UDC 678.01:53+541.6

PHYSICAL CHEMISTRY

V. E. ESKIN, A. E. NESTEROV

VALUES OF COHESIVE ENERGY FOR SOME POLYMERS

(Presented by Academician V. A. Kargin, 12 IV 1965)

P. Debye proposed a method for determining the mean radius of action of intermolecular forces in polymer solutions, \(l\), based on measurements of the asymmetry of critical opalescence \((^1)\). Similar determinations of \(l\) were carried out in a number of works \((^{2-7})\). According to Debye’s theory \((^5)\), the value \(l^2\) depends on the mean-square radius of inertia of polymer coils in solution \(\overline{R^2}\) (at the critical concentration and near the critical solution temperature \(T_k\)—the precipitation point), and also on the cohesive-energy densities polymer—polymer \(\delta_{22}\), solvent—solvent \(\delta_{11}\), and polymer—solvent \(\delta_{12}\):

\[ l^2 = \frac{l_{11}^2 \delta_{11}}{\delta_{11}+\delta_{22}-2\delta_{12}} + \frac{2(\delta_{22}-\delta_{12})}{\delta_{11}+\delta_{22}-2\delta_{12}} \,\overline{R^2}, \tag{1} \]

(here \(l_{11}\) is the value of \(l\) in the solvent). The value \(\overline{R^2}\) can be determined, along with \(l^2\), from the asymmetry of critical opalescence of solutions, if the molecular weight of the polymer fraction is sufficiently large \((^{4,5})\). Since \(\overline{R^2} \sim p\) (\(p\) is the degree of polymerization), one should expect that \((l^2-l_0^2)\sim p\), where

\[ l_0^2 = \frac{\delta_{11}^2 \delta_{11}}{\delta_{11}+\delta_{22}-2\delta_{12}} . \tag{2} \]

Figure 1 shows the dependence of \(l^2\) on \(p\) for fractions of poly-\(\beta\)-vinylnaphthalene (PVN) and polynaphthyl methacrylate (PNMA) in a number of solvents, and also for polybutyl methacrylate (PBMA) in isopropyl alcohol.

Fig. 1. Dependence of the square of the mean radius of action of intermolecular forces \(l^2\) on the degree of polymerization \(p\):
Ia—poly-\(\beta\)-vinylnaphthalene in phenylethyl alcohol; Ib—poly-\(\beta\)-vinylnaphthalene in benzyl alcohol; Ic—poly-\(\beta\)-vinylnaphthalene in a mixture of toluene—decalin (1:1.3); IIa—polynaphthyl methacrylate in benzyl alcohol; IIb—polynaphthyl methacrylate in phenylethyl alcohol; IIc—polynaphthyl methacrylate in tetralin; IId—polynaphthyl methacrylate in toluene; III—polybutyl methacrylate in isopropyl alcohol.

Since the quantity \(\delta_{11}=(Q-RT)/V_1\) is known in principle (\(Q\) is the heat of evaporation of 1 mole of solvent at temperature \(T_k\); \(R\) is the universal gas constant; \(V_1\) is the molar volume of the solvent), then, having determined \(l^2\) and \(\overline{R^2}\) for some polymer fraction and using the graph \(l^2=f(p)\) to determine \(l_0^2\), one can calculate the cohesive-energy densities \(\delta_{22}\) and \(\delta_{12}\) from relations (1) and (2), transformed into the form

\[ a = \frac{2\overline{R^2}-(l^2-l_0^2)}{l^2-l_0^2} = \frac{\delta_{11}-\delta_{12}}{\delta_{22}-\delta_{12}}, \tag{1a} \]

\[ b=\frac{l_0^2}{l_{11}^2}=\frac{\delta_{11}}{\delta_{11}+\delta_{22}-2\delta_{12}} \tag{2a} \]

The value of \(l_{11}\), according to measurements of critical opalescence in mixtures of low-molecular liquids, is 10–14 Å \((8–11)\) and, without significant error, may be taken equal to 12 Å. Eliminating \(\delta_{12}\) from (1a), (2a), one can obtain

\[ \delta_{22}=\delta_{11}\left[1-\frac{a-1}{(a+1)b}\right], \tag{3} \]

or, per 1 mole of monomer units of the polymer,

\[ \delta_{22}V_2=(Q-RT)\frac{V_2}{V_1}\left[1-\frac{a-1}{(a+1)b}\right], \tag{3a} \]

where \(V_2=M_0\bar v\), \(M_0\) is the molecular weight of the monomer unit, and \(\bar v\) is the partial specific volume of the polymer in solution.

The result of calculating the molar cohesive energy \(\delta_{22}V_2\) for PVN, PNMA, and PBMA is presented in Table 1. From consideration of the available data—

Table 1

—some preliminary conclusions may be drawn. The cohesive-energy values of a number of polymers, determined by the method of critical opalescence, have the same order of magnitude as \(\delta_{22}V_2\) obtained for some polymers (polystyrene, polyethylene, polyisobutylene, natural rubber) by other methods \((12, 13)\). For PNMA, the value of \(\delta_{22}V_2\) obtained in alcohols proves to be substantially higher than in nonpolar solvents with a low dielectric constant \(\varepsilon\), such as toluene or tetralin. Within the group of polar or nonpolar solvents, the values of \(\delta_{22}V_2\) for a given polymer are sufficiently close.

The values of \(\delta_{22}V_2\) for three fractions of PBMA (in one solvent) are very close, although one may note a tendency toward some decrease in \(\delta_{22}V_2\) with increasing \(M\), apparently associated with deviation of the points on the plot \(l^2=f(p)\) from a straight line (Fig. 1).

Sources of quantitative data on the cohesive-energy densities of polymers are few. The traditional method for determining \(\delta_{22}\) is the investigation of polymer swelling (see, for example, \((12)\)). Comparatively recently, it was proposed to use the relation between the cohesive energy and the internal pressure in a polymer (thermal pressure coefficient) \((13)\). Attempts to calculate \(\delta_{22}\) on the basis of

of additivity of cohesion energies for individual atomic groups (see, for example, (¹⁴)). The indicated methods do not give entirely coincident results. Obtaining additional information is therefore highly desirable. In addition, in a number of technological processes the interaction of polymer molecules in solutions plays an essential role. In this connection, comparison of the average radii of action of intermolecular forces \(l\), measured by the critical-opalescence method, and of the cohesion energies for a given polymer \(\delta_{22}V_2\) in different solvents may have certain advantages.

Institute of High-Molecular Compounds
Academy of Sciences of the USSR

Received
18 III 1965

CITED LITERATURE

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