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65-439: Physical chemistry, in contrast to chemical physics , is predominantly (but not always) a supra-molecular science, as the majority of the principles on which it was founded relate to the bulk rather than the molecular or atomic structure alone (for example, chemical equilibrium and colloids ). Some of the relationships that physical chemistry strives to understand include the effects of: The key concepts of physical chemistry are

130-446: A chemical compound. Spectroscopy is the related sub-discipline of physical chemistry which is specifically concerned with the interaction of electromagnetic radiation with matter. Another set of important questions in chemistry concerns what kind of reactions can happen spontaneously and which properties are possible for a given chemical mixture. This is studied in chemical thermodynamics , which sets limits on quantities like how far

195-601: A few of the possible states of the system, with the states chosen randomly (with a fair weight). As long as these states form a representative sample of the whole set of states of the system, the approximate characteristic function is obtained. As more and more random samples are included, the errors are reduced to an arbitrarily low level. Many physical phenomena involve quasi-thermodynamic processes out of equilibrium, for example: All of these processes occur over time with characteristic rates. These rates are important in engineering. The field of non-equilibrium statistical mechanics

260-455: A finite volume. These are the most often discussed ensembles in statistical thermodynamics. In the macroscopic limit (defined below) they all correspond to classical thermodynamics. For systems containing many particles (the thermodynamic limit ), all three of the ensembles listed above tend to give identical behaviour. It is then simply a matter of mathematical convenience which ensemble is used. The Gibbs theorem about equivalence of ensembles

325-438: A limited extent, quasi-equilibrium and non-equilibrium thermodynamics can describe irreversible changes. However, classical thermodynamics is mostly concerned with systems in equilibrium and reversible changes and not what actually does happen, or how fast, away from equilibrium. Which reactions do occur and how fast is the subject of chemical kinetics , another branch of physical chemistry. A key idea in chemical kinetics

390-470: A mixture, is a special case of another key concept in physical chemistry, which is that to the extent an engineer needs to know, everything going on in a mixture of very large numbers (perhaps of the order of the Avogadro constant , 6 x 10) of particles can often be described by just a few variables like pressure, temperature, and concentration. The precise reasons for this are described in statistical mechanics ,

455-401: A reaction can proceed, or how much energy can be converted into work in an internal combustion engine , and which provides links between properties like the thermal expansion coefficient and rate of change of entropy with pressure for a gas or a liquid . It can frequently be used to assess whether a reactor or engine design is feasible, or to check the validity of experimental data. To

520-424: A role in materials science, nuclear physics, astrophysics, chemistry, biology and medicine (e.g. study of the spread of infectious diseases). Analytical and computational techniques derived from statistical physics of disordered systems, can be extended to large-scale problems, including machine learning, e.g., to analyze the weight space of deep neural networks . Statistical physics is thus finding applications in

585-539: A specialty within physical chemistry which is also shared with physics. Statistical mechanics also provides ways to predict the properties we see in everyday life from molecular properties without relying on empirical correlations based on chemical similarities. The term "physical chemistry" was coined by Mikhail Lomonosov in 1752, when he presented a lecture course entitled "A Course in True Physical Chemistry" ( Russian : Курс истинной физической химии ) before

650-407: A state with a balance of forces that has ceased to evolve.) The study of equilibrium ensembles of isolated systems is the focus of statistical thermodynamics. Non-equilibrium statistical mechanics addresses the more general case of ensembles that change over time, and/or ensembles of non-isolated systems. The primary goal of statistical thermodynamics (also known as equilibrium statistical mechanics)

715-477: A surface causes the gas pressure that we feel, and that what we experience as heat is simply the kinetic energy of their motion. The founding of the field of statistical mechanics is generally credited to three physicists: In 1859, after reading a paper on the diffusion of molecules by Rudolf Clausius , Scottish physicist James Clerk Maxwell formulated the Maxwell distribution of molecular velocities, which gave

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780-499: Is concerned with understanding these non-equilibrium processes at the microscopic level. (Statistical thermodynamics can only be used to calculate the final result, after the external imbalances have been removed and the ensemble has settled back down to equilibrium.) In principle, non-equilibrium statistical mechanics could be mathematically exact: ensembles for an isolated system evolve over time according to deterministic equations such as Liouville's equation or its quantum equivalent,

845-429: Is distinct from physical chemistry as it focuses more on using physical theories to understand and explain chemical phenomena at the microscopic level, such as quantum mechanics, statistical mechanics, and molecular dynamics. Meanwhile, physical chemistry uses a broader range of methods, such as thermodynamics and kinetics, to study the physical nature of chemical processes. On the other hand, physical chemistry deals with

910-504: Is firmly entrenched. Shortly before his death, Gibbs published in 1902 Elementary Principles in Statistical Mechanics , a book which formalized statistical mechanics as a fully general approach to address all mechanical systems—macroscopic or microscopic, gaseous or non-gaseous. Gibbs' methods were initially derived in the framework classical mechanics , however they were of such generality that they were found to adapt easily to

975-417: Is however a disconnect between these laws and everyday life experiences, as we do not find it necessary (nor even theoretically possible) to know exactly at a microscopic level the simultaneous positions and velocities of each molecule while carrying out processes at the human scale (for example, when performing a chemical reaction). Statistical mechanics fills this disconnection between the laws of mechanics and

1040-449: Is preserved). In order to make headway in modelling irreversible processes, it is necessary to consider additional factors besides probability and reversible mechanics. Non-equilibrium mechanics is therefore an active area of theoretical research as the range of validity of these additional assumptions continues to be explored. A few approaches are described in the following subsections. One approach to non-equilibrium statistical mechanics

1105-469: Is primarily concerned with thermodynamic equilibrium , statistical mechanics has been applied in non-equilibrium statistical mechanics to the issues of microscopically modeling the speed of irreversible processes that are driven by imbalances. Examples of such processes include chemical reactions and flows of particles and heat. The fluctuation–dissipation theorem is the basic knowledge obtained from applying non-equilibrium statistical mechanics to study

1170-585: Is probably the most important 20th century development. Further development in physical chemistry may be attributed to discoveries in nuclear chemistry , especially in isotope separation (before and during World War II), more recent discoveries in astrochemistry , as well as the development of calculation algorithms in the field of "additive physicochemical properties" (practically all physicochemical properties, such as boiling point, critical point, surface tension, vapor pressure, etc.—more than 20 in all—can be precisely calculated from chemical structure alone, even if

1235-566: Is significant overlap in the topics and techniques used. Journals like PCCP ( Physical Chemistry Chemical Physics ) cover research in both areas, highlighting their overlap. The term "chemical physics" in its modern sense was first used by the German scientist A. Eucken, who published "A Course in Chemical Physics" in 1930. Prior to this, in 1927, the publication "Electronic Chemistry" by V. N. Kondrat'ev, N. N. Semenov, and Iu. B. Khariton hinted at

1300-441: Is that for reactants to react and form products , most chemical species must go through transition states which are higher in energy than either the reactants or the products and serve as a barrier to reaction. In general, the higher the barrier, the slower the reaction. A second is that most chemical reactions occur as a sequence of elementary reactions , each with its own transition state. Key questions in kinetics include how

1365-400: Is those ensembles that do not evolve over time. These ensembles are known as equilibrium ensembles and their condition is known as statistical equilibrium . Statistical equilibrium occurs if, for each state in the ensemble, the ensemble also contains all of its future and past states with probabilities equal to the probability of being in that state. (By contrast, mechanical equilibrium is

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1430-431: Is to derive the classical thermodynamics of materials in terms of the properties of their constituent particles and the interactions between them. In other words, statistical thermodynamics provides a connection between the macroscopic properties of materials in thermodynamic equilibrium , and the microscopic behaviours and motions occurring inside the material. Whereas statistical mechanics proper involves dynamics, here

1495-411: Is to incorporate stochastic (random) behaviour into the system. Stochastic behaviour destroys information contained in the ensemble. While this is technically inaccurate (aside from hypothetical situations involving black holes , a system cannot in itself cause loss of information), the randomness is added to reflect that information of interest becomes converted over time into subtle correlations within

1560-417: Is usual for probabilities, the ensemble can be interpreted in different ways: These two meanings are equivalent for many purposes, and will be used interchangeably in this article. However the probability is interpreted, each state in the ensemble evolves over time according to the equation of motion. Thus, the ensemble itself (the probability distribution over states) also evolves, as the virtual systems in

1625-432: The von Neumann equation . These equations are the result of applying the mechanical equations of motion independently to each state in the ensemble. These ensemble evolution equations inherit much of the complexity of the underlying mechanical motion, and so exact solutions are very difficult to obtain. Moreover, the ensemble evolution equations are fully reversible and do not destroy information (the ensemble's Gibbs entropy

1690-560: The "interesting" information is immediately (after just one collision) scrambled up into subtle correlations, which essentially restricts them to rarefied gases. The Boltzmann transport equation has been found to be very useful in simulations of electron transport in lightly doped semiconductors (in transistors ), where the electrons are indeed analogous to a rarefied gas. Another important class of non-equilibrium statistical mechanical models deals with systems that are only very slightly perturbed from equilibrium. With very small perturbations,

1755-529: The Nobel Laureate Irving Langmuir , the award recognizes significant contributions to understanding chemical phenomena through physics principles, impacting areas such as surface chemistry and quantum mechanics. Chemical physicists investigate the structure and dynamics of ions , free radicals , polymers , clusters , and molecules . Their research includes studying the quantum mechanical aspects of chemical reactions, solvation processes, and

1820-448: The area of medical diagnostics . Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems . In quantum mechanics, a statistical ensemble (probability distribution over possible quantum states ) is described by a density operator S , which is a non-negative, self-adjoint , trace-class operator of trace 1 on the Hilbert space H describing

1885-412: The atoms and bonds precisely, it is necessary to know both where the nuclei of the atoms are, and how electrons are distributed around them. Quantum chemistry , a subfield of physical chemistry especially concerned with the application of quantum mechanics to chemical problems, provides tools to determine how strong and what shape bonds are, how nuclei move, and how light can be absorbed or emitted by

1950-625: The attention is focussed on statistical equilibrium (steady state). Statistical equilibrium does not mean that the particles have stopped moving ( mechanical equilibrium ), rather, only that the ensemble is not evolving. A sufficient (but not necessary) condition for statistical equilibrium with an isolated system is that the probability distribution is a function only of conserved properties (total energy, total particle numbers, etc.). There are many different equilibrium ensembles that can be considered, and only some of them correspond to thermodynamics. Additional postulates are necessary to motivate why

2015-650: The characteristic state function). Calculating the characteristic state function of a thermodynamic ensemble is not necessarily a simple task, however, since it involves considering every possible state of the system. While some hypothetical systems have been exactly solved, the most general (and realistic) case is too complex for an exact solution. Various approaches exist to approximate the true ensemble and allow calculation of average quantities. There are some cases which allow exact solutions. Although some problems in statistical physics can be solved analytically using approximations and expansions, most current research utilizes

Physical chemistry - Misplaced Pages Continue

2080-473: The chemical molecule remains unsynthesized), and herein lies the practical importance of contemporary physical chemistry. See Group contribution method , Lydersen method , Joback method , Benson group increment theory , quantitative structure–activity relationship Some journals that deal with physical chemistry include Historical journals that covered both chemistry and physics include Annales de chimie et de physique (started in 1789, published under

2145-626: The conductance of an electronic system is the use of the Green–Kubo relations, with the inclusion of stochastic dephasing by interactions between various electrons by use of the Keldysh method. The ensemble formalism can be used to analyze general mechanical systems with uncertainty in knowledge about the state of a system. Ensembles are also used in: Statistical physics explains and quantitatively describes superconductivity , superfluidity , turbulence , collective phenomena in solids and plasma , and

2210-414: The development of quantum mechanics into quantum chemistry from the 1930s, where Linus Pauling was one of the leading names. Theoretical developments have gone hand in hand with developments in experimental methods, where the use of different forms of spectroscopy , such as infrared spectroscopy , microwave spectroscopy , electron paramagnetic resonance and nuclear magnetic resonance spectroscopy ,

2275-463: The energy flow within and between molecules, and nanomaterials such as quantum dots. Experiments in chemical physics typically involve using spectroscopic methods to understand hydrogen bonding , electron transfer , the formation and dissolution of chemical bonds , chemical reactions, and the formation of nanoparticles . The research objectives in the theoretical aspect of chemical physics are to understand how chemical structures and reactions work at

2340-531: The ensemble continually leave one state and enter another. The ensemble evolution is given by the Liouville equation (classical mechanics) or the von Neumann equation (quantum mechanics). These equations are simply derived by the application of the mechanical equation of motion separately to each virtual system contained in the ensemble, with the probability of the virtual system being conserved over time as it evolves from state to state. One special class of ensemble

2405-524: The ensemble for a given system should have one form or another. A common approach found in many textbooks is to take the equal a priori probability postulate . This postulate states that The equal a priori probability postulate therefore provides a motivation for the microcanonical ensemble described below. There are various arguments in favour of the equal a priori probability postulate: Other fundamental postulates for statistical mechanics have also been proposed. For example, recent studies shows that

2470-629: The fields of physics, biology , chemistry , neuroscience , computer science , information theory and sociology . Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion. Statistical mechanics arose out of the development of classical thermodynamics , a field for which it was successful in explaining macroscopic physical properties—such as temperature , pressure , and heat capacity —in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions . While classical thermodynamics

2535-410: The fluctuation–dissipation connection can be a convenient shortcut for calculations in near-equilibrium statistical mechanics. A few of the theoretical tools used to make this connection include: An advanced approach uses a combination of stochastic methods and linear response theory . As an example, one approach to compute quantum coherence effects ( weak localization , conductance fluctuations ) in

2600-518: The large processing power of modern computers to simulate or approximate solutions. A common approach to statistical problems is to use a Monte Carlo simulation to yield insight into the properties of a complex system . Monte Carlo methods are important in computational physics , physical chemistry , and related fields, and have diverse applications including medical physics , where they are used to model radiation transport for radiation dosimetry calculations. The Monte Carlo method examines just

2665-409: The later quantum mechanics , and still form the foundation of statistical mechanics to this day. In physics, two types of mechanics are usually examined: classical mechanics and quantum mechanics . For both types of mechanics, the standard mathematical approach is to consider two concepts: Using these two concepts, the state at any other time, past or future, can in principle be calculated. There

Physical chemistry - Misplaced Pages Continue

2730-507: The leading figures in physical chemistry in the late 19th century and early 20th century. All three were awarded the Nobel Prize in Chemistry between 1901 and 1909. Developments in the following decades include the application of statistical mechanics to chemical systems and work on colloids and surface chemistry , where Irving Langmuir made many contributions. Another important step was

2795-709: The meaning of "chemical physics" through its title. The Institute of Chemical Physics of the Academy of Sciences of the USSR was established in 1931. In the United States, " The Journal of Chemical Physics " has been published since 1933. In 1964, the General Electric Foundation established the Irving Langmuir Award in Chemical Physics to honor outstanding achievements in the field of chemical physics. Named after

2860-545: The name given here from 1815 to 1914). Chemical physics Chemical physics is a branch of physics that studies chemical processes from a physical point of view. It focuses on understanding the physical properties and behavior of chemical systems, using principles from both physics and chemistry. This field investigates physicochemical phenomena using techniques from atomic and molecular physics and condensed matter physics . The United States Department of Education defines chemical physics as "A program that focuses on

2925-406: The physical properties and behavior of matter in chemical reactions, covering a broader range of topics such as thermodynamics , kinetics , and spectroscopy , and often links the macroscopic and microscopic chemical behavior. The distinction between the two fields still needs to be clarified as both fields share common grounds. Scientists often practice in both fields during their research, as there

2990-427: The practical experience of incomplete knowledge, by adding some uncertainty about which state the system is in. Whereas ordinary mechanics only considers the behaviour of a single state, statistical mechanics introduces the statistical ensemble , which is a large collection of virtual, independent copies of the system in various states. The statistical ensemble is a probability distribution over all possible states of

3055-558: The proceedings of the Vienna Academy and other societies. Boltzmann introduced the concept of an equilibrium statistical ensemble and also investigated for the first time non-equilibrium statistical mechanics, with his H -theorem . The term "statistical mechanics" was coined by the American mathematical physicist J. Willard Gibbs in 1884. According to Gibbs, the term "statistical", in the context of mechanics, i.e. statistical mechanics,

3120-473: The proportion of molecules having a certain velocity in a specific range. This was the first-ever statistical law in physics. Maxwell also gave the first mechanical argument that molecular collisions entail an equalization of temperatures and hence a tendency towards equilibrium. Five years later, in 1864, Ludwig Boltzmann , a young student in Vienna, came across Maxwell's paper and spent much of his life developing

3185-612: The quantum mechanical level. This field also aims to clarify how ions and radicals behave and react in the gas phase and to develop precise approximations that simplify the computation of the physics of chemical phenomena. Chemical physicists are looking for answers to such questions as: Statistical mechanics In physics , statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics , its applications include many problems in

3250-412: The rate of reaction depends on temperature and on the concentrations of reactants and catalysts in the reaction mixture, as well as how catalysts and reaction conditions can be engineered to optimize the reaction rate. The fact that how fast reactions occur can often be specified with just a few concentrations and a temperature, instead of needing to know all the positions and speeds of every molecule in

3315-432: The response can be analysed in linear response theory . A remarkable result, as formalized by the fluctuation–dissipation theorem , is that the response of a system when near equilibrium is precisely related to the fluctuations that occur when the system is in total equilibrium. Essentially, a system that is slightly away from equilibrium—whether put there by external forces or by fluctuations—relaxes towards equilibrium in

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3380-408: The same way, since the system cannot tell the difference or "know" how it came to be away from equilibrium. This provides an indirect avenue for obtaining numbers such as ohmic conductivity and thermal conductivity by extracting results from equilibrium statistical mechanics. Since equilibrium statistical mechanics is mathematically well defined and (in some cases) more amenable for calculations,

3445-400: The scientific study of structural phenomena combining the disciplines of physical chemistry and atomic/molecular physics. Includes instruction in heterogeneous structures, alignment and surface phenomena, quantum theory , mathematical physics , statistical and classical mechanics, chemical kinetics , and laser physics ." While at the interface of physics and chemistry, chemical physics

3510-413: The simplest non-equilibrium situation of a steady state current flow in a system of many particles. In 1738, Swiss physicist and mathematician Daniel Bernoulli published Hydrodynamica which laid the basis for the kinetic theory of gases . In this work, Bernoulli posited the argument, still used to this day, that gases consist of great numbers of molecules moving in all directions, that their impact on

3575-445: The size of fluctuations, but also in average quantities such as the distribution of particles. The correct ensemble is that which corresponds to the way the system has been prepared and characterized—in other words, the ensemble that reflects the knowledge about that system. Once the characteristic state function for an ensemble has been calculated for a given system, that system is 'solved' (macroscopic observables can be extracted from

3640-419: The structural features of liquid . It underlies the modern astrophysics . In solid state physics, statistical physics aids the study of liquid crystals , phase transitions , and critical phenomena . Many experimental studies of matter are entirely based on the statistical description of a system. These include the scattering of cold neutrons , X-ray , visible light , and more. Statistical physics also plays

3705-458: The students of Petersburg University . In the preamble to these lectures he gives the definition: "Physical chemistry is the science that must explain under provisions of physical experiments the reason for what is happening in complex bodies through chemical operations". Modern physical chemistry originated in the 1860s to 1880s with work on chemical thermodynamics , electrolytes in solutions, chemical kinetics and other subjects. One milestone

3770-455: The subject further. Statistical mechanics was initiated in the 1870s with the work of Boltzmann, much of which was collectively published in his 1896 Lectures on Gas Theory . Boltzmann's original papers on the statistical interpretation of thermodynamics, the H-theorem , transport theory , thermal equilibrium , the equation of state of gases, and similar subjects, occupy about 2,000 pages in

3835-462: The system, or to correlations between the system and environment. These correlations appear as chaotic or pseudorandom influences on the variables of interest. By replacing these correlations with randomness proper, the calculations can be made much easier. The Boltzmann transport equation and related approaches are important tools in non-equilibrium statistical mechanics due to their extreme simplicity. These approximations work well in systems where

3900-413: The system. In classical statistical mechanics, the ensemble is a probability distribution over phase points (as opposed to a single phase point in ordinary mechanics), usually represented as a distribution in a phase space with canonical coordinate axes. In quantum statistical mechanics, the ensemble is a probability distribution over pure states and can be compactly summarized as a density matrix . As

3965-403: The theory of statistical mechanics can be built without the equal a priori probability postulate. One such formalism is based on the fundamental thermodynamic relation together with the following set of postulates: where the third postulate can be replaced by the following: There are three equilibrium ensembles with a simple form that can be defined for any isolated system bounded inside

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4030-443: The ways in which pure physics is applied to chemical problems. One of the key concepts in classical chemistry is that all chemical compounds can be described as groups of atoms bonded together and chemical reactions can be described as the making and breaking of those bonds. Predicting the properties of chemical compounds from a description of atoms and how they bond is one of the major goals of physical chemistry. To describe

4095-446: Was developed into the theory of concentration of measure phenomenon, which has applications in many areas of science, from functional analysis to methods of artificial intelligence and big data technology. Important cases where the thermodynamic ensembles do not give identical results include: In these cases the correct thermodynamic ensemble must be chosen as there are observable differences between these ensembles not just in

4160-491: Was first used by the Scottish physicist James Clerk Maxwell in 1871: "In dealing with masses of matter, while we do not perceive the individual molecules, we are compelled to adopt what I have described as the statistical method of calculation, and to abandon the strict dynamical method, in which we follow every motion by the calculus." "Probabilistic mechanics" might today seem a more appropriate term, but "statistical mechanics"

4225-592: Was the publication in 1876 by Josiah Willard Gibbs of his paper, On the Equilibrium of Heterogeneous Substances . This paper introduced several of the cornerstones of physical chemistry, such as Gibbs energy , chemical potentials , and Gibbs' phase rule . The first scientific journal specifically in the field of physical chemistry was the German journal, Zeitschrift für Physikalische Chemie , founded in 1887 by Wilhelm Ostwald and Jacobus Henricus van 't Hoff . Together with Svante August Arrhenius , these were

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