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Molecular liquids formed by nanoparticles
Journal of Molecular Liquids 286 (2019) 110852
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Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Molecular liquids formed by nanoparticles A.Ya Malkin a,⁎, M. Yu Polyakova a, A.V. Subbotin a,d, I.B. Meshkov b,c, A.V. Bystrova b,c, V.G. Kulichikhin a, A.M. Muzafarov b,c a
A.V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Moscow, Russia N.S. Enikolopov Institute of Synthetic Polymeric Materials, Russian Academy of Sciences, Moscow, Russia A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Moscow, Russia d AN. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Moscow, Russia b c
a r t i c l e
i n f o
Article history: Received 28 February 2019 Received in revised form 18 April 2019 Accepted 24 April 2019 Available online 3 May 2019 Keywords: Nanoliquids Viscosity Organosilicon compounds Viscoelasticity Molecular weight Physical gelation
a b s t r a c t The rheology of a rather special case of molecular nanoliquids formed by polymethylsilsesquioxane nanoparticles which occupy an intermediate position between colloidal particles and macromolecules has been studied. These objects are liquids, homogeneous up to submicron size in a wide temperature range. They demonstrate viscoelastic behavior with very strong dependence of viscosity on molecular weight of these nanoobjects. A new scaling model based on the concept of friction in viscoelastic outer layers describing this kind of behavior has been proposed. Relaxation properties of smaller nanoparticles can be described by a single-mode Maxwell model, while relaxation for larger particles takes place in a wide frequency rage covering three orders. Interpretation of the temperature dependence of viscosity within the framework of the standard WLF equation allowed us to find the “glass” (or gel)transition point. Transition from fluid to global gel-like state was clearly observed at this temperature. As part of finding on the nature of this transition, it was shown that no structural effects are related to this transition and it should be treated as a relaxation phenomenon. © 2019 Elsevier B.V. All rights reserved.
1. Introduction The emergence of new polymeric forms, such as hyperbranched systems and their regular counterparts – dendrimers, multiarm stars, dense macromolecular brushes, and molecular nanogels, that is, everything that we call nanoobjects [1], requires a comprehensive study of their properties and interpretation of the results obtained in the coordinates of the classical polymer science. Pioneering research of dendrimer rheology immediately demonstrated their unusual solution and bulk behavior [2–4], and lately unique results were obtained [5,6] for the behavior of carbosilane dendrimers in the bulk. The subject of our research was polymethylsilsesquioxane nanosized densely cross-linked polycyclic formations, the transition of which to cross-linked systems of infinite size is artificially limited by blocking agents [7]. The number of similar nanoobjects is gradually increasing, and most importantly, many of the previously known objects that have many practical applications can be unambiguously attributed to this type (MQ resins, many organoelement systems), and, therefore, the study of their rheological properties is highly relevant.
⁎ Corresponding author. E-mail address: [email protected] (A.Y. Malkin).
https://doi.org/10.1016/j.molliq.2019.04.129 0167-7322/© 2019 Elsevier B.V. All rights reserved.
Interest in these objects also arises from the fact that they lie in the borderline between the polymers and colloidal particles [8,9]. The thermodynamics and the phase state of such systems were an object of intensive investigations [10–12] as well as their behavior in solutions [13], rheological properties of MQ-systems [14], and correlation between their phase state and the rheological properties [15]. These materials are of wide practical interest including oil recovery [16], improving compatibility of polymer blends [17], platform for targeted drugdelivery [18] and others. Different aspects of silica-soles processing and various fields of their applications were discussed in [19]. Earlier we dealt with particles of a rigid silica core and trimethylsiloxane shell – molecular silica-sols [20–22], in this work molecular nanoparticles with polymethylsilsesquioxane core and trimethylsiloxane shell were investigated. That is, the outer shell of the new objects remained the same, but the rigidity of the core became substantially less with the replacement of the silica structure by the methylsilsesquioxane one, as the functionality of monomer units changed from 4 to 3. This led to the fact that in the whole range of the core-shell ratios the synthesized systems remained liquids, which allowed us to investigate these objects in a wide range of molecular weights and core-shell ratios. At the same time, they remained close analogues of particles with silica cores, retained a compact form, core-shell morphology, and very low intrinsic viscosity [13]. These objects could be classified as nanoparticles, but are completely different from solid
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nanoparticle, such as metal oxides, carbon allotropic derivatives (nanotubes, fullerenes, graphenes), some clays. Thus, the subject of this study was quite new nanoobjects, namely fluids formed by polymethylsilsequioxane nanoparticles, which stay homogeneous up to submicron size level and can flow in a wide temperature range. We expected that the mode of flow of these molecular liquids is different from the mechanism of flow of usual long-chain linear polymers and therefore it was necessary to understand the nature of their viscosity-MW dependence.
Table 1 Main characteristics of the samples under study.
2. Objects and methods
the range of shear rates of 10−3–104 rad/s in a step mode with duration of each step 20 s. Viscoelastic (dynamic) properties were measured in the frequency (ω) range of 0.00628–628 rad/s and frequency dependences of the storage modulus G′(ω) and the loss modulus G″(ω) were determined in the linear domain of the viscoelasticity, which was controlled by varying the strain. Frequency was changed by steps of 10 s duration. It is worth mentioning that all dynamic measurements were carried out in the isothermal conditions because the temperature growth due to energy dissipation did not exceed 1 K. As known, wall slip can influence the results of measurements of the rheological properties of different media [23,24]. Therefore, the following tests have been made: comparison of data obtained in plate-plate and come-plate geometry with smooth and rough surfaces, correlation of the results obtained in rotational devices and capillary viscometer. A possibility for comparison was facilitated by the Newtonian behavior of the samples studied. The results of the viscosity measurements when initial data were treated by the standard methods matched in all cases within the confidence limits. So we can be sure that wall slip is absent (or negligibly small). For low temperature IR studies, the S10 sample was placed on the copper support, which was transferred into a cryostat connected with vacuum pump. The IR spectra were registered in the reflection mode. The referent spectrum was registered at 20 °C. Then the cryostat was evacuated to residual pressure of 1 Pa cooled by passing cold nitrogen vapor from 30 °C to −50 °C in an increment of 10 °C. Temperature control was performed by heating the nitrogen stream. Temperature was measured by a copper-constantan thermocouple with junction embedded into the copper support. IR spectra were registered using FTIR spectrometer Tensor II (Bruker, Germany) with standard mirror reflection
The object of this study were polymethylsilsesquioxane nanoparticles, synthesized as described earlier [7,13] by condensation and blocking of hyperbranched polymethylethoxysiloxane. Principle stages of synthesis and structure are shown in Fig. 1. Samples of different molecular weight were obtained by varying condensation time. Main characteristics of the samples under study are summarized in Table 1 where the objects of the study are denoted as S-samples and the subscript designates approximate MW of a sample. Molecular weights of the nanoparticles were estimated from the GPC data using PS standard. The size and polydispersity of the samples was determined using the Zeta-Sizer ZS instrument (Malvern Panalytic, GB) with isopropanol as a medium (Fig. 2). The size distributions are close to Gaussian and the volume-to-surface average size of dispersed particles, D32, are collected in Table 1. Thermal properties over a wide temperature range were studied using the DSC method (Mettler-Toledo Instrument). The protocol of the experiments was as follows: samples were carefully dried in a thermo-oven at 10 °C for 4 h and placed into a desiccator and stored there for four days. Then the samples were quickly transferred into the working cell of the DSC instrument. The samples were cooled to minus 40 °C, this temperature maintained for 10 min, and then the temperature increased to 70 °C at a rate of 5 K·min−1. The heating-cooling cycle was repeated three times. The rheological properties were measured with rotation rheometers Physica MCR301 (Anton Paar, Austria-Germany) and RheoStress RS600 (Thermo Haake, Germany) using different operating units. Two regimes of measuring were carried out. The apparent viscosity was measured in
Sample designation
Mw
S10 S7 S4 S3
10,000 7000 4200 2800
Diameter, D32, nm 4.85 2.70 2.01 0.72
Fig. 1. The scheme of synthesis and the molecular structure of polymethylsilsesquioxane nanoparticles.
Polydispersity Index 2.67 2.06 1.56 1.24
Viscosity at 25 °C, Pa*s 6540 198 2.48 0.14
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30 25
3
Share, % S3 S4
20
S7
15
S10
10 5 0 1
10
100
Size, nm Fig. 2. Size distribution of the studied samples.
accessory. Spectra were obtained in the range of 500–8000 cm−1 with resolution of 1 cm−1, number of scans was 32. The lower limit of 500 cm−1 was due to cryostat windows made of zinc celenide. 3. Results and discussion 3.1. Rheology and structure of nanoparticles 3.1.1. Viscosity at room temperature The results of measuring viscous properties are shown in Fig. 3 for room temperature. All samples are Newtonian liquids and the viscosity strongly increases with the growth of MW as shown in Fig. 4. The dependence of the viscosity on MW as presented in Fig. 4 has a typical power law type, but the exponent is very high, close to 8.3, that is rather unusual for the η(M) dependence. At present, there is more or less general agreement about rheological properties of linear polymers [25–27]. However, the role of branching continues to be the subject of active discussion both on the fundamental level and in relation to industrial polymers. In earlier publications, it was established that ratio of viscosities of linear and branched polymers is determined by the size of a statistical coil [28,29]. Modern approach to determining the viscoelastic properties of branched polymers is based on the so-named Pom-Pom model, which is an advanced version of the general tube model [30,31]. Branching of linear chains is especially
Fig. 3. Viscosity of the S liquids (designations are shown at the curves) measured at 25 0С.
Fig. 4. Dependence of the viscosity on molecular weight at 25 °C.
important for example for polyethylene [32–36]. However, the rheology of branched polymers was considered mainly for rarely statistically distributed short or long branches. The situation with nanoparticles is quite different because they are intramolecularly cross-linked branched polymers with relatively thick and hard homogeneous packing of branches without any central macromolecular chain and movable cover. In this case, it is rather difficult to characterize the molecular structure of nanoparticles which is determined not only by molecular weight, but also density of chain packing inside the particle. As said above, the value of the exponent in the η(M) dependence is approximately 8. This value is much larger than a typical value of the exponent (close to 3.5) for linear polymers, which is assumed to be induced by intermolecular entanglements. There is no reasonable entanglement model, which can be responsible for the observed high value of the exponent. That is why we should suppose that the very high value of the exponent in the η(M) dependence for studied samples is related to some other mechanism of interparticle interaction different from that for linear polymers. The structure of these samples can be also treated as granular suspensions which can flow due to soft outer layer. Meanwhile strong contact friction between neighboring particles should be also taken in consideration. The rheology of similar (but not colloidal size) solid particles was discussed in several publications [37–39]. However, as seen from Fig. 3, our samples are Newtonian liquids and they do not demonstrate tendency to shear thickening and jamming at high shear rates that are typical for concentrated suspensions [40–45].
Fig. 5. Comparison of the experimental data (points) with prediction of Eq. (1) (line).
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S10
S10
a
S7
S7
S4
S3
S4
Fig. 6. Frequency dependences of the storage (a) and loss (b) modulus for S-nanoparticles at room temperature.
Thus, we considered a model of friction of particles with viscoelastic outer layer and activation model of relaxation, and proposed the following model of the flow of nanoparticles describing the observed η(M) dependence. This model is based on simple scaling arguments. The nanoliquid is considered as a volume tightly filled with deformable elastic objects with a shape close to spherical. Individual particles do not interpenetrate each other. The volume V of the individual particle is proportional to MW: V ~ M. 1=3
The intrinsic radius of a particle is estimated as R ~ ð3V and the 4π Þ pffiffiffi 2=3 surface area is A ~ ð6V πÞ . Elasticity of the particle is characterized by the elastic modulus G, which is assumed to be independent on MW. In the limit of linear viscoelasticity, the elastic energy stored in the particle, U, is defined by well-known formula U ~ Gε2V, where ε is the elastic deformation. The viscosity is defined from the scaling relation η ~ Gτ, where τ is the characteristic relaxation time. In order to estimate the relaxation time we assume that dissipation in the system arises due to external friction between nanoparticles while they slip along each other like in concentrated suspensions. It is assumed that nanoparticles slightly penetrate into each other and the dissipative processes happening in the interpenetration layer are characterized by the friction coefficient which is considered as a measure of this phenomenon. In this way, the total friction coefficient ζ is proportional to the surface area of the particle, A, ζ = ζ0A, where ζ0 is the friction coefficient per unit area. The relaxation time was estimated as a diffusion time of the 2
U
particle on a distance of the order of R: τ∝ ζkBRT ekB T , where U* ~ GV is the
energy barrier which should be overcome. This barrier is related to deformation of the given particle when it moves between other particles and the value of this strain is ε~ 1. Thus, the final formula for viscosity can be written as η η∝
Gζ 0 V 4=3 kGVT e B ∝M 4=3 eβM kB T
ð1Þ
Here the coefficient β does not depend on M. Therefore, as opposed to the standard power law η(M) dependence, we have come to more complicated dependence including an exponential factor. Comparison of this result with the experimental data is presented in Fig. 5 plotted in the coordinates of this equation as ln(η/M4/3) vs. M. The proposed model of quasi-suspensions of molecular nanoliquids is in good agreement with experimental observations (Pearson's r = 0.993, R-square = 0.981). 3.1.2. Viscoelastic properties at room temperature The frequency dependences of the elastic modulus and loss modulus for all S-samples are presented in Fig. 6. For three low MW samples, the moduli are almost the same and the G′(ω) dependencies of the storage modulus are close to squared. This means that their properties can be characterized by a single-mode Maxwell model with the dependence of the relaxation time on MW similar to that dependence of the viscosity. The behavior of the high MW nanoparticles (sample S10) is more interesting and complicated. The observed G′(ω) dependence is the transient part of the wide frequency dependence corresponding to the
S10
S10
S7
S7 S4
S4 S3
S3
Fig. 7. Temperature dependences of the viscosity in the Arrhenius coordinates.
Fig. 8. Temperature dependences of the viscosity in coordinates of the WLF equation. Parameter A is the right part of Eq. (2), i.e. the function of (T − Ts).
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taken at the lowest frequency from Fig. 6a. However, the short-time side of the relaxation spectrum is long because G′(ω) and G″(ω) dependences do not cross till 104 s−1, i.e. the minimal relaxation time is definitely less than 10−4 s and the spectrum in whole covers more than 3 orders. 3.1.3. Temperature dependence of viscosity and viscoelastic properties With decreasing temperature, the viscosities of all samples remain Newtonian though demonstrate strong temperature dependence (Fig. 7). Temperature dependencies of the viscosity in a rather wide temperature range do not obey the Arrhenius equation that is typical for amorphous media in a wide temperature range. The Williams-Landel-Ferry (WLF) equation with some averaged (or “universal”) constants is the most appropriate for describing temperature dependences of such materials. This equation can be written as [46]: Fig. 9. Dependence of the reference temperature on molecular weight of nanoparticles.
lgηðTÞ ¼ lgηs −
1 Hz, 5 K/min 0.1 Hz, 5 K/min
0.1 Hz, 2 K/min
Fig. 10. Temperature dependences of the elastic modulus of the nanoliquid (sample S10) at different regimes of scanning.
transition from the terminal (flow) zone to the rubbery plateau. The relaxation spectrum of this sample is very wide. The terminal relaxation 0
time is estimated as θterm ¼ G =ω η ¼ 0:135s where the value of G′ was 2
8:86ðT−T s Þ 101:6 þ ðT−T s Þ
ð2Þ
where Ts is the reference temperature lying app. at 45–50 K above the glass transition temperature and ηs is the viscosity at this temperature. This equation quite satisfactory describes the experimental data (see Fig. 8). Indeed, this equation quite satisfactory describes the experimental data for the viscosity changing at least by 4 orders of magnitude in the rather wide range of the difference (T − Ts) values except the boundary temperatures lying far above the Ts values. As is known, the transition from the free volume model to the activation model takes place and this is the reason of the deviation from the WLF equation [44]. The logηsvalues in Eq. (2) for four samples lie in the range 4.0–4.4. The Ts values obtained by fitting the experimental data as a function of MW are shown in Fig. 9. The reference temperature increases monotonously approaching 275 K for particles of the largest size. This temperature should be treated as mechanical glass transition temperature typical for highly concentrated suspensions [42–45]. However, in the case of nanoparticles it is more correct to treat this temperature as the physical gelation temperature because of rather low modulus values at T b Ts (see below) and low logηs values (4.2 ± 0.2). These values are extremely low for the glass point but can correspond to physical gelation.
Fig. 11. IR spectra of S10 in a wide temperature range covering the gelation temperature.
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0.1 W/g
1st test
2nd test
3rd test
Fig. 12. The results of three repeated DSC measurements for the S10 nanoliquid. The rate of temperature change is 5 K/min.
The experimental data for the temperature dependence of the storage modulus are presented in Fig. 10 for different frequencies. This data clearly demonstrate that at temperature close to Ts (in Fig. 9) a transition to the new state takes place where the elastic modulus does not depend on frequency and on the rate of temperature change. The modulus value at this plateau is 106 Pa. It is reasonable to believe that nanoparticles at temperatures below Ts form a global solid gel-like structure. For understanding the nature of the fluid-to-gel transition, it was necessary to make sure this transition is not related to any physical process of interchain interaction. Fig. 11 presents comparison of spectra obtained in the temperature range from −50 °C to 30 °C in the range of 500–8000 cm−1 In all cases, the baseline was corrected in interactive re. gime. One can see that there is no special changes in IR spectra. It means that the observed gelation is completely explained by a relaxation mechanism, i.e. loss of mobility of outer layers of the particles. If we estimate the value of the energetic barrier U* = GV from η(T) dependence of the sample S10 for the temperature range close to Ts (Eq. (1)), we obtain the value of 143 kJ/mol. This is rather high value showing the hindrance for movement (flow) of particles. This can be treated as the solidification of the outer layers of the particles and their relative displacement becomes impossible due to high interparticle friction like it happens in jamming of suspensions. Thus, in this situation, we deal with the dual behavior of molecular nanoparticles transition from flow of a liquid to solidification of suspension. The effect of the liquid-to-gel transition is supported by the DSC data presented in Fig. 12. These measurements confirm that the transition
10 Hz
takes place in the temperature interval from −7 to −10 °C and this is not a phase transition. Examined nanoliquids are amorphous homogeneous matter which do not exhibit any phase transitions in a wide temperature range. Meanwhile something similar to the second-order transition happens below 270 K. The above discussed experimental data allow us to consider S10 sample as a material close to polymeric substances. Decreasing MW changes the situation remarkably. Fig. 13 presents experimental data for temperature dependencies of the storage modulus for S7 sample at three frequencies (changing by two orders). One can see that the storage modulus depends on frequency. This proves the viscoelastic nature of S-samples possibly obliged to deformation of nanoparticles as a matter similar to rubbery balls. No gelation is observed even at high modulus values (much higher than corresponding to gelation transition in Fig. 10). Even more interesting is temperature-frequency superposition. Shifting the curves shown in Fig. 13 along the temperature axis to the dependence corresponding to 0.1 Hz gives the results presented in Fig. 14. The temperature coefficient chosen for the middle parts of the curves was 10 °C for 1 Hz and 20 °C for 10 Hz. One can see that no gelation happens even at −40 °C. Meanwhile the following result draws attention. This is a possibility of satisfactory temperature-frequency superposition in the low temperature domain and no superposition at higher temperatures. This indicates a change of the flow mechanism and mode of relaxation in transition from low to higher temperatures. Absence of temperature dependence of the elastic modulus at high temperatures may evidence, that molecular movement in the lower MW nanoliquids occurs like in simple liquids. 4. Conclusion 1. The study of polymethylsilsesquioxane nanoparticles showed that these objects are viscoelastic liquids in the temperatures above 0 °C in opposite to usual nanoparticles which are always solids. 2. The viscosity of these nanoliquids strongly depends on the size of particles and in flow they demonstrate their dual nature (like colloidal particles and like liquids). Unusual strong dependence of the viscosity on MW is explained by a new molecular model based on scaling arguments. 3. According to the temperature dependence of viscosity, these objects should be treated as amorphous materials but at temperatures below app. −5 °C physical gelation of the nanoliquid takes place. This effect is not accompanied by any chemical transformations of the structure and thus should be treated as a relaxation phenomenon.
10 Hz
1 Hz
1 Hz 0.1 Hz
Fig. 13. Temperature dependencies of the storage modulus for the S7. Rate of temperature scanning was 5 K/min.
Fig. 14. Superimposed temperature dependencies of the storage modulus shifted to 0.1 Hz.
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Acknowledgements The authors are grateful for the financial support of Russian Science Foundation (grant 17-79-30108). Synthesis of polymethylsilsesquioxane nanoparticles was supported by the Ministry of Science and Higher Education of the Russian Federation (Grant of the Government of the Russian Federation No. 14. W03.31.0018). Polymethylsilsesquioxane nanoparticles were examined within the State Program of TIPS RAS. The authors are grateful for measuring particle size distribution to Mr. M. Kuzin from TIPS RAS (Fig. 2), DSC of dry samples to Dr. G. Shandryuk from TIPS RAS (Fig. 12), and the low temperature FTIR spectra (Fig. 11) to Dr. Yu. N. Morozov from Moscow State University. References [1] A.M. Muzafarov, N.G. Vasilenko, E.A. Tatarinova, G.M. Ignat'eva, V.M. Myakushev, M.A. Obrezkova, I.B. Meshkov, N.V. Voronina, O.V. Novozhilov, Macromolecular nano-objects as a promising direction of polymer chemistry, Polym. Sci. Ser. 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Contents lists available at ScienceDirect
Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq
Molecular liquids formed by nanoparticles A.Ya Malkin a,⁎, M. Yu Polyakova a, A.V. Subbotin a,d, I.B. Meshkov b,c, A.V. Bystrova b,c, V.G. Kulichikhin a, A.M. Muzafarov b,c a
A.V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Moscow, Russia N.S. Enikolopov Institute of Synthetic Polymeric Materials, Russian Academy of Sciences, Moscow, Russia A.N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences, Moscow, Russia d AN. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Moscow, Russia b c
a r t i c l e
i n f o
Article history: Received 28 February 2019 Received in revised form 18 April 2019 Accepted 24 April 2019 Available online 3 May 2019 Keywords: Nanoliquids Viscosity Organosilicon compounds Viscoelasticity Molecular weight Physical gelation
a b s t r a c t The rheology of a rather special case of molecular nanoliquids formed by polymethylsilsesquioxane nanoparticles which occupy an intermediate position between colloidal particles and macromolecules has been studied. These objects are liquids, homogeneous up to submicron size in a wide temperature range. They demonstrate viscoelastic behavior with very strong dependence of viscosity on molecular weight of these nanoobjects. A new scaling model based on the concept of friction in viscoelastic outer layers describing this kind of behavior has been proposed. Relaxation properties of smaller nanoparticles can be described by a single-mode Maxwell model, while relaxation for larger particles takes place in a wide frequency rage covering three orders. Interpretation of the temperature dependence of viscosity within the framework of the standard WLF equation allowed us to find the “glass” (or gel)transition point. Transition from fluid to global gel-like state was clearly observed at this temperature. As part of finding on the nature of this transition, it was shown that no structural effects are related to this transition and it should be treated as a relaxation phenomenon. © 2019 Elsevier B.V. All rights reserved.
1. Introduction The emergence of new polymeric forms, such as hyperbranched systems and their regular counterparts – dendrimers, multiarm stars, dense macromolecular brushes, and molecular nanogels, that is, everything that we call nanoobjects [1], requires a comprehensive study of their properties and interpretation of the results obtained in the coordinates of the classical polymer science. Pioneering research of dendrimer rheology immediately demonstrated their unusual solution and bulk behavior [2–4], and lately unique results were obtained [5,6] for the behavior of carbosilane dendrimers in the bulk. The subject of our research was polymethylsilsesquioxane nanosized densely cross-linked polycyclic formations, the transition of which to cross-linked systems of infinite size is artificially limited by blocking agents [7]. The number of similar nanoobjects is gradually increasing, and most importantly, many of the previously known objects that have many practical applications can be unambiguously attributed to this type (MQ resins, many organoelement systems), and, therefore, the study of their rheological properties is highly relevant.
⁎ Corresponding author. E-mail address: [email protected] (A.Y. Malkin).
https://doi.org/10.1016/j.molliq.2019.04.129 0167-7322/© 2019 Elsevier B.V. All rights reserved.
Interest in these objects also arises from the fact that they lie in the borderline between the polymers and colloidal particles [8,9]. The thermodynamics and the phase state of such systems were an object of intensive investigations [10–12] as well as their behavior in solutions [13], rheological properties of MQ-systems [14], and correlation between their phase state and the rheological properties [15]. These materials are of wide practical interest including oil recovery [16], improving compatibility of polymer blends [17], platform for targeted drugdelivery [18] and others. Different aspects of silica-soles processing and various fields of their applications were discussed in [19]. Earlier we dealt with particles of a rigid silica core and trimethylsiloxane shell – molecular silica-sols [20–22], in this work molecular nanoparticles with polymethylsilsesquioxane core and trimethylsiloxane shell were investigated. That is, the outer shell of the new objects remained the same, but the rigidity of the core became substantially less with the replacement of the silica structure by the methylsilsesquioxane one, as the functionality of monomer units changed from 4 to 3. This led to the fact that in the whole range of the core-shell ratios the synthesized systems remained liquids, which allowed us to investigate these objects in a wide range of molecular weights and core-shell ratios. At the same time, they remained close analogues of particles with silica cores, retained a compact form, core-shell morphology, and very low intrinsic viscosity [13]. These objects could be classified as nanoparticles, but are completely different from solid
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nanoparticle, such as metal oxides, carbon allotropic derivatives (nanotubes, fullerenes, graphenes), some clays. Thus, the subject of this study was quite new nanoobjects, namely fluids formed by polymethylsilsequioxane nanoparticles, which stay homogeneous up to submicron size level and can flow in a wide temperature range. We expected that the mode of flow of these molecular liquids is different from the mechanism of flow of usual long-chain linear polymers and therefore it was necessary to understand the nature of their viscosity-MW dependence.
Table 1 Main characteristics of the samples under study.
2. Objects and methods
the range of shear rates of 10−3–104 rad/s in a step mode with duration of each step 20 s. Viscoelastic (dynamic) properties were measured in the frequency (ω) range of 0.00628–628 rad/s and frequency dependences of the storage modulus G′(ω) and the loss modulus G″(ω) were determined in the linear domain of the viscoelasticity, which was controlled by varying the strain. Frequency was changed by steps of 10 s duration. It is worth mentioning that all dynamic measurements were carried out in the isothermal conditions because the temperature growth due to energy dissipation did not exceed 1 K. As known, wall slip can influence the results of measurements of the rheological properties of different media [23,24]. Therefore, the following tests have been made: comparison of data obtained in plate-plate and come-plate geometry with smooth and rough surfaces, correlation of the results obtained in rotational devices and capillary viscometer. A possibility for comparison was facilitated by the Newtonian behavior of the samples studied. The results of the viscosity measurements when initial data were treated by the standard methods matched in all cases within the confidence limits. So we can be sure that wall slip is absent (or negligibly small). For low temperature IR studies, the S10 sample was placed on the copper support, which was transferred into a cryostat connected with vacuum pump. The IR spectra were registered in the reflection mode. The referent spectrum was registered at 20 °C. Then the cryostat was evacuated to residual pressure of 1 Pa cooled by passing cold nitrogen vapor from 30 °C to −50 °C in an increment of 10 °C. Temperature control was performed by heating the nitrogen stream. Temperature was measured by a copper-constantan thermocouple with junction embedded into the copper support. IR spectra were registered using FTIR spectrometer Tensor II (Bruker, Germany) with standard mirror reflection
The object of this study were polymethylsilsesquioxane nanoparticles, synthesized as described earlier [7,13] by condensation and blocking of hyperbranched polymethylethoxysiloxane. Principle stages of synthesis and structure are shown in Fig. 1. Samples of different molecular weight were obtained by varying condensation time. Main characteristics of the samples under study are summarized in Table 1 where the objects of the study are denoted as S-samples and the subscript designates approximate MW of a sample. Molecular weights of the nanoparticles were estimated from the GPC data using PS standard. The size and polydispersity of the samples was determined using the Zeta-Sizer ZS instrument (Malvern Panalytic, GB) with isopropanol as a medium (Fig. 2). The size distributions are close to Gaussian and the volume-to-surface average size of dispersed particles, D32, are collected in Table 1. Thermal properties over a wide temperature range were studied using the DSC method (Mettler-Toledo Instrument). The protocol of the experiments was as follows: samples were carefully dried in a thermo-oven at 10 °C for 4 h and placed into a desiccator and stored there for four days. Then the samples were quickly transferred into the working cell of the DSC instrument. The samples were cooled to minus 40 °C, this temperature maintained for 10 min, and then the temperature increased to 70 °C at a rate of 5 K·min−1. The heating-cooling cycle was repeated three times. The rheological properties were measured with rotation rheometers Physica MCR301 (Anton Paar, Austria-Germany) and RheoStress RS600 (Thermo Haake, Germany) using different operating units. Two regimes of measuring were carried out. The apparent viscosity was measured in
Sample designation
Mw
S10 S7 S4 S3
10,000 7000 4200 2800
Diameter, D32, nm 4.85 2.70 2.01 0.72
Fig. 1. The scheme of synthesis and the molecular structure of polymethylsilsesquioxane nanoparticles.
Polydispersity Index 2.67 2.06 1.56 1.24
Viscosity at 25 °C, Pa*s 6540 198 2.48 0.14
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30 25
3
Share, % S3 S4
20
S7
15
S10
10 5 0 1
10
100
Size, nm Fig. 2. Size distribution of the studied samples.
accessory. Spectra were obtained in the range of 500–8000 cm−1 with resolution of 1 cm−1, number of scans was 32. The lower limit of 500 cm−1 was due to cryostat windows made of zinc celenide. 3. Results and discussion 3.1. Rheology and structure of nanoparticles 3.1.1. Viscosity at room temperature The results of measuring viscous properties are shown in Fig. 3 for room temperature. All samples are Newtonian liquids and the viscosity strongly increases with the growth of MW as shown in Fig. 4. The dependence of the viscosity on MW as presented in Fig. 4 has a typical power law type, but the exponent is very high, close to 8.3, that is rather unusual for the η(M) dependence. At present, there is more or less general agreement about rheological properties of linear polymers [25–27]. However, the role of branching continues to be the subject of active discussion both on the fundamental level and in relation to industrial polymers. In earlier publications, it was established that ratio of viscosities of linear and branched polymers is determined by the size of a statistical coil [28,29]. Modern approach to determining the viscoelastic properties of branched polymers is based on the so-named Pom-Pom model, which is an advanced version of the general tube model [30,31]. Branching of linear chains is especially
Fig. 3. Viscosity of the S liquids (designations are shown at the curves) measured at 25 0С.
Fig. 4. Dependence of the viscosity on molecular weight at 25 °C.
important for example for polyethylene [32–36]. However, the rheology of branched polymers was considered mainly for rarely statistically distributed short or long branches. The situation with nanoparticles is quite different because they are intramolecularly cross-linked branched polymers with relatively thick and hard homogeneous packing of branches without any central macromolecular chain and movable cover. In this case, it is rather difficult to characterize the molecular structure of nanoparticles which is determined not only by molecular weight, but also density of chain packing inside the particle. As said above, the value of the exponent in the η(M) dependence is approximately 8. This value is much larger than a typical value of the exponent (close to 3.5) for linear polymers, which is assumed to be induced by intermolecular entanglements. There is no reasonable entanglement model, which can be responsible for the observed high value of the exponent. That is why we should suppose that the very high value of the exponent in the η(M) dependence for studied samples is related to some other mechanism of interparticle interaction different from that for linear polymers. The structure of these samples can be also treated as granular suspensions which can flow due to soft outer layer. Meanwhile strong contact friction between neighboring particles should be also taken in consideration. The rheology of similar (but not colloidal size) solid particles was discussed in several publications [37–39]. However, as seen from Fig. 3, our samples are Newtonian liquids and they do not demonstrate tendency to shear thickening and jamming at high shear rates that are typical for concentrated suspensions [40–45].
Fig. 5. Comparison of the experimental data (points) with prediction of Eq. (1) (line).
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S10
S10
a
S7
S7
S4
S3
S4
Fig. 6. Frequency dependences of the storage (a) and loss (b) modulus for S-nanoparticles at room temperature.
Thus, we considered a model of friction of particles with viscoelastic outer layer and activation model of relaxation, and proposed the following model of the flow of nanoparticles describing the observed η(M) dependence. This model is based on simple scaling arguments. The nanoliquid is considered as a volume tightly filled with deformable elastic objects with a shape close to spherical. Individual particles do not interpenetrate each other. The volume V of the individual particle is proportional to MW: V ~ M. 1=3
The intrinsic radius of a particle is estimated as R ~ ð3V and the 4π Þ pffiffiffi 2=3 surface area is A ~ ð6V πÞ . Elasticity of the particle is characterized by the elastic modulus G, which is assumed to be independent on MW. In the limit of linear viscoelasticity, the elastic energy stored in the particle, U, is defined by well-known formula U ~ Gε2V, where ε is the elastic deformation. The viscosity is defined from the scaling relation η ~ Gτ, where τ is the characteristic relaxation time. In order to estimate the relaxation time we assume that dissipation in the system arises due to external friction between nanoparticles while they slip along each other like in concentrated suspensions. It is assumed that nanoparticles slightly penetrate into each other and the dissipative processes happening in the interpenetration layer are characterized by the friction coefficient which is considered as a measure of this phenomenon. In this way, the total friction coefficient ζ is proportional to the surface area of the particle, A, ζ = ζ0A, where ζ0 is the friction coefficient per unit area. The relaxation time was estimated as a diffusion time of the 2
U
particle on a distance of the order of R: τ∝ ζkBRT ekB T , where U* ~ GV is the
energy barrier which should be overcome. This barrier is related to deformation of the given particle when it moves between other particles and the value of this strain is ε~ 1. Thus, the final formula for viscosity can be written as η η∝
Gζ 0 V 4=3 kGVT e B ∝M 4=3 eβM kB T
ð1Þ
Here the coefficient β does not depend on M. Therefore, as opposed to the standard power law η(M) dependence, we have come to more complicated dependence including an exponential factor. Comparison of this result with the experimental data is presented in Fig. 5 plotted in the coordinates of this equation as ln(η/M4/3) vs. M. The proposed model of quasi-suspensions of molecular nanoliquids is in good agreement with experimental observations (Pearson's r = 0.993, R-square = 0.981). 3.1.2. Viscoelastic properties at room temperature The frequency dependences of the elastic modulus and loss modulus for all S-samples are presented in Fig. 6. For three low MW samples, the moduli are almost the same and the G′(ω) dependencies of the storage modulus are close to squared. This means that their properties can be characterized by a single-mode Maxwell model with the dependence of the relaxation time on MW similar to that dependence of the viscosity. The behavior of the high MW nanoparticles (sample S10) is more interesting and complicated. The observed G′(ω) dependence is the transient part of the wide frequency dependence corresponding to the
S10
S10
S7
S7 S4
S4 S3
S3
Fig. 7. Temperature dependences of the viscosity in the Arrhenius coordinates.
Fig. 8. Temperature dependences of the viscosity in coordinates of the WLF equation. Parameter A is the right part of Eq. (2), i.e. the function of (T − Ts).
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taken at the lowest frequency from Fig. 6a. However, the short-time side of the relaxation spectrum is long because G′(ω) and G″(ω) dependences do not cross till 104 s−1, i.e. the minimal relaxation time is definitely less than 10−4 s and the spectrum in whole covers more than 3 orders. 3.1.3. Temperature dependence of viscosity and viscoelastic properties With decreasing temperature, the viscosities of all samples remain Newtonian though demonstrate strong temperature dependence (Fig. 7). Temperature dependencies of the viscosity in a rather wide temperature range do not obey the Arrhenius equation that is typical for amorphous media in a wide temperature range. The Williams-Landel-Ferry (WLF) equation with some averaged (or “universal”) constants is the most appropriate for describing temperature dependences of such materials. This equation can be written as [46]: Fig. 9. Dependence of the reference temperature on molecular weight of nanoparticles.
lgηðTÞ ¼ lgηs −
1 Hz, 5 K/min 0.1 Hz, 5 K/min
0.1 Hz, 2 K/min
Fig. 10. Temperature dependences of the elastic modulus of the nanoliquid (sample S10) at different regimes of scanning.
transition from the terminal (flow) zone to the rubbery plateau. The relaxation spectrum of this sample is very wide. The terminal relaxation 0
time is estimated as θterm ¼ G =ω η ¼ 0:135s where the value of G′ was 2
8:86ðT−T s Þ 101:6 þ ðT−T s Þ
ð2Þ
where Ts is the reference temperature lying app. at 45–50 K above the glass transition temperature and ηs is the viscosity at this temperature. This equation quite satisfactory describes the experimental data (see Fig. 8). Indeed, this equation quite satisfactory describes the experimental data for the viscosity changing at least by 4 orders of magnitude in the rather wide range of the difference (T − Ts) values except the boundary temperatures lying far above the Ts values. As is known, the transition from the free volume model to the activation model takes place and this is the reason of the deviation from the WLF equation [44]. The logηsvalues in Eq. (2) for four samples lie in the range 4.0–4.4. The Ts values obtained by fitting the experimental data as a function of MW are shown in Fig. 9. The reference temperature increases monotonously approaching 275 K for particles of the largest size. This temperature should be treated as mechanical glass transition temperature typical for highly concentrated suspensions [42–45]. However, in the case of nanoparticles it is more correct to treat this temperature as the physical gelation temperature because of rather low modulus values at T b Ts (see below) and low logηs values (4.2 ± 0.2). These values are extremely low for the glass point but can correspond to physical gelation.
Fig. 11. IR spectra of S10 in a wide temperature range covering the gelation temperature.
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0.1 W/g
1st test
2nd test
3rd test
Fig. 12. The results of three repeated DSC measurements for the S10 nanoliquid. The rate of temperature change is 5 K/min.
The experimental data for the temperature dependence of the storage modulus are presented in Fig. 10 for different frequencies. This data clearly demonstrate that at temperature close to Ts (in Fig. 9) a transition to the new state takes place where the elastic modulus does not depend on frequency and on the rate of temperature change. The modulus value at this plateau is 106 Pa. It is reasonable to believe that nanoparticles at temperatures below Ts form a global solid gel-like structure. For understanding the nature of the fluid-to-gel transition, it was necessary to make sure this transition is not related to any physical process of interchain interaction. Fig. 11 presents comparison of spectra obtained in the temperature range from −50 °C to 30 °C in the range of 500–8000 cm−1 In all cases, the baseline was corrected in interactive re. gime. One can see that there is no special changes in IR spectra. It means that the observed gelation is completely explained by a relaxation mechanism, i.e. loss of mobility of outer layers of the particles. If we estimate the value of the energetic barrier U* = GV from η(T) dependence of the sample S10 for the temperature range close to Ts (Eq. (1)), we obtain the value of 143 kJ/mol. This is rather high value showing the hindrance for movement (flow) of particles. This can be treated as the solidification of the outer layers of the particles and their relative displacement becomes impossible due to high interparticle friction like it happens in jamming of suspensions. Thus, in this situation, we deal with the dual behavior of molecular nanoparticles transition from flow of a liquid to solidification of suspension. The effect of the liquid-to-gel transition is supported by the DSC data presented in Fig. 12. These measurements confirm that the transition
10 Hz
takes place in the temperature interval from −7 to −10 °C and this is not a phase transition. Examined nanoliquids are amorphous homogeneous matter which do not exhibit any phase transitions in a wide temperature range. Meanwhile something similar to the second-order transition happens below 270 K. The above discussed experimental data allow us to consider S10 sample as a material close to polymeric substances. Decreasing MW changes the situation remarkably. Fig. 13 presents experimental data for temperature dependencies of the storage modulus for S7 sample at three frequencies (changing by two orders). One can see that the storage modulus depends on frequency. This proves the viscoelastic nature of S-samples possibly obliged to deformation of nanoparticles as a matter similar to rubbery balls. No gelation is observed even at high modulus values (much higher than corresponding to gelation transition in Fig. 10). Even more interesting is temperature-frequency superposition. Shifting the curves shown in Fig. 13 along the temperature axis to the dependence corresponding to 0.1 Hz gives the results presented in Fig. 14. The temperature coefficient chosen for the middle parts of the curves was 10 °C for 1 Hz and 20 °C for 10 Hz. One can see that no gelation happens even at −40 °C. Meanwhile the following result draws attention. This is a possibility of satisfactory temperature-frequency superposition in the low temperature domain and no superposition at higher temperatures. This indicates a change of the flow mechanism and mode of relaxation in transition from low to higher temperatures. Absence of temperature dependence of the elastic modulus at high temperatures may evidence, that molecular movement in the lower MW nanoliquids occurs like in simple liquids. 4. Conclusion 1. The study of polymethylsilsesquioxane nanoparticles showed that these objects are viscoelastic liquids in the temperatures above 0 °C in opposite to usual nanoparticles which are always solids. 2. The viscosity of these nanoliquids strongly depends on the size of particles and in flow they demonstrate their dual nature (like colloidal particles and like liquids). Unusual strong dependence of the viscosity on MW is explained by a new molecular model based on scaling arguments. 3. According to the temperature dependence of viscosity, these objects should be treated as amorphous materials but at temperatures below app. −5 °C physical gelation of the nanoliquid takes place. This effect is not accompanied by any chemical transformations of the structure and thus should be treated as a relaxation phenomenon.
10 Hz
1 Hz
1 Hz 0.1 Hz
Fig. 13. Temperature dependencies of the storage modulus for the S7. Rate of temperature scanning was 5 K/min.
Fig. 14. Superimposed temperature dependencies of the storage modulus shifted to 0.1 Hz.
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Acknowledgements The authors are grateful for the financial support of Russian Science Foundation (grant 17-79-30108). Synthesis of polymethylsilsesquioxane nanoparticles was supported by the Ministry of Science and Higher Education of the Russian Federation (Grant of the Government of the Russian Federation No. 14. W03.31.0018). Polymethylsilsesquioxane nanoparticles were examined within the State Program of TIPS RAS. The authors are grateful for measuring particle size distribution to Mr. M. Kuzin from TIPS RAS (Fig. 2), DSC of dry samples to Dr. G. Shandryuk from TIPS RAS (Fig. 12), and the low temperature FTIR spectra (Fig. 11) to Dr. Yu. N. Morozov from Moscow State University. References [1] A.M. Muzafarov, N.G. Vasilenko, E.A. Tatarinova, G.M. Ignat'eva, V.M. Myakushev, M.A. Obrezkova, I.B. Meshkov, N.V. Voronina, O.V. Novozhilov, Macromolecular nano-objects as a promising direction of polymer chemistry, Polym. Sci. Ser. 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