Hydrodynamic, Conformational, and Optical

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makromolekul v rastvorakh (Structure of Macromolecules in Solutions), Moscow: Nauka, 1964. 14. Tsvetkov, N.V., Khripunov, A.K., Astapenko, E.P., et al.,.
ISSN 1070-4272, Russian Journal of Applied Chemistry, 2012, Vol. 85, No. 6, pp. 963−968. © Pleiades Publishing, Ltd., 2012. Original Russian Text © S.V. Bushin, N.V. Tsvetkov, M.A. Bezrukova, E.P. Astapenko, E.V. Lebedeva, A.N. Podseval’nikova, V.O. Ivanova, A.V. Pavlov, A.K. Khripunov, 2012, published in Zhurnal Prikladnoi Khimii, 2012, Vol. 85, No. 6, pp. 983−989.

MACROMOLECULAR COMPOUNDS AND POLYMERIC MATERIALS

Hydrodynamic, Conformational, and Optical Properties of Cellulose Tridecanoate Molecules in Solutions S. V. Bushina, N. V. Tsvetkovb, M. A. Bezrukovaa, E. P. Astapenkoa, E. V. Lebedevab, A. N. Podseval’nikovab, V. O. Ivanovab, A. V. Pavlovb, and A. K. Khripunova a

Institute of Macromolecular Compounds, Russian Academy of Sciences, St. Petersburg, Russia b St. Petersburg State University, St. Petersburg, Russia e-mail: [email protected] Received April 4, 2012

Abstract—Cellulose tridecanoates of various molecular weights were synthesized, and their characteristics in chloroform and tetrachloroethane solutions were studied by methods of translational diffusion, velocity sedimentation, flow birefringence (Maxwell’s method), and viscometry. The effects of solvent and temperature on the conformational characteristics of the macromolecules under consideration were examined. The anisotropy of the monomeric unit of cellulose tridecanoates was studied, and the contribution of pendant chains to the optical anisotropy of macromolecules of cellulose esters with aliphatic substituents was analyzed. DOI: 10.1134/S1070427212050225

the temperature was varied in the interval 21–51°С. The diffusion coefficients D were measured with a polarization diffusometer [5] in a glass cell 3 cm long (along the beam) at 24°С. The solution concentration c did not exceed 0.1 × 10–2 g cm–3, which corresponded to practically limiting dilution. The flotation coefficients –s0 of CTD samples in chloroform (24°С) were determined with an analytical ultracentrifuge (МОМ, model 3180/В, Hungary) equipped with a polarization-interferometric attachment [5]. We used a layering two-sector cell with a polyamide insert. The rotor rotation rate was 40 × 103 rpm. The coefficients –s were extrapolated to zero concentration. The concentration was varied from 0.12 to 0.5 × 10–2 g cm–3. The molecular weights of the samples were determined from the measured diffusion (D) and flotation (–s0) coefficients by Svedberg’s formula МsD = RТ(s0/D)(v– ρ0 – 1)–1. The partial specific volume of the polymer is v– = 1.012 cm3 g–1. The refractive indices of the solutions and solvents were determined with a Mettler Toledo refractometer (model RM40, Switzerland) with an accuracy of 10–4 ± 5 × 10–5. The intrinsic viscosities [η] (dl g–1) at 21°С, diffusion (D) and flotation (–s0) coefficients at 24°C, temperature

Amphiphilic properties of aliphatically substituted cellulose in combination with high equilibrium rigidity of the molecules make it an attractive object for preparing mono- and multilayer Langmuir– Blodgett nanofilms. Successful use of such films in micro- and nanoelectronics, analytical biotechnology, bioelectronics, and membrane technologies stimulates interest in studying the structure and conformational properties of the molecules of the starting compounds [1–4]. In this work, we studied cellulose tridecanoate [CTD, pendant group CH3–(CH2)11–CO–] by methods of molecular hydrodynamics and optics. We examined nine samples differing in the origin of the base (bacterial, wood, cotton, linter, microcrystalline cellulose) in chloroform (CF) and tetrachloroethane (TCE). The mean degree of substitution DS was 210. EXPERIMENTAL The intrinsic viscosity [η] was measured with an Ostwald capillary viscometer following the standard procedure [5]. In the measurements in CF, 963

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Table 1. Molecular-hydrodynamics and optical characteristics of CTD in CF Sample no.

[η], dl g–1

D × 107, cm2 s–1

–s0, Sv

(dln[η])/dT × 103, K–1

DS

М0, g mol–1

1

0.33

5.0

8.0

–3.0

215

584

2

0.39

4.0

7.1

–3.6

200

3

0.65

4.6

8.1



4

0.38

3.9

8.5

5

0.45

3.1

6

0.70

7

Z

A0 × 1010, erg K–1

8.0

138

2.6

554

8.9

160

2.3

165

486

8.8

181

3.2

–8.9

205

564

11

194

2.4

10.0

–5.6

225

610

17

277

2.3

3.6

10.0

–4.7

165

486

14

288

3.0

1.75

2.4

16.0

–5.2

237

657.5

34

536

3.6

8

2.00

1.4

17.0

–5.4

203

561

60

1066

2.7

9

2.90

1.3

24.0

–6.3

240

633

92

1455

3.2

log (M0[η]), log(D × 109.5), log(–s0 × 1014)

coefficients of the viscosity αη = dln[η]/dT × 103, degrees of substitution (DS) of the samples, molecular weights of the recurrent units (М0) and samples (MSD), degrees of their polymerization Z, and Tsvetkov–Klenin’s constants А0 are given in Table 1. The dynamic flow birefringence (Maxwell’s effect, FBR) was studied in a dynamooptimeter with an internal rotor 3 cm in diameter and 3.21 cm high. The gap between the stator and rotor was 0.022 cm. We used a photoelectric recording scheme with modulation of the light polarization ellipticity to enhance the sensitivity [5, 6] and with a semiconductor laser (HLDPM 12.655.5, wavelength λ ≈ 655 nm) as the light source. The elliptical rotary compensator had the relative path difference Δλ/λ = 0.04. The FBR measurements were performed at

MSD × 10–4, g mol–1

24°С, with forced temperature control using water. Hydrodynamic and conformational characteristics of macromolecules. The dependences of M0[η] (dl mol–1), D, and s0 on the degree of polymerization Z in CF in the interval Z = 137.5–1455 are given in logarithmic coordinates in Fig. 1. The dependences are approximated by straight lines. The Mark–Kuhn–Houwink equations have the form M0[η] = 1.60 Z0.97 (dl mol–1), D = 8.05 × 10–6 Z–0.57, –s0 = 6.79 × 10–14 Z0.48.

High values of the exponents and negative temperature coefficients of the intrinsic viscosities suggest high equilibrium rigidity and draining of the molecules. The volume effects are weak and noticeably affect neither the hydrodynamic characteristics nor their dependence on Z. The Tsvetkov–Klenin’s constants А0 for the majority of the samples are low (the value averaged over the samples is А0,av = 2.8 × 10–10 erg K–1), which is due to large relative hydrodynamic diameter of the macromolecules. The Mark–Kuhn–Houwink equation for the viscosity in TCE has the form

M0[η] = 3.4 Z0.73 (dl mol–1). log Z

Fig. 1. Plots of (1) log(M0[η]), (2) log(D × 109.5), and (3) log(–s0 × 1014) vs. log Z.

(1)

(2)

The lower exponent in the Mark–Kuhn–Houwink equation for the viscosity in TCE, compared to CF, suggests more compact conformation of the polymer

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macromolecules in this solvent, which is due to lower equilibrium rigidity of the molecular chains of cellulose esters in more polar solvents. The dependences of [η] and D were interpreted on the molecular level using the model of a wormlike chain without volume effects [7, 8]. The points in Fig. 2 are the experimental values of η0DZ/RT × 1017 (1) and (A0,av/R)(Z2/[η]M0)1/3 × 1017 (2), presented as functions of Z1/2. The factor A0,av/R (R is the universal gas constant) was introduced to match the diffusion and viscometric experimental points along the ordinate. The experimental points are fitted by the theoretical curve [7] (NAλP∞)–1Ψ(Zλ/A; d/A)(Zλ/A)1/2 = F(Z1/2),

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η0DZ/RT × 1017, (A0,av/R)(Z2/[η]M0)1/3 × 1017

HYDRODYNAMIC, CONFORMATIONAL, AND OPTICAL PROPERTIES

Fig. 2. Plots of (1) η0DZ/RT × 1017 and (2) (A0,av/R)(Z2/[η] × M0)1/3 × 1017 vs. Z1/2.

(3)

where the function Ψ(Zλ/A; d/A) is equal to the ratio of the coefficient Р in the translational friction theory to its limiting value P∞ = 5.11 at Zλ/A → ∞ [7]; Zλ/A, number of statistical chain segments, d/A, relative segment diameter; A, segment length; and d, segment diameter. The matching was achieved at A = 280 × 10–8 cm and d = 17 × 10–8 cm. High value of the segment asymmetry, А/d = 16.5, allows the polymer to be considered as rigid-chain [5]. The segment diameter d = 17 × 10–8 cm coincides with the polymer chain diameter, dv = 15.5 × 10–8 cm, calculated from the partial specific volume of the polymer v– =1.012 cm3 g–1 by the formula dv = 2√(πNA)–1(M0v– /λ)], which demonstrates the adequacy of using the simple worm-like model (characterized by coincidence of the directions of the rigidity segments and polymer chain as a whole). The rotation hindrance factor is σ = (A/Af)1/2 = 4.83 (Af = 12 × 10–8 cm is the Kuhn segment length at fully free rotations around the С1О and С4О bonds in the oxygen bridges of the polyglucoside chain). The σ value obtained is characteristic of cellulose esters and suggests considerable stabilization of the intramolecular structure of bonds in the backbone whose flexibility corresponds to small deformation vibrations around rotation bonds of the oxygen bridges. The plotting used for determining the hydrodynamic characteristics of CTD from viscometric data in TCE (Fig. 3) is similar to that in Fig. 2. The hydrodynamic invariant А0 in TCE is taken equal to 2.8 × 10–10 erg K–1, as in CF. The experimental points are best fitted by the theoretical dependence at A = 220 × 10–8 cm and d = 11 × 10–8 cm. Appreciably lower rigidity of CTD macromolecules in TCE, compared to CF, is due to the

Fig. 3. Bushin plot for the examined samples in TCE. A = 220 Å, d = 11 Å, d/A = 0.05.

fact that the rigidity of molecular chains of cellulose esters is largely determined by intramolecular hydrogen bonds which can be weakened under the action of a polar solvent capable of breaking these bonds. This feature is manifested not only in hydrodynamic properties of cellulose derivatives, but also, no less clearly, in FBR [5, 9, 10]. In accordance with the lower equilibrium rigidity of CTD in TCE, the intramolecular rotation hindrance factor in this solvent is also lower: σ = 4.28. Lower value of the effective hydrodynamic diameter of CTD macromolecules in TCE, compared to CF, may be due to more rolled-up conformations of the pendant aliphatic nonpolar substituents in the relatively polar solvent. According to the theory of the deformation flexibility of structures with coplanar arrangement of rotation bonds, the mean quantity (φ is the angle of twisting vibrations around bonds of the oxygen bridges),

, (4)

is determined by the activation energy U0 of the trans–cis transformation of the configuration of the

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BUSHIN et al.

effective rotation bonds in three recurrent units of the polyglucoside chain. The quantity was calculated from the relationship = (σ2 – 1)/(σ2 + 1).

(5)

We found = 0.917 and the internal rotation hindrance energy U0 = 30.9 kJ mol–1 in CF, = 0.896 and U0 = 25 kJ mol–1 in TCE. Intramolecular interactions in the CTD chain determine both the high interaction energy U0 and the character and extent of variation of the unperturbed chain size

and of U0 with temperature. To determine the temperature coefficient of the unperturbed chain size α S = dln/dT and the intramolecular rotation hindrance energy dU0/dT, we studied how the temperature coefficients of the intrinsic viscosity, αη, in CF depend on the molecular weight M. Figure 4 shows the dependences of (M 2/[η]) 1/3 (straight line 1) and (M 2/[η])1/3dln[η]/dT (straigt line 2) on M1/2. Dependences 1 and 2 correspond to the equations [11] (M2/[η])1/3 = Ф–1/3(M0/Aλ)1/2M1/2 + 0.73Ф–1/3(M0/λ)[ln(A/d) – 0.75],

(6)

(M2/[η])1/3d(ln[η]/dT) = Ф–1/3(3/2)αS(M0/Aλ)1/2M1/2 – 2.2Ф–1/3(M0/Aλ)dln(A/d)/dT,

(7)

where Eq. (7) is the temperature derivative of Eq. (6). The ratio of the slopes Ф–1/3(3/2)αS(M0/Aλ)1/2 and Ф–1/3(M0/Aλ)1/2 of straight lines 2 and 1 (Fig. 4) is equal to (3/2)αS, and αS = dln

/dT = –5.7 × 10–3 K–1 is the temperature coefficient of the unperturbed macromol-

× 100 Fig. 4. Plots of (1) (M2/[η])1/3 and (2) (M2/[η])1/3dln[η]/dT vs. М1/2.

ecule size. The equilibrium rigidity and unperturbed chain size decrease with increasing temperature Т, as already noted, in accordance with the rigid-chain character of the polymer. Using the equation [12] αS = (3/2RT)(–U0/T + dU0/dT)[( – 2)/(1 – 2)]

(8)

and formula (9) for calculating at U 0 = 30.9 kJ mol–1,

,

(9)

w e f o u n d < c o s 2φ > = 0 . 8 5 5 a n d d U 0/ d T = –0.055 kJ mol–1 K. The activation potential U0 of CTD decreases to an extent comparable to that observed for cellulose acetocinnamate (ACC) (dU0/dT = –0.057 kJ mol–1 K [12]) and cellulose valerate (dU0/dT = –0.058 kJ mol–1 K [3]), which do not contain aliphatic substituents (ACC) or contain short aliphatic substituents (valeric acid residues as pendant groups, at moderate DS 190). On the contrary, the polymers characterized by high density of aliphatic substituents along the chain direction (cellulose acetomyristate CAM and cellulose pelargonate CP) have positive values of dU0/dT: +0.034 and +0.016 kJ mol–1 K, respectively. The mechanism of the increase in U0 with temperature may be associated with unrolling of the aliphatic chains and with an increase in the volume of the aliphatic phase surrounding the cellulose backbone. Optical properties of cellulose tridecanoate. To study the optical characteristics of CTD, we chose TCE as solvent. This choice is governed by the fact that the refractive index increment for CTD in TCE does not exceed 0.02 cm3 g–1; therefore, the role of micro- and macroform optical effects in this case is negligible. Hence, in TCE we can determine the intrinsic values of the optical shear coefficient and of the optical anisotropy of the Kuhn segment and monomeric unit of the polymer. Figure 5 shows the dependences of the birefringence Δn on the flow velocity gradient g for sample no. 9 in TCE (Table 2) for three concentrations of the polymer solution. As seen from the figure, they are linear. Similar results were observed for the other samples studied.

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Table 2. Molecular-hydrodynamics and optical characteristics of CTD in TCE Sample no.

MSD × 10–4, g mol–1

[η], dl g–1

Δn/Δτ × 1010, cm s2 g–1

1

8.0

0.26

–7.2

2

8.9

0.29

–8.0

3

8.8

0.39



11

0.35

–6.4

5

17

0.24

–8.6

6

14

0.32

–7.4

7

34

1.11

–12.4

8

60

0.89

–10.2

9

92

1.11

–13.1

g × 10–3, s–1 Fig. 5. Flow birefringence Δn as a function of the flow velocity gradient g for sample no. 9 in TCE. c, %: (1) 0.65, (2) 0.32, and (3) 0.25; the same for Fig. 6.

Δn × 10–8, s–1

4

Figure 6 shows the dependences of FBR Δn on the shear stress Δτ for the same sample. As can be seen, the points referring to different concentrations are well fitted by a common straight line. This means that the optical shear coefficient of the polymers under consideration is independent of concentration. The optical shear coefficient is negative for all the samples studied. This is due to negative contributions of pendant aliphatic substituents to the optical anisotropy of the polymer macromolecules and to the negligible influence of the micro- and macroform effects. Taking into account high molecular weight of the majority of the samples studied, we can consider their macromolecules as occurring in the Gaussian coil state. Then the optical anisotropy of the molecular segment, α1 – α2, of CTD can be determined using the well-known Kuhn relationship [13] 4π (ns2 + 2)2 Δn/Δτ = ——– –——— (α1 – α2), 5kT ns

967

Δn × 10–8, s–1

HYDRODYNAMIC, CONFORMATIONAL, AND OPTICAL PROPERTIES

(10)

where ns is the solvent refractive index, T is the absolute temperature, and k is the Boltzmann constant. Knowing the number of monomeric units in the Kuhn segment, S = 43 (determined by the equilibrium rigidity А), we can calculate the optical anisotropy of the monomeric unit of CTD by the relationship

Δτ × 10–2, g cm–1 s–2 Fig. 6. Flow birefringence Δn as a function of the shear stress Δτ for sample no. 9 in TCE.

Δa = (α1 – α2)/S.

(11)

Using the Kuhn relationship, we determined the optical anisotropy of the CTD molecular segment in TCE, α1 – α2 = –180 × 10–25 cm3, and, correspondingly, the optical anisotropy of the CTD monomeric unit for Δа = –4.3 × 10–25 cm3. As already noted, the polymer–solvent refractive index increment is extremely low; therefore, the quantity Δa obtained can be considered as intrinsic optical anisotropy of the CTD monomeric unit. The data we obtained are well consistent with the results obtained previously in studying other cellulose esters with aliphatic pendant groups [4, 5, 14]. Figure 7 shows how Δai depends on the number ν of carbon atoms in the pendant substituent linked to the ester group. The points are the experimental data, and the curve is the theoretical dependence calculated by the relationship Δа = –1/16 nΔb(1 – e–6ν/n).

(12)

Expression (12) defines the optical anisotropy of

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BUSHIN et al. –Δai × 10–25, cm3

(3) The conformational and optical properties of cellulose tridecanoate macromolecules are well consistent with the corresponding characteristics of the previously studied cellulose esters with aliphatic pendant substituents. REFERENCES

Fig. 7. Intrinsic optical anisotropy of the monomeric unit, Δai, of cellulose esters as a function of the number ν of carbon atoms in the pendant group (linked to the ester group).

a worm-like chain in axes of the first element [5, 14], taking into account the fact that the angle formed by the first element of the pendant chain with the backbone is 60°. The experimental data are best fitted by the theoretical dependence at the following parameters: Δb = 3.4 × 10–25 cm3 (anisotropy per valence bond in the aliphatic chain) and n = 20 (number of valence bonds in the Kuhn segment for the aliphatic chain). The data we obtained confirm the conclusion made in [14] that, for cellulose esters with aliphatic pendant groups, the optical anisotropy is determined only by pendant substituents of the macromolecules, whereas the optical anisotropy of the cellulose chain with ester groups linked to it is close to zero. CONCLUSIONS (1) The equilibrium rigidity of cellulose tridecanoate in chloroform and tetrachloroethane was determined by methods of molecular hydrodynamics. With an increase in the solvent polarity and in temperature, the equilibrium rigidity of cellulose tridecanoate macromolecules decreases. (2) The intrinsic optical anisotropy of the monomeric unit of cellulose tridecanoates was determined experimentally. The negative sign of this quantity is due to the comb-like structure of the polymer macromolecules.

1. Bushin, S.V., Astapenko, E.P., Belyaeva, E.V., et al., Vysokomol. Soedin., Ser. A, 1999, vol. 41, no. 6, pp. 1021–1027. 2. Bushin, S.V., Khripunov, A.K., Bezrukova, M.A., et al., Vysokomol. Soedin., Ser. A, 2007, vol. 49, no. 1, pp. 88–96. 3. Bushin, S.V., Khripunov, A.K., Astapenko, E.P., et al., Vysokomol. Soedin., Ser. A, 2009, vol. 51, no. 7, pp. 1096– 1103. 4. Tsvetkov, N.V., Bushin, S.V., Bezrukova, M.A., et al., Zh. Prikl. Khim., 2011, vol. 84, no. 1, pp. 156–163. 5. Tsvetkov, V.N., Zhestkotsepnye polimernye molekuly (Rigid-Chain Polymer Molecules), Leningrad: Nauka, 1986. 6. Tsvetkov, V.N. and Andreeva, L.N., Adv. Polym. Sci., 1981, vol. 39, pp. 95–207. 7. Norisuye, T., Motowoka, M., and Fujita, H., Macromolecules, 1979, vol. 12, no. 2, pp. 320–323. 8. Yamakawa, H. and Fujii, M., Macromolecules, 1973, vol. 6, no. 3, pp. 407–415. 9. Tsvetkov, V.N. and Tsvetkov, N.V., Usp. Khim., 1993, vol. 62, no. 9, pp. 900–927. 10. Tsvetkov, V.N., Lezov, A.V., Tsvetkov, N.V., et al., Eur. Polym. J., 1990, vol. 26, no. 10, pp. 1103–1107. 11. Bushin, S.V., Tsvetkov, V.N., Lysenko, E.B., et al., Vysokomol. Soedin., Ser. A, 1981, vol. 23, no. 11, pp. 2494–2503. 12. Tsvetkov, V.N., Bushin, S.V., Bezrukova, M.A., et al., Vysokomol. Soedin., Ser. A, 1993, vol. 35, no. 10, pp. 1632– 1640. 13. Tsvetkov, V.N., Eskin, V.E., and Frenkel’, S.Ya., Struktura makromolekul v rastvorakh (Structure of Macromolecules in Solutions), Moscow: Nauka, 1964. 14. Tsvetkov, N.V., Khripunov, A.K., Astapenko, E.P., et al., Vysokomol. Soedin., Ser. A, 1995, vol. 37, no. 8, pp. 1306– 1313.

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