Time evolution of polymer distribution functions from moment equations and maximum-entropy methods

Divergent Mechanistic Avenues to an Aliphatic Polyesteracetal or Polyester from a Single Cyclic Esteracetal

The cyclic esteracetal 2-methyl-1,3-dioxane-4-one (MDO) was polymerized in bulk using diethyl zinc as the catalyst and benzyl alcohol as the initiator to yield either the corresponding polyesteracetal (PMDO) or the aliphatic polyester poly(3-hydroxypropionic acid) (PHPA) at low and high catalyst concentrations, respectively. Spectral analysis gave evidence for distinct propagating species in the two catalyst concentration regimes. At low zinc concentrations ring opening by attack of the initiating species at the acetal functionality, yielding a zinc carboxylate, followed by propagation to yield pure PMDO was implicated. At high zinc concentrations we propose that ring opening via attack at the ester functionality produced a labile zinc hemiacetal, which rapidly and irreversibly expelled acetaldehyde to form a propagating zinc alkoxide and ultimately pure PHPA. Initial rate studies indicated that the rate of PHPA formation had a second-order dependence on zinc concentration; in contrast, the rate of PMDO formation was first order in zinc concentration. High molar mass PMDO exhibited only a glass transition temperature (T_g) ≈ -30 °C, whereas high molar mass PHPA had a T_g ≈ -30 °C and a melting temperature (T_m) ≈ 77 °C. When PHPA and PMDO were subjected to neutral or slightly acidic environments, PMDO exhibited expedited degradation as compared with PHPA.

Entropy production during reversible polymerization in nonideal systems

A general route is shown to calculate the entropy production sigma as function of time t in a closed system during reversible polymerization. We treat the polymer molecules to behave nonideal and apply exemplarily the classical Flory-Huggins theory to get explicit expressions for the activity coefficient. At the beginning of the polymerization the system is in a nonequilibrium state where chemical reactions take place that irreversibly drive the system towards equilibrium with sigma approaching zero in the limit t-->infinity. The time-dependent course of the entropy production is explicitly calculated for two cases where the reaction starts (i) from monomer molecules polymerizing to a defined number average chain length xn,eq and (ii) from monodisperse polymer molecules reacting with each other under the constrain that xn is the same at the beginning and the end of the reaction. In both cases we find that the nature of the activity coefficient has an important effect on the curvature of sigma which may considerably differ from that of an ideal behavior.

Enthalpy distributions in proteins

Experimental data on the temperature dependence of the heat capacity of proteins can be used to calculate approximate enthalpy distributions for these molecules using the maximum-entropy method. C(p) (T) data is first used to calculate a set of moments of the enthalpy distribution, and these are then used to estimate the enthalpy distribution. If one knows the temperature expansion of the heat capacity through the (n - 2)th power of DeltaT (measured from the expansion center), then this is enough information to calculate the nth moment of the enthalpy distribution. Using four or more moments is in turn enough information to resolve bimodal behavior in the distribution. If the enthalpy distribution of a protein exhibits two distinct peaks, then this is direct experimental confirmation of a two-state mechanism of denaturation, the two peaks corresponding to the enthalpy of the native and unfolded species respectively. If the heat capacity of a protein exhibits a maximum at the denaturation temperature, then there is the possibility that the enthalpy distribution will be bimodal, but the presence of a maximum in the heat capacity is not a sufficient condition for this kind of behavior. We construct a phase diagram in terms of the appropriate variables to indicate when a maximum in the heat capacity will also give rise to bimodal behavior in the enthalpy distribution. We illustrate the phase diagram using literature data for a set of proteins.