Calorimetric and infrared studies of carbosilane dendrimers of the third generation with ethyleneoxide terminal groups

Thermochimica Acta 617 (2015) 144–151

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Calorimetric and infrared studies of carbosilane dendrimers of the third generation with ethyleneoxide terminal groups b ˛ A.V. Markin a,∗ , S.S. Sologubov a , N.N. Smirnova a , A.V. Knyazev a , M. Maczka , M. Ptak b , c c c N.A. Novozhilova , E.A. Tatarinova , A.M. Muzafarov a

Lobachevsky State University of Nizhni Novgorod, 23/5 Gagarin Av., 603950 Nizhni Novgorod, Russia Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950 Wroclaw, Poland c Enikolopov Institute of Synthetic Polymeric Materials, Russian Academy of Sciences, 70 Profsoyuznaya St., 117393 Moscow, Russia b

a r t i c l e

i n f o

Article history: Received 13 April 2015 Received in revised form 21 August 2015 Accepted 22 August 2015 Available online 24 August 2015 Keywords: Carbosilane dendrimers AC DSC Heat capacity Glass transition Thermodynamic functions IR spectroscopy

a b s t r a c t In the present work, temperature dependences of heat capacities of carbosilane dendrimers of the third generation with ethyleneoxide terminal groups, denoted as G3[(OCH2 CH2 )1 OCH3 ]32 and G3[(OCH2 CH2 )3 OCH3 ]32 , have been measured in the temperature ranges from T = 6 to 520 K by precision adiabatic calorimetry (AC) and differential scanning calorimetry (DSC). In the above temperature range the physical transformations, such as glass transition and anomalies, have been detected, and their standard thermodynamic characteristics have been determined and analyzed. Complementary temperature-dependent infrared (IR) studies of carbosilane dendrimer G3[(OCH2 CH2 )1 OCH3 ]32 have been performed in the range from T = 4 to 298 K in order to study the nature of the revealed transformations. The standard thermodynamic functions of dendrimers under study, namely, heat capacity Cp0 (T ), enthalpy H◦ (T) − H◦ (0), entropy S◦ (T) − S◦ (0), and Gibbs energy G◦ (T) − H◦ (0) have been calculated for the range from T → 0 to 520 K. The standard thermodynamic properties of the investigated dendrimers have been discussed and compared with literature data for carbosilane dendrimers with different functional terminal groups. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The synthesis, study and application of dendrimers are one of new and rapidly developing directions of polymer science. Dendrimers are complex monodisperse macromolecules with a regular and highly branched three-dimensional architecture and welldefined chemical structure [1,2]. Together with the hyperbranched polymers they represent a new class of polymeric materials, so-called macromolecular nanoobjects [3]. The synthesis of dendrimers is realized by repeating sequences of reaction steps. These sequences of reactions allow controlling the dendrimers composition, chemical structure, molecular weight and their outer layers nature. Dendrimers combine the properties of macromolecules and individual particles; when compared to linear polymers, dendrimers have significantly increased solubility and very low viscosity in solutions [4]. The combination of structural perfection of dendrimers and possibilities of modification of their terminal

∗ Corresponding author. E-mail address: [email protected] (A.V. Markin). http://dx.doi.org/10.1016/j.tca.2015.08.028 0040-6031/© 2015 Elsevier B.V. All rights reserved.

functional groups enable to control the properties of dendrimers over wide ranges. Therefore, dendrimers have been widely and successfully applied to different up-to-date investigations [5–8]. The study of the standard thermodynamic properties of carbosilane dendrimers with different terminal groups in a wide temperature range by precision AC and DSC makes possible to determine and analyze their dependences on composition and structure [9–15]. The discovery of structural anomalies for carbosilane dendrimers of lower generations [9–11] and relaxation transitions for carbosilane dendrimers of higher generations [12–14] is an important result of the calorimetric studies. This work continues previous studies of the thermodynamic properties of various carbosilane dendrimers with different terminal groups on the outer layer. The heat capacity and thermodynamic properties of dendrimer G3[(OCH2 CH2 )3 OCH3 ]32 were earlier studied in the range from T = 6 to 350 K [9]. The goals of the present work were to study calorimetrically the temperature dependences of heat capacities of carbosilane dendrimers of the third generation with ethyleneoxide terminal groups G3[(OCH2 CH2 )1 OCH3 ]32 in the temperature range from T = 6 to 520 K and G3[(OCH2 CH2 )3 OCH3 ]32 in the temperature range from T = 350 to 520 K; to reveal and determine the thermodynamic

A.V. Markin et al. / Thermochimica Acta 617 (2015) 144–151

characteristics of possible physical transformations upon heating and cooling, and to investigate these transformations by IR spectroscopy; to calculate the standard thermodynamic functions for the range from T → 0 to 520 K, and the standard entropies of formation of dendrimers in the devitrified state at T = 298.15 K; to compare the standard thermodynamic properties of the investigated dendrimers with literature data for carbosilane dendrimers with different functional terminal groups. 2. Experimental 2.1. Samples The notional scheme of the investigated carbosilane dendrimers is presented in Fig. 1a. The general designation of dendrimers is Gn[X]m , where G is the dendrimer generation, n is the number of generation, X is the terminal groups on the outer layer of dendrimer macromolecules, and m is the number of terminal groups.

145

For example, the structure of carbosilane dendrimer of the third generation with terminal butyl groups G3[Bu]32 is illustrated in Fig. 1b. The samples of carbosilane dendrimers with ethyleneoxide terminal groups G3[(OCH2 CH2 )1 OCH3 ]32 and G3[(OCH2 CH2 )3 OCH3 ]32 were synthesized at the Enikolopov Institute of Synthetic Polymeric Materials, Russian Academy of Sciences (Moscow). Under standard conditions the investigated dendrimers were colorless transparent viscous liquids. The composition and structure of the synthesized samples were confirmed by data of elemental analysis and 1 H NMR spectroscopy. The gel permeation chromatography (GPC) curves show that dendrimers under study are characterized by a narrow monomodal distribution. The purity of the tested dendrimers was confirmed by gas-liquid chromatography (GLC) results. The true molecular masses of the synthesized dendritic macromolecules were determined by the static light scattering method. For G3[(OCH2 CH2 )1 OCH3 ]32 : found Mw = 10,900 g mol−1 ,

Fig. 1. (a) The scheme of carbosilane dendrimers of the third generation with ethyleneoxide terminal groups (n = 1, 3; i = the modifying agent containing ethyleneoxide units, Karstedt catalyst, toluene). (b) The structure of carbosilane dendrimer of the third generation with butyl terminal groups.

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Table 1 Sample information. Chemical name

Source

State

Mole fraction purity

Purification method

Analysis method

G3[(OCH2 CH2 )1 OCH3 ]32 G3[(OCH2 CH2 )3 OCH3 ]32

This work This work

Viscous liquid Viscous liquid

0.99 0.98

GLC GLC

Elemental analysis, NMR, GPC Elemental analysis, NMR, GPC

calculated Mw = 11,743.5 g mol−1 . For G3[(OCH2 CH2 )3 OCH3 ]32 : found Mw = 13,400 g mol−1 , calculated Mw = 14,562.9 g mol−1 . The molecular masses were determined with the relative standard uncertainty ur (Mw ) = 0.04. Synthesis of dendrimers under study and the above-listed data are presented in detail in [16]. The information for the investigated carbosilane dendrimers is listed in Table 1. For G3[(OCH2 CH2 )1 OCH3 ]32 : found (%): C, 53.83; H, 10.53; Si, 22.21. Calculated (%): C, 54.00; H, 10.68; Si, 22.24. 1 H NMR (CDCl3 ), ı: −0.10 (s, 84 H, CH2 Si(CH3 )CH2 CH2 CH2 Si); 0.02 (d, 384 H, CH2 Si(CH3 )2 OSi(CH3 )2 CH2 , J = 3.7 Hz); 0.44−0.59 (m, 304 H, CH2 SiCH2 , SiOSiCH2 CH2 CH2 O); 1.22−1.40 (m, 120 H, SiCH2 CH2 CH2 Si); 1.54−1.66 (m, 64 H, SiOSiCH2 CH2 CH2 O); 3.40 (t, 64 H, SiOSiCH2 CH2 CH2 O, J = 7.3 Hz); 3.37 (s, 96 H, OCH3 ); 3.50−3.59 (m, 128 H, OCH2 CH2 O). For G3[(OCH2 CH2 )3 OCH3 ]32 : found (%): C, 54.04; H, 10.30; Si, 18.26. Calculated (%): C, 54.10; H, 10.38; Si, 17.94. 1 H NMR (CDCl3 ), ı: −0.11 (s, 84 H, CH2 Si(CH3 )CH2 CH2 CH2 Si); 0.00−0.08 (m, 384 H, CH2 Si(CH3 )2 OSi(CH3 )2 CH2 ); 0.42−0.58 (m, 304 H, CH2 SiCH2 , SiOSiCH2 CH2 CH2 O); 1.23−1.36 (m, 120 H, SiCH2 CH2 CH2 Si); 1.50−1.63 (m, 64 H, SiOSiCH2 CH2 CH2 O); 3.38 (t, 64 H, SiOSiCH2 CH2 CH2 O, J = 6.7 Hz); 3.35 (s, 96 H, OCH3 ); 3.51−3.64 (m, 384 H, OCH2 CH2 O). The molar masses of dendrimers under study were calculated from the International Union of Pure and Applied Chemistry (IUPAC) table of atomic weights [17]. The standard thermodynamic functions of the investigated compounds were determined per mole of the macromolecules.

temperatures and the enthalpies of phase transitions were evaluated according to the standard Netzsch Proteus Software procedure. The heat capacity was determined by the ratio approach, with sapphire used as a standard reference sample. The measurement uncertainty of the heat capacities of studied samples in the temperature range from T = 300 to 520 K was within to 2 × 10−2 Cpo . The technique for determining of the temperatures and the enthalpies of transitions is described in detail elsewhere [22,23] and in Netzsch Proteus Software. The heating and cooling rates were 5 K min−1 ; the measurement was carried out in argon atmosphere. 2.2.3. IR spectroscopy Temperature-dependent infrared (IR) spectra in the 400−3500 cm−1 range were measured with a Biorad 575C FT-IR spectrometer equipped with a KBr beam splitter. For performing these measurements, a pellet was prepared from well-dried KBr by a standard cold pressing method. Then a thin film of the dendrimer was placed on this pellet and the pellet was mounted in a helium-flow Oxford cryostat. IR spectra were measured every 10 K in the temperature range from T = 10 to 300 K. Additional measurement was also performed at T = 5 K. Blackmann–Harris four-term apodization was applied and the number of collected scans was 128. The spectral resolution was 2 cm−1 . The description of IR spectroscopic experiments is given in detail elsewhere [24]. 3. Results and discussion 3.1. Heat capacity

2.2. Apparatus and measurement procedure 2.2.1. Adiabatic calorimetry A precision automatic adiabatic calorimeter (Block Calorimetric Thermophysical, BCT-3) with discrete heating was used to measure the heat capacities over the temperature range from T = 6 to 350 K. The calorimeter design and the operation procedure were described in detail elsewhere [18]. The calorimeter was tested by measuring heat capacities of the standard reference samples (K-2 benzoic acid and ␣-Al2 O3 ) [19,20]. It was established that the measurement uncertainty of the heat capacities of studied samples at helium temperatures from T = 6 to 15 K was within to 2 × 10−2 Cpo ,

Experimental molar heat capacities and smoothed curves for dendrimers G3[(OCH2 CH2 )1 OCH3 ]32 and G3[(OCH2 CH2 )3 OCH3 ]32 in the temperature range from T = 6 to 520 K are illustrated in Fig. 2. The mass of the investigated compound loaded into the calorimetric ampoule of BCT-3 device was 0.1951 g of G3[(OCH2 CH2 )1 OCH3 ]32 . The masses of samples loaded into the ampoules of DSC were 22.3 and 35.9 mg of G3[(OCH2 CH2 )1 OCH3 ]32 and G3[(OCH2 CH2 )3 OCH3 ]32 , respectively. All experimental values of heat capacities of the investigated dendrimers are given in Tables 1S and 2S in the Supplementary file.

and then it decreased down to 0.5 × 10−2 Cpo in the temperature

range from T = 15 to 40 K, and was equal to 2 × 10−3 Cpo over the range from T = 40 to 350 K. The temperatures of phase transitions can be determined with standard uncertainty u(T) = 0.02 K. 2.2.2. Differential scanning calorimetry To investigate the thermal behavior and to measure the heat capacities of dendrimers under study over the temperature range from T = 300 to 520 K, the differential scanning calorimeter (model: DSC 204 F1 Phoenix with ␮-sensor, Netzsch−Gerätebau, Germany) was used. The calorimeter was calibrated and tested against melting of standard calibration set (indium, bismuth, zinc, tin, biphenyl, mercury, cesium chloride, and potassium nitrate) [21]. It was established that the apparatus and measurement procedure enabled to measure the temperature of phase transitions with the standard uncertainty u(T) = 0.5 K, and the enthalpies of transitions o ) = 0.01. The with the combined expanded uncertainty Uc,r (Htr

Fig. 2. Temperature dependences of heat capacities of carbosilane dendrimers of the third generation with ethyleneoxide terminal groups (1) G3[(OCH2 CH2 )1 OCH3 ]32 , (2) G3[(OCH2 CH2 )3 OCH3 ]32 : Tgo (1), Tgo (2) − the glass transition temperatures.

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147

Table 2 Standard thermodynamic characteristics of revealed anomalies for carbosilane dendrimers with different functional terminal groups at pressure p = 0.1 MPa.a Compound

Tan (K)

o Han (kJ mol−1 )

o San (J K−1 mol−1 )

Reference

G3[(OCH2 CH2 )1 OCH3 ]32 G3[(OCH2 CH2 )3 OCH3 ]32 G3[All]32 G3[Bu]32

55−70 46−73 55−72 68−90

4.261 ± 0.043 6.955 ± 0.070 2.422 1.397

71.7 ± 0.9 99.3 ± 1.3 35.4 12.9

This work This work [10] [11]

a

Standard uncertainty u is u(p) = 10 kPa; reported uncertainties correspond to the combined expanded uncertainties for 0.95 level of confidence (k ≈ 2).

The heat capacities of dendrimers under study in the range between T = 6 and 520 K varied from 30% to 60% of the total heat capacities of calorimetric ampoule + compound. The experimental points of Cpo in the above temperature range were fitted using exponential and semilogarithmic polynomial equations, and the corresponding coefficients were found with special computer software. 3.2. Standard thermodynamic characteristics of anomalies The tested samples of dendrimers G3[(OCH2 CH2 )1 OCH3 ]32 and G3[(OCH2 CH2 )3 OCH3 ]32 were cooled from room temperature to the temperature of the measurement onset (T ∼ 6 K) at a flow rate of 0.02 K s−1 . Under conditions of our apparatus dendrimers were supercooled and vitrified. On subsequent heating of the investigated dendrimers, anomalies were detected on the curves of heat capacities in the interval from T = 55 to 70 K for G3[(OCH2 CH2 )1 OCH3 ]32 and in the range between T = 46 and 73 K for G3[(OCH2 CH2 )3 OCH3 ]32 (see Fig. 2). These anomalies expressed by positive deviations from the normal (interpolated) trends of Cpo curves. The revealed anomalies were reproduced on cooling and subsequent Cpo measurements in the above temperature intervals. The similar anomalies in the same temperature ranges were also detected in the case of carbosilane dendrimers (as a rule, lower than fifth generation) with other terminal groups, in particular, with allyl [10] and butyl [11] terminal groups. These anomalies are due to the excitation of vibrations of shielded atomic groups of repeating fragments (e.g., methyl groups) in macromolecules on their heating and by vibrations freezing on their cooling. The standard thermodynamic characteristics of the anomalies for dendrimers under study and for dendrimers studied earlier are presented in Table 2. The enthalpies of anomalies were calculated as the differences between the areas under the Cpo (T ) curves in the intervals of anomalies. The entropies were calculated analogously using the corresponding Cpo (ln T ) curves.

a certain value of it. Thus, the thermodynamic properties of dendrimers are more dependent on the nature of the outer layer, than on the number of generation. It was confirmed in previous calorimetric studies of carbosilane dendrimers with different functional terminal groups. The standard thermodynamic characteristics of glass transition and glassy state of dendrimers under study and dendrimers studied earlier are listed in Table 3. The glass transition temperature Tgo was determined using the method of Alford and Dole [25] from the inflection of the plot of S◦ (T) = f(T). The interval of glass transition T and the increase in heat capacity on glass transition Cpo (Tgo ) were determined graphically [26]. Also the glass transition parameters, such as Tgo and Cpo (Tgo ) were earlier determined for the investigated dendrimers by DSC [16]. The glass transition temperature Tgo values from Ref. [16] are in good agreement with results of the present work. The comparison of results for dendrimers under study shows that the value of increase in heat capacity on glass transition Cpo (Tgo ) for G3[(OCH2 CH2 )3 OCH3 ]32 is higher than for G3[(OCH2 CH2 )1 OCH3 ]32 . This can be explained by the increased content of ethyleneoxide fragments. o The configuration entropy Sconf was calculated using Eq. (1) [27]: o Sconf = Cpo (Tgo ) ln(Tgo /T2o ),

(1)

where T2o is the Kauzmann temperature [28], and (Tgo /T2o ) is equal to (1.29 ± 0.14) [29]. It was suggested that this ratio is also valid for o the investigated dendrimers. It was assumed that Sconf = S ◦ (0), and then can be used for estimating the absolute value of entropy S◦ (0) of dendrimers. 3.4. IR studies Temperature-dependent IR spectra of dendrimer G3[(OCH2 CH2 )1 OCH3 ]32 are presented in Figs. 3 and 4. Table 4 lists wavenumbers of the observed bands together with the proposed assignment. The proposed assignment of majority of

3.3. Standard thermodynamic characteristics of glass transition and glassy state The investigated carbosilane dendrimers G3[(OCH2 CH2 )1 OCH3 ]32 and G3[(OCH2 CH2 )3 OCH3 ]32 were devitrified upon heating, and glass transition reproduced each time upon cooling to temperatures below the glass transition temperature Tgo and on subsequent heating during new Cpo measurements. The process characteristics did not change even during new Cpo measurements after cooling of dendrimers from the devitrified state. The heat capacities of dendrimers under study changed smoothly and quite naturally (except for regions with anomalies) at increasing of temperature. Expectedly, the heat capacities increased more slowly in the devitrified state with rising of temperature. It should be noted that structure, chemical nature and number of terminal groups on the outer layer of dendrimers are most important factors to determine the Tgo values. Comparison of the glass transition temperatures of dendrimers shows that Tgo does not depend on the number of generation of dendrimers, starting with

Fig. 3. IR spectra of dendrimer G3[(OCH2 CH2 )1 OCH3 ]32 in the 3050−2700 cm−1 range at a few selected temperatures.

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Table 3 Standard thermodynamic characteristics of glass transition and glassy state of carbosilane dendrimers with different functional terminal groups at pressure p = 0.1 MPa.a Compound

T

Tgo ± 1

Cpo (Tgo )

a

156−188 160−190 170−180 175−195

S◦ (0)

Reference

1.7 2.9 0.417 0.485

This work This work [10] [11]

kJ K−1 mol−1

K G3[(OCH2 CH2 )1 OCH3 ]32 G3[(OCH2 CH2 )3 OCH3 ]32 G3[All]32 G3[Bu]32

o Sconf

175 176 173 180

6.730 ± 0.067 11.33 ± 0.11 1.640 1.904

1.714 ± 0.032 2.885 ± 0.057 0.417 0.485

Standard uncertainty u is u(p) = 10 kPa; reported uncertainties correspond to the combined expanded uncertainties for 0.95 level of confidence (k ≈ 2).

modes can be proposed by comparison of the present IR data with the experimental and calculated IR data for carbosilane dendrimers and allyltrimethoxysilane [30–33]. The studied dendrimer G3[(OCH2 CH2 )1 OCH3 ]32 has, however, also an ether part that should give rise to two additional bands related to antisymmetric and symmetric stretching vibration of the COC group. We assign to these vibrations the bands located at 1253 and 909 cm−1 . Temperature-dependent IR studies show that upon cooling the IR bands observed in the 2700−3000 cm−1 exhibit a few cm−1 shifts toward lower wavenumbers. Since these bands correspond to the C−H stretching modes of the CH3 and CH2 groups, the observed shift toward lower wavenumbers point to increase of the C−H bond lengths upon cooling due most likely to increased intramolecular and intermolecular interactions. In contrast to this behavior, majority of bands observed in the 1600−450 cm−1 range exhibit a few cm−1 shifts toward higher wavenumbers. Figs. 3 and 4 also show that upon cooling the IR bands become usually narrower and intensity of some bands increases. Especially significant changes are observed for the 1385, 1282, 1160, 1102, 965, 957, 813 and 742 cm−1 bands (values at T = 5 K), which are not clearly seen at room temperature due to very weak intensity and large bandwidth but they become very clear at T = 5 K (see Fig. 4). In order to better observe if IR modes exhibit any anomalies near T = 180 K and T = 60 K, where clear heat capacity anomalies were observed, we present for a few selected modes temperature evolution of their wavenumbers and full width at half maximum (FWHM) values (Figs. 1S–6S in the Supplementary file). Fig. 1S confirms that the C−H stretching modes soften upon cooling. It also shows that these modes do not exhibit any clear anomalies near T = 180 K and T = 60 K. In contrast to the C−H stretching mode wavenumbers, FWHM values of the 2914 and 2873 cm−1 bands show clear change of slopes near T = 180 K (see Fig. 2S). Interestingly, whereas FWHM values exhibits usual decrease upon cooling from T = 298 K to until T = 180 K, they increase below T = 180 K. As discussed above,

the heat capacity anomaly near T = 180 K corresponds to transition of dendrimer G3[(OCH2 CH2 )1 OCH3 ]32 into a glass state. Cooling of the glass state should also lead to decrease of the FWHM values due to decrease of the phonon–phonon anharmonic interactions. The observed increase of FWHM values below T = 180 K for the 2914 and 2873 cm−1 bands may be, therefore, attributed to presence of unresolved components and increased separation of these components upon cooling. The HCH and CCH bending modes show very clear anomalies at the glass transition, that is, the 1412 and 1305 cm−1 bands exhibit usual and relatively strong hardening upon cooling down

Table 4 IR wavenumbers at T = 295 K and T = 5 K together with the proposed assignments. T/K 295

5

2983sh 2954s 2929sh 2914s 2873s 2850sh 2827vw 2811w 2794vw 1470sh 1450w 1412m 1382w 1358w 1340sh 1331w 1305w

2983sh 2952s 2927sh 2912s 2872s 2846m 2826w 2008w 2788w 1472w 1450w 1413m 1385w 1357w 1340sh 1332w 1308w 1282w 1251s 1217w 1203m 1185m 1160w 1135s 1118s 1102s 1054s,b 1017sh 989m, 980m 965w, 957w 947w, 942w 910s, 901sh 887sh 860sh 842s 813w 795s 774s 742w 703m 680w 631vw 603vw 569vw 535w,b

1253s 1217w 1201m 1189w 1140s 1116s 1056s,b 1019sh 980m 944w 910m

841s 796s 778s

Fig. 4. IR spectra of dendrimer G3[(OCH2 CH2 )1 OCH3 ]32 in the 1600−450 cm−1 range at a few selected temperatures. Arrows indicate the bands that exhibit pronounced intensity increase and/or narrowing.

Assignment

702m 682sh 630vw 604vw 569vw 528w,b

Combination band as (CH3 ) as (CH2 ) as (CH3 ) s (CH3 ) s (CH2 ) Combination band s (CH3 ) Combination band ı(HCH) ı(HCH) ı(HCH) ı(CCH) ı(CCH) ı(CCH) ı(CCH) ı(CCH) ı(CCH) as (COC) ı(HCH), ı(SiCH) ı(HCH), ı(SiCH) ı(HCH), ı(SiCH), (CC) ı(HCH), ı(SiCH), (CC) ı(HCH), ı(SiCH), (CC) ı(HCH), ı(SiCH), (CC) ı(HCH), ı(SiCH), (CC) as (SiOSi) (CC) (CC) (CC) (CC) s (COC) ı(SiCH), ı(CCH) ı(SiCH), ı(CCH) s (SiOSi) (SiC), ı(SiCH), ı(CCH) (SiC), ı(SiCH), ı(CCH) (SiC), ı(SiCH), ı(CCH) ı(SiCH), ı(CCH) (SiC), ı(SiCH) (SiC), ı(SiCH) (SiC) (SiC) (SiC), ı(CCC) (CH)

A.V. Markin et al. / Thermochimica Acta 617 (2015) 144–151

to T = 180 K, followed by very weak temperature dependence in the glass phase (Fig. 3S). The 1358 cm−1 band exhibits strong softening and narrowing upon cooling to T = 180 K and nearly no change in FWHM and wavenumber below T = 180 K (see Fig. 3S). The bending modes in the 1100−1210 cm−1 range, which have significant contribution of the SiCH vibrations, also show significant decrease or increase of their wavenumbers in the liquid phase followed by weak temperature dependence in the glass phase (see Fig. 4S). The only exception is the 1201 cm−1 mode, which does not show any clear change in the slope of wavenumber versus temperature near T = 180 K. This mode shows, however, clear change in the slope for FWHM (see Fig. 5S). Fast decrease in FWHM upon cooling to T = 180 K and weak temperature dependence in the glass phase is seen for the 1189 and 1116 cm−1 bands (Fig. 5S). However, the 1140 cm−1 band exhibits very unusual behavior: its FWHM increases with cooling to T = 180 K, followed by decrease upon further cooling below T = 180 K. Fig. 6S shows no anomaly in the temperature evolution of wavenumber or FWHM for the 1253 cm−1 mode corresponding to the as (COC) vibration. However, clear change of slope is noticed for the ␯s (COC) mode at 910 cm−1 . Fig. 6S also shows the temperature evolution of the 841 cm−1 mode that was attributed to ␯s (SiOSi) vibration. As can be noticed, this mode also shows nearly no anomaly near T = 180 K. The last Fig. 7S in the Supplementary file presents temperature evolution of wavenumbers and FWHM values for the 980 and 1019 cm−1 modes, which were attributed to stretching vibrations of the C−C bonds. Clear anomalies can be noticed only at T = 180 K (see Fig. 7S). In summary, the temperature evolution of wavenumbers and FWHM values show clear anomalies near the glass transition for many modes but no anomalies can be observed near T = 60 K. We suppose, therefore, that the low-temperature heat capacity anomaly observed near T = 60 K corresponds to some very subtle structural or conformational change. At such low temperature the mobility of different functional groups is very low but reorientational motions of some groups, for instance, methyl groups are still likely. In contrast to lack of any clear anomalies near T = 60 K, very clear changes in the spectra are observed at the glass transition near T = 180 K. That is, wavenumbers and FWHM values of the most modes exhibit significant changes upon cooling dendrimer G3[(OCH2 CH2 )1 OCH3 ]32 down to T = 180 K followed by weak temperature dependence in the glass phase. This result is consistent with higher mobility of functional groups in the liquid phase and thus stronger temperature dependence of the molecular environment and conformations that in turn affect vibrational properties of the dendrimer. Our data show that the most significant temperature-dependent changes occur for the modes in the 1100−1200 cm−1 range that correspond mainly to ı(HCH) and ı(SiCH) vibrations. This result suggests that upon cooling the most significant changes occur in the −(CH3 )2 −Si−O−Si−(CH3 )2 − fragment of dendrimer G3[(OCH2 CH2 )1 OCH3 ]32 . Clear anomalies for the ı(HCH) and ı(CCH) modes also point to significant reorientational freedom of the methyl groups, both those attached to Si as well as those present in the terminal methoxy groups. 3.5. Standard thermodynamic functions To calculate the standard thermodynamic functions of the investigated dendrimers their heat capacities were extrapolated from the starting temperature of measurements to T → 0 K using the Debye function of heat capacity function [34]:





Cpo = nD D /T ,

(2)

where D is the symbol of Debye’s function, n and D are specially selected parameters. Using this equation, we obtained n = 5 for

149

Table 5 Standard thermodynamic functions of dendrimer (M = 11743.5 g mol−1 ) at pressure p = 0.1 MPa.a T (K)

S◦ (T) − S◦ (0)

Cpo (T )

H◦ (T) − H◦ (0)

kJ K−1 mol−1

G3[(OCH2 CH2 )1 OCH3 ]32 −[G◦ (T) − H◦ (0)] kJ mol−1

Glassy state 5 0.0453 10 0.298 15 0.769 20 1.296 25 1.810 30 2.337 35 2.861 40 3.381 45 3.898 50 4.390 60 5.734 70 6.351 80 7.081 90 7.762 100 8.495 110 9.158 120 9.748 130 10.40 140 11.13 150 11.67 160 12.46 170 13.25 175 13.47

0.0151 0.111 0.313 0.6077 0.9520 1.329 1.728 2.144 2.572 3.009 3.891 4.853 5.748 6.621 7.474 8.316 9.137 9.944 10.74 11.53 12.31 13.08 13.47

0.0560 0.825 3.40 8.576 16.34 26.70 39.69 55.30 73.51 94.25 142.8 205.2 272.2 346.4 427.7 515.8 610.6 711.3 818.6 932.7 1053 1181 1249

Devitrified state 175 20.20 180 20.26 190 20.33 200 20.46 210 20.61 220 20.65 230 20.82 240 20.90 250 21.08 260 21.15 270 21.32 280 21.54 290 21.79 298.15 22.01 300 22.04 310 22.34 320 22.60 330 22.85 340 23.19 350 23.45 360 23.55 370 23.72 380 23.83 390 24.00 400 24.18 410 24.39 420 24.60 430 24.81 440 25.02 450 25.23 460 25.44 470 25.62 480 25.83 490 26.04 500 26.25 510 26.46 520 26.60

13.47 14.04 15.14 16.18 17.19 18.15 19.07 19.96 20.82 21.64 22.44 23.22 23.98 24.59 24.73 25.45 26.17 26.86 27.55 28.23 28.88 29.55 30.18 30.77 31.41 32.00 32.60 33.16 33.72 34.32 34.84 35.41 35.93 36.49 37.02 37.55 38.04

1249 1350 1553 1757 1962 2169 2377 2585 2795 3005 3218 3432 3649 3828 3867 4091 4316 4541 4772 5004 5228 5474 5720 5965 6176 6421 6667 6913 7158 7439 7685 7930 8176 8456 8702 8983 9228

0.0190 0.290 1.30 3.579 7.463 13.16 20.79 30.46 42.25 56.21 90.67 134.5 187.5 249.4 319.9 399.0 486.0 581.4 684.9 796.2 915.5 1043 1109 1109 1178 1324 1480 1647 1824 2010 2205 2409 2621 2842 3070 3306 3504 3551 3800 4060 4323 4597 4874 5158 5439 5755 6070 6351 6702 7018 7334 7685 8000 8351 8702 9053 9439 9790 10,176 10,562

a Standard uncertainty of temperature u(T) = 0.02 K for range 6 K ≤ T ≤ 350 K, and u(T) = 0.5 K for range 350 K ≤ T ≤ 520 K. Combined expanded relative uncertainties for the heat capacity Uc (Cpo ) are 0.02, 0.005, 0.002 and 0.02; the combined expanded relative uncertainties Uc,r [H◦ (T) − H◦ (0)] are 0.022, 0.007, 0.005 and 0.022; Uc,r [S◦ (T) − S◦ (0)] are 0.023, 0.008, 0.006 and 0.023; Uc,r [G◦ (T) − H◦ (0)] are 0.03, 0.01, 0.009 and 0.03 in the ranges 6 K ≤ T ≤ 15 K, 15 ≤ T ≤ 40 K, 40 K ≤ T ≤ 350 K, and 350 K ≤ T ≤ 520 K, respectively for 0.95 level of confidence (k ≈ 2).

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A.V. Markin et al. / Thermochimica Acta 617 (2015) 144–151

Table 6 Standard thermodynamic functions of dendrimer (M = 14,562.9 g mol−1 ) at pressure p = 0.1 MPaa T/K

S◦ (T) − S◦ (0)

Cpo (T )

H◦ (T) − H◦ (0)

kJ K−1 mol−1 Glassy state 5 0.0735 10 0.386 15 0.958 20 1.634 25 2.351 30 3.005 35 3.583 40 4.134 45 4.664 50 5.498 60 6.627 70 7.922 80 8.453 90 9.612 100 10.53 110 11.31 120 12.04 130 12.76 140 13.48 150 14.24 160 15.03 170 15.79 176 16.28

0.0248 0.163 0.421 0.7876 1.230 1.717 2.225 2.739 3.257 3.792 4.905 6.042 7.107 8.170 9.233 10.27 11.29 12.28 13.25 14.21 15.15 16.09 16.68

Devitrified state 176 27.61 180 27.58 190 27.47 200 27.37 210 27.26 220 27.23 230 27.21 240 27.22 250 27.27 260 27.37 270 27.53 280 27.75 290 28.02 298.15 28.27 300 28.33 310 28.67 320 29.02 330 29.37 340 29.73 350 30.10 360 30.41 370 30.72 380 31.03 390 31.34 400 31.63 410 31.90 420 32.16 430 32.41 440 32.67 450 32.93 460 33.20 470 33.49 480 33.79 490 34.10 500 34.42 510 34.75 520 35.07

16.68 17.23 18.72 20.13 21.46 22.73 23.94 25.10 26.21 27.28 28.32 29.32 30.30 31.08 31.25 32.19 33.10 34.00 34.89 35.75 36.60 37.44 38.27 39.08 39.87 40.66 41.43 42.19 42.94 43.67 44.40 45.12 45.83 46.53 47.22 47.90 48.58

G3[(OCH2 CH2 )3 OCH3 ]32 −[G◦ (T) − H◦ (0)] kJ mol−1

0.0930 1.18 4.45 10.91 20.88 34.30 50.80 70.09 92.08 117.5 178.7 252.7 332.6 422.9 523.8 633.1 749.8 873.8 1005 1144 1290 1444 1547 1547 1646 1921 2195 2468 2741 3013 3285 3557 3830 4105 4381 4660 4889 4942 5227 5515 5807 6103 6402 6704 7010 7319 7631 7946 8263 8584 8906 9232 9560 9890 10,224 10,560 10,900 11,242 11,588 11,937

0.0310 0.451 1.86 4.842 9.863 17.22 27.07 39.48 54.47 72.07 115.6 170.2 236.0 312.4 399.4 497.0 604.8 722.7 850.4 987.7 1135 1291 1396 1396 1457 1636 1831 2039 2260 2493 2738 2995 3262 3540 3829 4127 4377 4435 4752 5078 5414 5758 6111 6473 6843 7222 7609 8003 8406 8817 9235 9660 10,093 10,534 10,981 11,436 11,898 12,367 12,842 13,325

Standard uncertainty of temperature u(T) = 0.02 K for range 6 K ≤ T ≤ 350 K, and u(T) = 0.5 K for range 350 K ≤ T ≤ 520 K. Combined expanded relative uncertainties for the heat capacity Uc (Cpo ) are 0.02, 0.005, 0.002 and 0.02; the combined expanded relative uncertainties Uc,r [H◦ (T) − H◦ (0)] are 0.022, 0.007, 0.005 and 0.022; Uc,r [S◦ (T) − S◦ (0)] are 0.023, 0.008, 0.006 and 0.023; Uc,r [G◦ (T) − H◦ (0)] are 0.03, 0.01, 0.009 and 0.03 in the ranges 6 K ≤ T ≤ 15 K, 15 K ≤ T ≤ 40 K, 40 K ≤ T ≤ 350 K, and 350 K ≤ T ≤ 520 K, respectively for 0.95 level of confidence (k ≈ 2).

both dendrimers, D = 63.5 and 59.0 K for G3[(OCH2 CH2 )1 OCH3 ]32 and G3[(OCH2 CH2 )3 OCH3 ]32 , respectively. Eq. (2) with the above parameters and in the above temperature ranges describes the experimental Cpo values with the relative standard uncertainty ur (Cpo ) = 0.017 for dendrimers under study. The standard thermodynamic functions of the investigated dendrimers are presented in Tables 5 and 6. The calculations of H◦ (T) − H◦ (0) and S◦ (T) − S◦ (0) were made by the numerical integration of Cpo = f (T ) and Cpo = f (ln T ) curves, respectively. The Gibbs energy G◦ (T) − H◦ (0) was calculated from the enthalpies and entropies at the corresponding temperatures. The calculation technique was described in [35]. The standard entropies of formation Sfo of dendrimers G3[(OCH2 CH2 )1 OCH3 ]32 and G3[(OCH2 CH2 )3 OCH3 ]32 in the devitrified state at T = 298.15 K were calculated from the S◦ (T) − S◦ (0) values of dendrimers at the identical temperatures (Tables 5 and 6), their residual entropies S◦ (0) (Table 4), and the absolute entropies of elemental substances Si(cr), C(gr), H2 (g), O2 (g) [36,37]. The Sfo values are −(69.49 ± 1.39) and −(85.82 ± 1.72) kJ K−1 mol−1 for G3[(OCH2 CH2 )1 OCH3 ]32 and G3[(OCH2 CH2 )3 OCH3 ]32 , respectively. 4. Conclusions The general aim of this investigation was to report the results of the calorimetric study of carbosilane dendrimers of the third generation with ethyleneoxide terminal groups. The heat capacities of compounds under study were measured in the temperature range from T = 6 to 520 K by precision AC and DSC. In the above range the physical transformations, such as glass transition and anomalies, were detected, and their thermodynamic characteristics were determined and discussed. Additionally, the revealed physical transformations for dendrimer G3[(OCH2 CH2 )1 OCH3 ]32 were studied by IR spectroscopy. As a result some peculiarities in IR spectra were detected and discussed. The results obtained by calorimetric and infrared investigations are consistent among themselves. The existence of low-temperature structural anomalies and the lack of a high-temperature “nanosized effect” (relaxation transition) on the heat capacities curves of carbosilane dendrimers of the third generation with ethyleneoxide terminal groups were confirmed. The standard thermodynamic functions of the investigated carbosilane dendrimers for the range from T → 0 to 520 K, as well as the standard entropies of formation at T = 298.15 K were calculated per mole of the macromolecules. It was shown that the thermodynamic properties of dendrimers are more dependent on the nature of the outer layer, than on the number of generation. Acknowledgments The work was performed with the financial support of the Ministry of Education and Science of the Russian Federation (Contract No. 4.1275.2014/K), the Russian Foundation for Basic Research (Project No. 15-03-02112), and the Russian President Grant supporting of scientific schools (NSh-1899.2014.3). Appendix A. Supplementary data

a

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