Relations between the Structural -Relaxation and the Johari-Goldstein

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Relations between the Structural #-Relaxation and the Johari-Goldstein #Relaxation in Two Monohydroxyl Alcohols: 1-Propanol and 5-Methyl-2-Hexanol Kia L. Ngai, and Li-Min Wang J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b11453 • Publication Date (Web): 02 Jan 2019 Downloaded from http://pubs.acs.org on January 6, 2019

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The Journal of Physical Chemistry

Relations between the Structural -Relaxation and the Johari-Goldstein β‑Relaxation in Two Monohydroxyl Alcohols: 1-Propanol and 5-Methyl-2-Hexanol K. L. Ngai1,2,*, Li-Min Wang2 1CNR-IPCF, 2State

Università di Pisa, Largo B. Pontecorvo 3, I-56127, Pisa, Italy

Key Lab of Metastable Materials Science and Technology, and College of Materials

Science and Engineering, Yanshan University, Qinhuangdao, Hebei, 066004 China

ABSTRACT: The hydrogen-bonded monohydroxyl alcohols form a large class of glass-formers studied more than one hundred years and still the structure and dynamics have continued to be a research problem. Recent advance suggests hydrogen-bonded transient supramolecular structure, which is the origin of the Debye relaxation dominating the dielectric loss spectra of many monohydroxyl alcohols. Obscured by the slower Debye relaxation, the structural -relaxation is either not resolved or showing up as a shoulder, and the supposedly universal Johari-Goldstein (JG) -relaxation is not always observed. Thus properties of the -relaxation and the JG -relaxation as well as the strong connection between the two relaxations generally observed in other classes of glass-formers are not commonly known in the monohydroxyl alcohols. Notwithstanding, extremely broadband dielectric relaxation and high precision light scattering experiments published recently have resolved the -relaxation and a secondary relaxation in two archetypal monohydroxyl alcohols, 1-propanol and 5-methyl-2-hexanol by Gabriel et al. We analyzed their experimental data and applied the Coupling Model to show the secondary relaxations in 1-propanol and 5M2H are JG -relaxations with strong connection to the -relaxation. The result is novel because it is not known before whether the secondary relaxations of these two monohydroxyl alcohols are JG -relaxation involving the entire molecule or are intramolecular relaxations. Based 1 ACS Paragon Plus Environment

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on this conclusion, we predict the secondary relaxation is pressure dependent and the ratio

(T,P)/(T,P) is invariant to variations of P and T while (T,P) is maintained constant and provided the frequency dispersion of the -relaxation is also constant. The prediction is compared with dielectric data of 5M2H at elevated pressures. Based on the identification of monohydroxyl alcohols as short-chain polymeric liquids by others, an explanation of the stronger T and P dependences of (T,P) than the Debye relaxation time D(T,P) is given. Corresponding author: [email protected] ; [email protected]

INTRODUCTION Dielectric relaxation study of the dynamics of monohydroxy alcohols is not only historic since the work of Debye1, but also it continues to be an active research topic till the present time2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30. The slowest Debye process in the dielectric spectra of many monohydroxy alcohols commands attention due its exceptionally high intensity and extremely narrow frequency dispersion or exponential time dependent relaxation function. The more recent efforts including nuclear magnetic resonance20, dielectric relaxation at elevated pressures24,28,29, shear mechanical relaxation25 and neutron scattering27 measurements have shown the Debye relaxation originates from the dynamics of transient supramolecular or short-chain structures22,25 of these hydrogen-bonded liquids. Despite the advances made in the research on the Debye relaxation, not much attention was paid on the dynamics of the faster structural -relaxation and the secondary -relaxation in the monohydroxyl alcohols. In other glass-formers, including van der Waals liquids, polymers,

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polyalcohols30,31,32,33,34,35,36,37,38,39, and other hydrogen-bonded liquids40,41, generally established is the existence of connection in properties and relaxation times between the -relaxation and a secondary -relaxation belonging to the special class called the Johari-Goldstein -relaxation. For example, the separation between of the -relaxation from the -relaxation measured by the ratio of their respective relaxation times (T,P) and (T,P) is approximately determined by the width of the frequency dispersion of the -relaxation for any fixed value of (T,P) independent of temperature T and pressure P.30-32 The Fourier transform of the Kohlrausch-Williams-Watts (KWW) function,

[

1―𝑛

𝜙(𝑡) = exp ― (𝑡 𝜏𝛼)

],

(1)

accounts well the frequency dispersion of the -relaxation and the width is proportional to n in the fractional exponent, the property can be restated as [log – log] is determined by n. Since the monhydroxyl alcohols have transient supramolecular structures different from the other glassformers, it is worthwhile to study in detail the dynamics of the  and  relaxations and check if the relation between [log – log] and n continues to hold or not. This is the main objective of the present paper. However, it is not an easy task because the slower Debye process makes it difficult to resolve the -relaxation and determine its frequency dispersion, even after the contribution of the former to the spectrum has been subtracted off 11,12. Located at higher frequencies, the -relaxation usually has weak relaxation strength and not resolved in the liquid, and rarely shown in the glassy state27-29. The situation is improved by the most recent experimental studies of two monohydroxyl alcohols, 1-propanol42 and 5-methyl-2-hexanol (5M2H)43, by very broadband dielectric



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spectroscopy (with additional time domain dielectric experiments) and depolarized dynamic light scattering (DDLS). The -relaxation as well as the -relaxation appear in the DDLS spectra in good agreement in the dynamics with that observed in the dielectric spectra. The wealth of information from these experiments enable us to address the dynamic properties of the  and  relaxations in these two archetypal monohydroxyl alcohols, and to verify that the relations between their relaxation times is the same as found in the other glass-formers, and hence the -relaxation belongs to the class of Johari-Goldstein (JG) -relaxations.

RESULTS AND DISCUSSIONS The existence of a secondary relaxation in all glass-formers with properties strongly connected to that of the structural -relaxation was suggested first in 199830 from the analogy it has to the primitive relaxation of the Coupling Model (CM). Such secondary relaxation is called the JohariGoldstein (JG) -relaxation30-32 to distinguish other secondary relaxations which involve internal degrees of freedom and parts of the molecule, while the JG -relaxation entails motion of the entire molecule. The primitive relaxation is closely related to the JG -relaxation, and hence (T,P) is approximate equal to 0(T,P), i.e.,

(T,P)  0(T,P)

(2)

In the CM, the -relaxation time (T,P) is determined by the primitive relaxation time 0(T,P) by the equation, 𝜏𝛼(𝑇,𝑃) = [𝑡𝑐―𝑛𝜏0(𝑇,𝑃)]

1/(1 ― 𝑛)

,

(3)


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where tc is a constant equal to about 1-2 ps for molecular glass-formers, and n is the fractional exponent appearing in the KWW function in Eq.(1). For readers not familiar with the long history of the CM since 1979, it is important to note that both the KWW form of the correlation function in Eq.(1) and also the key CM Eq.(3) were derived theoretically from several versions of the CM4448.

Also the value of tc 1-2 ps for molecular glass-formers and polymers is not ad hoc, and instead

was determined directly in neutron scattering experiments49-52, and molecular dynamics simulations32, and more can be found in the book 32. The microscopic JG -relaxation time, (T,P), can be obtained approximately from relation (2) by calculating the primitive 0(T,P) of the CM with the procedure described as follows. First, the value of n is determined by fitting the Fourier transform of the KWW function to the frequency dispersion of the -relaxation. After that, 0(T,P) is calculated from the companion equation of Eq.(3), 𝜏0(𝑇,𝑃) = [𝜏𝛼(𝑇,𝑃)]1 ― 𝑛(𝑡𝑐)𝑛

(4)

The approximate or order of magnitude agreement between the calculated 0(T,P) and the experimental (T,P) has been verified in many different glass-formers30-39. In turn, the verification leads to the strong connection of (T,P) to (T,P) in accord with the relation, 𝜏𝛽(𝑇,𝑃) ≈ [𝜏𝛼(𝑇,𝑃)]1 ― 𝑛(𝑡𝑐)𝑛

(5)

found in many studies30-39, It is worthwhile to mention that the JG -relaxation is composed of a distribution of processes53,54, and the text of the approximate relation (T,P)  0(T,P) is unequivocal only if

(T,P) can be extracted from the spectra such as the -loss peak frequency. On the other hand if 5 ACS Paragon Plus Environment


the spectra do not provide directly a characteristic (T,P) and an arbitrary or unjustified fitting procedure has to be used, the value of (T,P) obtained is artificial and larger deviation from the

(T,P)  0(T,P) is possible. Dielectric relaxation and DDLS data of 1 propanol We now make use of the dielectric and DDLS data of 1-propanol42 and 5M2H43 of Gabriel et al. to check if relation (2) holds also in these archetypal monohydroxyl alcohols. Fig.1 reproduces some of the dielectric loss (f) data of 1-propanol taken at 97.2, 99.2, 101, and 105.8 K. The contribution of the Debye relaxation has been subtracted off from the data to show the resolved -relaxation together with the -relaxation at higher frequencies as shown for the cases of 97.2 K and 105.8 K. The -relaxation loss peak at all temperatures are well fitted by the Fourier transform of the KWW function with n=0.40 as demonstrated for the result at 97.2 K in Fig.1. With the values of (T) determined from the fits, and n=0.40, we calculated the corresponding values of 0(T) by eq.(4). The resultant primitive frequencies f0(T)1/20(T) indicated by arrows are compared with the -relaxation frequency f(T)1/2(T) in Fig.1. There is approximate agreement between f(T) and f0(T) at temperatures where the loss peak frequency can be used to stand for f(T), and hence the relation (T)  0(T) holds for 1-propanol in dielectric relaxation. After subtracting off the Debye contribution, Hansen et al.11 had fitted the dielectric -relaxation by the Fourier transform of the KWW function with the same value of n=0.40. The dielectric f(T) and f(T), as well the DDLS f(T) from Hansen et al. plotted against reciprocal temperature are presented in Fig.S1 in the Supporting Information (SI). The primitive f0(T) calculated from dielectric f(T) and DDLS f(T) at two temperatures are depicted by the two filled triangles. The


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approximate relation, f(T)  f0(T), holds also in the dielectric and DDLS data of Hansen et al. as well as the dielectric data of Sillrén et al.27 shown in the same manner in Fig.S2. Gabriel et al.42 performed depolarized photon correlation (DDLS) experiments with an improved setup on 1-propanol and compare the light scattering data with the dielectric over a broad temperature range. The correlation function of the electric field g1(t) was Fourier transformed to obtain the susceptibility  in Fig.2. The Debye relaxation is absent in the DDLS spectra presented in Fig.2 for six temperatures. This makes it possible to directly observed the relaxation, and the improved DDLS setup allows Gabriel et al. to observe the JG β-process in conjunction with the -relaxation. They found the  and  relaxations in DDLS have almost identical spectral characteristics as in dielectric relaxation. This was already reported by Hansen et al.11 for the α process. For the DDLS -relaxation of Gabriel et al., this is clear from the same value of n=0.40 in the KWW function used to fit its frequency dispersion in Fig.2 as for the dielectric -relaxation in Fig.1. The values of (T) obtained from the KWW fits at the three lower temperatures were used to calculate the corresponding values of 0(T) by eq.(4). The locations of the primitive frequencies f0(T)1/20(T) in Fig.2 are indicated by arrows. Again there is approximate agreement between f0(T) and the -relaxation frequency f(T) at temperatures where the loss peak frequency can be used to stand for f(T). Therefore the relation (T)  0(T) holds for 1-propanol in DDLS as well in dielectric relaxation. The property, (T)  0(T), is one of the reliable criteria for JG -relaxation, i.e. secondary relaxation with properties connected to that of the -relaxation such as pressure dependence of . Since this property is verified by dielectric relaxation and DDLS in 1-propanol, hence the secondary relaxation is the Johari-Goldstein relaxation. We reach this conclusion despite the question is unsettled38 of whether the secondary 7 ACS Paragon Plus Environment


relaxation in 1-propanol is highly restricted reorientations of all molecules or it entails large angle reorientation and not all molecules are involved. Experiments at elevated pressure performed on 1-propanol near 100 K in the future will be helpful to strengthen the identification of the secondary relaxation as the JG -relaxation.

Figure 1. Replotting the dielectric loss (f) data of 1-propanol from Gabriel et al.42 at 97.2, 99.2, 101, and 105.8 K (from left to right). The + symbols at 97.2 and 105.8 K represent the results after subtracting the Debye relaxation from the data. The blue line is the KWW fit of the -relaxation at 97.2 K with n=0.40.


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Figure 2. Susceptibility () obtained by Fourier transform of the DDLS electric field correlation functions g1(t) of 1-propanol at temperatures of 99.0, 10104.8, 106.7, 112.7, 122.2, and 126.9 K (from left to right) from Gabriel et al.42. The dashed lines are the KWW fits with n=0.40. The locations of the arrows indicate logf0 calculated with n=0.40 for the three lower temperatures. Dielectric relaxation and DDLS data of 5-methyl-2-hexanol (5M2H) Gabriel et al. studied 5M2H, another monohydroxyl alcohol by isothermal dielectric relaxation and light scattering and compare the results after the electric field correlation function g1(t) was Fourier transformed to susceptibility (f). The results of (f) and (f) from the two spectroscopies are compared at one selected temperature of 157 K in Fig. 3. Like in 1-propanol, the dielectric Debye relaxation in 5M2H shows up as the intense loss peak and fitted by the line in Fig.3. The dielectric  relaxation is resolved after subtracting off the fit of the Debye relaxation from the data.



The Debye relaxation is much suppressed in intensity in (f) of light scattering but still visible, and appears together with the prominent α relaxation in the intermediate time range and a β process at shorter times. Gabriel et al. fitted the DDLS susceptibility spectra and resolved the Debye relaxation. The resultant DDLS α and  relaxation appear to be almost identical in their line shapes and time constants as those in the dielectric spectra as demonstrated in Fig.3. The overlapping DDLS and dielectric -relaxation data are well fitted by the Fourier transform of the KWW function with n=0.44 (blue line), slightly larger than the value of 0.40 of 1-propanol. From the values of  and n determined by the fit, the primitive relaxation time 0 was calculated by eq.(4). The value of the corresponding f0 indicated by the arrow in Fig.3 is in rough agreement with the -loss peak frequency, verifying once more that the -relaxation in 5M2H conforms to the relation

(T)  0(T), and it is the JG -relaxation. There is corroborating evidence from the dielectric data of 5M2H previously published12. We have analyzed the data and the results confirm the same conclusion as shown in Fig.S2 of SI. Relation (5) also predicts strong connection of the (T,P) to that of (T,P) in 5M2H via their pressure dependences. In particular relation, the pressure dependence of (T,P) is predicted. Pawlus et al.24 did measure the dielectric relaxation of 5M2H over a wide range of temperatures and pressures up to 1750 MPa. Their results at four pressures, 0.1, 512, 780, and 1750 MPa, verify the pressure dependence of JG -relaxation by showing At pressures ∼500 MPa and higher, the -relaxation merges with the Debye process to form a single dominant process, making it impossible to extract the characteristics of the -relaxation unambiguously. The frequency dispersion and relaxation time of the -relaxation at the elevated pressures are not known. Hence the invariance of frequency dispersion of the -relaxation and the ratio (T,P)/(T,P) to variations of P and T at constant (T,P) found in other glass-formers cannot be checked in the 10 ACS Paragon Plus Environment

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case of 5M2H. Notwithstanding, it is worthwhile to examine the dielectric loss spectra for four different combinations of P and T, all having the same peak frequency or the same relaxation time for the dominating process presented by Pawlus et al. in their Fig.6. The high frequency excess loss is the JG -relaxation, and it seems to occur at about the same frequency range.

Figure 3. Direct comparison of dielectric (green squares) and DDLS data of 5M2H (black circles, and black line is fit by Gabriel et al.43) at 157 K, demonstrating that α and  relaxation appear to be almost identical in both methods in their line shapes and time constants (DDLS, red circles). Fit of the Debye relaxation (light blue dashed line for dielectric data, and green dashed line for DDLS data were done by Gabriel et al.). The blue solid line is the KWW fit to -relaxation for both dielectric and DDSL data with n=0.44.



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Differences in T and P dependences of Debye relaxation and structural -relaxation There are two advances in the dynamics of the Debye relaxation that we can use to address the empirical fact that the faster structural -relaxation has stronger temperature dependence than the slower Debye process, which causes the merging of the two relaxation by lowering temperatures 6,42,43

or by elevating pressure24. One advance is the identification of the Debye process with

rheological behavior from oligomeric chains in monohydroxyl alcohols by Gainaru et al.25 based on shear mechanical study. This has led them to suggest theoretical concepts of polymer science are applicable to understand the anomalous physical behavior of a wide range of hydrogen-bonded liquids. We not only agree but also point out the relaxation time of the chain or Rouse modes in low molecular weight and unentangled linear polymers have temperature and pressure dependences weaker than the segmental -relaxation time

58,59,

and the explanation by the

Coupling Model59,60 based on two properties: (1) the presence of intermolecular coupling (i.e. nonzero coupling parameter) of the segmental -relaxation and the lack of it in the Rouse modes (i.e., zero coupling parameter), and (2) the same primitive monomeric friction factor for the two modes. In monohydroxyl alcohols, the Debye process has zero coupling parameter supported by either the analogy of the oligomeric chains to Rouse chains in polymers or the exponential time dependence of its correlation function, while the structural -relaxation has nonzero coupling parameter such as 0.40 of 1-propanol and 0.44 of 5M2H. Therefore the explanation of thermorheological and piezo-rheological complexities of low molecular weight polymers59,60 applies verbatim to the weaker temperature and pressure dependences of the Debye process than the relaxation in monohydroxyl alcohols. Quantitative test can be difficult because it requires the relaxation times (T,P) at T and P close to the Debye relaxation times D(T,P), and the merging of the two relaxations together makes it difficult to determine (T,P). 12 ACS Paragon Plus Environment

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Property (2) is also satisfied in monohydroxyl alcohols as suggested by the other advance of Thoms et al. from the pressure dependence of the Debye relaxation time of the branched monohydroxyl alcohol 2-butyl-1-octanol by dielectric spectroscopy. They found evidence of a crossover from slower to faster than exponential pressure dependence at different temperatures, and similar behavior in the viscosity. Thoms et al., concluded that these interesting findings indicate that the Debye relaxation time and the structural -relaxation time stem from some common origin, which implies they have the same primitive friction factor.

CONCLUSIONS The monohydroxyl alcohols form a large class of glass-formers by the multiple variations of the molecular structures from the different lengths and branching of the alkyl chain. There is a long history in the research on the monohydroxyl alcohols, particularly from the use of dielectric relaxation. There is a lack of consensus on microscopic understanding of the structure and dynamics for a long time. Recently the characteristic Debye relaxation observed has been identified as transient supramolecular structure originating from hydrogen bonding. Notwithstanding, the primary structural -relaxation and secondary -relaxation in monohydroxyl alcohols have been studied occasionally in the past. Consequently their dynamics are largely unknown, particularly whether monohydroxyl alcohols possess a general property found in many glass-formers with different chemical and physical structures. The property is the ubiquitous existence of a secondary relaxation, called the Johari-Goldstein (JG) -relaxation, with relaxation time (T,P) strongly connected in properties to that of (T,P). Taking advantage of the high quality dielectric and light scattering data recently obtained by Gabriel et al. we have verified that



(T) is approximately the same as the primitive relaxation time 0(T) of the Coupling Model. Since 0(T) is exactly connected to (T) in all properties, it follows that the secondary relaxations in 1propanol and 5M2H are JG -relaxations. This result is novel for the monohydroxyl alcohols. Based on this conclusion, we predict the secondary relaxation of 1-propanol and 5M2H is pressure dependent and the ratio (T,P)/(T,P) is invariant to variations of P and T while (T,P) is maintained constant, and provided the frequency dispersion of the -relaxation is constant. Dielectric study of 5M2H at elevated pressure verifies the secondary relaxation is pressure sensitive. However invariance of the ratio (T,P)/(T,P) cannot be fully verified due to the relaxation having merged with the Debye process at elevated pressures to form a single loss peak24, and it is impossible to determine (T,P) and frequency dispersion of the -relaxation. The property of (T,P) having stronger temperature and pressure dependences than D(T,P) is evidenced by the merging of the -relaxation with the Debye relaxation on lowering T or increasing P. This is analogous to the thermo-rheological and piezo-rheological complexities of low molecular weight linear polymers. It can be explained in the same way as done before for polymers since others have identified monohydroxyl alcohols as short-chain polymeric liquids, and the Debye relaxation originates from the motion of the chains.

Acknowledgements This work was supported by National Basic Research Program of China (973 Program No. 2015CB856805), National Natural Science Foundation of China (NSFC) (Nos. 11474247) and Key Research and Development Program of Hebei Province (No. 18391502D). 14 ACS Paragon Plus Environment

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Relations between the Structural -Relaxation and the Johari-Goldstein

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