Tarasov Function Research Articles

Heat capacity of solid-state biopolymers by thermal analysis

Heat capacities in the solid state of four globular proteins (bovine β-lactoglobulin, chicken lysozyme, ovalbumine, and horse myoglobin) and of the poly(amino acid) poly(L-tryptophan) have been determined using the Advanced THermal Analysis System (ATHAS). The experimental measurements were performed with adiabatic and differential scanning calorimetry over wide temperature ranges. The heat capacities were linked to an approximate vibrational spectrum by making use of known group vibrations and of a set of parameters, Θ1 and Θ3, of the Tarasov function for the skeletal vibrations. Good agreement was found between experiments and calculations with root mean square errors mostly within ±3%. The experimental data were analyzed also with an empirical addition scheme using the known data for poly(amino acid)s measured earlier. Based on this study, vibrational heat capacities can now be predicted for all proteins with an accuracy comparable to common experiments. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2093–2102, 1999

Computation of Heat Capacities of Solids Using a General Tarasov Equation

The general Tarasov function is fitted to the skeletal heat capacities of materials with widely different crystal structures. Examples are chosen from flexible macromolecules (polyethylene, polypropylene, poly(ethylene terephthalate), selenium, rigid macromolecules (diamond and graphite), and a small molecule (fullerene, C60). A new optimization approach using the MathematicaTM software is developed. It results in one-, two-, and three-dimensional Debye temperatures, Θ1, Θ2 and Θ3 the fitting parameters of the Tarasov function. In addition to the Tarasov function, the evaluation of the heat capacities makes use of approximate group-vibrational spectra. The results support the earlier assumption that Θ2=Θ3 for simple, solid, linear macromolecules. In more complicated bonding situations, Θ1, Θ2 and Θ3 are used as averaging fitting parameters. This general approach provides an improvement in the quantitative thermal analyses of polymers and other substances included in the ATHAS Data Bank. Sufficient programming information is provided to enable anyone the computation with a copy of the popular MathematicaTM software. The programming file is also downloadable from the WWW.

Heat capacity of poly-p-dioxanone

The heat capacity of poly-p-dioxanone (PPDX), (CH2‒CH2‒O‒CH2‒COO‒)x, was determined using both differential scanning calorimetry (DSC) and temperature-modulated DSC (TMDSC) from 200 K to 430 K. Based on the new data and literature data, the heat capacity of the solid state was analyzed using an approximate group vibrational spectrum and skeletal vibrations. The 10 skeletal vibrational modes are well represented by a Tarasov function with theta temperatures of θ1 = 478.7 K and θ3 = 50.4 K. The heat capacity of the liquid was fitted to a linear function, C liquid = 0.1484 T + 144.3 in units of J K−1 mol−1, which is close to the sum of equations developed earlier for the liquids of poly(oxyethylene) and polyglycolide. The change in heat capacity of amorphous PPDX at the glass transition temperature (264 K) is 69.9 J K−1 mol−1, and the heat of fusion for perfect crystals at the melting temperature (≈400 K) is 14.4 kJ mol−1. The integral thermodynamic functions were derived, and the residual entropy of the glass at 0 K, determined from these functions, is extrapolated as 13.4 J K1 mol−1 (or 2.7 J K−1 mol−1 per chain atom).

Heat capacity of solid state proteins

In an ongoing effort to understand the thermodynamic properties of proteins, ovalbumin, lactoglobulin, lysozyme are studied by adiabatic and differential scanning calorimetry over wide temperature ranges. The heat capacities of the samples in their pure, solid states are linked to an approximate vibrational spectrum with the ATHAS analysis that makes use of known group vibrations and a set of parameters, Θ1 and Θ3, of the Tarasov function for the skeletal vibrations. Good agreement is found between experiment and calculation with rms errors mostly within ±3%. The analyses were also carried out with an empirical addition scheme using data from polypeptides of naturally occurring amino acids. Due to space limitation, only selected results are reported.

Heat capacities of solid, globular proteins

AbstractIn an ongoing effort to understand the thermodynamic properties of proteins, solid‐state heat capacities of poly(amino acid)s of all 20 naturally occurring amino acids and 4 copoly(amino acid)s were previously determined using our Advance Thermal Analysis System (ATHAS). Recently, poly(L‐methionine) and poly(L‐phenylalanine) were further studied with new low‐temperature measurements from 10 to 340 K. In addition, an analysis was performed on literature data of a first protein, zinc bovine insulin dimer C508H752O150N130S12Zn. Good agreement was found between experiment and calculation. In the present work, we have investigated four additional anhydrous globular proteins, α‐chymotrypsinogen, β‐lactoglobulin, ovalbumin, and ribonuclease A. The heat capacity of each protein was measured from 130 to 420 K with differential scanning calorimetry, and the data were analyzed with both the ATHAS empirical addition scheme and a fitting to computations using an approximate vibrational spectrum. For the solid state, agreement between measurement and computation scheme could be accomplished to an average and root mean square percentage error of 0.5 ± 3.2% for α‐chymotrypsinogen, −0.8 ± 2.5% for β‐lactoglobulin, −0.4 ± 1.8% for ovalbumin, and −0.7 ± 2.2% for ribonuclease A. With these calculations, it was possible to link the macroscopic heat capacities to their macroscopic causes, the group and skeletal vibrational motion. For each protein one set of parameters of the Tarasov function, Θ1 and Θ3, represent the skeletal vibrational contributions to the heat capacity. They are obtained from a new optimization procedure [α‐chymotrypsinogen: 631 K and 79 K (number of skeletal vibrators Ns = 3005); β‐lactoglobulin: 582 K and (79 K) (Ns = 2188); ovalbumin: 651 K and (79 K) (Ns = 5008) and ribonuclease A: 717 K and (79 K) (Ns = 1574), respectively]. Enthalpy, entropy, and Gibbs free energy can be derived for the solid state.

A new method of fitting approximate vibrational spectra to heat capacities of solids with Tarasov functions

A new, least-squares optimization method with interpolation is devised to fit skeletal vibrational heat capacities to the two parameters θ1 and θ3 in the Tarasov function used for heat capacity calculations of linear macromolecules. When heat capacities are available in the proper temperature range, θ1 and θ3 can be determined uniquely in a single computer run. Appended to our Advanced THermal Analysis System (ATHAS), this new method offers an improvement in analyzing heat capacity data and facilitates the systematic study of the physical significance of θ1 and θ3 values for all polymers and related molecules of the ATHAS data bank.

Heat capacities of poly(amino acid)s and proteins

AbstractIn an ongoing effort to understand the thermodynamic properties of proteins, solid‐state heat capacities of poly(amino acid)s of all 20 naturally occurring amino acids and 4 copoly(amino acid)s have been previously reported on and were analyzed using our Advanced THermal Analysis System (ATHAS). We extend the heat capacities of poly(L‐methionine) (PLMFT) and poly(L‐phenylalanine) (PLPHEA) with new low temperature measurements from 10 to 340 K. In addition, analyses were performed on literature data of a first protein, zinc bovine insulin dimer C508H752O150N130S12Zn, using both the ATHAS empirical addition scheme and computation with an approximate vibrational spectrum for the protein. For the solid state, agreement with the measurement could be accomplished to ±1.6% for PLMET, ±3.5% for PLPHEA, and ±3.2% for insulin, linking the macroscopic heat capacity to its microscopic cause, the group and skeletal vibrational motion. For each polymer, one set of parameters, Θ1 and Θ3, of the Tarasov function representing the skeletal vibrational contribution to the heat capacity are obtained from a new optimization procedure [PLMET: 542 K and 83 K (number of skeletal vibrations Ns = 15); PLPHEA: 396 K and 67 K (Ns = 11); and insulin monomer: 599 K and 79 K (Ns = 628), respectively]. Enthalpy, entropy, and Gibbs free energy have been derived for the solid state. © 1995 John Wiley & Sons, Inc.

Heat capacities of solid poly(amino acid)s. II. The remaining polymers

AbstractIn the first paper heat capacities Cp, of polyglycine, poly(L‐alanine), and poly (L‐valine) were analyzed using approximate group vibrations and fitting the Cp contributions of the skeletal vibrations to a two‐parameter Tarasov function. In this second paper all other poly (amino acid) s are similarly analyzed. Heat capacities were measured by differential scanning calorimetry in the temperature range of 230–390 K for poly(L‐leucine), poly(L‐serine), poly (sodium‐L‐aspartate), poly(sodium‐L‐glutamate), poly(L‐asparagine), poly(L‐phenylalanine), poly(L‐tyrosine), poly(L‐methionine), poly (L‐tryptophane), poly(L‐proline), poly(L‐lysine · HBr), poly(L‐histidine), poly(L‐histidine‐ HCl), and poly(L‐arginine · HCl). Good agreement exists between experiment and calculation. Predictions of heat capacities were made for all not‐measured poly (amino acid) s. Enthalpies, entropies, and Gibbs functions for the solid state have been derived. © 1993 John Wiley & Sons, Inc.

Heat capacities of solid copoly(amino acid)s

AbstractRecently heat capacities Cp of poly(amino acid)s of all naturally occurring amino acids have been determined. In a second step the heat capacities of four copoly(amino acid) s are studied in this research. Poly(L‐lysine · HBr‐alanine), poly(L‐Lysine · HBr‐phenylalanine), poly(sodium‐L‐glutamate‐tyrosine), and poly(L‐proline‐glycine‐proline) heat capacities are measured by differential scanning calorimetry in the temperature range 230–390 K. This is followed by an analysis using approximate group vibrations and fitting the Cp contributions of the skeletal vibrations of the corresponding homopolymers to a two‐parameter Tarasov function. Good agreement is found between experiment and calculation. Predictions of heat capacities based on homopoly(amino acid)s are thus expected to be possible for all polypeptides, and enthalpies, entropies, and Gibbs functions for the solid state can be derived.

Neural network inversion of the Tarasov function used for the computation of polymer heat capacities

The neural network method is trained using back propagation with a series of heat capacities (C v) in the temperature range 10 to 200 K for the skeletal vibration of 36 linear macromolecules. The trained network could then accurately extract both parameters of the Tarasov function (Θ1 and Θ3) from heat capacities of three computed test cases and a set of experimental measurements for polyethylene. The neural network method offers a major improvement in handling heat capacity data.

Heat capacities of solid poly(amino acids). I. Polyglycine, poly(L‐alanine), and poly(L‐valine)

AbstractHeat capacities of polyglycine, poly(L‐alanine), and poly(L‐valine) were analyzed using approximate group vibrations and fitting of the skeletal vibrations to a two‐parameter (Θ1, Θ3) Tarasov function. New experimental data were measured by differential scanning calorimetry in the temperature range of 230–390 K. Good agreement between our experimental data and the calculated data was observed for all three poly(amino acids). Previous investigations showed agreement between calculation and reported experimental data for only limited low temperature ranges. At higher temperatures, discrepancies of up to 55% existed between experiment and calculation. The cause of this discrepancy must be assumed to be experimental error. Recommended experimental data are revised on the basis of this investigation. Computed heat capacities are available for the three biopolymers in the solid state from 0 to 1000 K.

Heat capacities of solid polyamides

Heat capacities of 10 polyamides were analysed by using an approximate group vibration spectrum and fitting the skeletal heat capacity to a Tarasov function. New data were measured between 230 and 320 K for nylon 11, nylon 12, nylon 6.9, nylon 6.10 and nylon 6.12 by differential scanning calorimetry. A new method to account for the difference between C p and C v was tested. For all synthetic nylons good agreement could be obtained between experiment and calculation (nylon 6, nylon 11, nylon 12, nylon 6.6, nylon 6.9, nylon 6.10, nylon 6.12 and polymethacrylamide). Two poly(amino acids), (polyglycine and polyalanine) were also analysed and found to have larger discrepancies at higher temperatures, perhaps due to experimental error. The θ temperatures are similar for most polyamides and extrapolate to polyethylene for larger numbers of CH 2 groups.

Heat capacities of linear aliphatic polyesters

Heat capacities of solid polypentadecanolactone, polytridecanolactone, polyundecanolactone, polycaprolactone, polyvalerolactone, polybutyrolactone, polypropiolactone, polyglycolide, poly(ethylene oxalate), poly(butylene adipate) and poly(ethylene sebacate) were analysed using an approximate group vibration spectrum and fitting of the skeletal heat capacity to a Tarasov function. All polyesters have the same Θ 1 (513.6 ± 19 K) and Θ 3 varies less than would be expected with the variations due to crystallinity for polyethylene, and can be represented by a quadratic function of COO CH 2 . An addition scheme is proposed that is capable of predicting heat capacities of the polyesters with a precision close to experimental accuracy.

Heat capacities of high melting polymers containing phenylene groups

Heat capacities of solid polyparaphenylene, two variously substituted poly(oxy-1,4-phenylene)s, poly(thio-1,4-phenylene), polyparaxylylene, poly(4,4′-isopropylidenediphenylene carbonate), poly(ethylene terephthalate) and poly(oxy-1,4-phenylene-oxy-1,4-phenylene-carbonyl-1,4-phenylene) were analysed using an approximate group vibration spectrum and fitting of the skeletal heat capacity to a corrected Tarasov function. The prior developed calculation scheme needed adjustment by two vibrational modes when introducing the phenylene groups. The characteristic parameter θ 1 of these polymers has been found to follow a linear relationship with the square root of the weight fraction of phenylene groups in the repeating units, and θ 3 varies little from polymer to polymer in this group ( θ 3 = 40 K). An addition scheme based on approximate frequency spectra for heat capacities of polymers containing phenylene groups is proposed. Its precision is close to experimental accuracy.

Heat capacities of polyethylene and linear fluoropolymers

Heat capacities at constant pressure, C p, and at constant volume C v, were calculated with the help of normal mode frequency spectra and compared to experimental data for crystalline or semicrystalline polyethylene, poly(vinyl fluoride), poly(vinylidene fluoride), polytrifluooroethylene and poly(tetrafluoroethylene). A calculation scheme using a Tarasov function for 2 N skeletal vibrational modes and an approximation of the residual 7 N normal modes from known data on polyethylene and polytetrafluoroethylene is developed for all homologous, linear fluoropolymers. N is the number of carbon backbone atoms of the repeating unit. Calculations can be carried out over the whole temperature range 0 K to melting. For the two theta temperatures and the constant A 0 used for C v to C p conversion, fluorine-concentration dependent curves are given. The relations are expected to hold also for copolymers and blends of intermediate fluorine contents. Recommended experimental (data bank) heat capacities agree to ±2.5% with the calculations.