Cluster Origin of Solvation Features of C-Nanostructures in Organic Solvents

2016 ◽  
pp. 189-293
Author(s):  
Francisco Torrens ◽  
Gloria Castellano
Keyword(s):  
Experimental Data ◽  
Free Energy ◽  
Distribution Function ◽  
Diffusion Coefficient ◽  
Organic Solvents ◽  
Distribution Functions ◽  
Heat Of Solution ◽  
Carbon Nanocones ◽  
Single Wall Carbon ◽  
Sharp Concentration

The existence of fullerenes, Single-Wall Carbon Nanocones (SWNCs), especially Nanohorns (SWNHs), Single-Wall Carbon Nanotube (SWNT) (CNT) (NT), NT-Fullerene Bud (NT-BUD), Nanographene (GR) and GR-Fullerene Bud (GR-BUD) in cluster form is discussed in organic solvents. Theories are developed based on columnlet, bundlet and droplet models describing size-distribution functions. The phenomena present a unified explanation in the columnlet model in which free energy of cluster-involved GR comes from its volume, proportional to number of molecules n in cluster. Columnlet model enables describing distribution function of GR stacks by size. From geometrical considerations, columnlet (GR/GR-BUD), bundlet (SWNT/NT-BUD) and droplet (fullerene) models predict dissimilar behaviours. Interaction-energy parameters are derived from C60. An NT-BUD behaviour or further is expected. Solubility decays with temperature result smaller for GR/GR-BUD than SWNT/NT-BUD than C60 in agreement with lesser numbers of units in clusters. Discrepancy between experimental data of the heat of solution of fullerenes, CNT/NT-BUDs and GR/GR-BUDs is ascribed to the sharp concentration dependence of the heat of solution. Diffusion coefficient drops with temperature result greater for GR/GR-BUD than SWNT/NT-BUD than C60 corresponding to lesser number of units in clusters. Aggregates (C60)13, SWNT/NT-BUD7 and GR/GR-BUD3 are representative of droplet, bundlet and columnlet models.

Bundlet Model for Single-Wall Carbon Nanotubes, Nanocones and Nanohorns

2012 ◽  
Vol 2 (1) ◽  
pp. 48-98 ◽  
Author(s):  
Francisco Torrens ◽  
Gloria Castellano
Keyword(s):  
Carbon Nanotubes ◽  
Free Energy ◽  
Distribution Function ◽  
Carbon Nanotube ◽  
Interaction Energy ◽  
Organic Solvents ◽  
Cone Angle ◽  
Single Wall Carbon Nanotubes ◽  
Carbon Nanocones ◽  
Single Wall Carbon

This paper discusses the existence of single-wall carbon nanocones (SWNCs), especially nanohorns (SWNHs), in organic solvents in the form of clusters. A theory is developed based on a bundlet model describing their distribution function by size. Phenomena have a unified explanation in bundlet model in which free energy of an SWNC, involved in a cluster, is combined from two components: a volume one, proportional to number of molecules n in a cluster, and a surface one proportional to n1/2. Bundlet model enables describing distribution function of SWNC clusters by size. From purely geometrical differences, bundlet (SWNCs) and droplet (fullerene) models predict different behaviours. The SWNCs of various disclinations are investigated via energetic–structural analyses. Several SWNC’s terminations are studied, which are different among one another because of type of closing structure and arrangement. The packing efficiencies and interaction-energy parameters of SWNCs/SWNHs are intermediate between fullerene and single-wall carbon nanotube (SWNT) clusters; an in-between behaviour is expected. However, the properties of SWNCs, especially SWNHs, are calculated close to SWNTs. The structural asymmetry in the different SWNCs, entirely characterized by their cone angle, distinguishes the properties of some, such as P2.

Cluster Origin of Solvent Features of Fullerenes, Single-Wall Carbon Nanotubes, Nanocones, and Nanohorns

2014 ◽  
pp. 262-318
Author(s):  
Francisco Torrens ◽  
Gloria Castellano
Keyword(s):  
Carbon Nanotubes ◽  
Free Energy ◽  
Distribution Function ◽  
Carbon Nanotube ◽  
Interaction Energy ◽  
Organic Solvents ◽  
Single Wall Carbon Nanotubes ◽  
Single Wall Carbon Nanotube ◽  
Carbon Nanocones ◽  
Single Wall Carbon

This chapter discusses the existence of single-wall carbon nanocones (SWNCs), especially nanohorns (SWNHs) in organic solvents in the form of clusters. A theory is developed based on a bundlet model describing their distribution function by size. Phenomena have a unified explanation in bundlet model in which free energy of an SWNC, involved in a cluster, is combined from two components: a volume one, proportional to number of molecules n in a cluster, and a surface one proportional to n1/2. A bundlet model enables describing distribution function of SWNC clusters by size. From purely geometrical differences, bundlet (SWNCs) and droplet (fullerene) models predict different behaviours. The SWNCs of various disclinations are investigated via energetic–structural analyses. Several SWNC’s terminations are studied which are different among one another because of the type of closing structure and arrangement. Packing efficiencies and interaction-energy parameters of SWNCs/SWNHs are intermediate between fullerene and single-wall carbon nanotube (SWNT) clusters.

Cluster Origin of Solvent Features of Fullerenes, Single-Wall Carbon Nanotubes, Nanocones, and Nanohorns

2012 ◽  
pp. 1-57
Author(s):  
Francisco Torrens ◽  
Gloria Castellano
Keyword(s):  
Carbon Nanotubes ◽  
Free Energy ◽  
Distribution Function ◽  
Carbon Nanotube ◽  
Interaction Energy ◽  
Organic Solvents ◽  
Single Wall Carbon Nanotubes ◽  
Single Wall Carbon Nanotube ◽  
Carbon Nanocones ◽  
Single Wall Carbon

This chapter discusses the existence of single-wall carbon nanocones (SWNCs), especially nanohorns (SWNHs) in organic solvents in the form of clusters. A theory is developed based on a bundlet model describing their distribution function by size. Phenomena have a unified explanation in bundlet model in which free energy of an SWNC, involved in a cluster, is combined from two components: a volume one, proportional to number of molecules n in a cluster, and a surface one proportional to n1/2. A bundlet model enables describing distribution function of SWNC clusters by size. From purely geometrical differences, bundlet (SWNCs) and droplet (fullerene) models predict different behaviours. The SWNCs of various disclinations are investigated via energetic–structural analyses. Several SWNC’s terminations are studied which are different among one another because of the type of closing structure and arrangement. Packing efficiencies and interaction-energy parameters of SWNCs/SWNHs are intermediate between fullerene and single-wall carbon nanotube (SWNT) clusters.

Bundlet Model for Single-Wall Carbon Nanotubes, Nanocones and Nanohorns

2013 ◽  
pp. 228-284 ◽  
Author(s):  
Francisco Torrens ◽  
Gloria Castellano
Keyword(s):  
Carbon Nanotubes ◽  
Free Energy ◽  
Distribution Function ◽  
Carbon Nanotube ◽  
Interaction Energy ◽  
Cone Angle ◽  
Single Wall Carbon Nanotubes ◽  
Carbon Nanocones ◽  
Structural Asymmetry ◽  
Single Wall Carbon

This paper discusses the existence of single-wall carbon nanocones (SWNCs), especially nanohorns (SWNHs), in organic solvents in the form of clusters. A theory is developed based on a bundlet model describing their distribution function by size. Phenomena have a unified explanation in bundlet model in which free energy of an SWNC, involved in a cluster, is combined from two components: a volume one, proportional to number of molecules n in a cluster, and a surface one proportional to n1/2. Bundlet model enables describing distribution function of SWNC clusters by size. From purely geometrical differences, bundlet (SWNCs) and droplet (fullerene) models predict different behaviours. The SWNCs of various disclinations are investigated via energetic–structural analyses. Several SWNC’s terminations are studied, which are different among one another because of type of closing structure and arrangement. The packing efficiencies and interaction-energy parameters of SWNCs/SWNHs are intermediate between fullerene and single-wall carbon nanotube (SWNT) clusters; an in-between behaviour is expected. However, the properties of SWNCs, especially SWNHs, are calculated close to SWNTs. The structural asymmetry in the different SWNCs, entirely characterized by their cone angle, distinguishes the properties of some, such as P2.

scholarly journals INVESTIGATION OF ELECTRONS DIFFUSION COEFFICIENT DEPENDENCE ON TEMPERATURE IN PLASMA GAS CO2, N2, HE AND MIXTURES

2020 ◽  
pp. 31-41
Author(s):  
Nisaan Saud ORAIBI
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Diffusion Coefficient ◽  
Boltzmann Equation ◽  
Energy Distribution ◽  
Cross Section ◽  
Diffusion Coefficients ◽  
Equation Solution ◽  
Different Temperatures ◽  
Momentum Transfer Cross Section

The evolution of the μNth value at different temperatures was achieved through the drift velocity of electron. The results were show when the temperature was increased, the number of the electrons will be decreased because using the momentum transfer cross section for CO2 molecules through collisions. The calculation of the diffusion coefficient was used to deduce the μNth values of CO2 electrons at temperature between 288 to 573 k by utilization numerically the Boltzmann equation solution. The results were appearing the agreement with the theoretical and experimental data. Keywords: Diffusion Coefficients, Boltzmann Equation, Swarms Parameters, Energy Distribution Function.

scholarly journals IDENTIFICATION OF THE DISTRIBUTION FUNCTION AND CHARACTERIZATION OF THE NANO– AND MICROPOWDERS SIZES

2021 ◽  
pp. 231-239
Author(s):  
И.С. Бондарчук ◽  
С.С. Титов ◽  
С.С. Бондарчук
Keyword(s):  
Experimental Data ◽  
Distribution Function ◽  
Inverse Problems ◽  
Efficient Algorithms ◽  
Distribution Functions ◽  
Differential Distribution ◽  
Program Code ◽  
Lognormal Distributions ◽  
Short Program

В работе предлагаются два новых эффективных алгоритма, реализованных коротким программным кодом в MS Excel, предназначенных для идентификации и характеризации размеров нано– и микропорошков частиц в виде обобщенного гамма или логнормального распределений по данным опытных гистограмм. Предлагаемый метод представляет собой новый и достаточно общий подход к решению обратных задач идентификации параметров дифференциальных функций распределения по экспериментальным данным на основе на минимизации функционала, представляющего собой коэффициент детерминации.Алгоритм реализован формулами (менее 10) наиболее распространенного инструментария (электронных таблиц MS Excel без использования макросов), позволяющего исследователям, не обладающими навыками профессиональных программистов, простоту проверки и воспроизведения представленного материала, а также возможность модификации кода для решения более широкого круга задач. Текст статьи и комментарии на рабочих листах скриншотов представляют собой готовые инструкции по решению задач идентификация функций распределения и характеризации размеров нано– и микропорошков. The paper proposes two new efficient algorithms, implemented by a short program code in MS Excel, designed to identify and characterize the sizes of nano- and micropowders of particles in the form of generalized gamma or lognormal distributions according to experimental histograms. The proposed method is a new general approach to solving inverse problems of identifying the parameters of differential distribution functions from experimental data based on minimizing the functional that is the coefficient of determination.The algorithm is implemented with formulas (less than 10) of the most common tools (MS Excel spreadsheets without the use of macros), which allow researchers without the skills of professional programmers to easily check and reproduce the presented material, as well as the ability to modify the code to solve a wider range of problems. The text of the article and comments on the worksheets of screenshots represent ready-made instructions for solving problems of identification of distribution functions and characterization of the sizes of nano- and micropowders.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

scholarly journals Run-and-Tumble Motion: The Role of Reversibility

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Bart van Ginkel ◽  
Bart van Gisbergen ◽  
Frank Redig
Keyword(s):  
Free Energy ◽  
Diffusion Coefficient ◽  
Large Deviations ◽  
Energy Function ◽  
Internal State ◽  
Rate Function ◽  
Free Energy Function ◽  
Large Deviations Principle ◽  
Preferred Direction ◽  
State Process

AbstractWe study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

scholarly journals Development and Evaluation of a Fluctuating Plume Model for Odor Impact Assessment

2021 ◽  
Vol 11 (8) ◽  
pp. 3310
Author(s):  
Marzio Invernizzi ◽  
Federica Capra ◽  
Roberto Sozzi ◽  
Laura Capelli ◽  
Selena Sironi
Keyword(s):  
Experimental Data ◽  
Distribution Functions ◽  
Plume Model ◽  
Probability Distribution Functions ◽  
Weibull Pdf ◽  
Fluctuating Plume ◽  
Concentration Statistics ◽  
Modified Weibull ◽  
Instantaneous Concentration ◽  
Mean Concentration

For environmental odor nuisance, it is extremely important to identify the instantaneous concentration statistics. In this work, a Fluctuating Plume Model for different statistical moments is proposed. It provides data in terms of mean concentrations, variance, and intensity of concentration. The 90th percentile peak-to-mean factor, R90, was tested here by comparing it with the experimental results (Uttenweiler field experiment), considering different Probability Distribution Functions (PDFs): Gamma and the Modified Weibull. Seventy-two percent of the simulated mean concentration values fell within a factor 2 compared to the experimental ones: the model was judged acceptable. Both the modelled results for standard deviation, σC, and concentration intensity, Ic, overestimate the experimental data. This evidence can be due to the non-ideality of the measurement system. The propagation of those errors to the estimation of R90 is complex, but the ranges covered are quite repeatable: the obtained values are 1–3 for the Gamma, 1.5–4 for Modified Weibull PDF, and experimental ones from 1.4 to 3.6.

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