c = *cis*-1, 4-unit; t = *trans*-1, 4-unit; v = *vinyl*-1, 2-unit; v-T\*-v = *vinyl*-1, 2-CH2-CH=CH\*-CH2- *vinyl*-1, 2-unit; and v-\*C-t = *vinyl*-1, 2-CH2-\*CH=CH-CH2- *trans*-1, 4-unit.

**Table 2.** 13C{1H} Assignment of triad sequence of free radical HTPB prepolymer (δ 127-132 region).

In the aliphatic region (δ 24-44), the DEPT spectrum showed six sharp negative resonances at δ 38.6, 34.4, 32.8, 30.4, 27.4, and 24.9. A positive signal at δ 43.4, was assigned to the methine carbon of *vinyl*-1,2- unit. The chemical shift of each aliphatic carbon atom in HTPB polymer can be calculated by using empirical equation for branched and linear alkanes. According to Furukawa, the equation for calculating chemical shift of aliphatic carbon atom is given as ����� ��� ∑� �� ��� � ��, where������ is the chemical shifts of � carbon,�� is a constant,��� are the parameters away from various positions of � carbon,���� is the number of carbon away from various positions of � carbon, �� is the parameter of characteristic structure for � carbon itself. The numerical values of all these parameters were taken from literature (Zheyen et al., 1983). The chemical shifts of the aliphatic carbon atoms in various sequence distribution were calculated and then, compared with the observed one to assign the signals. Besides, the assignment of the diad/triad resonances was made based on the values reported by Sato et al., (1987). The results, thus, obtained are given in Table 3. In the carbon bearing hydroxyl end group region (δ 56-65), the DEPT spectrum showed only the negative resonances (-CH2-). Therefore, all the resonance signals belong to the adjacent methylene carbon to hydroxyl end group of HTPB prepolymer. Fig.4 shows the expanded 13C{1H} NMR spectrum of δ 56-65 region along with the assignment of carbon signals. The assignment of various resonances in this region was based on the report by Haas, (1985). The resonance at δ 58.50 is assigned to methylene carbon of *cis*-1,4-hydroxyl structure while other resonances at δ 63.67 and 65.06 are assigned to the methylene carbon of *trans*-1,4-hydroxyl and *vinyl*-1,2 hydroxyl structure, respectively. Further, the resonance line at δ 56.66 is attributed to the *cis*-1,4-epoxide carbon, while the resonance line at δ 58.26 is assigned to the *trans*-1,4 epoxide carbon.

HTPB-Polyurethane: A Versatile Fuel Binder for Composite Solid Propellant 237

**Figure 4.** Expanded 13C{1H} NMR spectrum of δ 56-65 region of HTPB prepolymer along with the

The assignment of the various methylene and methine carbons from 1H/13C-HMQC helped to assign the corresponding protons in the 1H NMR spectrum.Figs.5, 6, and 7 show the 1H/13C-HMQC spectrum of HTPB prepolymer in olefinic region, carbon bearing hydroxyl end group region, and aliphatic region respectively. In the olefinic region, the 13C resonances at δ 113-144, showed three contours in the 2D HMQC spectrum (Fig.5) which corresponded to δ 4.9-5.7, in the 1H NMR spectrum. Further, the fine splitting may be attributed to compositional sequences and tactic reasons. Thus, resonances observed in the HMQC spectrum (Fig.5) at δ 142.8-142.04, 132-127, and 114.9-114.2 corresponded to the protons in the 1H NMR spectrum at δ 5.7-5.4, 5.44-5.41, and 5.0-4.9, respectively. Further, three signals seen in the HMQC spectrum at δ 65.06, 63.67, and 58.5 correspond to the protons at δ 3.4-3.7, 4.1-4.0, and 4.2, respectively (Fig.6). Similarly, in the aliphatic region (Fig.7), the 13C resonance at δ 43.4 and 41.8 is correlated to protons at δ 2.12. The remaining resonances at δ 32.1, 27.4 and 24.9 correspond to the protons at δ 2.10, while the signals at δ 38.6, 32.8 and 30.4 belong to carbons associated with proton signals at δ 2.06. The signals at δ 30.02 and 29.0 are correlated to the protons at δ 1.48 and 1.23 respectively. Based on the above assignments, chemical shifts of various protons observed in the 1H NMR spectrum of the polymer are summarized in Table 4. The proton resonance at 1.23 is assigned to the methyl group of isopropyl ether end group of the polymer. This isopropyl ether end group could be formed as isopropyl alcohol used as solvent in the synthesis of HTPB prepolymer also takes part in the free radical reactions. In presence of hydroxyl radical, isopropoxy radical is formed that leads to the formation of ether terminated polymer (Poletto & Pham, 1994).

assignment of carbon signals.


\*C: *cis*-1, 4-unit; T: *trans*-1, 4-unit; V: *vinyl*-1, 2-unit; (1, 4): C+T; and m: meso.

**Table 3.** Assignment of 13C{1H} NMR resonances of Diad and Triad sequences of free radical HTPB prepolymer (δ 24-44 region).

epoxide carbon.

prepolymer (δ 24-44 region).

assigned to the methine carbon of *vinyl*-1,2- unit. The chemical shift of each aliphatic carbon atom in HTPB polymer can be calculated by using empirical equation for branched and linear alkanes. According to Furukawa, the equation for calculating chemical shift of aliphatic carbon atom is given as ����� ��� ∑� �� ��� � ��, where������ is the chemical shifts of � carbon,�� is a constant,��� are the parameters away from various positions of � carbon,���� is the number of carbon away from various positions of � carbon, �� is the parameter of characteristic structure for � carbon itself. The numerical values of all these parameters were taken from literature (Zheyen et al., 1983). The chemical shifts of the aliphatic carbon atoms in various sequence distribution were calculated and then, compared with the observed one to assign the signals. Besides, the assignment of the diad/triad resonances was made based on the values reported by Sato et al., (1987). The results, thus, obtained are given in Table 3. In the carbon bearing hydroxyl end group region (δ 56-65), the DEPT spectrum showed only the negative resonances (-CH2-). Therefore, all the resonance signals belong to the adjacent methylene carbon to hydroxyl end group of HTPB prepolymer. Fig.4 shows the expanded 13C{1H} NMR spectrum of δ 56-65 region along with the assignment of carbon signals. The assignment of various resonances in this region was based on the report by Haas, (1985). The resonance at δ 58.50 is assigned to methylene carbon of *cis*-1,4-hydroxyl structure while other resonances at δ 63.67 and 65.06 are assigned to the methylene carbon of *trans*-1,4-hydroxyl and *vinyl*-1,2 hydroxyl structure, respectively. Further, the resonance line at δ 56.66 is attributed to the *cis*-1,4-epoxide carbon, while the resonance line at δ 58.26 is assigned to the *trans*-1,4-

Signal Sequence\* Chemical shift (<sup>δ</sup> values)

\*C: *cis*-1, 4-unit; T: *trans*-1, 4-unit; V: *vinyl*-1, 2-unit; (1, 4): C+T; and m: meso.

a (1,4)-V-(1,4) 43.10 43.4 b (1,4)-v-T 35.80 38.6 c (1,4)-V-v (m) 35.70 34.5 d (1,4)-V-(1,4) 34.80 34.2 e T-(1,4) +(1,4)-v-C 33.30-33.40 32.8 f v-v-C (m) 34.60 32.1 g T-v/v-V-v 31.0/31.4 30.4 h (1,4)-C 28.10 27.5 i C-(1,4) 28.10 27.4 j C-v 26.40 24.9

**Table 3.** Assignment of 13C{1H} NMR resonances of Diad and Triad sequences of free radical HTPB

calculated observed

**Figure 4.** Expanded 13C{1H} NMR spectrum of δ 56-65 region of HTPB prepolymer along with the assignment of carbon signals.

The assignment of the various methylene and methine carbons from 1H/13C-HMQC helped to assign the corresponding protons in the 1H NMR spectrum.Figs.5, 6, and 7 show the 1H/13C-HMQC spectrum of HTPB prepolymer in olefinic region, carbon bearing hydroxyl end group region, and aliphatic region respectively. In the olefinic region, the 13C resonances at δ 113-144, showed three contours in the 2D HMQC spectrum (Fig.5) which corresponded to δ 4.9-5.7, in the 1H NMR spectrum. Further, the fine splitting may be attributed to compositional sequences and tactic reasons. Thus, resonances observed in the HMQC spectrum (Fig.5) at δ 142.8-142.04, 132-127, and 114.9-114.2 corresponded to the protons in the 1H NMR spectrum at δ 5.7-5.4, 5.44-5.41, and 5.0-4.9, respectively. Further, three signals seen in the HMQC spectrum at δ 65.06, 63.67, and 58.5 correspond to the protons at δ 3.4-3.7, 4.1-4.0, and 4.2, respectively (Fig.6). Similarly, in the aliphatic region (Fig.7), the 13C resonance at δ 43.4 and 41.8 is correlated to protons at δ 2.12. The remaining resonances at δ 32.1, 27.4 and 24.9 correspond to the protons at δ 2.10, while the signals at δ 38.6, 32.8 and 30.4 belong to carbons associated with proton signals at δ 2.06. The signals at δ 30.02 and 29.0 are correlated to the protons at δ 1.48 and 1.23 respectively. Based on the above assignments, chemical shifts of various protons observed in the 1H NMR spectrum of the polymer are summarized in Table 4. The proton resonance at 1.23 is assigned to the methyl group of isopropyl ether end group of the polymer. This isopropyl ether end group could be formed as isopropyl alcohol used as solvent in the synthesis of HTPB prepolymer also takes part in the free radical reactions. In presence of hydroxyl radical, isopropoxy radical is formed that leads to the formation of ether terminated polymer (Poletto & Pham, 1994).

HTPB-Polyurethane: A Versatile Fuel Binder for Composite Solid Propellant 239

**Figure 7.** 1H/13C HMQC spectra of free radical HTPB prepolymer: aliphatic region.

Hydrogen Chemical Shifts ()



*3.1.1. Chain microstructure and relative distribution* 


The integration of a resonance in NMR is directly proportional to the number of equivalent nuclei contributing to the particular resonance, under suitable experimental conditions. In polymer molecule, these nuclei are part of the chemical structure of a particular repeating unit. Therefore, quantitative result may be obtained by determining the ratio of resonance areas that corresponds to different structural units of the polymer. In Fig.8, the peak


**Figure 5.** 1H/13C HMQC spectra of free radical HTPB prepolymer: olefinic region.

**Figure 6.** 1H/13C HMQC spectra of free radical HTPB prepolymer: carbon bearing hydroxyl end group region.

region.

**Figure 5.** 1H/13C HMQC spectra of free radical HTPB prepolymer: olefinic region.

**Figure 6.** 1H/13C HMQC spectra of free radical HTPB prepolymer: carbon bearing hydroxyl end group

**Figure 7.** 1H/13C HMQC spectra of free radical HTPB prepolymer: aliphatic region.


**Table 4.** Assignments of Chemical shifts () in the 1H NMR spectrum of free radical HTPB prepolymer.

#### *3.1.1. Chain microstructure and relative distribution*

The integration of a resonance in NMR is directly proportional to the number of equivalent nuclei contributing to the particular resonance, under suitable experimental conditions. In polymer molecule, these nuclei are part of the chemical structure of a particular repeating unit. Therefore, quantitative result may be obtained by determining the ratio of resonance areas that corresponds to different structural units of the polymer. In Fig.8, the peak

$$\alpha = 2a\_2/(2a\_1 + a\_2) \tag{1}$$

$$\mathbf{y} = [(2a\_3 - a\_2)(2a\_1 - a\_2)]/[(2a\_3 - a\_2 + 2a\_4)(2a\_1 + a\_2)]\tag{2}$$

$$z = \left[2a\_4(2a\_1 - a\_2)\right] / \left[ (2a\_3 - a\_2 + 2a\_4)(2a\_1 + a\_2) \right] \tag{3}$$

$$
\overrightarrow{DP}\_n = \overrightarrow{a}\_n + \overrightarrow{\beta}\_n + \overrightarrow{\gamma}\_n = [(a\_2 + 2a\_1) \times \overrightarrow{F}\_n(OH)] / [2(a\_C + a\_T + a\_V)] \tag{4}
$$


shows the effect of temperature on viscosity of the prepolymers (HTPB). The viscosity versus temperature data for Krasol LBH-2000 and LBH-3000 are also included for comparison. It is evident from Fig. 12 that the viscosity decreases with increase in temperature. The temperature dependence of viscosity followed the Arrhenius exponential relation as ���� � ������⁄��, where ��=1.32 x10-3, 7.7 x 10-7 and 2.11 x10-6 mPas and activation energy of viscous flow of the prepolymers ��� = 38.7, 59.23 and 56.54 kJmol-1 for free radical HTPB, Krasol LBH-2000 and LBH-3000, respectively (with�� in mPas and T in Kelvin). The viscosity dependence on temperature can also be fitted with a Power Law model of the form����� � ���. The Power Law index is the characteristic parameter of the prepolymer. It shows the sensitivity of viscosity to temperature changes (�� �� ⁄ ) of the prepolymer. The � values were determined from the log-log plot of viscosity versus temperature (°C) and found to be -2.09, -3.16 and -3.07 for free radical HTPB, Krasol LBH-2000, and LBH-3000, respectively. This indicates that the anionic HTPB prepolymers are more sensitive to the temperature change as compared to the free radical one. Both the Arrhenius and Power Law model satisfactorily described the viscosity dependence on temperature of the polymers as the correlation coefficients were > 0.98.

HTPB-Polyurethane: A Versatile Fuel Binder for Composite Solid Propellant 245

and hydroxyl groups, respectively. The viscosity of the curing PU system is determined by two factors: (a) the degree of cure, and (b) the temperature. We have carried out the chemorheological experiments at different temperatures and different shear rates. As the cure proceeds, the molecular size increases and so does the cross linking density, which in turn, decreases the mobility of the molecules. On the other hand, the temperature exerts direct effects on the dynamics of the reacting molecules and so, on the viscosity. To check whether shear thinning was occurring, viscosity of all the PU samples was measured at different shear rates (rpm) ranging from 5 to 100 rpm (AB-4 spindle) for PU-I and PU-II, whereas for PU-IIp, the shear rate was ranged from 0.5 to 10 rpm (T-E spindle). The samples were also sheared for 10 minutes at a constant shear rate to check the time dependent effect of the PUs. For PU-I and PU-II, we observed that the viscosity remained more or less same with respect to shear rates, which revealed the Newtonian characteristic of the binder resin. Also, no significant effect was observed with time of shearing. However, the PU-IIp (propellant slurry) is found to be shear sensitive. Fig. 13 depicts a typical viscosity build up plots with cure time at various temperatures for PU-I. We observed that viscosity decreased with an increase in temperature. In the initial period of the reaction, when the polymer molecules were small in size, viscosity varied considerably with temperature, higher temperatures resulted in lower viscosities. As the reaction proceeds and molecular size goes up, viscosity rises sharply with respect to time and temperature. This is because the effect of curing

reaction overtakes the effect of temperature on viscosity (Reji et al., 1991).

40 °C

50 °C

60 °C

70 °C

**Figure 13.** Plots of viscosity (ɊሻǤ at various temperatures for PU-1.

0

10

20

30

**Viscosity x 10-3**

**(mPa s)**

40

50

60

70

The fact that the temperature changes the viscosity of the slurry means that special consideration must be given to kinetic and thermodynamic factors. In kinetics, the emphasis is on the reaction rate. Navarchian et al. (2005) used exponential function to model the viscosity versus time data and found that the semi-logarithmic plots were of good linearity.

0.0 2.0 4.0 6.0 8.0 10.0 12.0

**Time x 10-3 (s)**

**Figure 12.** Plots of �������t�� �� vs. temperature for prepolymers (HTPB).

#### **3.3. Chemo-rheology of PU-I, PU-II and PU-IIp: Temperature and time modelling**

Chemo-rheology is the study of chemo-viscosity which is the variation of viscosity caused by chemical reactions. Although the exact reaction mechanism of PU formation is more complex, the kinetics of reaction of diisocyanate with dihydroxyl compound is often expressed successfully by a second order rate equation, *i.e.* �������⁄�� � �����������, where �� is the kinetic rate constant. The �����and ���� are the concentration of isocyanate and hydroxyl groups, respectively. The viscosity of the curing PU system is determined by two factors: (a) the degree of cure, and (b) the temperature. We have carried out the chemorheological experiments at different temperatures and different shear rates. As the cure proceeds, the molecular size increases and so does the cross linking density, which in turn, decreases the mobility of the molecules. On the other hand, the temperature exerts direct effects on the dynamics of the reacting molecules and so, on the viscosity. To check whether shear thinning was occurring, viscosity of all the PU samples was measured at different shear rates (rpm) ranging from 5 to 100 rpm (AB-4 spindle) for PU-I and PU-II, whereas for PU-IIp, the shear rate was ranged from 0.5 to 10 rpm (T-E spindle). The samples were also sheared for 10 minutes at a constant shear rate to check the time dependent effect of the PUs. For PU-I and PU-II, we observed that the viscosity remained more or less same with respect to shear rates, which revealed the Newtonian characteristic of the binder resin. Also, no significant effect was observed with time of shearing. However, the PU-IIp (propellant slurry) is found to be shear sensitive. Fig. 13 depicts a typical viscosity build up plots with cure time at various temperatures for PU-I. We observed that viscosity decreased with an increase in temperature. In the initial period of the reaction, when the polymer molecules were small in size, viscosity varied considerably with temperature, higher temperatures resulted in lower viscosities. As the reaction proceeds and molecular size goes up, viscosity rises sharply with respect to time and temperature. This is because the effect of curing reaction overtakes the effect of temperature on viscosity (Reji et al., 1991).

244 Polyurethane

the correlation coefficients were > 0.98.

**modelling** 

**Figure 12.** Plots of �������t�� �� vs. temperature for prepolymers (HTPB).

4

24

44

**Viscosity x 10‐2 (mPa s)**

64

84

104

**3.3. Chemo-rheology of PU-I, PU-II and PU-IIp: Temperature and time** 

Chemo-rheology is the study of chemo-viscosity which is the variation of viscosity caused by chemical reactions. Although the exact reaction mechanism of PU formation is more complex, the kinetics of reaction of diisocyanate with dihydroxyl compound is often expressed successfully by a second order rate equation, *i.e.* �������⁄�� � �����������, where �� is the kinetic rate constant. The �����and ���� are the concentration of isocyanate

302 312 322 332 342

**Temperature (K)**

Free radical HTPB

Krasol LBH-2000

Krasol LBH-3000

shows the effect of temperature on viscosity of the prepolymers (HTPB). The viscosity versus temperature data for Krasol LBH-2000 and LBH-3000 are also included for comparison. It is evident from Fig. 12 that the viscosity decreases with increase in temperature. The temperature dependence of viscosity followed the Arrhenius exponential relation as ���� � ������⁄��, where ��=1.32 x10-3, 7.7 x 10-7 and 2.11 x10-6 mPas and activation energy of viscous flow of the prepolymers ��� = 38.7, 59.23 and 56.54 kJmol-1 for free radical HTPB, Krasol LBH-2000 and LBH-3000, respectively (with�� in mPas and T in Kelvin). The viscosity dependence on temperature can also be fitted with a Power Law model of the form����� � ���. The Power Law index is the characteristic parameter of the prepolymer. It shows the sensitivity of viscosity to temperature changes (�� �� ⁄ ) of the prepolymer. The � values were determined from the log-log plot of viscosity versus temperature (°C) and found to be -2.09, -3.16 and -3.07 for free radical HTPB, Krasol LBH-2000, and LBH-3000, respectively. This indicates that the anionic HTPB prepolymers are more sensitive to the temperature change as compared to the free radical one. Both the Arrhenius and Power Law model satisfactorily described the viscosity dependence on temperature of the polymers as

**Figure 13.** Plots of viscosity (ɊሻǤ at various temperatures for PU-1.

The fact that the temperature changes the viscosity of the slurry means that special consideration must be given to kinetic and thermodynamic factors. In kinetics, the emphasis is on the reaction rate. Navarchian et al. (2005) used exponential function to model the viscosity versus time data and found that the semi-logarithmic plots were of good linearity. The model representing the change of viscosity (�) with reaction time (t) has the following form:

$$
\mu(t) = \mu\_0 e^{k\_{\mu}t} \tag{5}
$$

HTPB-Polyurethane: A Versatile Fuel Binder for Composite Solid Propellant 247

30 min. 60 min. 90 min. 120 min. 150 min. 180 min.

**Figure 14.** Viscosity (at various intervals) versus shear rate of PU-IIp at 40 °C.

**Table 7.** Kinetic and thermodynamic parameters for different PU-systems.

���

���

���

function of cure time (Fig.15).

5.0

7.0

9.0

11.0

**Viscosity x 10-5**

**(mPa s)**

13.0

15.0

17.0

Parameters Unfilled polyurethane Filled polyurethane

0 2 4 6 8 10

**Shear rate (rpm)**

��(kJ mol-1) 35.3 32.3 35.8 ��(kJ mol-1) 58.6 35.0 53.8 ��(min-1) 7423 3020 1707 ��(mPas) 7.99 x 10-7 9.03 x 10-3 1.13x10-5
