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Molecular dynamics study on the glass forming process of asphalt
Construction and Building Materials 214 (2019) 430–440
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Molecular dynamics study on the glass forming process of asphalt Yang Kang a,⇑, Dunhong Zhou b, Qiang Wu a, Rui Liang a, Shaoxin Shangguan a, Zhiwei Liao a, Ning Wei a,⇑ a b
College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, Shaanxi, China Nanjing ASFT Neomaterials LLC., Xinmofan Road, Nanjing 210009, Jiangsu, China
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Molecular dynamic simulations were
used to study glass forming process of asphalt. Glass transition of asphalt spans a wide temperature range from ca. 400 K to ca. 250 K. Non-Arrhenius temperature dependence of viscosity implies a transition at ca. 400 K. Breakdown of Stokes-Einstein relation verifies the transition at ca. 400 K. Viscoelastic liquid-Newtonian liquid transition at ca. 400 K explained by cage effect.
a r t i c l e
i n f o
Article history: Received 5 July 2018 Received in revised form 10 April 2019 Accepted 17 April 2019
Keywords: Molecular dynamics Asphalt Glass transition Liquid-liquid transition Glass forming liquid
a b s t r a c t Glass transition temperature (Tg) is a significant parameter that determines the viscoelastic properties of asphalt. However, the understanding of glass transition process of asphalt is ambiguous, especially at the molecular level. In this paper, molecular dynamic (MD) simulations were used to help understanding the glass forming process from the viewpoint of glass forming liquid. The temperature dependence of volumetric properties, such as free volume, fractional free volume, specific volume and coefficients of volume thermal expansion etc., for AAA-1 asphalt were computed. Results show that there are two transition temperatures with temperature decreasing from 575 K to 50 K, i.e., one is Tg at ca. 250 K, the other is ca. 400 K. The nonArrhenius type temperature dependence of viscosity and the breakdown of Stokes-Einstein relation imply that the transition at ca. 400 K is responsible to the liquid–liquid transition of asphalt from viscoelastic liquid to Newtonian fluid. Furthermore, molecular trajectory demonstrated that at ca. 400 K, AAA-1 asphalt system experienced the transition from non-ergodic local thermal vibrations and restricted movement to temperature-independent ergodic movement, and this observation verified that the liquid–liquid transition of asphalt did occur at ca. 400 K. Namely, at temperatures higher than 400 K, the rearrangement process of asphalt colloid cage is a temperature-independent a-relaxation, and in the temperature range from 400 K to 250 K, the relaxation associated with diffusional movement is a slow a-relaxation, i.e., structure relaxation of glass transition, and at temperatures lower than 250 K, asphalt is truly frozen glassy. Moreover, the good agreement between the rheological experiments and simulation results demonstrated that the MD results are reliable. This paper helps understanding microscopic picture of glass forming asphalt and its relaxation mechanisms with temperature, which could enable new additives and new additive strategies to modify asphalt and facilitate crude oil exploitation, transportation and refining processes, etc. Ó 2019 Elsevier Ltd. All rights reserved.
⇑ Corresponding authors. E-mail addresses: [email protected] (Y. Kang), [email protected] (N. Wei). https://doi.org/10.1016/j.conbuildmat.2019.04.138 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
Y. Kang et al. / Construction and Building Materials 214 (2019) 430–440
1. Introduction Asphalt is a typical amorphous material, which is a complex heterogeneous mixture of hydrocarbons usually collected as a byproduct of the refining process of crude oil in petroleum refineries [1]. The existence of asphalt within crude oil greatly influences the exploitation, transportation, and refining etc. of crude oil for their mechanical responses vary with temperature and time dramatically. Asphalt has numerous applications and the most important one of them is as a binder for aggregates in building roads [2,3]. To pave an asphalt concrete road properly, operation temperatures, e.g., the temperature for transport and storage, the temperature during mixing, laying and compacting operations, etc., have to be controlled rigorously. When paved, performances of asphalt concretes vary dramatically from ca. 200 K to ca. 400 K. With the decrease of temperature, mechanical states of asphalt change from Newtonian fluid to a viscoelastic state and to a glassy solid [4,5]. Temperature at which mechanical states of asphalt change from viscoelastic state to glass state is called the glass transition temperature (Tg) [4]. Tg is a significant parameter that determines the viscoelastic properties of asphalt, which can influence the mechanical properties such as toughness and creep critically and also cause major changes in its physiochemical and rheological properties, giving rise to a huge impact on the pavement [6]. Several researchers [7–10] had studied the Tg of the Strategic Highway Research Program (SHRP) core asphalts by experiments and molecular dynamic simulations. Therein, from differential scanning calorimetry, the Tg for AAA-1 asphalt spans a range from 232.7 K to 264.4 K [7]. Zhang and Greenfield proposed several SHRP core asphalt models [8], and the glass transition temperatures were estimated to be within the range of 298.2–385.2 K [7]. Sun et al. computed the Tg of 3-component neat asphalt model proposed by Zhang and Greenfield and it is of 261.8 K [9]. Khabaz and Khare [10] simulated the Tg of the AAA-1 and AAM-1 [8] asphalt systems, while the results show Tg values are of 350.0 ± 6.9 and 348.3 ± 7.7 K, respectively. Obviously, there are different understandings on the glass transition process of asphalt. Liquid fragility provides an approach to understand the process from time-independent Newtonian fluid to truly frozen glassy solid of glass-forming liquids and its effects on physical properties, as shown in Fig. 1(a) [11–13]. As shown in Fig. 1(b), fragility is the measurement of the deviation of viscosity or relaxation time to the Arrhenius form, which is usually characterized by fragility index m [14],
" m¼
dlogx d T g =T
431
# ð1Þ T¼T g
where x can be viscosity, relaxation time, shift factors or other dynamic variables. T is the absolute temperature. Therein, temperature corresponding to viscosity of 1012Pa.s [15] (or the structural relaxation time equals to 100 s [11]) is regarded to be a common definition of Tg, avoiding directly determine the definite Tg value. According to fragility index m, glass formers can be divided into two types: strong liquids whose temperature dependence of viscosity obey Arrhenius law and fragile liquids satisfy Vogel-FulcherTammann (VFT) Eq. [16],
g ¼ g0 exp
DT 0 T T0
ð2Þ
where g is the viscosity and, D; T 0 and g0 are the constants of the VTF equation. The larger m value, i.e., the more deviation from the linear Arrhenius behavior, the more fragile the material is. Asphalt has been accepted to be a typical fragile liquid for that its m value is over 230 [16–18], which is bigger than most known glassforming materials [14]. Including fragile liquids, a number of theoretical models and concepts have been proposed to describe the glass transition process of glass forming liquids, e.g., free volume, mode coupling theory (MCT), etc. [19–22]. However, existed studies of glass forming liquid of asphalt do not focus on the glass forming process [10,17,23]. From the viewpoint of glass forming liquid, this paper aims to improve the understanding of the glass forming process in a wider temperature range from Newtonian fluid state to glassy state that typical asphalt materials would experience in actual environments by using MD simulations. Detailed speaking, in this study, the volumetric related properties of AAA-1 model asphalt, such as free volume, fractional free volume, specific volume and coefficients of volume thermal expansion (CVTE) etc., were obtained at various temperatures to observe the processes of liquid–liquid transition and glass transition. Meanwhile, the temperature dependence of viscosities and the Stokes-Einstein relation were used to verify the liquid–liquid transition temperature. And lastly, cage effect of MCT theory was borrowed to explain the microscopic dynamics transition mechanism at molecular level. In addition, rheological experiments were conducted to further verify the MD simulation results.
Fig. 1. (a) Definition of the regions of glass-former phenomenology I, II, and III. In domain I, the system is in internal equilibrium, and has no history dependence at all temperatures. In domain II, it is relaxing during the experiment, and in domain III, it is fully frozen. (b) Schematic Angell plot of strong and fragile liquids and slope of the red line represents fragility index m.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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2. MD simulation and rheological experiments methods 2.1. MD simulation details All MD simulations were carried out by using Materials Studio simulation software [24]. In this paper, a 12-component asphalt model system proposed by Li and Greenfield [8] which contains four types of constituent molecules (saturates, naphthene aromatics, polar aromatics (resins), and asphaltenes), i.e., AAA-1 asphalt model [8], was constructed by ‘Amorphous Cell’ module, as shown in Fig. 2 and further details of the system are given in Table 1. Subsequently, the structural optimization was carried out using the energy minimization process for 20,000 iterations to eliminate the unreasonable contacts, such as overlapping and close contact, for which the energy convergence level, force and displacement were set to 2.0 105 kcal mol1 Å1, 1.0 103 kcal mol1 Å1 and 1.0 105 Å, respectively. After that, the annealing process was applied to overcome the energy barriers and avoid capturing the structure in a conformation that represents a local energy minimum. Next, a series of NPT (constant number of particles, constant pressure and constant temperature) MD was adopted to calculate physical properties, such as densities, volumes, and energies like kinetics and potentials, at different temperatures from 600 K to 50 K every 25 K by ‘Forcite’ module. Notably, each subsequent simulation was started from the final configuration obtained at the preceding temperature. And lastly, MD simulations were conducted for 2 ns under NVT (constant number of particles, constant volume and constant temperature) ensemble and 20,001 configurations were generated for self-diffusion coefficient and viscosity analysis. The Condensed-phase Optimized Molecular Potential for Atomistic Simulation Studies (COMPASS) [25] force field was employed to calculate interatomic interactions in the systems and conduct the MD computation of the molecular models. In this study, Ewald summation method [26] was selected to sum the long-range electrostatic interaction terms with an accuracy of 1 103 kcal mol1. And, van der Waals(vdW) interactions
involved were calculated by group-based method [26] with a cutoff distance of 12.5 Å. Meanwhile, the temperature and pressure of the systems were controlled by using the Nosé-Hoover thermostat and Berendsen barostat, respectively. And all molecular dynamics simulations were performed with a step interval of 1 fs (fs, i.e., 1015 s). 2.2. Rheological experiment details The rheological properties of asphalt (Tahua 90#, commercial available, in Table 2) were measured by using a dynamic shear rheological device, MCR-302 (Anton Parr Inc., Graz, Austria). The parallel plate geometry of 4 mm diameter with 1 mm gap was used for the temperature range from 35 to 60 °C, and when the temperatures vary from 60 to 135 °C, a parallel plate geometry of 25 mm diameter with 1 mm gap was used. Strain sweep of asphalt was conducted by MCR-302 with an oscillation frequency of 10 rad/s, temperatures increased from 30 to 130 °C every 20 °C and strains increased from 0.0001% to 100%. After that, temperature sweeps was performed with a strain of 0.1%, oscillation frequency of 10 rad/s, and the temperature range reduced at the interval of 1 °C per minute from 35 to 135 °C. Finally, checking time continued for 10 min to eliminate thermo-history and attain an equilibrium state.
3. Results and discussions 3.1. Volumetric properties Domains of I, II and III in Fig. 1(a) are phenomenology defined for glass-former based on the variation with temperature of extensive thermodynamic properties such as volume and enthalpy during heating and cooling cycles without annealing [11]. Domain I is defined by the temperature range in which the properties of the system have no history dependence; i.e., the system is always of Newtonian fluid. Domain III is focused on the properties of systems
Fig. 2. Chemical structure of 12-component in the AAA-1 asphalt model, therein, asphaltenes are marked with green color, polar aromatics are in red color, naphthene aromatics are represented by blue color and saturates are indicated purple color.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Y. Kang et al. / Construction and Building Materials 214 (2019) 430–440 Table 1 Details of the AAA-1 asphalt model System. Molecular Label
Molecular Formula
Number of Atoms
Molar Mass (g/mol)
Number in Model system
Mass Ratio (%)
APhenol APyrrole AThiophene SHopane SSqualane NADOCHN NAPHPN PABBTP PAPNH PATMBO PATIRE PAQNP Total
C42H54O C66H81N C51H62S C35H62 C30H62 C30H46 C35H44 C18H10S2 C36H57N C29H50O C40H60S C40H59N C452H585O2N3S4
97 148 114 97 92 76 79 30 94 80 101 100 5572
574.9 888.4 707.1 483.0 422.9 406.7 464.8 290.4 503.9 414.7 573.0 553.9
3 2 3 4 4 13 11 15 4 5 4 4 72
5.08 5.27 6.23 5.66 4.99 15.54 15.06 12.85 5.95 6.14 6.71 6.52 96.0
Table 2 Model value of AAA-1 asphalt, experiment value of AAA-1 and Tahua 90# asphalt.
a b c
Asphalt system
Asphaltenes
Naphthene aromatics
Polar aromatics
Saturates
AAA-1 (Model)a AAA-1 (Experiment)b Tahua 90# (Experiment)c
16.5 16.2 17.3
38.1 37.3 22.3
30.6 31.8 37.2
10.7 10.6 23.4
Model value of AAA-1 asphalt from Li and Greenfield [8]. Experiment value of AAA-1 asphalt from Jones [27]. Experiment value of Tahua 90# asphalt from Xu [28].
truly frozen, i.e., glassy solid. The domain II, i.e., the temperature range BC, is an important transition domain. The calculated density of the AAA-1 asphalt model system is 1.002 g/cm3 at 325 K, which is consistent with that of tested by experiment (1.01–1.04 g/cm3, at 333.15 K) [7,8,13]. This consistent result validates the correctness of the simulation procedure. Therefore, we have used MD simulations to investigate the dependence of volumetric properties of the AAA-1 asphalt systems, such as free volume, fractional free volume, specific volume and coefficients of volume thermal expansion (CVTE) etc. Fig. 3 plotted the volume- and density-temperature diagrams of the AAA-1 asphalt model and error bars from the statistical results of the six MD replicas. Therein, each dot in the graph is a representative for a system state at a specific temperature. Here, compared with Fig. 1(a), linear fittings were carried out within temperature ranges of 50 K–250 K and 400 K–575 K, and we speculate that there are two transition points as shown in Fig. 3(a). With temperature increasing, the first change (around 245 K) in the slope of the curve is known as the glass transition temperature (Tg) of the asphalt, which is about 3 K higher than the experimental results (248.6 K [29]) for the same system. Therefore, the intermediate
(250 < T < 400 K) temperature region represents the rubbery state (or viscoelastic region or transition domain, which can be apparently fitting using a linear). When temperatures are higher than Tx (ca. 388 K), asphalt would turn to Newtonian flow state, i.e., we think that Tx is the transition temperature of asphalt which transforms from viscoelastic liquid into Newtonian fluid. In addition, fitted slope of volume vs. temperature is volume expansion ratio, and they would correspond to the average volume expansion ratios of the three mechanical states of glassy solid, viscoelastic and Newtonian fluid state. That is, average volume expansion ratios of the three stages are of 2.2 104 K1, 4.0 104 K1 and 6.7 104 K1, respectively. As shown in Fig. 3(b), with the increase of temperature, the average volume of asphalt increased, and thus, the density of asphalt decreasing is also consistent to the three volume expansion stages. Therein, the Tg and Tx are in concerted with the results of Fig. 3(a). To compare the simulation results with other researcher [10], the specific volume (reciprocal of density) under each temperature of six MD replicas was shown in Fig. 4(a). Tg of asphalt is approximately 246 K, which is about 2 K lower than the experimental results (248.6 K [29]) of the same asphalt, and it is almost the same
Fig. 3. (a) Volume versus temperature of the AAA-1 asphalt systems, from 50 K to 575 K. (b) Density versus temperature of the AAA-1 asphalt model, from 50 to 575 K.
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Fig. 4. (a) Specific volume versus temperature diagrams for AAA-1 asphalt model from 50 K to 575 K; (b) Specific volume versus temperature diagrams, whose data were abstracted from Khabaz and Khare [10].
with the calculation result from Fig. 3. Meanwhile, it shows that the speculated transition temperature of viscoelastic liquid to Newtonian fluid is at Tx (ca. 391 K), which is very near to the result from Fig. 3. As shown in Fig. 4(b), the similar trend was also observed by other researcher [10]. However, the understanding about the results is different. We think that there is not only one glass transition temperature of about 350 K, but are two transition temperatures within this temperature range; i.e., one is Tg (ca. 250 K), at which asphalt changes from viscoelastic liquid to glassy solid, the other is Tx (ca. 390 K), at which asphalt transforms from Newtonian liquid to viscoelastic liquid. Frankly speaking, the judgment of two transition points is somewhat empirical. To verify the assumption, the coefficient of volume thermal expansion at each temperature was calculated. 3.2. The coefficient of volume thermal expansion (CVTE) CVTE is a definition at constant pressure to measure the volume expansion of pure substances, and it can be approximately simplified as follows:
av ¼
1 @V 1 DV ffi V 0 @T V 0 DT
ð3Þ
where V 0 is the reference volume at 300 K and @V=@T is the first derivative of the volume-temperature curve. Therefore, this method is more sensitive than previous methods as described in Section 3.1 to discern the number of transition decently. As shown in Fig. 5(a), the values of CVTE of AAA-1 asphalt model show three distinct regions: high temperature region
(T > 400 K), intermediate temperature region (250 K < T < 400 K) and low temperature region (T < 250 K), which would correspond to the viscous state (or Newtonian fluid), viscoelastic liquid state and glassy solid state, respectively, so do in Fig. 5(b), whose data were abstracted from Khabaz and Khare [10]. It is worthy of noting that the average CVTE values of AAA-1 asphalt systems in the three regions are consistent in Fig. 5(a) and (b) as listed in Table 3, which are good in agreement with the results of Section 3.1, and also, it is in good accordance with the experimental value in glassy state [30]. However, unlike Fig. 4(a) and (b), data tendencies in Fig. 5(a) and (b) look quite different. It is attributed that 1) the two simulation systems took into the glassy solid state with different initial paths at temperatures of 250 K–400 K [11], and 2) the shorter simulation duration of ours leaded to the greater data fluctuation, especially at temperatures >400 K. Fortunately, the transition temperatures of Tg obtained from Fig. 5(a) and (b) are in good agreement the experimental result (248.6 K [29]) of the same asphalt and the results from Section 3.1. Also, the transition temperatures of Tx are also in concert with each other well. These results confirm our previous assumption to a great extent that there are two transition temperatures within this temperature range. 3.3. Free volume and fractional free volume The free volume theory proposed by Fox and Flory has been extensively used to explain the molecular motion and physical behavior of glassy and liquid states. Usually, hard sphere scanning probe method is used for the characterization of free volume in
Fig. 5. CVTE versus temperature for AAA-1 asphalt model, (a) whose data was from our MD simulation; (b) whose data was abstracted from Khabaz and Khare [10].
Y. Kang et al. / Construction and Building Materials 214 (2019) 430–440 Table 3 Average CVTE (104K1) of different temperature ranges of the AAA-1 asphalt model system obtained from various methods.
Experimental [30] Volume method, in Fig. 3(a) CVTE, in Fig. 5(a) CVTE, in Fig. 5(b) [10]
[400 K, 575 K]
[250 K, 400 K]
[50 K, 250 K]
NA 6.7 7.3 7.0
NA 4.0 4.3 4.5
3.5 2.2 2.3 2.4
NA: not availability for experimental data.
simulation, and the space where the hard sphere can access is considered to be the free volume (in Fig. 6(a)) [31]. In general, free volume (V f ) is equivalent to the total volume (V) minus the occupied volume (V 0 ):
Vf ¼ V V0
ð4aÞ
V 0 ¼ 1:3V w
ð4bÞ
While, the fractional free volume (FFV) value of the asphalt model can be estimated by using the following equations:
FFV Sim: ¼
V V0 V
ð4cÞ
where V is the cell volume at T = 300 K, V w is the van der Waals volume obtained from the van der Waals surface, and V 0 is the occupied volume. In this paper, we apply a probe sphere with a radius of 0.01 nm (the distance between two neighboring atoms) to probe the equilibrated cells and calculate the free volume of them. Fifty replicas were conducted to obtain the statistical results. As shown in Fig. 7(a), similar to results from Section 3.2, the Tg is approximately of 249 K (Fig. 7(a)), which is in good agreement the experimental results (248.6 K [29]). And it shows that the asphalt would probably transform from viscoelastic state to Newtonian fluid state at 398 K. As shown in Fig. 7(b), the FFV values also show two obvious transition temperatures of 247 K and 401 K, which is regarded as Tg and Tx, respectively, that is also consistent with the above results. To further verify the transition of asphalt at Tx is occurred, transport properties were calculated. 3.4. Temperature dependent of viscosity and diffusion coefficients properties Equilibrium MD method was used to calculate the viscosity g of asphalt by integrating the autocorrelation function of the pressure tensor based on the Green-Kubo relation [32,33],
+ Z 1 *X V g¼ Pab ðtÞPab ð0Þ dt kB T 0 a–b where Pab ¼
P
j¼1 N
P aj P bj mj
435
ð5Þ
þ r ja F jb , ða; b ¼ x; y; zÞwhere V is the sys-
tem volume, kB is the Boltzmann constant, T is the absolute temperature, Pab is the off-diagonal element (a – b) of the pressure tensor; Paj and Pbj are the momenta of the jth atom along a and b directions and rja and Fjb are the components of the position and force on the jth atom, respectively. As shown in Fig. 8(a), the viscosity estimated for AAA-1 asphalt system at T = 533.15 K is of 4.18 mPas, which is in good agreement with the viscosity that was reported in the literature [23]. Fig. 8(b) shows the results of viscosity (log(g)) versus the inverse of temperature from 298 K to 533 K. Obviously, the viscosity decreases as temperature increases, the data points cannot be fitted by the Arrhenius law, i.e., they do not obey the same temperaturedependence. However, the temperature dependence of viscoelasticity was well fitted by the empirical VFT equation, which indicates that asphalt is typical of a fragile liquid [23], as expected. And, Tg of AAA-1 asphalt system was extrapolated by both VFT equation and Arrhenius law (dash line crossover in Fig. 8(b)). We readily obtained the Tg = 261 K that is ca. 5% higher than the results of Sections 3.1 to 3.3 (ca. 250 K) and the experimental result (248.6 K [29]). Notably, the temperature dependences of the viscosity were piecewise fitted with the Arrhenius law, and it can be readily see that there is a crossover temperature at about T = 387 K. To verify this crossover temperature T, the product of self-diffusion coefficient D and viscosity g vs. temperature was plotted in Fig. 9. According to the Stokes-Einstein (SE) relation [34]:
Dg ¼
kB T 6pr
ð6Þ
where g is the viscosity, D is the diffusion coefficient, r is the effective radius of particles, and kB is the Boltzmann’s constant, the product of self-diffusivity and viscosity (Dg) would linearly depend on temperature. Therein, self-diffusion coefficient was calculated through the time evolution of the mean squared displacement (MSD). And the quantitative relationship between diffusivity and MSD can be written as following:
Di ¼
n i2 X 1 1 h ðiÞ ð iÞ lim r ij ðt þ t 0 Þ r ij ðt 0 Þ 6Ni t!1 j¼1 t
ð7Þ
Fig. 6. (a) Schematic representation of Connolly surface defined by three-dimensional molecules, which can be used to calculate the free volume; (b) Three-dimensional view of an amorphous cell of AAA-1 asphalt model containing 5572 atoms, therein, the grey surface shows the van der Waals surface, blue surface is the Connolly surface with probe radius of 0.01 nm.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 7. (a) Free volumes versus temperature of the AAA-1 asphalt model, from 50 to 575 K. (b) Fractional free volume versus temperature of the AAA-1 asphalt model, from 50 to 575 K.
Fig. 8. (a) Viscosity results as a function of simulation time at 533.15 K for AAA-1 asphalt system. The horizontal line is the averaged viscosity estimate by using Green-Kubo methods. (b) log(g) versus reciprocal temperature, whose data were from Li and Greenfield (in blue triangle) [23]. Straight lines are linear fitting by using the Arrhenius law. The curve (in red) is resulted from a fit by the VFT equation. And extrapolations are used to determine the Tg of AAA-1 asphalt system (hollow triangle), which plotted in dashes.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
As is shown in Fig. 9, the calculated Dg of each molecular in the semilog plot suggests that SE relation breakdown at about Tb400K. It reveals that there is a decoupling of diffusion and viscous transport properties at this temperature [34], i.e., asphalt transforms from viscoelastic liquid to viscous liquid. Thus, we can conclude that there must be a liquid-liquid transition taking place at temperature approximately Tb=400K. Furthermore, it is the consistency of transition temperatures which were obtained from Sections 3.1 to 3.4 that implies Tb = Tx. To illuminate the implication of Tx, microscopic dynamics of asphalt in the glass forming process was conducted. 3.5. Microscopic dynamics mechanism
Fig. 9. The product of Dg for asphaltene as a function of temperature in the AAA-1 asphalt system, whose data from Li and Greenfield [23]. Meanwhile, our results are well validated (in pink diamond). The gray region bounded by black dash lines of Dg ¼ kB T=6pr, 0.1 nm r 3.0 nm. ð iÞ
ð iÞ
where N i is the atomic number of type i, rij ðt þ t0 Þ, rij ðt 0 Þ are the position vector of particle i at time t þ t 0 and time t 0 , respectively, and the angular bracket represents the ensemble average of the MSD of the molecular.
As shown in Fig. 10, the mobility of the asphaltene-phenol molecular and movement details through the simulation cells can be directly visualized by using 3-D Cartesian trajectory range from 325 K to 500 K. Cage effect was borrowed from the MCT liquid theory to understand the dynamics of asphalt in this glass forming process, as shown in Fig. 11. As illustrated in Fig. 11(a), at lower temperatures, motion of the hard sphere is constrained by a small number of neighbors which restrict and eventually arrest its macroscopic motion (on the scale of its size), forming an effective cage [35], i.e., particles are thermal vibration in cages formed by their neighbors. Only a part of the configuration space is available for motion due to the strong short range repulsive potentials, i.e., the system states are non-ergodic. The life of cage
Y. Kang et al. / Construction and Building Materials 214 (2019) 430–440
437
Fig. 10. (a) The diffusion displacement of asphaltene-phenol as a function of temperature range from 325 K to 500 K. With temperature increasing, the asphaltene-phenol molecular transits from local thermal vibrations (325 K-350 K) to restricted movement (375 K), then jumps from one cage to another (400 K), and eventually performs temperature-independent ergodic movements (>400 K). (b)–(d) The trajectories of asphaltene-phenol at partially representative temperature at 325 K (local thermal vibrations), 400 K (jumped) and 475 K (colloidal cage rearrangements).
Fig. 11. Schematic representation of: (a) the repulsive colloidal hard spheres: cage model, adapted from [35]; (b) the asphalt colloidal structure model of one imaginary of asphaltenes in a dispersing medium of lighter polar aromatics, naphthenic aromatics and saturates.
decreases as the temperature increases, while, when the temperature approaches a critical temperature Tc, the life of cage tends to be finite, i.e., the system states are ergodic, of which the system is in the state of Newtonian fluid [11]. As for the asphalt colloidal
structure model, components with the heaviest molecular weight (like asphaltene) are located in the center of colloids [1,36], and lighter components (like aromatics) constitute outer shells. Fig. 11(b) shows the SARA (the acronym of saturates, aromatics
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(naphthenic aromatics), resins (polar aromatics), and asphaltene) constitute in one hypothetical colloid, which can consider a modified cage model. As shown in Fig. 10(a) and (b), at 325 K and 350 K, the asphaltene-phenol molecular thermally vibrates within its cage, and with temperature increasing to 375 K, most of the time the asphaltene-phenol molecular is still rattling in its cage, but the whole cage vibrates enhanced. When temperature in the vicinity of 400 K, asphaltene-phenol molecular jumps from one cage to a neighboring one as shown in Fig. 10(c) [35,37]. That is, the neighborhood of 400 K is the critical temperature of Tc. At temperatures higher than Tc = 400 K, in addition to the regular vibrations and random walks of the particles in the cage, the position of the cage where the asphaltene-phenol molecular is located also changes with the rearrangement of the surrounding colloids. The relaxation associated with diffusional movement is a slow a-relaxation, i.e., structure relaxation of glass transition, whereas at temperatures higher than Tc = 400 K, the rearrangement process of cage is a fast 0 a -relaxation, showing ergodic characteristics [38,39]. Namely, as shown in Fig. 10(a) (temperatures higher than 400 K) and Fig. 10 (d), the normalized displacement of the asphaltene-phenol with its cage stochastically changes greatly with temperature increasing. It is worthy of noting that Tc = 400 K is the liquid–liquid transition (Tll) temperature of asphalt. In general, with temperature increasing, the asphaltene-phenol molecular transits from local thermal vibrations to restricted movement, then jumps from one cage to another, and eventually perform temperature-independent ergodic movements. And, the critical transition temperature of asphalt (ca. Tc = 400 K) is well coincided with Tx and Tb, at which asphalt transits from viscoelastic liquid to Newtonian fluid (Tll).
3.6. Experimental verification 3.6.1. Linear viscoelastic region and viscosity To identify the linear viscoelastic region (LVE), strain sweep measurements of Tahua 90# asphalt were carried out from 35 °C to 135 °C. As shown in the Fig. 12(a)–(c), at 30 °C, the asphalt retained its linear viscoelastic property when the strains were smaller than 0.5% or shear stress were less than 107Pa; when beyond these ranges, brittle fracture would occurred obviously. With the increase of temperature (30–10°C), moduli and stresses at the end of the linear regions decreased slightly. When the temperature increases from 10 to 110 °C, moduli decreased several orders of magnitude and the LVE region significantly turns to wider than those of lower temperatures, i.e., asphalt gradually transforms from viscoelastic solid to viscoelastic liquid. As Fig. 12(d) presented, stress and viscosity versus shear rate keeps constant at T = 130 °C compared with those at T = 90 °C; obviously, asphalt has been completely transformed into Newtonian fluids at T = 130 °C. 3.6.2. Temperature dependence of asphalt’s mechanics In concert with the results of the strain sweep tests (Fig. 12), the strains are controlled to be of 0.1% to ensure the whole thermorheological measurements are conducted in the LVE region. Temperature sweep of Tahua 90# asphalt were conducted at an angular velocity frequency of 10 rad/s. As Fig. 13 presented, the temperature sweep curves of Tahua 90# asphalt were divided into four sections (as printed in the plots, glassy, viscoelastic solid, viscoelastic liquid, and Newtonian fluid) by three transition temperatures, i.e., glass transition temperature, solid–liquid transition temperature and viscoelastic liquid-Newtonian fluid transition temperature;
Fig. 12. Strain sweep results of the Tahua 90# asphalt, temperature range from (a) 30 to 10 °C; (b) 10 to 70 °C; (c) 90 to 130 °C; (d) shear stress and viscosity versus shear rate at temperature T = 90 °C and T = 130 °C.
Y. Kang et al. / Construction and Building Materials 214 (2019) 430–440
439
Fig. 13. Temperature sweep results of Tahua 90# asphalt; (a) Modulus versus temperature; (b) Phase angle and damping factor versus temperature from 35 to 135 °C.
therein, when the loss modulus approaches the maximum platform over the whole range of temperatures, the corresponding temperature is the glass transition temperature Tg (about 14 °C); at temperature when G’ = G”, viscoelastic asphalt transforms their mechanical state from solid to liquid, and this transition temperature is ca. 32 °C. Also, G’ of Tahua 90# asphalt decreases rapidly and the corresponding phase angle approaches 90° when the temperature is above 130 °C, that is, the corresponding temperature is the transition temperature of asphalt from viscoelastic liquid to Newtonian fluid, after that, asphalt exhibits pure viscous flow state with temperature. Obviously, there is still a slight difference between the simulation and the laboratory results (for AAA-1 asphalt: Tg = 247 ± 4 K, Tll = 400 K; for Tahua 90# asphalt: Tg = 259 K, Tll = 395 K). However, experimental results are consistent with the MD results in overall trends. 4. Conclusions In this paper, the MD simulations were used to study the glass forming process of AAA-1 asphalt from the viewpoint of glass forming liquid. The volume-temperature of asphalt was obtained at various temperatures to observe the processes of liquid–liquid transition and glass transition. Meanwhile, the temperature dependence of viscosity and the Stokes-Einstein relation were used to verify the liquid–liquid transition temperature. And lastly, cage effect of MCT theory was borrowed to explain the microscopic dynamics transition mechanism at molecular level. The main conclusions can be drawn as follows: (1) With temperature decreasing, asphalt evolves from timeindependent Newtonian fluid at above 394 ± 7 K to truly frozen glassy solid at beneath 247 ± 4 K. That is, from the viewpoint of glass forming liquid, the glass transition of asphalt spans a distinct broadening temperature range from 394 ± 7 K to 247 ± 4 K. (2) In practice, Tg = 247 ± 4 K is thought of glass transition temperature which is quantitatively consistent to experimental result. Further, temperature dependences of coefficient of volume thermal expansion (CVTE) and free volume of AAA1 verified above-mentioned results. (3) The temperature dependence of the viscosity of AAA-1 asphalt system is not satisfied with Arrhenius law but satisfied with Vogel-Fulcher-Tammann (VFT) equation, which also reveals that asphalt is typical of a fragile liquid. Moreover, piecewise fittings with Arrhenius law reveal that there would be a transition at above 387 K.
(4) The product of self-diffusivity and viscosity (Dg) strongly deviates from the Stokes-Einstein relation in the vicinity of temperature Tc = 400 K, which verifies that there is a transition at about this temperature. (5) Normalized displacement of asphaltene-phenol revealed that Tc (i.e., Tll) is the critical temperature, above which arelaxation transforms to fast a-relaxation of asphalt. And it was explained by colloidal cage effect similar to that of mode coupling theory (MCT), i.e., with temperature increasing, the asphaltene-phenol molecular transits from local thermal vibrations to restricted movement, then jumps from one colloidal cage to another at ca. 400 K, and eventually performs temperature-independent ergodic movements at above 400 K. That is, viscoelastic liquid-Newtonian liquid transition of AAA-1 asphalt did occur at ca. 400 K. Moreover, the good agreement between the rheological experiments and simulation results demonstrated that these MD results are reliable. This paper may help understanding microscopic picture of asphalt relaxation processes with temperature, which would enable new additives and new additive strategies to modify asphalt and facilitate crude oil exploitation, transportation and refining processes, etc. And also, this paper may improve the understanding of glass forming liquid of asphalt. Acknowledgements The research is financially supported by China Postdoctoral Science Foundation (Nos. 2016M592841, 2017T100774), the Fundamental Research Funds for the Central Universities (No. 2452015054), and the National Natural Science Foundation of China (NSFC) (No. 51308461). We thank the National Supercomputing Center in Shenzhen, HPC of NWAFU for the use of the supercomputer. Conflict of interest The authors declare no conflict of interest. References [1] O.C. Mullins, The asphaltenes, Ann. Rev. Anal. Chem. 4 (2011) 393–418, https:// doi.org/10.1146/annurev-anchem-061010-113849. [2] A. Zare-Shahabadi, A. Shokuhfar, S. Ebrahimi-Nejad, Preparation and rheological characterization of asphalt binders reinforced with layered silicate nanoparticles, Construct. Build. Mater. 24 (7) (2010) 1239–1244, https://doi.org/10.1016/j.conbuildmat.2009.12.013.
440
Y. Kang et al. / Construction and Building Materials 214 (2019) 430–440
[3] Y. Ding, B. Huang, X. Shu, Y. Zhang, M.E. Woods, Use of molecular dynamics to investigate diffusion between virgin and aged asphalt binders, Fuel 174 (2016) 267–273, https://doi.org/10.1016/j.fuel.2016.02.022. [4] J.M. Krishnan, K.R. Rajagopal, On the mechanical behavior of asphalt, Mechan. Mater. 37 (11) (2005) 1085–1100, https://doi.org/10.1016/j. mechmat.2004.09.005. [5] P. Kriz, J. Stastna, L. Zanzotto, Glass transition and phase stability in asphalt binders, Road Mater. Pave. Design 9 (sup1) (2011) 37–65, https://doi.org/ 10.1080/14680629.2008.9690158. [6] M. Mousavi, F. Pahlavan, D. Oldham, S. Hosseinnezhad, E.H. Fini, Multiscale investigation of oxidative aging in biomodified asphalt binder, J. Phys. Chem. C 120 (31) (2016) 17224–17233, https://doi.org/10.1021/acs.jpcc.6b05004. [7] L. Zhang, M.L. Greenfield, Effects of polymer modification on properties and microstructure of model asphalt systems, Energy Fuels 22 (5) (2008) 3363– 3375, https://doi.org/10.1021/ef700699p. [8] D.D. Li, M.L. Greenfield, Chemical compositions of improved model asphalt systems for molecular simulations, Fuel 115 (2014) 347–356, https://doi.org/ 10.1016/j.fuel.2013.07.012. [9] D. Sun, T. Lin, X. Zhu, Y. Tian, F. Liu, Indices for self-healing performance assessments based on molecular dynamics simulation of asphalt binders, Computat. Mater. Sci. 114 (2016) 86–93, https://doi.org/10.1016/ j.commatsci.2015.12.017. [10] F. Khabaz, R. Khare, Glass transition and molecular mobility in styrenebutadiene rubber modified asphalt, J. Phys. Chem. B 119 (44) (2015) 14261– 14269, https://doi.org/10.1021/acs.jpcb.5b06191. [11] C.A. Angell, K.L. Ngai, G.B. McKenna, P.F. McMillan, S.W. Martin, Relaxation in glassforming liquids and amorphous solids, J. Appl. Phys. 88 (6) (2000) 3113– 3157, https://doi.org/10.1063/1.1286035. [12] C. Zhang, L. Hu, Y. Yue, J.C. Mauro, Fragile-to-strong transition in metallic glass-forming liquids, J. Chem. Phys. 133 (1) (2010), https://doi.org/10.1063/ 1.3457670. [13] L. Zhang, M.L. Greenfield, Relaxation time, diffusion, and viscosity analysis of model asphalt systems using molecular simulation, J. Chem. Phys. 127 (19) (2007), https://doi.org/10.1063/1.2799189. [14] Q. Qin, G.B. McKenna, Correlation between dynamic fragility and glass transition temperature for different classes of glass forming liquids, J. NonCrystal. Solid. 352 (28–29) (2006) 2977–2985, https://doi.org/10.1016/j. jnoncrysol.2006.04.014. [15] P.G. Debenedetti, F.H. Stillinger, Supercooled liquids and the glass transition, Nature 410 (6825) (2001) 259–267, https://doi.org/10.1038/35065704. [16] H. Zhai, D. Salomon, Evaluation of low-temperature properties and the fragility of asphalt binders with non-arrhenius viscosity-temperature dependence, J. Transport. Res. Board 2005 (1901) 44–51. [17] Q. Qin, J.F. Schabron, R.B. Boysen, M.J. Farrar, Field aging effect on chemistry and rheology of asphalt binders and rheological predictions for field aging, Fuel 121 (2014) 86–94, https://doi.org/10.1016/j.fuel.2013.12.040. [18] A. Samieadel, D. Oldham, E.H. Fini, Investigating molecular conformation and packing of oxidized asphaltene molecules in presence of paraffin wax, Fuel 220 (2018) 503–512, https://doi.org/10.1016/j.fuel.2018.02.031. [19] S. Sastry, P.G. Debenedetti, F.H. Stillinger, Signatures of distinct dynamical regimes in the energy landscape of a glass-forming liquid, Nature 393 (6685) (1998) 554–557, https://doi.org/10.1038/31189.
[20] J.L. Barrat, W. Gotze, A. Latz, The liquid-glass transition of the hard-sphere system, J. Phys.: Conden. Matter 1 (39) (1989) 7163–7170, https://doi.org/ 10.1088/0953-8984/1/39/027. [21] J. Jackle, Models of the glass transition, Report. Progr. Phys. 49 (2) (1986) 171– 231, https://doi.org/10.1088/0034-4885/49/2/002. [22] M.H. Cohen, D. Turnbull, Molecular transport in liquids and glasses, J. Chem. Phys. 31 (5) (1959) 1164–1169, https://doi.org/10.1063/1.1730566. [23] D.D. Li, M.L. Greenfield, Viscosity, relaxation time, and dynamics within a model asphalt of larger molecules, J. Chem. Phys. 140 (3) (2014), https://doi. org/10.1063/1.4848736. [24] Accelrys Inc, San Diego. http://accelrys.com/products/collaborative-science/ biovia-materials-studio/. [25] H. Sun, COMPASS: An ab initio force-field optimized for condensed-phase applicationssoverview with details on alkane and benzene compounds, J. Phys. Chem. B 102 (1998) 7338–7364. [26] F. Daan, S. Berend, Understanding Molecular Simulation From Algorithms to Applications, Academic Press, San Diego, 2002. [27] D.R. Jones, SHRP materials reference library, asphalt cements: a concise data compilation. SHRP-A-645, Strategic Highway Research Program National Research Council, Washington, DC, 1993. [28] X. Pei, Modeling and Analysis of molecular dynamics for characterizing asphalt-aggregate interaction [dissertation], Chang’an University, Xi’an(SN), 2013. in chinese. [29] A. Usmani, Asphalt Science and Technology, CRC Press, New York, 1997. [30] D.A. Anderson, D.W. Christensen, H.U. Bahia, R. Dongre, M.G. Sharma, C.E. Antle, J. Button, Binder characterization and evaluation. Volume 3: physical characterization, Strategic Highway Research Program, Washington, D.C.,, 1994. [31] M.L. Connolly, Analytical molecular surface calculation, J. Appl. Crystallogr. 16 (5) (1983) 548–558, https://doi.org/10.1107/s0021889883010985. [32] M.S. Green, Markoff random processes and the statistical mechanics of timedependent phenomena, J. Chem. Phys. 20 (8) (1952) 1281–1295, https://doi. org/10.1063/1.1700722. [33] M.S. Green, Markoff random processes and the statistical mechanics of timedependent phenomena. II. Irreversible processes in fluids, J. Chem. Phys. 22 (3) (1954) 398–413, https://doi.org/10.1063/1.1740082. [34] B. Liu, J. Goree, O.S. Vaulina, Test of the Stokes-Einstein relation in a twodimensional Yukawa liquid, Phys. Rev. Lett. 96 (1) (2006), https://doi.org/ 10.1103/PhysRevLett. 96.015005. [35] D. Vlassopoulos, G. Fytas, From Polymers to Colloids: Engineering the Dynamic Properties of Hairy Particles, 236 (2009) 1-54, doi: /10.1007/12_2009_31. [36] M. Mousavi, T. Abdollahi, F. Pahlavan, E.H. Fini, The influence of asphalteneresin molecular interactions on the colloidal stability of crude oil, Fuel 183 (2016) 262–271, https://doi.org/10.1016/j.fuel.2016.06.100. [37] M.E. Helgeson, N.J. Wagner, D. Vlassopoulos, Viscoelasticity and shear melting of colloidal star polymer glasses, J. Rheol. 51 (2) (2007) 297–316, https://doi. org/10.1122/1.2433935. [38] S.J. Stadnicki, J.K. Gillham, R.F. Boyer, The Tll (>Tg) transition of atactic polystyrene, J. Appl. Polym. Sci. 20 (5) (1976) 1245–1275, https://doi.org/ 10.1002/app.1976.070200510. [39] M. Fuchs, W. Gotze, S. Hildebrand, A. Latz, A theory for the beta -relaxation process near the liquid-to-glass crossover, J. Phys. Conden. Matter. 4 (38) (1992) 7709–7744, https://doi.org/10.1088/0953-8984/4/38/007.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Molecular dynamics study on the glass forming process of asphalt Yang Kang a,⇑, Dunhong Zhou b, Qiang Wu a, Rui Liang a, Shaoxin Shangguan a, Zhiwei Liao a, Ning Wei a,⇑ a b
College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, Shaanxi, China Nanjing ASFT Neomaterials LLC., Xinmofan Road, Nanjing 210009, Jiangsu, China
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Molecular dynamic simulations were
used to study glass forming process of asphalt. Glass transition of asphalt spans a wide temperature range from ca. 400 K to ca. 250 K. Non-Arrhenius temperature dependence of viscosity implies a transition at ca. 400 K. Breakdown of Stokes-Einstein relation verifies the transition at ca. 400 K. Viscoelastic liquid-Newtonian liquid transition at ca. 400 K explained by cage effect.
a r t i c l e
i n f o
Article history: Received 5 July 2018 Received in revised form 10 April 2019 Accepted 17 April 2019
Keywords: Molecular dynamics Asphalt Glass transition Liquid-liquid transition Glass forming liquid
a b s t r a c t Glass transition temperature (Tg) is a significant parameter that determines the viscoelastic properties of asphalt. However, the understanding of glass transition process of asphalt is ambiguous, especially at the molecular level. In this paper, molecular dynamic (MD) simulations were used to help understanding the glass forming process from the viewpoint of glass forming liquid. The temperature dependence of volumetric properties, such as free volume, fractional free volume, specific volume and coefficients of volume thermal expansion etc., for AAA-1 asphalt were computed. Results show that there are two transition temperatures with temperature decreasing from 575 K to 50 K, i.e., one is Tg at ca. 250 K, the other is ca. 400 K. The nonArrhenius type temperature dependence of viscosity and the breakdown of Stokes-Einstein relation imply that the transition at ca. 400 K is responsible to the liquid–liquid transition of asphalt from viscoelastic liquid to Newtonian fluid. Furthermore, molecular trajectory demonstrated that at ca. 400 K, AAA-1 asphalt system experienced the transition from non-ergodic local thermal vibrations and restricted movement to temperature-independent ergodic movement, and this observation verified that the liquid–liquid transition of asphalt did occur at ca. 400 K. Namely, at temperatures higher than 400 K, the rearrangement process of asphalt colloid cage is a temperature-independent a-relaxation, and in the temperature range from 400 K to 250 K, the relaxation associated with diffusional movement is a slow a-relaxation, i.e., structure relaxation of glass transition, and at temperatures lower than 250 K, asphalt is truly frozen glassy. Moreover, the good agreement between the rheological experiments and simulation results demonstrated that the MD results are reliable. This paper helps understanding microscopic picture of glass forming asphalt and its relaxation mechanisms with temperature, which could enable new additives and new additive strategies to modify asphalt and facilitate crude oil exploitation, transportation and refining processes, etc. Ó 2019 Elsevier Ltd. All rights reserved.
⇑ Corresponding authors. E-mail addresses: [email protected] (Y. Kang), [email protected] (N. Wei). https://doi.org/10.1016/j.conbuildmat.2019.04.138 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
Y. Kang et al. / Construction and Building Materials 214 (2019) 430–440
1. Introduction Asphalt is a typical amorphous material, which is a complex heterogeneous mixture of hydrocarbons usually collected as a byproduct of the refining process of crude oil in petroleum refineries [1]. The existence of asphalt within crude oil greatly influences the exploitation, transportation, and refining etc. of crude oil for their mechanical responses vary with temperature and time dramatically. Asphalt has numerous applications and the most important one of them is as a binder for aggregates in building roads [2,3]. To pave an asphalt concrete road properly, operation temperatures, e.g., the temperature for transport and storage, the temperature during mixing, laying and compacting operations, etc., have to be controlled rigorously. When paved, performances of asphalt concretes vary dramatically from ca. 200 K to ca. 400 K. With the decrease of temperature, mechanical states of asphalt change from Newtonian fluid to a viscoelastic state and to a glassy solid [4,5]. Temperature at which mechanical states of asphalt change from viscoelastic state to glass state is called the glass transition temperature (Tg) [4]. Tg is a significant parameter that determines the viscoelastic properties of asphalt, which can influence the mechanical properties such as toughness and creep critically and also cause major changes in its physiochemical and rheological properties, giving rise to a huge impact on the pavement [6]. Several researchers [7–10] had studied the Tg of the Strategic Highway Research Program (SHRP) core asphalts by experiments and molecular dynamic simulations. Therein, from differential scanning calorimetry, the Tg for AAA-1 asphalt spans a range from 232.7 K to 264.4 K [7]. Zhang and Greenfield proposed several SHRP core asphalt models [8], and the glass transition temperatures were estimated to be within the range of 298.2–385.2 K [7]. Sun et al. computed the Tg of 3-component neat asphalt model proposed by Zhang and Greenfield and it is of 261.8 K [9]. Khabaz and Khare [10] simulated the Tg of the AAA-1 and AAM-1 [8] asphalt systems, while the results show Tg values are of 350.0 ± 6.9 and 348.3 ± 7.7 K, respectively. Obviously, there are different understandings on the glass transition process of asphalt. Liquid fragility provides an approach to understand the process from time-independent Newtonian fluid to truly frozen glassy solid of glass-forming liquids and its effects on physical properties, as shown in Fig. 1(a) [11–13]. As shown in Fig. 1(b), fragility is the measurement of the deviation of viscosity or relaxation time to the Arrhenius form, which is usually characterized by fragility index m [14],
" m¼
dlogx d T g =T
431
# ð1Þ T¼T g
where x can be viscosity, relaxation time, shift factors or other dynamic variables. T is the absolute temperature. Therein, temperature corresponding to viscosity of 1012Pa.s [15] (or the structural relaxation time equals to 100 s [11]) is regarded to be a common definition of Tg, avoiding directly determine the definite Tg value. According to fragility index m, glass formers can be divided into two types: strong liquids whose temperature dependence of viscosity obey Arrhenius law and fragile liquids satisfy Vogel-FulcherTammann (VFT) Eq. [16],
g ¼ g0 exp
DT 0 T T0
ð2Þ
where g is the viscosity and, D; T 0 and g0 are the constants of the VTF equation. The larger m value, i.e., the more deviation from the linear Arrhenius behavior, the more fragile the material is. Asphalt has been accepted to be a typical fragile liquid for that its m value is over 230 [16–18], which is bigger than most known glassforming materials [14]. Including fragile liquids, a number of theoretical models and concepts have been proposed to describe the glass transition process of glass forming liquids, e.g., free volume, mode coupling theory (MCT), etc. [19–22]. However, existed studies of glass forming liquid of asphalt do not focus on the glass forming process [10,17,23]. From the viewpoint of glass forming liquid, this paper aims to improve the understanding of the glass forming process in a wider temperature range from Newtonian fluid state to glassy state that typical asphalt materials would experience in actual environments by using MD simulations. Detailed speaking, in this study, the volumetric related properties of AAA-1 model asphalt, such as free volume, fractional free volume, specific volume and coefficients of volume thermal expansion (CVTE) etc., were obtained at various temperatures to observe the processes of liquid–liquid transition and glass transition. Meanwhile, the temperature dependence of viscosities and the Stokes-Einstein relation were used to verify the liquid–liquid transition temperature. And lastly, cage effect of MCT theory was borrowed to explain the microscopic dynamics transition mechanism at molecular level. In addition, rheological experiments were conducted to further verify the MD simulation results.
Fig. 1. (a) Definition of the regions of glass-former phenomenology I, II, and III. In domain I, the system is in internal equilibrium, and has no history dependence at all temperatures. In domain II, it is relaxing during the experiment, and in domain III, it is fully frozen. (b) Schematic Angell plot of strong and fragile liquids and slope of the red line represents fragility index m.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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2. MD simulation and rheological experiments methods 2.1. MD simulation details All MD simulations were carried out by using Materials Studio simulation software [24]. In this paper, a 12-component asphalt model system proposed by Li and Greenfield [8] which contains four types of constituent molecules (saturates, naphthene aromatics, polar aromatics (resins), and asphaltenes), i.e., AAA-1 asphalt model [8], was constructed by ‘Amorphous Cell’ module, as shown in Fig. 2 and further details of the system are given in Table 1. Subsequently, the structural optimization was carried out using the energy minimization process for 20,000 iterations to eliminate the unreasonable contacts, such as overlapping and close contact, for which the energy convergence level, force and displacement were set to 2.0 105 kcal mol1 Å1, 1.0 103 kcal mol1 Å1 and 1.0 105 Å, respectively. After that, the annealing process was applied to overcome the energy barriers and avoid capturing the structure in a conformation that represents a local energy minimum. Next, a series of NPT (constant number of particles, constant pressure and constant temperature) MD was adopted to calculate physical properties, such as densities, volumes, and energies like kinetics and potentials, at different temperatures from 600 K to 50 K every 25 K by ‘Forcite’ module. Notably, each subsequent simulation was started from the final configuration obtained at the preceding temperature. And lastly, MD simulations were conducted for 2 ns under NVT (constant number of particles, constant volume and constant temperature) ensemble and 20,001 configurations were generated for self-diffusion coefficient and viscosity analysis. The Condensed-phase Optimized Molecular Potential for Atomistic Simulation Studies (COMPASS) [25] force field was employed to calculate interatomic interactions in the systems and conduct the MD computation of the molecular models. In this study, Ewald summation method [26] was selected to sum the long-range electrostatic interaction terms with an accuracy of 1 103 kcal mol1. And, van der Waals(vdW) interactions
involved were calculated by group-based method [26] with a cutoff distance of 12.5 Å. Meanwhile, the temperature and pressure of the systems were controlled by using the Nosé-Hoover thermostat and Berendsen barostat, respectively. And all molecular dynamics simulations were performed with a step interval of 1 fs (fs, i.e., 1015 s). 2.2. Rheological experiment details The rheological properties of asphalt (Tahua 90#, commercial available, in Table 2) were measured by using a dynamic shear rheological device, MCR-302 (Anton Parr Inc., Graz, Austria). The parallel plate geometry of 4 mm diameter with 1 mm gap was used for the temperature range from 35 to 60 °C, and when the temperatures vary from 60 to 135 °C, a parallel plate geometry of 25 mm diameter with 1 mm gap was used. Strain sweep of asphalt was conducted by MCR-302 with an oscillation frequency of 10 rad/s, temperatures increased from 30 to 130 °C every 20 °C and strains increased from 0.0001% to 100%. After that, temperature sweeps was performed with a strain of 0.1%, oscillation frequency of 10 rad/s, and the temperature range reduced at the interval of 1 °C per minute from 35 to 135 °C. Finally, checking time continued for 10 min to eliminate thermo-history and attain an equilibrium state.
3. Results and discussions 3.1. Volumetric properties Domains of I, II and III in Fig. 1(a) are phenomenology defined for glass-former based on the variation with temperature of extensive thermodynamic properties such as volume and enthalpy during heating and cooling cycles without annealing [11]. Domain I is defined by the temperature range in which the properties of the system have no history dependence; i.e., the system is always of Newtonian fluid. Domain III is focused on the properties of systems
Fig. 2. Chemical structure of 12-component in the AAA-1 asphalt model, therein, asphaltenes are marked with green color, polar aromatics are in red color, naphthene aromatics are represented by blue color and saturates are indicated purple color.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Y. Kang et al. / Construction and Building Materials 214 (2019) 430–440 Table 1 Details of the AAA-1 asphalt model System. Molecular Label
Molecular Formula
Number of Atoms
Molar Mass (g/mol)
Number in Model system
Mass Ratio (%)
APhenol APyrrole AThiophene SHopane SSqualane NADOCHN NAPHPN PABBTP PAPNH PATMBO PATIRE PAQNP Total
C42H54O C66H81N C51H62S C35H62 C30H62 C30H46 C35H44 C18H10S2 C36H57N C29H50O C40H60S C40H59N C452H585O2N3S4
97 148 114 97 92 76 79 30 94 80 101 100 5572
574.9 888.4 707.1 483.0 422.9 406.7 464.8 290.4 503.9 414.7 573.0 553.9
3 2 3 4 4 13 11 15 4 5 4 4 72
5.08 5.27 6.23 5.66 4.99 15.54 15.06 12.85 5.95 6.14 6.71 6.52 96.0
Table 2 Model value of AAA-1 asphalt, experiment value of AAA-1 and Tahua 90# asphalt.
a b c
Asphalt system
Asphaltenes
Naphthene aromatics
Polar aromatics
Saturates
AAA-1 (Model)a AAA-1 (Experiment)b Tahua 90# (Experiment)c
16.5 16.2 17.3
38.1 37.3 22.3
30.6 31.8 37.2
10.7 10.6 23.4
Model value of AAA-1 asphalt from Li and Greenfield [8]. Experiment value of AAA-1 asphalt from Jones [27]. Experiment value of Tahua 90# asphalt from Xu [28].
truly frozen, i.e., glassy solid. The domain II, i.e., the temperature range BC, is an important transition domain. The calculated density of the AAA-1 asphalt model system is 1.002 g/cm3 at 325 K, which is consistent with that of tested by experiment (1.01–1.04 g/cm3, at 333.15 K) [7,8,13]. This consistent result validates the correctness of the simulation procedure. Therefore, we have used MD simulations to investigate the dependence of volumetric properties of the AAA-1 asphalt systems, such as free volume, fractional free volume, specific volume and coefficients of volume thermal expansion (CVTE) etc. Fig. 3 plotted the volume- and density-temperature diagrams of the AAA-1 asphalt model and error bars from the statistical results of the six MD replicas. Therein, each dot in the graph is a representative for a system state at a specific temperature. Here, compared with Fig. 1(a), linear fittings were carried out within temperature ranges of 50 K–250 K and 400 K–575 K, and we speculate that there are two transition points as shown in Fig. 3(a). With temperature increasing, the first change (around 245 K) in the slope of the curve is known as the glass transition temperature (Tg) of the asphalt, which is about 3 K higher than the experimental results (248.6 K [29]) for the same system. Therefore, the intermediate
(250 < T < 400 K) temperature region represents the rubbery state (or viscoelastic region or transition domain, which can be apparently fitting using a linear). When temperatures are higher than Tx (ca. 388 K), asphalt would turn to Newtonian flow state, i.e., we think that Tx is the transition temperature of asphalt which transforms from viscoelastic liquid into Newtonian fluid. In addition, fitted slope of volume vs. temperature is volume expansion ratio, and they would correspond to the average volume expansion ratios of the three mechanical states of glassy solid, viscoelastic and Newtonian fluid state. That is, average volume expansion ratios of the three stages are of 2.2 104 K1, 4.0 104 K1 and 6.7 104 K1, respectively. As shown in Fig. 3(b), with the increase of temperature, the average volume of asphalt increased, and thus, the density of asphalt decreasing is also consistent to the three volume expansion stages. Therein, the Tg and Tx are in concerted with the results of Fig. 3(a). To compare the simulation results with other researcher [10], the specific volume (reciprocal of density) under each temperature of six MD replicas was shown in Fig. 4(a). Tg of asphalt is approximately 246 K, which is about 2 K lower than the experimental results (248.6 K [29]) of the same asphalt, and it is almost the same
Fig. 3. (a) Volume versus temperature of the AAA-1 asphalt systems, from 50 K to 575 K. (b) Density versus temperature of the AAA-1 asphalt model, from 50 to 575 K.
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Fig. 4. (a) Specific volume versus temperature diagrams for AAA-1 asphalt model from 50 K to 575 K; (b) Specific volume versus temperature diagrams, whose data were abstracted from Khabaz and Khare [10].
with the calculation result from Fig. 3. Meanwhile, it shows that the speculated transition temperature of viscoelastic liquid to Newtonian fluid is at Tx (ca. 391 K), which is very near to the result from Fig. 3. As shown in Fig. 4(b), the similar trend was also observed by other researcher [10]. However, the understanding about the results is different. We think that there is not only one glass transition temperature of about 350 K, but are two transition temperatures within this temperature range; i.e., one is Tg (ca. 250 K), at which asphalt changes from viscoelastic liquid to glassy solid, the other is Tx (ca. 390 K), at which asphalt transforms from Newtonian liquid to viscoelastic liquid. Frankly speaking, the judgment of two transition points is somewhat empirical. To verify the assumption, the coefficient of volume thermal expansion at each temperature was calculated. 3.2. The coefficient of volume thermal expansion (CVTE) CVTE is a definition at constant pressure to measure the volume expansion of pure substances, and it can be approximately simplified as follows:
av ¼
1 @V 1 DV ffi V 0 @T V 0 DT
ð3Þ
where V 0 is the reference volume at 300 K and @V=@T is the first derivative of the volume-temperature curve. Therefore, this method is more sensitive than previous methods as described in Section 3.1 to discern the number of transition decently. As shown in Fig. 5(a), the values of CVTE of AAA-1 asphalt model show three distinct regions: high temperature region
(T > 400 K), intermediate temperature region (250 K < T < 400 K) and low temperature region (T < 250 K), which would correspond to the viscous state (or Newtonian fluid), viscoelastic liquid state and glassy solid state, respectively, so do in Fig. 5(b), whose data were abstracted from Khabaz and Khare [10]. It is worthy of noting that the average CVTE values of AAA-1 asphalt systems in the three regions are consistent in Fig. 5(a) and (b) as listed in Table 3, which are good in agreement with the results of Section 3.1, and also, it is in good accordance with the experimental value in glassy state [30]. However, unlike Fig. 4(a) and (b), data tendencies in Fig. 5(a) and (b) look quite different. It is attributed that 1) the two simulation systems took into the glassy solid state with different initial paths at temperatures of 250 K–400 K [11], and 2) the shorter simulation duration of ours leaded to the greater data fluctuation, especially at temperatures >400 K. Fortunately, the transition temperatures of Tg obtained from Fig. 5(a) and (b) are in good agreement the experimental result (248.6 K [29]) of the same asphalt and the results from Section 3.1. Also, the transition temperatures of Tx are also in concert with each other well. These results confirm our previous assumption to a great extent that there are two transition temperatures within this temperature range. 3.3. Free volume and fractional free volume The free volume theory proposed by Fox and Flory has been extensively used to explain the molecular motion and physical behavior of glassy and liquid states. Usually, hard sphere scanning probe method is used for the characterization of free volume in
Fig. 5. CVTE versus temperature for AAA-1 asphalt model, (a) whose data was from our MD simulation; (b) whose data was abstracted from Khabaz and Khare [10].
Y. Kang et al. / Construction and Building Materials 214 (2019) 430–440 Table 3 Average CVTE (104K1) of different temperature ranges of the AAA-1 asphalt model system obtained from various methods.
Experimental [30] Volume method, in Fig. 3(a) CVTE, in Fig. 5(a) CVTE, in Fig. 5(b) [10]
[400 K, 575 K]
[250 K, 400 K]
[50 K, 250 K]
NA 6.7 7.3 7.0
NA 4.0 4.3 4.5
3.5 2.2 2.3 2.4
NA: not availability for experimental data.
simulation, and the space where the hard sphere can access is considered to be the free volume (in Fig. 6(a)) [31]. In general, free volume (V f ) is equivalent to the total volume (V) minus the occupied volume (V 0 ):
Vf ¼ V V0
ð4aÞ
V 0 ¼ 1:3V w
ð4bÞ
While, the fractional free volume (FFV) value of the asphalt model can be estimated by using the following equations:
FFV Sim: ¼
V V0 V
ð4cÞ
where V is the cell volume at T = 300 K, V w is the van der Waals volume obtained from the van der Waals surface, and V 0 is the occupied volume. In this paper, we apply a probe sphere with a radius of 0.01 nm (the distance between two neighboring atoms) to probe the equilibrated cells and calculate the free volume of them. Fifty replicas were conducted to obtain the statistical results. As shown in Fig. 7(a), similar to results from Section 3.2, the Tg is approximately of 249 K (Fig. 7(a)), which is in good agreement the experimental results (248.6 K [29]). And it shows that the asphalt would probably transform from viscoelastic state to Newtonian fluid state at 398 K. As shown in Fig. 7(b), the FFV values also show two obvious transition temperatures of 247 K and 401 K, which is regarded as Tg and Tx, respectively, that is also consistent with the above results. To further verify the transition of asphalt at Tx is occurred, transport properties were calculated. 3.4. Temperature dependent of viscosity and diffusion coefficients properties Equilibrium MD method was used to calculate the viscosity g of asphalt by integrating the autocorrelation function of the pressure tensor based on the Green-Kubo relation [32,33],
+ Z 1 *X V g¼ Pab ðtÞPab ð0Þ dt kB T 0 a–b where Pab ¼
P
j¼1 N
P aj P bj mj
435
ð5Þ
þ r ja F jb , ða; b ¼ x; y; zÞwhere V is the sys-
tem volume, kB is the Boltzmann constant, T is the absolute temperature, Pab is the off-diagonal element (a – b) of the pressure tensor; Paj and Pbj are the momenta of the jth atom along a and b directions and rja and Fjb are the components of the position and force on the jth atom, respectively. As shown in Fig. 8(a), the viscosity estimated for AAA-1 asphalt system at T = 533.15 K is of 4.18 mPas, which is in good agreement with the viscosity that was reported in the literature [23]. Fig. 8(b) shows the results of viscosity (log(g)) versus the inverse of temperature from 298 K to 533 K. Obviously, the viscosity decreases as temperature increases, the data points cannot be fitted by the Arrhenius law, i.e., they do not obey the same temperaturedependence. However, the temperature dependence of viscoelasticity was well fitted by the empirical VFT equation, which indicates that asphalt is typical of a fragile liquid [23], as expected. And, Tg of AAA-1 asphalt system was extrapolated by both VFT equation and Arrhenius law (dash line crossover in Fig. 8(b)). We readily obtained the Tg = 261 K that is ca. 5% higher than the results of Sections 3.1 to 3.3 (ca. 250 K) and the experimental result (248.6 K [29]). Notably, the temperature dependences of the viscosity were piecewise fitted with the Arrhenius law, and it can be readily see that there is a crossover temperature at about T = 387 K. To verify this crossover temperature T, the product of self-diffusion coefficient D and viscosity g vs. temperature was plotted in Fig. 9. According to the Stokes-Einstein (SE) relation [34]:
Dg ¼
kB T 6pr
ð6Þ
where g is the viscosity, D is the diffusion coefficient, r is the effective radius of particles, and kB is the Boltzmann’s constant, the product of self-diffusivity and viscosity (Dg) would linearly depend on temperature. Therein, self-diffusion coefficient was calculated through the time evolution of the mean squared displacement (MSD). And the quantitative relationship between diffusivity and MSD can be written as following:
Di ¼
n i2 X 1 1 h ðiÞ ð iÞ lim r ij ðt þ t 0 Þ r ij ðt 0 Þ 6Ni t!1 j¼1 t
ð7Þ
Fig. 6. (a) Schematic representation of Connolly surface defined by three-dimensional molecules, which can be used to calculate the free volume; (b) Three-dimensional view of an amorphous cell of AAA-1 asphalt model containing 5572 atoms, therein, the grey surface shows the van der Waals surface, blue surface is the Connolly surface with probe radius of 0.01 nm.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 7. (a) Free volumes versus temperature of the AAA-1 asphalt model, from 50 to 575 K. (b) Fractional free volume versus temperature of the AAA-1 asphalt model, from 50 to 575 K.
Fig. 8. (a) Viscosity results as a function of simulation time at 533.15 K for AAA-1 asphalt system. The horizontal line is the averaged viscosity estimate by using Green-Kubo methods. (b) log(g) versus reciprocal temperature, whose data were from Li and Greenfield (in blue triangle) [23]. Straight lines are linear fitting by using the Arrhenius law. The curve (in red) is resulted from a fit by the VFT equation. And extrapolations are used to determine the Tg of AAA-1 asphalt system (hollow triangle), which plotted in dashes.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
As is shown in Fig. 9, the calculated Dg of each molecular in the semilog plot suggests that SE relation breakdown at about Tb400K. It reveals that there is a decoupling of diffusion and viscous transport properties at this temperature [34], i.e., asphalt transforms from viscoelastic liquid to viscous liquid. Thus, we can conclude that there must be a liquid-liquid transition taking place at temperature approximately Tb=400K. Furthermore, it is the consistency of transition temperatures which were obtained from Sections 3.1 to 3.4 that implies Tb = Tx. To illuminate the implication of Tx, microscopic dynamics of asphalt in the glass forming process was conducted. 3.5. Microscopic dynamics mechanism
Fig. 9. The product of Dg for asphaltene as a function of temperature in the AAA-1 asphalt system, whose data from Li and Greenfield [23]. Meanwhile, our results are well validated (in pink diamond). The gray region bounded by black dash lines of Dg ¼ kB T=6pr, 0.1 nm r 3.0 nm. ð iÞ
ð iÞ
where N i is the atomic number of type i, rij ðt þ t0 Þ, rij ðt 0 Þ are the position vector of particle i at time t þ t 0 and time t 0 , respectively, and the angular bracket represents the ensemble average of the MSD of the molecular.
As shown in Fig. 10, the mobility of the asphaltene-phenol molecular and movement details through the simulation cells can be directly visualized by using 3-D Cartesian trajectory range from 325 K to 500 K. Cage effect was borrowed from the MCT liquid theory to understand the dynamics of asphalt in this glass forming process, as shown in Fig. 11. As illustrated in Fig. 11(a), at lower temperatures, motion of the hard sphere is constrained by a small number of neighbors which restrict and eventually arrest its macroscopic motion (on the scale of its size), forming an effective cage [35], i.e., particles are thermal vibration in cages formed by their neighbors. Only a part of the configuration space is available for motion due to the strong short range repulsive potentials, i.e., the system states are non-ergodic. The life of cage
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Fig. 10. (a) The diffusion displacement of asphaltene-phenol as a function of temperature range from 325 K to 500 K. With temperature increasing, the asphaltene-phenol molecular transits from local thermal vibrations (325 K-350 K) to restricted movement (375 K), then jumps from one cage to another (400 K), and eventually performs temperature-independent ergodic movements (>400 K). (b)–(d) The trajectories of asphaltene-phenol at partially representative temperature at 325 K (local thermal vibrations), 400 K (jumped) and 475 K (colloidal cage rearrangements).
Fig. 11. Schematic representation of: (a) the repulsive colloidal hard spheres: cage model, adapted from [35]; (b) the asphalt colloidal structure model of one imaginary of asphaltenes in a dispersing medium of lighter polar aromatics, naphthenic aromatics and saturates.
decreases as the temperature increases, while, when the temperature approaches a critical temperature Tc, the life of cage tends to be finite, i.e., the system states are ergodic, of which the system is in the state of Newtonian fluid [11]. As for the asphalt colloidal
structure model, components with the heaviest molecular weight (like asphaltene) are located in the center of colloids [1,36], and lighter components (like aromatics) constitute outer shells. Fig. 11(b) shows the SARA (the acronym of saturates, aromatics
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(naphthenic aromatics), resins (polar aromatics), and asphaltene) constitute in one hypothetical colloid, which can consider a modified cage model. As shown in Fig. 10(a) and (b), at 325 K and 350 K, the asphaltene-phenol molecular thermally vibrates within its cage, and with temperature increasing to 375 K, most of the time the asphaltene-phenol molecular is still rattling in its cage, but the whole cage vibrates enhanced. When temperature in the vicinity of 400 K, asphaltene-phenol molecular jumps from one cage to a neighboring one as shown in Fig. 10(c) [35,37]. That is, the neighborhood of 400 K is the critical temperature of Tc. At temperatures higher than Tc = 400 K, in addition to the regular vibrations and random walks of the particles in the cage, the position of the cage where the asphaltene-phenol molecular is located also changes with the rearrangement of the surrounding colloids. The relaxation associated with diffusional movement is a slow a-relaxation, i.e., structure relaxation of glass transition, whereas at temperatures higher than Tc = 400 K, the rearrangement process of cage is a fast 0 a -relaxation, showing ergodic characteristics [38,39]. Namely, as shown in Fig. 10(a) (temperatures higher than 400 K) and Fig. 10 (d), the normalized displacement of the asphaltene-phenol with its cage stochastically changes greatly with temperature increasing. It is worthy of noting that Tc = 400 K is the liquid–liquid transition (Tll) temperature of asphalt. In general, with temperature increasing, the asphaltene-phenol molecular transits from local thermal vibrations to restricted movement, then jumps from one cage to another, and eventually perform temperature-independent ergodic movements. And, the critical transition temperature of asphalt (ca. Tc = 400 K) is well coincided with Tx and Tb, at which asphalt transits from viscoelastic liquid to Newtonian fluid (Tll).
3.6. Experimental verification 3.6.1. Linear viscoelastic region and viscosity To identify the linear viscoelastic region (LVE), strain sweep measurements of Tahua 90# asphalt were carried out from 35 °C to 135 °C. As shown in the Fig. 12(a)–(c), at 30 °C, the asphalt retained its linear viscoelastic property when the strains were smaller than 0.5% or shear stress were less than 107Pa; when beyond these ranges, brittle fracture would occurred obviously. With the increase of temperature (30–10°C), moduli and stresses at the end of the linear regions decreased slightly. When the temperature increases from 10 to 110 °C, moduli decreased several orders of magnitude and the LVE region significantly turns to wider than those of lower temperatures, i.e., asphalt gradually transforms from viscoelastic solid to viscoelastic liquid. As Fig. 12(d) presented, stress and viscosity versus shear rate keeps constant at T = 130 °C compared with those at T = 90 °C; obviously, asphalt has been completely transformed into Newtonian fluids at T = 130 °C. 3.6.2. Temperature dependence of asphalt’s mechanics In concert with the results of the strain sweep tests (Fig. 12), the strains are controlled to be of 0.1% to ensure the whole thermorheological measurements are conducted in the LVE region. Temperature sweep of Tahua 90# asphalt were conducted at an angular velocity frequency of 10 rad/s. As Fig. 13 presented, the temperature sweep curves of Tahua 90# asphalt were divided into four sections (as printed in the plots, glassy, viscoelastic solid, viscoelastic liquid, and Newtonian fluid) by three transition temperatures, i.e., glass transition temperature, solid–liquid transition temperature and viscoelastic liquid-Newtonian fluid transition temperature;
Fig. 12. Strain sweep results of the Tahua 90# asphalt, temperature range from (a) 30 to 10 °C; (b) 10 to 70 °C; (c) 90 to 130 °C; (d) shear stress and viscosity versus shear rate at temperature T = 90 °C and T = 130 °C.
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Fig. 13. Temperature sweep results of Tahua 90# asphalt; (a) Modulus versus temperature; (b) Phase angle and damping factor versus temperature from 35 to 135 °C.
therein, when the loss modulus approaches the maximum platform over the whole range of temperatures, the corresponding temperature is the glass transition temperature Tg (about 14 °C); at temperature when G’ = G”, viscoelastic asphalt transforms their mechanical state from solid to liquid, and this transition temperature is ca. 32 °C. Also, G’ of Tahua 90# asphalt decreases rapidly and the corresponding phase angle approaches 90° when the temperature is above 130 °C, that is, the corresponding temperature is the transition temperature of asphalt from viscoelastic liquid to Newtonian fluid, after that, asphalt exhibits pure viscous flow state with temperature. Obviously, there is still a slight difference between the simulation and the laboratory results (for AAA-1 asphalt: Tg = 247 ± 4 K, Tll = 400 K; for Tahua 90# asphalt: Tg = 259 K, Tll = 395 K). However, experimental results are consistent with the MD results in overall trends. 4. Conclusions In this paper, the MD simulations were used to study the glass forming process of AAA-1 asphalt from the viewpoint of glass forming liquid. The volume-temperature of asphalt was obtained at various temperatures to observe the processes of liquid–liquid transition and glass transition. Meanwhile, the temperature dependence of viscosity and the Stokes-Einstein relation were used to verify the liquid–liquid transition temperature. And lastly, cage effect of MCT theory was borrowed to explain the microscopic dynamics transition mechanism at molecular level. The main conclusions can be drawn as follows: (1) With temperature decreasing, asphalt evolves from timeindependent Newtonian fluid at above 394 ± 7 K to truly frozen glassy solid at beneath 247 ± 4 K. That is, from the viewpoint of glass forming liquid, the glass transition of asphalt spans a distinct broadening temperature range from 394 ± 7 K to 247 ± 4 K. (2) In practice, Tg = 247 ± 4 K is thought of glass transition temperature which is quantitatively consistent to experimental result. Further, temperature dependences of coefficient of volume thermal expansion (CVTE) and free volume of AAA1 verified above-mentioned results. (3) The temperature dependence of the viscosity of AAA-1 asphalt system is not satisfied with Arrhenius law but satisfied with Vogel-Fulcher-Tammann (VFT) equation, which also reveals that asphalt is typical of a fragile liquid. Moreover, piecewise fittings with Arrhenius law reveal that there would be a transition at above 387 K.
(4) The product of self-diffusivity and viscosity (Dg) strongly deviates from the Stokes-Einstein relation in the vicinity of temperature Tc = 400 K, which verifies that there is a transition at about this temperature. (5) Normalized displacement of asphaltene-phenol revealed that Tc (i.e., Tll) is the critical temperature, above which arelaxation transforms to fast a-relaxation of asphalt. And it was explained by colloidal cage effect similar to that of mode coupling theory (MCT), i.e., with temperature increasing, the asphaltene-phenol molecular transits from local thermal vibrations to restricted movement, then jumps from one colloidal cage to another at ca. 400 K, and eventually performs temperature-independent ergodic movements at above 400 K. That is, viscoelastic liquid-Newtonian liquid transition of AAA-1 asphalt did occur at ca. 400 K. Moreover, the good agreement between the rheological experiments and simulation results demonstrated that these MD results are reliable. This paper may help understanding microscopic picture of asphalt relaxation processes with temperature, which would enable new additives and new additive strategies to modify asphalt and facilitate crude oil exploitation, transportation and refining processes, etc. And also, this paper may improve the understanding of glass forming liquid of asphalt. Acknowledgements The research is financially supported by China Postdoctoral Science Foundation (Nos. 2016M592841, 2017T100774), the Fundamental Research Funds for the Central Universities (No. 2452015054), and the National Natural Science Foundation of China (NSFC) (No. 51308461). We thank the National Supercomputing Center in Shenzhen, HPC of NWAFU for the use of the supercomputer. Conflict of interest The authors declare no conflict of interest. References [1] O.C. Mullins, The asphaltenes, Ann. Rev. Anal. Chem. 4 (2011) 393–418, https:// doi.org/10.1146/annurev-anchem-061010-113849. [2] A. Zare-Shahabadi, A. Shokuhfar, S. Ebrahimi-Nejad, Preparation and rheological characterization of asphalt binders reinforced with layered silicate nanoparticles, Construct. Build. Mater. 24 (7) (2010) 1239–1244, https://doi.org/10.1016/j.conbuildmat.2009.12.013.
440
Y. Kang et al. / Construction and Building Materials 214 (2019) 430–440
[3] Y. Ding, B. Huang, X. Shu, Y. Zhang, M.E. Woods, Use of molecular dynamics to investigate diffusion between virgin and aged asphalt binders, Fuel 174 (2016) 267–273, https://doi.org/10.1016/j.fuel.2016.02.022. [4] J.M. Krishnan, K.R. Rajagopal, On the mechanical behavior of asphalt, Mechan. Mater. 37 (11) (2005) 1085–1100, https://doi.org/10.1016/j. mechmat.2004.09.005. [5] P. Kriz, J. Stastna, L. Zanzotto, Glass transition and phase stability in asphalt binders, Road Mater. Pave. Design 9 (sup1) (2011) 37–65, https://doi.org/ 10.1080/14680629.2008.9690158. [6] M. Mousavi, F. Pahlavan, D. Oldham, S. Hosseinnezhad, E.H. Fini, Multiscale investigation of oxidative aging in biomodified asphalt binder, J. Phys. Chem. C 120 (31) (2016) 17224–17233, https://doi.org/10.1021/acs.jpcc.6b05004. [7] L. Zhang, M.L. Greenfield, Effects of polymer modification on properties and microstructure of model asphalt systems, Energy Fuels 22 (5) (2008) 3363– 3375, https://doi.org/10.1021/ef700699p. [8] D.D. Li, M.L. Greenfield, Chemical compositions of improved model asphalt systems for molecular simulations, Fuel 115 (2014) 347–356, https://doi.org/ 10.1016/j.fuel.2013.07.012. [9] D. Sun, T. Lin, X. Zhu, Y. Tian, F. Liu, Indices for self-healing performance assessments based on molecular dynamics simulation of asphalt binders, Computat. Mater. Sci. 114 (2016) 86–93, https://doi.org/10.1016/ j.commatsci.2015.12.017. [10] F. Khabaz, R. Khare, Glass transition and molecular mobility in styrenebutadiene rubber modified asphalt, J. Phys. Chem. B 119 (44) (2015) 14261– 14269, https://doi.org/10.1021/acs.jpcb.5b06191. [11] C.A. Angell, K.L. Ngai, G.B. McKenna, P.F. McMillan, S.W. Martin, Relaxation in glassforming liquids and amorphous solids, J. Appl. Phys. 88 (6) (2000) 3113– 3157, https://doi.org/10.1063/1.1286035. [12] C. Zhang, L. Hu, Y. Yue, J.C. Mauro, Fragile-to-strong transition in metallic glass-forming liquids, J. Chem. Phys. 133 (1) (2010), https://doi.org/10.1063/ 1.3457670. [13] L. Zhang, M.L. Greenfield, Relaxation time, diffusion, and viscosity analysis of model asphalt systems using molecular simulation, J. Chem. Phys. 127 (19) (2007), https://doi.org/10.1063/1.2799189. [14] Q. Qin, G.B. McKenna, Correlation between dynamic fragility and glass transition temperature for different classes of glass forming liquids, J. NonCrystal. Solid. 352 (28–29) (2006) 2977–2985, https://doi.org/10.1016/j. jnoncrysol.2006.04.014. [15] P.G. Debenedetti, F.H. Stillinger, Supercooled liquids and the glass transition, Nature 410 (6825) (2001) 259–267, https://doi.org/10.1038/35065704. [16] H. Zhai, D. Salomon, Evaluation of low-temperature properties and the fragility of asphalt binders with non-arrhenius viscosity-temperature dependence, J. Transport. Res. Board 2005 (1901) 44–51. [17] Q. Qin, J.F. Schabron, R.B. Boysen, M.J. Farrar, Field aging effect on chemistry and rheology of asphalt binders and rheological predictions for field aging, Fuel 121 (2014) 86–94, https://doi.org/10.1016/j.fuel.2013.12.040. [18] A. Samieadel, D. Oldham, E.H. Fini, Investigating molecular conformation and packing of oxidized asphaltene molecules in presence of paraffin wax, Fuel 220 (2018) 503–512, https://doi.org/10.1016/j.fuel.2018.02.031. [19] S. Sastry, P.G. Debenedetti, F.H. Stillinger, Signatures of distinct dynamical regimes in the energy landscape of a glass-forming liquid, Nature 393 (6685) (1998) 554–557, https://doi.org/10.1038/31189.
[20] J.L. Barrat, W. Gotze, A. Latz, The liquid-glass transition of the hard-sphere system, J. Phys.: Conden. Matter 1 (39) (1989) 7163–7170, https://doi.org/ 10.1088/0953-8984/1/39/027. [21] J. Jackle, Models of the glass transition, Report. Progr. Phys. 49 (2) (1986) 171– 231, https://doi.org/10.1088/0034-4885/49/2/002. [22] M.H. Cohen, D. Turnbull, Molecular transport in liquids and glasses, J. Chem. Phys. 31 (5) (1959) 1164–1169, https://doi.org/10.1063/1.1730566. [23] D.D. Li, M.L. Greenfield, Viscosity, relaxation time, and dynamics within a model asphalt of larger molecules, J. Chem. Phys. 140 (3) (2014), https://doi. org/10.1063/1.4848736. [24] Accelrys Inc, San Diego. http://accelrys.com/products/collaborative-science/ biovia-materials-studio/. [25] H. Sun, COMPASS: An ab initio force-field optimized for condensed-phase applicationssoverview with details on alkane and benzene compounds, J. Phys. Chem. B 102 (1998) 7338–7364. [26] F. Daan, S. Berend, Understanding Molecular Simulation From Algorithms to Applications, Academic Press, San Diego, 2002. [27] D.R. Jones, SHRP materials reference library, asphalt cements: a concise data compilation. SHRP-A-645, Strategic Highway Research Program National Research Council, Washington, DC, 1993. [28] X. Pei, Modeling and Analysis of molecular dynamics for characterizing asphalt-aggregate interaction [dissertation], Chang’an University, Xi’an(SN), 2013. in chinese. [29] A. Usmani, Asphalt Science and Technology, CRC Press, New York, 1997. [30] D.A. Anderson, D.W. Christensen, H.U. Bahia, R. Dongre, M.G. Sharma, C.E. Antle, J. Button, Binder characterization and evaluation. Volume 3: physical characterization, Strategic Highway Research Program, Washington, D.C.,, 1994. [31] M.L. Connolly, Analytical molecular surface calculation, J. Appl. Crystallogr. 16 (5) (1983) 548–558, https://doi.org/10.1107/s0021889883010985. [32] M.S. Green, Markoff random processes and the statistical mechanics of timedependent phenomena, J. Chem. Phys. 20 (8) (1952) 1281–1295, https://doi. org/10.1063/1.1700722. [33] M.S. Green, Markoff random processes and the statistical mechanics of timedependent phenomena. II. Irreversible processes in fluids, J. Chem. Phys. 22 (3) (1954) 398–413, https://doi.org/10.1063/1.1740082. [34] B. Liu, J. Goree, O.S. Vaulina, Test of the Stokes-Einstein relation in a twodimensional Yukawa liquid, Phys. Rev. Lett. 96 (1) (2006), https://doi.org/ 10.1103/PhysRevLett. 96.015005. [35] D. Vlassopoulos, G. Fytas, From Polymers to Colloids: Engineering the Dynamic Properties of Hairy Particles, 236 (2009) 1-54, doi: /10.1007/12_2009_31. [36] M. Mousavi, T. Abdollahi, F. Pahlavan, E.H. Fini, The influence of asphalteneresin molecular interactions on the colloidal stability of crude oil, Fuel 183 (2016) 262–271, https://doi.org/10.1016/j.fuel.2016.06.100. [37] M.E. Helgeson, N.J. Wagner, D. Vlassopoulos, Viscoelasticity and shear melting of colloidal star polymer glasses, J. Rheol. 51 (2) (2007) 297–316, https://doi. org/10.1122/1.2433935. [38] S.J. Stadnicki, J.K. Gillham, R.F. Boyer, The Tll (>Tg) transition of atactic polystyrene, J. Appl. Polym. Sci. 20 (5) (1976) 1245–1275, https://doi.org/ 10.1002/app.1976.070200510. [39] M. Fuchs, W. Gotze, S. Hildebrand, A. Latz, A theory for the beta -relaxation process near the liquid-to-glass crossover, J. Phys. Conden. Matter. 4 (38) (1992) 7709–7744, https://doi.org/10.1088/0953-8984/4/38/007.