Entropy of polymerization

Larger rings may exhibit a positive change of entropy. For instance, the entropy of polymerization of elemental sulfur (8-membered ring) is AS = 20 J mol-1 x deg-138) due to the gain in the vibrational and internal rotational entropy. 

The entropy of polymerization of higher unstrained cycles increases and, for e.g., the 42-membered cyclic hexamer of s-caprolactone, exceeds 40 J -mol-1 - deg-1. Similar values were reported for the polymerization of cyclic oligomers (n = 3-7) of 1,3,6-trioxacyclooctane35). This phenomenon has its origin in the increase of vibrational and rotational freedom in the large cycle. 

In small rings the angular strain is sufficiently high to compensate the conformational strain in the macromolecule. Thus, even fully substituted oxiranes can polymerize. Cationic polymerization of 1,1,2,2-tetramethyloxirane is a good example of this countereffect  

R c2h5 ch3 C6H5CH2 H CHjOCH2 c6h5 C6H5OCH2 CH2C1 

Substituted oxetanes (4-membered rings) polymerize as readily as oxiranes, particularly those disubstituted at the 3-position. Thus, even oxetanes with large substitu-tents like benzoxymethyl or iodomethyl  

The accumulation of a great number of small particles into one polymer chain is an aggregation process resulting in a decrease in the translational entropy of the system. In the polymerization of cyclic monomers, the decrease of translational entropy is partially counterbalanced by the increase in rotational and vibrational entropy resulting from the conversion of a more or less rigid cyclic monomer into a flexible monomer unit inside a polymer chain. Thus the net entropy of polymerization of lactams is more positive (e.g. —3 eu for seven-membered lactams) than the entropy of polymerization of vinyl monomers (—25 to —30 eu). 

Skuratov et al. [39] tried to estimate the polymerization entropy from specific heat measurements of the monomer and polymer. However, the calculated value of AS29 8 -g- foi caprolactam (+1.1 eu), is too positive because the authors disregarded the fact that the polymer was not completely crystalline. Making allowance for the partial crystallinity, the value of ASp becomes more negative and approaches the value —3.2 eu calculated from the monomer-polymer equilibria [45]. 

The equilibrium concentrations [M] of the monomer at the poly-merization equilibrium fluctuate widely according to the constitution. At 25°C, it is found, for example, in bulk polymerization that [M] is 10 mol/dm for vinyl acetate, 10 mol/dm for styrene, 10 mol/dm for methyl methacrylate, and 2.8 mol/dm for a-methyl styrene. Since the equilibrium concentrations are related to the free energy of polymerization, and this depends on the enthalpy and entropy of polymerization, then it is necessary to determine the influence of the constitution on HZp and S p. 

The change in entropy on the transition from a gaseous monomer to a (hypothetical) gaseous polymer consists of four components translational entropy external and internal rotational entropies A5gr and AS r, and vibrational entropy ASjb  

Calculations for ethylene, styrene, and isobutylene have shown that on polymerization the loss in external rotational entropy is directly balanced by a gain in the internal rotational and vibrational entropies (Table 16-9). It therefore follows that AS , AS , -f AS b. Thus, AS must be practically equal in magnitude to the translational entropy of the monomer (AS = -AS ,). 

If gaseous monomers are polymerized to condensed crystalline polymers, then the contribution of the entropy of vaporization AS and the entropy of fusion AS also have to be taken into account  

In certain cases, the entropy of polymerization can also be calculated using an increment method. A direct determination, for example, of from the heat capacity is possible, but this method can give incorrect values in some circumstances. Incorrect values are observed when a monomer associates in the vapor phase, or when physical transitions occur in polymers in the range of temperatures between calorimetric measurements and equilibrium measurements. If such effects are excluded, then the quotient S%s/Cp 298 is remarkably constant for the most dissimilar monomer-polymer systems (Table 16-10). Determination of the entropy of polymerization from the temperature dependence of the equilibrium concentrations of the monomer is relatively unambiguous. Alternatively, it can be determined from the Arrhenius parameters Ap of polymerization and A p of depolymerization [of equation (16-52)]. 

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The thermodynamic ceiling temperature (26) T for a polymerization is computed by dividing the AfTp by the standard entropy of polymerization, The T is the temperature at which monomer and polymer are in equHibrium in their standard states at 25°C (298.15 K) and 101.3... 

The polymerization of THE is an equilibrium polymerization. It fits the equation that relates the enthalpy of polymerization, AH, and entropy of polymerization at 1 Af, to the equilibrium monomer concentration, [Af as a function of the absolute temperature, T, where R is the gas constant... 

Polymerization thermodynamics has been reviewed by Allen and Patrick,323 lvin,JM [vin and Busfield,325 Sawada326 and Busfield/27 In most radical polymerizations, the propagation steps are facile (kp typically > 102 M 1 s l -Section 4.5.2) and highly exothermic. Heats of polymerization (A//,) for addition polymerizations may be measured by analyzing the equilibrium between monomer and polymer or from calorimetric data using standard thermochemical techniques. Data for polymerization of some common monomers are collected in Table 4.10. Entropy of polymerization ( SP) data are more scarce. The scatter in experimental numbers for AHp obtained by different methods appears quite large and direct comparisons are often complicated by effects of the physical state of the monomei-and polymers (i.e whether for solid, liquid or solution, degree of crystallinity of the polymer). 

Knowing this, we can add monomers together at a series of temperatures and determine the point at which no further polymerization occurs, regardless of how long the reaction is observed. We use this temperature and the enthalpy of polymerization to determine the entropy of polymerization. 

How can we determine the entropy of polymerization for step growth polymers ... 

Table III. Summary of Published Data of Enthalpy and Entropy of Polymerization of THE...

Monomer Ring size Monomer polymer states Enthalpy of polymerization, AHp (kJ/mol) Entropy of polymerization, ASp (J/mol K) Monomer concentration at equilibrium, [M]eq (mol4-) Ceiling temperature, (°K)... 

Progress in the polymerization of the carbonyl linkage did not result until there was an understanding of the effect of ceiling temperature (Tc) on polymerization (Sec. 3-9c). With the major exception of formaldehyde and one or two other aldehydes, carbonyl monomers have low ceiling temperatures (Table 5-13). Most carbonyl monomers have ceiling temperatures at or appreciably below room temperature. The low Tc values for carbonyl polymerizations are due primarily to the AH factor. The entropy of polymerization of the carbonyl double bond in aldehydes is approximately the same as that for the alkene double bond. The enthalpy of polymerization for the carbonyl double bond, however, is appreciably lower. Thus AH for acetaldehyde polymerization is only about 29 kJ mol-1 compared to the usual 80-90 kJ mol-1 for polymerization of the carbon-carbon double bond (Table 3-14) [Hashimoto et al., 1076, 1978],... 

Busfield, W. K., Heats and Entropies of Polymerization, Ceiling Temperatures, Equilibrium Monomer Concentrations, and Polymerizability of Heterocyclic Compounds, pp. 295-334 in Chap. II in Polymer Handbook, 2nd ed., J. Brandrup and E. H. Immergut, eds., Wiley-Interscience, New York, 1989. 

It should be remarked that dilution of the monomer decreases the entropy of polymerization and, hence, even if its value were positive for pure monomer it eventually becomes negative at a sufficiently high dilution. Therefore, for any system showing the phenomenon of floor temperature, polymerization becomes impossible at any temperature below a certain critical monomer concentration. 

The thermodynamic ceiling temperature (26) T for a polymerization is computed by dividing the Afi°polym by the standard entropy of polymerization, A+°polym. The T is the temperature at which monomer and polymer are in equilibrium in their standard states at 25°C (298.15 K) and 101.3 kPa (1 atm). (In the case of p-xylylene, such a state is, of course, purely hypothetical.) The T quantifies the binding forces between monomer units in a polymer and measures the tendency of the polymer to revert back to monomer. In other systems, the T indicates a temperature above which the polymer is unstable with respect to its monomer, but in the case of parylene it serves rather as a means of comparing the relative stability of the polymer with... 

Equation 3 shows that for a given monomer concentration [M]eq at temperatures above a critical value Tc the rate of the depolymerization step becomes greater than the rate of the polymerization step and dominates the reaction. The critical temperature Tc is called ceiling temperature (22, 23). (AH is the enthalpy of polymerization, and AS° is the entropy of polymerization at the monomer concentration [M] = 1 mole/liter.) The concentration of the monomer at equilibrium [M]eq is identical to the equilibrium constant K, which is defined by the rate constants kp and kd. 

In most vinyl monomer polymerizations measurable monomer concentrations at equilibrium are only apparent at elevated temperatures (T > 150°C). However, the corresponding concentrations of -methyl-styrene are measurable at room temperature. This is caused by the enthalpy of polymerization which is, compared with other monomers, relatively low (at a comparable entropy of polymerization). 

Ivin KJ, "Heats and Entropies of Polymerization, Ceiling Temperatures and Equilibrium Monomer Concentrations , in "Polymer Handbook , Brandrup J and Immergut EH (Eds), Interscience, New York, 2nd Ed, 1975, Part II pp 421M50. 

Thermodynamics determines whether or not a monomer will polymerize, to what extent it polymerizes, and what conditions such as solvent, temperature, and concentrations are required. As discussed in Chapter 1, the thermodynamic polymerizability of a monomer is independent of the mechanism and is therefore identical for radical, anionic, cationic, and coordinative mechanisms if structurally identical polymers are obtained. Although this requires that both the end groups and the microstructure are the same, the influence of regioselectivity and stereoselectivity on the enthalpy and/or entropy of polymerization has not been confirmed experimentally yet. 

Before discussing in more detail the factors influencing the enthalpy and entropy of polymerization of heterocyclic monomers, it is worth reviewing some practical consequences of the reversibility of polymerization ... 

Analysis of the changes of entropy upon passage from monomer to polymer unit leads to the conclusion, that the loss of rotational entropy of monomer is nearly balanced by the gain in internal rotation and vibrational entropy in polymer unit [58,59]. Thus, the overall entropy of polymerization is governed mainly by the loss of translational entropy of monomer. 

It is quite difficult to analyze the data obtained in real systems, because the scattering of the results given by different authors is significant moreover, in many cases the nonideality of the system has not been considered. The analysis of the collected experimental data [53] indicates, however, that the upper limit for 45 values is not very far from this predicted on the assumption that the magnitude of the entropy of polymerization is governed mainly by the loss of translational entropy of monomer. 

Now, according to the transition-state theory of chemical reaction rates, the pre-exponential factors are related to the entropy of activation, A5 , of the particular reaction [A = kT ere k and h are the Boltzmann and Planck constants, respectively, and An is the change in the number of molecules when the transition state complex is formed.] Entropies of polymerization are usually negative, since there is a net decrease in disorder when the discrete radical and monomer combine. The range of values for vinyl monomers of major interest in connection with free radical copolymerization is not large (about —100 to —150 JK mol ) and it is not unreasonable to suppose, therefore, that the A values in Eq. (7-73) will be approximately equal. It follows then that... 

The entropy of polymerization is negative, i.e., randomly oriented monomer molecules are transformed to a highly ordered chain molecule. In order to have a... 

Irrespective of the reaction mechanism, the polymerization of lactams leads to an equilibrium between monomer, cyclic oligomers and polymer. Tobolsky and Eisenberg [9] showed that the thermodynamic parameters are independent of the reaction mechanism, so that the polymerizability may be rationalized in terms of the ease of formation of the cyclic monomer, or, its opening into a linear chain unit. The simple relation between the equilibrium monomer concentration [L]e, temperature, and standard heat and entropy of polymerization. 

Fig. 3. Ring size and entropy of polymerization. Calculated values for lactams [43] compared with values obtained from the equilibrium content of caprolactam and its oligomers [16].

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