Physikalische Chemie

Job, Georg; Rüffler, Regina

doi:10.1007/978-3-8348-9834-0

Cited by 14 publications

(7 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Thus, entropy fulfills a unilateral conservation law. The authors of several textbooks proposed that entropy should replace the role of "heat" ( [8,9,24,37], e. g.). This causes a dilemma, since "thermal energy" TdS replaces "heat" already: The notion "entropy" for "heat" would confuse, as it would replace also the notion "thermal energy".…”

Section: General Results and Remarksmentioning

confidence: 99%

“…Thus, Eqs. (9) and (10) are a parameter representation of the function U S V ð Þ for constant volume and number of particles. It is to be pointed out that transition entropies and energies at the temperatures of phase transitions of first order have to be taken into account, to be dealt with in a later section in more detail.…”

Section: Approaching Negligible Transfer Of Differential Heatmentioning

confidence: 99%

“…(The procedure is similar to Eqs. (9) and (10) except that C p ðTÞ replaces C V ðTÞ.) The results using the experimental data from Figure 3 are depicted in Figure 4.…”

Section: From Internal Energy To Enthalpymentioning

confidence: 99%

See 2 more Smart Citations

From heat to entropy

Hoffmann

2020

Materialwissenschaft Werkst

View full text Add to dashboard Cite

Milestones in the development of thermodynamics are the discovery of the absolute temperature scale and the recognition that differential “heat” is a form of energy given as the product of absolute temperature and differential entropy. Following a new path, the last statement results from a careful analysis of the heat transfer applying the first theorem without reference to the usual cycles in thermodynamics. This confirms also characteristic properties of entropy. In particular, the total entropy can never decrease in a process. In thermal equilibrium, the differential thermal energy is proportional to the differential entropy with the constant of proportionality being the temperature of the heat and entropy. Hence, thermal energy and entropy are transferred simultaneously into the same storage facilities, some of which are mentioned. However, the issue which one is the superior quantity is obsolete. The entropy is maximum for a given amount of exchanged thermal energy and, vice versa, for a given amount of exchanged entropy the concomitant energy is minimum. We calculate the thermal energy and entropy of phonons (as bosons) in oscillators and of electrons (as fermions) in their states of solids and melts as examples from statistical thermodynamics. The thermal energy or heat is the sum of the energies of all bosons and fermions in their elementary states or quantum states according to Bose Einstein and Fermi Dirac statistics in thermal equilibrium minus the total energy in the limit T→0 K. The entropy can be written as mixing entropy of all of these quantum states weighted with their occupancies, in agreement with an earlier publication. Thus, entropy is a logarithmic metrics of the number of all possible variants to distribute the respective total energy over all elementary states in thermal equilibrium.

show abstract

Section: General Results and Remarksmentioning

confidence: 99%

Section: Approaching Negligible Transfer Of Differential Heatmentioning

confidence: 99%

See 1 more Smart Citation

From heat to entropy

Hoffmann

2020

Materialwissenschaft Werkst

View full text Add to dashboard Cite

show abstract

“…Herein, c A is the concentration of particles and w A ðTÞ is the mechanical mobility of the particles at location x in the system (see many textbooks on diffusion, e. g. pages 430 + in [12]). The minus sign in (1) takes into account that the particles move to ranges with lower chemical potential, i. e. against the gradient of m A ðx; TÞ.…”

Section: Basic Laws and Notionsmentioning

confidence: 99%

“…The present article refers to such processes and materials. Abundant publications on diffusion are available from the literature, of which references are selected arbitrarily [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Transitions of electrons and holes drive diffusion in crystals, glasses and melts

Hoffmann

2020

Materialwissenschaft Werkst

View full text Add to dashboard Cite

Diffusion of atoms or molecules (generally: particles) is driven by differences and gradients of the chemical potential of the particles in their accessible space. If the difference of the chemical potential is due to differences of concentrations alone, one arrives at the diffusion equations of Fick. The diffusion coefficients are described in known models by vibrations of atoms in condensed matter which cause the exchange of preferentially neutral particles with neighbouring particles, impurities, interstitial places and vacancies near or on surfaces, grain boundaries, dislocation lines and in the homogeneous bulk. The rates of electronic transitions, however, increase also in melts and solids of chemically bonded particles with increasing temperature. Such transitions cause large fluctuating deviations of the local energy, the charge distribution and the local chemical and electrical potentials. The fluctuating deviations interact with the core ions and drive particles to interchange. This mechanism that supplements the known mechanisms of diffusion has not yet found adequate attention in the literature until now. Foundations, experimental results, evidence and consequences for diffusion are discussed.

show abstract

DMAP Immobilized on Porous Silica Particles and Monoliths for the Esterification of Phenylethanol in Continuous Flow

et al. 2022

View full text Add to dashboard Cite

We report the immobilization of 4-dimethylaminopyridine (DMAP), a versatile organocatalyst for sterically demanding esterifications, on mesoporous silica particles and macromesoporous silica monoliths, both possessing optimized properties for continuous flow synthesis. An alkyne-functionalized DMAP derivative was immobilized via click chemistry; the materials were characterized by physisorption analysis, diffuse reflectance infrared Fourier transform spectroscopy (DRIFT) and elemental analysis. While silica particles were functionalized in batch and packed into a packed-bed reactor, monoliths were cladded with a polyether ether ketone (PEEK) tube after sol-gel synthesis and functionalized in a circulating flow process. Samples with three different catalyst loadings were prepared, in order to study the impact of the catalyst amount on the mesopore space as well as the catalytic performance. In continuous flow experiments, complete conversion of 1-phenylethanol to phenylethylacetate was achieved with both materials and short contact times. Monoliths exhibited far lower pressures than packed bed reactors (7 bar at a flow rate of 1 mL min À 1 ) and reached turnover rates up to 9.3x10 À 2 s À 1 , which is almost twice as high as a comparable batch experiment. The absence of diffusion limitations in monoliths made investigations on reaction kinetics with microkinetics-dominated experiments possible. This study demonstrates that all properties needed for a successful transfer of immobilized organocatalysts to sophisticated flow syntheses with complex organocatalysts can be met with functionalized meso-macroporous monoliths.

show abstract

Physikalische Chemie

Cited by 14 publications

References 0 publications

From heat to entropy

From heat to entropy

Transitions of electrons and holes drive diffusion in crystals, glasses and melts

DMAP Immobilized on Porous Silica Particles and Monoliths for the Esterification of Phenylethanol in Continuous Flow

Contact Info

Product

Resources

About