Statistic thermodynamic analysis of fructans – Part 3: Relationship between polymer structure and mixing entropy at equilibrium conditions

2017 ◽  
pp. 151-157
Author(s):  
Roland H.F. Beck
Keyword(s):  
Thermodynamic Analysis ◽  
Polymer Structure ◽  
Degree Of Polymerization ◽  
Average Degree ◽  
Equilibrium Conditions ◽  
Mixing Entropy ◽  
Branching Structures ◽  
Probable Distribution ◽  
Extremum Value ◽  
Most Probable Distribution

The reduced mixing entropy, which is a concentration and unimer independent equivalent to the polymer mixing entropy defined by Flory, for various probabilistic distributed polymer distributions is calculated. The unbranched most probable distribution proves to reach an extremum value at any given number average degree of polymerization, clearly differentiating it from both broader and narrower polymer distributions with branching structures. Entropy driven polymerization reactions thus inevitably produce unbranched polymer structures as discussed for the case of inulin biosynthesis.

Theory of molecular size distribution In multichain polymers

1970 ◽  
Vol 48 (1) ◽  
pp. 33-45 ◽  
Author(s):  
S. G. Whiteway ◽  
I. B. Smith ◽  
C. R. Masson
Keyword(s):  
Functional Groups ◽  
Entire Range ◽  
Molecular Size ◽  
Degree Of Polymerization ◽  
Probable Distribution ◽  
Molecular Sizes ◽  
Intramolecular Condensation ◽  
Meaningful Existence ◽  
Molecular Size Distribution ◽  
Most Probable Distribution

Expressions are derived for the most probable distribution of molecular sizes in multi-chain polymers formed by the self-condensation of the monomer A—R—Xf − 1, where A and X are functional groups and X may be either A or B. It is assumed that all functional groups of the same kind are chemically equivalent and that intramolecular condensation may be neglected. For the case A—R—Bf − 1 the results are identical with those of Flory, although it is shown that this is fortuitous and due to a cancellation of two errors in Flory's method. For the case R—Af the results differ significantly from expressions derived by Flory and sources of error in previous work are discussed. In theory, the mole and weight fractions of individual x-mers vary continuously with the extent of reaction α over the entire range up to αmax = 2/f. The ratio of the weight average to the number average degree of polymerization is finite for all values of α below αmax. The critical point for the formation of infinitely large (wall-to-wall) molecules occurs, not at α = 1/(f − 1) as predicted by Flory, but at α = 2/f. The prediction of actual gel points is discussed in terms of the largest molecule which can have a physically meaningful existence at any fixed value of α.

Combined Implementation of Dynamic Rating-based Protection and Calculating the Average Degree of Polymerization for Power Transformers

2021 ◽  
Vol 141 (7) ◽  
pp. 528-534
Author(s):  
Kohei Ito ◽  
Mutsumi Aoki ◽  
Toru Amau ◽  
Tetsuo Otani ◽  
Tatsuya Ozawa ◽  
...  
Keyword(s):  
Degree Of Polymerization ◽  
Average Degree ◽  
Power Transformers

scholarly journals Extraction and Characterization of Inulin-Type Fructans from Artichoke Wastes and Their Effect on the Growth of Intestinal Bacteria Associated with Health

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Zahraa Zeaiter ◽  
Maria Elena Regonesi ◽  
Sofia Cavini ◽  
Massimo Labra ◽  
Guido Sello ◽  
...  
Keyword(s):  
Intestinal Bacteria ◽  
Degree Of Polymerization ◽  
Average Degree ◽  
Globe Artichoke ◽  
Ethanol Precipitation ◽  
Long Chain ◽  
Simpler Method

Globe artichoke is an intriguing source of indigestible sugar polymers such as inulin-type fructans. In this study, the effect of ultrasound in combination with ethanol precipitation to enhance the extraction of long chain fructans from artichoke wastes has been evaluated. The inulin-type fructans content both from bracts and stems was measured using an enzymatic fructanase-based assay, while its average degree of polymerization (DP) was determined by HPLC-RID analysis. Results show that this method provides artichoke extracts with an inulin-type fructans content of 70% with an average DP between 32 and 42 both in bracts and in stems. The prebiotic effect of long chain inulins from artichoke extract wastes was demonstrated by its ability to support the growth of five Lactobacillus and four Bifidobacterium species, previously characterized as probiotics. Besides, we considered the possibility to industrialize the process developing a simpler method for the production of inulin-type fructans from the artichoke wastes so that the artichoke inulin preparation could be suitable for its use in synbiotic formulations in combination with different probiotics for further studies including in vivo trials.

THE MECHANISM OF DEGRADATION OF A CELLODEXTRIN BY MYROTHECIUM CELLULASE

1956 ◽  
Vol 34 (1) ◽  
pp. 488-494 ◽  
Author(s):  
D. R. Whitaker
Keyword(s):  
Degree Of Polymerization ◽  
Average Degree ◽  
Transfer Reactions ◽  
Mechanism Of Degradation ◽  
Specific Activities

A cellodextrin with a number-average degree of polymerization (D.P.) of 24 was hydrolyzed by Myrothecium cellulase in the presence of C14-labelled cellobiose. The specific activities of cellotriose and cellotetraose isolated at various stages of the hydrolysis were less than 20% of that of cellobiose isolated at the same time. It is concluded that transfer reactions involving cellobiose contributed little to the formation of cellotriose and cellotetraose. The ratio moles of cellotriose formed/mole of cellobiose formed was at least 0.7 and the corresponding ratio for cellotetraose at least 0.4. The number-average D.P. of the substrate decreased slightly during the hydrolysis. The results exclude a degradation of the substrate by cleavage of cellobiose units from the ends of its chains but are consistent with degradation by random cleavage.

Application of Boltzmann Statistical Mechanics in the Validation of the Gaussian Summit-Height Distribution in Rough Surfaces

1997 ◽  
Vol 119 (4) ◽  
pp. 846-850 ◽  
Author(s):  
M. Leung ◽  
C. K. Hsieh ◽  
D. Y. Goswami
Keyword(s):  
Surface Roughness ◽  
Statistical Mechanics ◽  
Theoretical Basis ◽  
Rough Surfaces ◽  
Electrical Contact ◽  
Height Distribution ◽  
Probable Distribution ◽  
Theoretical Predictions ◽  
Most Probable Distribution ◽  
Roughness Measurements

In theoretical modeling of contact mechanics, a homogeneously, isotropically rough surface is usually assumed to be a flat plane covered with asperities of a Gaussian summit-height distribution. This assumption yields satisfactory results between theoretical predictions and experimental measurements of the physical characteristics, such as thermal/electrical contact conductance and friction coefficient. However, lack of theoretical basis of this assumption motivates further study in surface modeling. This paper presents a theoretical investigation by statistical mechanics to determine surface roughness in terms of the most probable distribution of surface asperities. Based upon the surface roughness measurements as statistical constraints, the Boltzmann statistical model derives a distribution equivalent to Gaussian. The Boltzmann statistical mechanics derivation in this paper provides a rigorous validation of the Gaussian summit-height assumption presently in use for study of rough surfaces.

Method of most probable distribution: New solutions and results

Pramana ◽  
1989 ◽  
Vol 33 (4) ◽  
pp. 455-465 ◽  
Author(s):  
V J Menon ◽  
D C Agrawal
Keyword(s):  
Probable Distribution ◽  
Most Probable Distribution
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