Flory–Rehner Equation
   HOME





Flory–Rehner Equation
In polymer science Flory–Rehner equation is an equation that describes the mixing of polymer and liquid molecules as predicted by the equilibrium swelling theory of Flory and Rehner. It describes the equilibrium swelling of a lightly crosslinked polymer in terms of crosslink density and the quality of the solvent. The Flory–Rehner equation is written as: : -\left \ln+\nu_2+ \chi_1 \nu_2^2 \right= V_1 n \left(\nu_2^\frac-\frac\right) where, \nu_2 is the volume fraction of polymer in the swollen mass, V_1 the molar volume of the solvent, n is the number of network chain segments bounded on both ends by crosslinks, and \chi_1 is the Flory solvent-polymer interaction term. In its full form, the Flory–Rehner equation is written as: : -\left \ln+\nu_2+ \chi_1 \nu_2^2 \right= \frac \left(1-\frac\frac\right) \left(\nu_2^\frac-\frac\right) where \bar is the specific volume of the polymer; M is the primary molecular mass; f is the crosslink functionality (4 for perfect network); ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


Polymer Science
Polymer science or macromolecular science is a subfield of materials science concerned with polymers, primarily synthetic polymers such as plastics and elastomers. The field of polymer science includes researchers in multiple disciplines including chemistry, physics, and engineering. Subdisciplines This science comprises three main sub-disciplines: * Polymer chemistry or macromolecular chemistry is concerned with the chemical synthesis and chemical properties of polymers. * Polymer physics is concerned with the physical properties of polymer materials and engineering applications. Specifically, it seeks to present the mechanical, thermal, electronic and optical properties of polymers with respect to the underlying physics governing a polymer microstructure. Despite originating as an application of statistical physics to chain structures, polymer physics has now evolved into a discipline in its own right. * Polymer characterization is concerned with the analysis of chemical ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American Multinational corporation, multinational Publishing, publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and produces books, Academic journal, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, Technology, technical, and engineering subject areas, abandoning its literary interests. Wiley's son Joh ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Polymers
A polymer () is a substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeating subunits derived from one or more species of monomers. Due to their broad spectrum of properties, both synthetic and natural polymers play essential and ubiquitous roles in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure and function. Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. Their consequently large molecular mass, relative to small molecule compounds, produces unique physical properties including toughness, high elasticity, viscoelasticity, and a tendency to form amorphous and semicrystalline structures rather than crystals. Polymers are studied in the fields of polymer science (which includes polymer chemistry and polymer p ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Materials Science
Materials science is an interdisciplinary field of researching and discovering materials. Materials engineering is an engineering field of finding uses for materials in other fields and industries. The intellectual origins of materials science stem from the Age of Enlightenment, when researchers began to use analytical thinking from chemistry, physics, and engineering to understand ancient, phenomenological observations in metallurgy and mineralogy. Materials science still incorporates elements of physics, chemistry, and engineering. As such, the field was long considered by academic institutions as a sub-field of these related fields. Beginning in the 1940s, materials science began to be more widely recognized as a specific and distinct field of science and engineering, and major technical universities around the world created dedicated schools for its study. Materials scientists emphasize understanding how the history of a material (''processing'') influences its struc ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Soft Matter
Soft matter or soft condensed matter is a type of matter that can be deformed or structurally altered by thermal or mechanical stress which is of similar magnitude to thermal fluctuations. The science of soft matter is a subfield of condensed matter physics. Soft materials include liquids, colloids, polymers, foams, gels, granular materials, liquid crystals, flesh, and a number of biomaterials. These materials share an important common feature in that predominant physical behaviors occur at an energy scale comparable with room temperature thermal energy (of order of kT), and that entropy is considered the dominant factor. At these temperatures, quantum aspects are generally unimportant. When soft materials interact favorably with surfaces, they become squashed without an external compressive force. Pierre-Gilles de Gennes, who has been called the "founding father of soft matter," received the Nobel Prize in Physics in 1991 for discovering that methods developed f ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


Polymer Physics
Polymer physics is the field of physics that studies polymers, their fluctuations, mechanical properties, as well as the kinetics of reactions involving degradation of polymers and polymerisation of monomers.P. Flory, ''Principles of Polymer Chemistry'', Cornell University Press, 1953. .Pierre Gilles De Gennes, ''Scaling Concepts in Polymer Physics'' CORNELL UNIVERSITY PRESS Ithaca and London, 1979M. Doi and S. F. Edwards, ''The Theory of Polymer Dynamics'' Oxford University Inc NY, 1986 While it focuses on the perspective of condensed matter physics, polymer physics was originally a branch of statistical physics. Polymer physics and polymer chemistry are also related to the field of polymer science, which is considered to be the applicative part of polymers. Polymers are large molecules and thus are very complicated for solving using a deterministic method. Yet, statistical approaches can yield results and are often pertinent, since large polymers (i.e., polymers with many ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

London
London is the Capital city, capital and List of urban areas in the United Kingdom, largest city of both England and the United Kingdom, with a population of in . London metropolitan area, Its wider metropolitan area is the largest in Western Europe, with a population of 14.9 million. London stands on the River Thames in southeast England, at the head of a tidal estuary down to the North Sea, and has been a major settlement for nearly 2,000 years. Its ancient core and financial centre, the City of London, was founded by the Roman Empire, Romans as Londinium and has retained its medieval boundaries. The City of Westminster, to the west of the City of London, has been the centuries-long host of Government of the United Kingdom, the national government and Parliament of the United Kingdom, parliament. London grew rapidly 19th-century London, in the 19th century, becoming the world's List of largest cities throughout history, largest city at the time. Since the 19th cen ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


Chapman & Hall
Chapman & Hall is an imprint owned by CRC Press, originally founded as a British publishing house in London in the first half of the 19th century by Edward Chapman and William Hall. Chapman & Hall were publishers for Charles Dickens (from 1840 until 1844 and again from 1858 until 1870), Thomas Carlyle, William Thackeray, Elizabeth Barrett Browning, Anthony Trollope, Eadweard Muybridge and Evelyn Waugh. History Upon Hall's death in 1847, Chapman's cousin Frederic Chapman began his progress through the ranks of the company and eventually becoming a partner in 1858 and sole proprietor on Edward Chapman's retirement from Chapman & Hall in 1866. In 1868 author Anthony Trollope bought a third of the company for his son, Henry Merivale Trollope. From 1902 to 1930 the company's managing director was Arthur Waugh. In the 1930s the company merged with Methuen & Co. Ltd., Methuen, a merger which, in 1955, participated in forming the Associated Book Publishers. The latter was acquire ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Entropy
Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change and information systems including the transmission of information in telecommunication. Entropy is central to the second law of thermodynamics, which states that the entropy of an isolated system left to spontaneous evolution cannot decrease with time. As a result, isolated systems evolve toward thermodynamic equilibrium, where the entropy is highest. A consequence of the second law of thermodynamics is that certain processes are irreversible. The thermodynami ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Polymer
A polymer () is a chemical substance, substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeat unit, repeating subunits derived from one or more species of monomers. Due to their broad spectrum of properties, both synthetic and natural polymers play essential and ubiquitous roles in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure and function. Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. Their consequently large molecular mass, relative to small molecule compound (chemistry), compounds, produces unique physical property, physical properties including toughness, high rubber elasticity, elasticity, viscoelasticity, and a tendency to form Amorphous solid, amorphous and crystallization of polymers, semicrystalline structures rath ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  


picture info

Flory–Huggins Solution Theory
Flory–Huggins solution theory is a lattice model (physics), lattice model of the thermodynamics of polymer solutions which takes account of the great dissimilarity in molecule, molecular sizes in adapting the usual expression (mathematics), expression for the entropy of mixing. The result is an equation for the Gibbs free energy change \Delta G_ for mixing a polymer with a solvent. Although it makes simplifying assumptions, it generates useful results for interpreting experiments. Theory The thermodynamic potentials, thermodynamic equation for the Gibbs energy change accompanying mixing at constant temperature and (external) pressure is : \Delta G_ = \Delta H_ - T\Delta S_ A change, denoted by \Delta, is the number, value of a Variable (mathematics), variable for a Solution (chemistry), solution or mixture minus the values for the pure Component (thermodynamics), components considered separately. The objective is to find explicit formulas for \Delta H_ and \Delta S_, the en ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  




Free-energy Relationship
In physical organic chemistry, a free-energy relationship or Gibbs energy relation relates the logarithm of a reaction rate constant or equilibrium constant for one series of chemical reactions with the logarithm of the rate or equilibrium constant for a related series of reactions. Free energy relationships establish the extent at which bond formation and breakage happen in the transition state of a reaction, and in combination with kinetic isotope experiments a reaction mechanism can be determined. Free energy relationships are often used to calculate equilibrium constants since they are experimentally difficult to determine. The most common form of free-energy relationships are linear free-energy relationships (LFER). The Brønsted catalysis equation describes the relationship between the ionization constant of a series of catalysts and the reaction rate constant for a reaction on which the catalyst operates. The Hammett equation predicts the equilibrium constant or react ...
[...More Info...]      
[...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]