648.
21. Z. Wojnarowska, A. Swiety-Pospiech, K. Grzybowska, L. Hawelek, M. Paluch and K. L. Ngai, J. Chem. Phys., 2012, 136, 164507.
22. Z. Wojnarowska, J. Knapik, M. Rams-Baron, A. Jedrzejowska, M. Paczkowska, A. Krause, J. Cielecka-Piontek, M. Jaworska, P. Lodowski and M. Paluch, Mol. Pharm., 2016, 13, 1111–1122.
23. Z. Wojnarowska, K. J. Paluch, E. Shoifet, C. Schick, L. Tajber, J. Knapik, P. Wlodarczyk, K. Grzybowska, S. Hensel-Bielowka, S. P. Verevkin and M. Paluch, J. Am. Chem. Soc., 2015, 137, 1157–1164.
24. R. D. Deegan, R. L. Leheny, N. Menon, S. R. Nagel and D. C. Venerus, J. Phys. Chem. B, 1999, 103, 4066–4070.
25. T. Psurek, S. Hensel-Bielowka, J. Ziolo and M. Paluch, J. Chem. Phys., 2002, 116, 9882.
26. Z. Wojnarowska, Y. Wang, K. J. Paluch, A. P. Sokolov and M. Paluch, Phys. Chem. Chem. Phys., 2014, 16, 9123.
27. T. L. Greaves and C. J. Drummond, Chem. Rev., 2015, 115, 11379–11448.
28. K. Fumino, A. Wulfa and R. Ludwig, Phys. Chem. Chem. Phys., 2009, 11, 8790–8794.
29. F. Dommert, K. Wendler, R. Berger, L. Delle Site and C. Holm, ChemPhysChem, 2012, 13(7), 1625–1637.
30. H. Shirota and E. W. Castner, J. Phys. Chem. A, 2005, 109(42), 9388–9392.
31. D. Roy, N. Patel, S. Conte and M. Maroncelli, J. Phys. Chem. B, 2010, 114, 8410–8424.
32. L. Berthier, G. Biroli, J. P. Bouchaud, L. Cipelletti, D. El Masri, D. L'Hote, F. Ladieu and M. Pierno, Science, 2005, 310, 1797–1800.
33. S. Capaccioli, G. Ruocco and F. Zamponi, J. Phys. Chem. B, 2008, 112, 10652–10658.
34. K. Grzybowska, A. Grzybowski, Z. Wojnarowska, J. Knapik and M. Paluch, Sci. Rep., 2015, 5, 16876.
35. K. Ueno, Z. Zhao, M. Watanabe and C. A. Angell, J. Phys. Chem. B, 2012, 116, 63–70.
36. C. M. Roland, S. Hensel-Bielowka, M. Paluch and R. Casalini, Rep. Prog. Phys., 2005, 68, 1405–1478.
37. Y. Zhao, X. Liu, X. Lu, S. Zhang, J. Wang, H. Wang, G. Gurau, R. D. Rogers, L. Su and H. Li, J. Phys. Chem. B, 2012, 116, 10876–10884.
38. A. Andersson and O. Andersson, Macromolecules, 1998, 31(9), 2999–3006.
39. K. Koperwas, A. Grzybowski, S. N. Tripathy, E. Masiewicz and M. Paluch, Sci. Rep., 2015, 5, 17782.
40. C. M. Roland, R. Casalini, R. Bergman and J. Mattsson, Phys. Rev. B: Solid State, 2008, 77, 012201.
41. W. A. Bueno and E. G. Sobrinho, Spectrochim. Acta, 1995, 51(2), 287–292.
42. M. Barańska and L. M. Proniewicz, J. Mol. Struct., 1999, 511–512, 153–162.
43. H. Tecle, L. Robichaud and C. F. Schwender, J. Med. Chem., 1981, 24, 1095–1097.
44. G. Karpińska, J. C. Dobrowolski and A. P. Mazurek, J. Mol. Struct., 2003, 645, 37–43.
45. N. L. Calvo, S. O. Simonetti, R. M. Maggio and T. S. Kaufman, Anal. Chim. Acta, 2015, 875, 22–32.
46. M. Sekula, S. Pawlus, S. Hensel-Bielowka, J. Ziolo, M. Paluch and C. M. Roland, J. Phys. Chem. B, 2004, 108, 4997–5003.
47. A. Swiety-Pospiech, Z. Wojnarowska, S. Hensel-Bielowka, J. Pionteck and M. Paluch, J. Chem. Phys., 2013, 138(20), 204502.
48. Z. Wojnarowska, Y. Wang, J. Pionteck, K. Grzybowska, A. P. Sokolov and M. Paluch, Phys. Rev. Lett., 2013, 111, 225703.
49. Z. Wojnarowska, M. Paluch, A. Grzybowski, K. Adrjanowicz, K. Grzybowska, K. Kaminski, P. Wlodarczyk and J. Pionteck, J. Chem. Phys., 2009, 131, 104505.
50. A. Swiety-Pospiech, Z. Wojnarowska, J. Pionteck, S. Pawlus, A. Grzybowski, S. Hensel-Bielowka, K. Grzybowska, A. Szulc and M. Paluch, J. Chem. Phys., 2012, 136, 224501.
51. Z. Wojnarowska, C. M. Roland, A. Swiety-Pospiech, K. Grzybowska and M. Paluch, Phys. Rev. Lett., 2012, 108, 015701.
52. S. Hensel-Bielowka, K. L. Ngai, A. Swiety-Pospiech, L. Hawelek, J. Knapik, W. Sawicki and M. Paluch, J. Non-Cryst. Solids, 2015, 407, 81–87.
53. Z. Wojnarowska, K. Grzybowska, L. Hawelek, A. Swiety-Pospiech, E. Masiewicz, M. Paluch, W. Sawicki, A. Chmielewska, P. Bujak and J. Markowski, Mol. Pharm., 2012, 9, 1250.
54. G. P. Johari and M. Goldstein, J. Chem. Phys., 1970, 53, 2372.
55. S. Capaccioli, D. Prevosto, M. Lucchesi, P. A. Rolla, R. Casalini and K. L. Ngai, J. Non-Cryst. Solids, 2005, 351, 2643–2651.
56. C. M. Roland, M. J. Schroeder, J. J. Fontanella and K. L. Ngai, Macromolecules, 2004, 37, 2630–2635.
57. J. C. Dyre, P. Maass, B. Roling and D. L. Sidebottom, Rep. Prog. Phys., 2009, 72, 046501.
58. S. N. Tripathy, Z. Wojnarowska, J. Knapik, H. Shirota, R. Biswas and M. Paluch, J. Chem. Phys., 2015, 142, 184504.
59. K. L. Ngai and M. Paluch, J. Chem. Phys., 2004, 20(2), 857–873.
60. K. L. Ngai and S. Capaccioli, J. Phys.: Condens. Matter, 2008, 20, 244101.
61. K. L. Ngai, J. Phys.: Condens. Matter, 2003, 15, S1107–S1112.
62. K. L. Ngai, J. Chem. Phys., 1998, 109, 6982.
63. R. Casalini and C. M. Roland, Phys. Rev. Lett., 2009, 102, 035701.
64. I. M. Hodge and A. R. Berens, Macromolecules, 1982, 15, 762–770.
65. R. Xiao, J. Choi, N. Lakhera, C. M. Yakacki, C. P. Frick and T. D. Nguyen, J. Mech. Phys. Solids, 2013, 61, 1612–1635.
66. R. Xiao and T. D. Nguyen, J. Mech. Phys. Solids, 2015, 82, 62–81.
67. P. Lunkenheimer, R. Wehn, U. Schneider and A. Loidl, Phys. Rev. Lett., 2005, 95, 055702.
68. M. Paluch, Z. Wojnarowska and S. Hansel-Bielowka, Phys. Rev. Lett., 2013, 110, 015702.
69. Z. Wojnarowska, C. M. Roland, K. Kolodziejczyk, A. Swiety-Pospiech, K. Grzybowska and M. Paluch, J. Phys. Chem. Lett., 2012, 3, 1238.

---